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.
b = diameter of armature bearings.
d c = diameter of core-portion of armature shaft.
d t = mean diameter of magnetic field.
<4 = diameter of front head of (drum) armature.
d\ diameter of back head of (drum) armature.
<4 = diameter of commutator.
^m diameter of magnet core.
d v = diameter of bore of polepieces.
dy, = diameter of car wheel, in inches.
d & = diameter of armature wire, in mils.
6' a = width of insulated armature conductor, in inches.
6" & = height of insulated armature conductor, in inches.
d'" & pitch of conductors on armature circumference.
di = thickness of iron laminae in armature core, in inches.
6 m = diameter of magnet wire, bare, in mils.
6' m = diameter of magnet wire, insulated, in mils.
xxvili LIST OF SYMBOLS.
<5 se = diameter of series field wire.
tf sh diameter of shunt field wire.
(tf a ) 2 = sectional area of armature conductor, in circular mils.
(#a) 2 rnm = sectional area of armature conductor in square
millimetres.
(# ai ) 2 sectional area of single armature wire, in circular
mils.
t e = electromotive force, or pressure, in volts.
E normal E. M. F. output, or voltage, of generator; ter-
minal E. M. F., or supply voltage of motor.
E' total E. M. F. induced in armature of generator; counter
E. M. F. of motor.
E = total E. M. F. active in armature, on open circuit.
E l = total E. M. F. active in armature, at minimum load.
E^ = total E. M. F. active in armature, at maximum load.
E m = E. M. F. between terminals of magnet winding.
e unit armature induction per pair of poles, volts per foot.
*, = unit armature induction per pair of poles, volts per metre.
e' = specific induction of active armature conductor, volts per
foot.
e\ = specific induction of active armature conductor, volts per
metre.
*" = specific generating power of motor, /. e., volts of counter
E. M. F., produced at a speed of i revolution per
minute.
<2 = volts generated per 100 conductors, per TOO revolutions
per minute, and i megaline of flux per pole.
^ 3 = average volts between commutator segments per megaline
and per 100 revolutions per minute.
^ a drop of voltage due to armature resistance.
= factor of eddy current loss in armature, English measure
(watts per cubic foot).
e 1 = factor of eddy current loss in armature, metric measure
(watts per cubic metre).
f l = eddy current constant.
$ = magneto-motive force, in gilberts.
F, / = force, or pull, in pounds.
F^ =.- total peripheral force of armature, in pounds.
F' & peripheral force corresponding to safe working strength
of armature spokes, in pounds.
LIST OF SYMBOLS. xxix
J^ B = tension on tight side of belt, in pounds.
Jf p = pull at pulley circumference, in pounds.
/ a = peripheral force per armature conductor, in pounds.
/ = tension on slack side of belt, in pounds.
/ h = horizontal effort, or draw-bar pull of railway motor.
/ k = specific tangential pull due to brush-friction, at 1000 feet
per second, in pounds per square inch of contact
area.
/' k = specific tangential pull due to brush-friction, at any
velocity, in pounds per square inch of contact area.
f t = armature thrust, /. ^., displacing force acting on arma-
ture due to unsymmetrical field.
# = useful flux, /. ^., number of lines of force cutting arma-
ture conductors, at normal output.
# = useful flux, /. ., number of lines of force cutting arma-
ture conductors, at open circuit.
$' = total flux, or total number of lines generated, at normal
output (maxwells).
4>" = 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; /. ., output
of generator, intake of motor.
P' total electrical energy, active in armature, or electrical
activity of machine.
P" = mechanical energy at dynamo shaft; /. ., driving power
of generator, output of motor.
P^ =total energy absorbed in armature.
P^ = total energy absorbed in field circuits.
/> 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 min = o and ^ max = E', the mean
E. M. F. is
9]
CURRENT GENERATION IN ARMATURE.
and the amount of fluctuation, with a two-division commuta-
tor, is
E'
'max 'mean
'min
E 1
o
> = .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'
'max .70711 '
'rain-^nean = (-5 -.60356)^'
^max .70711 E'
= ^.= ..465,
or 14.65$.
If each of the two coils i and 2, Fig. 19, is again subdivided
into two coils of half the number of turns, four coils, i', 2', 3',
225
M35*
Fig. 22. Four Coil Armature.
and 4', are obtained which make angles of 45 with each other,.
Fig. 22. Plotting the curves of E. M. Fs., therefore, we get
T"
~ 22^ 45
360'
22>$ 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 2 ", the addition of
which, finally, renders the resultant curve of reduced E. M. F.,
e'", which fluctuates between the values
t'" mtit = (O^x + (O-. = 2 X ^ sin 45 +
4 4
= X ^ VT~ +^- = C35356 + .25) E' = .60356
and
.38268 -f- .92388 '
-^ -E = . 65328.6 .
From this follows the mean E. M. F. obtained with an
eight-division commutator:
'"'mean = \ (-60356 + .65328) E' = .62842 ',
giving a fluctuation of the maximum E. M. F. in the amount of
'"'max - '"'mean (-65328 - .62842) '
.65328^' I = 02486
min
(.60356 - .62842) E' I -65328
.65328,?'
= .0386, or 3.86$.
The above calculations show that the percentage of fluctua-
tion rapidly diminishes as the number of armature coils
increases, and in continuing the process of subdividing the
coils into sections symmetrically spaced at equal angles, we
will get for resultants curves which more and more resemble
a straight line, and thus indicate the approaching entire dis-
appearance of fluctuations and, therefore, continuity of the
E. M. F. In the following Table I. the numerical results of
such continued subdivision of the armature coils are given,
the original maximum E. M. F. E' being for convenience
taken as unity:
9] CURRENT GENERATION IN ARMATURE. 19
TABLE I. FLUCTUATION OF E. M. F. OF COMMUTATED CURRENTS.
NUMBER OP
ANGLE
AMOUNT
FLUCTUA-
COMMUTA-
EMBRACED
MAXIMUM
MINIMUM
MEAN
OF
TION
TOR
BY
E. M. F.
E. M. F.
E. M. F.
FLUCTUA-
IN P. CENT.
DIVISIONS.
EACH COIL.
TION.
OF MAX.
E. M. F.
2
180
1.
0.
.5
.5
50#
4
90
.70711
.5
.60356
.10356
14.65
8
45
.65328
.60356
.62842
.02456
3.86
12
30
.64395
.62201
.63298
.01097
1.70
18
20
.63987
.63014
.63500
.00487
.76
24
15
.63844
.63298
.63571
.00273
.43
36
10
.63743
.63501
.63622
.00121
.19
48
H
.63708
.63571
.636395
.000685
.107
60
6
.63691
.63604
.636475
.000435
.068
90
4
.63675
.63637
.63656
.000190
.030
180
2
.63665
.63656
.636605
.000045
.007
360
1
.63664
.63660
.63662
.000020
.003
The average E. M. F., that is, the geometrical mean of all
the sums of instantaneous E. M. Fs. induced in the various
45 90 180 270 360
Fig. 24. Average E. M. F. Induced in Rotating Armature.
subdivisions of the coil, must be the same in every case, for,
the total number of turns, the speed, and the field-strength
remain the same for any number of commutator divisions.
Fig. 25. Average E. M. F. of One-Coil j Armature.
Numerically, the average E. M. F. is the height of a rectangle
having an area equal to the surface extending between the
axis of abscissae, the two end-ordinates, and the curve of
20
D YNAMO-ELECTRIC MA CHINES.
E. M. F., as shown in Fig. 24. In case of the one-coil
armature the average E. M. F. , in considering one-half of
a revolution, is the height of a rectangle equal to the area of
a single wave having ' as its amplitude. The area S inclosed,
by a sinusoid of amplitude E' and length /, Fig. 25, is:
/ f 77 E' I
S - E ' sin x dx = ( cos 180 ( cos o))
therefore the average E. M. F.
= - =-X E' = .636622'.
.(7)
Fig. 26. Average E. M. F. of Two-Coil Armature.
