UNIVERSITY OF CALIFORNIA ANDREW SMITH HALLIDIE; PRACTICAL CALCULATION OF DYNAMO-ELECTRIC MACHINES A MANUAL FOR ELECTRICAL AND MECHANICAL ENGINEERS AND A TEXT-BOOK FOR STUDENTS OF ELECTRICAL ENGINEERING CONTINUOUS CURRENT MACHINERY BY ALFRED E. WIENER, E. E., M. E. M. A. I. E. E SECOND EDITION, REVISED AND ENLARGED NEW YORK ELECTRICAL WORLD AND ENGINEER 1902 T tf COPYRIGHT, 1901, BY ELECTRICAL WORLD AND ENGINEER PREFACE. IN the following volume an entirely practical treatise on dynamo-calculation is developed, differing from the usual text-book methods, in which the application of the various formulae given requires more or less experience in dynamo- design. The present treatment of the subject is based upon results obtained in practice and therefore, contrary to the theoretical methods, gives such practical experience. Informa- tion of this kind is presented in the form of more than a hundred original tables and of nearly five hundred formulae derived from the data and tests of over two hundred of the best modern dynamos of American as well as European make, comprising all the usual types of field magnets and of arma- tures, and ranging in all existing sizes. The author's collection of dynamo-data made use of for this purpose contains full particulars of the following types of con- tinuous current machines: American Machines. Edison Single Horseshoe Type, ... .20 sizes. " Iron-clad Type, . . 10 " " Multipolar Central Station Type, . 10 " " Bipolar Arc Light Type, . . . 6 " " Fourpolar Marine Type, . . .. 4 " Small Low-Speed Motor Type, . 4 " " Railway Motor Type, . , 3 " Thomson-Houston Arc Light Type, . 9 " " " Spherical Incandescent Type, 4 " " " Multipolar Type, . 3 " " " Railway Motor Type, . 2 " General Electric Radial Outerpole Type, . 12 " Westinghouse Engine Type (" Kodak ") . 12 " Belt Type, . . . 8 " " Arc Light Type, . . 3 " Brush Double Horseshoe (" Victoria ") Type, 16 " 103844 PREFACE. Sprague Double Magnet Type, . . .13 sizes. Crocker-Wheeler Bipolar Motor Type, . . 6 " " " Multipolar Generator Type, 2 " Entz Multipolar Marine Type, . . 5 " Weston Double Horseshoe Type, . . 3 " Lundell Multipolar Type, . . . 3 " Short Multipolar Railway Motor Type, . 2 " Walker Multipolar Type, . . . 2 " 162 English Machines. Kapp Inverted Horseshoe Type, ... 4 sizes. Edison-Hopkinson Single Horseshoe Type, . 3 " Patterson & Cooper " Phoenix " Type, . 3 " Mather & Platt " Manchester " Type, . 3 " Paris & Scott Double Horseshoe Type, . 2 " Crompton Double Horseshoe Type, . . i size. Kennedy Single Magnet Type, . . i " 11 Leeds" Single Magnet Type, . . . i " Immisch Double Magnet Type, . . i " *' Silvertown" Single Horseshoe Type, . i " Elwell-Parker Single Horseshoe Type, . i " Sayers Double Magnet Type, . . i " 22 German Machines. Siemens & Halske Innerpole Type, . . 3 sizes. 11 " Single Horseshoe Type, . 2 " Allgemeine E. G., Innerpole Type, . . 3 " " " Outerpole Type, . . 3 " Schuckert Muttipolar Flat Ring Type, . 3 " Lahmeyer Iron-clad Type, .' , . . 3 " Naglo Bros. Innerpole Type, . . . 2 '* Fein Innerpole Type, . . '. . . 2 " " Iron-clad Type, . .* . . * . 2 '* " Inward Pole Horseshoe Type, . - . 2 '* Guelcher Multipolar Type, . . 2 " Schorch Inward Pole Type, . . . . i size. Kummer & Co. Radial Multipolar Type, . i " Bollmann Multipolar Disc Type, . . i ll 30 PREFACE. Hi French Machines. Gramme Bipolar Type, 3 sizes. Marcel Deprez Multipolar Type, . . 2 " Desrozier Multipolar Disc Type, i size. Alsacian Electric Construction Co. Innerpole Type, i " Swiss Machines. Oerlikon Multipolar Type, . . . 4 sizes. " Bipolar Iron-clad Type, . . 2 " " Bipolar Double Magnet Type, . 2 " Brown Double Magnet Type (Brown, Boveri & Co.), ..... . . 2 " Thury Multipolar Type, . . . . i size. Alioth & Co. Radial Outerpole Type (" Helvetia"), . . . . < . i " 12 In this list are contained the generators used in the central stations of New York, Brooklyn, Boston, Chicago, St. Louis, and San Francisco, United States; of Berlin, Hamburg, Han- over, Duesseldorf, and Darmstadt, Germany; of London, England; of Paris, France; and others; also the General Electric Company's large power generator for the Intra- mural Railway plant at the Chicago World's Fair, and other dynamos of fame. The author believes that the abundance and variety of his working material entitles him to consider his formulae and tabfes as universally applicable to the calculation of any dynamo. Although being intended as a text-book for students and a manual for practical dynamo-designers, anyone possessing a but fundamental knowledge of arithmetic and algebra will by means of this work be able to successfully calculate and design any kind of a continuous-current dynamo, the matter being so arranged that all the required practical information is given wherever it is needed for a formula. The treatise as here presented has originated from notes prepared by the author for the purpose of instructing his IV PREFACE. classes of practical workers in the electrical field, and upon the success experienced with these it was decided to publish the method for the benefit of others. Since the book is to be used for actual workshop practice, the formulae are so prepared that the results are obtained in inches, feet, pounds, etc. But since the time is approaching when the metric system will be universally employed, and as the book is written for the future as well as for the present, the tables are given both for the English and metric systems of measurement. As far as the principles of dynamo-electric machinery are concerned, the time-honored method of filling one-third to one-half of each and every treatise on dynamo design with chapters on magnetism, electro-magnetic induction, etc., has in the present volume been departed from, the subject of it being the calculation and not the theory of the dynamo. For the latter the reader is referred to the numerous text-books, notably those of Professor Silvanus P. Thompson, Houston and Kennelly, Professor D. C. Jackson, Carl Hering, and Professor Dr. E. Kittler. Descriptions of executed machines have also been omitted from this volume, a fairly com- plete list of references being given instead, in Chapter XIV. The arrangement of the Parts and Chapters has been care- fully worked out with regard to the natural sequence of the subject, the process of dynamo-calculation, in general, con- sisting (i) in the calculation of the length and size of con- ductor required for a given output at a certain speed; (2) in the arrangement of this conductor upon a suitable armature; (3) in supplying a magnet frame of proper cross-section to carry the magnetic flux required by that armature, and (4) in determining the field winding necessary to excite the magnet- izing force required to produce the desired flux. Numerous complete examples of practical dynamo calcula- tion are given in Part VIII., the single cases being chosen with a view of obtaining the greatest possible variety of dif- ferent designs and varying conditions. The leakage examples in Chapter XXX. not only demonstrate the practical applica- tion of the formulae given in Chapters XII. and XIII. , but also show the accuracy to which the leakage factor of a PREFACE. dynamo can be estimated from the dimensions of its magnet frame by the author's formulae. A small portion of the subject matter of this volume first appeared as a serial entitled " Practical Notes on Dynamo Calculation," in the Electrical World, May 19, 1894 (vol. xxiii. p. 675) to June 8, 1895 (vol. xxv. p. 662), and reprinted in the Electrical Engineer (London), June i, 1894 (vol. xiii., new series, p. 640), to July 12, 1895 (vol. xvi. p. 43). This por- tion has been thoroughly revised, and by considering all the literature that has appeared on the subject since the serial was written has been brought to date. It has been the aim of the author to make the book thor- oughly practical from beginning to end, and he expresses the hope that he may have attained this end. The author's thanks are extended to all those firms who upon his request have so courteously supplied him with the data of their latest machines, without which it would not have been possible to bring this work up to date. Due credit, finally, should also be given to the publishers, who have spared neither trouble nor expense in the production of this volume. ALFRED E. WIENER. SCHENECTADY, N. Y., September 20, 1897. PREFACE TO THE SECOND EDITION. In preparing the second edition, it has been the aim to bring this volume up to date in every particular. For this purpose, data of the latest machines of the most prominent manufacturers were procured by the author and compared with the information given in the book. Since the practice in regard to direct-current machinery has changed but little during the past few years, however, only comparatively few changes in the tables have been found necessary. A number of new tables have been inserted, in order to facilitate the work of the inexperienced designer to a still greater extent. The most import of these additions to the text are those to 17 and to 89. The new matter in 17 gives additional guidance in the selection of the conductor-velocity, it having been found that too much uncertainty was formerly left in the assumption of this most important factor. With the added help, even a novice in dynamo designing is now enabled to obtain a practical value of the conductor-velocity for any kind of machine. Table LXXXIXa, 89, serves to check the design with respect to the relation between arma- ture and field. By its use, the performance of a machine in operation can be predicted, thereby avoiding the liability of building a dynamo which would give trouble due to excessive sparking. The importance of such a check will be appreciated by designers who have had experience. Other new matter has been added, referring to double-cur- rent generators, multi-circuit arc dynamos, secondary gener- ators, etc. Besides these additions to the text, three appendices have been added to the book. Appendix I. gives dimensions and armature data of various types of modern dynamos, thus affording to the student a means of comparing his results with existing machines as he proceeds in the design. Appendix II. contains wire tables and winding data necessary in determining viii PREFACE TO THE SECOND EDITION. the windings of dynamos; these tables are added in order to make the book complete in itself, the designer now having close at hand all the necessary data referring to standard wires, rods, cables, etc. Appendix III., finally, in which the causes, localization, and remedies of the usual troubles oc- curring in dynamo-electric machines are compiled, is given for two purposes: first, to enable the designer, by calling his attention to the ordinary short- comings of electrical ma- chinery, to take such preventive measures in designing a machine as will reduce the liability of trouble in operation to a minimum, thus making his dynamo good in performance as well as economical in operation; and second, to assist the attendant of a dynamo plant in going about in a systematic manner in finding the causes of troubles, so that, by their prompt elimination, unnecessary delay or even a shut-down may be obviated. In conclusion, the author takes this opportunity to express his sincere thanks to his professional confreres in this country as well as abroad, for the encouraging comments on the first edition of his book. A. E. W. BROOKLYN, November, 1901. CONTENTS. PAGE LIST OF SYMBOLS, . . . . . . . . . . xxv Part I. Physical Principles of Dynamo-Electric Machines. CHAPTER I. PRINCIPLES OF CURRENT GENERATION IN ARMATURE. 1. Definition of Dynamo-Electric Machinery, . . .. . 3 2. Classification of Armatures, . "- ; * . -. >. - . 4. 3. Production of Electromotive Force, . . ... . . 4 4. Magnitude of Electromotive Force, . . * . . . . 6 5. Average Electromotive Force, . ; ." . . . . 8 6. Direction of Electromotive Force, 9 7. Collection of Currents from Armature Coil, .... 12 8. Rectification of Alternating Currents, ; ". , . . . . .13 9. Fluctuations of Commutated Currents 14 Table I. Fluctuation of E. M. F. of Commutated Currents, . .-.''. . . . 19 CHAPTER II. THE MAGNETIC FIELD OF DYNAMO-ELECTRIC MACHINES. 10. Unipolar, Bipolar, and Multipolar Induction, . . ... 22 11. Unipolar Dynamos, . . . . . . . . .23 12. Bipolar Dynamos, . . . . . . . . .26 13. Multipolar Dynamos, . . . . . . . -33 14. Methods of Exciting Field Magnetism, 35 a. Series Dynamo 36 b. Shunt Dynamo, 37 Table II. Ratio of Shunt Resistance to Armature Resistance for Different Efficiencies, . . 40 c. Compound Dynamo, ' . 41 Part II. Calculation of Armature. CHAPTER III. FUNDAMENTAL CALCULATION FOR ARMATURE WINDING. 15. Unit Armature Induction, . .47 Table III. Unit Induction 48 Table IV. Practical Values of Unit Armature Inductions, . 50 ix X CONTENTS. PAGE 16. Specific Armature Induction, 51 17. Conductor Velocity 52 Table V. Average Conductor Velocities, . . 520 Table Va. High, Medium, and Low Dynamo Speeds, 52^ 18. Field Density, 52^ Table VI. Field Densities, in English Measure, . 54 Table VII. Field Densities, in Metric Measure, . 54 19. Length of Armature Conductor, . . . . . -55 Table VIII. E. M. F. Allowed for Internal Resist- ances, . 56 20. Size of Armature Conductor, 56 CHAPTER IV. DIMENSIONS OF ARMATURE CORE. 21. Diameter of Armature Core, ....... 58 Table IX. Ratio between Core Diameter and Mean Winding Diameter for Small Armatures, 59 Table X. Speeds and Diameters for Drum Arma- tures, ......... 60 Table XI. Speeds and Diameters for High-Speed Ring Armatures, . ' M j , . .... . 60 Table XII. Speeds and Diameters for Low-Speed Ring Armatures, -. JL. .,:_ 6l 22. Dimensioning of Toothed and Perforated Armatures, . . 61 a. Toothed Armatures, . . . . , . .65 Table XIII. Number of Slots in Toothed Arma- tures . . .66 Table XIV. Specific Hysteresis Heat in Toothed Armatures, for Different Widths of Slots, . 69 Table XV. Dimensions of Toothed Armatures, English Measure, . . . . . .70 Table XVI. Dimensions of Toothed Armatures, Metric Measure, . .... . . . 71 b. Perforated Armatures, '*,-,",. . 7* 23. Length of Armature Core, ....? 7 2 a. Number of Wires per Layer, ... ./ . . . 72 Table XVII. Allowance for Division-Strips in Drum Armatures, Y ""-.. V" ... 73 b. Height of Winding Space, Number of Layers, . . 74 Table XVIII. Height of Winding Space in Arma- tures, . . . ; ' .' 75 Table X Villa. Data for Armature Binding, . 75 c. Total Number of Conductors, Length of Armature Core, 76 24. Armature Insulations, ' .. ' . ' ... .. .., , . 78 a. Thickness of Armature Insulations, . . . .78 Table XIX. Thickness of Armature Insulation, . 82 CONTENTS. xr PAGE. b. Selection of Insulating Material, ..... 83 Table XX. Resistivity and Specific Disruptive Strength of Various Insulating Materials, . 85 CHAPTER V. FINAL CALCULATION OF ARMATURE WINDING. 25. Arrangement of Armature Winding, . . . .87 a. Number of Commutator Divisions, ..... 87 Table XXI. Difference of Potential between Com- mutator Divisions, ' 88 b. Number of Convolutions per Armature Division, . .89 c. Number of Armature Divisions, . . . . .90 26. Radial Depth of Armature Core Density of Magnetic Lines in Armature Body, \ . . . . - , . . . 90 Table XXII. Core Densities for Various Kinds of Armatures, . . . ' . = . . . 91 Table XXIII. Ratio of Net Iron Section to Total Cross-section of Armature Core, ... 94 27. Total Length of Armature Conductor, . . . . .94 a. Drum Armatures, ...''<" 95 Table XXIV. Ratio between Total and Active Length of Wire on Drum Armatures, . . 96 b. Ring Armatures, . . ... . . .98 c. Drum-Wound Ring Armatures, . . . . 99 Table XXV. Total Length of Conductor on Drum- Wound Ring Armatures, ...'"." . ^ 100 28. Weight of Armature Winding, . . ^ 100 Table XXVI. Weight of Insulation on Round Copper Wire, . . .. -,; . . .103 29. Armature Resistance, i 102- CHAPTER VI. ENERGY LOSSES IN ARMATURE. RISE OF ARMATURE TEMPERATURE. 30. Total Energy Loss in Armature, . . . . . . 107 31. Energy Dissipated in Armature Winding, .... 108 Table XXVII. Total Armature Current in Shunt- and Compound- Wound Dynamos, . . . 109 32. Energy Dissipated by Hysteresis, . " *,< IO 9' Table XXVIII. Hysteretic Resistance of Various Kinds of Iron, ... . . .. m Table XXIX. Hysteresis Factors for Different ; Core Densities, English Measure, . . . 113 Table XXX. Hysteresis Factors for Different Core Densities, Metric Measure, . . .115 Table XXXI. Hysteretic Exponents for Various Magnetizations, . . . f . y . 116 Table XXXII. Variation of Hysteresis Loss with Temperature, , . . ..^. _>.... . '. II8 x'ii CONTENTS. PAGE 33. Energy Dissipated by Eddy Currents, . . . '. .119 Table XXXIII. Eddy Current Factors for Differ- ent Core Densities and for Various Laminations, English Measure, ...... 120 Table XXXIV. Eddy Current Factors for Differ- ent Core Densities and for Various Laminations, Metric Measure, 122 34. Radiating Surface of Armature, 122 a. Radiating Surface of Drum Armatures, .... 123 Table XXXV. Length of Heads in Drum Arma- tures 124 b. Radiating Surface of Ring Armatures, . . . .125 35. Specific Energy Loss, Rise of Armature Temperature, . . 126 Table XXXVI. Specific Temperature Increase in Armatures, . . ... . .127 36. Empirical Formula for Heating of Drum Armatures, . .129 37. Circumferential Current Density of Armature, . . . 130 Table XXXVII. Rise of Armature Temperature Corresponding to Various Circumferential Cur- rent Densities, . . .. in .. ) _., . ~ . 132 38. Load Limit and Maximum Safe Capacity of Armature, . . 132 Table XXXVIII. Percentage of Effective Gap- Circumference for Various Ratios of Polar Arc, 135 39. Running Value of Armatures, . . . . . . .135 Table XXXIX. Running Values of Various Kinds of Armatures, 136 CHAPTER VII. MECHANICAL EFFECTS OF ARMATURE WINDING. 40. Armature Torque, ......... 137 41. Peripheral Force of Armature Conductors, .... 138 42. Armature Thrust, ......... 140 CHAPTER VIII. ARMATURE WINDING OF DYNAMO-ELECTRIC MACHINES. 43. Types of Armature Winding, 143 a. Closed Coil Winding and Open Coil Winding, . . 143 b. Spiral Winding, Lap Winding, and Wave Winding, . 144 44. Grouping of Armature Coils, 147 Table XL. Symbols for Different Kinds of Arma- ture Winding, . . . . . . .150 Table XLI. E. M. F. Generated in Armature at Various Grouping of Conductors, .' . .151 45. Formula for Connecting Armature Coils, ..... 152 a. Connecting Formula and its Application to the Different Methods of Grouping, 152 CONTENTS. xiil $ PAGE b. Application of Connecting Formula to the Various Prac- tical Cases, 153 46. Armature Winding Data, . . . . . . . .155 a. Series Windings for Multipolar Machines, . . .155 Table XLII. Kinds of Series Winding Possible for Multipolar Machines, . . . . .156 b. Qualification of Number of Conductors for the Various Windings, . . 4 . . . . . . .157 Table XLIII. Number of Conductors and Con- necting Pitches for Simplex Series Drum Wind- ings, . ;. . . . 159 Table XLIV. Number of Conductors and Con- necting Pitches for Duplex Series Drum Wind- ing, . . . . _ . . __ . . . 160 Table XLV. Number of Conductors and Con- necting Pitches for Triplex Series Drum Wind- ings, . '..'' .V; : " < ^ *62 Example showing use of Table XLIII., . . 158 Example showing use of Tables XLIV. and XLV. , 162 Example of Multiplex Parallel Windings, . . 167 CHAPTER IX. DIMENSIONING OF COMMUTATORS, BRUSHES, AND CURRENT-CONVEYING PARTS OF DYNAMO. 47. Diameter and Length of Commutator Brush Surface, . . 168 48. Commutator Insulation, . . 170 Table XLVI. Commutator Insulation for Various Voltages, . . . . ... .171 49. Dynamo Brushes, . . ... 171 a. Material and Kinds of Brushes, . .:-. . . . 171 b. Area of Brush Contact, - _ - .. j . . . . .174 c. Energy Lost in Collecting Armature-current; Determina- tion of Best Brush-tension, .--.,-. . . .176 Table XLVII. Contact Resistance and Friction for Different Brush Tensions, . . . .179 50. Current-conveying Parts, . . ... . . . 181 Table XLVIII. Current Densities for Various Kinds of Contacts, and for Cross-section of Dif- ferent Materials, . . .. ... ' . . .183 CHAPTER X. MECHANICAL CALCULATIONS ABOUT ARMATURE. 51. Armature Shaft, , . . . . .184 Table XLIX. Value of Constant in Formula for Journal Diameter of Armature Shaft, . . . 185 Table L. Value of Constant in Formula for Di- ameter of Core Portion of Armature Shaft, . 185 xiv CONTENTS. PAGE Table LI. Diameters of Shafts for Drum Arma- tures, . 186 Table LIT. Diameters of Shafts for High-Speed Ring Armatures, ....... 187 Table LIII. Diameters of Shafts for Low-Speed Ring Armatures, 187 52. Driving Spokes, . . . . . . . ' . . 186 53. Armature Bearings, . . . . ... . . 190 Table LIV. Value of Constant in Formula for Length of Armature Bearings, . . . . 190 Table LV. Bearings for Drum Armatures, . . 191 Table LVI. Bearings for High-Speed Ring Arma- tures, . . . . . '":,'. . ' . . 192 Table LVII. Bearings for Low-Speed Ring Arma- tures, . . . . . . . . . 192 54. Pulley and Belt, .191 Table LVIII. Belt Velocities of High-Speed Dy- namos of Various Capacities, .... 193 Table LIX. Sizes of Belts for Dynamos, . . 194 Part III. Calculation of Magnetic Flux. CHAPTER XI. USEFUL AND TOTAL MAGNETIC FLUX. 55. Magnetic Field, Lines of Magnetic Force, Magnetic Flux, Field Density, . . . v . ... . . . . 199^ 56. Useful Flux of Dynamo, . "... . . . . 200 57. Actual Field Density of Dynamo, . 2O2 a. Smooth Armatures, .... . ' . <. . . . 204 b. Toothed and Perforated Armatures, .... 205 58. Percentage of Polar Arc, . . . . . .. . . . 207 a. Distance between Pole Corners, . . . . . 207 Table LX. Ratio of Distance between Pole Cor- ners to Length of Gap-Spaces for Various Kinds and Sizes of Dynamos, ... . . 208 b. Bore of Polepieces, . . . ... . 209 Table LXI. Radial Clearance for Various Kinds and Sizes of Armatures, 209 c. Polar Embrace, . .... ... . . . 210 59. Relative Efficiency of Magnetic Field 211 Table LXII. Field Efficiency for Various Sizes of Dynamos, . . . V \ . 212 Table LXIII. Variation of Field Efficiency with Output of Dynamo, . ,- . . . .213 Table LXIV. Useful Flux for Various Sizes of Dynamos at Different Conductor Velocities, . 214 60. Total Flux to be Generated in Machine 214 CONTENTS. XV PAGE CHAPTER XII. CALCULATION OF LEAKAGE FACTOR, FROM DIMENSIONS OF MACHINE. A. formula for Probable Leakage Factor. 61 . Coefficient of Magnetic Leakage in Dynamo-Electric Machines, 217 a. Smooth Armatures, . . '. . . . . .217 b. Toothed and Perforated Armatures, . . J ' . . . 218 Table LXV. Core Leakage in Toothed and Per- forated Armatures, . '.-".. . . . 219 B. General Formula for Relative Permeances. 62. Fundamental Permeance Formula and Practical Derivations, 219 a. Two Plane Surfaces Inclined to each other, . . . 220 b. Two Parallel Plane Surfaces Facing each other, . . 220 c. Two Equal Rectangular Surfaces Lying in one Plane, . 221 d. Two Equal Rectangles at Right Angles to each other, . 221 e. Two Parallel Cylinders, .' ... . . .221 /. Two Parallel Cylinder-halves, 223 C. Relative Permeances in Dynamo-Electric Machines. 63. Principle of Magnetic Potential, ''"".' '. ~'\' .... 224 64. Relative Permeance of the Air Gaps, .<;.... 224 a. Smooth Armature, 224 Table LXVI. Factor of Field Deflection in Dy- namos with Smooth Surface Armatures, . . 225 b. Toothed and Perforated Armature, ..... 227 Table LXVII. Factor of Field Deflection in Dy- namos with Toothed Armatures, . . . 230 65. Relative Average Permeance across the Magnet Cores, . .231 66. Relative Permeance across Polepieces, ..... 238 67. Relative Permeance between Polepieces and Yoke, . . 244 D. Comparison of Various Types of Dynamos. 68. Application of Leakage Formulae for Comparison of Various Types of Dynamos, . . Y - 248 (1) Upright Horseshoe Type, 249 (2) Inverted Horseshoe Type, 250 (3) Horizontal Horseshoe Type, ..... 251 (4) Single Magnet Type, . ._*... . .251 (5) Vertical Double Magnet Type, ... . .252 (6) Vertical Double Horseshoe Type, . . . .252 (7) Horizontal Double Horseshoe Type, . . . 253 (8) Horizontal Double Magnet Type, . . . . 254 (9) Bipolar Iron-clad Type, . . . ... * 255 (10) Fourpolar Iron-clad Type, . .^ . . . .225 XVI CONTENTS. $ PAGE CHAPTER XIII. CALCULATION OF LEAKAGE FACTOR, FROM MACHINE TEST. 69. Calculation of Total Flux, 257 a. Magnet Frame Consisting of but One Material, . . 259 b. Magnet Frame Consisting of Two Different Materials, . 260 70. Actual Leakage Factor of Machine, . .. .-. . . 261 Table LXVIII. Leakage Factors, .. . . 263 Table LXVIII^. Usual Limits of Leakage Fac- tor for Most Common Types of Dynamos, . 265 Part IV. Dimensions of Field-Magnet Frame. CHAPTER XIV. FORMS OF FIELD-MAGNET FRAMES. 71. Classification of Field-Magnet Frames, 269 72. Bipolar Types, . . . . . . . . 270 73. Multipolar Types, . '',' .-. ...... 279 74. Selection of Type, . . . . . ... . . . 285 Advantages and Disadvantages of Multipolar Machines, . 287 Comparison of Bipolar and Multipolar Types, . . . 287^ Proper Number of Poles for Multipolar Field Magnets, . 287^ Table LXVIII^. Number of Magnet Poles for Various Speeds, 287^ CHAPTER XV. GENERAL CONSTRUCTION RULES. 75. Magnet Cores, .. .- . ' . . . . . . . 288 a. Material, . . . . ... . . .288 b. Form of Cross-section, . 289 Table LXIX. Circumference of Various Forms of Cross-sections of Equal Area, .... 291 c. Ratio of Core Area to Cross-section of Armature, . . 292 76. Polepieces, ........... 293 a. Material, .......... 293 b. Shape, _.....-.. 295 77. Base, ............ 299 78. Zinc Blocks, ........... 300 Table LXX. Height of Zinc Blocks for High- Speed Dynamos with Smooth Drum Armatures, 301 Table LXXI. Height of Zinc Blocks for High- Speed Dynamos with Smooth Ring Armatures, 302 Table LXXII. Height of Zinc Blocks for Low- Speed Dynamos with Toothed Armatures, . 302 Table LXXI II. Comparison of Zinc Blocks for Dynamos with Various Kinds of Armatures, 303 79. Pedestals and Bearings, ........ 303 80. Joints in Field-Magnet Frame, ....... 305 a. Joints in Frames of One Material, 305 CONTENTS. xv 11 PAGE Table LXXIV. Influence of Magnetic Density upon the Effect of Joints in Wrought Iron, . 307 b. Joints in Combination Frames, 306 CHAPTER XVI. CALCULATION OF FIELD-MAGNET FRAME. 81. Permeability of Various Kinds of Iron, Absolute and Prac- tical Limits of Magnetization, . . . . 310 Table LXXV. Permeability of Different Kinds of Iron at Various Magnetizations, . . . 311 Table LXXVI. Practical Working Densities and Limits of Magnetization for Various Materials, 313 82. Sectional Area of Magnet Frame, . . . . . 313 Table LXXVI I. Sectional Areas of Field-Magnet Frame for High-Speed Drum Dynamos, . . 315 Table LXXVIII. Sectional Areas of Field-Magnet Frame for High-Speed Ring Dynamos, . . 315 Table LXXIX. Sectional Areas of Field-Magnet Frame for Low-Speed Ring Dynamos, . .316 83. Dimensioning of Magnet Cores, ; 316 a. Length of Magnet Cores .316 Table LXXX. Height of Winding Space for Dy- namo Magnets, ....... 317 Table LXXXI. Dimensions of Cylindrical Magnet Cores for Bipolar Types, 319 Table LXXXII. Dimensions of Cylindrical Mag- net Cores for Multipolar Types, . . . 320 Table LXXXIII. Dimensions of Rectangular Magnet Cores (Wrought Iron and Cast Steel), . 321 Table LXXXIV. Dimensions of Oval Magnet Cores (Wrought Iron and Cast Steel), . . 322 b. Relative Position of Magnet Cores, 319 Table LXXXV. Distance between Cylindrical Magnet Cores, ....... 32.' Table LXXXVI. Distance between Rectangular and Oval Magnet Cores 324 84. Dimensioning of Yokes, ........ 3 2 5 85. Dimensioning of Polepieces 325 Table LXXXVII. Dimensions of Polepieces for Bipolar Horseshoe Type Dynamos, . . . 326 Part V. Calculation of Magnetizing Force. CHAPTER XVII. THEORY OF THE MAGNETIC CIRCUIT. 86. Law of the Magnetic Circuit, 33* 87. Unit Magnetomotive Force. Relation between M. M. F. and Exciting Power, . . . . . ~. . . 332 xviii CONTENTS. * PAGE 88. Magnetizing Force required for any Portion of a Magnetic Circuit, 333 Table LXXXVIII. Specific Magnetizing Forces, in English Measure, . . . . "' . . . 336 Table LXXXIX. Specific Magnetizing Forces, in Metric Measure, . 337 CHAPTER XVIII. MAGNETIZING FORCES. 89. Total Magnetizing Force of Machine, 339 Table LXXXIXa. Greatest Permissible Angle of Field Deflection and Corresponding Maximum Ratio of Armature Ampere-Turns to Field Ampere-Turns, . . . .... 90. Ampere-Turns for Air Gaps, . . ... . 91. Ampere-Turns for Armature Core, . . ... ,-. . . . 340 92. Ampere-Turns for Field-Magnet Frame, . . . . 344 93. Ampere-Turns for Compensating Armature Reactions, . . 348 Table XC. Coefficient of Brush Lead in Toothed and Perforated Armatures, . . . .350 Table XCI. Coefficient of Armature Reaction for Various Densities and Different Materials, 352 94. Grouping of Magnetic Circuits in Various Types of Dynamos, 353 Part VI. Calculation of Magnet Winding. CHAPTER XIX. COIL WINDING CALCULATIONS. 95. General Formulae for Coil Windings, . f . . . 359 96. Size of Wire Producing Given Magnetizing Force at Given Voltage between Field Terminals. Current Density in Mag- net Wire, . . . . '- . . . . . . 363 Table XCII. Specific Weights of Copper Wire Coils, Single Cotton Insulation, . . . 367 97. Heating of Magnet Coils, . . . . . . . . 368 Table XCIII. Specific Temperature Increase in Magnet Coils of Various Proportions, at Unit Energy Loss per Square Inch of Core Surface, 371 98. Allowable Energy Dissipation for Given Rise of Temperature in Magnet Winding, 370 CHAPTER XX. SERIES WINDING. 99. Calculation of Series Winding for Given Temperature In- crease, . ..,....-. 374 Table XCIV. Length of Mean Turn for Cylin- drical Magnets, . ..... 375 loo. Series Winding with Shunt-Coil Regulation 375 CONTENTS. xix PAGE CHAPTER XXI. SHUNT WINDING. 101. Calculation of Shunt Winding for Given Temperature In- crease, . . ... . 383 102. Computation of Resistance and Weight of Magnet Winding, 388 103. Calculation of Shunt Field Regulator, . . . . . 390 CHAPTER XXII. COMPOUND WINDING. 104. Determination of the Number of Shunt and Series Ampere- Turns, . . . ... '. . . .... 395 Table XCV. Influence of Armature Current on Relative Distribution of Magnetic Flux, . . 398 105. Calculation of Compound Winding for Given Temperature Increase, . . ....... . 399 Part VII. Efficiency of Generators and Motors ; Designing of a Number of Dynamos of Same Type ; Calculation of Electric Motors, Unipolar Dynamos, Motor-Generators, etc.; and Dynamo- Graphics. CHAPTER XXIII. EFFICIENCY OF GENERATORS AND MOTORS. 106. Electrical Efficiency, . . . . . . . . . 405 107. Commercial Efficiency, ........ 406 Table XCVI. Losses in Dynamo Belting, . . 409 108. Efficiency of Conversion, .... .... 409 109. Weight-Efficiency and Cost of Dynamos, .... 410 Table XCVII. Average Weight and Weight-Effi- ciency of Dynamos, 412 CHAPTER XXIV. DESIGNING OF A NUMBER OF DYNAMOS OF SAME TYPE. no. Simplified Method of Armature Calculation 4^3 in. Output as a Function of Size, 4 l6 Table XCVIII. Exponent of Output-Ratio in Formula for Size- Ratio, for Various Combina- tions of Potentials and Sizes, . . . .41? CHAPTER XXV. CALCULATION OF ELECTRIC MOTORS. 112. Application of Generator Formulae to Motor Calculation, . 419 Table XCIX. Average Efficiencies and Electrical Activity of Electric Motors of Various Sizes, . 422 113. Counter E. M. F., 4-23 .114. Speed Calculation of Electric Motors, 424 Table C. Tests on Speed Variation of Shunt Motors, . ...' 427 XX CONTENTS. PAGE. i 5. Calculation of Current for Electric Motors, . . . .427 a. Current for any Given Load 427 b. Current for Maximum Commercial and Electrical Effi- ciency, . ' . 428 116. Designing of Motors for Different Purposes, .... 429 Table CI. Comparison of Efficiencies of Two Mo- tors Built for Different Purposes, . . . 430 117. Railway Motors, 431 a. Railway Motor Construction, 431 (1) Compact Design and Accessibility, . . ... 432 (2) Maximum Output with Minimum Weight, . . 432 (3) Speed, and Reduction-Gearing, .... 433 Table CII. General Data of Railway Motors, . 435 (4) S-peed Regulation, . . . . . . . 436 (5) Selection of Type, 437 b. Calculations Connected with Railway Motor Design, . 438 (1) Counter E. M. F., Current, and Output of Motor, 438 (2) Speed of Motor for Given Car Velocity, . """.' . 439 (3) Horizontal Effort and Capacity of Motor Equip- ment for Given Conditions 440 Table GUI. Specific Propelling Power Re- quired for Different Grades and Speeds, . 441 Table CIV. Horizontal Effort of Motors of Va- rious Capacities at Different Speeds, . . 442 (4) Line Potential for Given Speed and Grade, . . 442 CHAPTER XXVI. CALCULATION OF UNIPOLAR DYNAMOS. 118. Formulae for Dimensions Relative to Armature Diameter, . 443 119. Calculation of Armature Diameter and Output of Unipolar Cylinder Dynamo, ..... . . . . . . 446 120. Formulae for Unipolar Double Dynamo, . . . . . 449 121. Calculation for Magnet Winding for Unipolar Cylinder Dy- namos, ... . . -. . . . . 450 CHAPTER XXVII. CALCULATION OF DYNAMOTORS; GEN- ERATORS FOR SPECIAL PURPOSES, ETC. 122. Calculation of Dynamotors, . . ''i . . . 452 123. Designing of Generators for Special Purposes, . . .455 a. Arc Light Machines (Constant-Current Generators), . 455 b. Dynamos for Electro-Metallurgy, ..... 459 c. Generators for Charging Accumulators, .... 461 d. Machines for Very High Potentials, .... 462 e. Multi-Circuit Arc Dynamos, . . , . . . 462^ f. Double-Current Generators, ... . . . 462^ 124. Prevention of Armature Reaction, . . . . . . 463 a. Ryan's Balancing Field Coil Method 464 CONTENTS. xxh PAGE ' b. Sayers' Compensating Armature Coil Method, . . 467 c. Thomson's Auxiliary Pole Method, ..... 469 125. Size of Air Gaps for Sparkless Collection, .... 470 126. Irdn Wire for Armature and Magnet Winding, . . . 472 CHAPTER XXVIII. DYNAMO GRAPHICS. 127. Construction of Characteristic Curves, 476 Table CV. Factor of Armature Ampere-Turns for Various Mean Full-Load Densities, . . . 480 Practical Example, 481 128. Modification in the Characteristic Due to Change of Air Gap, 483 129. Determination of the E. M. F. of a Shunt Dynamo for a Given Load, . 485 130. Determination of the Number of Series Ampere-Turns for a Compound Dynamo, . . f . . . . . . 486' 131. Determination of Shunt Regulators, ..... 487 a. Regulators for Shunt Machines of Varying Load, . 487 Practical Example, . . .-. . . . . 488 b. Regulators for Shunt Machines of Varying Speed, . . 490 Practical Example, . '.' 492 c. Regulators for Shunt Machines of Varying Load and Varying Speed, . . . 493 Practical Example, . . . . . . . . 495 d. Regulators for Varying the Potential of Shunt Dynamos, 496 132. Transmission of Power at Constant Speed by Means of Two Series Dynamos, . . . .' - . . . . 497 133. Determination of Speed and Current Consumption of Rail- way Motors at Varying Load, . . - '; ' . ... . ' ; 500- Practical Example, . . . . . . 501 Part VIII. Practical Examples of Dynamo Calculation. CHAPTER XXIX. EXAMPLES OF CALCULATIONS FOR ELECTRIC GENERATORS. 134. Calculation of a Bipolar, Single Magnetic Circuit, Smooth Ring, High-Speed Series Dynamo (10 KW. Single Magnet Type. 250 V. 40 Amp. 1200 Revs.), .... 505 135. Calculation of Bipolar, Single Magnetic Circuit, Smooth Drum, High-Speed Shunt Dynamo (300 KW. Upright Horseshoe Type. 500 V. 600 Amp. 400 Revs.), . . 527 136. Calculation of a Bipolar, Single Magnetic Circuit, Smooth Drum, High-Speed, Compound Dynamo (300 KW. Up- right Horseshoe Type. 500 V. 600 Amp. 400 Revs.), . 547 137. Calculation of a Bipolar Double Magnetic Circuit, Toothed Ring, Low-Speed Compound Dynamo (50 KW. Double Magnet Type. 125 V. 400 Amp. 200 Revs.), . . . 552 xxii CONTENTS. PAGE 138. Calculation of a Multipolar, Multiple Magnet, Smooth Ring,- High-Speed Shunt Dynamo (1200 KW. Radial Innerpole Type. 10 Poles. 150 V. 8000 Amp. 232 Revs.), ""!*: . 566 139. Calculation of a Multipolar, Single Magnet, Smooth Ring, Moderate-Speed Series Dynamo (30 KW. Single Magnet Innerpole Type. 6 Poles. 600 V. 50 Amp. 400 Revs.), 580 140. Calculation of a Multipolar, Multiple Magnet, Toothed Ring, Low-Speed Compound Dynamo (2000 KW. Radial Outer- pole Type. 16 Poles. 540 V. 3700 Amp. 70 Revs.), . 587 Table CVI. Factor of Hysteresis Loss in Arma- ture Teeth, .... . . . . 592 141. Calculation of a Multipolar, Consequent Pole, Perforated Ring, High-Speed Shunt Dynamo (100 KW. Fourpolar Iron-Clad Type. 200 V. 500 Amp. 600 Revs.), in Metric Units, . . . .... . . . 603 CHAPTER XXX. EXAMPLES OF LEAKAGE CALCULATIONS, ELECTRIC MOTOR DESIGN, ETC. 142. Leakage Calculation for a Smooth Ring, One-Material Frame, Inverted Horseshoe Type Dynamo (9.5 KW. "Phoenix" Dynamo: 105 V. 90 Amp. 1420 Revs.), .... 614 143. Leakage Calculation for a Smooth Ring, One-Material Frame, Double Magnet Type Dynamo (40 KW. " Immisch " Dy- namo: 690 V. 59 Amp. 480 Revs.), 618 144. Leakage Calculation for a Smooth Drum, Combination Frame, Upright Horseshoe Type Dynamo (200 KW. " Ed- ison " Bipolar Railway Generator: 500 V. 400 Amp. 450 Revs.), . . .. . 621 145. Leakage Calculation for a Toothed Ring, One-Material Frame, Multipolar Dynamo (360 KW. " Thomson-Hous- ton" Fourpolar Railway Generator: 600 V. 600 Amp. 400 Revs.), 624 146. Calculation of a Series Motor for Constant-Power Work (In- verted Horseshoe Type. 25 HP. 220 V. 850 Revs.), . 628 147. Calculation of a Shunt Motor for Intermittent Work (Bipolar Iron-Clad Type. 15 HP. 125 V. 1400 Revs.), . . .637 148. Calculation of a Compound Motor for Constant Speed at Varying Load (Radial Outerpole Type. 4 Poles. 75 HP. 440 V. 500 Revs.), 644 149. Calculation of a Unipolar Dynamo (Cylinder Single Type. 300 KW. 10 V. 30,000 Amp. looo Revs.), . . . 652 150. Calculation of a Dynamotor (Bipolar Double Horseshoe Type, s/4 KW. 1450 Revs. Primary: 500 V. n Amp. Secondary: uoV. 44 Amp.), 655 CONTENTS. xxin APPENDIX I. TABLES OF DIMENSIONS OF MODERN DYNAMOS. TABLE PAGE CVII. Dimensions of Crocker- Wheeler Bipolar Medium-Speed Ring-Armature Motors, . . . . . . 664 CV1II. Dimensions of Edison Bipolar High-Speed Drum-Arma- ture Dynamos and Motors, ; .. . ,,. . .. . 665 CIX. Dimensions of Westing house Four-Pole Medium and High-Speed Drum-Armature Dynamos and Motors, 666 CX. Dimensions of General Electric Four-Pole Moderate and High-Speed Ring-Armature Generators, . . 667 CXI. Dimensions of Crocker- Wheeler Multipolar Low, Medium and High-Speed Surface-Wound Ring- Armature Dynamos 668 CXII. Dimensions of General Electric Multipolar Low-Speed Ring-Armature Generators, 669 CXIII. Ring-Armature Dimensions, 670 CXIV. Drum-Armature Dimensions, ...... 671 APPENDIX II. WIRE TABLES AND WINDING DATA. TABLE CXV. Resistance, Weight, and Length of Cool, Warm, and Hot Copper Wire, 676-677 CXVI. Data for Armature Wire (D. C. C ), . . . . 678 CXVII. Data for Magnet Wire (S. C. C.), 679 CXVIII. Limiting Currents for Copper Wires 680 CXIX. Carrying Capacity of Copper Wires, . . . .681 CXX. Carrying Capacity of Circular Copper Rods, . . 682 CXXI. Equivalents of Wires 684-685 CXXII. Stranding of Standard Cables 686 CXXIII. Number and Size of Wires in Cable of Given Cross- Section 687 CXXIV. Size and Weight of Rubber-Covered Cables, . . 688 CXXV. Iron Wire for Rheostats and Starting Boxes, . . 689 CXXVI. Carrying Capacity of German Silver Rheostat Coils, . 690 APPENDIX III. LOCALIZATION AND REMEDY OF TROUBLES IN DYNAMOS AND MOTORS IN OPERATION. Classification of Dynamo Troubles, 695 i. Sparking at Commutator 695 Causes of Sparking, 696 Prevention of Sparking, 696 Faulty Adjustment 696 Faulty Construction and Wrong Connection 697 Wear and Tear 698 Excessive Current, . . . .699 xx iv CONTENTS. PAGE 2. Heating of Armature and Field Magnets, . . . . 699 3. Heating of Commutator and Brushes, 700 4. Heating of Bearings, . . . . . . . . . 701 5. Causes and-Prevention of Noises in Dynamos, . . . 701 6. Adjustment of Speed, 702 7. Failure of Self -Excitation, , . 703. 8. Failure of Motor, , . 704 INDEX, . 707 LIST OF SYMBOLS. Throughout the book a uniform system of notation, based upon the standard Congress-notation, is adhered to, the same quantity always being denoted by the same symbol. The fol- lowing is a complete list of these symbols, here compiled for convenient reference: AT, at ampere-turns. AT '= total number of ampere-turns on magnets, at normal load, or magnetizing force. AT' total magnetizing force required for maximum output of machine. AT" total magnetizing force required for minimum output of machine. =. total magnetizing force required for maximum speed of machine. total magnetizing force required for minimum speed of machine. AT total magnetizing force required at open circuit. at & = magnetizing force required for armature core, normal load. #4 o = magnetizing force required for armature core, open circuit. 0/e.i. = magnetizing force required for cast iron portion of magnetic circuit, normal load. at c io = magnetizing force required for cast iron portion of magnetic circuit, no load. -0/ c>8> = magnetizing force required for cast steel portion of magnetic circuit, normal load. ^c.s. = magnetizing force required for cast steel portion of magnetic circuit, no load. at^ = magnetizing force required for air gaps, normal load. af so = magnetizing force required for air gaps, open circuit.. X xvi LIST OF SYMBOLS. #/ gan = combined magnetizing force required for air gaps, armature core, and reactions. at m magnetizing force required for magnet frame, normal output. at mo = magnetizing force required for magnet frame, open circuit. <7/ p , tf/ po = magnetizing forces required for polepieces. at r magnetizing force required for compensation of armature reactions. at s = magnetizing force required to produce a reversing field of sufficient strength for sparkless collection. #/ wi = magnetizing force required for wrought iron portion of magnetic circuit, normal load. ^Av.i.o magnetizing force required for wrought iron portion of magnetic circuit, no load. aty, at yo = magnetizing forces required for yoke, or yokes. a = half pole-space angle (also angle of brush-displacement). (B = magnetic flux density in magnetic material, in lines per square centimetre. &" = magnetic flux density in magnetic material, in lines per square inch. (B t , (ft" a = average density of magnetic lines in armature core. <&*, 'ai maximum density of magnetic lines in armature core. a 2 > "a 2 minimum density of magnetic lines in armature core. o.i.> " C i. mean density of magnetic lines in cast iron portion of frame. ^"PI = max i mum density of magnetic lines in polepieces. (B P2 , (B" P2 = minimum magnetic density in polepieces. t , &" t = magnetic density in armature teeth. <& w .i> &Vi.= magnetic density in wrought iron portion of mag- netic circuit. b breadth, width. b & = breadth of armature cross-section, or radial depth of armature core. b\ maximum depth of armature core. LIST OF SYMBOLS. xxvii b^ = width of commutator brush. ^ B = breadth of belt. k = circumferential breadth of brush contact. b s = width of armature slot. b\ available width of armature slot. b" s width of armature slot for minimum tooth-density. s = smallest breadth of armature spoke (parallel to shaft). b t = width, at top, of armature tooth. b\ = radial depth to which armature tooth is exposed to mag- netic field. b'\ width, at root, of armature tooth. b y = breadth of yoke. fi = angle embraced by each pole. /3 t = percentage of polar arc. ft\ = percentage of effective arc, or effective field circum- ference. y = electrical conductivity, in mhos. Z>, d t d = diameter. D m = external diameter of magnet coil. Z> p = diameter of armature pulley. d & diameter of armature core. d' & mean diameter of armature winding. d\ external diameter of armature (over winding). d'" & = mean diameter of armature core. " = total flux per magnetic circuit. $' P == relative efficiency of magnetic field (maxwells per watt of output at unit conductor velocity). g = grade of railway track, in per cent. 3C = magnetic flux density in air, or field density, in gausses (lines of force per square centimetre). 3C" = field density, in lines of force per square inch. 5C t , 3C\ = density on stronger side of an unsymmetrical field. 3C 2 , 3C" 2 = density on weaker side of an unsymmetrical field. h = height, thickness. /i & = total height of winding space in armature (depth of slots). h\ available height of armature winding space. // B = thickness of belt, in inches. // c radial height of clearance between external diameter of finished armature and polepieces. //i = thickness of commutator side insulation, in inches. h \ = thickness of commutator bottom insulation, in inches. ti \ = thickness of commutator end insulation, in inches. h m = height of winding space on field magnets. h' m = net height of field winding. /i p height of polepieces. xxx LIST OF SYMBOLS. h & = smallest thickness of armature spoke (perpendicular to, shaft). fi y = height of yoke. h z = height of zinc block. HP, hp horse power. rj factor of hysteresis loss in armature, English measure (watts per cubic foot). tf = factor of hysteresis loss in armature, metric measure (watts per cubic metre). rj l == hysteretic resistance. r} G = commercial efficiency. rj Q = electrical efficiency. rf K = gross efficiency, or efficiency of conversion. /, i = intensity of current, amperes. f= current output, or amperage, of generator; current sup- plied to motor terminals. /' total current active in armature, in amperes. /j, / n ,... = currents flowing in coils /, //, ... of series field regulator. / m = current in magnet winding, in amperes. /^ total series current, in amperes. /^ = total shunt current, in amperes. / a = current density in armature conductor, circular mils per ampere. *e = circumferential current density of armature (amperes per unit length of core circumference). t m = current density in magnet wire, circular mils per ampere. / se = current density in series wire, circular mils per ampere. / Bh = current density in shunt wire, circular mils per ampere. K, k = constants. ^i> ^2> ^3, ... = various constants depending upon material. manner of manufacture, and similar conditions. Z, / = length, distance. Z a = active length of armature conductor, in feet. Z e = effective length of armature conductor, in feet. Z m = total length of magnet wire, in feet. Z se = total length of series wire, in feet. Z Bh = total length of shunt wire, in feet. Z t = total length of armature conductor. / a = length of armature core, in inches. LIST OF SYMBOLS. xxxi /" a = length of magnetic circuit in armature core, in inches. / b = length of armature bearings, in inches. /' b = length of gap between adjacent commutator brushes. / c = total length of commutator brush contact surface. ^"c.i. = length of magnetic circuit in cast iron portion of field frame. l" cs =. length of magnetic circuit in cast steel portion of field frame. / f = mean length of magnetic field. l" g = length of magnetic circuit in air gaps, in inches. / h r= length of drum armature heads. 4 = effective axial length of commutator brush contact sur- face. / m = length of magnet core, in inches. l' m = total length of magnet cores, in inches. r m total length of magnetic circuit in entire field magnet frame. /p = length of polepieces, parallel to armature inductors. /' p = mean distance between pole-corners, in inches. /" p = length of magnetic circuit in polepieces, in inches. / 8 = distance of smallest armature spoke section from active conductors, or leverage at smallest section of armature spokes. / t mean length of turn of field magnet winding, in feet. / T mean length of turn of field magnet winding, in inches. /' T length of mean series turn, in inches. l\ = length of mean shunt turn, in inches. /* wjt = length of magnetic circuit in wrought iron portion of field frame, in inches. /' y = length of yoke, in inches. /" y = length of magnetic circuit in yoke, in inches. A = factor of magnetic leakage. A' = factor of core leakage in machines with toothed or per- forated armature. A m = = specific length of magnet wire, in feet per ohm /'m X.' m = specific length of magnet wire, in feet per pound. A se = specific length of series wire, in feet per ohm. A 8h = specific length of shunt wire, in feet per ohm. J\f, J/, , . . . = mass, volume. xxxii LIST OF SYMBOLS. M = mass of iron in armature core, in cubic feet. M l = mass of iron in armature core, in cubic metres. M\ = mass of iron in armature core, in cubic centimetres. M m = volume of coil space on field magnets, in cubic inches. w = magnetizing force per centimetre length. w" = magnetizing force per inch length. 7# a , #/ a = specific magnetizing force of armature core. w c.i.> m "c.i. specific magnetizing force of cast iron portion of magnetic circuit. m c,s,> m "c,s. specific magnetizing force of cast steel portion of magnetic circuit. w m , m" m = specific magnetizing force of magnet frame. w p , m" v = specific magnetizing force of polepieces. w t , m\ = specific magnetizing force of armature teeth. w wi , m\ Af = specific magnetizing force of wrought iron por- tion of magnetic circuit. m y , m" y = specific magnetizing force of yoke. fjL = magnetic permeability. JV, n = number. N = number of revolutions of armature per minute. JV' = number of revolutions of armature per second. JV t = frequency of magnetic reversals, or number of cycles per second. JV a =' speed of dynamo, when run as motor. JV r a = total number of turns on armature. JV C = number of conductors around pole-facing circumference of armature. .JV m = number of turns on magnets. .JVge = number of series turns. 7V sh number of shunt turns. j* = speed ratio, /. e., abnormal divided by normal speed of machine. x = speed ratio for maximum speed. a = speed ratio for minimum speed. n & = number of turns per armature coil. n b = number of commutator brushes, at one point of commu- tation. n c number of armature coils, or number of commutator divisions. n' = number of armature slots. LIST OF SYMBOLS. xxxiii n$ = number of wires stranded in parallel to make up one armature conductor. n t = number of separate field coils in each magnetic circuit. ;/ k number of commutator bars covered by one set of brushes. ! =z number of layers of wire on armature. n m = number of independent armature windings in multiple. ;/ p = number of pairs of magnet poles. //'p = number of pairs of parallel branches in armature, or number of bifurcations of current in armature. ;/ p = number of pairs of brush sets. n r = number of steps, or divisions, in shunt field regulator. />/ s = number of armature circuits connected in series in each of the parallel branches. s = total number of spokes in armature spiders. n S3 = number of wires constituting one series field conductor. w = number of armature wires per layer. // z number of magnetic circuits in dynamo. 2, = relative permeance of gap-spaces. ^ 2 = relative average permeance across magnet cores. ^ 3 = relative permeance across polepieces. ^ 4 = relative permeance between polepieces and yoke. $' relative permeance of clearance space between poles and external surface of armature. <$" = relative permeance of teeth. ( $"' = relative permeance of slots. P electrical energy at terminals of machine; /. a = energy absorbed in armature winding (C'VvMoss). P' A = running value of armature; /. e., energy developed per unit weight of copper at unit speed and unit field density. P & = energy absorbed by eddy currents, in watts. xxxiv LIST OF SYMBOLS. P' e = energy absorbed by eddy currents, in ergs. P t = energy absorbed by brush-friction. ./V energy absorbed by hysteresis, in entire armature core. P' h = energy absorbed by hysteresis, in solid portion of slotted armature core. P ff h energy absorbed by hysteresis, in iron projections of toothed and perforated armatures. P k = energy absorbed by contact resistance of brushes. P m = energy absorbed in magnet windings. P = energy loss due to air-resistance, brush friction, journal friction, etc. P' .= energy required to run dynamo at normal speed on open circuit. P 8e energy absorbed in series winding. jP Bh = energy absorbed in shunt winding. jP'gb = energy absorbed in entire shunt-circuit, at normal load. P r = energy absorbed in shunt regulating resistance. P\ = any load of a motor, in watts. / B = safe pressure, or working load, of materials, in pounds per square inch. TT = ratio of circumference to diameter of circle, = 3.1416. 61 = reluctance of magnetic circuit, in oersteds. .A?, r = electrical resistance, in ohms. It resistance of external circuit. J? & total resistance of armature wire, all in series. r a = armature resistance, cold, at 15.5 Centigrade. r' a armature resistance, hot, at (15.5 -f- 6 a ) degrees Cent. r m = magnet-resistance, cold, at 15.5 Centigrade. r' m = magnet-resistance, warm, at (15.5 -f- 6 m ) degrees Cent. r r = resistance of shunt field regulator. ^ = resistance of series winding, cold, at 15.5 Centigrade. r^ = resistance of series winding, warm, at (15.5 + 6 m ) de- grees Centigrade. r h resistance of shunt winding, cold, at 15.5 Centigrade. r sh = resistance of shunt winding, warm, at (15.5 + 6 m ) de- grees Centigrade. r x = extra-resistance, or shunt regulating resistance in circuit at normal load, in per cent, of magnet resistance. r i> r n> resistances of coils I, II, ... of series field regulator. LIST OF SYMBOLS. xxxv yck = resistivity of brush-contact, in ohms per square inch of surface. p m resistivity of magnet-wire, in ohms per foot. S surface, sectional area. S A = radiating surface of armature. *S a sectional area (corresponding to average specific mag- netizing force) of magnetic circuit in armature core. S &1 minimum cross-section of armature core. S^ = maximum cross-section of armature core. S Cm i. = sectional area of magnetic circuit in cast iron portion of field frame. .S CfS _ = sectional area of magnetic circuit in cast steel portion of field frame. S t actual field area ; i. e., area occupied by effective inductors. Sg = sectional area of magnetic circuit in air gaps. .S' g = area of clearance spaces in toothed and perforated armature. S m = radiating surface of magnets. S'u = surface of magnet-cores. S m = sectional area of magnet-frame, consisting of but one material. Sp = area of magnet circuit in polepieces of uniform cross- section. .S PI minimum cross-section of polepieces. .S^ = maximum area of magnetic circuit in polepieces. .S s = sectional area of armature slot, in metric units. S" s = sectional area of armature slot, in square inches. Sw. i. sectional area of magnetic circuit in wrought iron por- tion of field frame. S y area of magnetic circuit in yoke. a = factor of magnetic saturation. 7 T , / time. r = torque, or torsional moment. '0 a = rise of temperature in armature, in degrees Centigrade. 6' a = specific temperature increase in armature, in degrees Centigrade. 6 m = rise of temperature in magnets, in degrees Centigrade. ,' m specific temperature increase in magnets, in degrees Centigrade. xxxvi LIST OF SYMBOLS. v = velocity, linear speed. V B = belt velocity, in feet per minute. v' B belt velocity, in feet per second. v = conductor velocity, or cutting speed, in feet (or metres) per second. z' k = commutator velocity, in feet per second. v m = velocity of railway car, in miles per hour. W^n wt = weight. W t = total weight to be propelled by railway motor, in tons. wt & = weight of armature winding, bare wire, in pounds. wt' & = weight of armature winding, covered wire. wt m = weight of magnet winding, bare wire. wt' m = weight of magnet winding, covered wire. wf M = weight of series winding, bare wire. w/'ae = weight of series winding, covered wire. w/ sh = weight of shunt winding, bare wire. wt' A weight of shunt winding, covered wire. X X X (1) In practical dynamos the inductors are usually so arranged upon the armature that their axes are perpendicular to the direction of the motion, i. e., so that a = 90, and for this practical case we have: L x sin 90 x v X 3C = L x v X OC (2) The E. M. F. induced in the moving inductor is propor- tional to this number, hence: . = X# = XZX.' X 3C, (3) where E = E. M. F. induced in moving inductor; $ = total number of lines cut per second; L = length of moving inductor; v = linear velocity of inductor per second; 5C = average density of magnetic field; k = constant, whose value depends upon units chosen. Now, the absolute electric and magnetic systems of units are so related with each other that, if the number of magnetic lines cut per second is expressed in C. G. S. units, the result of formula (3) gives directly the E. M. F. induced, expressed in absolute units, or in other words, if an inductor cuts i C. G. S. line per second, the difference of potential induced in its length by the motion causing such cutting, is i absolute unit of E. M. F. In the C. G. S. system, consequently, the constant k = i. The practical unit of E. M. F., i volt, is one hundred million times greater than the absolute unit, which is inconveniently small,and, in consequence, 100,000,000 C. G. S. lines of force cut per second produce one volt of E. M. F. If,, therefore, # is reckoned in C. G. S. lines, and E is to be measured, as usual, in volts, the value of the constant is k = 1 : = 10 -., IOO,000,OOO 8 DYNAMO-ELECTRIC MACHINES. [ 5 and the formula for the E. M. F., in practical units, becomes: =LXVXWX io~ 8 volts, (4) and now: L length of inductor, in centimetres; v = cutting-velocity, in centimetres per second; 5C = density of field, in C. G. S. lines per square centimetre. 5. Average Electromotive Force. If the rate of cutting lines of force is constant, the E. M. F. induced at any instant is the same throughout the motion of 16 Fig. 4. Inductor Describing Circle in Magnetic Field. the conductor, but if either the cutting-speed or the density of the field varies, the instantaneous values of the E. M. F. vary accordingly, and the average E. M. F. generated in the inductor is the geometrical mean of all the instantaneous values. In a dynamo each inductor is carried in a circle through a more or less homogeneous field; in two diametrically opposite positions therefore, at a and a', Fig. 4, its motion is parallel to the lines of force, while at two positions, b and ', at right angles to a and a', the inductor moves perpendicular to the lines. In positions a and a', consequently, no lines are cut, and the induced E. M. F. is E o, while at b and b' the maxi- mum number of lines is cut in unit time, and E has its maxi- mum value. Between these two extremes any possible value of E exists, according to the angular position of the inductor. 6] CURRENT GENERA TION IN ARM A TURE. 9 The average value of the induced E. M. F. for any movement with a varying number of lines cut is given by the average rate of cutting lines during that movement, and the average rate is the quotient of the total number of lines cut divided by the time required to cut them. The average E. M. F., therefore, is = ~X iQ- 8 volts, (5) where E average value of E. M. F., in volts; $ total number of lines of force cut; / = time required to cut lines, in seconds. If the inductor of Fig. 4 is moved with an angular velocity of N revolutions per minute, or of : 6oT revolutions per second, the number of lines cut in the half- revolution from a to a 1 is , and the time taken by this half-revolution is = ~2N~' seconds; consequently the average E. M. F. for this case is: E = x io~ 8 2 > jy X 10" i (6) 60 "3 in which E = average value of E. M. F., in volts; $> i= total number of lines of force cut; N cutting speed, in revolutions per minute; N' =. cutting speed, in revolutions per second. 6. Direction of Electromotive Force. The direction of the current flowing due to the induced E. M. F. in any inductor depends upon the direction of the lines of force and upon the direction of the motion, and can be determined by applying the well-known " finger-rule" of IO DYNAMO-ELECTRIC MACHINES. 6 Professor Fleming. The directions of the magnetic lines, of the motion, and of the current being perpendicular to each other, three fingers of the hand, placed at right angles to one another, are used to determine any one of these directions when the other two are known. To find the direction of the induced E. M. F. the right hand is employed, being placed in such a position that the tJCumb points in the direction of the magnetic lines (of density 5C), and the middle finger in the direction of the motion, Fig. 5, when the/orefinger will indicate Fig. 5. Finger Rule for Direction of Current. (Right Hand.) P'ig. 6. Finger Rule for Direction of Motion. (Left Hand.) the direction of the /low of the current. Conversely, the direction of the motion which results if a conductor carrying an electric current is placed in the magnetic field of a magnet, is obtained by using in the same manner the respective fingers of the left hand, as shown in Fig. 6, and then the widdle finger will point to the direction in which the motion of the conductor will take place. If, in case of a generator, either the direction of the lines of force or the direction of the motion is reversed, the induced E. M. F. will also be reversed in direction; and if, in case of a motor, either the polarity of the field or the direction of the current in the armature conductors is reversed, the rotation will also change its direction. In the armatures of practical machines the inductors, for the purpose of collecting the E. M. Fs. induced in each, are elec- trically connected with each other, and thereby a system of 6] CURRENT GENERATION IN ARMATURE. II armature coils is formed. According to the number of inductors in each loop there are two kinds of armature coils. In ring armatures, Fig. 7, each coil contains but one inductor per turn, while in drum armatures, Fig. 8, every convolution of the coil is formed of two inductors and two connecting conductors. A CON DUG-TOR CONDU Fig. 7. King Armature Coil. MAGNET POLE Fig. 8. Drum Armature Coil. ring armature coil, therefore, when moved so as to' cut the lines of a magnetic field, has only one E. M. F. induced in it; in a drum armature coil, however, E. M. Fs. are induced in both the inductors, and these two E. M. Fs. may be of the same or of opposite directions, according to the manner in which the coil Fig. 9. Closed Coil moving Horizontally in Magnetic Field. is moved with respect to the lines of force. If the relative position between the magnetic axis of the coil and the direc- tion of the lines does not change, that is, if the angle enclosed by them remains the same during the entire motion of the coil, as in Fig. 9, the E. M. Fs. induced in the two halves counter- 12 DYNAMO-ELECTRIC MACHINES. [V act each other, while when the coil is revolved about an axis perpendicular to the direction of the lines of force, as in Figs. 10 and n, the E. M. Fs. in the two inductors have opposite directions, and therefore add each other when flowing around the coil. Since in the former case, Fig. 9, the number of lines through the coil does not change, while in the latter case, Figs. 10 and n, it does, it follows that E. M. F. is induced in a closed circuit, if this circuit moves in a magnetic field so that the number of lines of force passing through it is altered during the motion. By applying the finger-rule to the single elements of the coil it is found that Figs. 10 and n. Closed Coil Revolving in Magnetic Field. the direction of the induced current is clockwise, viewed in the direction with the lines, if the motion is such as to cause a decreases the number of lines; and is counter-clockwise, if the motion effects an increase in the number of lines. 7. Collection of Current from Armature Coil. If a coil is revolved in a uniform magnetic field, the number of lines threading through it will twice in each revolution be zero, once a maximum in one direction, and once in the other. If, therefore, the current of that coil is collected by means of collector-rings and brushes, Figs. 12 and 13, it will traverse the external circuit, from brush to brush, in one direction for one- half of a revolution^aqxl in the opposite direction in the other half, or an alternating current is produced by the coil. In plotting the positions of the coil in the magnetic field as ordi- nates and the corresponding instantaneous values of the 8] CURRENT GENERATION IN ARMATURE. induced E. M. F. as abscissae, the curve of induced E. M. Fs. y or, since the electrical resistance of the circuit is constant during the motion of the coil, the curve of induced currents is Figs. 12 and 13. Collection of Armature Current. obtained, Fig. 14. Since the instantaneous value e^ at any moment is expressed by the product of the maximum value and the sine of the angle through which the coil has moved, 360' -V- Fig. 14. Curve of Induced E. M. Fs. viz., e 9 = E' X sin cp, the curve of the induced E. M. Fs., in a uniform magnetic field, is a sine-wave, or a sinusoid. 8. Rectification of Alternating Currents. By means of a device called a commutator, the alternating current delivered by the coil to the external circuit can be rectified so as to flow always in the same direction, the negative inductions being commutated into positive ones, and the alternat- ing current transformed into a uni-directed or continuous current. A commutator employed for this purpose in continuous cur- rent dynamos consists of as many conducting cylinder segments DYNAMO-ELECTRIC MACHINES. or circle-sectors as there are coils, in case of a ring armature, and has twice as many commutator-bars or -divisions as there are coils in the case of a drum armature, each commutator-bar being insulated from its neighbors, but in electrical connection with the armature coils and rotating with them. The process Figs. 15 and 16. Commutation of Armature Current. of rectification of the currents generated in the drum armature coil of Figs. 12 and 13 by means of a two-division commutator is shown in Figs. 15 and 16, of which the former refers to the first and the latter to the second half-revolution of the coil. The corresponding curve of the induced E. M. Fs. is repre- sented in Fig. 17, which shows that the current issuing from a Fig. 17. Rectified Curve of E. M. Fs. single coil is of a pulsating character, its value periodically increasing from zero to a maximum, and decreasing again to zero. 9. Fluctuations of Com mutated Currents. The instantaneous E. M. Fs. induced in a single coil vary- ing between the values = .5, or 50$. In order to obtain a less fluctuating current, it is necessary to employ more than one armature coil, the current growing Fig. 1 8. One-Coil Armature. the steadier, the greater the number of the coils. If a coil of, say, 16 turns, Fig. 18, generating a maximum E. M. F. of 'max E' volts, is split up into two coils of half the number of turns each, which are set at right angles to each other, Fig. 19, each will only generate half the maximum E. M. F. 360 V Fig. 19. Two-Coil Armature. of the original coil, viz. : ('i)max (' 2 )max = i6 D YNAMO-ELECTRIC MA CHINES. [ but each of them will have this maximum value while the other one passes through the position of zero induction, as is shown in Fig. 20. Hence, if the E. M. Fs. of the two coils are 90" ISO 870 Fig. 20. Fluctuation of E. M. F. in Two-Coil Armature. added by means of a four-division commutator, the minimum joint E. M. F. in this case is while the total maximum E. M. F., the maximum inductions in the two coils not occurring at the same time, does not reach the maximum valued' of the undivided coil, but, being the "XI / N \ s x 4'' \ i / >,, AA ' % 4 / / 62 \ \ \ i \ / v ; K l y ^ ^135 2 Fig. 21. E. M. Fs. in Two-Coil Armature at one-eighth Revolution. sum of the E. M. Fs. induced at one-eighth revolution, when both partial E. M. Fs. are equal, is, with reference to Fig. 21 f 'ma* = (',) + M*' = ~ (sin 45 + cos 45) E' R' The mean E. M. F., therefore, is = T -(/ min + / max ) = ^ (-5 + - ' = -60356 CURRENT GENERATION IN ARMATURE. 17 and the fluctuation of the E. M. F., with a four-division com- mutator, amounts to 'max-^mean __(.7<>7" ~ -60356) E' $ u 45 90 180 270 Fig. 23. Fluctuations of E. M. F. in Four-Coil Armature. four waves, */, * a ', e s ' and ^', Fig. 23, each varying between the values \?i /rain V^a /rain (?$ /rain (^4 /rain and E f /., '\ /^ '\ _ (p t\ (, '\ \ c i /max \ C 3 /max V^a /max V.^4 /max > and each starting 45 from its neighbor. In combining each two waves 90 apart, by adding their respective ordinates, the 1 8 DYNAMO-ELECTRIC MACHINES. [ 9 four waves are reduced to two, viz., e" and n * + J o COS * - - 9] CURRENT GENERATION IN ARMATURE. 21 = E'l I -- - - cos x +- sin ^ - * ) I 2 /. J The average E. M. F. in this case is: 2 ^ ' / 2 _. -- r~ = - E' . 63662 ^ / 7T which is the same as obtained above for the case of a one-coil armature. In the same manner the average E. M. F. is obtained for any number of coils and is invariably found to be .63662 of the maximum E. M. F. produced if all of the inductive wire is wound in but one coil and connected to the external circuit by a two-division commutator. As might be expected from the definition of the average E. M. F., it will be noted that the values of the mean E. M. F., column 5, Table I., for increasing number of commutator divisions, approach the figure .63662 for the average E. M. F. as a limit. CHAPTER II. THE MAGNETIC FIELD OF DYNAMO-ELECTRIC MACHINES. 10. Unipolar, Bipolar, and Multipolar Induction. From the previous chapter it is evident that an E. M. F, will be induced in a conductor: (1) When the conductor is moved across the lines of force of the field in a direction perpendicular to its own axis and per- pendicular to the direction of the lines, Fig. 27; and (2) When the conductor is revolved in the field about an axis perpendicular to the direction of the lines, Fig. 28. In the first case, the inductor aa, Fig. 27, as it cuts the lines Fig. 27. Unipolar Induction. Fig. 28. Bipolar Induction. of the magnetic field but once in each revolution around the axis oo, and in the same direction each time, is the seat of a uni- directed or continuous E. M. F. In the second case, however, the inductor a, Fig. 28, in revolving about the axis 0, cuts the lines of the field twice in each revolution, and cuts them in the opposite direction alternately; the inductor a, therefore, is the seat of an alternating E. M. F. whose direction undergoes reversal twice every revolution. If the conductor a is made to rotate in a multiple field formed of more than one pair of mag- net poles, Fig. 29, it cuts the lines of all the individual fields, between each two poles, in alternate directions, and an alternating E. M. F. is induced in it, whose direction reverses. 11] THE MAGNETIC FIELD. as many times in every revolution as there are poles to form the multiple field. Since the induced E. M. F. in the first case always has the same direction along the length of the con- ductor, in the second case has two reversals in every revolu- tion, and in the third case reverses its direction as many times as there are poles, three different kinds of inductions are dis- Fig. 29. Multipolar Induction. tinguished accordingly, viz. : Unipolar, Bipolar, and Multipolar induction, respectively. As induction due to but one pole cannot exist, the term " uni- polar induction," if strictly interpreted, is both incorrect and misleading, and Professor Silvanus P. Thompson, in the latest (fifth) edition of his " Dynamo-Electric Machinery," there- fore uses the word homopolar (homo=alike) for unipolar, and heteropolar (hetero=:different) for bi- and multipolar induction. 11. Unipolar Dynamos. In carrying out practically the principle of unipolar induc- tion, as illustrated in Fig. 27, the poles of the magnet are made tubular and the conductor extended into the form of a disc or of a cylinder-ring, Figs. 30 and 31, respectively, in order to cause the unidirected E. M. F. to be maintained continuously at a constant value. The solid disc or solid cylinder-ring inductor is to be considered as a number of contiguous strips, in electrical contact with each other, thus forming a number of conductors in parallel which carry a correspondingly larger DYNAMO-ELECTRIC MACHINES. [H current, but which do not increase the amount of E. M. F. induced. In order to increase the E. M. F. it would be necessary to connect two or more conductors in series, thereby multiplying the inducing length. But heretofore all methods which have been experimented with to achieve the end of grouping in series the conductors on a unipolar dynamo armature have failed, for the reason that the conductor which would have to Fig. 30. Unipolar Disc Dynamo. Fig. 31. Unipolar Cylinder Dynamo. be used to connect the two inductors with each other will itself become an inductor, and, being joined to oppositely situ- ated ends of the two adjoining inductors, will neutralize the E. M. F. produced in a length of inductor equal to its own length. No matter, therefore, how many inductors are placed "in series" on the armature, the resulting E. M. F. will cor- respond to the length of but one of them. By adapting the ring armature to this class of machines, winding the conductor alternately backward and forward across the field which is made discontinuous by dividing up the polefaces into separate projections, loops of several inductors in series can be formed, round which the E. M. F. and current alternate, the character- istic feature of the unipolar continuous current dynamo being thereby lost, and unipolar alternators being obtained. Unipolar dynamos being the only natural continuous current 11] THE MAGNETIC FIELD. 25 machines not requiring commutating devices, 2t (s but a matter of course that attempts are continually being made to render these machines useful for technical purposes; but unless the points brought out in the following are kept in mind, such attempts will be of no avail. 1 From the fact that unipolar dynamos have practically but one conductor, it is evident that its length must be made rather great, and the whole machine rather cumbersome in consequence, in order to obtain sufficient voltage for commer- cial uses. But since a very large amount of current may be drawn from a solid disc or cylinder-ring, it follows that uni- polar dynamos can be practical machines only if built for very large current outputs, such as will be required for metallur- gical purposes and for central station incandescent lighting. Professor F. B. Crocker and C. H. Parmly'have recently taken up this subject in a paper presented to the American Institute of Electrical Engineers, and have shown that the only practical manner in which the unipolar dynamo problem can be solved, is by the use of large solid discs or cylinder- rings of wrought iron or steel run at very high speed between the poles of strong tubular magnets. The greatest advantage of such unipolar machines is their extreme simplicity, thb armature having no winding and nr commutator. The almost infinitesimal armature resistance not only effects increased efficiency and decreased heating, but also causes the machine to regulate more closely either as a generator or as a motor. Furthermore, there is no hysteresis, because the armature and field are always magnetized in exactly the same direction and 1 See " Unipolar Dynamos which will Generate No Current," by Carl Hering, Electrical World, vol. xxiii. p. 53 (January 13, 1894); A. Randolph, Electrical World, vol. xxiii. p. 145 (February 3, 1894); Bruce Ford, Electrical World, Tol. xxiii. p. 238 (February 24, 1894); G. M. Warner, Electrical World, vol. txiii. p. 431 (March 31, 1894); A. G. Webster, Electrical World, vol. xxiii. p. 491 (April 14, 1894); Professor Lecher, Elekirotechn. Zeitschr., January I, 2895, Electrical World, vol. xxv. p. 147 (February 2, 1895); Professor Arnold, Elektrotechn. Zeilschr., March 7, 1895, Electrical World, vol. xxv. p. 427 (April 6, 1895). 2 " Unipolar Dynamos for Electric Light and Power," by F. B. Crocker and C. H. Parmly, Trans. A. I. E. E., vol. xi. p. 406 (May 16, 1894); Electrical World, vol. xxiii. p. 738 (June 2, 1894); Electrical Engineer, vol. xvii. p. 46* .'May 30, 1894). 26 DYNAMO-ELECTRIC MACHINES. [12: to precisely the same intensity. For similar reasons there are no eddy currents, since the E. M. F. generated in any element of the armature is exactly equal to that induced in any other element, the magnetic field being perfectly uniform, owing to the exactly symmetrical construction of the magnet frame. The armature conductor consists of only one single length, conse- quently the maximum magnetizing effect of the armature in am- pere turns is numerically equal to its current capacity, and since the field excitation is considerably greater than this, the arma- ture reaction cannot be great. The armature reaction has the effect of distorting and slightly lengthening the lines of force,, so that they do not pass perpendicularly from one pole surface to the other in the air gap and have a spiral path in the iron. For, the field current tends to produce lines in planes passing through the axis, while the armature current acts at right angles to the field current and produces an inclined resultant. There can, of course, be no change of distribution of magnet- ism as a result of armature reaction, which is the really objec- tionable effect that it produces in bipolar and multipolar machines. Unipolar machines having no back ampere turns, an extremely small air gap, and but very little magnetic leak- age, their exciting power needs to be but very small, compara- tively, and they have, therefore, a very economical magnetic field. Machines of the type recommended by Professor Crocker, finally, are practically indestructible, since they are so simple and can be made so strong that they are not likely to be damaged mechanically, while it is almost impossible to conceive of an armature being burnt out or otherwise injured electrically, as the engine would be stalled by the current before it reached the enormous strength necessary to fuse the armature. Machines possessing all these important advantages certainly deserve a prominent place in electrical engineering, whereas they now have practically no existence whatever. 12. Bipolar Dynamos. While the homopolar (unipolar) dynamo is naturally a con- tinuous current dynamo, the heteropolar (bipolar and multi- polar) dynamo is naturally an alternating current machine, and has to be artificially made to render continuous currents by 12] THE MAGNETIC FIELD. 27 means of a commutator. But in heteropolar machines any number of inductors may be connected in series, and con- sequently high E. M. Fs. may be produced with comparatively small-sized armatures. In Fig. 32 a ring armature placed in a bipolar field is shown. The magnetic lines emanating from the ^V-pole, in passing over to the ,S-pole of the field magnet, first cross the adjacent gap-space, then traverse the armature core, and finally pass across the gap-space at the opposite side. The inductors of the armature as they revolve will cut these magnetic lines twice in every revolution, once each as Fig. 32. Ring Armature in Bipolar Field. they pass through either gap. If the rule for the direction of the induced E. M. F. , as given in 6, is now applied, it is found that in all the inductors that descend through the right- hand gap-space the direction of the induced current is from the observer, while in all inductors that ascend through the left- hand gap-space it is toward the observer. If an armature is wound as a ring, the currents which are produced in the inductors in the gap-space are added up by conductors carrying the currents through the inside of the ring; when, however, the armature is wound as a drum, the currents simply cross at the ends of the core through connect- ing conductors provided to complete a closed electric circuit. In this manner armature coils are formed, in ring as well as in drum armatures, which are grouped symmetrically around the armature core. In order to yield a continuous current these coils must be connected at regular intervals to the respective bars of a commutator, as illustrated by Fig. 33. The currents 28 DYNAMO-ELECTRIC MACHINES, [12 induced in the two gap-spaces will then unite at the top-bar b y and will flow together in the upper brush, which, therefore, is the positive brush in this case, and thence will return, through the external circuit, to the lower or negative brush and will there re-enter the armature at the lowest bar b v of the commu- tator, dividing again into two parts and flowing through the two halves of the winding in parallel circuits. The preceding equally applies to a drum winding, but owing to the overlapping 1 Fig. 33- Commutator Connections of Bipolar Ring Armature. of the two halves of the windings, the paths of the currents cannot be followed up as easily as in a ring winding. By inspection of the diagram, Fig. 33, it is seen that the .current after having divided in its two paths goes from coil to coil without flowing down in any of the commutator bars, until both streams unite at the other side and pass down into the bar of the commutator which is at the time passing under the brush. At the instant when one of the commutator segments is just leaving contact with the brush and another one is coming into contact with it, the brush will rest upon two adjacent bars and will momentarily short-circuit one of the coils. While this lasts the two streams will unite by both flowing into the same brush from the two adjacent com- mutator segments. A moment later the short-circuited coil when it has passed the brush will belong to the other half of the armature, that is to say, in the act of passing the brush 12] THE MAGNETIC FIELD. 29 every coil will be transferred from one half of the armature to the other, and will have its current reversed. This is, in fact, the act of commutation, and the conditions under which it takes place govern the proper functioning of the machine when running, as they directly control the presence and amount of sparking at the brushes. The production of sparks is a consequence of the property of self-induction in virtue of which, owing to the current in a conductor setting up a magnetic field of its own, it is im- possible to instantaneously start, stop, or reverse a current. If the act of commutation occurs exactly at the point when the short-circuited coils under the two brushes are not cutting any magnetic lines at all, no E. M. F. is induced in them at the time and they are perfectly idle when entering the other half of the armature winding. On account of the self- induction the current cannot instantly rise to its full strength in these idle coils, and it will spark across the commutator bars as the brushes leave them. From this can be concluded that the ideal arrangement is attained if the brushes are shifted just so far beyond the point of maximum E. M. F. that, while each successive coil passes under the brush and is short-circuited, it should actually have a reverse E. M. F. of such an amount induced in it as to cause a current of the opposite direction to circulate in it, exactly equal in strength to that which is flowing in the other half of the armature which it is then ready to join without sparking. A magnetic field of the proper intensity to cause the current in the short- circuited coil to be stopped, reversed, and started at equal strength in the opposite direction can usually be found just outside the tip of the polepiece, for here the fringe of mag- netic lines presents a density which increases very rapidly toward the polepiece. Since a more intense field is needed to reverse a large current than is required for a small one, it follows that for sparkless commutation the brushes must be shifted through the greater an angle the greater the current output of the armature. Since it takes a certain length of time to reverse a current, the brushes must be of sufficient thickness to short-circuit the coils for that length of time, while on the other hand they must not be so wide as to short- circuit a number of coils at the time, as this again would 30 D YNA MO- EL ECTRIC MA CHINE S. [12 increase the tendency to sparking on account of increased self-induction. From the preceding, then, it is evident that sparkless commutation will be promoted (i) by dividing up the armature into many sections so as to do the reversing of the current in detail; (2) by making the field magnet relatively powerful, thereby securing between the pole tips a fringe of field of sufficient strength to reverse the currents in the short- circuited coils; (3) by so shaping the pole surfaces as to give a fringe of magnetic field of suitable extent; (4) by choosing brushes of proper thickness and keeping their contact surfaces well trimmed. Since the direction of a current causing a certain motion is opposite to the direction of the current caused by that motion, it follows that in a generator the current induced in the short- circuited coil at a certain position has just the opposite direction with relation to the current flowing in the armature from that induced in the short-circuited coil of a motor in the same position, when rotating in the same direction. That is to say, if in a generator the brushes are shifted so that the current induced in the short-circuited coil has the same direction as the current flowing in the half of the armature it is about to join, in a motor revolving in the same direction and having its brushes set in exactly the same position, the current in the commuted coil, which absolutely of course has the same direction as in case of the generator, would relatively have a direction opposite to that flowing in the half of the armature to which it is transferred by the act of commutation. While the brushes, in order to attain sparkless commutation, must therefore be shifted with the direction of rotation, or must be given an angle of lead in a generator, in a motor they have to be shifted backward, or have to be given an angle of lag. In a generator the effect of commutation is a tendency to increase the aggregate magnetomotive force and therefore to strengthen the field; in a motor, however, the effect of com- mutation is to decrease the magnetomotive force and to weaken the field. Iron is very sensitive to slight increases of magnetomotive force, while on the other hand it is com- paratively insensible to considerable decrease of magneto- motive force; in generators, therefore, the danger of 12] THE MAGNETIC FIELD. sparking due to improper setting of the brushes is much greater than in motors. If the magnetic field is perfectly uniform in strength all around the armature, the E. M. Fs. generated in the separate coils will be all of equal amount; but in actual dynamos the distribution of the magnetic lines in the gaps is always more or less uneven, and the E. M. Fs. in the different coils, therefore, have more or less varying strengths. In well- designed machines, however, the magnetic lines, although unevenly distributed around the armature, are symmetrically Figs. 34 and 35. Methods of Exploring Distribution of Potential around Armature. situated in the two air gaps, and the total E. M. F. of either half of the winding, being the sum of the individual E. M. Fs. of the separate coils, will be equal to the total E. M. F. of the other half, from brush to brush. As the distribution of the magnetic flux around the armature directly affects the distribution of the potential, an examination of the latter will .allow conclusions to be drawn as to the former. There are two ways of studying the distribution of the potential around the armature : (i) by observing the voltmeter- deflections caused by the individual coils, a set of exploring brushes being placed, in turn, against every two adjacent com- mutator bars, Fig. 34, and (2) by taking a voltmeter-reading for every bar, the voltmeter being connected- between one of the main brushes and an exploring brush sliding upon the -commutator, Fig, 35. .By plotting the voltmeter readings, in the first case a curve is obtained which shows the relative 3 2 DYNAMO-ELECTRIC MACHINES. [12; amount of E. M. F. induced in each armature coil when brought in the various parts of the magnetic field, while the curve received in the second case gives the totalized or " integrated " potential around the armature, such as is found for any point in one of the armature halves by adding up the E. M. Fs. of all the coils from the brush to that point. The investigation of the distribution of the potential around the commutator is very useful in practice, as it may disclose unsymmetrical distribution of the magnetic field due to faulty design of the magnet frame, or to incorrect shape of the pole- pieces, or to other causes. Fig. 36 shows the curves of s 90 180 270 J Fig' 36. Curves of Potentials around Armature at No Load. 90 180 270 300 Fig. 37. Curves of Potentials around Armature at Full Load. potentials around an armature rotating in an evenly dis- tributed field, such as will exist in a well-proportioned dynamo when there is no current flowing in the armature, that is to say, when the machine is running on open circuit. In Fig. 37 similar curves are given for a correctly designed dynamo with unevenly but symmetrically distributed field, as distorted by the action of the armature current when running on closed circuit. In both diagrams A is the curve of potentials in each coil, obtained by the first method, and B the curve of inte- grated potential, obtained by the second method of exploring the distribution of potential around the commutator. If either one of the curves A or B is given by experiment, the ordinates of the other may be directly obtained by one of the following formulae given by George P. Huhn: 1 1 " On Distribution of Potential," by George P. Huhn, Electrical Engineer, vol. xv. p. 186 (February 15, 1893). 13] THE MAGNETIC FIELD. 33 and X a X sin a: sin a 7T i cos a X in which X a = ordinate, at angle a from starting position of curve of integral potential; x a = ordinate, at angle a from starting position of curve of potential in each coil; n c = number of commutator divisions. The potentials may also with advantage be plotted out round a circle corresponding to the circumference of the commutator, the reading for each coil being projected radially from the Fig. 38. Distribu- tion of Potential around Commu- tator at No Load. ig- 39- Distribution of Potential around Commutator at Full Load. Fig. 40. Distribution of Potential around Commutator of Faulty Dynamo. respective commutator division. Fig. 38 shows, thus plotted, the curve of potentials at no load, and Fig. 39 that at full load of a well-arranged dynamo, while Fig. 40 depicts the distribu- tion of potential around the commutator of a badly designed machine. 13. Multipolar Dynamos. While bipolar dynamos offer advantages when small capaci- ties are required, their output per unit of weight does not materially increase with increasing size, and a more economical form of machine is therefore desired for large outputs. In order that the weight-efficiency (output per pound of weight) of a dynamo may be increased without increasing the periphery velocity of the armature, or dangerously increasing the tern- 34 DYNAMO-ELECTRIC MACHINES. [13 perature limit, it is necessary to decrease the reluctance of the magnetic circuit, that is, to reduce the ratio of the length of the air gap to the area of its cross section. Since the length of the armature cannot be increased beyond certain limits governed by mechanical as well as magnetical conditions, the only means of increasing the gap area remains to increase the armature diameter. Increasing the diameter of an armature allows a greater circumference on which to wind conductors, and therefore the depth of the winding may be proportionally decreased. Thus the increase of the armature diameter not only increases the gap area, but also decreases its length, and consequently very effectively reduces the reluctance of the ^magnetic circuit. With armatures of such large diameters, in order to more evenly distribute the magnetic flux, and to more economically make use of space and weight of the magnet frame, it is advantageous to divide the magnetic circuit, resulting in dynamos with more than one pair of poles, or multi- .-polar dynamos. For small multipolar dynamos drum armatures are often used ; large machines for continuous current work, however, have always ring armatures. In a multipolar armature there are as many neutral and commutating planes as there are pairs of poles, -and, therefore, as many sets of brushes as there are poles. Often, however, all commutator segments that are symmetri- cally situated with respect to the separate magnetic circuits are cross-connected among each other, so that the separate portions of the armature winding corresponding to the separate magnetic circuits are actually connected in parallel within the machine, and then only two brushes, in any two subsequent planes of commutation, are necessary. But unless the arma- ture is in excellent electric and magnetic balance, and all the magnetic circuits of the machine have an equal effect on the armature, excessive heating and sparking are bound to result from this arrangement. This trouble may be avoided by wind- ing the armature so that the current is divided between only two paths, exactly as in a bipolar machine. When such ;a two-path, or scries, winding is used, the wire of each coil must cross the face of the core as many times as there are field- poles, the turns being spaced at a distance equal to nearly the pitch of the poles. Series-wound multipolar armatures will 14] THE MAGNETIC FIELD. 35 operate satisfactorily regardless of inequalities in the strength of the magnetic circuits. Unless specially arranged, these armatures require only two brushes which are 180 apart in machines having an odd number of pairs of poles, and at an angular distance apart equal to the pitch of the poles in machines having an even number of pairs of poles. Sometimes the commutators of series armatures are arranged with twice as many bars as there are coils in the armature, in which case the extra bars are properly cross-connected to the active bars, so that four brushes may be used in order to give a greater current-carrying capacity. To economize wire in multipolar armatures, it is of advantage to arrange the winding so that no wires have to pass through the inside of the ring, the inductors being connected by conductors on either face of the core. An armature so wound is termed a drum-wound ring armattire. If the dynamos are to be directly coupled to the steam engines, particularly low rotative speeds of the armatures are required, and their diameters are then made extra large in order to give them low speed without too great a reduction of periphery velocity. To fully utilize the large armature circum- ference of such low speed multipolar machines, the number of poles is usually made very high, their actual number depending upon the capacity of the machine and the service required of it. Great reductions of rotative speed can, however, only be obtained either by considerable sacrifice of weight-efficiency, or by sacrificing sparkless operation. The former, when carried to an extreme, makes too expensive a machine, and the latter causes increased repairs and depreciation; a mean between the two must therefore be followed in practice. 14. Methods of Exciting Field Magnetism. In modern dynamos the field magnetism is excited by current from the armature of the machine itself. According to the manner in which current is taken from the armature and sent through the field winding, we distinguish, as far as continuous current machines are concerned, the following classes of dynamos: (a) Series-wound, or Series dynamo; (b) Shunt- wound, or Shunt dynamo, and (c) Compound-wound, or Com- pound dynamo. DYNAMO-ELECTRIC MACHINES. [14 a. Series Dynamo. In the series-wound dynamo the whole current from the armature is carried through the field-magnet coils, the latter being wound with comparatively few turns of heavy copper Fig. 41. Diagram of Series- Wound Dynamo. wire, cable, or ribbon, and connected in series with the main circuit, Fig. 41. Denoting by E = total E. M. F. generated in armature; /' = total current generated in armature; r & = armature resistance; E = terminal voltage, or potential of dynamo; 7 = useful current flowing in external circuit; R =. resistance of external or working circuit; 7 ge = current in series field; r se = resistance of series-field coil; 7/ e = electrical efficiency; the following equations exist, by virtue of Ohm's law of the electric circuit, for the series dynamo: /' = E' (8) = / =/' 14] THE MAGNETIC FIELD. 37 (9) useful energy _ E I _ E total energy : ~ ~E r T ~ ~E~' X From equations (8) it is evident that an increase in the working resistance directly diminishes the current in the field coils, therefore reducing the amount of the effective magnetic flux, and that on the other hand a decrease of the external resistance tends to increase the excitation and, in consequence, the flux. The constancy of the flux thus depending upon the constancy of the current strength in series-wound dynamos, these machines are best adapted for service requiring a con- stant current, such as series arc lighting. Equation (9) shows that the current generated in the arma- ture of a series dynamo, in order to overcome the resistances of armature and series field, loses a portion of its E. M. F. ; the E. M. F. to be generated in the armature of a series-wound machine, therefore, is equal to the required useful potential, increased by the drops in the armature and in the series-field winding. Series machines having but one circuit the current intensity is the same throughout, and consequently the current to be generated in the armature is equal to the current required in the external circuit. The end result of equation (10) shows that the electrical efficiency of a series dynamo is obviously a maximum when the armature resistance and field resistance are both as small as possible. In practice they are usually about equal. The series-wound dynamo has the disadvantage of not start- ing action until a certain speed has been attained, or unless the resistance of the circuit is below a certain limit, the machine refusing to excite when there is too much resistance or too little speed. b. Shunt Dynamo. In the shunt-wound dynamo the field-magnet coils are wound with many turns of fine wire, and are connected to the brushes of the machine, constituting a by-pass circuit of high D YNA MO- ELE C 7 'R1C MA CHINES. resistance through which only a small portion of the armature current passes, Fig. 42. Using similar symbols as in the case of the series dynamo, Fig. 42. Diagram of Shunt-Wound Dynamo. the following fundamental equations for the shunt dynamo can be derived: /' = /+/, = /+ A > , X R - E - T ~' sh " ' = ..(11) 7 2 "a + ^sh) R , (13) 14] 7 'HE MAGNETIC FIELD. 39- Equations (n) show that in a shunt dynamo an increase of the external resistance, by diminishing the current in the working circuit, increases the shunt current, and with it the magnetic flux, while a decrease of the working resistance increases the useful current, the sum of which and the shunt current is a constant as long as the total current generated in the armature remains the same, thereby reducing the exciting current and ultimately decreasing the magnetic flux. The flux remains constant only when the potential of the machine is kept the same, as then the shunt current, which is the quotient of the terminal pressure and the constant shunt resistance, is also constant; shunt-wound machines, therefore, are best adapted for service demanding a constant supply of pressure, such as parallel incandescent lighting. Since the stronger a current flows through the shunt circuit the less is the current intensity of the main circuit, a shunt machine will refuse to excite itself if the resistance of the main circuit is too low. From (n) and (12) it is seen that the armature current of a shunt dynamo suffers a loss both in E. M. F. and in intensity within the machine; E. M. F. being lost in overcoming the armature resistance, and current intensity in supplying the shunt circuit. In consequence, the E. M. F. to be generated in a shunt dynamo must be equal to the potential required in the working circuit, plus the drop in the armature; and the total current is equal to the useful amperage required, plus the current strength used for field excitation. The efficiency of a shunt dynamo, by equation (13), becomes maximum under the condition ' that (14) Inserting this value in (13) we obtain the equation for the max- imum electrical efficiency of a shunt dynamo: V '* 1 Sir W. Thomson (Lord Kelvin), La Lumiere Electr., iv., p. 385 (1881), 4 o D YNAMO-ELECTRIC MA CHINES. [14 Now, since the armature resistance is usually very small com- pared with the shunt-field resistance, the sum r & -f- r sh may be replaced by r ah , and the quotient may be neglected, when the following very simple approximate value of the efficiency is obtained: (16) and this, by transformation, furnishes (17) By means of equation (16) the approximate electrical efficiency of any shunt dynamo can be computed if armature and magnet resistance are known; and from formula (17) the ratio of shunt resistance to armature resistance for any given per- centage of efficiency can directly be calculated. In the follow- ing Table II. these ratios are given for electrical efficiencies from 7/ e = .8, to ^ e = .995, or from 80 to 99.5 per cent. : TABLE II. RATIO OF SHUNT TO ARMATURE RESISTANCE FOR DIFFERENT EFFICIENCIES. PERCENTAGE OF ELECTRICAL EFFICIENCY. RATIO OF SHUNT TO ARMATURE RESISTANCE. PERCENTAGE OF ELECTRICAL EFFICIENCY. RATIO OF SHUNT TO ARMATURE RESISTANCE. 100 ?e rsh ra 100 rje rsh 7'a 80# 64 95.5$ 1,802 85 128 96 2,304 87.5 196 96.5 3,041 90 324 97 4,182 91 409 97.5 6,084 92 529 98 9.604 93 706 98.5 17,248 94 983 99 39,204 95 1,444 99.5 158,404 14] THE MAGNETIC FIELD. c. Compound Dynamo. Compound winding is a combination of shunt and series excitation. The field coils of a compound dynamo are partly wound with fine wire and partly with heavy conductors, the fine winding being traversed by a shunt current and the heavy winding by the main current. The shunt circuit may be derived from the brushes of the machine or from the terminals of the external circuit; in the former case the combination is termed a short shunt compound winding, or an ordinary compound winding, Fig. 43, in the latter case a long shunt compound wind- ing, Fig. 44. Employing the same symbols as before, the application of Fig. 43. Diagram of Ordinary Compound- Wound Dynamo. Ohm's law furnishes the following equations for the compound dynamo: (i) Ordinary Compound Dynamo (Fig. 43). = /X sh sh sh J ....(18) 42 DYNAMO-ELECTRIC MACHINES. = ^ + El TV/? E'i' -/'V a + / 8h v 8h + / 2 (je + I (2) ZtfTZg" Shunt Compound Dynamo (Fig. 44). ,...(19) >...(20> v E_J R Fig. 44. Diagram of Long Shunt Compound-Wound Dynamo. (21) sh $14] THE MAGNETIC FIELD. 43 r R (23) , ^(r. + r, ~ V By combining the shunt and series windings, the excitation of the dynamo can be held constant, as the main current diminishes and the shunt current increases with increasing working resistance, and the main current rises and the shunt current decreases with decreasing external resistance. A compound-wound dynamo, therefore, if properly proportioned, will maintain a constant potential for varying load. In the case of the ordinary compound dynamo, the potential between the brushes is thus kept constant, in case of the long shunt compound dynamo the potential between the terminals of the working circuit. Although, therefore, the latter arrangement is the more desirable in practice, in a well-designed dynamo it makes very little difference whether the shunt is connected across the brushes or across the terminals of the external circuit. In the ordinary compound dynamo the series winding sup- plies the excitation necessary to produce a potential equal in amount to the voltage lost by armature resistance and by arma- ture reaction; in the long shunt compound dynamo the series winding compensates for armature reaction, and for the drop in the series field as well as for that in the armature. The series winding may even be so proportioned that the increase of pressure due to it exceeds the lost voltage, and then the dynamo is said to be over-compounded, and gives higher voltage at full load than on open circuit. Compound dynamos used for incandescent lighting are usually about 5 per cent, over- compounded in order to compensate for drop in the line from the machine to the lamps. The armature current of a compound dynamo suffering a drop both in potential and in intensity within the machine, in calcu- 44 DYNAMO-ELECTRIC MACHINES. [14 lating a compound-wound machine the total E. M. F. to be generated must be taken equal to the required potential plus the voltage necessary to overcome armature and series-field resistances; and the total current strength of the armature equal to the intensity of the external circuit increased by the current used in exciting the shunt field. PART II. CALCULATION OF ARMATURE. CHAPTER III. FUNDAMENTAL CALCULATIONS FOR ARMATURE WINDING. 15. Unit Armature Induction. It is evident that a certain length of wire moving with the same speed in magnetic fields of equal strengths will invariably generate the same electromotive force, no matter whether the said length of wire be placed on the circumference of a drum or of a ring armature, and no matter whatever may be the shape of the field magnet frame, or the number of poles of the different magnetic fields. In order to obtain such a constant, suitable for practical purposes, we start from the definition: " One volt E. M. F. is generated by a conductor when cutting a magnetic field at the rate of 100,000,000 C. G. S. lines of force per second." Since the English system of measurement is still the standard in this country, we will take one foot as the unit length of wire, and one foot per second as its unit linear velocity, and for the unit of field strength we take an intensity of one line of force per square inch. At the same time, however, for calculation in the metric system, one metre is taken as the unit for the length of the conductor, one metre per second as the unit velocity, and one line per square centimetre as the unit of field density. Based upon the law: "The E. M. F. generated in a con- ductor is directly proportional to the length and the cutting speed of the conductor, and to the number of lines of force cut per unit of time," we can then derive the unit amounts of E. M. F. generated in the respective systems of measure- ment, with the following results: " Every foot of inductor moving with the velocity of one foot per .second in a magnetic field of the density of one line of force per square inch generates an electromotive force of 144 X io~* volt" and " Every metre of inductor cutting at a speed of one metre per second through a field having a density of one line per square centi- metre generates io~* volt." 47 4 8 D YNA MO-ELEC TRIG MA CHINE S. [15- The derivation of these two laws from the fundamental defi- nition is given in the following Table III.: TABLE III. UNIT INDUCTIONS. LENGTH OP INDUCTOR. CUTTING VELOCITY. DENSITY OP FIELD. E. M. F. GENERATED. 1 foot 1 foot 1 foot 1 ft. per second 1 ft. per second 1 ft. per second 100,000,000 lines per sq. ft. 100,000,000 lines per sq. in. 1 line per sq. in. 1 Volt 144 Volts 144X10- 8 Volt 1 cm. 1 metre 1 metre 1 metre 1 cm. per second 1 m. per second 1 m. per second 1 m. per second 100,000,000 lines per sq. cm. 100,000,000 lines per sq. m. 100,000,000 lines persq. cm. 1 line per sq. cm. 1 Volt 1 Volt 10,000 Volts 10-* Volt If two or more equal lengths are connected in parallel, in each of these wires every unit of length will produce the respec- tive unit of induction, but these parallel E. M. Fs. will not add, but the total E. M. F. generated in one length will also be the total E. M. F. output of the combination. In an ordinary bipolar armature, now, there are two such parallel branches, each branch generating the total E. M. F. This necessitates one foot of generating wire in each of these two parallel circuits, or altogether two feet of wire, under our unit conditions, in order to obtain an E. M. F. output of 144 x io~ 8 volt; or, in other words: Every foot of the total gen- erating wire on a bipolar armature, at a cutting speed of one foot per second, in a field of one line per square inch, generates 72 X io~* volt of the output E. M. F. And by a similar consideration we find for the metric system : Every metre of the actual inductive wire on a bipolar armature revolving with a cutting velocity of one metre per second in a field of one line per square centimetre, gen- erates 5 X icr* volt of the output E. M. F. In multipolar armatures the number of the electrically paral- lel portions of the winding generally is 2#' p , the number of pairs of parallel armature circuits, or the number of bifurca- tions of the current in the armature being denoted by ' p , and usually 2' p is equal to the number of poles, 2 p , the number of pairs of poles being denoted by p . In such armatures it therefore takes 2' p feet of generating conductor to produce 144 x io~ 8 volt of output, or the share of E. M. F. contrib- 15] FUNDAMENTAL CALCULATIONS FOR WINDING. 49- uted to the total output by every foot of the generating wire on the entire pole-facing circumference is 144 x io~ 8 _ 72 x iQ- 8 volt ; that is, 72 x icr* volt per pair of armature circuits, or per pair of poles, respectively. In metric units the share of the E. M. F. contributed to the output of a multipolar arma- ture by every metre of the inductive length of the armature conductor is 5 X io~ 5 volt, or 5 x io~* volt per bifurcation. These theoretical values of the " unit armature induction" however, have to undergo a slight modification for prac- tical use, owing to the fact that generally only a portion of the total generating or active wire of an armature is effective. ' 'Active" is all the wire that is placed upon the pole-facing surface of the armature, "effective" only that portion of it which is actually generating E. M. F. at any time; that is, the portion immediately opposite the poles and within the reach of the lines of force, at that time. The percentage of effective polar arc, in modern dynamos, according to the number and arrangement of the poles, varies from 50 to 100 per cent, and, usually, lies between 70 and 80 per cent., corresponding to a pole angle of 120 to 144, respectively. The lowest values of the effective arc, 50 to 60 per cent, of the total circumference, are found in the multipo- lar machines made by Schuckert, with poles parallel to the armature shaft, and having no separate pole shoes; in these the space taken up by the magnet winding prevents the poles from being as close together as in machines of other types. The highest figure, 100 per cent., is met in some of the Allgemeine Elektricitaets Gesellschaft dynamos, in which the poles are united by a common cast-iron ring (Dobrowohky* s pole bushing. See 76, Chap. XV.). In fixing a preliminary value of this precentage, fi lt in case of a new design, take 67 to 80 per cent., or ^ = .67 to .80, for smooth drum armatures; /?, = .75 to .85 for smooth rings, and D YNA MO-ELECTRIC MA CHINES. [15 A = -7 to -9 for toothed and perforated armatures. The lower of the given limits refers to small, and the upper to large sizes, for the final value of p l is determined with reference to the length of the air gaps, and the latter are comparatively much smaller in large than in small dynamos. Also the num- ber of the magnet poles somewhat affects the selection of /? the smaller a percentage usually being preferable the larger the number of field poles. For these various percentages the author has found the average values of the unit armature induction given in the following Table IV. : TABLE IV. PRACTICAL VALUES OF UNIT ARMATURE INDUCTION. E. M. F. PER PAIR OF ARMATURE CIRCUITS. PERCENTAGE ENGLISH UNITS. METRIC UNITS. OF Volt per Foot. Volt per Metre. POLAR ARC. BIPOLAR MULTIPOLAR BIPOLAR MULTIPOLAR DYNAMOS. DYNAMOS. DYNAMOS. DYNAMOS. ft e e ei i 1.00 72 X 10- 72 X 10- 8 5 X 10-' 5 X 10- 5 .95 71 68 4.9 48 .90 70 65 48 4.6 .85 67.5 62.5 4.7 4.4 .80 65 60 4.6 4.2 .75 625 57.5 4.4 4 .70 60 55 4.2 3.8 .65 57.5 52.5 4 3.6 .60 55 50 3.8 3.4 .55 52.5 47.5 3.6 3.2 .50 50 45 3.4 3 It will be noticed that the values for multipolar machines run somewhat below those for bipolar ones. This means that, at the same rate of polar embrace, a greater percentage of the total active wire is effective in the case of a bipolar machine, which is undoubtedly due to a greater circumferential spread of the lines of force of bipolar fields. 