ELECTRO-DYNAMIC MACHINERY FOR CONTINUOUS CURRENTS BY EDWIN J. HOUSTON, PH. D. (PRINCETON) AND A. E. KENNELLY, Sc. D. ^N HE \ UNIVERSITY; f^tMhltX* ^*r NEW YORK t THE W. J. JOHNSTON COMPANY 253 BROADWAY 1896 COPYRIGHT, 1896, BY THE W. J. JOHNSTON COMPANY. PREFACE. ALTHOUGH several excellent treatises on machinery employed in electro-dynamics already exist, yet the authors believe that there remains a demand for a work on electro-dynamic ma- chinery based upon a treatment differing essentially from any that has perhaps yet appeared. Nearly all preceding treatises are essentially symbolic in their mathematical treatment of the quantities which are invoJv-ed, even although such treat- ment is associated with much practical information. It has been the object of the authors in this work to employ only the simplest mathematical treatment, and to base this treatment, as far as possible, on actual observations, taken from practice, and illustrated by arithmetical examples. By thus bringing the reader into intimate association with the nature of the quantities involved, it is believed that a more thorough appre- ciation and grasp of the subject can be obtained than would be practicable where a symbolic treatment from a purely algebraic point of view is employed. In accordance with these principles, the authors have in- serted, wherever practicable, arithmetical examples, illustrat- ing formulas as they arise. The fundamental principles involved in the construction and use of dynamos and motors have been considered, rather than the details of construction and winding. The notation adopted throughout the book is that recom- mended by the Committee on Notation of the Chamber of Delegates at the Chicago International Electric Congress of 1893. ia iv PREFACE. The magnetic units of the C. G. S. system, as provisionally adopted by the American Institute of Electrical Engineers, are employed throughout the book. The advantages which are believed to accrue to the concep- tion of a working analogy between the magnetic and voltaic circuits, are especially developed, for which purpose the con- ception of reluctivity and reluctance are fully availed of. CONTENTS. CHAPTER I. GENERAL PRINCIPLES OF DYNAMOS. Definition of Electro-Dynamic Machinery. General Laws of the Genera- tion of E. M. F. in Dynamos. Electric Capability. Output. Intake. Commercial Efficiency. Electrical Efficiency. Maximum Output. Maximum Efficiency. Relation between Output and Efficiency, . I CHAPTER II. STRUCTURAL ELEMENTS OF DYNAMO-ELECTRIC MACHINES. Armatures. Field Magnets. Magnetic Flux. Commutator Brushes. Constant-Potential Machines. Constant-Current Machines. Magneto. Electric Machines. Separately-Excited Machines. Self-Excited Machines. Series-Wound Machines. Shunt- Wound Machines. Compound- Wound Machines. Bipolar Machines. Multipolar Ma- chines. Quadripolar, Sextipolar, Octopolar and Decipolar Machines. Number of Poles Required for Continuous and Alternating-Current Machines. Consequent Poles. Ring Armatures. Drum Armatures. Disc Armatures. Pole Armatures. Smooth-Core Armatures. Toothed- Core Armatures. Inductor Dynamos. Diphascrs. Triphasers. Single Field-Coil Multipolar Machines. Commutatorless Continuous- Current Machines, 9 CHAPTER III. MAGNETIC FLUX. Working Theory Outlined. Magnetic Fields. Direction, Intensity, Dis- tribution. Uniformity, Convergence, Divergence. Flux Density. Tubes of Force. Lines of Magnetic Force. The Gauss. Properties of Magnetic Flux. M. M. F. Ampere-Turn. The Gilbert. Flux Paths, . ....... 29 CHAPTER IV. NON-FERRIC MAGNETIC CIRCUITS. Reluctance. The Oersted. Ohm's Law Applied to Magnetic Circuits. Ferric, Non-Ferric, and Aero-Ferric Circuits. Magnetizing Force. Magnetic Potential. Laws of Non-Ferric Circuits, . . . .48 CHAPTER V. FERRIC MAGNETIC CIRCUIT. Residual Magnetism. Permeability. Theory of Magnetization in Iron. Prime M. M. F. Structural M. M. F. Counter M. M. F. Reluc- tivity. Laws of Reluctivity. . . *. .* . ; . 55 viii CONTENTS. CHAPTER VI. AERO-FERRIC MAGNETIC CIRCUITS. Magnetic Stresses. Laws of Magnetic Attraction. Leakage, . . .68 CHAPTER VII. LAWS OF ELECTRO-DYNAMIC INDUCTION. Fleming's Hand Rule. Cutting and Enclosure of Magnetic Flux, . . 74 CHAPTER VIII. ELECTRO-DYNAMIC INDUCTION IN DYNAMO ARMATURES. Curves of E. M. F. Generated in Armature Windings. Idle-Wire, . 90 CHAPTER IX. ELECTROMOTIVE FORCE INDUCED BY MAGNETO GENERATORS, IO3 CHAPTER X. POLE ARMATURES, IIO CHAPTER XI. GRAMME-RING ARMATURES. E. M. Fs. Induced in. Effect of Magnetic Dissymmetry. Commuta- tor-Brushes. Effect of Dissymmetry in Winding. Best Cross- Section of Armature, . . . . . . . . .117 CHAPTER XII. CALCULATION OF THE WINDINGS OF A GRAMME-RING DYNAMO, I2& CHAPTER XIII. MULTIPOLAR GRAMME-RING DYNAMOS. Belt-Driven versus Direct-Driven Generators. Reasons for Employing Multipolar Field Magnets. Multipolar Armature Connections. Effect of Dissymmetry in Magnetic Circuits of Multipolar Generators. Com- putations for Multipolar Gramme-Ring Generator, .... 135 CHAPTER XIV. DRUM ARMATURES. Smooth-Core and Toothed-Core Armatures. Armature Windings. Lap Windings. Wave Windings, ..,.... 152 CHAPTER XV. ARMATURE JOURNAL BEARINGS. Frictional Losses of Energy in Dynamos. Sight-Feed Oilers and Self- Oiling Bearings, .......... 159 CONTENTS. IX CHAPTER XVI. EDDY CURRENTS. Methods of Lamination of Core. Transposition of Conductors, . . 164 CHAPTER XVII. MAGNETIC HYSTERESIS. Nature and Laws of Hysteresis. Hysteretic Loss of Energy. Table of Hysteretic Loss. Hysteretic Torque, . . , . . . .172 CHAPTER XVIII. ARMATURE REACTION AND SPARKING AT COMMUTATORS. Diameter of Commutation. E. M. F. of Self-induction. Inductance of Coils. Cross- Magnetization. Back-Magnetization. Leading and Following Polar Edges. Lead of Brushes. Distortion of Field. Con- ditions Favoring Sparking at Commutator. Conditions Favoring Sparkless Commutation. Methods Adopted for Preventing Sparking, 179 CHAPTER XIX. HEATING OF DYNAMOS. Losses of Energy in Magnetizing, Eddies, Hysteresis and Friction. Safe Temperature of Armatures, . . . . . . . . 199 CHAPTER XX. REGULATION OF DYNAMOS. Series- Wound, Shunt-Wound and Compound-Wound Generators. Over- compounding. Characteristic Curves of Machines. Internal and External Characteristic. Computation of Characteristics. Field Rheostats. Series- Wound Machines and their Regulation. Open-Coil and Closed-Coil Armatures, , , 206 CHAPTER XXL COMBINATIONS OF DYNAMOS IN SERIES AND PARALLEL. Generator Units. Series-Wound Machines Coupled in Series. Shunt- Wound Machines Coupled in Parallel. Equalizing Bars. Omnibus Bars, ... . 220 CHAPTER XXII. DISC-ARMATURES AND SINGLE-FIELD COIL MACHINES, 228 CHAPTER XXIII. COMMUTATORLESS CONTINUOUS-CURRENT GENERATORS. Disc and Cylinder Machines, .... ^ : r "~"*-s! ' 2 ^ x CONTENTS. CHAPTER XXIV. ELECTRO-DYNAMIC FORCE. Fleming's Hand-Rule. Ideal Electro-dynamic Motor, .... 241 CHAPTER XXV. MOTOR TORQUE. Torque of Single Active Turn. Torque of Armature-Windings. Torque of Multipolar Armatures. Dynamo- Power, 251 CHAPTER XXVI. EFFICIENCY OF MOTORS. Commercial Efficiency in Generators and Motors Compared. Slow-Speed versus High-Speed Motors. Torque-per-pound of Weight, . . 268 CHAPTER XXVII. REGULATION OF MOTORS. Control of Speed and Torque under Various Conditions. Control of Series- Wound Motors, 280 CHAPTER XXVIII. STARTING AND REVERSING OF MOTORS. Starting Rheostats. Starting Coils. Automatic Switches. Direction of Rotation in Motors, .......... 297 CHAPTER XXIX. METER-MOTORS. Conditions under which Motors may act as Meters, 309 CHAPTER XXX. MOTOR DYNAMOS. Construction and Operation of Motor-Dynamos, . 318 OF THE EVERSITY ' ELECTRO-DYNAMIC MACHINERY FOR CONTINUOUS CURRENTS. CHAPTER I. GENERAL PRINCIPLES OF DYNAMOS. I. By electro-dynamic machinery is meant any apparatus designed for the production, transference, utilization or measurement of energy through the medium of electricity. Electro-dynamic machinery may, therefore, be classified under the following heads : (i.) Generators, or apparatus for converting mechanical energy into electrical energy. (2.) Transmission circuits, or apparatus designed to receive, modify and transfer the electric energy from the generators to the receptive devices. (3.) Devices for the reception and conversion of electric energy into some other desired form of energy. (4.) Devices for the measurement of electric energy. Under generating apparatus are included all forms of con- tinuous or alternating-current dynamos. Under transmission circuits are included not only conduct- ing lines or circuits in their various forms, but also the means whereby the electric pressure may be varied in transit between the generating and the receptive devices. This would, therefore, include not only the circuit conductors proper, but also various types of transformers, either station- ary or rotary. Under receptive devices are included any devices for con- verting electrical energy into mechanical energy. Strictly speaking, however, it is but fair to give to the term mechanical energy a wide interpretation, such for example, as would per- 2 ELECTRO-DYNAMIC MACHINERY. mit the introduction of any device for translating electric energy into telephonic or telegraphic vibrations. Under devices for the measurement of electric energy would be included all electric measuring and testing apparatus. In this volume the principles underlying the construction and use of the apparatus employed with continuous-current machinery will be considered, rather than the technique in- volved in their application. 2. A consideration of the foregoing classification will show that in all cases of the application of electro-dynamic machin- ery, mechanical energy is transformed, by various devices, into electric energy, and utilized by various electro-receptive devices connected with the generators by means of conducting lines. The electro-technical problem, involved in the practi- cal application of electro-dynamic machinery, is, therefore, that of economically generating a current and transferring it to the point of utilization with as little loss in transit as possible. The engineering problem is the solution of the electro-technical problem with the least expense. 3. A dynamo-electric generator is a machine in which con- ductors are caused to cut magnetic flux-paths, under conditions in which an expenditure of energy is required to maintain the electric current. Under these conditions, electromotive forces are generated in the conductors. Since the object of the electromotive force generated in the armature is the production of a current, it is evident that, in order to obtain a powerful current strength, either the electro- motive force of the generator must be great, or the resistance of the circuit small. Electromotive sources must be regarded as primarily producing, not electric currents, but electromotive forces. Other things being equal, that type of dynamo will be the best electrically, which produces, under given conditions of resistance, speed, etc., the highest electromotive force (generally contracted E. M. F.). In designing a dynamo, therefore, the electromo- tive force of which is fixed by the character of the work it is required to perform, the problem resolves itself into obtaining a machine which will satisfactorily perform its work at a given GENERAL PRINCIPLES OF DYNAMOS. 3 efficiency, and without overheating, with, however, the maxi- mum economy of construction and operation. In other words, that dynamo will be the best, electrically, which for a given weight, resistance and friction, produces the greatest electro- motive force. 4. There are various ways in which the electromotive force of a dynamo may be increased; viz., (i.) By increasing the speed of revolution. (2.) By increasing the magnetic flux through the machine. (3.) By increasing the number of turns on the armature. The increase in the speed of revolution is limited by well- known mechanical considerations. Such increase in speed means that the same wire is brought through the same mag- netic flux more rapidly. To double the electromotive force from this cause, we require to double the rate of rotation, which would, in ordinary cases, carry the speed far beyond the limits of safe commercial practice. Since the E. M. F. produced in any wire is proportional to its rate of cutting magnetic flux, it is evident that in order to double the E. M. F. .in a given wire or conductor, its rate of motion through the flux must be doubled. This can be done, either by doubling the rapidity of rotation of the armature ; or, by doubling the density of the flux through which it cuts, the rate of motion of tne armature remaining the same. Since the total E. M. F. in any circuit is the sum of the separate E. M. Fs. contained in that circuit, if a number of separate wires, each of which is the seat of an E. M. F., be connected in series, the total E. M. F. will be the sum of the separate E. M. Fs. If, therefore, several loops of wire be moved through a magnetic field, and these loops be con- nected in series, it is evident that, with the same rotational speed and flux density, the E. M. F. generated will be pro- portional to the number of turns. An increase in E. M. F. under any of these heads is limited by the conditions which arise in actual practice. As we have already seen, the speed is limited by mechanical considerations. An increase in the magnetic flux is limited by the magnetic permeability of the iron that is, its capability of conducting magnetic flux and the increase in the number of turns is 4 ELECTRO-DYNAMIC MACHINERY. limited by the space on the armature which can properly be devoted to the winding. 5. It will be shown subsequently that a definite relation exists between the output of a dynamo, and the relative amounts of iron and copper it contains that is to say, the type of machine being determined upon, given dimensions and weight should produce, at a given speed, a certain output. The conditions under which these relations exist will form the subject of future consideration. 6. Generally speaking, in the case of every machine, there exists a constant relation between its electromotive force and E* resistance, which may be expressed by the ratio, , where , is the E. M. F. of the machine at its brushes, in volts, and r, the resistance of the machine; i. , the pilot lamp; i. e., a lamp connected across the terminals of the machine, to show that the generator is at work. S, the main circuit switch, , the rocker-arm carrying the brushes B, B. STRUCTURAL ELEMENTS. 13 16. Self-excited machines maybe divided into three classes; viz., (i.) Series wound. (2.) Shunt wound. (3.) Compound wound. Series-wound machines have their field magnets connected in series with their armatures. The field winding consists of FIG. 4. ALTERNATING- CURRENT MULTIPOLAR SEPARATELY-EXCITED GENERATOR. stout wire, in comparatively few turns. Arc-light machines are almost always series wound. Fig. 6 represents a particular form of series-wound machine for arc-light circuits. Here the current from the armature passes round the cylindrical mag- nets M, J/, through the regulating magnet m, and thence to the external circuit. The machine in Fig. 2 is also series wound. Shunt-wound machines have their field magnets connected to the main terminals, that is, placed in shunt with the external circuit. In order to employ only a small fraction of .the total current from the armature for this purpose, the resistance of the field magnets is made many times higher than the resist- 14 ELECTRO-DYNAMIC MACHINERY. ance of the external circuit. This is accomplished by winding- the magnets with many turns of fine wire, carefully insulated. A particular form of shunt-wound machine is represented in Fig. 7. Here the fine wire windings of the four magnets coils are supplied in one series through the connecting wires W> W, W Y FIG. 5. SELF-EXCITED CONTINUOUS-CURRENT GENERATOR. from the main terminals of the machine, one of which is shown at M. In order to regulate the strength of the exciting cur- rent through the magnet circuit, it is usual to insert a hand- regulating resistance box, called the field regulating box y in series with them. (d.) Compound-wound machines. These are machines that are partly shunt wound and partly series wound. It is found that when the load increases on a series-wound generator, it tends to increase the pressure at its terminals ; i.e., to raise its E. M. F. On the other hand, when the load increases on a shunt-wound generator, it tends to diminish the pressure at its terminals; i. t., to lower its E. M. F. In order, therefore, to obtain good automatic regulation of pressure STRUCTURAL ELEMENTS. , 15 from a machine under all loads, these two tendencies' are so directed as to cancel each other ; this is accomplished by employing a winding that is partly shunt and partly series. Fig. 8 represents a particular form of a compound-wound machine. Here there are two spools placed side by side on each mag- net-core, one of fine wire in the shunt circuit, carrying a cur- rent, and exciting the fields, even when no current is supplied externally by the machine, and the other of stout wire making FIG. 6. SELF-EXCITED SERIES-WOUND CONTINUOUS-CURRENT GENERATOR. comparatively few turns. This is part of the series winding which carries the current to the external circuit. The excita- tion of the magnets from this winding, therefore, depends upon the current delivered by the machine; *'. ^., upon its load. Many generators for incandescent lamp circuits, as well as many generators for power circuits are compound wound. 