For the two-coil armature the area S lt Fig. 26, of one-quarter
of a revolution is the sum of a rectangle of length
and height
and of a wave of amplitude
V f \
-| (sin 45 + cos 45)- i [
and length
or:
^?*f^fl> 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;
a = diameter of armature wire, in mils;
/' = total current generated in armature, in amperes;
and
' p = number of pairs of parallel armature circuits.
In the metric system, taking .4 square millimetre per am-
pere ( 2.5 amperes per square millimetre) as the average
current density in the armature conductor, the sectional area
of the inductor, in square millimetres, is obtained:
WLn =^4^=.2X -C ..... (28)
from which, in case of a circular conductor, the diameter can
be derived:
4- ()
The size of conductor may be taken from the wire gauge
tables by selecting a wire, the sectional area of one or more
of which makes up, as nearly as possible, the cross-section
obtained by formula (27).
The total armature current, /', in shunt and compound
dynamos is the sum of the current output, /, and the exciting
current of the shunt circuit. The latter quantity, however,
generally is very small compared with the former, and in all
practical cases, consequently, it will be sufficient to use the
given /instead of the unknown /' for the calculation of the
conductor area. A supplementary allowance may, then, be
made by correspondingly rounding off the figures obtained
by (27), or by selecting the wires of such a gauge that the
actual conductor area is somewhat in excess of the calculated
amount.
CHAPTER IV.
DIMENSIONS OF ARMATURE CORE.
21. Diameter of Armature Core.
If the speed of the dynamo is given, the proper conductor
velocity taken from Table V. will at once determine the
diameter of the armature. Let N denote this known speed,
in revolutions per minute, and d' & the mean diameter of the
Fig. 45- Principal Dimensions of Armature.
armature winding, in inches, then the cutting speed, in feet
per second, is
12
X 6cT'
from which follows:
12 X 60 I
n
x ^ = 230X 2vr-
.(30)
In the metric system the mean diameter of the armature
winding, in centimetres, is given by
100 x 60 v c
..... (31)
in which v c is to be expressed in metres per second.
58
21]
DIMENSIONS OF ARMATURE CORE.
59
From this mean winding diameter, d' &y then, the diameter
of the armature core, d M Fig. 45, is found by making allow-
ance for the height of the armature winding. For small
armatures under two feet in diameter the coefficients given
in the following Table IX. may be used for this purpose; for
larger ones it is sufficient to simply round off the result of
formula (30), or (31), respectively, to the next lower round
figure:
TABLE IX. RATIO BETWEEN CORE DIAMETER AND MEAN WINDING
DIAMETER FOR SMALL ARMATURES.
SIZE OF ARMATURE.
RATIO A.
a
English Measure.
Metric Measure.
Drum Armatures.
Ring Armatures.
Up to 2 ins. dia.
Up to 5 cm. dia.
.88
_
4
10
.92
.95
8
20
.94
.97
12
30
.95
.975
16
40
.96
.98
20
50
.965
.9825
24
60
.97
.985
For dynamos with internal poles, the reciprocals of these
-coefficients are to be taken, or the result is to be rounded off
to the next higher round figure, respectively; and the dimen-
sion thus obtained is the internal diameter of the armature
core. In the case of machines with internal as well as external
poles, the mean winding diameter, ' a , is identical with the
mean diameter of the armature body.
If the speed of the dynamo is not prescribed by the condi-
tions for its service, the following Tables X., XL, and XII.
will be found useful. Table X. gives practical data for speeds,
conductor velocities, and corresponding diameters of drum
armatures. Table XI. contains similar information relating
to high-speed ring armatures, and in Table XII. data for the
speeds of low-speed ring armatures are compiled and the cor-
responding armature diameters computed:
60 DYNAMO-ELECTRIC MACHINES. [21
TABLE X. SPEEDS AND DIAMETERS OP DRUM ARMATURES.
ENGLISH MEASURE.
METRIC MEASURE.
CAPACITY
SPEED,
IN
IN
KILOWATTS.
REVOLUTIONS
PER
MINUTE.
JV
Conductor
Velocity,
in ft. per sec.
Armature
Diameter,
in inches.
Conductor
Velocity,
in m. per sec.
Armature
Diameter,
in cm.
Vc
da,
Vc
da.
.1
3,000
25
U
8
45
.25
2,700
30
2;
9
5.5
.5
2,400
32
2 !
10
7
1
2,200
34
3
11
8.5-
2
2,000
36
3]
12
10
3
1,900
40
4 1
i-
13
12
5
1,800
45
5
b ^
14
14
10
1,700
50
6
15
16
15
1,600
50
6^
i
'-
15
17
20
1,500
50
7i
15
IS
25
1,350
50
8
15
20
30
1,200
50
9
15
23
50
1,050
50
lOi
?
15
2H
75
900
50
12
f
15
30
100
750
50
15
15
37
150
600
50
18]
r
15
46.5
200
500
50
99
NM91
15
56
300
400
50
28'
15
70
TABLE XI. SPEEDS AND DIAMETERS OF HIGH-SPEED RING
ARMATURES.
ENGLISH MEASURE.
METRIC MEASURE.
CAPACITY
SPEED,
IN
IN
REVOLUTIONS
PER
Conductor
Armature
Conductor
Armature
KILOWATTS.
MINUTE.
JN
Velocity,
in ft. per sec.
Diameter,
in inches.
Velocity,
in m. per sec.
Diameter,
in cm.
Vc
da.
Vc
da
.1
2,600
50
4
15
10
.25
2,400
55
5
17
12.5
.5
2,200
60
6
18.5
15
1
2,000
65
7
20
18
2.5
1,700
70
9
21.5
23
5
1,500
75
11
23
28
10
1,250
80
14
24
35
25
1,000
80
18
25
46
50
800
85
24
26
60
100
600
85
32
26
80
200
500
88
40
27
100
300
450
90
46
28
115
400
400
92
52
28
130
600
350
95
62
28
150
800
300
95
72
29
180
1,000
250
95
87
30
225
1,500
225
100
102
30
250
2,000
200
100
115
32
300
22] DIMENSIONS OF ARM A TURE CORE.
TABLE XII. SPEEDS AND DIAMETERS OF LOW-SPEED RING
ARMATURES.
61
ENGLISH MEASURE.
METRIC MEASURE.
CAPACITY
SPEED,
IN
IN
KILOWATTS.
REVOLUTIONS
PER
MINUTE.
N
Conductor
Velocity,
in ft. per sec.
Armature
Diameter,
in inches.
Conductor
Velocity,
in m. per sec.
Armature
Diameter,
in cm.
c
d &
c
da
2.5
400
25
14
7.5
35
5
350
26
17
8
42
10
300
28
21
8.5
53
25
250
30
27
9
70
50
200
32
36
9.5
90
100
175
35
46
11
115
200
150
40
60
12
150
300
125
42
78
13.25
200
400
100
44
100
13.25
250
600
90
45
115
13.75
290
800
80
45
129
13.75
325
1,000
75
45
138
13.75
350
1,500
70
45
148
13.75
375
2,000
65
45
158
13.75
400
I
22. Dimensioning of Toothed and Perforated Arma-
tures.
Armatures with toothed and with perforated core discs,
which have been much used in recent years, offer the following
advantages over smooth armatures: (i) Excellent means for
driving the conductors; (2) mechanical protection of the
winding, especially in cores with tangentially projecting
teeth, and in perforated bodies; (3) lessening of the resistance
of the magnetic circuit, and, therefore, saving in exciting
power; (4) prevention of eddy currents in the conductors;
(5) lessening of the difference between the amounts of field-
distortion at open circuit and at maximum output, and there-
fore possibility of sparkless commutation for varying load
without shifting brushes; and (6) taking up of the magnetic
drag by the core instead of by the conductors. Their dis-
advantages art: (i) Increased cost of manufacture; (2) neces-
sity for special devices to insulate the winding from the core;
(3) eddy currents set up by the teeth in the polar faces;
(4) additional heat generated in the iron projections by
62 DYNAMO-ELECTRIC MACHINES. [22
hysteresis; (5) increase of self-induction in short-circuited
armature coils due to imbedding them in iron, especially in
high amperage machines; (6) increased length of the gap-
space and consequent greater expenditure in exciting power
when saturation of the teeth takes place; and (7) leakage of
lines of force through the armature core, exterior to the
winding, particularly in case of projecting teeth and of per-
forated cores.