16] FUNDAMENTAL CALCULATIONS FOR WINDING. 5 1 16. Specific Armature Induction. Knowing the values of the induction per unit length of active armature wire under unit conditions, a general ex- pression can now easily be derived for the " specific armature induction" at any given conductor speed and field density. The induction per unit length of active conductor, in any armature, is *' = - X v e X OC", ......... where *' = specific induction of active armature conductor, in volts per foot; ^ = unit armature induction per pair of armature cir- cuits, in volts per foot, from Table IV. ; ' p number of bifurcations of current in armature, or number of pairs of parallel armature circuits; 'p has the following values, to be multiplied by the number of independent windings in case of multiplex grouping ( 44): ' p = i for bipolar dynamos and for multipolar ma- chines having ordinary series grouping, 'p = ;/ p for multipolar dynamos with parallel group- ing, ;/ p being the number of pairs of mag- net poles, ' p = ^ for multipolar dynamo with series-parallel 3 grouping, n s being the number of arma- ture circuits connected in series in each of the 2#'p parallel circuits; v = conductor-velocity, or cutting speed, in feet per second, from Table V. ; OC" = field density, in lines of force per square inch, from Table VI. In order to obtain the specific armature induction in the metric system, * is to be replaced by the corresponding value of *j, Table IV. ; the conductor velocity is to be expressed in metres per second, Table V., and the field density, X, in lines per square centimetre, from Table VII. ; then (24) gives the specific armature induction in volts per metre of active conductor. 52 D YNA MO-ELECTRIC MA CHINES. [17 17. Conductor Telocity. The E.M.F. of a dynamo, according to formula (4), is pro- portional to the velocity v c of the moving conductor; since, therefore, the output of a given dynamo can be raised by simply increasing its speed, it will be best economy to run a dynamo-electric machine at as high a conductor speed as practically possible. The velocity, however, is limited mechanically as well as electrically; mechanically, because the friction in the bearings and the strain in the revolving parts due to centrifugal force, must not exceed certain limits; and electrically, because the heating of the armature caused by the resistance of the wind- ing and by hysteresis and eddy currents in the iron, must be kept reasonably low by limiting the power loss, which increases with the output, and therefore is the greater, the higher the conductor speed is chosen. Furthermore, if the number of revolutions of the armature is given, either by the speed of the engine in case of a direct-driven machine, or otherwise, the above mechanical and electrical limitations alone are not sufficient for choosing the conductor velocity, for, when the number of revolutions is fixed, the diameter of the armature is proportional to the peripheral velocity, and abnormal sizes may be obtained by assuming a value of v c , which is permissible from all the other considerations. The limits of v established by practice are from 25 to 100 feet per second, according to the kind, size, and revolving speed of the machine. A common value is 50 feet per second, or 3000 feet per minute, which in the metric system corre- sponds to about 15 metres per second, or 900 metres per min- ute. For drum armatures, the average practical values of the conductor velocity range between 25 and 50 feet per second, and for ring armatures, which offer a better ventilation and are lighter than drum armatures of the same diameter, con- ductor velocities up to 100 feet per second are employed. Values near the upper limits are chosen for high-speed machines, in which the selection of a low peripheral velocity would re- sult in too small an armature diameter; the radiating surface, or more properly called the cooling surface, of the armature would consequently be inadequate, and excessive heating would be inevitable. Values near the lower limit, on the 17J FUNDAMENTAL CALCULATIONS FOR WINDING. S 2a other hand, are taken for low-speed machines, because too large a conductor velocity would in their case excessively increase the diameter of the armature, and in consequence would bring the size of the entire machine out of proportion to its output. The following Table V will serve the unexperienced designer as a guide in selecting the proper value of v c for various sizes of drum and ring armature machines. This table is compiled from the data of a great many practical machines, the scope of which can best be seen from the list of machines given in the Preface. The averages given for drum armatures are intended for the usual case of high-speed drum machines, but they hold also good for medium and low-speeds, if it is considered that the figures given in the table are in each case averaged from widely differing actual values of the conductor velocity, so that good practical values of v c for each size may be taken from about 20 to 25 per cent, below to about as much above the TABLE V. AVERAGE CONDUCTOR VELOCITIES. CONDUCTOR VELOCITY, IN FEET CONDUCTOR VELOCITY, IN METRBS PER SECOND. PER SECOND. CAPACITY IN Ring Armature. Ring Armature. Drum Drum KILOWATTS. Armature Armature High Medium Low High Medium Low Speed. Speed. Speed. Speed. Speed. Speed. .1 25 50 25 7.5 15 7.5 .25 27 55 27 8 16.5 8 .5 30 60 30 25 9 18 9 '7.5 1 35 65 30 25 10.5 19.5 9 7.5 2.5 40 70 35 25 12 21 10.5 7.5 5 45 70 40 26 13.5 21 12 8 10 45 75 40 28 13.5 22.5 12 8.5 25 50 75 45 30 15 22.5 13.5 9 50 50 80 50 32 15 24 15 10 100 50 80 50 35 15 24 15 11 200 50 85 50 40 15 25.5 15 12 300 50 85 55 40 15 25.5 16.5 12 500 90 55 45 27 16.5 13.5 1000 90 60 45 27 18 13.5 2000 95 60 45 28.5 18 13.5 5000 100 65 50 30 19.5 15 given average. Thus, for instance, the conductor velocity of a 2.5-KW drum armature may be chosen between .75 x 40 = 30 and 1.25 x 40 = 50 feet per second ; and the velocity of drum D YNA MO- RLE CTR1C MA CHINE S. [17 machines above 25 KW output may be taken within the limits of .75 X 50 = 37.5 and 1.25 x 50 = 62.5 feet per second. In the case of ring armatures, in which the peripheral veloc- ities vary in much wider limits than in drum armatures, separate averages are given for high, medium, and low speeds; and in each case a deviation of about 15 per cent, above or below the given average is within good practical limits. For example, the value of v c for a 5-KW high-speed ring armature may be selected between .85 x 70 = 60 and 1. 15 x 70 = 80 feet per second. It will be noted that the value of v c for a ring armature of given output varies considerably with the speed at which the machine is run, for the reasons given above. Since the size of the armature, and therefore the general proportion of the entire machine, depends directly upon the value chosen for v c , it is evident that the proper selection of the conductor velocity is one of the most important assumptions to be made by the designer. TABLE Va. HIGH, MEDIUM, AND Low DYNAMO SPEEDS. CAPACITY DRUM ARMATURES. RING ARMATURES. IN High .Medium Low High Medium Low KILOWATTS. Speeds. Speeds. Speeds. Speeds. Speeds. Speeds. .1 3000 to 2400 2400 to 1800 1800 to 1200 2600 to 2200 2200 to 1600 .25 2800 2200 2200 16(JO 1600 10002400 2000 am 1400 .5 2600 2000 2000 1500 1500 8002200 1800 1800 1200 120o"t "eoo 1 2400 1800 1800 1400 1400 7002000 160013(0 1000 1000 5('0 2.5 2200 1600 1600 1200 1300 6001800 1400 1400 800 800 400 5 12000 1400 1400 1000 1000 500il600 1200 1200 700 700 300 10 1800 1200 1200 800 800 400 1400 1000 1000 600 600 250 25 1500 1000 1000 600 600 3001200 850 850 500 500 200 50 1200 800 800 500 500 2501000 700 700 400 400 150 100 1000 600 600 400 400 200 800 550 550 300 300 125 200 800 450 450 300 300 150 600 400 400 200 200 100 500 200 inn nnn 300 300 150 150 80 1000 400 250 250 125 125 ' 70 2000 ! ann 200 200 100 100 4 ftft 5000 250 150 150 80 80 " 50 The diameter of the armature must be of such magnitude that the required length of armature conductor can be placed upon the core, if made of the proper length for that diameter, without causing the winding depth to be too great, or without causing an abnormal length of the armature when 17] FUNDAMENTAL CALCULATIONS FOR WINDING. $2C wound to a certain depth proper for the diameter in question. And furthermore, the dimensions of the armature must be such that the size of its superficial area is adequate to liberate the heat generated in 'the winding .and. in the core. For these reasons it is an advantage to calculate the armature for several values of the conductor velocity, and to select the best size obtained, all things considered. In Table Va, p. 52^, the usual speeds of various sizes of dynamos and their classification into high, medium, and low speeds are given. The values of ^ c for ring armatures, in Table V., refer to the average of the respective speeds in Table Va. If the dynamo in the given problem is a high-speed machine running near the lower limit, or a medium-speed machine running at a speed near the upper limit given in Table V#, a value of v c about halfway between the high-speed and the medium- speed average is to be taken. If the speed specified for the dynamo to be designed is near the lower medium, or the upper low-speed limit, a value near the mean of the medium and the low-speed values of v c should be selected. For speeds near the upper high-speed or the lower low-speed limits, a value of z> c somewhat higher than the high-speed average, or lower than the low-speed average, respectively, should be chosen. For instance, if a ring armature for a 25-KW dynamo is to be designed to run at 800 revolutions per minute, the average conductor velocity is obtained as follows: From Table Va it is seen that the given speed, though found under the head of ''medium speed," approaches the lower limit given for high speeds; the average value of v c for medium-speed machines of the size in question is 45 ; the average for 25-KW high-speed ring armatures is 75; the mean of the two averages is secon( j. Therefore, in the present case, an average value of v c of about 55 feet per second should be chosen. In order to check the value of the conductor velocity so obtained, the tables of dimensions of modern machines which, have been added for the guidance of the student may be used. DYNAMO-ELECTRIC MACHINES. [18 These tables, which will be found in Appendix I., include drum as well as ring armature machines, and give the principal dimensions of armatures and field frames for all ordinary sizes of high-, medium-, and low-speed dynamos. Tables CX1II. and CXIV., which contain the armature diameters and lengths of all the machines given in the Dynamo Tables CVII. to CXIL, have been prepared especially for the purpose of checking the conductor velocity and the consequent armature dimensions. The conductor velocity having been ascertained by the method given above, the armature diameter is computed by means of formula (30), p. 58, and is compared with the di- ameter of the machine of nearest size and speed given in Table CXIII. or CXIV., respectively. Thus, for the above example of a 25-KW Soo-revolution dynamo, formula (30) gives a diameter of \ = 230 X ~ = 15! inches. The nearest machine in Table CXIII. is a 20-KW dynamo running at 700 revolutions, which would furnish 25 KW at 875 revolutions; its diameter is 16 inches. The close agree- ment of the two diameters shows that the conductor velocity chosen is a good value for the case on hand. If Table CXIII. or CXIV. contains no machine of sufficiently near output and speed to allow of a comparison, the required diameter may be obtained by interpolation as shown in Appen- dix I , p. 663. 18. Field Density. The specific strength of the magnetic field is chosen accord- ing to the size of the machine, the number of poles, the form of the armature, and the material of the polepieces. In gen- eral, higher field densities are taken for large than for small dynamos, and in multipolar machines higher values of 3C are admitted than in bipolar ones. In dynamos with smooth-core armatures, the field densities are usually taken somewhat greater than in those with toothed armature bodies, for the reason that in the latter a portion of the lines enters the teeth 18] FUNDAMENTAL CALCULATIONS FOR WINDING. 5 3 and passes from tooth to tooth without cutting the conductors, and that in such armatures it therefore takes more lines per square inch of pole area to produce the same field density (per square inch of area occupied by armature conductors) than for smooth cores; consequently, smaller field densities must be employed with toothed armatures in order to prevent over- saturation of the polepieces, and, eventually, of the frame. This leakage through the armature teeth takes place in the higher a degree, the greater the width of the teeth compared to that of the slots, and therefore still smaller field densities are to be chosen in case of armature cores with tangentially projecting teeth, and of those with closed slots. Finally, in machines having wrought iron or cast steel polepieces, the densities can be taken about fifty per cent, higher than those with cast iron pole-shoes. Practical average values of OC" for ordinary dynamos and motors are tabulated in Table VI., which gives the average densities in lines of force per square inch, while Table VII. contains the corresponding values of JC in lines per square centimetre. The values of 3C will also depend on the method to be em- ployed for obviating armature reaction. Modern designers often rely upon a strong magnetic field to assist in preventing the distorting effect of the armature reaction (see 93 and 124), and, therefore, higher gap inductions are generally used now than were a few years ago. If a strong field is desired for the above purpose, a value of the field density about 20 or 30 per cent, in excess of the respective value given in Table VI. or VII., respectively, is advisable. For machines designed for a very low voltage, such as electro-plating dynamos, battery motors, etc., or for dynamos in which the amperage is very high, comparatively, as in incandescent generators of large outputs, the field density is usually made about two-thirds or three-quarters of the corre- sponding density employed under similar conditions for ordi- nary machines. For machines generating very high voltages, the field density should, on the other hand, be chosen considerably higher than the averages given, values from 25 to 50 per cent, in excess of those given being quite common for such machines. 54 D YNA MO-ELEC 7 VvVC MA CHINE S. For considerations governing the design of the above and other special kinds of machines, the student is referred to I2 3> PP- 455 10463. TABLE VI. PRACTICAL FIELD DENSITIES, IN ENGLISH MEASURE. Field Densities, in Lines of Force per square inch , Bipolar Dynamos Toothed Armature Cor* Btnlg ht Tth __ risr _._ _ P.UpUoM P.l.pi~ PoltriMM Pl.pi KtUUpoIar Dynamos B W - H S Toothed Armature Core 8lrigbt Teeth .26 .5 1 .5 7.5 100 300 1000 2000 10000 12000 14000 15000 16000 17000 18000 19000 20000 22000 24000 27000 80000 15000 18000 20000 22000 24000 26000 26000 28000 80000 88000 86000 40000 45000 10000 12000 13000 14000 15000 16000 17000 18000 20000 22000 24000 27000 12000 15000 18000 19000 20000 22000 24000 25000 27000 30000 33000 86000 40000 9000 10000 11000 12000 13000 14000 16000 18000 20000 12000 14000 15000 16000 18000 20000 22000 24000 27000 30000 14000 16000 19000 20000 21000 22000 24000 26000 38000 30000 32000 35000 41000 45000 20000 24000 27000 28000 29000 30000 41000 44000 47000 50000 53000 56000 12000 14000 16000 17000 18000 19000 20000 21000 27000 29000 31000 33000 35000 18000 21000 24000 25000 80000 85000 40000 42000 44000 46000 48000 50000- 10000 11000 12000 13000 14000 15000 16000 17000 18000 19000 24000 15000 16000 18000 20000 21000 28000 24000 25000 26000 28000 30000 82000 85000 .1 .25 .5 1 2.5 5 7.5 10 25 50 100 500 1000 TABLE VII. PRACTICAL FIELD DENSITIES, IN METRIC MEASURE. Reid Dendtleft, in lines of Force per sqpnrre Centimetre , Blpolar-Pyi USS, Toothed Armature Core Piqjectini T.eth Multtpolmr Dynamos Armature Core Toothed Armature Core BUlrht Teeth .6 1 8.5 5 7.5 10 85 50 100 900 800 500 1000 2000 1550 1850 2150 2800 2600 2600 2950 3100 8400 8700 4200 4700 2800 8100 8400 8700 4000 4700 6100 6WO 7000 1250 1550 2000 2150 2800 8100 8400 3700 1850 2800 2800 2950 3100 3400 8700 4200 4700 5100 1250 1400 1550 1700 1850 2000 2150 2500 2800. 8100 1860 2500 2800 8100 3400 8700 4200 4700 2800 2950 3400 8700 4000 4850 4700 5000 5400 6400 7000 3700 4500 4700 5000 5400 6900 6400 6800 7300 7750 8700 1860 2150 2500 2650 2800 2950 3100 3250 8400 8550 3850 4200 4500 4800 5100 5400 2800 8250 8700 8850 4000 4350 4700 5000 5400 6600 6800 7200 7600 7800 1700 1860 2000 2150 3100 8700 2300 8100 8300 8500 8700 3850 4000 4850 4700 5000 5400 .1 .26 .5 "l 2.5 5 7.5 10 35 50 100 200 800 500 1000 2000 19] FUNDAMENTAL CALCULATIONS FOR WINDING. 55 19. Length of Armature Conductor. By means of the specific armature induction obtained from formula (24), the total length of active wire to be wound upon the pole-facing surface of any armature can be readily deter- mined. If E ! denotes the total E. M. F. generated in an armature, and Z a the total length of active wire wound on it, then E' divided by L & will give the specific armature induction, e '. The length of active conductor for any armature can therefore be obtained from the formula (25) in which Z a total length of active conductor (on whole cir- cumference opposite polepieces), in feet, or in metres; E' = total E. M. F. to be generated in armature, /. e., volt output plus additional volts to be allowed for internal resistances (see Table VIII.); and e 1 = specific induction of active armature wire, cal- culated by formula (24), in volts per foot, or in volts per metre, respectively. Introducing the value of e' from (24) into (25), the formula for the length of active armature conductor becomes: 4- x - x n The length Z a is obtained in feet, if e is given in volts per foot, 7' c in feet per second, and 3C" in lines per square inch; and is obtained in metres, if e is replaced by *, in volt per metre, f c expressed in metres per second, and if 3C" is replaced by 3C in lines per square centimetre. To find the total electromotive force, ', to be generated by the armature, increase the electromotive force E wanted in the external circuit, by the percentages given in Table VIII. The figures in the second column of this table refer to shunt- wound dynamos, and, therefore, take into account the arma- ture resistance only. The percentages in the third and fourth DYNAMO-ELECTRIC MACHINES, [20 columns are to be used for series- and for compound-wound dynamos respectively, and, consequently, include allowances for armature resistance as well as for series field resistance: TABLE VIII. E. M. F. ALLOWED FOB INTERNAL RESISTANCES. ADDITIONAL E. M. F. IN PER CEKT. OF OUTPUT E. M. F. CAPACITY IN KILOWATTS. Shunt Dynamos. Series Dynamos. Compound Dynamos. Up to .5 20 % to 12 % 40 % to 25 % 30 % to 20 % 1 12 10 25 20 20 15 2.5 10 8 20 16 15 12 5 8 7 16 14 12 10 10 7 6 14 12 10 8 25 6 5 12 10 8 7 50 5 4 10 8 7 6 100 4 3i 8 6 6 5 200 3i 3 6 5 5 4 500 3 2i 5 4 4 3 1,000 2i 2 4 3 3 2i 2,000 2 H 3 a* 2| 2 20. Size of Armature Conductor. The sectional area of the armature conductor is determined by the strength of the current it has to carry. For general work the current densities usually taken vary between 400 and 800 circular mils (.25 to .5 square millimetre) per ampere; in special cases, however, a conductor area may be provided at the rate of as low as 200 to 400 circular mils (.125 to .5 square millimetre) per ampere, or as high as 800 to 1,200 circular mils (-5 to -75 square millimetre) per ampefe. The low rate refers to machines which only are to run for a short while at the time, as, for instance, motors to drive special machinery (private elevators, pumps, sewing machines, dental drills, etc.), while the high rate is to be employed for dynamos which have a fifteen or twenty hours' daily duty, as is the case for central- station, power-house, and marine generators, etc. Taking 600 circular mils per ampere as the average current density (= 475 square mils, or .000475 square inch per ampere, or about 2,100 amperes per square inch), the sectional area of the armature conductor, in circular mils, is to be 20] FUNDAMENTAL CALCULATIONS FOR WINDING. 57 x 7 ', .....(27) ' where d a a = sectional area of armature conductor, in circular mils; K X A S a ) the symbol A standing for the expression: " n n' c X b s A - 1 80' 2n' X tan j- (32) in which Y = hysteresis heat per unit volume of teeth divided by a constant that depends upon the machine under consideration; d\ external diameter of armature (in millimetres); ' c = number of slots; b % width of slots (in millimetres); s = 7t - n' X a. maximum; and the value of b s which does the latter is 271 X S'. (33) D YNA MO- ELEC TRIG MA CHINE S. [ 22 where b" s width of slot for minimum tooth density, in inches or in centimetres; S" s cross-section of slot, in square inches, or in square centimetres; n' c number of slots. While formula (33) in connection with Table XIV. is very useful for the determination of the best width of the slots in case their cross-section is given, ordinarily the problem is to be attacked by first selecting the number of teeth, then deter- mining the width, and finally the depth of the slot. Consider- ing all the adverse conditions, the author has found it a good practical rule to make the width of the slots x -(34) TABLE XV. DIMENSIONS OF TOOTHED ARMATURES, IN ENGLISH MEASURE. DIAMETER DIMENSIONS OP SLOTS. NUMBER OP CORE WIDTH AT OP SLOTS. DIAMETER, BOTTOM OB* ARMATURE, IN INCHES. d\ Depth, in inches. Width, in inches. Ratio of Depth to Width. n' c = IN INCHES. TOOTH, IN INCHES. da T 2b 8 n'c 5 { [ t 2.50 30 3f .14 6 H ft 2.59 36 4f .14 8 i \ & 266 44 6* .18 10 \ fl 2.95 52 s| .20 12 i 3.20 60 10 .21 15 i 3.43 72 12f .23 18 i 3.64 80 15* .26 21 i f 3.66 88 .28 25 i H 3.69 98 22 .30 30 40 i i ft 3.71 3.73 108 136 27| .37 .38 50 IT ? 3.75 160 46j .41 60 2 A 3.76 180 56 .45 70 80 1 ; 3.78 3.79 196 212 65f 75^- .51 .52 90 2- r ? 4 228 85 .55 100 2; I 4 232 94^ .59 125 3 8 4 264 119 .67 150 3 ^ 7. 4 272 143 .78 200 4 1 4 320 192 .89 22] DIMENSIONS OF ARMATURE CORE. that is to say, to make the width of the slots equal to half their pitch on the outer circumference, for the special case of a straight-tooth core, then the width of the slots is equal to the top width of the teeth. The proper sectional area S\ of the slots to accommodate a sufficient amount of armature winding is obtained by making the depth of the slot from 2^ to 4 times its width, according to the size of the armature, the minimum value referring to very small and the maximum value to the largest machines. Applying these rules to armatures of various sizes, the ac- companying Tables XV. (see page 70) and XVI. have been calculated, giving the dimensions of toothed armatures, the former in English and the latter in metric measure: TABLE XVI. DIMENSIONS OP TOOTHED ARMATURES, IN METRIC MEASURE. DIAMETER DIMENSIONS OF SLOTS. NUMBER OP SLOTS. CORE DIAMETER, WIDTH AT BOTTOM op OF ARMATURE, Depth, Width, Ratio n' c = IN CM. TOOTH, IN CM. IN CM. in cm. in cm. of Depth to fj" ~ d i Width. u u, /r A d\ n & 5s 2b s d\ - 2A a ^T~ 8 10 1.5 .6 2.50 24 7 .32 15 1.75 .65 2.69 36 11.5 .36 20 2 .7 2.86 44 16 .44 25 2.25 .75 3.00 52 20.5 .49 30 2.5 .8 3.13 60 25 .51 40 3 .9 3.34 70 36 .72 50 3.5 1.0 3.50 78 43 .75 60 4 1.1 3.64 86 52 .80 75 4.5 1.2 3.75 98 66 .92 100 5 1.3 3.85 120 90 1.06 150 5.5 1.4 3.95 168 139 1.20 200 6 1.5 4.0 210 188 1.32 250 7 1.75 4.0 224 236 1.56 300 8 2.0 4.0 236 286 1.81 400 9 2.25 4.0 288 382 1.92 500 10 2.5 4.0 320 480 2.21 1 b. Perforated Armatures. The same considerations that prevailed in determining the number and the width of the slots in toothed armatures are also decisive for the dimensioning of perforated cores. The DYNAMO-ELECTRIC MACHINES. [23 number of perforations, for this reason, can be taken in the same limits as the number of slots for toothed cores. See Table XIII. In case of round holes, Fig. 51, the thickness of the iron between two adjacent perforations should be taken between 0.4 and 0.75 times the diameter of the hole. For rectangular holes, Fig. 52, the thickness of the iron ,0.5b g T00.9b s Figs. 51 and 52. Dimensions of Perforated-Core Discs. between them is to be taken somewhat greater than for round holes, namely, from 0.5 to 0.9 times the width of the channel. The distance of the holes from the outer periphery is to be made as small as possible, and may vary between 1/32 and 1/8 inch, according to the size of the armature. 23. Length of Armature Core. The number of wires that can be placed in one layer around the armature circumference, and the depth of the winding- space, determine the total number of conductors on the arma- ture, and the latter, together with the length of active wire, gives the length of the armature core. a. Number of Wires per Layer. For smooth armatures the number of wires per layer is ob- tained in dividing the available core circumference by the thickness of the insulated armature wire. If the whole circum- ference is to be filled by the winding, then & X (35) 23] DIMENSIONS OF ARMATURE CORE 73 where n w = number of armature wires per layer; d & = diameter of armature core, in inches; and sometimes of iron: TABLE XVII. ALLOWANCE FOR DIVISION STRIPS IN DRUM ARMATURES. DIAMETER OP ARMATURE CORE. PERCENTAGE OP CORE CIRCUMFERENCE OCCUPIED BY DIVISION STRIPS. Inches. Centimetres. Up to 300 Volts. 400 to 750 Volts. SOOtoSOOOVolts. Up to 3 " 6 " 12 " 20 " 30 Up to 7.5 11 15 " 30 " 50 " 75 12 % 10 8 7 6 15 % 12 10 9 8 15 % 12 10 9 Denoting one-hundredth of these percentages by ,, the core circumference being unity, the formula for the number of wires per layer in a drum armature in English measure becomes: _ x (37) 74 DYNAMO-ELECTRIC MACHINES. [23 In metric measure the same value of ;/ w is obtained by multi- plying the numerator of (37) by 10, thus deriving the metric formula similarly as (36) is derived from (35). In toothed armatures the number of wires in one layer is found from the number, ' c , and the available width, b' B , of the slots by the equation: (38) In this formula the value of b' s , is to be derived from the actual width, b s , of the armature slots ( 22), by deducting the thickness of insulation used for lining their sides, data for the latter being given in 24. For calculation in metric system the factor 10 is to be em- ployed, as before. b. Height of Winding Space. Number of Layers. In dividing the available height, h' M of the winding space by the height d" M of the insulated armature conductor, the number of layers of wire on the armature is found: n\ = number of layers of armature wire; h\ available height of winding space, in inches; d" & = height of insulated armature conductor, in inch. The height of the insulated armature conductor, d" M in the case of round or square wire, is identical with its width, d' & . If h & is expressed in cm. and d" & in mm., the right-hand side of (39) must be multiplied by 10 in order to correct the for- mula for the metric system. The available height, h\, of the winding space is obtained from its total height, /? a , averages for which are given in Table XVIII. (page 75) by deducting from 1/32 to 1/4 inch (see 24), according to size and voltage of machine, for the insulation of the armature core, insulation between the layers, thickness of binding wires, etc. The nearest whole number is to be substituted for the value of !. 23] DIMENSIONS OF ARMATURE CORE. 75 TABLE XVIII. HEIGHT OF WINDING SPACE IN ARMATURES. ENGLISH MEASURE. METRIC MEASURE. Height of Winding Space, in inches. Height of Winding Space, in centimetres. Diameter of Smooth Armature Diameter of Smooth Armature Armature, in inches. Core. Toothed Armature Armature, in cm. Core. Toothed Armature Drum Armature. Ring Armature. Core. Drum Armature. Ring Armature. Core. 2 r 5 .6 4 A A* 10 .8 .5 6 10 i r 15 25 1 1.2 .6 .7 1.5 2 15 5 T 5 * i 35 1.5 .8 2.5 20 |. | li 50 2 1 3 30 50 * f 1! 75 100 2.2 1.2 1.4 3.5 4 75 5 2 200 1.6 5 100 3 24 300 1.8 6 150 7 31 400 2.1 8 200 1 4 500 2.5 10 The approximate radial height taken up by the armature- binding in smooth armatures may be taken from the following table: TABLE X Villa. DATA, FOR ARMATURE BINDING. Capacity of Dynamo in Kilowatts. Thickness of Armature Binding. Size of Binding Wire. Thickness of Mica Insu- lating Strip.? Average T of Baud Vidth 5. 1 .030" No. 24 B. & S. .010" 5 .035 22 .010 10 .040 ' 21 .012 50 .050 1 19 .014 100 .060 ' 17 .015 200 .070 ' 16 .016 i 500 .080 ' 14 .018 1 1000 .090 ' 13 .018 M r 2000 .100 1 12 .020 2 These figures, besides allowing for the binding wires, which range from No. 24 B. & S. (.020") to No. 12 B. & S. gauge {.080") respectively, as indicated, include the insulation of the ?6 DYNAMO-ELECTRIC MACHINES. [23 bands, the thickness of which, therefore, varies from .010 to .020 inch, according to the size of the armature. The bands usually consist of from 12 to 25 convolutions of phosphor bronze or steel wire, their width varying from ^ inch to 2 inches. They are insulated from the winding by strips of mica from ^ to i inch wider than themselves, and are placed at distances apart equal to about twice the width of a band. In straight-tooth armatures recesses are usually turned to receive a few light bands, while armatures with projecting teeth and with perforated cores need, of course, no binding at all. c. Total Number of Armature Conductors. Length of Armature Core. The product of the number of layers and the number of conductors per layer gives the total number of conductors on the armature; and this, divided into the total length of active armature conductor, furnishes the active length of one con- ductor, that is, the length of the armature body: 12 X n s X A X n, where / a = length of armature core parallel to pole faces, in. inches; Z a length of active armature conductor, in feet, from formula (26); n w = number of wires per layer, from formula (35), (37), or (38), respectively; ! = number of layers of armature wire, from formula (39); n $ = number of wires stranded in parallel to make up one armature conductor of area # a 2 , formula (27); = total number of conductors on armature. In the metric system, Z a being expressed in metres, the length / a is found in centimetres by replacing the factor 12 in (40) by 100. For preliminary calculations an approximate value of the 23] DIMENSIONS OF ARMATURE CORE. TT number of conductors, W et all around the polefacing circum- ference of the armature, may be obtained by dividing the con- ductor area found from formula (27) into the net area of the winding space. Taking .6 of the total area of the winding space as an average for its net area in smooth armatures with winding filling the entire circumference, we obtain: w X i _ _ 1,000,000 X .6 X d & x TC X h & = 1,885,000 x ........ (41) This result is to be correspondingly reduced for windings- filling only part of circumference, or to be multiplied by ( x _ &J, see formula (37), in case of a drum armature, re- spectively. In toothed armatures the average net height of the winding space is about three-fourths of the total depth of the slot, hence the approximate number of armature conductors: = 750,000 X * y */; X ** ......... () ^a In (41) and (42) the values of ........ (68) II.: Z t = - f- -x a ........ (54) *a III.: = .2(4 + *a)+/*a?r xZa 4 + 2 J a + ^ * h n In these formulae / a , a , and Z a are known by virtue of equa- tions (40), (48) and (26), respectively, and /$ a can be taken from Table XVIII., if the actual winding depth is not already known by having previously determined the winding and its arrangement. A formula for Case V. is not given, because, in the first place, the arrangement shown in Fig. 66 is not at all practical, and the makers who first introduced the same have long since discarded it, and, second, because the distance of the internal pole projections depends upon the construction and manner of supporting of the armature core, and, consequently, cannot be definitely expressed. c. Drum- Wound Ring Armatures. In modern ring armatures of the types indicated by Figs. 59 and 60, the conductors facing two adjacent poles of opposite polarity are often connected in the fashion of a bipolar drum, by completing their turns across the end surfaces of the arma- ture body, thus converting the multipolar ring armature into the combination of as many bipolar drum armatures as there are pairs of poles in the field frame ; see 43. By this arrangement, which is illustrated in Fig. 67, not only a con- 100 DYNAMO-ELECTRIC MACHINES. [28 siderable saving of dead wire is experienced, but also the exchanging of conductors in case of repair is rendered much more convenient, especially when formed coils are used, which is the almost universal practice now. The total length of the armature conductor can, in this case, be calculated by applying, for both smooth and toothed bodies, the above formula (51), replacing in the same the core diam- eter, d M by the chordal distance of two neighboring poles, measured from centre to centre along the circumference of the armature over the winding. The formula for the total length of conductor on a drum-wound ring armature, therefore, is (see Fig. 67, page 101) : d" X sin X i8o\ 2 * P } x (57) Inserting in this formula the numerical value for the size of half the pole angle, we obtain the following set of formulae for the various pole numbers that may be used in practice: TABLE XXV. TOTAL LENGTH OF CONDUCTOR ON DRUM WOUND RING ARMATURES. NUMBER OP POLES. HALF POLE- ANGLE. 180 LENGTH op POLE-CHORD (DIAMETER = 1) eiw 180 TOTAL LENGTH OP ARMATURE CONDUCTOR (FORMULA 57). 4 45 0.707 Lt = (l+ 1.161 X -y^) X L & 6 30 .500 0.750 8 22 .383 .574 10 18 .309 .464 12 15 .259 .388 14 12f .222 .333 16 Jii .195 .293 18 10 .174 .261 20 9 .156 .235 24 7^ .131 .196 30 6 .105 .157 28. Weight of Armature Winding. A copper wire of i circular mil \ 1,000, 000 7T X square 4 inch I %28] FINAL CALCULATION OF WINDING. ioi area weighs .00000303 pound per foot of length; our armature conductor of # a 2 circular mils sectional area, therefore, has a weight per foot of .00000303 x # a 2 pound. And the total Z t feet of it, used in winding the armature, will weigh: wt & = .00000303 x # a 2 X A ; (58) wt & = weight of bare armature winding, in pounds; tf a 2 = sectional area of armature conductor, in circular mils, from formula (27); L t total length of armature conductor, in feet, formulae (49) to (57), respectively. Fig. 67. Face Connections of Drum-Wound Ring Armature. In case of round gauge wires, the product .00000303 x # a s is contained in the gauge table under the heading " Ibs. per foot," and consequently the bare weight of the winding is found by simply multiplying the respective table-value by the total length, Z t , and, eventually, by the number of wires, n stranded in parallel. If, in case of heavy rectangular or trapezoidal armature bars, the cross-section, # a 2 , is given in square inches, the numerical constant in the above formula (58) should be replaced by 3.858, this being the weight per foot of a copper bar of i square inch sectional area. When the length of the wire is given in metres and its sec- tional area in square millimetres, formula (58) will give the weight of the armature-winding in kilogrammes, if the factor .0089 is used as the numerical constant, 8.9 being the specific gravity of copper, and .0089, therefore, the weight in kilo- grammes of one metre of copper wire having a cross-section of one square millimetre area. 102 DYNAMO-ELECTRIC MACHINES. [29' When standard gauge wire is to be employed in winding the armature, it is desirable to know the weight of the winding, including its covering, particularly in the case when insulated wire, such as is obtainable from wire manufacturers, is to be used. This covered weight of the winding can be expressed as a multiple of the bare weight, by the equation: wt' & = k b x wt* , (59) in which 6 is a constant depending upon the ratio of the bare diameter of the wire to the thickness of its insulation. In Fig. 68. Armature-Circuits of Multipolar Dynamo. Table XXVI., page 103, these ratios and the corresponding values of 5 are given for all standard gauge wires likely to be used for winding armatures, for single and for double cotton covering. 29. Armature Resistance. The electrical resistance of the armature winding can be determined by the total length of wire wound on the armature, and by the sectional area of the conductor. If R & denotes the total resistance of the armature wire, all in one continuous length, and if there are #' p bifurcations in the armature, and, therefore, 2 n' p electrically parallel armature portions, then the 29 J FINAL CALCULA TION OF WINDING. 103 armature forms the combination of 2 n' p parallel branches of lohms resistance each. TABLE XXVI. WEIGHT OF INSULATION ON ROUND COPPER WIRE. GAUGE SINGLTS COTTON INSULATION. DOUBLE COTTON INSULATION. OF WIRE. DIAMETER |M 1 < OF WIRE 2 * *-< 4) . . , (BABE). .Thickness of insulatioi Inch. Ratio of bare diame to thickness of insulatioi Weight of insulatioi per 100 Ibs. of covered wi * * Thickness of insulatiol Inch. Ratio of bare diame to thicknesg of insulation Weight of insnlatior per 100 Ibs. of covered wi "o *" O pq 02 CQ inch mm 1 .300 7.62 030 15 2.28 1.0228 'i .289 7.34 ]) || .020 14.45 2.32 .0232 '2 .284 7.21 .020 14.2 2.33 10233 3 .259 6.58 020 12.95 2.40 .024 '2 .258 655 020 129 2.40 1.024 '4 .238 604 020 11.9 2.50 1.025 '3 .229 5891 020 11 45 2.55 1.0255 '5 .220 5.59 >4 .0.0 11 2.65 1.0265 '4 .204 5.18 .012 17*' 2.20 1 022 .021) 10.2 2.85 1.0285 'e . . .203 5.16 .012 16.9 220 1.022 .020 10.15 2.86 1.0286 5 .182 4.62 .012 15.15 2.27 0227 .018 10.1 2.87 1.0287 *7 .ISO 4.57 .012 15 2.28 0228 .018 10 2.90 1.029 8 .165 4.19 .012 13.75 2.33 0233 .018 9.17 3.20 1.032 . . 'e .162 4.12 .010 16.2 2.24 .0244 .018 9 3.25 1.0325 9 .148 3.76 .010 14.8 2.30 023 .016 9.25 3.15 1.0315 . . 7 .144 366 .010 14.4 232 .0232 .016 9 3.25 1.0325 10 .134 3.40 .010 13.4 2.36 0236 .016 8.4 3.55 1.0355 8 .1285 3.27 .010 12.85 2.40 .024 .016 8 3.75 1.0375 ii .120 3.05 .010 12 2.50 .025 .016 7.5 4.10 1041 . , '9 .1144 2.91 .010 11.4 2.55 .0255 .016 7.1 4.35 10435 12 .109 2.77 .010 10.9 2.66 .0266 .016 6.8 4.60 1.046 io .102 2.59 .010 10.2 285 .0285 .016 6.4 5.00 1.05 is .095 2.41 .010 9.5 310 1.031 .016 5.9 5.55 1.0C55 ii .091 2.31 .010 9.1 3.25 1.0325 .016 5.7 5.85 1.0585 i4 .083 2.11 .007 12 2.50 .025 .016 5.2 6.60 1.066 12 .081 2.06 .007 11.6 2.54 .0254 .016 5.1 6.80 1.068 is 13 .072 1.83 .007 10.3 2.80 .028 .016 4.5 7.80 1.078 16 .065 :.65 .007 9.3 3.15 1.0315 .016 4.1 8.60 1.086 i4 .064 1.63 .007 91 3.25 .0325 .016 4 8.80 1.088 17 .058 1.47 .007 8.3 3.60 .036 .014 41 8.60 1.086 is .057 1.45 .007 8.1 3.70 1037 .014 41 8.60 1.086 16 .051 1.30 .007 7.3 4.20 .042 014 3.6 9.60 1.096 18 .049 1.25 .007 7 4.40 1.044 .014 8.5 9.83 1.098 if .045 1.15 .005 9 3.25 1.0325 .012 3.75 9.30 1.093 i9 .042 1.07 .005 8.4 3.55 .0355 .012 35 9.80 1.098 is .040 102 .005 8 3.75 .0375 .012 333 10.10 1.101 19 .036 0.91 .005 7.2 4.30 .043 .005* 7.2 560 1.05ft 20 035 089 .005 7 440 1.044 .005* 6.00 1.06 21 20 032 081 .005 6.4 5.00 1.05 .005* 6.4 6.60 1.066 22 21 .028 0.71 .005 5.6 6.00 106 .004* 7 6.00 1.06 23 22 .025 0.64 .005 5 7.00 1.07 .004* 625 7.00 1.07 24 23 .022 0.56 .005 4.4 8.00 1.08 .004* 5.5 8.00 1.08 25 24 .020 0.51 .005 4 8.80 1.088 .004* 5 8.K) 1.088" 26 25 .018 0.46 .005 3.6 9.60 1.096 .004* 4.5 9.60 1.096 27 26 .016 0.41 .005 3.2 10.40 .104 .004* 4 10.40 .104 28 27 .014 0.36 .005 2.8 11.25 1125 .004* 3.5 11.25 .1125 29 28 .013 0.33 .005 26 11.65 .1165 .004* 3.25 11.65 .1165 30 .012 0.31 .005 2.4 12.05 .1205 .004* 3 12.05 .1205 29 .011 0.28 .005 2.2 12.45 .1245 .004* 2.75 12.45 .1245 * Double silk : covering. mil of silk insulation taken equal in weight to 1.25 mil of cotton 104 DYNAMO-ELECTRIC MACHINES. [29 In case of a multipolar dynamo with parallel grouping the number of parallel armature branches, 2 ' p , is equal to the num- ber of poles 2 n p , and the resistance of each branch becomes see Fig. 68, page 102. The joint resistance of these 2 n' p circuits, that is, the actual armature resistance, will consequently be " (2 ' p )' 4 X (' p ) a ' The total resistance, R & , of all the armature wire in series can be calculated from the total length, Z t , and the sectional area, tf a a > of the conductor by the formula where 10.5 is the resistance, in ohms, at 15.5 C. ( = 60 Fahr.) of a copper wire of i circular mil sectional area and i foot length, and of a conductivity of about 98 per cent, of that of pure copper. The quotient for commercial copper, or iQ.3 2 If the temperatures are measured by the Fahrenheit scale, i per cent, is to be added to the resistance for every 4^ over 60 Fahr., and the formula becomes: F . = e F. - __ . (64) In both (63) and (64), r & is the resistance at 15.5 C. ( = 60 Fahr.) found from formula (61) or (62), respectively. CHAPTER VI. ENERGY LOSSES IN ARMATURE. RISE OF ARMATURE- TEMPERATURE. 30. Total Energy Loss in Armature, There are three sources of energy-dissipation in the arma- ture which cause a portion of the energy generated to be wasted, and which give rise to injurious heating of the armature. These sources are (i) overcoming of electrical resistance of armature winding, (2) overcoming of magnetic resistance of iron, and (3) generation of electric currents in the armature core. The energy spent for the first cause, that is, the energy spent by the current in overcoming the ohmic resistance of the conductors, is often called the C*R loss {C = current, R resistance), for reasons evident from 31. The energy consumed from the second cause, or spent in continually reversing the magnetism of the iron core, as the armature revolves in the field, is called the hysteresis .loss (see 32), and the energy spent from the third cause, in setting up useless currents in the iron and, in a small degree, also in the armature conductors, is styled the eddy .current loss, or Foucault current loss (see 33). The total energy transformed into heat in the armature of .a dynamo-electric machine is the sum of the C*R loss, of the hysteresis loss, and of the eddy current loss, and can be expressed by the formula: A = A+ A + A, (65) in which P A = total watts absorbed in armature; P & = watts consumed by armature winding, form- ula (68) ; JP h = watts consumed by hysteresis, formula (73); jP e = watts consumed by eddy currents, formula (75). I0 7 108 DYNAMO-ELECTRIC MACHINES. [31 31. Energy Dissipated in Armature Winding. The energy required to pass an electric current through any resistance is given, in watts, by the product of the square of the current intensity, in amperes, into the resistance, in ohms. The energy absorbed by the armature winding, therefore, is: A = (/')' X r' a , (66) where P & = energy dissipated in armature winding, in watts; /' = total current generated in armature, in amperes; r' & = resistance of armature winding, hot, in ohms; see formulae (60) to (64), respectively. The total current, /', in series-wound dynamos, is identical, with the current output // in shunt- and compound-wound dynamos, however,' /' consists of the sum of the external current, and the current necessary to excite the shunt mag- net winding. The amount of current passing through the shunt winding is the quotient of the potential difference, , at the terminals of the machine, by the resistances of the shunt circuit, r m , that is the sum of the resistance of the shunt winding and of the regulating rheostat, in series with the shunt winding. For the resistance, r' & , of the armature winding, when hot, in order to be on the safe side in determining the armature losses, we will take that at, say 65.5 C. (= 150 Fahr.), or, according to formula (63), the resistance, r M at 15.5 C. (= 60 Fahr.), multiplied by = 1.2 . The energy dissipated in overcoming the resistance of the armature winding, consequently, for shunt- and compound- dynamos can be obtained from the formula: A= 1.2 X (l + \ X r & ..(67) / = current-output of dynamo, in amperes; E = E. M. F. output of dynamo, in volts; r a = resistance of armature, at 15.5 C. (=60 Fahr.), in ohms; 32] ENERGY LOSSES IN ARMATURE. 109 r m = resistance of shunt-circuit (magnet resistance -f- reg- ulating resistance) at 15.5 C. (for series dynamos If jP a is to be computed before the field calculations are made, that is to say, before r m is known, it is sufficiently accurate for practical purposes to express, from experience, the total armature current, /', as a multiple of the current output, I; and, therefore, we have approximately /> a = 1.2 X (*. X /)' X r & ........ (68) and in this the coefficient k 6 for series dynamos is 6 = i, and for shunt- and compound-wound dynamos can be taken from the following Table XXVII. : TABLE XXVII. TOTAL ARMATURE CURRENT IN SHUNT- AND COMPOUND WOUND DYNAMOS. CAPACITY IN KILOWATTS. SHUNT CURRENT IN PER CENT. or CURRENT OUTPUT. TOTAL CURRENT, AS MULTIPLE OP CURRENT OUTPUT. *6 .1 15* 1.15 .25 12 1.12 .5 10 1.10 1 8 1.08 25 7 1.07 5 6 1.06 10 5 1.05 20 4 1.04 30 3.5 1.035 50 3 1.03 100 2.75 1.0275 200 2.5 1.025 300 2.25 1.0225 500 2 1.02 1,000 1.75 1.0175 2,000 1.5 1.015 32. Energy Dissipated by Hysteresis. The iron of the armature core is subjected to successive magnetizations and demagnetizations. Owing to the mole- cular friction in the iron, a lag in phase is caused of the effected magnetization behind the magnetizing force that produces it, and energy is dissipated during every reversal no D YNA MO-ELECTRIC MA CHINES. [32 of the magnetization. The name of ''Hysteresis" (from the Greek vGrsptoo, to lag behind) was given by Ewing, in 1881, to this property of paramagnetic materials, by virtue of which the magnetizing and demagnetizing effects lag behind the causes that produce them. Although Warburg, 1 Ewing, 2 Hopkinson, 3 and others have made numerous researches about the nature of this property of paramagnetic substances, it was not until recently that a definite Law of Hysteresis was established. In an elaborate paper presented to the American Institute of Electrical Engineers on January 19, 1892, Charles Proteus Steinmetz 4 gave the results of his experiments, showing that the energy dissipated by hysteresis is proportional to the i.6th power of the magnetic density, directly proportional to the number of magnetic reversals and directly proportional to the mass of the iron. This law he expressed by the empirical formula: /" h = r ll x <' 6 X JVT X M' where P' h energy consumed by hysteresis, in ergs; rj l = constant depending upon magnetic hardness of material (" Hysteretic Resistance"); (B a = density of lines per square centimetre of iron; JV t = frequency, or number of complete cycles of 2 reversals each, per second; M\ = mass of iron, in cubic centimetres. The values of the hysteretic resistance found by Steinmetz for various kinds of iron are given in Table XXVIII. , page in. For the materials employed in building up the armature core, according to this table, we can take the following aver- age values of the hysteretic resistance: Sheet iron : rj^ = .0035, Iron wire : rj^ =. .040. 1 Warburg, Wiedem. Ann., vol. xiii. p. 141 (1881) ; Warburg and Hoenig, Wiedem. Ann., vol. xx. p. 814 (1884). 2 Ewing, Proceed. Royal Sac., vol. xxxiv. p. 39, 1882 ; P kilos. Trans., part ii. p. 526 (1885). 3 J. Hopkinson, Philos. Trans. Royal Soc., part ii. p. 455 (1885). 4 Steinmetz, Trans. A. I. E. E., vol. ix. p. 3 ; Electrical World, vol. xix. pp. 73 and 89 (1892); vol. xx. p. 285 (1892). 32] ENERGY LOSSES IN ARMATURE. ill TABLE XXVIII. HYSTERETIC RESISTANCE FOR VARIOUS KINDS OF IRON. KIND or IRON. HYSTERETIC RESISTANCE. Sheet Iron, magnetized lengthwise 0025 to 005 .0165" thick ( .42 mm.).. 0035 .015" " ( .38 " ) 004 .006" " ( .15 " ) 005 " magnetized across Lamination 007 * Iron Wire length-magnetization 0035 cross- 040 Wrought Iron, Norway Iron 0023 " ordinary mean 0033 Cast Iron ordinary, mean 013 " containing % % Aluminium 0137 0146 Mitis Metal 0043 Tool Steel glass hard 070 oil hardened 027 ' ' annealed 0165 Cast Steel, hardened .012 to 028 annealed 003 to 009 Inserting the average values given on page no into Stein- metz's equation, and reducing the latter to our practical units, we obtain for the energy loss by hysteresis in any armature having core built of discs or ribbon : ^- j P h = io- 7 x .0035 x - j X -#i X 28,316 X M = 5 X io- 7 X (BY* X NI X M, ......... (69) and in any armature with core of iron wire : P h = 5.7 X io- X (BY' 6 XWXM, ......... (70) where P h = energy absorbed by hysteresis, in watts ; i watt io 7 ergs ; (B" a = density, in lines per square inch, correspond- ing to average specific magnetizing force of armature core, see 91; N NI = frequency, in cycles per second, = - X p ; JV = number of revs, per min., p = num- ber of pairs of poles ; M = mass of iron in armature core, in cubic feet; i cu. ft. = 28,316 cm. 3 112 DYNAMO-ELECTRIC MACHINES. [32 The mass, in cubic feet, for both drum and ring armatures with smooth core is : J/ = d '" & X TT X ^ X 4 X d'" & = mean diameter of armature core, in inches, = 6 and 5.7 X io~ 6 X (B" a 1<6 > respectively, into one factor, rj, the factor of hysteresis; that is, the energy absorbed by hysteresis in one cubic foot of iron, when subjected to magnetization and demagnetization at the rate of one complete cycle (two reversals) per second. For convenience, the author, in Table XXIX., has calcu- lated the numerical values of these hysteresis factors, 77, for all core densities from 10,000 to 125,000 lines per square inch, thus simplifying the equation for the hysteresis loss into the formula: A = ff X N, x M ............. (73) In Table XXIX., columns headed 77 -i- 480, are added for the case the hysteresis loss is to be calculated for an arma- ture, of which the weight, in pounds, of the iron core is known: 32] ENERGY LOSSES IN ARMATURE. TABLE XXIX. HYSTERESIS FACTORS FOR DIFFERENT CORE DENSITIES, IN ENGLISH MEASURE. WATTS DISSIPATED WATTS DISSIPATED MAGNETIC DENSITY AT A FREQUENCY OF ONE COMPLETE MAGNETIC CYCLE PER SECOND. . MAGNETIC DENSITY AT A FREQUENCY OF ONE COMPLETE MAGNETIC CYCLE PER SECOND. IN IN ARMATURE CORE. Sheet Iron. Iron Wire. ARMATURE CORE. Sheet Iron. Iron Wire. LINES OF LINES OF FORCB FORCE PER SQ. IN. per cu. ft. per Ib. per cu. ft. per Ib. PER SQ. IN. per cu. ft. per Ib. per cu. ft. per Ib. rj+480 17 TJ-H480 " Tj+480 * rj-f-480 10,000 1.25 .0026 143 .030 66,000 25.72 .0537 294.0 .613 15,000 2.40 .0050 27.4 .057 67,000 26.34 .0550 301.0 .628 20,000 3.79 .0079 43.3 .090 68,000 26.97 .0563 308.2 .643 25,000 5.42 .0113 62.0 .129 69,000 27.61 .0576 315.5 .658 30,000 7.30 .0152 83.5 .174 70,000 28.26 .0589 322.8 .673 31,000 7.70 .0160 88.0 .183 71,000 28.91 .0603 330.1 .688 32,000 8.10 .0168 92.6 .192 72,000 29.56 .0617 337.6 .704 33,000 8.50 .0177 97.2 .202 73,000 30.22 .0631 345.1 .720 34-,000 8.91 .0186 101.8 .212 74,000 30.89 .0645 352.9 .736 35,000 9.33 .0195 106.5 .222 75,000 31.56 .0659 360.7 .752 36,000 9.76 .0204 111.5 .232 76.000 32.23 .0673 368.5 .768 37,000 10.20 .0213 116.5 .242 77,000 32.91 .0687 3763 .784 38,000 10.65 .0222 121.6 .253 78,000 33.60 .0701 384.2 .800 39,000 11.10 .0231 126.8 .264 79,000 34.29 .0715 392.1 .817 40,000 11.55 .0240 132.0 .275 80,000 34.* X 4 X 2 _ n' c X S s X 4 X 1,000,000 M. =- , (74) 1,000,000 the second term of which refers to toothed and perforated armatures only, and in which M l = mass of iron in armature body, in cubic metres; d'" & =-mean diameter of armature core, in centimetres; FIG. 69. Hysteresis Factor for Sheet Iron and Iron Wire, at Different Core Densities. d'" & = d & b & , for smooth armatures; = d" & (b & -\- /^ a ), for toothed armatures; / a = length of armature core, in centimetres; b & = radial depth of armature core, in centimetres; ri c = number of slots; S a = slot area, in square centimetres; 2 = ratio of magnetic to total length of armature core, Table XXL, 26. Then, formula (73) will give the hysteresis loss in watts, if the factor of hysteresis rj is replaced by rf from the following Table XXX., rf being calculated from 3.5 X io~ 4 x (B a 1>6 , in case of sheet-iron, and from 4 x io~ 3 X & a 16 > in case of iron wire: 32] ENERGY LOSSES IN ARMATURE. TABLE XXX. HYSTERESIS FACTORS FOR DIFFERENT CORE DENSITIES, IN METRIC MEASURE. WATTS DISSIPATED WATTS DISSIPATED MAGNETIC DENSITY IN AT A FREQUENCY OF ONE COMPLETE MAGNETIC CYCLE PER SECOND. MAGNETIC DENSITY IN AT A FREQUENCY OP ONE COMPLETE MAGNETIC CYCLE PER SECOND. ARMATURE ARMATURE CORE. LINES OP FORCE Sheet Iron. Iron Wire. CORE. LINES OP FORCE Sheet Iron. Iron Wire. PER CM. 2 PER CM ^ (GAUSSES) &a per cu. m. per kg. per cu. m. per kg. (GAUSSES) &a per cu. m. per kg. per cu. m. per kg. * V+7,700 Y V+7,700 V V+7,700 V V+7,700- 2,000 67.0 .0087 765.1 .0994 12,000 1,177.0 .1529 13,451.0 1.7469 3,000 128.1 .0166 1,467.1 .1905 12,250 1,216.5 .1580 13,902.3 1.8054 3,500 163.9 .0213 1,873.1 .2432 12,500 1,256.4 .1632 14,359.0 1.8648 4,000 202.9 .0264 2,319.3 .3012 12,750 1.296.9 .1685 14,821.0 1.9248 4,500 245.0 .0318 2.800.2 .3637 13,000 ,337.8 .1737 15,288.7 1.9855 5,000 290.0 .0377 3,314.6 .4305 13.250 ,379.2 .1791 15,7C1.7 2.0470 5,250 313.6 .0407 3,583.6 .4654 13,500 ,421.0 .1845 16,240.0 2.1091 5,500 337.8 .0439 3,8605 .5014 13,750 ,463.4 .1901 16,724.0 2.1730 5,750 362.7 .0471 4,145.1 .5383 14,000 ,506.2 .1952 17,213.0 2.2355 6,000 388.3 .0504 4,437.1 .5763 14,250 ,549.4 .2012 17,708.0 2.2997 6,250 414.5 .0588 4.848.0 .6151 14,500 1,593.2 .2069 18,207.4 2.3646. 6,500 441.3 .0573 5,043.3 .6550 14,750 ,637.3 .2126 18,712.0 2.4301 6.750 468.8 .0609 5,857.8 .69.58 15,000 ,681.9 .2179 19,222.0 2.4964 7,000 496.9 .0645 5,678.3 .7375 15,250 ,727.0 .2243 19,742.0 2.5639 7.250 525.6 .0683 6,006.1 .7800 15,500 .792.6 .2302 20,257.4 2.6309- 7,500 554.8 .0721 6,355.3 .8254 15,750 1,818.6 .2362 20,783.0 2.6991 7.750 584.7 .0759 6,682.4 .8679 16,000 ,864.9 .2422 21,313.5 2.7681 8,000 615.2 .0799 7,030.7 .9131 16,250 ,911.8 .2484 21,848.5 2.8375- 8,250 646.2 .0839 7,385.5 .9592 16,500 1,959.0 .2544 22,389.0 2.9076 8,500 677.9 .0880 7.747.0 1.0061 16,750 2,006.7 .2606 22,934.0 2.9785- 8,750 710.1 .09-22 8,114.8 1.0539 17,000 2,054.9 .2609 23,484.5 3.0499 9,000 742.8 .0965 8,488.6 .1024 17,250 2,103.5 .2732 24,039.5 3.1220 9,250 776.1 .1101 8,869.2 .1152 17,500 2,152.5 .2795 24,599.0 3.1947 9,500 809.9 .1105 9,255.6 .1202 17,750 2,201.9 .2860 25,164.0 3.2681 9,750 844.2 .1110 9.649.0 .2532 18,000 2,251.7 .2924 25.733.6 3.3420 10,000 879.2 .1142 10,047.7 .3049 18,250 2,301.9 .2990 26,307.6 3.4165 10,250 914.6 .1188 10,452.2 .3574 18,500 2,352.6 .3055 26,886.0 3.4918 10,500 950.5 .12:34 10,863.2 .4108 18,750 2,403.7 .3122 27,470.0 3.5676 10,750 987.0 .1282 11,284.0 1.4650 19,000 2,455 1 .3189 28,058.6 3.6440 11,000 1,024.0 .1330 11,702.5 1.5198 19,250 2,507.1 .3256 28,652.0 3.7210 11,250 1,061.5 .1379 12,131.0 1.5755 19,500 2,559.3 .3324 29,248 6 3.7986 11,500 1,099.5 .1428 12,565.3 1.6319 19.750 2,636.2 .3424 29,814.6 3.8760 11,750 1,138.0 .1478 13,005.3 1.6890 20,000 2,665.1 .3461 30,458.7 3.9556 With regard to the exponent of (B" a , in formulae (69) and (70), Steinmetz's value, which in the preceding is given as 1.6 over the whole range of magnetization, has been attacked by Professor Ewing, 1 who by recent investigations has found it to vary with the density of magnetization. In the case of sheet 1 J. A. Ewing and Miss Helen G. Klaassen, Philos. Trans. Roy. Soc.; Elec- trician (London), vol. xxxii. pp. 636, 668, 713 ; vol. xxxiii. pp. 6, 38 (April and May, 1894); Electrical World, vol. xxiii. pp. 569, 573, 614, 680, 714, 740 (April and May, 1894); Electrical Engineer, vol. xvii. p. 647 (May 9, 1894). n6 D YNAMO-ELECTRIC MA CHINES. [32 iron of .0185 inch ( =.47 mrn.) thickness, for instance, the hysteretic. exponent ranged as follows: TABLE XXXI. HYSTERETIC EXPONENTS FOR VARIOUS MAGNETIZATIONS. DENSITY OP MAGNETIZATION. HTSTEUETIC EXPONENT. Lines of Force per Square Inch. &"a Lines per cm. a (Gausses.) &a 1,300 to 3,000 3,000 " 6,500 6,500 " 13,000 13000 " 50,000 50,000 " 90,000 200 to 500 500 " 1,000 1,000 " 2,000 2,000 " 8,000 8,000 " 14,000 1.9 1.68 1.55 1.475 1.7 Although Ewing thus has shown that no formula with a constant exponent can represent the hysteretic losses within anything like the limits of experimental accuracy, he con- cludes that Steinmetz's exponent 1.6 gives values which are nowhere so grossly divergent from the truth as to unfit them for use in practical calculations. This conclusion holds par- ticularly good for the densities applied in dynamo-electric machinery, as from the above Table XXXI. can be seen that for densities between 4 and 14 kilogausses (25,000 and 90,000 lines per square inch, respectively), compare Table XXII., 26, the hysteretic exponent, according to Ewing's experiments, varies from 1.475 to I -7 tne average of which is 1.59, indeed a good agreement with Steinmetz's value. Experiments on the variation of the hysteretic loss per cycle as function of the temperature have been made by Dr. W. Kunz, 1 for the temperatures up to 800 C. ( = 1,472 Fahr.). They show that .with rising temperature the hyster- esis loss decreases according to a law expressed by the formula P' h = a + b , where P' h = hysteresis loss per cycle, in ergs; = temperature, in centigrade degrees; a and b = constants for the material, depending upon the temperature and on the maximal density of magnetization. J Dr. W. Kunz, Elektrotechn. Zeitschr., vol. xv. p. 194 (April 5, 1894); Electrical World, vol. xxiii. p. 647 (May 12, 1894). 32] ENERGY LOSSES IN ARMATUKE. 117 The decrease of the hysteretic loss, consequently, consists of two parts: one part, 0, which is proportional to the in- crease of the temperature, and another part, a, which becomes permanent, and seems to be due to a permanent change of the molecular structure, produced by heating. This latter part, in soft iron, is also proportional to the temperature, thus 30 100 ^.200 300 400 50O 60O 700 8OO 9OO Fig. 70. Influence of Temperature upon Hysteresis in Iron and Steel. making the hysteretic loss of soft iron a linear function of the temperature, but is irregular in steel. The curves in the latter case show a slightly ascending line to about 300 C. ( = 572 Fahr.), then change into a rapidly descending straight portion to about 600 C. (= 1,112 Fahr.), when a second "knee" occurs, and the descension becomes more gradual. The author has refigured all of Kunz's test results, basing th-e same upon the hysteresis loss at 20 C. ( 68 Fahr.) as unity n8 D YNAMO-ELECTRIC MA CHINES. [ 32 in every set of observations. In Fig. 70 dotted lines have then been drawn, inclosing all the values thus obtained, for soft iron and for steel, respectively, and two full lines, one for each quality of iron, are placed centrally in the planes bounded by the two sets of dotted lines, thus indicating the average values of the hysteretic losses, in per cent, of the energy loss at 20 C. Arranging the same in form of a table, the following law is obtained: TABLE XXXII. VARIATION OF HYSTERESIS Loss WITH TEMPERATURE. TEMPERATURE. ENERGY DISSIPATED BY HYSTERESIS IN PER CENT. OF HYSTERESIS Loss AT 20 C. (= 68 FAHR.) In Centigrade Degrees. In Fahrenheit Degrees. Soft Iron. Steel. 20 68 WQfc 100 100 212 90 103 200 392 80 106 300 572 70 110 400 752 60 80 500 932 50 50 600 1,112 40 20 700 1,292 30 15 800 1,472 20 10 20 68 70 40 The last row of this table, which gives the hysteresis loss at 20 C., at the end of the test, shows that the energy required to overcome the hysteretic resistance is reduced to about 70 per cent, in case of soft iron and to about 40 per cent, in case of steel, after having been subjected to magnetic cycles at high temperatures. Kunz further found that the hysteretic energy loss can thus be considerably reduced by repeatedly applying high temperatures while iron is under cyclic influence. For soft iron a set of straight lines was obtained in this way, each following of which had a lower starting point, and de- scended less rapidly than the foregoing one, until, finally, after the fourth repetition of the heating process, a stationary condition was reached. For steel, already the second set of tests with the same sample did not show the characteristic form of the, at first 33] ENERGY LOSSES IN ARMATURE. 119 ascending, then rapidly, and finally slowly descending steel curve, but furnished a rapidly descending straight line. For every further repetition, the corresponding line becomes less inclined, and for the fifth test is parallel to the axis of abscissae. Steel, therefore, after heating it but once as high as 800 C. (= i, 472 Fahr.), loses its characteristic properties, and with every further repetition becomes a softer, less car- bonaceous iron. 33. Energy Dissipated by Eddy Currents. From his experiments Steinmetz also derived that the energy consumed in setting up induced currents in a body of iron increases with the square of the magnetic density, with the square of the frequency, and in direct proportion with the mass of the iron: P' e = e' x &, 2 X N*X M\; P' e energy dissipated by eddy currents, in ergs; (Bj, = density of lines of foree, per square centimetre of iron; N N^ = frequency, in cycles per second, = X p ; M\ = mass of iron, in cubic centimetres; f = eddy current constant, depending upon the thickness and the specific electric conductivity of the mate- rial; for the numerical value of this constant Stein- metz gives the formula: 2 X y X io" 9 = 1-645 X & X y X I0 ~- 6 = thickness of material, in centimetres. y = electrical conductivity, in mhos; for iron : y = 100,000 mhos; for copper: y = 700,000 mhos. Inserting the value of e 1 with reference to iron, into the above equation expressing the Eddy Current Law, and trans- forming into practical units, the eddy current loss in an arma- ture, in watts, is obtained: P e = io- 7 X 1.645 X (2.54 dj* X io- 4 X I J&J X N? X 28,316 X M= 7.22 X io- e X " 12 1C 80 .55 to .45 = .50 X d" a -\ - 2 Ji " 18 " 45 .50 to .40 = .45 X d" & -\ - 2 h & " 24 " 60 .45 to .35 = .40 X d\-\ - 2 h " 30 75 .40 to .30 = .35 X d\-\ -a*. As to the diameters at the ends of the heads, that of the front head, 00 = ^ * I8>ooa # = useful flux through armature,in maxwells; 2 tf p number of poles; a X / a X / 2 = net area of least cross-sec- tion of armature core, in square centi- metres; (B a = flux-density in armature core, in gausses; N number of revolutions per minute; M\ = mass of armature core, in cubic centimetres; S\ surface of armature-core, in square centimetres, = d & n X / a + ~ ~> ^ or smooth armatures, = d\ 7t X 4 H -- , for toothed and perforated armatures. The numerical constant in this formula is averaged from values ranging between .008 and .012 for smooth-core machines, and between .010 and .0125 for toothed armatures. 'Ernst Schulz, Elektrotechn. Zeitschr., vol. xiv. p. 367 (June 30, 1893); Electrical World, vol. xxii. p. 118 (August 12, 1893). 130 DYNAMO-ELECTRIC MACHINES. [37 Translating (82) into the English system of measurement, we obtain the formula: " a x ?/p X N X M . e a = .00045 x - -^7 -; ....(83) a = rise of armature temperature, in degrees Centigrade; (B" a = density of magnetization, in lines per square inch; n p = number of pairs of poles; JV number of revolutions per minute; M = mass of iron, in cubic feet; S" A = armature core surface, in square inches. The value of the constant in the English system, for the type of machines experimented upon by Schulz, varies between the limits .0003 and .0005. The numerical factor depends upon the units chosen, upon the ventilation of the armature, upon the quality of the iron, and upon the thickness of the lamination, and consequently varies considerably in different machines. For this reason it is advisable not to use formula (82) or (83), respectively, except in case of calculating an armature of an existing type for which this constant is known by experiment. In the latter case, Schulz's formula, although not as exact, is even more con- venient than the direct equation (81) which necessitates the separate calculation of the energy losses, while (82) and (83) contain the factors determining these losses, and therefore will give the result quicker, provided that the numerical factor has been previously determined from similar machines. Another empirical formula for the temperature increase of drum armatures, which, however, requires the specific energy- loss to be calculated, and which therefore is not as practical as that of Schulz, and which cannot give as accurate results as can be obtained by the use of Table XXXVI. in connection with formula (81), has recently been given by Ernest Wilson. 1 37. Circumferential Current Density of Armature. An excellent. check on the heat calculation of the armature, and in most cases all that is really necessary for an examina- 1 Ernest Wilson, Electrician (London), vol. xxxv. p. 784 (October u, 1895); Elektrotechn. Zeitschr., vol. xvi. p. 712 (November 7, 1895). 37] ENERGY LOSSES IN ARMATURE. 131 tion of its electrical qualities, is the computation of the cir- cumferential current density of the armature. This is the sum of the currents flowing through a number of active arma- ture conductors corresponding to unit length of core-periphery, and is found by dividing the total number of amperes all around the armature by the core circumference: / c = circumferential current density, in amperes per inch length of core periphery, or in amperes per centi- metre; N c = total number of armature conductors, all around periphery; /' = total current generated in armature, in amperes; 2 ' p = number of electrically parallel armature portions, eventually equal to the number of poles; - = current flowing through each conductor, in amperes; JV C x r = total number of amperes all around armature; this quantity is called "volume of the armature cur- rent" by W. B. Esson, and " cir cum flux of the arma- ture" by Silvanus P. Thompson; d & == diameter of armature core, in inches; in case of a toothed armature, on account of the considerably greater winding depth, the external diameter, d" M is to be taken instead of d & , in order to bring toothed and smooth armatures to about the same basis; for a similar reason, for an inner-pole dy- namo, the mean diameter, d'" M should be substituted for d & . By comparing the values of * c found from (84) with the averages given in the following Table XXXVII., the rise of the armature temperature can be approximately determined, and thus a measure for the electrical quality of the armature be gained. The degree of fitness of the proportion between the armature winding and the dimensions of the core is indicated by 132 DYNAMO-ELECTRIC MACHINES. [38 the amount of increase of the armature temperature. If the latter is too high, it can be concluded that the winding is pro- portioned excessively, and either should be reduced or divided over a larger armature surface : TABLE XXXVII. RISE OF AKMATURE TEMPERATURE, CORRESPONDING TO VARIOUS CIRCUMFERENTIAL CURRENT DENSITIES. CIRCUMFERENTIAL RISE or ARMATURE TEMPERATURE, & . High Speed (Belt-Driven) Dynamos. Low Speed (Direct-Driven) Dynamos. per inch. per cm. Centigrade. Fahrenheit. Centigrade. Fahrenheit. 50 to 100 20 to 40 15 to 25 27 to 45 10 to 20 18 to 36. 100 200 40 80 20 35 36 63 15 25 27 45 200 300 80 120 30 50 54 90 20 35 36 63 300 400 120 160 40 60 72 108 25 40 45 72 400 500 160 200 50 70 90 126 30 45 54 81 500 600 200 240 60 80 108 144 86 50 63 90 600 700 240 280 70 90 126 162 40 60 72 108 700 800 280 320 80 100 144 180 50 70 90 126 The difference in the temperature-rise at same circumferen- tial current density for high-speed and low-speed dynamos (columns 3 and 5, or 4 and 6, respectively, of the above table) is due to the fact that, other conditions being equal, in a low- speed machine less energy is absorbed by hysteresis and eddy currents; that, consequently, less total heat is generated in the armature, and, therefore, more cooling surface is available for the radiation of every degree of heat generated. 38. Load Limit and Maximum Safe Capacity of Arma- tures. From Table XXXVII. also follows that, according to the temperature increase desired, the load carried by an arma- ture varies between 50 and 800 amperes per inch (= 20 to 320 amperes per centimetre) of circumference, or between about 150 and 2,500 amperes per inch (= 60 to 1,000 amperes per centimetre) of armature diameter. As a limiting value for safe working, Esson 1 gives 1,000 amperes per inch diameter {= 600 amperes per centimetre) for ring armatures, and 1,500 1 Esson, Journal I. E. E., vol. xx. p. 142. (1890.) 38J ENERGY LOOSES IN ARMATURE. 133 amperes (= 400 amperes per centimetre) for drums. Kapp 1 allows 2,000 amperes per inch (= 800 amperes per centimetre) diametral current density for diameters over 12 inches as a safe load. Taking 1,900 amperes per inch diameter (= 600 amperes per inch circumference) as the average limiting value of the arma- ture-load in high-speed dynamos, corresponding to a tempera- ture rise of about 70 to 80 Centigrade (= 126 to 144 Fahrenheit), compare Table XXXVII., we have: ^c X 7- = 1,900 X <4, ......... (85) 2 p and since for the total electrical energy of the armature we can write, see formula (136), 56, in which P' = total electrical energy generated in dynamo, in watts; E' = total E. M. F., generated in armature, in volts; /' = total current generated in armature, in am- peres; JV C = number of armature conductors; = number of useful lines of force; N = speed, in revolutions per minute; ' p = half number of parallel armature circuits (eventually also number of pairs of poles); we obtain for the limit of the capacity, by inserting (85) into (86): f = T ' 9 y x x * X N = 63 X 1-* x 4.x N x ft (87) But the useful flux, $, is the product of gap area and field density, or, approximately, # - ^^ X ft\ X 4 X 3C", Kapp, S. P. Thompson's "Dynamo-Electric Machinery," 4th edition, p. 439. 134 DYNAMO-ELECTRIC MACHINES. [38 and consequently the safe capacity of a high-speed dynamo : p' = 6 3 x 10 - 8 x d & x N x d ^~^- x ft\ x /a x oe" = icr" X d; X / a X ft\ X N X 5C" (88) For low-speed machines, 2,500 amperes per inch diameter, or 800 amperes per inch circumference, can safely be allowed, hence, in order to obtain the safe capacity of a direct-driven machine^ the factor i.jj must be adjoined to formula (88). In (88), P 1 = maximum safe capacity of armature, in watts; d & diameter of armature core, in inches; / a = length of armature core, in inches; /J'j = percentage of useful gap circumference; to be taken somewhat higher than the percentage of polar arc, to allow for circumferential spread of the lines of force, see Table XXXVIII. ; 3C" = field density, in lines of force per square inch; N speed, in revolutions per minute. Inserting into (85) the equivalent limit current density in metric units, of 240 amperes per centimetre circumference (= 765 amperes per centimetre diameter), the maximum safe capacity, in watts, of a high-speed armature given in metric measure is obtained: p , _ 765 X d & x N X $ io 8 X 30 = 4 X io- 7 X d; X 4 X ft\ X N X OC, . .(89) wherein all dimensions are expressed in centimetres. For low-speed machines the factor 4 in this formula must be replaced; by 5-33- Average values for ft' lt taken from practice, are given in Table XXXVIII. on the opposite page. In this table the percentages given for toothed arma- tures refer to straight tooth cores only; for projecting teeth a value between the straight tooth and the perforated arma- ture should be taken, proportional to the size of the opening; between the tooth projections. 39] ENERGY LOSSES JN ARMATURE. '35 TABLE XXXVIII. PERCENTAGE OF EFFECTIVE GAP CIRCUMFERENCE FOR VARIOUS RATIOS OF POLAR ARC. PERCENTAGE OP EFFECTIVE GAP CIRCUMFERENCE. ft', PERCENTAGE 2 Poles. 4 to 6 Poles. 8 to 12 Poles. 14 to 20 Poles. OP POLAR AKC. j fa ' '-* - 1 o*g a> gs O g, gj TJ g olg s 8 | g> fr 11! Z =3 11 ||| 11 Pi j| jji 11 0!^ OJ cc^ 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 .95 .98 .96 .97 .955 .965 .955 .96 .955 .90 .96 .915 .94 .91 .93 .91 .92 .91 .85 .94 .87 .905 .865 .89 .865 .88 .865 .80 .91 .825 .87 .82 .85 .82 .84 .82 .75 .88 .78 .835 .775 .815 .775 .80 .775 .70 .85 .735 .80 .73 .78 .725 .76 .725 .65 .82 .69 .765 .685 .74 .68 .72 .675 .60 .78 .645 .73 .635 .70 .63 .68 .62-1 .55 .74 .60 .69 .59 .665 .58 .64 .575 .50 .70 .55 .65 .54 .625 .53 .60 .525 39. Running Yalue of Armature. In order to form an "idea of the efficiency of an armature as an inductor, its "running value" has to be determined. In forming the quotient of the total energy induced by the product of the weight of copper on the armature and the field density, the number of watts generated per pound of copper at unit field density is obtained, an expression which indicates the relative inducing power of the armature: (90) 77' v /' pt _- Ci X J . a w;/ V "V" ' ' '* 'a ^ **** P' & = running value of armature in watts per unit weight of copper, at unit field density; ' = total E. M. F. generated in armature, in volts; . /' = total current generated in armature, in amperes; wt & = weight of copper in armature, in pounds or in kilo- grammes, formula (58); 3C" = field density, in lines of force per square inch, or per square centimetre, respectively. 136 DYNAMO-ELECTRIC MACHINES. [39 The value of P' & for a newly designed armature being found, its relative inductor efficiency can then be judged at by com- parison with other machines. The running value of modern dynamos, according to the type of machine and the kind of armature, varies between very wide limits, and the following- are the averages for well-designed machines: TABLE XXXIX. RUNNING VALUES OF VARIOUS KINDS OF ARMATURES. TYPE OF MACHINE. KIND OP ARMATURE. RUNNING VALUE, P' & (Watts per unit weight of copper at unit field density.) English Measure. Metric Measure. Watts per Ib. at 1 line per zq. inch. Watts per kg. at 1 line per cm. 3 High Speed Bipolar Drum .015 to .03 .045 to. 09 Ring .01 " .02 .03 " .06 Multipolar Drum .01 " .02 .03 " .06 Ring .0075 .015 .022" .045 Low Speed Bipolar Drum .0075 " .015 .022" .045 Ring .005 " .01 .015" .03 Multipolar Drum .005 " .01 .015" .03 Ring .00375 " .0075 .011" .022 CHAPTER VII. MECHANICAL EFFECTS OF ARMATURE WINDING. 40. Armature Torque, The work done by the armature of a dynamo can be ex- pressed in two ways: electrically, as the product of E. M. F. and current strength, P' E' X /' watts; and mechanically, as the product of circumferential speed and turning moment, or torque, 746 P' = 27rxNxrx- - = .142 X N X r watts; 33,000 P' =. total energy developed by machine, in watts; E' = total E. M. F. generated in armature, in volts; /' = total current generated in armature, in amperes; JV = speed, in revolutions per minute; T = torque, in foot-pounds; 746 = number of watts making one horse power; 33,000 = number of foot-pounds per minute making one horse power. Equating the above two expressions, we obtain: JE' X /' = .142 X N X r, from which follows : E' X /' E' X /' 7 = .i 42 x N = 7 ' 42 X ~^~N~~ foot-pounds. ..(91) Or, in metric system, i kilogramme-metre being = 7.233 foot- pounds, ..... (92) Inserting into (91) and (92) the expression for the E. M. F. from 56, viz. : _ N c X $ X W ' 'X io 8 X 60' P 137 138 DYNAMO-ELECTRIC MACHINES. [41 the equation for the torque becomes: N c . x $ X N v , /' ~- 7' 042 X ,' p X io X 60 X IV X r X ^ c X # foot-pounds IO (93) 1.625 /' if X r X ^c X $ kg. -metres n p from which follows that in a given machine the torque depends in nowise upon the speed, but only upon the current flowing through the armature, and upon the magnetic flux. 41. Peripheral Force of Armature Conductors. By means of the armature torque we can now calculate the drag of the armature conductors in a generator, respectively the pull exerted by the armature conductors in a motor. The torque divided by the mean radius of the armature winding gives the total peripheral force acting on the arma- ture; and the latter, divided by the number of effective con- ductors, gives the peripheral force acting on each armature conductor. In English measure, if the torque is expressed in foot-pounds and the radius of the winding in inches, the peripheral force of each conductor is: f t 24 x r f* i/s ~ = , ^ AT ^ H, pounds (94) 76* a x JV G x & X -w c X A, Inserting into this equation the value of r from formula (91), we obtain: ' x /' 24 X 7-042 X ^v a a X ^V c X p\ _ 2 X 7.042 X 7t E' x /' : ~2 " /N ' 60 or, $41] EFFECTS OF ARMATURE WINDING. 139 / a = peripheral force per armature conductor, in pounds; ' X /' = total output of armature, in watts; v c mean conductor velocity, in feet per second; N c = total number of armature conductors; fi\ percentage of effective armature conductors, see Table XXXVIII., 38. A second expression for the peripheral force can be obtained by substituting in the original equation (94) the value of -c from formula (93), thus: [ 24x11.74 r_ ^c * io 10 < n X N X d' & Replacing in this the useful flux $ by its equivalent, the product of gap area and field density, we find a third formula for the peripheral force: 2.82 2 ' X ^ X X ^ X ** X ^ . /a =I ~ X ^ a X = ^ X ~ X 4 X OC" pounds; .......... (97) io ' ' p /' - r - = total current flowing in each armature conductor, in 2 tl p amperes; 4 = length of armature core, in inches; 3C 7 = field density, in lines of force per square inch. If the dimensions of the armature are given in centimetres, the conductor velocity in metres per second, and the field density in gausses, the peripheral force is obtained in kilo- grammes from the following formulae: A = I02 x ' kil s rammes ' - and / a = ~ 8 X ^r X 4 X 3C kilogrammes, . ..(100) which correspond to (95), (96) and (97), respectively. 140 DYNAMO-ELECTRIC MACHINES. [42 It is on account of this peripheral force exerted by the magnetic field upon the armature conductors that there is need of a good positive method of conveying the driving power from the shaft to the conductors, or vice versa; in the gener- ator it is the conductors, and not the core discs, that have to be driven; in the motor it is they that drive the shaft. Thus. the construction of the armature is aggravated 'by the condi- tion that, while the copper conductors must be mechanically connected to the shaft in the most positive way, yet they must be electrically insulated from all metallic parts of the core. In drum armatures the centrifugal force still more complicates. matters in tending to lift the conductors from the core; in smooth drum armatures it has therefore been found necessary to employ driving horns, which either are inserted into nicks in the periphery of the discs, or are supported from hubs keyed to the armature shaft at each end of the core. In ring armatures the centrifugal force presses the conductors at the inner circumference toward the armature core, and thus helps to drive, while the spider arms, by interlocking into the arma- ture winding, serve as driving horns. If toothed discs are used, no better means of driving can be desired. 42, Armature Thrust. If the field frame of a dynamo is not symmetrical, which is- particularly the case in most of the bipolar types (see Figs. 77 to 85), unless special precautions are taken there will be a denser magnetic field at one side of the armature than at the other, and an attractive force will be exerted upon the arma- ture, resulting in an armature thrust toward the side of the denser field. The force with which the armature would be attracted, if only one-half of the field were acting, is: / = 2 7t X ^ X ( ) = - OI 99 X -S s X OC 2 dynes, or, since 981,000 dynes = i kilogramme, / = g- X S g X 3C 2 = 2.03 x io- 8 X S e X 3C 2 kilogrammes; S g = gap area, in square centimetres; 3C = field density, in lines of force per square centimetre. 42] EFFECTS OF ARMATURE WINDING. 14* Expressing the gap area by the dimensions of the armature, we obtain : / = 2.03 x io- 8 X ^-^ X / a X ft\ X X 2 = 32 x io- 9 X <4 X 4 X ft\ X 3C 2 kilogrammes. . . (101) If, now, both halves of the field are in action, but one half is stronger than the other, the armature will be acted upon by two forces: /! = 32 x io~ 9 X a || M 00 M t>o 1 11 evs s s HI ii S'S si ti 13 11 1-1 Q ^ :_ j^ OoS fiS ^ ^ r75 ^s: PS & *fr p ^ ^ ^ ^ > F * ^ ft L > 2 1.667 .833 .556 1.667 .833 .556 .067 .033 .022 .067 .033 .022 4 3.333 1.667 1.111 1.667 .833 .556 .267 .133 .089 .133 .067 .044 5.000 2.500 1.667 1.667 .833 .556 .600 .300 .200 .200 .100 .067 8 6.667 3.333 2.222 1.667 .833 .556 1.067 .533 .356 .267 .133 .089 10 8.333 4.167 2.778 1.667 .833 .556 1.667 .833 .556 .333 .167 .111 12 10.000 5.000 3.333 1.667 .833 .556 2.400 1.200 .800 .400 .200 .133 14 11.667 5.833 3.889 1.667 .833 .556 3.267 1.633 1.089 .467 .233 .156 16 13.333 6.667 4.444 1.667 .833 .556 4.2672.133 1.422 .533 .267 .178 Designating the voltages in columns 2 to 7 of this table by * a , the number of conductors required for any particular case can be calculated from : E X io 10 (104) X X in which JV C = number of armature conductors; E = E. M. F. to be generated; e^ = volts per 100 conductors per 100 revolutions per minute and i megaline per pole, see Table XLI. ; JV = speed, in revolutions per minute; # = useful flux per pole, in webers. The average voltage between adjoining commutator-bars can be found from = ' x ..(105) 152 DYNAMO-ELECTRIC MACHINES. [45 where e s is the average voltage between segments at 100 revo- lutions per minute and at i megaline flux, as given in columns 8 to 13 of Table XLI. 45. Formula for Connecting Armature Coils. a. Connecting Formula and its Application to the Different Methods of Grouping. ,- A general formula for connecting the conductors of a closed coil armature has been given by Arnold 1 as follows: If JV C i= number of conductors arranged around armature core; ;/ a number of conductors per commutator segment; ;/' p number of bifurcations of current in armature; ;/ p = i, single bifurcation, or 2 parallel circuits. 'p = 2, double bifurcation, or 4 parallel circuits, etc. ;/ p = number of pairs of magnet poles; y = " pitch," or " spacing" of armature winding; /". e., the numerical step by which is to be advanced in con- necting the armature conductors; then the number of armature conductors can be expressed by W* = a X ( p X y 'p) , from which follows the connecting formula for any armature: (106) The general rule, then, for connecting any armature is: Connect the end (beginning) of any coil, x, of the armature to the beginning (end) of the (x -\- jy) th coil. For the various methods of grouping the armature coils, the above formula is applied as follows: I. Parallel Grouping. In this method of connecting there are as many parallel armature branches as there are poles, viz. 2 p circuits, or # p bifurcations. Spiral winding, lap winding, and wave winding may be applied: (i) Spiral Winding and Lap Winding. In this case the multipolar armature is considered as consisting of # p bipolar 1 E. Arnold, " Die Ankerwicklungen der Gleichstrom Dynamomaschinen." Berlin, 1891. 45] ARMATURE WINDING. 153 ones, and independently of the number of poles, p = i and n' P = i is to be inserted in (106), and the formula applied to a set of conductors lying between two poles of the same polarity. (2) Wave Winding, Here the actual number of pairs of poles, p, and the actual number of bifurcations, n' p = p , is to be introduced in (106), and the formula applied to the entire number of conductors. II. Series Grouping. This is characterized by having but two parallel armature circuits, or one bifurcation, no matter what the number of poles may be; for series connecting, therefore, we have n' p = i. In the special case of # p = i, bipolar dynamos, the series connecting is identical with the parallel grouping, and the winding may be either a lap winding (spiral winding) or a wave winding; the latter holds good also for # p = 2 ; /. 2, however, series grouping is only possible by means of wave winding. III. Series Parallel Grouping. In the mixed grouping the number of bifurcations is greater than i, and must be less than ;/ p ; hence, in the connecting formula we have //' p > i and ' p < ;/ p . In this case there are either several circuits closed in itself, with separate neutral points on the commutator, or one single closed winding with ' p parallel branches. The latter is the case N if y and -- are prime to each other; the former if they have a common factor; this factor, then, indicates the number of independent circuits. b. Application of Connecting Formula to the Various Practical Cases. I. Bipolar Armatures. (i) For any bipolar armature the number of pairs of poles, as well as the number of bifurcations is i; furthermore, the number of coils per commutator-bar is usually = i ; conse- quently // a = i, if in the connecting formula the number of conductors, N c , is replaced by the number of coils, n c . For ordinary bipolar armatures, therefore: tf p = i, . a = r > ' P = i ; y = c T J (107) 154 DYNAMO-ELECTRIC MACHINES. [45 (2) If the number of commutator segments is half the num- ber of armature coils, /. e., two coils per commutator-bar, then n = .y- - T i (108) II. Multipolar Armatures with Parallel Grouping. (1) By multiplying the bipolar method of connecting, we have: p = i, a = i, ' p = i ; y = n c =F i (109) This is a spiral winding; beginning and end of neighbor- ing coils are connected with each other, and a commutator connection made between each two coils. The number of sets of brushes is 2 n v . For multipolar parallel connection and spiral winding with but two sets of brushes, either n c divisions may be used in the commutator, and the bars, symmetrically situated with refer- ence to the field, cross-connected into groups of p bars each, or on iy __. segments may be employed, and n p coils of same ;/ P relative position to the poles connected to each bar by means of p separate connection wires. (2) In connecting after the wave fashion by joining coils of similar positions in different fields to the same commutator segments, the following formula is obtained: (110) \i y and n c have a common factor, this method of connecting furnishes several distinct circuits closed in itself, the common factor indicating their number. (3) If n v similarly situated coils are connected in series between each two consecutive commutator bars, only seg- /Z P ments, but 2 n p sets of brushes are needed; the winding is of the wave type, and the connecting formula becomes: 46] ARMATURE WINDING, 155 III. Multipolar Armatures with Series Grouping. (i) If all symmetrically situated coils exposed to the same polarity, by joining the commutator segments into groups of n p bars each, are connected to each other, they can be consid- ered as one single coil, and we obtain: Each brush, in this case, short circuits n v coils simultaneously. The same formula holds good, if beginning and end of every coil are connected to a commutator-bar each. The latter can always be done if n v is an uneven number; but if n v is even, the number of coils, n c , must be odd. In the case of n v uneven, if n c is even, the brushes embrace an angle of 180; but if n G is T 8n odd, an angle of only - - is inclosed by the brushes. p (2) Instead of cross-connecting the commutator, the wind- ing itself can be so arranged that only bars are required. In p this case the connections have to be made by the formula: NOTE. In drum armatures the beginning and end of a coil being situated in different portions of the circumference, they should be numbered alike, and yet marked differently, in order to facilitate the application of the above connecting formulae. By designating the beginnings of the coils by i, 2, 3, , and the ends by i', 2', 3', , this dis- tinction is attained. 46. Armature Winding Data. a. Series Windings for Multipolar Machines. While a parallel winding for a multipolar armature is always possible if the number of coils is even, the possibility of a series winding depends upon the relation between the number of poles and the number of conductors per armature division, or the number of conductors per slot in case of a toothed or perforated armature, respectively. In the following Table XLII., which is compiled from data contained in Parshall and DYNAMO-ELECTRIC MACHINES. [46 Hobart's work, 1 the various kinds of series windings possible for different cases are given, the symbols shown in Table XL., 44, being employed: TABLE XLIL KINDS OP SERIES WINDINGS POSSIBLE FOR MULTIPOLAR MACHINES. onductors per Armature Division or per Slot) Kind of Series inding SERIES WINDINGS possible for various numbers of Poles Poles Poles 8 Poles 10 Poles 12 Poles 14 Poles 16 Poles Simplex Duplex && && && riplex Simplex Duplex <& Q o GD GD Triplex Q <)() Simplex Duplex o O ffl GDffl Triplex 6 Simplex Duplex && && && Triplex S8 8 Simplex Duplex 00 G) (S Triplex 10 Simplex Duplex <2> ffl o Triplex o Simplex 12 Duplex o sa Triplex && 16 Simplex Duplex GDO Triplex Singly reentrant Simplex Winding Doubly '' = Triply ;;' Duplex Triplex 1 "Armature Windings for Electric Machines," H. F. Parshall and H. M. Hobart, New York, 1895. 46] ARM A TV RE WINDING. b. Qualification of Number of Conductors for the Various Windings. The approximate number of conductors for the generation of a certain E. M. F. being calculated from formula (104) and Table XXXIX., it is important to find the accurate number which is qualified to give correct connections for the desired kind of winding. In the following, practical rules and a num- ber of tables are given for the various cases. (i) Simplex Series Windings. Simplex series windings may be arranged either so that coils in adjacent fields, or so that coils in fields of same polarity are connected to each other. In Fig. 99. Short Connection Type Series Winding. Fig. 100. Long Connection Type Series Winding. the former case, which is sometimes called the short connection type of series winding, each of the two armature circuits is influenced by all the poles ; in the latter case, which is similarly styled the long connection type of series winding, each circuit is controlled by only half the number of poles. In the former, therefore, the E. M. Fs. of the two circuits are always equal, in the latter only then when the sum of all the lines of one polarity is equal to that of the other; a condition which, how- ever, is fulfilled in all well designed machines. In Fig. 99 a winding of the first kind, and in Fig. 100 one o the second kind is shown. The formula controlling simple series windings is: JV C = 2 (# p y i), for drum armatures, and # c = n v y i , for ring armatures; in which: 158 DYNAMO-ELECl^RIC MACHINES. [46 N c = number of conductors; n c = number of coils; n p = number of pairs of poles; y = average pitch. While for the short connection type there are as many com- mutator segments as there are coils, in a ring armature, or half as many as there are conductors, in a drum armature, the number of commutator-bars for the long connection type of .series winding is , T It is preferable to have the pitchy the same at both ends, in order to have all end connections of same length, but the number of conductors is less restricted (when n p > 2), if the front and back pitches differ by 2. Each pitch must be an odd number, so, in order that the winding passes through all conductors before returning upon itself, it must pass alter- nately through odd and even numbered conductors. Also when the bars, as is usually the case, occupy two layers, it is necessary to connect from a conductor of the upper to one of the lower layer, so as to obviate interference in the position of the spiral end connections. The following Table XLIII., page 159, gives formulae for the number of conductors for which simplex series windings are possible in various cases, and also gives the pitches for prop- erly connecting the conductors among each other. The formulae given refer to drum armatures, but can be used for ring armatures by replacing in every case half the number of conductors, -**c 2 by the number of coils, n c . Example, showing use of Table XLIII. : A 6-pole simplex series-wound drum armature is to yield 1.25 volt of E. M. F. at 3,000 revolutions per minute, with a flux of 27,000 webers per pole. How many conductors are required, and how are they to be connected? From (104) and Table XLI. we have ;v c = . '-'S x .0" _ 5 x 3> X 27,000 and Table XLIII. shows that the number of conductors in this 46] ARMATURE WINDING. TABLE XLIII. NUMBER OF CONDUCTORS AND CONNECTING PITCHES FOR SIMPLEX SERIES DRUM WINDINGS. 1 QUALIFICATION +- OF NUMBER OF CONDUCTORS, JVJ.. ** ^ n K^ Equation Degree of Description. M H M i torJY ' Evenness. < I o -1 N 2 **.* N c even Any even number not divisible by 3. y = T -i y y' y y' Any singly even num- lA#c \ y y 4 V odd ber, i. e., any odd multiple of 2. ^2ly 1 J y-i y'+l 6 ,.=,.,, ^V c even Any even number not a multiple of 3. -4(f-) y y 8 ^=8* 2 fodd Any singly even num- ber. ^(f* 1 ) y y'-i y'+i *, Any even number, having either 2 or 3 as remainder 1 / 7V7" V y 10 A- c =l L Any singly even num- 16 ^ =16* 3 ^Vc ber having either 2 or 14 as remain- der when divided -l(f-) y y'-i y by 16. * General formula: N G = 2 n x 2 ; 2 p = number of poles, x = any integer. t For ring armatures replace - by n c (number of coils). % The front and back pitches must always be odd numbers. If the average pitch, y, is odd, both the front and back pitches are equal to y ; but if y is even, then the front pitch is y i, and the back pitch = y -f- i. If the average pitch is either odd (y] i or even (y^), ac- cording to whether the -f- or sign in the formula is used, then two connections are possible, one having the pitches y t y, and the other the pitches y' i, y 1 -\- 1. iCo D YXA MO-ELE C TRIG MA CHINES. case must fulfill the condition N c = 6 x 2, which, for x = 5, and for the -f sign makes N c = 30 + 2 = 32 . The same table gives the average pitch from which follows that at both ends of the armature each conductor is to be connected to the sixth following (see Fig. 99, P a g e J 57). (2) Multiplex Series Windings. In case of multiplex series drum windings the number of conductors must be NC = 2 (p y m) i TABLE XLIV. NUMBER OF CONDUCTORS AND CONNECTING PITCHES FOR DUPLEX SERIES DRUM WINDINGS. 1 QUALIFICATION 1 OF NUMBER OF CONDUCTORS, JVc 09 a C00 t- a 2 AVERAGE H O NUMBER c 2r i; H Equation for JVe.t Degree of Evenness. Description. PITCH.* FRONT Pi I 9, LZV C =4 a 2 ^odd Any singly even num- ber. ^=^2 y y' 2/ y' AT (2) (5) ^,z=4 # 4 ^-even Any multiple of 4. y =-^- 2 y'-i y+i O O AT" Q -> /V c O */ "4~ G Any multiple of 8. 2 '=i(| +2 ) y IT 4 y g ^ 3 2j y 2/ r lA#c_i_9\ _.. (5) (5) N c 8 # 4 ^L odd Any quadruple of an y ~ ~2\ "3 "*". / ^ 4 odd integer. ^-i^- 2 ) y'-l 2/'+l iVc=12 x2 ~2~ Any singly even num- ber, not divisible by 3. y 2/ & N e =12 x 4 ^even Any multiply even number (even multi- ple of 2) not divisi- ble by 3. y =3A~2~ 2 j y ~ l y+t 8 ^" c =16 a; 4 4 Any quadruple of an odd integer. -S4 f-i y 46] ARMATURE WINDING. 161 TABLE XLIV. NUMBER OF CONDUCTORS AND CONNECTING PITCHES FOR DUPLEX SERIES DRUM WINDINGS. Continued. NUMBER OF POLKS. 2// p . KIND OF SERIES WINDING.* QUALIFICATION OF NUMBER OF CONDUCTORS, JV C AVERAGE PITCH. $ FRONT PITCH vn H Equation for.V c .t Degree of Evenness. Description. 10 O JV C =20 x 6 odd Any singly even num- ber having a 4 or a 6 as its unit digit. V l ( Nc 2] y If (S)(S)' JVc=20 a? 4 ^_even 2 Any multiply even number having a 4 or a 6 as its unit digit. y 5V 2 **) ?/'-! y'+i 12 JVc-24 a; 8 ^-even 4 ^ToTd Any multiple of 8, not divisible by 8. 1/^c 2 \ y y JV C =84 x 4 Any quadruple of an odd integer, not di- visible by 3. y ~Q\ 2 2 ) y'-i y'+i 14 O O # c =28ar 10 ^Odd Any singly even num- ber having 3 or 4 as remainder when di- vided by 7. -$H y y y'4-i y y'+i <>); .V =28 aj 4 =^- even Any multiply even number having 3 or 4 as remainder when divided by 7. y'-i 16 JV c =32o! 12 ^Lodd 4 Any quadruple of an odd integer of the form 8 x 3. V *( Nc 2\ y J!V C =32 4 ^odd 4 Any quadruple of an odd integer of the form 8 x 1. y 8V 2 **) y'-i * O O = singly re-entrant duplex winding ($) (J) = doubly re-entrant duplex winding. t General formula for O O ' N c = 4 p x (2 p 4); I a p = number of poles. General formula for(jj}CE>: -We = 4p-*4- \ x = any integer. ^ In case of ring windings replace ~ by c (number of coils). (/), the pitches may be either _y, j, or , the pitches are y i and y -\- i; if the average pitch has two e either y, y, or y',y'; if i, jf'-f- i, respectively. If v is 0W,both pitches are = y; \i y is *zv, the pitches different ,vW values, jj/ andy, the pitches may be either y, y, or y',y'; if the average pitch is either odd O) Ot and for ring windings the number of coils = p ^ in which m is the number of multiplex windings. The great- est common factor of y and m indicates the number of re- entrancies. In Tables XLIV. and XLV., pages 160 to 163, data for duplex and triplex series windings, respectively, are given. 162 Z> YNA MO-ELE C TRIG MA CHINE S. Example: The flux of a lo-pole dynamo is 8 megalines per pole. It is to give 145 volts at 125 revolutions per minute, with a triplex series drum winding. To find the number of conductors and the winding pitches. The approximate number of conductors is, by (104): N = X 2.778 X 125 X 8,000,000 TABLE XLV. NUMBER OP CONDUCTORS AND CONNECTING PITCHES FOR TRIPLEX SERIES DRUM WINDINGS. (2 i p ft KIND OP SERIES WINDING.* QUALIFICATION OP NUMBER OP CONDUCTORS, Nc. AVERAGE PITCH 4 FRONT PITCH. H i PH 1 Equation for ^Vc.t Degree of Evenness. Description. 000 N = 6 x 2 -ZV C even Any even number, not a multiple of 3. a/ c _l_ Q y 4x (3)(S)(as) N c = 6 x 6 N even Any multiple of 6. 2 y y'-i A* 4 000 N c =12 x 2 -^- odd Any singly even num- ber, not a multiple of 3. U|(f+) y y'-i y 0~ N C -=12 x 6 odd Any odd multiple of 6. ^](f-) y y 6 000 N C =1S x -ZV C even Any multiple of 18. " = i ( f + 3 3) *-i /+i 000 N e =lS x 6 ^V c even Any even multiple of 3, not divisible by 9. -! Ai 8 000 TW- 04. * 2 * 10 ^.Odd Any singly even num- ber, not a multiple of 3. l(N c /-i Ai QCSXfifl) JV C =24 # 6 fodd Any odd multiple of 6. y 4V 2 8 J /-i y v'+t 10 000 ^c=30 x * J 4 Nc even Any even number not divisible by 3, and having either a 4 or a 6 as unit digit. HfM /-i y'-hi ao iV c =30 * 6 Nc even Any odd multiple of 6, having either a 4 or a 6 as unit digit. '-! 46] ARMATURE WINDING. I6 3 TABLE XLV. NUMBER OF CONDUCTORS AND CONNECTING PITCHES FOR TRIPLEX SERIES DRUM WINDINGS. Continued. t * 1 QUALIFICATION 3 O OF NUMBER OF CONDUCTORS, N~ c . C^9 1 bi i g I* ^ c 2 AVERAGE PH a g^ PITCH.* 1" 02 Equation for jVc.t Degree of Evenness. Description. ! I 10 000 No= 36 x 18 - odd Any odd multiple of 18. '=+) /-i fk 000 ^Vc=36 x 6 - odd Any odd multiple of 6, not divisible by 9. y ' = l(^~~ 3 ) /-i y+i Any even number, not 8 a, multiple of 3, hav- y .y 14 000 * 22 JV C even ing either 1 or 6 as remainder when di- vided by 7. y = l(K s \ y'-i y+i Any multiple of 6, hav- y V ^=42 x 6 NO even ing either 1 or 6 as remainder when di- vided by 7. Any singly even num- ooo ^- 48 * 10 26 IT Odd ber, not a multiple of 3, having either 6 or 10 as remainder y i/'-\-L 16 when divided by 16. Any odd multiple of 6, 8 V 2 J ( ^c = 48 # 6 f-dd having either 6 or 10 as remainder when y y divided by 16. y'-i y+i * O O O = singly re-entrant triplex winding ;(2)(5Xufi) = triply re-entrant triplex winding. t General formula for O O O : : c = 6 p x ( 2 p - 6), or | a ^ = num General formula for: ^^enp^ot" 13 f -^ = ^y integer. $ For ring windings replace _i: by c (number of coils). Jlf y is <7rfi/, both pitches are = _y/ if y is ^^, the pitches are y i and y -\- i ; if the average pitch is ( (y), or even (_j/), the pitches may be either^j/, or^' i.jy'-j- i, respectively. By Table XLV., the number of conductors qualified for a singly re-entrant triplex series drum winding must be either ^0 = 3* * 4, or ^"c = 3 x 14 , the latter of which, for x = 17, when using the + sl S n t ^ ur * nishes the nearest number, e = 3 X 17 -f 14 = 524, 1 64 DYNAMO-ELECTRIC MACHINES. [46 for which a singly re-entrant triplex winding is possible. The average pitch, being odd, the front and back pitches are equal, both being the same as the average pitch. If a triply re-entrant triplex winding were desired the num- ber of conductors would have to be determined from N c = 30 x 6 ; and the two nearest numbers that fulfill this equation are N c = 30 x 17 + 6 = 516, and -#c = 3 X 18 6 = 534 . According to whether the former or the latter number of con- ductors is chosen, the average pitch will be either or respectively. In the former case both pitches are y = 51; in the latter case, however, the front pitch has to be taken / i = 53, and the back pitch/ -f i = 55. (3) Simplex Parallel Windings. For simplex parallel wind- ings there may be any even number of conductors, except that in toothed and perforated armatures the number of conductors must also be a multiple of the number of conductors per slot. If it is desired to have exactly the same number of coils in each of the parallel branches, the number of coils must further be a multiple of the number of poles. The pitches in parallel windings are alternately forward and backward, instead of being always forward, as in the series windings. The front and back pitches must both be odd, and should preferably differ by 2; therefore, the average pitch 46] ARMATURE WINDING. 165 should be even. The average pitch should not be very much different from the number of conductors per pole, ** For drum fashioned ring windings, or " chord" windings, the average pitch, y, should preferably be smaller than and should differ from it by as great an amount as other con ditions will permit. Fig. 101. Simplex Parallel Ring Winding. Fig. 101 shows a simplex parallel ring winding for 4 poles and 16 coils. The average pitch is consequently the front pitch, y 1=3, and the back pitch y + i = 5- (4) Multiplex Parallel Windings. In multiplex parallel wind- ings the number of conductors, N& must be even. The con- necting pitches must be odd. If the front pitch is = y', then the back pitch is = (/ -f- 2 ;z m ), where n m = number of mul- tiple windings. The number of conductors (TV^), the average pitch (y) and the number of poles (2 p ) should be so chosen that 2 n p = y is somewhere nearly = 7V C , preferably a little smaller than JV. 1 66 DYNAMO-ELECTRIC MACHINES. [ 4ft The greatest common factor of - and n m 2// p indicates the number of re-entrancies of the windings. If the number of conductors per pole, 2n r is not divisible by the number of multiple windings, n m , there will be a singly re-entrant winding; and if it is divisible by Fig. 102. Duplex Parallel Drum Winding. m , there will be a doubly re-entrant winding in case of n m 2 (duplex winding), and a triply re-entrant winding in case of n m = 3 (triplex winding). The winding pitches for multiple parallel windings are: Average pitch y = - - x ( - 1 n p \^ 2 Front pitch y t y n m) Back pitch y b = y -f- n m . In case of a duplex parallel winding y should be chosen an odd number, so as to makejy 2 and y + 2 odd numbers also; and in case of a triplex parallel winding the average pitch should be taken even, in order to make the connecting pitches, y 3 and y -|- 3, odd. In Fig. 102 a singly re-entrant multiplex parallel winding is 46] ARMATURE WINDING. 167 given for n p = 2, n' p = 2, n m = 2, and N e = 28. The pitches in this case are y 2 = 5> and y + 2 = 9 . There are two independent singly re-entrant windings, each having 4 parallel branches, making 8 paths altogether; 6 of these paths contain 4 conductors each, and the remaining 2 but 2 conductors each. In order to have an equal number of conductors in all branches, N must be a multiple of 2 n' v x m , or in the present example the number of conductors should be either 24 or 32; in the former case each of the 8 parallel branches would have 3, and in the latter case 4, conductors. As further illustrations of the rules given above we take (i) N c 486, n p 3, 'p = 3, ;/ m = 2; this is a 6-pole duplex parallel winding; since N c 486 - 5i 2 p 6 is not divisible by n m = 2, we have a singly re-entrant duplex winding (oo), for which the pitches are: 7 2 = 79, and . v + 2 = 8 3 - (2) N c = 1,368, p = 6, ' p = 6, m = 3; in this case, which represents a triplex parallel winding for 12 poles, 12 is a multiple of m = 3, and therefore we have a triply re- entrant triplex winding ( (^(20)); the average pitch for this winding is - hence the front and back pitches are y - 3 = in, and;; + 3 = 117, respectively. CHAPTER IX. DIMENSIONING OF COMMUTATORS, BRUSHES, AND CURRENT- CONVEYING PARTS OF DYNAMO. 47. Diameter and Length of Commutator Brush Sur- face. In small and medium-sized machines the commutator is usu- ally placed upon the shaft concentric with the armature, and has the collecting brushes sliding upon its peripheral surface. In large ring dynamos the armature winding is often performed by means of bare copper bars, and the current is then taken off directly from the winding; thus, in the Siemens Innerpole dy- namo the brushes rest upon the external periphery of the arma- ture, and in the Edison Radial Outerpole machine the two end surfaces of the armature are formed into commutators. If it is not convenient to use part of the armature winding itself as the commutator, in large diameter machines it is of advantage to provide a separate face-commutator, that is, a commutator with the brush surface perpendicular to the arma- ture shaft; for in this case the otherwise unavailable space between the armature periphery and the shaft is made use of, and a saving in length of machine and in weight will be effected. For the peripheral as well as for the face type commutator the same principles of construction hold good; the only differ- ence is that in the latter case the outer diameter of the brush surface is fixed by the external diameter of the armature, and that therewith the top width of the bars is directly given by the number of commutator divisions, while in the former case the dimensions of the brush surface can be chosen between comparatively much wider limits. In low potential machines with small number of divisions, the thickness of the substructure determines the diameter of the commutator; in high potential machines, however, espe- cially those of multipolar type, where the number of commuta- 168 47] COMMUTATORS, BRUSHES, AND CONNECTIONS. 169 tor segments is very great, the width, at top, of the commu- tator bars, their number, and the thickness of the insulation between them fix the outside diameter. The bars must be large enough in cross-section to carry the whole current generated in the armature without undue heat- ing, and shall continue so after a reasonable amount of wear. They must be of sufficient length to allow a proper number of brushes to take off the" current. The same brush contact surface may be obtained by employ- ing either a broad thin brush on a small diameter commutator,, or a narrow thick one on a large diameter, the number of bars being the same in both cases, their width, consequently, larger in the latter case. With larger diameter and greater conse- quent peripheral velocity there will be more wear of both brushes and segments, and greater consumption of energy due to the increased friction of the brushes. The segments are usually made of copper (cast, rolled, or forged), phosphor bronze, or gun metal, sometimes brass, and even iron being used; the materials for the substructure are phosphor bronze, brass, or cast iron. From all this it will be obvious that a general formula for the diameter of the commutator cannot be established, and that, on the contrary, this dimension has to be properly chosen in every case with reference to the armature diameter to the design of the commutator, to the materials employed, to the strength of the substructure, or the thickness of the bar, respectively, and, finally, with reference to the wear of the segments. The commutator diameter being decided upon, the size of the brushes can now be calculated, as shown in 49, and, from this, the length of the commutator can be found. In order to prevent annular grooves being cut around the commutator, the brushes ought to be so adjusted that the gaps between those in one set do not come opposite the gaps in the other set. Denoting, Fig. 103, the width of each brush by ^ b , their number per .set by b , and the gap between them by /' b , we consequently obtain the total length of the commu- tator brush surface from : - ix I yo DYNAMO-ELECTRIC MACHINES. [48 This length of brush surface should be available even after the commutator has been turned down to its final diameter; the original diameter must therefore have a somewhat larger con- Fig. 103. Arrangement of Commutator Brushes. tact length. An addition to / c of from ^ to i inch, according to the depth of the bar, is thus necessitated. As to the practical design of commutators, while the same general plan is followed in all, the details of construction are almost numberless. Structural cross-sections and descriptions of the commutators manufactured by the Electron Manufac- turing Company, the Storey Motor and Tool Company, the Royal Electric Company, the Fort Wayne Electric Corpora- tion, Paterson & Cooper, the Gulcher Company, the General Electric Company, the Triumph Electric Company, the Sie- mens & Halske Electric Company, the Walker Company, and others, are given in an article l in American Electrician. 48. Commutator Insulations. In a commutator the insulation has to form a part of the general structure, and has to take strain in common with other material used; from its natural cleavage and hardness, therefore, mica is particularly suitable for commutator insula- tions, and is, in fact, almost exclusively used for this purpose, only asbestos and vulcanized fibre being employed in rare cases. 1 " Modern Commutator Construction," American Electrician, vol. viii. p. 83 (July, 1896). 49] COMMUTATORS, BRUSHES, AND CONNECTIONS. i?i The thickness of the commutator insulation ought to be proportional to the voltage of the machine, and, for the various Fig. 104. Commutator Insulations. positions with reference to the bars, see // t , h' iy h'\^ Fig. 104, should be selected within the following limits: TABLE XL VI. COMMUTATOR INSULATIONS FOR VARIOUS VOLTAGES. POSITION OP INSULATION. THICKNESS OP INSULATION (MICA): Up to 300 Volts. 400 to 700 Volts. 800 to 3,000 Volts. inch. mm. inch. mm. inch. mm. Side Insulation (hi) Bottom Insulation (h'\) End Insulation (h"i) .020 to .040 * :: * IB 35 .5 to 1.0 1.25 " 2.5 1.5 " 2.5 .030 to .050 i " ! .75 to 1.25 1.5 " 3 2.5 " 3 .040 to .060 t 1 1 to 1.5 2.5 " 5 3 " 5 49. Dynamo Brushes. 1 a. Material and Kinds of Brushes. For low potential machines having a large current output, it is the practice to employ thick copper brushes, made up either of copper wires, or copper strips, or copper wire gauze, in order to secure a large number of contact points, and to set them so as to make an angle of about 45 with the commutator surface, as shown in Fig. 105. In small dynamos, often springy copperplates are used which are placed tangentially to the commutator periphery, as illustrated in Fig. 106. For high potential machines, especially for railway genera- tors and motors, carbon brushes are used in order to aid in the sparkless collection of the current at varying load. As each 1 " Commutator Brushes for Dynamo-Electric Machines: their selection, their proper contact-area, and their best tension," by A. E. Wiener, American Elec- trician, vol. viii. p. 152 (September, 1896). 