17. Besides the preceding classes, dynamo-electric machines may be conveniently divided into other classes, according to a variety of circumstances; for example, they may be divided according to the number of magnetic poles in the field frame, as follows : i6 ELECTRO-D Y NAM 1C MA CHINER Y. (a) Bipolar machines, or machines having only two magnetic field poles. Bipolar machines may be subdivided, according to the num- ber of separate magnetic circuits passing through the exciting FIG. 7. SELF-EXCITED SHUNT-WOUND CONTINUOUS-CURRENT GENERATOR. coils, into single-circuit bipolar, double-circuit bipolar machines, and so on. Generally, however, modern bipolar machines are not constructed with more than two magnetic circuits. Figs, i, 2, 3 represent bipolar machines. Of these, Fig. i possesses a single magnetic circuit, and Fig. 2 a double magnetic circuit. (b) Multipolar machines, or machines having more than two magnetic poles. Fig. 9 represents a multipolar, diphase alternator of many STRUCTURAL ELEMENTS. 17 poles. This machine was employed at the World's Columbian Exhibition. 18. Multipolar machines may be divided into the following sub-classes : Quadripolar, or those having four poles. Sextipolar, or those having six poles. Octopolar, or those having eight poles. Decipolar, or those having ten poles. Beyond the number of ten poles, it is more convenient to omit the Latin prefix, and to characterise the machine by the FIG. 8. COMPOUND-WOUND CONTINUOUS-CURRENT GENERATOR. number of poles, as, for example, a i4-pole, or i6-pole machine, etc. Quadripolar machines are common. Fig. 10 shows a quadri- polar machine. This machine has four brushes and is com- pound wound. It is designed to supply from 500 to 600 volts pressure at its brushes, and is surmounted by a group of six pilot lights in series. Fig. 7 also represents a quadripolar generator. Fig. ii shows a form of continuous-current, self-exciting, compound-wound, sextipolar machine, arranged for direct con- nection to the main shaft of an engine. The machine is pro- vided, as shown, with six collecting brushes. Fig. 12 shows an alternating-current, self-exciting, octopolar generator for arc circuits. Although this machine is an alter- nator ; i. e., supplies alternating currents, it, nevertheless, i8 ELECTRO-D YNA MIC MA CHINER Y. supplies its field-magnet coils in series with continuous cur- rents from the commutator C, at one end of its shaft. The magnet M, forms an essential part of a short-circuiting device, whereby the machine is automatically short-circuited, on the external circuit becoming accidentally broken, in which case FIG. 9. ALTERNATING-CURRENT, 75O-KILOWATT DIPHASE MULTIPOLAR GENERATOR. the pressure generated by the machine might become so great as to endanger the insulation of the armature. Fig. 13 shows a decipolar alternator, separately excited, and compensating. This machine is belt-driven, and it drives in turn a small dynamo D, employed for exciting the ten field magnets. The commutator, shown at C, is provided for the purpose of automatically increasing the pressure at the brushes of the machine with the load, so as to compensate for drop of pressure in the line or armature. In other words, the machine is compound-wound. STRUCTURAL ELEMENTS. 19 As we have already observed, bipolar machines may be sub- divided into classes according to the number of magnetic circuits passing through their exciting coils. In general, multipolar machines may be similarly classified. But, as usually constructed, there are as many independent magnetic circuits as there are poles. Thus, a quadripolar generator has FIG. IO. CONTINUOUS-CURRENT SELF-EXCITED COMPOUND-WOUND QUADRIPOLAR GENERATOR. usually four magnetic circuits, a sextipolar six, and so on. In some cases, however, a double system of field magnets is pro- vided, one on each side of the armature; in this case, the number of magnetic circuits may be double the number of poles. Ip. In designing a continuous-current generator, the num- ber of poles in the field is, to a certain degree, a matter of 20 ELECTRO-DYNAMIC MACHINERY. choice. In almost all cases, directly-coupled, continuous-cur- rent dynamos are multipolar, while belt-driven dynamos are frequently bipolar. Directly-coupled, continuous-current dy- namos are usually multipolar machines, owing to the fact that, in order to conform with engine construction, they have to be made with a comparatively slow speed of rotation, and, since FIG. II. CONTINUOUS-CURRENT SELF-EXCITED GENERATOR. the E. M. F. generated depends upon the rate of cutting mag- netic flux, if the speed of the conductor is decreased, the total amount of flux must be correspondingly increased. This necessitates a greater cross-section of iron in the field magnets in order to carry the flux, and this large amount of iron is most conveniently and effectively disposed in multiple magnetic cir- cuits. To a certain extent the number of poles is arbitrary, but usually, in the United States, the greater the output of a direct-driven generator, the greater the number of poles. In alternators, however, the case is different. Here, in order to conform with a given system of distribution, the frequency of alternation in the current is fixed, and, since the speed of revolution of the armature is determined within certain limits, STRUCTURAL ELEMENTS. 21 by mechanical considerations, or by the speed of the driving" engine, the number of poles is not open to choice, but is fixed by the two preceding considerations. In any alternator, the number of alternations of E. M. F. induced per revolution in the coils of its revolving armature, is equal to the number of M FIG. 12. ALTERNATING-CURRENT SELF-EXCITED OCTOPOLAR GENERATOR. poles. Consequently, an alternator producing a frequency of X 33~ 5 tnat i s a frequency of 133 complete periods or cycles per second, delivers 266 alternations from each coil, and its arma- ture must, therefore, pass 266 poles per second. 20. Fig. 16 shows a i2-pole alternator. The wires a, a, are in circuit with the field magnets, and serve to carry the current which excites them, while the wires b, b, lead from the brushes. 21. Dynamo-electric machines may also be divided, accord- ing to their magnetic circuits, into the two following classes: 22 ELEC TRO-D YNA MIC MA CHINER Y. (a.) Those having simple magnetic circuits formed by a single core and winding. FIG. 13. ALTERNATING-CURRENT SEPARATELY-EXCITED DECIPOLAR COMPENSATING GENERATOR. FIG. 14. CONTINUOUS-CURRENT CONSEQUENT-POLE BIPOLAR SHUNT- WOUND GENERATOR. (b.) Those having consequent poles, or poles formed by a double winding; that is, by the juxtaposition of two poles of the same name. Dynamo-electric machines belonging to the Sl^RUCTURAL ELEMENTS. 23 first class are shown in Figs, i, 3 and 5. A type of machine belonging to the consequent-pole class is shown in Figs. 14 and 15. The poles are shown at^V, N, and S, S, in each case, the field coils being so wound and excited as to produce consequent poles. FIG. 15. CONTINUOUS-CURRENT CONSEQUENT-POLE BIPOLAR GENERATOR. 22. Dynamo machines may also be classified according to the shape of the armature, as follows; namely, (a.) Ring armatures. (b. ) Cylinder or drum armatures. (c. ) Disc armatures. (d. ) Radial or pole armatures. (e. ) Smooth-core armatures. (f. ) Toothed-core armatures. Figs. 2 and n represent examples of ring armatures. Since Gramme was the first to introduce the ring type of armature, this form is frequently called a Gramme-ring armature. Figs, i, 5 and 14, show examples of cylinder or drum arma- tures. Disc armatures are very seldom employed in the United States. An example of a disc armature is shown in Fig. 19. An example of a radial or pole armature is seen in Fig. 17. 24 ELECTRO-DYNAMIC MACHINERY. A smooth-core armature is one on which the wire is wound over the cylindrical iron core, so as to cover the armature sur- face completely; or, if the wire does not cover the surface com- pletely, the space between the wires may either be left vacant or filled with some non-magnetic metal. Such armatures are represented in Figs, i, 2, 5, 15. A toothed-core armature, on the other hand, is one on which FIG. 16. ALTERNATING-CURRENT SEPARATELY-EXCITED I2-POLE GENERATOR. the wire is so wound in grooves or depressions, on the surface of the laminated iron core, that the finished armature pre- sents an ironclad surface, but with slots containing insulated copper wire. Such an armature is shown in Fig. 18 and also in Figs. 7, 10 and n. It is frequently called an iron-clad armature. STRUCTURAL ELEMENTS. 2 5 23. Dynamos may also be divided, according to the actual or relative movement of armature or field, into the following classes; namely, (a.) Those in which the field is fixed and the armature ^. FIG. 17. DIAGRAM OF POLE ARMATURE. revolves. This class includes all the machines previously described, except that represented in Fig. 19. (b.) Those in which the armature is fixed and the field revolves. An example of this type of machine is shown in FIG. l8. A TOOTHED-CORE ARMATURE SHOWING THE STAGES OF WINDING. Fig. 19 A and B, where two sets of field magnets, mounted on a common shaft, revolve together around a fixed disc arma- ture, shown in Fig. 19 B, which is rigidly supported vertically in the space between them. (c.) Those in which the field and armature are both fixed, but the magnetic connection between the two is revolved. These dynamos are usually called inductor dynamos. 26 ELECTRO-D YNAMIC MACHINER Y. 24. Dynamo machines may also be divided, according to the character of the work they are intended to perform, into the following classes; namely, (a.) Arc-light generators. (b. ) Incandescent-light generators. (c. ) Plating generators. (d.) Generators for operating motors. FIG. ALTERNATING-CURRENT DOUBLE I2-POLE GENERATOR WITH FIXED ARMATURE AND REVOLVING FIELD FRAMES. (e. ) Telegraphic generators, (f. ) Therapeutic generators. (g.) Welding generators. 25. Alternating-current generators may be divided, accord- ing to the number of separate alternating currents furnished by the machine, into the following classes; namely, (a.) Uniphase alternators, or those that deliver a single alter- nating current. To this class of machines belong all the ordinary alternators employed for electric lighting purposes. (b.) Multiphase alternators, or those that deliver two or more alternating currents which are not in step. STRUCTURAL ELEMENTS. 27 Some multiphase alternators can supply both single-pHase and multiphase currents to different circuits. Multiphase machines may be further subdivided into the following classes; namely, (i.) Diphase machines, or those delivering two separate alter- nating currents. These two currents are, in almost all cases, FIG. IQB. DISC ARMATURE. quarter-phase currents, that is to say, they are separated by a quarter of a complete cycle. Although it is possible to employ any other difference of phase between two currents, yet the quarter-phase is in present practice nearly always employed. Fig. 9 represents a diphase generator, or diphaser. (2.) Triphase machines, or triphasers, are generators deliver- ing three separate alternating currents. These three currents are, in all cases, separated by one third of a complete cycle. Uniphase machines are sometimes called single-phase machines, and diphase machines are sometimes called two-phase machines or tivo-phasers, while triphase machines are sometimes called three-phase machines or three-phasers. The terminology above employed, however, is to be preferred. 26. In addition to the above classification there are the fol- lowing outstanding types : 28 ELECTRO-DYNAMIC MACHINERY. (a.) Single-field-coil multipolar machines, or machines in which multipolar magnets are operated by a single exciting field coil. (b.) Commutatorless continuous-current machines, or so-called unipolar machines, in which the E. M. Fs. generated in the arma- ture, being obtained by the continuous cutting of flux in a uniform field, have always the same direction in the circuit, and do not, therefore, need commutation. The term unipolar is both inaccurate and misleading, as a single magnetic pole does not exist. CHAPTER III. MAGNETIC FLUX. 27. A magnet is invariably accompanied by an activity in the space or region surrounding it. Every magnet produces a magnetic field or flux, which not only passes through the sub- stance of the magnet itself, but also pervades the space sur- rounding it. In other words, the property ordinarily called magnetism is in reality a peculiar activity in the surrounding ether, known technically 3&*mctgiutic flux. By a simple convention magnetic flux is regarded as passing out of the north-seeking pole of a magnet, traversing the space "surrounding the magnet, and finally re-entering the magnet at its south-seeking pole. Magnetic flux, or magnetism, is cir- cuital; that is, the flux is active along closed, re-entrant curves. 28. Although we are ignorant of the true nature of magnetic flux, yet, perhaps, the most satisfactory working conception we can form concerning it, is that of the ether in translatory motion ; in other words, in a magnet, the ether is actually streaming out from the north-seeking pole and re-entering at the south-seeking pole. Since the ether is assumed to possess the properties of a perfect fluid ; /. = 43,070 webers, with an intensity of 43 = 13,710 gausses. 65. In cases where the flux is confined to definite paths, as in a closed circular coil, or in a very long, straight, and uni- formly wrapped bar, the preceding calculations are strictly applicable*. When, however, an air-gap is introduced into the closed ring, that is, when its circuit becomes aero-ferric, the results begin to be vitiated, partly owing to the influence of diffusion, and partly to the results of the C. M. M. F. which is established at the air-gap. As the length of the air- gap increases, the degree of accuracy which can be attained by the application of the formula diminishes, but in dynamos, the aero-ferric circuits are in almost all cases of such a char- acter, that the degree of approximation, which can be reached by these computations, is sufficient for all practical purposes; for, while it is impossible strictly to compute the magnetic circuit of a dynamo by any means at present within our reach, yet the E. M. F. of dynamos, and the speed of motors, can be predicted by computation within the limits of commercial requirements. 