Comparing these advantages and disadvantages with each
other we find that the conditions that have to be fulfilled in
order to bring to prominence certain advantages will also
favor the conspicuousness of certain of the disadvantages,
and moreover we see that what is an advantage in one case
may be a decided disadvantage in another. All considered,
therefore, there are no such striking advantages in either the
toothed or the smooth core as to make any one of them
superior in all cases over the other, and a general decision
whether a toothed or a smooth-core armature is preferable,
cannot be arrived at. As a matter of fact, in practice it
chiefly depends upon the purpose of the machine to be
designed whether a smooth or a toothed core is preferably
used in its armature. In machines with toothed and with
perforated armatures an increase of the load has the effect of
increasing the saturation of the iron projections and therewith
the reluctance of the air gap; the counter-magnetomotive
force of the armature, which also increases with the load, has
therefore to overcome a greater reluctance as it increases
itself, in consequence of which the demagnetizing effect of
the armature is kept very nearly constant at all loads. Hence
the distribution of the field in the gap remains nearly the same
and the angle inclosed between the planes of commutation at
no load and at maximum output is reduced to a minimum.
For cases where sparkless commutation is required without
shifting the brushes for varying loads, as for instance in rail-
way generators, in which due to the continual and sudden
fluctuations of the load a shifting of the brushes is impractica-
ble, the employment of toothed armatures is preferable, for
the attainment of the desired end in this case outweighs all
their disadvantages. On the other hand, the self-induction in
smooth-core armatures, owing to the absence of iron between
22] DIMENSIONS OF ARMATURE CORE. 63
the conductors, is much less, and consequently they are chosen
in cases of machines in which large currents are commutated
at low voltages, such as in central station lighting generators
and in electro-metallurgical machines. In the latter case the
disadvantage of increased self-induction in the toothed arma-
ture is the main consideration and drives it out of competi-
tion with the smooth armature, in spite of all advantages which
it may have otherwise. Again, in the case of motors, where
a large torque is the desideratum, especially in low-speed
motors, such as single reduction and gearless railway motors,
the toothed armature answers best, as in this instance its
advantage of increased drag upon the teeth is considered the
prominent one. Toothed armatures must further be em-
ployed if, in a series motor, a constant speed under all loads
is to be attained, for at light loads the teeth, being worked
.at a low point of magnetization, offer but 'little reluctance to
the flux through the armature, while at heavy loads the teeth
become saturated and considerably increase the reluctance of
the magnetic circuit, thereby preventing the induction from
increasing with increased field excitation, the result being
a motor that comes much nearer being self-regulating than
one with a smooth-core armature.
In order to more definitely determine the mechanical advan-
tage of the iron projections, W. B. Sayers ' compared the
pull on the conductors in toothed and smooth-core armatures.
He found that in toothed armatures the driving force is borne
directly by the iron instead of by the conductors as in case
of smooth-core machines. Taking the case of an armature in
which the thickness of the tooth is equal to the width of the
slot, he shows that, when the density in the teeth is 100,000
lines per square inch (= 15,500 lines per square centimetre),
that in the slots is about 300 lines per square inch (= 47 per
square centimetre), while in a smooth-core armature the field
density would be about 50,000 per square inch ( 7,750 per
square centimetre), from which follows that the force acting
upon the conductors is about 167 times greater in the latter case
than in the former. In another example he takes a higher mag-
netic density and finds that the pull in case of the toothed arma-
1 London Electrician, April 19, 1895; Electrical World, vol. xxv. p. 562
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 ft , h M and b' a are given in.
inches, and d^ in circular mils.
For metric calculations formula (41) takes the form:
TOO X .6 X d & 7t X h &
and formula (42) is replaced by:
100 X Q X^ r 8 X
A7
x ^ ? c x ^, x h & ......... (44)
In (43) and (44) the dimensions d M h M and b\ are expressed
in centimetres, and (tf a )mm. in square millimetres.
7 8 DYNAMO-ELECTRIC MACHINES. [24
2. Armature Insulations.
a. Thickness of Armature Insulations.
According to the size and the voltage of a dynamo the thick-
nesses of the insulations in its armature vary in very wide
limits.
The coating of the armature conductor, if single wire is em-
ployed, usually is effected by a double cotton covering ranging
in diametral thickness from .012 to .020 inch (0.3 to 0.5 mm.),
according to the size of the wire and the voltage, see Table
XXVI., 28. If stranded cable is used for winding the
armature, either bare or single cotton-covered wire is used to
make up the cable, and the whole is covered with two or three
layers of cotton. The thickness of the single cotton insula-
tion in this case varies from .005 to .010 inch (0.125 too. 25 mm.)
in diameter. For very thin wires, from No. 20 B. W. G. (.035
inch = 0.9 mm.) down, a double silk covering from .004 to
.005 inch (o. i to 0.125 mm.) diametral thickness is applied.
In case of rectangular or wedge-shaped conductors, accord-
ing to their size and to the voltage of the machine, either a
double cotton covering, as with wires, is used, or oiled paper,
cardboard, asbestos, or mica is employed for their enwrapping
or separation. The thickness of the insulation in the latter
case. varies between .010 and .0125 inch (0.25 and 3 mm.) each
side, see columns e of the following Table XIX.
Besides this coating of the single conductors, sometimes
particularly in high voltage machines one or more sheets of
insulating material are employed to separate the layers from
one another. The thickness of this insulation, for which either
oiled paper, rubber tape, silk, or mica is used, ranges from
.004 to .030 inch (o. i to 0.75 mm.), columns/, Table XIX.
The insulation of the conductors from the iron body in
smooth armatures is effected by serving the core with one or
two coatings of enamel or japan and then covering it by either
oiled paper, cardboard, canvas, silk, tape, sheet rubber, cotton
cloth, asbestos, or mica, varying in radial thickness between
.010 and .200 inch (0.25 and 5 mm.), columns a, Table XIX.
In drum armatures the complete core insulation, besides this
circumferential coating, a, consists of coverings, , over the
core edges, of core-face insulations, c, and of shaft-insulations,
24]
DIMENSIONS OF ARM A TURE CORE.
79
, all overlapping each other as shown in Fig. 53. The edge
insulation is effected by first covering the core with layers of
oiled paper, oiled muslin, or canvas, then winding with rubber
tape, and finally adding a layer of mica or asbestos; according
to the voltage and size of machine this edge insulation varies
Fig- 53- Core Insulations on Drum Armature.
from .020 to .250 inch (0.5 to 6.4 mm.), see columns b, Table
XIX. The core-face insulation is made up of circular sheets
of oiled paper, muslin, linen, cardboard, asbestos, vulcanized
fibre, or leatheroid, in thicknesses varying from .030 to .400
inch (0.75 to 10 mm.), columns ........ (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,
= a - a , see Fig. 45, page 58 ;
/ a = length of armature core, in inches;
b & = radial depth of armature core, in inches;
2 = ratio of net iron section to total cross-section, see
Table XXL, 26;
1,728 = multiplier to convert cubic feet into cubic inches.
And for toothed and perforated armatures :
^ (d'" & n X b & - ;/' c S\) X 4 X *,. n9 .
1,728
<'" a = mean core-diameter, in inches = d\ ( a + ^ a ), see:
Fig. 48, page 65 ;
n' c = number of slots;
S" a = sectional area of slots, in square inches.
Formulae (69) and (70) can be rendered more convenient
for practical use by uniting the terms 5 X io~ 7 X (B" a 1>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, h , at commutator end of armature, is generally
made from 0.75 d\ to i.o a" M while the diameter of the end
washer of the back head, ' h , ranges in size from 0.5 d\ to
-75 d\- Taking d h = 0.9 d\ as the average diameter of the
front head, and flT' h =0.6 a" & as that on the back head (Figs. 73
and 74, page 125), we obtain the following formula for the
radiating surface of a drum armature:
= d\ x
X
34]
ENERGY LOSSES IN ARMATURE.