172 D YNAMO-ELECTRIC MA CHINES. [ 49 commutator segment enters under the brush, the area of con- tact is, at first, very small and, owing to the high specific re- sistance of carbon, a considerable resistance is offered to the passage of the current from the branch of the armature of which that segment at the time is the terminal, into the exter- nal circuit. This gives rise to a considerable local fall of potential, which diverts a comparatively large portion of the armature current through the neighboring coil into which it flows against the existing current, causing the latter to reverse quickly in opposition to the E. M. F. of self-induction, thereby Fig. 105. Sloping Copper Wire (or Fig. 106. Tangential Copper Plate leaf) Brush. Brush. preparing the short-circuited coil to join the successive arma- ture circuit of opposite polarity without sparking. (Compare with sections on sparkless commutation of armature cur- rent, in 13.) The resistance of the carbon brushes cannot be depended upon for the complete commutation of the entire current, but in most generators, especially in those with toothed and perforated armatures, fully half the armature current may be thus commutated. In railway generators it is usual to adjust the brushes so that at no load they are in the neighborhood of the forward pole-tips where the pole- fringe E. M. Fs. generated are sufficient to reverse one-half of the normal current, the remaining half being then taken care of by the brushes. Carbon brushes are either set tangentially (Fig. 107), or radially (Fig. 108), with respect to the commutator circumfer- ence, the latter arrangement having the advantage of admitting of reversal of the rotation, without changing the brushes. To use carbon brushes exclusively on machines of low volt- age would be very bad practice, because carbon has so much 49] COMMUTATORS, BRUSHES, AND CONNECTIONS. 173 higher resistance than copper that the drop of potential would be excessive, and too great a percentage of the power of the machine would be used up for commutation. If, therefore, the resistance of an ordinary copper brush is not high enough Fig. 107. Tangential Carbon Brush. Fig. 108. Radial Carbon Brush. for sparkless collection, a copper gauze brush must be em- ployed, which has a much higher resistance than a copper leaf brush, and while there are some mechanical advantages in using it, such as cooling effects and smoother wear of the commutator, yet the principal reason it stops sparking is that it has a higher resistance. In case the resistance is still too low, the next step is the application of a brass gauze brush having about twice the resistance of copper gauze. If that is not enough yet, some form of carbon brush which has its resistance reduced, must be resorted to. Carbon itself cannot have its resistivity changed, but by mixing copper filings with the carbon powder, or by molding layers of gauze in it, the conductivity of the brush can be increased. Instead of arti- Figs. 109 and no. Combination Copper-Carbon Brushes. ficially decreasing the resistance of carbon, combination brushes consisting either in copper brushes provided with carbon tips, Fig. 109, or in carbon brushes sliding upon the commutator and having, in turn, copper brushes resting against themselves, Fig. no, are sometimes employed, and in case of very heavy D YNA MO-ELE C TRIG MA CHINE S. [49 currents, the addition to each set of copper brushes, of a com- bination brush set somewhat ahead of the copper brushes as shown in Fig. in, has been found to greatly improve the COMBINATION BRUSH COPPER BRUSH Fig. in. Arrangement of Copper and Combination Brushes for Collection of Large Currents. sparkless running of the machines. With the latter arrange- ment, the tension on the combination brushes should exceed that on the copper brushes sufficiently to enable them to take their full share of the current as nearly as possible. b. Area of Brush Contact. The thickness of the brushes, according to the current capa- city of the machine, to the grouping of the armature coils, to the material and kind of the brush and to the dimensions of the commutator, varies between less than the width of one to Figs. 112 and 113. Circumferential Breadth of Brush Contact. that of three and even more commutator segments. In case the brush covers not more than the width of one bar, as in Fig. 112, only one armature coil is short-circuited at any time, 49] COMMUTATORS, BRUSHES, AND CONNECTIONS. 175 while in case of brushes thicker than the width of one bar plus two side insulations, Fig. 113, two or even more coils, at times, are simultaneously short-circuited under each set of brushes. The breadth of the brush contact surface in the former case (Fig. 112) is equal to the thickness of the beveled end of the brush measured along the commutator circumference; in the latter case (Fig. 113) is the breadth of the brush bevel dimin- ished by the sum of the thickness of the commutator insula- tions covered by the brush, and can be generally expressed by the formula where ^ k = circumferential breadth of brush contact, in inches; k = number of commutator-bars covered by the thick- ness of one brush; dT k = diameter of commutator, in inches; c = number of commutator-divisions; ^i = thickness of commutator side-insulation, in inches, see Table XLVI. If the brush covers less than one bar, as in Fig. 112, n k is a fraction; if the width of the brush is from one bar to one bar plus two side insulations, n k = i; when between two bars plus one insulation and two bars plus three insulations, n k = 2, etc. ; and if the brush covers from one bar plus two insulations to two bars plus one insulation, or from two bars plus three insula- tions to three bars plus two insulations, etc., the value of k is a mixed number, consisting of an integer and a fraction. Having decided upon k and having calculated b^ from (115), the width of the contact area, and subsequently the width of the brushes, can be found for a given current output of the dynamo by providing contact area in proportion to the current intensity. In order to keep the brushes at a moderate tem- perature, and the loss of commutation within practical limits, the current density of the brush contact should not exceed 150 to 175 amperes per square inch in case of copper brushes (wire, leaf plate, and gauze), 100 to 125 amperes per square inch for brass gauze brushes, and 30 to 40 amperes per square inch in case of carbon brushes. 176 D YNAMO-ELECTRIC MA CHINES. |_ 4- Taking the lower of the above limits of the current densities, the effective length of the brush contact can consequently be expressed by for copper brushes, by for brass brushes, and by / k = i- (118) 30 X n\ X k for carbon brushes, the symbols employed being / k = effective length of brush contact surface, in inches; = n \> X ^b (b = number of brushes per set, b = width of brush); / total current output of dynamo, in amperes; n"^ = number of pairs of brush sets (usually either n" v = i, or equal to the number of bifurcations of the armature current, n\ #' p ). For the purpose of securing a good contact, the length / k should be subdivided into a set of n b individual brushes, of a width b each, not exceeding \y 2 to 2 inches. In small machines, where one such brush would suffice, it is good practice to employ two narrow brushes, even down as low as 3/8 inch each, in order to facilitate their adjusting or exchang- ing while the machine is running. c. Energy- Loss in Collecting Armature Current. Determination of Best Brush Tension. The brushes give rise to two losses of energy: an electrical energy-loss due to overcoming contact resistance, and a mechan- ical loss caused by friction. Both of these losses depend upon the pressure with which the brushes are resting upon the com- mutator, the electrical loss decreasing and the mechanical loss increasing with increasing brush tension. There will, there- fore, in every single case, be one certain pressure per unit area of brush contact, for which the sum of the brush losses will be a minimum. With the object of determining this criti- 49] COMMUTATORS, BRUSHES, AND CONNECTIONS. 177 cal pressure, E. V. Cox and H. W. Buck 1 have investigated the influence of the brush tension upon the contact resistance and upon the friction, for various kinds of brushes. They found (i) that the friction increases in direct proportion RESISTANCE, TANGENTIAL COPPER LEAF BRUSH BRUSH PRESSURE, IN POUNDS PER SQUARE INCH Tig. 1 14. Contact Resistance and Friction per Square Inch of Brush Surface, on Copper Commutator (dry), at Peripheral Velocity of 1,000 Feet per Minute. with the tension; (2) that the contact resistance decreases at first very rapidly, but that beyond a certain point a great increase in pressure produces only a slight diminution of resistance; (3) that slightly oiling the contact surface, while not perceptibly increasing the electrical resistance, greatly 1 The Relation between Pressure, Electrical Resistance, and Friction in Brush Contact," Electrical Engineering Thesis, Columbia College, by E. V. Cox and H. W. Buck. Electrical Engineer, vol. xx. p. 125 (August 7, 1895); Electrical World, vol. xxvi. p. 217 (August 24, 1895). i 7 8 D YNAMO-ELECTRIC MACHINES. [49 diminishes the friction; (4) that for a copper brush the friction is greater and the contact resistance smaller than fur a carbon brush of same area at the same pressure; (5) that the friction of a radial carbon brush is greater than that of a tangential carbon brush at the same pressure; (6) that for the same brush both the contact resistance and the friction are consid- erably less on a cast-iron cylinder than on a commutator; and [STANCE, RADI RES/STANCETfAWG 0-51 1-5 2 2-5 3 3-5 4 BRUSH PRESSURE, IN POUNDS PER SQUARE INCH Fig. 115. Contact Resistance and Friction per Square Inch of Brush Surface,, on Cast-iron Cylinder. (7) that for all kinds of brushes the friction is less at high than at low peripheral speeds, while the contact resistance is but slightly increased by raising the velocity. In Figs. 114 and 115 the averages of their results are plotted, the former giving the curves of contact resistance and friction for an ordinary commutator, without lubrication, and the latter the corresponding curves for the case that the commutator is replaced by a cast-iron cylinder. From Fig. 114 the following Table XLVII. is derived, which, in addition to the data obtained from the curves, also- 49J COMMUTATORS, BRUSHES, AND CONNECTIONS. 179 contains the brush friction for the case the commutator is slightly oiled: TABLE XLVII. CONTACT RESISTANCE AND FRICTION FOR DIFFERENT BRUSH TENSIONS. CONTACT RESISTANCE PER SQUARE INCH OF BRUSH SURFACE, TANGENTIAL PULL DUE TO BRUSH FRICTION PER SQUARE INCH OF CONTACT AT PERIPHERAL SPEED OF 1,000 FEET PER MINUTE. /9 k , IN OHM. flu IN POUNDS. BRUSH IN POUNDS A Commutator Dry. Commutator Oiled. PER ~2 a'S | SQUARE INCH. .Scq p .5 s 1 b/oa s ll cW si i sl ^jg "cM "7 JS 5. *j la ii l s M a3 ig " a t^ 32 o. s s W^g 5 S PH ^ 5 l l H S g| | 1 .5 .010 .50 .40 .6 .3 .5 .16 .10 .15 1 .009 .24 .20 1.15 .63 1 .32 .20 .30 1.5 .008 .15 .13 1.7 .95 1.5 .48 .30 .45 2 .007 .12 .10 2.25 1.25 2 .64 .40 .60 2.5 .006 .10 .087 2.8 1.6 2.5 .80 .50 .75 3 .0055 .09 .08 3.4 1.9 3 .96 .60 .90 3.5 .0052 .083 .075 3.95 2.2 8.5 1.12 .70 1.05 4 .005 .08 .07 4.5 2.5 4 1.30 .80 1.20 The specific pull, / k , due to brush friction, in columns 5 to 10 of the above table, is given for a peripheral velocity of 1,000 feet per minute; at 2,000 feet per minute it is 7/8, at 3,000 feet per minute 3/4, at 4,000 feet per minute 5/8, and at 5,000 feet per minute only 1/2 of what it is for that pres- sure at 1,000 feet per minute, and for any commutator velocity > ?' k , can be found from the formula (119) From Table XLVII. the electrical brush loss is calculated by dividing the contact resistance given for the particular brush tension employed, by the contact area, and multiplying the 1 80 D YNAMO-ELECTRIC MA CHINES. [ 49 quotient by the number of sets of brushes and by the square of the current passing through each set, thus: watts = .00268 X Pk . X /2 horse power, ..... (120) 'k X ^k X # p where P^ energy absorbed by contact resistance of brushes; p k = resistivity of brush contact, ohm per square inch surface, from Table XLVIL; / k x ^ k = contact area of one set of brushes, in square inches; n\ number of pairs of brush sets; / = current output of dynamo. And the frictional loss is obtained in multiplying the tan- gential pull, given for the respective brusli tension and cor- rected to the proper peripheral velocity according to formula (119), by the total brush contact area and by the peripheral velocity of the commutator, and dividing the product by 33,000, the equivalent of one horse power in foot-pounds per minute: p = X 4 X k X 33,000 6 x io- 5 X A X 4 X k X n\ X < in which P t = energy absorbed by brush friction, in HP; y' k specific tangential pull due to friction, at ve- locity z; k , in pounds, see formula (119); 2 #"p X 4 X ^ total area of brush contact surfaces, in square inches; z> k = peripheral velocity of commutator, in feet per minute, <4 X fr X JV 12 By calculating the amounts of P^ and P t , from (120) and (121) respectively, for different brush tensions, the best tension giving a minimum value of the total brush-loss, P -f- P t , can readily be found. 50] COMMUTATORS, BRUSHES, AND CONNECTIONS. 181 oO. Current-Conveying Parts. Care must also be exercised in the proportioning of those parts of a dynamo which serve to convey the current, col- lected by the brushes, to the external circuit. For, if mate- rial is wasted in these, the cost of the machine is unneces- sarily increased; and if, on the contrary, too little material is used, an appreciable drop in the voltage and undue heating will be the result. In the. design of such current-conveying parts, among which may be classed brush holders, cables, conductor rods, cable lugs, binding posts, and switches, the attention should Figs. 116 to 118. Various Forms of Spring Contacts. therefore be directed to the smallest cross-section through which the current has to pass, and to the surfaces of contact transferring the current from one part to another. The max- imum permissible current density in the cross-section, while depending in a small degree upon the ratio of circumference to area of cross-section, is chiefly determined by the choice of the material; that in the area of contact between two parts, how- ever, although the conductivity of the material employed is of some consequence, depends mainly upon the condition of the contact surfaces and upon the amount of pressure that can be applied to the joint. The most usual forms of contact are those shown in Figs. 116 to 125. Figs. 116 to 118 represent spring contacts as used in switches; in Fig. 116 the switchblade is cast in one with the lever, while in Figs. 117 and 118 the levers are provided with separate copper blades. The former is a single switch making and breaking contact between the blade and the clips, the lever itself forming the terminal of one pole; the. latter two are double switches, the connection being established between two sets of clips by way of the blade, when the switch is closed. 1 82 DYNAMO-ELECTRIC MACHINES. [50 In order to prevent the forming of an arc in opening a switch, especially a double switch, each blade must leave all the clips with which it engages simultaneously over its entire length. For this purpose either the blade, or the clips, or both (Figs. 117, 118, and 116, respectively) have to be cut off at such an. angle that, in the closed position of the switch, the enter-line of the blade and the line through the tops of the clips are both tangents to the same circle (shown in dotted lines in Figs. 116 to 1 18), described from the centre of the lever fulcrum. If all clips are then made of equal widths, as in Fig. 117, those Fid. 11 9. -LAMINATED JOINT. FIG. 122. -LUG CLAMPED BETWEEN WASHERS. FIG. 123.-TAPER PLUG, FITTED INTO SOCKET. Flo' f24. -TAPER PLUG INSERTED BETWEEN TWO SURFACES. /IG. 126. -TAPER PLUG GROUND TO SEAT ' AND BOLTED. Figs. 119 to 125. Various Forms of Screwed, Clamped, and Fitted Contacts. nearest to the fulcrum, in case of a double switch, have less contact area than the remote ones, and in designing such a switch this smaller contact area is to be made of sufficient size to carry half the armature current, if there is but one blade, and one-quarter of the total current when the lever has two blades. By making the clips near the fulcrum correspondingly wider than those at the other end of the blade, as in Fig. 118, all the contact surfaces can, however, be made of equal area. Various forms of screwed or bolted contacts are shown in Figs. 119, 120, and 121; a clamped contact is illustrated in Fig. 122; two common forms of fitted contact in Figs. 123 and 124;^ and an excellent fitted and screwed contact in Fig. 125. 50] COMMUTATORS, BRUSHES, AND CONNECTIONS. 183 The permissible current densities for all these different kinds of contact as well as for the cross-section of different materials are compiled in the following Table XLVIII., which more in particular refers to the larger sizes of dynamos, since in small machines purely mechanical considerations lead to much heavier pieces than are required for electrical purposes: TABLE XLVIII. CURRENT DENSITIES FOR VARIOUS KINDS OP CONTACTS AND FOK CROSS-SECTION OF DIFFERENT MATERIALS. KIND OF CONTACT. MATERIAL. CURRENT DENSITY. ENGLISH MEASURE. METRIC MEASURE, Amps, per square inch. Square mils per amp. Amps, per cm. 2 mm. 2 per ampere. 3.5 to 4.5 Sliding Contact (Brushes) Copper Brush 150 to 175 5,700 to 6,700 23 to 28 Brass Gauze Brush 100 to 125 8,000 to 10,000 15 to 20 4.5 to 6 5 to 7 16 to 22 Carbon Brush 30 to 40 25,000 to 33,300 Spring Contact (Switch Blades) Copper on Copper 60 to 80 12,500 to 16,700 9 to 12.5 8 to 11 Composition on Copper 50 to 60 16,700 to 20,000 7.5 to 9.5 11.5 to 13.5 Brass on Brass 40 to 50 20,000 to 25,000 5.000 to 6,700 6 to 8 12.5 to 16.5 Screwed Contact Copper to Copper 150 to 200 23 to 31 3 to 4.5 Composition to Copper 125 to 150 6,700 to 8,000 19 to 23 4.5 to 5.5 Composition to Composition 100 to 125 8,000 to 10,000 15 to 20 5 to 6.5 Clamped Contact Copper to Copper 100 to 125 8,000 to 10,000 15 to 20 5 to 6.5 Composition to Copper 75 to 100 10,000 to 13,000 12 to 16 6 to 8.5 Composition to Composition 70 to 90 11,000 to 14,000 11 to 14 7 to 9 3.5 to 5 5 to 7 l Fitted Contact (Taper Plugs) Copper to Copper 125 to 175 5,700 to 8,000 20 to 28 Composition to Copper 100 to 125 8,000 to 10,000 15 to 20 Composition to Composition 75 to 100 200 to 250 10,000 to 13,000 4,000 to 5,000 12 to 16 6 to 8.5 Pitted and Screwed Contact Copper to Copper 30 to 40 2.5 to 3.5 Composition to Copper 175 to 200 5,000 to 5,700 28 to 31 3 to 3.5 Composition to Composition 150 to 175 5,700 to 6,700 23 to 28 3.5 to 4.5 Cross-section Copper Wire 1,200 to 2,000 500 to 800 175 to 300 .35 to .55 Copper Wire Cable 1,000 to 1,600 600 to 1,000 150 to 250 .4 to .65 Copper Rod 800 to 1,200 800 to 1,200 1,400 to 2,000 125 to 175 .55 to .80 Composition Casting 500 to 700 75 to 110 .90 to 1.35 Brass Casting 300 to 400 2,500 to 3,300 45 to 60 .60 to 2.25 CHAPTER X. MECHANICAL CALCULATIONS ABOUT ARMATURE. 51. Armature Shaft. The length of the armature shaft, varying considerably foi the different arrangements of the field magnet frame, depends upon the type chosen, and, since the length of the commutatoi depends upon the current output of the machine, even varies in dynamos of equal capacity and of same design, but of differ, ent voltage, a general rule for the length of the shaft can therefore not be given. Its diameter, however, directly depends only upon the out- put and the speed of the dynamo, and can be expressed as a function of these quantities, different functions, however, being employed for various portions of its length. For, while Fig. 126. Dimensions of Armature Shaft. in the bearing portions, <4, Fig. 126, torsional strength only has to be taken into account, the center portion, d c , between the bearings, which carries the armature core, is to be calcu- lated to withstand the torsional force as well as the trending due to the weight. For steel shafts the author has found the following empirical formulae to give good results in practice: For bearing portions: ^ = ,x x where c Dividing F' & by the total number of spokes, we have the pull for each spoke, and this multiplied by the leverage gives the external momentum acting on each; the latter must be equal to the internal momentum, *. e., the product of the modulus of the cross-section and the safe working stress of the material. In consequence, we have the equation: P' ' , - or, , ^^"x-^Xsrh; ...... (125) in which b$ = smallest width of spoke (parallel to shaft), in inches; /t s = smallest thickness of spoke (perpendicular to shaft), in inches; / s = leverage at smallest spoke section, /. e., distance of smallest section from active armature con- ductors, in inches; s = total number of spokes per armature; P' = total capacity of dynamo, in watts; v c = conductor velocity of armature, in feet per second; / s = safe working load of material, in pounds per square inch; for cast iron ....... ./ s = 5,000 Ibs. per square inch. " brass ........... = 6,000 " " " phosphor-bronze = 7,000 " wrought iron. ... = 10,000 " aluminum bronze = 12,000 " " cast steel ....... =15,000 " " For spiral windings, now, s , as stated above, is given by making it as large as possible, and from (125) we therefore obtain: _ x ..... (126) 190 DYNAMO-ELECTRIC MACHINES. [53 For windings external to the core, 7/ s may be fixed and then calculated from: I 6* = 18 X X x x For very heavy duty dynamos a larger factor of safety should be taken, say from 6 to 8; this will change the numeri- cal coefficient of formulae (125) and (127) into 27 to 36, and that of equation (126) into 5.3 to 6, respectively. 53. Armature Bearings. To determine the size of the armature bearings, ordinary engineering practice ought to be followed. In machine design, on account of the increased heat generation at higher velocities, it is the rule to provide a larger bearing surface the higher the speed of the revolving shaft. This rule may, for dynamo shafts, be expressed by the formula: 4 = X (128) where / b = length of bearing, in inches; */ b = diameter of bearing, in inches, from formula (122); JV= speed of shaft in revolutions per minute; 10 =r constant depending upon kind of armature and on capacity of dynamo. (See Table LIV.) The numerical values of 10 range between .1 and .225 for high-speed armatures, and from .15 to .3 for low-speed arma- tures, as follows: TABLE LIV. VALUE OF CONSTANT IN FORMULA FOB LENGTH OF ARMATURE BEARINGS. CAPACITY, IN KILOWATTS. VALUE OP CONSTANT &io. High-Speed Armatures. Low-Speed Armatures. Up to 5 10 50 100 500 1,000 2,000 .1 .1 .125 .15 .175 .2 .225 .15 .175 .2 .225 .25 .275 .3 53] MECHANICAL CALCULATIONS. 191 Applying these values to formula (128), and using the jour- nal diameters previously determined, the following Tables LV., LVL, and LVII. are obtained, giving the sizes of bearings for drum armatures, high-speed ring armatures, and low-speed ring armatures, respectively: TABLE LV. BEARINGS FOR DRUM ARMATURES. SIZE OP BEARING. SPEED CAPACITY, VALUB IN REVS. IN KILO- WATTS. OP CONSTANT *. PER MIN. (FROM TABLK X.) N. Diameter (from Table LI.) b Length. *b = *,o X d b X ffi Ratio. ^ b : <*b .1 .1 3,000 A 1 5.3 .25 .5 .1 .1 2,700 2,400 * 11 5.2 4.9 1 .1 2,200 X 2f 4.7 2 .1 2.000 8f 4.5 3 .1 1,900 If 4 4.3 5 .1 1,800 H 4f 4.2 10 .1 1,700 H 6* 4.2 15 .105 1,600 1* n 4.2 20 .11 1,500 2i 9 4.2 25 .115 1,350 at 10 4.2 30 .12 1,200 2i 10i 4.2 50 .125 1,050 8 12 4.0 75 .13 900 8f 14 3.9 100 .14 750 4i 15| 3.8 150 .15 600 4f TO 3.7 200 .16 500 5i 18f 3.6 300 .175 400 6 21 3.5 54. Pulley and Belt. The pulley diameter is determined by the speed of the dynamo and the linear belt velocity: 12 X ^ B n X N = 3-7 T7 (129) where Z> p = diameter of pulley, in inches; r; B = belt speed, in feet per minute, see Table LVIII. ; N =. speed of dynamo, in revolutions per minute. The belt speed in modern dynamos ranges between 2,000 192 DYNAMO-ELECTRIC MACHINES. [53 TABLE LVI. BEARINGS FOR HIGH-SPEED RING ARMATURES. SIZE OF BEARING. SPEED CAPACITY, IN KILO- WATTS. VALUJB OP CONSTANT &10. - IN REVS. PKB MIN. (FROM TABLE XI.) N. Diameter (from Table LII.) ^ Length. f b = *w x rf b x VN. Batio. 'b ^b .1 .1 2,600 i U 5.0 .25 .1 2,400 if 5.0 .5 .1 2,200 i 2f 4.75 1 .1 2,000 i 2f 4.4 2.5 .1 1,700 1 4i 4.1 5 .1 1,500 11 5f 3.9 10 .11 1,250 If 6* 3.85 25 .12 1,000 2f 10 3.8 50 .13 800 8* 13 3.7 100 .15 600 4f 17i 3.7 200 .16 500 6f 23 3.6 300 .17 450 7* 27 3.6 400 .175 400 8i 30 8.5 600 .18 350 10 33i 3.35 800 .19 300 11 36 3.3 1,000 .2 250 12 38 3.2 1,500 .21 225 14 45 3.2 2,000 .225 200 16 51 3.2 TABLE L VII. BEARINGS FOR LOW-SPEED RING ARMATURES. SIZE OP BEARING. SPEED CAPACITY, IN KILO- WATTS. VALUE OP CONSTANT fao. IN REVS. PER MIN. (FROM TABLE XII.) N. Diameter (from Table Lin.) <*b Length. l b = k M X d b X V^ r . Ratio. 'b'A 2.5 .15 400 H 3f 3.0 5 .16 350 H 4i 3.0 10 .17 300 2 5| 2.9 25 .18 250 8i 8f 28 50 .19 200 3 IH 2.7 100 .20 175 5| 15i 2.65 200 .21 150 7f 20 2.6 300 .23 125 9i 23f 2.6 400 .25 100 10 25 2.5 600 .265 90 12 30 2.5 800 1,000 .27 .28 80 75 13| 15 32^ 36 2.4 2.4 1,500 .29 70 18 43i 24 2,000 .30 65 20 48 2.4 54] MECHANICAL CALCULA TIONS. and 6,000 feet per minute (= 600 and 1,800 metres per minute), as follows: TABLE LVIII. BELT VELOCITIES FOR HIGH-SPEED DYNAMOS OF VARIOUS CAPACITIES. CAPACITY, IN KILOWATTS. BELT SPEED, U B Feet per Minute. Metres per Minute. Up to 5 2.5 " 25 10 " 100 50 " 500 2,000 to 3,000 3,000 " 4,000 4,000 " 5,000 5,000 " 6,000 600 to 900 900 " 1,200 1,200 " 1,500 1,500 " 1,800 The pull at the pulley circumference, in pounds, is: 33,000 X HP _ 33,ooo X HP ' A. x n XJV ~ v, 12 Watts 33,000 X - f- = 44. 2 X - - . For an arc of belt contact of 180, which can safely be as- sumed for dynamo pulleys, the pull F v , is to be multiplied by 1.4 in order to obtain the tension on the tight side of the belt; hence the greatest strain upon the belt: = 1.4 X P' = 62 X . Allowing 300 pounds per square inch as the safe working strain of leather, the necessary sectional area of the belt can be found from F P' ^ ,, -*^., x 4-; (130) ^ B = width of belt, in inches; // B = thickness of belt, in inches; FV greatest strain in belt, /. e., tension on its tight side, in pounds; P' = capacity of dynamo, in watts; # B = belt speed, in feet per minute, Table LVIII. 194 D YNA MO-ELECTRIC MA CHINES. [54 The approximate thicknesses for the various kinds of belts are: Single belt h^ -f$ inch Light double belt " = & " Heavy double belt " = JJ- " Three-ply belt " = T V " Inserting these figures into (130), the width of the belt is obtained: \ Single belt & B = X = i.V X (131) 1 6 B B Light double belt. . . A = - X = .7 X (132) TABLE LIX. SIZES OF BELTS FOR DYNAMOS. WIDTH OF BELT, IN INCHES. OUTPUT OF THICKNESS DYNAMO IN OF BELT, Belt Speed, in Feet per Minute : KILO INCH* WATTS. 2,000 2,500 3,000 3,500 4,000 4,500 5,000 5,500 6,000 1 r 3 .8 .7 .6 2 ft 1.1 ^ 3 ft 2^3 1.8 1.5 1.3 1.2 _ 5 ft 3.1 3.0 2.5 2.1 1.9 7.5 ft 5.4 4.4 36 3.1 2.7 . . . . . . 10 13 ft 7.1 5.6 4.7 4.0 3.5 3.1 2.8 . . 15 10.3 8.3 6.9 5.9 5.2 4.6 4.1 . . 20 0} 8 13.4 10.7 9.0 7.7 6.7 6.0 5.4 . . . 25 a ft . . 10.9 9.4 8.2 7.3 6.6 . . . 30 33 ft . . . . 13 11.1 9.7 8.6 7.8 . . . . 40 ft 17 14.6 12.8 11.4 10.2 50 ft 21 18.0 15.8 14 12.7 11.5 10.5 60 ft . . . 25 21.4 18.8 16.7 15 13.7 12.5 75 ft 31 26.5 23.2 20 18.5 17 15.5 100 I ft 30 27 24.4 22.2 20.4 150 J2 ^ pa 29 25.7 23 21 19.3 200 33 29.2 26.3 24 22 250 cpii . . . . 40.7 36.2 32.6 29.6 27.2 300 C^ 11 51.3 45.5 41 37.3 34.2 400 . ^-rV 48.5 43 38.7 35.2 32.2 500 "^ft 60 53.5 48 44 40 54] MECHANICAL CALCULATIONS. 195 Heavy double belt. ... = -| X = .6 X (133) Three-ply belt b = ~ x = .45 X (134) TV * ; B ^B Single belts are used for all the smaller sizes, up to 100 KW output, light double belts up to 200 KW, heavy doubles up to 400 KW, and three-ply belts for capacities from 400 KW up. Based upon the above formulae the author has prepared the, preceding Table LIX., from which the belt dimensions for vari- ous outputs and for different belt speeds can readily be taken. The width of the belt being thus determined, the breadth of the pulley-rim is found by adding from ^ inch to 2 inches according to the width of the belt. PART III. CALCULATION OF MAGNETIC FLUX. CHAPTER XI. USEFUL AND TOTAL MAGNETIC FLUX. 55. Magnetic Field. Lines of Magnetic Force. Magnetic Flux. Field-Density. The surrounding of a magnetic body, as far as the magnetic effects of the latter extend, is called its Magnetic Field. According to the modern theory of magnetism, magnetic attractions and repulsions are assumed to take place along certain lines, called Lines of Magnetic Force; the magnetic field of a magnet, therefore, is the region traversed by the magnetic lines of force emanating from its poles. The lines of magnetic force are assumed to pass out from the north pole and back again into the magnet at its south pole; their direction, therefore, indicates ihe polarity of the mag- netic field. The total number of lines of magnetic force in any magnetic field is termed its Magnetic Flow, or Magnetic Flux, and is a measure of the amount, or quantity of its magnetism. The density of the magnetism at any point within the region of magnetic influence of a magnet, or the Field Density of a magnet, is expressed by the number of these magnetic lines of force per unit of field area at that point, measured perpendicu- larly to their direction. The Unit of Field Density that is, the field density of a unit pole is i line of magnetic force per square centimetre of field area, and is called i gauss. A Single Line of Force, or the Unit of Magnetic Flux, is that amount of magnetism th#t passes through every square centi- metre of cross-section of a magnetic field whose density is unity. To this unit, which was formerly called i weber, the name of i maxwell was given at the Paris Electrical Congress, in 1900. A Magnet Pole of Unit Strength is that which exerts unit force upon a second unit pole, placed at unit distance from the former. The lines of force of a single pole, concentrated in one point, are straight lines emanating from this point to all 200 DYNAMO-ELECTRIC MACHINES. [56 directions; /. e., radii of a sphere. The surface of a sphere of i centimetre radius is 4 n square centimetres; a pole of unit strength, therefore, has a magnetic flux of 4 n absolute or C. G. S. lines of magnetic force, or of 4 n maxwells. The number of C. G. S. lines of force, or the number of webers expressing the strength of a certain magnetic field, must consequently be divided by 4 n, or by 12.5664, in. order to give that same field strength in absolute units of magnetism, /. for drum armatures and for drum- wound ring armatures ; 56] USEFUL AND TOTAL MAGNETIC FLUX. 201 (where n c = number of commutator-divisions, a = number of turns per commutator- division, n c x a = tota l number of convolutions of armature, see 25); IV = speed, in revolutions per minute; and ' p number of bifurcations of current in armature, /*. ^., number of pairs of armature portions connected in parallel, see 45 ; then, i conductor in i revolution cuts 2 3> lines of force, for, the $ lines emanating from all the north poles, after pass- ing the armature core, return to the south poles, hence pass twice across the air-gaps, and, in consequence, are cut twice in each revolution by every armature conductor. The armature makes N_ 60 revolutions in i second, hence, N i conductor in i second cuts 2 $ X - - lines. oo Each one of the 2 ' p parallel armature portions contains- conductors connected in series; in each of these 2 ' p arma- ture circuits, therefore, N N N - T- conductors in i second cut 2 $ X -r- X r- lines. 2 ' p 60 2 n' p But, according to the law of the divided circuit, the E. M. F. generated in one of the parallel branches is the output voltage of the machine; the E. M. F. generated by any armature, con- sequently, by virtue of (135), is cvol >>: ..... (136) ' p X 60 X io 8 and from this we obtain the number of useful lines required to produce the E. M. F. of E volts, thus: = 6__X *' X E X X N 202 DYNAMO-ELECTRIC MACHINES, [57 For dynamos with but one pair of parallel circuits in the armature, /. e. y for bipolar machines and for multipolar dynamos with series connections, we have n' p = i, see (112) and (113), and the useful flux for this special case is: This formula also gives the useful flux per pole in multipolar dynamos, with parallel grouping, and therefore in text-books is usually given instead of (137) as the general formula for the useful flux of a dynamo, which, however, is not strictly correct, and, in consequence, misleading. 57. Actual Field Density of Dynamo. According to the definition given in 55, the actual field density of a dynamo is the total useful flux cutting the armature conductors, divided by the area of the actual magnetic field, thus: (139) where X" = field density, in lines of force per square inch; $ = useful flux, in maxwells, from formula (137) or (138), respectively; and S t = actual field-area, in square inches, /. c where 5C" = actual field density of dynamo, in lines of force per square inch; #' p number of bifurcations of current in armature; E' = total E. M. F. to be generated in armature, in volts; /^ = percentage of polar arc, see 58; Z a = length of active armature conductor, in feet, for- mula (26) or (148); v c = conductor speed, in feet per second. The field density in metric units is obtained from 5C = 20,000 X -0^,* "x v ' (1 ^ if Z a is expressed in metres and v c in metres per second. Since, in a newly designed armature, on account of rounding off the number of conductors to a readily divisible number and the length of the armature to a round dimension, the actual length, Z a , of the armature conductor, in general, is somewhat different from that found by formula (26), (as a rule, a little greater a value is taken), it is preferable to deduce the accurate value of Z a from the data of the finished armature: Z a = N c x A = ^-*^! X ^- (148) 12 f/& 12 where JV C = total number of conductors on armature; / a = length of armature core, in inches; w = number of wires per layer; j ! = number of layers of armature wire; > see 23. ns = number of wires stranded in parallel. ) Formula (146) for the actual field density of toothed and perforated armatures, can also be used for smooth cores, and may be applied to check the result obtained from (142). 358] USEFUL AND TOTAL MAGNETIC FLUX. 207 For the application to smooth armatures, however, the polar embrace, /?, , in formula (146) and (147), is to be replaced by the corresponding value of the effective field circumference, ft t , obtained from the former by means of Table XXXVIII., 38. If it is desired to know the real field area in toothed and perforated armatures, an expression for 6" f can be obtained by combining formulae (139) and (146), thus: Si = = 7 2 x /?. x z a x V Q x ' p X E' X io 8 ..(149) This formula, which gives the mean effective area actually traversed by the useful lines cutting the armature conductors, is very useful for the investigation of the magnetic field of toothed and perforated armatures. 58. Percentage of Polar Arc. The ratio of polar embrace, to which frequent reference has been had in 57, is determined by the distance between the pole-corners and by the bore of the polepieces. a. Distance Between Pole-corners. The mean distance between the pole-corners, / p , Fig. 130, depends upon the length of the gap-space between the arma- Fig. 130. Distance Between Pole-corners, and Pole Space Angle. ture core and the pole face, and is determined by the rule of making that distance from 1.25 to 8 times the length of the two gap-spaces, according to the kind and size of the armature and to the number of poles, see Table LX. Denoting this ratio of the distance between the pole-corners 208 DYNAMO-ELECTRIC MACHINES. [ to the length of the gaps by n , this rule can be expressed by the formula: /, = * xK-4), (150) where / p = mean distance between pole-corners; d p = diameter of polepieces; d & diameter of armature core; for toothed and per- forated armatures, d & is the diameter at the bot- tom of the slots. The value of u for various cases may be chosen within the- following limits: TABLE LX. RATIO OF DISTANCE BETWEEN POLE-CORNERS TO LENGTH OF GAP-SPACES, FOR VARIOUS KINDS AND SIZES OF ARMATURES. VALUE OF RATIO ku. CAPACITY Smooth Armature. IN KILO- Toothed or WATTS. Bipolar. Multipolar. Perforated Armature. Drum. Ring. Drum. Ring. Bipolar. Multipolar. .1 1.5 2.5 1.5 2.5 1.25 1.25 .25 1.75 3 1.75 2.75 1.5 1.3 .5 2 3.5 2 3 1.75 1.4 1 2.25 4 2.25 3.25 2 1.5 2.5 2.5 4.5 2.75 3.5 2.25 1.6 5 3 5 3 3.75 2.5 1.7 10 3.5 5.5 3.25 4 2.75 1.8 25 4 6 3.5 4.25 3 1.9 50 4.5 6.5 3.75 4.5 8.25 2 100 5 7 4 4.75 3.5 2.1 200 5.5 7.5 4.25 5 3.75 2.2 300 6 8 4.5 5.25 4 2.3 400 .... . 4.75 5.5 .... 2.4 600 .... . . . 5 5.75 .... 2.5 800 6 .... 2.6 1,000 .... .... 6.5 .... 2.7 1,200 .... . . . .... 7 .... 2.8 1,500 .... . 7.5 .... 2.9 2,000 ... 8 3 Whenever n can be made larger than given in the above table without reducing the percentage of the polar embrace below its practical limit, it is advisable to do so, and in fact this ratio in some modern machines has values as high as k n = 12. 58] USEFUL AND TOTAL MAGNETIC FLUX. 209 b. Bore of Polepieces. The diameter of the polepieces, or the bore of the field, d v , is given by the diameter of the armature core, the height of the armature winding, and the clearance between the armature winding and the polepieces: 2 x (151) d & = diameter of armature core, in inches; h & = height of winding space, including insulations and binding wires, in inches; // c = radial height of clearance between external surface of finished armature and polepieces, in inches; see Table LXI. TABLE LXI. RADIAL CLEARANCE FOR VARIOUS KINDS AND SIZES OP ARMATURES. RADIAL CLEARANCE, h c . Smooth Armature. DIAMETER OF Disc or Ribbon Core. Wire Core. Toothed ARMATURE. or Perforated Wire Wound. Armature. Copper Bars. Wire Wound. Copper Bars. Drum. Ring. inches. cm. inch. mm. inch. mm. inch. mm. inch. mm. inch. mm. inch.' mm. 2 5 3 2.4 ^ 4.0 TV 1.6 4 10 | 3.2 A 2.4 . 4.8 . . A 2.0 8 15 A 4.0 f 3.2 7 5.6 . . . A 2.4 12 18 30 45 t 4.8 5.6 A 4.0 4.8 A 4.0 4.4 f 6.4 7.2 7 5.6 6.4 | 3.2 4.0 24 30 60 75 \ A 6.4 7.2 A 5.6 6.4 t 4.8 5.6 H 8.0 8.8 A A 7.2 8.0 4.8 5.6 40 100 9 7.2 \ 6.4 Y 9.6 8.8 | 64 50 125 A 8.0 7.2 10.4 f 9.6 7.2 75 100 200 250 I 9.6 11.2 a 8.0 8.8 t 11.2 12.8 if TV 10.4 11.2 I! 8.0 8.8 125 300 Y 12.8 i 9.6 f 9.6 150 400 A 14.4 TV 11.2 . . . . . TV 11.2 200 500 f 16.0 12.8 12.0 210 DYNAMO-ELECTRIC MACHINES. [58 The radial clearance, which is to be taken as small as pos- sible, in order to* keep the air-gap reluctance at a minimum, ranges between 1/32 and 7/16 inch, according to the kind of the armature and its size. The preceding Table LXI. may serve as a guide in fixing its limits for any particular case. The above table shows that with toothed and perforated armatures the smallest clearance can be used, a fact which is explained by the consideration that the exteriors of these armatures offer a solid body, and may be turned off true to the field-bore. For a similar reason wire-core armatures need a larger clearance than disc-core armatures, since the former cannot be tooled in the lathe, and have to be used in the more or less oval form in which they come from the press. Since copper bars can be put upon the body with greater precision than wires, a somewhat larger clearance is to be allowed in the latter case. Finally, a drum armature, in general, has a higher winding space than a ring armature of same size; the unevenness in winding will, consequently, be more prominent in the former case, and therefore a drum armature should be provided with a somewhat larger clearance than a ring of equal diameter. The figures given in Table LXI. may be considered as aver- age values, and, in specially favorable cases, may be reduced, while under certain unfavorable conditions an increase of the clearance may be desirable. c. Polar Embrace. The dimensions of the magnetic field having thus been determined, half the pole-space angle, a, Fig. 130, can be found from the trigonometrical equation: " (152) / p = pole distance, from formula (150); d p = diameter of polepieces, from formula (151). The ratio of polar embrace, or the percentage of polar arc, then, is: 59] USEFUL AND TOTAL MAGNETIC FLUX. 211 in which a = half pole-space angle, from (152); p = number of pairs of magnet poles. From (153) follows, by transposition: from which the pole-space angle, a, can be calculated in the case that the ratio of embrace, ft l , of the polepieces is given. 59. Relative Efficiency of Magnetic Field. The useful flux of the dynamo being found from formula (137), the number of lines of force per watt of output, at unit conductor-velocity, will be a measure for the magnetic quali- ties of the machine, and may be regarded as the relative efficiency of the magnetic field. The field efficiency for any dynamo can accordingly be obtained from the equation: # ^ * = E' X /' X Vc = P 1 " X Vc ' '( 155 ) where #' P = relative efficiency of magnetic field, in maxwells per watt of output at a conductor velocity of i foot per second. <2> = useful flux of dynamo, from formula (137) or (138); E' = total E. M. F. to be generated in machine, in volts; /' total current to be generated in machine, in amperes; P' = E X /' = total capacity of machine, in watts; v c = conductor velocity, in feet per second. The numerical value of this constant, $' P , varies between 4,000 and 40,000 lines of force per watt at i foot per second, according to the size of the machine, the lower figure corre- sponding to the highest field efficiency; and for outputs from 1/4 KW to 2,000 KW, for bipolar and for multipolar fields, respectively, ranges as per the following Table LXII., which is averaged from a great number of modern dynamos of all types of field-magnets: 212 DYNAMO-ELECTRIC MACHINES. [59 TABLE LXIL FIELD EFFICIENCY FOR VARIOUS SIZES OF DYNAMOS. CAPACITY, IN KILOWATTS. VALUE OP 1.02 1.06 " 1.04 .65 1.04 ^ 1.01 1.05 1.03 .7 1.03 " 1.01 1.04 i* 1.02 B. GENERAL FORMULAE FOR RELATIVE PERMEANCES. 62. Fundamental Permeance Formula and Practical Derivations. In order to obtain the values of the permeances of the vari- ous paths, we start from the general law of conductance: Area of medium Distance in medium Conductance = or, in our case of magnetic conductance: Area Permeance = Permeability x Len th - Since the permeability of air = i, the relative leakage per- meance between two surfaces can be expressed by the general formula : '_ Mean area of surfaces exposed Mean length of path between them ' From this, formulae for the various cases occurring in prac- tice can be derived. (159) 22O D YNA MO-ELECTRIC MA CHINES. [62 a. Two plane surfaces, inclined to each other. In order to express, algebraically, the relative permeance of the air space between two inclined plane surfaces, Fig. 132, the mean path is assumed to consist of two circular arcs joined by a straight line tangent to both circles, said arcs to be de- scribed from the edges of the planes nearest to each other, as Fig. 132. Two Plane Surfaces Inclined to Each Other. centres, with radii equal to the distances of the respective cen- tres of gravity from those edges. Hence: (160) where S lt S 9 = areas of magnetic surfaces; c least distance between them; a i , # 2 = widths of surfaces S l and *S 2 , respectively; a = angle between surfaces ^ and S^. b. Two parallel plane surfaces facing each other. If the two surfaces S t and *S" a are parallel to one another, Fig. 133, the angle inclosed is a 0, and the formula for Fig- I 33- Two Parallel Plane Surfaces Facing Each Other. the relative permeance, as a special case of (160), becomes: 3 = i (5 + S (161 y 6 2] PREDE TERM IN A TION OF MA GNE TIC L EA KA GE. 221 c. Two equal rectangular surfaces lying in one plane. In case the two surfaces lie in the same plane, Fig. 134, they inclose an angle of a 180, and the permeance of ( a H- c-^fc- -a- - Fig. 134. Two Equal Rectangular Surfaces Lying in One Plane. the air between them, by formula (160), is: a X b ,(162) 71 X - a width of rectangular surface; b = length of rectangular surface; c = least distance between surfaces. d. Two equal rectangles at right angles to each other. If the two surfaces are rectangular to each other, Fig. 135,. Fig- !35- Two Equal Rectangles at Right Angles to Each Other, the angle a = 90, formula (160), consequently, reduces to 3 = ax * ..(163) e. Two parallel cylinders. In case the two surfaces are cylinders of diameter, d, and length, /, Fig. 136, the areas of their surfaces are d x TT X I; and if they are placed parallel to each other, at a distance, c, apart, the mean length of the magnetic path is c -j- \d; hence the permeance of the air between them: d X 7t x / 2 = (164) 222 D YNAMO-ELECTRIC MA CHINES. [62 In this formula the expression for the mean length of the path is deduced from Fig. 137, in which it is assumed that the Fig. 136. Two Parallel Cylinders. mean path consists of two quadrants joined by a straight line of length <:, and extends between two points of the cylinder- peripheries situated at angles of 60 from the centre line. Since in an equilateral triangle the perpendicular, dropped from any one corner upon the opposite side, bisects that side, \ Fig. 137. Leakage Path Between Parallel Cylinders. the perpendicular, from either of the endpoints of the mean path upon the centre line, bisects the radius of the corre- sponding cylinder-circle, and the radius of the leakage-path quadrant is d hence the length of the mean path: x + y x -re c -\- d x -> 4 or, approximately: x c -f \d . This approximation even better meets the practical truth, as most of the leakage takes place directly across the cylinders. 6 2] PREDE TERMINA TION OF MA GNE TIC LEA KAGE. 223 and the mean path, therefore, in reality is situated at an angle of somewhat less than 60, which was taken for convenience in the geometrical consideration. /. Two parallel cylinder-halves. If two cylinder-halves face each other with their curved surfaces, Fig. 138, the mean length of the magnetic path is c ~h -3 d, where c is the least distance apart of the curved sur- Fig. 138. Two Parallel Cylinder-Halves. faces, and d the diameter of the cylinders, and we have for the permeance: 2 X / & The symbols used in these formulae are: %' = relative permeance of clearance spaces; *$" = relative permeance of teeth; %"' = relative permeance of slots; d & = diameter at bottom of slots; d" & = diameter at top of teeth; d v = diameter of bore of polefaces; b s = breadth of armature slots; b t top width of armature teeth; b\ radial spread of magnetic lines along teeth; 4 length of armature core; / f = length of magnetic field; n' c = number of armature slots; fi i = percentage of polar arc, _ ;; p X . 180 ' n p = number of pairs of poles, ft = pole angle; ft\ = percentage of effective gap circumference, see Table XXXVIII., 38; k^ ratio of magnetic to total length of armature core, Table XXIIL, 26; k^~ factor of field deflection, see Table LXVIL, below; IJL permeability of iron in armature teeth, at density employed, see Table LXXV., 81. Formulae (170) and (171) apply directly only to straight- tooth armatures. For projecting teeth the same formulae, how- ever, can be used if the dimensions of the projecting tooth are . 64] PREDETERMINATION OF MAGNETIC LEAKAGE. 229 replaced by those of a straight tooth of equal volume, as indi- cated by Fig. 142, the reduced width of the slot, b Sl , taking the place of the actual width, b s . For perforated armatures with rectangular holes (Fig. 143) the slot permeance is directly expressed by formula (171), while the permeance of the iron projections is equal to that of straight teeth having equal vol- ume. In formula (170), consequently, the reduced width, 8l , and in (171) the actual width, s , of the holes is to be used. For round and oval perforations, Figs. 144 and 145, respect- ively, the iron projections being transformed into straight Fig. 142. Fig. 143. Fig. 144. Fig. 145. Figs. 142 to 145. Geometrical Substitution of Projecting Teeth and Hole- Projections by Straight Teeth of Equal Volume. teeth of equal volume, the reduced width, b si , of the perfora- tion is to be used in both (170) and (171). The permeance of the teeth, ^", on account of the high value of the permeability, / K 12 XN \ p a/ and for perforated armatures : 7T x A + d "* x /0\) x / f ^12 X (^p - d\) ' '" TABLE LXVII. FACTOR OF FIELD DEFLECTION IN DYNAMOS WITH TOOTHED ARMATURES. FACTOR OP FIELD DEFLECTION, fc FOR TOOTHED ARMATURES. RATIO OP RADIAL CLEARANCE TO PITCH OP SLOTS ON Product of Conductor Velocity and Field Density, in English Measure. OUTER CIRCUMFERENCE. 500,000 1,000,000 1,500,000 2,000,000 2,500,000 0.1 .90 2.00 2.10 2.20 2.30 .15 .80 1.90 2.00 2.10 '2.20 .2 .70 1.80 1.90 2.00 2.10 .25* .60 1.70 1.80 1.90 2.00 .3 .50 1.60 1.70 1.80 1.90 .35 .40 1.50 1.60 1.70 1.80 .4 .35 1.40 1.50 1.60 1.70 .45 .30 1.35 1.40 1.50 1.60 .5 .25 1.30 1.35 1.40 1.50 .55 .20 1.25 1.30 1.35 1.40 .6 1.15 1.20 1.25 1.30 1.35 .65 1.12 1.15 1.20 1.25 1.30 .7 1.10 1.12 1.15 1.20 1.25 The amount of the field deflection in machines with toothed armatures is primarily governed by the ratio of the clearance space to the pitch of the slots, and only secondarily depends upon the product of conductor velocity and field density. 65] PREDE TERM IN A TION OF MA GNE TIC LEAK A GE. 231 The values for use with formulae (174) and (175) are compiled in the above Table LXVII., while those for use with formula (176) are contained in the previous Table LXVI. Table LXVII. refers to straight teeth only; in case of armatures with projecting teeth, the average of the values from Table LXVII. and from LXVI. for a corresponding perforated armature must be taken. 65. Relative Average Permeance between the Magnet Cores (2,). Since in dynamo-electric machines the magnet cores, with their ends averted from the armature, are magnetically joined by special "yokes" or by the frame of the machine, forming the magnetic return circuit, the magnetic potential between these joined ends is practically = o, while the full magnetic potential is operating between the free ends toward the arma- ture. The average magnetic potential over the whole length of the magnet cores, therefore, is one-half of the maximum potential, and the average relative permeance, consequently, one-half of that which would exist between the cores, if they had the same magnetic potential all over their length. For the various forms of magnet cores, by virtue of for- mulae (160) to (165), respectively, we therefore obtain the following relative average permeances: a. Rectangular Cores. The permeance between two rectangular magnet cores, Fig. 146, is the sum of the permeances between the inner surfaces Fig. 146. Rectangular Magnet Cores. which face each other, formula (161), and between the end surfaces which lie in the same plane, formula (162); and there- fore the average permeance: 2 3 2 DYNAMO-ELECTRIC MACHINES. a X / , b X / 2 ^ c + l> X 2 [65 (177) where a, b, c, and / are the dimensions of the cores in inches, see Fig. 146. b. Round Cores. According to formula 164, we have in this case, see Fig. 147 . c. Oval Cores. Fig 147. Round Magnet Cores. _ i dn X I _ dn X I mft , ~ 2 X c + \d" 2^ + 1.5 ^ ' U^) For oval cores, Fig. 148, the permeance path consists of two parts, a straight portion between the inner surfaces, and a Fig. 148. Oval Magnet Cores. curved portion between the round end surfaces. Combining, therefore, formulae (161) and (164), we obtain: (a b} X I , b 7t X / 2 C 2 c -\- 1.5 b ' (179) 6 5] PREDE TERM IN A TION OF MA GNE TIC LEA KA GE. 233 d. Inclined Cores. If the cores, instead of being parallel to each other, are set at an angle, Fig. 149, the distance, c, in formulae (177), (178), Fig. 149. Inclined Magnet Cores. and (179), respectively, has to be averaged from the least and greatest distance of the cores: (180) e. Multipolar Types. In case of multipolar dynamos of p pairs of poles, the total permeance across the magnet cores is 2 // p times that between each pair of cores. In calculating the latter, it has to be con- sidered that, while the permeance across two opposite side surfaces of the cores does not change by increasing their number, the leakage across two end surfaces is reduced, half of the lines leaking to the neighboring core at one side, and half to that on the other side. For rectangular cores, therefore, we have, with reference to Fig 150: Fig. 150 Multipolar Frame with Rectangular Cores. = 2 D X = P x . , X (181) 234 DYNAMO-ELECTRIC MACHINES. for round cores, according to formula (165): [65 and for oval cores: In multipolar machines, for _ h X (i+y) e -f i X - (196) 7. Radial Multipolar Type. In radial multipolar dynamos, Fig. 168, lines pass from the end surfaces of the polepieces across the pole gaps: = 2 Fig. 168. Radial Multipolar Type. g X / hXj ..(197) p = number of pairs of magnet poles. 244 DYNAMO-ELECTRIC MACHINES. [67 8. Tangential Multipolar Type. The leakage between adjacent polepieces in tangential mul- tipolar machines, Fig. 169, takes place across the length of the magnet cores: \ Fig. 169. Tangential Multipolar Type. S t half area of external surface of polepiece;_ S 2 = area of side surface of polepiece; S a area of projecting portion of end surface, '= end surface area of magnet core. '67. Relative Permeance between Polepieces and Yoke According to the general principle of calculating relative permeances, the magnetic potential between polepieces and yoke is to be taken = J, with reference to the potential be- tween two polepieces of opposite polarity. For, the yokes serve to join two magnet cores in series, magnetically, and are therefore separated from the polepieces by but one magnet core. If the yokes join the magnets in parallel, thn they usually serve as polepieces also, and must be considered as such in leakage calculations. Since the amounts of the leakages in the various paths are proportional to their permeances, in dynamos having an ex- ternal iron surface near the polepieces, most of the leakage takes place between the polepieces through that external sur- face; and in such machines the leakage from the polepieces to .the yoke is comparatively small. 6 7] PREDE TERMINA 7 'ION OF MA GNE TIC LEA KA GE. 2 45 a. Polepieces Having an External Iron Surface Opposite Them. i . Upright Horseshoe Type. From the polepiece area facing the yoke, S 3 , Fig. 170, the leakage takes place in a straight line equal in length to that of Fig. 170. Upright Horseshoe Type. the magnet cores, while from the end surfaces the leakage paths are quadrants joined by straight lines: . (199) S 3 projecting area of polepiece, = top area of pole- piece minus area of magnet core. 2. Horizontal Horseshoe Type. The leakage from the polepieces to the yoke partly passes directly across the cores, and partly takes its path through the iron bed; hence, with reference to Fig. 159, page 239, we have approximately: <* _ 4 (200) S l = half area of external surface of polepiece; S 3 = projecting area of polepiece, = area of yoke-end of polepiece minus area of magnet core; / length of magnet core; 2 = distance of polepiece from iron bedplate. 246 D YNAMO-ELECTRIC MA CHINES. [67 b. Polepieces Having No External Iron Surface Opposite Them. i. Inverted Horseshoe Type with Rectangular Polepieces. In this case the leakage from the side surfaces of the pole- Fig. 171. Inverted Horseshoe Type with Rectangular Polepieces. pieces to the yoke, Fig. 171, is twice that of the upright type: O X f /. (201) 7T 2. Inverted Horseshoe Type with Beveled or Rounded Polepieces. Similar to the former case we have for these forms of the polepieces, Figs. 172 and 173, respectively: Figs. 172 and 173. Inverted Horseshoe Type with Beveled and Rounded Polepieces. $ -= ^ 4- f X U t ' 7 I (202) 3. Horizontal Double Magnet Type. If in this type special polepieces are applied, Fig. 174, lines- tS* Fig. 174. Horizontal Double Magnet Type. pass from the lower surfaces of the same to the yoke: 67] PREDETERMINATION OF MAGNETIC LEAKAGE. 247 j: vx _ o (203) Here it is supposed that the path from the projecting back surfaces of the polepieces to the yoke below them is shorter than the length of magnet cores; if the latter is not the case, the term (-MX!) in the denominator of the second portion of formula (203) is to be replaced by /, the length of the cores. 4. Iron-clad Types. In the bipolar iron-clad type, with separate poleshoes, Fig. 175, lines leak to the yoke from the back surfaces of the pole- Fig. J 75- Bipolar Iron-clad Type with Poleshoes. pieces; hence the relative permeance, half of the total mag- netic potential existing between polepieces and yoke: . . . (204) As to the denominator of the second term, see remark to formula (203). This amount, formula (204), as well as the relative permeance across the side surfaces of the polepieces, formula (196), is to be added to the relative permeance found by formula (184), iron-clad type without polepieces, in order to obtain the total relative permeance of this type. In the fourpolar iron-clad type, since the total magnetizing force of each circuit is supplied by one magnet only, there is 248 DYNAMO-ELECTRIC MACHINES. [68 full magnetic potential between polepieces and frame, and both terms of formula (204) must consequently be multiplied by 2. 5. Radial Multipolar Type. In this type leakage lines pass from the projecting portions, S 3 , Fig. 176, of the back surfaces of the polepieces to those of r Fig. 176. Radial Multipolar Type. the yoke, *S" 4 ; and if the yoke is relatively near to the pole gap, leakage also takes place from the end surfaces of the polepieces to the yoke: ...(205) According to the design of the frame, then, either formula (205) is to be used together with the latter portion of formula (197), or the entire formula (197) is to be combined with the first portion of formula (205), in order to obtain the total joint permeance across the polepieces and from polepieces to yoke of the radial multipolar type. By the proper combination of formulae (167) to (205) the probable leakage factor of any dynamo can be calculated from the dimensions of the machine. D. COMPARISON OF VARIOUS TYPES OF DYNAMOS. 68. Application of Leakage Formulae for Comparison of Tarious Types of Dynamos. In order to illustrate the application of the above for- mulae, and at the same time to afford the means of comparing the relative leakages in various well-known types of dynamos, in the following, frames of various types are designed for the same armature, and the leakage factor for each machine thus obtained is calculated. 68] PREDE TERM1NA TION OF MA GNE TIC LEAK A GE. 249 In order to accommodate all the types to be considered here, the armature has been chosen of a square cross-section, viz., 16 inches core diameter, and 16 inches long. This armature, if wound to a height of about -| inch, and driven at a speed of 800 revolutions per minute, will yield an output of 50 KW. The polepieces for this armature must have a bore of 17^ inches, and must be 16 inches long; the pole angle, for all bipolar types, is chosen fi 136. and the distance between the pole corners, therefore, is 17^ X sin ^ (180 136) = 6 inches. Figs. 177 to 186 give the dimensions of various types of frames for this armature, viz., (i) Upright Horseshoe Type; sq.ins* Fig. 177. Upright Horseshoe Type. (2) Inverted Horseshoe Type; (3) Horizontal Horseshoe Type; (4) Single Magnet Type; (5) Vertical Double Magnet Type; (6) Vertical Double Horseshoe Type; (7) Horizontal Double Horseshoe Type; (8) Horizontal Double Magnet Type; (9) Bipolar Iron-clad Type; and (10) Fourpolar Iron-clad Type, respectively. The probable leakage factors of these machines figure out as follows: i . Upright Horseshoe Type, Fig. 777. By (167): - X 16 X (17} - 16) = !*L=i9. 25 DYNAMO-ELECTRIC MACHINES. [68 By (178): i 14 X 7t X 20 _ 43.98 X 20 _ 2 X 7} + i-5 X 14 15 + 2I By (188): = 24-5- X 8f) + 300] By (199): 2 X 5t 16 X = 7T = 4-3 + 3-3 = 7-6. 2 X 20 + (17$.+ n)- By (157): A = !9 2 +24.5 + 29.1 + 7-6 _ 253.2 _ 192 192 2. Inverted Horseshoe Type, Fig. 178. j = 192. 2 = 24.5- By (192): Fig. 178. Inverted Horseshoe Type. l 6 2XI7JX7 = By (202): 16 X 20 20 -|- (n 7T X * 4 = 4-3 + 4-9 = 9- 2 - 6 8] PREDE TERMINA TION OF MA GNE TIC LEA KA GE. 251 By (157): A = * 9 24 ' 5 192 9 ' 2 = 241 ' 3 = 1.255. 192 3. Horizontal Horseshoe Type, Fig. 2, = 192. 2, = 24.5. By (189): Fig. 179. Horizontal Horseshoe Type. 14X22+2 By (200): (14 X 22) + | 15' = 27.6. A = T 9 2 + 24.5 + 53-3 + 27-6 192 4. Single Magnet Type, Fig. 180. ^ = 192. By (193): 297.4 = 192 *, = I22 . 6 2 5 2 DYNAMO-ELECTRIC MACHINES. [ea _ 192 + 6l -7 _ 2 53-7 _ 192 192 sq.uis. Fig. 180. Single Magnet Type. 5. Vertical Double Magnet Type, Fig. 181. Fig. 181. Vertical Double Magnet Type. , = 192. By (194): .. 2 j (49t + 16) X 7 + (228.5 ~ 78.5) 1 16 X 4j ~ = 2 (38.2 + 6.8) = 90. _ 192 + 90 ._ 282 _ /v - - X T I * 192 192 6. Vertical Double Horseshoe Type, Fig. 182. \ = 192. By (177): 2. = I4 X l6 + 2 X 5 ^ X l6 7 * = 29.9 n.i= 68] PREDE TERM IN A TION OF MA GNE TIC LEAK A GE. 253 By (195): = 2 X (4-6 + 1.6 + i.i) = 14.6. Fig. 182. Vertical Double Horseshoe Type. By (201): = ( l6 X 6|- 14 X 5f) + M X 3f , 16 X 1 _ = 5 + 10.2 = 15.2. 41 + M.6 +T5.2 _ 262.8 7. Horizontal Double Horseshoe Type, Fig. 183. Fig. 183. Horizontal Double Horseshoe Type. , = 192. By (179): 8| X 16 . 6 X 7t X 16 .= 1 Tr -+ 7i + 3 x 6 = 19.3 + 25.7 =45. 254 DYNAMO^ELECTRIC MACHINES. By (195): [68 X i7j | X 16 " X 16 '3 = 2 X = 2 X (4-6 + 1.6 + .6) = 13-6. By (201): , __ (16 X 6} - 80.8) + 25 X 16 16 X 16 + ii X 18 + = 14.2 + 4.45 + 6.15 = 24.8. 192 + 45 + 13-6 + 24.8 _ 275.4 " 8. Horizontal Double Magnet Type, Fig. 184. Fig 184. Horizontal Double Magnet Type. , = 192. By (187): X 16 X 25? I6X7 I6XI4 + 7X- = 8 -5 + 5-1 + 12.3= 192 192 68] PREDE TERM IN A TION OF MAGNE TIC LEA KA GE. 255 -9. Bipolar Iron- clad Type, Fig. 185. Fig. 185. Bipolar Iron-clad Type. = I 9 2. By (184): ,6 X X Jl = 3 1-285 X = - = 1.15. <* + Si X - = 8 -5 + 7-9 + s 3-6 = 3- 192 192 10. Four polar Iron- clad Type, Fig. 186. Fig. 1 86. Fourpolar Iron-clad Type. By (167): 16 7t + i7i 7t X 5 \ x 16 '2. = i-95 -a-* By (185): 256 DYNAMO-ELECTRIC MACHINES. 16 X (nl + I4f) , 8 1 X (nt -\ [68 = 88.8 -+- 19 = 107.8. '74+ IQ7.8 = 174 174 Taking now the leakage proper, that is, leakage factor minus i, of the bipolar iron-clad type, which is the smallest found, as unity, we can express the amounts of the stray fields of the remaining types as multiples of this unity, thus obtain- ing the following comparative leakages of the types consid- ered : Upright horseshoe type 0.32 Inverted horseshoe type - 2 55 Horizontal horseshoe type 0.55 Single magnet type 0.32 Vertical double magnet type 0.47 Horizontal double horseshoe type.. 0.37 Vertical double horseshoe type 0.43 Horizontal double magnet type.... o. 16 Bipolar iron-clad type o. 15 Fourpolar iron-clad type 0.62 o. 15 = 2.14 o. 15 = i. 70 o-i5 = 3-67 0.15 = 2.13 -i5 = 3-i3 o. 15 = 2.46 0.15 = 2.87 0.15 = 1.07 0.15 = i 0.15 = 4.14 If, in the latter machine, the stray field of which is some- what excessive, an armature of larger diameter and smaller axial length would be chosen and the dimensions of the frame altered accordingly, the leakage would be found within the usual limits of the fourpolar iron-clad type. CHAPTER XIII. CALCULATION OF LEAKAGE FROM MACHINE TEST. 69. Calculation of Total Flux. The machine having been built, its actual leakage can be determined from the ordinary machine test. It is only neces- sary, for this purpose, to run the machine at its normal speed, and to regulate the field current by changing the series-regu- lating resistance in a shunt dynamo, or by altering the num- ber of turns in a series machine, or by regulating both in a compound-wound dynamo until the required output is ob- tained. Noting then the exciting ampere-turns, we can calcu- late the total magnetic flux, <', through the magnet frame, by a comparatively simple method which is given below; and >' divided by the useful flux, <, gives the factor A of the actual leakage. The observed magnetizing force of AT ampere-turns per magnetic circuit made up of T sh shunt turns, through which a current of 7 sh = amperes m {E = potential at terminals, r m = total resistance of shunt circuit) is flowing, in a shunt machine; or of T se series turns traversed by a current of /^ = / amperes (/ = current output of dynamo), in a series machine; or partly of the one and partly of the other, in a compound dynamo is supplying the requisite magnetizing forces used in the different portions of that circuit, viz., the ampere turns needed to overcome the magnetic resistance of the air gaps, of the armature core, and of the field frame, and the magnetizing force required to compensate the reaction of the armature winding upon the magnetic field; hence we have: A T = at g + tf/ a + at m + at v , (206) 258 DYNAMO-ELECTRIC MACHINES. [69 where AT total magnetomotive force required per mag- netic circuit for normal output, in ampere- turns, observed; at s = magnetomotive force used per circuit to over- come the magnetic resistance of the air gaps in ampere-turns, see 90; #4 = magnetomotive force used per circuit to over- come magnetic resistance of armature core in. ampere-turns, see 91; at m = magnetomotive force used per circuit to over- come magnetic resistance of magnet frame, in ampere-turns, see 92; af r magnetomotive force required per circuit for compensating armature reactions, in ampere- turns, see 93. Since the magnet frame alone carries the total flux gen- erated in the machine, while the air gaps and the armature core are traversed by the useful lines, only the ampere-turns used in overcoming the resistance of the magnet frame depend upon the total magnetic flux, and all others of these partial magnetomotive forces can be determined from the useful flux. The latter, however, is known from the armature data of the machine by virtue of equations (137) anol (138), respectively; consequently, from (206) we can determine at m , and this, in turn, will furnish the value of the total flux, $'. Transposing (206), we obtain: at m = AT- (af g + ta & + at r ), (207) in which AT is known from the machine test, at^ and #4 can be calculated from the useful flux, and at r is given by the data of the armature. The numerical value of at m having been found, we can then calculate the total magnetic flux through the machine. In the following, the two cases occurring in practice are con- sidered separately, viz. : (i) but one material, and (2) two different materials being used in building the magnet frame of the machine. 69] CALCULA TION OF A CTUAL MA GNE TIC LEAK A GE. 259 a. Calculation of Total Flux when Magnet Frame Consists of but One Material. If but one single material either cast iron, wrought iron, mitis metal, or steel is used in the magnet frame, the calcu- lation of the total magnetic flux is a very simple operation. For, if /" m denotes the length of the magnetic circuit in the magnet frame, from air gap to air gap, and m" m is the cor- responding mean specific magnetizing force, then, according to formula (226), 88, we have: (208) from which follows, by substituting the value of at m from (207): nf - a J^ - AT --Kr + < + O , 9ftt . " m /// ~ jjf - . ..(6O\9) m ' m Dividing the numerical value of #/ m , as found by formula (207), by the length, /" m , of the circuit, we therefore obtain the numerical value of the specific magnetizing force per inch length for the respective material. By means of Table LXXXVIIL, p. 336, or Fig. 256, p. 338, then, the density ", in an indirect manner, as follows: The useful flux, $, being known by virtue of formula (137) or (138), respectively, an assumption can be made of the total flux per circuit, $", by adding to the useful flux per circuit, {n z being the number of the magnetic circuits in the machine), from 10 to 100 per cent., according to the size and the type of the dynamo (see Table LXVIIL, p. 263, and Table LXVIILz, p. 265). In dividing this approximate value of 3>" by the areas S Wti and S cAt) respectively, the densities (B" w .i. an ^ (B" c .i, are obtained, and by means of Table LXXXVIII. (Fig. 256) the corresponding value of w" w" was taken too large. A second assumption of >" is now made so that the corresponding value of Z obtained in a similar manner from Table LXXXVIII. and formula (213) will be on the other side of #/ m , z. 2 O b cx n J3 -< hV' 1 ^ tr" -^ 2 .5 }i ^^^s-f^w.. s s I ^ 5 ^ 5 * | & S ** v5 s .' J ts ^ c/i ^^ O vi_i !J - ( "*-*/-, w ^ 8 o S &^ 6 | C tJ3 t^ O D^^.,^-" ^ >PH rt OXi } -S o ^-^^ 5j3'S ! flf5u*s^ I 1 e gl 15 |.a S l-^|flls"l 8 g^ J|| i-f ls**-lMl f ijlf jP^tft ? lil 111 1 !? o s i3 ^. ^^ o a C = rt P. 3 o -rt '.^r-.i-.-rr-a s^^^l g ^.g-l^ i .2 Isli 6 2*2 I ^ ^ "5 1 M rt '> oT "5 Q. ^ u r- i ' ar ' J S- S '"OS^S^^^-^'S'S C^ *-*I3 rt C2 Q *~* O O rt S-^ti^bbjosc! | 3 2^ ||^| 264 DYNAMO-ELECTRIC MACHINES. [70 distances of the leakage surfaces much smaller than in large dynamos ; the permeance of the air gaps, therefore, is relatively much smaller, while the permeances of the leakage paths are considerably larger, comparatively, than in large machines, and formula (157), in consequence, will produce a high value of the leakage coefficient for a small dynamo. It further follows from Table LXVIII. that the leakage factor for various types o and sizes of dynamos varies within the wide range of from i.io to 2.00, which result agrees with observa- tions of Mavor, 1 who, however, seems not to have considered capacities over 100 KW, By comparing the values of A for any one capacity," the rela- tive merits of the various types considered may be deduced. Thus it is learned that, as far as magnetic leakage is con- cerned, the Horizontal Double Magnet Type (column 6) and the Bipolar Jlron-clad Type (column 7) are superior to any of the other types, which undoubtedly is due to the common feature of these types of having the cores of opposite magnetic potential in tine with each other on opposite sides of the arma- ture, thus reducing the magnetic leakage between them to a minimum. Next in line, considering bipolar dynamos, are the Inverted Horseshoe Type (column 2), the Single Magnet Type (column 4), the Upright Horseshoe Type (column i), and the Vertical Double Horseshoe Type (column 8). Of multipolar machines the two best forms, magnetically, are, respectively, the Innerpole Type (column 13), and the Radial Multipolar Type (column 12). In the first named of these types the magnet cores form a star, having a common yoke in the centre and the polepieces at the periphery; thus the dis- tances of the leakage paths increase the direct proportion to the difference of magnetic potential, a feature which is most desirable, and which accounts fdr the low values of A for the type in question. The most leaky of all types seem to be the Horizontal Single Horseshoe Type (column 3), and the Axial Multipolar Type (column 15). 1 Mavor, Electrical Engineer (London), April 13, 1894 ; Electrical World, vol. xxiii. p. 615, May 5, 1894. 70] CA LCULA TION OF A CTUAL MA GNE TIC LEAK A GE. 265 In the former type the excessive leakage is due to the mag- netic circuit being suspended over an iron surface extending over its entire length, while in the latter type it is due to the comparatively close relative proximity of a great number of magnet cores (two for each pole) parallel to each other. When making the allowances for improvements referred to in the note to Table LXVIII., the following Table LXVIIIa is obtained, which gives the usual limits of the leakage factor for various sizes of the most common types of continuous current dynamos: TABLE LXVIIIrt. USUAL LIMITS OP LEAKAGE FACTOR FOR MOST COM- MON TYPES OF DYNAMOS. Capacity of Dynamo in Kilo- watts. .25 1 2. 5 10 25 50 100 500 1,000 2,000 Ordinary Horseshoe Type. n il.45 .40 !: 35 1.30 1.25 1.22 1.20 1.18 1.16 1.14 1.12 801 1.50 to 2.001.40 to .35 .80 .86 .20 1.18 .16 1.14 1.12 1.10 1. 1. 1. 1. 1.55 1. 1.45 1.40 1.35 1.30 1.25 70 1 651 601 501 Inverted Horseshoe Type. Double Magnet Type. 1.75 1.601.45 to 2.00 1 1.501.40 .80 .451.35 .401 30 .351.25 .301.20 .251.18 .221.16 .201.15 .90 1 .701 .60 .55 1 .50 .48 .40 Bipolar Iron Clad Type. Fourpolar Iron Clad Type. 1.25 to .22 .20 1.18 .16 1.14 .12 1.10 1.09 1.08 .60 .40 .35 .30 .28 1.35 to .251. .2211.30 .20 .181.26 .15 1.28 1.24 1.22 1.20 Multipolar Ring Type. .75 .65 .60 1 .55 .50J1 .45 J .401 .351 1.08 to 1.50 1.40 1.35 .30 PART IV. DIMENSIONING OF FIELD MAGNET FRAME. CHAPTER XIV. FORMS OF FIELD MAGNETS. 71. Classification of Field Magnet Frames. With reference to the type of the field magnet frame mod- ern dynamos may be classified as follows: /. Bipolar Machines. 1. Single Horseshoe Type. a. Upright single horseshoe type (Fig. 187). b. Inverted single horseshoe type (Fig. 188). c. Horizontal single horseshoe type (Fig. 189). d. Vertical single horseshoe type (Fig. 190). 2. Single Magnet Type. a. Horizontal single magnet type (Figs. 191 and 192). b. Vertical single magnet type (Fig. 193). c. Single magnet ring type (Fig. 194). 3. Double Magnet Type. a. Horizontal double magnet type (Figs. 195 and 197). b. Vertical double magnet type (Figs. 196 and 199). c. Inclined double magnet type (Fig. 198). d. Double magnet ring type (Fig. 200). 4. Double Horseshoe Type. a. Horizontal double horseshoe type (Fig. 201). b. Vertical double horseshoe type (Fig. 202). 5. Iron-clad Type. a. Horizontal iron-clad type (Figs. 203 and 204). b. Vertical iron-clad type. a. Single magnet vertical iron-clad type (Figs. 205 and 206). ft. Double magnet vertical iron-clad type (Fig. 207). //. Multipolar Machines. i. Radial Multipolar Type. a. Radial outerpole type (Fig. 208). b. Radial innerpole type (Fig. 209). 369 270 DYNAMO-ELECTRIC MACHINES. [72 2. Tangential Multipolar Type. a. Tangential outerpole type (Fig. 210). b. Tangential innerpole type ^Fig. 211). . 3. Axial Multipolar Type (Fig. 212). 4. Radi-tangent Multipolar Type (Fig. 213). 5. Single Magnet Multipolar Type. a. Axial pole single magnet multipolar type (Fig. 214). b. Outer-innerpole single magnet multipolar type (Fig. 215)- 6. Double Magnet Multipolar Type (Fig. 216). 7. Multipolar Iron-clad Type (Fig. 217). Horizontal fourpolar iron-clad type (Figs. 218 and 220). Vertical fourpolar iron-clad type (Fig. 219). 8. Multiple Horseshoe Type (Figs. 221 and 222). 9. Fourpolar Double Magnet Type (Fig. 223). 10. Quadruple Magnet Type (Fig. 224). 72. Bipolar Types. The simplest form of field magnet frame is that resembling the shape of a horseshoe. Such a horseshoe-shaped frame may be composed of two magnet cores joined by a yoke, or may be formed of but one electromagnet provided with suit- ably shaped polepieces. The former is called the single horse- shoe type, the latter the single magnet type. A single horseshoe frame may be placed in four different posi- tions with reference to the armature, the two cores either being above or below the armature, or situated symmetrically. one on each side, in a horizontal or in a vertical position. The upright single horseshoe type, Fig. 187, is the realization of the first named arrangement, having the armature below the cores, and is therefore often called the li under type." This form is now used in the Edison dynamo, 1 built by the General Electric Co., Schenectady, N. Y., in the motors of the "C & C" (Curtis & Crocker) Electric Co., 2 New York, and is fur- ther employed by the Adams Electric Co., Worcester, Mass.; 1 Electrical Engineer, vol. xiii. p. 391 (1891); Electrical World, vol. xix. p. 220 (1892). 2 Martin and Wetzler, " The Electric Motor," third edition, p 230. 72] FORMS OF FIELD MAGNETS. 271 by the E. G. Bernard Company, Troy, N. Y. ; by the Detroit Electrical Works, l Detroit, Mich. (" King'' dynamo); the Com- FlQ. 205 FlQ. 206 FIG. 207 Figs. 187 to 207. Types of Bipolar Fields. mercial Electric Co. 8 (A. D. Adams), Indianapolis, Ind. ; the Novelty Electric Co., 3 Philadelphia, Pa.; the Elektron Manu- 1 Electrical World, vol. xxi. p. 165 (1893). 2 Electrical World, vol. xx. p. 430 (1892). 3 Electrical World, vol. xvi. p. 404 (1890). 272 DYNAMO-ELECTRIC MACHINES. [72 facturing Co. 1 (Ferret), Springfield, Mass.; by Siemens Bros., 2 London, Eng. ; Mather & Platt 3 (Hopkinson), Man- chester, Eng. ; the India-rubber, Guttapercha and Telegraph Works Co., 4 Silvertown, Eng., and by Clarke, Muirhead & Co., London. The inverted horseshoe type, Fig. 188, having the armature above the cores, is also called the "overtype" Of this form are the General Electric Co. 's "Thomson-Houston Motors," the standard motors of the Crocker-Wheeler Electric Co., 5 Ampere, N. J.; further, machines of the Keysto'ne Electric Co., 6 Erie, Pa. ; the Belknap Motor Co., 7 Portland, Me. ; the Holtzer-Cabot Electric Co., 6 Boston, Mass.; the Card Electric Motor and Dynamo Co., 9 Cincinnati, O. ; the La Roche Elec- trical Works, 10 Philadelphia, Pa. ; the Excelsior Electric Co., 11 New York; the Zucker & Levett Chemical Co., 12 New York (American " Giant" dynamo); the Knapp Electric and Nov- elty Co., 13 New York; the Aurora Electric Co., 14 Philadelphia, Pa.; the Detroit Motor Co., 15 Detroit, Mich.; the National Electric Manufacturing Co., 16 Eau Claire, Wis. ; Patterson & j 1 Electrical Engineer, vol. xiii. p. 8 (1892). 2 Silv. P. Thompson, " Dynamo-Electric Machinery," fourth edition, p. 509. 3 Silv. P. Thompson, " Dynamo-Electric Machinery," fourth edition, pp. 519 and 522. 4 Electrical World, vol. xiii. p. 84 (1889). 5 Electrical World, vol. xvii. p. 130 (1891); Electrical Engineer, vol. xiv. p. 199 (1892). 6 Electrical World, vol. xix. p. 220 (1892). 7 Electrical World, vol. xxi. p. 470 (1893); Electrical Engineer, vol. xiv. p. 210 (1892). 8 Electrical Engineer, vol. xvii. p. 291 (1894). 9 Electrical World, vol. xxiii. p. 499 (1894); Electrical Engineer, vol. xi. p. 13(1891). (This company is now the Bullock Electric Manufacturing Company.) 10 Electrical World, vol. xvii. p. 17 (1893); Electrical Engineer, vol. xiv. p. 559 (1892); vol. xv. p. 491 (1893). 11 Electrical Engineer, vol. xiv. p. 240 (1892). 12 Electrical Engineer, vol. xiv. p. 187 (1892); Electrical World, vol. xxii. p. 210 (1893). (Now the Zucker, Levett & Loeb Company.) 13 Electrical 'World, vol. xxi. pp. 286, 306, 471 (1893). 14 Electrical World, vol. xv. p. n (1890). 16 Electrical World, vol. xvi. p. 437 (1890); Electrical Engineer, vol. x. p. 695 (1890). 16 Electrical World, vol. xvi. pp. 121, 419 (1890); vol. xxiv. p. 220 (1894); Electrical Engineer, vol. xviii. p. '178 (1894). 72] FORMS OF FIELD MAGNETS. 273 Cooper 1 (Esson), London; Johnson & Phillips 2 (Kapp), Lon- don; Siemens & Halske, 3 Berlin, Germany; Ganz & Co., 4 Budapest, Austria ; Allgemeine Elektricitats Gesellschaft, 6 Berlin; Berliner Maschinenbau Actien-gesellschaft, vorm. L. Schwartzkopff, 6 Berlin; and Zuricher Telephon Gesellschaft, 7 Zurich, Switzerland. Machines of the horizontal single horseshoe type, Fig. 189, in which the centre lines of the two magnet cores and the axis of the armature lie in the same horizontal plane, are built by the Jenney Electric Co., 8 New Bedford, Mass. (''Star" dynamo), by the Great Western Manufacturing Co. 9 (Bain), Chicago, 111., and by O. L. Kummer & Co., 10 Dresden, Germany. The vertical single horseshoe type, Fig. 190, finally, having the axes of magnet cores and armature in one vertical plane, is employed by the Excelsior Electric Co. 11 (Hochhausen), New York, and by the Donaldson-Macrae Electric Co., 12 Baltimore, Md. Single core honseshoe frames may be designed by placing the magnet either in a horizontal or in a vertical position, or by joining two polepieces of suitable shape by a magnet of circu- lar form. The types thus obtained are the horizontal single magnet type, the vertical single magnet type, and the single magnet ring type. In the horizontal single magnet type, Figs. 191 and 192 respect- ively, the armature may either be situated above or below the core. Machines of the former type (Fig. 191) are built by the I S. P. Thompson, " Dynamo-Electric Machinery," plate v. 2 S. P. Thompson, " Dynamo-Electric Machinery," plates i and ii. 8 Elektrotechn. Zeitschr., vol. vii. p. 13 (1886); Kittler, "Handbuch," vol. i. p. 851. * Zeitschr. f. Electrotechn., vol. vii, p. 78 (1889); Kfttler, " Handbuch," vol. i. p. 930. 5 Grawinkel and Strecker, " Hilfsbuch," fourth edition (1895), p. 287. 8 Gra\vinkel and Strecker, " Hilfsbuch," fourth edition, p. 288. 7 Grawinkel and Strieker, " Hilfsbuch," fourth edition, p. 328. 8 Electrical World, vol. xix. p. 172 (1892); Electrical Engineer, vol. xiii. p. 182 (1892). 9 Electrical Engineer, vol. xvii. p. 421 (1894). (Now the Western Elec- tric Co. ) 10 Kittler, " Handbuch," vol. i. p. 949. II Electrical Engineer, vol. xvii. p. 465 (1894). 12 Electrical Engineer, vol. xiii. p. 397 (1892). 274 DYNAMO-ELECTRIC MACHINES. [72 Jenney Electric Motor Co., 1 Indianapolis, Ind. ; the Porter Standard Motor Co., New York; the Fort Wayne Electric Corp., 2 Fort Wayne, Ind. ; the United States Electric Co., New York; the Holtzer-Cabot Electric Co., 3 Boston; the Card Electric Motor and Dynamo Co., 4 Cincinnati, O. ; the Simp- son Electrical Manufacturing Co., 5 Chicago; the Chicago Electric Motor Co., 6 Chicago; the Bernstein Electric Co., 7 Boston; and by the Premier Electric Co., 8 Brooklyn. The latter type, Fig. 192, is employed by the Elektr9n Manufac- turing Co., 9 Springfield, Mass.; by the Riker Electric Motor Co., 10 Brooklyn; and by the Actiengesellschaft Elektricitat- vverke, vorm. O. L. Kummer & Co., 11 Dresden. The vertical single magnet type, Fig. 193, is used by the " D. & D." Electric Manufacturing Company, 12 Minneapolis, Minn. ; the Packard Electric Company, 18 Warren, O. ; the Bos- ton Motor Company, 14 Boston; the Elbridge Electric Man- ufacturing Company, Elbridge, N. Y. ; the Woodside Electric Works 1B (Rankin Kennedy), Glasgow, Scotland ; by Greenwood & Batley, 16 Leeds, England ; by Goolden & Trotter 17 (Atkinson), England; and by Naglo Bros., 18 Berlin. 1 Electrical Engineer, vol. xiii. p. i 2 Electrical Engineer, vol. xiii. p. 408 (1892); Electrical World, vol. xxviii. p. 394 (1896). 3 Electrical World, vol. xix. p. 107 (1892). 4 Electrical World, vol. xxiii. p. 499 (1894). 5 Electrical World, vol. xxii. p. 30 (1893). 6 Electrical World, vol. xxii. p. 31 (1893). 7 Electrical World, vol. xix. p. 283 (1892). 8 Electrical World, vol. xix. p. 186 (1892). * Electrical Engineer, vol. xv. p. 540(1893). Electrical Engineer , vol. xvi. p. 436 (1893). 11 Grawinkel and Strecker, " Hilfsbuch," fourth edition, p. 277. ^Electrical World, vol. xx. p. 183(1892); Electrical Engineer, vol. xiv. p. 272 (1892). 13 Electrical World, vol. xx. p. 265 (1892), Electrical Engineer, vol. xiv. p. 414(1892). 14 Electrical World, vol. xxi. p. 471 (1893). 15 l^he Electrician (London), March I, 1889; Electrical World, vol. xiii., April, 1889. 16 Silv. P. Thompson, " Dynamo-Electric Machinery," fourth edition, p. 531. 17 Silv. P. Thompson, "Dynamo-Electric Machinery," fourth edition, p. 615. 18 Grawinkel and Strecker, " Hilfsbuch," fourth edition, p. 314. 72] FORMS OF FIELD MAGNETS. 275 Fig. 194 shows the single magnet ring type, which is employed by the Mather Electric Company, 1 Manchester, Conn. Two magnets, instead of forming the limbs of a horseshoe, can also be set in line with each other, one on each side of the armature, or may be arranged so as to be symmetrical to the armature, but with like poles pointing to the same direction, instead of forming a single magnetic circuit with salient poles; the frame will then constitute a double circuit with consequent poles in the yokes joining the respective ends of the magnet cores. In both of these cases the cores may be put in a hori- zontal or vertical position, and in consequence we obtain two horizontal double magnet types, Figs. 195 and 197, and two vertical double magnet types, Figs. 196 and 199. The salient pole horizontal double magnet type, Fig. 195, is em- ployed by Naglo Bros., 3 Berlin, and by Fein & Company, Stutt- gart, Germany ; and the salient pole vertical double magnet type, Fig. 196, by the Edison Manufacturing Company, 3 New York; and by Siemens & Halske, 4 Berlin. The consequent pole horizontal double magnet type, Fig. 197, is used in the Feldkamp motor, built by the Electrical Piano Company, 5 Newark, N. J. ; and in the fan motor of the De Mott Motor and Battery Company; 6 and the consequent pole vertical double magnet type, Fig. 199, by the Columbia Electric Company, 7 Worcester, Mass. ; the Keystone Electric Company, Erie, Pa. ; the Akron Electrical Manufacturing Company, 8 Akron, O. ; the Mather Electric Company, 9 Manchester, Conn.; the Duplex Electric Company, 10 Corry, Pa.; the Gen- 1 Electrical Engineer, vol. xvii. p. 181 (1894). 2 Kittler, " Handbuch," vol. i. p. 908; Jos. Kramer, " Berechnung der Dy- namo Gleichstrom Maschinen." 3 " Composite" Fan Motor, Electrical Engineer, vol. xiv. p. 140(1893) ; Elec- trical World, vol. xxviii. p. 375 (1896); Electrical Age, vol. xix. p. 269 (1897^ 4 Grawinkel and Strecker, " Hilfsbuch," fourth edition, p. 326. 5 Electrical World, vol. xxi. p. 240 (1893). 6 Electrical World, vol. xxi. p. 395 (1893). 7 Electrical World, vol. xxiii. p. 849(1894). 8 Electrical World, vol. xx. p. 264 (1892). 9 Electrical World, vol. xxiv. p. 112 (1894); Electrical Engineer, vol. xviii, p. 99 (1894). 10 Electrical World, vol. xix. pp. 107, 171 (1892); Electrical Engineer, vol xiii. p. 198(1892). 276 D YNAMO-ELECTRIC MA CHINES. [72 eral Electric Traction Company (Snell), England; Mather & Platt (Hopkinson), 1 Manchester, England; Tmmish & Com- pany, 2 England; Oerlikon Works (Brown), 3 Zurich, Switzer- land; Helios Company, 4 Cologne; and by Naglo Bros./ Berlin. If in the latter form the magnets are made of circular shape, the double magnet ring type, Fig. 200, is obtained, which is built by the " C & C " Electric Company, 6 New York, and which has .been used in the Griscom motor 7 of the Electro-dynamic Company, Philadelphia. The inclined double magnet type, illustrated in Fig. 198, forms the connecting link between the double magnet and the single horseshoe types; it is employed by the Baxter Electrical Manu- facturing Company, 8 Baltimore, Md. ; by Fein & Company, 9 Stuttgart; and by Schorch 10 in Darmstadt. The combination of two horseshoes with common polepieces furnishes two further forms of field magnet frames. Fig. 201 shows the horizontal double horseshoe type, and Fig. 202 the -ver- tical double horseshoe type. Machines of the former type (Fig. 201) are built by the United States Electric Company " (Weston), New York; the Brush Electric Company, 12 Cleveland, O. ; the Ford-Washburn Storelectric Company, Cleveland, O. ; the Western Electric Company, 13 Chicago, 111. ; the Fontaine Crossing and Electric Company (Fuller), Detroit, Mich. ; by Crompton & Com- pany, 14 London, England; by Lawrence, Paris & Scott, Eng- land, and by Schuckert & Company, Nuremberg, Germany. The latter form (Fig. 202) is employed in dynamos of Fort 1 Silv. P. Thompson, " Dynamo-Electric Machinery," fourth edition, p. 496. 2 Gisbert Kapp, " Transmission of Energy," p. 272. 3 Kittler, " Handbuch," vol. i. p. 921. 4 Kittler, " Handbuch," vol. i. p. 904. 5 Grawinkel and Strecker, " Hilfsbuch," fourth edition, p. 312. Electrical World, vol. xxii. p. 247 (1892). 7 Martin and Wetzler, " The Electric Motor," third edition, p. 126. 8 Martin and Wetzler, " The Electric Motor," third edition, p. 228. 9 Kittler, " Handbuch," vol. i. p. 944. 10 Jos. Kramer, " Berechnung der Gleichstrom Dynamo Maschinen." 11 Kittler, " Handbuch," vol. i. p. 879. 12 Electrical Engineer , vol. xiv. p. 50 (1892). 13 Electrical Engineer, vol. xvi. p. 323 (1893). 34 Kapp, " Transmission of Energy," p. 292. g 72] FORMS OF FIELD MAGNETS. 277 Wayne Electric Corporation 1 (Wood), Fort Wayne, Ind. ; La Roche Electric Works, 2 Philadelphia; Granite State Electric Company, 3 Concord, N. H. ; Onondaga Dynamo Company, Syracuse, N. Y. ; Electric Construction Corporation 4 (Elwell- Parker); and Crompton Company, 6 London, England. If one or both the polepieces of a consequent pole double magnet type are prolonged in the axial direction, that is, to- ward the armature, and the winding is transferred from the cores to these elongated polepieces, then a type is obtained in which the magnet frame forms a closed iron wrappage with in- wardly protruding poles. Forms of this feature are known as iron-clad types, and, according to the number of magnets and to their position, are single magnet and double magnet, horizontal and vertical iron-clad types. Fig. 203 shows the horizontal iron-clad type, having two hori- zontal magnets. It is used by the General Electric Com- pany, 6 Schenectady, N.Y. (Thomson-Houston Arc Light type), Detroit Electric Works, 7 Detroit, Mich. ; Eickemeyer Com- pany, 8 Yonkers, N. Y. ; Fein & Company, 9 Stuttgart; and Aachen Electrical Works 10 (Lahmeyer), Aachen, Germany. A modification of this type consists in letting the poles pro- ject parallel to the shaft, one above and one below, or one on each side of the armature; the only magnetizing coil required in this case will completely surround the armature. This spe- cial horizontal iron-clad form, which is illustrated in Fig. 204, is realized in the Lundell machine, 11 built by the Interior Con- duit and Insulation Company, New York. 1 Electrical World, vol. xxiii. p. 845 (1894); vol. xxviii. p. 390 (1896); Elec- trical Engineer, vol. xvii. p. 598 (1894). 2 Electrical Engineer, vol. xiii. p. 439 (1892). 3 Electrical Engineer, vol. xvi. p. 45 (1893). 4 Electrical Engineer, vol. xv. p. 166(1893). 5 Silv. P. Thompson, " Dynamo-Electric Machinery," fourth edition, p. 486. 6 Silv. P. Thompson, " Dynamo-Electric Machinery," fourth edition, p. 465. 7 Electrical World, vol. xx. p. 46 (1892) ; Electrical Engineer, vol. xiv. p. 27(1892). 8 Kittler, " Handbuch," vol. i. p. 941. 9 Kittler, " Handbuch," vol. i. p. 944. 10 Kittler, " Handbuch," vol. i. p. 917. 11 Electrical World, vol. xx. pp. 13. 381 (1892); vol. xxiii. p. 32 (1894); Electrical Engineer, vol. xiii. p. 643 (1892); vol. xiv. p. 544(1892); vol. xvii. p. 17 (1894.) 278 DYNAMO-ELECTRIC MACHINES. [72 In Figs. 205 and 206 the two possible cases of the vertical single magnet iron-clad type are depicted, the magnet being placed above the armature in the former and below the armature in the latter case. The single magnet iron-clad overtype, Fig. 205, is adopted in the street-car motors of the General Electric Com- pany, Schenectady, N. Y. ; in the machines of the Muncie Electrical Works, 1 Muncie, Ind. ; of the Lafayette Engineering and Electric Works," Lafayette, Ind., and rn the battery fan motor of the Edison Manufacturing Company, 3 New York. Machines of the single magnet iron-clad undertype, Fig. 206, are built by the Brush Electrical Engineering Company 4 (Mor- dey), London, and by Stafford and Eaves, 5 England. The vertical double magnet iron- clad type, Fig. 207, having two vertically projecting magnets, one above and one below the armature, is employed in the machines of the Wenstrom Elec- tric Company, 6 Baltimore; the Triumph Electric Company, 7 Cincinnati, O. ; the Shawhan-Thresher Electric Company, 8 Dayton, O. ; the Card Motor Company, 9 Cincinnati, O. ; the Johnson Electric Service Company, 10 Milwaukee, Wis. ; the Erie Machinery Supply Company, 11 Erie, Pa.; O. L. Kummer & Company, 12 Dresden ; Deutsche Elektrizitats-Werke 13 (Garbe, Lahmeyer & Co.), Aachen; Schuckert & Company, 14 Nuremburg, Germany; Oerlikon Works, 15 Zurich; and the Zurich Telephone Company, 16 Zurich, Switzerland. There are various other bipolar types, which, however,, ^Electrical Engineer, vol. xv. p. 606 (1893). 2 Western Electrician, vol. xviii. p. 273 (1896). 3 Electrical World, vol. xxi. p. 347 (1893). 4 Elektrotechn, Zeitschr., vol. xi. p. 135 (1890). 5 S. P. Thompson, " Dynamo-Electric Machinery," fourth edition, p. 202., * Elektrotechn. Zeitschr., vol. xi. p. 122 (1890). 7 Electrical Engineer, vol. xvii. p. 314 (1894). 8 Electrical World, vol. xxiii. p. 191 (1894). 9 Electrical World, vol. xxii. p. 15 (1893). 10 Electrical Engineer, vol. xvii. p. 290(1894). 11 Electrical World, vol. xix. p. 283 (1892). 12 Grawinkel and Strecker, " Hilfsbuch," fourth edition, p. 278. 13 Grawinkel and Strecker, " Hilfsbuch," fourth edition, p. 293. 14 Grawinkel and Strecker, " Hilfsbuch," fourth edition, p. 299. 15 Grawinkel and Strecker, " Hilfsbuch," fourth edition, p. 320. 16 Elektrotechn. Zeitschr., vol. ix. pp. 181, 347, 410 and 485 (1888)^ 73] FORMS OF FIELD MAGNETS. 279 mostly are out of date, and, therefore, of very little practical importance. These can easily be regarded as special cases of the types enumerated above. 73. Multipolar Types. Multipolar field magnet frames can have one or two mag- nets for every pole, or each magnet can independently supply FIG. 221 FIG. 222 FIG. 223 FIG. 224 Figs. 208 to 224. Types of Multipolar Fields. two poles, or one single magnet, or two magnets, may be pro- vided with polepieces of such shape as to form the desired number of poles of opposite polarity. 280 DYNAMO-ELECTRIC MACHINES. [73 If the number of magnets is identical with the number of poles, the magnets may either be placed in a radial, a tangetial, or an axial position with reference to the armature, and in the two first-named cases they may be put either outside or inside of the armature. The Radial Outerpole Type is shown in Fig. 208; this form has been adopted as the standard type for large dynamos of the General Electric Company, 1 Schenectady, N. Y. ; of the Westinghouse Electric and Manufacturing Company, 2 Pitts- burg, Pa.; the Crocker-Wheeler Electric Company, 3 Ampere, N. J. ; the Riker Electric Motor Company, 4 Brooklyn; the Stanley Electric Manufacturing Company, 5 Pittsfield, Mass.; the Fort Wayne Electric Company, 6 Fort Wayne, Ind. ; the Eddy Electric Manufacturing Company, 7 Windsor, Conn.; the Belknap Motor Company, 8 Portland, Me.; the Shawhan- Thresher Electric Company, 9 Dayton, O. ; the Great Western Electric Company 10 (Bain), Chicago ; the Walker Manufactur- ing Company, 11 Cleveland, O. ; the Mather Electric Com- pany, 12 Manchester, Conn.; the Claus Electric Company, 13 New York; the Commercial Electric Company, 14 Indianapolis; I Electrical World, vol. xxi. p. 335 (1893); vol. xxiv. pp. 557 and 652 (1894); Electrical Engineer, vol. xiii. p. 165 (1892) ; vol. xiv. p. 562 (1892); vol. xviii. pp. 426, 507 (1894). 2 Electrical World, vol. xxi. p. 91 (1893); vol. xxiv. p. 421 (1894); Electrical Engineer, vol. xviii. p. 330 (1894). 3 Electrical World, vol. xxiii. p. 307 (1894); Electrical Engineer, vol. xvii. p. 193 (1894). 4 Electrical World, vol. xxiii. p. 687 (1894); Electrical Engineer, vol. xvii. p. 442 (1894). 5 Electrical World, vol. xxiii. p. 815 (1894); Electrical Engineer, vol. xvii. p. 507 (1894). 6 Electrical World, vol. xxiii. p. 878 (1894); vol. xxviii. p. 395 (1896). ^Electrical World, vol. xxv. p. 34 (1895). 8 Electrical Engineer, vol. xvii. p. 502 (1894). 9 Electrical Engineer , vol. xvii. p. 463 (1894). 10 Electrical World, vol. xxiii. p. 161 (1894). II Electrical World, vol. xxiii. pp. 475 and 785 (1894); vol. xxviii. p. 423 (1896); Electrical Age, vol. xviii. p. 605 (1896). 12 Electrical Engineer, vol. xiv. p. 364 (1892). 13 Electrical Engineer, vol. xvi. p. 3 (1893). 14 Electrical World, vol. xxiv. p. 627 (1894); vol. xxviii. p. 437 (1896); Elec- trical Engineer, vol. xviii. p. 506 (1894). 73] FORMS OF FIELD MAGNETS. 281 the Zucker, Levitt & Loeb Company, 1 New York; the All- gemeine Electric Company 2 (Dobrowolsky), Berlin, Germany; O. L. Kummer & Company, 3 Dresden; Garbe, Lahmeyer & Company, 4 Aachen; Elektricitats Actien-Gesellschaft, vor- mals W. Lahmeyer & Company, 5 Frankfurt a. M. ; Schuckert & Company, 6 Nuremburg; C. & E. Fein, 7 Stuttgart; Naglo Bros., 8 Berlin; the Zurich Telephone Company, 9 Zurich; the Oerlikon Machine Works, 1 * Zurich, Switzerland; R. Alioth & Company, 11 Basel, Switzerland; the Berlin Electric Construc- tion Company (Schwartzkopff), 12 Berlin, Germany; and numer- ous others. In Fig. 209 is represented the Radial Innerpole Type, which is used by the Siemens & Halske Electric Company, 13 Chicago, 111., and Berlin, Germany; by the Alsacian Electric Construc- tion Company, 14 Belfort, Alsace; by Naglo Bros., 15 Berlin, Germany; by Fein & Co., 16 Stuttgart, Germany; and by Ganz & Co., 17 Budapest, Austria. The Tangential Outerpole Type, Fig. 210, is employed by the Riker Electric Motor Company, Brooklyn; by the Baxter Motor Company, 18 Baltimore, Md. ; the Mather Electric Com- pany, 19 Manchester, Conn.; the Dahl Electric Motor Com- 1 "Improved American Giant Dynamo," Electrical Age, vol. xviii. p. 600 (Oct. 17, 1896). 2 Electrical Engineer, vol xii. p. 596 (1891); vol. xvi. p. 103 (1893) 3 Grawinkel and Strecker, " Hilfsbuch," fourth edition, p. 278. 4 Grawinkel and Strecker, " Hilfsbuch," fourth edition, p. 291. 5 Grawinkel and Strecker, " Hilfsbuch," fourth edition, p. 294. 6 Grawinkel and Strecker, " Hilfsbuch," fourth edition, p. 299. 7 Grawinkel and Strecker, " Hilfsbuch," fourth edition, p. 304. 8 Grawinkel and Strecker, " Hilfsbuch," fourth edition, p. 311. 9 Grawinkel and Strecker, " Hilfsbuch," fourth edition, p. 327. 10 Electrical Engineer, vol. xii. p. 597(1891). 11 Kittler, " Handbuch," vol. i. p. 934. 12 Kittler, " Handbuch," vol. i. p. 939. 13 Electrical World, vol. xxii., p. 61 (1893); Electrical Engineer, vol. xii. p. 572(1891); vol. xiv. p. 313 (1892). 14 L'Electricien, vol. i. p. 33 (1891). 15 Kittler, " Handbuch," vol. i. p. 916. "Zeitsckr.f. Elektrotechn., vol. v. p. 545 (1887). 17 Electrotechn. Zeitschr., vol. viii. p. 233 (1887). 18 Hering, " Electric Railways," p. 294. 19 Electrical World, vol. xxiv. p. 134 (1894); Electrical Engineer, vol. xviii. p. 177(1894). 282 DYNAMO-ELECTRIC MACHINES. [73 pany, 1 New York; the Electrochemical and Specialty Com- pany, 2 New York (''Atlantic Fan Motor "), and by Cuenod, Sauter & Co. 3 (Thury), Geneva, Switzerland; generators of this type are further used in the power station of the General Electric Company, 4 Schenectady, N. Y., and in the Herstal, 5 Belgium, Arsenal. Machines of the Tagential Innerpole Type, Fig. 211, are built by the Helios Electric Company, 6 Cologne, Germany. In the Axial Multipolar Type, Fig. 212, there are usually two magnets for each pole, one on each side of the armature, in order to produce a symmetrical magnetic field. This form is used by the Short Electric Railway Company, 7 Cleveland, O. ; Schuckert & Co., 8 Nuremberg, Germany; Fritsche & Pischon, 9 Berlin, Germany; Brush Electric Engineering Company, 10 London, England ("Victoria" Dynamo); by M. E. Desro- ziers, 11 Paris, and by Fabius Henrion, 12 Nancy, France. The type recently brought out by the C. & C. Electric Company, 13 New York, has but one magnet per pole, and the polepieces are arranged opposite the external circumference of the armature. Fig. 213 shows the Raditangent Multipolar Type, which is a combination of the Radial and Tangential Outerpole Types, Figs. 208 and 210 respectively, and which is employed by the Standard Electric Company, 14 Chicago, 111. ^Electrical World, vol. xxi. p. 213 (1893). 2 Electrical World, vol. xxi. p. 394 (1893). 3 Kittler, " Handbuch," vol. i. p. 936. 4 Thompson, "Dynamo-Electric Machinery," fourth edition, p. 517. 6 500 HP. Generator, Electrical World, vol. xx. p. 224 (1892). 6 Kittler, " Handbuch," vol. i. p. 905. ^Electrical World, vol. xviii. p. 165 (1891). 8 Elektrotechn. Zeitschr., vol. xiv. p. 513 (1893); Electrical Engineer, vol. xii. p. 595 (1891). 9 Electrical World, vol. xx. p. 308 (1892); Electrical Engineer, vol. xii. p. 572 (1891). 10 Thompson, " Dynamo Electric Machinery," fourth edition, p. 498. n Electrical Engineer , vol. xiv. p. 259 (1892); vol. xv. p. 340 (1893). 12 Grawinkel and Strecker, " Hilfsbuch," fourth edition, p. 317. 13 Electrical World, vol. xxviii. p. 372 (1896). l * Electrical World, vol. xxiii. pp. 342, 549 (1894); Electrical Engineer, vol. xvii. pp. 189, 379 (1894). g 73] FORMS OF FIELD MAGNETS. 283 If only one magnet is used in multipolar fields, the pole- pieces may be so shaped as to face the armature in an axial or in a radial direction. In the former case the Axial Pole Single Magnet Multipolar Type, Fig. 214, is obtained, which is used by the Brush Electrical Engineering Company 1 (Mordey), London, England, and by the Fort Wayne Electric Company 3 (Wood), Fort Wayne, Ind. In the latter case the Outer-Inner Pole Single Magnet Type, Fig. 215, results, in which the polepieces may either all be opposite the outer or the inner armature surface, or alter- nately outside and inside of the armature; the latter arrange- ment, which is the most usual, is illustrated in Fig. 215, and is employed by the Waddell-Entz Company, 3 Bridgeport, Conn., and by the Esslinger Works, 4 W T urtemberg, Germany; the all outerpole arrangement is employed in the direct con- nected multipolar type of the C & C Electric Company, 5 New York. If two magnets furnish the magnetic flux, they are placed concentric to the armature, and the two sets of polepieces so arranged that adjacent poles on either side of the armature are of unlike polarity, but that poles facing each other on opposite sides of the armature have the same polarity. Such a Double Magnet Multipolar Type is shown in Fig. 216; it is that designed by Lundell, 6 and built by the Interior Conduit and Insulation Company, New York. In giving the yoke of the Radial Multipolar Type (Fig. 208) such a shape as to form a polepiece between each two consec- utive magnets, an iron-clad form is obtained having alternate salient and consequent poles, and requiring but one-half the number of magnets as a radial multipolar machine of same .number of poles. Fig. 217 shows a field frame of the Multipolar Iron-clad Type, having six poles, which is the form employed in the :gearless street car motor of the Short Electric Railway Com- 1 Thompson, " Dynamo Electric Machinery," fourth edition, p. 678. 2 Electrical Engineer vol. xv. p. 46 (1893). 3 Electrical World, vol. xix. p. 13 (1892); vol. xxii. p. 120(1893). 4 Kittler, "Handbuch," vol. i. p. 945. 5 Electrical World, vol. xxv. p. 33 (1895). Electrical World, vol. xx. p. 85 (1892). 284 DYNAMO-ELECTRIC MACHINES. [ 7$ pany, 1 Cleveland, O. In Figs. 218 and 219, two special cases of this type are depicted, both representing Fourpolar Iron- clad Types, and differing only in the position of the magnets. The Horizontal Fourpolar Iron-clad Type, Fig. 218, is used in the Edison Iron-clad Motor 2 (General Electric Company), and in the dynamos of the Wenstrom Electric Company, 3 Balti- more, Md. The Vertical Fourpolar Iron-clad Type, Fig. 219, is employed by the Elliott-Lincoln Electric Company, 4 'Cleve- land, O. Fig. 220 shows a special case of the Horizontal Fourpolar Iron-clad Type, obtained by symmetrically doubling the frame illustrated in Fig. 204, and providing four poles instead of two. The cores are so wound that the centre of the cylindri- cal iron wrappage has one polarity and the ends the opposite polarity. Two oppositely situated polepieces are joined to the middle, and the two sets of intermediate ones to the ends of the magnet frame; the lower half of Fig. 220, consequently, is a section taken at right angles to'the upper half, the diamet- rically opposite section being identical. This type has been developed by the Storey Motor and Tool Company, 5 New York. Multipolar fields may also be formed by a number of inde- pendent horseshoes arranged symmetrically around the outer armature periphery. Figs. 221 and 222 show two such Mul- tiple Horseshoe Types, double magnet horseshoes being employed in the former, and single magnet horseshoes in the latter type. Multiple horseshoe machines of the double magnet form (Fig. 221) have been designed by Elphihstone & Vincent, and by Elwell-Parker Electric Construction Corporation, 6 England; while the single-magnet form (Fig. 222) is employed by the Electron Manufacturing Company 7 (Ferret), Springfield, Mass. 1 Electrical World, vol. xx. p. 241 (1892); Electrical Engineer, vol. xiv. p. 395 (1895). 3 Electrical Engineer, vol. xii. p. 598 (1891). 3 Electrical World, vol. xxiv. p. 183 (1894). 4 Electrical World, vol. xxi. p. 193 (1893); vol. xxii. p. 484 (1893). 5 Electrical World, vol. xxi. p. 214(1893); Electrical Engineer, vol. xv. p. 263 (1893). 6 The Electrician (London), vol. xxi. p. 183 (1888). 7 Electrical Engineer, vol. x. p. 592 (1890); vol. xiii. p. 2 (1892). 74] FORMS OF FIELD MAGNETS. 285 Further forms of multipolar fields can be derived from the bipolar horizontal and vertical double magnet types respec- tively. If, in the Vertical -Double Magnet Type, Fig. 196, an additional polepiece is provided at the centre of the frame so as to face the internal surface of the armature at right angles to the outer polepieces, the Fourpolar Vertical Double Magnet Type is created, which, when laid on its side, will constitute the Fourpolar Horizontal Double Magnet Type, Fig. 223. If, in the Vertical Double Magnet Type, Fig. 199, the two cores are cut in halves and additional polepieces inserted at right angles to the existing ones, the Vertical Quadruple Magnet Type, Fig. 224, is obtained; the same operation performed with the Hori- zontal Double Magnet Type, Fig. 197, will give the Horizontal Quadruple Magnet Type. Fourpolar Horizontal Double Magnet Dynamos, Fig. 223, are built by the Zurich Telephone Company, 1 Zurich, Switzerland; and Vertical Quadruple Magnet Machine, Fig. 224, by the Duplex Electric Company, 2 Corry, Pa. Numerous other multipolar types have been invented and patented, but either are of historical value only, or have not yet come into practical use. 74. Selection of Type. If the type is not specified, the field magnet frame for a large output machine should be chosen of one of the multipolar types, as in these the advantage of a better proportioning and a higher efficiency of the armature winding, and the possibility of a symmetrical arrangement of the magnetic frame, results in a saving of copper as well as of iron; while for smaller machines below 10 KW capacity the bipolar forms are pref- erable on account of the great complication caused by the increased number of armature sections, commutator-divisions, field coils, etc., necessary in multipolar machines, and on account of the narrowness of the neutral or non-sparking space on a multipolar commutator. The field, moreover, should have as few separate magnetic 'Kittler, " Handbuch," vol. i. p. 947. 2 Electrical World, vol. xx. p. 14(1892); Electrical Engineer, vol. xiv. p, I (1892). .286 DYNAMO-ELECTRIC MACHINES. [74 -circuits as possible; thus, in the case of a bipolar type, it should be a single magnetic circuit rather than the consequent pole type which is formed by two or more magnetic circuits, of one or two magnets each, in parallel, because the former is more economical in wire and in current required for excita- tion. In two-circuit consequent pole machines, for instance, .such as the double magnet types, Figs. 197, 199, and 200, and the double horseshoe types, Figs. 201 and 202, according to Table LXIX., 75, there is 1.41 times the length of wire, and -consequently also 1.41 times the energy of magnetization required than in a single circuit, round cores being used in both cases, and the single circuit having exactly twice the area of each of the two parallel circuits in the consequent pole ma- chines. Triple and quadruple magnetic circuits, /'. e., 3 or 4 cores, or sets of cores, magnetically in parallel, are still more objectionable, requiring, when the cores are of circular cross- section, 1.73 and 2.00 times as much wire, respectively, as a single magnetic circuit having a round core of equal total sec- tional area. If a machine has several magnetic circuits, each of which, however, passes through all the magnets in series, then the frame is to be considered as consisting of but one single cir- cuit, for the subdivision only takes place in the yokes, and it is immaterial as to the length of exciting wire whether the return path of a single circuit is formed by one yoke, or by a number of yokes magnetically in parallel. The above-named objection to divided circuit types, consequently, does not apply in the case of the iron-clad forms, Figs. 203 to 207. According to Table LXVIII., 70, the horizontal double magnet type, Fig. 195, and the horizontal iron-clad type, Fig. 203, are the best bipolar forms, magnetically. The iron- clad types, furthermore, possess the mechanical advantage of having the field windings and the armature protected from external injuries by the frame of the machines, which makes them eminently adaptable to motors for railway, mining, and similar work. The inverted horseshoe type, Fig. 188, which ranks very highly, as far as its magnetic qualities are concerned, has the centre of its armature at a comparatively very great distance from the base, requiring very high pillow-blocks, which have 74] FORMS OF FIELD MAGNETS. 287 to carry the weight as well as the downward thrust of the armature inherent to the inverted forms having the field wind- ings below the centre of revolution; see 42. The side pull of the belt with a high centre line of shaft tends to tip the .machine, and the changes in the pull due even to the undula- tions of the belt will cause a tremor in the frame which jars the brushes, and, eventually, loosens their holders, and which lias a disastrous influence upon the wearing of the commutator. On this account the inverted forms, or Bunder-types," can only be used for small and medium-sized machines, in which the height of the pillow-blocks remains within practical limits. In selecting a multipolar type, Table LXVIII. shows that the radial innerpole type, Fig. 209, offers the best advantage with regard to the magnetical disposition; with this type, however, are connected some mechanical difficulties, due to the necessity of supporting the frame from one of its ends, laterally, and the armature from the other. In the outerpole types the armature core can be supported centrally from the inner circumference, and the frame suit- ably provided with external lugs or flanges resting upon the foundation, a most desirable arrangement for mechanical strength and convenience. The most favorite of the out- erpole forms is the radial outerpole type, Fig. 208, on account of its superiority, magnetically, over the tangential and axial multipolar types. In all dynamo designs the consideration is especially to be borne in mind that the whole machine as well as its various parts should be easily accessible for inspection, and so arranged that they can conveniently be removed for repair or exchange. A large number of machines owe their popularity chiefly to their good disposition in this respect. The shape of the frame in all cases is preferably to be so chosen that the length of the magnetic circuit in the same is as short as possible, Advantages and Disadvantages of Multipolar Machines. The advantages of multipolar over bipolar dynamos can be summarized as follows: (i) By the multipolar construction a saving in weight of DYNAMO-ELECTRIC MACHINES. [74 material is effected both in the armature and in the field magnet, due to the subdivision of the magnetic circuit. (2) Multipolar machines have a more compact and sym- metrical form, because the component parts of the magnet frame are much smaller than a corresponding bipolar magnet, and are evenly spaced around the armature. (3) Since there are as many openings around the armature as there are poles, the ventilation of the armature is much better; and since a number of small cores have a greater sur- face than one large core of equal cross-section and length, the dissipation of heat is facilitated, so that under the same condi- tions multipolar machines run cooler than bipolar ones. (4) For armatures of the same diameter, the individual parts of the field frame are much smaller and more easily handled in the multipolar than in the bipolar type. The disadvantages of multipolar machines are: (1) Greater complication in constructing, fitting, winding, and connecting, owing to the increased number of parts and consequent larger number of magnetic and electrical circuits. (2) Strong magnetic side pull on the armature in case of eccentricity of field; much greater than in bipolar machines. (3) Greater difficulty in balancing field; with multiple-cir- cuit armature winding, the flux must be exactly the same for each pole, otherwise the E. M. F. of the circuits will be un- equal, producing wasteful currents in them which, in turn, cause excessive sparking and heating. This difficulty, how- ever, is not present in two-circuit windings. Comparison of Bipolar and Multipolar Types. The saving in material effected by the multipolar construc- tion is seen by comparing the three designs shown in Fig. 224^7, representing armatures of equal size in bipolar, four-pole, and eight-pole fields. Assuming that in all three cases the poles cover a like portion of the armature periphery, and that the gap induction is the same, then evidently the total armature flux is the same in the three designs. In practice, the gap density is usually less in bipolar than in multipolar machines, but this difference is not a necessity, and need not be con- sidered in this comparison. In the bipolar type, it will be seen that the armature must 74] FORMS OF FIELD MAGNETS. 