66. If the ring of Fig. 45 be provided with a small air-gap of 0.5 cm. in width, the intensity in the circuit, before the intro- 64 ELECTRO-DYNAMIC MACHINERY. duction of the iron core, will be practically unchanged by the existence of the gap, that is to say, with the same 1,000 ampere- turns, or 1,257 gilberts of M. M. F., the prime intensity exist- ing in the ring will be practically 20.95 gausses. In Ihe air- gap itself, the intensity will be less than this, owing to lateral diffusion of the flux; but, neglecting these influences, we may consider the intensity to be uniform. Now, introducing a soft, Norway iron core into the ring, the iron is subjected to an intensity of approximately, 20.95 gausses throughout the cir- cuit. The reluctivity of the iron at this intensity, is, as we have seen, 0.001596. The length of the circuit in the iron will be 59.5 cms., and its cross section 10 sq. cms., making the ferric reluctance A?l_ x 0.001594 = 0.009484 oersted. The 10 reluctance of the air-gap, neglecting the influence of lateral diffusion, will be X i =0.05 oersted, and the total reluct- ance of the circuit therefore, will be 0.009484 + 0.05 = 0.059484 oersted. The flux in the circuit will be ' = 0.059484 21,130 webers, and the intensity in the iron, 2,113 gausses. The existence of the air-gap has, therefore, reduced the flux from 131 kilowebers to 21 kilowebers. 67. In practical cases, however, the problem which presents itself is not to determine the amount of flux produced in a magnetic circuit under a given magnetizing force, but rather to ascertain the M. M. F., which must be impressed on a cir- cuit in order to obtain a given magnetic flux. When the total required flux in a circuit is assigned, the mean intensity of flux in all portions of the circuit is approximately determinable, being simply the flux divided by the cross section of the circuit from point to point. What is required, is the reluctivity of iron at an assigned flux density and this we now proceed to determine. ftr> From the equations, v = a -\- b 3C, and (B = , correspond- ing in a magnetic circuit, to / = in the electric circuit, /, being the electric flux density or amperes-per-sq.-cm. and p f the resistivity, we obtain, v = FERRIC MAGNETIC CIRCUITS. 65 This equation gives the reluctivity of any magnetic metal for any value of the flux density & passing through it, when the value of the constants a and , have been experimentally determined. The values of v, so obtained are only true for reluctivities beyond the critical value, where the linear relation expressed in the equation v = a -f- b 5C commences. 68. The following table gives the values of the reluctivity constants a and <, for various samples of iron : Sample. a b Observer. Soft Iron, . . .. ., . 0.000,2 0.000,056 Stoletow. . O.OOO,! 0.000,059 Rowland. O OOO O^Q^ Fessenden. < < (i . O.OOO,2275 ^ *-**--* , \j 3 \j j 0.000,0654 " " . 0.000,3325 O.OOO,O64 11 . O.OOO,2I3 0.000,05605 " Cast Steel, . . 0.000,45 0.000,05125 " < . 0.000,314 0.000,0563 " Mitis Iron, . . 0.000,25 0.000,0575 it Cast Iron, . . . . 0.001,031 0.000,129 " Improved Cast Iron, . . 0.000,9025 O.OOO,IO6 it Wrought Iron, . 0.000,22 O.OOO,O58 Hopkinson. Dynamo Wrought Iron, . 0.000,4 0.000,057 Kennelly. " Cast Iron, . 0.002,6 O.OOO,O93 M Annealed Norway Iron, . 0.000,3 O.OOO,O57 U 69. Fig. 47 shows curves of reluctivity of various samples of iron and steel at different flux densities. The descending branches are of practically little importance in connection with dynamo-electric machinery. They are included in the curves, however, in order to bring these into coincidence with actual observations. It will be seen, that while the reluctivity of Norway iron is only 0.000,5 at 8 kilogausses, that of cast iron is commonly about o.oio, or twenty times as great. 70. In order to show the application of the above curves of reluctivity, we will take the simplest case of the ferric circuit; namely, that of a soft Norway iron anchor ring, shaped as shown in Fig. 44, of 10 square centimetres cross section and 60 cms. mean circumference, uniformly wrapped with insulated wire. If it be required to produce a total flux of 80 kilowebers in this circuit, the intensity in the iron will be 8 kilogausses, 66 ELECTRO-DYNAMIC MACHINERY. 0.012 7 8 Kilogausses Flux Density in Iron URVES OF RELUCTIVITY IN RELATION TO FLUX DENSITY. 17 J18 and, by following the curve for Norway iron, in Fig 47, it will be seen that its reluctivity at this density is 0.000,5. The re- luctance of the circuit, therefore, will be X 0.000,5 -3 FERRIC MAGNETIC CIRCUITS. 67 oersted, and the M. M. F. necessary to produce the requisite magnetic flux will be F = $ (R = 80,000 x 0.003 = 2 4 &l~ berts, or 240 x 0.7958 = 191 ampere-turns. 71. If, however, the ring be of cast iron, instead of soft Nor- way iron, its reluctivity at this density would be say o.oio, and its reluctance - x o.oio = 0.06 oersted, from which the 10 required M. M. F. will be 80,000 X 0.06 = 4,800 gilberts = 3,820 ampere-turns. The importance of employing soft iron for ferric magnetic circuits, in which a large total flux is re- quired, will, therefore, be evident. OF THE TJNIVERSITT CHAPTER VI. AERO-FERRIC MAGNETIC CIRCUITS. 72. We will now consider the case of the aero-ferric magnetic circuit. Fig. 48 is a representation of a simple ferric circuit consisting of two closely fitting iron cores, the upper of which is wrapped with a magnetizing coil M. The polar surfaces are made to correspond so closely, that when the coil M, has a magnetizing current sent through it, the magnetic attraction between the two cores will cause them to exclude all sensible air-gaps. The general direction of the flux-paths is shown by the dotted arrows, and a mechanical stress is exerted within the iron along the flux-paths. These stresses cannot be rendered manifest, so long as the iron is continuous. In other words, the continuous anchor ring, as shown in Fig. 44, would give no evidence of the existence of stress along its flux-paths. In the case shown in Fig. 48, the stress is rendered evident by the force which must be applied to the two magnetized cores in order to separate them. The amount of this force depends upon the magnetic intensity in the iron at the polar surfaces, and, if (B, represents this intensity in gausses, the attractive force exerted along the flux-paths at the /T>2 polar surfaces; /. e., perpendicularly across them, will be =r ^ dynes-per-square-centimetre of polar surface. The dyne is the fundamental unit of force employed in the system of C. G. S. units universally employed in the scientific world, and is equal to the weight of 1.0203 milligrammes at Washington; that is to say, the attractive force which the earth exerts upon one milligramme of matter, is approximately, equal to one dyne. 73. If the magnetic circuit shown in Fig. 48 has a uniform area of cross section of 12 square centimetres, and the mag- netic intensity in the circuit be everywhere 17 kilogausses, 68 AERO-FERRIC MAGNETIC CIRCUITS. 6 9 then the attractive force exerted across each square centi- metre of the polar surfaces at R lt and R^ will be 17,000 X 17,000 8 x 3-J4 16 = 11,500,000 dynes, or 11,500,000 X 1.0203 = 11,730,000 milligrammes weight = 11,730 grammes weight = 25.86 Ibs. weight. As there are twelve square centimetres in each polar surface,, 6,324 VOLTS 7-0.081 OHM 0.00029 OHM O.C0023 OHM 1 = 204,000 AMPERES FIGS. 48 AND 49. DIAGRAMS REPRESENTING A SIMPLE FERRIC, AND AN AERO-FERRIC, CIRCUIT, AND THEIR ELECTRIC ANALOGUES. the total pull across each gap will be 12 x 25.86 = 310.32 Ibs. weight; and since there are two gaps, the total pull between the iron cores will be 620.64 Ibs. weight, so that, if the whole magnet were suspended in the position shown in Fig. 48, this weight should be required to be suspended from the lower core (less, of course, the weight of the lower core) in order to effect a separation; or, in other words, this should be the maximum weight which the magnet could support. 74. In order to ascertain the M. M. F. needed to produce the required intensity of 17 kilogausses through the circuit in order to cause this attraction, we find, by reference to Fig. 47, that the reluctivity of Norway iron at this intensity is 0.0073; 73 10,000 that of air. The reluctance of the magnetic cir- 70 ELECTRO-DYNAMIC MACHINERY. CQ cuit will, therefore, be -- X 0.0073 = 0.03042 oersted. The total flux through the circuit will be 17,000 x 12 = 204,000 webers, and the M. M. F. required to produce the flux, there- fore, will be 204,000 x 0.03042 = 6,206 gilberts, or 6,206 x 0.7958 = 4,937 ampere-turns. If, then, the coil J/, has 2,000 turns, it will be necessary to send through it a current of 2.469 amperes, in order to produce the flux required. The electric circuit analogue of this case is represented in the same figure, where E, represents the E. M. F. in the electric circuit as a voltaic battery, and the amount of this E. M. F. necessary to produce a current of strength /, amperes, when the total resistance of the circuit is r, ohms, will be E = i r volts. 75. So far we have considered that no sensible reluctance existed at the polar surfaces R l9 and R^. Practically, how- ever, it is found, that, no matter how smooth the surfaces may be, and, therefore, how closely they may be brought into con- tact, a small reluctance does exist, owing, apparently, to the absence of molecular continuity. This reluctance has been found experimentally, in case of very smooth joints, to be equivalent to the reluctance of an air-gap, from 0.003 to 0.004 cm. wide (0.0012" to 0.0016"). Taking this reluctance into account we have at R^ and at R^ an equivalent reluctance of air path, say 0.0035 cm - l n g an d 12 cms. in cross-sectional area. Since the reluctivity of air is unity, the reluctance at each gap becomes 0.000,29 oersted, and the reluctance of the circuit has, there- fore, to be increased by 0.000,58 oersted, making a total of 0.03042 -f- 0.000,58 = 0.031 oersted, and requiring the M. M. F. of 204,000 x 0.031 or 6,324 gilberts = 5,032 ampere-turns, or an increase of current strength to 2.516 amperes. ,76. It is evident, since the attractive force exerted across a /02 square centimetre of polar ^surface is equal to dynes, that STT doubling the intensity at the polar surface will quadruple the attraction per square centimetre. Therefore, all electro- magnets, which are intended to attract or support heavy weights, are designed to have as great a cross-sectional area AERO-FERRIC MAGNETIC CIRCUITS. 71 of polar surface as possible, combined with a high magnetic in- tensity across these surfaces. If, however, *the increase of the area of polar surface is attended by a corresponding diminu- tion of flux density, the total attractive force across the surface will be diminished, because the intensity, per-unit-area, will be reduced in the ratio of the square of the intensity, while the pull will only increase directly with the surface. It is evident, therefore, that soft iron of low reluctivity is especially desira- ble in powerful electro-magnets. If, for example, cast iron was employed in the construction of the magnet of Fig. 48, instead of soft Norway iron, and the same M. M. F., namely, 6,324 gilberts were applied, the mean magnetizing force would be this M. M. F. , divided by the mean length of the circuit in cms., or X >3 = 126.48 gilberts- per-centimetre. At this magnetizing force, a sample of cast iron would have a reluctivity represented by the formula v = (a -j- ^5C), where a, may be 0.0027, and , 0.000,09, so tnat i ts reluctivity at 133.92 gilberts per centimetre of magnetizing force would be (0.0027 -f- 0.000,09 X 126.48) = 0.01407. The reluctance of the cast iron circuit, including the small reluctance in the air-gaps, would be 5 - X 0.01407 =0.05863 oersted, and the flux in the circuit would be ' -= 108,700 webers, or an intensity of 9,058 gausses. The magnetic attraction between the surfaces per-square- centimetre, would, therefore, be ^ ^ = 3,264,000 dynes, or 3, 331 grammes weight, or 7.342 Ibs. weight; and, since the total polar surface amounts to 24 square centimetres, the total attractive force exerted between and across them is 176.2 Ibs. weight. The effect of introducing cast iron instead of wrought iron into the magnetic circuit, keeping the dimen- sions and M. M. F. the same, has, then, been to reduce the total pull from 620.64 Ibs. to 176.2 Ibs., or 71.6 per cent. 77. If now an air-gap be placed in the circuit at JR l9 and JR^ of half an inch (1.27 cm.) in width, as in Fig 49, two results will follow; viz., 72 ELECTRO-DYNAMIC MACHINERY. (i.) A greater reluctance will be produced in the circuit. (2.) A leakage or shunt path will now be formed through the air between the poles TV^and S. Strictly speaking, there will be some leakage in the preceding case of Fig. 48, but with a ferric circuit of comparatively short length, it will have been so small as to be practically negligible. In Fig. 49, however, the reluc- tance of the main circuit between the poles including the air- gaps will be so great as to give rise to a considerable difference of magnetic potential between the poles N and S, so that appre- ciable leakage will occur between these points. The reluctance of the leakage-paths through the air will usually be very com- plex, and difficult to compute, but, in simple geometrical cases, it may be approximately obtained without great difficulty. In this case we may proceed to determine the magnetic circuit first on the assumption that no leakage exists, and second on the assumption of the existence of a known amount of leakage. Assuming that the cores are of soft Norway iron, and that it is required to establish a total flux of 204,000 webers through the circuit, then the flux density in the iron will be 17 kilogausses and its reluctivity 0.0073. The reluctance of the circuit, so far as it is composed of iron, will be 0.03042 oersted, I 27 while the reluctance of each air-gap will be - - X i = 0.1058; or, in all, 0.2016 oersted. The total reluctance of the circuit will, therefore, be 0.23202 oersted, and the M. M. F. required will be 204,000 x 0.23202 = 47,330 gilberts = 37,660 ampere- turns; or, with 2,000 turns, 18.83 amperes. The attractive force on the armature will be 620 Ibs. as in the previous case. 78. Considering now the effect of leakage, we may assume that the reluctance of the leakage path through the air Jt 3 , is o. 5 oersted, and that a flux of 108 kilowebers has to be produced through the lower core; the length of mean path in the lower core being 20 cms., and in the upper core 30 cms., it is required to find the M. M. F., which will produce this flux through the lower core. The intensity in the lower core will be - * c - = 9,000 gausses, at which intensity the reluctivity of Norway iron will AERO-FERRIC MAGNETIC CIRCUITS. 73 be, by Fig. 47, 0.000,6, so that the reluctance of the lower core will be X 0.000,6 = o.ooi oersted, and this added to the re- 12 luctance of the two air-gaps, 1.27 cms. in width, = 0.2016 -f-o.ooi = o. 2026 oersted. The magnetic difference of potential in this branch of the double circuit will, therefore, be 108,000 x 0.2026 = 21,880 gilberts. This will also be the difference of magnetic potential between the terminals of the leakage path R^ and the leakage flux will, therefore, be 43,760 webers. The total flux in the main circuit through the upper core will be the sum of the flux in the two branches, or 108,000 -}- 43,760 = 151,760 webers, making the intensity in the upper core * = 12,647 gausses, at which intensity the reluctivity is 0.00121, so that the reluctance of the upper core is X 0.0012 = 12 0.003 oersted. The drop of potential in the upper core will, therefore, be 151,760 x 0.003 = 455 gilberts, and the total difference of potential in the circuit, or the M. M. F., will be 21,880 -|- 455 = 22,335 gilberts = 17,775 ampere-turns, or 8.89 amperes at 2,000 turns. 79. It is obvious that the results obtained by the preceding method of calculation cannot be strictly accurate, since no account has been taken of any magnetic leakage except that whicH occurs directly between the poles N and S. Also we have assumed that the flux density remains uniform through- out the lengths of the two cores. When a greater degree of accuracy is desired, corrections may be introduced for the effects of these erroneous assumptions, but the examples illus- trate the general methods by which the magnetic circuits of practical dynamo-electric machines may be computed with fair limits of accuracy. CHAPTER VII. LAWS OF ELECTRO-DYNAMIC INDUCTION. 