125
or approximately:
*=.<, X TT X (4 + 1-8 x 4); ...... (78)
6* A = radiating surface of armature, in square inches, or in
square centimetres;
d" & = external diameter of armature, in inches, or in centi-
metres, = d & -f- 2 h & ;
4 length of armature body, in inches, or in centimetres,
formula (40) ;
4 = length of armature head, in inches, or centimetres; from
formula (77) and Table XXXV.
Figs. 73 and 74. Size of Heads in Drum Armatures.
b. Radiating Surface of Ring Armature.
In ring armatures the construction and mounting of the core
may be such that either one, two, or three, or all four sides of
the cross-section are in contact with the air, but in modern
--- |.+Sfc- *
1 fl
Fig. 75- Dimensions of Ring Armature.
machines almost without exception, all four, or at least three
of the surfaces constituting the ring are radiating areas.
Fig. 75 shows the cross-section of a ring armature.
In the first mentioned case (four sides) we have the formula:
S A = 2 x d'\ X n X (4 + *+ + 4 X /U, (79)
126 DYNAMO-ELECTRIC MACHINES. [35
and in the latter case (three sides):
S A = d\ x n x (4 + 2 /y
+ 2 X d'\ X 7t X (^ + 2 // a ); (80)
,S A radiating surface of armature, in square inches, or in
square centimetres;
d" & = external diameter of armature, in inches, or in centi-
metres;
V' a = mean diameter of armature core, in inches, or in centi-
metres;
4 = length of armature core, in inches, or in centimetres;
b & = radial depth of armature core, in inches, or in centi-
metres;
// a height of winding space, in inches, or in centimetres.
35. Specific Energy Loss. Rise of Armature Temper-
ature.
While the amount of the total energy consumed, P ' A , formula
(65), determines directly the quantity of heat generated in the
armature, the amount of heat liberated from it depends upon
the size of its radiating surface, upon its circumferential
velocity, and upon the ratio of the pole area to the radiating
surface.
The most important of these factors in the heat conduction
from an armature naturally is the size of the radiating surface,
while the speed and the ratio of polar embrace are of minor
influence only; and it is, therefore, the ratio of the energy
consumed in the armature to the size of the cooling surface,
that is, the specific energy loss, which limits the proportion of
heat generated to heat radiated, and which consequently
affords a measure for the degree of the temperature increase
of the armature.
A. H. and C. E. Timmermann, 1 of Cornell University, who
made the armature radiation the subject of their paper read
before the American Institute of Electrical Engineers, in May,
1893, from a series of elaborate experiments drew the follow-
ing conclusions:
(i) An increase of the temperature of the armature causes
an increased radiation of heat per degree rise in tempera-
1 A. H. and C. E. Timmermann, Transactions Am. Inst. of Elec. Eng. y vol.
x. p. 336 (1893).
' 35]
ENERGY LOSSES IiV ARMATURE.
127
ture, but the ratio of increase diminishes as the temperature
increases, and an increase of the amount of "heat generated in
the armature increases the temperature of the armature, but
less than proportionately.
(2) As the peripheral velocity is increased, the amount of
heat liberated per degree rise in temperature is increased, but
the rate of increase becomes less with the higher speeds.
(3) The effect of the field-poles is to prevent the radiation of
heat; as the percentage of the polar embrace is increased, the
.amount of heat radiated per degree rise in temperature
becomes less.
Combining these results with the data and tests of various
dynamos, the author finds the following values, given in Table
XXXVI., of the temperature increase per unit of specific energy
loss, that is, for every watt of energy dissipated per square
inch of radiating surface, under various conditions of periph-
eral velocity and polar embrace :
TABLE XXXVI. SPECIFIC TEMPERATURE INCREASE IN ARMATURES.
RISE OF TEMPERATURE PER UNIT OP SPECIFIC ENERGY Loss,
PERIPHERAL
IN DEGREES CENTIGRADE, 0'a.
VELOCITY.
Ratio of Pole Area to Total Radiating Surface.
Feet
Metres
per sec.
per sec.
.8
.7
.6
.5
.4
.3
.2
110
100
95
90
86
83
80 Q
10
3
80
74
70
67
64
62
60
20
6
64
61
58
56
54
52
50
30
9
55
53
51
49|
48
46i
45
40
12
50
48
47
46
45
44
43
50
15
48
47
46
45
44
43
42
75
22.5
47
46
45
44
43
42
41
100
30
46
45
44
43
42
41
40
150
45
45
44
43
42
41
40
40
In Fig. 76 these temperatures are represented graphically;
Curves I., II. . . VII., corresponding to Columns 3, 4, . .
9, of Table XXXVI., respectively.
Multiplying this specific temperature increase by the respec-
tive specific energy loss, the rise of temperature can be found
from:
e a = e'a x t* . . (81)
128
where a
r.
D YNA MO- EL E C TRIG MA CHINES.
[35
rise of temperature in armature, in degrees Centi-
grade;
specific temperature increase, or rise of armature
temperature, per unit of specific energy loss, from
Table XXXVI., or Fig. 76;
no
g 40
I. POLE AREA = .8 OF TOTAL RADIATING SURFACE
= .5
*= .4
=5.3
= .2
10 20 30 40 50 60 70 SO 90 KO -
PERIPHERAL VELOCITY, IN FEET P. SEC.
Fig. 76. Specific Temperature Increase in Armatures.
P = total energy consumed in armature, in watts,
formula (65);
^A = radiating surface of armature, in square inches,
from formula (78), (79), or (80), respectively;
p
^ - specific energy loss, i. e., watts energy loss per
square inch of radiating surface.
In order to obtain the temperature increase in Fahrenheit
degrees, the result obtained by (81) is to be multiplied by
36] ENERGY LOSSES IN ARMATURE. 129
and if S A is expressed in square centimetres, the factor 6.45 must
be adjoined.
36. Empirical Formula for Heating of Drum Armatures.
From tests made with drum armatures, Ernst Schulz 1 derived
the following empirical formula:
X "" * N X "'
= . 012 X
in which a = rise of armature temperature, in degrees Centi-
grade;
a = factor of magnetic saturation in smallest cross-
section of armature core,
- * I8>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 X 4 X ft\ X 3C, 2 kilogrammes,
and
/, = 32 X io- 9 X a X 4 X ft' i X OC 2 2 kilogrammes,
and will be drawn toward the stronger side by the amount of
the difference of their attractive forces. The armature thrust,
therefore, is:
/t=/i-/ 2 -32Xio- 9 x^ a x/aX/5' 1 x(ac l 2 -ac.;)kg.; ...(102)
/ t = thrusting force acting on armature, due to unsym-
metrical field, in kilogrammes;
d & = diameter of armature, in centimetres;
/ a = length of armature, in centimetres;
ft\ = percentage of effective gap-circumference, see Table
XXXVI. ;
3C t = density of field, on stronger side, lines per square-
centimetre;
5C 2 = density of field, on weaker side, lines per square centi-
metre.
In English measure, i pound being = .4536 kilogrammes,
and i square inch = 6.4515 square centimetres, the formula for
the armature thrust becomes:
/' = 3X0 X X 4 X * X (*'/ - *Y)
= iiX io-^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 ; /. ., for
four-polar machines. For dynamos with more than four poles,
;/' p > 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 b = diameter of armature shaft, at bearings, in inches;
P' = capacity of dynamo, in watts;
N = speed, in revolutions per minute;
g = constant, depending upon the kind of armature,
see Table XLIX.
51]
MECHANICAL CALCULATIONS.
185
The value of 8 varies between .0025 and .005, as follows:
TABLE XLIX. VALUE OP CONSTANT IN FORMULA FOR JOURNAL-
DIAMETER OP ARMATURE SHAFT.
KIND OP ARMATURE.
VALUE OF
k t .
High speed drum armature
0025
High speed ring "
003
Low speed drum "
004
Low speed ring
005
For core portion :
(123)
where d c = diameter of core portion of armature shaft, in
inches;
P' = capacity of machine, in watts;
N speed, in revolutions per minute;
k 9 = constant depending upon output of machine,
see Table L.