287^ carry \ the total flux between its shaft and periphery, while in the four-pole machine the armature cross-section is only required to carry the total flux, hence the radial depth B of the armature core in the four-pole machine need be only one-half as great as A in the bipolar type, thus reducing its weight. The flux passing through each core 'of the four-pole machine is |, and that passing through its yoke ring is j of the corresponding bipolar flux, as is indicated by the dotted lines, each of which represents -J- of the total flux. Owing to this subdivision of the flux, the weight of the multipolar magnet frame is less than that of the bipolar. The difference is still more marked when we compare the eight-pole machine shown in Fig. 2240 with the bipolar and Fig. 224^. Comparison of Bipolar and Multipolar Types. four-pole types. The radial thickness of the field ring in the eight-pole machine is only -| as much as in the four-pole machine, and ^ as great as the thickness of the yoke in the bipolar machine, and the armature may be hollowed out to a radial thickness C of only J that of the bipolar armature, A, as shown, the total flux being the same for all three designs. Proper Number of Poles for Multipolar Field Magnets. If a multipolar field has been adopted, the best number of poles must next be decided upon. This is a question, partly, of selecting a size and number of field cores, coils, etc., con- venient for making and handling, but it is chiefly a matter of the number of magnetic cycles occurring in the armature core. The number of cycles per second, as stated on p. in, is .Af = X M 287^ DYNAMO-ELECTRIC MACHINES. [ 74 if N is the number of revolutions per minute, and ;/ p the number of pairs of magnet poles. Direct-current machinery is designed, generally, so that N is between 10 and 35 cycles per second. This limits the number of poles, the object being to reduce the core losses due to hysteresis and eddy currents, the former, as we have seen in 32, being proportional to N^ whereas the latter increase with the square of N^ see 33. The lower frequency of about 10 or 15 cycles applies to low-speed machines for direct connection to engines, and the higher frequency of 30 or 35 is adopted in high-speed belt-connected generators and motors. By transformation of the above formula for N^ it therefore follows that, for instance, the maximum speed of a four-pole machine, having 2 pairs of poles, should be N = 60 XJVT = 60 x 35 = I050 revs . min . P 2 In some instances, four-pole machines are run at higher speeds than this, for example 1200 revs, per min., which gives 40 cycles. But this is rather too high a frequency, and should not be adopted except for special reasons. If the values ;/ p i, 2, 3, 4, etc., and N^ 10, 15, 25, and 35, respectively, be inserted into the above formula for IV, the following table of dynamo speeds for various numbers of poles is obtained, from which the proper number of poles for any particular speed can be taken: TABLE LXVIII&. NUMBER OP MAGNET POLES FOR VARIOUS SPEEDS. LIMITS OP SPEED. NUMBER OP Low-Speed Machines. Medium-Speed Machines. High-Speed Machines. POLES. Ni = 10 to 15 cycles 2Vi = 15 to 25 cycles. Ni = 25 to 35 cycles. 2 600 to 900 900 to 1500 1500 to 2100 4 300 450 450 750 750 1050 6 200 300 300 500 500 700 8 150 225 225 375 375 525 10 120 180 180 300 300 420 12 100 150 150 250 250 350 14 85 130 130 215 215 300 16 75 115 115 190 190 260 18 70 100 100 170 170 230 20 60 90 90 ' 150 150 210 74] FOKMS CF FIELD MAGNETS. 287^ Generally speaking, the bipolar type is used for high speeds, such as 1500 revs, per min. or more. A further reason for selecting the bipolar type for very high speeds is the fact that machines running at 1500 revolutions, or more, are usually quite small. For speeds between 400 and 900 revs, per min., the four-pole construction is especially suitable, giving fre- quencies from 13^ to 30 cycles. This includes nearly all belted dynamos and motors, from the large sizes of 200 KW, or more, down to about 10 KW, below which the bipolar form is generally used for the reasons given. Between 200 and 400 revs, per min., six poles are commonly adopted, the corresponding frequencies being from 10 to 20 cycles. This range of speed comprises practically all generators directly connected to high-speed engines, from the largest to the smallest, excepting combinations with very high speed engines of 600 revs, per min., or more, for which four poles would be preferable. When a dynamo is directly driven by a steam turbine, at an extremely high speed without reducing gear, the field should be of the bipolar type. For speeds below 200 revs, per min. the number of poles is generally increased to eight, or more. This applies to most generators directly con- nected to low-speed engines. In some cases motors of various sizes, even down to i or 2 HP, are required to run at low speeds in order to be con- nected directly to the machines which they drive. For this purpose six poles are suitable for speeds from 200 to 400 revs, per min., and eight, or more, poles, if the speed is below 200 revs, per min. Railway motors are nearly always con- structed with four poles, the speed being very variable, but hav- ing a maximum value in most cases of about 800 revs, per min. This gives a rather high frequency of 26| cycles, but as the maximum speed is rarely maintained for more than a few minutes at a time, the heating due to hysteresis and eddy currents in the armature core does not rise above the limit allowed. The average speed corresponds to a moderate frequency of 15 to 20 cycles. CHAPTER XV. GENERAL CONSTRUCTION RULES. 75. Magnet Cores. a. Material. *' ' The field cores should preferably be of wrought iron, or of cast steel, in order to economize in magnet wire, for the use of cast iron, on account of its low permeability, would require cores of at least if, /. e., almost twice the cross-section, and therefore a much greater length of wire, to obtain the neces- sary magnetizing force. With the smaller wrought-iron cores the leakage would also be less. In spite of the decided advantage of wrought-iron cores, cast-iron field magnets are very common, since the temptation to use castings instead of forgings is very great. Where weight and bulk are of no consequence, a cast-iron field mag- net may prove nearly as economical as one of wrought iron costing considerably more, but the former requires from \ to \ times more wire to encircle it than a wrought-iron one of similar magnetic density, in case of circular cross-section, and it is evident that this, by introducing additional electrical resistance, will prove a constant source of unnecessary running expense. As to the use of steel in dynamos, H. F. Parshall, in a paper delivered before the Franklin Institute, 1 states that magnet frames made of cast steel are 25 per cent, cheaper than those of cast iron, but possess the disadvantage of being not as uni- form in magnetic qualities as cast iron. He further asserts that good cast steel should not have greater percentages of impurities than .25 per cent, of carbon, .6 per cent, of man- ganese, .2 per cent, of silicon, .08 per cent, of phosphorus, and .05 per cent, of sulphur. The effect of carbon is to lessen the magnetic continuity and to greatly reduce the permeability ; 1 Electrical World, vol. xxiii. p. 214, February 17, 1894. $ 75] GENERAL CONSTRUCTION RULES. 289 carbon, therefore, is the most objectionable impurity, and, if possible, should be restricted to smaller amounts than the maximum above quoted. Manganese, in quantities larger than stated, seriously reduces the magnetic susceptibility of the steel, a 12 per cent, mixture having scarcely greater suscepti- bility than air. Silicon is objectionable through facilitating the formation of blowholes, and from its hardening effect. E. Schulz, 1 in comparing two dynamos differing only in the material of the field frame and in the magnet winding, finds that the weight of a cast-steel magnet frame is about one-half of that of cast iron, and that the weight of the copper for the magnets, on account of the smaller cross-section and the greater permeability of the cast steel, is reduced to somewhat less than one-half. The price of the frame will accordingly be about ij times that of the cast-iron one, but, on account of the reduction of the copper weight, the cost of the whole ma- chine will be less for a cast-steel than for a cast-iron frame, the total weight being less than one-half in the former case. According to Professor Ewing 2 the permeability of good cast steel at low magnetic forces is less than that of wrought iron, but the reverse is the case with high forces. In a specially good sample tested by G. Kapp and Professor Ewing, a magnetic density of 18,000 lines per square centimetre { 116,000 lines per square inch) was reached, with but Httle more than one-half the magnetizing force as is necessary for the same induction in ordinary wrought iron. b. Form of Cross- Section. The best form of cross-section for a magnet-core is undoubt- edly that which possesses the smallest circumference for a given area, and this most economical section is the circle. It is, however, often preferable on account of reducing the dimen- sion of the machine perpendicular to the armature shaft, to use cores of other than circular section; in this case either rectangular, elliptical, or oval cores are employed, or several. 1 Elektrisches Echo, August II, 1894; Electrical World, vol. xxiv., p. 238 (September 8, 1894). ^Electrical Engineer, London, October 5, 1894; Electrical World, vol. ocxiv. p. 446 (October 27, 1894). 290 DYNAMO-ELECTRIC MACHINES. [75- round cores are placed side by side and connected in parallel to each other, magnetically. The latter method, however, is not recommendable for the reason that the magnetizing effects- of the neighboring coils partly neutralize each other, because of the currents of equal polarity flowing in opposite lateral directions in the parts of the coils facing each other, as indi- cated by arrows in Fig. 225. There is, consequently,, a double oo Fig. 225. Direction of Current in Parallel Magnet Cores of same Polarity.. loss connected with this arrangement, a larger expenditure of copper, connected with higher magnet resistance, and decrease of the magnetizing effects by mutual influence of the coils. Besides the forms mentioned, also square cores and hollow magnets of ring-section are frequently used. An idea of the economy of the form of cross-section to be chosen can be formed by means of the following Table LXIX., which gives the circumferences for unit area of the various forms of cross-sections employed in modern machines, and compares the same with the circumference of the most eco- nomical form, the circle. In the case of rectangular and elliptical cores, four forms each are considered, the lengths being, re- spectively, 2, 3, 4, and 8 times the width of the sections. For oval cores three sections are examined, the semicircular end portions being attached to a centre portion formed of i, 2, and: 4 adjacent squares, respectively. Next come four sections consisting of several round cores in parallel, namely, 2, 3, 4, and 8 separate circles. Of hollow cores, finally, five cases are con- sidered, the internal diameter being, respectively, i, 2, 3, 4, and 8 times the radial thickness of the cross-section. Hollow Magnets are used in some special types, such as shown in Figs. 84, 94, 95, 96, and 100, where large circumfer- ences of the cores are required but not the total area inclosed by these circumferences, and where the armature or its shaft has to pass through the centre of the magnet. As to the use of hollow magnets in place of solid ones, Profes- 75] GENERAL CONSTRUCTION RULES. 291 TABLE LXIX. CIRCUMFERENCE OF VARIOUS FORMS OF CROSS- SECTIONS OF EQUAL AREA. Form of Cross-Section Description Circumference for Unit Area Relative Circumference (Circle=1) % Circle 3.545 1 . Square 4.000 1.13 Rectangle, 1:2 4.243 1.20 1:3 4.62 1.305 wmtm 1:4 5.00 1.41 w%0m0m> 1:8 6.364 1.80 Ellipse, 1:2 3.87 1.09 1:3 4.35 1.23 1:4 ~ 1:8 4.84 6.53 1.37 1.84 Oval, lequ, 2 g;?;; 3.85 1.085 mn^ " 2 ' 2 " 4.28 1.21 wmm .. 4. ,< 2 " 5.09 1.44 @ H 2 Circles 5.01 1.41 3 " 6.14 1.73 4 " 7-09 2.00 8 " 10.03 2.83 IS Ring, 1:1 3.85 1.085 O 1 .* 1;2 4.09 1,155 O 1:3 4.43 1.25 1:4 4.76 1.34 1:8 5.91 1.67 sor Grotrian 1 states that with weak magnetizing forces o outer layers of the iron, next to the winding, are magn< 1 Elektrotechn. Zeitschr., vol. xv. p. 36 (January 18, 1894); Electrical World, vol. xxiii. p. 216 (February 17, 1894). 292 DYNAMO-ELECTRIC MACHINES. [75 E. Schulz, 1 however, showed by practical experiments that the magnetization is exactly proportional to the area of the core- section, even at the low induction due to the remanent mag- netism; from this can be concluded that Professor Grotrian's results do not apply to the case of dynamo magnets under prac- tical conditions. A. Foppl 2 claims that the theory of Professor Grotrian is correct, /'. e. , that the flux gradually penetrates the magnet from its circumference, and that under certain cir- cumstances it may not reach the centre of the core, but he admits that this theory has no practical bearing upon such magnets as are now used in practical dynamo design. * c. Ratio of Core-area to Cross-section of Armature. The relation between the cross-section of iron in the magnet cores to that of the armature core is a very important one, as on its proper adjustment depends the attainment of maximum output per pound of wire with minimum weight of iron. According to tests made at the Cornell University under the direction of Professor Dugald C. Jackson, 3 the best area of cross-section of the magnet cores for drum machines is i^ times that of least cross-section of armature, if the cores are of good wrought iron, or about 2\ times the minimum arma- ture section if cast iron cores are used. According to Table XXII., 26, the maximum core den- sity in ring armatures is from i-J. to if times that of drum armatures; for equal amounts of active wire, therefore, the former require i-J to if times as great a magnetic flux as the latter, and the cross-sections of the magnet cross, con- sequently, have to be taken correspondingly greater in case of ring machines, namely, if to 2j times the minimum armature section in case of wrought iron cores, and 3 to 4 times the arma- ture section for cast iron field magnets. Professor S. P. Thompson, in his ''Manual on Dynamo- 1 Elektrotechn. Zeitsckr., vol. xv. p. 50 (February 8, 1894); Electrical World, vol. xxiii. p. 337 (March 10, 1894). 2 Elektrotechn. Zeitschr., vol. xv. p. 206 (April 12, 1894); Electrical World, vol. xxiii. p. 680 (May 19, 1894). 3 Transactions Am. Inst of El. Eng., vol. iv. (May 18, 1887); Electrical Engineer, vol. iii. p. 221 (June, 1887). 76] GENERAL CONSTRUCTION RULES. 293 Electric Machinery," ' gives 1.25 for wrought iron and 2.3 for cast iron as the usual ratio in drum machines, and 1.66 and 3 respectively, in ring-armature dynamos. In the experiments conducted by Professor Jackson, ten different armatures, all of same length and same external diameter, but of different bores, were used in the same field, thus including a range of from .5 to 1.4 for the ratio of least armature section to core area. The curves obtained show that the total induction through the armature increased quite rapidly when the armature was increased in area from .5 of that of the magnets to about .75 of the core area. From. 75 to. 9 there is still an increase of induction with increase of armature section, though comparatively small, and beyond .9 the increase is of no practical importance. 76. Polepieces. a. Material. The polepieces, if the shape and the construction of the magnet frame permits, should be of wrought iron or cast steel, in order to reduce their size, and therefore their magnetic leak- age, they being of the highest magnetic potential of any part of the magnetic circuit. In forging, care should be taken that the " grain" or texture of the iron runs in the direction of the lines of force. The polepieces, however, ^usually have to em- brace from .7 to .8 of the armature surface (compare 15), and are, therefore, particularly in the case of bipolar machines, often comparatively large. If in such a case their cross-sec- tion, in order to give sufficient mechanical strength, is to be far in excess of the area needed for the magnetic flux, there is no gain in using wrought iron or cast steel, and the pole- pieces should be made of cast iron. The cast iron used should be as soft and free from impurities as possible. It is prefer- able, whenever practicable, to have it annealed, and, if not too large in bulk, to have it converted into malleable iron; this is especially to be recommended for small machines. An admixture of aluminum has been found to increase the permeability of the cast iron; by adding i per cent, by weight, of aluminum, the maximum carrying capacity of the 1 S. P. Thompson, " Dynamo-Electric Machinery,'' fifth edition, p. 378. 294 DYNAMO-ELECTRIC MACHINES. [76 cast iron is increased about 5 per cent.; by 3 per cent, admix- ture it is increased 7 per cent. ; and by adding 6 per cent, of aluminum, the induction increases about 9 per cent. ; above 7 per cent, of admixture the permeability decreases, and at 12 per cent, addition of aluminum the gain in magnetic conduc- tivity falls down to 7 per cent. From this it follows that an addition of from 6 to 7 per cent., by weight, of aluminum is the proper admixture for the purpose of improving the mag- netic qualities of cast iron, which is explained by the fact that the latter percentage is the limit from which up the hardening influence of the aluminum upon the cast iron becomes appre- ciable. ' In large multipolar machines combination frames consisting of wrought-iron magnet cores, cast-iron yokes, and cast-steel polepieces give excellent results, having the advantages of the high permeability and uniformity in the magnetic qualities of the wrought iron, of cheapness of the cast iron, and of re- duction in size of the cast-steel pblepieces, and being easier to machine, requiring less chipping, and being more easily fin- ished than a magnet frame made entirely of cast steel. A material which a few years ago was quite a favorite with dynamo builders, but which since has to a great extent been displaced by the cheaper cast steel, is the so-called " Mitis metal" or cast ivrought iron, obtained by melting down scrap wrought iron in crucibles, and by rendering it fluid by the addition of a small quantity of aluminum. The trouble with this material was that a great many extra precautions had to be taken to procure sound castings, and that as a rule the castings were rough and difficult to work on account of their toughness. The magnetic value of Mitis iron differs very little from that offcast steel, its permeability at the inductions used in practice being but a trifle lower than that of the latter. Edges and sharp corners are to be avoided as much as pos- sible, for if they protrude sufficiently they will act to a certain extent as poles, and give cause to a source of loss. In cast- ings thin projections are apt to chill while being cast, thus making them quite hard and destroying their magnetic quali- ties; when necessary for mechanical reasons, they should, therefore, be cast quite thick and massive, and may afterward be planed or turned down to the required size. 76] GENERAL CONSTRUCTION RULES. 295 b. Shape. The polepieces have for their object the transmission to the armature of the magnetic flux set up by the field magnet, and the establishment of a magnetic field space around the armature. The shape to be given to them must, therefore, effect the concentration of the lines of force upon the arma- ture, and not their diffusion through the air. This, in general, is achieved by making the polar surfaces as large as possible, and bringing them as near to the armature as mechanical con- siderations permit, and by reducing the' leakage areas of the free pole surfaces as much as possible. For practical rules of fixing the distance between the pole corners and the clearance between armature surface and polepieces for various kinds and sizes of armatures, see Tables LX. and LXL, 58, re- spectively. Since eddy currents are produced in all metallic masses, either by their motion through magnetic fields or by variations in the strength of electric currents flowing near them, the pole- pieces of a dynamo-electric machine are seats of such currents, which form closed circuits of comparatively low resistance, and thereby cause undue heating. These currents are strong- est where the changes in the intensity of the magnetic field or of the electric current are the greatest and the most sudden; this is the case, and consequently the eddy currents are strong- est at those corners of the polepieces from which the arma- ture is moved in its rotation, for, owing to the distortion of the magnetic field by the revolving armature, a density greater than the average is created at the corners where the armature leaves the polepieces, and a density smaller than the average at the corners where it enters. In order to reduce and eventually to avoid the generation of these eddy currents in the polepieces, as well as in the armature conductors, it is therefore necessary to prevent the crowding of the mag- netic lines toward the tips of the polepieces, and to so arrange the poles that the magnetic field does not suddenly fall off at the pole corners, but gradually decreases in strength toward the neutral zone. This object in a smooth arma- ture machine can be attained (i) by gradually increasing the air gap from the centres of the poles toward the 296 DYNAMO-ELECTRIC MACHINES. [76 neutral spaces in boring the polar faces to a diameter larger than their least diametrical distance apart, thus giving an elliptical shape to the field space, as illustrated in Fig. 226; (2) by providing wrought iron polepieces with cast iron tips form- ing the pole corners and terminating the arcs embraced by the pole faces (see Figs. 227 and 228); or (3) by establishing a magnetic shunt between two neighboring poles in connecting the polepieces, either by a cast-iron ring of small sectional FIG 226 FIG. 227 FIG. 228 FIG 229 FIG. 235 FIG. 236 FIG. 237 Figs. 226 to 237. Types of Polepieces. area (Dobrowolsky's pole-bushing] or by placing thin bridges across the neighboring pole corners, as shown in Figs. 229 and 230, respectively. The ellipsity of the field space has the advantage that it con- fines the lines of force within the sphere of the pole faces by proportionately increasing the reluctance toward the pole cor- ners, thus preventing an increase of the magnetic density at any particular portion of the polepiece. The application of cast-iron pole tips with wrought iron (or cast-steel) polepieces does not prevent the crowding of the lines at the pole corners, but, by reason of the low permeability of the cast iron, re- duces their density to a figure below that in the wrought iron, and consequently effects a graduation of the field strength near the neutral space, the maximum density being in the 76] GENERAL CONSTRUCTION RULES. 297 wrought iron at the point where the cast-iron tips are joined. In the pole bushing or its equivalent, the pole bridges, the reach of the magnetic field is greatly increased, the percentage of the polar arc being practically 100, and also a more or less gradual decrease of the field strength at the neutral point is obtained, but the length of the non-sparking space is greatly reduced and thereby its uncertainty increased, thus making the proper setting of the brushes a very difficult operation. It has also been recommended to laminate both the polepieces and the magnet cores in the direction parallel to the armature shaft, in order to prevent the production of eddy currents, but this can only be applied to small dynamos, as the additional cost connected with such a lamination in large machines would be in no proportion to the small gain obtained. Besides, there is another reason against lamination : a laminated magnet frame is very sensitive to the fluctuations in the load of the machine, which naturally react upon the magnetic field, and in following these fluctuations an unsteady magnetization is pro- duced, which, in turn, again tends to increase the fluctuations causing its variability; while in a solid magnet frame the eddy currents induced by the changes of magnetization caused by the fluctuations of the load tend to counteract the very changes producing them, and therefore exercise a steadying influence upon the field, thus reducing the fluctuations in the external circuit of the machine. An expedient sometimes used instead of laminating the pole- pieces is to cut narrow longitudinal slots in the polepieces, Fig. 231, thus laminating a portion of the polepieces only. These slots at the same time serve to increase the length of the path traversed by the lines of force set up by the action of the armature current, and to thus reduce the armature reaction upon the magnetic field, checking the sparking connected therewith. When the commutator brushes, after having short-circuited an armature coil, break this short circuit, the sudden reversal of the current in the same, produced in passing the neutral line of the field, together with the self-induction set up by the extra current on breaking, causes a spark to appear at the brushes, which maybe considerable, since in the comparatively low resistance of the short-circuited coil a small electromotive- 298 DYNAMO-ELECTRIC MACHINES. [76 force is sufficient to produce a heavy current. If a dynamo, therefore, is otherwise well designed, that is, if the armature is subdivided into a sufficient number of sections, if the field is strong enough so as not to be overpowered by the armature, and if the thickness of the brushes is so chosen as to not short- circuit more than one or two armature sections each simulta- neously, and as not to leave one commutator-bar before making connection with the next strip, then the sparking at the com- mutator can be reduced to a practically unappreciable degree by so shaping the pole surfaces as to give a suitable fringe of magnetic field of graduated intensity, thus not only causing the current in the short-circuited coils to die out by degrees, but also compelling the coils to enter the field of opposite polarity gradually. This is achieved by giving the pole corners an oblique, or a double conichl, or a hyperbolical form, as illus- trated by top views in Figs. 232, 233, and 234, respectively. For the purpose of counteracting the magnetic pull due to the armature thrust in bipolar machines, see 42, the pole- pieces are often mounted eccentrically ', leaving a smaller gap- space at the side averted from the field coils than at the side toward the same, Fig. 235, or in case of wrought-iron or steel polepieces, cast-iron pole tips are used at the side toward the exciting coils, and wrought-iron or steel tips at the other, Fig. 236. Both the eccentricity of the pole faces and the cast-iron pole tips, if suitably dimensioned, have the effect of increasing the reluctance of the stronger side of the field in the same propor- tion as the density rises on account of the dissymmetry of the field, thus making the product of density and permeance the same in both halves. In a very instructive paper, entitled "On the Relation of the Air Gap and the Shape of the Poles to the Performance of Dynamo-electric Machinery," Professor Harris J. Ryan 1 has demonstrated the importance of making the polepieces of such shape that saturation at the pole corners cannot occur even at full load; for, the armature ampere turns cannot change the total magnetization established by the field when the pole cor- ners are unsaturated. He further proved by experiment that for a sparkless operation at all loads of a constant current 1 Transactions A. I. E. ., vol. viii. p. 451 (September 22, 1891); Electrical World, vol. xviii. p. 252 (October 3, 1891). 77] GENERAL CONSTRUCTION RULES. 299 generator, it is necessary that the air gap be made of such a depth that the ampere turns required to set up the magnetiza- tion through the armature without current, and for the produc- tion of the maximum E. M. F. of the machine, shall be a little more than the ampere turns of the armature when it furnishes its normal current. As long as the brushes were kept under the pole faces the non-sparking point was wherever the brushes were placed, no matter whether the armature core was satu- rated or not. In order to enable currents to be taken from a machine at various voltages, Rankine Kennedy 1 has proposed to subdivide the pole faces by deep, wide slots parallel to the armature shaft, Fig. 237, thus providing a number of neutral points on the commutator, at which brushes may be placed without sparking. If, for instance, there are two such grooves in each polepiece, the total voltage of the machine is divided into three equal parts, and by employing an intermediate brush at one of the additional neutral spaces, two circuits can be sup- plied by the machine, one each between the intermediate brush and one of the main brushes, one having two-thirds and the other one-third of the total voltage furnished by the dynamo. 77. Base. The base is the only part of the machine where weight is not only not objectionable but very beneficial, and it should there- fore be a heavy iron casting, especially as the extra cost of plain cast iron is insignificant as compared with the entire cost of the machine. A heavy base brings the centre of gravity low, and consequently gives great stability and strength to the whole machine. Besides this mechanical argument in favor of a massive cast- ing, there is a magnetical reason which applies to all types in which the base constitutes a part of the magnetic circuit, as is the case in the inverted horseshoe type, Fig. 188, in the ver- tical single-magnet type, Fig. 193, in the inclined and vertical double-magnet types, Figs. 198 and 199, respectively, in the iron-clad types, Figs. 203, 205, 206, 207, 218, and 219, respec- tively, and in the vertical quadruple magnet machine, Fig. 224. 1 English Patent No. 1640, issued April 4, 1892. 300 DYNAMO-ELECTRIC MACHINES. [ 7& In these and similar types a heavy base of consequent high permeance reduces the reluctance of the entire magnetic cir- cuit, and effects a saving in exciting power which usually is sufficient to repay the extra expense involved, and often even reduces the total cost of the machine. If the base forms a part of the magnetic circuit of the ma- chine, constituting either the yoke or one of the polepieces, its least cross-section perpendicular to the flow of the mag- netic lines should be dimensioned by the rules given for cast- iron magnets that is, it should be at least i| to 2 times the area of the magnet cores, if the latter are of wrought iron or cast steel, and .at least of equal area if they are of the same material as the base, /. tne tangential multipolar type, Fig. 210, etc., the magnet frame rests upon two polepieces of opposite polarity, and if these were joined by the iron base, the latter would con- stitute a stray path of very much lower reluctance than the useful path through air gaps and armature, and the lines of force emanating from these two polepieces would thus be shunted away from the armature, instead of forming a mag- netic field for the conductors. In order to prevent such a short-circuiting of the magnetic lines it is necessary either to use material different from iron for the base, or to interpose blocks of a non-magnetic substance between the polepieces and the bed-plate. The former method can be applied to small machines only, and in this case the magnet frame is mounted upon a base of either wood or brass. For large ma- chines a wooden base would be too weak and too light, and a brass one too expensive, and resort has to be taken to the second method of interposing a non-magnetic block, zinc being most usually employed. These zinc blocks must be of the necessary strength, not only to carry the weight of the frame, but also to withstand the tremor of the machine, and must be made high enough to introduce a sufficient amount of reluc- tance into the path of leakage through the base. The reluctance 78] GENERAL CONSTRUCTION RULES. 301 required in that path must be at least four times, and preferably should be up to ten or twelve times that of the air gaps; that is, its relative permeance calculated from formula (161), 62, according to the size of the machine, should range between |- and -J^ of the relative permeance of the air gaps, as found from formula (167) or (168), 64, the amount of leakage through the iron base being thereby limited to 25 per cent, of the useful flux in small dynamos, and to 8 per cent, in the largest machines. This condition is fulfilled if the height of the zinc blocks, .according to the kind and the size of the machine, is from three to fifteen times greater than the radial length of the gap-space. The following Tables, LXX., LXXI., and LXXII., give the value of this ratio, the consequent height of the zinc blocks, and the corresponding approximate leakage through the base for high-speed dynamos with smooth-core drum armatures, for high-speed dynamos with smooth-core ring armatures, and for low-speed machines with toothed and perforated armatures, respectively: TABLE LXX. HEIGHT OF Zrxc BLOCKS FOR HIGH-SPEED DYNAMOS WITH SMOOTH-CORE DRUM ARMATURES. O> 2 . M 5^ S^o.^ 'g^.c's la c ^l S^iS Lj <5g^ 3 1 3F .3" .03" .045 .375" 5 11" 25^ 2 3| .325 .03 .045 .4 5 2 25 3 44 .35 .03 .045 .425 5^ H 25 5 .375 .03 .045 .45 54 24 20 10 6 .4 .04 .06 .5 54 2f 20 15 6J .425 .04 .06 .525 6 18 20 74 .45 .04 .06 .55 6* 34 18 25 81 .475 .04 .06 .575 7 4 16 30 9 .5 .05 .075 .625 7i 44 16 50 104 .525 .05 .075 .65 7| 5 15 75 124 .55 .06 .09 .7 84 6 14 100 15 .6 .06 .09 .75 0i 14 150 184 .65 .065 .125 .84 9 74 12 200 224 .7 .07 .16 .93 9f 9 10 300 28 .8 .07 .19 L06 11 10 302 D YNAMO-ELECTRIC MA CHINES. TABLE LXXI. HEIGHT OF ZINC BLOCKS FOR HIGH-SPEED DYNAMOS WITH SMOOTH-CORE RING ARMATURES. CAPACITY IN KILOWATTS. Diameter of Armature Core (from Table XI.) 1 S3* i s| fl SB Radial Clearance (from Table LXII.) Radial Length of Gap-Space. Inch. Ratio of Height of Zinc Block to Length of Gap-Space. pi M JL 53 S s 5 o Approximate Leakage through IBnse in p. c. of UsefuJFlux. 1 2 7" v8 .25" .25 Toir~ .03 .045" .045 .325" .325 8 9 ~zV~ 3 15* 14 3 94 .275 .04 .06 .375 94 3 14 5 11 .3 .04 .06 .4 10 4 12 10 14 .325 .05 .075 .45 11 5 12 15 15 .325 .05 .075 .45 11 5 12 20 16 .35 .06 .09 5 12 6 10 25 18 .35 .06 .09 .5 12 6 10 30 20 .375 .07 .13 .575 12 7 10 50 24 .4 .07 .13 .6 18* 8 9- 75 28 .425 .07 .155 .65 144 94 9 100 32 .45 .07 .155 .675 154 104 8 150 36 .475 .07 .18 .725 16 114 8 TABLE LXXIL HEIGHT OF ZINC BLOCKS FOR LOW-SPEED DYNAMOS WITH TOOTHED AND PERFORATED ARMATURE. 7 CAPACITY IN KILOWATTS. Diameter of Armature Core (from Table XII.) Height of Winding Space (from Table XVIII.) Radial Clearance (from Table LXI.) Maximum Radial Length of Gap-Space. Inch. Ratio of Height of Zinc Block to Maximum Length of Gap-Space Height of Zinc Blocks. Inches. !'! a^d&H t-3 'S 2 12" 14" A" 1- 1 " 3 34" 15^ 3 15 TV 1 r? 3 4 15 5 10 17 21 1! % 1- 1 & 34 3f 5 6 12 12 15 23 H 4 6f 10 20 25 IT & 1^ f 4i 74 10 25 27 If A 1^ 4 4| 8 10 30 80 HI 1J 1 44 8| 8 50 36 If i 2 4f 94 8 From the comparison of the above Tables LXX., LXXI. and LXXIL, it follows that the height of the zinc blocks increases in a nearly direct proportion with the diameter of the armature 79] GENERAL CONSTRUCTION RULES. core, and that, for the same armature diameter, a smooth- drum machine requires a higher, and a toothed or perforated armature machine a lower zinc than a smooth-ring dynamo. By compiling the results of Tables LXX., LXXL, and LXXII.,, the following Table, LXXIIL, is obtained, from which it can be seen that the heights of zinc blocks for smooth-ring machines, are from 18 to 30 per cent, less than for smooth-drum dyna- mos, and those for machines with toothed and perforated armatures are from n to 20 percent, less than for smooth-ring armature dynamos: TABLE LXXIIL COMPARISON OF ZINC BLOCKS FOR DYNAMOS WITH VARIOUS KINDS OF ARMATURE. HEIGHT OF ZINC BLOCKS. DIAMETER OP Smooth Armature. Toothed ARMATURE CORE. or Perforated Drum. Ring. Armature. Inches. Inches. Inches. Inches. 3 If 4 2 , 6 2| 2 U 8 4 3 2* 10 5 3* 3 12 5f 4* 3i 15 6* 5 4 18 7i 6 5 21 8f 7 6 24 H 8 7 27 11 9 8 30 . . 10 8| 36 11* 94 79. Pedestals and Bearings. In the design of the base, especially when the portion of the field frame above the armature centre cannot be lifted off, care should be taken that the armature can easily be withdrawn longitudinally by removing one of the bearing pedestals, which, therefore, should be a separate casting. In machines where the lowest point of the armature periphery is at a con- siderable height above the base, as for instance in dynamos of 304 DYNAMO-ELECTRIC MACHINES. [79 the overtypes, Figs. 188, 191, 198, and 206, respectively, fur- ther of the vertical double types, Figs. 197, 202, 207, 219, and 224, respectively, and of the radial and tangential outerpole types, Figs. 208 and 210, respectively, it is preferable that the pedestals should be made of two parts, the upper part, which should have a depth from the shaft centre a little in excess of the radius of the finished armature, being removable, while the lower portion, which may be cast in one with the base, will form a convenient resting place for the armature in removal. In most cases this problem of making high pedestals of two parts can practically be solved by boring out the pedestal seats together with the polepieces, thus providing a cylindrical seat for the pillow blocks, as shown in Fig. 238. This design is particularly advantageous also for machines in which the base forms one of the polepieces, as for example, the forms shown in Figs. 193, 199 and 219, as in this case, outside of the finish- ing of the core seats, this boring to a uniform radius is the only tooling necessary for the base. If the field frame is symmetrical with reference to the hori- zontal plane through the armature centre, the frame of the machine is usually made in halves, and the armature, in case of repair, can be removed by lifting it from its bed without disturbing the bearing pedestals. The bearing boxes must for this purpose be made divided so that all parts of the machine above the shaft centre are removable. This design affords the further advantage that the bearing caps can be taken off at anytime and the bearings inspected, and it has for this reason become a general practice in dynamo design to employ split bearings, even for types in which the armature cannot be lifted. It is, further, of great importance that the bearing should not only be exactly concentric, but that they also should be accurately in line with each other; for large machines it is therefore advisable to effect automatic alignment by providing the bearings with spherical seats. This can be attained either by giving the enlarged central portion of the shell a spherical shape, Fig. 239, or in providing the bottom part of the box with a spherical extension fitting into a spherical recess in the pedestal, Fig. 240. In order to prevent heating of the bearings, the shells in modern dynamos are usually furnished with some automatic 80] GENERAL CONSTRUCTION RULES. 35 oiling device, the most common form of which, shown in Fig. 241, consists of a brass ring or chain dipping into the oil chamber of the box and resting upon and turning with the shaft, thereby causing a continuous supply of oil at the top of the shaft. A further improvement of this self-oiling arrange- ment, patented in 1888 by the Edison General Electric Com- pany, is illustrated in Fig. 242. In this the interior of the FIG. 238 FIG. 239 FIG. 240 FIG. 242 Figs. 238 to 242. Pedestals and Bearings. shell is provided with spiral grooves filled with soft metal and forming channels for conveying oil from each end of the bear- ing to a circumferential groove which surrounds the shaft at the centre of the shell, and which communicates with the oil chamber beneath the bearing. These grooves not only effect a steady supply, but a continuous circulation of oil, the latter being lifted from the reservoir into the shell by the oiling rings, thence forced by the spiral channels into the central groove, from where it flows back into the oil chamber. 80. Joints in Field Magnet Frame. a. Joints in Frames of One Material. Magnet frames consisting of but one material may either be formed of one single piece or may be composed of several parts. If the frame is of cast iron or cast steel, in small 306 DYNAMO-ELECTRIC MACHINES. [ 8O dynamos usually the former is the case, /. e., the whole frame is cast in one, while in large machines it generally consists of two castings; if, however, wrought iron is used, it is, as a rule, much more convenient to forge each part separately and to build up the frame by butt-jointing the parts. In so joint- ing a magnet frame, it is of the utmost importance to accu- rately adjust and finish the surfaces to be united, so as to make the joint as perfect as possible, for every poorly fitted joint, by reduction of the sectional area at that point, introduces a considerable reluctance in the magnetic circuit. If, however, the contact between the two surfaces is as good as planing and scraping can make it, a practically perfect joint is obtained, and the additional reluctance, which then only depends upon the degree of magnetization, is entirely inappreciable for such high magnetic densities as are employed in modern dynamos. Experiments have shown that at low densities the additional' magnetomotive force required to overcome the reluctance of a joint is very much greater, comparatively, than at high in- ductions, which is undoubtedly due to the pressure created by the magnetic attraction of the two surfaces across the joint, this pressure being proportional to the square of the density. The following Table LXXIV. shows the influence of the den- sity of magnetization upon the effect of a well-fitted joint in a wrought iron magnet frame, the induction in the iron ranging from 10,000 to 120,000 lines per square inch, and indicates that the reluctance of the joint becomes the less significant the nearer saturation of the iron is approached. At a magnetic density of ($>" m = 10,000 lines of force per square inch, each joint in the circuit is equivalent to an air space of .0016 inch, or has a reluctance equal to that of an additional length of 3 inches of wrought iron; at <&" m 100,000 lines per square inch, the thickness of an equivalent air space is only .00065 inch, which corresponds to the reluctance of .22 inch of wrought iron at that density; and at or above (B* m = 120,000, finally, a good joint is found to have no effect whatever upon the reluctance of the circuit. b. Joints in Combination Frames. For magnet frames consisting of two or three different mate- rials the same rule as for frames of one material holds good as 80] GENERAL CONSTRUCTION RULES. 307 to the nature of the joint, but since the ordinary butt-jointing would limit the capacity of the joint to that of the inferior magnetic material, it is essential in the case of combination frames to increase the area of contact in the proportion of the relative permeabilities of the two materials joined. Thus, if wrought and cast iron are butt-jointed, the capacity of the joint is reduced to that of the cast iron, whereby the advantage of the high permeability of the wrought iron is destroyed and the permeance of the circuit is considerably increased; and in order to have the full benefit of the wrought iron, the contact area of the joint must be increased proportionally to the ratio of the permeability of the wrought iron to that of the cast iron at the particular density employed. TABLE LXXIV. INFLUENCE OP MAGNETIC DENSITY UPON THE EFFECT OF JOINTS IN WROUGHT IRON. PRESSURE ON JOINT MAGNETIZING FORCE REQUIRED FOR 1 INCH. DIFFER- EQUIVALENT OF JOINT DENSITY or MAGNET- IZATION. DUE TO MAGNETIC ATTRAC- ENCE DUE TO JOINT, Air Space, Length of Iron, (ft" TION. /D// 2 Solid. Jointed. OC OC oe Lines per sq. in. JC, Amp. turns. Amp. turns. ae.-oe, Amp. turns. 3C Inch. 72,134,000 IDS. .3133X(B" m Inch. per. sq. in. 10,000 1.4 1.7 6.7 5 .0016 3.0 20.000 5.5 3.2 12.6 9.4 .00155 2.9 30,000 125 5 19.1 14.1 .0015 2.8 40,000 22 7 25.2 18.2 .00145 2.6 50,000 35 9.5 31.4 21.9 .0014 2.3 60,000 50 12.7 38.1 25.4 .00135 2.0 70,000 68 18.3 45.7 27.4 .00125 1.5 80,000 89 27.6 55.2 27.6 .0011 1.0 90,000 112 508 76.2 25.4 .0009 0.5 95,000 125 68 91.8 23.8 .0008 .35 100,000 139 90 110 20 .00065 .22 105,000 153 134 150 16 .0005 .12 110,000 168 288 300 12 .00035 .04 112,500 176 391 400 9 .00025 .023 115,000 183 500 506 6 .00016 .012 117,500 192 600 603 3 .00008 .005 120,000 200 700 700 .00000 .000 For a density in wrought iron of 100,000 lines of force per square inch, for example, a magnetomotive force of 90 ampere- turns is required per inch length of the circuit, and the same 3 o8 DYNAMO-ELECTRIC MACHINES. [80 specific magnetomotive force is capable of setting up about 40,000 lines per square inch in cast iron; the contact area of a joint between wrought iron and cast iron in this case must therefore be increased in the ratio of 100,000 : 40,000, or must be made 2\ times the cross-section of the wrought iron in order to reduce the permeability of the joint to that of the wrought iron. In practice this problem of providing a sufficiently large con- tact area between a wrought and a cast iron part of the mag- FiQ.243 FiQ.244 Fl3. 245 FIQ. 246 FiQ. 247 FIG 248 FIQ. 249 FIQ 250 Figs. 243 to 250. Joints in Magnetic Circuits. netic circuit may be solved either by setting the wrought iron into the cast iron, or by extending the surface of the wrought iron part near the joint by means of flanges; or, finally, by in- serting an intermediate wrought-iron plate into the joint. In Figs. 243, 244, 245 and 246 are shown four methods of increasing the area of the joint by means of projecting the wrought-iron core into the cast-iron yoke or polepiece, differing only in the manner of securing a good contact between the parts, the first one employing a set-screw, the second one a wrought-iron nut, and the third one using a conical fit with draw-screw for this purpose, while in the fourth one the threaded projection of the core itself forms the tightening screw. Fig. 247 illustrates a modification of the method shown in Fig. 246, a separate screw- stud being used instead of the threaded extension of the wrought-iron core. In case of rectangular magnet cores the arrangement shown by plan in Fig. 248 effects an excellent 80] GENERAL CONSTRUCTION RULES. 309 joint; in this the cores are inserted into the base from the sides, thus offering three surfaces to form the contact area. The manner of supplying the necessary joint surface by flanged ex- tensions of the wrought-iron core is illustrated in Fig. 249, which shows the method of fastening employed in large multi- polar machines, feather-keys being used to secure exact rela- tive position of the cores. In Fig. 250, finally, a joint is shown in which a wrought-iron contact plate is inserted between the wrought-iron core and the cast-iron yoke or polepiece with the object of increasing the area of the joint and of spreading the lines of force gradually from the smaller area of the wrought iron to the larger of the cast iron. CHAPTER XVI. CALCULATION OF FIELD MAGNET FRAME. 81. Permeability of the Yarious Kinds of Iron, Ab- solute and Practical Limits of Magnetization. The field magnet of a dynamo has the function of supplying to the-interpolar space in which the armature conductors revolve magnetic lines of force in a number sufficient either to cause the generation of the required electromotive force, in case of a generator, or to produce a motion of the desired power, in case of a motor. The cross-sections of the various parts of the field magnet frame, that is, of the iron structure consti- tuting the path or paths, for the flow of these magnetic lines, consequently, must be dimensioned with reference to the num- ber of lines of force to be carried, and to the magnetic con- ductivity of the material used. The number of lines which by a certain exciting power or magnetomotive force can be passed through a portion of a magnetic circuit depends upon the area of the cross-section and on the magnetic conductivity of the material of that part of the circuit. The various magnetic materials, according to their hardness, have a different capability of conducting magnetic lines, the softest material being the best magnetic conductor. The specific magnetic conductance of air being taken as unity, the relative magnetic conductance, or the rela- tive permeance, of the various magnetic materials is indicated by the ratio of the number of lines of force produced in unit cross-section of these materials to the number of lines set up by the same magnetizing force in unit cross-sections of air. This ratio, or coefficient of magnetic induction, is called the magnetic conductivity, or \k& permeability of the material. The number of lines per square centimetre of sectional area set up by a certain magnetizing force in air is conventionally designated by X, that in iron by (B, and the permeability by 81] CALCULATION OF FIELD MAGNET FRAME, the symbol jj, ; between these three quantities, therefore, exists the relation /n = -, or (B = X (215) Since for air the permeability p = i, the number of lines of force per square centimetre of air is numerically equal to the magnetizing force in magnetic measure, /'. ^., in current-turns. Permeability is therefore often also defined as the ratio of the magnetization produced to the magnetizing force producing it. TABLE LXXV. PERMEABILITY OP DIFFERENT KINDS OF IRON AT VAR- IOUS MAGNETIZATIONS. DENSITY OP MAGNETIZATION. PERMEABILITY, /* Lines per sq. inch , for dynamos of various kinds and sizes is obtained, and, then by applying formulae (217) to (221), the sectional areas of the field frame for various kinds and sizes of machines can be found. In this manner the following Tables LXXVIL, LXXVIIL, andLXXIX,, have been prepared, which give the cross-sections of field magnet frames of different materials for high-speed drum machines, high-speed ring dynamos, and low speed ring machines, respectively. The figures given for the areas directly apply to single circuit bipolar dynamos only; for double circuit bipolar, and for multipolar machines they represent the total cross-section of all the magnetic circuits in parallel, or for frames of only one material, the total area of all the cores of same free polarity, the cross-sections of the various portions of the field magnet frame are therefore obtained in dividing these figures by the number of magnetic circuits, /. e., by the number of pairs of magnet poles: 82] CALCULATION OF FIELD MAGNET FRAME. 315 TABLE LXXVII. SECTIONAL AREA OF FIELD MAGNET FRAME FOR HIGH-SPEED DRUM DYNAMOS. >. AREA OF FIELD MAGNET FRAME. Capacity in Kilowatts. iductor Veloc (Table X). 't. per second Average Useful Flux. Table LXIV. Lines of force. Av'age Leak'ge Coeffi- cient. Table LXVIII Average total flux, *'. Lines of force. Wr'ght Iron, Sm *' Cast Steel, Sm *' Mitis Iron, Sm $/ Cast Iron, 6.5*; Al. Sm & Cast Iron, ordin'y Sm 4>' ~ 90,000 85,000 ~ 80,000 45,000 40,000 sq. in. sq. in. q. in. sq. in. sq. in. .1 25 200,000 2.00 400,000 4.5 4.7 5 9 10 .25 30 333,000 1.90 630,000 7 7.4 7.9 14 15.8 .5 32 550,000 1.80 990,000 11 11.7 12.4 22 24.8 1 34 880,000 1.75 1,640,00) 17.1 18.1 19.3 34.2 38.6 2 36 1,530,000 1.70 2,600,000 289 30.( 32.5 57.8 65 3 40 1,875,000 1.65 3,100,000 34.5 36.5 38.8 69 77.6 5 45 2,550,000 1.60 4,080,000 45.5 48 51 91 102 10 50 4.000,000 1.55 6,200,000 69 73 77.5 138 155 15 50 5,700,000 1.50 8,550,000 95 101 107 190 214 20 50 7.200,000 1.45 10,400 000 115.5 122 130 231 260 25 50 8,500.000 1.40 11,900,000 132 140 149 264 298 30 50 9,900,000 1.40 13,850.000 154 163 173 308 346 50 50 15,500,000 1.35 20,900,000 232 246 261 464 522 75 50 22,000,000 1.35 29,700,000 330 350 371 660 742 100 50 28,000,000 1.30 36,400.000 405 430 455 810 910 150 50 39,500,000 1.30 51,400,000 572 605 643 1,144 1,286 200 50 50.000,000 125 62,500.000 695 735 782 1,390 1,564 300 50 70000,000 1.20 84,000.000 933 990 1,050 1,866 2,100 TABLE LXXVIII. SECTIONAL AREA OF FIELD MAGNET FRAME FOR HIGH-SPEED RING DYNAMOS. >, AREA OF FIELD MAGNET FRAME. Capacity in Kilowatts. iductor Veloc (Table XI). 't. per second Average Useful Flux. (Table LXIV.) Lines of force. Av'age Leak'ge Coeffi- cient. Table LXVIII Average Total Flux, V. Lines of force. Wr'ght Iron, Sm *' Cast Steel, Sm $/ Mitis Iron, Sm <&' Cast Iron, 6.5* Al. Sm _ *' Cast Iron, ordin'y Sm V 1 90,000 85,000 80,000 ~ 45,000 40,000 sq. in. sq. in. eq. in. sq. in. sq. in. .1 50 100,000 1.80 180.000 2 2.1 2.2 4 4.5 .25 55 182,000 1.70 310.000 3.5 3.7 3.9 7 7.8 .5 60 292,000 1.60 467,000 5.2 5.5 5.8 10.4 11.6 1. 65 462.000 1.55 715,000 8 8.4 8.9 16 17.8 2.5 70 930,000 1.50 1,400,000 15.5 16.5 175 31 35 5 75 1.500,000 1.45 2,180,000 24.2 25.6 27.3 48.4 54.5 10 80 2,500,000 1.40 3,500,000 39 41.2 43.8 78 87.5 25 80 5,320,000 1.35 7,200,000 80 &5 90 160 180 50 85 9,120,000 1.30 11,900,000 132 140 149 264 298 75 85 13,000,000 1.26 16,250,000 180 191 203 360 406 100 85 16,500,000 1.22 20,100,000 224 236 251 448 502 200 88 28,400,000 1.20 34,000,000 378 400 425 756 850 300 90 39,000,000 1.18 46,000,000 512 542 575 1,024 1,150 400 92 47,800,000 1.18 56,500,000 628 665 707 1,256 1,415 600 95 62,000,000 1.17 72,500,000 806 855 905 1,612 1,810 800 95 74,200,000 1.17 87,000,000 967 1,025 1,085 1,935 2,170 1,000 95 84.200,000 1.16 97,700,000 1,085 1,150 1,240 2,170 2,480 1,500 100 97,500,000 1.16 113,000,000 1,255 1,330 1,410 2,510 2,820 2,000 100 110,000,000 1.15 126,500,000 1,400 1,490 1,580 2,800 3,160 3,6 D YNA MO-ELECTRIC MA CHINES. [83 TABLE LXXIX. SECTIONAL AREA OF FIELD MAGNET FRAME FOR LOW- SPEED RING DYNAMOS. >* AREA OP FIELD MAGNET FRAME. Capacity in Kilowatts. ductor Veloc :Table XII.) t. per second Average Useful Flux. (Table LXIV.) Liius of Av'age Leak'ge Coeffi- cient. Table LXVIII Average Total Flux. *'. Lines of force. Wr'ght Iron, Sm $' Cast Steel, Sin 4>' Mitis Iron, Sm *' Cast Iron, 6.5# Al. Sm $' Cast Iron, ordin'y Sm *' g * 90,000 85,000 80,000 45,000 40.000 sq. in. sq. in. sq. in. eq. in. sq. in. .5 25 2,600,000 .50 3,900,000 43.3 46 48.7 86.6 97.5 5 26 4,420,000 .45 6,400,000 71.2 75.3 80 142.4 160 10 28 7,150,000 .40 10,000,000 111 117.5 125 822 S50 25 30 14,200.000 .35 19,200,000 213.5 226 240 417 480 50 32 24,200,000 .30 31,500,000 350 360 394 700 788 75 33 33,500,000 .25 42,000,000 467 495 525 934 1,050 100 35 40,000,000 .22 48,800,000 543 575 610 1,086 1.220 200 40 62,500,000 .20 75,000,000 833 883 938 1,666 1,875 300 42 83,300,000 .18 98,500,000 1,095 1,160 1,230 2,190 2,460 400 44 100,000,000 .18 118,000,000 1,310 1,390 1,475 2,620 2,950 600 45 131,000,000 .17 153,500,000 1,725 1,810 1,940 3,450 3,880 800 45 157,000,000 .17 184,000,000 2,050 2,165 2,300 4,100 4,600 1,000 45 178,000.000 .16 206,500,000 2,300 2,430 2,580 4,600 5,160 1,500 45 217,000,000 .16 252,000,000 2,800 2,970 3,150 5,600 6,300 2,000 45 245,000,000 1.15 282,000,000 3,140 3,320 3,525 6,280 7,050 For cases of practical design, in which the fundamental con- ditions materially differ from those forming the base for the above tables, the areas obtained by formula (216) may also widely vary from the figures given, but, by proper considera- tion, these tables will answer even for such a case, and will be found useful for comparing the results of calculations. 83. Dimensioning of Magnet Cores. The sectional area of the magnet cores being found by means of the formulae and tables given in 82, their length and their relative position must be determined. a. Length of Magnet Cores. In the majority of types the length of the magnet cores has a more or less fixed relation to the dimensions of the armature, and definite rules can only be laid down for such cases where the length of the magnets is not already limited by the selec- tion of the type. Two points have to be considered in dimensioning the length of the magnets. The longer the cores are made, the less height will be taken up by the magnet winding; the mean length of a convolution of the magnet wire, and, consequently, the total length of wire required for a certain magnetomotive force will, therefore, be smaller the greater the length of the 83] CALCULATION OF FIELD MAGNET FRAME. 317 core. On the other hand, the shorter the cores are chosen the shorter will be the magnetic circuit of the machine, and, in consequence, the less magnetomotive force will be required to set up the necessary magnetic flux. Of these two considerations economy of copper at the ex- pense of additional iron on the one hand, and saving in mag- netomotive force and in weight of iron on the other the latter predominates over the former, from which fact follows the general rule to make the cores as short as is possible without increasing the height of the winding space to an undue amount. In order to enable the proper carrying out of this rule, the author has compiled the following Table LXXX., which gives practical values of the height of the winding space for magnets of various types, shapes and sizes: TABLE LXXX. HEIGHT OF WINDING SPACE FOR DYNAMO MAGNETS. BIPOLAR TYPES. MULTIPOLAR TYPES. SIZE OP CORE. Cylindrical Cores. Rectangular or Oval Cores. Cylindrical Cores. Rectangular or Oval Cores. M 2 . Tc SJD IJ i M! =' 8 ?J jj lag Diameter of Circular Cross-Section. Area of Rectangular or Oval Section. .3 02 3*2 a | i Ratio of Winding Heij to Diameter of < a QQ hj =3 1 i Ratio of Winding to Diam. of EC Circular Secti Height of Winding Spa Ratio of Winding Hei< to Diameter of Ihs! w 1 Ratio of Winding to Diam. of Ei Circular Secti Ins. cm. Sq. ins. Sq. cm. Inch. Inch. Inch. Inch. 1 2.5 .8 4 9 L .50 Q/ .75 2 5.1 3.1 20.4 1 .375 'i" .50 \y. .625 1*^ .75 3 7.6 7.1 45.4 1 .33 1J4 .42 1% .58 2 .67 4 10.2 12.6 81.7 ; J1X .31 l*i? .38 2 .50 2*^ .625 6 15.3 28.3 184 1*1 .25 2 .33 2*4 .375 24 .46 8 20.3 50.3 324 1% .22 2**> .31 2*12 .31 3 .375 10 25.5 78.5 511 m .19 2% .275 2% .28 3*4 .33 12 30.5 113.1 731 2 .17 3 .25 3 .25 31^ .29 15 38.1 176.7 1140 2*6 .14 3J4 .22 3/4 .22 3M .25 18 45.7 254.5 1640 2*4 .125 3/4 .20 3*4 .20 4 .22 21 53.3 346 2231 2% .113 3% .18 3?| .18 4/4 .215 24 61. 452 2922 2*i> .104 4 .17 4 .17 5 .21 27 68.6 573 3696 2% .097 .16 4*4 .16 5*^ .205 30 762 707 4560 2% .092 4*f .15 4*1 .15 6 .20 33 83.8 855 5515 2% .087 5 .15 4M .145 6J4 .197 36 91.5 1018 6576 3 .083 5* .15 5 .14 7 .195 318 DYNAMO-ELECTRIC MACHINES. [83 In bipolar machines, such as the various horseshoe types, in which the length of the magnet cores is not limited by the form of the field magnet frame, the radial height of the magnet winding in case of cylindrical magnets varies from one-half to- one-twelfth the core diameter, according to the size of the magnets, and in case of rectangular or oval magnets, is made from .5 to .15 of the diameter of the equivalent circular cross- section. For multipolar types, in which the length of the mag- rrets is of a comparatively much greater influence upon size and weight of the machine, it is customary to set the limit of the winding height considerably higher, in order to reduce the length necessary for the magnet winding. For cylindrical mag- nets to be used in multipolar machines, therefore, the prac- tical limit of winding height ranges from .75 to .14 of the core diameter, and for rectangular or oval magnets, from .75 to .195 of the diameter of the equivalent circular area, according to the size. In case of emergency the figures given for rectangular cores may be used in calculating circular magnets, or those given for multipolar types may be employed for bipolar machines. In order to keep the winding heights within the limits given in Table LXXX. the lengths of. cylindrical magnets have to be made from 3 to i times the core diameter for bipolar types, and from i to \ the core diameter for multipolar types; those of rec- tangular magnets from i| to f the equivalent diameter for bipolar types, and from i to f the equivalent diameter for multipolar types; and the lengths of oval magnets, finally, from i| to I the diameter of the equivalent circular area for bipolar types, and from i| to -f the equivalent diameter for multipolar types. In the following Tables LXXXI., LXXXII., LXXXIIL, and LXXXIV., the dimensions of cylindrical magnet cores for bipolar types, of cylindrical magnet cores for multipolar types, of rectangular magnet cores, and of oval magnet cores, respec- tively, have been calculated. In the former two of these tables the lengths and corresponding ratios are given for cast- iron as well as for wrought-iron and cast-steel cores ; in the latter two for wrought iron and cast steel only. From Tables LXXXI. and LXXXII. it follows that cast-iron cores are made from 20 to 10 per cent, longer, according to the size, than wrought-iron 83] CALCULA 7702V OF FIELD MAGNET FRAME. 3 T 9 or cast-steel ones of the same diameter, the lengths of cast-iron cores of rectangular or oval cross-section can therefore be easily deduced from the figures given in Tables LXXXIII. and LXXXIV. TABLE LXXXI. DIMENSIONS OF .CYLINDRICAL MAGNET CORES FOR BIPOLAR TYPES. DIMENSIONS OF MAGNET CORES, IN INCHES. TOTAL FLUX, Wrought Iron and Cast Steel. Cast Iron. IN WEBEBS. Diam. Length. Ratio Diam. Length. Ratio 70,000 1 3 3.0 li 4* 3.0 150,000 1* 3f 2.5 2* 5f 2.56 275,000 2 44- 2.25 3 7 2.33 425,000 24; 5" 2.0 8* 8* 2.20 600,000 3 5f 1.92 4* 2.11 850,000 8* 1.86 5* 10f 2.05 1,100,000 4 7-j- 1.87 6 12 2.0 1,700,000 5 9 1.80 * 14i .9 2,500,000 6 10* 1.75 9 164; .83 3,300.000 7 12 1.72 10* 18 .71 4,500,000 8 18* 1.70 12 20 .67 5,500,000 9 15 1.67 18* 22 .63 7,000,000 10 16 1.60 15 24 .60 8,500,000 11 17 1.55 ie* 254; 1.55 10,000,000 12 18 1.50 18 27 1.50 15,000,000 15 22 1.46 224, 32 1.42 22,500,000 18 25 1.39 27 37 1.37 30,000,000 21 28 1.33 81* 41 1.30 40,000,000 24 31 1.29 36 45 1.25 50,000,000 27 34 1.26 .... .... .... 60,000,000 30 36 1.20 .... .... .... 75,000,000 33 38 1.15 .... .... .... 90,000,000 36 40 1.11 b. Relative Position of Magnet Cores. The majority of types having two or more magnets, the rela- tive position of the magnet cores is next to be considered. In a great number of forms, having the magnets arranged symmet- rically with reference to the armature circumference, the exact relative position of the magnet cores is given by the shape of the field magnet frame; in other types, however, having parallel 3 20 D YNA MO-ELECTRIC MA CHINES. [83 magnets on the same side of the armature, diametrically or axially, the shape of the frame does not fix their relative position, and the distance between them is to be properly determined. This is done by limiting the magnetic leakage across the cores to a certain amount, according to the size of the machine, namely, from about 33 per cent, of the useful flux in small machines, to 8 per cent, in large dynamos. ' The relative amount of the leakage across the magnet cores is determined by the ratio of the permeance between the cores to the permeance of the useful path, and the percentage of the core leakage is kept within the limits given above, if the average permeance of the space between the magnet cores does not exceed one-third of the permeance of the gap-space in small machines, and one-twelfth of the gap permeance in large dynamos, or if the reluctance across the core is at least three to twelve times, respectively, that of the gaps. TABLE LXXXII. DIMENSIONS OF CYLINDRICAL MAGNET CORES FOR MULTIPOLAR TYPES. DIMENSIONS OP MAGNET CORES, IN INCHES. TOTAL FLUX PER Wrought Iron and Cast Steel. Cast Iron. MAGNETIC CIRCUIT, IN MAXWELLS. Diam. 4n Length. An Ratio. / m :<4 Diam. 4n Length. 'm Ratio. / m :4. 275,000 2 2 1.00 3 3* 1.17 600,000 3 2| .92 4| 4* 1.00 1,100,000 4 3* .875 6 5* .92 1,700,000 5 4 .80 7| 6f .90 2,500,000 6 4| .75 9 8 .89 4,500,000 8 6 .75 12 10* .875 7,000,000 10 H .75 15 13 .87 10,000,000 12 9 .75 18 15 .83 15,000,000 15 11 .73 22| 18 .80 22,500,000 18 13 .72 27 20 .74 30,000,000 21 14* .69 si* 22 .70 40,000,000 24 16 .67 36 24 .67 50,000,000 27 17 .63 .... .... ..... 60,000,000 30 18 .60 .... .... 75,000,000 33 19 .58 .... .... .... 90,000,000 36 20 .56 83] CALCULATION OF FIELD MAGNET FRAME, 321 TABLE LXXXIII. DIMENSIONS OP RECTANGULAR MAGNET CORES. (WROUGHT IRON AND CAST STEEL.) TOTAL FLUX PER MAGNETIC CIRCUIT, IN MAXWELLS. CROSS-SECTION. LENGTH. II 8 = OQ M 4i e o M I '1 0* 02 Diam. of Equiv. Circular Area 4 Bipolar Types. Multipolar Types. Length An Ratio /m:4u Length An Ratio /m^m 500,000 700,000 1,000,000 1,400,000 2 2 2 2 3 4 6 8 6 8 12 16 1 ?* JL 1.64 1.57 1.40 1.33 1.31 1.30 1.28 1.26 9* P 1.27 1.25 1.14 1.11 1,200,000 1,600,000 2,400,000 3,200,000 3 3 3 3 9* 9 12 13.5 18 27 36 1 P 6 6^ 1.08 1.04 1.02 .96 i.03~ .98 .95 95 .96 .94 .94 .93 2,000,000 2,750,000 4,250,000 5,500,000 4 4 4 4 6 6 6 6 6 8 12 16 9 12 18 24 24 32 48 64 54 78 108 144 9 7 8 1.26 1.26 1.24 1.20 1 4,750,000 6,500,000 9,500,000 12,500,000 10 11^ IttJ 15^ 1.20 1.20 1.15 1.15 8 9 11 ia 8,500,000 11,000,000 17,000,000 13,000,000 17,500,000 2(3,000,000 19,000,000" 25.000,000 38,000,000 8 8 8 10 10 10 12 16 24 15 20 30 96 128 192 11 "IF 19^ 13 15 1% 1.18 1.18 1.12 i** 14 .96 .94 .90 150 200 300 16 18 20 1.15 1.12 1.03 a* 16 .90 .875 .82 12 12 12 18 24 36 216 288 432 23)^ ~%*~ 21% 18 20 22 20 22 24 1.08 1.05 .94 15 16 18 17 18 19 .90 .84 .77 30,000,000 40,000,000 50,000,000 15 15 15 22^ 30 37^ 337.5 450 562.5 .96 .92 .90 .82 .75 .71 38.000,000 47,500,000 57,000,000 18 18 18 24 30 36 432 540 648 i 22 24 25 .94 .915 .87 18 19 20 .765 .74 .70 .71 .68 .66 55,000,000 66,000,000 77,000,000 21 21 21 30 36 42 630 756 882 28% 31 33^ 35% 25 26 27 ~27 28 30 .85 .83 .81 20 21 22 75,000.000 90,000,000 100,000,000 24 24 24 36 42 48 864 1008 1152 .81 .80 .785 22 23 24 .66 .66 .64 The area of the cross section and the length of the cores being given, the reluctance of the space between them depends upon the shape of their cross section and upon the distance between them. In case of round cores the shape is given by 322 DYNAMO-ELECTRIC MACHINES. [83 TABLE LXXXIV. DIMENSIONS OF OVAL MAGNET CORES. (WROUGHT IRON AND CAST STEEL.) TOTAL FLUX PER MAGNETIC CIRCUIT, IN MAXWELLS. CROSS-SECTION. LENGTH. Breadth, Inches. if* S 1 o < H 11 o* 00 Diameter of Equiv. Circular Area d m Bipolar Types. Multipolar Types. Length. 4. Inches. Ratio /. : 4* Length ^m Inches. Ratio 4:4. 600,000 1,000,000 1,300,000 2 2 2 4 6 8 7.14 11.14 15.14 3 4^2 5J4 6 1.50 1.40 1.37 4yf 5 1.17 1.18 1.14 1,400,000 2,200,000 3,000,000 3 3 3 6 9 12 16.06 25.06 34.06 28.56 44.56 60.56 1 6 t 1.33 1.33 1.28 5 6 7 6 & 1.11 1.07 1.05 2,500,000 3,900,000 5.250,000 4 4 4 8 12 16 6 11 4 1.29 1.27 1.26 1.00 1.00 .97 5,500,000 8,750,000 12,000,000 i 6 6 6 12 18 24 64.26 100.26 136.26 9 11M i8 11 13 15 1.22 1.16 1.14 BM |P .945 .93 .915 10,000,000 15,000,000 8 8 16 24 114.14 178.14 12 15 14 16 1.17 1.065 11 13 .92 .87 15,000,000 24,000,000 10 10 20 30 178.5 278.5 15 18% 16 20 1.065 1.065 13 16 .87 .85 22,500,000 35,000,000 12 12 15 15 24 36 257 401 18 8*K 18 21 21 25 1.00 .93 ^93 .885 15 17 .835 .755 35,000,000 55,000,000 30 45 400 625 2'% 28>| 17 20 .755 .71 50,000,000 50,000,000 18 18 36 42 578 686 SI 24 25 .885 .85 19 20 .70 .68 70,000,000 80,000,000 21 21 42 48 787 913 31% 34^ 26 27 .82 .79 21 22 .66 .645 90,000,000 100,000,000 24 24 48 54 1028 1172 36J6 38% 28 30 .78 .78 ^ .625 .62 the area of the cross-section, and the reluctance of the path from core to core, in consequence, only depends upon their distance apart, directly increasing with the same. The reluc- tance of the air gaps is determined by the diameter and length of the armature, by the percentage of polar embrace, and by the radial length of the gap-space, decreasing with the area of the gap and increasing with its length. The cross-section of the cores and the gap area, both depending upon the output of the machine, have a more or less fixed relation to each other varying with the type, the voltage, the speed, and the 83] CALCULATION OF FIELD MAGNET FRAME. 323 kind of armature and the relation between the reluctance across the cores to that of the air gaps can approximately be expressed by the ratio of the average distance apart of the cores to the radial length of the gap-space. In dynamos with smooth-drum armature this ratio is made from 6 to 16, in smooth- ring machines from 8 to 20, and for toothed and perforated armatures the distance apart of the cores is taken from 3 to 6 times the maximum radial length of the gap-space, /. e.\ from 3 to 6 times the distance between pole face and bottom of armature slot. The following Table LXXXV. gives the average distance between cylindrical magnet cores for various kinds and sizes of armatures, the ratio of this distance to the radial length of the gap-space, and the corresponding approxi- mate leakage between the magnet cores, expressed in per cent, of the useful flux: TABLE LXXXV. DISTANCE BETWEEN CYLINDRICAL MAGNET CORES. SMOOTH CORE ARMATURE. Drum. Ring. TOOTHED OR PERFORATED ARMATURE. 40 s* ai 53 OS 5.8 6.8 (5.9 75 8.0 8.8 10.2 11.3 12.3 13.5 15 16 16 25 IB IS i 8.7 10.0 11.7 13.1 14.9 16.5 16.9 17.6 18.9 1 oj II M *O es 8 t* 2.9 8.1 3.5 3.8 4.0 4.2 4.8 4.6 4.9 5.3 15* 14 18 12 11 10 10 ?* r* In case of inclined cylindrical magnets the figures given in Table LXXXV. for the least distances apart are to be consid- ered as the mean least distances, taken across the magnets midway between their ends. (Compare formula 180, 65.) 324 DYNAMO-ELECTRIC MACHINES. 83 In dynamos with rectangular and oval cores the leakage across, for the same distance apart, is greater than in case of circular cores of equal sectional area, increasing in proportion to the ratio of the width of the cores to their breadth. For rectangular and oval cores, therefore, the distance apart is to be made greater than for round cores in order to limit the leakage between them to the same amount; and the distance must be the greater the wider the cores are in proportion to their thickness. The following Table LXXXVI. gives the minimum, average and maximum values of the ratio of the dis- tance across rectangular and oval cores of various shapes of cross-sections to the distance which, between round cores of equal sectional area, effects approximately the same leakage, in small, in medium-sized, and in large dynamos, respectively: TABLE LXXXVI. DISTANCE BETWEEN RECTANGULAR AND OVAL MAGNET CORES. EATIO Distance between Rectangular and Oval Magnet Cores, as compared with that between Round Cores of Equal Area, OF THICKNESS TO W IDTH causing approximately the same leakage across. OF CORES. Minimum. (Small Machines.) Average. Maximum. (Large Machines.) 1 1 1.0 1.0 1.0 3 4 1.05 1.07 1.1 2 3 1.1 1.15 1.2 1 2 1.15 1.22 1.3 1 3 1.2 1.3 1.4 1 4 1.25 1.37 1.5 1 5 1.3 1.45 1.6 1 6 1.35 .55 1.75 1 7 1.4 .65 19 1 8 1.5 .75 2.05 1 : 9 1.6 1.9 2.25 1 : 10 1.7 2.1 2.5 In order to determine the proper distance apart of rectan- gular and oval magnet cores, the corresponding distance be- tween round cores of equal cross-section is taken from Table LXXXIIL, in multiplying the radial length of the gap-space by the ratio of distance apart to length of gap for the particu- lar size of armature. The distance thus obtained is then mul- tiplied by the respective figure found for the shape in question from Table LXXXVI. 85] CALCULATION OF FIELD MAGNET FRAME. 325 84. Dimensioning of Yokes. In bipolar types the dimensions of the magnet cores being given by Tables LXXXL, LXXXIII. or LXXXIV., 83, and their least distance apart by Table LXXX. or LXXXVI., 83, thus fixing the length of the yoke, and the sectional area of the yokes being found from formula (216), 82 the dimen- sioning of the yoke consists in arranging its cross-section with reference to the shape of the section of the cores, and, for the case that its material is different from that of the cores, in providing a sufficient contact area, conforming to the rules given in 80. In multipolar types the total cross-section found for the frame from formula (216), 82, is to be divided by the total number of magnetic circuits in the machine and multiplied by the number of circuits passing through any part of the yoke in order to obtain the sectional area required for that part of the yoke; otherwise the above rules also govern the dimen- sioning of the yokes for multipolar machines. 85. Dimensioning of Polepieces. In dimensioning the polepieces, three cases have to be con- sidered: (i) the path of the lines of force leaving the pole- pieces has the same direction as their path through the magnets (Fig. 251); (2) the path of the lines leaving the pole- FlQ.251 FiQ.252 FiQ. 253 FlQ. 254 Figs. 251 to 255. Various Kinds of Polepieces. pieces-makesa right angle to that through the cores (Fig. 252); and (3) the path of the lines leaving the polepieces is parallel but of opposite direction to that through the cores, making two turns at right angles in the polepieces (Fig. 253). In the first case, Fig. 251, which occurs in dynamos of the iron-clad, the radial and the axial multipolar types, the shape 336 DYNAMO-ELECTRIC MACPIINES. [85 of the cross-section is fixed by the form of the magnet core at one end and by the axial length or the radial width of the armature, respectively, and the percentage of polar arc at the other, while the height, in the direction of the lines of force, is to be made as small as possible, in order not to increase the total length of the magnetic circuit more than necessary. TABLE LXXXVII. DIMENSIONS OP POLEPIECES FOR BIPOLAR HORSE- SHOE TYPE DYNAMOS. DRUM ARMATURE. KINO ARMATURE. I l Dimensions of Polepiece. S3 Dimensions of Polepiece. o tf O 34 Thick- >4 a; J3 03 1-1 a 5 ness in 2 Area in Centre r * 1y lslf| 8 A O i (= Leng rmature. CCE Inc tre. ties. 1;!! I* C !~ i I Square Inches. 4> O< 1 K !| II 1 8? 33 i Wrought Iron. Cast Iron. 3 5 w 5 QJ a 3 * 5 w ft a .1 350,000 if 2| 3* * 9 1 175,000 4 4f If .25 500,000 3 4* 1* 250,000 5 Sf 1* 2* .5 650,000 2f 3* -i u 325,000 6 6f If 1 900,000 3i 4 6 f 1* 450,000 7 7f 4* 2 1,400,000 3f 4* 7 i 2 675,000 8 9 3f 6f 3 1,800,000 6f 8i H 2* 900,000 9* 10^ 4* 9 5 2,500,000 5 6* 9* 1| 2| 1,300,000 11 12 6* 13 10 3,500,000 6 7 10* if 3f 2,100,000 14 15 10* 21 15 5,000,000 6| 7f 12 2* 4* 2,800,000 15 16 14 28 20 6,000,000 ?* 13 %T5 4f 3,500,000 16 17 17* 35 25 7,000,000 8* 9! 14 2* 5 4,200,000 18 19 21 42 30 8,000,000 9 15 2f 5.2 4,800,000 20 21 24 48 50 12,500,000 10* H| 18 3* 7 7,000,000 24 25 35 70 75 16,500,000 12* 13| 20 4* 8* 9,500,000 28 29* 47* 95 100 21,000,000 15 16* 22 9* 12,000,000 32 33* 60 120 150 30,000,000 18* 20i 26 5f 11* 17,000,000 36 37* 85 170 200 38.000,000 22* 24* 31 6* 12* 21,500,000 40 42 107* 215 300 57,000,000 28 30* 38 7* 15 30,000,000 46 48 150 300 In the second case, Fig. 252, met with in bipolar and multi- ple horseshoe and in tangential multipolar types, the height of the polepieces is determined by the diameter, and the length of the polepiece by the length of the armature, while the area of the cross-section, perpendicular to the flow of the lines, is to be made of the size obtained by formula (216) at the end next to the magnet core, and to be gradually decreased in amount from that end to the opposite end or to the centre of 85] CALCULATION OF FIELD MAGNET FRAME. 327 the polepiece, respectively, according to whether there is but one magnetic circuit, or whether two circuits are passing through the same polepiece. Since, in bipolar machines, the lines of force are supposed to divide equally between the two halves of the armature, only one-half of the total flux passes the centre of the polepieces, in order to reach the half of the armature opposite the magnets, and the area in the centre of the polepiece consequently needs to be but one-half that at the end next to the core. In case the two circuits passing through each polepiece, Fig. 254, the same applies to the cross-section of the polepiece, at one-quarter the height from either end. For ready use, in the preceding Table LXXXVIL, the dimen- sions of wrought- and cast-iron polepieces for various sizes of bipolar horseshoe type dynamos are calculated for drum and ring armatures, by combining the respective data given in former tables. In the third case, Fig. 253, finally, which is found in single and double magnet types, the length of the magnetic circuit in the polepiece is determined by the diameter of the armature, by the cross-section of the magnet core, and by the height of their winding space; the width, parallel to the armature shaft of the polepiece near the magnet, is given by the width of the magnet core, and that near the armature by the axial length of the latter. The heights, parallel to the axis of the magnet core, in case of a single circuit, are to be so chosen that all of the cross-sections, up to that in line with the pole corner next to the magnet core, have an area at least equal in amount to that obtained by formula (216), and that the section in line with the armature centre has an area of one-half that amount. In case of two circuits meeting at the polepieces (consequent pole types), Fig. 255, the full area has to be provided from either end of the polepiece to the sections in line with the pole corners, half the full area at quarter distance from each pole corner, that is, midway between each pole corner and the pole centre, and sufficient cross-section for mechanical strength only is needed at the centre of the polepiece. PART V. CALCULATION OF MAGNETIZING FORCES CHAPTER XVII. THEORY OF THE MAGNETIC CIRCUIT 86. Law of the Magnetic Circuit. The magnetic flux through the various parts of the mag- netic circuit being known by means of formulae (137), 56, and (156), 60, respectively, and the dimensions of the magnet frame being determined by the rules and formulae given in Chapters XV. and XVI., the magnetomotive force necessary to drive the required flux through the circuit of given reluctance can now be calculated by virtue of the "Law of the Mag- netic Circuit." For the magnetic circuit a law holds good similar to Ohm's Law of the electric circuit; in the electric circuit: Electromotive Force Current (or Electric Flux) = and analogously, in the magnetic circuit: Magnetomotive Force Magnet,cFlux : Reluctance -- ' from which follows: Magnetomotive Force Magnetic Flux x Reluc- tance ....................................... (222) The Reluctance of a magnetic circuit, similar to the electric case of resistance, can be expressed by the specific reluctance, or reluctivity, of the material, and the dimensions of the mag- netic conductor, thus: Reluctance = Reluctivity X Lengt - . Area But the reluctivity of a magnetic material is the reciprocal of its permeability (similarly as the resistivity of an electric con- ducting material is the reciprocal of its conductivity), and con- sequently we have: Reluctance = - - u L , ength A - ..... (223) Permeability X Area 331 332 DYNAMO-ELECTRIC MACHINES. [87 Combining (222) and (223), we obtain: Magnetic Flux Length Magnetomotive Force = - X s , ... , Area Permeability and since the quotient of magnetic flux by area is the mag- netic density, we have : Magnetomotive Force = Magnetic Density x ^ Permeability r Phe permeability of magnetic materials depending upon the magnetic density employed in the circuit, see Table LXXV., 81, the quotient of magnetic density and permeability also depends upon the density, and has a fixed value for every degree of saturation and for each material. But this quotient- multiplied by the length of the circuit gives the magneto- motive force required for that circuit, and consequently represents the magnetomotive force per unit of length, or the specific magnetomotive force of the circuit. In order to obtain the M.M.F. required for any material, any density and any length, therefore, the specific M. M. F. for the respective material at the density employed is to be multiplied by the length of the circuit: Magnetomotive Force = Specific M. M. F. x Length. (224:) 87. Unit Magnetomotive Force. Relation Between Magnetomotive Force and Exciting Power. An infinitely long solenoid of unit cross-sectional area (i square centimetre), having unit magnetizing force or exciting power (i current-turn) per unit of length (i centimetre) pos- sesses poles of unit strength at its ultimate extremities. If the exciting power per centimetre length, therefore, is i ampere- turn, /. e., T V of a current-turn (the ampere being the tenth part of the absolute unit of current-strength), the poles pro- duced at the ends of the solenoid will be of the strength of yL- of a unit pole. Since a unit pole disperses 4 n lines of force, or maxwells, see 55, the magnetic flux of a unit solenoid of infinite length and of a special exciting power of i ampere-turn per centimetre is maxwells. 10 88] THEORY OF THE MAGNETIC CIRCUIT. 333 and the density of the flux is webers per square centimetre, or - gausses. The reluctance per unit length of the solenoid, the latter being of i square centimetre sectional area, is that of i cubic centimetre of air, and therefore is unity, or i oersted, hence the M. M. F. of the coil per ampere-turn of exciting power being the product of magnetic flux and reluctance, is 10 C. G. S units of magnetomotive force, or 4 ^gilberts. A magnetomotive force of 4 n 10 gilberts being excited by one ampere-turn of magnetizing force, and the magnetomotive force being proportional to the magnet- izing force producing the same, it follows that the entire M. M. F. of a circuit, in gilberts, is 4 n 10 times the total number of ampere-turns; and inversely, in order to express the exciting power necessary to produce a certain M. M. F., the number of gilberts to be multiplied by 10 = 796; 4 n thus: Number of Ampere-turns = -^ . x Number of Gil- berts (225) 88. Magnetizing Force Required for any Portion of a Magnetic Circuit. The magnetizing force required for any circuit is the sum of the magnetizing forces used for its different parts. 334 D YNAMO-ELECTRIC MA CHINES, [ 88 From (224) and (225), 87, follows that the exciting power required for any part of a magnetic circuit is 10 4 n times the product of the specific M. M. F. and the length of that portion of the circuit: Magnetizing Force = -I x Specific M. M. F. x Length. 4 n The product of the specific magnetomotive force, for the particular material and density in question, with the constant factor 10 represents the exciting power per unit length of the circuit, or the Specific Magnetizing Force; consequently we have: Magnetizing Force = Specific Magnetizing Force X Length, or, Number of Ampere-turns = Ampere-turns per unit of Length x Length. Denoting the density of the lines of force in any particular portion of a magnetic circuit by (R, the specific magnetizing force by m, and the length by /, the number of ampere-turns required for that portion of the magnetic circuit can be calcu- lated from the general formula: where m = specific magnetizing force, in ampere-turns per inch, or per centimetre, of length, for the particular material and density employed, see Tables LXXXVIII. and LXXXIX., or Fig. 256; /= length of the magnetic circuit in the respec- tive material in inches, or centimetres, re- spectively. The values of the specific magnetizing forces, ;, for vari- ous densities, as averaged from a great number of tests by 88] THEORY OF THE MAGNETIC CIRCUIT. 335 Ewing, 1 Negbauer, 2 Kennelly, 3 Steinmetz, 4 Thompson, 5 and others, for the various materials are compiled in the following Tables LXXXVIII. and LXXXIX., which give the specific magnetizing force in ampere-turns per inch length, and in ampere-turns per centimetre length, respectively. The figures in the last column of these tables, referring to air, are obtained by multiplying the magnetic density, (B, by 10 47T in the metric, and by 10 i in the English system; for in case of air, the permeability, being unity, does not depend upon the density, and the mag- netizing force, in consequence, is directly proportional to the density. For convenient reference the values of m contained in Tables LXXXVIII. and LXXXIX., for the various kinds of iron, are plotted in Fig. 256, p. 338. The said Tables LXXXVIII. and LXXXIX., although carefully averaged with reference to commercial tests of various kinds of iron, cannot be expected to give accurate results in specific cases of actual design, since different sam- ples of one and the same kind of iron often vary as much as- 10 per cent, and more in permeability. These tables are, therefore, intended only for the use of the student, while the practical designer is supposed to make up his own table or 1 J. A. Ewing, " Magnetism in Iron and Other Metals," The Electrician (London, 1890-91). 2 Walter Negbauer, Electrical Engineer, vol. ix. p. 56 (February, 1890). 3 A. E. Kennelly, Trans. Am. Inst. El. Eng., vol. viii. p. 485 (October 27, 1891) ; Electrical Engineer, vol. xii. p. 508 (November 4, 1891); Electrical World, vol. xviii. p. 350 (November 7, 1891). 4 Charles P. Steinmetz, Trans. Am. Inst. El. Eng., vol. ix. p. 3 (January 19, 1892); Electrical Engineer, vol. xiii. pp. 91, 121, 143, 167, 261, 282 (Jan- uary 27, February 3, 10, 17, March 9, 16, 1892); Electrical World, voh xix. pp. 73. 89 (January 30, February 6, 1892). 6 Milton E. Thompson, Percy H. Knight, and George W. Bacon, Trans* Am. Inst. El. Eng., vol. ix. p. 250 (June 7, 1892); Electrical Engineer, voL xiv. p. 40 (July 13, 1892); Electrical World, vol. xix. p. 436 (June 25, '892). 33 DYNAMO-ELECTRIC MACHINES. . . [88 TABLE LXXXVIII. SPECIFIC MAGNETIZING FORCES FOR VARIOUS MATERIALS AT DIFFERENT DENSITIES, IN ENGLISH MEASURE. MAGNETIC DENSITY. Lines of Force per square inch. &" UNIT MAGNETIZING FORCE. Ampere-Turns per Inch Length. Annealed Soft Wrought Cast Iron. Steel. Mitis Iron. Cast Iron containing 6.5 % of Aluminum. Cast Iron (ordinary). Air, (=.3133X(B*). f 2,500 1.2 2 2.5 7 9 783 5,000 1.7 2.8 3.4 9.6 13 1,566 7,500 2.1 3.4 4 11.6 16 2,350 10.000 2.2 3.7 4.4 13.5 18.5 3,133 12,500 2.4 4 4.8 15.7 21.3 3,916 15,000 27 4.3 5.2 18.2 24.1 4,700 17,500 3.1 4.6 5.6 21 27.1 5,483 20,000 3.5 5 6 24 30.5 6,266 22,500 4 5.4 6.5 27.2 34.5 7,050 25,000 4.5 5.8 7 31 39 7,833 27,500 5 6.2 7.5 35.5 44 8,616 30,000 5.5 6.6 8.1 41.5 50 9,400 32,500 6 7.1 8.7 47.5 57 10,162 35,000 6.5 7.6 9.4 54 65 10,966 37,500 7 8.2 10.1 62 76 11,750 40,000 7.5 8.8 10.9 72 88 12,532 42,500 8 9.4 11.7 83 101 13,315 45,000 8.5 10.1 12.6 95 116 14,100 - 47,500 9 10.9 13.6 110 136 14,882 50,000 9.6 11.8 14.7 128 160 15,665 52,500 10.3 12.8 15.9 149 189 16,450 55,000 11.1 13.9 17.3 173 222 17,233 57,500 12 15.1 19 200 257 18,016 CO 000 13 16.4 21 230 295 18,800 (52,500 14.2 17.8 23.2 263 340 65,000 15.7 19.3 25.6 300 400 67,500 17.5 20.9 28.5 345 470 70,000 19.6 22.7 32 400 570 72,500 22 24.7 36 460 700 75,000 24.7 27 41 525 77,500 27.7 30 47 600 80,000 31.2 34 54 700 82,500 352 39 62 85.000 39.7 44 70 87,500 44.7 50 80 90.000 50.7 57 92 92,500 58 65 109 95.000 67 75 131 97,500 78 86 159 . 100.000 91 100 193 102,500 108 121 245 105,000 137 159 290 107,500 190 227 345 110,000 290 325 410 112,500 395 430 500 115,000 500 550 600 117,500 600 650 700 120,000 700 750 800 122,500 8tiO 850 125,000 900 950 88] THEORY OF THE MAGNETIC CIRCUIT. 337 curve, by actually testing the very iron he is going to use for his machine. TABLE LXXXIX. SPECIFIC MAGNETIZING FORCES FOB VARIOUS MATERIALS AT DIFFERENT DENSITIES, IN METRIC MEASURE. UNIT MAGNETIZING FORCE. MAGNETIC AMPERE-TURNS PER CENTIMETRE LENGTH. DENSITY. Lines of Force per cm 2 (B Annealed Wrought Iron. Soft Cast Steel. Mitis Iron. Cast Iron containing 6.5 % of Aluminum Cast Iron (Ordinary) Air, (=*) 500 .5 .9 1.1 3 5 400 1,000 .8 1.25 1.5 4 6 800 1,500 .9 1.45 1.7 5 7 1,200 2,000 .95 1.6 1.9 6.5 8.5 1,600 2,500 1.1 1.75 2.1 8 10 2,000 3,000 1.35 1.95 2.3 9.5 12 2,400 3,500 1.6 2.15 2.6 11 14 2,800 4,000 1.8 2.35 2.8 13 16 3,200 4,500 2.1 2.55 3.1 15 19 3,600 5,000 2.35 2.8 3.4 19 22 4,000 5,500 2.6 3.05 3.7 22.5 26 4,400 6,000 2.85 3.35 4.1 26.5 32 4,800 6,500 3.1 3.65 4.5 31.5 38 5,200 7,000 3.35 4 5 37.5 46 5,600 7,500 3.6 4.4 5.5 45 57 6,000 8,000 3.95 4.9 6.1 56 71 6,400 8,500 4.35 5.5 6.75 68 87 6,800 9,000 4.8 6.0 7.6 81 105 7,200 9,500 5.4 6.7 8.7 99 125 7,600 10,000 6.1 7.5 10.0 118 153 8,000 10,500 7 8.3 11.5 138 190 . 11,000 8 9.2 13.5 163 240 11,500 9.4 10.3 16 195 12,000 10.8 11.7 18.5 235 12,500 12 14 22 285 f 13,000 15 16 26 13,500 17 20 30.5 14,000 20 23 37 14,500 24 27 46 15,000 30 32 58 15,500 36 40 74 16,000 47 52 96 16,500 68 80 124 17,000 108 124 160 17,500 160 176 204 18,000 212 228 250 18,500 264 280 300 19,000 316 333 350 19,500 368 386 400 . 20,000 420 440 450 333 DYNAMO-ELECTRIC MACHINES. [88 MAGNETIC DENSITY. IN LINES OF FORCE PER SQUARF INCH JS S S 8 3 8 S I | t? tn' to ? cr *S o 1 . ii- O 30 - o s i? s 5 ^A < C i I i i i i i i i i i MAGNETIC DENSITY, IN LINES OF FORCE' PER SQUARE CENTIMETRE CHAPTER XVIII. MAGNETIZING FORCES. 89. Total Magnetizing Force of Machine. The total exciting power required for each magnetic circuit of a dynamo-electric machine is the sum of the magnetizing forces needed to overcome the reluctances due to the gap- spaces, to the armature core, and to the field frame, and of the magnetizing force required to compensate the reaction of the armature winding upon the magnetic field; or, in symbols: A T = where AT = total magnetizing force required for normal output of machine in ampere-turns; af g = ampere-turns needed to overcome reluctance of gap-spaces; see formula (228), 90; at* =. ampere-turns needed to overcome reluctance of armature core; see formula (230), 91; at m = ampere-turns needed to overcome reluctance of magnet frame; see formula (238), 92; at t = ampere-turns needed to compensate armature reactions; see formula (250), 93. In order to keep the angle of field-distortion, upon which depends the amount of spar king > below its practical limit, the ratio of the armature ampere-turns per magnetic circuit to the aboiie number A T of field ampere-turns per magnetic circuit must not ex- ceed the value of the trigonometric tangent of the greatest permissible angle of field distortion for the type of machine under consider- ation. (See page 349.) If for some reason this important condition isnot fulfilled, although the rules and formulae given in the previous chapters have been carefully followed, the ma- chine must be re-designed. The angle of field distortion of any dynamo depends upon the number of its poles and upon the type of its armature. 339 DYNAMO-ELECTRIC MACHINES. [89 The following table gives the usual limiting values of the dis- tortion angle and the corresponding value of its trigonometric tangent for smooth and toothed armature machines with va- rious numbers of poles: TABLE LXXXIXa. GREATEST PERMISSIBLE ANGLE OF FIELD DIS- TORTION AND CORRESPONDING MAXIMUM RATIO OP ARMATURE AM- PERE-TURNS TO FIELD AMPERE-TURNS. GREATEST PERMISSIBLE ANGLE OP FIELD DISTORTION. MAXIMUM RATIO OP ARMATURE AMPERE-TURNS TO FIELD AMPERE-TURNS. NUMBER OP Toothed Toothed Smooth or Perforated Smooth or Perforated POLES. Armature. Armature. Armature. Armature. a a' tan a. tan a'. 2 36 24 .727 .445 4 18 12 .325 .213 6 12 8 .213 .141 8 9 6 .158 .105 10 7 5 .123 .087 12 6 4 .105 .070 14 5 3^ .087 .061 16 . 4* 3 .075 .052 18 20 3i II .070 .061 .046 .040 24 3 2 .052 .035 In dividing the armature ampere-turns per magnetic circuit, X by the field ampere-turns, AT, the actual ratio of armature ampere-turns to field ampere-turns for the machine under consideration is obtained; and by comparing this ratio with the value of the corresponding tangent in the above table it can easily be decided whether or not it will be necessary to alter the design of the machine. Since, for the purpose of the above check, an approximate value f the field ampere-turns i-s all that is required, it is not necessary for this preliminary determination of AT to make the detailed calculations treated in 91, 92, and 93, but it will be sufficient to proceed as follows: 90] MAGNETIZING FORCES. 339^ To find the gap ampere-turns, at & which in all but excep- tional cases constitute at least one-half of the total number AT of the field ampere-turns, use formula (228), employing for 5C" the value chosen from Table VI. as the basis of the arma- ture calculation. Next make a rough scale drawing of the magnetic circuit and indicate by lines therein the mean paths of the flux in the various parts, thereby obtaining /" a , /" wi , and /" ci> (or /'' CA , as the case may be) directly by measurement. From Table LXXXVIIL, page 336, find the specific magnetizing forces m" & , ;/z" w .i.> etc., corresponding to the flux densities (B" a , (B" w .i. etc., employed in computing the various cross-sections, and form the respective products /" ft x w" a , /" w .i. X ^" w .i.> etc. In this manner the values of at & and at m are obtained, the latter by one single multiplication if the field frame is all of the same material, or by adding several products if various portions of the magnet frame are made of different materials. The compensating ampere-turns af n finally, need not be computed at all, it being sufficiently accurate for the purpose on hand to increase the sum of the gap, armature, and frame ampere-turns thus far obtained by 75 or 20 per cent. 90. Ampere-Turns for Air Gaps. The magnetizing force required to produce a magnetic den- sity of OC" lines of force per square inch in the air spaces, ac- cording to 88, is: af g = X 3C" X -^L =.3133 X 3C" X /' (228) 4 ^ 2 -54 where X" = field density, in lines offeree per square inch; from formula (142), 57, for smooth armature # dynamos, and from -^ for machine's with toothed ^ K or perforated armatures, the area of the gap- space, S g , to be "taken, respectively, from the numerators of equations (174), (175), or ( 1 76)> p. 230; and 340 DYNAMO-ELECTRIC MACHINES. [91 /" g = length of magnetic circuit in air gaps, in inches; the magnetic length of the gaps is obtained by multiplying twice the distance between arma- ture core surface and polepieces by the factor of field-deflection; see Table LXVI., p. 225, for smooth armatures, and Table LXVIL, p. 230, for toothed and perforated armatures, respectively. If the field density is given in lines of force per square cen- timetre, and the length of the circuit in centimetres, the mag- netizing force in ampere-turns is obtained from af e = X 3C X / g = .8 X OC X t e . . . .(229) 91. Ampere-Turns for Armature Core. For the magnetizing force needed to overcome the reluc- tance of the armature core we find, according to formula (226): */k = \ x /"., .............. (230) where m" & average specific magnetizing force, in ampere- turns per inch length, formulae (231) to (235); l" & mean length of magnetic circuit in armature core in inches, formula (236) or (237), respect- ively. Owing to the cylindrical shape of the armature, the area of the surface presented to the lines when entering and leaving the core is much greater than that of the actual cross-section of the armature body. Hence, since every useful line of force, on its way from a north pole to the adjoining south pole, must pass through the smallest core section, it is evident that the magnetizing force required per unit of path length is smallest near the polepieces and greatest opposite the neutral points of the field, while it gradually increases from the minimum to the maximum value as the flux passes from the peripheral surface opposite the north pole to the neutral cross-section, and grad- ually decreases again to minimum as the flux proceeds from the neutral section to the periphery opposite the south pole. 91] MAGNETIZING FORCES. 341 The average specific magnetizing force, therefore, is obtained by taking the arithmetical mean of the extreme values: *'. = ~ ('\ + *v- < 231 ) in which m" ai = maximum specific magnetizing force, for smallest area of magnetic circuit, in armature; see Table LXXXYIII., col- umn for annealed wrought iron; m ff M = minimum specific magnetizing force, for largest area of magnetic circuit in arma- ture, Table LXXXVIII. The maximum specific magnetizing force m" &l corresponds to the maximum density of (B ai = -^ lines, and the mini- 5 *i mum specific magnetizing force ;;/' aa to a minimum density of > w " c . s . = specific magnetizing forces for wrought iron, cast iron, and cast steel, re- spectively, from Table LXXXVIII., or Fig. 256; corresponding to the magnetic densi- ties " w .i, (B" e .i., and " c . s . in the respective materials; n _ M'WJ. X /Vi. + "/" c .j. X /" c ,. + m\^ X /" c . 8 . "* m /// | /// | /// / W.i. + * C . T ' C.8. =^ average specific magnetizing force of magnet frame in ampere-turns per inch length; ^Vi. > ^c.i. > ^C.B. lengths of magnetic circuit in wrought iron, in cast iron, and in cast steel, respectively, in inches; /" m = /" w> i. -f- /" c i. -|- /^g. = total length of magnetic circuit in magnet frame, in inches. The densities (B lV .i., (B c .i. , and (B c . s . are the quotients of the total magnetic flux, $', by the mean total areas, S" W . L , S' f cAt , .and S" c)> (241) in which m^ = average specific magnetizing force, of pole- pieces, in ampere-turns per inch; m l = specific magnetizing force, corresponding to cross-section Sj_ of polepieces near magnet- core (or to twice the minimum cross-section at center of polepiece, Fig. 262), in square inches; m 2 = specific magnetizing force, corresponding to pole face area S 2 (maximum cross-section of polepiece), in square inches. If, on the other hand, the area is partly uniform and partly varying, as in the polepieces shown in Figs. 264 and 265, the geometrical mean of the specific magnetizing force of the uniform portion and of the average specific magnetizing force of the varying portion has to be taken as follows: Figs. 264 and 265. Polepieces with Partly Uniform and Partly Varying Cross Section. _ i A + + ) x /, + 4 92] MAGNETIZING FORCES. 347 where m^ = specific magnetizing force corresponding to area 6*! of minimum cross-section, in sq. in. ; m 2 = specific magnetizing force corresponding to pole face area S 2 (maximum cross-section), in sq.in. ; /! = length of uniform cross-section, in inches; / 2 = mean length of varying cross-section, in inches. In formulae (241) and (242) it is assumed that the smallest sec- tion of the polepiece is entered by the entire total flux, $', and that the pole area only carries the useful flux, #. Neither Figs. 266 and 267. Mean Length of Magnetic Circuit in Cores and Yokes. of these assumptions is quite correct (the number of lines entering the polepieces being smaller than $', and the flux at the pole face somewhat larger than $) but, since their devia- tions from the facts are in opposite directions, they practically cancel in forming the arithmetical mean of the respective specific magneting forces and give a result as accurate as can be desired. The mean length of the magnetic circuit in portions of the field frame having a homogenous cross-section (cores andjto&tf) is measured along the centre line of the frame, as shown in Fig. 266, if there is but one magnetic circuit through that por- tion. In case of two or more magnetic circuits passing in parallel through any part of the frame, as in Fig. 267, that part is to be correspondingly subdivided parallel with the direction of the magnetic lines, and the mean length of the magnetic circuit, then, is given by the centre-line through a part of the frame thus apportioned to one circuit. In the illustration, Fig. 267, two parallel circuits being shown through each core, the average line of force passes through the cores at a distance from their edges equal to one-quarter of their breadth. D YNAMO-ELECl^RIC MA CHINES. [93 In parts with varying cross-section (polepieces) the mean length of the magnetic circuit, depending altogether upon their shape, can only be estimated, one approximation being Figs. 268 and 269. Mean Length of Magnetic Circuit in Polepieces. the arithmetical mean between the shortest and the longest line of force (see Figs. 268 and 269): /" p = mean length of magnetic circuit in polepieces, in inches; /j = shortest line of force in polepiece; / a = longest line of force in polepiece. 93. Ampere-Turns for Compensating Armature Re- actions. The armature current in magnetizing the armature core exerts a double influence upon the magnetic circuit: (i) a direct weakening influence-upon the magnetic field, due to the lines of force set up by the armature winding, and (2) an indi- rect, secondary influence by shifting the magnetic field in the direction of the rotation, thereby causing greater magnetic density to take place in those portions of the polepieces at which the armature leaves the pole than in those at which it enters. The direct effect of the armature current on the field has been studied experimentally by Professor Harris J. Ryan, 1 who, in his paper presented to the American Institute of Electrical Engineers, on September 22, 1891, has shown that the arma- 1 Harris J. Ryan, Trans. A. /. E. E., vol. viii. p. 451 (September 22, 1891); Electrical Engineer, vol. xii. pp. 377, 404 (September 30 and October 7, 1891); Electrical World, vol. xvii. p. 252 (October 3, 1891). 93] MAGNETIZING FORCES. 349 ture ampere-turns acting directly against the field ampere turns can be expressed by: N* X /' X a where at' T = counter magnetizing force of armature per mag- netic circuit, in ampere-turns, to be compen- sated for by additional windings on field frame; N & total number of turns on armature, JV a = JV C , for ring armatures, JV A =.J JV C , for drum- wound armatures, (JV C = total number of armature conductors); /' total current-capacity of dynamo, in amperes; 2/z' p = number of armature circuits electrically connected in parallel; N X /' i 3 = total number of ampere-turns on armature; 2' p J3 X OL = angle of brush lead. For smooth-core armatures the angle of lead is approximately equal to half the angle between two adjacent pole corners, the constant 13 being very nearly = i, and is accurately expressed by formula (245). Since the angle of field-distortion depends upon the relative magnitudes of the armature- and field magnetomotive forces acting at right angles to each other, the direction of the dis- torted field is the resultant of both forces; that is, the diag- onal of a rectangle, having the two determining M. M. Fs. as its sides, as shown in Fig. 270, in which OA represents the direction and magnitude of the direct M. M. F., and OB that of the counter M. M. F. The angle of lead can, con- sequently, be mathematically expressed by: _ OB Total Armature Ampere-Turns OA ~ Total Field Ampere-Turns N & X I' 2n ' N * X 7/ n z X AT~ 2' p X n z X AT a = arc tan p or 35 DYNAMO-ELECTRIC MACHINES. [93 the total number of field ampere-turns being the product of the number, AT, of ampere-turns per magnetic circuit, and of the number, n z , of magnetic circuits. In toothed Z.K& perforated machines the weakening effect of the armature magnetomotive force is checked by the presence of iron surrounding the conductors, this checking influence being the stronger the greater the ratio of tooth section to. field den- sity, that is, the smaller the tooth density. In a minor degree, the coefficient of brush lead depends upon the ratio of gap length to pitch of slots, and upon the peripheral velocity of the armature. In the following Table XC. averages for this co- efficient, 13 , for toothed and perforated armatures are given, the upper limits referring to small gaps and high-speed arma- tures, and the smaller values to large air gaps and to armatures of low circumferential velocity: TABLE XC. COEFFICIENT OF BRUSH LEAD IN TOOTHED AND PER- FORATED ARMATURES. MAXIMUM DENSITY OF MAGNETIC LINES IN ARMATURE PROJECTIONS AT NORMAL LOAD. COEFFICIENT OF BRUSH LEAD, *,. Toothed Armatures. Perforated Armatures. Lines per sq. in. Lines per sq. cm. Straight Teeth. Projecting Teeth. 50,000 75,000 100,000 125,000 150,000 7,750 11,600 15,500 19,400 23,250 0.30 to 0.45 .35 " .60 .40 " .80 .50 " .90 .70 " 1.00 0.25 to 0.35 .30 " .45 .40 " .60 .50" .70 .60 " .90 0.20 to 0.30 .25 " .35 .30 " .45 .40 " .60 .50 " .80 Formula (244) is directly applicable to single magnetic circuit bipolar and to the radial types of multipolar machines. In double circuit bipolar types, and for axial multipolar dynamos, however, in which the number of magnetic circuits per pole space is twice that of the former machines, respectively, the result of (244), must be divided by 2 in order to furnish the direct counter magnetizing force per magnetic circuit. As to the second, indirect, influence of the armature field, the density in the Sections I, I, Fig. 270, of the polepieces, on account of the distortion of the field caused by the action of the armature current, is greater, in the Sections II, II, how- 93] MAGNETIZING FORCES. 351 ever, smaller than the average density obtained by dividing the total flux by the sectional area of the polepieces. Fig. 270. Influence of Armature Current upon Magnetic Density in Polepieces. If the average density in the polepieces, $' -f- S p , is denoted by &" p , then the distorted densities are in Sections I, I : (B" DI = (&'' x sina \ (246) in Sections II, II: (B* = (B" D X pn i sin a The magnetizing force required to produce these densities in the polepieces can be found from aff = /" x m " + m "", . ...... (247) where /" p = length of magnetic circuit in the polepieces, in inches; m" plj m rf pn = specific magnetizing forces per inch length for the densities (&" pl and (&" pn , respectively, for- mula (245), for the material used; to be taken from Table LXXXVL, or from Fig. 256. But since the magnetic force necessary to produce the original average density is which is smaller than at' p , we can find the number of ampere- turns by which the field magnetomotive force is diminished on account of this indirect effect of the armature current, by sub- tracting at p from (247). Doing this, we obtain: at\ = at\ - at, ................ (248) 35 2 DYNAMO-ELECTRIC MACHINES. [%93- The total weakening effect of the armature winding per mag- netic circuit can therefore be found by combining (244) and (248), thus: This is the total number of ampere-turns by the amount of which the exciting power of each magnetic circuit is to be in- creased in order to compensate for the reactions of the arma- ture current upon the field. Making the above calculation of at r , by formula (249), for a great number of practical machines, the author has found that with sufficient accuracy the complex formula (249) can be re- placed by the simple equation: at r = X X /' X a i8o c (250) if the following values of the coefficient u are employed: TABLE XCI. COEFFICIENT OF ARMATURE REACTION FOR VARIOUS DENSITIES AND DIFFERENT MATERIALS. AVERAGE MAGNETIC DENSITY IN POLEPIECES. Wrought Iron and Cast Steel. Mitis Iron. Cast Iron. Coefficient of Armature Roue tion Lines Lines Lines Lines Lines Lines per sq. in. per sq. cm. per sq. in. per sq. cm. per sq, in. per pq. cm. . <*P <&p a 7 ; (B p < P * 80,000* 12,400* 1.25 90,000 13,950 7o,'6oo* 10,'850* .... . 1.30 100,000 15,500 80,000 12,400 .... .... 1.40 105,000 16,250 90,000 13,950 20,000* 3,100* 1.50 110,000 17,000 100,000 15,500 30,000 4,650 1.60 115,000 17,800 105,000 16,250 40,000 6,200 1.70 120,000 18,600 110,000 17,000 50,000 7,750 1.80 .... .... 115,000 17,800 55,000 8,500 1.90 . . .... 120,000 18,600 60,000 9,300 2.00 .... .... .... .... 65,000 10,100 2.10 .... 70,000 10,850 2.25 Or less. 94] MAGNETIZING FORCES. 353 94. Grouping of Magnetic Circuits in Yarious Types of Dynamos. In applying formula (227), 89, for the total magnetizing power of a dynamo, the number of the magnetic circuits and their grouping has to be taken into account. Considering each magnet, or each group of magnet coils wound upon the same core, as a separate source of M. M. F., we can classify the various types of dynamos according to the number of sources of magnetomotive force, and according to their grouping, as follows: (1) One source of M. M. F., single circuit, Figs. 271 and 272; (2) One source of M. M. F., double circuit, Figs. 273 and 274; (3) One source of M. M. F., multiple circuit, Figs. 275 and 276; (4) Two sources of M. M. F. in series, single circuit, Figs. 277 and 278; (5) Two sources of M. M. F. in series, double circuit, Figs. 279 and 280; (6) Two sources of M. M. F. in parallel, single circuit, Figs. 281 and 282 ; (7) Two sources of M. M. F. in parallel, double circuit, Figs. 283 and 284; (8) Two sources of M. M. F. in parallel, multiple cir- cuit, Figs. 285 and 286; (9) Two sources of M. M. F. in series, each also sup- plying a shunt circuit, Figs. 287 and 288; (10) Three or more sources of M. M. F. in parallel, multiple circuit, Figs. 289 and 290; (n) Three or more sources of M. M. F. in series, each having a shunt circuit, Figs. 291 and 292; (12) Four sources of M. M. F., two in series and two in parallel, single circuit, Figs. 293 and 294; (13) Four sources of M. M. F. in series, each pair also supplying a shunt circuit, Figs. 295 and 296; (14) Four or more sources of M. M. F. in series, paral- lel, two sources in series in each circuit, Figs. 297 and 298; 354 DYNAMO-ELECTRIC MACHINES. [94 (15) Four or more sources of M. M. F., all in parallel, multiple circuit, Figs. 299 and 300; (16) Four^or more sources of M. M. F., arranged in one or more parallel branches in each of which two separate sources are placed in series with a group of two in parallel, Figs. 301, 302 and 303. In order to facilitate the conception of the grouping of the magnetomotive forces, to the following illustrations of the 16 classes enumerated above the electrical analogues of corre- sponding grouping of E. M. Fs. have been added: FIG. 271 F.G.272 FiG.'273 F.G 274 Fiq. 275 F.G. 2?6 FIG. 277 F'G. 278 1O BOO FIG 279 FIG. 280 FIG. 281 FIG. 282 FIG. 285 FIG. 286 FIG. 287 FIG. 288 FIG. 289 FIG. 290 FIG. 291 FIG. 292 FIG. 293 FIG. 294 FIG. 295 FIG. 296 FIG. 297 FIG. 298 FIG. 299 FIG. 300 FIG. 301 FIG. 302 FIG. 303 Figs. 271 10303. Grouping of Magnetic Circuits in Various Types of Dyna- mos, and Electrical Analogues. Of the first class, Fig. 271, which has but one magnetic cir- cuit, are the bipolar single magnet types shown in Figs. 191, 192, 193 and 194. In the second class, Fig. 273, there are two parallel magnetic 94] MAGNETIZING FORCES. 