80. When a conducting wire is moved through a magnetic flux, there will always be an E. M. F. induced in the wire, unless the motion of the wire coincides with the direction of the flux; or, in other words, unless the wire in its motion does FIG. 50. CONDUCTOR PERPENDICULAR TO UNIFORM MAGNETIC FLUX, AND MOVING AT RIGHT ANGLES TO SAME. not pass through or cut the flux. Thus, if, as in Fig. 50, a straight wire A B, of / cms. length, extending across a uniform flux, be moved at right angles to the flux, either upwards or downwards, to the position, for example, a b, or a' b\ it will have an E. M. F. induced in it, the direction of which will change with the direction of the motion. 8l. A convenient rule for memorizing the direction of the E. M. F. induced in a wire cutting, or moving across, magnetic flux, is known as Fleming's hand rule. Here, as in Fig. 51, the right hand being held, with the thumb, the forefinger and the middle finger extended as shown, the thumb being so pointed as to indicate the direction of wotion, and the /brefinger the direction of the magnetic /lux, then the middle finger will indi- cate the direction of induced E. M. F. For example, if, as in 74 LAWS OF ELECTRO-DYNAMIC INDUCTION. 75 Fig. 50, a wire be moved vertically downwards from A B, to a b ', and the thumb be held in that direction, the forefinger pointing in the direction of the flux, the E. M. F. induced in the wire will take the direction a' ', during the motion, follow- ing the direction of the middle finger. If, however, the wire be moved upwards through the flux, an application of the same FIG. 51. FLEMING S HAND RULE. rule will show that the direction of the induced E. M. F., as indicated by the middle finger, is now changed. 82. The induction of electromotive force in a conductor, moving so as to pass through or cut magnetic flux, is called electro-dynamic induction. The value of the E. M. F. induced in a wire by electro-dynamic induction depends, (i.) Onthe density of the magnetic flux. (2.) On the velocity of the motion, and (3.) On the length of the wire. This is equivalent to the statement that the E. M. F., in- duced in a given length of wire, depends upon the total amount 76 ELECTRO-DYNAMIC MACHINERY. of flux cut by the wire per second in the same direction; or, e = ($>lv C. G. S. units of E. M. F. Where (B, is the intensity of the flux in gausses, /, the length of the conductor in cms., v, the velocity of motion in cms.-per- second, and ^, the induced electromotive force as measured in C. G. S. units. Since one international volt is equal to FIG. 52. CONDUCTOR OBLIQUE TO UNIFORM MAGNETIC FLUX, AND MOVING AT RIGHT ANGLES TO SAME. 100,000,000 C. G. S. units of E. M. F., the E. M. F. induced in the wire will be e = volts. 100,000,000 83. The preceding equation assumes that the wire is not only lying at right angles to the flux, but also that it is moved in a direction at right angles to the direction of the flux. If instead of being at right angles to the flux, the wire makes an angle /?, with the perpendicular to the same, as shown in Fig. 52, then the length of the wire has to be considered as the virtual length across the flux, or as its projection on the normal plane, so that the formula becomes, (B / v cos fi e = volts. 100,000,000 If the motion of the wire, instead of being directed perpendic- ularly to the flux, is such as to make an angle a, with the per- pendicular plane, the effective velocity is that virtually taking LAWS OF ELECTRO-DYNAMIC INDUCTION. ^^ place perpendicular to the flux, or v cos a, as shown in Fig. 53, so that the formula becomes in the most general case, e = & l cos f '" cos a volts 100,000,000 84. It will be seen that in all cases the amount of flux cut through uniformly in one second, gives the value of the E. M. F: FIG. 53. CONDUCTOR OBLIQUE TO UNIFORM MAGNETIC FLUX, AND MOVING OBLIQUELY TO SAME. induced in the wire, and that the value of the E. M. F. does not depend upon the amount of flux that has been cut through, or that has to be cut through, but upon the instantaneous rate of cutting. The E. M. F. ceases the moment the cutting ceases. 85. If the loop A B C >, Fig. 54, be rotated about its axis O O', in the direction of the curved arrows, then, while the side C D, is ascending, the side A B, is descending; con- sequently, the E. M. F. in the side C D, will be oppositely directed to the E. M. F. in the side A B. Applying Fleming's hand rule to this case, we observe that the directions of these E. M. Fs. are as indicated by the double-headed arrows, and, regarding the conductors CD and A B, as forming parts of the complete circuit C D A B, it is evident that the E. M. Fs. induced in A B and C D, will aid each other, while, if they are permitted to produce a current, the current will flow through the circuit in the same direction. 86. We have seen that no E. M. F. is induced in a wire unless it cuts flux. Consequently, the portions B C and A D, of the circuit which move in the plane of the flux, will con- tribute nothing to the E. M. F. of the circuit. 78 ELECTRO-DYNAMIC MACHINERY. If the dimensions of the wires forming this loop shown in the figure, are such that C D and A B, having each a length of 12 cms., while A B and B C, are 4 cms. each., the circumfer- ence traced by the wires A B and C D, in their revolution about the axis, will be 3.1416 x 4 = 12.567 cms. ; and, if the rate of rotation be 50 revolutions per second, the speed with which the wires A B and C Z>, revolve will be 628.3 cms. per second. If the intensity of the magnetic flux B, is uniformly 5 kilogausses, the E. M. F. induced in each of the wires A B FIG. 54. RECTANGULAR CONDUCTING LOOP ROTATING IN UNIFORM MAGNETIC FLUX. and C D, will be, 5,000 x 12 x 628.32=37,699,200 C. G. S, units of E. M. F., or 0.377 volt. This value of the E. M. F. only exists at the instant when the loop has its plane coincident with the plane of the flux, and the sides cut the flux at right angles. In any other position, the motion of these sides is not at right angles to the flux, so that the E. M. F. is reduced. 87. In order that the E. M. F. induced in a wire may estab- lish a current in it, it is necessary that such wire should form a complete curcuit or loop, as indicated in Fig. 55. When such a conducting loop is moved in a magnetic field, some or all portions of the loop will cut flux, and will thereby contribute a certain E. M. F. around the loop. If the loop moves in its. own plane, in a uniform magnetic flux, there will be no resultant E. M. F. generated in it. For example, considering a circular loop, we may compare any two diametrically opposite segments, when it is evident that each member of such a pair cuts through the same amount of flux per second, and will, therefore, gener- ate the same amount of E. M. F., but in directions opposite to each other in the loop. At the same time, it is clear that LAWS OF ELECTRO-DYNAMIC INDUCTION. 79 the total amount of flux in the loop does not change; for, while the flux is being left by the loop at its receding edge, it is entering the loop at the same rate at its advancing edge, and, since these two quantities of flux are equal, the total amount of flux enclosed by the loop remains constant. 88. The cutting of flux by the edges of a moving loop, there- fore, resolves itself into the more general condition of enclos- ing flux in a loop. The value of the E. M. F. induced around FIG. 55. CIRCULAR CONDUCTING LOOP PERPENDICULAR TO UNIFORM MAGNETIC FLUX. the loop does not depend upon the actual quantity of flux enclosed, but on the rate at which the enclosure is being made. If, as we have already seen, the loop is so moved that the total flux it encloses undergoes no variation, the amount entering the loop being balanced by the amount leav- ing it, although E. M. Fs. will be induced in those parts of the loop where the flux is entering and where it is leaving, yet these E. M. Fs. being opposite, exactly neutralize each other, and leave no resultant E. M. F. Consequently, the value or" the E. M. F. induced at any moment in the loop by any motion, does not depend upon the flux density within the loop, but on the rate of change of flux enclosed. 89. If $, be the total flux in webers contained within a single loop, such as shown at A B C, in Fig. 55, the mean rate at which this flux is changing during any given period of time, will be the quotient of the change in the enclosure, divided by So ELECTRO-DYNAMIC MACHINERY. that amount of time, so that if $, changes by 20,000 webers in two seconds, the mean rate of change during that time will be 10,000 webers per second, and this will be the E. M. F. in the loop expressed in C. G. S. units. But, during these two seconds of time, the change may not have been progressing uniformly, in which case only the average E. M. F. can be stated as being equal to the 10,000 C. G. S. units. Where the change is not uniform, the rate at any moment has to be determined by taking an extremely short interval, so that if dt, represents $2s> &.>- x^ tiiiti FIG. 55A. RECTANGULAR CONDUCTING LOOP IN NON-UNIFORM MAGNETIC FLUX. this indefinitely small interval of time, and d$, the correspond- ing change in the flux enclosed during that interval in webers, d the rate of change will be webers-per-second, and this will be the value of the induced E. M. F. at each instant. 90. If a small square loop of wire A B C Z>, one cm. in length of edge, placed at right angles to the flux as shown in Fig. 55 A, contains a total quantity of flux amounting to 10,000 webers, the mean flux density at the position occupied by the square, will be 10,000 gausses. If now, the loop be moved uniformly upward in its own plane to the position a bed, so as to accomplish the journey in the th part of a second, and if the flux enclosed by the loop at the position a bed, be 1,000 webers, then 9,000 webers will have escaped from the loop during the motion. Assuming that the distribution of flux density in the field was such that the emission took LAWS OF ELECTRO-DYNAMIC INDUCTION. 81 place uniformly, the E. M. F. in the loop, during the passage, will have been, j = - 900,000 C. G. S. units 0.009 volt. A* rro 91. If, however, the rate of emptying, during the motion, were not uniform, 0.009 vo ^ would be the average E. M. F., and not the E. M. F. sustained during the interval; or, in other words, the instantaneous value of the E. M. F. in the loop would vary at different portions of this short interval of time, or at corresponding different positions during the jour- ney ; but, in all cases, the time integral of the E. M. F. will be equal to the change in > ; thus, the change in <&, is, in this case, 9,000 webers. If the motion is made in th of a 100 second, the E. M. F., will be 900,000 C. G. S. units of E. M. F., which, multiplied by the time (o.oi second), gives 9,000 webers. If, however, the motion were uniformly made in half a second, the E. M. F. would have been 18,000 C. G. S. units, which, multiplied by the time, would give as before 9,000 webers; and under whatever circumstances of velocity the change were made, the sum of the products of the instantaneous values of E. M. F. multiplied into the intervals of time during which they existed, would give the total change in flux of 9,000 webers. Or in symbols, c . d Since e --=-- at fe dt = A $> The first equation simply expresses that the E. M. F., ^, is the instantaneous rate of change in the flux enclosed, and the second equation shows that the difference in the enclosure between any two conditions of the loop is the time integral of the E. M. F., which has been induced in the loop during the change, assuming of course, that the change continues in the same direction ; i. e. , that the flux through the loop has con- tinually increased or decreased. 92. If a circuit contains more than one loop, as, for example, when composed in whole, or in part, of a coil, the turns of which are all in series, the E. M. F. induced in any one turn 82 ELECTRO-DYNAMIC MACHINERY. or loop of the coil, may be regarded as being established inde- pendently of all the other loops, so that the total E. M. F. in the circuit will be the sum of all the separate E. M. Fs. exist- ing at any instant in the loops, and may, therefore, be regarded as the instantaneous rate of change in the flux linked with the entire circuit. A coil, therefore, may be regarded as a device for increasing the amount of flux magnetically linked with an electric circuit, so that by increasing the number of loops of conductor in the circuit, the value of the induced E. M. F. corresponding to any change in the flux, is proportionally increased, and if the coil or system of loops forming the. cir- c FIG. 56. CLOSED CIRCULAR HELIX LINKED WITH A LOOP OF WIRE. cuit, contains in the aggregate $ webers of flux linked with it, taking each turn separately and summing the enclosures, then the time integral of E. M. F. in the circuit will be the total change in $>, and this will be true, whether the loop is chang- ing its position, or whether the flux is changing in intensity or in direction. 93. It is evident from the preceding, that there are two different standpoints from which we may regard the produc- tion of electromotive force in a conducting circuit by electro- dynamic induction ; namely, that of cutting magnetic flux, and that of enclosing magnetic flux. These two conceptions are equivalent, being but different ways of regarding the same phenomenon. The amount of flux enclosed by a loop can only vary by the flux being cut at the entering edge or edges at a different rate to that at the receding edge; or, in mathe- matical language, the surface integral of enclosing is equal to LAWS OF ELECTRO-DYNAMIC INDUCTION. 83 the line integral of cutting, taken once round the loop. This statement is equally true whether the flux is at rest and the conductor moving, or the conductor at rest and the flux mov- ing, or whether both conductor and flux are in relative motion. 94. Cases of electro-dynamic induction may occur where the equivalence of cutting and enclosing magnetic flux apparently fails. On closer examination, however, the equivalence will be manifest. For example, in Fig. 56, let A B C D be a wooden anchor ring uniformly wound with wire, as shown in Fig. 44, and a b c d, a circular loop of conductor linked with the ring. FIG. 57. SQUARE CONDUCTING LOOP ROTATED IN UNIFORM FLUX. FIRST POSITION. It has been experimentally observed that when a powerful cur- rent is sent through the winding of the anchor ring, no appreci- able magnetic flux is to be found at any point outside the ring, although within the core of the ring a powerful magnetic flux is developed. Nevertheless, both at the moment of applying and at the moment of removing the exciting current through the winding of the ring, an E. M. F. is induced in the loop a b c d, whose time integral in C. G. S. units, is the total number of webers of change of flux in the ring core. It might appear at first sight that this E. M. F. so induced in the loop cannot be due to the cutting of flux by the loop, but must be due to simple threading or enclosing of flux. It is clear, how- ever, that the mere act of enclosure will not account for the induction of the E. M. -F., since the passage of flux through the centre of the loop cannot produce E. M. F. in the loop itself, unless activity is transmitted from the centre of the loop 84 ELECTRO-DYNAMIC MACHINERY. to its periphery. In other words, action at a distance, with- out intervening mechanism of propagation, is believed to be impossible. Could we see the action which occurs when the current first passes through the ring-winding, we should observe flux apparently issuing from all parts of the ring and passing into surrounding space, at a definite speed. The loop a b c d, would receive the impact of flux from the adjacent portions of the ring before receiving that from the more distant parts of the ring, and, in this sense, would actually be cut by the flux. As soon as the flux has become established, and the current in x ^ S* ivr *-- +* _* >> FIG. 58. SQUARE CONDUCTING LOOP ROTATED IN UNIFORM FLUX. SECOND POSITION. the winding steady, it is found that the flux from any particu- lar portion of the ring is equal and opposite to that from the remainder of the ring, and is, therefore, cancelled or annulled at all points except within the ring core. It is evident, there- fore, that we may regard the E. M. F induced in the loop a b c d as due either to the cutting of the boundary by flux, or to the enclosure of flux. 95. Let us consider the case of a square conducting loop A B C D, Fig. 57, having its plane parallel with the uniform magnetic flux shown by the dotted arrows. If this loop be rotated about the axis O O', which is at right angles to the magnetic flux, and symmetrically placed with regard to the loop, so that A D, descends, and B C, ascends, these sides, which cut flux during the rotation, will have E. M. Fs. gene- rated in them, in accordance with Fleming's hand rule already LAWS OF ELECTRO-DYNAMIC INDUCTION. 