This constant indicates the dependence of the diameter of
the shaft upon the length between its supports; and since the
weight supported and also the length supporting it increase
with the output, it is evident that 9 has a greater value the
larger the output of the machine. For capacities up to 2,000
kilowatts, k 9 numerically ranges between i and 1.8, thus:
TABLE L. VALUE OP CONSTANT IN FORMULA FOR DIAMETER OF CORE
PORTION OF ARMATURE SHAFT.
CAPACITY, IN WATTS.
P
VALUE OF
Jc 9 .
Up
to 1,000 WE
5,000
10,000
50,000
100,000
200,000
500,000
1,000,000
2,000,000
itts
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1 86
DYNAMO-ELECTRIC MACHINES.
[51
Considering the speeds given in Tables X., XI., and XII.,
21, for various outputs, we obtain the following Tables LI.,
LIL, and LIII., giving, respectively, the diameters of shafts
for drum armatures, for high-speed ring armatures, and for low-
speed ring armatures :
TABLE LI. DIAMETERS OP SHAFTS FOR DRUM ARMATURES.
SPEED,
IN
DIAMETER OF ARMATURE SHAFT, IN INCHES.
CAPACITY,
IN
EEVOLUTIONS
PER MINUTE
Bearing Portion.
Core Portion.
WATTS.
P
(FROM
TABLE X.)
jr.
d b = .0025 /P 7 X yW<
*9
4/p
d = * x y *
100
3,000
A
.9
250
2,700
T 5 .
.95
*
500
1,000
2,400
2,200
s
1
1
it
2,000
2,000
T f
1.05
i
3,000
1,900
it
1.1
lir
5,000
1,800
H
1.15
H
10,000
1,700
if
1.2
2
15,000
1,600
11
1.25
2i
20,000
1.500
2i
1.25
8*
25,000
1,350
2|
1.25
2f
30,000
1,200
2*
1.3
3
50,000
1,050
3
1.3
3i
75,000
900
8f
1.35
4i
100,000
750
4i
1.4
41
150,000
6uO
4f
1.45
5|
200,000
500
5i
1.5
6|
300,000
400
6
1.55
8
For wrought iron shafts the diameters obtained by formulae
(122) and (123), or those taken from Tables LI., LIL, and
LIII., respectively, are to be multiplied by 1.25, that is, in-
creased by 25 per cent.
52, DriTing Spokes.
Ring armature cores usually are attached to the shaft either
by means of spider frames or of skeleton pulleys. In both
cases the driving of the conductors is effected by a number of
spokes, which respectively form part of the spider itself, Fig.
127, or of a separate driving frame keyed to the skeleton pulley,
Fig. 128, page 188.
51] MECHANICAL CALCULATIONS. 187
TABLE LIL DIAMETERS OF SHAFTS FOR HIGH-SPEED RING ARMATURES.
SPEED,
DIAMETER OF ARMATURE SHAFT, IN INCHES.
IN
CAPACITY,
IN
REVOLUTIONS
PER MINUTE
Bearing Portion.
Core Portion.
WATTS.
(FROM
4 /"
TABLE XI.)
4
/ f
P
N.
d^.mvr-xsn
kg
dc= gx V w
100
2,600
i
.9
i
250
2,400
.95
500
2,200
1
1
H
1,000
2,000
4
2,500
1,700
1
.05
i^
5,000
10,000
1,500
1,250
if
.1
.2
if
2
25,000
1,000
3*
.25
u
50,000
800
.3
3f
100,000
600
4f
.4
5
200,000
500
.5
6f
300,000
450
7*
.55
400,000
400
8*
.55
9
600,000
350
10
.6
10*
800,000
300
11
.65
12
1,000.000
250
12
.7
18*
1,500,000
225
14
1.75
15f
2,000,000
200
16
1.8
18
TABLE LIII. DIAMETERS OF SHAFTS FOR LOW-SPEED RING ARMATURES.
SPEED,
DIAMETER OF ARMATURE SHAFT, IN INCHES.
IN
CAPACITY,
IN
REVOLUTIONS
PER MlNTITE
Bearing Portion.
Core Portion.
WATTS.
(FROM
4 / "
P
TABLE XII.)
N.
d b = .005 t/P'X \/W
*
*-**yV
2,500
400
li
1.05
H
5,000
350
1*
1.1
2*
10,000
300
2
1.2
H
25,000
250
1.25
4
50,000
200
4
1.3
5i
100,000
175
5f
1.4
6
200,000
150
7f
1.5
9
300,000
125
1.55
10^
400,000
100
10
1.55
12 J
600,000
90
12
1.6
14*
800,000
80
m
1.65
16*
1,000,000
75
15
1.7
18*
1,500,000
70
18
1.75
22
2,000,000
65
20
1.8
24*
1 88
D YNA MO-ELE C TRIG MA CHINE S.
[52
In dimensioning these driving spokes, on the one hand suf-
ficient mechanical strength for driving should be provided,
while on the other hand, if spiral winding is to be used, not
+"~ ---"" """" 1 ~*~ -. ^ *""' fc ^
Fig. 127. Ring Armature Driven by Spiders.
more than necessary of the inner winding circumference should
be made unavailable.
For the latter reason the axial breadth of the spokes, ^ s ,
Figs. 127 and 128, is to be made as large as the construction
of the armature allows, and their thickness, /i s , calculated ta
give the requisite strength.
Multiplying equation (95) for the circumferential force per
Fig. 128. Ring Armature Driven by Pulley and End Rings.
armature conductor ( 41) by the number of effective conduc-
tors, we obtain the total peripheral force of the armature:
* =/. X
X
= .7375 X
E *
....(124)
52] MECHANICAL CALCULATIONS. 189
and, allowing a factor of safety of about 4, we get:
P"
*Y=3X-^>
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,
/. ., in unit-poles.
A magnetic field of unit intensity also exists at the center of
curvature of an arc of a circle whose radius is i centimetre
and whose length is i centimetre, when a current of i
absolute electromagnetic unft of intensity, or of 10 practical
electromagnetic units, that is, of 10 amperes, flows through
this arc. Therefore, the unit of magnetic flux, /. e., i
C. G. S. line of force, or i maxwell, is equal to
10
practical electromagnetic units, or one practical electromag-
netic unit
4 TT
maxwells.
10
56. Useful Flux of Dynamo.
The total number of lines of force cutting the armature con-
ductors is called the Useful Flux of the dynamo.
According to the definition given in 15, we have:
Volts Dumber f C- G. S. Lines cut per second
Let now # = total number of useful lines, or useful flux, in
maxwells;
N c = number of conductors all around pole-facing
circumference of armature;
-^c = n c X n & , for ring armatures ;
AT C = 2 x n c x # a > 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, /. ., area occu-
pied by the effective armature conductors.
The same formula also holds good for the metric system,
the density, 3C, in gausses, being obtained, if the area, S t , is
expressed in square centimetres.
The actual field density, calculated from (139), is, in general,
slightly different from the original field density, selected from
Table VI., 18, and used for the determination of the length
of armature conductor, for the reason that, in practice, the
length of the polar arc is not fixed with relation to exactly ob-
taining the assumed field density, but is dimensioned according
to a construction rule having reference to the ratio of the
distance between pole-corners to the length of gap-spaces
(see 58).
It would be an easy matter to obtain the length of the polar
arc and the percentage of its embrace from the assumed field
' 57] USEFUL AND TOTAL MAGNETIC FLUX. 203
density, for, supposing that, in a machine with smooth arma-
ture, the length of the polepieces is equal to that of the arma-
ture core, we would simply have to make the sum of the
lengths of the polar arcs of half the number of poles equal to
3C" X 4 '
or the percentage of the polar arc:
3C' X / a X d t X J
2
in which /? t = percentage of polar arc, or quotient of sum of
all polar arcs by circumference of mean field-
circle;
= useful flux, in maxwells, from (137) or (138);
3C" = assumed field density, in lines per square inch,
from Table VL, 18;
/ a = length of armature core, in inches, formula (40);
and
d t = mean diameter of magnetic field, in inches,
which is given by the core diameter of the
armature, by the height of its winding space,
and by the clearance between the armature
winding and the polepieces: d t = d & -\- h & -j- h c ;
see 58.