355 circuits, each containing the entire magnetizing force; of this class are the single magnet bipolar iron-clad types, illustrated in Figs. 204, 205 and 206. The third class, Fig. 275, has as many magnetic circuits as there are pairs of magnet poles, and each circuit contains the entire magnetizing force; the single magnet multipolar types, Figs. 214 and 215, belong to this class. T V\& fourth class, Fig. 277, has but one magnetic circuit, and is represented by the single horseshoe types, Figs. 187 to 190, and by the bipolar double magnet types, Figs. 195, 196 and 198. In the fifth class, Fig. 279, there are two magnetic circuits, each of which contains both magnets; the bipolar double mag- net iron-clad types shown in Figs. 203 and 207 belong to this class. The sixth class, Fig. 281, has also two magnetic circuits, but each one contains only one magnet; of this class are the bipolar double magnet types illustrated in Figs. 197, 199 and 200. In the seventh class, Fig. 283, there are four parallel mag- netic circuits, each of which contains but one magnet; the fourpolar iron-clad types, Figs. 218, 219 and 220, and the fourpolar double magnet type, Fig. 223, belong to this class. In the eighth class, Fig. 285, the number of magnetic cir- cuits is equal to twice the number of poles, opposite pole faces of same polarity considered as one pole, and each circuit con- tains one magnet; this class Js represented by the double magnet multipolar type, Fig. 216. The ninth class, Fig. 287, has three magnetic circuits, two* of which contain one magnet each, while the third one con- tains both the magnets. In the tenth class, Fig. 289, there are as many magnetic cir- cuits as there are poles, two circuits passing through each magnet; the multipolar iron-clad type, Fig. 217, is of this class. The eleventh class, Fig. 291, has one more circuit than there are pairs of poles, one circuit containing all the magnets, while all the rest contain but one magnet each; to this class belongs the multiple horseshoe type, Fig. 222. In the twelfth class, Fig. 293, there are two magnetic cir- 356 DYNAMO-ELECTRIC MACHINES. [94 cuits, each containing two magnets; it is represented by the double horseshoe types, Figs. 201 and 202. Class thirteen, Fig. 295, has three circuits, two containing two magnets each and the third one all four magneis; to this class belongs the fourpolar horseshoe type, Fig. 221. In class fourteen, Fig. 297, there are as many circuits as there are poles, each circuit containing two magnetomotive forces in series; this class of grouping is common to the radial multipolar types, Figs. 208 and 209, and to the axial multipolar type, Fig. 212. In class fifteen, Fig. 299, the number of magnetic circuits is equal to the number of poles, and each circuit contains one magnet; the tangential multipolar types, Figs. 210 and 211, and the quadruple magnet type, Fig. 224, are the varieties of this class. The sixteenth class, Fig. 301, finally, has as many magnetic circuits as there are poles, and each circuit contains three magnets; the raditangent multipolar type which is shown in Fig. 213, represents this class of grouping. Similarly as the total joint E. M. F. of a number of sources of electricity connected in series-parallel is the sum of the E. M. Fs. placed in series in any of the parallel branches, so the total M. M. F. of a dynamo-electric machine is the sum of the M. M. Fs. in series in any of its magnetic circuits. In considering, therefore, one single magnetic circuit for the computation of the magnetizing forces required for over- coming the reluctances of the air gaps, armature core and field frame, the result obtained by formula (227) represents the exciting force to be distributed over all the magnets in that one circuit, and, consequently, the same magnetizing force is to be applied to all the remaining magnetic circuits, pro- vided all circuits contain the same number of magnets. In case of several magnetic circuits with a different number of M. M. Fs. in series, as in classes 9, n and 13, which have one long circuit containing all the magnets, and several small circuits with but one or two magnets, respectively, the total M. M. F. of the machine is either the sum of all M. M. Fs. or the joint M. M. F. of one of the small circuits, according to whether the long, or one of the small circuits has been used in calculating the magnetizing force required for the machine. PART n. CALCULATION OF MAGNET WINDING. CHAPTER XIX. COIL WINDING CALCULATIONS. 95. General Formulae for Coil Windings, In practice it frequently is desired to make calculations con- cerning the arrangement, etc., of magnet windings, without reference to their magnetizing forces; and it is for the simpli- fication of such computations that the following general for- mulae for coil windings are compiled. In Fig. 304 a coil bobbin is represented, and the following symbols are used: D m = external diameter of coil space, in inches; d m internal diameter of coil space, in inches; / m = length of coil space, in inches; // m = height of coil space, in inches; y m = volume of coil space, in cubic inches; d m = diameter of magnet wire, bare, in inches; 6' m diameter of magnet wire, insulated, in inches; N m total number of convolutions; Z m = total length of magnet wire, in feet; wt m = total weight of magnet wire, in pounds; r m = resistance of magnet wire, in ohms; Pm resistivity of magnet wire, in ohms per foot; A m = = specific length of magnet wire, in feet per Pm ohm; ^'m specific length of magnet wire, in feet per pound. The total number of convolutions filling a coil space of given, dimensions with a wire of given size is: 359 360 D YNA MO-ELECTRIC MA CHINES. [95 The diameter (insulated) of wire required to fill a bobbin of given size with a given number of convolutions, irrespective of resistance, is: M'. -'-. '-'.:. tsjj J_ * TO Fig. 304. Dimensions of Coil Bobbin. The total length of wire of given diameter which can be wound on a bobbin of given dimensions, is: T . ~ / m X x or: = x 04 = .262 x x x * x + x (253) (254) From (254) the dimensions of a coil can be calculated on which a certain length of wire of given diameter can be wound. If the internal diameter and the height of the coil space are given, the length can be computed from: " 12 x Z m x m ' - and of the mean length of one turn, / t , in feet, thus: An = N m X /t ; furthermore, by (259): z = !=.' m ~ p ' hence, jj> N v T v / m ^m A * m ^ * ~" /} > Pm from which follows the specific length of the wire which gives the desired magnetizing force at the specified voltage between the field terminals, viz. : i (N m X / m ) X / t AT X l t m = 7T ~~^ ~^ A'm -^m ** 364 DYNAMO-ELECTRIC MACHINES. [96 that is to say, the specific length (feet per ohm) of the required wire is the quotient of the number of ampere-feet by the given voltage. In taking from the gauge table the standard size of wire whose feet per ohm are nearest to the figure found by (268), the size of magnet wire that furnishes the required num- ber of ampere-turns, AT, at the given potential difference^, can directly be determined by the length, / t , of the mean turn. Since the value of -i- , from (268), gives the specific length of the hot magnet wire, the next smaller gauge number should be chosen. Inserting (259) into (267) we obtain: E Zm X m which, multiplied by the sectional area of the wire, d^ , gives the cross-section of the wire per unit of current strength, that is, its current density: / m = y=^x (* x p m ). y m ^m The product (# m 2 x Pm) of tne sectional area (in circular mils) of a wire into its specific resistance (in ohms per foot) gives the resistance of one mil-foot of wire of the given material, *'. > * m and since by (272) we have, approximately: ^m X tf m * = 12 X ^r x / tr 96] COIL WINDING CALCULATIONS. we finally obtain: M 2" X / t ) a wf m = 144 X io~ 6 X 15 X s 75 ~ * m or, 367 IOOO (274) The constant 16 is = 144 x ^ 16 , and can be taken from the following Table XCII. : TABLE XCII. SPECIFIC WEIGHTS OP COPPER WIRE COILS, SINGLE COTTON INSULATION. Total Area Specific Value GAUGE OF WIRE. Diam eter. Bare, Inch. Insula- tion S. C. C. Inch. Space Occupied by Wire. Cir. Mils. of Copper. Square Mils. Eatio of Copper to Weight Winding. Ibs. per of Constant in Formula Total cu. inch. (274). Volume of 6 2 X - Coil. B. W. G. B. &S. 6m m m m 4 K\$ Ill re) 4 .204 .012 46,656 32,685 .702 .225 32.5 (7) 5 .182 .012 37,637 26,016 .69 .221 31.8 8 .165 .012 31,329 21,383 .683 .218 31.4 *6 .162 .010 29,584 20,612 .697 .223 32.2 9 10 S .148 .134 .010 .010 24,964 20,736 17.203 14,103 .688 .682 .220 .218 31.7 31.4 11 (9) .120 .010 16,900 11,310 .669 .214 30.8 12 .109 .010 14.161 9,331 .66 .211 30.4 io .102 .010 12.544 8,171 .65 .208 30.0 13 .095 .010 11,025 7,088 .644 .206 29.7 ii .091 .010 10,209 6,504 .637 .204 29.4 (14) 12 .081 .007 7,744 5,153 .665 .213 30.7 15 13 .072 .007 6,241 4.072 .65 .208 30.4 16 (14) .065 .007 5,184 3.318 .64 .205 29.5 17 (15) .058 .007 4,225 2,642 .625 .200 28.8 (18) 16 .051 .007 3,364 2,043 .607 .194 27.9 17 .045 .005 2.500 1,590 .637 .204 29.5 19 .042 .005 2,209 1,385 .627 .201 290 is .040 .005 2.025 1,257 .628 .201 29.0 19 .036 .005 1,681 1,018 .607 .194 27.9 20 .035 .005 1,600 962 .601 .1925 27.7 21 20 .032 .005 1369 804 .587 .187 27.0 22 21 .028 .005 1,089 616 .546 .175 25.2 23 22 .025 .005 900 491 .565 .181 26.1 24 23 .022 .005 729 380 .521 .167 24.1 25 24 .020 .005 625 314 .503 .161 23.2 26 25 .018 .005 529 254.5 .48 .1535 22.1 27 26 .016 .005 441 201 .457 .146 21.0 28 27 .014 .005 361 154 .428 .137 19.8 29 28 .013 .005 324 133 .41 .131 18.9 30 .012 .005 289 113 .391 .125 18.0 29 .011 .005 256 95 .371 .119 17.2 From the above Table it is found that for the most usual sizes of magnet wire (No. 6 B. W. G. to No. 20 B. W. G.) the 368 DYNAMO-ELECTRIC MACHINES. [97 average value of ]6 is .21, and that of 16 is = 30, and therefore approximately: (AT X/tV 30 x ( - I \ 1000 / t> \ / (275) m that is to say: /Ampere-feetV \ 1000 I Weight of winding = Watts absorb ed by Magnet By means of (275) the weight of wire can be found that sup- plies a given magnetizing force at a fixed loss of energy in the field winding. 97. Heating of Magnet Coils. The conditions of heat radiation from an electro-magnet being similar to those of an armature at rest, with polepieces removed, the unit temperature increase of magnet coils can be obtained by extending Table XXXVI., 35, for the specific increase of armatures, to conform with the above conditions. Plotting for this purpose the temperatures given in the first horizontal row for zero peripheral velocity, as functions of the ratio of pole-area to total radiating surface, and prolonging the temperature curve so obtained until it intersects the zero ordinate, the specific temperature rise 6' m = 75 C.(= 135 F.) for i watt of energy loss per square inch of radiating sur- face, is found. The actual temperature increase of any mag- net coil can, therefore, be obtained by the formula: P P 6 B' V m TC O v m m u m A c 75 A c > where m = rise of temperature in magnets, in Centigrade degrees; P m energy absorbed in magnet-winding, in watts; / m = current in magnet wind- ing, in amperes; 2 # = E - M - F - between field -5L ; ] terminals, in volts; m = resistance of magnet winding, in ohms; = radiating surface of magnet coils, in square inches. 97] COIL WINDING CALCULATIONS. 369 The radiating surface of the magnets depends upon the shape and size of the cores as well as the upon the arrangement of the field frame, and can be readily deduced geometrically from the dimensions of the coil. If the polepieces, or yokes, com- pletely overlap the end flanges of the magnet coils, air has access to the prismatical surface only, and the radiating sur- face is for cylindrical magnets: 5 M = An X 7t X /' m = ( m external diameter of cylindrical magnet coil; h m height of magnet winding, see Table LXXX., 83; /' m = total length of magnet coils per magnetic circuit; / length of rectangular or oval core-section; b breadth of rectangular or oval core-section; / T = length of mean turn of magnet wire; by breadth of yoke, or polepiece; n m = number of separate magnet coils in each mag- netic circuit. If the surface, S'u, of the magnet cores is given instead of the radiating surface, 5 M , of the coils, the value of 6' m in (276), instead of being constant at 75 C., ranges between 75 and 4 C. (or 135 and 7 F., respectively), according to the ratio of depth of magnet winding to thickness of core; that is, according to the ratio of radiating surface to core surface. In the following, Table XCIIL, the specific temperature rise, 0' m , is given for round magnets, varying in winding depth from .01 to 2 core diameters, and for rectangular and oval cores ranging in radiating surface from 1.02 to 15 times the surface of the cores. If, for a given type of machine, the approximate ratio of radiating surface to core surface is known, the calculation of the magnet winding can, by means of Table XCIII., directly be based upon the given surface of the magnet cores. 98. Allowable Energy Dissipation for Given Rise of Temperature in Magnet Winding. From formula (276), 97, it is evident that for a given coil the temperature rise depends solely upon the amount of energy consumed, and conversely it follows that by limiting the tern- 97] C0/Z WINDING CALCULATIONS. 37* O QG S Z IS B* 5 p i P l ^8 .2 sSlHl, BJiSl 33 siT aW W o5 nm oo o S3 2 I'll 8 ! I ^ A iota 100 00 00 10 10 i ** oi oo ^ oo et oo O 10 10 (N i CO lO' 00 IN - J-i' CO 10 372 DYNAMO-ELECTRIC MACHINES. [98 perature increase of the coil, the maximum of its energy dissi- pation is also fixed. By transposition of (276) we obtain: % ?** = - 9m 6 x S M , .... ........ (283) and f m = L X 5' M ; ............. (284) where P m = energy dissipation in magnet winding, in watts; m = temperature increase of magnet coils, in degrees Centigrade; 0' m = specific temperature rise of magnet coils, for one watt per square inch of core-surface; SM = radiating surface of magnet coils, in square inches; see formulae (277) to (282); *S" M = surface of magnet cores, in square inches. The temperature rise of magnet coils in practice varies be- tween 10 and 50 C., and in exceptional cases reaches 75 C., the latter increase causing, in summer, a final temperature of the magnets of about 100 C., which is the limit of safe heating of coils of insulated wire. For ordinary cases, therefore, the allowable energy dissipation in the field magnets ranges between P m = ~X .5, = . 133$ and that is, between .133 and .667 watt per square inch (= .02 to .10 watt per square centimetre), or radiating surface is to be provided at the rate of from 7^ to \y 2 square inches per watt (= 50 to 10 square centimetres per watt). The arith- metical mean of these limits, .4 watt per square inch (= .062 watt per square centimetre), or 2% square inches ( 16 square centimetres) per watt, is a good practical average for medium-sized machines, and corresponds to a rise of magnet temperature of 30 C. (= 54 F.). The energy dissipation, P mt thus being fixed by the temper- 98] COIL WINDING CALCULATIONS. 373 ature increase specified, the working resistance of the magnet winding can be obtained by means of Ohm's Law, thus: 77 p v T P i J -'m '-'m /N * m * m /OOC\ - = -7-7 , (285) / / 2 / 2 ' * m * m * m or, *'.= ^-= /m x^ m = ^' ( 286 > according to whether the intensity of the current flowing through the field circuit, or the E. M. F. between the field ter- minals, respectively, is given, the former being the case in series-wound machines and the latter in shunt-wound dynamos. In a series machine the field current is equal to the given cur- rent output, / m /; while in a shunt dynamo the potential .between the field terminals is identical with the known E. M. F. output of the machine, m = E\ see 14, Chapter II. CHAPTER XX. SERIES WINDING. 99, Calculation of Series Winding for Given Tempera- ture Increase. The number of ampere-turns, AT, being found by the for- mulae given in Chapter XVIII., and the field current in a series- dynamo being equal to the given current output, /, of the machine, the number of series turns, -A^, can readily be obtained by dividing the former by the latter: A T N = ~ -(287) The number of turns multiplied by the mean length of one convolution, in feet, gives the total length of the series field wire: A. = N ~* /T (288) in which the length of the mean turn, in inches, is for cylindrical magnets : 4 = ( *^M where A T= ampere-turns required for field excitation, for- mula (227); / T = length of mean turn, in inches, formulae (289) to (292), respectively; 7 = current output of dynamo, in amperes; m = specified temperature increase of magnet wind- ing, in Centigrade degrees; SK = radiating surface of magnet coils, in square inches, formulae (277) to (282). The conclusion of the series field calculation, now, consists in selecting, from the standard wire gauge tables, a wire whose " feet per ohm " most nearly correspond to the result of formula (295). If no one single wire will satisfactorily answer, either ;/ wires of a specific length of A, 'se n feet per ohm each may be suitable stranded into a cable, or a -copper ribbon may be employed for winding the series coil. In the latter case it is desirable to have an expression for the sectional area of the series field conductor. Such an expres- sion is easily obtained by multiplying the specific length, A 89 , by the specific resistance, for, since ohms = specific resistance X -, n circular mils 100] SERIES WINDING. 377 we have: circular mils = specific resistance X feet per ohm; the specific resistance of copper is 10.5 ohms per mil-foot, at 15.5 C.,and the area of the series field conductor, conse- quently, is: tf 8 e 2 = 10.5 X A se = 6 5 x ^T x A X/ x (i +.004 x * m ) . ..(296) In formulae (293) to (296), it is supposed that all the mag- net coils of the machine are connected in series. If this, however, is not the case, the main current must be divided by the number of parallel series-circuits, in order to obtain the proper value of / for these formulae. Having found the size of the conductor, the number of turns, -W se , from (287), will render the effective height, h' mj of the winding space for given total length, /' m , of coil, by transposition of formula (252), 95, thus: V m = ^ 8e x ^!, (297) ' m (#'se) 2 being the area, in square inches, of the square, or rectan- gle, that contains one insulated series field conductor (wire, cable, or ribbon). If h' m , from (297), should prove materially different from the average winding depth taken from Table LXXX., the actual values of / T and S M should be calculated, and the size of the series field conductor checked by inserting these actual values into formula (295) or (296). The product of the number of turns by the actual mean length of one convolution will give the actual length, Z se , of the series field winding, and from the latter the real resistance and the weight of the winding can be calculated. (See 102.) 100. Series Winding with Shunt Coil Regulation. For some purposes it is desired to employ a series dynamo whose voltage can be readily adjusted between given limits. Such adjustment can best be attained by connecting across the terminals of the series field winding a shunt of variable 373 D YNAMO-ELECTRIC MA CHINES. [100 resistance which is opened if the maximum voltage is desired, while its least resistance is offered for obtaining the minimum voltage of the machine, intermediate grades of resistance being used for regulating the voltage of the machine between the maximum and the minimum limits. The series winding in this case is calculated, according to 99, for the maximum voltage of the machine, and then the various combinations of the shunt-coils are so figured as to produce the desired regu- lation, and to safely carry the proper amount of current. As an example let us take five coils arranged, as shown in Fig. 305, so as to permit of being grouped, by moving the SERIES FIELD WINDING Flo. 305 DIAGRAM OF SERIES WINDING WITH SHUNT COIL.REGULATION. FIG. 309 4TH COMBINATION FIG. 310 5TH COMBINATION. Figs. 305 to 310. Shunt Coil Combinations. slider of the adjusting switch into five different combinations, illustrated by Figs. 306 to 310. The resistances and sectional areas of these coils are to be so determined as to enable 60, 66f, 75, 83^, and 90 per cent, of the maximum voltage to be taken from the machine. It is evident that in this case 40, 33^, 25, i6f, and 10 per cent, re- spectively, of the maximum field current will have to be absorbed by the respective combinations of the shunt coils, and their resistance, therefore, must be: Resistance first combination 60 = X resistance of series field = 1.5 r r K . Resistance second combination resistance of series field = 2 100] SERIES WINDING. 379 Resistance third combination = - X resistance of series field = 3 r' se . Resistance fourth combination = |f- X resistance of series field = 5 r' K . Resistance fifth combination oo = - - X resistance of series field = o r' . 10 For the arrangement shown in Figs. 305 to 310, the first combination consists of coils I, II, and III, in parallel, the second combination of coils II and III in parallel, in the third combination only coil III is in circuit, in the fourth combina- tion coils III and IV are in series, and the fifth combination has coils III, IV, and V in series. In all combinations there are, furthermore, the flexible leads carrying the current from the field terminal to the adjusting slider; these are in series to the group of coils in every case, and their resistance, r t , consequently is to be deducted from the resistance of the combination in order to obtain the resistance of the group of coils alone. Expressing the resistances of the various groups by the resistances of the single shunt-coils, we therefore obtain : First group: t ; ...... (298) Second group: - -- r = a^-n; ........ (299) r u r m Third group: 'm = 3^'se - n; ........ (300) Fourth group: r m + r n zsSm-ri; ........ (301) Fifth group: , ........ (302) From this set of equations the resistances of the separate shunt-coils can be derived as follows: 380 DYNAMO-ELECTRIC MACHINES. [ 10O Inserting (299) into (298): >-i 2 r' se - whence: 'se - n) X (1.5 r r _ " The resistance of the leads being very small, rf can ber neglected, hence the resistance of coil I: r, = 6r' se - 7n (303) (300) into (299) gives: i 4-+ or: - (3 ^^ ~ n) X (2 r y M - rQ (3 ^ - rO - ( 2 r' se - rj se ' se Neglecting again r^ , the resistance of coil II is obtained : r n s=6^-Sn .............. (304) From (300) we have, directly : 'HI = 3^'se- n .............. (305) By subtracting (300) from (301): riv - 2 ,' ............... (306) By subtracting (301) from (302): r v = 4r' se ............... (307) In the above formulae, r'^ is the resistance of the series field, hot, at maximum E. M. F. output of machine; and ^ the resistance of the current-leads at the temperature of the 100] SERIES WINDING. 381 room. The resistance r\ is determined by finding the length and the sectional area of the leads, the former being depend- ent upon the distance of the adjusting switch from the field terminal, and the latter upon the maximum current to be car- ried, which in the present case is 40 per cent, of the current output of the machine. The currents flowing through the shunt coils in the various combinations can be obtained by the well-known law of the divided circuit, by virtue of which the relative strengths of the currents in the different branches are directly proportional to their conductances, or in inverse proportion to their resistances. The first combination consists in three parallel branches having the resistances r^ r tt , and r m , respectively, and carries a total current of .4 / amperes, hence the currents in the branches: T" r i r m ~r r v . X -4 i u / f i f m v r -* n i ~ X 4 * > 'n r m + r T r m + r x r n and 7 m=7 /;? , rr x.4/. r n ^ui T r i r in T r i r n Inserting into these equations the values of the resistances from (303) to (307), respectively, we obtain: T- (6r'se sn) (3^'se r\) (6r'se 5^1) (sr'se r\) -j- (e^'se yri) (sr'se n) + (6r'se 7n) (6r r se 5^1) X.4/ = - Tf ~ 2Ir " ri T 5ri 2 x .4 / = - x .4 / = . i /, 72/ 8e a -- 121^^ + 47^ 4 and + * 3 ' 1 X.4/--X .4/=,2/. In the second combination there are but two parallel 382 DYNAMO-ELECTRIC MACHINES. [ 100 branches, having the resistances r u and r m , and the total cur- rent carried is .333 /amperes ; therefore: /n = ~r X -333 / = 3 '" ~ X .333 / = 7 X .333 ! = - 111 7 > o and / ^ n v i?? / 6r ' se ~ 5 r i v 7 ~, / m ~ ^ j_ X -333 y > -- z^ X .333 J r u ~r r m 9 r ae 0^1 = - X -333 7 = - 222 7 - 9 The third, fourth, and fifth combinations are simple circuits only, the current through the coils therefore is identical with the total current flowing through the combination, viz. : .25 /, .167 /and .1 /amperes respectively; the first named current, consequently, flows through coil III when in the third com- bination, the second current through coils III and IV, when in the fourth combination, and the last figure given is the cur- rent intensity in coils III, IV, and V, when in the fifth com- bination. Taking the maximum value for the current flowing in each coil, the following must be their current capacities: Coil I and V: /! = / v = . i / = , " II: / n = .ii v i " HI: /m=.25 " IV: / IV = .i6 7 /=, ........ (311) By allowing 1000 circular mils per ampere current intensity, the proper size of wire for the different shunt coils can then readily be determined from formulae (308) to (311). The preceding formulae (298) to (311) of course only apply to the special arrangement and to the particular regulation selected as an example, but can easily be modified for any given case [see formulae (457) to (466), 134], the method of their derivation being thoroughly explained. ' / (309) 9 ' / ..(310) 4 ' CHAPTER XXI. SHUNT WINDING. 101. Calculation of Shunt Winding for Given Tem- perature Increase. The problem here to be considered is to find the data for a shunt winding which will furnish the requisite magnetizing force at the specified rise of the magnet temperature, and with a given regulating resistance in series to the shunt coils, at normal output. The shunt regulating resistance, or as it is sometimes called, the extra-resistance, admits of an adjustment of the resistance of the shunt-circuit within the limits prescribed, thereby inversely varying the strength of the shunt-current, which in turn correspondingly influences the magnetizing force and, ultimately, regulates the E. M. F. of the dynamo. In cutting out this regulating resistance, the maximum E. M. F. at the given speed is obtained while the minimum E. M. F. obtaina- ble is limited by the total resistance of the regulating coil. By specifying the percentage of extra-resistance in circuit at normal load, and the total resistance of the coil, any desired range may be obtained; see 103. Designating the given percentage of extra-resistance by r x , the total energy absorbed in the shunt-circuit, consisting of magnet winding and regulating coil, can be expressed by: where f\ ^ sh = SM = energy absorbed in the magnet winding alone. 75 The potential between the field terminals of a shunt dynamo being equal to the E. M. F. output, , of the machine, the current flowing through the shunt-circuit is: '* = ^T .......... ..... (313) 383 384 DYNAMO-ELECTRIC MACHINES. [ 10L and the number of shunt turns, therefore : AT ATX E /Q1 (314:) By means of formulae (289) to (292), which apply equally well to shunt as to series windings, the approximate mean length of one turn is found, and the latter multiplied by the number of turns gives the total length of the shunt wire: ...(315) " X 75 By Ohm's Law we next find the total resistance of the shunt- circuit at normal load, viz.: x 1, 75 This contains the r x per cent, of extra resistance; in order to obtain the resistance of the shunt winding alone, r" sh must be decreased in the ratio of i : and we have: i n T IOO jm v 9 S 75 M , IOQ X , (317) which is the resistance of the magnet winding when hot, at a temperature of (15.5 -j- e m ) degrees Centigrade; the magnet resistance, cold, at 15.5 C, consequently, is : = r * X i + .004 X 101] SHUNT WINDING. 385 E* i i The division of (315) by (318), then, furnishes the specific length of the required shunt wire: The size of the shunt wire can then be readily taken from a wire-gauge table; if a wire of exactly this specific length is not a standard gauge wire, either a length of Z 8h feet of the next larger size is to be taken, and the difference in resistance made up by additional extra-resistance, or such quantities of the next larger and the next smaller gauge wires are to be combined as to produce the required resistance, r eh , by the correct length, Z sh . To fulfill the latter condition, the geo- metrical mean of the specific lengths of the two sizes must correspond to the result obtained by formula (319); thus, if A' sh is the specific length of one size of wire and A" 8h that of the other, such proportions, Z' sh and Z" 8h , of the total length, Z sh Z' sh -f Z" 8h , are to be taken of each that: ^ sh X Z ah -\- A sh X Z sli -\ /QOA\ 77 i 777 -=^8h, (dV) Since in this equation every term contains a length as a factor, any length, for instance Z' sh , may be unity, and we have: from which follows the proper ratio of the lengths of the two wires: Sh 8h 386 DYNAMO-ELECTRIC MACHINES. [101 If the two sizes are combined by their weight, the specific weights, in pound per ohm, are to be substituted for the specific lengths in the above equations. The sectional area of the shunt wire which exactly furnishes the requisite magnetizing power at the given voltage between field terminals, with the prescribed percentage of extra- resistance in circuit, and at the specified increase of magnet temperature, may be directly obtained by the formulae = - 8 75 X ^X / T X fl + jSy X (i + .004 X 8 m ). (322) In the above formulae, E is the E. M. F. supplying the shunt coils of one magnetic circuit, and is identical with the terminal voltage of the machine, if the shunt coils are grouped in as many parallel rows as there are magnetic cir- cuits. But if the number of parallel shunt-circuits differs from the number of magnetic circuits, the output E. M. F. of the machine, in order to obtain the proper value of E for cal- culating the shunt winding, must be multiplied by the ratio of the former to the latter number. The size, or sizes, of the shunt wire thus being decided upon, by means of formulae (319) or (322), the actual value of ft m , and therefrom the real length of the mean turn is to be computed (see formulae (289) to (291)), and to be inserted into formulae (319), or (322), respectively. In case of two sizes of wire being used, the winding depth can with sufficient accuracy in most cases be found by means of the formula: + which, however, on account of the fact that the mean length of a turn of the one size of wire is different from that of the other, and that, therefore, the ratio of the number of turns of the two sizes differs from the ratio of their length, is only approximately correct and gives accurate results in case of 101] SHUNT WINDING. 387 comparatively long and shallow coils only. For short and deep coils, Fig. 311, the heights of the winding spaces for the ~t~ 11 T T Fig. 311. Dimensions of Shunt Coil. two sizes are to be separately determined by formula (257), thus: X X ' A or: X amp.'xohm-s' 31.3 x ( -feet s (327) watts which agrees, substantially, with formula (275), 96. The denominator of equation (327), since the specific length of the magnet wire in (326) is given at 15.5 C., represents the energy lost in the magnets at that temperature, that is, the actual energy consumption, at the final temperature (15.5 -f m ), of the magnet winding, divided by (i -f- .004 x 9 m ); hence the weight of bare magnet wire necessary to produce a given mag- 39 DYNAMO-ELECTRIC MACHINES. [106 netizing force, AT, at a specified rise, 6 m , of the magnet tem- perature: 1000 * m = 31-3 x-Y- -^-x (i.+ .004 x e m ), (328) 75" > M in which AT number of ampere-turns required; / t = mean length of one turn, in feet; m = specified rise of temperature, in Centigrade degrees; S x = radiating surface of magnets, in square inches. In case of a compound winding, (328) will give the weights of the series and shunt wires, respectively, if A T is replaced by ^7* se and AT sh , and if the energies consumed by each of the two windings individually are substituted for the total energy loss in the magnets. By, transformation, the above formula (328) can be employed to calculate the temperature increase m , caused in exciting a magnetizing force of A T ampere-turns by a given weight, wt m pounds, of bare wire filling a coil of known radiating surface, S M square inches. Solving (328) for m , we obtain: [ : ^~i . (329) "m ~ wt m .004 X The weight of copper contained in a coil of given dimen- sions is: w/ m = /. X /' m X t m X .21 , (330) where / T = mean length of one turn, in inches; /' m = length of coil, in inches; h m = height of winding space, in inches; .21 = average specific weight, in pounds per cubic inch, of insulated copper wire, see Table XCIL, 96. 103. Calculation of Shunt Field Regulator. The voltage of a shunt-wound machine is regulated by means of a variable rheostat inserted into the shunt-circuit. 103J SHUNT WINDING. 391 The total resistance of this shunt regulator must be the sum. of the resistances that are to be cut out of, and added to, the shunt-circuit in order to effect, respectively, an increase and a decrease of the exciting current sufficient to cause the normal E. M. F. to rise and fall to the desired limits. The amount of regulating resistance required to produce a given maximum or minimum E. M. F. is obtained, in per cent, of the magnet resistance, by determining the additional ampere-turns needed, for maximum voltage, or the difference between the magnet- izing forces for normal and for minimum voltage respectively, for, the magnetic flux, and with it the magnetic densities in. the various portions of the magnetic circuit, must be varied in, direct proportion with the E. M. F. to be generated. If the dynamo is to be regulated between a maximum E. M. F., E' m&K , and a minimum E. M. F., -' min , the magnet- izing forces required for the resulting maximum and minimum flux are found as follows: The exciting power required for the air gaps varies directly with the field density, hence the maximum magnetizing force,, by (228): X (f \ IP" N/ max \ E } and the minimum magnetizing force: The values of l\ in these formulae may differ from each other, and also from that for normal voltage, owing to the fact that the product of field density and conductor velocity may have increased or decreased sufficiently to influence the constant 13 in formula (166). For each value of 3C", there- fore, Table LXVL, 64, must be consulted. For the iron portions of the magnetic circuit the specific magnetizing forces for the new densities are to be found from Table LXXXVIII., 88, and to be multiplied by the length of the path in the frame; thus, for maximum voltage: I n > in a * m "* max A * m 1 EV w/r max corresponding to a density of &' i/ 1 / m 392 DYNAMO-ELECTRIC MACHINES. [ 103 and for minimum voltage: <*t"m m "mm X I" m , EV ^min corresponding to a density of (B" m X -^r 9 ' The magnetizing force required to compensate the armature reactions, finally, is affected by the change of density in the polepieces, the latter determining the constant ]B in formula (250); in calculating the compensating ampere-turns for the maximum voltage, the value of 15 from Table XCI. is to be taken for a density of <&' max p ^ 77' and in case of the minimum voltage, for a density of F 1 (nn ^ -^ min * p x &- lines per square inch. Having determined the maximum and minimum magnetizing forces for the various portions of the circuit, their respective sums are the excitations, AT m&Ji and AT min , needed for the maximum and minimum voltage. The number of turns be- ing constant, the magnetizing force is varied by proportion- ally adjusting the exciting current, and this in turn is effected by inversely altering the resistance of the field circuit. The excitation for maximum voltage is AT times that for normal load, hence the corresponding minimum shunt resistance, that is, the resistance of the magnet winding alone, must be AT times the normal resistance of the shunt-circuit, or, the extra resistance in circuit at normal load is: A r max -AT r* = 100 X - 103] SHUNT WINDING. 393 per cent, of the magnet resistance. The magnetizing force for minimum voltage, similarly being AT times that for normal output, the maximum shunt resistance is AT ~AT~* times the normal, or, regulating resistance amounting to ' " per cent, of the normal resistance, which is , OX -H- A ^ per cent, of the magnet resistance, is to be added to the nor- mal shunt resistance in order to reduce the E. M. F. to the required limit. Expressing the sum of these percentages in terms of the magnet resistance, we obtain the total resistance of the shunt regulator: A T max AT AT mSLX AT A T -- -~ X - This resistance is to be divided into a number of subdi- visions, or "steps," said number to be greater the finer the degree of regulation desired. Since the shunt-current de- creases with the number of steps included into the circuit, material can be saved by winding the coils last in circuit with finer wires than the first ones. At the maximum voltage the shunt-current, by virtue of Ohm's Law, is: (^Oma* = ^, (332) and at minimum voltage we have: (/d)min= ^^ , (333) ^sh + r r the current capacity of any coil of the regulator, therefore, can with sufficient accuracy be determined by proper interpolation 394 DYNAMO-ELECTRIC MACHINES. [103 between the values obtained by formula (332) and (333). Thus, the current passing through the shunt-circuit when /z x coils of the regulator are contained in the same, is found : IT \ - (T \ r V * sh)max (^sh)min /QQJX V/shjx (/shjmax ~ n x X ~ , (od4r) n r where n r is the total number of the coils, or steps, of the reg- ulator. From (334) we obtain by transposition: _ (^shjmax V/sh)x v, X the latter formula giving the number of coils which must be added to the magnet winding in order to cause any given cur- rent, (/sh) x , to flow through the shunt-circuit. CHAPTER XXII. COMPOUND WINDING. 104. Determination of Number of Shunt and Series Ampere-Turns. Since in a compound dynamo the series winding is to supply the excitation necessary to produce a potential equal to that lost by armature and series field resistance, and by armature reaction, the number of shunt ampere-turns for a compound- wound machine is the magnetizing force needed on open circuit, and the number of series ampere-turns required for perfect regulation is the difference between the excitation needed for normal load and that on open circuit. The proper number of shunt and series ampere-turns can, therefore, be computed as follows: The useful flux required on open circuit is that number of lines of force which will produce the output E. M. F., E, of the dynamo, viz. : _ 6 X n' 9 X E X io 9 ~ N e X N hence the ampere-turns needed to overcome, on open circuit, the reluctances of air gaps, armature core, and magnet frame, respectively, are: <*t go - .3133 x -j- x r g , at &o = m\ Q X / r/ a , and tf/ mo = w" w .i. X /" W .L + "ej. X /" c .i + ^" c . 8 . X /'., in which m\ , m" w , L , ;;/" Cii and w" c . s . are the specific mag- . , .. o netizing forces corresponding to densities - -^ ? > ~ A < a w f r ordinary compound wind- ing; see formula (19), 14; and E' = E -f /' x (r\ -\- r'^), for long-shunt compound winding; see formula (22), 14. Since, however, / and /' are very nearly alike, E' is practi- cally the same in either case. Besides, E' can only be approxi- mately determined at this stage of the calculation, since the series field resistance is not yet known. Taking the latter as .25 of the armature resistance, we therefore have for either kind of a compound winding: '= E+ i.2 5 /'r' a ............ (337) In case the machine is to be over compounded for loss in the line, the percentage of drop usually 5 percent. is to be in- cluded into the output E. M. F., hence the total E. M. F. generated at normal load, for 5 per cent, overcompounding: '= 1.05^+ i.2 5 7'/ a .......... (338) The magnetizing forces required at normal load, then, are: # af g = -3133 x -~-x /'; and = m\ X /" a ; " c .i. x /" c .i. + m"^ x N x 7 ' ^ X a i*i"r "-14 /\ i '^ p 180 w/r a > w "w.i.> w " c .i. an d w "c.s. are tne specific magnetizing forces corresponding to the densities -j-' -^ ' and ' re- OoOtwi *J{ O a w.i. " c,i. "a -' w.i. c.i. spectively, A, being the leakage factor at normal output. 104] COMPOUND WINDING. 397 Their sum is the total number of ampere-turns needed for excitation at normal output: this is supplied by shunt and series winding combined, conse- quently the compounding number of series ampere-turns: ..... (339) In the above formulae for at m& and at m , the factors A and A are the leakage coefficients of the machine on open circuit and 312 and 313. Positions of Exploring Coils for Determining Distribu- tion of Flux in Dynamos. at normal load, respectively. Although the effect of the armature current upon the distribution of the magnetic flux in the different parts of the machine is very marked, as shown by tests made by H. D. Frisbee and A. Stratton, ' the ratio of the total leakage factors in the two cases, especially in com- pound-wound machines, is so small that the factor A, as obtained from formulae (157), can be used for the calculation of both the shunt and the total ampere-turns. Since, however, it is very instructive to note the actual difference between the distribu- tion of the magnetic flux at normal output and that on open circuit, the results of the tests mentioned above are compiled in the following Table XCV., in which all the flux intensities in the various parts of the different machines experimented upon are given in per cent, of the useful flux through the 1 "The Effect of Armature Current on Magnetic Leakage in Dynamos and Motors," graduation thesis by Harry D. Frisbee and Alex. Stratton, Columbia College ; Electrical World, vol. xxv. p. 200 (February 16, 1895). 398 DYNAMO-ELECTRIC MACHINES. [104 10 10 10 10 1C 1C CO 1C O O OS Tt< -*' TH & 10 t- i-J ?O- CO 00 i-H < IO 1O IO CO -^ rt< t- l l "3*5 si IO 1O 1O SOS lO O 1> TH T-I IO IO 10 O CO & w co 05 w e rt< co oi Saoo 0? TH (75 TH TH rH IO IO CO 1O So TH -THOOS TJ< co oqi^odo G-?THrHCO OS T-I CO 25 IO 1OI> 'CO ^^ .^H 10 CO 10 GO CO C4O5CO TH 10 CO ^ g .& t :M 105] COMPOUND WINDING. 399 armature, the various positions of the exploring coils being shown in the accompanying Figs. 312 and 313. Appended to this table are the respective leakage factors, obtained in divid- ing for each case the maximum percentage of flux by 100, and also the ratios of the leakage factor at normal output to that on open circuit. 105. Calculation of Compound Winding for Given Temperature Increase. After having determined the number of shunt and series ampere-turns giving the desired regulation, the calculation of the compound winding itself merely consists in a combination of the methods treated in Chapters XX. and XXI. The total energy dissipation, P m , allowable in the magnet winding for the given rise of m degrees being obtained from for- mula (283), this energy loss is to be suitably apportioned to the two windings, preferably in the ratio of their respective mag- netizing forces, so that the amount to be absorbed by the series winding is: P K = f X f m = f X f s X S. watts; (340) hence, by (294), the resistance of the series winding, at 15.5 C. : /* i + .004 X 6 m * ~ X ya X , fl ~ (4:1) The number of series turns being readily found from -se T the total length of the series field conductor is: /' AT r Ae = ^ se X - = * x ji feet, and this, divided by the series field resistance, furnishes the specific length of the required series field conductor, thus: 400 DYNAMO-ELECTRIC MACHINES. [105 /' AT *?e 7 2 x ~ x -p-x ^x (. +.004 x U se * l2 ** 2 ae m *->M x/ T 7 V / V /' = 6 ' 2S x -sTxl x (I + ' 04 x U ..... (342) where /' T = mean length of one series turn, in inches. The sectional area of the series field conductor, therefore. analogous to (296), is: = 10.5 x A^ 7 v /' X(i+.oo 4 xe m ) ...... (343) If one single wire of this cross-section would be impractical, one or more cables stranded of n^ wires, each of circular mils, may be used, or a copper ribbon may be em ployed. The actual series field resistance, at 15.5 C, then being: L = 10.5 X , = 10.5 X the actual energy consumption in the series winding is: f = i" x f> m = - 8?5 X / ' X ' X * X f + - 04 X "- and, consequently, the energy loss permissible in the shunt winding: -* sh -^m -* se = ~ X ^ - / f X ^ X (i + .004 X fl m ) ...... (346) If the extra-resistance at normal load is to be r^ per cent. of the shunt resistance, the total watts consumed by the entire- 105] COMPOUND WINDING. 401 shunt-circuit can be obtained by (312); formulae (313) to (317) then furnish the number of shunt turns, the total length, and the resistance of the shunt wire, and from (318) and (319) the specific length and the sectional area are finally received: AT I" / r \ ^ = ^x~ x/i + ^ o jx(i+.oo 4 xe m ) ....(347) - .875 x x /', x + \x(i+.oo 4 in ) (348) In estimating the mean lengths of series and shunt turns, /' T and /" T , respectively, all depends upon the manner of plac- ing the field winding upon the cores. If the winding is per- formed by means of two or more bobbins upon each core, the series winding filling one spool, preferably that nearest to the brush cable terminals, and the shunt winding occupying the remaining ones, then the approximate mean length, /' T , of one series-turn is equal to that of one shunt turn, /" T , and also identical with the average turn, / T , given by Tables LXXX., 83, and XCIV., 99. But, if the field coils are wound directly upon the cores the series winding usually being wound on first the lengths /' T and /" T differ from each other, and can be approximately determined by apportioning from J to ^ of the average winding height, given in Table LXXX., to the series winding, and the remainder to the shunt winding. TART 11. EFFICIENCY OF GENERATORS AND MOTORS. DESIGNING OF A NUMBER OF DYNAMOS OF SAME TYPE. CALCULATION OF ELECTRIC MOTORS, UNIPOLAR DYNAMOS, MOTOR-GENERATORS, ETC. DYNAMO-GRAPHICS. CHAPTER XXIII. EFFICIENCY OF GENERATORS AND MOTORS. l 106. Electrical Efficiency. The electrical efficiency, or the economic coefficient of a dynamo, is the ratio of its useful to the total electrical energy in its armature, the latter being the sum of the former and of the energy losses due to the armature and field resistances; hence the electrical efficiency of a generator : P P Ve ~~pT " p I ~~p i p > V**^^) and that of a motor : 7. = P p = P ~ (P j, + P *\ (850) where 7/ e = electrical efficiency of machine; P electrical energy, at terminals of machine; P = electrical activity in armature, or total energy engaged in electromagnetic induction; P & energy absorbed by armature winding; /> M = energy used for field excitation. In case of a generator, P is the output available at the brushes, while in a motor it is the total energy delivered to the terminals, that is, the intake of the motor. Inserting into (349) and (350) the expressions for P, P M and P M in terms of E. M. F. current-strength and resistance, the following formulae for the electrical efficiency are obtained: Series-wound generator: 1 See "Efficiency of Dynamo-Electric Machinery," by Alfred E. Wiener; American Electrician, vol. ix. p. 259 (July, 1897). 45 406 DYNAMO-ELECTRIC MACHINES. [107 Shunt-wound generator: ^QK\ ; Compound-wound generator: Series-wound motor: .e=* 7 - 7 ;^ + ^; ............ (354> Shunt-wound motor: Compound-wound motor: Since the electrical efficiency does not include waste by hys- teresis, eddy currents, and friction, but is depending upon the energy losses due to heating by the current only, it may be adjusted to any desired value by properly proportioning the resistances of the machine; see formulae (10), (13), (20), and (23), 14. The electrical efficiency of modern dynamos is. very high, ranging from rj e = .85, or 85 per cent., for small machines, to as high as 7/ e = .99, or 99 percent., for very large generators. 107. Commercial Efficiency. By the commercial or net efficiency of a dynamo-electric machine is meant the ratio of its output to its intake. The intake of a generator is the mechanical energy required to drive it, and is the sum of the total energy generated in the armature and of the energy losses due to hysteresis, eddy cur- rents, and friction; the intake of a motor is the electrical energy delivered to its terminals. The output of a generator is the electrical energy disposable at its terminals; the output of a motor is the mechanical energy disposable at its shaft, and 1O7] EFFICIENCY OF GENERATORS AND MOTORS. 4 7 consists in the useful energy of the armature diminished by hysteresis, eddy current, and friction losses. The commercial efficiency of a generator, therefore, is: P" ~ P' P' - P' (357) and that of a motor : P' - P'. P' - (A + P, + /o) _ ' p ~ p P in which /7 C = commercial or net efficiency of dynamo; P = electrical energy at terminals, /". e. y output of generator, or intake of motor; P' electrical activity in armature; P" = mechanical energy at dynamo shaft, /. e., driv- ing power of generator, or mechanical out- put of motor, respectively; P & = energy absorbed by armature winding; /* M energy used for field excitation; P h = energy consumed by hysteresis; P e = energy consumed by eddy currents; P = energy loss due to air resistance, brush fric- tion, journal friction, etc. ; P' = energy required to run machine at normal speed on open circuit. Substituting in the above formulae the values of P, P M and PM, the following set of formulas, resembling (351) to (356), is obtained : Series-wound generator: (359) Shunt-wound generator: I T '2 < ~\- J ^a 408 DYNAMO-ELECTRIC MACHINES. [107 > ; (3< Compound-wound generator: El Series-wound motor: . ih= *f-v(,. + ,j + j>.l, .......... (362) Shunt-wound motor: -[/'V- a + 7 sh 3 r* sh + / o] . Compound-wound motor: /- r ' /' r" f -/ y In case of belt-driving, the mechanical energy at the dynamo shaft, in foot-pounds per second, can also be expressed by the product of the belt-speed, in feet per second, and of the effect- ive driving power of the belt, in pounds, or, converted into watts : = ..3564 x v'* x (F, -A), .................. (365) where V B belt velocity, in feet per minute; z/ B = belt velocity, in feet per second; jF B = tension on tight side of belt, in pounds; y B = tension on slack side of belt, in pounds. The commercial efficiency of a generator, therefore, may be expressed by: 64 X*-x (*-.-/.) and the commercial efficiency of a motor, by: P" 1.3564 X v'y X (F* -/B) '- The commercial efficiency, 7/ c , of a dynamo is always smaller than its electrical efficiency, 7/ e , since the former, besides the electrical energy-dissipation, includes all mechanical and mag- 108] EFFICIENCY OF GENERATORS AND MOTORS. 4 9 netic energy losses, such as are due to journal bearing fric- tion, to hysteresis, to eddy currents, and to magnetic leakage. The commercial efficiency, therefore, depends upon the .amount of the electrical efficiency, upon the shape of the armature, upon the design, workmanship, and alignment of the bearings, upon the pressure of the brushes, upon the quality of the iron employed in its armature and field magnets, and upon the degree of lamination of the armature core; while the electrical efficiency is a function of the electrical resistances only. The mechanical and magnetical losses vary very nearly proportional to the speed; the no load energy consumption for any speed, consequently, is approximately equal to the open circuit loss at normal speed multiplied by the ratio of the given to the normal speed. The commercial efficiency of well-designed machines ranges from ;/ c .70, or 70 per cent., for small dynamos, to ^ c = .96, or 96 per cent., for large ones. Since in a direct-driven generator the commercial efficiency is the ratio of the mechanical power available at the engine shaft to the electrical energy at the machine terminals, for comparisons between direct and belt-driven dynamos the loss in belting should also be included into the commercial effi- ciency of the belt-driven generator. The following Table XCVI. contains averages of these losses for various arrange- ments of belts: TABLE XCVI. LOSSES IN DYNAMO BELTING. ARRANGEMENT OP BELTS. Loss IN BELTING IN PER CENT. op POWER TRANSMITTED. Horizontal Belt 5 to 10 per cent. Vertical Belt 7 " 12 Countershaft and Horizontal Belt 10 " 15 Countershaft and Vertical Belt 12 " 20 Main and Countershaft with Belts 20 " 30 108. Efficiency of Conversion. The efficiency of conversion, or the gross-efficiency, is the ratio of the electrical activity in the armature to the mechanical energy at the shaft, or vice versa; that is to say, in a generator 4io DYNAMO-ELECTRIC MACHINES. [109 it is the ratio between the total electrical energy generated and the gross mechanical power delivered to the shaft, and in a motor is the ratio of the mechanical output to the useful electrical energy in the armature. Or, in symbols, for a generator: P' P ' 2 (r a + r se ) + 7 sh 2 r" s P' _ _ _ " 746 hp ~ 1.3564 X Z/B X (-/? - /B) ' and for a motor : P P'-P' P-P P ...(368) 7 - [/' 2 (r a El- [/''K + ^ _ 746 ^/ _ 1.3564 X PB X - ^'y E 1 r -A) - ...(369) The efficiency of conversion, ^ g , is the quotient of the com- mercial and electrical efficiencies, ancl therefore varies between ri s = = ^ .82, or 82 per cent., -85 for small dynamos, and ife = - = l- = .97, or 97 per cent, Tor large machines. 109. Weight-Efficiency and Cost of Dynamos. As the commercial efficiency increases with the size of the machine, so the weight-efficiency that is, the output per unit weight of the machine in general is greater for a large than for a small dynamo, and the cost of the machine per unit out- put, therefore, gradually decreases as the output increases. If all the different sized machines of a firm were made of the 109] EFFICIENCY OF GENERATORS AND MOTORS. 411 same type, all having the same linear proportions, and if all had the same, or a gradually increasing circumferential velocity, and were all figured for the same temperature increase in their windings, then the weight-efficiency would gradually increase according to a certain definite law, and the cost per KW would decrease by a similar law. In practice, however, such definite laws do not exist for the following reasons: (i) Up to a certain output a bipolar type is usually employed, while for the larger capacities the multipolar types are more economical; this change in the type causes a sudden jump to take place, both in the weight-efficiency and in the specific cost, between the largest bipolar and the smallest multipolar sizes. (2) The machines of the different capacities are not all built in linear proportion to each other, but, in order to economize material, tools, and patterns the outputs of two or three consecutive sizes are often varied by simply increasing the length of armature and polepieces; in this case a small machine with a long armature may be of greater weight-efficiency and of a smaller specific price than the next larger size with a short armature. (3) The conductor-velocity is not the same in all sizes; as a general rule, it is higher in the bigger machines, but often the increase from size to size is very irregular, causing deviation in the gradual increase of the weight-efficiency. (4) Certain sizes of machines being more popular than others, a greater number of these can be manufactured simultaneously, and therefore these sizes can be turned out cheaper than others, and the specific cost of such sizes will likely be smaller than that of the next larger ones. (5) Large generators frequently are fitted with special parts, such as devices for the simultaneous adjustment and raising of the brushes, arrangements for operating the switches, brackets for supporting the heavy main and cross-connecting cables, platforms, stairways, etc., the additional weight and cost of these extra parts often lowering the weight efficiency and increasing the specific cost beyond those of smaller sizes not possessing such complications. These various considera- tions, then, show why prices differ so widely, and why the ratio of weight to output is so varied; and they offer a reason for the fact that the data derived from different makers' price- lists are at such a great variance from each other. 4 I2 D YNA MO-ELECTRIC MA CHINES. [ 109 In the following Table XCVII. the author has compiled the average weights and weight-efficiencies (watts per pound), for all sizes of high-, medium-, and low-speed dynamos as averaged from the catalogues of numerous representative American manufacturers of high grade electrical machinery: TABLE XCVII. AVERAGE WEIGHT AND WEIGHT-EFFICIENCY OF DYNAMOS. CAPAC- HI 19 , ^ and ;z' p are constant, and may be transferred from (373) to (374), still more simplifying the working formula, which under these con- ditions becomes: <4 = K' X iTx'rf 7 ". , .......... (375) 416 DYNAMO-ELECTRIC MACHINES. [ 111 while the corresponding preliminary formula is : x n ' x K' = 2887 x A/ _ E> v . .(376) V (B'm X * 18 X z' c X Having found the armature diameters for the various sizes, their lengths can then be readily obtained by multiplication with/ 18 ; and diameter and length of the armature determine the principal dimensions of the field frame. The calculation of the total magnetizing force and of the field winding, for the number of dynamos of the same type, by similarly extracting from the respective formulae all the fixed quantities, may also be somewhat simplified, but the direct methods given for the field calculation are already so simple that not much can be gained by so doing, and it is therefore preferable to separately consider every single case. 111. Output as a Function of Size. If the ratio of the dimensions of two dynamos of the same type is i : ;;/, the ratio of their respective outputs can be expressed as an exponential function of this ratio of size, as follows: If the exponent x is given for the various practical condi- tions, the dimensions of any dynamo for a required output can, therefore, be calculated from the dimensions, and the known output of one machine of the type in question, from the formula: (377) which gives the multiplier, by which the linear dimensions of the known machine are to be altered in order to obtain the required output. The author, by a mathematical deduction, ' has found the theoretical value of the required exponent to be : * = 2.5. 1 " Relation Between Increase of Dimensions and Rise of Output of Dynamos," by Alfred E. Wiener, Electrical World, vol. xxii. pp. 395 and 409 (November 18 and 25, 1893) ; Elektrotech. Zeitschr., vol. xv. p. 57 (February J, 1894). 111] DESIGNING DYNAMOS OF SAME TYPE. 417 In the mathematical determination of x, however, the thick- ness of the insulation around the armature conductor has, for convenience, been neglected. The theoretical value found, therefore, holds good only for the imaginary case that the entire winding space is filled with copper. Since the per- centage of the winding space occupied by insulating material is the larger the smaller the armature, the difference between the actual and the theoretical output will be the greater, com- paratively, the smaller the dynamo, and it follows that the exponent, x, varies with the sizes of the machines to be compared. Furthermore, the area of the armature conductor decreases with the voltage of the machine; in a high-voltage dynamo, therefore, a larger portion of the winding space is occupied by the insulation than would be the case if the same machine were wound for low tension. From this it follows that the output of any dynamo, if wound for low voltage, is greater than if wound for high potential, and the value of the expo- nent x, consequently, also depends upon the voltages of the machines to be compared. Taking up by actual calculation the influence of size and of voltage upon the value of x, the general law was found that the exponent of the ratio of outputs of two dynamos of the same type increases with decreasing ratio of their linear dimensions as well as with decreasing ratio of their voltages; the theoretical value being correct only for the case that the dynamo to be newly designed is to have 10 or more times the voltage, and at least the 8-fold size of the given one. This law is observed to really hold in practice, as can be derived from the following Table XCVIIL, which gives average values of the exponent x for all the different ratios of size and voltage : TABLE XCVIII. EXPONENT OP OUTPUT-RATIO IN FORMULA FOR SIZE- RATIO FOR VARIOUS COMBINATIONS OF POTENTIALS AND SIZES. VALUE OP EXPONENT x, RATIO OP POTENTIALS, FOR RATIO OP LINEAR DIMENSIONS, Wl = JL> I fis Ito2 8 to 6 8 and over. Uptoi 3.00 2.85 2.70 t to 4 2.80 2.70 2.60 10 and over 2.60 2.55 2.50 4 1 8 D YNA MO-ELE C TRIG MA CHINE S. [ 1 1 1 The values given in the above table, besides for the com- parison of machines of the same type, are found to hold good also for the comparison of the outputs of similar armatures in frames of different types. But the figures contained in Table XCVIII. are based upon the assumption that the field- densities and the conductor-velocities of the two machines to be compared are identical, a condition which is very seldom fulfilled in practice, particularly not in dynamos of .different type, as, for instance, when comparing a bipolar with a multi- polar machine. Hence, any difference in the field-densities and in the peripheral speeds of the two machines to be com- pared must be properly considered, that is to say, the expo- nent x given in the preceding table for the voltage-ratio and the size-ratio in question must be multiplied by the ratio of their products of field-density and conductor-velocity, for, the E. M. F., and therefore the output, of a dynamo is directly proportional to the flux-density of its magnetic field and to the cutting-speed of its armature conductors. CHAPTER XXV. CALCULATION OF ELECTRIC MOTORS. Application of Generator Formulae to Motor Calculation. All the formulae previously given for generators apply equally well to the case of an electric motor; for, in general, a well-designed generator will also be a good motor. Hence the first step in calculating an electric motor is to determine the electrical capacity and E. M. F. of this motor when driven as a generator, at the specified speed. 1 Considering a given dynamo as a generator, its output, P l , in watts, at the terminals, is the total energy, P', generated in its armature by electromagnetic induction, diminished by the amount of energy absorbed between the armature conductors and the machine terminals; that is, by the loss due to inter- nal electrical resistances. In other words, the output is the total electrical energy produced in the armature multiplied by the electrical efficiency of the dynamo. The output, P\, of the same machine, when run with the same speed as a motor, is the useful electrical energy, P' t active within its armature in setting up electromagnetic induction, less the energy lost between armature and pulley; that is, less the loss caused by hysteresis, eddy currents, and friction, or is the product of electrical activity and gross efficiency. Conversely, the power, P\ , to be supplied to the generator pulley, must be the total energy, P', produced in the armature, increased by an amount equal to the magnetic and frictional losses, or must be P' divided by the gross efficiency. And the energy, P 9t finally, required at the motor terminals in order to set up in the arma- ture an electrical activity of P' watts, is found by adding to P' the energy needed to overcome the internal resistances of 1 "Calculation of Electric Motors," by Alfred E. Wiener, Electrical World, vol. xxviii., pp. 693 and 725 (December 5 and 12, 1896). 419 420 DYNAMO-ELECTRIC MACHINES. [ 112 the motor, or by dividing P' by the electrical efficiency. Des- ignating the electrical efficiency of the machine, /. e. t the ratio. of its useful to the total electrical energy in its armature, by 7/ e , and its gross efficiency, or efficiency of conversion, /. e., the ratio between the electrical activity in the armature and the mechanical power at the pulley, by rj gt we therefore have: Output of machine as generator: P^K-Xfj ............. (378) Output of machine* as motor: P\ = ng xP'j ............. (379) Power to be supplied to machine when run as generator (driving power): *">=} .............. (380) 'IS Energy to be supplied to machine when run as motor (intake of motor) : ' = ............... '<*> Where P lt P z = electrical energy at terminals of machine, as generator and motor, respectively; P' electric energy active in armature conduc- tors, being the same in both cases; P" l> P" z = mechanical energy at dynamo pulley, for generator and motor, respectively. By transposition of (379) the electrical capacity of the machine can be expressed by the motor output, thus:. which is to say that, in order to find the dimensions and wind- ings for a motor of P" hp = ^ horse-power, it is necessary to figure a generator which at the given speed has a total capacity of p , = P^ = 74 6 x hp 112] CALCULATION OF ELECTRIC MOTORS. 421 The E. M. F. for which the generator is to be calculated, or the Counter E. M. F. of the motor, is the voltage at the motor terminals diminished by the drop of potential within the machine, or: E = E - I X (r' a + r' 8e ) , (383) in which E = E. M. F. active in armature, in volts; E voltage supplied to motor terminals; / = current intensity at motor terminals; r' & armature resistance, at working temperature, in ohms; r' s& = resistance of series field, warm, in ohms, for series and compound machines; in case of shunt dynamo r' ee = o. Formula (383), though theoretically accurate, is not prac- tically so, since for the same excitation, armature current and speed, the counter E. M. F. of a motor is greater than the E. M. F. when used as a generator, for the following reason: While in a generator a forward displacement, or a lead, of the brushes has the effect of weakening, and a backward displace- ment, or a lag, that of strengthening the field magnet, in a motor a lead tends to magnetize, and a lag to demagnetize the field. Sparkless running, however, requires a lead of the brushes in a generator and a lag of the same in a motor, so that in both cases the armature reactions weaken the field. Since hysteresis as well as eddy currents have the effect of shifting the magnetic field in the direction of the rotation, thereby increasing the lead in a generator and diminishing the lag in a motor, it follows that for equal magnetizing force, equal current inten- sity, and equal speed the lag in a motor is less than the lead in a corresponding generator. For the purpose at hand, however, formula (383) gives the required counter E. M. F. with sufficient accuracy, particularly because neither the cur- rent strength nor the resistances usually being prescribed, the drop must be estimated by means of Table VIII., 19. By dividing the electrical activity, P\ as obtained from formula (382), by the E. M. F., E ', the current-capacity of the corresponding generator is found: /' = (384) 422 DYNAMO-ELECTRIC MACHINES. [ For the purpose of simplifying this conversion of a motor into a generator of equal electrical activity, the following Table XCIX. is given, which contains the average efficiencies, and the active energy for motors of various sizes: TABLE XCIX. AVERAGE EFFICIENCIES AND ELECTRICAL ACTIVITY OF ELECTRIC MOTORS OF VARIOUS SIZES. ELECTRICAL .OUTPUT ACTIVITY OF MOTOR ELECTRICAL GROSS COMMERCIAL IN ARMATURE, IN EFFICIENCY. EFFICIENCY. EFFICIENCY. IN KILOWATTS. HOUSE-POWER. hp % Vs %=1? e X Tf K p , . 746 X hp *!* r .85 .87 .89 .82 .83 .84 .70 .72 .75 .08 .13 .22 t .90 .87 .78 .43 .91 .88 .80 .85 2 .92 .89 .82 1.7 5 .93 .90 .84 4.1 10 .94 .92 .86 8.1 20 .95 .93 .88 16 30 .96 .935 .90 24 50 .97 94 .91 40 100 .975 .945 .92 79 200 .98 .95 .93 157 500 -985 .955 .94 390 1000 .985 .96 .95 780 2000 .99 .97 .96 1540 If a dynamo which has been connected for working as a gen- erator is supplied with current from the mains instead, it will run as a motor, the direction of rotation depending upon the man- ner of field excitation. A series dynamo, since both the arma- ture and field currents are then reversed, will run in the opposite direction from that which it was driven as generator, and must therefore have its brushes reversed and given a lead in the opposite direction; or, if direction in the original gen- erator direction is desired, must have either its armature or its field connections reversed. A shunt dynamo will turn in the same direction when run as a motor, for, while the armature 113J CALCULATION OF ELECTRIC MOTORS. 4 2 3- current is reversed, the exciting current will have the same direction as when worked as a generator. A compound dynamo, finally, will run as a motor in the opposite direction, if the series winding is more powerful than the shunt, and in the same sense, if the shunt is the more powerful ; and while the field excitation as a generator is the sum of the series and shunt windings as a motor it is their difference. 113. Counter E. M. F. Whereas in a generator there is but one E. M. F., in a motor there must always be two. If / = current at machine terminals, E = direct E. M. F., E = counter E. M. F., J? = total resistance of circuit, and r internal resistance of machine, this difference between a generator and a motor can be best expressed l by the formulae for the current in the two- cases, thus for generator: _ E ~ R'' for motor: E E _ / = , or E = E Ir. The current and direct E. M. F. are the same in both cases,, but the resistance is much less in case of a motor, the differ- ence being replaced by the counter E. M. F., which acts like a resistance to reduce the current. Upon the amount of this counter E. M. F. depend the speed and the current, and therefore the power of an electric motor. For, since the E. M. F. generated by electromagnetic induction is proportional to the peripheral velocity of the armature, it follows that, other factors remaining unchanged, the speed conversely depends upon the counter E. M. F. only. The latter is the case in a series motor run from constant cur- rent supply, since in this the magnetizing force is constant at all loads. In a shunt motor, however, the field current varies with the load, and the speed, therefore, depends upon the field magnetism as well as upon the counter E. M. F. If the exciting current in a constant potential shunt motor is de- creased, the E. M. F. decreases correspondingly, and a rise of 1 "The Electric Motor," by Francis B. Crocker, Electrical World, vol. xxiii. p. 673 (May 19, 1894). 424 DYNAMO-ELECTRIC MACHINES. [ 114 the current flowing in the motor is the consequence, as fol- lows directly from the above equation for the motor current. The speed in this case, therefore, rises until the counter E. M. F. reaches a sufficient value to shut off the excess of current. If the counter E. M. F. is low, which is the case when the motor is starting or running slowly, resistance has to take its place in order to govern the current of the motor. The intro- duction of resistance in series with the armature, the so-called starting resistance, is usually resorted to for this regulation, but this is very wasteful of energy and involves the use of a large and clumsy rheostat, while the counter E. M. F. itself affords a means to easily design a motor to run at the same, or at a higher, speed at full load than when lightly loaded. This may be done by slightly exaggerating the effect of armature reac- tion, so that the field .magnetism will be considerably reduced by the large armature current which flows at full load, thus diminishing the counter E. M. F. and increasing the speed in the manner explained above. In this way the remarkable effect of greater speed with heavier load is obtained without any special device or construction; all that is necessary being a slight modification in design, involving no increase in cost or complication. 114. Speed Calculation of Electric Motors. If a generator, which at a speed of N^ revolutions per minute produces a total E. M. F. of E\ = E + /' X (r' & + r'J volts, is run as a motor having same current strength in armature, the motor armature, in order that no more nor less than this current, /', its full load as a generator, shall flow, must gen- erate a counter E. M. F. of ' t = -f X (r' a + ry volts. The speed necessary to generate this back voltage, speed being proportional to voltage, is: E\ ~ E + /' X (r' & + r' 8e ) X 114] CALCULATION OF ELECTRIC MOTORS. 425 which is the speed of the motor at full load, provided the E. M. F., , supplied to its terminals is equal to the voltage when run as generator. The speed of the motor for any given E. M. F., applied to its armature terminals, depends (i) upon the load impressed upon the motor armature, or the torque t , it has to exert; (2) on the electrical resistance (r' & -f ;-' se ), of the armature and the series field; and (3) upon its specific generating power, or its capability of producing counter E. M. F. ; *'. e., the number of volts, e\ it produces at a speed of one revolution per second. The specific generating power of the motor being N e $ x -r 2 X io~ 8 volts at i rev. per sec. , (386) ;/ P where = useful flux, in maxwells; N c = number of conductors on armature; ;/' p = number of pairs of armature circuits electrically in parallel; the total counter E. M. F. at the required speed of JV 9 revolu- tions per minute, will be and the current flowing in the armature, therefore, is: The activity of this current expended upon the counter E. M. F. will be their product, E\ X /' watts, and this must be equal to the total rate of working, which is the product of circumferential speed and turning moment, or torque; that is, it must be equal to 74.6 2 7t X NS X r X - watts , 33,000 where the torque, r, is calculated from formula (93), 40; hence we have: E - e" 2 -^ 1 x < 6 - > 7t y N * x r X ^~ *- ) X r& + rse - 2 * X 60" X * X 550 426 D YNA MO-ELECTRIC MA CHINES. [ 1 1 4 from which N^ = 60 X (-2- - 8.52 X ^^L^-\ (389) From (389) follows that, if either the internal resistance or the torque is zero, since the second term in the parenthesis then disappears, the speed of the motor is: ..(390) This reduced formula (390), indeed, holds very nearly in practice for very large motors (in which the internal resistance is very small), and also is approximately followed in case of motors running free (the torque then being only that necessary to overcome the frictions). The important requirement of constant speed under variable load may be almost perfectly met by the compound-wound motor, is nearly met by the shunt-wound motor, and is not met without the aid of special mechanism by the series-wound motor. A compound-wound motor will maintain its speed perfectly constant under all loads, if the series winding is so adjusted that the increase of current strength through the series coils and armature shall diminish the M. M. F. of the field magnets to the degree necessary to compensate for the drop of pressure in the armature winding. (See 148.) If constant speed is required, such as is the case in operating silk mills and textile machinery, the compound motor will therefore be found to give the best satisfaction, since in shunt motors, although running with " practically constant " speed, the variation may be too great to be without influence upon the product of manufacture. When started without load the speed of a shunt motor grad- ually increases and reaches a maximum, from which it falls down again as soon as the load is put on. The rise at no load is due to the fact that since the potential at the field terminals is constant, the field current decreases as the resistance of the field coils increases, owing to their heating, thereby decreasing the magnetizing power, and in consequence the counter E. M. F. of the motor. The subsequent decrease of the speed is caused by the increase of the armature current with increas- 115] CALCULATION OF ELECTRIC MOTORS. 427 ing load, and by the heating of the armature due to the passing current, the counter E. M. F. decreasing with increasing drop of voltage in the armature. Tests made by Thomas J. Fay ' with shunt motors of various sizes gave the results compiled in the following Table C. : TABLE C. TESTS ON SPEED- VARIATION OF SHUNT MOTORS. Normal CAPACITY OF MOTOR, Speed, at No Load, Cold, Revs, per Increase of Speed from No Load, Cold, to No Load, Hot, Due to Heating of Field Coils. Decrease of Speed from No Load, Hot, to Full Load, Hot, Due to Heating of Armature. Final Change in Speed. 4- = Increase. = Decrease. HP. Mm. 3 1400 20 % of normal speed 12 % of normal speed -+- 8 % of normal speed. 5 1200 8% 5 -4- 3V4 fc 7Vij 1360 sy 4 _j_ \\ i 10 1200 2 " 8^ " " 52^ ' 15 1180 2^ 3V " " -1 20 860 X " 4 -8J* From this table it will be seen that the resistance of the field and of the armature can be so proportioned with relation to each other that the final speed at full load hot is equal to the normal speed at no load cold. But in order to reduce to a minimum the variation of the speed during the period of heat- ing up of the motor, it is necessary that both the increase due to the heating of the magnet coils and the decrease due to the heating of the armature should be reduced as much as possible. For this purpose the field winding should be so proportioned as not to heat very much above the temperature of the sur- rounding air, and the armature resistance should be as low as possible. 115. Calculation of Current for Electric Motors. a. Current for Any Given Load. The current in the armature of a motor for any load, P"^ watts = 746 X hp^ horse power, at the pulley, since at any in- stant the entire energy supplied to the motor must be equal to the sum of the expenditures, can be found from the equation: X (/' x + / sh ) = P\ + /V X (/ a + r' M ) + E X / sh + P , ' " Constant Speed Motors," by Thomas J. Fay, Electrical Age, vol. xv. p. 38 (January 19, 1895). 428 ' DYNAMO-ELECTRIC MACHINES. [ 115 which gives: E- VE' - 4 (/-'. + *'.) X (f\ + A) .,-,. ^T'lT^T where E line potential supplied to motor terminals, in volts; /' x current in armature of motor, in amperes, for any given load; 7 sh = current in shunt field of motor, in amperes; P"^ = useful load of motor, in watts; jP = energy required for no load, in watts; r' & = armature resistance, in ohm; r' se = series field resistance, in ohm. Formula (391) directly applies to series- and compound- wound motors; in case of shunt-wound motors, r' M being = o, it reduces it to: b. Current for Maximum Commercial and Electrical Efficiency. ' As the energy commercially utilized in a motor is: P\ = E X /' - r X (r' & + r'J - P and the entire energy supplied is: P\ = E X /' + P* ; the commercial efficiency can be expressed by ExI' and similarly the electrical efficiency, by: ^ being the energy absorbed in the shunt. 1 " Shunt Motors," by W. D. Weaver, Electrical World, vol. xxi. p. 137,, (February 25, 1893). 116] CALCULATION OF ELECTRIC MOTORS. 4 2 9 These efficiencies are maxima for: r and ^J - m- (39*) respectively. Formula (393), therefore, gives the current that must be supplied to the armature of a motor in order to have the maximum commercial efficiency, and formula (394) the current for maximum electrical efficiency. 116. Designing of Motors for Different Purposes. According to the purpose a motor has to serve, its efficiency is desired to either be high and nearly constant over a wide range of its load, or to increase in proportion with the output and be highest at the maximal load the motor can carry. The shape of the efficiency curve of a motor depends upon the proportioning of its various losses. The losses in a motor are of two kinds, fixed and variable. The fixed losses are those due to the shunt field current, hysteresis, and eddy cur- rents, brush friction, bearing friction, and air resistance. The variable losses are those due to armature and series resistance, and to commutation, and increase with the load. If the fixed losses are small compared with the variable ones, the efficiency at light loads will be high and will rapidly drop as the load, and with it the variable loss, increases. If, on the other hand, the fixed losses are very large, and the variable losses small, the efficiency with small loads will be low, but will increase as the load becomes greater, for the reason that the total energy increases proportional to the load while the losses in this case remain nearly constant, increasing but very little with the load. In order to have the fixed losses in a motor small and the variable losses great, it is necessary to employ a massive mag- netic circuit with few shunt ampere-turns, an ample cross-sec- tion of iron in the armature core, and a large number of turns on armature and series field; hence the energy lost in shunt field excitation, in hysteresis, and eddy currents is small, but that lost by armature and series field resistance and by com- 43 D YNAMO-ELECTRIC MACHINES. [116 mutation is great. The reverse of these conditions insures an increase in the fixed, or a decrease in the variable, losses. Curves I. and II., Fig. 315, show the variation of the com- mercial efficiency with the load in two motors of different de- sign, both having the same efficiency, T/ C = 80 per cent, at 100 IJ^LOAD Fig. 315. Efficiency Curves of Two Motors of Different Design. normal load, but I. having very high efficiencies at light loads, while II. has very low efficiencies at small loads, but even greater than normal efficiency with overloads: TABLE CL COMPARISON OP EFFICIENCIES OF Two MOTORS BUILT FOR DIFFERENT PURPOSES. EFFICIENCY AT VARIOUS LOADS. J Load. ^ Load. % Load. Normal Load. 25 Per cent. Overload. 50 Per cent. Overload. Percent. Per cent. Per cent. Per cent. Per cent. Per cent. I. 70 80 83 80 73 65 II. 40 60 72 80 86 90 An efficiency curve similar to I. is desired in constant power work where the greatest load is put on the motor but once in starting, and where, after the friction of rest has been over- come, the motor is called upon to work on half to three-fourths its normal output continually; motors, consequently, which are to be employed for running printing presses, machine- 117] CALCULATION OF ELECTRIC MOTORS. 43* shop tools, power pumps, etc., must be designed with a heavy frame of low magnetic density, a weak field, small excitation, and a powerful armature. In order to obtain an efficiency curve similar to II., which is preferable in all cases where the motor is not doing steady work, but is called upon to give more than its normal power at frequent intervals, as, for in- stance, in operating electric railways, elevators, cranes, hoists, etc., the motor must be provided with a light frame of high magnetic density, a strong field, powerful excitation, and a weak armature. 117. Railway Motors. a. RAILWAY MOTOR CONSTRUCTION. * The construction of motors used for railway propulsion deviates in many respects, electrically as well as mechanically, from that of ordinary motors. The principal conditions that must be fulfilled in the design of a railway motor are the fol- lowing: (1) The motor should be extremely compact, so that it may be easily placed in the space available within the truck; yet it must be easily accessible, and all its parts subject to wear must be easily exchangeable. All parts of the machine must furthermore be so designed and the winding so executed that the continual vibrations due to the motion of the car are un- able to loosen the same, or to get them out of working order, (2) A railway motor must be so designed that with minimum weight a maximum output is obtained. (3) The speed of the armature must be properly chosen with regard to the minimum and maximum load, to the speed of the car, the diameter of the car wheels, and the ratio of speed reduction. (4) The regulation of the speed should be simple, reliable, and perfectly adapted to all grades and curvatures of the track. (5) The type of the motor should be so chosen, and the de- sign so carried out, that there is no external magnetic leakage, 1 See " Praktische Gesichtspunkte ftir die Konstruction von Motoren fiir Strassenbahnbetrieb," by Emil Kolben, Elektrotechn. Zeitschrift, vol. xiii. No. 34 and 35 (August 19 and 26, 1892). 432 D YNA MO-ELE C TRIG MA CHINE S. [ 1 1 7 that at the same time all the vital parts of the motor are pro- tected from mechanical injuries, and that it can be so sup- ported from the truck that, if possible, none of its weight is resting directly upon the car axle. Particular care must also be bestowed upon the selection of insulating materials and the manner of insulation, in order to guard the machine against the influence of dampness, mud, and water. (i) Compact Design and Accessibility. Since it is usual to equip each car with two motors which are directly suspended from the car axles and the frame of the truck, the extreme dimensions of the motor are limited by the diameter of the wheels, their distance apart longitudinally, and by the gauge of the track. The trucks most commonly used have 30 or 33-inch wheels, a wheel base of 6 to 7 feet, and the standard gauge of 4 feet 8 inches. The height of the motor is further limited by the condition that a space of at least 3 inches should be left between the lowest point of the motor and the top of the rails in order to enable the motor to pass over stones or other small obstructions upon the track. The arrangement should be such that the working parts can. be easily inspected during the trip from a trapdoor in the flooring of the car. If it is impracticable to provide the car- barn with pits below the tracks, the motor should be so arranged that the armature, the field coils, and the brushes can be taken out through the same trapdoor. In order to facilitate the quick replacing of a disabled armature, it is ad- visable to split the motor frame horizontally, and to make one part revolvable by means of strong hinges. (2) Maximum Output with Minimum Weight. The energy required for propelling a car being proportional to its weight, it must be the aim to make the entire equipment as light as is consistent with strength and durability. In order to reduce the weight of the motor to a minimum, it is of the utmost importance to use only the best materials suitable for the respective parts, namely, the softest annealed sheet iron for the armature core, silicon bronze or drop-forged copper 117] CALCULATION OF ELECTRIC MOTORS. 433 for the commutator segments, and softest cast steel for the field frame. If reduction gears are used, the pinions should be of hard bronze or of good tool steel, and the gear wheels of cast steel, or of fine grain cast-iron. In order to obtain the maximum possible output, the magnetic circuit of the motor should have as small a reluctance as possible, and the magnetic leakage should likewise be reduced as much as pos- sible. The former is attained by the use of toothed or perfor- ated armatures with very small air gaps; and the latter by proper selection of the type. The armature should be made most effective by providing it with a great number of turns; the sparking which would thus result under ordinary condi- tions being checked by the use of carbon brushes which are set radially in order to enable reversibility in the direction of rota- tion of the motor. The weight efficiency of various railway motors is given in Table GIL, p. 435. (3) Speed, and Reduction Gearing. The speed of the motor naturally depends upon the car velocity desired, upon the size of the car wheels, and upon the method used for the mechanical transmission of the motion from the armature-shaft to the car axle. The maximum speed of the car, according to local conditions (size of town, amount of traffic in streets, etc.) varies from 8 to 15 miles per hour, the greatest speed of the car axle, therefore, provided that 30- inch wheels are used with the slow, and 33-inch wheels with the fast running cars, ranges between 90 and 150 revolutions, respectively. The methods of transmission most commonly employed in electric railway cars are the double and single spur gearing, and the direct coupling; worm gearing, bevel gearing, link- chains, and crank-rods' being used only in single cases. The employment of double spur gearing was necessary with the earlier railway motors which were run at from 1000 to 1200 revolu- tions per minute, and which, therefore, had to have their speed reduced in the ratio of from 10: i to 15: i. High-speed railway motors, however, on account of the noise and wear connected with the presence of four gear wheels for each motor, that is eight gears per car, proved too inconvenient 434 DYNAMO-ELECTRIC MACHINES. [ 117 and too expensive to maintain, and low-speed motors of from 400 to 500 revolutions per minute, necessitating but a single spur gearing with a reduction ratio of from 4:1 to 5 : i, were next resorted to. If the spur gears for such single reduction motors are provided with broad and carefully cut teeth, and are run in oil, both noise and wpar are very small, and the effi- ciency is comparatively high. Worm gearing can be employed for any speed ratio within the limits of railway motor reduction, and by proper design very high efficiencies may be attained. Jf the worm is carefully cut from a solid piece of tool steel, and the rim of the worm wheel made of hard phosphor bronze, and if the dimensions are so chosen that an initial speed of 20 to 40 feet per second is obtained, the efficiency when run in oil may reach 90 per cent, and over. ! If no speed reduction at all is desired, that is to say, if the motor is to be directly coupled with the car axle, its normal speed must be between 100 and 150 revolutions per minute. From tests made by Professor S. H. Short, 2 the saving of power consumed in operating a directly coupled, gearless street car motor is found to be from 10 to 30 per cent, as compared with double spur gearing, and from 5 to 10 per cent, as compared with single spur gearing, according to the load. In order to show what has been done in the way of compact design and weight-efficiency of railway motors of various speed reductions, the following Table CII. has been prepared, giving the specific weight, the speed, kind and ratio of reduction, the type and dimensions of the frame, the space-efficiency, and the size of the armature, of the most common railway motors in practical use. The figures given for the dimensions of the field frame do not include any supporting or suspension brackets, lugs, or other extensions that may be attached to, -or cast in one with the frame, but relate only to the magnetic portion of the field casting. This is done to bring all the space efficiencies to a common basis, thus enabling a fair com- parison of the various types: 1 See " Schneckengetriebe in Verbindung mit Elektromotoren," by Emil Kolben, Elektrotechn. Zeitschr., vol. xvi. p. 514 (August 15, 1895). 2 " Gearless Motors," by Sidney H. Short, Electrical Engineer, vol. xiii. p. 386 (April 13, 1892) ; Electrical World, vol. xix. p. 263 (April 16, 1892). 117] CALCULATION OF ELECTRIC MOTORS. 435 **ll -no i pi paidnooo .9 aoareo'ao'iri'of otr' ocD oTr-Ii-Ti-Teo' Sqjat?8Q jo puiH SITJ9O . 03 CC Q3Q . 03 C <0 C rf III ia * SS* c o : IS'S 436 DYNAMO-ELECTRIC MACHINES. [117 (4) Speed Regulation. In order to effect the variation of the speed of railway motors within wide limits it is desirable that their field mag- nets should be series wound. The strength of the magnetic field can then be regulated either by inserting resistance into the main circuit, in connection with partial short-circuiting of the field coils, or by altering the combination of the magnet spools, or by series-parallel grouping of the armatures and field coils of the two motors. In the Resistance Method the insertion of rheostat-resistance into the main circuit, by reducing the effective E. M. F., causes a decrease in the speed of the motor; in this case the cross section of the magnet wire must be so dimensioned as to carry the maximum current, but the number of turns must be chosen fargreater than is required for the production of the requisite number of ampere-turns at maximum current and maximum speed. For, almost the full field strength must be obtained with a comparatively small current-intensity, and it it therefore necessary to short-circuit a portion of the magnet coils at maximum load. That is to say, in order to raise the torque of the motor for increased loads, only one of the two factors determining the same is increased, namely the current strength in the armature, while the field current remains the same. In order to do this without excessive sparking, caused by the fact that the brushes, not being adjustable, are never at the neutral points of the resultant field, carbon brushes must be used, whose large contact resistance considerably re- duces the current in the coils short-circuited by the brushes. The Combination Method of speed regulation consists in suit- ably changing the grouping of the magnet-spools. For this purpose it is necessary to wind the magnet coil in sections, equal portions of which are placed on each magnet, and to connect the terminals of these sections, usually three in num- ber, to a switch, or controller, of proper design. At the max- imum load of the motor the three sections are connected in parallel, and for this combination, therefore, the cross-section of the winding is to be calculated. For starting the car all sections are connected in series, and, if no precaution were taken, the magnet winding would, in consequence, have to 117] CALCULATION OF ELECTRIC MOTORS. 437 carry the full starting current, which may be 4 to 6 times the maximum normal current. In order to avoid overheating and damage due to this starting current, a starting rheostat must be placed in circuit, the resistance of this rheostat being so dimensioned that the starting current is brought down in strength to that of the maximum working current. While with the two former methods of speed regulation the two motors of the car are permanently connected in parallel, in the Series- Parallel Method of control, finally, both the arma- tures and magnet-coils of the two motors can be grouped in any desired combination. The same number of combinations is therefore possible with less elements, and only two sections per magnet-coil are necessitated. Since by placing both arma- tures and all four field-sections in series the starting current is considerably reduced, less resistance is needed in the start- ing rheostat, and a saving of energy is effected by this method. For calculating the carrying capacity of the magnet-wire the last two positions of the series-parallel controller are essential: for maximum speed the two motors, each having one coil cut out, are placed in parallel; and in the position for the next lower speed both motors with their two coils in series are grouped in parallel. (5) Selection of Type. The most important consideration in the selection of the type for a railway motor is the condition that there should be no external magnetic leakage, as otherwise the neighboring iron parts of the truck may seriously influence the magnetic distribution, and, furthermore, small iron objects, such as nails, screws, etc., may be attracted into the gap-space and may injure the armature. In order to protect the motor from dampness and mechanical injuries, such types are to be pre- ferred in which the yoke surrounds the armature, and which therefore can easily be so arranged that the frame completely encases all parts of the machine. The types possessing the latter feature are the iron-clad types, Figs. 203 to 207, 72, and Figs. 217 to 220, 73, the radial outerpole type, Fig. 208, and the axial multipolar type, Fig. 212; and as can be seen from the preceding Table CIL, these are in fact the forms of machines that are used in modern railway motor design. 43 8 DYNAMO-ELECTRIC MACHINES. [ 117 b. CALCULATIONS CONNECTED WITH RAILWAY MOTOR DESIGN/ (i) Counter E. M. F., Current, and Energy Output of Motor. Inserting into the formula for the counter E. M. F., io 8 , the value of the useful flux from 86 and 87, 4 ^ v AT 10 ' &*> X / ^e X (R " (R where SF magnetomotive force, in gilberts; AT N^ X / = magnetizing force, in ampere-turns; (R = reluctance of magnetic circuit, in oersteds; io io i /" 6V = X & = X X m r, *S ra /^ =r permeability of magnet-frame, at normal load; /" m = length of magnetic circuit, in inches; S m = area of magnet-frame, in square inches; we obtain: If the internal resistance of the motor, /. *?., armature resist- ance plus series field resistance, is designated by r, and the line potential by E, the current flowing in the armature, there- fore is: ,. _ N y N I N p ^ v c A ^Vge v J V V J?r 7n~> - ~ X 7 A -^ X Jb (R n 60 1 See " Some Practical Formulae for Street-Car Motors," by Thorburn Reid,. Electrical Engineer, vol. xii. p. 688 (December 23, 1891); " Capacity of Rail- way Motors," byE. A. Merrill, Electrical Engineer, vol. xvii. p. 231 (March 14, 1894). 117] CALCULATION OF ELECTRIC MOTORS. 439 and solving for /, we have: N c X N i JV~ r + - ^r-^ X -T- X 7- X io 8 (R n p 60 ' (396) Hence the work done by the motor: /v v iv r* iv ^ = ^ x / = -^ s xf p xgx I o'. (397) 7V" C , .A^e, and n' p are constants of the motor, and (R.' varies somewhat with the saturation of the field, but may be consid- ered practically constant; if, therefore, we unite all constants by substituting: '^ c x J\r i io 8 (R' < ' p X 60 ' the above formulae (395), (396), and (397) become: E' = x x ix *r, .......... (398) and p' = KX r x N .......... (400) The value of the constant K can be readily calculated from the windings of the machine and from the dimensions and flux densities of its magnetic circuit. If, however, the values of E, /, and ^Vfor any load are given, and it is required to find the counter E. M. Fs., the currents, and the mechanical out- puts for other loads, then K can, far simpler and more accu- rately, be determined by substituting the given values in: K- - . /X-AT ' which is obtained from (399) by transformation. (2) Speed of Motor for Given Car Velocity. The speed of the motor required to move the car at a given velocity, with a given reduction gear, is: 440 DYNAMO-ELECTRIC MACHINES. [117 _ feet per min. 5280 X 12 X z ; m X z m = speed of car, in miles per hour; z = ratio of speed reduction, /. e., ratio of arma- ture revolutions to those of the car axle; d w = diameter of car wheel, in inches. ^(3) Horizontal Effort, and Capacity of Motor Equipment for Given Conditions. The power required to propel a car depends upon five things: friction, grade, condition of track, curvature of track, and speed. No accurate formula can be given for the resist- ance due to friction, condition of track, and curvature, for this resistance will vary largely at different times with the same car, depending upon the care with which the bearings and gears are oiled, and whether the track is wet or dry, clean or dusty, or muddy. A good average practical value of the specific traction resistance, verified by numerous tests, is 30 pounds per ton of weight on the level, and (30 20 X g) pounds per ton on grades, g being the percentage of the grade, that is, the number of feet rise or fall, respectively, in a -length of 100 feet. The horizontal force necessary to over- come the traction-resistance caused by a total weight of W t tons, therefore, is: A = Wt X (30 20 X g) pounds, ....(403) and the power, in watts, required to exert this horizontal -effort, at a speed of v m miles per hour, will be: U __ A X ft. per min. X 746 = 2 A x v m (404) 5280 A X 2 v m X 746 33,000 117] CALCULATION OF ELECTRIC MOTORS. 441 In order to facilitate the calculation of the propelling power, or of the motor capacity required for given conditions of trac- tion, the following Table CIII. has been calculated, which gives the power required to propel one ton at different grades and speeds, and which, therefore, furnishes P" by simply mul- tiplying the respective table-value by the total weight, Wt tons, to be propelled, /. *>., the weight of car plus passengers {average weight of passenger = 125 Ibs.): TABLE GUI. SPECIFIC PROPELLING POWER REQUIRED FOR DIFFERENT GRADES AND SPEEDS. HORSE-POWER REQUIRED TO PROPEL 1 TON, PERCENTAGE IP RATED SPEED OP OAR, V m > IN MILES PER HOUR, is : OP GRADE, g 8 10 12 15 18 20 25 30 .64 .80 .96 1.21 1.45 1.61 2.01 2.41 1 1.0? 1.34 1.61 2.01 2.41 2.68 3.35 4.02 2 1.50 1.88 2.25 2.82 3.38 3.76 4.69 5.63 3 1.93 2.41 2.90 3.62 4.34 4.83 6.03 7.24 4 2.36 2.95 3.54 4.42 5.31 5.90 7.37 8.85 5 2.78 3.48 4.17 5.22 6.26 6.97 8.71 10.44 6 3.22 4.02 4.83 6.03 7.23 8.05 10.04 12.06 7 3.65 4.56 5.47 6.84 8.20 9.12 11.40 13.67 8 4.07 5.09 6.11 7.63 9.15 10.18 12.73 15.28 9 4.50 5.62 6.75 8.43 10.10 11.25 14.07 16.89 10 4.93 6.16 7.39 9.24 11.07 12.32 15.40 18.50 12 5.78 7.23 8.68 10.84 13.01 14.47 18.10 21.70 15 7.07 8.84 10.60 13.25 15.90 17.70 22.10 26.55 From (404) the horizontal pull required to exert a given power at given speed is found thus: A = 33,000 X 60 P" 5280 746 Giving to hp values from 15 to 60 horse-power, and to 7/ m from 8 to 30 miles per hour, the following Table CIV. is obtained, which at a glance gives the horizontal effort, or draw-bar pull, exerted by any motor-capacity at a given speed, whereupon, from (403), the load Wt, in tons, can be computed, which the equipment under consideration is able to propel at any given grade : 442 D YNA MO-ELECTRIC MACHINES. [H7 TABLE CIV. HORIZONTAL EFFORT OF MOTORS OF VARIOUS CAPACITIES AT DIFFERENT SPEEDS. HATED CAPACITY OP MOTOR EQUIPMENT. PULL AT PERIPHERY OP WHEEL, f h IN POUNDS, AT RATED SPEED OP CAR, V mt IN MILES PER HOUR, OF : 8 10 12 15 18 20 25 30 15 703 563 469 375 313 281 225 188 20 938 750 625 500 417 375 300 250 25 1,172 938 781 625 521 469 375 313 30 1,406 1,125 938 750 625 563 450 375 40 1,875 1,500 1,250 1,000 833 750 600 500 50 4,344 1,875 1,562 1,250 1,043 938 750 625 60 2,812 2,250 1,875 1,500 1,250 1,125 900 750 A simple graphical method of determining the car velocity and the current consumption under various conditions of traffic is shown in 133, Chapter XXVIII. (4) Line Potential for Given Speed of Car and Grade of Track. The E. M. F. required at the motor terminals to drive a car up a particular grade at a certain rate of speed may be found as follows. From (399) we have: E = Ix(r + KxN), (406) in which everything is known except E and 2. But /can be obtained from formula (400), provided we know the work P" that is to be done by the motor under the prevailing condi- tions. The value of P" being given by (404), the current / can be expressed by transposition of formula (400), and by substituting the expression so found into (406) the required E. M. F. is obtained : E= (r + K 2 /h X K X 1 ..(407) Inserting into (407) the value of N found from (402), we have : 304 X A X v m X 2 j v t ^ / j h ^ lt , w /AAC^ x Knowing E, we are enabled to determine the size of wire required in the feeders to maintain a certain speed at any point on the line. CHAPTER XXVI. CALCULATION OF UNIPOLAR DYNAMOS. 118. Formulae for Dimensions Relative to Armature Diameter. Assuming the armature diameter of a unipolar dynamo as given, the ratio of the working density of the lines in the material chosen for the frame to the flux-density permissible in the air gaps will determine the dimensions of the frame. The armature consisting in a solid iron or steel core without winding, the only air gap necessary is the clearance required for untrue running, and, on account of the short air gaps so obtained, a comparatively high field density, namely, 3C" = 40,000 lines per square inch (or 3C = 6200 lines per square centimetre) can be admitted. The practical working densi- ties, as given in Table LXXVL, 81, are: = 13,200 lines per square centimetre), for cast steel, and (ft" = 45,000 to 40,000 lines per square inch ((& = 7000 to 6200 lines per square centimetre), for cast iron. By comparison, then, it follows that the area of the gap spaces should be about twice the cross-section of the frame, if wrought iron or cast steel is used, and about equal to the frame section if cast iron is employed. The cylinder type, on account of its smaller diameter and more compact form, being more practical than the disc type of unipolar machines, the former only will here be considered, inasmuch as it will not be difficult to derive similar formulae for the latter. Moreover, since for the same size of armature 444 D YNA MO-ELE C TRIG MA CHINES. [ H8 a cast-iron frame requires about twice the weight of a cast- steel one, the use of the former material is limited to special cases, and formulae are given only for machines having cast- steel magnets. Adopting the general design indicated by Fig. 31, n, good practical dimensions of the frame are obtained by making the Fig. 316. Dimensions of Cast Steel Unipolar Cylinder Dynamo. active length of the armature conductor, that is, the length of the poles, see Fig 316: / P = .3<4, ....(409) d & being the mean diameter of the armature-cylinder; and by providing for the winding an annular space of length: / m = .i25d a , (410) and height: *. = .*, (411) The gap area, then, will be : S g = d & 7r X .3*4 = -94<4 a , 118] CALCULATION OF UNIPOLAR DYNAMOS. 445 and the cross-section of the magnet frame, in order to have a magnetic density of 85,000 lines per square inch, must be: Tlie radial thickness of the armature, being that of the rim of a pulley of diameter 4> is taken : ** = .2V, ............. (412) which, by adding for clearance, makes the total distance between the two pole faces : Allowing .05 y~rf for the recess at the outer pole face, the internal diameter of the yoke is found: 4 = 4 + -3 |/4~? and the diameter at the bottom of the annular winding groove, or the diameter of the magnet core is: 4i = 4 - -25 1/4"- 2 X .14 = .84 -- .25 t/^7 The thicknesses of the frame section at these diameters must be: and - .25 |/ 7T respectively. For the radial thicknesses of the outer and inner tube por- tions of the field frame we have the equations: -444 s (4 446 DYNAMO-ELECTRIC MACHINES. [ 119 and (.8 <4 - . 25 t/Z~- 4) n .I4<4" .84- -25/4 - respectively, from which we obtain, for the radial thickness of the yoke: = .1254 -.03*^ ........................... (416) and for the radial thickness of the core portion of the frame: h ^_ .84 - ;25 V _ (.84 -.25 _ < = .264 +.23^ .......................... (417) The total axial length of the frame is: 4 = .34 + .1254 + 2^ = .6254 ; ..... (418) and for the mean length of the magnetic circuit in the frame we find by scaling the path : /* = i.t* ............... (419) 119. Calculation of Armature Diameter and Output of Unipolar Cylinder Dynamo. All the dimensions of the machine being given, by 118, as multiples of the armature diameter, , and field density, X", and geometrically, as a cylinder surface of diameter d & and length .3*4. The number of parallel circuits as well as the number of conductors in the unipolar armature is unity, and the lines are cut but once in each revolution, the useful flux necessary to 119] CALCULATION OF UNIPOLAR DYNAMOS. 447 generate E volts at the speed of N revolutions, therefore, from formula (137), 56, is: ' hence the gap area can be expressed, electrically, by: 6 X E X io 9 while geometrically we have from Fig. 316: S 8 = d & x n X -3<4 = -94<4 a ...... (421) Equating (420) and (421), we obtain: 6 X X io 9 N X from which follows: = 80,000X1/^1^" ....... (422) Inserting in this the value of the field density given in 118, namely, 3C" = 40,000 lines per square inch, we find: d & = 400 x Mjf> (* 23 ) in which d & = mean diameter of armature, in inches; E = E. M. F. required, in volts; N = speed, in revolutions per minute. From (423) the armature diameter of a unipolar cylinder dynamo can be computed which generates the required E. M. F. at a given speed. If, however, the minimum value of d & , at the maximum safe speed permissible, is desired, JV must be eliminated from the above equation (423), and replaced by the peripheral velocity. For this purpose the value of d & from (423) is inserted into the equation <4 = 230 x ^-[see (30), 21]; by this process we obtain: 400 X V E X N = 230 z; c or: (424) 448 DYNAMO-ELECTRIC MACHINES. and this in (423) gives: & = 400 X 33 ^c = 690 X ..(425) The values of v ct i. e., the limiting safe velocities, for the materials used in unipolar armatures are: v c 400 feet per second, for forged steel; v c = 300 feet per second, for wrought iron and cast steel ;. v c = 200 feet per second, for cast iron. Inserting these values into (425), the following formula giving the minimum armature diameter for unipolar cylinder dynamos of E volts E. M. F. are arrived at: ^Q^ forged steel armature : d & = ? X E = i. 73 E. 400 For wrought iron or cast steel armature : d t For cast iron armature : d f 200 E 3.45 E. ^ > (426) The corresponding minimum speeds are found by formula (424), as follows: For forged steel armature : N = . 33 X For wrought iron or cast steel armature: N = .33 X For cast iron armature : N . 33 X 300 _ 30,000 fij j^i 2OO 2 _ 13,200 JLL (427) The output of the machine is limited only by the carrying capacity of the armature; the current carrying cross-section of the latter is: & n X . = -2 and since iron or steel will carry at least 200 amperes per square inch, the current capacity, in amperes, is: 1= 200 X .2 n X ^= 1254*, ....(428) 120] CALCULATION OF UNIPOLAR DYNAMOS. 449 which, at E volts E. M. F., gives th-e output of the dynamo, in watts: P = EXS=I2$XX d?. (429) 120. Formulae for Unipolar Double Dynamo. In duplicating the design shown in Fig. 316, a unipolar dynamo with an armature of twice the effective length of the former is obtained, Fig. 317. Fig. 3 J 7- Dimensions of Cast-Steel Unipolar Double Dynamo. The pole area for this type is: S g = 2 x d & it X .3*4 = i.88<4', . . . .(430) hence, by equating (430) and (420), the diameter is obtained: <4 = 56,400 X N X3C" (431) which, for 3C" = 40,000 lines per square inch, becomes: The minimum diameter which produces E volts is: ' - (433) 450 DYNAMO-ELECTRIC MACHINES. [121 from which, ,\ 49 for forged steel armature: d & = - X E = 1*22 E; 400 for wrought iron or cast steel armature: d & = ? X E = 1.63 E; 300 and for cast iron armature : d & = ? X E 2.45 E. .-..(434) For the double machine, the current carrying capacity and the output are found from the same formulae (428) and (429) respectively, as for the single-frame machine, and since the diameter of the frame is smaller, also its current intensity, and, in consequence, its total output will be smaller than that of a single-cylinder machine of the same E. M. F. Calculation of Magnet Winding for Unipolar Cylinder Dynamos. The dimensions of both the single and double cylinder types being generally expressed as multiples of the armature diameter, see Figs. 316 and 317, the magnetizing forces re- quired for the various portions of their magnetic circuit can be computed from the following formulae. The magnetizing force required for the air gaps, their density being X" = 40,000, is: <** -3133 x 40,000 x .05 Vd & x 1.2 = 750 V~d & , ..(435) where 1.2 is taken to be the probable factor of field deflec- tion, see Table LXVL, 64. Magnetizing force required for armature: ] ^/J & . Since (B" a = 40,000 lines, we have: for wrought iron: at & = 1.5 for cast steel: at & 1.8 for cast iron: at & 17.6 Magnetizing force required for magnet frame (cast steel of density &" m = 85,000): 1.2*4 = 44 X 1.2/4 = 53<4- .