85 described in Par. 81, and in the direction shown by the double arrows. The sides A B and D C, which do not cut ftux during the motion, will add nothing to the E. M. F. generated. The figure shows that while the sides AD and C B, have oppo- sitely directed E. M. Fs., yet regarding the entire loop as a conducting circuit, these E. M. Fs. tend to produce a current which circulates in the same direction. 96. As already pointed out, the value of the E. M. F. gene- rated in the sides A D and C B, of the loop, by the cutting of the ftux, will depend upon the rate of filling and emptying the FIG. 59. SQUARE CONDUCTING LOOP ROTATED IN UNIFORM FLUX. THIRD POSITION. loop with flux, and it is evident that this rate is at a maximum when the loop is empty; /. , instead of from D to A, in the conducting branch A Dj and from C to B, instead of from B to C, in the conducting branch B C. The direction of E. M. F.. around the loop, will, therefore, be FIG. 60. SQUARE CONDUCTING LOOP ROTATED IN UNIFORM FLUX. FOURTH POSITION. reversed. Consequently, the loop A B C D, during its first half revolution as shown in Figs. 57 to 59, has an E. M. F. in it in the same direction; and, during the remaining half-revolu- tion, has its E. M. F. in the reverse direction, as shown. S?CL JK -*.->.-. -..- .+ *^ A*-.*. >. - *-!*-. FIG. 6l. FLUX OBLIQUE TO PLANE OF ROTATING LOOP. 98. The value of the E. M. F. generated in a loop, during its rotation, depends upon the flux density, on the area of the loop, and on the rate of rotation. Assuming the side of the loop C Z>, to occupy the position shown in Fig. 61, making an angle a, with the direction H K, of the flux, then the E. M. F. generated in the loop at this instant is the rate at which flux is being admitted into the loop. If /cms., be the length of the side of the loop or the length of A Z>, in Fig. 57, the amount of flux embraced at this instant will be / ($> X 2 D K. During the next succeeding small interval LAWS OF ELECTRO-DYNAMIC INDUCTION. 87 of time dt, if the angular velocity of the loop, GO radians per second, carries it to the position C ' D ', the amount of flux admitted during that time will be / (B X 2 D L. But D L = D D' X cosine of angle D' D L, and this angle is equal to the FIG. 62. FLUX COINCIDENT WITH PLANE OF ROTATING LOOP. angle <*, so that D L D D' xcos a, and D D', will be oodt cms. in length, since the radius O D = ; consequently, the flux admitted into the loop during this brief interval of time dt, will be GO cos a dt, or / 2 (& GO cos a dt = <& GO cos a dt d <& so that 7- = $ GO cos a. at Thus, at the instant of time in which the loop has reached the D D H *** --- c u c/ FIG. 63. FLUX PERPENDICULAR TO PLANE OF ROTATING LOOP. position O D, if , be the angle which the loop makes at any time with the direction of the flux, the E. M. F. , while when the loop is at right angles to the flux, or as shown in Figure 63, D D', the succeeding small FIG. 65. CURVE OF E. M. F. INDUCED IN LOOP ROTATING AT DOUBLED SPEED. excursion of the loop, is at right angles to D Z, or cosine a = o, so that e o. 99. If (B, as in the case represented by Figs. 57 to 60, be twa kilogausses, and / = 100 cms., then $ = 100 x 100 X 2,000 = 20- LAWS OF ELECTRO-DYNAMIC INDUCTION. 89 megawebers. If the loop be rotated in the direction shown at an angular velocity of 50 radians per second ( -- revolutions per second), the E. M. F. ^., will be e = 20,000,000 X 50 X cos a, or 100,000,000 cos a = i cos a volt. The E. M. F. generated by the loop, therefore, varies periodically between i, o, i, o, and i. If these values be 0.5- g I 1! FIG. 66. CURVE OF E. M. F. COMMUTED IN EXTERNAL CIRCUIT. plotted graphically as ordinates, to a scale of time as abscissas, the curve shown in Fig. 64 will be obtained, where the distance A O, represents the time occupied by one half revolution of the loop, the E. M. F. being positive from O to A, and negative from A to B. If now, the speed of revolution be doubled; i. e., increased to TOO radians per second, the time occupied in each revolution will be halved, and O'A', Fig. 65, will be half the length of O A, but e, will be doubled as shown. The shaded area O' C' A', in Fig. 65, is equal to the area O C A, of of Fig. 64. The E. M. F. generated by the loop is alternating, being positive and negative during successive half revolutions, but, by the aid of a suitable commutator, the E. M. F. can be made unidirectional in the external circuit, as represented in Fig. 66, where the curve P S Q, corresponds to OCA, in Fig. 64 and Q T R, to A D B. CHAPTER VIII. ELECTRO-DYNAMIC INDUCTION IN DYNAMO ARMATURES. 100. The type of curve represented in Figs. 64, 65, and 66, showing the E. M. F. generated by the rotation of a conduct- ing loop in a uniform magnetic flux, may be produced by the rotation of the coil represented in Fig. 67. Here a number of circular loops, formed by winding a long insulated wire upon FIG . 67. COIL FOR INDUCING FEEBLE E. M. FS. BY REVOLUTION IN EARTH'S MAGNETIC FLUX. a circular wooden frame, are capable of being rotated by the handle, in the uniform magnetic flux of the earth. If the mean area of the loops be 1,000 sq. cms., the number of loops 500, and the intensity of the earth's magnetic flux threading the loop 0.6 gauss, then the E. M. F. generated by rotating the loop will depend only on the speed of rotation. Assuming this to be 5 revolutions-per-second, or an angular velocity of 5 x 2 n 15.708 radians-per-second, the E. M. F. will vary between -\- 3> GO and > &?, in each half revolution. Here $, the total flux linked with the coil is 500 X 1,000 X 0.6 300,000 INDUCTION IN DYNAMO ARMATURES. 91 webers, and GO 15.708, so that the maximum value of the E. M. F. generated in the coil will be 4,712,400 C. G. S units 0.047 volt, or roughly th volt. This corresponds to the peaks C and >, of the waves of induced E. M. F. shown in Fig. 64. 101. In practice, however, continuous-current generators do not produce this type of E. M. F. Fig. 68 represents, in cross-section, a common type of generator armature, situated between two field poles JV, and S. A type of generator, armature and field poles, similar to this, is seen in Fig. i. The flux from these poles passes readily into and out of the armature surface as indicated by the arrows. In other words, FIG. 68. CROSS-SECTION OF BIPOLAR DRUM ARMATURE. the flux cuts the surface of the armature at right angles, while, in the cases shown in Figs. 57 to 60, the conducting loop is only cut by the flux at right angles in two positions 180 apart, so that the curve of E. M. F. is peaked at these points, and descends rapidly from them on each side. 102. Suppose in Fig. 68 that the difference of magnetic potential, maintained between .Wand S, is 2,000 gilberts, that the diameter of the armature core g o h, is 40 cms., that its length is 100 cms., and that the air-gap or entrefer is i cm.; then, if the reluctance of the iron armature core be regarded as negligibly small, the magnetic potential between the polar surfaces and the armature surface on each side, that is between c N e and A g B, also between d S f and A h B, will be 1,000 gilberts. The magnetic intensity in the air may be obtained in two ways. (i.) By considering the total reluctance of the air-gap and obtaining, by this means, the total flux. Thus the polar surface represented is 55 cms. in arc x 100 cms. in breadth = 5,500 92 ELECTRO-DYNAMIC MACHINERY. sq. cms. The reluctance of the air-gap on either side of the armature is, therefore, oersted, and the total flux passing 5>5 F 1,000 through the air will, therefore, be $ = = -y- = 5,500,000 webers. This flux, divided by the area through which it passes, gives the intensity, or 5o 00 > 000 __ Ij000 gausses. 5>5 (2.) The magnetic intensity is, as we have seen (Par. 53), numerically equal to the drop of magnetic potential in air, or other non-magnetic material, per centimetre, so that the drop 1000- -flwo- t 1 DEGREES OF ANGULAR DEVIATION FROM VERTICALRAPI'JSOA. FIG. 69. DIAGRAM OF MAGNETIC INTENSITY IN AIR-GAP. of potential being here 1,000 gilberts in i cm. of distance in air, the intensity must be 1,000 gausses. Representing the in- tensity graphically, as shown in Fig. 69, it will be seen that the intensity is uniform from c to 40 : 60 30 60 90 120 150 DEGREES ANGULAR DISPLACEMENT OF ARMATURE 100- FIG. 89. DIAGRAM OF FLUX PASSING THROUGH ARMATURE IN DIFFERENT ANGULAR POSITIONS. the armature core at different positions of angular displacement from the initial position shown in Fig. 85, from actual measure- ments 6f a particular shuttle-wound machine of this type. An inspection of this figure will show that at 30 displacement the flux through the armature will amount to above 40 kilowebers, while at 90 displacement, the position of maximum flux, it will reach about 93 kilowebers. From this position the flux decreases until its value is zero at 180, the position assumed by the armature when it has completed one half of a rotation and is again in the position represented in Fig. 85, but in the reverse direction. From this position onward, the direction of flux is reversed, the maximum flux being reached at an angular displacement of 270, or ^ of an entire rotation, completing a cycle at 360. Il8. Having thus obtained the value of the flux passing through the armature, it is a simple matter to determine the MAGNETO GENERATORS. 107 E. M. F. at any speed of rotation; for, we have only to recon- struct the flux diagram of Fig. 89, to a horizontal scale of time in seconds, instead of angular displacement. This is shown in Fig. 90, for an assumed rate of rotation of 1.5 revolutions per second, or 90 revolutions per minute, the horizontal distance of o m, being taken as one second, and the vertical scale being taken for convenience smaller than in Fig. 89. FIG. QO. DIAGRAM OF FLUX PASSING THROUGH ARMATURE AT DIFFERENT PERIODS OF TIME. The E. M. F. produced in any single loop or turn around the armature will be the rate of increase in the flux passing through the armature. If at the position <9, commencing the curve, we continue the curve along the dotted tangent of O O\ for one second of time, we reach the ordinate m O f , of 770 kilowebers, and this is the rate at which flux is entering the loop at that moment; for, if the rate at O, were continued uniformly for an entire second, we should evidently reach the point O'. The E. M. F. existing at the moment of starting is, io8 ELECTRO-DYNAMIC MACHINERY. therefore, 770,000 C. G. S. units (of which 100,000,000 make one volt) or 0.0077 volt, and, if the number of turns around the armature core be 1,000, the total E. M. F. in the armature winding will be 7.7 volts. Again, if after a lapse of %th of a second, the flux curve o a b c d efg hi k I m n, be examined, it will be found that the curve has reached the point b, or its maximum positive value when it commences to descend toward g, so that the tangent is horizontal, representing that the rate of change of flux is zero, or similar to the condition of slack water in a tide-way. At this point, therefore, the E. M. F. in each turn on the armature is zero, and the curve of E. M. F. O A BCD, etc., touches the zero line at this point B. Again at the point ^, on the flux curve, if the change of flux were to continue for one second uniformly at this rate, we should follow the dotted line or tangent q q', which reaches the ordinate 400, or 500 below q ', so that the rate of change at the point q, on the curve is 500 kilowebers, represented by the point Q, on the E. M. F. curve at that ordinate. Con- tinuing in this way we trace the E. M. F. curve O A B C D, etc., showing that an alternating E. M. F. is produced in the armature, varying between +7.7 and 7.7 volts. At the rate of rotation assumed; namely, i^ revolutions per second, there will be three alternations of E. M. F. per second, or twice the number of revolutions in that time. 119. Having now examined the means for determining the value of the E. M. F. developed in the armature, we will con- sider the effect of the commutator. It will be seen by refer- ence to Figs. 85 to 88, the brushes B, B ', resting on the segments of the two-part commutator, that the direction of E. M. F. from the armature toward the external circuit is reversed at the moment when the core passes the position of maximum contained flux, as indicated by the change in the direction of the dotted loops C .D' E' and L' M' N', relatively to the horizontal line. The E. M. F. generated by the armature as produced at the brushes B, B', will be represented by the pulsating E. M. F., O A B C D' E F G H I K L' M' N'. It is evident that had we selected a higher rate of rotation, the E. M. F. of the machine would have been correspondingly increased. MAGNETO GENERATORS. 109 120. The preceding considerations can only determine the value of the E. M. F. at the brushes, while the external circuit is open. As soon as the circuit of the armature is closed, the E. M. F. at the brushes is reduced, for the following reasons; viz., (i.) The current in the armature always produces an M. M. F., counter, or opposite to the M. M. F. of the field magnet, and, therefore, diminishes the flux through the magnetic circuit, thus causing a corresponding diminution in the value of the E. M. F. produced. Indeed, this opposing M. M. F. may, under certain circumstances, assume a magnitude sufficient to neutralize and destroy the permanent M. M. F. in the field magnets. This is one of the reasons why magneto generators are not employed on a large scale in practice. (2.) The current through the armature produces in the resistance of the armature, a drop in the E. M. F. If, for example, the current through the armature at any instant be one ampere, and the resistance of the armature be 10 ohms, then in accordance with Ohm's law, the drop of E. M. F. pro- duced in the armature, will be i X 10 10 volts. (3.) The current through the armature not being steady, but pulsating, the variations in current strength will induce E. M. Fs. in the coil opposed to the change and, therefore, reducing the effective E. M. F. CHAPTER X. POLE ARMATURES. 121. The form of armature, which stands next in order of complexity to the shuttle-wound armature last described, is the radial or pole armature, represented in Figs. .91 and 92. Here the armature coils c, c, are wrapped, usually by hand, around radially extending laminated pole-pieces, formed from sheet iron punchings laid side by side. This type of machine is rarely found in continuous current generators, but is some- times adopted in very small motors. The winding of such an armature is carried out as represented in Fig. 93, where the pole-pieces are shown at P P, and P' P '. Starting the wind- ing at the point M, the coil A, is wound from A to B, as shown; the coil C, is then wound from B^ through C to D; the coil E, from Z>, through E to E; the coil G, from F, through G to H; the coil /, from H 9 through J to K; the coil Z, from K, through L to M y finally connecting the last end of the coil M, to the first end of the coil A, thus making the closed-coil winding shown in the figure. The connections of this winding to the six-part commutator will be seen from an inspection of the figure. The points M, B, Z>, E, .