But since the polar embrace so determined may not be within
the limits of practical design in accordance with the construc-
tion rule referred to, it is advisable not to follow the process
indicated by formula (140), but to fix the distance between the
pole-corners, and thereby the percentage ft l , by that rule, and
to calculate the actual field density corresponding to the same
by formula (142) or (146), respectively.
This latter method is in no way objectionable, as the new,
actual value of 3C" only enters the calculation of the magneto-
motive force, and the change does not affect any of the previ-
ous calculations concerning the dimensions and the winding
data of the armature. For, according to formula (136), the
same E. M. F. will be generated by a certain number of con-
ductors moving at a constant speed, as long as the total useful
204 DYNAMO-ELECTRIC MACHINES. [57
flux remains the same; the E. M. F. generated by a certain
armature, therefore, remains constant as long as the product
field density and field area is kept at the same value, and it
matters not whether this product is made up of the original
field density and an area corresponding to the polar embrace
found from formula (140), or of a larger actual density and a-
Fig. 129. Field Area of Bipolar Dynamo.
corresponding reduced field area, or of a smaller density-
spread over a larger area.
a. Smooth Armatures.
In smooth-core armatures, Fig. 129, the area, S l9 occupied by
the effective conductors, is obtained from:
S t = d t x ~ X ft\ X l t ; ........ (141)
the actual field density, therefore, by inserting (141) into (139)
can be found:
4 x x ft\ x
(U2)
where 3C" = actual field density of dynamo, in lines of force
per square inch;
= total useful flux of machine, in maxwells, from for-
mula (137) or (138);
f = mean diameter of magnetic field, in inches;
a = diameter of armature core, in inches;
57] USEFUL AND TOTAL MAGNETIC FLUX. 205.
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, /, at even comparatively high satura-
tion of the teeth, is very large compared with the permeance
of the slots, ^"', so that for all practical purposes b $'" in (168)
may be neglected, and we have:
The permeance of the clearance space, 2 ; , furthermore, is so
all compared with $*, that their sum 2' + *$" is practically
equal to 2*, and by canceling we obtain the approximate
formula:
(173)
which can be used with sufficient accuracy in all cases where
the magnetization in the teeth is not driven beyond 100,000
lines per square inch (= 15,500 gausses).
230
D YNAMO-ELECTRIC MA CHINES.
[64
Inserting the values from (169) into (173) we obtain for
straight-tooth armatures:
; (in)
X 7t X A +*t +* X n' c X /3'x / f
k \i X (a p \)
iQ? projecting-tooth armatures:
- [ p X TT X A + (^t + ^'t) X ' c X ^'i] X /f
.= ^ X tf -rf-) -;d75>
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. ., larger than at m in the former, and
smaller in the latter case.
By properly interpolating between the first and second
assumption, a third assumption of $" is now made which will
produce a value of Z very near the actual value of at m . A
fourth, or eventually a fifth assumption, will then make the
value of Z practically equal to #/ m from formula (207), and that
final value of $", which satisfies the equation (212), is the re-
quired total flux per magnetic circuit of the dynamo.
70. Actual Leakage Factor of Machine.
Being thus able to calculate the total flux of magnetic lines
through any dynamo from the ordinary machine test, that is,
262 D YNAMO-ELECTRIC MA CHINES. [ 70
from its ordinary running conditions, the actual factor of mag-
netic leakage can be found from
where $' = total flux through magnet frame, in lines of
force;
<&" = total flux per magnetic circuit, calculated from
formula (210), or (212), respectively;
$ = useful flux cutting armature conductors, from
(137) or (138), respectively;
n z = total number of magnetic circuits in machine.
The author, by employing his method of calculating the leak-
age from the ordinary machine test, 69, has figured the leakage
factors for a great number of practical dynamos 1 of which the
test data were at his command, and by combining his results
with the researches of Hopkinson, 2 Lahmeyer, 3 Corsepius,*
Esson, 6 Wedding/ Ives, 7 Edser, 8 and Puffer, 9 has averaged the
following Table LXVIII. of leakage factors for dynamos of
various types and sizes, which is intended as a guide in making
the first assumption of the total flux, for solving equation (212),
as well as for dimensioning the field^magnet frame (see 60),
but which may also be made use of in obtaining, an approxi-
mate value of the leakage coefficient for rough calculations.
From this table the general fact will be noted that the leak-
age is the greater the smaller the dynamo, which is due to the
difficulty, or rather impossibility, of advantageously dimension-
ing the magnetic circuit in small machines. In these the length
of the air gaps is comparatively much larger, and the relative
1 For list of machines considered see Preface.
2 J. and E. Hopkinson, Phil. Trans., 1886, part i.
3 Lahmeyer, Elektrotechn. Zeitsckr., vol. ix. pp. 89 and 283 (1888).
4 Corsepius, Elektrotechn. Zeitschr., vol. ix. p. 235 (1888).
6 W. B, Esson, The Electrician (London), vol. xxiv. p. 424 (1890); Journal
Jnst. El. Eng., vol. xix. p. 122 (1890).
6 W. Wedding, Elektrotechn. Zeitschr., vol. xiii. p. 67 (1892).
'Arthur Stanley Ives, Electrical World, vol. xix. p. u (January 2, 1892).
* Edwin Edser and Herbert Stansfield, Electrical World, vol. xx. p. 180
(September 17, 1892).
9 Puffer, Electrical Review (London), vol. xxx. p. 487 (1892).
87O] CALCULATION OF ACTUAL MAGNETIC LEAKAGE. 263
I | S.
S-SI8,
SJJ.VMO-IIM Nl
A-LIOVdVO
3
Ilii
.111
DO*-
S s
HI
2
Is 1
n-
-Hi
6JJ.VM Ol IX Nl
AXlOV.dVO
: :8ggS83$S!i58
83888O88SS3
S 2
O T5
S
Hi
C
8 a
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, /. ., of cast iron.
78. Zinc Blocks.
In some forms of machines, such as the upright horseshoe
type, Fig. 187, the horizontal single-magnet types^ Figs. 191
and 192, the consequent pole, horizontal double magnet type,
Fig. I 97> 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 2
n + * m X 7t X
95] COIL WINDING CALCULATIONS. 361
When length and winding depth are known, the internal
coil diameter is found from:
_ 12 X An X 6V - /i m * X l m X n
/ X h m X 7T
7" v tf' a
= 3-82X 7=-Tr r% (256)
*m A " m
And if the length and the internal diameter of the coil are
given, its winding depth can be obtained from:
, " - + 3S-S-. ..(257)
'm X " 42
Since the length of a wire is the product of its weight and
its specific length, formula (257) can be modified so as to give
the height of the coil space required to wind a given weight of
wire of given diameter upon a core of known dimensions:
/v = /^H1f^ + T-^- < 858 )
The resistance which a coil of wire of known resistivity will
offer when wound on a given bobbin, is:
r m = An X p m ohms, (259)
or, by inserting the value of Z m from (254):
r m = .262 X p m X (d m + h m ) X m ** m . (260) %
Ml
The diameter of a wire which shall fill a bobbin of given
dimensions and offer a given resistance can be found as fol-
lows: The coil space occupied by Z m feet of wire having a
diameter (insulated) of d' m inch, is:
F m = 12 Z m X ' m a , (261)
while, expressed in the dimensions of the bobbin, the same
volume is:
7 ^ s ,
(Z> m ' - m 2 )
4
. +
= / x 7r(A 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, *'. ., in the case of copper:
tf m a X p m = 12 ohms, at about 60 Cent. (= 140 Fahr.);
consequently the current density in the magnet wire:
(269)
For a given machine, therefore, (E m being constant) the cur-
rent density only depends upon the total length of the wire,
and is independent of its size.
Formula (269) may be used to determine the practical limits
of Z m , by limiting the value of the current density, / m . From
(269) follows directly:
m =ix m ; (270)
96] COIL WINDING CALCULA TIONS. 365
and since the practical value of i m ranges between 240 and
1800 Circular Mils per ampere (= 5300 to 700 amperes per
square inch, or 8. 2 to i.i amperes per square millimetre),
we have:
for(/ m ) min = 240 CM. per amp. ..(Z m ) min = 20 m -)
for(/ m ) max = i,8ooC.M. per amp. . .(Z m ) max = 150 m . j ^
The total length of magnet wire, in feet, should therefore
be from 20 to 150 times the difference of potential between the
field terminals, in volts.