-(437) 121] CALCULATION OF UNIPOLAR DYNAMOS. 451 There being no armature-reaction, the total number of ampere-turns, AT, required for excitation at full output, see (227), 89, is the sum of the magnetizing forces obtained by formulae (435), (436), and (437). The voltage of a unipolar dynamo being comparatively small, but of constant value if the speed is kept constant, the excitation should be effected by a shunt-winding. The dimensions of the magnet-coil being fixed by the design, the mean length of one turn, the radiating surface, and the weight, respectively, can be expressed thus: /T = (4n + /V) * =_(.8<4 - .25 V7 a + .1,4) n = 2.83,4 - .785 *V a ; (438) SM = (d m + 2// m ) 7t >^ l m = (d & - .25 Vd & ) 7t X .125^ = .39*4'-. i V^; (439) and wt m / T X / m X // m X .21 = ( 2 .83^a - .785 V?a)_X .I25^ a X .I<4 X .21 = .oo 74 <4 3 - .002 1/^ , (440) The gauge of the wire, then, is determined by means of formula (319), and the temperature increase that is obtained by filling the entire space provided for this purpose, is found from (329). See example, 149. If the temperature rise corresponding to the given dimen- sions should be higher than desired in a particular case, the cross-section of the winding space must be suitably increased, preferably by extending its length, / m , and a greater weight of wire must be employed. CHAPTER XXVII. CALCULATION OF DYNAMOTORS, GENERATORS FOR SPECIAL PURPOSES, ETC. 122. Calculation of Dynamotors. Dynamo-electric generators which are energized, not by mechanical power, but by the electric current derived from another source of electricity, are, in general, called Secondary Generators, and serve the purpose of transforming a current of one kind or voltage into a current of another kind or voltage. According to the nature of the currents to be transformed and to that of the secondary currents generated, secondary generators can be divided into two classes: (1) Secondary generators for transforming continuous cur- rents of any voltage into a continuous current of any other voltage; (2) Secondary generators for transforming continuous cur- rents of any voltage into .single-phase or polyphase alternating currents of any voltage, or vice versa. Secondary generators of the first class may be of two kinds: (1) Motor -dynamos, or those in which a separate motor oper- ates a dynamo, both machines either being mounted on a common base and having a common shaft, or being entirely separate and having their shafts coupled together; (2) Dynamotors, or those in which the motor and dynamo are placed upon the same armature, or upon two separate armatures revolving in the same magnetic field, the former arrangement being the usual case. Motor-dynamos and dynamotors are used for the following purposes: (1) For transforming high-voltage currents transmitted from a central station to distributing centers located at convenient places into currents suitable for lighting, etc. (2) For transforming ordinary lighting currents into com- 452 122] CALCULATION OF DYNAMOTORS. 452^ paratively large currents at very low voltage, as used for electro-metallurgical purposes, telegraph or telephone oper- ating, meter testing, etc. (3) For compensating the drop in voltage on long mains by inserting into the mains at the distant point a series motor driving a generator armature placed as a shunt across the mains. An arrangement of this kind is called a Booster. (4) For charging accumulators at a higher voltage than that of the line, so that lamps may be operated either directly from the circuit or from the cells. (5) For 3-wire and 5-wire systems of distribution, a number of armatures or windings on the same shaft being connected Equalizer Field Coil H-i JT Equalizer rn^m -HOVol -110 Volts , Fig. 317^. Connections of Equalizing Dynamo. across the various pairs of mains, so that, if the potential drops at any one pair of mains, its armature will feed this pair, driven by the other armatures as motor. Such a device is called an Equalizing Dynamo. In the Eddy Company's equalizing system, a dynamotor having two no-volt windings is connected across the terminals of a 220-volt generator for the purpose of enabling its use for supplying a no-volt 3-wire system. The two dynamotor armature windings are con- 45 2 ^ D YNA MO- RLE C TRIC MA CHINES. [ 122 nected in series, and the neutral wire is run from the common connection of the two windings, as shown in Fig. 3170. .When the system is unbalanced, that armature winding of the dynamotor which is connected with the side of the smaller load (having the lesser drop) acts as a motor, runs the armature, and thereby causes the other armature to run as a generator, thus raising the pressure of the heavier loaded side of the system. (6) For starting and controlling large motors, especially those used for driving large printing presses supplied from lighting circuits. Printing presses have many sets of gears Fig. 3i7<$. Connections for Teaser System of Motor Control. and possess very large moments of inertia, so that an unusually large torque is required to start them. Sometimes the start- ing torque is as much as 5 or 6 times the normal torque of the motor when running at full load. The torque exerted by a motor depends upon the strength of the current flowing through its armature. Since the current which is required to produce the normal running torque of these motors is already of considerable magnitude, it is desirable that a continuous- current transformation by means of a dynamotor be employed to avoid drawing the excessive starting current from the line. 122] CALCULATION OF DYNAMOTORS. 4$2<: The dynamotor used for this purpose is designed so that its- motor side may be supplied by the line voltage while its generator side is usually wound for a voltage of about one-fifth that of the line. By this arrangement, which has been intro- duced by the Bullock Electrical Manufacturing Co., and is by them called the Teaser System of Motor Speed Control, the excessive current for starting a motor is derived without necessitating an increase of the supply current above the normal amount. The two teaser armature windings are con- nected in series with a rheostat across the supply mains; the dynamotor field winding is excited directly from the line; the negative brush of the motor side is connected with the positive brush of the dynamo side; see Fig. 317^. At starting, the main motor armature is supplied from the generator end of the dynamotor with a voltage somewhat less than one-fifth of the line voltage, depending upon the magnitude of the regulating resistance; thus, the current which passes through the main motor is about five times as great as that taken from the supply mains, so that the required amount of starting torque is pro- duced with normal supply current. Since the speed of the motor is dependent upon the E. M. F. impressed upon it, the starting speed is only about one-fifth of the normal running speed. The E. M. F. of the motor, and with it its speed, is raised by manipulating the dynamo-regulating resistance, and when the proper speed is attained the main motor connections are switched to the supply mains through a second series-reg- ulating resistance, thus establishing the required conditions for running under workingload. Regulation of the resistances and changes of the connections are accomplished by the aid of a controller, and thus the motor may be operated by the manipulation of a single hand-wheel. Secondary generators of the second class consist in a com- bination of a continuous-current motor with an alternating- current generator, or of an alternating-current motor with a continuous-current generator. They are usually called Notary Converters, and are employed in all cases where an alternating current is to be derived from continuous-current supply cir- cuits, or continuous currents from alternating circuits. Since one of the windings involves an alternating current design, the calculation of rotary converters will be taken up in the 45 2 ^ DYNAMO-ELECTRIC MACHINES. [122 second volume of this book under the head of Alternating-Cur- rent Machinery. The calculation of a motor-dynamo consists in the design of a motor which is supplied by the given current, and in the design of a generator which produces the desired current and voltage when run at the speed attained by the driving motor. The former design is accomplished by means of the formulae contained in Chapter XXV., the latter by the methods given in Parts II. to VI.; hence the calculation of motor-dynamos need not be specially considered. The calculation of dynamotors, however, involves some points of special interest, and is separately treated for this reason. The armature of a dynamotor, as previously stated, is provided with two separate windings, each connected to its own commutator, usually placed at opposite sides of the armature core. These two armature windings may be placed one above the other upon the core, or they may be interspersed by leaving suitable spaces upon the core surface for the second winding, when putting on the first. The electrical activity of the generator winding is equal to that of the motor winding, therefore the space occupied by each winding will be approximately the same, and half the winding space of the armature should be apportioned to each. The armature and frame of a dynamotor will, consequently, be of a size and weight corresponding to a machine of double the capacity to be transformed by it. Since the magnetomotive force of the motor armature wind- ing, or primary winding, is opposite in direction to that of the generator winding, or secondary winding, and since these two magnetomotive forces are nearly equal to one another and are produced in the same core, they will practically neutralize each other, the result being that in a dynamotor there is no appreciable armature-reaction, and the brushes never require to be shifted during variations of load. The size of the machine depends upon the speed, the latter being chosen with respect to the heating of armature and bearings only, for, the transformation itself is not influenced by it, because, in calculating the motor portion of the arma- ture, any change in the selection of the speed, for the same winding, calls for an alteration of the field density in exactly [ 122 CALCULATION OF DYNAMO TORS. 453 the inverse proportion, so that the product of conductor- velocity and field density remains constant, and the E. M. F. produced in the generator winding, therefore, is always the same. The field magnets of a dynamotor must, at least in part, always be excited from the primary circuit, that is, from the motor side, since otherwise the motor would not start. In case of transformation from low to high tension the fields are usually shunt wound, but in transforming from very low to high pressure it is more economical to start the motor action by a few turns of series winding connected to the motor cir- cuit and to supply the remainder of the field excitation by a shunt winding from the secondary or generator side, which commences to be actuated as soon as the machine has started to run. The counter E. M. F. of the motor winding is found by deducting from the primary voltage the drop due to internal motor resistance, and the E. M. F. active in the generator winding is the sum of the secondary voltage required and of the potential absorbed by the secondary winding. The quotient of these two E. M. Fs. gives the ratio of the number of armature turns of the primary to that needed in the secondary winding. The active length and the cross-section of either the primary or the secondary armature conductor is then calculated in the ordinary manner, and the winding so obtained is arranged upon an armature of twice the winding space necessary to accommodate it. The number of con- ductors and the area of the other winding, then, is simply obtained in multiplying or dividing, respectively, by the ratio of the E. M. Fs. to be induced in the two windings. For practical example see 150. If the primary E. M. F. be E v volts, the primary current I I amperes, the resistance of the primary winding r l ohms, and the number of primary armature turns JV &1 , while the cor- responding quantities in the secondary circuit are E^ , / a , r tt and 7V a2 , respectively, the counter E. M. F. of the primary winding will be: E\ = E l - I I r lt and the E. M. F. induced in the generator armature: 454 DYNAMO-ELECTRIC MACHINES. [122 where HI is the given ratio of transformation. The ratio of the E. M. Fs. induced in the two windings, therefore, is: But since the weight of copper in the two windings is approximately equal, the drop in the primary winding will practically be : so that the ratio of the number of turns of the secondary to that of the primary winding becomes: 1 k *(*E,+f,r,) _ E, + 7. r. - * X The terminal E. M. F. of the generator side can then be expressed thus: ,*=' t -f t ,. = ', X -/.r. = fa- -iPY^ -'.'. = '- -',".' .-(442) The machine, therefore, as far as its efficiency is concerned, acts as though it were a motor of terminal E. M. F. E, = E^ ^ volts, ^ V ai / with an internal resistance of 2 r a ohms, that is, twice the resistance of the secondary winding. 123] GENERATORS FOR SPECIAL PURPOSES. 455 123. Designing of Generators for Special Purposes. a. Arc Light Machines (Constant Current Generators). Ordinary arc lamps for commercial use are so adjusted that the pressure required to force the current through the arc is from 45 to 50 volts. A 2000 candle-power lamp will then require a current intensity of about 10 amperes, a 1200 candle- power lamp a current of about 6.5 amperes, and a 600 candle- power lamp a current of about 4 amperes. The energy consumed in the arc will therefore be about 450 watts for each 2000 candle-power lamp, about 300 watts for each 1200 candle- power lamp, and about 200 watts for each 600 candle power lamp. An arc light dynamo for n lamps must therefore have a capacity of 450^, or 300/2, or 200^ watts, respectively, and, since arc lamps are usually arranged in series, must be able to give an E. M. F. of from 50 to n X 50 volts, and a constant current of 10, or 6.5, or 4 amperes, respectively. For search- lights and lighthouse reflector lamps higher currents are used, up to 200 amperes or more; but only a few of these are ever fed from the same dynamo, which, consequently, is of a com- paratively low voltage. For all arc lamps, however, the constancy of the current is essential, and in arc light dynamos, therefore, the current must be kept practically constant for all variations of load. The problems to be considered in the design of constant cur- rent machines are so radically different from those of a con- stant potential dynamo, that, in general, a well-designed machine of the one class will not answer for the other. The ordinary shunt dynamo has the tendency to regulate for constant current, 1 because the induced E. M. F., if the magnetic circuit is suitably dimensioned, is proportional to the ampere-turns in the field, and if the resistance and the reaction of the armature are negligible, the machine will at any voltage just give the ampere-turns required to produce this voltage; that is to say, it will produce any voltage required by the con- ditions of the external circuit. This theoretical condition is 1 See " Test of a Closed Coil Arc Dynamo," by Professor R. B. Owens and C. A. Skinner; discussion by C. P. Steinmetz; Transactions Am. Inst. E. E., vol. xi. p. 441 (May 16, 1894); Electrical World, vol. xxiv. p. 150 (August 18, 1894); Electrical Engineer, vol. xviii. p. 144 (August 12, 1894). 456 DYNAMO-ELECTRIC MACHINES. [123 fulfilled in practice if the variable shunt excitation, which for low saturations is proportional to the terminal voltage, is aug- mented by the constant exciting force necessary to compensate for the drop of E. M. F. due to armature resistance and for the cross ampere-turns due to armature reaction. Thus, a shunt dynamo with a constant separate excitation will fulfill the con- dition of giving a terminal E. M. F. proportional to the ex- ternal resistance, and consequently a constant current, for all voltages below the bend of the magnetic saturation curve; that is, for all voltages for which the magnetic density is below 25,000 lines per square inch in cast iron, and below 70,000- lines per square inch in wrought iron or cast steel. (See Fig, 256, 88). Such a shunt machine will be a constant current dynamo,. and will do very well for feeding incandescent lamps in series,, but will be very unsatisfactory as an arc light generator, because it does not regulate quickly enough. If the load is changed suddenly, as often occurs in arc light working, it would take too long a time before the magnetism changes to the altered conditions of load and excitation, and thus either a sudden rush or a sudden decrease of current would take place. In an arc light machine the current intensity must not go above or below its normal value when the load is suddenly varied; the armature, therefore, must regulate instantly; that is to say, a small change of the armature current must essen- tially influence the effective field if necessary, destroy it, for even when short-circuiting the machine the field may not dis- appear entirely, but may only be so distorted as to be ineffective with regard to the terminal voltage. Consequently a machine of a large and unvariable field flux and of very large armature reaction is required, so that the armature magnetomotive force is of nearly the same magnitude as the field M. M. F., and very large compared with the resultant effective M. M. F. necessary to produce the magnetism. All successful arc light generators are based upon this prin- ciple of regulating for constant current by their armature re- action, and in their design, therefore, the following conditions, which lead to a great armature reaction, have to be fulfilled [see formulae (244) and (248), 93]: (i) The number of turns on the armature must be great; (2) the distortion of the field 123] GENERATORS FOR SPECIAL PURPOSES. 457 must be large; (3) the number of bifurcations of the armature current must be small; (4) the length of path of the field lines of force in the polepieces must be great and its area small; (5) the length of path of the armature lines of force in the pole- pieces must be small and its area large; and (6) the polepieces must require a high specific magnetizing force. Conditions (i), (3), and (4) will be fulfilled if a ring armature of small axial length, and therefore of large diameter, is chosen, and if the polepieces are shaped so as to have large circumferential projections; condition (2) points to an armature with smooth core, and condition (3) makes a bipolar type preferable, while (6) calls for high densities in the polepieces, and is most nearly attained by the use of highly saturated cast iron for that part of the magnetic circuit. In order to have constant flux, a con- stant current dynamo must be series wound and worked to very high densities in the magnetic circuit, the latter being the more insensitive to sudden changes in the exciting power the higher it is saturated. If wrought iron or cast steel is used in the magnet frame its cross-section should be so dimensioned that the resulting magnetic density has a value between 110,000 and 120,000 lines of force per square inch (= 17,000 to 18,500 lines per square centimetre), and in case of cast iron, between 60,000 and 75,000 lines per square inch (= 9300 to 11,500 lines per square centimetre). The radial thickness of the armature core should be chosen so as to obtain in the minimum armature cross-section a density of from 110,000 to 130,000 lines per square inch (= 17,000 to 20,000 lines per square centimetre) in case of bipolar machines, and from 100,000 to 120,000 lines per square inch (= 15,500 to 18,500 lines per square centime- tre) for multipolar machines. This high saturation of the armature is required for still another purpose, viz., to guard against sudden rise of the E. M. F. when the armature current is broken. For, since the magnetomotive force effective in producing the field magnetism, if current is flowing in the arma- ture, is the difference between the total field M. M. F. and the armature M. M. F., the effective M. M. F., when the current is broken, will rise by the amount of the armature reaction and become equal to the total field M. M. F. But, the total M. M. F. being very large compared with the effective M. M. F. necessary to send the normal flux through the armature, an 458 DYNAMO-ELECTRIC MACHINES. [123 enormous E. M. F. would be produced in the moment of open- ing the circuit if the saturation in the armature core were capable of a corresponding increase. In using the above den- sities, however, ever so great an increase of M. M. F. cannot raise the saturation, and thereby the voltage, seriously. For the reasons set forth in 43, open coil windings are fre- quently used in arc light dynamo armatures, although good results have also been attained with closed coil windings. In the manner explained in the foregoing, a machine can be designed which automatically keeps the current intensity con- stant under all loads without any artificial means; it will, how- ever, require an enormous magnetizing force on both field and armature in order to obtain very close regulation. But if artificial regulation is employed, very much less magnetizing force is needed, since then only just enough ampere-turns are sufficient so as not to get too large a fluctuation of the arma- ture current by a very sudden change of load before the regu- lator can act; hence, the arc light regulator is merely for the purpose of making the inherent automatic regulation of the machine still closer. There are two distinct systems of arc dynamo regulation : (i) By generating the maximum voltage at all times, but taking off by the brushes only such a portion of it as is required by the load. This is effected by shifting the brushes from the neutral line; in a closed coil armature this has the effect that the E. M. F. induced in some of the coils is in the opposite direction to that induced in the other coils in the same half of the armature, and their algebraical sum, consequently, can be made any part of the maximum E. M. F. ; in an open coil armature the brushes in the neutral position collect the current from the group of coils having maximum E. M. F., by moving them either way; therefore, groups will be connected to the brushes which have a smaller E. M. F. than the maximum potential of the machine. This method of regulation is em- ployed in the Edison, Thomson-Houston, Fort Wayne, Sperry, Western Electric, Standard Electric, and Bain arc machines. (2) By changing the whole E. M. F. generated by the dynamos as the load varies. The E. M. F. depends upon the number of conductors, the cutting speed, and the field density. It is impracticable to vary the former two while the machine is run- 123] GENERATORS FOR SPECIAL PURPOSES, 459 ning, but the field density can easily be adjusted. The field strength depends upon the number of turns on the magnets and upon the current passing through them, and can therefore be varied by changing either of them. The variation of the num- ber of field turns is performed by automatically cutting out, or short-circuiting, a portion of them, and the regulation of the field current, by placing a variable shunt across the field wind- ing. The Excelsior arc light machine is regulated in the former manner, while the Brush and the Schuyler dynamos have a variable shunt. The employment of external regulation introduces another problem. Whether the brushes are shifted in a constant field, or whether they remain stationary in a changing field, the posi- tion of the neutral line relative to the brush contact diameter varies with every change of the load, and means must be pro- vided to collect the current without sparking in any position. The best solution of this problem is, of course, to so design the dynamo that the field is perfectly uniform all around the armature, for then the brushes will actually commutate in any position of the field. To attain this, a low density is required in the gap, from 10,000 to 20,000 lines per square inch (= 1550 to 3100 lines per square centimetre); hence the pole area must be made as great as possible by large extending polepieces. If this solution is not feasible in practice, but if the resultant den- sity at any position of the brush varies with the amount of shift- ing necessary to bring the brush to that position, sparkless commutation can be obtained by varying the frequency of com- mutation; that is, the circumferential width of the brush, in employing two brushes connected in parallel, and shifting the one against the other. b. Dynamos for Electro- Metallurgy. For electroplating, electrotyping (galvano-plastics), electro- lytic precipitation of metals (refining of crude metals and ex- tracting of metals from ores), electro-smelting (reduction of metals), and for other electrolytical purposes, low electromo- tive forces and very large current intensities are requisite, as the quantity of metal extracted from the electrolyte depends upon the intensity of the current only, and not upon its poten- tial. The latter, however, affects the quality of the deposit, 460 DYNAMO-ELECTRIC MACHINES. [123 for, if too great an E. M. F. is permitted, the precipitate will not be homogeneous. The E. M. F. required for any electro- lytical process is the sum of the counter E. M. F. of the elec- trolytic cell, or the E. M. F. of chemical reaction, and the drop of potential caused by the resistance of the electrolyte. In dynamos for very low voltage, in order not to reduce the speed too much, as this would unduly increase the weight and cost, both the number of convolutions on the armature and the field density must be brought down to their minimum values. Machines with weak fields give trouble in sparking on account of the armature reaction; dynamos with few massive con- ductors and few divisions in the commutator are subject to sparking, and are liable to heat from local eddy currents. Elec- tro-metallurgical machines, therefore, should be designed with short magnetic circuit, especially the length of the flux-path in the polepieces should be as small as possible. The pole- pieces should further have a large cross-section in the direc- tion of the field flux, but a small transverse area and a great length for the lines of force set up by the armature current; that is to say, the armature itself should be of small diameter and of comparatively great length (hence, preferably a smooth- drum armature), and the polepieces should embrace only a small portion of its periphery, and, if possible, be provided with longitudinal slots parallel to the direction of the field flux. In order to avoid eddy currents as much as possible, a stranded conductor, or a multiplex winding (see 44), or both com- bined, should be used, and the poles should be either ellipti- cally bored, or given slanting pole corners, or, if of wrought iron, should be provided with cast-iron tips (see 76). If it is desired to use the machine for different voltages, the polepieces may be designed in accordance with Fig. 173, 76. Dynamos for electrolytical purposes must be shunt wound, as otherwise they are liable to have their polarity reversed by the action of the counter E. M. F. In case of bipolar types the field density of metallurgical dynamos, according to their size, should range between 7000 and 20,000 lines per square inch (= uoo to 3100 lines per square centimetre), if the polepieces are of cast iron, and between 10,000 and 30,000 lines per square inch (=: 1550 to 4650 lines per square centimetre), if they are of wrought iron 123] GENERATORS FOR SPECIAL PURPOSES. 461 or cast steel. For multipolar types the corresponding values are 9000 to 30,000 lines per square inch (= 1400 to 4650 lines per square centimetre), and 15,000 to 40,000 lines per square inch (= 2300 to 6200 lines per square centimetre), respectively. The densities employed in the field frame are slightly less than those given in Table LXXVL, 81, namely, about 80,000 lines per square inch (= 12,500 lines per square centimetre) for wrought iron and cast steel, and about 35,000 lines per square inch (= 5500 lines per square centimetre) for cast iron. The armature core densities are given in Table XXII., 26. c. Generators for Charging Accumulators. Owing to the well-known fact that the counter E. M. F. of a storage battery gradually rises about 25 per cent, during charging, generators to serve the purpose of charging accumu- lators, in order to keep the charging current constant, should be so designed that their voltage increases automatically with increasing load. Such machines, therefore, must be excited by a shunt winding, and must have a very massive field frame of consequent low magnetic saturation. The former is neces- sary to cause an automatic increase of the magnetizing force with increasing external load, and the latter to effect a cor- responding rise of the flux-density, and thereby of the E. M. F. generated in the armature. Thus for generating the minimum voltage, at start of the charging period, the magnetic density in the frame should be from 30,000 to 35,000 lines per square inch ( 4600 to 5500 lines per square centimetre) in case of cast-iron magnets, and from 70,000 to 80,000 lines per square inch (= n,ooo to 12,500 lines per square centimetre) in case of ivrought-iron or steel magnets. The armature should have a smooth core of large cross-section, so that the reluctance of the gap remains constant, and therefore the total reluctance of the circuit approximately constant for the entire range of the magnetiz- ing force. In central station working the usual practice is to employ the charging dynamos also for directly supplying the lighting circuits, either separately or by connecting them in parallel to 462 DYNAMO-ELECTRIC MACHINES. [ 123 the accumulators at the time of maximum load. In this case the dynamos must be capable (i) of supplying a constant minimum potential, namely the lamp pressure, which is not to vary with change of load, and (2) of giving a voltage from 25 to 30 per cent, higher, /". e., the charging E. M. F. which must automatically regulate for variation of load. These two con- tradictory conditions can be fulfilled by designing a shunt dynamo of low magnetic density in armature core and mag- net frame, and by providing the armature core with high teeth of such peripheral thickness that the flux required for the generation of the lamp-potential is sufficient to almost com- pletely saturate the same, the density in the teetH at lamp- pressure to be 130,000 lines per square inch (= 20,000 lines per square centimetre) or more. The reluctance of the gap for light loads, up to the lamp-pressure, will then increase with the load, and as the magnetizing force in a weakly mag- netized shunt dynamo also varies directly with the load, the flux, and thereby the E. M. F., will remain constant. But as soon as the saturation of the teeth is reached, that is to say, as soon as the machine is used for voltages above that of the lighting circuit, the gap reluctance, then being equivalent to that of air, will become constant, hence the E. M. F. of the machine will vary in direct proportion with the load, as long as all parts of the magnetic circuit are well below the point of saturation. d. Machines for Very High Potentials. For transmission of power to long distances, for testing pur- poses, and for laboratory work, dynamos of 10,000 volts and over are sometimes needed. Professor Crocker, 1 in an address before the Electrical Congress, Chicago, August 24, 1893, has given the chief points to be observed in the success- ful construction of such machines, as follows: (i) The insula- tion must be excellent, and for no two parts that have the full potential between them should measure less than 1000 megohms; (2) the side-mica of the commutator should be at least ^g- of an inch, and the end insulations at least of 1 "On Direct Current Dynamos for Very High Potential," by F. B. Crocker, Electrical World, vol. xxii. p. 2OI (September 9, 1893). GENERATORS FOR SPECIAL PURPOSES. 463 an inch thick, and, if possible, the surface distance at the ends should be increased by having the insulation project, the number of commutator divisions can then be so chosen that the potential between adjacent bars is 100 volts per pair of poles; (3) hard, smooth, and fine-grained carbon brushes should be used, as the employment of metallic brushes, owing to the film of the brush-material that is rubbed into the sur- face of the mica insulation, and which at a voltage of 10,000 or above, is a sufficiently good conductor to carry many watts of electrical energy, would lead to the destruction of the com- mutator; (4) the brush-pressure should not be any greater than necessary to insure good contact, because otherwise a layer of carbon dust might be produced on the commutator, when a similar effect as with metallic brushes, but not to the same degree, would be caused; (5) the armature should have a slotted core (toothed or perforated), and should be wound with double silk-covered wire, the former with the object of reducing the reluctance of the magnetic circuit and enabling the employment of very high field-densities, from ij to ij- those given in Tables VI. and VII., 18; (6) the magnet frame should be well saturated, densities of about 100,000 lines per square inch (= 15,500 lines per square centimetre) for wrought iron or cast steel, and of about 50,000 lines per square inch (= 7750 lines per square centimetre) for cast iron being best suited for the purpose; (7) the potential of the frame must be kept at one-half the terminal E. M. F., a con- dition which, however, is fulfilled if the machine is highly insulated; and (8) for reasons of economy, the field excitation of a high potential machine has to be supplied by a series winding, as otherwise the space occupied by the covering of the wire, and thereby the winding depth, would become exces- sive and a waste of copper, besides increased labor and diffi- culty in handling the extremely fine wire, would result e. Multi-Circuit Arc Dynamos. The one serious objection to the use of the ordinary arc dynamo is the restriction of its capacity by the limitation of the line voltage. Since 7500 volts is considered the maximum for commercial work, ordinary arc machines are able to supply 463 tf D YNAMO-ELECTRIC MA CHINE S. [123 only 150 open or 100 inclosed arc lamps, corresponding to a maximum capacity of about 75 KW, or about 50 KW, respectively. In the multi-circuit dynamo a number of separate and inde- pendently regulable circuits are supplied, and thus it is possi- ble to build arc-lighting generators of much larger capacity without exceeding the limit of line voltage. Each pair of poles, the portion of armature thereunder, and the corresponding pair of brushes, constitute a separate series machine, the current leading from one brush to one of the line circuits, through two of the field coils, through the other brush of the pair, and dividing through the armature winding to the first-named brush. Each pair of brushes is carried upon a separate rocker segment, and the regulation is effected by shifting the separate rockers. In the Brush and in the Rushmore multi-circuit arc machines there is a small oil-pressure cylinder for each rocker, and oil is admitted under pressure to one end or*he other by a small magnet-controlled valve, and thus each pair of brushes occu- pies at all times a position on the commutator corresponding to the line voltage required. All regulating mechanism is placed in a small tank in the base of the machine, which also contains a small rotary oil pump, belted to the armature shaft to supply oil at the needed pressure. By this arrange- ment each circuit is able to be abruptly open-circuited or short-circuited under any load without the least effect upon the other circuit. /. Double-Current Generators. A double-current generator is a dynamo producing at the same time two different currents, either two continuous currents of different voltages, or one continuous current and an alternating current, or two alternating currents of different phase-rela- tions or of different frequencies. A double-current generator is therefore nothing more or less than a dynamotor which is driven by mechanical power, and the same principles of con- .struction apply as set forth in 122. Though numerous writers have during the last few years 124] PREVENTION OF ARMATURE-REACTION. 463^ recommended the use of double-current generators, they have not been introduced into practice to any extent, chiefly for the reason that there is usually no advantage gained by com- bining two generators for different purposes into one machine, while in most cases such a combination would be likely to complicate matters very much by introducing unnecessary difficulties. The only possible benefit obtained by the use of double-cur- rent generators is the ability to supply two kinds of currents .and still have but one type of station machinery. On the other hand, however, there are two decided disadvantages: (i) in- terference with the regulation of one system by certain fluc- tuations in the load of the other system; (2) in case of alter- nating current, the necessity of expensive station transformers capable of carrying the total alternating current load, and of auxiliary regulating apparatus. The latter is required on account of the poor regulating properties of the alternating current side of a double-current generator, and even the use of the auxiliary regulators will not always insure satisfactory results. Furthermore, the continuous current output of a continuous-alternating generator limits the frequency to about 35 cycles ( 74), making compulsory the use of a low-fre- quency alternating current. This low frequency may or may not be of disadvantage, according to the nature of the plant and to conditions of operation. For plants of such size as to permit the employment of very large units, facilitating the use of many magnet poles, double- current generators might be tolerable, provided the characters of the two loads are such as to justify the expense, but even in this case it is questionable whether any actual operating advantage would be conferred by double-current machines as compared with ordinary alternators and direct-current dynamos, 124. Prevention of Armature-Reaction. Not only the heating, but also, even to a higher degree, the amount of sparking at the brushes limits the output of an armature. The increased sparking with rise of load is due to the interference of the magnetic field set up by the current flowing in the armature, the tendency of the latter being to 464 DYNAMO-ELECTRIC MACHINES. [124: produce a cross magnetization through the armature core, at right angles to the useful lines of force, resulting in the dis- tortion of the field of the dynamo, that is, in increased field density under the trailing pole corners, and in decreased density under the leading pole-corners; see Fig. 140, 64, and Fig. 270, 93. This distortion, depending in a given machine directly upon the magnetizing force of the armature, naturally increases with the current furnished by the dynamo, and the result is that the amount of shifting of the neutral line, or diameter of commutation, and therefore the sparking at the brushes, increases with the load on the machine. Con- sequently, it becomes necessary to change the position of the brushes to meet every variation in load, and unless the pole- tips or the armature-teeth are saturated (see 22), a point of loading is soon reached for which no diameter of sparkless commutation can be found, and the output of the machine has reached a maximum at this point, notwithstanding the fact that the load may be below that allowed by a safe heating limit. In order, therefore, to increase the output of a dynamo, the arma- ture reaction itself, or its distorting effects, must be checked. Besides the means for this purpose already alluded to in 22, 76, and 122, consisting in specially shaping the pole- pieces, the air gaps, and the armature teeth so as to increase the reluctance of the cross-magnetization path, either perma- nently or proportionably to the load, three distinct methods for preventing armature reaction have recently been devised: (a) Balancing of armature cross-magnetization by means of special field coils (Professor H. J. Ryan) ; (b) compensation by additional armature winding (Wm. B. Sayers); and (c) checking of armature reaction by the employment of auxiliary magnet poles (Professor Elihu Thomson). a. Ryans Balancing Field Coil Method. ' This method, which in principle was first suggested by Fischer-Hinnen, 2 and independently also by Professor G. 1 " A Method for Preventing Armature Reaction," by Harris J. Ryan and Milton E. Thompson, Transactions Am. Inst. E. E., vol. xii. p. 84 (March 20, 1895); Electrical World, vol. xx. p. 329 (November 19, 1892); Electrical Engineer, vol. xix. p. 293 (March 27, 1895). 2 " Berechnung Elektrischer Gleichstrom Maschinen," by J. Fischer-Hinnen > Zurich, 1892. 124] PREVENTION OF ARMATURE REACTION. 465 Forbes, Professor S. P. Thompson, and W. H. Mordey, con- sists, in general, in surrounding the armature with a stationary winding exactly equal in its magnetizing effects to the arma- ture winding, but directly opposed to the latter, and thus completely balancing all armature-reaction. It is practically carried out by placing a number of balancing coils, one per pole, having a total number of turns equal to that of the arma- ture, into longitudinal slots cut into the polepieces parallel to the shaft, and by connecting these coils in series to the arma- ture, thus making their magnetizing force of equal number of ampere-turns as, but of opposite direction to, that of the armature. The two M. M. Fs. thus counterbalance and neutralize each other, leaving the field-flux practically un- changed at all loads of the machine. By this means all spark- ing due to distortion of the field is prevented, and only the sparking due to the self-induction in the short-circuited coil, and to the current reversal in the same, is left. In order to check the latter, each pole-space is provided with a commuta- tion magnet, or lug, which is made the centre of the respective balancing coil, and which is energized by an additional wind- ing consisting in a few extra turns of the balancing coil. If no current is flowing in the armature, and therefore also the balancing coils are without current, the commutation magnet is not energized and the field opposite the latter is neutral, but as soon as load is put on the armature the commutation lug is magnetized by the additional turns of the balancing coil, and a reversing field for the short-circuited armature-coil is created; the strength of this reversing field, being energized by the armature current, increases with the load, thus fulfill- ing the conditions for sparkless commutation. Fig. 318 shows two half polepieces slotted to receive a bal- ancing coil of eight turns, the half-turns being numbered con- secutively to indicate the manner in which the coil is wound. In Fig. 319 the field of a bipolar dynamo with commutation lugs and balancing coils is represented; the two polepieces in this case are in one piece, the commutation lugs being arranged in the centre line. The same effect, however, can be pro- duced by connecting each two polepieces by a pole-bridge. Fig. 320, or by employing a special pole-ring, Fig. 321, carrying the commutation lugs as well as the balancing coils. In any case 4 66 D YNA MO-ELECTRIC MA CHINES. [124 the slots A and B, adjoining the commutation lugs, C, are larger than the remaining slots, for the purpose of receiving the extra turns for magnetizing the commutation lugs. The disadvantages of this method are (i) increased reluct- Fig. 318. Polepiece Provided with Ryan Balancing Coils. ance of the magnetic circuit on account of reducing, by virtue of the slots for the balancing coils, the cross-section of the pole- pieces; this requires additional field-excitation; (2) increased magnetic leakage owing to the close proximity of the pole-tips, Fig. 319. Bipolar Dynamo Field with Commutation Lug and Ryan Balancing Coils. or to the bridging of the pole spaces, necessitated to form the commutation lugs; this leakage must also be made up by extra field-winding; (3) reduction of the ventilating space around the armature, and consequent increased heating of the latter; and (4) increased weight and cost of machine. The increase 124J PREVENTION OF ARMATURE REACTION. 467 in exciting power due to (i) and (2) alone may be sufficient to overcome an additional length of air gap large enough to Fig. 320. Dynamo Field with Pole Bridge, Carrying Commutation Lug for Ryan Balancing Coil. nearly or quite check the armature reaction without the use of .balancing coils. b. Sayers' Compensating Armature Coil Method. ' While in the former method the compensating coils are placed on the fields, in the present one additional series wind- ings are put on the armature; a series dynamo on this princi- ple, therefore, requires no field winding at all, and a compound machine is to be provided with shunt coils only. This end is attained by connecting the main loops of the armature to the commutator-bars by means of connecting coils which form open circuits except when in contact with the brushes; then Fig. 321. Dynamo Field Frame with Pole-Ring for Ryan Balancing Coils. they carry the whole armature current, and thus exercise their function of creating a sufficient E. M. F. to balance the self- 1 " Reversible Regenerative Armatures and Short Air Space Dynamos," by W. B. Sayers ; Trans. Inst. El. Eng., vol. xxii. p. 377 (July, 1893), and vol. xxiv. p. 122 (February 14, 1895) ; Electrical Engineer (London), vol. xv. (new series) p. 191 (February 15, 1895) ; Electrician (London), vol. xxxvi, p. 341 (January 10, 1896). 468 DYNAMO-ELECTRIC MACHINES. [ 124 induction of the short-circuited armature coils. These "com- mutator-coils" form loops under the field-poles and thereby produce a forward field, which excites the magnets. By this means it is possible to control sparking, to reduce the magnetic reluctance of the frame and, in consequence, the exciting power, and to raise the weight-efficiency. The sparking being under perfect control, the brushes in a generator can be placed backward, instead of giving them a forward lead, and the armature-current consequently exercises a helpful magnetizing action instead of having a destroying effect as in the ordinary case. Fig. 322 shows the principle of this winding, A, A, being the main armature coils, and B, B, the compensating, or commuta- Fig. 322. Diagram of Sayers' Compensating Armature Winding. tor coils. An auxiliary magnet, or pole extension, C, having a similar function as the commutator lug in the previous method, is employed to supply the proper strength of the re- versing field for the short-circuited armature coil. Sayers uses toothed and perforated armature cores, placing the main winding at the bottom and the commutator coils at the top in each slot. In order to keep down self-induc- tion, the opening at the top of the slot, that is, the distance between the tooth-projections, should be made as wide as can be done without exceeding the limit where appreciable loss would occur through eddies in the polar surfaces of the field magnets. For the latter reason the width of this opening should not exceed i^ times the length of the air space; Sayers 124] PREVENTION OF ARMATURE REACTION. usually makes it about 1} times that length. The number of conductors in each slot must be as small as is consistent with considerations of cost of manufacture, and since the number of commutator segments should be as small as possible, it is advantageous to connect the armature winding so that the conductors in two or more pairs of slots form but one coil. By placing the conductors of opposite potential, or connected at the time of commutation to opposite brushes, into separate slots, the self-induction of the armature winding can be reduced to about one-half. For reversible motors the rocking arm carrying the brush- holders is mounted on the shaft so as to move freely between two stops, the friction of the brushes, upon reversal of direc- tion, changing the position of the brushes automatically and without sparking from the stop at one side to that of the other, the stops being so adjusted as to keep the brushes in proper position for sparkless commutation. While in the case of a generator it may be inadvisable tc reduce the air space below a given value on account of the crowding up of lines due to the large armature reaction, caus- ing a diminution in the total flux, in the case of a motor this action can be taken advantage of, and the air space reduced to a safe mechanical clearance; the reduction of the total flux due to crowding up will then tend to compensate for drop of pressure due to dead resistance, so that in the case of a motor we obtain the happy concurrence of lightest weight and mini- mum cost with best regulating qualities. c. Thomsons Auxiliary Pole Method* By the employment of auxiliary, or blank poles, one between each two active or excited poles, the current in the armature is made to react under load to magnetize a portion of the field frame which at no load is neutral or nearly so. The armature reaction may thus be made to give rise to a magnetic flux suf- ficient, or even more than sufficient, to compensate for its diminishing effect upon the useful field flux. This result is 1 " Compounding Dynamos for Armature Reaction," by Elihu Thomson, Trans. A. I. E. E,, vol. xii. p. 288 (June 26, 1895); Electrical Engineer, vol. xx. p. 35 (July 10, 1895). 470 D YNA MO-ELECTRIC MA CHINES. [ 125 accomplished by dividing each field pole into a portion which is left unwound and a portion which is wound and excited in shunt, or separate. At no load, only the wound polar portions act to generate the open circuit E. M. F. ; as the load is put on, the unwound auxiliary poles become active in consequence of a magnetic flux developed in them by the armature current itself, that is in consequence of the armature M. M. F. The disposition of the poles is shown in Figs. 323 and 324, the un- N S Figs. 323 and 324. Magnetic Circuits of Dynamos with Thomson Auxiliary Poles, at no Load and with Current in Armature. wound poles being presented to the armature at right angles to the useful field flux. Fig. 323 gives the magnetic circuits at no load when the unwound poles are neutral, magnetically, while in Fig. 324 the grouping of the magnetic circuits is repre- sented, if current is flowing in the armature, the cross-flux then being taken up by the auxiliary poles and led off into the backs of the wound poles, thereby strengthening the useful field instead of weakening it. By properly choosing the position and spread of the auxili- ary poles in relation to that of the main poles, and by adjust- ing the magnetizing force of the field relatively to that of the armature, the effect of compounding, or any degree of over- compounding, may easily be obtained, or the blank poles may be made adjustable in position so as to vary the effect of the armature M. M. F. upon them. 125. Size of Air Gaps for Sparkless Collection. Although from the magnetic standpoint as small an air gap as possible is desired, the distance between armature core and polepieces should not be cut down too much, for the following 125] SIZE OF AIR GAPS. 47 J reasons: (i) With a very small air space the excitation is too low to maintain a stiff field at full load; (2) eddy currents be- come troublesome; (3) a great difficulty arises in maintaining the armature exactly centred, which is much more essential in a multipolar than in a bipolar machine; and (4) dynamos constructed with a very small air gap require a larger angle of lead, and do not generate as high a voltage as others of the same type having a larger air gap; this is due to the greater armature reaction, which causes a greater distortion of the lines, and owing to this increased obliquity of the lines, a short air gap may have a greater reluctance than a longer one; in fact, there is a certain value for each dynamo, beyond which there is no advantage in diminishing the air gap, as the ob- liquity of the lines becomes too great. For sparkless collection of the current the gaps should be so proportioned that the magnetizing force required to give the correct flow of lines for the normal voltage and speed is the sum of the magnetizing force necessary to balance the armature cross turns, and of the magnetizing force required to give a reversing field of sufficient strength to effect sparkless collection. If it is less than this amount, there will be spark- ing, while if it is greater, the excess constitutes a useless waste of energy. The magnetizing force necessary to produce the proper strength of the reversing field has been found by Claude W. Hill ' to be 11.25 tjmes the ampere-turns per armature coil in machines with ring armatures and wrought -iroti magnets, and from 26.5 to 29.6 times the ampere-turns per coil in drum armatures of various sizes. Taking 12 and 30 times the mag- netizing force of one armature coil, for ring and drum arma- tures, respectively, the length of the air gaps for sparkless collection can be derived as follows: By (228), 90, the ampere-turns needed for the air gaps are: *tg = -3133 x oe" x r e = .3133 x x" x k^ x (d v - ~ 2 // p "i8^~ and the ampere-turns required to produce the proper strength of the reversing field by means of the above figures based upon Hill's results, can be expressed by: at s = 12 X a X -- -i for n'/ig armatures, 2 P ; ... #/ s = 30 X a X , for drum armatures. 2 p For sparkless collection then we must make: or, for ring armatures : .3133 x oe" x 12 x K - <4) 7V a /' >&.. X -^XT^-X-^S whence: /' * X * X T- + I2 // J. = ^r X and similarly for drum armatures: , * M X,X^|^+30 126. Iron Wire for Armature and Magnet Winding. Small dynamos, up to 5 KW. capacity, are very uneconomi- cal, for the reason that the armature-winding with its binding wires occupies a comparatively large depth, which with the clearance between the finished armature and the polepieces makes the air gaps unduly large. The leakage factor, being the quotient of the total permeance (which in small machines is particularly large on account of the comparatively large sur- faces and small distances in the frame) and of the useful per- meance (which is extra small owing to the long air gaps), is therefore very high, and a comparatively large exciting power is required in consequence. 126] IRON WIRE FOR WINDING. 473 For the purpose of removing the main cause of low efficiency of small dynamos, viz. , excessive ratio of gap-space to arma- ture diameter, it has been repeatedly suggested ' to employ iron wire for winding the armature. It is certain that the winding of an armature with iron wire will materially reduce the reluctance of the gap-spaces, and thereby will economize in exciting power, (i) directly, by lessening the total reluctance of the magnetic circuit of which the air gap is the predominant portion, and (2) indirectly by reducing the magnetic leakage of the machine. Magnetically, therefore, the use of iron wire for the armature coils offers a great advantage over copper. Another advantage of employing iron wire for winding the armatures of small machines is the increase of the total effect- ive length of the armature conductor thereby made possible. In order to limit the leakage across the tips of the polepieces, the distance between the pole-corners must be larger than the length of the two gaps; in small copper-wound armatures this distance therefore is excessive compared with large dynamos, even if it is reduced so that quite a good deal of leakage does take place across the pole-tips; and, if iron armature coils are employed, may be considerably decreased, thereby rendering a larger portion of the armature circumference useful, and in- creasing the effective length of the armature conductor, while the ratio of the decreased pole-distance to the gap-length, which then only consists in the height taken up by binding and in the mechanical clearance, will even be greater, and thus effect a decrease in the percentage of leakage from pole to pole. On the other hand, the electrical resistivity of iron being about six times that of commercial copper, for the same cur- rent output an iron wire of about six times the cross-section of a copper wire will be required, and this will occupy about six times the space on the ends of a drum, or in the interior of a ring armature, eventually necessitating an increase in the diameter of the latter. Since the winding is very deep, and consists of magnetic conducting material, the outer layers will form a shorter path for the magnetic lines than the inner ones, so that only a portion of the useful flux will cut the inner 1 See editorial, Electrical Engineer , vol. xviii. p. 150 (August 22, 1894). 474 DYNAMO-ELECTRIC MACHINES. [126 layers, and the latter therefore will not generate their full share of E. M. F. The presence of the iron wire in the in- terior of the ring armature, moreover, would allow magnetic lines to cross the internal ring-space, and these, in cutting the winding, would produce an E. M. F. opposite in direction to the E. M. F. of the machine, thus reducing the latter by its amount. Finally, the total revolving mass of iron in the armature being greater in the case of iron coils, both the hys- teresis and eddy current losses will be in excess of those in a copper-wound armature. As to cost, the fine copper wire commonly used in small armatures is difficult to insulate with thin cotton covering, and, therefore, expensive silk insulation is usually applied, while an iron wire of six times its area, that is, about 2j times its diameter, may conveniently be insulated with the cheaper cotton. But since the weight of the iron wire, oa account of its sixfold area and of the higher winding space and consequent larger armature-heads, is at least seven to eight times that of a corresponding copper winding, it is doubtful whether there is a direct saving in cost by the employment of iron wire. Furthermore, an increase in the length of arma- ture shaft and machine-base being necessitated by the much larger heads, while the reduction of the gap reluctance and of the magnetic leakage effects a saving in magnet-wire and a decrease in field frame area and length of magnetic circuit, the cost of the machine frame is influenced positively as well as negatively, and it will depend upon the circumstances in every single case whether copper or iron armature coils are preferable. It has also been recommended to use iron wire for winding the magnet coils. In this case the winding itself may be con- sidered a part of the magnetic circuit, hence the cores may be diminished in area and the length of the wire thereby reduced, but on account of the insulation on the winding, its reluctivity is much greater than that of the solid core, and the winding therefore can only take the place of a portion of the core much smaller than itself, leaving the outside diameter of the magnet cores still larger than if wound with copper wire. Owing to this increase in diameter, the core surfaces are in- creased and their distance apart is diminished, hence the per- 126] IRON WIRE FOR WINDING. 475 meance of the path between them is increased and rise for greater leakage is given, unless the frame area, by the simul- taneous use of iron for the armature coils, is reduced suffi- ciently to make up for this increase in diameter. In case of a small shunt-wound machine, the magnet wire is extremely fine, and the reduction of both the number of turns and their mean length would necessitate the selection of a still smaller sized wire in order to have a sufficiently high resistance in the field coils, and then the use of iron wire would be particularly desirable. From these considerations it follows that the advisability of using iron wire for the magnet coils likewise depends upon the circumstances connected with the machine in question. The fact, however, that various makers have practically tried iron wire armature and magnet windings without adopt- ing their use for small dynamos, seems to indicate that there is nothing to be gained by the change. CHAPTER XXVIII. DYNAMO-GRAPHICS. 127. Construction of Characteristic Curves. The majority of the practical problems connected with the construction of dynamo-electric machines can readily be solved graphically, by the use of certain curves, technically called characteristics, which express the dependence upon one another of the various quantities involved. For distinction the curves relating to quantities of the external circuit are termed external characteristics, while those referring to quantities within the machine itself are known as internal characteristics. In most problems the magnetic characteristics, showing the variation of the E. M. F, with increasing magnetizing power, is employed, and the construction of this curve, from the data of the machine calculated, forms, therefore, the fundamental problem of dynamo-graphics. This problem is solved by means of the formula for the total magnetizing force of the machine. Inserting into (227) the values given in (228), (230), (238), and (250), Chapter XVIII., we obtain for the total number of ampere-turns per magnetic circuit, in English measure: AT = .3133 X l\ X 3C" + l\ X m\ + / But m\ and m" m depend upon the values (B" a and (E* m of the magnetic densities of the armature core and the magnet-frame, respectively, and, since (B" a = 3C" X ^ and &" m = A X 3C" X -j*> o a ^m S g , S & , S m being the areas of the magnetic circuit in air gaps, armature core, and field frame, and A the leakage factor, "it is 47 6 I 127] DYNAMO-GRAPHICS. 477 evident that m\ and m" m depend upon the value of the field- density 3C", and can be mathematically expressed as " func- tions" of X", thus; "a=/i(OC") and / m =/ 2 (X"), /! (5C") and / 2 (X") reading "function one of (X")" and '* function two of (3C")", respectively. Furthermore, since the angle of brush lead, 'm X /' m = V X / Vi. + **"c.i. X /' CJ + m" c , s , X l\. s , .. m" Wtit corresponding to a density of A x 3C" x -^-> m " c .i. cor- ^w.i. responding to \ X 3C* X -=^-i and m'^ to A X OC" X -^- ^c-i. ^->c.8 D YNA MO- GRA PHICS. 479 In cases where the armature reaction is small and where the magnetic density in the armature core is low, that is, in all machines except those designed for certain special purposes (see 123), the curves OB and OD are very nearly straight lines, and can be united with curve OA by means of the approx- imate formula: = -3133 x ae" x i\ + 20 x A x ae" x x i\ *^a -f .00001 X ^V" a X r X 3C" 2 n = oe" x ( . 3133 x i' 9 + ao x A x -~ x /" a + .00001 X X r ) , 2n v/ (448), thus simplifying the construction of the magnetic characteris- tic into the addition of the abscissae of but a single curve and a Fig. 326. Simplified Method of Constructing Magnetic Characteristic. single straight line. Formula (448) gives practically accurate results if the mean density in the armature core, 91, at maxi- mum load of dynamo, is within 80,000 lines per square inch, or 12,500 lines per square centimetre, and if the values of the 480 D YNA MO-ELECTRIC MA CHINES. [ 127 constant / 20 for different mean maximum load densities are taken from the following Table CV. : TABLE CV. FACTOR OF ARMATURE AMPERE-TURNS FOR VARIOUS MEAN FULL-LOAD DENSITIES. ENGLISH UNITS. METRIC UNITS. Mean Ampere- Constant Mean Ampere- Constant Density in Armature Core at Maximum Output. Turns per inch of Magnetic Circuit in Armature in Approximate Formula for Armature Ampere- TuruH. Density in Armature Core at Maximum Output. Turns per cm. of Magnetic Circuit in Armature . in Approximate Formula for Armature Ampere- Turns. Lines p. sq. in. (B a Core. n " l a k ~ ~W^ Lines per cm 8 Core. k' m& (B 25,000 4.5 .00018 4,000 1.8 .00045 30,000 5.5 4 .00018 5,000 2.35 .00047 35,000 6.5 .00019 6,000 2.85 .000475 40,000 7.5 .00019 7,000 3.35 .00048 45,000 8.5 .00019 8,000 3.95 .00049 50,000 9.6 .00019 9,000 4.8 .00053 55,000 11.1 .00020 10,000 6.1 .00061 60,000 13 .00022 10,500 7 .00067 65,000 15.7 .00024 11,000 8 .00073 70,000 19.6 .00028 11,500 9.4 .00082 75,000 24.7 .00033 12,000 10.8 .00090 80,000 31.2 .00039 12,500 12 .00096 For calculations in metric units the coefficient of gap ampere- turns, .3133, must be replaced by .8 (see 90), and the value .0000645 is to De taken for the factor of compensating am- pere-turns, instead of .0000 1, which has been averaged from a great number of bipolar and multipolar dynamos, having drum as well as ring, and smooth as well as toothed and perforated armatures. In the majority of cases the value of this factor, in English units, ranges between .0000075 anc ^ .0000125, while the actual minimum and maximum limits found were .0000040 and .0000160, respectively. The metric value is derived from the average in English measure by multiplying with the number of square centimetres in one square inch. The simplified process of constructing the characteristic, then, is as follows : The value of the combined magnetizing force, #/g ar , calculated from (448) for any one, preferably high, value of the~ field density, 3C", is plotted as abscissa XA, Fig. 326, with that value, XO, of 3C" as ordinate, and the point A 127] DYNAMO-GRAPHICS. 481 thus found is connected with the co-ordinate centre <9, by a straight line. Next the saturation curve OC of the field frame is plotted by computing A X 3C" X -^ ^m for a series of values of 5C", multiplying the corresponding magnetizing forces, m" m , taken from Table LXXXVIIL, p. 336, or LXXXIX, p. 337, or from Fig. 259, p. 338, for the re- spective material, with the length /" m , of the magnetic circuit in the field frame, and connecting the points so obtained by a continuous curved line OC. In case of a composition frame this process is to be performed according to formula (447), that is to say, by adding all the component magnetizing forces for each value of the density JC". The required characteristic OE is then obtained by drawing horizontal lines, such as XE in Fig. 326, and making CE, measured from curve OC, equal to the distance XA of line OA from the axis OX. Example : To construct the characteristic of a bipolar gen- erator of 125 volts and 160 amperes at 1200 revolutions per minute, having a ring armature and a cast-iron field frame, the following data being given: Length of magnetic circuit in cast iron, /" m = 80 inches; in armature core, l\ = 15 inches; in gap spaces, l\ = i^ inch. Mean area in cast iron, S m = 79 square inches; in armature, S & = 50 square inches; in gaps, S g 158 square inches. Number of armature conductors, N c = 216. Coefficient of magnetic leakage, A, = 1.25. If the field frame, as in the present case, consists of but one material, the magnetization curve for that material of which a supply may be prepared for this purpose can be directly utilized. It is only necessary to multiply the scale of the abscissae by /" m , and to divide that of the ordinates by g A X -^ ; in the present case the magnetizing force per inch ^>m length of circuit is to be multiplied by 80 to obtain the total number of ampere-turns, and the density per square inch of field frame is to be divided by 158 482 DYNAMO-ELECTRIC MACHINES. [127 in order to reduce the ordinates to the corresponding values of the field density. In this manner the second scales in Fig. 327, marked "Total Number of Ampere-turns" and " Field E ac (Bm /Har C^^ ^ - 24000 60000 / ^^^ tf^C 150- - / <^^ *>^Z ~ J 22000 UJ / <^ ^^ ' _ Z ...10200 _V,<^ ^^ f0125- . 20000 OL <50000 ^^ ^ 18000 "u. ~ Q ~ 7 ^^ o Qj _l > - 2ioo- 16000 LJ C 40000 / *<$s / s ul 111 ? 14000 z / *y y ? 12000 1- co 30000 Z 111 / / ty S : ticooo CO _ Q - O - / 50- jj 8000 Q _ -1- 20000 UJ - 3 6000 UJ - 'I - 1 / % S5- U. 4000 Z loooo i / o~ 2000 o 1 I// AMPERE TURNS PER INCH LE ^ i i i i i i i i 1 i i i 1 i i i i 1 . i i i 1 NQTH, m" m , , , 1 , . , . I fi n r , . * 100 200 j 300 400) ! 12000 ' 16000 20000 24000 28000 32000 TOTAL NUMBER OF AMPERE TURNS Fig. 327. Practical Example of Construction of Characteristic. Density," respectively, are obtained, and now the line at g&r can be plotted. For this purpose the mean density in the arma- ture core at maximum output, and from this the value of the constant 20 must first be determined. From formula (138) we have, for the useful flux, at normal load : 6 X ( 5 + 5) X .o' = Q maxwel , 216 X 1200 hence, _, $ 3,000,000 . , & a = ; = -i '- 60,000 lines per square inch, for which Table CV. gives: k nn .00022. 128] DYNAMO-GRAPHICS. 4 8 3 Calculating now the value of at^ for JC" = 20,000, we find by formula (448) : I5 8 3 1 33 X i-gV + .00022 X 1.25 X --- X 15 >,ooo/. i6o\ .00001 X 216 X I = 20,000 (.324 + .013 + .173) = 20,000 x .510 = 10,200 ampere-turns. Plotting this value as abscissa for an ordinate of 5C" = 20,000, the point A is obtained, which, when connected with the co- ordinate centre (9, gives the line OA, representing the sum of the gap, armature, and compensating ampere-turns for any field density. The addition of the abscissa of this line to those of the curve OB, which gives the magnetizing force, at m , required for the field frame, furnishes the required characteristic. In order to read the ordinates in volts,- a third scale of ordinates is yet to be added; since the field density at full load is 000 = 19,000, 6 g 158 this third scale is obtained by placing "125 volts" opposite that density, and by subdividing accordingly, the resulting scale giving the output E. M. F. for varying magnetizing force. 128. Modification in the Characteristic Due to Change of Air Gap. 1 In practice it often becomes necessary to change the length of the air gap in order to secure sparkless collection of the current (compare 125), and it is then important to investi- gate the influence of different air gaps upon exciting power and E. M. F. The characteristic OBC, Fig. 328, for the original air gap constructed according to 127, is replaced by the curve ABC, consisting of the straight-line portion, AB, and of the curved 1 Brunswick, L Eclair age Elec., August 31, 1895; Electrical World, vol. xxvi. p. 349 (September 28, 1895). 4 8 4 D YNAMO-ELECTRIC MA CHINES. [ 128 portion, BC. Since for low densities the magnetizing force required for the iron portion of the magnetic circuit is very small, the straight line portion, AB, can be considered as the magnetizing force due to the air gap alone, and therefore the curved portion, BC, as the sum of the elongation, BD, of this- straight line plus the magnetizing force due to the iron. Any AMPER.E TURNS . A K H' Fig. 328. Conversion of Characteristics for Different Air Gaps, change in the length of the air gaps will, consequently, for any given ordinate, OE, only alter the abscissa, EF, of the straight line AD, but will leave unaffected the abscissa-difference, FG, between the curve BC and the straight line BD. Hence the new characteristic OC for an increased air gap is obtained by increasing the abscissa EF to EF ', in the ratio of the old to the new air gap, and by adding to the abscissa thus found the original difference between BC and BD, making F'G FG. Then OH' is the magnetizing force required to produce the E. M. F. OE, corresponding to the point G' on the new characteristic; the portion OK' of the magnetizing force is the exciting power used for the new air gap, and K'H' that for the remaining parts of the magnetic circuit, and is therefore independent of the air gap. - 129] D YNAMO-GRAPHICS. 485 129. Determination of the E. M. F. of a Shunt Dy- namo for a Given Load. ' If E, Fig. 329, is the E. M. F. developed by the machine at no load, viz. : E = / 8h X r sh , and if the E. M. F., E l , at a certain load corresponding to an armature current of 7 amperes is to be found, draw QA, b.j connecting the co-ordinate centre, O, with the point A on the AMP. TURNS AT, AT Fig. 329. Determination of E. M. F. of Shunt Dynamo for Given Load. characteristic corresponding to the E. M. F. , then make OB equal to the total drop of E. M. F. caused by the armature current /, or OB = e & = /X r & + e r , where f X r & is the drop caused by the armature resistance r a , and e T that due to armature reaction. The latter may ap- proximately be taken as half the former, /. e.: thus making the total drop _ = OT= ~^T =A-=>w + ^ and: The required regulating resistance, therefore, is directly: r = -. , Example: A shunt dynamo for 100 volt? and 40 amperes having an armature resistance of r & = .12 ohm, a magnet winding of JV m = 4200 turns per magnetic circuit, and the magnetic characteristic shown in Fig. 332, is to be provided with a regulator for constant pressure at variable load. 131] DYNAMO-GRAPHICS. 489 The drop at 40 amperes is: e & = 1.5 x / X r & = 1.5 X 40 X .12 = 7.2 volts, and the characteristic gives, for E = ioo and E' = ioo -f- 7.2 = 107.2 volts, respectively: Magnetizing force at no load, AT = 8100 ampere-turns; Magnetizing force at full load, AT' = 10,500 ampere-turns. Hence, by (449) : and X E 4200 X ioo AT 8100 X E 1 4200 X ioo AT' 10,500 r r = 51.8 40.0 = ii. 8 ohms. = 51.8 ohms, = 40.0 ohms, O 70 h 50 uj 40 1 1 AMPERE TURNS I I Fig. 332. Practical Example of Graphical Determination of Shunt Regulator for Constant Potential at Varying Load. These values can also be directly derived from the charac- teristic by erecting, at OA 4200, the perpendicular AB, and by drawing the lines OE and OF\ the resistances can then be read off on AB from the scale of ordinates. 490 DYNAMO-ELECTRIC MACHINES. [13L b. Regulators for Shunt Machines of Varying Speed. If N is the normal, and N^ the maximal, or minimal abnor- mal speed, as the case may be % then the speed ratio, is greater or smaller than i, according to whether the speed- variation is in the form of an increase or of a decrease. In. AT AT' AT n Fig. 333- Shunt Regulating Resistance for Constant Potential at Increasing Speed. order to obtain the characteristic of the machine for the abnormal speed, all ordinates of the original characteristic, /, must be multiplied by the speed-ratio, n. The result of this multiplication is shown by curve II, Fig. 333, for increasing, and by curve II, Fig. 334, for decreasing speed. If the point E on curve /, corresponding to the E. M. F. at normal speed, N, is connected with O, then the intersec- tion, n , of the line OE with curve 7, is the E. M. F. which the machine would yield at the speed N^ . For, in the first moment, the E. M. F. E, Fig. 333, on account of the increased speed, will rise to the amount E'\ at the same time, however, the exciting current rises, and with it the magnetizing force increases from ^7* to AT', causing an increase of the E. M. F. to E", on account of which the magnetizing power is further increased to AT\ and so on, until at E n the equilibrium is reached. But the potential of the machine is to be kept con- 131] D YNA MO- GRA PHJCS. 491 stant; for this purpose, that magnetizing force, AT^ is to be found which produces the E. M. F. E at the speed N^ . This, however, can be done without the use of curves II, which therefore need not be constructed at all. For, since the num- Fig. 334. Shunt Regulating Resistance for Constant Potential at Decreasing Speed. ber of ampere-turns required to produce E volts at N^ revolu- tions is identical with the magnetizing force needed to generate E x N" E 1 " N l ' ~^T volts at normal speed, IV, it follows that it is only necessary to draw EA J_ OA, to make and to draw BE l fl OA. The abscissa of the intersection, E l , of this parallel with the characteristic / is the required number of ampere-turns, AT^ . The latter will be smaller than AT if n > i, and greater if n < i; in the former case, therefore, the excitation must be reduced by adding resistance, while in the latter case it must be increased by cutting out resistance. AT^ being known, the regulating resistance can be computed as follows: For N^ > N: E ~AT, AT, r m = AT 492 D YNA MO-ELE C TRIG MA CHINES. [131 whence: % }. ,..(450) T t AT) AT AT^ For NI < N: r m ~T~ r v ^ T> or: If at distance OC = N m a parallel, CD, to the axis of ordinates is drawn, then resistances can be directly derived graphically, as shown in Figs. 333 and 334. Example: A dynamo of 125 amperes current output, hav- ing the characteristic OA, Fig. 335, is to be regulated to give a constant potential of 120 volts for a speed variation of 9 per cent, below and 10 per cent, above the normal speed; to deter- mine the magnet and regulator resistance, if at normal speed a current consumption of 3.2 per cent, is prescribed. Under the given conditions the speed ratio and correspond- ing E. M. F. for increasing speed is: JVr W+o.io.W E 120 n = j\r~- ^r =I - I; ^i= = ='9 voits; and for decreasing speed: N' JV - 0.09 N E 120 n' = -^- = j^-^ = .91 ; E'. = = - - = 132 volts. N JV n .91 For these E. M. Fs. the characteristic furnishes the follow- ing magnetizing forces: Ampere-turns at normal speed, AT = 20,000; Ampere-turns at maximum speed, AT l = 15,400; Ampere-turns at minimum speed, AT\ = 27,600. Hence: 20,000 , . N m = - = 5000 convolutions; .032 X 125 and consequently: 131] D YNAMO-GRAPHICS. 493 5000 X 120 ^V I5 , 400 = 39. 5000 X 120 r m = - - = 21.8 ohms. 27,600 r r = 39.0 21.8 = 17.2 ohms. This value is directly given by the ordinate scale in the dia- gram, Fig. 335, being the distance between the lines OF and m - = 5000-*- 132_V_, = 120 V. ,= 1,09 y. 1 1 c 1 AMPERE TURNS 335- Practical Example of Graphical Determination of Shunt Regulator for Constant Potential at Varying Speed. ^ measured on the ordinate CD, in distance OC N m = 5000 from the co-ordinate centre. c. Regulators for Shunt Machines of Varying Load and Varying Speed. In this case the required resistance must be capable of keeping the potential the same at no load and maximum speed as at full load and minimum speed. The former of these two extreme cases no load and maximum speed, N^ , has already been treated under subdivision b\ to consider the latter case full load and minimum speed reference is 494 D YNAMO-ELEC TRIG MA CHINES. [131 had to the open circuit curves I and II, Fig. 336, for normal speed, N, and for minimum speed, N^ , respectively. If AT ampere-turns are requisite to produce, at normal speed and on open circuit, the potential, E, to be regulated, AT AT 2 Fig. 336. Shunt Regulating Resi'stance for Constant Potential at Variable Load and Variable Speed. the magnetizing force for minimum speed is found by deter- mining the abscissa AT^ for on curve II, which at the same time also is the abscissa for the potential on curve I, 2 being the ratio of minimum to normal speed. The value of A 7' 2 can therefore be derived without plotting curve II, by adding to E the drop e & , dividing the sum by and finding the abscissa for the potential so obtained. If the magnetizing force for open circuit and maximum speed is A T l , the desired regulating resistance for variable load and variable speed is: (452) where N m is the number of turns per magnetic circuit. 131] D YNAMO-GRAPH1CS. 495 Example : A shunt dynamo having a potential of 60 volts, a drop in the armature of 3 volts, a current-intensity of 50 amperes, 6 per cent, of which is to be used for excitation at full load, and having the characteristic given in Fig. 337, is to i AMPERE TURNS Fig. 337. Practical Example of Graphical Determination of Shunt Regulator for Constant Potential at Varying Load and Varying Speed. be regulated for a speed variation of 10 per cent, above and below normal speed, and for loads varying from zero to full capacity. For no load and maximum speed we have in this case: N = i.i A = - = == 54-5 AT^ = 2500 ampere-turns (from Fig. 337); and for full load and minimum speed: E' = E -J- e & = 60 -f 3 = 63 volts, N N .iN = -9, E_ = 63 , -9 496 DYNAMO-ELECTRIC MACHINES. [ 131 AT^ 5500 ampere-turns (from Fig.. 337), N m = ~ ~ - = 1833 convolutions. -8h 'O X 5 Connecting the points A and B, in which the 2500 and 5500 ampere-turn lines, respectively, intersect the 6o-volt line, with the co-ordinate centre O, and erecting, at OC = 1833, the perpendicular CD, the intersections F and G are obtained, and the lengths CF and FG give the required resistances of the magnet-winding and of the shunt-regulator, respectively. The result thus found can be checked by the following computation: 60 = 20 ohms, .06 X 50 r r = 44 20 = 24 ohms; or, directly, by formula (452): . r,= 1833 X 60 X - = 24 ohms. d. Regulators for Varying the Potential of Shunt Dynamos. The potential of the machine is to be adjustable between a minimum limit 1 and a maximum limit E^ , and the ad- justed potential is to be kept constant for varying load. These conditions are fulfilled by so proportioning the magnet- winding and the regulator-resistance that at full load the maximum potential E^ is generated with the regulator cut out entirely, and that at no load the minimum potential E l is pro- duced with all the regulator-resistance in circuit. From the characteristic, Fig. 338, the magnetizing forces AT^, corresponding to the potential E^ at no load, and AT^, corresponding to the potential z at full load, or to the internal E. M. F., E\ = E^ -f- ^ a , are obtained; and if again jV m denotes the number of field-convolutions per magnetic circuit, we have: 132] D YNAMO-GRAPHICS. 497 _ tf m x E, AT. and from which follows: r* = (453) In order to derive the values of the resistances r m and r T graphically, the points 1 , on the characteristic, and E\ , "on the ampere-turn line AT at are connected with O, and a per- Fig. 338. Shunt Regulating Resistance for Adjusting Potential Between Given Limits at Varying Load. pendicular, AB, is erected upon the axis of abscissae at the distance OA JV m from the ordinate axis. Then the por- tions AC and CD of AB, cut off by the lines OE\ and O l , represent the required resistances r m and r r , respectively. 132. Transmission of Power at Constant Speed by Means of Two Series Dynamos. 1 Since two exactly identical series machines do not solve the problem of transmission at constant speed with varying load, it is now to be investigated graphically, how generator and motor must be designed, electrically, for that purpose. 1 J. Fischer-Hinnen, Elektrotechn. Zeitsckr., vol. xv. p. 400 (July 19, 1894). 498 DYNAMO-ELECTRIC MACHINES. [132 Let I, Fig. 339, represent the external characteristic, giving the E. M. F. as function of the current intensity of the generator, and also of the motor when run as a generator, thereby indicating that both machines are identical in design. CURRENT INTENSITY I Fig. 339- External Characteristics of Generator and Motor of Identical Design. If R is the total resistance of both machines plus the resist- ance of the line, the total drop of E. M. F. at any current- intensity, /, is e & = I X R, and the E. M. F. at the motor terminals, therefore: E" = E I X volts. By plotting the straight line Oe & and subtracting the ordinate values from those of curve I, we obtain curve II, which repre- sents the external characteristic of the motor. The speed of the motor for any load is then found by taking its E. M. F. E" at the current-intensity, /, corresponding to that load, from the characteristic II, and inserting it into the formula: N" = E" X 60 X io 8 K" X X n" X ..(464) where N" speed of motor, at certain load; E" E. M. F. required on motor-terminals for that load ; N\ number of turns on the motor armature; 132] DYNAMO-GRAPHICS. 499 n\ = number of bifurcations of current in armature; <&" number of useful lines of force; K" - 1 r TTf r- constant for motor under con- N " a X 'p sideration. But since the E. M. F. of the generator is, with similar denotation: AT" v AT" v ' v , however, is a direct function of the exciting power, and is inversely proportional to the reluctance of the magnetic circuit; approximate constancy of W", consequently, can be produced (i) by making the motor of a higher reluctance than 5 oo DYNAMO-ELECTRIC MACHINES. [133 the generator, either by increasing the length of the air gap or by reducing the section of the iron in the former, or (2) by making the magnetizing force of the generator greater than that of the motor by winding a greater number of field turns on its magnets. The proper way, however, is to select for the motor a somewhat smaller type, corresponding to the smaller capacity required for it, and to so design its magnet frame, air gap, and windings as to create a characteristic whose ordinates for any current intensity are proportional to the corresponding ordinates of curve II, Fig. 339. 133. Determination of Speed and Current Consumption of Railway Motors at Varying Load. 1 The speed of the car and the current required for the motor equipment are to be found for different grades of track, /'. 28 = 9 + 9 + I0 > an( l 32 = 10 -|- ii + n, it follows 508 DYNAMO-ELECTRIC MACHINES. [134 that in the first case alone the number of wires per layer is uniform, while for each of the two latter windings the number of wires in one of the three layers would differ by i from the other two. Substituting, therefore, n c = 56 into (46) the number of convolutions per coil is obtained: that is to say, the armature winding is composed of 56 coils, each having 12 turns of 2 No. 15 B. W. G. wires. The arrangement of the winding is shown by the diagram, Fig. 342, which represents the cross-section of one armature @ @ @a )@(k Fig 342. Arrangement of Armature Winding, lo-KW. Single-Magnet Type Generator. coil. In order to have both ends of the coil terminate at the outside layer, at the inner circumference of the armature, and at the commutator end, as is most desirable for convenience in connecting and for avoidance of crossings, the centre, C, of each coil must be placed at the inner armature circumference on the commutator end, and, starting from C, one-half, Cy, 7', 8, 8'. ... 12 must be wound right-handedly, and the other half, C6', 6, 5', 5 .... i, left-handedly, as indicated. The wind- ing in the interior of the armature is shown arranged in five layers, this being necessary on account of the smaller interior circumference. 134] EXAMPLES OF GENERATOR CALCULATION. 59 6. Radial Depth, Minimum and Maximum Cross- Section, and Average Magnetic Density of Armature Core. The useful mag- netic flux, according to formula (138), 56, being 6 X 280 x io 9 the radial depth of the armature core, by (48), 26, is obtained : 2,083,000 rt _ . b & - = 21 inches. 2 x 80,000 X5j X .90 In this the density in the minimum core section is taken at the upper of the limits prescribed by Table XXII., while the ratio k^ is selected from Table XXIII., under the assumption that .010" iron discs with oxide coating are employed. Subtracting twice the radial depth from the core diameter, we find the internal diameter of the armature core: 15 2 x 2 -J = 9-} inches, and the arithmetical mean of the external and internal diame- ters is the mean diameter of the core: d'\ = (15 + 9 J) = 12! inches. Inserting the value of b & into formula (234), 91, the maxi- mum depth of the armature core is obtained: 'a = 2-J X /I/ -^| i = 5.92 inches; hence, by (232) and (233), the minimum and maximum cross* sections: S" &1 = 2 x 5-J- X 2-J X .90 = 26.5 square inches, and S\ = 2 x 5i X 5.92 X .90 = 54.7 square inches, respectively. Dividing with these areas into the useful flux, we find the maximum and minimum densities: 2,083,000 ai = ^ = 78,700 lines per square inch, and _. 2,083,000 Q> M = = 38,100 lines per square inch, 54" 7 510 DYNAMO-ELECTRIC MACHINES. [ 134 for which Table LXXXVIII., p. 336, gives the specific mag- netizing forces m rr &i = 29.5, and m" &2 =7.1 ampere-turns per inch. According to formula (231), therefore, the mean specific magnetizing force is: m\ = (29.5 + 7.1) = 18.3 ampere-turns per inch, and to this, according to Table LXXXVIII., corresponds an average density of: (&" a = 68,500 lines per square inch. 7. Weight and Resistance of Armature Winding; Insulation Resistance of Armature. The poles being situated exterior to the armature, as in Fig. 59, 27, formula (53) gives the total length of the armature conductor: L - 2 x (5i + 2 D + -325 X 7t __ St ~ Hence, by (58), p. 101, the bare weight of the armature winding: w/ a = .00000303 x 10,368 x 955 = 30 pounds. The same result can also be obtained by means of the specific weight given in the wire gauge table; No. 15 B. W. G. wire weighing .0157 pound per foot, and two wires being connected in parallel, we have: wt & = 2 x 955 X .0157 = 30 pounds. From this the covered weight of the winding is deduced by means of formula (59) and Table XXVI., thus: wt' & = 1.078 x 30 = 32 J pounds. The resistance of the armature winding, at 15.5 C., is ob- tained from (61), 29: r - = dh x 9SS x (iS) = - 24 ohm> 134] EXAMPLES OF GENERATOR CALCULATION. 511 By Fig. 343 the surface of the armature core is: 2 X (5i + 2 1) X I2-J- X TT = 610 square inches; if oiled muslin whose average resistivity, by Table XX., 24, is 650 megohms per square inch-mil at 30 C., and 650 -h 25 = 26 megohms per square inch-mil at ioo p C., is employed to make up the 40 mils of core insulation given by Table XIX., the insulation resistance of the armature is found: 65 6i X o 40 = 42.6 megohms at 30 C, and 26 x 4 610 = 1.7 megohm at 100 C. 8. Energy Losses in Armature, and Temperature Increase. The energy dissipated by the armature winding, by formula (68), 31, is found: 9 P & = 1.2 X 40' X .24 = 460 watts. The frequency is: 1200 JV l = = 20 cycles per second; the mass of iron in the armature core, from (71), 32: SiX. 9 o = 292 cubic feet . for &" a = 68,500, Table XXIX. gives the hysteresis factor: *? = 2 7-3, and Table XXXIII., the eddy current factor: = .034. Hence, the energy losses due to the hysteresis and eddy cur- rents, from (73), p. 112, and (76), p. 120, respectively: A = 27.3 X 20 x .292 = 160 watts, P e = .034 x 2o 2 x .292 = 4 watts. By (65), p. 107, then, the total energy dissipation in the armature is : P A 460 -f 1 60 -f 4 = 624 watts. 512 D YNAMO-ELECTRIC MA CHINES. [134 The heat generated by this energy, according to (79), 34, is liberated from a radiating surface of ,5; = 2 X I2-J- X TT X (5j + 2| + if) = 715 square inches, whence follows the rise in armature temperature, by (81), p. 127 : e a = 42x^1= sere., the specific temperature increase, O' a = 42 C., being taken from Table XXXVI. for a peripheral velocity of 80 feet per second, and for a ratio of pole area to radiating surface of .78 X i5JX it x 51 6 Inserting the above value of 6 a into formula (63), p. 106, the armature resistance, hot, at 15.5 + 36.5 52 degrees, Centi- grade, is obtained : / * -\ = .275 ohm. 9. Circumferential Current Density, Safe Capacity and Run- ning Value of Armature; Relative Efficiency of Magnetic Field. From formula (84), 37, the circumferential current density is obtained: 67 2 X 2O /c = -- -- - - = 285 amperes per inch, 15 X 7t for which Table XXXVII. gives a temperature increase of 30 to 50 Cent., the result obtained being indeed within these limits. For the maximum safe capacity we find, by formula (88), 38, and by the use of Table XXXVIII. : p< = I 5 2 X 5i X .89 X 1200 X 19,000 X io-' = 23,500 watts, and for the running value of the armature, by formula (90), 39: ' = .0197 watt per pound of copper at unit Q field density (i line per square inch). 134] EXAMPLES OF GENERATOR CALCULATION. 513. The values of P' and P' & show that the armature is a very good one, electrically, for, according to the former, an over- load of over 100 per cent, can be stood without injury, and by comparing the latter with the respective limits of Table XXXIX. it is learned that the inductor efficiency is as high as in the best modern dynamos. The relative efficiency of the magnetic field, by formula (i55), 59, is: _ 2083,000 x go = u 880 maxwe i ls per watt 2OO X 4O at unit velocity, and, according to Table LXIL, page 212, this is within the limits of good design. 10. Torque, Peripheral Force, and Lateral Thrust of Arma- ture. By means of formula (93), 40, we obtain the torque: t 1 ilr X 40 X 672 X 2,083,000 = 65.7 foot-pounds. 10 and by (95), 41, the force acting at each armature con- ductor: 280 X 40 / = '"75 X 8o x 6?2 * . 89 -.173 pound. The force tending to move the armature toward the magnet core is found by formula (103), 42; the reluctance of the path through the averted half of the armature being about 10 per cent, in excess of that through the armature half nearest to the magnet core, the field density in the former will be about 10 per cent, smaller than in the latter; that is to say, the stronger density, 3C", is about 5 per cent, above, and the weaker density, 3C" a , about 5 per cent, below the average den- sity JC", or 3C", = 19,000 X 1.05 = 20,000, and 3C" 2 = 19,000 x .95 = 18,000; hence the side thrust: / t = n X io- 9 X 15 X 5i X (2o,ooo a 18,000') = 64J pounds. 5H D YNA MO-ELEC TRIC MA CHINE S. [134 This pull is to be added to or subtracted from the belt pull, according to whether the dynamo is driven from the magnet or from the armature side. ii. Commutator, Brushes, and Connecting Cables. The in- ternal diameter of the wound armature being 9^ 2 x (.040 + 5 X .088) = 8J inches, the brush-surface diameter of the commutator is chosen 4 = 8J- 2X|=7 inches, by allowing -|" radially for the height of the connecting lugs, as shown in Fig. 343. If we make the thickness of the side 5 13/ 16 " Fig. 343. Dimensions of Armature and Commutator, IO-KW. Single-Magnet Type Generator. mica hi = .030", Table XLVL, 48, and if we fix the number of bars to be covered by the brush as k = i-J, the circum- ferential breadth of the brush contact, by (115), becomes: = .68'. Adding to this the thickness of one side insulation, which is also covered by the brush, we obtain the breadth of the brush- bevel, .68 -f- .030 = 71", which, for an angle of contact of 45, gives the actual thickness of the brush as = - inch. Tangential carbon brushes being best suited for the machine under consideration, formula (118), page 176, gives the effec- tive length of the brush contact surface: 134] EXAMPLES OF GENERATOR CALCULATION. 515 /k = 5^T68 = 2 inches ' .' - which we subdivide into two brushes of i inch width, each. Allowing -J-" between them for their separation in the holder, and adding ft" for wear, we obtain the length of the brush- surface from (114), page 169, thus: 4 = (2 + ) X (i + i) + ft = 2i| + ft = 3} inches. The best tension with which the brushes are to be pressed against the commutator is found by means of formulae (119) to (121) and Table XLVIL, as follows: The peripheral velocity of the commutator is: 7 x 7f x 1200 = 2200 feet per minute, hence the speed-correction factor for the specific friction pull, by (119), p. 179: 2200 1000 Inserting the values into (120) and (121), the formulae for the energies absorbed by contact resistance and by friction re- duce to and P t = 6 X io- 5 X .85 / k X 2 X .68 X 2200 = .i526/ k . Taking from Table XLVII. the values of p k and / k for brush tensions of i, 2, 2^, and 3 pounds per square inch, respec- tively, for tangential carbon brush and dry commutator, we find: for i Ibs. per sq. in., P k -f P t = 3.15 x .15 + -IS 26 X .95 = .618 HP.; "2 " P* + P t = 3.15 X .12 +.1526 X 1.25 -.569 HP.; 11 2j " P k + P t = 3.15 x .10 + .1526 X 1.6 = 559 HP.; 3 *' " P k + P t = 3-15 X .09 + .1526 X 1.9 = 574 HP., " 516 DYNAMO-ELECTRIC MACHINES. [134 from which follows that the most economical pressure is about 2| pounds per square inch of contact. The proper cross-section of the connecting cables, by allow- ing 900 square mils per ampere, in accordance with Table XLVIIL, 50, is found to be: 40 x 900 36,000 square mils, or 36,000 x = 46,000 circular mils. Taking 7 strands of 3 X 7 wires each, or a i47-wire cable, each wire must have an area of 46,000 - 315 circular mils, J 47 and the cable will have to be made up of No. 25 B. & S. wire, which is the nearest gauge-number. 12. Armature Shaft and Bearings. By (123) and Table L., 31, the diameter of the core portion of the shaft is: 4 = ,. a X l~ = 2J inches; by (122), p. 185, and Table XLVIL, the journal diameter: b -3 X /v/ 2 8o X 40 X 1/1200 = 1J inch; and, by (128), p. 190, and Table LIV., the length of the journal: 4 = .1 X 1 1 X V I20 = 6J- inches. 13. Driving Spokes. Selecting 4-arm spiders, similar to those- shown in Fig. 127, 52, the leverage of the smallest spoke- section, determined by the radial depth of the armature, is / s = 3-1", and the width of the spokes, fixed by the length of the armature core, is b$ = 2"; hence, by formula (126), p. 189, their thickness: *. = 4.25 X ,/ ".'X 3 j = . inch . y 80 x s x 2 x 7000 ** 134] EXAMPLES OF GENERATOR CALCULATION. 517 14. Ptdley and Belt. Taking a belt-speed of z' B = 3500 feet per .minute, Table LVIIL, 54, the pulley diameter becomes, t>7 (129), P. I9 1 ' 10f inches. ' ' the size of the belt, by Table LIX. : ^B = A incn , ^B = 4 inches, and the width of the pulley: p = 4 -| -- = 4J inches. b. DIMENSIONING OF MAGNET FRAME. 1. Total Magnetic J?tux.rom Table LXVIII., 70, the average leakage factor for a lo-KW single-magnet type machine, with high-speed drum armature and cast-iron pole pieces, is A = 1.40; the present machine having a ring arma- ture and a cast-steel frame, the leakage is about 22 -|- n = 33 per cent, less (see note to Table LXVIII., p. 263), and the leakage factor is reduced to A. 1.27. The total flux, conse- quently, by (156) : #' = 1.27 x 2,083,000 = 2,650,000 maxwells. 2. Sectional Area of Magnet Frame. According to formula <2i6) and Table LXXVIIL, 82, we obtain the cross-section of the magnet frame : = 2,650,000 = 29 4 e inches 90,000 The axial length of the frame, limited by the length of the armature core on the one hand and by the length over the armature winding on the other, being chosen / p = 5-J", its thickness is: 20.4 = 5 inches. D 8 3. Polepieces and Magnet Core. The bore of the field is found by summing up as follows: DYNAMO-ELECTRIC MACHINES. l134 Diameter of armature core i c.ooo inr.he*; Winding 6 x .088 = .528 " 2 x .080 = .160 " 2 X & = .312 " Insulation and binding Clearance (Table LXI.).... 7 ^ n es p. sq. in. ; m'^ = 29.5. Maximum area of circuit, by (233), p. 341, and (234), p. 342: = 2 X 5i X 2| x /l - i X .90 = 54-7 sq. in. ' 8 = 38,000 lines p. sq. in.; m\ = 7.1. Average specific magnetizing force, by (231), p. 341: m" A = -^ - *. = 18.3 ampere-turns per inch. 134] EXAMPLES OF GENERATOR CALCULATION. 521 Magnetizing force required, by (230), p. 340: at & = 18.3 x 14^ = 265 ampere-turns. 3. Magnet Frame (all cast steel). Length of portion with uniform cross-section (core and yokes) : /* m = 1 1 -f 2 x (5 + 2 J) = 26 inches. Area of magnet core and yokes: S m = 5 x 5-j- = 29.4 square inches. Density: 2,6e;o,ooo (B m = -i-= -- 90,000 lines per square inch. Specific magnetizing force (Table LXXXVIII., or Fig. 256): m" m = 57 ampere-turns per inch. Mean length of portion with varying cross-section (pole- pieces), from formula (243) and Fig. 344: /" p = 2 f + 8i + 7 f X ~ - SA = i inches. Minimum area: ,S"' Pi = 5 x 5-J = 29.4 square inches. " PI = 2> 5 - = 9 , 000 line s P- sq. in. ; m" Pl = 57. Maximum area: s \= ( I 5l X j X .78+2 X Y) X 5t =i2osq. in. 2,08^,000 ..(B" P2 = -! 21 -- = 17,400 lines p. sq. in.; m \ = 4.6. Average specific magnetizing force, by formula (241): m" p = " = 30.8 ampere-turns per inch. Corresponding flux density by Table LXXXVIII., p. 336: &" p = 78,000 lines per square inch. Magnetizing force required for magnet frame, by (238), P. 344: 4n = 57 X 26 + 30.8 x 18 = 2035 ampere-turns. 522 DYNAMO-ELECTRIC MACHINES. [ 134 4. Armature Reaction. According to Table XCI., 93, the coefficient of armature-reaction for gives the number of series turns: Nm = = 375. 40 The length of the mean turn, by (290), being *r = 2 (5} + 5) + 2 x it = 28 inches, the total length of the series field wire is obtained, by for- mula (288) p. 374: feet . Formulae (278) and (282) give the radiating surface of the magnet: S M3 = 2 X ii X (51 + 5 + 2 X n) + 2 X 2 X (28 - 5 |) = 466 square inches, hence by (294) the resistance required for the specified tem- perature increase : 134] EXAMPLES OF GENERATOR CALCULATION. 5 2 3 and therefore by (294) the specific length of the magnet-wire: A se = J*l = 6170 feet per ohm. . 104 The nearest gauge wire is No. 2 B. & S., which is too incon- venient to handle; we therefore take 2 No. 7 B. W. G. wires (.180" -f- .012" = .192"), which have a joint specific length of 2 X 3138.6 = 6277 feet per ohm. Allowing | inch at each end of the magnet spool for insulation and discs, formula (297), p. 377, gives an effective winding depth of 2 X .i92 2 . u h' m = 27^ X - r = 1.9 inch. II 2 X f Actual resistance of magnet-winding (from wire gauge table): 642 X = .1025 ohm at .5.5 C, or r' se = .1025 x 1. 12 = .115 ohm at 45.5 C. Weight of magnet winding, bare: wt m 2 x 642 x .098 = 126 pounds; weight, covered, from Table XXVI., 28: wt' m 1.0228 X 126 = 130 pounds. 2. Regulator (see diagrams, 100). The difference of 5 volts between each of the five steps being - 2 per cent, of the full load output, the shunt coil regulator has to be calculated for 90, 92, 94, 96, and 98 per cent, of the maximum E. M. F., the resistances of the five combinations, therefore, are: Resistance, first combination -9-g. x r'^ 9 x r' se> second " = ^ x r' se = 11.5 x r'* 9 third = Y X r' 8e = 15.67 X r' se , u fourth " = -V 6 - X r'^ 24 X r' se , fifth = -V 8 - X r' Ke = 49 X r> m > 524 DYNAMO-ELECTRIC MACHINES. [134 By the proceeding shown in 100 we then obtain the follow- ing formulae for the resistances of the five coils: _ (11.5 r' se - rj X (9^'se - n) T T ; _ " .$r' - rj - (9^8e - rJ _ II3-5 r*~ - 20-5 r '** r \ + r \ 2.5 r' se = 45-5 r'se - 8.2 r i; (457) 67 r' w - rJ X (11.5 ^'se - n) (15.67 ^'se - n) - (ll-S 160.2 r' 8e a 27.2 ?', n -f 4-167 r' 8e = 38.2^-6.5^; ............................. (458) r m = resistance of third combination minus res. of leads = 15-67 r^-n; .............................. (459) r iv res. of fourth comb, minus res. third comb. = (24-15.67)^ = 8.33^; ................. (460) r v = res. of fifth comb, minus res. fourth comb. = (49 - 24) r' se = 25 r' se ...................... (461) These formulae apply to all cases in which a total regulation of 10 per cent., in five steps of 2 per cent, each, is desired. In the present example, the resistance of the series winding, hot, being r' se = .115 ohm, and the resistance of the leads r\ = .01 ohm (assuming 4 feet of 4000 circular mil cable, carrying 10 per cent, of the maximum current output, or 4 am- peres), we have: r \ 45-5 X .115 8.2 X .01 5.15 ohms, r u = 38.2 x .115 - 6.2 x .01 = 4.32 " >m= 15-67 X .115 - .01 =1.79 " rrr = 8.33 X .115 = .96 " >v = 25 X .115 = 2.88 " The currents flowing in the various coils, at the different combinations, are: 134] EXAMPLES OF GENERATOR CALCULATION. 525 First combination: 7l = r a r m + ? i r % I + r 1 - u X- 1 ' . 4 ' 32XI ' 79 X.IX40 X 1-79 + 5- J 5 X 1.79 + 5- 15 X 4-3 2 7-73 7.73 -f 9.22 + 22.35 39.3 r r l r III Q- 22 /n = -- : . - x .1 / = - x 4 = . 39.3 /m== - ^^r - X . i/=^ 'i >n + r x r m + r n r m 39.3 Second combination: 4 = X 4 = .8 ampere. 95 amp. X .o8/= X 3.2 = -95 ampere. o. J i X .o87 = x 3-2 = 2.3 amperes. n T ni Third combination: 7 m = .06 7 = 2.4 amperes. Fourth combination: 7 m = 7 IV = .047 = 1.6 amperes. Fifth combination: /in = /iv = /v - 02 / = .8 ampere. By comparison, the maximum current passing through each of the five coils, in the present case of a machine of 40 amps, ca- pacity, is found : /i = .8 amp. ; or, for the general case of current output 7, we have: 7 X = .2 X .1 7= .02 /, (462) 7 n = .95 amp. ; or, in general: 7 n = .3 X .08 7= .024 7, (463) 7 in = 2.4 amp. ; or, in general : / m = .06 /, .......... (464) /iv = 1.6 amp. ; or, in general : 7 IV = .04 /, .......... (465) 7 V = .8 amp. ; or, in general : 7 V = .02 /, .......... (466) From the wire gauge table, finally, the size of the wire suffi- cient to carry the maximum current, and the length and weight of the same, required to make up the necessary resist- ance, is obtained: 526 DYNAMO-ELECTRIC MACHINES. [134 d COIL HP, 2 Ill ** Esl !" |J*j ! NUMBER. O.<2 GO^ 3* . 3*~ GU oS 02 o Oflg <|w o MO ^0 O I .8 No. 21 B. & S. 810 1012 5.15 400 1.05 II .95 No. 20 B. & S. 1021 1073 4.32 427 1.29 III 2.4 No. 18 B. W. G. 2401 1000 1.79 414 3.15 IV 1.6 No. 18 B. & S. 1624 1015 .96 150 .76 V .8 No. 21 B. & S. 810 1012 2.88 224 .58 /. CALCULATION OF EFFICIENCIES. i. Electrical Efficiency. The electrical efficiency of the above dynamo, by formula (351), p. 405, is: 250 X 40 250 x 40 4- 4o 2 X (.275 4- .115) 10,000 2. Commercial Efficieticy and Gross Efficiency. The energy losses due to hysteresis, eddy currents, brush contact, and brush friction were found P h = 160, P 9 = 4, P k = .315 X 746 = 235, and P t = .244 x 746 = 182 watts, respectively; as- suming that journal friction and air resistance cause a further energy loss of 500 watts, the commercial, or net efficiency of the machine will be, by (359), p. 361 : 10,000 10,624 + 160 4- 4 4- 235 4- 182 4- 500 10,000 II, 705 = .855, or 85.5 In dividing this by the electrical efficiency, the efficiency of conversion, or the gross efficiency, is obtained: or 3. Weight Efficiency. The weights of the various parts of our dynamo are as follows : 135] EXAMPLES OF GENERATOR CALCULATION. 527 Armature : Core, .292 cu. ft. of sheet iron, . ' . 140 Ibs. Winding ( 134, a, 7), core insulation, binding, and connecting wires, . ^ . 40 Ibs. Shaft, spiders, pulley, keys, and bolts (estimated), ... . . . 100 Ibs. Commutator, 7" dia. X 3^" length, . 20 Ibs. Armature, complete, . : . . ; . , 300 Ibs. Frame : Magnet core and polepieces (see Fig. 344 and 134, c, 2), (5 X 26 -f 54) X 5^ = 1080 cu. ins. of cast steel, . 300 Ibs. Field winding ( 134, c, i), core insu- lation, flanges, etc., . . . 150 Ibs. Bedplate (cast-iron), bearings, etc., (estimated), . . . . . 250 Ibs. Frame, complete, . ^ . . 7 lbs - Fittings: Brushes, holders, and brush-rocker, (estimated), 20 Ibs. Field regulator (winding, see 134, e, 2), . . . . .15 Ibs. Switches, cables, etc. (estimated), . 15 Ibs. Fittings, complete, ... 50 Ibs. Hence the total net weight of the machine, . 1050 Ibs. The useful output is 10 KW, therefore the weight-efficiency, by 109: ? 9.5 watts per pound. 1050 135. Calculation of a Bipolar, Single Magnetic Circuit, Smooth-Drum, High-Speed Shunt Dynamo : 300 KW. Upright Horseshoe Type. Wrought-Iron Cores and Yoke, Cast-Iron Polepieces. 500 Volts. 600 Amps. 400 Revs, per Min. a. CALCULATION OF ARMATURE. i. Length of Armature Conductor. For this machine, since 300 KW is a large output for a bipolar type, we take the upper limit given for the ratio of polar embrace of smooth- 528 DYNAMO-ELECTRIC MACHINES. [135 drum armatures, namely, ft l .75. Hence, by Table IV., p. 50: e = 62.5 X io~* volt per bifurcation; the number of bifur- cations is #'p = i. The mean conductor velocity, from Table V., p. 52: v c 50 feet per second; and the field density, from Table VI., p. 54: 3C" = 30,000 lines per square inch. The total E. M. F. to be generated, by Table VIII., p. 56: E' = 1.025 x 500 = 512.5 volts. Consequently, by (26): 512.5x10- _ = 547feet 62.5 X 50 X 30,000 2. Sectional Area of Armature Conductor, and Selection of Wire.Ky (27), p. 57: d a 2 300 x 600 = 180,000 circular mils. Taking 3 cables made up of 7 No. 13 B. W. G. wires having .095" diameter and 9025 circular mils area each, we have a total actual cross-section of 3 X 7 X 9025 189,525 circular mils, the excess over the calculated area amply allowing for the dif- ference between the current output and the total current generated in the armature, see 20. For large drum armatures cables are preferable to thick wires or copper rods, because they can be bent much easier, are much less liable to wasteful eddy currents, and, since air can circulate in the spaces between the single wires, effect a better ventilation of the armatures. In accordance with 24, a, a single covering of .007" is selected for the single wires, and an additional double coating of .016* is chosen for each cable of seven wires, making the total diameter of the insulated cable, see Fig. 345 : tf'a = 3 X (.095" + .007*) + .016" = 322 inch. 3. Diameter of Armature Core. From (30): d' & = 230 X = 284- inches. 400 By Table IX. : <4 = -97 X 28f 28 inches. 135] EXAMPLES OF GENERATOR CALCULATION. 529 4. Length of Armature Core. By (37) and Table XVII , p. 73: 28 X ?rX(i-.o8) .322 B 7 (39), P- 74, and Tables XVIII. and XIX. : B y (40), P. 76: n __ .8 (.090 + .070) __ .322 (547) V ?*/ . 12 X 3 X \ 1 .U_L / = 37 inches. * 5 * x In this the active length of the armature conductor has been divided by 1.04, taking into consideration the lateral spread of Fig. 345. Armature Cable, 3OO-KW Bipolar Horseshoe-Type Generator. the field in the axial direction, and assuming the same to amount to 4 per cent, of the length of the armature core. 5. Arrangement of Armature Winding. By (45) P- 89, and Table XXI: and to) = Two values of n c between these limits can be obtained, viz. : and 3 For the latter number of divisions, however, there are three conductors per commutator-bar, and since the armature is a. 53 D YNA MO -EL E C TRIG MA CHINES. [135 drum, there would be \\ turn to each coil, which is impossi- ble; therefore, the number of coils employed: c = 84. By (47), P- 89, then: 25 2 X 2 - 2 X 84 X 3 ~ hence, summary of armature winding: 84 coils, each .consisting of 1 turn of 3 cables made up of 7 No. 13 B. W. G. wires. He FIBRE 84 DIVISIONS Fig. 346. Arrangement of Armature Winding, 3OO-KW Bipolar Horseshoe- Type Generator. One armature division containing the beginning of one coil and the end of the one diametrically opposite, is shown in Fig. 346. 6. Weight and Resistance of Armature Winding. By (50), P- 96: A = 547 X /i + 1.3 X ~j j = 1070 feet. Here the original value of Z a , without reduction, is used, in regard of the fact that, in a cable, due to the helical arrange- ment of the wires, the actual length of each strand is greater than the length of the cable itself, and under the assumption that 4 per cent, is the proper allowance for this increase in the present case. By (58), p. 101, then: wt K = .00000303 x 189,525 x 1070 = 615 pounds. By (59), P. 102, and Table XXVI. : w/' a = 1.031 x 615 = 634 pounds. From (61), p. 105: r& ~ X I0 7 x -001144 = .0146 ohm, at 15.5 C. 135] EXAMPLES OF GENERATOR CALCULATION. 53* 7. Radial Depth, Minimum and Maximum Cross- Section, and Average Magnetic Density of Armature Core. By (123), and Table XLVIIL, p. 183: 4 / 700,000 4, = 1.55 x - = 8 mches "> see also Table XLIX., p. 185; therefore: b & = i (d & - 4) = p- = 10 inches, -and from (234), p. 342, or Fig. 347: b\ 10 x A/- - i = 13.4 inches. -28" 1 Fig. 347. Dimensions of Armature Core, 3OO-KW Bipolar Horseshoe- Type Generator. Hence by (232), p. 341: S" &1 = 2 x 37i X 10 X .95 = 712 square inches, and, by (233), p. 341: S" a2 =' 2 X 37i X 13-4 X -95 = 956 square inches. From (138), p. 202 : 6 X 5*2.5 X io 9 _ 6o Q maxw ells; 2 x 84 X 400 consequently: ^ _ 45>76o,ooo_ = 6 OQ Unes S q U are inch, 712 53 2 DYNAMO-ELECTRIC MACHINES. [135 45,760,000 &" = ^ J " = 47,8oo lines per square inch. 95 From Table LXXXVIIL, page 336: m" &L = 15.2 ampere-turns per inch; \ = 9.1 " " " " .. m\= -^ ^- = 12.15 ampere-turns per inch. To the latter corresponds a mean density of: (E" a = 58,000 lines per square inch. 8. Energy Losses in Armature^ and Temperature Increase. By (68), p. 109: jP a = 1.2 x 6oo 3 x .0146 = 6307 watts. JVj = -j = 6.67 cycles per second; 18 X 7t x 37i X 10 X .9 , . , M-- ^-^- - = 11.05 cubic feet \ From Table XXIX., (&" a = 58,000): ij = 20.92 watts per cubic feet; From XXXIII., ($ = .010"): = .0242 watt per cubic feet. By (73), P- 112: P h = 20.92 x 6.67 x 11.05 = 1540 watts. B 7 (76), p. 120: P 9 .0242 X 6.67 2 x 11.05 = 12 watts. B Y (65), p- 107: P^ = 6307 + 1540 + 12 = 7859 watts. From Table XXXV., p. 124: 4 = 35 X 28 -f 2 x .8 = ni inches. By (78), p. 124: S= (28 + 2 X .8) X ?r(37i+ 1.8 X ni) = 5412 sq. ins. 135] EXAMPLES OF GENERATOR CALCULATION. 