//and K, are branches connected to the separate insulating segments of the commu- tator, brushes being provided in the position shown on a line connecting the centres of the pole-pieces. This commutator is shown in cross-section at P, Fig. 92. It will be seen that, owing to the conical boundaries of each armature coil, the winding is difficult to arrange. This type of generator is always operated by an electro-magnetic field. 122. Since the dimensions of machines with pole or radial armatures are always small, the reluctance of the circuit is practically wholly resident in the air spaces between the poles and armature projections, provided care be taken that the iron in the armature is not worked at an intensity above 10 kilo- POLE ARMATURES. Ill gausses, or above 7 kilogausses in the field magnet, if the latter be of cast iron. If S, be the area of the polar face of a radial armature projection in square centimetres, and d, be the clear- ance or entrefer in cms., then will be the reluctance of the o entrefer over each armature projection. Since there are four FIG. 91. POLE ARMATURE AT RIGHT ANGLES TO AXIS. such air-gaps in multiple-series the total reluctance of the cir- cuit provided in the case represented, by Fig. 91, will be FIG. 92. SECTION OF POLE ARMATURE THROUGH AXIS. ~r oersteds, assuming that the reluctance existing in the iron o is neglected. 123. The distribution of the flux through the armature is diagrammatically represented in Fig. 95. If the cross-section of each armature core be s, square centimeters, then at no time will there be less than two radial projections carrying the total flux, and if 10 kilogausses be the limit permitted by the H2 ELECTRO-DYNAMIC MACHINERY. reluctance of the air-gap, the total flux to be forced through the armature will be 2 s X 10,000 = 20,000 s, webers. The M. M. F. necessary on the field magnets will be 20,000 .y x -~- gil- berts. For example, if s = 1.3 sq. cms., */ = o. 2 cm., s 10 sq. cms., the M. M. F. required will be 26,000 x 0.02 = 520 gil- berts = 416 ampere-turns, and this must be the total excitation included on the limbs of the electro-magnet. 124. In order to determine the amount of flux passing through a single projection, let the armature be considered as slowly rotated counter-clockwise. Starting with the core i, p FIG. 93. DIAGRAM SHOWING CONNECTIONS OF COIL WITH COMMUTATOR. Fig. 95, the magnetic flux passing through it will be found by dividing half the M. M. F. by the reluctance of the air-gap over its face, or = 13,000 webers. As it moves counter-clock- 10 wise towards 2, no appreciable change is effected in the amount of flux it carries, until the advancing edge of 2 emerges from beneath the polar face W a . The flux through i, rapidly dimin- ishes until before i becomes halfway between the pole faces -A^ and S t , it is entirely deprived of flux. When the position 3 is reached, the flux re-enters the coil of i, but in the opposite direction, and when it passes position 3, the total maximum flux of 13 kilowebers is in the reverse direction. The curve, Fig. 94^ commences at 13 kilowebers in the position corresponding to i, Fig. 91, falls steadily from B to (7, and, after a short pause, from C to Z>, where the coil lies midway between the poles, falls again from D to E, until the flux is 13 kilowebers negative, corresponding to the position 4. Con- POLE ARMATURES. tinuing at this value to F, it rises to G, corresponding to the position 5, and then pauses at the zero line, in the gap between "the poles, rising finally to /, corresponding to the original position i, at K. 125. The E. M. F. established in any turn of the coil is found by ascertaining, from the speed of rotation, the rapidity with which the flux, threading through the coil, changes in value. Jf, for example, the armature be driven at a speed of 1,500 Q H -ANGULAR -DISPLACEMENT co 5 8 -10 FIG. 94. DIAGRAM SHOWING FLUX PASSING THROUGH ONE ARMATURE PRO- JECTION DURING A COMPLETE REVOLUTION. revolutions per minute, or 25 revolutions per second, cor- responding to the time of 0.04 second per revolution, the E. M. F. will evidently be zero at the positions represented by the straight line A B, CD, E F, G H, and / K of Fig. 94, since here, the rate of change in the flux is practically zero, and the E. M. F. will be nearly uniform during the periods repre- sented by B C, D E, F G, and H /, since the rate of change is nearly uniform in one direction or the other during those periods. As shown in Fig. 97, the E. M. F. in the single turn on the projection commencing at the position i, is zero from o to b. From fr, through b' to ^, the flux diminishing at the rate of 13,000 webers in 0.00433 second, and, therefore, at the rate of 3,000,000 webers (3 megawebers) per second, and since 100 megawebers per second correspond to an E. M. F. of one volt, the E. M. F. in a single turn is 0.03 volt. Assuming 10 turns of wire on each armature projection, the total E. M. F. will be 0.3 volt at this period, and the ordinate bb, represents ,114 ELECTRO-DYNAMIC MACHINERY. 0.3 volt in Fig. 97. At c'd, corresponding to the position C >, Fig. 94, the E. M. F. is zero, falling again to 0.3 volt from d to e' t corresponding to a change in flux from D to , Fig. 94. After 0.02 second has elapsed, the E. M. F. re- verses in direction and becomes positive, tracing the curve ff 1 gg' hti jf k. By the aid of the commutator, the E. M. Fs. in the coils, as soon as they change their direction, are reversed relatively FIGS. 95 AND 96. DISTRIBUTION OF FLUX AND E. M. F. AT POSITION SHOWN. to the external circuit, and, therefore, preserve their direction externally, as can be seen by examination of Fig. 93. 126. We have thus far traced the E. M. F. as developed in a single polar projection, and so resulting from the variation of flux passing through it. During the time that the E. M. F. is being generated in this coil, a similar E. M. F. is being gener- rated in the other coils, displaced, however, in time, by por- tions of a revolution. As shown in Fig. 96, the six coils on the armature have E. M. Fs. developed in them, being con- nected with the external circuit through the brushes in two parallel series, each of 3 series-connected coils. Each coil is, therefore, acting in its circuit for one half of a revolution before it is transferred to the opposite side, and while Fig. 97 represents the E. M. F. generated in any half revolution of one coil, we have to consider the E. M. Fs. coincidently being generated in .its next neighbor on either side. This is shown in Fig. 98, where the E. M. F. of all three coils is de- POLE ARMATURES. veloped independently on parallel lines one above the other, each E. M. F. being a repetition of that in Fig. 98, but dis- placed the -J-th of a complete revolution. Fig. 99 represents O w SECONDS FIG. 98. FIGS. 97, 98, AND 99. E. M. F. WAVES GENERATED IN POLE ARMATURE. the effects of combining or summing these three separately generated E. M. Fs. in the same circuit, and it will be seen that the E. M. F. pulsates between 0.2 and 0.6 volt. i 127. If the resistance of the wire on each coil be r ohms, then the resistance of the three coils on each side of the arma- ture will be 3 r, and the resistance of these two sides in parallel will, except at changes of segments, be 1.5 r, so that, neglect- ing the resistance of the brushes and brush contacts, the resist- ance of the armature will be 1.5 r ohms. n6 ELECTRO-DYNAMIC MACHINERY. The current strength which should be maintained by the generator, when on short circuit, would, therefore, reach 0.6 amperes, but in reality, the current will not reach this amount, owing, among other things, to the effect of self-in- duction in the armature, which, under load, tends to check the pulsations, and, consequently, renders them more nearly uniform, thus reducing the mean E. M. F. CHAPTER XI. GRAMME-RING ARMATURES. 128. The armature of the dynamo-electric machine which comes next in order of complexity, is that devised by Gramme, and now known generally as the Gramme-ring arma- ture. This armature, as its name indicates, belongs to the type of ring armatures, and consists essentially of a ring-shaped laminated iron core wound with coils of insulated wire. In FIG. IOO. DIAGRAM OF GRAMME-RING ARMATURE IN BIPOLAR FIELD, TWENTY-FOUR SEPARATE TURNS. the Gramme-ring armature shown in Fig. 100, the core is a simple ring of iron, wound with 24 separate turns of wire, placed so as to be able to revolve about its axis in the bipolar field JV, S. Considering the ring to be first at rest, the turns 6, 7, 8, 18, 19 and 20 are represented as being linked with the total flux passing through the cross-section of the ring. If the total flux entering the armature at the north pole and leaving at the south pole, that is, passing from JV to *$*, be two mega- webers, then one megaweber passes through the upper half of the ring, and one megaweber through the lower half. The loops 5, 9, 17 and 21 are diagrammatically represented as hav- ing 900 kilowebers passing through them. The loops 4, 10, 16 and 22 carry 700 kilowebers ; 3, u, 15 and 23 carry 500 kilowebers ; 2, 12, 14 and 24, 300 kilowebers ; while i and 13, carry no flux. 117 Il8 ELECTRO-DYNAMIC MACHINERY. 129. Suppose now, the ring be given a uniform rotation of one revolution per second, in the direction of the large arrows. It is evident, that at any instant there is no change in the amount of flux linked with the turns occupying the positions 6, 7, 8, 18, 19 and 20 ; so that, although these contain a maxi- mum amount of flux, they will have no E. M. F. generated in them. Loops 5 and 9, however, are in a position at which the flux they contain is changing ; that is to say, the amount of flux that is passing through them at each instant has neither reached a maximum nor minimum ; and the same is true with regard to the loops 17 and 21. In 5, the flux is increasing, and in 9, it is decreasing ; consequently, the E. M. F. in 5 is directed oppositely to that in 9, and, according to rule, is in- dicated by the curved arrows (Par. 105); for, if coil 5 be regarded by an observer facing it from S, the flux, as the ring moves on, will thread the loop in the opposite direction 1 to that of light coming from the face of the loop, considered as a watch dial, to the observer, and the E. M. F. generated in the loop will be directed counter-clockwise, while the E. M. F. in the loop 9 must have the opposite direction. Moreover, simi- lar reasoning will show that all the coils to the left of the line J3 B ', that have E. M. Fs. generated in them, will have these E. M. Fs. similarly directed ; /. e., outwards, as shown, while all on the left-hand side of the line, will have the E. M. Fs. also similarly directed, but inwards. Loops i and 13, which lie parallel to the direction of the flux, will, in the position shown, have no flux threading through them, but during rota- tion, the rate of change of flux linked with them is a maxi- mum ; consequently, the E. M. F. induced in them is a maximum. 130. Instead of conceiving separate conducting loops to be wound on the surface of the armature, as shown in Fig. 100, let us suppose a continuous coil is wound on the surface of the armature as shown in Fig. 101, the first and last ends of the coils being connected together so as to make the winding con- tinuous; then it is evident that the E. M. Fs. so acting being similarly directed on each side of the vertical line B JB', might be made to produce continuously an E. M. F. in the conduct- ing wire. Moreover, if two wires, or collecting brushes, were GRAMME-RING ARMATURES. 119 employed in the positions B, B ', the E. M. Fs. from the two halves of the ring would unite at the brushes B, B'. Such a condition finds its analogue in the E. M. Fs. pro- duced by two series-connected voltaic batteries connected as shown in Fig. 102, with their positive poles united at B, and their negative poles united at B'. The figure shows two bat- teries each of 9 cells connected in series. Here, as indicated, all the cells have equal E. M. F. This condition of affairs need not, however, exist in the Gramme-ring analogue, since the only requirement is that the sum of all the E. M. Fs. FIG. 101. DIAGRAM OF GRAMME-RING ARMATURE IN BIPOLAR FIELD, TWENTY;FOUR SEPARATE TURNS. generated in the coils on 1 the right-hand side be equal to the sum of those on the left-hand side. In point of fact, as already observed, the E. M. Fs. are not the same in each of the coils, those at i and 13 having a maximum E. M. F., and those at 7 and 19 having zero E. M. F. Since these oppositely directed E. M. Fs. balance each other, no current will be pro- duced in the armature unless an external circuit be provided, by joining the brushes B, B'. 131. Figure 100 shows no difference between the amount of flux threaded through the coils 6, 7 and 8 ; or 18, 19 and 20, and, consequently, according to theory, a total absence of induced E. M. F. in these coils. In practice, however, owing to leakage (Par. 77) and other causes, no coil is entirely free from having E. M. F. generated in it. Moreover, the difference in the E. M. F. generated in coils 13, 12, ii and 10, is not as great as might be inferred from their angular position on the armature, owing to the fact that 120 ELECTRO-DYNAMIC MACHINERY. (Par. 100) the flux enters the armature core nearly uniformly all around its surface. In order to determine the total E. M. F. generated in such an armature as is represented in Fig. 101, it is first necessary to determine the E. M. F. generated in a single turn. Let us. consider a turn starting from the position 7, and therefore, generating no E. M. F., being carried by the uniform rotation of the armature in the direction of the arrows to the position 19, in a time / seconds. During this time the flux threading through it changes from webers in one direction, to - we*bers in the opposite direction, and, therefore, the change in flux linkage will be $ webers, $, being the total flux pass- ing from N into S, through the armature. Whatever may be the distribution of flux through the armature, and in the air- gap, the average E. M. F. generated in the coil during this & time will be C. G. S. units of E. M. F. If the number of revolutions made by the armature per second be /z, then one revolution takes place in the th of a second, and a half revolu- tion in the - th of a second, so that / = , and the average 2/2 272 E. M. F. is - , = 2n $ i 132. If, for example, the armature be revolved at a speed of 600 revolutions per minute, or 10 revolutions per second, n 10, and since $, has been assumed to be 2 megawebers, the average E. M. F. generated in any loop in passing from the position 7, to the position 19, will be 20x2,000,000 = 40,000,000 C. G. S. units, or 0.4 volt (Par. 82). The same E. M. F., oppositely directed, however, will exist on the average in any turn on the right-hand side of the line B B '. If the ring were wound with only four turns, say i, 7, 13 and 19, the E. M. F. generated in these turns when placed in series and connected to the brushes B and B', would evi- dently fluctuate considerably; since, when the coils occupy the GRAMME-RING ARMATURES. 121 position shown, the E. M. Fs. would be a maximum in i and 13, and zero in 7 and 19, while, after */&th of a revolution, all four coils would be active. If, however, numerous turns are wound on the coil, it is evident that the total E. M. F. between the brushes B and B ', will be very nearly uniform, since the only fluctuation which can take place is that coin- cident with the transfer of a single turn beneath the brush; consequently, in order to determine the total E. M. F. gener- ated by the rotation of a Gramme-ring armature, it is only necessary to multiply the average E. M. F. in each turn by half the number of turns on the armature; /. e., by the number FIG. 102. VOLTAIC ANALOGUE OF E. M. Fs, GENERATED IN GRAMME RING. of turns active between B and B ', on each side, so that if w y be the number of turns on the armature, counted once around, will be the number of turns active between brush and brush. 