From (269) we can also derive the following formula, which
gives, directly in Circular Mils, the area of a magnet wire
effecting a certain magnetizing force at given potential between
field terminals, viz. :
, 12 X An X / m 12 X W m X / m X/ t
m := ~^~
**i **m
_ (N m X /...) X (12 X / t ) _
that is to say, the area of the requisite magnet wire is the
quotient of the number of ampere-inches (/ T being the length
of the mean turn in inches) to be wound upon the cores, by
the potential between the field terminals. Assuming an ap-
proximate value for the mean turn, / T , the minimal limit of
which is always given by the circumference of the magnet
core, a preliminary value of tf m can be quickly determined, and
from this the value of / T is easily adjusted if necessary; a re-
calculation with the correct value of / T will then furnish the
final value of the area of the magnet wire.
A set of valuable curves which show the relation between
ampere-turns and mean length of turn, and between current
and total length of wire, respectively, and which can be used
for graphically obtaining the results of formula (272) as well
as other data concerning the magnet winding, has been
devised by Harrison H. Wood. 1
Formula (272) is only approximate, being based upon the
assumption that the final temperature of the magnet coils is
1 "Curves for Winding Magnets," by H. H. Wood; Electrical World, vol.
xxv. pp. 503 and 529 (April 27 and May 4, 1895),
366 DYNAMO-ELECTRIC MACHINES. [96
about 60 C. If the actual rise above 15.5 C. of the magnet
temperature is denoted by 6 m , the accurate formula for the
area of the wire would be :
/. x (i + .004 x e m ) , (273)
10.5 being the resistance, in ohms, of a copper wire, one foot
long and one mil in diameter, at a temperature of 15.5 C.
-(= 60 F.).
From (273) a very useful formula for the weight of the mag-
net winding can be derived. By Ohm's Law we have:
p
F T \f r V
"in y m A ' m 77 A A m
^m
in which P m = energy absorbed in magnet winding, in watts
(see 98); consequently:
But the resistance of the magnet winding can be ex-
pressed by:
/ 1 /i \ 2
-^ x [ ^rj
io. q X io
r m = - x (i + .004 x e m ) x
v/here wt' m = weight of magnet winding, including insulation,
in pounds;
15 = specific weight of magnet winding, in pounds
per cubic inch, depending upon size of wire
and thickness of insulation; see Table XCII.
Hence:
rt 2 v *2 X io- 6 X X AT X / t X E m X m 4
^ m X W /' m
or,
/' _ 12 x io- 6 x ,. x ^r x / t x^ m x ^ m 3
w ^m r> >
* 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 + 2/; m ) x n X /' m ; (277)
for rectangular magnets:
Si, = 2 X /' m X (/ + b + h m X *); . . . .(278)
and for magnets of oval cross-section (rectangle between two
semicircles) :
S* - 2 x /' m X (/-*) + ~ + h m X ?r . ..(279)
In case that also one of the end surfaces of each coil is
exposed to the air, or that one-half of each coil flange helps
the prismatical surface to liberate the heat developed by the
field current, the radiating surface becomes:
S^ = 5 M + X /T x h m ......... (280)
If there is a clearance between the magnet coils and the
yokes and polepieces such as to make both the entire end sur-
faces of each magnet coil active in giving off heat, the radiat-
ing surface is:
S Ma = .S M + 2 m X /T X * m ......... (281)
And when, finally, the yokes and polepieces touch the end
flanges of the coils, but the latter project over the former so
that heat can radiate from the projecting portions, the radiat-
ing surface will be:
^M 3 = -S-M + 2 m X h m X (/T - by) ..... (282)
In the above formulae (277) to (282):
SK = radiating surface of prismatic surface of magnet
coil;
*$M, radiating surface of prismatic surface plus one
end surface per coil;
37 DYNAMO-ELECTRIC MACHINES. [97
^MS radiating surface of prismatic surface plus two
end flanges per coil;
Syi 3 = radiating surface of prismatic surface plus pro-
jecting portions of coil flanges;
d m diameter of circular core-section;
> 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, a , the dimensioning of
the frame is reduced to the calculation of d & .
In order to obtain a formula for the armature diameter, we
express the polar area in two ways: electrically, as the quo-
tient of flux, >, 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 - a );
the magnetizing force necessary to compensate armature-
reactions, by (250), is:
1 "Armatures and Magnet-Coils," by Claude W. Hill, Electrical Review
(London), vol. xxxvii. p. 227 (August 23, 1895).
472 D YNA MO-ELECTRIC MA CHINES. [126
N & X /' 18 X a
atr ~ f" > ~ 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
_ . = 1.5 X / X r a .
1 Picou, " Traite des Machines dynamo-electriques."
486
DYNAMO-ELECTRIC MACHINES,
[ 13O
The point B thus being located, draw BC \ OA, and from
the intersection, C, of this parallel line with the characteristic
curve drop the perpendicular CD upon the axis of abscissae.
The portion FD of CD, from its intersection, F, with OA to
the axis of abscissae, is the required E. M. F., DF = E^ while
OD AT^is the corresponding exciting force of the field
magnets.
* The characteristic shows that the drop, CF, is the greater
the lower the saturation of the machine.
130. Determination of the Number of Series Ampere-
Turns for a Compound Dynamo.
Let the E. M. F., which is to be kept constant, be repre-
sented by E, Fig. 330. Draw EA parallel to the axis of
AMP. TURNS AT, A AT
Fig. 330. Determination of Compound Winding.
abscissae, and from A on the characteristic drop the perpen-
dicular AB. The length OB then gives the ampere-turns
required on open circuit, that is, the shunt excitation AT 8h .
If e & again denotes the total drop of E. M. F. caused by the
armature current at the given load (see 129), then in order
to keep the external E. M. F., E, constant, an internal E. M. F.,
E' == E + e & , must be generated. Drawing E'C || OB, and
CD J_ OB, we find that the latter requires a total magnetiz-
ing force of OD = AT ampere-turns.
131]
D YNAMO-GRAPHICS.
487
Hence the number of series ampere-turns necessary for
compounding:
= AT ee = AT - AT Bh ,
the series excitation being the difference between the total
number of ampere-turns required for the generation of r
volts, and the shunt excitation needed for E volts.
131. Determination of Shunt Regulators. 1
Shunt regulators are employed: (a) to keep the output
E. M. F. constant at variable load and constant speed; (b) to
keep the E. M. F. constant for variable speed; (c) to keep
the E. M. F. constant if both the load and the speed are var-
iable; and (d) to effect any variation in the E. M. F.
a. Regulators for Shunt Machines of Varying Load.
In Fig. 331, E is the constant potential of the dynamo, r m ,
the magnet resistance, r r , the resistance of the shunt regula-
i
AMP.TkjRNS
A AT AT 7
Fig. 33L Shunt Regulating Resistance for Constant Potential at
Varying Load.
tor, and N m the number of convolutions per magnetic circuit.
The dynamo is driven by a motor of constant speed, and so
1 " LOsung einiger praktischer Fragen tiber Gleichstrom-Maschinen auf
graphischem Wege," by J. Fischer-Hinnen, Elektrotechn. Zeitschr., vol. xv. p..
397 (July 19. 1894).
488 DYNAMO-ELECTRIC MACHINES. [131
arranged that at full load all resistance of the regulator is cut
out. The resistance is to be found which has to be put in
.series with the field magnets in order to keep the potential on
open circuit the same as at full load.
In the manner shown in 129 the exciting current intensi-
ties, 7 m and /' m , at no and full load, respectively, are first de-
termined by finding the magnetizing forces AT and AT', for
the E. M. Fs. E t and E' = E -(- a , respectively, and divid-
ing the same by the given number of shunt-turns, thus:
AT AT'
" #m' ' ^n
Then, according to Ohm's Law:
E N^ X E
tan
and
X E
...(449)
The values of r m and (r m -j- r r ) can be directly found as fol-
lows: In the distance OA = N m (Fig. 331) draw AB parallel
to the axis of the ordinates; find point F by drawing EF \\ OA
and E'F || AB; and draw the lines OE and OF. These will
intersect AB in points E l and E^ , respectively, for which hold
the following relations:
AE l N m X E,
* n *>= 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, /'. .,
for varying propelling power.