533 Ratio of pole area to radiating surface: 30 X n X 37^ X .75 _ -- 49 5412 For this ratio and a peripheral velocity of 29 ^* * x 4 = 51} feet per second. Table XXXVI., p. 127, gives: 0' a 44.7C. ; consequently by(8i): a = 44.7 x = 65 Centigrade, 54 12 and the resistance of the armature, when hot, is: r' & = .0146 X (i + .004 X 65) = .0184 ohm, at 80.5 C. 9. Circumferential Current Density, Safe Capacity, and Run- ning Value of Armature; Relative Efficiency of Magnetic Field. By (84), P. 131: 84 X 2 / c ^ -* = 572 amperes per inch. Corresponding increase of temperature, from Table XXXVII., p. 132: a = 60 to 80 C., which checks the above result. By (88), p. 134, and Table XXXVIII. : P' = 28" X 37i X .88 X 400 X 30,000 X io- 6 = 310,000 watts. By (9), P- J 35: P f & = 5I2 ' 5 - .0167 watt per pound of copper, at unit field density; this also verifies the calculation, see Table XXXIX., p. 136. By (155), P- *": #' p = 45,76o, ooo^ x 5Q = 7450 maxwe ll s per watt, at unit velocity; by Table LXII., p. 212, this is not too high. 534 DYNAMO-ELECTRIC MACHINES. [135 10. Torque, Peripheral Force, and Upward Thrust of Arma- ture. By (93), p- 138: r = ^^ x 600 X 168 X 45,760,000 = 5420 foot-pounds. By (95), P- 138: 512.5 X 600 ' = ' 7375 X 50 X 168 X .88 = 30 - 7 P Unds ' By (103), p. 141: / t = ii X io- 9 X 28 X 37i X (30,600 - 2 9 ,4oo 2 ) = 8321bs., under the assumption that the density of the upper half of the field is 2 per cent, above, and that of the lower half 2 per cent, below, the average. b. DIMENSIONING OF MAGNET FRAME. 1. Total Magnetic Flux, and Sectional Areas of Magnet Frame. By ( I 5 6 ) P- 2I 4, and Table LXVIII. : ^' = 1.20 x 45,760,000 = 55,000,000 maxwells. By (217), p. 314, wrought-iron cores and yoke being used: 55,000,000 S" . = ^- - = 611 square inches. 90,000 By (216), p. 313, and Table LXXVI., the minimum section of the cast-iron polepieces: = 55,, = n(K) e inches 5O,OOO 2. Magnet Cores. Selecting the circular form for the cross- section of the magnets, their diameter is: i x - = 28 inches. Length of cores, from Table LXXXL, p. 319, by interpola- tion: / m = 35 inches. 135] EXAMPLES OF GENERATOR CALCULATION. 535 Distance apart, from Table LXXXV., p. 323, c = 16 inches. 3. Yoke. Making the width of the yoke, parallel to the shaft, equal to the diameter of the cores, its height is found: h = ~ = 22 inches. SCALED I NCH=1 FT. Fig. 348. Dimensions of Field Magnet Frame, 3OO-KW Bipolar Horseshoe-Type Generator. The length of the yoke is given by the diameter of the cores,, and by their distance apart, see Fig. 348: / y = 2 x 28 -f 16 = 72 inches. 4. Polepieces. The bore of the field is the sum of: 536 DYNAMO-ELECTRIC MACHINES. [135 Diameter of armature core, = 28.000 Winding ........ 4 X .322", = 1.288 Insulation and binding, 2 X (.070*+ - 7") = - 28 Clearance (Table LXL, p. 209) ............ 2 X i", = .500 30.068 or, say, 30 inches, Pole distance, by (150), p. 208, and Table LX. : /' p = 6 X (30 - 28) = 12 inches. Length of polepieces equal to length of armature core, or: / p = 37J inches. Height of polepieces, same as bore: h 9 = 30 inches. Thickness in centre, requiring half of the full area: noo ~-i= M.7, say 15 inches. 2 X 37f Height of pole-tips: Ms A/30* - i 2 '' ) = li inch. Height of zinc blocks, from Table LXX., p. 301: h z = 11 inches. C. CALCULATION OF MAGNETIC LEAKAGE. 1. Permeance of Gap-Spaces. 3C" X z> = 3> 000 X 5 = i,5 000 therefore, by (167), p. 226, and Table LXVI. : ^-(284-30) X^X .88X37i 6 __ 2 2 JS 00 * - i. 35 x (30 - 28J- ' TT 2. Permeance by Stray Paths. By (178), p. 232: 28 X ^ X 35 * 1A " 2 x 16 + 1.5 x 28 135] EXAMPLES OF GENERATOR CALCULATION'. By (188), p. 239: 537 3. = r X [37* X (28 + 15) + 850] = 56, 2 X II the portion of the bed plate opposite one polepiece being esti- mated to have a surface of S = 850 square inches. The pro- jecting area of the polepiece, see Fig. 349, is ,-t.. Fig. 349. Top View of Polepiece, 300 KW Bipolar Horseshoe-Type Generator, Showing Projecting Area. S; = 16 X 37j + i6 a X - - 28 a - = 386 square inches, hence by (199), p. 245: 6j> _. 386 , 37i X 30 35 TC = ii + 7-4 = 18.4. 2 X 35 + (30 + 22) X - 3. Leakage Factor. y (i57), P- 218: i ._ 536'+ 41.6 + 56 + 18.4 652 ~~ Total flux: = 1.215 x 45,760,000 = 55,700,000 maxwells. d. CALCULATION OF MAGNETIZING FORCES. i. Air Gaps. length, by (166), p. 224: = I -35 X (30 28) = 2.7 inches. 538 DYNAMO-ELECTRIC MACHINES. Area, by (141), p. 204: [135 7t S g = 29 X - X .88 X 37i = 1500 square inches. Density, by (142), p. 204: 4.5. 760,000 3C" 222J ? = 30,500 lines per square inch. Magnetizing force required, by (228), p. 339: at g = .3133 X 30,500 x 2.7 = 25,800 ampere-turns. 2. Armature Core. Length, by (236), p. 343, see Fig. 350: l\ = 18 X n X ~fr- + 10 = 27.85 inches. Fig. 350. Flux Path in Armature, soo-KW Bipolar Horseshoe-Type Generator. Minimum area, by (232), p. 341 : S" &1 = 2 x 37i X 10 X -95 7 J 2 square inches. 4^,760,000 . . (&" ai - - = 64,200 lines p. sq. in. ; ar cj = 15.2. Maximum area, by (233), p. 341, and (234), p. 342: S"'^ = 2 x 37i X 13-4 X.95 = 956 square inches. ... fc"^ = 45,760,000 = Average specific magnetizing force, by (231), p. 341 : 15.2 -4- Q.I m\ - = 12.15 ampere-turns p. inch. Corresponding average density: (B'^ = 58,000 lines per sq. in. 135] EXAMPLES OF GENERATOR CALCULATION. 539 Magnetizing force required, by (230), p. 340: at & = 12.15 x 27.85 = 340 ampere-turns. 3. Wrought Iron Portion of Frame (Cores and Yoke). Length : /Vi. = 2 x 35 + 22 + 44 = 136 inches. Area : ,S"' wi = 28 2 - = 615.75 square inches. 4 Density and corresponding specific magnetizing force: . 700,000 .. = 9> 000 lmes ; m W.L = 5-7- w.. 6 Magnetizing force required: tf/Vi. = 5-7 X 136 = 6900 ampere-turns. 4. Cast Iron Portion of Frame (Polepieces). Length, by (243), page 348: ^ c .i. = 35 + 2 = 37 inches. Minimum area (at center): %.!.! = 15 X 37i - 5 62 -5 square inches. Corresponding maximum density and specific magnetizing force : ",.,, = < X 5 S 5 6 ' 2 7 5 ' 000 = 49,Soo lines; m> .^ = 155. Maximum area (at poleface) : ^"c.i. 2 = (30 X * X |^ + a X iij X 371 = HOO sq. ins. Corresponding minimum density and specific magnetizing force i lines ' m " = 5?- 6 - Average specific magnetizing force: m \.\. = -^ = 106.3 ampere-turns per inch. Corresponding average density: (B" ci> = 43,500 lines per square inch. 540 DYNAMO-ELECTRIC MACHINES. [135 Magnetizing force required: at oL = 106.3 X 37 = 3930 ampere-turns. 5. Armature Reaction. By (250), p. 352, and Table XCL: at r = 1.73 X - X " = 5700 ampere-turns. 2 IOO 6. Total Magnetizing Force Required. By (227), p. 339: AT 25,800 -f 340 -f 6900 + 3930 + 5700 = 41, 670 ampere-turns. e. CALCULATION OF MAGNET WINDING. Shunt winding to be figured for a temperature increase of 15 C. Regulating resistance to be adjustable for a maximum \oltage of 540, and a minimum voltage of 450. i. Percentage of Regulating Resistance at Normal Load. The maximum output of 540 volts requires a total E. M. F. of 512.5 -f 40 = 552.5 volts, which is 7.8 per cent, in excess of the total E. M. F. gen- erated at normal output; for the maximum voltage, therefore, 1.078 times the normal flux must be produced. The magnet- izing forces required for this increased flux are: Air gaps: at' g = .3133 X (30,500 X 1.078) x 2.7 = 27,800 ampere-turns. Armature core: (B' a = 58,000 x 1.078 = 62,500 lines; m' & = 14.2. at' & = 14.2 X 27.85 = 400 ampere-turns. Wrought iron: &'w.i. = 90,000 X 1.078 = 97,000 lines; ?// w .i. = 73.6. we receive: wt sh = 31.3 X io- 6 X 13,100 X { - \ X 834 = 2730 Ibs., which checks the above figure. Formula (257), p. 361, gives: / /.OQ C ? -f- .001 12 X 104,800 x - - + -oio .4-. 4 = 16. 2 14 = 2.2 inches. Allowing. 3 inch for insulation between the layers, thickness and insulation of bobbins, and clearance, the total height of the magnet winding becomes /i m = 2.2 -j- .3 = 2.5 inches, which is the same as used in calculating the winding. There are, consequently, no errors to be corrected, and the final result of the winding calculation is: 1400 Ibs. (covered) of No. 13 B.W.G. wire (.095* + .010") and 1400 Ibs. (covered) of No. 11 B. & S. wire (.091" -f .010"), each wound in 4 spools of 350 pounds, two spools of each size to be placed on each magnet, see Fig. 348. Total weight of magnet wire, 2800 pounds. 3. Shunt Field Regulator. The amount of regulating resist- ance in circuit at normal load required for the maximum volt- age in the preceding was found to be 18 per cent, of the magnet resistance. In order to reduce the voltage from the normal amount to the minimum of 450, the total E. M. F. gen- erated must be decreased from 512.5 to 512.5 50 = 462.5 volts, or by 9f per cent.; hence the minimum flux is .9025 of the normal flux, and the magnetizing forces for the minimum voltage are : 544 DYNAMO-ELECTRIC MACHINES. [135 Air gaps: ^'g = -3 J 33 X (30,50 X .9025) X 2.64* = 22,800 ampere- turns. Armature core: " a = 5 8 > 000 X .9025 = 52,35 lines; m\ = 10.3. .. at' & =. 10.3 X 27.85 = 270 ampere-turns. Wrought iron: &" wi = 90,000 X .9025 = 8120 lines; m\ A = 33.2. * 0*'w.L = 33-2 X 136 = 4520 ampere-turns. Cast iron: "c.i. = 43,5 X .9025 = 39,260 lines; m" ^ = 86.8. . . #/' ci =z 86.8 x 37 = 3210 ampere-turns. Armature reaction: ,/ , 8 4 X 600 23^ at r = 1.7 x X 5^ = 5600 ampere-turns. 2 loO The total excitation required for minimum voltage is the sum of the above magnetizing forces: AT 22,800 -f 270 + 4520 + 3210 x 5600 = 36 5 4:00 ampere-turns. This minimum excitation being IPO x (41,67 36,40) _ j2 41,670 smaller than the normal excitation, the normal resistance of the shunt circuit, in order to effect the corresponding increase in the exciting current, must be increased by 12.7 per cent., or the magnet resistance by 1.18 X 12.7 = 15 per cent. The total resistance of the regulator, therefore, by formula (33 1 ), P- 393, is: r r = (.18 + .15) X r' sh = .33 x 133 = 44 ohms. By (332), p. 393: (^sh)max = ^ = 4-6 amperes. J 33 * For the minimum density the product 3C" X # c being 1,500,000 X .9025 = T .35375 Table LXVI. gives a coefficient of field-deflection k^ 1.32, which makes the length of the magnetic circuit in the gaps /" g = 1.32 X (3^ 28) = 2.64 inches. 135] EXAMPLES OF GENERATOR CALCULATION. 545* % (333), P- 393 : (^sh)min = - ^ - = 2.54 amperes. Supposing that the regulator is to have 60 contact-steps, so as to give an average regulation of i J volt per step, the resist- ance of each coil of the rheostat will be - = .733 ohm; and if iron wire at 6500 circular mils per ampere is employed, the area of the wires for the various coils ranges between 4.06 X 6500 = 26,390 and 2.54 x 6500 = 16,510 circular mils. The data for the gauge numbers lying between these limits are: GAUGE DIAMETER SECTIONAL AREA CARRYING CAPACITY, AMPS. NUMBER. (inch). (Cir. Mils). (6500 Cir. Mils p. A.) No. 6. B. &S 162 26,251 4.04 No. 9B. W. G 148 21,904 3.38 No. 7B. &S 144 20,817 3.21 No. 10 B. W. G 134 17,956 2.76 No.SB.&S 1285.... 16,510 2.54 Inserting the above values of the current capacities into- formula (335), p. 394, we obtain: = 4.06 - 4.4 6o 4.06 2.54 4^6-^38 4.06 2.54 4.06 3.21 X3 = - X 60 = 33 , 4.06 2.54 _ 4.06 2.76 *** ~ 4.06 -- 2.54 and 4.06 2. 54 n^ = - ^ X 60 = 60 ; 4.06 -- 2.54 from which follows that coils i to 26 are to consist of No. 6 B. & S. wire, of which about 300 feet are needed for the required resistance of .733 ohm; that coils 27 to 32 are to be of No. 9 B. W. G., length per coil about 250 feet; coils 33 to 50 of No. 7 B. & S., length about 240 feet; coils 51 to 59 of No. 10 X 60 = 51 5 46 D YNA MO-ELECTRIC MA CHINES. [135 B. W. G., length about 205 feet; and coil 60 of No. 8 B. & S. wire, about 190 feet in length. /. CALCULATION OF EFFICIENCIES. 1. Electrical Efficiency. By (35 2 ) P- 4o6: 500 X 600 300,000 % = 500 X 600 + 603. i8 2 X .0184 + 3 .i8 2 X 157 " 3 8 > 28 = -975, or 97,5 #. 2. Commercial Efficiency and Gross Efficiency. The energy lost by hysteresis and eddy currents was found P h -f- P* =,1552 watts; energy losses by commutation and friction estimated at 12,000 watts; hence the commercial efficiency, by (360), p. 407 : 300,000 300,000 __ A 93.2 f, 308,280 -[ and the gross efficiency: rj K - ^2L .957, or 95.7 7oo 136. Calculation of a Bipolar, Single Magnetic Circuit, Smooth- Drum, High-Speed Compound Dynamo: 300 KW. Upright Horseshoe Type. Wrought-Iron Cores and Yoke. Cast-Iron Polepieces. 500 Yolts. 600 Amps. 400 Revs. per Min, The armature and field frame calculated in 135 are given; the machine is to be overcompounded for a line loss of 5 per cent. ; temperature of magnet winding to rise 22^ C. ; extra- resistance in shunt circuit to be not less than 18 per cent, at normal load. a. CALCULATION OF MAGNETIZING FORCES. i. Determination of Number of Shunt Ampere- Turns. Use- ful flux required on open circuit: hence by 104 and 135 : 44,700.000 , ox "t so = .3133 X 4> ; 50 ; X 1.3* (3 - a8) = -3 r 33 X 29,800 x 2.64 = 24,700 ampere-turns. I Q Q ..at -- ^^ - X 27.85 = 11.55 X 27.85 = 320 ampere- turns. 548 DYNAMO-ELECTRIC MACHINES. [136 / I *J ' ^Av.i. = 4^.4 X 136 = 6300 ampere-turns. I. 215 X 44,7OO,OOO .. (ft ci = 22Lf l = 48,250 lines per square inch; c '% 2 X 562.5 44,700,000 ,. (B c>i<2 - - - 32,000 lines per square inch; .-. at" ^ 5_li x 37 = 99.6 x 37 = 3680 amp. -turns. 2 AT sh AT = 24,700 + 320 -f 6300 -{- 3680 = 35,000 ampere-turns. 2. Determination of Number of Series Ampere- Turns. Total E. M. F. at normal output, by (333), p. 393: E' = 1.05 X 500 +1.25 X 603 X .0184 = 539 volts; and therefore: 6 x <^o X io 9 # = 6 a - = 48,200,000 maxwells. a * = -3I33 X 4 'i ~ x I -35 (3o 28) = -3I33 X 32,100 X 2.7 = 27,100 ampere-turns. 48,200, ooo =6 1}n 712 ^,, 48,200,000 .. * 2 = 956 = 50,500 lines; .'. fl/ a = I7>7 *" 9 ' 7 X 27.85 = 13.7 X 27.85 380 amp.-turns. _ 1.215 X 48,200,000 .. (B wj . -- ^5 m = 95,2oo lines per square inch. af wd. =67.8 x 136 = 9220 ampere-turns. _ 1.215 X 48,200,000 .. . , ($> ci<1 = - ^ =52, 200 lines per square inch; 48,200,000 = = 34,400 lines per square inch; 1400 184.7 4- 63. i ~ X 37 = 123.9 X 37 = 458o amp.-turnsv c.i. a t v = 1.76 x - 2 ^ X ^- 5820 ampere-turns, AT = 27,100 -|- 380 -|- 9220 -j- 4580 + 5820 = 47,100 ampere-turns. Consequently by (339), p. 397 : AT K = 47,100 35,000 = 12,100 ampere-turns. 136] EXAMPLES OF GENERATOR CALCULATION. 549 b. CALCULATION OF MAGNET WINDING. i. Series Winding. By (343), P. 4oo: = 1,267,000 circular mils. Taking 5 cables of 19 No. 9 B. & S. wires each, the actual area is: 5 Xi9 X 13,094 = 1,24-3,930 circular mils. The number of turns required is: 7V se = ? - = 20, or 10 turns per core; hence the series field resistance, at 15.5 C., by (344), p. 400: and the weight: wt SG = 20 x Y: X (5 X 19 X 13,094) = 6031bs., bare wire; or, //',= 1.028 x 603 = 620 Ibs., covered wire. 2. Shunt Winding. The potential across the shunt field being 1.05 x 500 = 525 volts, the specific length of the shunt wire, for 18 percent, extra-resistance, and 22^ C. rise in tem- perature, is, by (319), p. 385: ** = ^f^T X ~ X 1.18 X (i + -4 X 22|-) = 687 feet per ohm. The two nearest gauge numbers are No. n B. & S. (798 feet per ohm) and No. 14 B. W. G. (667 feet per ohm); taking two parts, by weight, of No. 14 B. W. G. to one part of No. n B. & S., we obtain: Agh = .0503 x 798 -MX. 0718x667 .0503 + 2 X .0718 which is a trifle more than 2 per cent, in excess of the re- quired specific length. By increasing the percentage of extra 550 D YNAMO-ELECTXIC MA CHINES. [ 1 36 resistance in the same ratio, that is, by making r^ = 20 per cent., formula (319) will give the specific length actually pos- sessed by the combination of shunt wires selected. Hence: by (346), p. 400: 22 10 P sh = 3- X 6730 - 6oo 2 X .00135 X (i + -4 X 2 2 ) = 2020 530 = 1490 watts; by (3 I2 )> P- 3 8 3 : -^sh = I 49 X 1.20 = 1788 watts; by (3H), P- 384: ^ sh= 34,980 X 5^5 = 10 ,270 turns; v ' -' by (315), P- 3 8 4: Z 8h = 10,270 x ^ = 82,160 feet; Weight: w / 8h = 82,160 X 2 X ' 2 85 + - 2493 = 1825 Ibs., bare wire, O wt' Bh = 1.035 x 1825 = 1890 Ibs., covered wire; Resistance: r sh =- = 117 ohms, resistance of shunt winding, 15.5 C.; by (318), p. 385: r' sh = 117 x (i + - 00 4 X 22j) = 127.5 ohms, resistance of shunt winding, 38 C. ; by (317), P- 384: /' Bh = 127.5 X 1.20 = 153 ohms, resistance of entire shunt circuit, normal load. C 2 C f sh = ~ - = 3.43 amperes, shunt current, normal load. 3. Arrangement of Winding on Cores. Total weight of series winding: . wt' SQ = 620 Ibs. Total weight of shunt winding: . w/' sh = 1890 Ibs. Total weight of magnet winding: . . 2510 Ibs. 136] EXAMPLES OF GENERATOR CALCULATION. 551 The weight of the series wire being just about one-quarter of the total weight, the winding is with advantage placed upon 8 spools, 4 per core, the lower one of each being used for the series wire, one of the upper three being wound with No. ii B. & S., and the remaining two with No. 14 B. W. G. wire; weight of wire per series spool, 310 pounds, per shunt spool, 315 pounds. Each series spool has 5 X 10 = 50 cables which are arranged in 4 layers, two of which contain 12, and two 13 cables. The diameter of each series cable, consisting of 19 No. 9 B. & S. wires, is 5 x (.1144"+ .010") = .622 inch, hence the winding depth in the series spools, 4 X .622" = 2.488 inches, and the length of one layer (13 cables) 13 X .622" = 8.086 inches. Since the available height of each spool is = 8 inches by this arrangement the spool will be just filled. In the shunt bobbins the total 10,270 turns are divided in the ratio of the quantities used and of the specific lengths (feet per pound) of the two sizes of wire, /. c., in the ratio of 2 x 48 : 40. i ; hence there are 10,270 x 2 -g = 724:0 turns of No. 14 B. W. G. and I0 ' 27 X aX +4o.. = 808 tUrnS f N - U B " & S - Each No. 14 B. W. G. spool, therefore, contains - = 1810 turns, 4 and, the number of turns per layer being 8 - "5 _ 87 .083 -f .010 ~ has a net winding depth of 1810 - X .093' ; = 1.95 inch. 55 2 DYNAMO-ELECTRIC MACHINES. [137 Each of the No. n B. & S. spools has ^- = 1515 turns; the number of turns per layer is: .091 -f .010 -and consequently, the net winding depth: 80 X IOI// = : 1 ' 92 inch ' Actual magnetizing force at full load : AMPERE-TURNS. Series magnetizing force, AT se = 20 X 600 = 12,000 Shunt magnetizing force, AT sh = 10,270 X 3.43 = 35,226 Total magnetizing force, .... 47,226 137. Calculation of a Bipolar, Double Magnetic Circuit, Toothed-Ring, Low-Speed Compound Dynamo: 50 KW. Double Magnet Type. Wrought-Iron Cores. Cast-Iron Yokes and Polepieces. 125 Tolts. 400 Amps. 200 Revs, per Min. a. CALCULATION OF ARMATURE. 1. Length of Armature Conductor. For ft l = .70 (a = 27), Table IV., p. 50, gives e = 60 X io~ 8 volt per foot; from Table V., p. 520, v c = 32 feet per second; from Table VI., p. 54, 3C" = 20,000 lines per square inch; and from Table VIII. , p. 56, E' = 1.064 X 125 = 133 volts; hence by (26), p. 55: _ 133 X io e _ 316 feet 60 X 32 X 20,000 2. Sectional Area of Armature Conductor, and Selection of Wire. B y (27), p- 57-. oV = 300 x 400 = 120,000 circular mils. For 20 No. 14 B. W. G. wires (.083" -f .016"), the actual area is : 20 x 6889 = 137,980 circular mils. 137] EXAMPLES OF GENERATOR CALCULATION. 553 The subdivision of the armature conductor into a large num- ber of wires has the particular advantage in toothed arma- tures, that by a simple regrouping of the wires, the same slot will answer for a number of different voltages. Thus, in the present case, for instance, the same number of wires arranged in groups of 10 will give 250 volts at 200 amperes, and arranged 5 in parallel will furnish 500 volts at 100 amperes. 3. Diameter of Armature Core and Dimensions of Slots. By (30), P. 58: d' & = 230 x = 36.8 inches. 200 From Table XV., p. 70, the approximate size of the slot is i-J* X -$". The width of this slot will accommodate 4 No. 14 B. W. G. wires, thus: s = (.083 + .016") x 4 + 2 X .020"= .436, or ^ inch, the slot insulation, e = .020", being taken from Table XIX., p. 82. Each conductor being made up of 20 wires, the number of layers in each slot must, therefore, be a multiple of 5. The nearest number of layers thus qualified is 15, hence the actual depth of the slots, if ;oio" is allowed for separating the conductors, and .035" for binding: // a (.083" + .016") X 15 + .020" + 2 X .010" + .035' = 1.6", or 1-j^- inch. External diameter of armature: d\ = 36.8 + i^ = 38} inches. Diameter at bottom of slots: <4 = 3H 2 x i A = 35f inches. Number of slots, by (34), p. 70: 4. Length of Armature Core. , P- 76: 554 D YNA MO-ELE C 7 *RIC MA CHINES. [137 5. Arrangement of Armature Winding. The number of com- mutator divisions must be between 40 and 60, and must be a divisor of the number of slots, 138, taking 3 slots per com- mutator section, we have <, = a> = 46; *5 therefore, by (46), p. 89: _ 138 X 4 X 15 _ n fl., 7 t7, 4 6 X 20 The armature winding, consequently, consists in 46 coils of 9 turns of 20 No. 14 B. W. G. wires, each coil occupying 3 Fig. 35L Arrangement of Armature Winding, so-KW Double-Magnet Type, Low-Speed Generator. slots. One slot, containing 3 turns, or one-third of an arma- ture coil, is shown in Fig. 351. 6. Radial Depth, Minimum and Maximum Cross- Section, and Average Magnetic Density of Armature Core. By (138), p. 202: < = X I33 x IQ9 = 9.630,000 maxwells. 414 x 200 By (48), p. 92, and Table XXII.: Internal diameter of armature core, Fig. 352: 35 1 - 2 X 6| = 21} inches. 137] EXAMPLES OF GENERATOR CALCULATION. Mean diameter of core: d'\ = 21-1 -f 6| + i-J>, = 30^ inches. Maximum depth of core, from (234), p. 342: 555 - i = 14.8 inches. Fig. 352. Dimensions of Armature Core, so-KW Double-Magnet Type, Low-Speed Generator. By (232), p. 341: S &1 2 x 10 X 6| x -90 = 121 square inches. By (233), p. 341: aa = 2 x 10 X 14-8 X .90 = 266 square inches. Therefore: ^' /ai = I2 i " ~ 79> 6o lines P er square inch- _ 9,630,000 82 ~ 266 = 3^ 200 l mes P er square inch. m "ai = 3-7 ampere-turns; m" &z = 6. 7 ampere-turnsp. inch, B y (231)1 P. 341: 30.7 -j- 6. 7 w// a : - = 18.7 ampere-turns per inch. Corresponding average density: &"a = 69,000 lines per square inch. 556 DYNAMO-ELECTRIC MACHINES. [ 137 7. Weight and Resistance of Armature Winding. By (53) P- 99- By (5$), P. 101: o/4 = .00000303 x 137,980 X 1360 = 568 Ibs., bare wire. By (59), P- 102: wt' & = i. 066 x 568 = 605 Ibs., covered wire. By (61), p. 105: X I36 X ' 15 ~ '^56 ohm at I $' 20 8. Energy Losses in Armature, and Temperature Increase. By (68), p. 109: jP a = 1.2 X 400* X .0256 = 4950 watts. From Fig. 352 : f 30 T 3 5- X n X 8^ - 138 X i T V X-^ j X 10 X .90 1728 = 3.61 cubic feet; >ir 20 N l = -- = 3.33 cycles per second; from Table XXIX. (&" a = 69,000): rj = 27.61 watts per cubic foot; from Table XXXI. (^ = .020"): s = .138 watts per cubic foot. By (73), P- U2: J> h = 27.61 x 3-33 X 3-61 = 320 watts; By (76), P. 120: ^ e = -i3 8 X 3-33' X 3.61 = 6 watts. By (65), p. 107: A = 4950 + 320 + 6 = 5276 watts. w 137] EXAMPLES OF GENERATOR CALCULATION. 557 B 7 (79), P. ^5: SA = 2 X 3rV X 7t X (10 + 6} + 4 X i^) = 4360 square inches. Ratio of pole-area to radiating surface: 38j X n X 10 X .70 _ 4360 From Table XXXVI., p. 127, by interpolation: 9 a = 44 C. By (81), p. 127: Armature resistance, hot: r' & = .0256 X (i + -004 X 53i) = .031^ ohm, at 69 C. 9. Circumferential Current Density, Safe Capacity and Running Value of Armature; Relative Efficiency of Magnetic Field. By (84), p. 131: / c = - = 685 amperes per inch circumference. X "ft Table XXXVII. , p. 132: a = 40 to 60 C. By (88), p. 134: P' 1.33 X 38 a X 10 X .85 X 200 X 20,000 X io~ 6 = 67,000 watts. By (90), p. 135 : p ,^ _ i33 X 400 _ ^004.7 watt per pound of copper, at unit field density. By (155)* P- 2II: ^ _ 9, 630, ooo x 5800 maxwe iis per watt, at unit J X b. DIMENSIONING OF MAGNET FRAME. i. Total Magnetic Flux, and Sectional Areas of Frame. By (156), p. 214, and Table LXVIII. : $ = 1.25 x 9,630,000 = 12,000,000 maxwells. 558 DYNAMO-ELECTRIC MACHINES. [137 By (217), p. 314: = 12,000,000 _ m 3 re inches 90,000 By (220), p. 314: = 12,000,000 = 266 7 e incheg 45,000 2. Magnet Cores. The two cores being magnetically in parallel, each must have one-half the area 6"' w .i. found above for wrought iron, and making their breadth equal to that of the armature core, their thickness is found: * 33 ' 3 = 6.67, or say 6| inches. 2 x 10 3. Polepieces. Thickness at ends joining cores: 2 x 6J = 18} inches. Bore, by Table LXI., p. 209: 2 J vo^ I" I0 ) X I3J + 3i X io io X = 2 (53-1 + -9) = 108. 3. Leakage Factor. By (i57), P- 218: 544 Ratio of width of slot to pitch: 4375 " 8765 therefore, by (158), p. 218, and Table LXV. : \' = 1.03 X 1.20 = 1.24. d. CALCULATION OF MAGNETIZING FORCES. I. Shunt Magnetizing Force. = 6 x 125 X io = maxwells. 414 X 200 Air gaps : at Ko =.3133 X > 8 X .75 = -3133 X 22,200 X .75 = 5216 ampere-turns. Armature core: 0,060,000 i ^,, 9,060,000 & \ = ~^T ^ 74,8oo Imes; (B" % = '-^ = lines; l\ = 2 8| X TT X 90027 + 6} + 3i = 39 inches; - ^^ 1 x 39 = J 5-5 X 39 = 6 5 ampere-turns. Magnet cores (wrought iron): 1.24 x 0,060,000 CB w.i. = 2 x 6 X io = -*.^ v .i. = 3 6 -5 X 38 = 1387 ampere-turns. 1.24 x 0,060,000 . , CB w.i. = 2 x 6 X io = 3 ' 3 CS per s ^ uare mch; 137J EXAMPLES OF GENERATOR CALCULATION. 561 Polepieces (cast iron with admixture of aluminum) : The pole- pieces consist of two end portions of uniform cross-section and of a centre portion of varying cross-section. The com- bined length of the uniform portions is, from Fig. 353: l\ = 2 x 3i = 6 inches, and the mean length of the varying cross-section, by (243), p. 348: ', = 4- T J 4. ij. = 22 inches. The flux-densities and the corresponding magnetizing forces are: 1.24 X 9,060,000 11,225,000 (B cil = ^1 ! = - = 41,700 lines per 2 X i3iXio 270 sq. inch; *, __ 9,060,000 9, 060, OOP _ ^^ f* i. ~~~ -4/^0 o ~^ r> o ' ~""~ A % A x^ m" ci = 79amp.-turnsp.inch;w" c = 6 x '37 X io 9 = 9 93Q maxwe ii s> 414 X 200 Air gaps: Q. 030,000 /g= -3I33 X -- X 75 = -3133 X 24,300 X .75 = 5710 ampere-turns. Armature core: 0,030,000 = - = 82,100 lines per square inch; (B = _ 37>400 neg per S q Uare 200 .. at & = - X 39 = 820 ampere-turns. 562 DYNAMO-ELECTRIC MACHINES. [137 Magnet cores: CSV, = ' 4Xft93o.ooo = 9i)2Qo Hnes; ;;;Vi = ^ 2 . * atwi. = 54- 2 X 38 = 2060 ampere-turns. Polepieces: (B' eAl = = 45,6oo lines; = 98,6; ' (*",i. 2 - > 42 8 8 = 23,200 lines; m" ^ - 28.2; .' <.i. = 9 8 -6 X 6| + 98 ' + 28 ' 2 x 22 = 640 + 1400 2 = 2040 ampere-turns. The average specific magnetizing force of the variable section, ^(98.6 + 28.2) = 63.4, corresponds to an average density of (&" p = 41,000 lines per square inch, from which Table XCL, p. 352, gives J4 = 1.71. The maximum density in the armature teeth, at normal load, is: _ 9,93 Q ,oo _ f X .7 X (351 X 7t - 138 X A) X 10 X .90 Q.Q^O.OOO -- = 62,000 lines per square inch, and for this, Table XC., p. 350, gives 13 = .36. Hence by (250), p. 352: at v = 1.71 X 4I4 X 2 X ' 36 Q X 27 = 3830 amp. -turns. 2 TOO .*. AT = 5710 -j- 820 -f- 2060 -J- 2040 -j- 3830 = 14^460 ampere-turns. AT se 14,460 8870 = 5590 ampere-turns. ^. CALCULATION OF MAGNET WINDING. Temperature-increase permitted, m = 19 C. Percentage of extra-resistance in circuit at normal load, r^ = 35 $. 137] EXAMPLES OF GENERATOR CALCULATION. 563 i. Series Winding. Apportioning one- third of the total winding depth, /i m = 2f", to the series winding (AT ae being -about one-third of AT), about i inch will be taken up by the latter, hence, if the series coil is wound next to the core, the mean length of a series turn: /' T = 2 (10 -f 6}) -f i X 7t = 36.64 inches, and the mean length of a shunt turn: /" T = 2 (12 -f 8}) + if X it = 47 inches. The radiating surface of each magnet is: SH = 2 (10 -j- 6J -f- 2f TT) x ( X 8" i") = 860 square inches. B 7 (343), P- 4oo, thus: = 910,000 circular mils. For 22 No. 4 B. & S. wires (.204" + .012") the actual area is: 22 x 4i,743 = 918,346 circular mils. Number of turns required per magnetic circuit, if both coils are in series: By (344), p. 400, for the two series coils: r - = ' 87 X 2 X46 ' ^ = - 00098 r'n = 1.078 X .00098 = .00106 ohm, at 34.5 C. and the total weight: 7// se = 2 x 14 X ^^ X 22 x .1264 = 238 Ibs., bare wire; wt' se = 1.029 X 238 = 245 Ibs., covered, or 122J Ibs. per magnet. 2. Shunt Winding. The two shunt coils to be connected in parallel. By (318), P. 385: A sh = -~- X X I-3SX (i + .004 X 19) =397 ft. per ohm. 564 DYNAMO-ELECTRIC MACHINES. [137 The nearest gauge wire is No. 14 B. and S. (.064" -j- .007"), with a specific length of 398 feet per ohm. By (346), p. 400: JP A . x 86o _ 400 * x > = 218 85 = 133 watts. By (312), p. 383: ^" S h = 133 x 1.35 = l8 watts - By (314), p. 384: = 8870 x 125 = 617Q tums per magnet> IoO By (315), P- 384: Z sh = 6170 X = 24,200 feet per core. Total weight: wt 8h = 2 x 24,200 x .01243 = 604 Ibs., bare wire. o//' 8h 1.0325 x 604 = 624 Ibs., covered, or 312 Ibs. per magnet. Shunt resistance per core: = 60.8 ohms, at 15.5 C. 39 s r' 8h = 60.8 X 1.076 = 65.5 ohms, at 34.5 C. r" sh = 65.5 X 1.35 = 88.4 ohms, each shunt circuit. Exciting current: I 2 C Ah = oo r5; 1*42 amperes, at normal load. 00.4 3. Arrangement of Magnet Winding on Cores. Number of series wires per layer: Number of layers of series wire: 14 x 22 = 4. 78 Height of series winding: 4 X .216 = .864 inch. 137] EXAMPLES OF GENERATOR CALCULATION. 565 Number of shunt wires per layer: 17 -240. .071 Number of layers of shunt wire: 6170 - A ^"- * 6 ' Height of shunt winding: 26 x .071 = 1.846 inch. Allowing .1 inch for core covering and insulation between layers, the actual total depth of magnet winding is: h m .864 -f 1.846 -f .1 = 2|f inches. Actual magnetizing force at full load : AMPERE- TURNS. Series magnetizing force, AT^^ 14 x 4 5600 Shunt magnetizing force, AT sh = 26 X 240 X 1.42 8850 Total magnetizing force, . . . . A 7 1 14,450 /. CALCULATION OF EFFICIENCIES. i. Electrical Efficiency. By (353), p. 406: .-, _ 125 X 400 Ye 125 X 400+ (400 + 2 X i-42) 3 X .0314 + 400" X .00106 + (2 X 1.42)' X " 2. Commercial Efficiency. Allowing 2500 watts for commuta- tor- and friction-losses, we have by (361), p. 408: 3. Weight Efficiency. The estimated weights of the different parts of our dynamo are: Armature : Core, 3.56 cubic feet of wrought iron, . 1710 Ibs. Winding, insulation, binding, etc., . . 640 " Shaft, commutator, spiders, etc., . . 500 " Armature complete, . . - . . 2850 Ibs. 566 DYNAMO-ELECTRIC MACHINES [138 Frame: Magnet cores, 2 x 45 X 10 X 6| = 6075 cubic inches of wrought iron, ';'* . " 1700 Ibs. Polepieces, [45 X 45 - (39 2 X | + 2 X 18 X 3i + 2 x 15 X i J)] X 10 = 6700 cubic inches of cast iron, . . . .. .-;.,. 1750 " Field-winding and insulation, 250 + 650 = 900 " Dynamo portion of bed, bearings, etc., . 800 " Frame, complete, , . . 5150 Ibs. Fittings: Brushes, holders, and brush-rocker, , . 100 Ibs. Switches, series field regulator, cables, etc., 100 " Fittings, complete, . . . . .. . 200 Ibs. Total net weight of dynamo, . . , 8200 Ibs. The specific output, therefore, is: - 6.1 watts per pound. o2OO 138. Calculation of a Multipolar, Multiple Magnet, Smooth Ring, High-Speed Shunt Dynamo : 1200 Kilowatts. Radial Innerpole Type. 10 Poles. Cast Steel Frame. 150 Volts. 8000 Amps. 232 Revs, per min. a. CALCULATION OF ARMATURE. i. Length of Armature Conductor. Assuming we find, from Table IV., p. 50: e = 60 X io~ 8 volt per foot. Table V., p. 520, gives an average conductor speed of 90 ft. p. sec. for a lOoo-KW high-speed ring armature; we will take in the present case: z/ c = 96 feet per second; 138] EXAMPLES OF GENERATOR CALCULATION. I 5 6 7 From Table VIII., p. 56, we obtain: E' = 1.02 x 150 = 153 volts. This machine being of comparatively low voltage and high current strength, the field-density obtained from Table VI. is. reduced according to the rule given on page 54, thus: OC" = f X 60,000 = 40,000 lines per square inch. Consequently, by (26), p. 55: L 5 X 153 X io 8 60 X 96 X 40,000 2. Area and Shape of Armature Conductor. By 20: c = 40,000 X 96 = 3,840,000-, by Table LXVL, p. 225, / 13 = 1.25; hence, by (167), p. 226: i (931 + 96) X 7t X .85 X 20 __ 2540 _ ^ 1.25 X ( 9 6- 9 3f) 2.8- 574 DYNAMO-ELECTRIC MACHINES. [138 2. Permeance of Stray Paths. Distance apart of cores, at yoke-end : ^ ( I7 j _ 13^) x cos 18 = 3.6 inches. Distance apart of cores, at pole-end: 3-6 X = 13.6 inches. tan 18' Fig. 356. Dimensions of Field-Magnet Frame, I2OO-KW ic-Pole Radial Innerpole-Type Generator. Projecting area of polepiece : S l = 22 x 20 19^ x 13^ = 177 square inches. Projecting area of yoke: S^ = 2v\ x 17^ 19^ X 13!- = 91 square inches. Total stray permeance, from Fig. 356: X 16 20 X i77 -6 + 3-6 6J 2 x 16 = 10 x (18.1 + 4-6 + 4.2) = 269, 138] EXAMPLES OF GENERATOR CALCULATION. 575 3. Leakage Factor, and Total Flux. By (157), P- 218: _ 907 -}- 269 1176 j OQ" 97 " 97 This is considerably higher than the value taken from Table LXVIII. and employed in the calculation of the frame area (see p. 572). The corrected total flux of #' = 1.295 X 99,000,000 = 128,000,000 maxwells brings the density in the frame up to "c. 8 . T = 97,500 lines per square inch, 5 X i9ir X 13 2 which, however, is within the practical limits of magnetization for cast steel (see Table LXXVL, p. 313), making a re-dimen- sioning of the frame unnecessary. d. CALCULATION OF MAGNETIZING FORCES. 1. Air Gaps. Actual density: 99,000,000 ^" 2540 ~ 39,000 lines per square inch. By (228), p. 339: af g 3 I 33 X 39,000 X 2.8 = 34,200 ampere-turns. 2. Armature Core. By (236), p. 343: + 4 /"a = 104 X 7t x -^-g (- 8 = 28 inches; m" & =12.5 ampere-turns per inch (p. 569): . . at & = 12.5 X 38 = 350 ampere-turns. 3. Magnet Frame. Length of path (see Fig. 356): 2 X (3i + 16 + 3i + 4i) = 54 inches. The specific magnetizing force correspondiug to the above flux density (B" c<8 . of 97,500 lines, for cast steel, is: m" cs 86 ampere-turns per inch. . . at m %6 x 54 = 4650 ampere-turns. 576 D YNAMO-ELECTRIC MA CHINES. [138 4. Armature Reaction. Mean density in polepieces: 128,000,000 = lines per square inch. 5 X 22| X 20 hence by (250), p. 352, and Table XCI. : atr = x., 5 X 2 X 8 X - = 4450 ampere-turns. 10 5. Total Magnetizing Force Required. By (227), p. 339: A T = 34, 200 + 350 -f 4650 + 4450 = 43,650 ampere-turns. 2080 By (315), P- 3 8 4: 3150 X 2080 e . . Z sh = - = 20,200 feet, per pair of magnets. ' r sh = ^ - = 7.67 ohms, 2 coils in series, at 15.5 C. 2637 By (318), p. 385: >-'sn = 7.67 X (i + .004 X 44) = 9.0 ohms, one group,. at 59.5* C. 578 D YNAMO-ELECTRIC MA CHINES. [138 By (317) P- 3 8 4: r "sb. 9- X 1.20 = 10.8 ohms, one shunt branch, at normal load. " ^sh = l = 13.9 amperes, current in each branch. 10. 8 There being 5 magnetic circuits with their magnetizing coils in parallel, the total exciting current is: 13.9 x 5 = 69.5 amperes, while the joint shunt resistance of the 10 coils is: = 1.8 ohm, at 59.5 C. Total weight: wtfr = 5 X 7 ' 67 = 8330 pounds, bare wire. .0046 wffr 8330 x i. 022 1 = 8530 pounds, covered wire, or 853 pounds of No. 8 B. W. G. wire per core. Actual magnetizing force at full load: AT = 3150 x 13.9 = 43,800 ampere-turns. Since in this example the dimensioning of the winding space was the starting point of the winding calculation, no checking of the result with reference to the length of mean turn, radi- ating surfaces, etc., is necessary. /. CALCULATION OF EFFICIENCIES. 1. Electrical Efficiency. By (35 2 ), P. 4o6: 150 X 8000 150 X 8000 -f- 8069. 5 2 X .000105 + 5 X 13. 9 2 X 10.8 1,200,000 = - - = .987, or 98.7 fo. 1,217,200 2. Commercial Efficiency. Taking the commutation- and fric- tion-losses at 40,000 watts, we obtain by (360), p. 407: 1,200,000 1,200,000 1,217,200+ 11,800 + 40,000 1,269,000 or 94.7 *. 138] EXAMPLES OF GENERATOR CALCULATION. 579 3. Weight- Efficiency. The weight of the machine is obtained as follows: Armature: Core, 27.2 cu. ft. of wrought iron, 13,000 Ibs. Winding and insulation, etc., . 4,000 " Armature spider, shaft, etc., 8,000 " Armature, complete, . . . . 25,000 Ibs. Frame: Magnet cores, 10 x 19^ X 13^ X 16 = 42, 100 cu. ins. of cast steel, . . . , ' . 1 1, 500 Ibs. Polepieces, 10 X 22% X 20 X 2} = 10,050 cu. ins. of cast steel, 2,800 " Yoke, / . 735 X 59* - 43" ~ J X 20 J- = 20,500 cu. ins. of cast steel, 57oo Field winding, spools, and insula- tion), . . . . . 10,000 Flange for fastening yoke to en- gine frame, outboard bearing, etc., . ... . . 12,000 " u Frame, complete, ..... 42,000 Ibs. Fittings: Brush shifting and raising de- vices, brushes, studs, etc., . 3,000 Ibs. Switches, cables, etc., . . 1,000 " Fittings, complete, 4,000 Ibs. Total net weight of dynamo, . . 71,000 Ibs. Weight efficiency: 1,200,000 71,000 580 DYNAMO-ELECTRIC MACHINES. [139 139. Calculation of a Multipolar, Single Magnet, Smooth Ring, Moderate Speed Series Dynamo : 30 KW. Single Magnet Innerpole Type. 6 Poles. Wrought-Iron Core. Cast Steel Polepieces. 600 Tolts. 50 Amps. 400 Revs, per Min. a. CALCULATION OF ARMATURE. i. Length of Armature Conductor. ' 8 ( ' 6 ~ ' 75) = .75; = '=7iV=57.5X io-' v. p. ft. z; c = 60 feet per second; 3C" = 15,000 lines per square inch; E' = i. io X 600 = 660 volts. By (26), p. 55 : Z *= 3 v 6 . 6 v Xl 8 -3870 feet. 57.5 X 60 X 15,000 2. Sectional Area of Armature Conductor. By (27), P. 57: a 3 = 300 X = 5000 circular mils. O No. 15 B. W. G. (.072" + -016") has a cross-section of 5184 circular mils. 3. Diameter of Armature Core, and Number of Conductors. By (30), P. 58: d* =i 230 X - = 35 inches. 400 The diameter over the winding on the internal circumfer- ence being about 34 inches, and 3 layers with its insula- tions making a well-proportioned winding space for the case ia question, the total number of conductors on the armature is: N = 34 X * x 3 = 3600 .072 + .Ol6 Actual depth of winding: h & = 3 x (.072" + .016") + .060" = .324 inch. 139] EXAMPLES OF GENERATOR CALCULATION. 581 4. Length of Armature Core. By (48), p. 92: 3870 X 12 / a = =13 inches. 3000 5. Arrangement of Armature Winding. By (45), P- 89: '. 660 X 3 (c)min = It = 172. Taking 180 commutator divisions, we have 30 coils of 20 convolutions per pole. 6. Radial Depth, Minimum and Maximum Cross- Section, and Average Magnetic Density of Armature Core. By (138), p. 202: , * = 6 X 3 X 660 X^ = OOQ maxwel , s _ 3600 X 400 By (48), p. 92 : ^ = S> 250,000 = 2i inches. 6 X 50,000 X 13 X .85 External diameter of armature core : 35 + 2 X 2j = 40 inches. Mean diameter of armature core: d "\ = 35 + 2| = 37^ inches. Maximum depth: *'a = ,9 2 -j- 2| 2 = 7f inches. Deducting f inch taken^up by armature bolt and insulation, the minimum core depth is reduced to 2 J f = if inch ; hence S" &1 = 6 X 13 X 1} X .85 116 square inches. S* 6 x 13 X 7| X .85 = 514 square inches. 582 DYNAMO-ELECTRIC MACHINES. [139 Maximum and minimum densities: 8,250,000 ,. 8,250,000 (B* aj J = 71,000 lines ;(B &2 = - -= 16,000 lines. Mean specific magnetizing force and corresponding average flux density: 20.5 4-2.9 m\ = 2 ! L = 11,7 ampere-turns per inch. (B" a = 57,000 lines per square inch. 7. Weight and Resistance of Armature Winding. By (53), P- 99' 13 By (58), P. 101: wt & = .00000303 x 5184 X 9500 = 149 Ibs. By (59), P.- 102: wt' & = 1.078 X 149 = 161 Ibs. By (61), p. 105: r & = ^ X 9500 = .002 = ,528 ohm, at 15.5 C. 8. Energy Losses in Armature, and Temperature Increase. - 37i X TT X 13 X 2! x .85 M = ^-^ 2 = 1.89 cubic feet. 1728 N l = ~p x 3 = 20 cycles per second. By (68), p. 109: P & = 1.2 X 50" x .528 = 1585 watts. By (73), p. 112: P h = 20.35 x 20 X 1.89 = 780 watts. By (76), p. 120: P* = .094 X 2o 2 X 1.89 70 watts. By (65), p. 107: A = 1585 + 780 + 70 = 2435 watts. By (79), p. 125: ^A = 2 X 37i * X (13 + 2$ + 4 X |) == 4000 sq. ins. 139] EXAMPLES OF GENERATOR CALCULATION. 583 Ratio of pole area to radiating surface : 34 X TT x 13 X .75 _ 26 4000 By (81), p. 127: a = 42 X - = 25J C. 4000 r' a = (i + .004 X 25!) x .528 = .583 ohm, at 41 C. b. DIMENSIONING OF MAGNET FRAME. 1. Total Magnetic Flux, and Sectional Areas of Frame. By (156), P- 214: <' = 1.30 x 8,250,000 = 10,700,000 maxwells. By (217), p. 314: * S wi = - - = 119 square inches. 90,000 By (218), p. 314: 10,700,000 . =" -=126 square inches. 05,000 2. Magnet Core. The magnet being hollow, its internal diameter must be determined first. Diameter of shaft, by (123), p. 185: = 1-3 X \ *~ - = 4 inches. r 400 Making the hole in the core 4^ inches in diameter, the ex- ternal core diameter becomes: 4n = y ("9 + I5-9) X ^ = 13 inches. 3. Polepieces. ^, - 35 - 2 X (.324 + A) = 33ff inch es. /; P = 33*1 X sin 7i = 4 inches. Providing the same distance between all projecting portions of opposite polarity, the shape shown in Fig. 357 is obtained, having a mean width of about 12 inches per magnetic circuit. The axial thickness of the polepieces, therefore, must be: 584 DYNAMO-ELECTRIC MACHINES. 126 . = 31 inches, 3X12 leaving the length of the magnet core: / m = 13 2 X 3i = 6 inches. [ 139 SCALE, 1:20. Tig. 357. Dimensions of Armature Core and Field Magnet Frame, 3O-KW 6-Pole, Single-Magnet Innerpole Type, Moderate-Speed Generator. C. CALCULATION OF MAGNETIC LEAKAGE. 1. Permeance of Gap Spaces. OC" X v c = 15,000 X 60 = 900,000. By (167), p. 226: 3> = 1 (33 + 35) X 7t X .835 X 13 _ 59 = i-i5 X (35 - 33*1) " I - 2 5. 2. Permeance of Stray Paths. From Fig. 357: / 2 _ 2 \ TT ( 2 * - 13 ) - 6 x (2 X 13 + 12 X 3j) 6 4i = 53-3 + 90.7 = 144. 139] EXAMPLES OF GENERATOR CALCULATION. 585 3. Leakage Factor. d. CALCULATION OF MAGNETIZING FORCES. 1. Air Gaps. Actual density: 8,250,000 .. OC - 2 - 2 - = 14,000 lines per square inch. By (228), p. 339: af g -3 *33 * 14,000 X 1.25 = 5480 ampere-turns. 2. Armature Core. B 7 (236), p. 343: f+7i* l\ = 371 * X ^_g -- h H = Hf inches. w'a =11.7 ampere-turns per inch, see p. 582; . . 0/ a = 11.7 x 14! = 170 ampere-turns. 3. Magnet Frame. Wrought iron portion: Length, /" w< i. =6 + 3^+^10 inches. Area, 6"' w .i. = (i3 2 4i 8 ) - = II6 - 8 square inches. 4 10,700,000 Density, (B w>i . = - n = 92,000 lines per square inch. I 10. O Specific magnetizing force: m "w.i. 5 6 -5 ampere-turns per inch. Magnetizing force required for wrought iron portion: fltf w = 56.5 x 10 = 565 ampere-turns. Cast steel portion: Length, /" c>8 ~ 2 X (9i + 6) = 30^ inches. Minimum cross-section, S CSi = 3 x ioj X 3^ = no square inches. 586 DYNAMO-ELECTRIC MACHINES. Maximum cross-section, S" CSz 3 x 1 8 X 3-J = 189 square inches. Maximum and minimum flux densities: 000 _ 10,700,000 = 97 ' 3Qo; M * = ~~ = 56 ' 7 - Average specific magnetizing force, 86 4- ic m C8t = - ! i = 50.5 ampere-turns per inch. Magnetizing force required for cast steel portion: a * CJi . = 5-5 X 3i 1540 ampere-turns. 4. Armature Reaction. Density in polepieces: 10,700,000 (B P = ^ - = 20,500 lines per square inch, \ X 34 X 7t x .75 X 13 By (250), p. 352, and Table XCI. : a/ r= j. 25 x 36 X 5 X ^ = 3130 ampere-turns. 3 I8 o 5. Total Magnetizing Force Required. AT= 5480+170 + 565 + 1540+3130 10,885 ampere-turns. e. CALCULATION OF MAGNET WINDING. Limit of temperature increase, m = 22 C. B y (287), p. 374: #. = *****-= 218 turns. 5o Allowing a winding depth of 7 inches, the mean length of one turn is / T = (13 + 7) X 7t = 62.8 inches; hence, by (288), p. 374: T 218 X 62.8 -- Af . , 4e = - = 1140 feet. 12 S K =27X^X6 + 6X14X3 = 760 square inches. "- = 77 X F X i +.004X 22 = 13 ' 900 eet P er ohm - 140] EXAMPLES OF GENERATOR CALCULATION. 5 8 7 The coil being round and of comparatively large diameter, a single wire, No. 00 B. W. G. (.380" -j- .020") can be em- ployed without difficulty. Number of turns per layer: 38 + .02- Number of layers: -17 13 Net depth of winding space: ^'m ~ i7 X (.38 + .02) = 6.8 inches. Adding to this the thickness of the bobbin and insulation, we have h m = 7 inches, as above. Weight of winding: wt w 1140 x .437 = 500 Ibs., bare wire; wt'se = 1.022 x 500 = 510 Ibs., covered wire. Resistance: r se = 500 X .00016 = .08 ohm, at 15.5 C. Actual magnetizing force: AT ^~ 13 X 17 X 50 = 11,050 ampere-turns. 140. Calculation of a Multipolar, Multiple Magnet, Toothed-Ring, Low-Speed Compound Dynamo : 2000 KW. Eadial Outerpole Type. 16 Poles. Cast- Steel Frame. Drum- Wound King Armature, 540 Yolts. 3700 Amps. 70 Keys, per Min. a. CALCULATION OF ARMATURE. i. Length of Armature Conductor. For /3 l = .70, we have g= i8o(i-.7) =3| . t and 588 DYNAMO-ELECTRIC MACHINES. [ 14O From Table IV., p. 50: e = 55 X io~ 8 volt per foot; 4- == =5* X io~ 8 = 6.875 X io~ 8 volt per foot. p From Table V., p. 520, the average conductor velocity for this case is 45 ft. p. sec. ; in order to obtain an external arma- ture diameter of exactly 12 feet, however, we will here take: V Q = 42.8 feet per second. From Table VI. , p. 54: 3C" = 35,ooo lines per square inch; and from Table VIII., p. 56: E' = 1.02 X 540 = 551 volts. Hence, by (26), p. 55 : 6.875 XX 35,oo 2. Mean Winding Diameter of Armature. By (30), P- 58: d\ = 230 x ^ = HOf inches. 3. Area and Shape of Armature Conductor; Size and Number of Slots. By 20: d a 2 = 600 X ^P - 278,000 circular mils, which is equivalent to 278,000 x - = 219,000 square mils. 4 A bar, -J inch high by J inch wide, has a cross-section of 218,750 square mils. Arranging 6 such bars in each slot, as shown in Fig. 358, the width of the slot is found fj- inch, and its total depth, 3^ inches. The distance between mean wind- ing diameter and external circumference is if inches, hence the external diameter: d\ = 140! + 2 X if = 144 inches, and by (34), p. 70: 'c = * 44 v X if = 329, or, say, 336 slots, 2 x T8" this being the nearest number divisible by 16. 140] EXAMPLES OF GENERATOR CALCULATION. 4. Length of Armature Core. By (48), p. 92 : 589 5. Arrangement of Armature Winding. By (45), P- 89: One commutator-division per slot making the number of commutator-bars smaller than this minimum, we have to take Fig. 358. Dimensions of Slot and Armature Conductors, 2OOO-KW i6-Pole, Radial Outerpole Type, Low-Speed Generator. two per slot, and the winding must be arranged in 772 coils of 3 turns each. 6. Radial Depth, Minimum and Maximum Cross- Section, and Average Magnetic Density of Armature Core. B y (is 8 )> P- 20I: # = 6X ** 5 6 5I X XI 0> = 188,000,000 maxwells. By (48), p. 92: 188,000,000 9 = Clinches, 59 DYNAMO-ELECTRIC MACHINES. [ 14O allowance being made for 6 air-ducts of J inch width, and for 2 phosphor-bronze end-frames of inch thickness, thus: 6xJ + 2Xi = 2| inches. Total radial depth of armature core: 6J + 3 | = 10 inches. Maximum depth of armature core : b\ y / 144 X sin-^ ) -f io 2 = Vio a + io a = 14 inches. Minimum and maximum cross-sections: S\ = 16 X 2pJ X 61 X .9 = 2920 square inches. S"^ = 1 6 X 29^ X 14 X .9 = 5950 square inches. Maximum and minimum flux densities: ^,, 188,000,000 188,000,000 ffl i= -^t = 6 4-4; \= ^^ =31,600. Mean specific magnetizing force and corresponding average density: m\ = ^^- t-^i- = 10.4 ampere-turns per inch. (& /; a = 53,000 lines per square inch. 7. Weight and Resistance of Armature Winding. B y(57), P. ioo : Z t = ( r -f .293 X ) X 535 = 12,400 feet. (58), p. 101: wt & = .0000303 X 278,000 X 12,400 = 10,425 Ibs. (61), p. 105: X '' 5 = .00183 ohm, at 15.5 C. 8. Energy Losses in Armature, and Temperature Increase. By (72), p. 112: 134 X n X io - 336 X 3 X H X 29! X .9 M=- 1728 = 55 cubic feet. 140] EXAMPLES OF GENERATOR CALCULATION. 591 In this the depth of the slot is taken 3 inches only, in order to allow for the volume of the lateral projections of the teeth. Frequency: N^ = j^ X 8 = 9.33 cycles per second. By (68), p. 109: P & = 1.2 X 37o 2 X 00183 = 30,000 watts. By (73> P- II2: P h = 18.1 X 9.33 X 55 = 9300 watts. By (76), p. 120: P e = .081 X 9.33' X 55 = 400 watts. By (65), p. 107: P A = 30,000 + 9300 -f 400 = 39,700 watts. By (79) P- T2 5' S A = 134 X 7t X 2 X (36 + 10) = 38,700 sq. inches. Ratio of pole area to radiating surface: 144-g- X 7t X 32 X .70 _ 10,200 _ . 3 8, 7 op ~ 38,700 ~~ hence by (81), with the iise of Table XXXVI., p. 127: and by (63), p. 106: r' ft = (i + .004 X 45) X .00183 = .00216 ohm, at 6o C. [NOTE. For the calculation of the hysteresis loss in toothed armatures, Dr. Max Breslauer 1 gives a more accurate expres- sion, consisting of two terms, P\ -\- P' f h ; the former, P'^ , rep- resenting the loss in the solid portion of the core, and the latter, P" h , the loss in the teeth only. While P' h is obtained from (73) by inserting for M the weight of the solid portion, the second term, P\ , is the hysteresis loss in the teeth, due to 1 " On the Calculation of the Energy Loss in Toothed Armatures," by Dr. Max Breslauer, Elektrotechn. Zeitschr., vol. xviii. p. 80 (February II, 1897); Electrical World, vol. xxix. p. 325 (March 6, 1897). 59 2 DYNAMO-ELECTRIC MACHINES. [140 the smallest density (in the largest section, at the periphery of the armature) multiplied by a factor, a, which depends upon the ratio, of minimum to maximum width of tooth, and upon the shape of the slot, ranging as follows: TABLE CVL FACTOR OF HYSTERESIS Loss IN ARMATURE TEETH. RATIO OP MINIMUM TO FACTOR a OP HYSTERESIS Loss IN ARMATURE TEETH. MAXIMUM WIDTH OP TOOTH, *L* Rectangular Circular ** Slot. Slot. 5.00 21.00 0.05 3.75 13.00 .1 3.04 8.75 .2 2.47 5.34 .3 2.10 3.77 .4 1.83 2.90 .5 1.61 2.25 .6 1.44 1.81 .7 1.30 1.51 .8 1.19 1.30 .9 1.09 1.14 1.0 1.00 1.00 The hysteresis loss in the mass of the teeth, however, ordi- narily is only a small fraction of the total hysteresis loss, P h , of the armature, and the total hysteresis loss in well-designed machines is so small compared with the C 2 ^-loss that the dif- ference in the total energy loss due to the use of the above method amounts to but a few per cent., and that, therefore, in the majority of practical cases such a refinement in the calcu- lation is unnecessary. Thus, in the present example, which is chosen to illustrate the above statement, because in it the difference between the approximate and the exact methods, on account of the great 140] EXAMPLES OF GENERATOR CALCULATION. 593 mass of the teeth about n cubic feet is near its maximum amount, the hysteresis loss in the solid portion of the arma- ture core is: P\ = 18.1 x 9-33 X (65 - n) = 7450 watts. Minimum density in teeth: 188,000,000 188,000,000 2 x .70 x (144*- rx 2 9 j- x .9 ('44 * - 3f = 55,000 lines per square inch; Hysteresis factor for this density: 77 = 19.21 watts per cubic foot Ratio of minimum to maximum width of tooth: '371 X n V* 336 = -^ = .545. J t 144 X n LI 336 Tooth-factor, by interpolation from the above table : * = i.53; hence, hysteresis loss in teeth: .-. P\ = 19.21 x 9-33 X ii X 1.53 = 3000 watts. The total hysteresis loss, therefore, theoretically accurate, is P h = 7450 + 3000 = 10,450 watts. This is about 12^ per cent, greater than the value found on p. 591 (JP h = 9300 watts), while the increase in the value of P due to this difference amounts to about 3 per cent, only.] b. DIMENSIONING OF MAGNET FRAME. i. Total Magnetic Flux and Sectional Area of Frame. By (156), p. 214: <' = 1.15 x 188,000,000 = 216,000,000 maxwells. By (218), p. 339: Scs = Jte222 = 2540 square inches. 05,000 594 D YNA MO-ELECTRIC MA CHINES. [140 2. Cores. The length of the polepieces being 32 inches (equal to length of armature core), and their circumferential width being jdSO I44-J X sin -- = 20 inches, the core section must be so dimensioned that the projecting strip of the polepiece has the same width both in. the lateral \ Fig. 359- Dimensions of Armature and Field Magnet Frame, 2000 KW, i6-Pole, Radial Outerpole Type, Low-Speed Generator. and in the circumferential directions; making this uniform width of the polepiece-shoulder 3^- inches, see Fig. 359, the total actual cross-section of the cores becomes: S"'c* = 8 X 2 5 X J 3 = 2600 square inches. Length of cores, by Table LXXXIIL, p. 321: / m = 16 inches. 3. Polepieces. Bore: ^ P X 144 + 2 x ~ = 144$ inches. Distance between pole-corners: X sin 3| = 8} inches. 140] EXAMPLES OF GENERATOR CALCULATION. 595 Radial thickness, in centre, If inch; at ends, i \ + (72^ -- \/75iV - io 2 ) = 2$ inches. 4. Yoke. Making the yoke of same width as the armature core, its radial thickness is: h = 5 inches. 16 X 32 In order to secure a straight seat for the cores and to allow room for the flanges of the magnet-coils, bosses of ^ inch ra- dial height must be provided at the internal periphery of the yoke, making the external diameter of the frame, Fig. 359, + 2 x (il + 16 + H + 5) = 191 i C. CALCULATION OF MAGNETIC LEAKAGE. i. Permeance of Gap -Spaces. A == ^j^ - i = i-35 - - 2 5 = LI inch; b\ = & inch. Ratio of radial clearance to pitch: Product of field-density and conductor-velocity: 35,000 x 42.8 = 1,500,000. By Table LXVIL, p. 230: 12 = i. 60. From Table LXVI., p. 225, for a corresponding perforated armature, k lz 1.20. Average factor of field deflection: i. 60 -f 1.20 ^t_ _ = , 40 . 59 6 DYNAMO-ELECTRIC MACHINES. [ 14Q By (l75), P- 230: 3, _ j(i44| X 7t X .70 + 1-29 X 336 X .76) X \ (32 + 31) 1.40 X (i44l - 144) = ^=3190. .-. --" 2. Permeance of Stray Paths. By (181), p. 233: - 3 X (16.8+ I4 ,> 19+ 13 X- -248. From Fig. 359: 3> 3 = 16 X 2i * 3 * = 16 X 9 = i From Fig. 359: 2< = g x ( 33 X 20) - (, 5 X -3) = 3. Leakage Factor; Total Flux. By (i57), P. 218: ^ _ 3190 -f 248 + 144+ i5 8 _ 374Q _ ^ 3190 3190 By (158), p. 218: A' = 1.025 X 1.17 = 1.20. .-. $' = 1.20 x 188,000,000 = 260,000,000 maxwells. d. CALCULATION OF MAGNETIZING FORCES. i. Shunt Magnetizing Force. No-load flux: X 5 6 40 x X 7 o' = M*00000 maxwells. Air gap ampere-turns: <*'g a = .3133 X T8 4 000 > 000 x 2>55 = 28, 800 ampere-turns, 5100 140] EXAMPLES OF GENERATOR CALCULATION. 597 Armature ampere-turns: - + 3t /" a = i 3 oj x n X -^-^ --- h 6J + 2 X 3i = 30 inches. 184,000,000 t 184,000,000 fc - 6 3>ooo, (B % - __- = 3 . . at &o = * 4 ' 5 "'" 5' X 30 300 ampere-turns. Magnet core ampere-turns: 1.20 X 184.000,000 .. H 2 + ^V ^.7 inches (see Fig. 359); ., 1.20 x 184,000,000 ,. . , (B v = - = 86,300 lines per square inch; yi o 16 X 5 X 32 i. 20 X 184,000,000 y 2 i6 X 8.7 X 32 = 49>6 P6r SqUarC mC Length of magnetic circuit in yoke (Fig. 359): I", = l -^-? - 6* + S = 36 inches; .. a/ yo = -1 - x 36 = 1060 ampere-turns. Total shunt magnetizing force: AT sh = 28,800 -}- 300 + I 4 I + X 3 + I0 6 = 31,700 ampere-turns. 2. & Magnetizing Force. Full-load flux: ^ = 188,000,000 maxwells. Air gap ampere-turns: at g = .3133 X ' 000>0 ? x 2.55 = 29,600 ampere-turns, 598 DYNAMO-ELECTRIC MACHINES. [ Armature ampere-turns, see pp. 590 and 597: at & 10.4 X 30 310 ampere-turns. Magnet core ampere-turns: _ 1.20 X 188,000,000 _ ( * m ~ 2600 . . at m = 49 X 32 = 1570 ampere-turns. Polepiece ampere-turns: = i.ao X 188,000,000 = oo ,. nes P l 2600 i. 20 X 188,000,000 .. . , (B = ! = 22,100 lines per square inch; P 2 10,200 .. af p = 49 ' 5 ' 4 X 5^ = 27.2 X 5^ = 150 ampere-turns. Yoke ampere-turns: ~ ff _ 1.20 X 188.000,000 _ 8 yi " 16 X 5 X 32 1.20 X 188,000,000 .. . , " = = 50,700 lines per square inch; 16 X 8.7 X 3 2 .*. aty = - X 36 = 32 X 36 = 1150 ampere-turns. Compensating ampere-turns: For (&" p = 75,000 (corresponding to m' f = 27.2), Table XCL, p. 352, gives *ii= 1-25. Maximum density in teeth: n 188,000.000 B * " i X .70 X (137} X n - 136 X H) X 2 9 X .9 188,000,000 = ^~ = 100,000 lines per square inch. looO For this density, the brush-lead coefficient is found, from Table XC, p. 350: ^8= -55* the value being taken near the upper limit, on account of the low conductor velocity. By (250), p. 352, therefore: ??6 X 6 X 3700 .cc X ^4 at r = 1.25 X ** 7 X ^ ^ ^ = 6000 amp. -turns, 10 1 80 Total magnetizing force required at full load: AT = 29,600 + 310 + 1570 -j- 150 + 1150 + 6000 = 38,780 ampere-turns. 140] EXAMPLES OF GENERATOR CALCULATION. 599 And the required series excitation: AT** 38,780 31,700 = 7080 ampere-turns. C. CALCULATION OF MAGNET WINDING. Rise of temperature, m = 37^ C. Percentage of Regulating Resistance, i\ = i. Series Winding. / T = 2 x (25 + 13) + 3^ X n = 87 inches. S* = 2 X (25 X + 13 + 3i X n) X (16 - -I) = 1460 square inches per core. Connecting all the 16 series coils in parallel, the current flow- ing in each will be: / 6e = = 231.25 amperes, and the number of series turns required on each core, two- magnets being in series in each magnetic circuit, l ~ X 7080 ^V 8e = = 16 turns. 231-25 By (343)> P- 4oo: l - X 38,780 X 231.25 X 87 *-' : = 6s x : 1460 x 37^ < (I + - 004 X 37i> = 532,000 circular mils. Using a iQ-wire cable, the area of the wire required is : 532,000 - = 28,000 circular mils. The nearest gauge wire is No. 8 B. W. G. (.165" + .010'% making a cable-diameter of 5 X (.165 + .010) = .875 inch. The winding depth available accommodates -ji- = 4 layers 600 DYNAMO-ELECTRIC MACHINES. [140 of this cable; hence there are required: - 4 turns per layer, 4 and the axial length of the series coil is 4 X .875 3 inches, leaving for the shunt coil a length of 1 6 \ 3^ = 12 inches. By (344), P. 400: Joint resistance of all series coils: = .000147 ohm at 15.5* C. 1U Total weight, bare: wt^ = 16 X 16 X X 19 X .0824 = 2910 pounds, or 182 pounds per core. 2. Shunt Winding. Grouping all the 16 shunt coils in series, the gauge of the shunt wire must be: I (3i,7oo) A 8h = X X 1.20 X (i + .004 X 37i) ~ X540 = 4690 feet per ohm. No. 5 B. W. G. wire (.220" -f .012') has 4688 feet per ohm, and therefore gives the required resistance. By (346), p. 400: ^ S h = y~- X 1460 231.25" X .00235 X (i + .004 X 37i) = 730 143 = 587 watts. By (312), p. 383: ^"sh = 587 X 1.20 = 705 watts per magnet. 140] EXAMPLES OF GENERATOR CALCULATION. 60 1 Jy (314), p. 383: j (3i,7oo) X ^ X 540 = 760 turns per core. Number of turns in one layer: 12 .232 Number of layers required: = 51; -15. Winding space taken up: 15 X .232 = 3j inches. B y (315), p- 384: Ah = 51 X 15 X = 5540 feet per core. Total weight, bare : wt^ 16 x 5540 X .1465 = 13,000 IDS., or 812 Ibs. per core, Total resistance: r sh = 16 X 5540 X .0002128 = 18.9 ohms, at 15.5 C. By (318), p. 385: r' sh = 18.9 X (1.004 X 37t) = 21.7 ohms, at 53 C. By (317), P. 384: /' sh = 21.7 X 1.20 = 26 ohms, entire shunt circuit. ,'. 7 sh 5-_ 20.8 amperes, shunt current, at normal load Actual magnetizing force : = 2 x 16 X 231.25 = 7,500 ampere-turns. ^r sh = 2 x 51 x 15 x 20.8 = 31,800 " Total exciting power: AT 39,300 ampere-turns. 602 DYNAMO-ELECTRIC MACHINES. [ 14D e. CALCULATION OF EFFICIENCIES. 1. Electrical Efficiency. B y (353)> P- 4o6: 540 X 3700 540 X 3700 + (372Q.8) 2 X .00216 -}- 37oo 2 X .000147 + 20.8 2 X 26 2,000,000 -. _. = - = .978, or 97.8 %. 2,043,300 2. Commercial Efficiency. By (361), p. 408: 2,000,000 2,000,000 ~. rf c = -- 2 =- = .947, or 94.7 #. 2,043,300 + 97 + 60,000 2,113,000 3. Weight- Efficiency. The weight of this machine is estimated as follows: Armature: Core, 55 cubic feet of wrought iron, . 26,500 Ibs. Winding and insulation, connections, etc., 12,000 " Commutator, ..... 15,000 " Skeleton pulley, spider frames, shaft, etc., 16,500 " Armature, complete, .... 70,000 Ibs, Frame : Magnet-cores, 16 X 13 X 25 X 16 = 83,200 cubic inches of cast steel, . 23,000 Ibs. Yoke 186 x TT X 32 X 5 = 93,500 cubic inches of cast steel, . . . 26,000 " Polepieces, 16 x 20 x 32 X 1} = 18,000 cubic inches of cast steel, . . . 5,000 " Field-winding, spools, and insulation, . 20,000 " Supporting lugs, flanges and bosses on frame, outboard bearing, etc., . . 16,000 < < Frame, complete, 90,000 Ibs. [141 EXAMPLES OF GENERATOR CALCULATION. 603 Fittings: Brush-shifting and raising devices, brushes and holders, etc., . , . . 4,000 Ibs. Switches, connections, cables, etc., . 1,000 " Fittings, complete, . . . .'',/ 5,ooolbs. Total net weight of dynamo, . . 105,000 Ibs. Weight efficiency; 2,000,000 t > - = 12.1 watts per pound. 165,000 141. Calculation of a Multipolar, Consequent Pole, Perforated King, High-Speed Shunt Dynamo: 100 KW. Fourpolar Iron Clad Type. Wrought-Iron Cores, Cast-Steel Yoke and Polepieces. 200 Volts. 500 Amps. 600 Revs, per Min. (Calculation in Metric Units.) a. CALCULATION OF ARMATURE. i. Length of Armature Conductor. From 15: ft l .70, From Table IV., p. 50: ^ = 3.8 x lo" 5 volt per metre per bifurcation. From Table V., p. 52: v c = 24 metres per second; From Table VII., p. 54: 3C = 3850 gausses; From Table VIII. , p. 56: ' = 1.04 x 200 = 208 volts. By (26), P . 55: 2 X 208 X io~ 5 L & = ^ - f 5 =118 metres. 3.8 x 24 X 3 8 5 604 DYNAMO-ELECTRIC MACHINES. [ 141 2. Sectional Area of Armature Conductor. By (28), p. 57: ( & =- ~ - - = 22.3 cm. Minimum and maximum cross-section: 5 61 = 4 X 23 X 10 X .88 = 810 cm 2 . 5 62 = 4 X 23 X 22.3 x .88 = 1810 cm 8 . Maximum and minimum densities: 8.120,000 810 8. 1 20,000 .. lmes P er cm ; .. 6r C i8io Mean specific magnetizing force: 6.1 -4- 2. i m & = - - = 4.1 ampere-turns per cm. Average density corresponding to m & = 4.1, from Table LXXXIX., p. 337: (B a = 8100 gausses. 7. Weight and Resistance of Armature Winding. By (53) P- 99: ^ = 2 (23 + 10) + 5 X n x iig = 42Q m By 28, p. 101: o/4 = .0089 X 8 a X * X 420 = 188 kg. 4 By (62), p. 105: ^ X 420 x ( '~' ) = .0089 ohm, at 15.5 C. .017 \ _ ' x -/ ~ 4X2 V8- X - 4 8. Energy-Losses in Armature, and Temperature Increase. By (74), p. 114: 65.5 X 7t X 23 X 15 X .88 128 X M l = 1,000,000 .0615 cbm. Frequency: 600 N^ = -- x 2 = 20 cycles per second. 141] EXAMPLES OF GENERATOR CALCULATION. 607 By Table XXX., p. 115 ( A = 2670 + 773 + 67 = 3510 watts. By (79), p. 125: ^S'X 5 i-2X5 X7rX2X(23 + I5 + 3X5) = 20,000 cm 2 . Ratio of pole area to radiating surface: 81 X n X 23 X .70 _ 20,000 From Table XXXVI, p. 127: <>'> = 41 C. By(8i), p. 127: Armature resistance, warm, by (63), p. 106 : r' a = .0089 X (i + .004 X 42) = .0104 ohm, at 57.5 C. b. DIMENSIONING OF MAGNET FRAME. i. Total Flux through Magnetic Circuit, and Sectional Areas of Frame. By (156) and Table LXVIII. : ' = 1.30 X 8,120,000 = 10,500,000 maxwells. 6o8 DYNAMO-ELECTRIC MACHINES. By Table LXXVL, p. 313: [ 141. and 10,500,000 _ I4>ooo 2. Magnet Cores. Each of the two magnet cores carries two , K-230," 1 /* im m / Fig. 361. Dimensions of Field-Magnet Frame, IOO-KW Fourpolar Iron- Clad Generator. of the four magnetic circuits, Fig. 361, hence the magnet, diameter: For a flux of 5,250,000 maxwells passing through each core, Table LXXXIL, p. 320, gives. 75 as the ratio of length to diameter, consequently 4 = -75 X 22 = 16,5 cm. 3. Polepieces.lhz radial clearance, from Table LXL, p. 209, being about 5 mm., the bore is: d v = 810 + 2X5= 820 mm. Pole distance: / p = 820 x sin 13! = 190 mm. 141] EXAMPLES OF GENERATOR CALCULATION. 609. Pole chord: h v = 820 x sin 31 y = 4:25 mm. Thickness in centre, 22 mm. ; at ends, 2 o + - - = 80 mm. 4. Yoke. Only one magnetic circuit passes through the yoke-section; for a breadth of 23 cm., equal to length of armature core, therefore, the thickness of the yoke is: 810 h y = - - = 9 cm. 4 X 23 Length over all (Fig. 361): 820 + 2 x (20 -f 165 + 90) = 1370 mm. Height of frame: 820 -f 2 x 90 = 1000 mm. C. CALCULATION OF MAGNETIC LEAKAGE. i. Permeance of Gap- Spaces. For v c X 3C = 24 X 3 8 5 = Table LXVI., p. 225, gives *u = 1-22; therefore, by (176), p. 230: (82 X.7 + 8i X .8)X 23 220 - 1.95 X (82 - 81) - a 2. Permeance of Stray Paths. By (165), p. 223, and (185), p. 237: <$ ^ (16.5 + 38.5) X (22 TT + 23 + 2 X 9) _ 3 + .3 X 22 By (196), p. 243: 4 2.5 X (8+ 2.2) _ E 3 2 X " - ~ 1 I 19 + 42.5 X - 6 io DYNAMO-ELECTRIC MACHINES. [_ By (204), p. 247 : 2 X /42-5 X 23 -22 2 *) 3 = 4^(8X23) V 4/ = n(K 19.75 16.5 3. Probable Leakage Coefficient, and Total Flux. By (157), p- 218: 1800 -}- 166 -j- 17 -f-iio 2093 11/5 A r o I.IO. By (158) p. 218, and Table LXV. : A' = 1.04 x 1.16 = 1.20, . . $' = T.2o x 8,120,000 = 9,750,000 maxwells. d. CALCULATION OF MAGNETIZING FORCES. 1. Air Gaps. Actual density: 8,120,000 30 ~ 2200 = 3<59 Busses. Magnetizing force: at g .8 x 3690 x 1.22 = 3600 ampere-turns. 2. Armature Core. By (237), p. 343, T + ^ l" & = 61 x ar X ^ - + 10 + 2 X 5 = 5i cm. Magnetizing force: at & = 4. i x 51 = 210 ampere-turns. 3. Magnet Cores. 0,7^0,000 (Bri = - = 12,800 gausses. 2 X 22* - 4 Magnetizing force: #/ wi 13.8 x 21 = 290 ampere-turns. 141] EXAMPLES OF GENERATOR CALCULATION. 611 4. Polepieces. Density at junction with cores: so - 9*750,000 ^PI - - = 12,800 gausses; 2 x 22* - 4 Density at poleface: ^ _ _ 8,120,000 ^pa - = 3940 gausses, -X 81.6 x n X 23 x .70 By (241), p. 346, and Table LXXXIX. : m 9 -^ 2 = 8.77 ampere-turns per cm. Corresponding average density: (B p = 10,750 gausses. Length of circuit in polepieces, see Fig. 361: / p = 10 cm. Magnetizing force: at p = S.Tj X 10 = 90 ampere-turns. 5. Yoke. m cs =11.1 ampere-turns per cm.; / c . s . = 90 cm. (Fig. 361). Magnetizing force: .-. 0/ cs = 1 1. 1 x 90 = 1000 ampere-turns. 6. Armature Reaction. For& p = 10,750 gausses, Table XCL, p. 352, gives 14 = 1.25, Maximum density in iron projections: - 8 - 120 ' 000 - =, 5> 700 gausses, - X .70 X (72.2 X 7t 128 X 1.2) X 23 X.88 for which Table XC., p. 350, gives an average coefficient of brush lead of > 13 = .4. 6l2 DYNAMO-ELECTRIC MACHINES, [ 14L Hence by (250), p. 352: , /r = x . 25 x 5I2 X X '-= 2400 ampere-turns. 4 i oo 7. Total Magnetizing Force Required. Summing up we have: AT = 3600 -f- 210 -}- 290 -(- 90 -{- 1000 -j- 2400 = 7590 ampere-turns. ' ^sh = -g = 2.35 amperes. Actual magnetizing force: AT 86 x 38 x 2.35 = 7670 ampere-turns. Weight per coil, bare: wt^ = ' sh 1000 17.8 being the weight, in kilogrammes, of 1000 metres of cop- per wire, of 1.6 mm diameter. CHAPTER XXX. EXAMPLES OF LEAKAGE CALCULATIONS, ELECTRIC MOTOR DESIGN, ETC. 142. Leakage Calculation for a Smooth Ring, One- Material Frame, Inverted Horseshoe Type Dynamo : 9.5 KW " Phcenix " Dynamo. 1 105 Yolts. 90 Amps. 1420 Keys, per Min. a. PROBABLE LEAKAGE FACTOR (FROM DIMENSIONS OF MACHINE). i. Permeance of Air Gaps. From Fig. 362, which shows the principal dimensions of this machine, its gap area is obtained: ~l * * r + n| X * X I -^- \ X 9 = I2 5 square ins. The useful flux (see below, 142, ., i, p. 616): $ = 2,600,000 maxwells, therefore the field density: . 2,600,000 3C = - - = 20,800 lines per square inch. The conductor velocity being ii X 7t 1420 # c = - - x ? = 68 feet per second, the product of density and speed is OC" X ^ c 20,800 X 68 = 1,415,000, for which Table LXVI., p. 225, gives a factor of field deflec- tion: k^ = 1.30. 1 Silvanus IP. Thompson, " Dynamo-Electric Machinery," fourth edition, p. 416 and Plate V. 614 142] EXAMPLES OF LEAKAGE CALCULATION. Hence, by (167), p. 226: <% = I2 5 1^_ ._ 12 o ' 1.30 X (n|- io|)-. 9 7 5 - 2. Stray Permeances. By (i77), P- 232: Fig. 362. 9.5 KW Phoenix Dynamo. (192), p. 241: 10 X 9 2 X 93 X- (7 + 4A) The projecting area of the yoke, at each core is: / 6 i \ -S -- ( ~ -f 2 I x 9 = 47-25 square inches, hence, by (202), p. 246, 616 DYNAMO-ELECTRIC MACHINES. [142 3. Probable Leakage Factor. By (157), P. 218: \ - 128 + 9.6 + io.6 + 7. 9 _ 156.1 _ ~~ "- 1 '^' & ACTUAL LEAKAGE FACTOR (FROM MACHINE TEST). 1. Total Magnetizing Force of Machine. The dynamo is compound-wound, having a series resistance of .021 ohm, and a shunt resistance of 39.76 ohms: its armature resistance is .04 ohm. Therefore, the total current generated: /' = 90 -] -- ^- = 92.65 amperes, and the total E. M. F. : ' = 105 -f 92.65 X .04 + 9 X .021 = 110.6 volts. There are 180 conductors on the periphery of the armature, hence by (138), p. 202: - 6 X 110.6 X io 9 = - - = 2,600.000 maxwells. 1 80 X 1420 The magnet winding consists of 108 series and 3454 shunt turns, and the two series coils are connected in parallel, the two shunt coils in series to each other, consequently: AT^ 108 X -- = 4860 ampere-turns, -and AT^ = 3454 X 2.65 = 9140 ampere-turns; making the total actual exciting power: AT 4860 -f 9140 = 14,000 ampere- turns. 2. Magnetizing Force Required for Magnet Frame. OC" = 20,800 (p. 614); l\ ='.975 (p. 615); .'. af e = .3133 X 20,800 x .975 = 6350 ampere-turns. / a = 9 inches; b & = i T 9 ^ inches; 00 lines per square inch, 6i8 DYNAMO-ELECTRIC MACHINES. 143 from which, by formula (210), p. 259, follows the total mag- netic flux: #' = 66 x 50,000 = 3,300,000 maxwells. The actual leakage coefficient, consequently, from (214), p. 262, is: The probable leakage factor computed from the dimensions of the frame has, on page 616, been found A = 1.22, which is 4 per cent, below the actual value. 143. Leakage Calculation for a Smooth Ring, One- Material Frame, Double Magnet Type Dynamo i 40 KW "Immisch " Dynamo. 1 690 Volts. 59 Amps. 480 Revs, per Min. a. Probable Leakage Factor. (From Fig. 363). Fig. 363. 40-KW " Immisch " Dynamo. By (167), p. 226: ~ 2 4) - == >-- = 267. 1 For data of this machine see Gisbert Kapp's " Transmission of Energy,' 5 third edition, p. 272. 143] EXAMPLES OF LEAKAGE CALCULATION. 619 By (194), p. 242: F(54+ 16) X TO + 4 X 16 16 X 7J . 2Xi6T_ ~^~ f rt+T* 4 ~9T-l~ Hence, by formula (157), p. 218, in which for the present type 2j, $ 2 , and ^ 4 are zero, b. Actual Leakage Factor. The armature is wound with 760 turns of No. 9 B. &S. wire, resistance .36 ohm; the field winding consists of 984 series turns (No. 4 S. W. G.) per core, two coils in parallel, joint resistance .25 ohm. B y (9), P. 37: E' = 690 -f 59 (.36 -f .25) = 690 + 36 = 726 volts. B y (138), p. 202: . 6 x 726 x io 9 7 6o X 480 ^ ">oo,ooo maxwells. By (i39)> P- 202 ' 12,000,000 .. . , 3C ; -- = 23,100 lines per square inch. By (228), p. 339: at -3 T 33 X 2 3 IO X 1.95 = 14, 100 ampere-turns. By (232), p. 341: ,S" ai = 2 X (16 2) X 4j X .865 = 109 square inches By ( 2 33), P- 34i: _ S" & , = 2 X (16 - 2) X 41 X y ^ - i X .865 = 230 square inches. By (231), P. 341: 290 -}- 10.2 m a = - - - = 150 ampere-turns per inch. 620 DYNAMO-ELECTRIC MACHINES. [ 143 B y (236), P. 343: l\ = i 9 x n X 9 " iy ^ + 4i = 22} inches. P- 34o: at & = 150 x 22} = 3400 ampere-turns. The angle of lead was measured to be about 20, therefore by (250), p. 352: at r = 1.40 X 760 X ^ X -^ = 35 ampere'-turns. The total magnetizing force of the machine is: AT = 984 x = 29,000 ampere-turns. The frame is all wrought iron, having a uniform cross-sec- tion of S m = 10 x 1 6 = 1 60 square inches, and the length of each circuit in the frame is: l" m = 75 inches. Hence we have: 75 X m" m = 29,000 (14,100 + 3400 + 3500) = 8000 ampere-turns. from which: 8000 . , m m = - - = 106.7 ampere-turns per inch. Consulting Table LXXXVIIL, p. 336, we find: 0' (B" m = = 102,000 lines per square inch; 160 or, the total flux: $' = 160 x 102,000 = 16,400,000 maxwells. m ^ _ 16,400,000 _ j g 12,000,000 The probable leakage factor found, In this case, is about 3 per cent, smaller than the actual one. 144] EXAMPLES OF LEAKAGE CALCULATION. 621 144. Leakage Calculation for a Smooth Drum, Com- bination Frame, Upright Horseshoe Type Dynamo: 200 KW "Edison "Bipolar Railway Generator. 1 500 Tolts. 400 Amps. 450 Revs, per Min. a. Probable Leakage Factor. (From Fig. 364). [H&^j ^AREA OFlBEDPLATE OPPOSITE FIELdS = 625 8Q. INS. Fig. 364. 200-KW " Edison " Bipolar Railway Generator. B y ( J 67), P- 226: <$ = X n X * X X 34 1.30 x B 7 (178), P. 232: 2 ~~ 2 X i2| + 1.5 X 25 - 2 3 J) 2.52 = 451' 1 For description see Electrical Engineer, vol. xiii. p. 321 (March 23, 1891); Electrical World, vol. xix. p. 220 (March 26, 1892). 622 DYNAMO-ELECTRIC MACHINES. [ 144 By (188), p. 239: (199), p- 2 X 3 1 + ( 2 6 + 2l)X - By (i57), P- 218: A = 45* + 38-7 + 60.9 + 16.5 = 567.1 = 45 1 45 * " A Actual Leakage Factor. The total E. M. F. generated, by considering the losses in armature and series field windings, is found: E' = 520 volts; and there are 228 conductors on the armature periphery; there- fore by (138), p. 202: 6 = 3 >5 00 > 000 maxwells. x 450 . . 3C" = = 27,000 lines per square inch. By (228), p. 339: at g = .3133 X 27,000 x 2.52 = 21,300 ampere-turns. By (232) and (233), p. 341: S"' ai = 2 x 34i X 8| x .85 = 502 square inches. S\ = 2 X 34} X 8f x -x ~ J X .85 = 665 sq. ins. Therefore: ,, 30,500,000 , 30, c;oo,ooo = ~ " ~ and by (231), p. 341: 13-2 + 8.6 m ' = = 10.9 ampere-turns per inch. 2 By (236), p. 343: l\ = i5i X n x 9 ~ 2 ^ + 8f = 23.9 inches. ~ 144] EXAMPLES OF LEAKAGE CALCULATION. 623 By (230), p. 340: at & = 10.9 X 23.9 = 260 ampere-turns. By (25), p- 352: at r '=2.15X114 X 4 t 3 ' 6 X?g 7000 ampere-turns. The magnet winding consists of about 8000 shunt turns and of 46 series turns. The shunt-circuit has a resistance of 139 ohms, making the shunt field current at normal load soo 7 sh = | = 3.6 amperes; hence, the total magnetizing force actually exciting this machine at full load: AT = 8000 X 3.6 -{- 46 X 400 = 47,200 ampere-turns; and by (207), p. 258: at m = 47,200 (21,300 -j- 260 + 7000) = 18,640 ampere-turns. The section of the cores is: S" m = 2 5 a X - = 490-9 square inches; 4 and that of the yoke : S" y = 25 x 21 = 525 square inches; the resultant area in wrought iron, therefore, can be taken at about S ff w . L = 500 square inches. The cross-section at centre of polepieces is: 34^ x ill 45 s i uare inches, and the vertical cross-section is: 34^ X 26 = 885 square inches. Increasing the minimal area by one-third of the difference between the maximum and minimum area, we obtain: *S"' ct = 405 -| 5 "" 4 ^ = 565 square inches, 624 DYNAMO-ELECTRIC MACHINES. [ 145 which we will take as the resultant area of the circuit in cast iron. The lengths of the magnetic circuit are: in wrought iron, /" w .i. = 120 inches; in cast iron, /" ci =36 inches. By (213), p. 261, we consequently have the equation: 120 x #/" w ,i. + 36 X /" o4 . = 18,640, which is satisfied by ^' = 37>5 00 > 000 > for, by employing this value of $', we obtain: 0' 37,^00,000 ' = 75>oo; w .i. = 24.7; fiv = _ = 37^000 ^ 66j3Qo; ^ therefore, the left member of the above equation becomes: 120 X 24.7 + 36 X 436 = 2960 + 15,700 = 18,600, which is practically identical with the actual number of ampere- turns. Hence, the actual leakage factor: A= 3y ' 5 ' 000 = 1.28. 30,500,000 In this instance, the probable value obtained is about 2^ per cent, in excess of the actual value. 145. Leakage Calculation for a Toothed Ring; One- Material Frame, Multipolar Dynamo : 360 KW "Thomson-Houston" Fourpolar Railway Generator. 1 600 Tolts. 600 Amps. 375 Revs, per Min. a. Probable Leakage Factor. (From Figs. 365 and 366). Effective total length of armature conductor: Z e = 90 x 4 X - 5 X 2 X Q 82 = 683 feet. 12 I oO J This machine, but bored for a 48-inch armature, is used in the power station of the West-End Railway Company of Boston, Mass. ; for description s&s Electrical Engineer, vol. xii. p. 456 (October 21, 1891). 145] EXAMPLES OF LEAKAGE CALCULATION 625 Conductor velocity: ' = 620, The total E. M. F. is Figs. 365 and 366. 36o-KW Thomson-Houston Fourpolar Railway Generator, hence, by (144), p. 205: 2 X 620 x io 8 50 = 72 x 683 x 70 = 3 ' per square ' . . v X 3C" = 70 X 36,000 = 2,520,000. Ratio of radial clearance between armature and field to pitch of slots: '553 therefore, by Table LXVL, p. 225: 12 = 1.4, and by Table LXVIL, p. 230: k n = 2.2\ average: k iz =. 1.8. Hence, by (175), p. 230: -[45 X 7t + (1.24 + .094) X 90] X 2 * 82 X 25 3> _4 loo 1.8 X (45 - 44 B <5 26 D YNAMO-ELECTRIC MA CHINES. [ 145 By (181), p. 233: , / \ Ir X - + 14 X 12! = 69.5 + 43 = 112.5. By (197), p- 243: = 132-5- i ._ 1656 + 112.5 + i3 2 -5 _ '9 01 _ -I6s6- -1656- ' IS ' Ratio of width of slot to pitch : if : 1-553 = -5 2 3- for which Table LXV., p. 219, gives a factof of armature leakage of Aj= 1.05; hence, the total probable leakage coefficient: A' = 1.05 x 1.15 = 1.21. b. Actual Leakage Factor. The machine is compound-wound, having 16,600 shunt am- pere-turns and 5500 series ampere-turns on each magnet; the total exciting power per circuit, two coils being magnetically in series, therefore, is: AT = 2 x (16,600 + 5500) = 44,200 ampere-turns. By (228), p. 339: af g = -3 X 33 X 36,000 x .9 = 10, 140 ampere-turns. y (232), P. 341: S' ; ai 4 x 9f X 25 x .85 = 828 square inches 145] EXAMPLES OF LEAKAGE CALCULATION. 627 _ 515,000,000 ' ' ai ~ 828 - 66 ,5 lln es per square inch. By (233), P. 341: S"^ = 4 X ^ X 25 X .85 = 1252 square inches. 55,000,000 .. . . (B a2 = -- - - = 44,000 lines per square inch. By ( 2 3i)> P- 34i: 18.6 -f 8.4 a = - = 13.5 ampere-turns per inch. By (236), p. 343: S T+< t l\ = 31* X n X 36o +9f + g X if = 26J inches. By (230), p. 340: 04 =13.5 X 26 J = 360 ampere-turns. The shunt current is 16 amperes, and the angle of brush lead, by measurement, about 5, hence by (250), p. 352: 616 5 04 = 2 x 360 x X %- = 3100 ampere-turns. 4 ioo The magnetizing force left for the magnet frame, con- sequently, is: at m = 44,200 (10,140 -|- 360 -(- 3100) = 30,600 ampere-turns. The magnet frame is of cast iron; each circuit has a length of /" m = 90 inches; the total cross-section of the cores is: 2 X 22 X 25 = i ioo square inches, and that of the yokes : 4 x i2j X 25 = 1250 square inches. Taking S" m =1125 square inches as the resultant sectional area, the value of #' is found as follows: 90 X *"m = 30,600; 628 D YNAMO-ELECTRIC MA CHINES. [ 146 m" m = 3 ? = 340 ampere-turns per inch; 90 (B" m = - - = 62,500 lines per square inch; >' = 1125 x 62,500 = 70,500,000 maxwells. The useful flux is: a X 6 X620X io 9 = ss 000,000 maxwells, 360 X 375 consequently, the actual leakage factor: ^, _ 70,500,000 _ i <)8 55,000,000 The formula for the probable leakage factor, for this ma- chine, gave a value of 5j per cent, below this actual figure. 146. Calculation of a Series Motor for Constant Power Work: Inverted Horseshoe Type. Toothed-Drum Armature. Wrought-Iron Cores and Polepieces, Cast-Iron Yoke. 25 HP. 210 Yolts, 850 Keys, per Min. a. Conversion into Generator of Equal Electrical Activity. Assuming- a gross efficiency of 93 per cent, and an electrical efficiency of 95 per cent, (see Table XCIX., p. 422), the elec- trical energy active in the armature of the motor is, by (382), p. 420: P' = 746 X 25 = 20,000 watts. 93 and the E. M. F. active, by (383), p. 421: ' = 210 X -95 = 200 volts; hence, by (384), p. 421, the current capacity: j, _ 20,000 200 which, in the present case of a series motor, is also the current intensity to be supplied to the motor terminals. 146] EXAMPLES OF MOTOR CALCULATION. 629 Intake of motor, by (381), p. 420: P t = - = 21,000 watts. b. Calculation of Armature. According to 146, #, the armature has to be designed to give a total E. M. F. of 200 volts and a total current of 100 amperes, at a speed of 850 revolutions. For the reason ad- vanced on p. 63, a toothed armature with its projections highly saturated at full load is chosen. In order to obtain high efficiencies at small loads, the armature, as explained in 116, must overpower the field, and therefore a low conductor velocity and a small field density must be taken: fi i .75; e = 62.5 x io~ 8 volt; v c = 40 feet per second; 3C" = 20,000 lines per square inch. ^ (26), p. 55: Z a = - _ ^-X^! _ = 400 feet. 62.5 X 40 X 20,000 By (27), P. 57: # a 2 300 X TOO = 30,000 circular mils. 2 No. 8 B. & S. (.i28 ff + .016") have 2 X 16,510 = 33,020 cir- cular mils area. By (30), p. 58: d\ = 230 X -]= iif inches - Approximate size of slot, by Table XV., p. 70: rx*r. 12 No. 8 B. & S. wires, arranged in 6 layers (see Fig. 368) with .020* slot-lining give a slot, tt'xtt'. Making the pitch y 2 inch, the number of slots is obtained, Fig. 367: nj X 7t * = *-T = 74- 630 DYNAMO-ELECTRIC MACHINES. [ Hence, by (40), p. 76: and by (138), p. 202: -64- 7. Figs. 367 and 368. Dimensions of Armature Core, 25-HP Inverted Horseshoe Type Series Motor. making the maximum density in the teeth at full load: ^ _ 3, i 80, OOP _ * ~ = ' ~7 - \ /9U<^ - fj ) X 74 X io X .90 X ilS V 74 / 2 = 130,000 lines per square inch. The shape-ratio of the armature core is: therefore by Table XXIV., p. 96: Z f = 2.90 X 400 = 1160 feet; whence: wt & = .00000303 X 33,020 X 1 1 60 = 116 Ibs. and " = - X 1160 x .000626 = .092 ohm, at 15.5 C. 4X2 146] EXAMPLES OF MOTOR CALCULATION'. 63 r c. Energy Losses in Armature, and Temperature Increase. Shaft diameter, by (123), p. 185: , */2o,8oo * = 1.3 X /*/ - = 3 inches; internal diameter of discs: 3J inches. S" ai = (pj 3^) x io| X .90 = 61.7 square inches, ^"ajj = JI i X 10} X .90 = 113.5 square inches. ' ' = 3 -^T = 5I ' soo; *'* = 3j ir = 28 ' ooo; m" & = I0 "*" 5 ' T = 7.5 ampere-turns per inch. Average density: (B" a = 40,000 lines per square inch. By (72), p. 112: M = 3*) X * X 4|-74X H XfjJxiofX - 1728 = .427 cubic inch. N l = ~ = 14. 2 cycles per second. By (68), p. 109: P & = 1.2 X 104* X .092 = 1194 watts. By (73), P. "2: A = 1^-55 X 14-2 x .427 = 70 watts. By (76), p. 120: /% = .046 X 14- 2 a X .427 = 4 watts. By (65), p. 107: P A = 1194 + 70 + 4 = 1268 watts. By (78), p. 125: ^ = n| X n X [iof + 1.8 X (.5 X iif + 2 X H)l = 913 square inches. 632 DYNAMO-ELECTRIC MACHINES. Ratio of pole area to radiating surface : nfl X n x i of- X .75 [ 146 for this ratio, and for v c = 40 feet per second, Table XXXVI., p. 127, gives: '. = 44 C, hence a = 44 x ^ = 61 C. .-. r' & = .092 X (i + .004 x 61) = .115 ohm, at 76.5 C. d. Dimensioning of Magnet Frame. In order to secure a small excitation, the density in the wrought iron is taken : (B" wi _ = 75,000 lines per square inch; Fig. 369. Dimensions of Magnet Frame, 25 HP Inverted Horseshoe Type Series Motor. and that in the cast iron: "c.i. 30,000 lines per square inch. $' = 1.20 x 3,180,000 = 3,820,000 maxwells. 3,820,000 S ', = = 51 square inches. 75,000 146] EXAMPLES OF MOTOR CALCULATION. 633 = 3,820,000 = 30,000 square inches. Cross-section of cores, rectangle, $y x 5^", between two semi-circles of 5^" diameter; (Figs. 369 and 370): 5 1 + 5i a X ~= 50.5 square inches. .k ------ ax-"- ..... >i Fig. 370. Joint of Magnet Core and Yoke, 25 HP Inverted Horseshoe Type Series Motor. Length of cores, by Table LXXXIIL, p. 321 : 4i = 71 inches. Cross-section of yoke: 15" X 8}^ (= 127.5 square inches). Core projection, rectangular: zoj X 2-J X 8J. Area of contact of same with yoke, Fig. 370: (zof -f 2 X 2f ) X 8 + ^^ = 160 square inches. Polepieces: d v = ll l + 2 x 4 = 12 inches. /' p = 12 X sin 22 J = 4J inches. * e = .295 X 23.33 a X .355 = 57 watts. ^ = 290 + 363 + 57 = 710 watts. 5 A = 2 X 12 x TT X (6| + 3 + 4 X i) = 780 sq. inches. r' a = .021 x (i + .004 x 38) = .024 ohm, at 53.5 C. d. Dimensioning of Magnet Frame. $' = 1.15 x 3,500,000 = 4,025,000 maxwells. = 4,025,000 = 96 square inches> 42,500 Breadth of cores: = 15 inches. 6 I 640 DYNAMO-ELECTRIC MACHINES. [147 Breadth of polepieces: 15! X sin 72 = 15 inches. These two dimensions being equal, no separate polepieces are required, and the frame may be cast in one piece, as shown, in Fig. 371. Fig. 371. Dimensions of Armature Core and Field-Magnet Frame, I5-HP Bipolar Iron-Clad Type Shunt Motor. e. Calculation of Magnetizing Forces. at g = .3133 X 26,008 x 1.2 X f = 7320 ampere-turns. at & 98.4 x 14 = 1380 ampere-turns. at m = ioi X 83 = 8300 ampere-turns. at, = i. 80 X I44 X I0? X ~ = 1400 ampere-turns. 2 loO A T = 7320 -j- 1380 -f- 8300 -}- 1400 = 18^400 ampere-turns, /. Calculation of Magnet Winding. Since the motor is not intended for continuous work, a high increase, m = 40 C., is permitted. Regulating resistance, at full load, r x = 23 per cent. Height of winding space, estimated: 2^ inches. A- = 2 (6| + 15) + 2\ x n = 50 inches. 147] EXAMPLES OF MOTOR CALCULATION. 641 18,400 50 8h = i 2 g X 77 X I>2 3^ V 1 + -4 X 40) = 874 feet per ohm, corresponding to No. 13 B. W. G. (.095' -j- .010"). SK = 2 X (6| + 15 -f 2j ?r) X 2 x 8 = 1000 sq. inches. P' sh = X 1000 X 1.23 = 655 watts. N Kh = I8>4 5 * 125 = 350() turn ^ tota ^ Qr 175Q per cor ^ Number of turns per layer: = 80 ; .095 -\- .010 Number of layers required : !252 = 22. 80 Depth of magnet winding: ft' m = 22 x (.095 + .010) = 2.32 inches. Z sh = 2 x 80 x 22 x -^ = 14,650 feet. T'sh = I4 Q >65 = 16 75 ohms, shunt resistance, at 15.5 C. 574 T-'sn = 16.75 x (i 4- -004 x 40) 19.45 ohms, shunt resistance, at 55.5 C. r"& = 19.45 X 1.23 = 23.9 ohms, res. of entire shunt-circuit, at full load. 7 sh = ~^- = 5.23 amperes, shunt current, at normal load Total actual magnetizing force : AT = 2 x 80 x 22 x 5.23 = 18,400 ampere-turns. Total weight, bare: = I Al5 _ 4QQ j bs or goo Ibs. per core. .0419 642 DYNAMO-ELECTRIC MACHINES. [147 g. Speed Calculations. E. M. F. consumed by armature winding: 107 x .024 = 2.6 volts. E. M. F. active in armature : E' = 125 - 2.6 = 122.4 volts. Torque: r = XI 'i 4 x 107 x 144 X 3,500,000 = 63.3 foot-pounds. Specific generating power: * - I22 " 4 x 6 = 5.25 volts. 1400 Speed, at any voltage, E : A-. = 60 x (^ - 8. 52 x - M4 5 * 5 fr 3 ) = n.48 J - 28. For E 125: N^ 1428 28 = 1400 revs, per minute. " E = 110: N^ = 1256 28 = 1228 revs, per minute. " E 100: -AT = 1142 28 = 1114 revs, per minute. h. Calculation of Current for Various Loads. Current for full load, by (392), p. 428: j, _ 125 Vi25 a 4 x .024 X (746 X 15 + 200 ) 2 X .024 = 107 amperes. Current for load : i 2 5 - /i/ I2 5 2 - 4 X .024 x (746 X 15 X - A + 2000) /' = - z- - _ -- 2 X .024 = 40 amperes. Current for ^ load : 125 "~ \l I2 5 3 - 4 X .024 x (746 X 15 X - + 2000) /'= - L _ I _ 2 X .024 = 63 amperes. 147] EXAMPLES OF MOTOR CALCULATION. 643 Current for load : I2 5 - /I/ 125" - 4 X .024 x (746 X 15 X ^ + 2000) ji _ r 4 2 X .024 = 86 amperes. Current for 25 per cent, overload: 7 , _ 125 V\2$* 4 X .024 X (746 X 15 X ij + 2000) 2 X .024 = 126 amperes. Current for 50 per cent, overload : j, _ 125 - V~i2^ 4 X .024 X (?46~X 15 X ij + 2 X .024 = 159 amperes. Current for maximum commercial efficiency, by (393), p. 429: /' = 4/535 + *ooo + /SJV 8 _ 535 = ^Q V .024 \ I2 5/ I2 5 from which follows that the maximum commercial efficiency is obtained at about five times the normal load. Current for maximum electrical efficiency, by (394), p. 429: = 145 amperes, .024 \i25/ 125 which corresponds to about ij times the normal load. i. Calculation of Efficiencies. Electrical efficiency, at normal load: I2 2.4 X 107 107" X .024 5.23' x 19-45 122.4 X 107 = 4 13,100 i3 Commercial efficiency, at normal load : _ 122.4 x 107 (107' x .024 + 535 + 35 2 + 2000) 7/0 ~ 13,100 13,100 644 DYNAMO-ELECTRIC MACHINES. [ Commercial efficiency at f load: 122.4 X 86 - (86 8 X .024 + 2887) 7455 % " 122.4 X 86 10,520 Commercial efficiency at load: 122.4 X 63 - (6 3 8 X .024 + 288 7) _ 4738 A1 ^ ~~ 722.4 X 63 ~ Commercial efficiency at load: _ 122.4 X 40 (40" X .024 + 2887) 1975 77 C - - .:rU 122.4 X 40 4900 Commercial efficiency at 25 per cent, overload: - *22-4 X 126 - (i 2 6 a X .024 + 2887) _ 12,153 _ 122.4 x 126 15,420 Commercial efficiency at 50 per cent, overload: - 122.4 x 159 - (159' X .024 + 2887) 16,006 122.4 X J59 i " In this case the efficiencies at overload are higher than the normal load efficiency. 14:8. Calculation of a Compound Motor for Constant Speed at Varying Load : Radial Outerpole Type. 4 Poles. Toothed Ring Armature. Cast-Steel Frame, 75 HP. 440 Volts. 500 Revs, per Min. a. Conversion into Generator of Equal Electrical Activity. P' = 60,000 watts (by Table XCIX., p. 422). E' = 440 .045 x 440 = 420 volts. .., 60,000 fl . / = - - = 143 amperes. 420 b. Calculation of Armature. # .70; e 55 x To~ 8 volt p. ft. ; z> c = 65 feet p. sec. ;. 3C" = 30,000 lines per square inch. T 2 X 420 X TO 8 A = - -7- - = 785 feet. 55 X 65 x 30,000 tf a a = 400 x 143 = 57,200 circular mils. EXAMPLES OF MOTOR CALCULATION. 645 4 No. ii B. W. G. wires (.120*4- .016"), have an actual area of: 4 X 14? 400 = 57,600 circular mils. d\ = 230 x = 29$ inches. 500 For this diameter, Table XV., p. 70, gives a slot of 1 1 X T V inch; actual slot for 36 No. n B. W. G. wires, see .Fig. 372, is 1-J-J- inch deep and J* inch wide. Fig. 372. Dimensions of Armature-Slot, 75 Fourpolar Compound Motor. Number of slots: 785 112 X = 9i inches. 3 6 6 x 2 X 420 X io 9 = - = 10,000,000 maxwells. 112 x 9 X 5 10,000,000 a 4 X 105,000 X 9i X .875 " ai = 105,000 lines; (B"a 2 = 4,5 lines; m'\ ~ 37 1~ / ampere-turns per inch. 646 DYNAMO-ELECTRIC MACHINES. [ 148 Average density: (B" a = 96,000 lines per square inch. o/4 = 2540 X 4 X .0436 = 4:4:2 Ibs. bare wire. r & = - X 2540 X .000717 = .114 ohm at 15.5 C. 4X4 c. Energy Losses in Armature, and Temperature Increase. M= (27 X TT X 4 T V " *H X tf X 112) X 9i X .875 1728 = 1.44 cubic foot. rOO N^ = X 2 = 16.67 cycles per second. P & = 1.2 X i43 s X .114 = 2800 watts. /> h = 46.85 X 16.67 X i.44 = 1120 watts. P e = .0665 X i6.67 3 X 1-44 = 30 watts. /> A 2800 -f- 1 1 20 -f 30 = 3950 watts. S; = 27 X *X 2 x (9i + 2j+ittX it = 3000 square inches. e a = 4 i X = 54 C. 3000 r' & = .114 X (i + -004 X 54) = .139 ohm, at 69^ C. d. Dimensioning of Magnet Frame. (Fig. 373.) $' = 1.20 x 10,000,000 - 12,000,000 maxwells. Width of frame (equal to length of armature core) : 9j- inches. Breadth of cores: 12,000,000 . = 8 inches. 2 X 80,000 X Thickness of yoke: 12,000,000 = 4 inches. 4 X 80,000 X Length of cores: / m = 7 inches. Breadth of polepieces: X sin 31^ = 16 J inches. 148J EXAMPLES OF MOfOR CALCULA TION. 647 Distance between pole-corners: /( P = 3 2 iV X sin 13 p = 7J inches. e. Calculation of Magnetizing Forces. The E. M. F. at no load being, E Q 440 volts, and that at full load being E' = 440 143 X .139 X 1.25 = 415 volts, the shunt winding is to be calculated to supply the total mag- netizing force necessary to produce 440 volts, and the series Fig. 373. Dimensions of Magnet Frame, 75 HP Fourpolar Compound Motor. winding, in order to regulate for constant speed at all loads, must provide the difference between the magnetizing forces required for 440 and 415 volts, respectively, and must be con- nected so as to act in opposition to the shunt winding. {Dif- ferential winding. ) Magnetizing Force Required at No Load : _ 6 x_ 2 x 44 X io' = maxwells. 112 X 9 X 500 2 X 440 X io 8 $0 = 72 X 112 X 9 X 12 = 29,500 lines p. sq. in X.8o x 65 X v c = 29,500 X 65 = 1,920,000. = 42 ' 5 648 DYNAMO-ELECTRIC MACHINES. [ 148 Ratio of clearance to pitch : 3i T V X n _ = .28. 112 From Table LXVIL, p. 230: k lz = 1.90; ... at gQ = .3133 X 29,500 X i X 1.90 = 9000 ampere-turns 10,500,000 -V, = 4 X 9 | X k X .875 IO, COO.OOO & \ = 4 X 9i X 7t X .875 200 + 8 .. at & = -- - X 20 = 3000 ampere-turns. 1.2 X 10,500,000 .. (B" mo = -- 2 x 8 X oi = 3 ' per S( l uare inch > . ^/ m = 36.1 X 60 = 2200 ampere-turns. .-.^(T^^ 9000 X 3000 + 2200 = 14,200 ampere-turns. Magnetizing Force required at Full Load. ^ = 6 X 2 x 415 X io 9 = 9 maxwe lis. 112 X 9 X 500 3C" = 29,500 X = 27, 800 lines per square inch; 44 .-. at e = .3133 X 27,800 x I X 1.90 = 8200 ampere-turns, (B" ai = 103,700 lines; (B"a 2 = 40,000 lines; .. at & = I22 '5 "t" 7-5 ^ 20 _ j^ 00 ampere-turns. (B" m = 78,300 lines per square inch; . -. at m 29.3 X 60 = 1750 ampere-turns. / r = 1.25 X 112 X 9 X X * 4 X I3ir = i35oamp.-turns. 4 loo .-. AT 8200 -|- 1300 + 1750 + 1350 = 12,600 amp. -turns. Magnetizing Force for Series Differential Winding. AT S& AT AT Q 12,600 14,200 = - 1600 amp. -turns. 148] EXAMPLES OF MOTOR CALCULATION. 649 As seen from the above, the armature reaction, by increas- ing the excitation needed for full load, in a motor reduces the difference between full load and no load magnetomotive force; and by properly adjusting the magnetizing forces required for the various portions of the magnetic circuit, the difference be- tween the ampere-turns required to overcome the reluctances of the circuit at no load and full load, respectively, can, indeed, be brought within the amount of the armature reactive ampere-turns, so that no series winding at all is needed for regulation, the armature-reaction (which may have to be made extra large for this purpose, either by widening the polepieces or in giving the brushes a greater backward lead) taking its place. In the present machine, this can be achieved by increas- ing the radial depth of the armature core from 2%" to 3-J", whereby the average specific magnetizing force is reduced to m\ Q = 29.5 ampere-turns per inch at no load and to m" & = 23.5 ampere-turns per inch at full load, making the corresponding magnetizing forces at^ 590 ampere-turns and at & = 470 ampere-turns, respectively. Substituting these figures for those in the above calculation, the total exciting power at no load is found AT = 11,790 ampere-turns, and at full load AT 11,770 ampere-turns. The remaining small difference of 20 ampere-turns is negligible, and we have then a self- regulating shunt-motor of practically constant speed for all variations of load. /. Calculation of Magnet Winding. Series Winding. N SQ = =12 turns per magnetic circuit, J 43 or 6 turns per core. Allowing 1000 circular mils per ampere, and taking 2 cables of 7 wires each, the size of each wire is: 6\ = I0 2 X I43 = 10,200 circular mils, or No. 10 B. &S. (.102"). 650 DYNAMO-ELECTRIC MACHINES. [ 148 Assuming h m 4 inches, twelve cables of 3 x (.102" -f- .008") = .33 inch diameter will just fill the winding space, and but one layer, axially, is therefore required. / T = 2 x (8 + 9 J) + 4 X n = 47| inches, tt'/ge = 12 X 14 X -^ X .0315 = 21 Ibs. per pair of cores, or 42 Ibs. total. r se = 12 x X '- - = .0034 ohm per pair of magnets, at 15-5 C. Shunt Winding. For fl m = 25 C., and r x = 45$. Connecting all four shunt coils in series, the potential across a pair of coils is 220 volts, and the size of the wire required: +.004X35) = 408 feet per ohm, which is the specific length of No. 16 B. W. G. wire (.065" -f- .007"). Allowing y of the length of the core for width of bobbin flanges, the radiating surface of one pair of shunt coils is: S* = 2 X (8 + 9i + 4 X 7f) X 2 X (7i - i) = 870 square inches. P * - 1~ X 8 7 - I43 2 X .0034 X (i + .004 X .25) = 290 77 = 213 watts. />' 8h = 213 x 1.45 = 309 watts. Allowing \ inch for the series winding and its insulation, the length available for the shunt winding is 6} inches, which holds :. 94 No. 16 B. W. G. wires; 148] EXAMPLES OF MOTOR CALCULATION. 651 hence, the height actually occupied by the shunt winding: ^m = - - X .072 = 54 x .072 3.89 inches. 2 x 94 = 2 x 94 X 54 X X .0128 = 512 Ibs. per pair of mag- nets, or 1024 Ibs., total. 12 x 49 r'& i9 6 X (i + .004 X 25) = 215.5 ohms, at 40.5 C. r"sh = 215.5 X 1.45 =312 ohms, entire shunt-circuit, at full load. / Bh = - - = 1.41 ampere, shunt current, full load. Actual magnetizing force at full load: AT = 2 X 94 X 54 X 1.41 - 12 X 143 = 14,300 - 1720 = 12,580 ampere-turns. g. Speed Calculations. Actual counter E. M. F. of motor at full load: E' = 440 143 x (.139 + .004) = 440 2o = 419J volts. Useful flux at full load : $ = 10,000,000 maxwells. Useful flux at no load : # o = 10,500,000 maxwells. Torque, at full load : r = iM4 x '43 X 1008 Torque, at no load (energy for overcoming frictions esti- mated at P = 5000 watts) : 11.74 cooo 1008 r = -^- X ^-X -^-X 10,500,000 ^ 71 foot-lbs. Specific generating power, at full load: 1008 tr 10,000,000 x - -X io~ 8 = 50.4 volts, 652 DYNAMO-ELECTRIC MACHINES. [149 at no load : 1008 e" 10,500,000 X - - Xio~ 8 = 52.9 volts. Speed, at full load : N, = 60 X 4 ^L- 8.52 X (*39 = 60 X (8.34 .0405) = 4:98 revolutions per minute. Speed, at no load : ^ 6o x __ 8 . 52 x . 5 2 -9 52-9 = 60 X (8.32 .0031) ~ 500 revolutions per minute. The difference in speed at full and no load being only 2 rev- olutions per minute, the condition of constant speed is fulfilled. 149. Calculation of a Unipolar Dynamo : Cylinder Single Type. Cast-Steel Frame. Cast-Iron Armature. 300 KW, 10 Yolts. 30,000 Amps. 1000 Revs. per Min. a. Diameter of Armature, Dimensioning of Frame, and Cur- rent Output. By (423), p. 447: 400 X \/ = 40 inches. The minimum diameter for the given voltage, by (426), p. 448, would be: <4 = 3-45 X 10 = 34^ inches, which would correspond to a maximum speed of N = .33 x = 1333 revolutions per minute. 10 The dimensions of the machine, by 118, are (see Fig-374): Length of field, by (409), p. 444: / = .3 x 40 = 12 inches. 149] EXAMPLE OF UNIPOLAR DYNAMO. Radial thickness of armature, by (412), p. 445: a .2 x 4/4o~= 1J inch. Radial distance of poles, by (413), p. 445: P = -25 X Vjo" = 1J inch. 653 Fig. 374. Dimensions of 300 KW Unipolar Cylinder Dynamo. 10 Volts. 30,000 Amps. 1000 Revs. Height of winding space, by (411), p. 444: 7* m = . i x 40 = 4 inches. Length of winding space, by (410), p. 444 4i = -125 X 40 5 inches. Thickness of yoke part of frame, opposite inner surface of exterior shell, by (414), p. 445 : ^ = .14 X 40 .042 X ^40 = 5| inches. Thickness of frame opposite bottom of winding space, by (415), p. 445: m -= -175 X 40 -f- .055 X V^o = 7| inches. Radial thickness of outer shell, by (416), p. 446: h y = .125 x 4 -03 X ^4 = 4| inches. 654 DYNAMO-ELECTRIC MACHINES. [149 Radial thickness of inner shell, by (417), p. 446: h Q = .26 X 40 + .23 X V^Q 12 inches. Total length of frame, by (418), p. 446: / F = .625 x 40 = 25 inches. Length of magnetic circuit in frame, by (419), p. 446: l" m = 1.2 x 40 = 4:8 inches. Current capacity, by (428), p. 448: /' = 125 x V4* = 30,600 amperes. b. Calculation of Magnetizing Forces. By (435), P. 45o: at^ 750 X V^ = 4740 ampere-turns. By (436), p. 45: dr/ a = 17.6 xV4 = no ampere-turns: B y (437), P- 45: at m = 53 x 40 = 2120 ampere-turns. Total magnetizing force: AT = 4740 -|- no + 2120 = 6970 ampere-turns. c. Calculation of Magnet Winding. By (438), p. 451: / T = 2.83 x 40 - .785 X ^40 = 108 inches. By (439), P- 45i: S* = .39 X 4o 3 -i X ^4o 3 600 square inches. By (440), P- 45 1: wt m .0074 x 40 s .002 x ^40^ = 453 Ibs. By (329), p- 390: 453 ~ -004 X [31-3 X (6. 97o X 9)' X 453 - 150J EXAMPLE OF DYNAMOTOR. 655 ;Size of wire, for 20 per cent, extra resistance: i ^97 ^ 8 h = -^ X 9 X 1.20 X (i + .004 x 39|) 8718 feet per ohm, or No. 1 B. W. G. (.300" + .020"). Number of wires per layer: = 12. .320 Number of layers: 4 .1 .320 Total length: Ah = 15 X 12 x 9 = 1620 feet. Resistance: r sh = 1620 X. 0001147 = .186 ohm, at 15.5 C. r' Bh = .186 x (i + .004 x 39i) = -215 ohm, at 55 C. r" sh = .215 x 1.20 = .254 ohm, entire shunt-circuit. ^sh = = 39.4 amperes. 2 54 Actual excitation: AT = 15 x 12 X 39.4 = 7080 ampere-turns. d. Weight- Efficiency. The weight of this machine, complete, will be in the neigh- borhood of 10,000 Ibs., thus making its weight-efficiency about 30 watts per pound. 150. Calculation of a Dynamotor : Bipolar Double Horseshoe Type. Cast-Steel Frame, Toothed Ring Armature. 5} KW. 1450 Revs, per Min. Primary: 500 Yolts, 11 Amps. Secondary: 110 Volts, 44 Amps. a. Ratio of Armature Turns ; Current Output of Secondary Winding. Electromotive forces active in armature: E\ 500 .064 x 500 = 468 volts, E' = no + .064 x no 117 volts, 656 DYNAMO-ELECTRIC MACHINES. [ 15O Ratio of number of armature turns: N^ _ , _ 468 #..-. 117 ~ Electrical activity in primary winding: E\ x /', = 468 x ii = 5150 watts. Current intensity of secondary winding: 7' a = . _ 44 amperes. . Calculation of Armature. /?, = .75; , ii| x ^ /o i , * =: 1T5<1I =68slots; One-half of the winding space being occupied by each winding, 34 slots of 24 wires constitute one winding. The secondary 150] EXAMPLE OF DYNAMOTOR. 657 winding requiring four times the area, 4 No. 16 wires in multiple form one secondary conductor. Making the primary commutator of 68, and the secondary of 34 divisions, the primary, or motor winding consists of 68 coils of 12 turns of 1 No. 16 B. W. G. ; and the secondary, or generator winding, of 34 coils of 6 turns of 4 No. 16 B. W. G. wires. Hence the length of the armature core: 2,240,000 b*. = - 9 Z-* - f - 24- inches. 2 X 85,000 X 6$ x .90 The length, weight, and resistance of the primary winding are, respectively: 7 r x 4 x 24 = 1355 12 wt &l = .00000303 X 4225 X 1355 = 17|lbs. r &l -i X 1355 X .00245 = .83 ohm, at 15.5 C. 4 The length of the secondary winding is one-quarter that of the primary, the weight is precisely the same, and the resist- ance is j times that of the primary, or 4 r & , = ^ = .052 ohm, at 15.5 C. c. Dimensioning of Magnet Frame. (Fig. 375.) $' 1.34 x 2,240,000 = 3,000,000 maxwells. ?. 000,000 ^ = 2 x 8^,000 = 17 ' 7 Square mCheS - Cylindrical cores being selected, their diameter is: 4 = y J 7-7 X I = 4| inches. 658 D YNAMO-ELECTRIC MA CHINES. Length of cores: Width of yoke: [150 / m =, 6J inches. 6 inches. Thickness of yoke : Bore of field: = 2} inches. \ = 42,500 lines; m\ = 39 ' 7 "*" =23.9 ampere- turns per inch. ., at & =23.9 x i if = 280 ampere- turns. /" m = 45 inches^ length of circuit in frame. "m = 85,000; m" m = 44 ampere-turns per inch (cast steel). ... r Mi 50.25 800 164 9 100 650 it; 25 150 450 18 | 264 200 450 M 34| second has a diameter of 68 inches and a length of 14 inches. The peripheral velocity in the first machine is v. = 5 -l^ X ^ = 37-3 feet per sec., 12 while in the second it is . = X = 44.6 feet persec. The length is f|, or |, of the diameter in the first armature, and |f, or about , of the diameter in the second armature. APPENDIX II. WIRE TABLES AND WINDING DATA. WIRE TABLES AND WINDING DATA. THE tables here compiled will be found useful in connection with dynamo calculation. Table CXV., on pages 676 and 677, gives the resistance per foot and per pound, the weight per ohm, and the length per ohm of pure copper wire at 20 C. (68 F. ), 6o Q C. (140 F.), and 100 C. (212 F.). The figures are substantially those adopted by the American Institute of Electrical Engineers upon the recommendation of the Committee on Standards, in 1893. The table is based on Matthiesson's standard of resis- tivity for soft copper, which is 1.5939 microhms per cu. cm. {i cm. length, i sq. cm. cross-section), corresponding to 10.32 ohms per mil-foot (i ft. length, * mil diameter, or i circular mil area), at o C. (32 F.). Specific gravity of copper wire, 3.90. The temperature coefficient of copper is taken as (i -f- .00388 /), in which / is the elevation of temperature in degrees C. The data are given for all sizes of the American, or Browne & Sharpe (B. 6 S.) gauge as well as of the Birming- ham wire gauge (B. W. G.). The wires are arranged accord- ing to size, so that the nearest standard gauge wire corre- sponding to any given resistance, weight, or length, can be obtained by referring to but one table. Table CXVL, page 678, gives the winding data for B. & S. and B. W. G. wires, when insulated for use as armature wires. In the first five columns the gauge numbers, diameters, sec- tional areas, and resistances of the sizes commonly employed are repeated for convenience; the sixth column, headed "Di- ameter of Insulated Wire," gives the diameter of the respec- tive wire when insulated with a double cotton covering (D. C. C.) which is the usual insulation on armature wires. The figures given in this column are in each case the maximum diameter of three samples of insulated wires furnished by dif- ferent manufacturers. The next two columns, Nos. 7 and 8, 675 TABLE CXV. RESISTANCE, WEIGHT, AND LENGTH: COOL SIZE op WIRE. at 20 C. (68 Fahr.) Gauge Number. Diameter. Area. Resistance. Weight. Length. B AS. B.W.G. Inches. Cir. Mils. Ohms p. Ib. Ohms p. ft. Ibs. p. ohm. Ibs. p. ft ft. p. ohm. feet p. Ib. 0000 .460 211,600 .0000764 .0000488 13,140 .6412 20,495 1.560 0000 .454 206,116 .0000802 .0000501 12,470 .6246 19,970 1.601 000 .425 180,625 .0001045 .0000571 9,570 .5472 17,500 1.827 000 .4096 167,772 .0001215 .0000615 8,260 .5084 16,250 1.967 00 .380 144,400 .0001634 .0000715 6,120 .4376 13,990 2.285 00 .365 133,225 .000193 .0000776 5,190 .4033 12,890 2.480 .340 115,600 .000255 .0000893 3,920 .3503 11,200 2.885 .325 105,625 .000307 .0000980 3,260 .3199 10,230 3.126 1 .300 90,000 .000421 .0001147 2,377 .2727 8,718 3.667 1 .289 83,521 .000488 .0001234 2,055 .2536 8,106 3.943 2 .284 80,656 .000524 .0001280 1,909 .2444 7,812 4.092 3 .259 67,081 .000757 .000154 1,320 .2033 6,497 4.919- 2 .258 66,564 .000776 .000156 1,290 .2011 6,428 4.973 4 .238 56,644 .001062 .000182 940 .1717 5,487 5.824 3 .229 52,441 .001235 .000196 813 .1595 5,098 6.270 5 .220 48,400 .001455 .000213 688 .1467 4.688 6.817 4 .204 41,616 .001960 .000247 510 .1265 4,043 7.905 6 .203 41,209 .00201 .000251 498 .1249 3,992 8.006. 5 .182 33,124 .00312 .000312 320 .1003 3,205 9.970 7 .180 32,400 .00325 .000319 308 .0982 3,138 10.135 8 .165 27,225 .00460 .000379 218 .0825 2,637 12.12 6 .162 26,244 .00496 .000393 202 .0795 2,542 12.57 9 .148 21,904 .00710 .000471 141 .0664 2,122 15.06 7 .1443 20,822 .00789 .000496 127 .063' 2,017 15.85 10 .134 17,956 .01060 .000575 95 .0544 ,739 18.38 8 .1285 16,512 .01255 .000625 80 .0500 ,600 19.98 11 .120 14,400 .0164 .000717 61.0 .0436 ,395 22.91 9 .1144 13,087 .0200 .000730 503 .0397 ,268 25.21 12 .109 11,881 .0242 .000869 414 .0360 ,151 27.78 10 .1019 10,384 .0316 .000994 31.6 .0315 1.006 31.78 13 .095 9,025 .0418 .001144 23.9 .0274 874 36.56 11 .0907 8,226 .0505 .001255 19.9 .0249 797 40.11 14 .083 6,889 .0718 .00150 13.9 .0209 667 47.89 12 .0808 6,529 .0802 .00158 12.5 .0198 633 50.53 13 15 .072 5,184 .1275 .00200 7.9 .0157 502 63.65 16 .065 4,225 .191 .00244 5.24 .0128 409 78.13 14 .0641 4,109 .203 .00251 4.95 .0125 398 80.32 17 .058 3,364 .301 .00307 3.32 .0102 326 98.04 15 .0571 3,260 .323 .00317 3.12 .00988 316 101.2 16 .0508 2.581 .513 .00400 1.96 .00782 250 127.8 18 .049 2,401 .591 .00430 1.69 .00728 233 137.4 17 .0453 2,052 .815 .00505 1.24 .00622 199 160.8 19 .042 ,764 1.095 .00585 .91 .00535 171 187.0 18 .0403 ,624 1.296 .00636 .77 .00492 157 203.0 19 .0359 ,289 2.05 .00801 .49 .00391 125 256 20 .035 ,225 2.27 .00843 .44 .00371 119 269 20 21 .032 ,024 3.25 .01010 .31 .00310 99.2 322 21 .0285 812 5.17 .0127 .19 .00246 78.7 406 22 .028 784 5.54 .0132 .18 .00238 75.9 421 22 .0253 640 8.32 .0161 .12 .00194 62.0 516 23 .025 625 8.73 .0165 .115 .00189 60.5 528 23 .0226 511 13.06 .0202 .077 .00155 49.5 646 24 .022 484 14.54 .0213 .069 .00147 46.9 682 24 25 .020 400 21.30 .0258 .047 .00121 38.8 825 25 26 .018 324 32.45 .0319 .0308 .000982 31.4 1,019 26 27 .016 256 52.00 .0403 .0192 .000776 24.8 1,289 27 28 .014 196 88.7 .0527 .0113 .000594 19.0 1,684 29 .013 169 i 119.3 .0611 .0084 .000512 16.4 1,952 28 .0126 159 135.1 .0650 .0074 .000481 15.4 2,078 30 .012 144 164.3 .0717 .0061 .000436 14.00 2,291 29 .0113 128 209.0 .0808 .0048 .000387 12.40 2,584 30 31 .010 100 341.0 .1032 .00293 .000303 9.69 3,300 31 32 .009 81 520 .1275 .00193 .000246 7.85 4,073 32 33 .008 64 832 .1613 .00120 .000194 6.20 5,155 33 34 .007 49 1419 .2111 .000705 .000149 4.74 6,734 34 .0063 40 2164 .260 .000462 .000120 3.85 8,313 35 .0056 31 3465 .329 .000289 .000095 3.04 10,530 36 35 .005 25 5453 .413 .0001 3 .0000758 2.42 13,200 OF COOL, WARM, AND HOT COPPER WIRE. 677 WARM HOT SIZE OF WIRE. at 60 C. (140 Fahr.) at 100 C. (212 Fahr.) -Oauge Number. Resistance. Weight. Length. Resistance. Weight. Length. JB&S. B.W.G. Ohms p. Ib. Ohms p. ft. Ibs. p. ohm. ft. p. ohm. ohms p. Ib. ohms p. ft. Ibs. p. ohm. ft. p. ohm. 0000 .0000871 .0000558 11,480 i 17,920 .0000980 .0000629 10,200 15,910 0000 .0000917 .0000573 10,900 17,460 .0001033 .0000645 9,681 15,500 000 .0001195; .0000654 8M8 ,15,300 .0001346 .0000736 7,429 13,580 000 .0001385 .0000704 7,220 14,200 .0001560 .0000793 6,410 12,610 00 .000187 .0000818 5,350 12,230 .0002105 .0000921 4,750 10,860 00 .000220 .0000887 ! 4,539 11,250 .0002481 .0001000 4,031 10.004 .000292 .0001021 3,427 9,797 .0003287 .0001151 3,042 8,688 .000350 .0001118 2,857 8,945 .0003942 .0001259 2,537 7,943 1 .000481 .0001312 2,078 7,622 .000542 .0001478 1,845 6,766 1 .000557 .0001411 1,797 7,087 .000627 .000159 1,595 6,289 2 .000599 .0001464 1,669 6,831 .000675 .000165 1,482 6,064 3 .000866 .0001761 1,155 5,679 .000975 .000198 1,025 5.043 2 .000885 .0001780 1,129 5,618 .000997 .000200 1,003 4,990 4 .001215 .0002084 823 4,798 .001368 .000235 731 4,261 3 .001408 .0002244 710 4,456 .001586 .000253 631 3,956 5 .001664 .000244 610 4,098 .001874 .000275 534 3,639 4 .002237 .000283 447 3,536 .002520 .000319 397 3,139 6 .00230 .000287 436 3,490 .002586 .000323 387 3,099 5 .00356 .000357 281 2,802 .004010 .000402 249 2,488 f .00371 .000365 269 2,743 .004180 .000411 239 2,435 8 .00526 .000434 190 2,306 .00592 .000489 169 2.047 6 .00566 .000450 177 2,222 .00638 .000507 159 ,974 9 .00812 .000539 123 1,855 .00915 .000607 109 ,647 7 .00899 .000567 111 1,763 .01013 .000639 98.7 ,565 10 .0121 .000658 83 1,521 .01362 .000741 73.4 ,350 8 .0143 .000715 70 1,399 .01611 .000805 62.1 ,242 11 .0188 .000820 53.2 1,220 .02117 .000923 47.2 1,083 9 .0228 .000902 44.0 1,101 .02563 .001016 39.0 984 12 .0276 .000994 36.2 1,006 .03111 .001119 32.1 894 10 .0362 .001137 27.7 880 .04074 .001281 24.6 781 13 .0479 .001309 20.9 764 .05391 .001474 18.6 678 11 .0576 .001436 17.4 696 .06487 .001617 15.4 618 14 .0821 .001713 12.2 584 .0925 .00193 10.80 518 1 .0914 .00181 10.9 553 .1030 .00204 9.71 491 13 15 .1450 .00228 6.9 439 .1634 .00257 6.12 390 16 .218 .00280 4.58 358 .246 .00315 4.07 318 14 .231 .00288 4.33 348 .260 .00324 3.85 309 17 .344 .00351 2.91 285 .388 .00395 2.68 253 15 .367 .00362 2.73 276 .413 .00408 2.42 245 16 .585 .00458 1.71 219 .659 .00515 1.52 194 ' 18 .676 .00492 1.48 203 .761 .00554 1.31 181 17 .926 00575 1 080 174 1.043 .OOS48 .959 154 19 1.253 .00669 .790 149 1.411 .00754 .709 133 18 1.478 .00727 .676 138 1.665 .00819 .601 122 19 235 .00916 .426 1090 2.64 .01031 .379 97 20 2.60 .00964 .385 104.0 2.93 .01086 .342 92 20 21 3.72 .01153 .269 86.7 4.19 .0130 .239 77 21 5.91 .01454 .169 68.8 6.66 .0164 .150 61 22 6.34 .01506 .158 66.4 7.14 .0170 .140 59 22 9.52 .01845 .105 54.2 10.72 .0208 .093 48 23 9.9S .0189 .100 52.9 11.24 .0213 .0890 47 23 14 94 .0231 .067 43.2 16.83 .0260 .0594 38.4 24 16.63 .0244 .060 40.9 18.73 .0275 .0534 36.4 24 25 24.4 .0295 .041 33.9 27.44 .0333 .0364 30.1 25 26 37.1 .0365 .0269 27.4 41.81 .0411 .0239 24.4 26 27 59.5 .0461 .0168 21.7 67.00 .0519 .0149 19.3 27 28 29 101.4 136.5 .0603 .0699 .0099 .0073 16.6 14.3 114 154 .0679 .0787 .00876 .00651 14.7 12.7 28 154.5 .0744 .0065 13.4 174 .0838 .00574 11.9 29 30 188 239 .0820 .0925 .00530 .00420 12.20 10.80 212 269 .0923 .1042 .00472 .00372 10.80 9.60 30 31 390 .1181 .00257 8.47 439 .1330 .00228 7.52 31 32 594 .1458 .001680 6.86 669 .1643 .00149 6.09 32 33 33 34 952 1623 .1845 .2415 .001050 .000616 5-42 4.14 1,072 1.828 .2078 .2719 .000933 .000547 4.81 3.68 34 2475 .2975 .000404 3.36 2,788 .335 .000359 2.98 35 36 35 3964 6237 .3766 .4723 .000252 .000160 2.66 2.12 4,464 7,026 .424 .532 .000224 .000142 2.36 1.88 678 D YNA MO- EL E C TRIG MA CHINE S. TABLE CXVL DATA OP ARMATURE WIRE. (D.C.C.) 1 O ^ 6 .0 .: SIZE OP WIRE. 1* " 1 ' o" q ^ c5g & J ~ H 5 o . ft" 5 P "5 fi a, 2 . a 13 * Or** o 1 *o *o ^ "* OOQ " S v a 85, H. g T & *""" u, ^ *-> 2 a t n a ~ G o Gauge Number. Diameter. Area. 111 Is l| | ' .S -^ fc_ ^ B. &S. B.W.G. Inches. Cir. Mils. i B * *g |1| 1 .300 90,000 .0001147 .320 3.1 9.8 .279 .000094 1 .289 83,521 .OJ01234 .309 3.25 10.5 .260 .000107 2 .284 80,656 .0001280 .304 3.3 10.8 .250 .000116 3 .259 67,081 .000154 .279 3.6 12.9 .208 .000167 2 .258 66,564 .000156 .278 3.6 13.0 .206 .000169 4 .238 56,644 .000182 .258 3.9 15.1' .176 .000230 3 .229 52,441 .000196 .249 4.0 16.2 .164 .000267 5 .220 48,400 .000213 .240 4.2 17.4 .150 .000310 4 .204 41,616 .000247 .224 4.45 20.0 .130 .000415 6 .203 41,209 .000251 .223 4.5 20.2 .1285 .000423 5 .182 33,124 .000312 .200 5.0 25.0 .1030 .OOC651 7 .180 32,400 .000319 .198 5.1 25.5 .1010 .000680 8 .165 27,225 .000379 .183 5.5 30.0 .0852 .00095 6 .162 26,244 .000393 .180 5.6 31.0 .0821 .00106 9 .148 21,904 .000471 .164 6.1 37.2 .0685 .00147 7 .1443 20,822 .000496 .160 6.3 39.0 .0652 .00162 10 .134 17,956 .000575 .150 6.7 44.6 .0563 .00215 8 .1285 16,512 .000625 .145 6.9 47.5 .0518 .00249 11 .120 14.400 .000717 .136 7.4 54.2 .0454 .00325 9 .1144 13,087 .000789 .130 7.7 58.3 .0415 .00442 12 .109 11,881 .000869 .125 80 64.0 .0376 .00465 10 .1019 10,384 .000994 .117 8.5 73.0 .0331 .00607 13 .095 9,025 .001144 .110 9.1 82.8 .0289 .00792 11 .0907 8,226 .001255 .106 9.4 89.0 .0264 .00934 14 .083 6,889 .00150 .095 10.5 1105 .0220 .01383 12 .0808 6,529 .00158 .093 10.8 1156 .0208 .01526 13 15 .072 5,184 .00199 .084 12.0 145.2 .t)166 .02410 16 .065 4,225 .00244 .077 13.0 169.0 .0136 .0345 14 .0641 4,109 .00251 .075 13.3 177.8 .0133 .0373 17 .058' 3,364 .00307 .068 14.7 216.0 .0108 .0553 15 .0571 3,260 .00317 .067 14.9 222.8 .01050 .0590 16 .0508 2,581 .00400 .061 16.4 2687 .00835 .0896 18 .049 2,401 .00430 .059 17.0 289.0 .00780 .1038 17 .0453 2,052 .00503 .055 18.2 330.6 .00672 .1392 19 .042 1,764 .00585 .052 19.3 371.0 .00580 .1815 18 .0403 1,624 .00636 .050 20.0 400.0 .00533 .2124 19 .0359 1,289 .00801 .046 21.7 473.5 .00426 .3172 20 .035 1,225 .00843 .045 22.2 495.0 .00407 .3480 20 21 .032 1,024 .01010 .042 23.8 566.9 .00343 .4790 21 .0285 812 .0127 .039 25.7 660.0 .00276 .7375 22 .028 784 .0132 .038 26.3 692.5 .00266 .76-20 22 .0253 640 .0161 .035 28.6 876.3 .00221 1.0963 23 .025 625 .0165 .035 28.6 876.3 .00215 1.210 23 .0226 511 .0202 .033 30.3 918.3 .00179 1.555 24 .022 484 .0213 .032 31.3 980.0 .00170 1.746 24 25 .020 400 .0258 .030 33.3 1111.1 .00142 2.373 25 26 .018 324 .0319 .028 35.7 1276.4 .00117 3.436 26 27 .016 256 .0403 .026 38.5 1479.3 .00094 5.022 TABLE CXVIL DATA OP MAGNET WIRE. (S.C.C.) 1 71 0.2 bi SIZE OP WIRE. lo S.C.C. WIRE IN COILS WEIGHT. "o "o w > tat o .5 .S 21 S^-3 111 gs> Gauge Number Diameter. Area. o 3 g tH Nbr. ol Nbr. o Nbr. o Pounds Pounds isi u g o X l g Turns Layer Turns p. Foo p. Cu. Incl O oi O 1 'ai QO o o a B. AS. B.W.G Inches. Cir. Mils. 5 p. Inch. p. Inch p.Sq.In S.C.C. of Winding f^ P- 1 .300 90,000 .320* 3.1* 3.5* 10.8* .279* .251* 76.8#* .0001 03( 1 .289 83,521 .309* 3.25* 3.65* 11.8* .260* .256* 77.9 .000121' 2 .284 80,656 .304* 3.3* 3.7* 12.2* .250* .254* 77.6 .000180E 3 .259 67,081 .279* 3.6* 4.05* 14.5* .208* .247* 76.7 .000186J 2 .258 66,564 .278* 3.6* 4.1* 14.7* .206* -253* 76.9 .000190E 4 .238 56,644 .258* 3.9* 4.4* 17.1* .176* .251* 76.4 .000260C 3 .229 52,441 .249* 4.0* 4.5* 18* .164* .246* 74.7 .000296=1 5 .220 48,400 .240* 4.2* 4.7* 19.8* .150* .248* 75.6 .000353 s1 4 .204 41,616 .216 4.6 5.15 23.7 .129 .255 78.0 .000492 6 .203 41,209 .215 4.5 5.2 24.2 .128 .258 78.6 .00051 5 .182 33,124 .194 5.15 5.8 29.9 .103 .257 78.2 .00078 7 .180 32,400 .192 5.2 5.85 30.4 .100 .254 77.7 .00081 8 .165 27,225 .177 5.65 6.35 35.9 .0845 .253 77.2 .00113 6 .162 26,244 .172 5.8 6.5 37.8 .081 .257 78.3 .00124 9 .148 21,904 .158 6.3 7.1 43.7 .068 .248 75.5 .00172 7 .1443 20,822 .154 6.5 7.3 47.5 .0645 .255 78.1. .00196 10 .134 17,956 .144 6.95 7.8 54.2 .0556 .251 76.8 .00261 8 .1285 16,512 .139 7.2 8.1 58.3 .0512 .249 76.0 .00308- 11 .120 14,400 .130 7.7 8.65 66.5 .0447 .248 75.4 .00350 9 .1144 13,087 .124 8.0 9.0 72 0407 .244 72.6 .00475 12 .109 11,881 .119 8.4 9.45 79.5 0369 .245 74.5 .00577 10 .1019 10,384 .112 8.9 10 89 0324 .240 73.0 .00738 13 .095 9,02o .105 9.5 10.7 102 0282 .239 72.8 .00975 11 .0907 8,226 .101 9.9 11.1 110 0257 .235 71.3 .01154 14 .083 6,889 .090 11.1 12.5 139 0214 .248 75.7 .0173 32 .0808 6,529 .088 11.3 12.7 144 0203 .243 74.3 .0190 13 15 .072 5,184 .079 12.6 14.2 179 0162 .241 73.1 .0298 16 .065 4,225 .072 13.9 15.6 217 0132 .239 72.4 .0443 14 .0641 4,109 .071 14.0 15.7 220 0129 .237 71.6 .0462 17 .058 3,364 .065 15.4 17.3 266 0106 .235 70.7 .0683, 15 .0571 3,260 .064 15.6 17.5 273 01024 .233 70.3 .072 16 .0508 2,581 .058 17.2 19.3 332 00815 .226 67.5 .111 18 .049 2,401 .056 17.8 20 356 00760 .225 67.5 .128 17 .0453 2,052 .051 19.6 22 431 00645 .232 69.8 .181 19 .042 1,764 .W 21.2 23.8 504 00554 .233 70.3 .216 18 .0403 1,624 .045 22.2 25 555 00510 .236 71.1 .295 19 .0359 1,289 .041 24.4 26.8 654 00408 .223 66.5 .437 20 .035 1,225 .040 25 28.1 703 00387 .227 68.0 .495 20 21 .032 1,024 .037 27 30.4 821 00325 .223 66.3 .690 21 .0285 812 .034 29.4 33 970 00261 .211 62.1 1.030 22 .028 784 .033 30.3 34 ,030 00252 .216 63.8 1.134 22 .0253 640 .030 33.0 37 ,220 00206 .209 61.5 1.643 23 .025 625 .030 33.3 37.5 ,250 00202 .211 61.6 1.725 23 .0226 511 .028 35.7 40 ,430 00168 .200 57.7 2.415 24 .022 484 .027 37 41.6 ,540 00159 .204 59.0 2.750 24 25 .020 400 .025 40 45 ,800 00132 .198 56.6 3.88 25 26 .018 324 .023 43.5 49 ,130 001075 .191 54.5 5.67 26 27 .016 256 .021 47.6 53.5 ,550 000856 .182 51.5 8.60 27 28 .014 196 .019 52.6 59 ,100 000660 .170 48.0 3.62 29 .013 169 .018 55.5 62.5 ,470 000570 .165 46.3 7.70 28 .0126 159 .018 56 63 ,530 000538 .158 442 9.20 30 .012 144 .017 58.8 66.2 ,900 000488 .159 44.2 4.4 29 .0113 128 .016 62.5 70.3 ,400 000435 .160 44.3 29.6 30 31 .010 100 .015 66.7 75 ,000 000342 .1425 89.5 43.1 l * Double Cotton Insulation. 