2 and the total E. M. F. on each side of the armature will be 2$nx~ = & n w C. G. S. units = volts. 2 100,000,000 If w = 24, as in the case represented, then the total E. M. F. will be 2,000,000 x 10 X 24 = 480,000,000 = 4.8 volts. 133. There is only one method, in practice, of connecting the separate coils of a Gramme-ring bipolar armature; namely, their continuous looping around the ring in a closed coil, as shown in Fig. 101. Suppose that it is desired to utilize the generated E. M. Fs. for the purpose of supplying a current to an external circuit; it is then only necessary to apply suitable brushes, or con- ductors, at B and B ', so as to rub continually against the external surface of the turns as they revolve, making the brushes sufficiently wide to maintain continuous contact. 122 ELECTRO-D YNAMIC MA CHINER Y. Under these circumstances, during the rotation of the armature, a steady current will flow through the circuit main- tained externally between Hand B\ B, being the positive pole of the machine, and B ', the negative pole. Reversing the direction of the armature rotation will, of course, reverse the polarity of the brushes, as will also the reversal of the direc- FIG. 103. GRAMME-RING SEXTIPOLAR GENERATOR WITH BRUSHES COM- MUTATING ON SURFACE OF ARMATURE. tion of the magnetic flux. If, therefore, it be required to change the polarity of the brushes without changing the direction of rotation, it is only necessary to reverse the magnetic flux through the armature. Fig. 103 shows a Gramme-ring sextipolar generator, with the commutating brushes bearing directly on the metallic surface of the turns of conductor on the surface of the armature. This method, however, of commuting the current from a Gramme-ring GRAMME-RING ARMATURES. 123 armature is not the one in most frequent use; for, not only are the conductors upon the surface of the armature usually too small to bear brush friction without destructive wear, but also the relative amount of friction offered by brushes, placed upon so large a diameter, is considerable, except in the case FIG. 104. COMMUTATION OF CURRENTS FROM A GRAMME-RING ARMATURE BY A COMMUTATOR. of very large machines. In order to avoid this, as well as for other reasons, it is usual to employ a special form of commu- tator, as represented diagrammatically in Fig. 104, where each turn is connected by a special conductor to a separately insu- lated segment of a commutator. This commutator, therefore, contains as many separate segments as there are turns on the FIG. 105. FORMS OF COMMUTATORS. armature. Usually, however, there are many turns of wire on the armature to each segment of the commutator. 134. It is customary, in practice, to give a considerable length of free surface to the commutator bars, so as to increase the surface of contact and thus diminish the pressure that has to be applied. Fig. 105 shows two forms of such commutator. The separate segments are insulated from each other by mica strips. In order to provide for the connection of the wires from the armature to the separate commutator segments or 124 ELEC7"RO-D YNAMIC MA CHINER Y. bars B, metal projections or lugs Z, attached to the bars, arc provided. The bars, after being assembled, are held rigidly in place by the nut N. Various forms of brushes are provided to maintain contact FIG. 106. FORM OF GENERATOR BRUSH. with the commutator bars. One form, consisting of wires and strips in alternate layers, is shown in Fig 106. 135. In the armature so far considered, it has been supposed that the condition as regards distribution of flux and the con- sequent generation of E. M. F. is symmetrical. It is possible, however, that in the construction of the machine this symme- FIG. IO7. DIAGRAM REPRESENTING INFLUENCE OF MAGNETIC DISSYMMETRY. try may not be secured. For example, in Fig. 107, the pole- piece S, is represented as being considerably further from the armature at its lower than at its upper edge, thereby increasing the reluctance of the air-gap at the lower edge, and producing magnetic dissymmetry, as represented by the distribution of flux arrows. It will be found, however, on examination, that despite this magnetic dissymmetry, the average E. M. F. produced in the coils would remain the same, although the distribution of this E. M. F. among the different turns neces- sarily varies. Thus if $, be, as before, the total flux through GRAMME-RING ARMATURES. 125 the armature, the lower half of the armature may take a cer- tain fraction n resistance of the entire armature winding, -^ will be the joint resistance between brushes, for there will be / sections in r> parallel, each of which will have ohms. Consequently, in P a six-pole armature, there will be six segments in parallel, r> each having a resistance of , making the joint resistance R_ R_ 36' r 6* Fig. 1 20 represents the mechanical arrangement for rigidly supporting the armature of a direct-driven octopolar Gramme- ring generator with eight sets of brushes pressing upon one side of the armature, thus dispensing with the use of a separate 142 ELECTRO-D Y NAM 1C MA CHINER Y. commutator. The central driving pulley PPP, supports upon its arched face two rings R,R '. These rings clamp between them the armature core, and are clamped together by 14 stout bolts. Where the supports ss, interfere with the winding of the conductor inside the armature, the conductors are carried on the supports as at a b c and d. FIG. 120. GRAMME-RING MULTIPOLAR ARMATURE. 151. It is not absolutely necessary, however, to employ six brushes in a sextipolar machine ; for, since in a machine of this type the three separate circuits are connected in parallel, con- nections may be carried within the armature between the various segments, permitting of the use of a single pair of brushes. Thus Fig. 121 represents a Gramme-ring armature, wound for a sextipolar field, with triangular cross-connections between its turns. In this case, the corresponding points p lt n i> n n v f Fig. 118, instead of being connected to- MULTIPOLAR GRAMME-RING DYNAMOS. 143 gather by brushes externally as in Figs. 119 or 120, are connected together by wires internally. It is not, of course, necessary that every turn on the armature should be so cross-connected, but that the coils or group of turns which are led to the com- mutator should be cross-connected, so that each of the 36 turns, shown in Fig. 121, may represent a coil of many turns. Although the brushes are shown in Fig. 121, as being placed on FIG. 121. ARMATURE CROSS-CONNECTIONS FOR A SEXTIPOLAR GRAMME-RING WITH TWO BRUSHES. adjacent segments, yet they may be 'equally well placed diametrically opposite to each other. Fig. 122 represents the corresponding cross-connections for a quadripolar Gramme generator, employing a single pair of brushes. The advantage of cross-connections is the reduction in the number of brushes. The disadvantage of cross-connec- tions lies in the extra complication of the armature connections. In large machines it is often an advantage to employ a number of brushes in order to carry off the current effectively. 152. Fig. 123 is a representation of a sextipolar generator whose magnetic field is produced by three magneto-motive forces, developed by coils placed as shown. The flux paths are represented diagrammatically by the dotted arrows at A. Each M. M. F. not only supplies magnetic flux through the segment of the armature immediately beneath it, but also con- tributes flux to the adjacent segments in combination with the neighboring M. M. Fs. 144 ELECTRO-D YNAMIC MA CHINER Y. 153. From the preceding considerations it is evident that while it is possible to design a bipolar generator for any desired output, yet, in practice, simple bipolar generators are not employed for outputs exceeding 150 KW, and, in fact, are seldom employed for more than 100 KW, since their dimen- sions become unwieldy and their output, per pound of weight, smaller than is capable of being obtained from a well-designed multipolar machine. In the same way, a quadripolar generator can be made to possess any desired capacity; but, in the United States, FIG. 122. CROSS-CONNECTIONS FOR QUADRIPOLAR GRAMME-RING WITH TWO BRUSHES. practice usually increases the number of the poles with an increase in the output of the machine. Thus, it is common to employ a four-pole or six-pole generator for outputs of from 25 to 100 KW, and 8 to 12 poles for a generator of 400 KW, capacity. 154. Should the armature of a multipolar generator not be concentric with \ht polar bore ; i. e., if it is nearer one particu- lar pole than any of the others, the reduction in the length of the air-gap opposite such pole, will reduce the reluctance of that particular magnetic circuit, and by reason of the increased flux through the armature at this point, induce a higher E. M. F. in the segments of the armature adjacent to the pole MULTIPOLAR GRAMME-RING DYNAMOS. than in the remaining segments. If the armature be not inter- connected ; i. e., if it employs as many pairs of brushes as there are poles, these unduly powerful E. M. Fs. can send no cur- rent through the armature as long as the brushes remain out of contact with the conductors; for an inspection of Figs. 118 and 119 will show that no abnormal increase of E. M. F. can exist in a single segment, but must be simultaneously generated in adjacent segments, and that such pairs of E. M. Fs. will counterbalance each other. When, however, the brushes are brought into contact with the armature conductors, thereby bringing the various segments into multiple connection with FIG. 123. SEXTIPOLAR GRAMME-RING SUPPLIED BY THREE MAGNET COILS. one another, a tendency will exist for the more powerful E. M. F. to reverse the direction of current through the weaker segments. 155. Whether this tendency will result in an actual reversal of current depends upon the difference of E. M. F. between the segments, their resistance, and the external resistance or load. Let A and B, Fig. 124, represent the E. M. Fs. of any two segments in a multiple-connected Gramme-ring armature, and let the E. M. F., E, of A, be greater than the E. M. F., E', of B. Owing to drop of pressure in the internal resistance r, the pressure e, at the terminals p, q, will be less than the E. M. F., E, of the stronger segment A. If e, is greater EV than E' , a current of ^ amperes will pass through the 146 ELECTRO-DYNAMIC MACHINERY. segment B, in the direction opposite to that in which its E. M. F. acts. If , at no load, with a useless expenditure of 500 watts. Consequently, between no load and full load, there will be a change from an expenditure of power with reversal of current in the weaker segments, to an excessive drop and expenditure of power without reversal of current. 159. Although this difficulty, arising from the unbalanced magnetic position of the armature, does not, in practice, give MULTIPOLAR GRAMME-RING DYNAMOS. 149 rise to any serious inconvenience, when mechanical construc- tion is carefully attended to, yet windings have been devised by which it maybe altogether avoided. For example, if all the turns be so connected that their E. M. Fs. are placed in series, then a single pair of brushes will be capable of carrying the current from the entire armature, which will only be divided into two circuits; or, the segments may be so interconnected that turns in distant segments may be connected in series so as to obtain a more general average in the total E. M. F. Such windings are always more or less complex, and the reader is referred to special treatises on this subject for fuller details. 160. The formula for determining the E. M. F. of a multi- polar Gramme generator armature is, E 3>nw C. G. S. units, where $, is the useful flux in webers, or the flux entering the armature through each pole, , the number of revolutions per second of the armature, and /, the number of turns on the surface of the armature counted once around. If, however, the armature be series connected, so that instead of having /, circuits through it between the brushes, where/, is the number of poles, there are only two circuits, then the E. M. F. will be E = 3>nw, while if, as in some alternators, the circuit between the brushes be a single one, the mean E. M. F. of the armature will 161. Fig. 129 represents the magnetic circuits of an octopolar generator, the dimensions being marked in inches and in centi- metres. The field frame is of cast steel, and the armature core is formed of soft iron discs. Let us assume that there are 768 turns of conductor in the armature winding, and that the speed of rotation is 172 revolutions per minute, or 2.867 per second. Assuming an intensity of 9,500 gausses in the armature, it may be required to determine the E. M. F. of the machine. The cross-section of the armature is 31.1X13 = 404.3 sq. cms., but allowing a reduction factor of 0.92 for the insulating material between the discs, the cross-section of iron is 372 sq. cms. The total flux passing through the cross-section of 150 ELECTRO-DYNAMIC MACHINERY. the armature will, therefore, be 372 x 9,500 = 3,534,000 webers. The useful flux through each pole will be twice this amount, or 7,068,000 webers, so that the E. M. F. of the generator will be : E $nw = 7,068,000 X 2.867 X 7 68 = r -557 X io 10 = 155.7 volts. This will be the E. M. F. of the generator, provided all the FIG. 129. GRAMME-RING OCTO POLAR GENERATOR. armature segments are connected in parallel, as shown in Fig. 115. If, however, the armature winding be so connected that only a single pair of brushes and a single pair of circuits exist through the armature, the E. M. F. would be 4 times as great, while if the armature could be connected in a single series, the E. M. F. would be 8 times as great. 162. In order to determine the M. M. F. necessary to drive this flux through the armature we proceed as follows: viz., MULTIPOLAR GRAMME-RING DYNAMOS. Cross-section. Sg. cms. Flux. Webers. Intensity. Gausses. Length Cms. 6n i$^ 9,188,400 13,430 40 354 S 3,534,000 9,980 7 6 *64J7V 3,534,000 9,500 50 We first determine the cross-section, the mean length, and the intensity in each portion of the magnetic circuits. One of the eight magnetic circuits through the armature is represented by the dotted arrows at A (Fig. 129). We may assume that the flux through the cores is 7,068,000 x 1.3 = 9,188,400 webers; 1.3, being the approximate leakage factor for a machine of this type; in other words, of all the flux passing through the cores X 100 = 76.9 per cent., approximately, may be O assumed to pass through the armature, half through each cross- section. Consequently, we have the following distribution : Field core, Yoke, . Armature, The entrefer, or gap, of copper, air and insulation, existing between the iron in the armature and in the pole faces, is 1.5 centimetres in length, while the polar area is 41 cms. X 34 cms., or 1,400 sq. cms. in cross-section. From these data, the reluctance in the magnetic circuit through the armature is Field core, n t c Yoke, Entrefer, . Armature, The M. M. F. required to drive a total flux of 3,534,000 webers through this circuit will be Cross-section carrying Cross- armature Length. Cms. Intensity. Gausses. Reluctivity. section. Sq. cms. flux. Sq. cms. Reluctance. Oersted. 40 13,430 O.OO2 342^ 263.1 0.000,304 40 13,430 0.002 342 263.1 O.OOO,3O4 76 9,980 O.OOI 354* 354-0 0.000,215 1-5 I. 700 i/ 0.002,142 1-5 I. 700 v' O.OO2,I42 50 9,500 0.0008 372^ 372 0.000,107,5 0.005,214,5 3,534,000 x 0.005,214 (18, t,5=1 i4, (7,3 ,430 gilberts. T ,66s ampere-turns. 333 ampere-turns on each spool. With 600 turns on each spool, the current would be 12.22 amperes. CHAPTER XIV. DRUM ARMATURES. 