To solve this problem, the speed characteristic of the motor
is
i
I CURRENT INTENSITY
Fig. 340. Speed Characteristic of Railway Motor.
giving the motor speed, or still better, the car velocity, as
a function of the current-intensityis plotted.
Let W t = total weight to be propelled, in tons;
v m velocity of car, in miles per hour;
g = grade of track, in per cent., *'. ., number of feet of
rise in a horizontal distance of 100 feet;
1 J. Fischer-Hinnen, Elektrotcchn. Zeitschr., vol. xv. p. 401 (July 19, 1894).
133]
D YNAMO-GRAPIIICS.
5 01
/ = current required to propel W t tons, at g
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.)....
= 16.000 inches
- - 1-16- -j
Fig. 344. Dimensions of Field Magnet Frame, lo-KW Single-Magnet Type
Generator.
Making the width at the centre of the polepiece one-half the
full width, or 2j inches, the total height of the machine is ob-
tained 1 6 -j- 5 = 21 inches, leaving the length of the magnet
core:
/ m = 21 2x5 11 inches.
The distance between the pole-tips is obtained by formula
(150) and Table LX., 58, as:
l 'v = 5-5 X (16 15) = 5$ inches.
The assumed percentage of polar arc corresponds to a pole
angle of /? = 140, or a pole space angle of a = 180 140 =
40, and therefore furnishes:
/' p = 16 x sin 20 =
inches.
If the two values of /' p so obtained differ from each other,
the larger figure is preferable on account of smaller leakage.
The distance between the magnet core and the adjoining
pole-tips is determined by Table LXXX., 83. In this, the
height of the magnet-winding for a 28 square inch rectangular
core is given as h m = 2 inches ; allowing J" clearance, we ob-
134] EXAMPLES OF GENERATOR CALCULATION. 519
tain the desired distance, and making the width of the pole-
shoes 1 6 inches, the total width of the frame becomes:
5 -f 21 -f 16 = 23J inches.
Fig. 344 shows the field magnet frame thus dimensioned.
C. CALCULATION OF MAGNETIC LEAKAGE.
i. Permeance of Gap- Spaces. The actual field-density, by
(142), p. 204, being
jg/r = _ 2,083,000 __
j(<5 + 16) X~ X .89 x i(5t + 5l)
= 17,500 lines per square inch,
the product of field density and conductor velocity is
OC" X v c = 17,500 x 80 = 1,400,000;
hence the permeance of the gaps, by Table LXVI. and formula
(167), page 226:
i5l X X - 8 9 X 51
i
1.19 X (16 15) 1.19
2. Permeance of Stray Paths. The area of the pole-shoe end
surface, 5 g , Fig. 164, is, according to Fig. 344:
54 square inches.
Substituting this value into (193), we obtain the total relative
permeance of the waste field:
X 54 + 5* X I 8J- + 7| X -
+
= 5-5 + I?- 2 + T -3 + 2.0 = 26.
'5^0 DYNAMO-ELECTRIC MACHINES. [134
3. Leakage Factor. From (157), p. 218:
IOO IOO
This being smaller than, and only i per cent, different from,
the leakage factor taken for the preliminary calculation of the
total flux, we will use the value found from the latter in the
subsequent calculations.
d. CALCULATION OF MAGNETIZING FORCES.
1. Air Gaps. Length, by (166), p. 224:
l\ = 1.19 X (16 15) = 1.19 inch.
Area, by (141), p. 204:
S" e = i5i X ~ X .89 x Si = 119 square inches.
Density, by (142), p. 204:
2,083,000
5C = - - = ^Soo lines per square inch.
119
Magnetizing force required, by (228), p. 339:
af % = .3133 X 17,500 X 1.19 = 6530 ampere-turns.
2. Armature Core. Length of path, by (236), p. 343:
l\ = 124 x n X 9 3 fo 20 + 2j --= 144 inches.
Minimum area of circuit, by (232), p. 341 :
S" &1 = 2 x 5i X 2| X .9 = 26.5 square inches.
2,083,000
'' ai = 26 5 = 7 8 >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:
p = 38^ + 2 x t = 39 inches.
Length of centre portion (equal to diameter of armature core) :
38} inches.
Depth of magnet winding (Table LXXX., p. 317):
^ m = 2} inches.
Allowing } inch clearance between the magnet winding and
the pole- tips, the total length of the polepieces is:
38} + 2 X (2f + }) = 45 inches.
Pole-distance:
^'P = 39 X sin 27 = 15 inches,
which is 4.45 times the total length of the gap space (compare
with Table LX., p. 208).
Thickness in centre, required for mechanical strength only:
3 inches.
Thickness of pole-tips:
\ (38} ~ V 7 39 2 - i5 2 ) = I
137] EXAMPLES OF GENERATOR CALCULATION. 559
All other dimensions of the frame can be directly derived
from Fig. 353.
45
. 353- Dimensions of Field-Magnet Frame, 50 KW Double-Magnet
Type, Low-Speed Generator.
C. CALCULATION OF MAGNETIC LEAKAGE.
i. Permeance of Gap Spaces.
' ' -~ 76
~ ' 4375 = " 439
Ratio of radial clearance to pitch :
.8765
= .286;
Product of field density and conductor velocity:
20,000 x 32 = 640,000,
hence by Table LXVII., p. 230, the factor of field deflection,
*= 1-5;
and by (174), p. 230:
<* . j [39 X n X .70 + (-439 + .219) X 138 X .85] X io
i-5 X (39 -
75
5 6 DYNAMO-ELECTRIC MACHINES. [137
2. Permeance of Stray Paths.
By (194), p. 242:
<-.'{
S> 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.
. CALCULATION OF MAGNET WINDING.
In the present machine the winding space is limited by the-
shape of the frame, the height available at the pole end of the
core being 4 inches, and at the yoke end only if inch, see Fig.
356. The larger depth can be employed until the distance
between two adjoining coils becomes the same as that allowed
at the yoke end; leaving J inch for the bobbin flanges, and for
insulation and clearance, it is thus found that 8f inches of the
available length of each core can be wound 4 inches deep, and
that for the remaining 7 inches the winding depth tapers from
4 inches to if inch. This gives a mean winding depth of
4 X 8f + L( 4 + T J)X7
= 3} inches.
m
Mean length of one turn:
/ T 2(19^- -f 13^) -f 3 x n = 77 inches.
Radiating surface of each magnet:
^M = 2 (i9i + 13^4- 3j x 7t) X i5f = 1585 square inches.
By means of formula (328), p. 390, we can now determine
the minimum temperature increase that can be obtained with
the present design (by entirely filling the given winding space).
The weight of bare copper wire filling one bobbin is, by (330),.
p. 390:
wf m = 77 X 15! X 3^ X .21 = 890 pounds.
138] EXAMPLES OF GENERATOR CALCULATION. 577
hence by (329), p. 390:
D-3 x (^ x ff )' x jjj
e _ _ v _ / _ i_f _ _ 4.4.0 p
m ~ r ?<; ~i
890 - .004 X |_3i-3 X 140 2 X ^J
Although this is rather high, especially for so large a
machine, it is yet within practical limits, and we therefore
base the winding calculation on the above dimensions of the
winding space.
Connecting the 10 coils in 5 groups of 2 each, the terminal
voltage of 150 volts will correspond to the total magnetizing
force of one circuit, and formula (318), p. 385, gives the specific
length of the wire required, for 20 per cent, extra-resistance:
A sh = x X 1.20 X (i -f . 004 x 44) = 2635
feet per ohm.
No. 8 B. W. G. wire (165" + .010*) has a specific length
of 2637 feet per ohm.
By 312, p. 383:
P' sh x 2 x 1480 X 1.20 = 2080 watts per magnetic
circuit.
By (314), p- 384:
^ = 43,650 x 150 _ 3150 turns per circuit>
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