68o DYNAMO-ELECTRIC MACHINES. headed " Number of D. C. C. Wires per Inch " and "Number of D. C. C. Wires per Square Inch," respectively, are conven- ient for computing the number of conductors that can be placed on a given armature. By multiplying the available TABLE CXVIII. LIMITING CURRENTS FOR COPPER WIRES. SIZE OF WIRE. Usual Limit given by Fire Underwriters. Amperes. Current producing a Rise of 40 C. (72 Fahr.) Amperes. Current producing Smoking Point of Insulation. Amperes. B. & S. B.W.G. 0000 210 360 630 0000 206 352 6^6 000 186 316 552 000 177 298 519 00 159 263 464 00 150 246 438 135 220 396 127 206 372 1 113 182 335 1 107 172 319 2 104 167 311 2 3 90 144 273 4 80 127 248 3 76 120 237 5 72 114 220 4 6 65 104 207 5 54 90 178 7 51 87 170 8 47 80 158 6 46 78 155 9 41 70 138 7 40 68 134 10 35 61 130 8 33 58 127 11 30 54 114 9 28 52 107 12 26 49 97 10 24 46 87 13 22 42 80 11 20 40 75 14 18 35 67 12 17 33 65 13 15 14 30 56 16 13 27 50 14 12 25 48 circumference of the armature core by the number of wires per inch (column 7), the approximate number of wires per layer of the armature is obtained; and when the sectional area of the winding space is multiplied by the number of wires per WIRE TABLES AND WINDING DATA. 68 1 TABLE CXIX. CARRYING CAPACITY OF COPPER WIRES. CAPACITY, IN AMPERES, FOB CURRENT-DENSITY OF: SIZE OP WIRE. 1000 2000 3000 4000 5000 6000 Amps, per sq. in., or 1275 Amps, per sq. in., or 640 Amps, per sq. in., or 425 Amps, per sq. in., or 320 Amps, per sq. in., or 255 Amps, per eq. in., or 212 Cir. Mils Cir. Mils Cir. Mils Cir. Mils Cir. Mils Cir. Mils . &S. B.W.G. per Amp. per Amp. per Amp. per Amp. per Amp. per Amp. 0000 166 332 498 664 840 996 0000 162 324 486 648 810 972 000 142 283 425 567 708 850 000 132 263 395 527 658 790 00 113 227 340 453 567 680 00 105 209 314 419 523 628 - o 92 183 275 367 458 550 83 166 249 332 415 498 1 71 141 212 283 353 424 1 66 131 197 263 328 394 2 63 127 190 253 317 380 3 53 105.5 158 211 263 316 2 52 104.5 157 209 262 314 4 45 89 133.5 178 223 267 3 41 82 123.5 165 206 247 5 38 76 114 152 190 228 4 33 65 98 131 163 196 6 32 64.5 97 129 161 194 5 26 52 78 104 130 156 7 25.5 51 71.5 102 127.5 153 8 21.3 43 64 83 107 128 6 20.7 41 62 83 103 124 9 17.2 34 51.5 69 86 103 7 16.3 33 49 65 82 98 10 14.1 28 42 56.5 71 85 8 13.0 26 39 52 65 78 11 11.3 23 34 45 57 68 9 10.3 20 31 41 51.5 62 12 9.35 19 28 37.4 47 56 10 8.2 16 24.5 32.6 41 49 13 7.1 14 21.3 28.4 35.5 43 11 6.5 13 19.4 25.9 32.4 39 14 5.4 10.8 16.3 21.7 27.1 32.5 12 51 10.3 15.4 20.6 25.7 30.8 13 15 4.1 8.2 12.3 16.3 20.4 24.5 16 3.3 6.6 10.0 13.2 16.6 19.9 14 3.2 6.5 9.7 12.9 16.2 19.4 17 2.65 53 8.0 10.6 13.3 15.9 15 2.57 525 7.7 10.3 12.8 15.4 16 2.03 4.1 6.1 8.1 10.3 12.2 18 1.88 3.8 5.7 7.3 94 11.3 17 1.61 3.2 4.85 6.4 8.1 9.7 19 1.39 2.8 4.15 5.6 7.0 8.3 18 1.23 2.56 3.83 5.1 6.4 7.7 19 1.01 2.02 304 4.0 5.1 6.1 20 .96 1.82 2.89 3.8 4.8 5.8 20 21 .81 1.61 2.42 3.2 4.0 4.8 21 .64 1.28 .92 2.56 3.2 383 22 .62 1.24 .85 2.48 3.1 370 22 .50 1.00 .51 201 2.5 302 23 .49 .98 .48 1.98 2.45 2.95 23 .40 .80 .21 1.61 2.0 2.41 24 .38 .76 .14 1.42 1.9 2.28 24 25 .32 .62 .95 1.24 1.58 1.89 25 26 .26 .51 .77 1.02 1.28 1.53 26 27 .20 .40 .61 .81 1.01 1.21 27 28 .15 .30 .46 .61 .75 .92 29 .13 .26 .40 .52 .65 .80 28 .125 .25 .375 .50 .625 .75 30 .11 .22 .34 .44 .55 .68 29 .10 .20 .30 .40 .50 .60 30 31 .08 .16 .235 .32 .40 .47 682 D YNA MO-ELEC TRIG MA CHINES. square inch (column 8), the approximate total number of wires on the armature is found. The ninth column, headed "Weight of D. C. C. Wire, Pounds per Foot," serves to compute the weight of the armature winding, and the last column (No. 10), headed " Resistance at 20 C. per Cubic Inch of D. C. C. Wire," can be used to find the approximate resistance of the armature wire, and from this the armature resistance, if only the size of the wire and the dimensions of the winding space are given. In Table CXVIL, page 679, data similar to Table CXVI. are given for wires having a single cotton covering (S. C. C.) TABLE CXX. CARRYING CAPACITY OP CIRCULAR COPPER RODS. AREA OP ROD, CURRENT, IN AMPERES, DIAMETER CAUSING A TEMPERATURE RISE OP OP ROD, IN INCHES. in in Square Inches. Circular Mils. 10 C. (18 F.) 20 C. (36 F.) 30 C. (54 F.) 40 C. (72 F.) i .196 250,000 300 400 450 550 f .442 562,500 500 650 800 950 .785 1,000,000 750 950 1,200 1,400 1 1.227 1,562,500 1,000 1,350 1,650 1,900 1* 1.767 2,250,000 1,300 1,800 2,200 2,550 H 2.405 3,062,500 1,600 2,300 2,800 3,200 2 3.142 4,000,000 2,000 2,800 3,450 3,950 2i 3.976 5,062,500 2,350 3,300 4,100 4,700 2i 4.909 6,250,000 2,750 3,900 4,800 5,550 24 5.940 7,562,500 3,250 4,500 5,500 6,500 3 7.069 9,000.000 3,600 5,600 6,300 7,200 3i 8.296 10,562,500 4,100 5,800 7,000 8,000 3i 9.621 12,250,000 4,600 6,500 7,800 9,000 3i 11.045 14,062,500 5,000 7,200 8,600 10,000 4 12.566 16,000,000 5,200 7,700 9,200 11,000 as is used for magnet winding. The fifth column, headed " Diameter of Insulated Wire, S. C. C.," contains the maximum outside diameter of a number of samples of single covered wire from different manufacturers. The sixth column, marked " Number of Turns per Inch," gives the number of wires which can be laid side by side in the length of one inch; this column serves to find the number of wires per layer on a magnet of given length. The figures in the seventh column represent the number of layers of the given size of wire that can be wound per inch height of winding space. In the table of WIRE TABLES AND WINDING DA7'A. 683 armature winding data the corresponding figures are omitted, because in an armature the wires of different layers are usu- ally placed in line, vertically, so that the number of layers per inch is identical with the number of turns per inch. In wind- ing a magnet, however, the wires of each following layer are placed into the hollows left between the wires of the preced- ing layer; more layers can therefore be wound per inch height on a magnet than on an armature, and the figures in the column headed " Number of Wires per Layer " are thus greater than the corresponding figures in the preceding column. While the number of wires per square inch for an armature is the square of the number of wires per inch, the number of turns per square inch for a magnet (given in column 8) is the product of the number of turns per inch by the number of lay- ers per inch. The two succeeding columns, Nos. 9 and jo, headed respectively " Pounds per Foot S. C. C." and " Pounds per Cubic Inch of Winding," serve to determine the weight of the magnet winding when the total length of wire, or the total space occupied by the winding, is known. From column n the percentage of solid copper in any volume wound with S. C. C. magnet wire can be taken. It will be noted that this percentage is greatest for the larger diameters given and diminishes with the size of wire, which is due to the fact that on a small wire the insulation occupies a relatively much greater space than on a large wire. Column 12, finally, gives the resistance of a length of each wire which will just fill a cubic inch of the winding space. Knowing the total con- tents of the latter, a simple multiplication will give the total resistance of the magnet winding at 20 C. Table CXVIII., page 680, gives (i) the maximum current allowed by the Fire Underwriters, in various sizes of wires for use in buildings, (2) the currents which produce a rise of 40 C. (72 F.) in the temperature of the wire, and (3) the currents which cause the wires to heat up to the smoking point of cot- ton insulation (about 180 C. or 356 F.). The Underwriters' limits are only given for comparison; they do not apply to dynamo windings, and therefore do not directly interest the dynamo designer. The figures contained in the two remain- ing columns are intended as a check on the wire calculation, the former limit corresponding to the usual rise of tempera- 68 4 TABLE CXXI. EQUIVALENTS OF WIRES. SIZE OP SINGLE WIRE. NEAREST GAUGE OP WIRE TO OBTAIN AREA EQUIVALENT TO SINGLE WIRE, IF NUMBER OP WIHES WHICH MAKE UP ONE CONDUCTOR, is: B. &S B.W.G 2 3 4 5 6 7 8 0000 B. & S 3 B.W.G. 3 B. & S. 4 B. & S. 5 B. & S. 7 B.W.G. 6 B. & 0000 B. & S 3 B.W.G. 3 B. & S. 6 B.W.G. 5 B. & S. 7 B.W.G. 6 B. & 000 1 B. & S 2 B. & 8. 5 B.W.G. 6 B.W.G. 7 B.W.G. 6 B. & S. 9 B.W. 000 1 B. & S. 4 B.W.G. 4 B. & S. 5 B. & S. 8 B.W.G. 6 B. & S. 7 B. & 00 2 B.W.G. 5 B.W.G. 6 B.W.G. 7 B.W.G. 6 B. & S. 7 B. & S. 10 B.W. 00 2 B. & 8 5 B.W.G. 5 B. & S. 8 B W.G. 9 B.W.G. 10 B.W.G. 8 B. & 4 B.W.G. 6 B.W.G. 8 B.W.G. 9 B.W.G. 7 B. & S. 8 B. & S. 11 B.W. 3 B. & S. 5 B. & S. 6 B. & S. 9 B.W.G. 10 B.W.G. 11 B.W.G. 9 B. & 1 5 B.W.G. 7 B.W.G 9 B.W.G. 10 B.W.G. 11 B.W.G. 9 B. & S. 12 B.W. 1 4 B. & 8. 8 B.W.G. 7 B. & S. 8 B. & S. 11 B.W.G. 12 B.W.GJIO B. & 2 6 B.W.G. 6 B. & S. 7 B. & S 8 B. & S. 9 B. & S. 12 B.W.G. 10 B. & 3 5 B. & S. 9 B.W.G. 8 B. & S. 9 B. & S. 12 B.W.G. 10 B. & S. 11 B. & 2 5 B. & S. 9 B.W.G. 8 B. & S. 9 B. & S. 12 B.W.G. 10 B. & S. 11 B. & 4 8 B.W.G. 10 B.W.G. 11 B.W.G. 12 B.W.G. 13 B.W.G. 11 B. & S. 14 B. & 3 6 B. & S 10 B.W.G. 9 B. & S. 10 B. & S. 13 B.W.G. 11 B. & S. 12 B. & 5 6 B. & S. 8 B. & S. 12 B.W.G. 10 B. & S. 11 B. & S. 14 B.W.G. 12 B. & 4 7 B. & S. 11 B.W.G. 10 B. & S 11 B. & S. 14 B.W.G. 12 B. & S. 13 B. & 6 7 B. & S. 11 B.W.G 10 B. & S. 11 B. & S. 14 B.W.G. 12 B. & S. 13 B. & 5 8 B. & S. 12 B.W.G. 11 B. & S. 14 B.W.G. 12 B. & S. 13 B. & S. 14 B. & 7 8 B. & S. 10 B. & S. 11 B. & S. 12 B. & S. 13 B. & 8. 16 B.W.G. 14 B. & 8 11 B.W.G. 13 B.W.G. 14 B.W.G. 13 B. & S 16 B.W.G. 14 B. & S. 17 B.W.( 6 9 B. & S. 13 B.W.G. 12 B. & S. 13 B. & S. 16 B.W.G. 14 B. & S. 15 B. & 9 12 B.W.G. 11 B. & S. 13 B. & S. 16 B.W.G. 14 B. & S. 15 B. & S. 16 B. & 7 10 B. & S. 14 B.W.G. 13 B. & S. 14 B. & S. 17 B.W.G. 15 B. & S. 16 B. & 10 13 B.W.G. 12 B. & S. 16 B.W G. 17 B.W.G. 15 B. & S. 16 B. & S 18 B.W. 8 11 B. & S. 13 B. & 8. 14 B. & S. 17 B.W.G. 16 B. & S. 18 B.W.G. 17 B. & 11 14 B.W.G. 13 B. & S. 17 B.W.G. 15 B. & S. 16 B. & S. 17 B. & S. 19 B.W. 9 12 B. & S. 16 B.W.G. 15 B. & 8. 16 B. & S. 18 B.W.G. 17 B. & S. 18 B. & 12 12 B. & S. 14 B. & S. 15 B. & S. 18 B.W.G. 17 B. & S. 18 B. & S.I18 B. & 10 13 B. & S. 17 B.W.G. 16 B. & S. 17 B. & S. 19 B.W.G. 18 B. & 8.! 19 B. & 13 16 B.W.G. 15 B. & S. 18 B.W.G. 19 B.W.G. 18 B. & S. 19 B. & SJ20 B.W. 11 14 B. & S. 16 B. & S. 17 B. & S. 18 B. & S. 19 B. & S. 20 B.W.G.I20 B. & 14 17 B.W.G. 18 B.W.G. 19 B.W.G. 18 B. & S. 20 B.W.G. 20 B. & S. 20 B. & 12 15 B. & S 17 B. & S 18 B. & S. 19 B. & S. 20 B. & S. 20 B. & S. 21 B. & 13 15 16 B & S. 19 B.W.G. 19 B. & S 20 B. & S. 21 B. & S. 22 B.W.G. 22 B. & 16 17 B. & S. 18 B. & S. 20 B. & S. 21 B. & S 22 B.W.G. 23 B.W.G. 23 B. & i 14 17 B. & S. 19 B. & S. 20 B. & S. 21 B. & S. 22 B. & S. 23 B.W.GJ23 B. & { 17 18 B. & S. 20 B.W.G. 21 B. & S. 22 B. & S. 23 B.W.G. 24 B.W.G. 24 B. & { 15 18 B. & S. 20 B. & S. 21 B. & S. 22 B. & S. 23 B.W.G. 24 B.W.G. 24 B. & 16 19 B. & S 21 B. & 8. 22 B. & S. 23 B. & S. 24 B.W.G. 24 B. & S.;25 B. & S 18 20 B.W.G. 21 B. & S. 23 B.W.G. 24 B.W.G. 24 B. & S. 25 B. & 8. 25 B. & 17 20 B. & 8. 22 B.W.G. 23 B. & S. 24 B. & S. 25 B. & S. 25 B. & S. 26 B. & S 19 20 B. & S 23 B.W.G. 24 B.W.G. 24 B. & 8. 25 B. & S. 26 B. & 8.126 B. & J 18 21 B. & S. 23 B. & S. 24 B. & S. 25 B. & S. 26 B. & S. 26 B. & S. 27 B. & J 19 22 B. & S. 24 B. & S. 25 B. & S. 26 B. & S. 27 B. & S. 27 B. & S. 28 B. & S 20 23 B.W.G. 24 B. & S. 25 B. & S 26 B. & S. 27 B. & S. 29 B.W.G. !28 B. & I 20 21 23 B. & S. 25 B. & S. 26 B. & S 27 B. & S. 29 B.W.G. 30 B.W.G. 29 B. & TABLE CXXL EQUIVALENTS OP WIRES. Continued. 685 SIZE OP ' SINGLE WIRE.. NEAREST GAUGE OF WIRE TO OBTAIN AREA EQUIVALENT TO SINOLB WIRE, IF NUMBER OF WIUES WHICH MAKE UP ONE CONDUCTOR, is.- B. AS. B.W.G. 9 10 12 14 16 20 24 0000 "~! 9 B.W.G. 7 B. & S. 10 B.W.G. 11 B.W.G. 9 B. & S. 10 B. & S. 13 B.W.G. 0000 9 B.W.G.! 7 B. & 8. 10 B.W.G. 11 B.W.G. 9 B. & S. 10 B. & S. 13 B.W.G. 000 7 B. & S. 10 B.W.G. 8 B. & S. 9 B. & S. 12 B.W.G. 13 B.W.G. 11 B. & S. 000 10 B.W.G. 8 B. & S. 11 B.W.G. 12 B.W.G. 10 B. & S. 11 B & S. 14 B.W.G. 00 8 B. & S. 11 B.W.G. 12 B.W.G. 10 B. & S 13 B.W.G. 14 B.W.G. 12 B. & S. 00 i 11 B.W.G. 9 B. & 8.112 B.W.G. 13 B.W.G. 11 B & S. 14 B.WG. 15 B.W.G. i 9 B. & 8. 12 B.W.G. 10 B. & S. 11 B. & S. 14 B.W.G. 12 B. & S. 13 B. & S. 12 B.W.G. 10 B. & S. 13 B.W.G. 11 B. & S. 14 B.W.G. 13 B. & S. 16 B.W.G. 1 10 B. & S. 13 B.W.G. 11 B. & S. 14 B.W.G. 12 B. & S. 16 B W.G. 14 B. & S. 1 13 B.W.G. 11 B. & S.|14 B.W.G. 12 B. & S. 13 B. & S. 14 B. & S 17 B.W.G. 2 13 B.W.G. 11 B. & S. 14 B.W.G. 12 B. & S. 13 B. & S 14 B. & S.|17 B W.G. 3 11 B. & S. 14 B.W.G. 12 B. & S 13 B. & S. 14 B. & S. 17 B.W.G. 15 B. & S. 2 11 B. & S. 14 B.W.G. 12 B. & S. 13 B. & 8. 14 B & S. 17 B.W.G. 15 B. & S. 4 12 B. & S 12 B. & 8. 13 B. & S. 14 B. & S. 17 B.W.G. 15 B. & S.jlS B.W.G. 3 12 B & S 13 B. & S 16 B.WG. 14 B. & S. 15 B. & S. 16 B. & S.J17 B. & S. 5 13 B. & S !13 B. & S 14 B. & 8 17 B.W.G. 15 B. & S. 18 B.W.G. 17 B. & S. 4 13 B. & S. 16 B.W.G 17 B.W.G. 15 B. & S. 16 B. & S. 17 B. & 8. 19 B.W.G. 6 16 B.W.G. 14 B. & S. 17 B.W.G 15 B. & S. 16 B. & S. 17 B. & S. 19 B.W.G. 5 14 B & S. 17 B.W.G. 15 B. & S. 18 B.W.G. 17 B. & S. 17 B. & S. 19 B. & S. 7 17 B.WG. 15 B. & S. 16 B. & S. 18 B.W.G. 17 B. & S. 19 B.W.G. 19 B. & S. 8 15 B. & S 16 B. & S. 18 B.W.G. 17 B. & S. 19 B.W.G. 19 B. & S. 20 B.W.G. 6 15 B. & S 16 B. & S 18 B.W.G. 17 B. & S. 18 B. & S. 19 B. & S 20 B. & S. 9 18 B.W.G 17 B. & S 19 B.W.G. 18 B. & S. 18 B. & S. 20 B.W.G. 20 B. & S. 7 18 B.W.G. 17 B. & S. 19 B.W G. 18 B. & S. 19 B. & 8. 20 B. & S. 21 B. & S. 10 17 B & S. 19 B.W.G. 18 B. & S. 19 B. & S. 20 B.W.G. 20 B. & S. 21 B. & S. 8 19 B.W.G. 18 B. & 8. 19 B. & S 20 B.W.G. 20 B. & S. 21 B. & S. 22 B. & S. 11 18 B. & S. 18 B. & S 19 B. & S. 20 B. & S. 20 B. & S. 22 B.W.G. 23 B.W.G. 9 18 B. & S. 19 B & S 20 B.W.G. 20 B. & S. 21 B. & S. 22 B. & S. 23 B.W.G. 12 19 B. & S. 20 B.W.G 20 B. & 8. 21 B. & S. 22 B.W.G. 23 B.W.G. 23 B. & S. 10 20 B.W.G. 20 B. & S. 21 B. & S. 21 B. & S 22 B & S 23 B. & S. 24 B.W.G. 13 20 B. & 8. 21 B. & S. 22 B.W.G. 22 B. & S. 23 B.W.G 24 B.W.G. 24 B. & S. 11 2i) B. & S 21 B. & S. 22 B. & S. 23 B.W.G. 23 B. & S 24 B. & S. 25 B. & S. 14 22 B.W.G 22 B. & S. 23 B.W.G. 24 B.W.G. 24 B.W.G !25 B. & S. 25 B. & S. 12 22 B.W.G. 22 B. & 8. 23 B. & S. 24 B.W.G. 24 B. & 8.125 B. & S. 26 B. & S. 13 15 23 B.W.G. 23 B. & S 24 B W.G. 24 B. & S. 25 B. & S. 26 B. & S. 27 B. & S. 16 24 B.W.G 24 B. & S. 24 B & S. 25 B. & S 26 B. & S. 27 B. & S 29 B.W.G. 14 24 B.W.G. 24 B. & S. 25 B. & S. 25 B. & S. 26 B. & 8. 27 B. & S. 29 B.W.G. 17 24 B. & S. 25 B. & S 25 B. & S. 26 B. & 8. 27 B. & S. 29 B.W.G 30 B.W.G. 15 24 B. & S. 25 B. & S. 26 B. & S. 26 B. & S. 27 B. & S. 28 B. & S. 29 B. & S. 16 25 B. & S 26 B. & S 27 B. & S. 27 B. & S. 28 B. & S. 29 B. & S. 30 B. & S. 18 26 B. & S. 26 B. & S. 27 B. & 8.29 B.W.G. 30 B.W.G.I29 B. & S. 30 15. & S. 17 26 B. & S. 27 B. & S. 29 B.W.G. 30 B.W.G 29 B. & S.,30 B. & S. 19 27 B. & S. 29 B.W.G. 30 B W.G. 29 B. & S 30 B. & S. 18 28 B. & S. 29 B. & S. 30 B.W.G. 29 B. & S 30 B. & S.j 19 30 B.W.G. 29 B. & S. 30 B. & S. 20 30 B.W.G. 29 B. & S 30 B. & S. 20 21 29 B. & S. 30 B. & S i m 686 D YNA MO-ELE C TRIG MA CHINE S. ture specified for dynamo magnets, and the currents given in the latter column being those which will injure the insulation. Table CXIX., page 681, is self-explanatory. It gives the carrying capacities of wires from No. oooo to No. 30 B. & S., and from No. oooo to No. 31 B. W. G. for current densities of 1000, 2000, 3000, 4000, 5000, and 6000 amperes per square inch, respectively. TABLE C XXII. STRANDING OF STANDARD CABLES. 1 i|l STRANDING OP CABLE. feg 3 ri la ||| O ^ 2g S *,S tf^ H S S ? OMOQ Number of Wires in Concentric Layers. p HS |{ ||1 (Commencing from Inner Layer.) "s ^ B 3 2* IX 3 1 3 7 3* IX 7 2 1- -e 12 4* IX 12 2 3- -9 19 5 IX 19 3 1- -6+12 27 8* IX 27 3 3- -9+15 37 7 IX 37 4 1- -6+12+18 48 8* IX 48 4 3+9+15+21 49 9 7X 7 2 1- r6 61 9 IX 61 5 1- -6+12+18+24 75 10* IX 75 5 3- -9+15+21+27 91 11 IX 91 6 1- -6+12+18+24+30 108 13* 1X108 6 3- -9+15+21+27+33 127 13 1X127 7 1- -6- -12+18+24+30+36 133 15 7X 19 3 1-1 147 14* 1X147 7 3+9- -15+21+27+33+39 169 192 15 16* 1X169 1X192 8 8 1- 3- -9- -12+18+24+30+36+42 -15+21+27+33+39+45 217 17 1X217 9 1- -6- -12+18+24+30+36+42+48 259 21 7X 37 4 1- -6+12+18 343 27 7X7X7 2 1- -6 427 27 7X 61 5 1- -6+12+18+24 In Table CXX., page 682, the current capacities of copper rods from J- inch to 4 inches in diameter, for temperature in- creases of 10, 20, 30, and 40 C., respectively, are compiled. The values contained in this table have been obtained from actual tests on bare rods of commercial copper of about 98 per cent, conductivity, horizontally suspended. Table CXXI., pages 684 and 685, is designed as a short-cut oojogogogogogogogogogogooooo rf Sj " m w^toiokJtototototocococo^^crbiCTj O O O ^ i-"- i-i (-A i-i 1-1. ,-i t-i h-i (->. i-i H-I h-i "^ '^ tO tO tO tO CO CO CO CO b b b b b o ^ ^ H^ ^ ^ J^ !^ H*. '^ K* h-i. J-i. J-. h-i w to to M> to co co CO *O ^^ ^^ O> ^^ ^> O - ^ ^ ^ -^^^^qpoooocxcDO^tocooTpsr? CO CO O 1 O 1 O , %*s ^ s / s /** /*s %s L_i L_I * i l_i r . CO ^GOtOOSOC00500i^^OJOOOCOOl-3?bOtOl-io60Tt0^6TOiCl ll bbbbbbbbbbbbbbbbbobboooooi-ii-'. l^lOtOtOCOCOCOCOCO^^^i^^t^C;TOC7p?05C!5^-JGC500 oooooooooooooooooooooooooo ^ 688 DYNAMO-ELECTRIC MACHINES. in armature winding calculations. The size of the single wire required to carry the given current having been found, this table gives directly, without further calculation, the size of wire for a subdivided armature conductor. The scope of this table, including all sizes from No. oooo to No. 20 B. & S., and from No. oooo to No. 21 B. W. G., and giving subdivisions from 2 to 24, is such that it will answer for all the usual cases occurring in practice. TABLE CXXIV. SIZE AND WEIGHT OP CABLES. SIZE OP CABLE, B. & S. GAUGE. AREA OP CABLE, ClRCULARMlLS. MAXIMUM DIAMETER OP COPPER STRAND, INCHES. OUTSIDE DIAMETER OF CABLE, INCHES. WEIGHT PER FOOT OP CABLE, POUNDS. 1,000,000 1* 11 3.7 900,000 If 1J . 3.0 . 800,000 itt 1- I ' 2.9 . 750,000 1- 1 2.8 . 700,000 l\ 2.5 ... 650,000 1. 1 2.4 . . . 600.000 1 T 8 * ly 9 * 2.1 . . . 550,000 U H 2.0 . . . 500,000 & i* 1.9 450,000 if 1.6 400,000 if 4 1.5 350,000 H 1.3 300,000 13 1ft 1.2 . 250,000 | H 1.0 OOOO 211,600 1ft .82 000 168,100 | 1 .65 00 133,225 ft if .55 105,625 ( 1 .46 1 83,521 I .38 2 66,564 T f .30 3 52,441 H I .27 4 41,616 ft 1 .22 5 33,124 X I .20 6 26,244 i .18 Tables CXXIL, CXXIIL, and CXXIV. give the data of flexible copper wire cables, such as are used for dynamo con- nections. In Table CXXIL, page 686, the diameter of the copper strand of cables containing from 3 to 427 wires is given, and the arrangement of the Various stranded cables is shown. The unit of the diameter in each case is the diame- ter of the wire employed in making up the cable, so that the diameter in inches is found by multiplying the given figure by the diameter of the wire. For instance, the diameter of the WIRE TABLES AND WINDING DATA. 689 copper strand of a cable consisting of 133 No. 13 B. & S. wires is 15 X .072 1.08 inches. From the last column it will be seen that cables are made up in either of two ways: (i) one single wire forms the center layer, 6 wires the second layer, 12 wires the third layer, etc.; or (2) the center layer consists of 3 wires, the second layer of 9 wires, the third of 15 wires, etc. Up to 9 concentric layers are used in this manner; cables requiring a larger number of wires are made TABLE CXXV. IRON WIRE FOR RHEOSTATS AND STARTING BOXES. SIZE OF WIRE. FOR RHEOSTATS. FOR STARTING BOXES. WOOD FRAME. IRON FRAME. i a fll. sf g, of, C i* fg S ? |l 1 ilj U !i if?! Is, Jfg'l S3 IS &! 00 DM o a S^o^s ~ s " O-S -2^0,C SI ^1 3 * 5 U> 9 fig 1 Ili a Jf g iS PQ cc 5 GO 00 8 .1285 17.4 6.32 20.3 5.42 436 2.52 .00398 250. .040 9 .1144 14.6 7.53 17.1 6.43 36.6 3.01 .00578 173. .033 10 .1019 12.3 8.94 14.3 7.69 30.8 357 .00728 137. .0*75 11 .0907 10.3 10.68 12.0 9.17 25.8 4.26 .00918 108. .0218 12 .0808 8.7 12.64 10.1 10.89 21.7 5.07 .01157 86.4 .0173 13 .072 7.3 15.07 85 12.94 18.3 6.01 .01459 68.5 .0137 14 .0641 6.1 18.03 7.1 15.49 15.3 7.19 i .01840 54.3 .0109 15 .0571 5 1 21.57 6.0 18.33 12.9 8.53 .02320 43.1 .0063 16 .0508 4.3 25.58 5.0 22.00 10.8 10.19 .02925 34.1 .00685 17 .0453 3.6 30.56 4.2 26.19 9.1 12.09 .03688 27.1 .00543 18 .0403 3.0 3667 3.5 31.43 7.6 14.47 .04652 21.4 .00480 19 .0359 2.52 4365 2.9 37.93 6.3 17.46 .06032 16.5 .00341 20 .032 2.17 5069 2.5 44.00 5.4 20.37 .07396 13.5 .00271 21 .0285 1.82 60.44 2.1 52.38 45 2444 .09332 10.7 .00231 22 .0253 1.53 71.90 1.77 62.15 3.8 2895 .11769 8.49 .001838 23 .0226 1.28 85.94 1.5 73.33 3.2 3438 .14843 . 6.73 .001457 24 .020 1.08 101.85 1.2 91.67 23 47.83 .18717 5.34 .001155 up by stranding together 7 individual cables, each composed of the proper number of concentric layers. In the 343-wire cable, each of the 7 cables so stranded is again subdivided into 7 cables, each of the small cables consisting of 7 wires in two concentric layers. The figures given in Table CXXIIL, page 687, are the diameters of the wire required to produce a given sectional area when used for making up a cable of a given number of wires. Thus, the size of wire for a 690 DYNAMO-ELECTRIC MACHINES. i47-wire cable of 400,000 circular mils sectional area is given as .052 inch. The nearest gauge sizes are No. 15 and No. 16 B. & S. ; the former is to be taken if it is not desirable to go below the specified area, and the latter may be used if a TABLE CXXVI. CARRYING CAPACITY OF GERMAN SILVER RHEOSTAT COILS. (18$ Commercial German Silver.) GO tilT <$ PERMISSIBLE CURRENT M g C H IN A f-lNCH SPIRAL, 3 INCHE* LONG, STRETCHED HORIZONTALLY TO 7 INCHES, FOR A RISE IN TEMPERATURE OF: I.JH g filii I " 63 S ft 1 50 C. (90 F.) 75C.(135F.) 100 C. (180 F.) 125 C. (225 F.) 150 C. (270 F.) gJ 72 10 923 12.03 14.04 16.15 17.03 1.100 11 7.75 1007 11.79 13.46 14.29 .964 12 6.52 8.47 9.88 11.31 12.03 .812 13 5.48 7.15 8.32 9.50 10.11 .703 14 4.50 6.00 7.00 8.00 8.50 .600 15 389 5.03 5.86 6.71 7.15 .481 16 3.22 4.21 4.90 5.62 5.99 .406 17 2.73 3.59 4.13 4.71 5.04 .311 18 2.28 2.98 3.47 3.95 4.22 .287 19 1.89 2.46 2.90 3.30 3.48 .236 20 1.62 2.12 2.46 2.76 2.98 .203 21 1.36 1.78 2.10 2.35 2.50 .170 22 1.14 1.50 1.76 2.00 2.11 .149 23 .96 1.25 1.47 1.61 1.78 .126 24 .81 1.04 1.23 1.39 1.48 .105 25 .68 .88 1.03 1.19 1.24 .089 26 .57 .74 .87 .99 1.05 .074 27 .48 .63 .73 .83 .885 .063 28 .40 .52 .61 .70 .74 .052 29 .34 .44 .51 .59 .625 .039 30 .29 .37 .43 .50 .52 .037 31 .24 .31 .36 .41 .44 .031 32 .20 .26 .31 .35 .37 .027 33 .17 .22 .25 .29 .31 .022 34 .14 .19 .21 .245 .256 .019 35 .12 .16 .18 .205 .215 .016 36 .10 .13 .15 .174 .185 .013 37 .084 .11 .13 .144 .156 .011 38 .071 .092 .11 .121 .130 .009 39 .060 .077 .090 .100 .110 .008 40 .050 .065 .077 .088 .092 .007 slight shortcoming of the cross-section is immaterial. Table CXXIV., page 688, gives the maximum bare and outside diameters and the weights of flexible cables from 1,000,000 circular mils down to 26,244 circular mils area, the latter being WIRE TABLES AND WINDING DATA. 691 equivalent to a 6 No. B. & S. wire. The figures in the third column are based on the data given in Table CXXIII. for 343- wire cables; to obtain the diameter given in the fourth column, 1 of an inch is added to the former dimensions, the thickness of insulation on flexible dynamo and power cables being usu- ally about T 3 g- of an inch. Table CXX1V. will be found useful for designing the cable-lugs of brush holders and the cable-re- ceiving parts of switches, etc. Tables CXXV. and CXXVL, finally, contain all the data necessary for selecting the proper size of wire for resistance coils. Table CXXV., page 689, gives the safe current-carry- ing capacities, the resistance required, the specific resistance, the specific length, and the specific weight of tinned iron wires from No. 8 to No. 24 B. & S. gauge for wooden and iron rheo- stats as well as for starting boxes. The resistance of the shunt circuit corresponding to each current strength is calculated for the case of no volts; this resistance must be multiplied by T? 2 for 220 volts, by 5 for 550 volts, and by , where E is the 1 10 E. M. F. at shunt terminals, for any other voltage E. The resist- ance so obtained is the minimum resistance that should be pro- vided for the voltage in question. Table CXXVL, page 690, gives the current capacities for temperature increases of 50, 75, 100, 125, and 150 C., respectively, of German Silver rheostat coils from No. 10 to No. 4oB.& S. wire. The figures are the results of tests made with spirals wound to a solid length of 3j inches on a f-inch mandrel, and afterwards stretched to a length of 7 inches; thus making the space between the turns equal to the diameter of the wire. The last column of this table serves to correct the values given for the 7-inch spiral in the case that its length, that is to say, its number of turns, is increased; twice the current strengths given in this column are to be deducted from the respective table-value for every additional inch length of spiral above 7 inches. Thus, for in- stance, the current capacity of an 8J-inch spiral of No. 12 Ger- man Silver wire for a temperature increase of 125 C. is 11.31 2 X (8|- 7) X .812 = 11.31 2.44 8.87 amperes. Table CXXVL refers to the so-called 18 per cent. German Silver, containing 18 per cent, of nickel, this alloy being usu- 692 DYNAMO-ELECTRIC MACHINES. ally employed for resistance coils. From a great number of tests it has been found that the average resistance of this ma- terial is a trifle over eighteen times the resistance of copper at 75 F. German Silver is also made with 30 per cent, of nickel, but in this composition it is now but rarely used for electrical purposes. The resistance of the 30 per cent, alloy is about twenty-eight times that of copper. APPENDIX III. LOCALIZATION AND REMEDY OF TROUBLES IN DYNAMOS AND MOTORS IN OPERATION. LOCALIZATION AND REMEDY OF TROUBLES IN DYNAMOS AND MOTORS IN OPERATION.* Classification of Dynamo Troubles. The constructive expedients to be employed when designing a dynamo having; been treated in the text, the following pages are intended for the consideration of the attendant in whose care the machine is placed, and upon whose competency depends, in no small measure, its efficiency and even its life. While general pre- cautions and preventive measures do not always insure free- dom from trouble, neglect and carelessness with any ma- chinery are usually followed by accidents of some sort. The success of an electric plant depends to a very great extent upon the promptness with which the attendant is able to remedy such difficulties. The usual troubles in dynamo-electric machinery may be clas- sified as follows: 1. Sparking at commutator. 2. Heating of armature and field magnets. 3. Heating of commutator and brushes. 4. Heating of bearings. 5. Noises. 6. Abnormal speed. 7. Dynamo fails to generate. 8. Motor stops or fails to start. 1. Sparking at Commutator. The most common trouble met with in running continuous-current dynamos and mo- tors is the sparking at the commutator. Since excessive sparking wears, and eventually even destroys, the commu- * Compiled from " Practical Management of Dynamos and Motors," by- Crocker and Wheeler. 695 696 DYNAMO-ELECTRIC MACHINES. tator and brushes, and produces heat which may become in- jurious to the armature and bearings, it is of the greatest importance that sparking, upon its discovery, should be promptly checked. CAUSES OF SPARKING. Sparking may be due to any of the fol- lowing causes: (i) Brushes not set at neutral points. (2) Brushes make poor contact with commutator. .(3) Vibra- tion, or chattering, of brushes. (4) Short-circuited or reversed coil in armature. (5) Weak field. (6) Unequal distribution of magnetism. (7) High resistance brush. (8) Vibration of machine. (9) Commutator rough, eccentric, or having " high " or "flat" bars. (10) Broken circuit in armature. (n) Ground in armature. (12) Armature overloaded. PREVENTION OF SPARKING. It is seen from the preceding that sparking at the commutator may be due to one, or more, of many causes. The first step in the speedy prevention of sparking, therefore, is the detection of the trouble that causes it. If due to any one cause, the finding of the trouble is comparatively easy, since in each case the symptoms are different and quite well pronounced; but when two or more causes combine in effecting excessive sparking, it requires more care to locate the faulty conditions. FAULTY ADJUSTMENT. Causes (i) to (3) are due to faulty ad- justment of the brushes, and sparking in consequence of these causes can be easily prevented by resetting the brushes. In the first case, when the brushes are not at neutral points, they must be set exactly opposite each other, if the machine is bi- polar; po apart, if it is fourpolar; 60, if it has six poles, etc. The proper points of contact for so setting the brushes are best determined by counting the commutator bars. To find the opposite bar to No. i, add i to half the. number of bars; to find the po bar, add i to one-quarter the number of bars; to find the 60 bar, add i to one-sixth the number of bars, etc. For instance, if the commutator has ^cPbars, one- half the number is 24, and 24 -|- i = 25, hence bar No. 25 is opposite bar No. i ; since one-quarter of 48 is 12, bar No. 13 is the one 90 from No. i; and i added to one-sixth of 48, LOCALIZATION AND REMEDY OF TROUBLES. 697 or 8, gives No. 9 as the bar 6o p from No. i. Mark bars Nos. i and 25 in case of a bipolar machine, bars i and 13 in case of a four-pole machine, or i and 9 in case of a six-pole machine, and adjust the brushes so that each set rests on one of the marked bars, taking care that all the brushes of one set are exactly in line with each other, so that none is ahead or behind the others. This being done, the rocker- arm or brush-yoke, as the movable bracket is called to which the brush-holders are attached, is shifted backward or for- ward until sparking is reduced to a minimum, or disappears. If the sparking is due to the second cause, poor contact, an ex- amination of the brushes will show that they touch only at one corner, or only at one edge, or that there is dirt or oil between them and the commutator. In case of metallic brushes, they should then be filed or bent until they rest evenly on the commutator. Carbon brushes are fitted by pasting a band of sandpaper around the commutator and revolving the armature while the brushes are firmly pressed in their proper positions. In this manner, the tips of the brushes are hollowed out to the exact shape of the commu- tator, and after removal of the sandpaper, the brush-contact is found to be perfect. The third cause, vibration of brushes, is frequently met with carbon brushes which are set radially to the commutator. Such brushes, when the commutator has become sticky, are thrown into rapid vibration by the running of the machine, and create a chattering noise. The ensuing spark is easily stopped by cleaning and slightly lubricating the commutator. In applying the lubricant, which may consist of ordinary machinery-oil, vaseline, or specially prepared commutator- compound, care should be exercised in using it very sparingly, preferably by rubbing it over the commutator with the finger. . For, since all oils are non-conductors of electricity, too much lubrication will insulate the brushes from the com- mutator, and will thus prevent the machine from operating. FAULTY CONSTRUCTION AND WRONG CONSTRUCTION. Causes (4) to (8) are a consequence either of faulty construction of, or wrong connections in, the machine, and can be properly eliminated only by repairing the machine. 698 DYNAMO-ELECTRIC MACHINES. If a coil in the armature ha's been accidentally short-circuited or reversed while connecting up the armature, it will, when ro- tated in the magnetic field, generate local currents which give rise to sparking. Short-circuits in the coils are frequently caused by solder dropping between two commutator bars when fastening the wires to the commutator. Defects of this kind can be readily detected by careful inspection, and are easily remedied by removal of the obstruction. Re- versals are due to mistaking the terminals of the armature coils, so that the end of a coil is connected to a bar where the beginning of the coil should be, or vice versa. In this case the faulty coils must be disconnected and properly re- attached to the commutator. A weak field may be due' to a break, or to a short-circuit, or to a ground in the field coils. These faults can be easily repaired if they are external or accessible. When internal, the only remedy is to partially, or wholly, rewind and replace the faulty coil. Unequal distribution of magnetism, which is usually traced to weak- ness of one of the pole-tips, causes one brush to spark more than the other. In this case the polepieces must be re-shaped so as to weaken the strong tip or to strengthen the weak tip. The brushes of a machine must be of sufficient conductivity to carry the current generated by the armature without undue heating. Their material as well as their cross-section must therefore be suitably selected. Brushes of abnormally high resistance become very hot, cause sparking, and reduce the output of the machine. By using new brushes of proper- material and thickness, the sparking due to this cause is immediately stopped. Vibration of machine is usually due to an imperfectly balanced armature or pulley, to a bad belt, or to an unsteady founda- tion, or sometimes to poor design of the field frame. In the two former cases, re-balancing of the rotating parts, or re- lacing the belt, respectively, will remove the vibration; in the two latter cases, the weak parts must be strengthened or rebuilt. WEAR AND TEAR. Causes (9) to (i i) are consequent upon wear and tear, and are therefore the most usual. LOCALIZATION AND REMEDY OF TROUBLES. 699 A commutator, after some time, shows grooves and ridges* wears more or less eccentric, and develops projections and fiats. To avoid sparking from these causes, the commutator should from time to time be smoothed by means of a fine file or sandpaper, but never by means of emery-paper. Emery, con- taining the metal particles taken from the commutator, would lodge in the insulation between the bars, and would thus cause short-circuits, which would give rise to worse sparking than the unevenness of the commutator did before smoothing. A broken circuit in the armature is either located in the com- mutator connection or in the coil itself. If the commutator connection has worked loose, the break can easily be re- paired; but if the wire inside the coil has broken, the coil must be removed and the armature rewound. Grounds in the armature are due to breakdown of the insula- tion between two wires or between a wire and the armature core. To repair a ground, the defective insulation must be replaced. EXCESSIVE CURRENT. If a machine is overloaded, cause (12), the winding is forced to carry too much current, which causes excessive heating of the armature. Sparking due to ex- cessive current can be reduced by decreasing the load upon the machine, or by decreasing the strength of the magnetic field in the case of a dynamo, or increasing it in the case of a motor. 2. Heating of Armature and Field Magnets. Injurious heating in a dynamo or motor can be detected by placing the hand on the various parts. If any part so examined feels so- hot that the hand cannot remain in touch without discomfort,, the safe limit of temperature has been passed, and the trouble should be remedied. If the heat has become so> great as to produce odor or smoke, the current should be shut off and the machine stopped immediately. The above sim- ple method of testing for heat should be applied shortly- after the machine has been started up, because after the machine has run for some time, any abnormal heating effect will spread until all parts are nearly equal in temperature,, and it will be almost impossible to locate the trouble. 700 DYNAMO-ELECTRIC MACHINES. Abnormal heating of the armature or field magnets may be due to excessive current, to short-circuits, to moisture in the coils, or to excessive generation of eddy currents in the armature core or polepieces. Excessive current in the armature is remedied by reducing the load, or eliminating whatever other cause is responsible for it, which may be either a short-circuit, or a leak, or a ground on the line. To decrease the current in the field circuit, in- crease the field resistance by inserting rheostat, in case of a shunt machine, or by shunting, in case of a series machine, or by both of these methods in a compound machine. If heating is caused by a short-circuit in the winding, the faulty coil must be located, and repaired or replaced by a new one. The presence of moisture is revealed by the formation of steam when the machine becomes hot. A moist machine should be stopped and the moisture expelled by baking the affected part in a moderately warm oven for 4 or 5 hours, or by pass- ing a current through it which should be regulated to main- tain a temperature of about 75 Centrigrade. Heating due to eddy currents in the iron is indicated by the fact that, after a short trial run, the iron parts will feel warmer than the windings; it is always the result of some construc- tional fault of the machine, such as insufficient lamination of the armature core, misproportioning of the armature teeth, improper arrangement of the polepieces, etc. 3. Heating of Commutator and Brushes. Heating of the commutator and brushes maybe due to sparking at the brushes, arcing in the commutator, or to excessive resistance. Sparking always heats both the commutator and the brushes. Heating from this cause is checked by shifting the rocker arm, or by applying the proper remedies for the sparking. Frequently heating of the commutator is produced by the -causes which induce sparking without being accompanied by the visible manifestation of the latter. .Arcing within the commutator, either between one bar and the next, or between the bars and the commutator shell, is due ito defective w punctured insulation; if the heating is traced to this cause, the commutator must be taken apart and re- paired. LOCALIZATION AND REMEDY OF TROUBLES. 701 Heating of commutator and brushes is often due to insufficient contact area, the cross-section of the brushes being too small to carry the current without overheating. In this case, either thicker brushes of the same material as the old ones, or new brushes of a higher-conductivity material, should be substituted. Sometimes connections or joints in the brush-holder or cable terminal become loose by the vibration of the machine, and cause heating of the joints due to increased contact resistance. By tightening all contacts before every run, however, this trouble can always be prevented. 4. Heating of Bearings. Heating of the bearings may arise from lack of lubrication, presence of grit, or from fric- tion due to roughness or tight fit of shaft, faulty alignment of bearings, excessive belt pull, or to end-thrust or side- thrust of armature. The first two causes, and also excessive belt tension, can be easily detected and remedied, while a rough, sprung, bent, or tight shaft has to be turned or filed down true in the lathe. When the bearings are out of line, they must be un- screwed and properly adjusted, by filing out the bolt holes if necessary, so that they will stay in line, with the armature central to the polepieces, when the screws are tightened. Friction due to end-thrust may be relieved by lining up the belt, shifting armature collar or pulley, turning off shoulder on, shaft, or filing off bearing until a sufficient clearance be- tween the two is obtained. In case of side-thrust, the arma- ture must be re-centered by adjusting the bearings or the polepieces. Water or ice cooling of the bearings should only be used in cases of extreme necessity, and should never be attempted if there is the slightest danger of wetting the commutator or the armature. 5. Causes and Prevention of Noises in Dynamos. The humming noise often issued by an electric machine is pro- duced by vibration due to armature or pulley being out of balance. The armature and pulley should always be bal- anced separately by slowly rolling the armature, first without 702 DYNAMO-ELECTRIC MACHINES. and then with pulley, upon a knife-edge track and attaching weights to the places which show a tendency to remain on top. An excess of weight on one side of the armature and an equal excess on the opposite side of the pulley will not produce a balance when running, though it does when standing still; on the contrary, it will give the shaft a strong tendency to wobble. A perfect balance is only obtained when the weights are directly opposite in the same line per- pendicular to the shaft. Rattling noises are sometimes caused by striking of the arma- ture against one or more of the polepieces, by scraping of the shaft collar or pulley hub against the bearing, or by looseness of screws or other parts. In these cases, the machine should be immediately stopped and the parts properly adjusted. Singing or hissing of the brushes is usually occasioned by rough or sticky commutator or by itnevenness of the brushes, especially when the commutator or the brushes are new, and have not yet worn smooth. A sparing application of oil or vaseline to the commutator, with a rag or the finger, will in most cases stop the noise. If not, shortening or lengthening of the brushes may be resorted to, and, if hissing still contin- ues, it will be necessary to sandpaper, file, or turn down the commutator. A humming sound is often heard in toothed-armature machines, due to the sudden changes of magnetic conditions as each tooth passes the edge of the polepieces. This sound is reduced or stopped by filing away the ends of the polepieces, so that the armature teeth pass each pole-edge gradually. Slipping of the belt causes an intermittent squeaking noise, which can be stopped by tightening the belt. If the belt is poorly laced, so that the joint is rough, a pounding is emitted every time the joint passes over the pulleys. A properly made joint will immediately obviate this difficulty. $. Adjustment of Speed. Too high or too low speed is generally a serious matter in either dynamo or motor, and it is always desirable and often imperative to shut off immedi- ately, and make a careful investigation of the trouble. Low speed m a motor may be caused by overloading, or short-cir- cuits, or grounds in armature, or by excessive friction in the LOCAL/ZA770AT AND REMEDY OF TROUBLES. 703 bearings. Accidental weakness of the field due to a break, short-circuit, or ground in the field coils, or to weakness of the field current, has the effect, on a constant-potential circuit, of making a motor run too fast if lightly loaded, or too slow if heavily loaded, or even to stop or to run backward if the overload is excessive. A series motor on a constant-potential circuit, or any motor on a constant-current circuit, is liable to run too fast if the load is very much reduced. Constant, current motors, except when directly coupled, must, there- fore, be provided with automatic governors or cut-outs, which act to reduce the power if the speed becomes too great. 7. Failure of Self-Excitation. The inability of a gener- ator to excite or build up its field magnetism is in most cases due to weakness or absence of the residual magnetism, caused either by vibration or jar, or by counter-magnetization effected by the proximity of another dynamo or by the earth's mag- netism, or by accidentally reversed current through the fields. Residual magnetism can be restored by sending a current from any dynamo or battery through the field coil ; if, upon starting the machine, it fails to generate, apply the battery current in the opposite direction, since the magnets may have enough polarity to prevent the battery from building them up in the direction first tried. By shifting the brushes backward from the neutral point, the armature magnetization can be made to assist the field. Other causes for dynamo failing to generate are reversed con- nections, reversed direction of rotation, short-circuit in machine or external circuit, connection of field coils in opposition, open circuit, and faulty position of brushes. Any of these troubles can be detected by carefully inspecting and testing the ma- chine, and, when found, can readily be eliminated. A break, poor contact, or excessive resistance in the field circuit or regulator of a shunt dynamo will make the magnetization weak, and prevent its building up. This may be detected and overcome by cutting out the rheostat for a moment, taking care not to make a short-circuit. An abnormally high resistance anywhere in the circuit of a series machine will prevent it from generating, since the field coil is in the main circuit. The magnetization in this case 704 DYNAMO-ELECl^RIC MACHINES. can be started up by short-circuiting the machine for an in- stant. Either of the above two expedients should be applied very carefully, and not until the polepieces have been tested with a piece of iron to make sure that the magnetization is weak. 8. Failure Of Motor. The stopping of a motor, or its re- fusal to start, may be due to excessive overload, to open circuit, or to a wrong connection. While a moderate overload causes the motor to run below its normal speed, an excessive overload vi\\\ stop it entirely. The abnormal load is not always exterior to the motor, but may be due to unusual friction in the motor itself, occasioned by jamming of the shaft, bearings, or other parts, or by arma- ture touching polepieces. In either case, the current should be turned off instantly, the load or the friction reduced, and the current supplied again for a moment, just long enough to see if trouble still exists. If the motor comes promptly up to speed, it may then be left in circuit. If the stopping of the motor is caused by open circuit, a melted fuse or broken wire will be found upon examination of the motor, provided its brushes are in contact and the external circuit is in proper order. If there is no visible break, the armature and field coils must be tested for continuity by means of a battery (or magneto) and electric bell. On a constant-potential circuit, if current is excessive, it indicates a short-circuit. If the field is at fault, the polepieces will be found non-magnetic, or but very weakly magnetized. The possible complications of wrong connections are so great that a very careful and systematic examination and comparison of the connections with the diagram furnished by the manu- facturer is necessary to locate the trouble. INDEX. {Numbers indicate pages.') Absolute units, 7, 47, 199, 332, 333 Accessibility of parts in dynamos, 287, 432 Accumulator charging dynamos, 91, 92, 461, 462 Act of commutation, 29 Active wire in armature, 49, 55 Activity, electrical, in armature, 405, 407, 420, 422, 628, 637, 644 Addenbrooke, on insulation-re- sistance of wood, 85 Addition of E. M. Fs. in closed coil, 12 Adjustment of brushes, 29 Advantages of combination mag- net-frames, 294 of drum-wound ring arma- tures, 35 of iron clad types, 286 of multipolar dynamos, 33, 34, 285 of open coil armatures, 144 of oxide coating of armature laminae, 93 of stranded armature con- ductor, 528, 553 of toothed and perforated armatures, 61, 62, 63 of unipolar dynamos, 25, 26 Air-ducts in armature, 94, 590 Air-friction, 407, 526 Air-gaps, ampere-turns required for, 339- 340 graduation of, 295 influence of change of, 483,484 length of, 62, 208, 433, 469, 470-472, 483 permeance of, 217, 224-231 Alignment of bearings, 304, 409 Allowance for armature-binding, 75, 507, 536 for clearance, 209, 210, 518, 536, 543, 558,576, 583, 604 for flanges on magnet-cores, 523, 542, 576, 595, 650 Allowance for height of commu- tator-lugs, 514 for spaces between armature- coils, 73, 506, 638 for spread of magnetic field, 529 for stranding of armature- conductor, 530 Alternating current, production of, 12 rectification of, 13 Alternators, unipolar, 24 Aluminum, in cast iron, in, 293, 312, 313, 314, 315, 316, 336, 337, 338 Aluminum-bronze, 189 "American Giant " dynamo, 272, 281 Amperage, permissible, 56, 57, 132, 133, 183 Ampere-turn, the unit of exciting power, 333 Ampere-turns, calculation of, 339- 356, 520, 537, 547, 560, 575, 585, 605, 638, 645, 657 Analogy between magnetic and electric circuit, 354 Angle of belt-contact, 193 of field-distortion, greatest permissible, for various num- bers of poles, 340 of lag or lead, 30, 349, 350, 421 of pole-space, 210, 211 Application of connecting for- mula, 152-155 of generator formulas to motor calculation, 419 Arc of belt-contact, 193 of polar embrace, 49 Arcing in commutator, 700 Arc-lighting dynamos, designing of, 455-459, 462tf flux density in armature of, 9i regulation of, 458, 459 series-excitation of, 37 705 yo6 INDEX. Area, see Sectional Area, Surface. Armature, calculation of, 45-195, 413-416, 505, 527, 552, 566, 580, 587, 603, 629, 638, 644, 652, 656 circumflux of, 131 closed coil- and open coil-, 143 cylinder-, or drum-, see Drum- Armature. definition of, 4 disc-, 4 energy-losses in, 107-122 load limit and maximum safe capacity of, 132-135 perforated, or pierced, or tunnel-armature, see Perfor- ated Armature. pole-, or star-, 4 principles of current-genera- tion in, 3 ring-, see Ring-Armature, running-value of, 135, 136 smooth core-, see Smooth Core Armature. toothed, or slotted, see Toothed Core Armature. Armature-calculation, formulae for, 45-195 practical examples of, 505, 527, 552, 566, 580, 587, 603, 629, 638, 644, 652, 656 simplified method of , 413-416 Armature-coils, formulae for con- necting of, 152-155 grouping of, 147-151 Armature-conductor, active and effective, 49 length of, 55, 94 size of, 56 Armature- conductors, number of, 76, 7.7 peripheral force of, 138-140 Armature-core, diameter of, 58 insulation of, 78-82 length of, 72, 76 magnetic density in, 90, 91 magnetizing force for, 340- 343 . radial depth of, 92 Armature-current, total, in shunt and compound dynamos, 109 volume of, 131 Armature-divisions, number of, 90 Armature-induction, specific, 51 unit, 47-50 Armature-insulations, selection of material for, 83-86 thickness of, 82 Armature-reaction, compounding motor by, 649 Armatures-reaction, magnetizing force for compensating, 348- 352 Armature-reaction, prevention of, 463-470 regulating for constant cur- rent by. 456 Armature-thrust, 140-142, 513, 534 Armature-torque, 63, 137, 138, 513, 534 Armature-winding, arrangement of, 87, 507, 529, 554, 581, 589, 604, 657 circumferential current-den- sity in, 130-132 connecting-formulae for, 152- 155 energy dissipated in, 108 fundamental calculations for, 47 grouping of, 147-151 mechanical effects of, 137-142 qualification of number of conductors for, 155-167 temperature rise in, 126-130 types of, 143-147 weight of, 101, 102 Armature wire (D.C.C), data of, 678 Arnold, Professor E., on arma- ture-winding, 152 on unipolar dynamos, 25 Arrangement of armature-wind- ing, 87, 507, 529, 554, 581, 589, 604, 657 of field-poles around ring- armature, 98 of magnet-winding on cores, 387, 401, 551, 564, 576, 599, 613, 635, 641, 655, 660 Asbestos, for armature-insulation, 78, 79, 85, 93, 94 " Atlantic " fan-motor, 282 Attracting force of magnetic field, 140, 141 Auxiliary pole method, 469 Available height of armature- winding, 74 of magnet-winding, 377 Average efficiencies of electric motors, 422 E. M. F., 8, 9, 19, 20, 21 magnet density in armature- core, III, I2O pitch of armature-winding, 158-167 relative permeance between magnet-cores, 231, 238 traction-resistance, 440 INDEX. 707 Average turn, length of, on mag- nets, 374 useful flux of dynamos, 212- 214 values of hysteretic resistance, no volts between commutator sections, 88, 151 weight and cost of dynamos, 412 Axial multipolar type, 270, 282 BackE.M.F.,or Counter E.M.F., 421, 423, 434, 438, 453, 461 pitch of armature-winding, 159-167 Backward lead, see Angle of Lag. Bacon, George W.,on magnetism of iron, 335 Bar armatures, 101, 567, 569, 588 Base, or bedplate, of dynamo, 299, 300 Battery-motors, 54, 91, 92 Baumgardt, L., on dimensioning of toothed armatures, 67 Baxter, William, on seat of elec- tro-dynamic force in iron clad armatures, 64 Bearings, 184, 186, 187, 190, 191, 192. 303-305, 516 Belt-velocity, 193 Belt-driven dynamos, 52^, 60, 132, 193, 194 Belts, calculation of, 193-195, 517 losses in, 409 Bifurcation of current in arma- ture, 48, 49, 51, 104 Binding-posts, contact area for, 183 Binding wires, for armatures, 75 Bipolar dynamos, act of commu- tation in, 29 classification of, 269, 270-278, 286 connecting formula for, 153 field densities for, 54 generation of current in, 27 running value of, 136 Bipolar iron clad type, 234, 235, 247, 255, 263, 637 Bipolar types, comparison of, 249- 256 practical forms of, 270-278 Blank poles, 469 Bobbin, formulae for winding of, 359-363 Bolted contact, 182, 183 Booster, 452 Bore of polepieces, 209, 210 Bottom-insulation of commutator, 171 Brass, current-densities for, 183 for brushes, 173, 176 for commutators, 169 for dynamo-base, 300 safe working load of, 189 Breadth of armature section, 92 of armature-spokes, 189, 516 of beltand pulley, 193-195, 517 of brush-contact, 175, 514 Breslauer, Dr. Max, on hysteresis- loss in toothed armatures, 591 Bristol-board, for armature-insu- lation, 85 Brunswick, on variation of air- gaps, 483 Brush, multi-circuit arc dynamo, 462 a Brushes, adjustment of, 696 arrangement of , on commuta- tor, 169, 170, 174 best tension for, 176-180, 515 dimensioning of, 175, 176, 515 displacement of, 30 material and kinds of, 171-174 number of, for multipolar dynamos, 34 Brush-holders, 181 Buck, H. W., on commutator- brushes, 177 Bullock Electric Mig. Co.'s teaser system of motor control, 452^ Burke, James, on insulating ma- terials, 86 Butt-joints in magnet-frame, 306 Cables, stranding of, 686, 687 size and weight of, Table, 688 Calculation of armature, 45-195, 413-416, 505, 527, 552, 566, 580, 587, 603, 629, 638, 644, 652, 656 of dynamotors, 452, 655 of efficiencies, 405-410, 526, 546, 565, 578, 602, 636, 643 of field magnet frame, 313- 327, 517, 534, 557, 572, 583, 593, 607, 632, 639, 646, 657 of generators for special pur- poses, 455-463 of leakage-factor, 217-263, 519, 536, 559. 573, 584, 595, 609, 614-628, 633 of magnetic flux, 200-216, 7oS INDEX. 517, 53i, 554, 568, 581, 589, 605, 638, 645, 657 Calculation of magnetizing forces, 339-356, 520, 537, 547, 56o, 575, 585, 596, 610, 634, 640, 647, 654, 658 of magnet-winding, 359-401, 486-497, 522, 540, 549, 562, 576, 599, 612, 635, 640, 649, 654, 659 of motors, 419-442, 628, 652 of railway motors, 431-442, 500-502 of unipolar dynamos, 443- 45i, 652 ific Canfield, M. C., on disruptive strength of insulating mate- rials, 86 Canvas, for armature-insulation, 78, 79 Capacity, maximum safe, of arma- ture, 132-135 of railway motor equipment, 440-442 Carbon-brushes, 171-180, 183 Card-board (press-board) for arma- ture-insulation, 78, 79, 80, 85 Carrying capacity of circular cop- per rods, Table, 682 of copper wires, Table, 681 Cast iron, in, 178, 189, 288, 312, 3i3, 448 Cast steel, in, 189, 288, 293, 448 Cast-wrought iron, or mitis metal, in, 294, 312,. 313 Causes of sparking, see Sparking. C.-G.-S. units, 7, 47, 199, 332, 333 Characteristic curves, 476-483 Charging accumulators, dynamos for, 91, 92, 461, 462 Checks on armature calculation, 130, 132, 135 Cheese-cloth, varnished, for arma- ture-insulation, 85 Chord-winding, or surface ring winding, 35, 89, 99, 165 Circuit, closed electric, 6, 317 magnetic, 317, 331 Circumflux of armature, 131 Clamped contact, 182, 183 Classification of armatures, 4 of armature-windings, 143, 144 of dynamos, 35, 269, 270 of field-magnet frames, 269, 270 of inductions, 23 Clearance between armature and pole-face, 209, 210 Clearance between pole-corners, 207, 208 Closed coil winding, 143, 144, 458 Coefficient, see Factor. Coil, closed, moving in magnetic field, u, 12 Coils, number of, in armature, 87-89. short-circuited, in armature, 28, 30, 149, 174, 175, 298 Coil-winding calculation, 359-373 Collection of current, by means of collector rings, 12 by means of commutator, 13 energy-loss in, 176-180 sparkless, see Sparking. Collection of large currents, 174 Collector, see Commutator. Combination brushes, 173, 174 Combination-frames, advantages of, 294 calculation of flux in, 260, 261, 621 joints in, 306-309 Combination-method of speed con- trol for railway motors, 436 Combination of shunt-coils for series field regulation, 378- 382, 523-526 Commercial or net efficiency, 406- 409, 422, 526, 546, 578, 602 copper, specific resistence of, 104, 105 wrought iron, permeability of, 311 Commutation, act of, 29 effect of, in generator and motor, 30 sparkless, in toothed and per- forated armature, 62 sparkless, promotion of, 30, 62, 172, 173, 297, 298, 299, 459, 463-470, 471, 472 Commutator, construction and di- mensioning of, 168-170, 514 principle of, 13, 14 thickness of insulation for, 171 trueing of, 699 Commutator-divisions, difference of potential between, 88, 151 number of, 87, 88 Compactness of railway motors, 432 Comparison of bipolar and multi- polar types, 487^ of efficiency-curves of motors, IXDEX. 709 Comparison of various types of dynamos, 248-256 Compensating ampere-turns, 348 Compound-dynamo, constant po- tential of, 43 efficiency of, 42, 43, 406, 408 E.' M. F. allowed for inter- nal resistance of, 56 Compound-dynamo, fundamental equations of, 41, 42, 43 over-compounding of, 43, 396 total armature current in, 109 Compound-motor, 406, 408, 426, 428, 644 Compound-winding, calculation of, 395-401, 456, 549. 563, 599, 649 principle of, 41-43 Conductivity, electrical, of copper and iron, 119 Conductor, armature-, see Arma- ture-Conductor. describing circle in magnetic field, 8 motion of, in uniform mag- netic field, 5 Conductor-velocities, 52 Connecting-formula for armature- winding, 152-155 Consequent poles, 275, 286, 327, 603 Constant current dynamos, see Arc-Lighting dynamos. excitation in compound dy- namo, 43 potential dynamos, 43 power work, motors for, 429, 431, 628 speed motors, 63, 426, 427 Construction-rules for field-frame, 288-309 Contact-area of commutator- brushes, 169, 174-176 Contact-resistance of commutator- brushes, 177-180 Contacts, various forms of, 181- 183 Continuous current, production of, 13, 14, 22 Conversion, efficiency of, see Effi- ciency, Gross. of motor into generator, 419, 628, 637, 644 Conveying parts, 181-183 Cooling surface, see Radiating Surface. Copper, current-densities for, 183 physical properties of, 101, 104^ 113, 362 Core, see Armature Core or Mag- net Core, respectively. Corsepius, on magnetic leakage, 262 Cost of dynamos, 288, 289, 300, 411, 412 Cotton, for armature-insulation, 78, 85 Cotton covering on wires, insulat- ing properties of, 85 weight of, 103, 367 Counter Electro-Motive Force, 421, 423, 434, 438, 453, 461 Magneto-Motive Force, see Armature-Reaction. Cox, E. V., on Cpmmutator- brushes, 177 Critical brush-tension, 176-179, 5i5 Crocker, Professor F. B., on high- potential dynamos, 462 on unipolar dynamos, 25, 26 Crocker Wheeler bipolar motors, dimensions of, 664 multipolar dynamos, dimen- sions of, 668 Cross-connection of commutator- bars, 35, 155 Cross-Induction, see Armature Re- action. Cross-Magnetization, see Arma- ture Reaction. Cross-Section, see Sectional Area. Crowding of magnetic lines in polepieces, 295 Current, alternating, 12, 13 collection of, from armature coil, 12 commutated, fluctuations of, 14-21 constant, see Constant Cur- rent. direction of, in closed coil, 12 in electric motors, 427-429, 642 in single inductor, 10 Current- density, circumferential, of armature, 130-132 in armature-conductor, 56, 57 in magnet-core, 364, 365 permissible, in materials, 183 Currents, eddy, or Foucault, see Eddy Currents. Curve of average E. M. F. in- duced in armature, 19 of E. M. Fs., rectified, 14 of induced current, 13 of induced E. M. F., 13 Curves, characteristic, 476-483 IO INDEX. Curves of contact-resistance and friction of commutator- brushes, 177, 178 of eddy current factors, 121 of hysteresis factors, 114 of potentials around arma- ture, 32, 33 of relative hysteresis-heat in armature-teeth, 68 of specific temperature-in- crease in armature, 128 of temperature-effect upon hysteresis, 117 Cutting of magnetic lines, 3, 5, 6, 8, 9, 12, 22, 27, 47, 48, 52, 200, 201 Cycle of magnetization, 109, no, in, 113, 115, 119, 121 Cylinder armature, see Drum Ar- mature. Cylindrical magnets, 232, 234, 291, 318, 319, 320, 323, 369, 374, 375 Data for winding armatures, 155- 167, 678 for winding magnets, 679 general, of railway motors, 435 Dead wire on armature, 94 Deflection of lines of force in gap- space, 225, 230, 349, 456 Definition of armature, 4 of closed and open coil wind- ing, 143 of dynamo-electric machine, of generator, 3 of magnetic units, 199 of motor, 3 of unipolar, bipolar, and mul- tipolar induction, 23 of unit induction, 47 Demagnetizing action of arma- ture, see Armature-Reaction. Density of current, 56, 57, 132, 133, 183 of magnetic lines, 54, 91, 313 Depth of armature-core, 92, 341, 342 of armature-winding, 70, 71, 74, 75 of magnet-winding, 317, 361, 371, 375, 377, 386, 387 Design of current conveying parts, 18,1-183 of generators for special pur- poses, 455-463 Design of magnet-frames, 270 309 of motors for different pur- poses, 429, 430 of railway motors, 432 Developed winding diagrams, 146,. 147 Diagram of closed coil armature- winding, 144 of doubly re-entrant winding^ 150 of duplex winding, 149 of drum-wound ring arma- ture, 101 of lap-winding, 145, 146 of long shunt compound- wound dynamo, 42 of mixed winding, 147 of open coil armature wind- ing, 144 of ordinary compound-wound dynamo, 41 of parallel armature winding, 165, 166 of series armature winding, 157 of series winding with shunt- coil regulation, 378 of series-wound dynamo, 36 of shunt-wound dynamo, 38 of simplex winding, 149 of singly re-entrant winding, 150 of spiral winding, 145 of wave winding, 146, 147 Diamagnetic materials, permea- bility of, 311 Diameter of armature-core, 58, 60, 61 of armature-shaft, 184-187, 516 of armature-wire, 57 of commutator brush-surface, 168, 514 of heads in drum armatures, 124 of magnet wire, 361, 362, 365 of pulley, 191, 517 Dielectrics, properties of, 83-86 Difference of potential, see Elec- tro-Motive Force. Differentially wound motor, 647, 648 Dimensions of armature-bearings, 184, 191, 516 of armature-core, 58-86 of belts, 194, 517 of driving-spokes, 188-190,. 5i6 of magnet-cores, 319-324 INDEX. 711 Dimensions of toothed and per- forated armatures, 65-72 of unipolar dynamos, 443- 446, 652 see also Length, Breadth, Diameter, Sectional Area, etc. Direct-driven machines, 52,61, 91, 132, 134, 136, 185, 187, 192 Direction of current, 10, 30 of E. M. F., 9 of rotation, 10, 12, 422 Disadvantages of laminated pole- pieces, 292 of multiple magnetic circuits, 286, 290 of multipolar frames for small dynamos, 285 of paper -insulation between armature-laminae, 93 of toothed and perforated ar- matures, 61, 62 Disc-armature, definition of, 4 Disruptive strength of insulating materials, 83, 84, 85 Dissipation of energy in armature core, T 10-122 in armature winding, 108, 109 in magnet winding, 370, 372 Distance between magnet-cores, 320-324 between pole-corners, 207, 208 Distortion of magnetic field, 225, 230, 349, 456 Distribution of flux in dynamo, 397-399 of potential around armature, 3i, 33 Division-strips in drum armatures, 73 Dobrowolsky's pole-ring, 49, 296 Double-current generators, 462^ Double horseshoe type, classifica- tion of, 269, 276 magnetic leakage in, 242, 252, 253, 263 Double magnet multipolar type, 270, 283 Double magnet type, classification of, 269, 275, 276 leakage factor of, 252, 254, 263 permeance across polepieces, in, 240. 242 permeance between magnet cores in, 237, 238 permeance between pole- pieces and yoke in, 246, 247 Doubly re-entrant armature-wind- ing, 150, 156, 160, 161 Drag, magnetic, see electro-dy- namic force, 63, 64 Draw-bar pull of railway motors, 440-442 Driving-horns for drum arma- tures, 73, 140 Driving-power for generator, 408, 420 Driving-spokes for ring armatures, 186, 188-190, 516 Drop of voltage, 37, 39, 43 Drum armature dimensions, Table of, 671 armatures, allowance for di- vision-strips in, 60 bearings for, 191 core densities for, 91 definition of, 4 diameters of shafts for, 186 heating of, 129, 130 height of winding in, 75 insulation of, 78, 79 radiating surface of, 123-125 size of heads in, 123, 124 speeds and diameters of, 60 total length of wire on, 95 Drum-wound ring armatures, 35, 89, 99, 165 Duplex, or double, armature wind- ing, 149, 151, 156, 160, 166, 167 Dynamo-electric machines, defini- tion of, 3 Dynamo-graphics, 476-502 Dynamo speeds, high, medium and low, Table of, 52^. Dynamos, bipolar, see Bipolar Dynamos. constant current, see Arc- Lighting Dynamos. Electro-plating, Electro-typ- ing, etc., see Electro-Metal- lurgical Dynamos. for charging accumulators, 91, 92, 461, 462 list of, considered in prepara- tion of Tables, see Preface iii-v. multipolar, see Multipolar Dynamos. unipolar, or homopolar, see Unipolar Dynamos. Dynamos of various Manufactur- ers: Aachen Electrical Works, 277 Actien-Gesellschaft Elektrici- tatswerke, 273, 274, 278, 281 712 INDEX. Dynamos of various Manufactur- ers Continued. Adams, A. D., see Commercial Electric Co. Adams Electric Co., 270 Akron Electric Manufacturing Co., 275 Alioth, R., & Co., 281 Allgemeine Electric Co., 49, 281 Alsacian Electric Construction Co., 281 Atkinson, see Goolden & Trot- ter Aurora Electric Co., 272 Bain, Force, see Great Western Electric Co. Baxter Electrical Manufactur- ing Co., 276, 281 Belknap Motor Co., 272, 280 Berliner Maschinenbau Actien- Gesellschaft, 273, 281 Bernard Co., 271 Bernstein Electric Co., 274 Boston Fan Motor Co., 274 Brown, C. E. L., see Oerlikon Machine Works. Brush Electrical Engineering Co., 278, 282, 283 . Brush Electric Co., 276, 459 <1 C. & C." (Curtis & Crocker) Electric Co., 270, 276, 282, 283 Card Electric Motor and Dy- namo Co., 272, 274, 278 Chicago Electric Motor Co., 274 Clarke, Muirhead & Co., 272 Glaus Electric Co., 280 Columbia Electric Co., 271, 280 Commercial Electric Co., 275 Crocker-Wheeler Electric Co., 272, 280, 398, 664, 668 Crompton & Co., 276, 277 Cuenot, Sauter & Co., 282 Dahl Electric Motor Co., 281 "D. & D." Electric Co., 274 De Mott Motor and Battery Co., 275 Desrozier, M. E , 282 Detroit Electrical Works, 271,. 277 . Detroit Motor Co., 272 Deutsche Elektricitatswerke, 278, 281 Dobrowolsky, M. von Dolivo-, see Allgemeine Electric Co. Donaldson-Macrae Electric Co. , 273 Duplex Electric Co., 275, 285 Eddy Electric Manufacturing Co., 280 Dynamos of various Manufactur- ers Continued. Edison General Electric Co.,i68, 270, 284, 305, 308, 435, 458, 621, 665 Edison Manufacturing Co., 275, 278 Eickemeyer Co., 277 Elbridge Electric Manufactur- ing Co., 274 Electrical Piano Co., 275 Electro-Chemical and Specialty Co., 282 Electro-Dynamic Co., 276 Electron Manufacturing Co., 170, 271, 274, 284 Elektricitats-A c t i e n-G e s e 1 1- schaft, 281 Elliot-Lincoln Electric Co,, 284 Elphinstone & Vincent, 284 Elwell-ParkerElectricConstruc- tion Corporation, 277, 284 Erie Machinery Supply Co., 278 Esson, W. B., see Patterson & Cooper. Esslinger Works, 283 Excelsior Electric Co., 272, 273, 459 Fein & Co., 275,^276, 277, 281 Fontaine Crossing and Electric Co., 276 Ford-Washburn Storelectric Co., 276 Fort Wayne Electric Corpora- tion, 170, 274, 277, 280, 283, 458 Fritsche & Pischon, 282 Fuller, see Fontaine Crossing and Electric Co. Garbe, Lahmeyer & Co., see Deutsche Elektricitatswerke. Ganz & Co., 273, 281 General Electric Co., 270, 277, 278, 280, 282, 284, 435, 667, 669 General Electric Traction Co., 275 Goolden & Trotter, 274 Granite State Electric Co., 277 Great Western Electric Manu- facturing Co., 273, 280, 458 Greenwood & Batley, 274 Gulcher Co., 170 Helios Electric Co., 276, 282 Henrion, Fabius, 282 Hochhausen, see Excelsior Elec- " trie Co. Holtzer-Cabot Electric Co., 272, 274 Hopkinson, Dr. J., see Mather and Platt. INDEX. 7'3 Dynamos of various Manufactur- ers Continued. Immisch & Co., 276, 618 India Rubber, Guttapercha and Telegraph Works Co., 272 Interior Conduit and Insulation Co , 277, 283 Jenney Electric Co., 273 Jenney Electric Motor Co., 274 Johnson & Phillips, 273 Johnson Electric Service Co., 278 Kapp, Gisbert, see Johnson & Phillips. Kennedy, Rankine, see Wood- side Electric Works. Keystone Electric Co., 272, 275 Knapp Electric and Novelty Co., 272 Kummer, O. L. & Co., see Ac- tien-Gesellschaft Elektrici- tatswerke. Lahmeyer, W., see Aachen Electrical Works. Lahmeyer, W. & Co., see Elek- tricitats-Actien-Gesellschaft. Lafayette Engineering and Electric Works, 278 La Roche Electrical Works, 272, 277 Lawrence, Paris & Scott, 276 Lundell, Robert, see Interior Conduit and Insulation Co. Mather & Platt, 272, 276 Mather Electric Co., 275, 280, 281 Mordey, W. H., see Brush Elec- trical Engineering Co. Muncie Electrical Works, 278 N agio Brothers, 274, 275, 276, 281 National Electric Manufactur- ing Co., 272 Novelty Electric Co., 271 Oerlikon Machine Works, 276, 278, 281, 435 Onondaga Dynamo Co., 277 Packard Electric Co., 274 Patterson & Cooper, 170, 273, 614 Ferret, see Electron Manufac- turing Co. Porter Standard Motor Co., 274 Premier Electric Co., 274 Riker Electric Motor Co., 274, 280, 281 Royal Electric Co., 170 Schorch, 276 Schuckert & Co., 49, 276, 278, 281, 282 Schuyler Electric Co., 459 Dynamos of various Manufactur- ers Con tin ued. Schwartzkopff, L., see Berliner Maschinenbau Actien-Gesell- schaft. Shawhan-Thresher Electric Co., 278, 280 Short Electric Railway Co., 282, 283, 435 Siemens & Halske Electric Co., 168, 170, 273, 275, 281 Siemens Brothers, 272 Simpson Electric Manufactur- ing Co., 274 Snell, Albion, see General Elec- tric Traction Co. Sperry Electric Co., 458 Sprague Electric Co., 398 Stafford & Eaves, 278 Standard Electric Co., 280, 458 Stanley Electric Manufacturing Co., 280 Storey Motor and Tool Co., 170, 284 Thomson-Houston Electric Co., 277, 458, 624 Thury, see Cuenod, Sauter & Co. Triumph Electric Co., 170, 278 United States Electric Co., 274, 276 Waddell-Entz Co., 283 Walker Electric Manufacturing Co., 170, 280, 435 Wenstrom Electric Co., 278, 284 Western Electric Co., 276, 458 Westinghouse Electric and Man- ufacturing Co., 280, 435, 666 Weston, see United States Elec- tric Co. Wood, see Fort Wayne Electric Corporation. Woodside Electric Works, 274 Zucker & Levitt & Loeb Co., 281 Zucker & Levitt Chemical Co., 271 Zurich Telephone Co., 273, 278, 281, 285 Dynamotors, 452-454, 655 Ebonite, see Hard Rubber. Ecentricity of polefaces, 298 Economic coefficient, 406-409 Eddy Co., Equalizing system, 452^ Eddy currents in armature con- ductors, 107, 119 714 INDEX. Eddy currents in armature core, 107, 119-122 in polepieces, 295 Edge-insulation of armature, 79, 82 Edison bipolar dynamos, dimen- sions of, 665 Edser, Edwin, on magnetic leak- age, 262 Effective height of armature wind- ing, 74 of magnet winding, 377 Effective length of armature con- ductor, 49 Effects, mechanical, of armature winding, 137-142 Efficiencies, average, of electric motors, 422 Efficiency, commercial, or net, 406-409, 422, 526, 546, 565, 578, 602 electrical, 37, 38, 39, 40, 42, 43, 405, 406, 422, 526, 546, 565, 578, 602 gross, 409, 410, 422, 526, 546 of armature as an inductor, 135 relative, of magnetic field, 211-214, 512, 533, 557, 572 space-, of various railway motors, 435 weight-, 33, 410-412, 527, 546, 565, 578, 602 Effort, horizontal, of railway mo- tors, 440-442 Electro-dynamic force, seat of, in toothed armatures, 63, 64 Electro-magnet, see Magnet. Electro-metallurgical dynamos, designing of, 459-461 field-density for, 54 magnetic density in armature of, 91, 92 unipolar forms of, 25, 652 Electro-motive Force, addition of, in closed coil, 12 allowed for internal resist- ances, 56 at various grouping of con- ductors, 151 average, 8, 9, 19, 20, 21 direction of, 9 fluctuation of, 19 magnitude of, 6 production of, 4 Elliptical bore of field, 296 magnet-cores, 289, 291 Embedding of armature-conduc- tors, see Perforated Armature. Emission of heat from armature, 126, 127 Empirical formula for heating of drum armatures, 129 Enamel, for armature-insulation, 78, 94 End-insulation of commutator, 171 End-rings for armature, 188, 590 Energy-dissipation, see Dissipa- tion of Energy. Energy-loss, specific, in armature, 126-128 in magnets, 368, 371, 372 Energy-losses in armature, 107- 122 in collecting armature cur- rent, 176-180, 515 in magnets, 366, 368, 372, 375, 383, 399- 4oo, 577 Equalizing dynamo, 452^: Equations, fundamental, for dif- ferent dynamos, 36-43 Equivalents of wires, Table of, 684-685 Esson, W. B., on capacity of ar- matures, 131 on magnetic leakage, 262 Evenness, degree of, of number of conductors for series wind- ings, 159-163 Ewing, Professor J. A., on hys- teresis, no, 115 on magnetism of iron, 335 on permeability of cast-steel, 289 Examples, 158, 162, 167, 249-256, 481, 488, 492, 495, 501, 505-660 Excitation of field-magnetism, methods of, 35 Exploration of magnetic field, 31 of magnetic flux, 397, 398 Exponent, hysteretic, 116 of output-ratio, 416, 417 External characteristic, 476 Extra-resistance, 383, 384, 385, 393, 540 Face-connection of drum-wound ring armature, 101 Face-insulation of armature-core, 79, 82 Face-type commutator, 168 Factor of armature ampere-turns, 480 of armature reaction, 352 of brush-lead in toothed and perforated armatures, 350 INDEX. 715 Factor of core-leakage in toothed and perforated armatures, 219 of eddy-current-loss, 120-122 of field-deflection, 225, 230 of hysteresis-loss, 112, 113, 115 of magnetic leakage, 215, 217- 265 of safety, 189, 190 Faults, remedy of, in dynamos and motors, 695-704 Fay, Thomas J., on constant speed motors, 427 Feather-keys, 309 Feldkamp motor, 275 Fibre, vulcanized, for armature- insulation, 79, 84, 85 Field-area, effective, 204, 207 Field-bore, diameter of, 209, 210 Field-density, actual, of dynamo, 202, 204, 205, 206 definition and unit of, 199 practical values of, 54 Field-distortion, 225, 230, 349, 456 Field-efficiency, 211-213 Field-excitation, methods of, 35-43 Field-magnet frame, see Magnet- Frame. Field, magnetic, see Magnetic Field. unsymmetrical, effect of, on armature, 140-142, 513, 534 Finger-rule for direction of cur- rent and motion, 10 Firms, see Dynamos of various Manufacturers. Fischer-Hinnen, J., on dynamo- . graphics, 487, 497, 500 on prevention of armature- reaction, 464 Fitted contact, 182, 183 Fittings (brush holders, conveying parts, switches, etc.), 181-183 Flanges for magnet-cores, 308, 523, 542, 576, 595, 650 on field-frames, 287 Flat-ring armatures, 93 Fleming, Professor J. A., on eddy current loss. 121 on rule for direction of cur- rent, 10 Flow of magnetic lines, see Flux. Fluctuations of E. M. F. of com- mutated currents, 14-21 Flux-density, magnetic, in air- gaps, 54 in armature-core, 91 in magnet-frame, 313 Flux, distribution of, in dynamo, 397-399 Flux, magnetic, 199, 331 total, of dynamo, 214, 257- 261 useful, of dynamo, 92, 133, 200-202, 211-214 Foppl, A., on hollow magnet- cores, 292 Forbes, Professor George, on leakage formulae, 216 on prevention of armature- reaction, 465 Force, attractive, of magnetic field, 140, 141, 513, 534 electro-dynamic, in toothed armatures, 63, 64 Electro-Motive, see Electro- motive Force. horizontal, exerted by railway motor, 440-442 magnetizing, see Magnetiz- ing Force. peripheral, of armature-con- ductors, 138-140, 188, 513, 534 thrusting, on armature, 140- 142, 513, 534 tangential, at pulley-circum- ference, 193, 287 due to brush-friction, 179, 515 Ford, Bruce, on unipolar dyna- mos, 25 Forged steel, 448, 450 Forms of cross-section for magnet- cores, 289-291 of dynamo-brushes, 172-174 of field magnet frames, 269- 287 of fields around ring arma- ture, 98 of polepieces, 30, 295-299 of slot-insulation for toothed and perforated armatures, 81 of unsymmetrical bipolar fields, 142 Formulae for dimensions, wind- ing data, etc. , see Dimensions, Diameter, Length, Breadth, Sectional Area, Number, etc. fundamental, 7, 8, 9, 36-43, 55, 57, 200, 201, 219, 314, 334, 377, 385 Foucault currents, see Eddy Cur- ents. Four-coil armature, 17, 1 8 Fourpolar double magnet type, 240, 270, 285 iron-clad type, 236, 255, 263, 270, 284, 603 Frame, see Magnet Frame. Frequency, no, in, 119, 287^ 7 i6 INDEX. Friction, losses by, 406-409, 526, 546, 565, 5?8, 602, 636, 643, 651 of commutator-brushes, 176- 180 Fringe of magnetic field, 29, 30 Frisbee, Harry D., on distribution of magnetic flux, 397 Front-pitch of magnetic-winding, 159-167 Fundamental calculations for ar- mature winding, 47-57 equations for different excita- tions, 36-43 permeance formula, 219 Gap, see Air Gap. Gap-circumference, effective, 135 Gauges of wire, 103, 367 Gauss, the unit of magnetic den- sity, 199 Gauze brushes, 171, 173 Gearing of railway motors, 433 Gearless railway motors, 434 General Electric Co. 's generators, dimensions of, 667, 669 Generation of E. M. F., 4, 22, 47 Generator, electric, definition of, 3 German Silver rheostat coils, Table of, 690 " Giant " dynamo, 272 Gilbert, the unit of magnetomo- tive force, 333 Grade of railway track, 440, 441 Graphic methods of dynamo-cal- culation, 476-502 Grawinkel & Strecker, on forms of field-magnets, 273, 274, 275, 276, 278, 281, 282 Griscom motor, 276 Gross Efficiency, 409, 410, 422, 526 Grotrian, Professor, on hollow magnet-cores, 291 Grouping of armature-coils, 147 of magnetic circuits, 353-356 'Gun-metal, 169 H Hard rubber, 85 Hardness, magnetic, no Head in drum-armatures, 123, 124 Heat, effect of, on hysteresis, 117 on insulation-resistance, 85 Heating of armatures, 127, 129, 130, 132, 699 of bearings, 701 Heating of commutator and brushes, 700 of magnet-coils, 368-371, 699 Height of armature winding, 70, 7i. 74, 75 of magnet winding, 317, 361, 3?r, 375, 377, 386, 387 of polepieces, 326 of zinc blocks, 301-303, 536 Hering, Carl, on unipolar dyna- mos, 25 Herrick, Albert B., on insulating materials, 86 Heteropolar induction, 23, 26 High-potential dynamos, 462, 463 High-speed dynamos, 52^, 60, 91, 132, 134, 136, 185, 187, 192, 193 Hill, Claude W., on strength of reversing field, 471 Hobart, H. M., on armature wind- ing, 156 Holes in core-discs, see Perforated Armature. Hollow magnet-cores, 290-292 Homopolar dynamos, see Unipolar Dynamos. Hopkinson, Dr. J., on hysteresis, no Hopkinson, J. & E., on magnetic leakage, 262 Horizontal effort of railway mo- tors, 438-442 magnet types, 238, 239, 245, 246, 251, 253, 254, 263, 269, 270, 273, 275, 276, 277, 284, 285 Horns for driving drum armatures, 73, 140 of polepieces, see Pole-Tips. Horsepower, the unit of work, 137 Horseshoe types, leakage factors of, 249-251, 252-254, 263 permeance across polepieces in, 238, 242 permeance between magnet cores in, 231-233 permeance between pole- pieces and yoke in, 245, 246 Huhn, George P. , on distribution of potential, 32 Hysteresis, definition of, no variation of, with density of magnetization, 116 variation of, with tempera- ture, 118 Hysteresis-heat, specific, in toothed armatures, 69 Hysteresis-loss in armature, cal- culation of, 107, 109-118, 591 INDEX. 717 Hysteretic exponent, 116 resistance, no, in I Ideal position of brushes, 29 Impurities in cast steel, 288, 289 Incandescent generators, large, field-densities for, 54 magnetic density in armature of, gi shunt-excitation of, 39 Inclined magnet types, 232, 269, 276 Induction, electro-magnetic, 3, 5, 22, 23, 47, 48, 405, 423 Inductor, see Armature Conduc- tor. Ineconomy of small dynamos, 472 Innerpole types, 131, 168, 263, 264, 269, 270, 281, 282, 287, 566, 580 Insulating materials, properties of, 83-86 Insulation, between laminae of armature core, 93, 94 of armature, resistance of, 86, 5io of armature, thickness of, 82 of commutator-bars, 171 of magnet-cores, thickness of, 543. 565, 576 weight of, on round gauge wire, 103 Intake of motor, 405, 420 Integrated curve of potentials, 32, 33 Intensity, see Density. Intermittent work, motors for, 429-431,637 Internal characteristic, 476 Inventors, see Dynamos of rarious Manufacturers. Inverted horseshoe type, 240, 241, 246, 250, 263, 264, 269, 272, 286, 299, 614 Iron-clad types, classification of, 269, 270, 277, 278, 284 leakage -factor for, 255, 256,263 permeance across polepieces in, 243 permeance between magnet cores in, 234-237 permeance between pole- pieces and yoke in, 247 Iron, for armature-cores, 93, 94, no, 113, 115, 118, 119, 120, 121, 122 for magnet-frame, 30, 288, 289, 293, 294, 300, 305-309 Iron, hysteretic resistance for va- rious kinds of, in permeability of different kinds of, 310-313 projections, effect of, in mag- netic field, 64 specific magnetizing forces, for different kinds of, 336-338 wire, for armature-, and mag- net winding, 472-475 wire, for armature-cores, 93^ 94, no, 113, 115 wire, for rheostats, 689 Ives, Arthur Stanley, on magnetic leakage, 262 Jackson, Professor Dugald C., on ratio, cross-section, 292, 293 Japan (enamel) for armature-insu- lation, 78, 94 Joints in magnetic circuit, 305-309 Journals, calculation of, 184, 186, 187, 190, 191, 192, 303-305, 5i6 friction in, 406-409, 526, 546, 565, 578, 602, 636, 643, 651 Kapp, Gisbert, on diametral cur- rent density of armature, 133 on magnetic leakage, 216 on permeability of cast steel 289 Kelvin, Lord, see Thomson, Sir William. Kennedy, Rankine, on shape of polepieces, 299. Kennelly, A. E., on magnetism of iron, 335 on seat of electro-dynamic force in iron-clad armatures, 64 "King" dynamo, 271 Kittler, Professor Dr. E., on forms of field magnets, 273, 275, 276., 277, 281, 282, 283, 285 Klaasen, Miss Helen G., on hys- teresis, 115 Knee of saturation curve, 312 Knight, Percy H., on magnetisms of iron, 335 Kolben, Emil, on railway motor construction, 431 on worm-gearing for electric motors, 434 Kunz, Dr. W., on hysteresis, ii& 7 i8 INDEX. Lag, angle of, 30, 421 Lahmeyer, W., on magnetic leak- age, 262 Laminated joint, 182 Lamination of armature core, 93, 94, 119-122 of polepieces, 297 Lap-, or loop-, winding, 144, 145, 152 Law of armature-induction, 47, 48, 49 of conductance, 219 of cutting lines of force, 47, 200 of hysteresis, no of magnetic circuit, 331 Ohm's, 36, 41, 384, 393 Layers, number of, of armature wire, 74, 508 Lead of brushes, 30, 349, 350, 421 Leads for current, 181-183, 379, 524 Leakage, magnetic, calculation of, from dimensions of frame, 217-256 calculation of, from machine- test, 257-265 in toothed armatures, 53, 218, 219 Leakage factors, Tables of, 263,265 Leather, safe working strength of, 193 Leatheroid for armature-insula- tion, 79, 85 Lecher, Professor, on unipolar dynamos, 25 Length of armature-conductor, 55, 95-100 of armature-bearings, 190-192 of armature-core, 76 of armature-shaft, 184 of commutator brush-surface, 168, 176, 515 of heads in drum armatures, 123, 124 of magnet-cores, 316-319 of magnetic circuit, 224, 230, 243, 347, 348 of magnet-wire, 360 of mean turn on magnets, 374 Liberation of heat from armature, 126, 127 Limit of armature capacity, 132 of magnetization, 313 Limiting currents for copper wires, 680 Line, neutral, of magnetic field, 225, 459 Line-potential for railway motor, 442 Lines of force, cutting of, 3, 5, 6, 8, 9, 12, 22, 27, 47, 48, 52, 200 definition and unit of, 199 Linseed oil ; for armature insula- tion, 83, 85 Load-limit of armature, 132-135 Localization and remedy of trou- bles in dynamos and motors, 695-704 Long connection type of series armature winding, 157, 158 Long shunt compound winding, 41 Loop winding, 144, 145, 152 Losses in armature, 107-126 in bearings, 406-409, 526, 546, 565, 578, 602, 636, 643, 651 in belting, 409 in commutator-brush-contact, 175, 176-180 Low-speed dynamos, 52, 61, 91, 132, 134, 136, 185, 187, 192 Lubrication of bearings, 305 of commutator, 177, 179 Lugs for connecting cables, 181, 182 M Magnet-cores, dimensioning of, 316-324 general construction rules for, 288-293 relative average permeance between, 231-238 Magnet-frame, classification of types of, 269, 270 dimensioning of, 313-327 general design of, 288-309 magnetizing force for, 344- 348 Magnetic circuit, air-gap in, see Air-Gaps. joints in, 305-309 law of, 331 reluctance of, 331 Magnetic field, definition and unit of, 199 exploration of, 31 fringe of, 29, 30 motion of conductor in, 5 relative efficiency of, 211 Magnetic flux, see Flux. intensity, or magnetic den- sity, 54, 91, 313 INDEX. 719 Magnetic leakage, see Leakage, Magnetic. permeability, 310-312 potential, 224 pull on armature, or arma- ture-thrust, 140-142, 513, 534 reluctance, 331 units, definition of, 199 Magnetization, absolute and prac- tical limits of, 313 influence of, on brush-lead in iron-clad armatures, 350 influence of, on hysteretic ex- ponent, 116 influence of, on magnetizing force, 336, 337 Magnetizing force for air-gaps, 339. 340 for any portion of a circuit, 333-338 for armature-core, 340-343 for compensating armature- reaction, 348-352 for field- frame, 344-348 Magnetomotive force, 331 Magnet-poles, number of, for va- rious speeds, Table, 287^: Magnet-winding, calculation of, 3 59-401, 450, 451, 486-497, 522, 540, 549, 562, 576, 599, 612, 635, 640, 649, 654, 659 methods of excitation of, 35 Magnet-wire (S.C.C.), data of, 679 " Manchester" dynamo, 276 Manganese, in cast steel, 288, 289 Martin & Wetzler, on electric motors, 270 Mass of iron in armature core, no, in, 112, 114, 119, 120 Materials for armature core, 93 for armature insulation, 83-86 for commutator, 169 for dynamo-base, 299, 300 for magnet-cores, 288 for polepieces, 53, 296 Mavor, on magnetic leakage, 264 Maximum efficiency, current for, of motors, 428, 429, 642 electrical efficiency, of shunt- dynamo, 39, 40 safe capacity of armature, 132-135 Maxwell, the unit of magnetic flux, 199, 200 Mean E. M. F., 21 Mechanical calculations about ar- mature, 184-195, 516, 517 effects of armature-winding, 137-142, 513, 534 Merrill, E. A., on capacity of rail- way motors, 438 Metallurgical dynamos, see Elec- tro-Metallurgical Dynamos. Mho, unit of electrical conductiv- ity, 119 Mica, for armature-insulation, 78, 79, 83, 85 for commutator-insulation, 170-171 Micanite, for armature-insulation, 80, 81, 84, 85 Mitis iron, in, 294, 312, 313 Mixed armature winding, 144, 147 Monell, A., on effect of tempera- ture on insulating materials, 86 Mordey, W. H., on prevention of armature-reaction, 465 Motion, relative, between conduct- ors and magnetic fields, 3-12 Motor, electric, calculation of, 419-442, 628-652 definition of, 3 failure of, 704 Motor-generators, 452 Multi-circuit arc dynamos, 462^ Multiple circuit winding, 148, 151, 152, 154 Multiplex, or multiple, winding, 149, 150, 151, 160, 165 Multipolar dynamos, classification of, 269, 270, 279-285, 287 connecting formula for, 154, 155 economy of, 33 field-densities for, 54 kinds of series windings pos- sible for, 156 number of brushes for, 34,102 permeance across polepieces in, 243, 244 permeance between magnet cores in, 233, 234 permeance between pole- pieces and yoke in, 247, 248 Multipolar types, practical forms of, 279-285 Monroe and Jamieson, on insula- tion-resistance of wood, 85 Muslin, for armature-insulation, 79,85 N Negbauer, Walter, on magnetism of iron, 335 Net-efficiency, 406-409 ' Neutral points, 148, 459 720 INDEX. Noises in dynamos, causes and prevention of, 701 Normal load, calculation of mag- netizing force for, 396 Number of ampere-turns, 333-352 of armature circuits in multi- polar dynamos, 49, 104 of armature conductors, 76, 77, 159-163 of armature divisions, 90 of brushes in multipolar ma- chines, 34, 102 of coils in armature, 15-21, 87, 9> 153-155, I ?. 8 -. I ^3 of commutator divisions, 87 of convolutions per commu- tator division, 89 of cycles of magnetization, iio, in, 112, 119, 121 of layers of wire on arma- ture, 74, 508 of lines of force per square inch, 54, 91 of pairs of magnet poles, 48, 51, 53, 287^ of reversals of E. M. F. in one revolution of conductor, 22, 23 of revolutions of armature, 58, 60, 61 of slots in toothed and per- forated armatures, 65, 66, 70, 71 of useful lines of force, 7, 9, 92, 133, 200-202, 2II-2I4 of wires per layer on arma- ture, 72, 73, 74 Oersted, the unit of magnetic re- luctance, 333 Ohm's law, 36, 41, 384, 393 Oiled fabrics (paper, cloth, silk) for armature insulation, 78, 85 One-coil armature, 15, 20 One-material magnet frame, cal- culation of flux in, 259, 614, 618, 624 joints in, 305, 306, 307 Open circuit, calculation of mag- netizing forces for, 395 Open-coil winding, 143, 144, 458 Ordinary compound dynamo, 41 Outer inner-pole type, 270, 283 Outerpole types, 269, 270, 280, 281, 287, 304 Output, formulae for, 405, 420, 438 maximum, of armature, 132- 135 Output of dynamo as a function of size, 416-418 Oval magnet cores, 232, 234, 289,. 291, 318, 322, 374 Over-compounding, 43, 396 Over-type, 272, 278, 304 Owens, Professor R. B., on closed coil arc dynamo, 455 Oxide coating for insulating ar- mature-laminae, 93, 94 Paper, for armature insulation, 78, 85, 94 Paraffined materials, for armature insulation, 83, 85 Parallel, or multiple circuit, arma- ture winding, 148, 151, 152, 154 Parchment, for armature insula- tion, 85 Parmly, C. H., on unipolar dyna- mos, 25 Parshall, H. F., on armature windings, 156 on use of steel in dynamos, 288 Pedestals for dynamos, 142, 303 Perforated armatures, advantages and disadvantages of, 61, 62, 63 core-leakage in, 53, 218, 219 definition of, 4 dimensioning of, 71, 72 effective field area of, 207 insulation of, 81 percentage of effective gap, circumference for, 135 percentage of polar arc for, 50 Peripheral force on armature-con- ductors, 138, 139 on pulley, 193 Peripheral speed of armature, 52, 53 of pulley, 193 Permeability of iron, 310-312 Permeance, law of, 219 relative, across polepieces, 238-244 relative average, between magnet cores, 231-238 relative, between polepieces and yoke, 244-248 relative, general formulae for, 220-223 relative, of air-gaps, 224-230 Permissible current densities, 180 energy-dissipation, in arma- ture, 127 INDEX. 721 Permissible energy-dissipation, in magnets, 372 Perry, C. L., on effect of tempera- ture on insulating materials, 86 " Phoenix " dynamo, 614 Phosphor-bronze, 169, 189, 434 Phosphorus, in cast steel, 288 Physical principles of dynamo- electric machines, 3-43 Picou, on E. M. F. of shunt dy- namo, 485 Pierced core-discs, see Perforated Armatures. Pitch of armature-conductors, 414, 415 of armature-winding, 152- 167 of slots in toothed armatures, 65. 7i Plating dynamos, see Electro- Metallurgical Dynamos. Plugs, for switch connections, 182, 183 Points, neutral, on commutator, 148 Polar arc, 49, 203, 207, 210 Pole-armature, 4 Pole-bridges, 296 Pole-bushing, 49, 296 Pole-corners, 207, 208, 298 Pole-faces, eccentricity of, 298 Pole-number for multipolar field- magnets, 287^ Pole-pieces, bore of, 209, 210 dimensioning of, 325-327 magnetic circuit in, 346, 348 material and shape of, 293- 299 Pole-strength, unit of. 199 Pole-surface, 127, 128, 204 Pole-tips, '296, 298 Poole, Cecil P., on simplified method of calculation, 413 Position of brushes, 29, 697 Potential, distribution of, around armature, 31-33 magnetic, 224 Power for driving generator, 420 for propelling car, 440-442 Power-losses, see Energy-losses. Power-transmission, dynamos for, 91 1 497 Practical field densities, 54 limit of magnetization, 313 values of armature induction, 50 working densities in magnet frame, 313 Press-board, for armature insula- tion, 78, 79, 80, 85 Pressure, best, of commutator brushes, 176-179, 515 effect of, on joints, 306, 307 electric, see Electro-Motive Force. Prevention of armature-reaction, 463-470 of armature-thrust, 298 of crowding of lines in pole- pieces, 295, 296 of eddy currents in pole- pieces, 297 of sparking, 30, 62, 172, 173, 297, 298, 299, 459, 465, 471, 472 of vibration, 287, 299, 431 Principles, physical, of dynamo- electric machines, 3-43 Production of continuous current, 13, 14, 22 -of E. M. F., 4 , 5, 47, 48 Projecting teeth, 76, 134, 219, 228, 229 Projections of magnet-frame, 294 Puffer, Professor, on magnetic leakage, 262 Pull, see Force. Pulley, calculation of, 191, 195 O Quadruple magnet type, 270, 285, 299 Quadruplex armature winding, 150 Quadruply re-entrant armature- winding, 150 Qualification of number of con- ductors for various windings, 157-167 Radial clearance of armature, 209 depth of armature core, 92 multipolar type, 243, 248, 269, 280, 281, 566, 587, 624, 644 Radiating surface of armature, 52, 122-126 of magnets, 369 Radiation of heat from armature, 126, 127 Radi-tangent multipolar type, 270, 282 Railway-generators, adjustment of carbon brushes in, 172 magnetic density in armature of, 91 722 INDEX. Railway-generators, toothed arm- atures for, 62 Railway-motors, calculation of, 438-442, 500-502 general data of, 435 magnetic density in armature of, QI Randolph, A., on unipolar dyna- mos, 25 Ratio of armature- to field ampere- turns, 340, 349 of clearance to pitch in slotted armatures, 230 of core-diameter to winding diameter of small armatures, 59 of height of zinc-blocks to length of gaps, 301, 302 of length to diameter of drum armatures, 96, 97 of length to diameter of mag- net-cores, 320-322 of magnet-, to armature cross- section, 292, 293 of mean turn to core diameter of cylindrical magnets, 375 of minimum to maximum width of tooth in iron clad armatures, 592 of net iron section to total cross-section of armature- core, 94 of pole-area to armature radi- ating surface, 127 of pole-distance to length of gaps, 208 of radiating surface to core surface of magnets, 371 of shunt-, to armature-resist- ance, 40 of speed-reduction, of rail- way motors, 433, 435 of transformation, of motor- generators, 454, 656 of width of slots to their pitch on armature circumference, 219, 230 of winding-height to diame- ter of magnet core, 317, 371 Reaction of armature, see Arma- ture-Reaction. Rectangular magnet-cores, 233, 289, 291, 318, 321, 369, 374 Rectification of alternating cur- rents, 13, 14 Re-entrancy of armature-wind- ing, 150 Regenerative armatures, reversi- ble, 467 Regulation of arc lighting dyna- mos, 458, 459 of railway motors, 436, 437 of series dynamos, 377-382, 523-526 of shunt dynamos, 390-394, 487-497 Reid, Thorburn, on railway mo- tor calculation, 438 Relation between brush-lead and density of lines in armature- teeth /3 50 between core-leakage and shape of slots in toothed ar- matures, 219 between effective gap circum- ference and polar embrace, 135 between electrical efficiency and ratio of shunt- to armature resistance, 40 between fluctuation of E. M. F. and number of commuta- tor divisions, 19 between horizontal effort and grade, 441 between size and output of dynamos, 416-418 between temperature in- crease and peripheral velocity of armature, 127, 128 between temperature in- crease and winding depth of magnets, 371 between total length of ar- mature wire and ratio of length to diameter of core, 96 Reluctance, 331 Reluctivity, 331 Resistance, hysteretic, of various kinds of iron, in insulation-, of various mate- rials, 85 internal, of dynamo, E. M. F. allowed for, 56 of armature-winding, 102-106 of copper wire, Table, 676- 677 of magnet-winding, 375, 376, 384, 388, 399, 400, 679 Resistance-method of speed-con- trol for railway motors, 436 Reversing field, strength of, 471 Rheostat for regulating series dy- namos, 377-382, 523-526 for regulating shunt dyna- mos, 390-394, 487-497, 543-546 for starting motors, 424 wire for, 689, 690 INDEX. 723 Ribbon armature-cores, 93 copper-, for series field wind- ing, 36, 376 Ring-armature dimensions, Table of, 670 Ring-armatures, bearings for, 192 core-densities for, 91 definition of, 4 diameters of shafts for, 187 drum- wound, 35, 89, 99, 165 height of winding space in, 75 insulation of, 80, 81 radiating surface of, 125, 126 speeds and diameters of, 60, 61 total length of conductor on, 9 s * 99 Ring-winding, 144, 152, 154, 189 Robinson, F. Gge., on disruptive strength of insulating mate- rials, 86 Rockers, 527 Rotary converters, 452^ Rotation, direction of, in genera- tor, 10 in motor, 422, 423 Round magnet cores, 232, 234, 291, 319, 320, 323, 369, 374, 375. Rubber, for armature-insulation, 78, 83, 85 Rule for direction of current, 10 for direction of motion, 10 Running value of armature, 135, 136 Rushtnore multi-circuit arc dy- namo, 4626 Ryan, Professor Harris J., on shape of polepieces, 298 -- on prevention of armature- reaction, 464 Safe capacity of armature, 132-135 peripheral velocities of uni- polar armatures, 448 working strain of materials, 189, 193 Safety, factor of, 189, 190 Salient poles, 275 Saturation, magnetic, 312, 313, 338 Sayers, W. B., on driving force in toothed armatures, 63 on prevention of armature- reaction, 467 Schulz, Ernst, on cast steel mag- net frames, 289 on heating of armatures, 129 Schulz, Ernst, on hollow magnet cores, 292 on lamination of armature core, 93 Screwed contact, 182, 183 Screw-stud, 308 Secondary generators, 452 Sectional area of armature-con- ductor, 57 of armature-core, 92 of magnet-frame, 313-316 of magnetic circuit, 204, 230, 34i, 345, 346 of magnet-wire, 363 of slots in toothed and per- forated armatures, 71 Selection of insulating material, 83 of magnet-type, 285-287, 437 of wire for armature con- ductor, 57, 506, 528, 567, 588, 638, 645 of wire for magnet-winding, 376, 386, 400, 523, 541, 549, 587, 599' 6 49 Self-excitation, failure of, 703 Self-induction, 29, 62, 172, 297,465 Self-oiling bearings, 305 Series dynamo, efficiency of, 37, 405, 407 E. M. F. allowed for internal resistance of, 56 fundamental equations of, 36 Series motor, 406, 408, 428, 429, 436, 628 Series, or two-circuit, armature- winding, 148, 151, 153, 155-164 Series parallel armature-winding, 148, 153 control of railway motors, 437 Series-winding, calculation of, 374-382, 522, 586, 635 principle of, 36, 37 Sever, George F., on effect of temperature on insulating materials, 86 Shaft, calculation of, 184-186, 516 insulation of, 79, 82 Shape, see Form. Sheet iron, for armature cores, 93, 94, IIO, 113, 115, 120, 121, 122 Shellacked materials, for arma- ture insulation, 85 Short-circuiting of armature-coils, 28, 30, 149. 174, 175, 298 Short-connection type of series, winding, 157, 158 Short, Professor Sidney H., on gearless railway motors, 434 724 INDEX. Shunt-coil regulator for series winding, 377-382, 523-526 Shunt-dynamo, efficiency of, 38, 39, 40, 406, 407, 408 E. M. P. allowed for internal resistance of, 56 fundamental equations of, 38, 39. 40 total armature current in, 109 Shunt, magnetic, across pole- pieces, 296 Shunt-motor, 406, 408, 426, 427, 428, 429, 637 Shunt-resistance, ratio of, to ar- mature-resistance for differ- ent efficiencies, 40 Shunt-winding, calculation of 383-394, 54i, 576, 612, 640, 654, 6 59 . principle of, 37-40 Side-insulation of commutator, 171 Silicon, in cast steel, 288, 289 Silk-covering of wires, weight of, 103 Silk for armature insulation, 78, 85 Simplex, or single, armature- winding, 149, 150, 151, 156, 157, 159, 164, 165 Simplified method of armature- calculation, 413-416 process of constructing mag- netic characteristic, 480 Sine curve, 13, 20 Single horseshoe type, classifica- tion of, 269, 270-273 magnetic leakage in, 231, 232, 239, 240, 241, 245, 246, 249, 250, 251, 263 Single magnet iron-clad type, 237, 263, 269, 278 multipolar types, 263, 270, 283. 580 ring type, 269, 275 type, classification of, 269, 273-275 type, magnetic leakage in, 241, 242, 251, 252, 263 Singly re-entrant armature-wind- ing, 150, 156, 160, 161, 162, 163, 164, 167 Sinusoid, 13 Size, see Dimensions. Skeleton pulleys, for driving ring armatures, 186, 188-190 Skinner, C. A., on closed coil arc dynamo, 455 Slanting pole-corners, 296, 460 Sliding contact, current density for, 183 Slotted armatures, see Toothed Core Armatures. Slotting of polepieces, 297 Smooth core armatures, definition of, 4 effective field area of, 204 factor of field-deflection for,. 225 gap-permeance of, 224-227 height of binding-bands on,- 75 height of winding space in, 75 percentage of effective gap circumference for, 135 percentage of polar arc for, 49 Sources of energy-dissipation in armature, 107 of magnetomotive force, grouping of, 353, 354 of sparking, see Sparking. Space-efficiency of railway mo- tors, 435 Spacing of armature-connections, see Pitch of Armature-Wind- ing, 152-167 Span, polar, 49, 203, 207, 210 Sparking, 29, 30, 62, 172, 173, 297, 298, 299, 459, 696 Specific armature induction, 51 energy-loss in armature, 126 energy-loss in magnets, 372 generating power of motor, 425, 636, 642, 651 magnetizing force, 334-338 resistance of insulating ma- terials, 85 temperature increase in ar- mature, 127 temperature increase in mag- net-coils, 371 weight and cost of dynamos, 412 Speed, see Velocity. Speed-calculation of electric mo- tors, 424-427, 636, 642, 651 Speed regulation of railway mo- tors, 436, 437 Speeds, table of, for armatures, 60, 61 Spherical bearings, 304 Spiders for ring armatures, 140, i 86, 188-190 Spiral winding, or ring winding, 144, 152, 154, 189 Spokes for ring armatures, 186, 188-190, 516 Spools for magnet-cores, 359-363, 543, 55i INDEX. 725 Sprague motor, 398 Spread, lateral, of magnetic field, 529 Spring contact, 181, 183 Spur gearing, 433, 435 Square wire, for armature-core, 94 Stansfield, Herbert, on magnetic leakage, 262 Star armature, definition of, 4 " Star " dynamo, 273 Starting resistance, 424 Stationary motor, see Motor. Steel, for armature-shafts, 184-186 for magnet-frame, 288, 293 safe working load of, 189 Steinmetz, Charles P., on arc lighting dynamos, 455 on disruptive strength of dielectrics, 86 on hysteresis, no. 116 on magnetism of iron, 335 Strain, greatest, in belt, 193 permissible specific, in mate- rials, 189, 193 Stranded wire conductors, 36, 105, 181, 183, 376, 528, 549 Stranding of standard cables, Tables, 686, 687 Stratton, Alex., on distribution of magnetic flux, 397 Stray paths of magnetic flux, 218, 300, 398 Street car motors, see Railway Motors. Strength, disruptive, of insulating materials, 83, 84, 85 tensile, of materials, 189, 193 Sulphur, in cast steel, 288 Surface of armature, 122-126 of brush- contact, 168, 174- 176, 514 of magnet-coils, 369 Switches, design of, 181-183 Symbols for armature windings, 15 used in formulae, see List of Symbols, xxv-xxxvi. Symmetry of magnetic field, 140, 304 Tables, list of, see Contents ix- xxiv. Tangential multipolar type, 244, 270, 281, 282 pull, see Force, peripheral and tangential. Tape, for armature-insulation, 78 Taper-plugs, 182, 183 Teaser system of motor control, 452^- Temperature-increase in arma- ture, 126-130 in magnet-coils, 368-371 Temperature, influence of, on hysteresis, 117, 118 on insulation-resistance, 85 Tension, best, for brush-contact, 176-179, 5i5 safe, in materials, 189, 193 Thickness of armature-insula- tions, 78-82 of armature-laminae, 94, in, 119-122 of armature-spokes, 189, 516 of belts, 194 of commutator-brushes, 174 of commutator-insulations, 171 Thompson, Milton E., on magnet- ism of iron, 335 Thompson, Professor Silvanus P., on circumflux of armature, 131 on diametral current density of armature, 133 on eddy current-loss in arma- ture, 121 on forms of field-magnets, 272, 273, 274, 276, 277, 278, 282, 283 on homopolar and hetero- polar induction, 23 on leakage formulae, 216 on prevention of armature- reaction, 465 on ratio of magnet-, to arma- ture-cross-section, 292, 293 on test of Westinghouse No. 3 railway motor, 435 Thomson, Professor Elihu, on prevention of armature-reac- tion, 469 Thomson, Sir William (Lord Kel- 'vin), on efficiency of shunt dynamo, 39 Thrusting force, acting on arma- ture, 140-142, 513, 534 Timmermann, A. H. and C. E., on armature-radiation, 126 Tool-steel, hysteretic resistance of, in Toothed core armatures, advan- tages and disadvantages of, 61, 62, 63 core-leakage in, 53, 218, 219 definition of, 4 726 INDEX. Toothed core armatures, dimen- sioning of, 65-72 effective field-area of, 207 factor of field-deflection for, 230, 231 gap-permeance ot, 227-231 height of winding-space in, 75 hysteresis heat in, 67, 68, 69, 5Qi ^- insulation of, 81 number of slots for, 66 percentage of effective gap circumference for, 135 percentage of polar arc for, 50 seat of electro-dynamic force in, 63, 64 various types of slots for, 66 Torque, calculation of, 137, 138, 513, 534 of toothed and perforated ar- matures, 63 Traction-resistance, 440 Transformation-ratio, in dyna- motors, 454, 656 Transformer, rotary or rotary con- verter, 452^- Transmission .of power, at con- stant speed, 497 Trapezoidal armature-bars, 78, 101, 567 Triplex, or triple, armature-wind- ing, 149, 150, 151, 156, 162, 163, 166, 167 Triply re-entrant armature-wind- ing, 150, 156, 162, 164, 167 Troughs, micanite, for insulating armature-slots, 81, 82 Trueing of commutator, 699 Tubes, insulating, for armature slots, 80, 82 Tunnel Armature, see Perforated Armature. Turn, mean, length of, on mag- nets, 374 Turning moment, see Torque. Two-circuit winding, see Series Armature-Winding. Two-coil armature, 15, 16, 20 Type, selection of, 285, 437 Types of armature-winding, 143 of field-magnets, 269-285 of polepieces, 296 of series-windings, 157, 158 of slots for armatures, 66 U Under-type, 270, 278, 287 Unequal distribution of magnet- ism, .698 Unipolar dynamos, calculation of, 443-451, 652 principle of, 25-26 Unipolar induction, 22, 23 Unit armature-induction, 47-50 Units, electric, 7, 47 electro-magnetic, 200, 332, 333 magnetic, 199, 200 Unsymmetrical magnetic field, ef- fect of, on armature, 140-142, 513, 534 Unwound poles, 470 Upright horseshoe type, 239, 245, 249, 263, 269, 270, 527, 547, 621 Useful magnetic flux, 92, 133, 200- 202, 211-214 Utilization of copper, specific, see efficiency of Magnetic Field. Variable resistance, see Rheostat. shunt method of regulation, 459 Varnish, for armature-insulation, 85, 94 Varying cross-section in magnetic circuit, 345, 346, 348 Velocity of armature-conductors, 6, 7, 52, 448 of belt, 193 of commutator, 179, 180, 515 Velocity of railway-cars, 433, 440- 442, 500-502 of unipolar armatures, 448 Ventilation of armature, 53, 94, 528, 590 Vertical magnet types, 252, 253, 263, 269, 270, 273, 274, 276, 278, 284, 285, 299, 304 Vibration of dynamo, 287, 300, 43i " Victoria " dynamo, 282 Volume of armature current, 131 Voltage, see Electromotive Force. Vulcabeston, 80, 84, 85 Vulcanized fibre, 79, 84, 85 W Warburg, on hysteresis, no Warner, G. M., on unipolar dy- namos, 25 Wave winding, or zigzag winding, 144, 146, 147, 153, 154 Weaver, W. D., on shunt motors, 428 Weber, the unit of magnetic flux, 199, 200 INDEX. 727 Webster, A. G., on unipolar dy- namos, 25 Wedding, W., on magnetic leak- age, 262 Wedge-shaped armature-conduct- ors, 78, 101, 567 Weight-efficiency of dynamos, 33, 410-412, 527, 546, 565, 578, 602 Weight of armature winding, 100 of insulation on round copper wire, 103 of magnet winding, 366-368, 388-390 of parts of dynamos, 527, 546, 565, 579- 602 Westinghouse four-pole drum-ar- mature dynamos, dimensions of, 666 Width, see Breadth. Wiener, Alfred E., on calculation of electric motors, 419 on commutator-brushes, 171 on dynamo-calculation, see Preface, iii-viii. on efficiency of dynamo-elec- tric machinery, 405 on magnetic leakage, 216 on ratio of output and size of dynamos, 416 Wilson, Ernest, on heating of drum armatures, 130 Winding of armatures, see Arma- ture-Winding. Winding of magnets, see Magnet- Winding. Winding-space, height of, in ar- matures, 70, 71, 74, 75 height of, in magnets, 317, 361, 371, 375, 377, 386, 387 Wire, copper, 101, 104, 119, 676- 681 Wire for armature-binding, 75 gauges, 103, 367 iron, for armature and mag- net winding, 472, 475 iron, for armature-cores, 93, 94, no, 113, 115 Wolcott, Townsend, on seat of electro-dynamic force in iron- clad armatures, 64 Wood, for armature-insulation, 85 for dynamo-base, 300 Wood, Harrison H,, on curves for winding magnets, 365 Work done by armature, 137 Working-stress, safe, of different metals, 189 of leather, 193 Worm gearing, 434, 435 Wrought iron, for armature-cores, 90-94, 109-122 for armature-shafts, 186 for magnet cores, 288 for polepieces, 293 for unipolar armatures, 448 magnetic properties of, in, 3ii. 313 safe working load of, 189 Yokes, dimensioning of, 325 length of magnetic circuit in, 347 Zigzag winding, or Wave-Wind- ing, 144, 146, 147, 153, 154 Zinc blocks, 300-303 UNIVERSITY YD 04 1 57 103844