163. The drum armature was first introduced into electrical engineering by Siemens, in the shape of the shuttle armature, and was modified by Hefner-Alteneck in 1873. The drum armature was subsequently modified in this country by the introduction of a laminated iron armature core, consisting of discs of soft iron, called core discs, provided with radial teeth or projections. This armature core, when assembled, had FIG. 130. TOOTHED-CORE ARMATURE IN VARIOUS STAGES OF CONSTRUCTION, space provided between the teeth for the reception of the armature loops on its surface, a completed armature showing, when wound, alternate spaces of iron and insulated wire, and formed what is called a toothed-core armature. Next followed the smooth-core drum armature, that is, a drum armature com- posed of similar core discs in which the teeth were absent, so that the completed armature had its external surface com- pletely covered with loops of insulated wire. Fig. 130 shows a common type of toothed-core armature in various stages of construction. The laminated iron core is shown at A, as assembled on the armature-shaft ready to receive its winding of conducting loops in the spaces between the radially project- ing teeth. At B, is shown the same core provided with wind- 152 DRUM ARMATURES. 153 ings of insulated wire. At C, is shown a completed armature. The detailed construction of a laminated armature core is illustrated in Fig. 131, which shows a portion of a drum arma- ture core already assembled by the aid of large bolts passing FIG. 131. TOOTHED-CORE ARMATURE IN PROCESS OF ASSEMBLING. through holes in the core-discs. On the right are other core-discs ready to be placed in position on the shaft. 164. Fig. 132 shows a laminated armature body of the smooth-core type. Here the separate core-discs are formed FIG. 132. SMOOTH-CORE ARMATURE BODY. of sheet iron rings assembled on the armature, shaft as shown. These discs, after being assembled, are pressed together hydraulically. The end rings are heavy bronze spiders, held 154 ELECTRO-DYNAMIC MACHINERY. together internally by six bolts shown in the figure. When the armature body is subjected to compression, these bolts are tightened on the spiders, which are firmly keyed to the shaft, so that on release of the hydraulic pressure, the lami- FIG. 133. COMPLETED ARMATURE, SMOOTH-CORE TYPE." nated iron core forms one piece mechanically. Fig. 133 shows the same armature completely wound. 165. In the drum armature, the conducting wire is entirely confined to the outer surface, and does not pass through the FIG. 134. TYPICAL FORM OF SMALL SIZE DRUM ARMATURE. interior of the core. In this respect, therefore, it differs from the Gramme-ring armature, already described, in which the winding is carried through the interior of the core, lying, therefore, partly on the interior and partly on the exterior. The armature core, or body, of a Gramme-ring machine differs markedly in appearance from the armature body of a drum machine, when both are in small sizes, since then the drum core is practically solid, having no hollow space, so that it would be impossible to wind it after the Gramme method. Such a drum-wound armature is shown in Fig. 134. When, however, DRUM ARMATURES. 155 the drum armature is increased in size, so as to be employed in multipolar fields, the form of the core or body passes from a solid cylinder to that of an open cylinder or ring, as is shown in Figs. 132 and 135, so that it would be possible to place a conducting wire on such a core either after the drum or Gramme type of winding. The tendency, however, in modern electrical engineering is, perhaps, toward the produc- tion of drum-wound rather than Gramme-wound generators. FIG. 135. LARGE DRUM ARMATURE FOR MULTIPOLAR FIELD. This tendency has arisen, probably more from mechanical and commercial reasons than from any inherent electrical objections. to armatures of the Gramme-ring type. 166. The windings of drum armatures are numerous and complicated in detail, but all may be embraced under two typi- cal classes ; namely, lap-winding and wave-winding. In lap- winding, the wire is arranged upon the surface of the armature in conducting loops, the successive loops overlapping each other, hence the term; while in wave-winding, the conducting 156 ELECTRO-DYNAMIC MACHINERY. wire makes successive passages across the surface of the armature, while being advanced around its periphery in the same direction. 167. Lap-winding is applicable particularly to bipolar arma- tures, while wave-winding is applicable only to multipolar armatures. b ti FIG. 136. SIMPLE BIPOLAR DRUM-WINDING. The simplest form of lap-winding is shown in Fig. 136, where the separate paths taken by the turns a y b, c, d, and the resistance of the local circuit in ohms. 174. It is evident that a dynamo machine can never be designed so as to be entirely free from eddy currents; for, con- ducting loops must be placed on the armature, and, moreover, in nearly all the types of practical dynamo machines, iron arma- ture cores are employed. All that can be done is to reduce these losses as far as is commercially practicable. In the case of the iron core, for EDDY CURRENTS. 165 example, the advantage arising from its use; namely, the decrease in the reluctance of the magnetic circuit, can be retained, provided the material of the core is laminated, /. e. , made continuous in the direction of the magnetic flux -paths, and discontinuous at right angles to this direction. 175. If a piece of metal be revolved in a magnetic field, it will enclose magnetic flux. A distribution of E. M. Fs. will be established in it according to the rate at which the enclosure takes place, and depending upon the shape of the piece. These E. M. Fs. will produce eddy currents in the moving metal. The rate of expending work in eddy currents will be, for a given flux intensity in the metal, in direct proportion to the conductivity of the material. A piece of revolving copper will have much more work expended in it by eddy currents than a piece of lead or German silver. If, however, we divide the mass of metal into a number of segments or smaller portions, the total E. M. F. at any instant will be divided into a num- ber of parts, one in each segment, and the resistance of each segment to its E. M. F. will be much greater than the ratio of the resistance of the entire mass to the total E. M. F. in such mass. The energy wasted in the mass will therefore be reduced. For this reason, the iron core of the armature is divided into sheets or laminae, in such a manner that the sheets afford a continuous path to the magnetic flux, but no circuit is provided for eddy currents across the sheets. The magnetic flux is conducted through the entire length of the sheet, but the circuits of the eddy currents are all in the cross-sections of the sheet. The division of the armature core does not, therefore, increase the magnetic resistance, or reluctance of the armature, but enormously increases its resistance to eddy currents. 176. Fig. 146 represents at Z>, an armature core of solid iron capable of being revolved in aquadripolar field JV 1 , S 1 , ^V a , *S" 3 , the arrows indicating the general directions of the flux paths. The cross-section of the armature is shown at A, and the arrows represents diagrammatically the distribution of the eddy cur- rents set up in the solid mass of iron during the rotation of the armature. At B, the cross-section is represented with lamina- i66 ELECTRO-D YNAMIC MA CHINER Y. tions, parallel to the axis of the armature, as, for example, when the armature core is composed of a spiral winding of sheet-iron ribbon. Here the eddy currents are limited to the cross- section of each band or lamina. The magnetic flux, however, has to penetrate all the discontinuities between the bands, in order to penetrate to the deepest layer, unless the flux be admitted to the armature on its sides, as shown in Fig. 8. At <7, the armature is laminated in planes perpendicular to the axis, or is built up of sheet discs. Here the eddy currents are confined, as in the last instance, to the section of each disc, but the flux passes directly along each sheet. While, therefore, the methods of construction indicated at N 2 FIG. 146. DIAGRAM ILLUSTRATING EFFECTS UPON EDDY CURRENTS OF LAMINATING ARMATURE CORES. B and C, are equally favorable to the suppression of eddy currents, B, tends to increase the reluctance of the armature, and to magnetically saturate the outer layers of the core, with a corresponding sparsity of flux in the inner layers, except when the field poles cover the sides of the armature. 177' Taking a single lamina of the armature core, it is clear that if the intensity in the core is, say, 12 kilogausses, each square centimetre of cross-section in the lamina is linked with 12 kilowebers, first in one direction and then in the opposite direction, as the armature moves from one pole to the next. The value of the E. M. F. round the cross-section of the lamina, considered as a loop, depends upon the speed with EDDY CURRENTS. 167 which the linkage takes place, and, therefore, on the intensity e , the formula for the amount of activity expended in one cubic centimetre of magnetic metal being P = n rj (B '* watts. Since the same loss of energy occurs in a cubic centi- metre during each cycle, the more rapidly the cycles recur, the greater will be the wasteful activity, and ;/, in the above formula, expresses the number of complete cycles through which the iron is carried per second. The coefficient 77, is the hysteresis coefficient for the metal considered, and has to be de- termined experimentally. It may be regarded as the activity in watts which would be expended in one cubic centimetre of the metal when magnetized and demagnetized to a flux density of one gauss at one complete cycle or double rever- sal per second. The following table gives the values of this coefficient, and also the amount of hysteretic loss produced in a cubic centimetre, and in a pound, of ordinary good com- mercial sheet iron at various frequencies and intensities. MAGNETIC HYSTERESIS. '75 Table Showing the Hysteritic Activity in Good ', Soft Sheet Iron or Steel Undergoing One Complete Magnetic Cycle per Second, in Watts per Cubic Centimetre, Watts per Cubic Inch, and Watts per Pound, for Various Magnetic Intensities in Gausses and in Webers Per Square Inch. Webers, per sq. in 6,452 12,900 19,360 25,8lO 32,260 38,710 45,160 51,620 58,060 Gausses[(BJ. 1,000 2,000 3,000 4,OOO 5,OOO 6,000 7,000 8,000 9,000 Watts, per cc. 8 1.58X10 -6 4.78x10 -5 9.I5XIO -4 1.45X10 -4 2.07X10 -4 2.78X10 -4 3-55X10 -4 4.40X10 -4. 5-31x10 Watts, per cubic in. . . -4 2.59X10 -4 7.84X10 -3 I.50XIO 2.38x10 3 3.40X10 3 4-55X10 -3 5.82X10 -3 7-20X10 -3 8.60JIIO Watts, per lb. -4 9.17X10 -3 2.78x10 -3 5.32X10 -3 8.43X10 -2 1. 21X10 -2 I.62XIO -2 2.06X10 -a 2.56x10 -2 3.09X10 Webers, per sq. in ... . 64,520 70,960 77,420 83,860 90,320 96,770 103,200 109,700 Il6,IOO Gausses [(B]. 10,000 II,OOO 12,000 13,000 14,000 15,000 l6,000 17,000 18,000 Watts, per cc. -4 6.28X10 -4 7-3IXIO -4 8.40X10 -4 9-55X10 -3 I.OSXIO -3 1. 20X10 3 I.33XIO -3 I.47XIO -3 1.61x10 Watts, per cubic in ... -2 1.03X10 -2 I.2OXIO -2 1.38x10 2 I.57XIO -2 1.76x10 -2 I.97XIO -2 2.I8XIO 9 2.4IXIO -2 2.64X10 Watts, per lb. -2 3.65X10 -2 4.25X10 -2 4.89X10 - 5.56x10 -2 6.26X10 -2 6.79X10 -2 7.75X10 -2 8.53XTO -2 9.35X10 IpO. As an example of the hysteretic activity, we may con- sider a pound of iron subjected to a periodic alternating flux density of ten kilogausses, with a frequency of 25 cycles-per second. From the preceding table, it is seen that at 10 kilo- gausses the hysteretic activity is 0.0365 watts-per-pound, at a frequency of one cycle per second. At 25 cycles per second this would be 25 x 0.0365 =0.9125 watt = 0.9125 joule-per- second = 0.6735 foot-pound per second. Consequently the hysteretic activity might be represented by lifting the pound at the rate of 0.6735 foot P er second against gravitational force. If, therefore, all the iron in an armature core be subjected to an intensity of ten kilogausses, and rotates 25 times per second in a bipolar field, 12.5 times per second in a quadripolar field, 176 ELECTRO-DYNAMIC MACHINERY. or 6.25 times per second, in an octopolar field, hysteretic activity is being expended at a rate which is probably repre- sented by the activity of raising the whole armature core about eight inches per second. It is to be observed that the table represents average samples of good commercial iron, and by no means the best quality of iron obtainable. 191. As an example of the application of this table, suppose that it is required to estimate the power expended in hysteresis during the rotation of the armature of the octopolar generator represented in Fig. 129, the weight of iron in the armature being 2,700 Ibs. At the maximum intensity of 9,500 gausses, or 61,290 webers- per-sq. in., the table shows that the hysteretic activity per pound at one cycle per second is about 3.4 X io~ a watts. In each revolution of the armature there would be eight reversals, . or four complete cycles, and at 2.867 revolutions per second, the frequency of reversal would be 11.468 cycles per second. The total hysterettc'activity is, therefore, P X 2,700 X 3-4 X io~ a X 11.468 = 1,053 watts. This would be the hysteretic activity in the armature when generating 155.7 volts. When generating a lower E.M.F., the flux intensity in the armature would be reduced, and, therefore, the hysteretic activity. 192. Hysteresis, therefore, occurs when a mass of iron undergoes successive magnetizations and demagnetizations, and this is true whether such are caused by the reversal of the magnetizing current, with the mass at rest, or by the reversal of the direction of the mass in a constant magnetic field. Conse- quently, the revolutions of the armature of a dynamo or motor, occasioning the successive magnetizations and demagnetiz- ations of its core, are accompanied by an hysteretic loss of energy. The amount of this hysteretic loss increases directly with the volume V, of iron in the armature in c. c., the number , of revolutions of the armature per second, the hysteretic coeffi- cient ff of the iron employed, and the i.6th power of the maximum magnetic intensity in the iron; for, it is evident that XTNIVERSITT) MAGNETIC H YSTERESI3* Q ^\ 1 77 in one complete revolution of the armature its direction of magnetization will have undergone two reversals, provided that the field is bipolar. In a multipolar field the number of revers- als increases with the number of poles/, and the hysteretic activity becomes P = nr l r - watts. In the case of a gen- erator, this activity must be supplied by the driving power, and in the case of a motor by the driving current. IQ3- When a generator armature is at rest in an unmagnet- ized field, the torque; i. e., the twisting moment of the force which must be applied to the armature in order to rotate it, is such as will overcome the friction of the journals and brushes. When, however, the field is excited, so that the armature becomes magnetized, the torque which is necessary to rotate the armature is increased, even when the armature is symmet- rically placed in regard to the poles. This extra torque is due to hysteresis. It is sometimes called the hysteretic torque, and is equal to V 77 /(B 1 ' 8 t = -- megadyne-decimetres. 194. The total useless expenditure, therefore, of power in an armature core is the sum of the hysteretic and eddy current loss. The former increases as the speed of revolution directly, but the latter, as already pointed out, increases as the square of the speed. Consequently, if we have an unwound armature core, and rotate it on its shaft through a field which is at first unexcited, we expend an activity which might be measured, and which would be entirely frictional loss. When the field is ex- cited, we expend activity against mechanical friction, hysteresis and eddy currents combined. By varying the speed of rotation, and observing the rate at which the activity given to the rotat- ing armature increases, it is possible to separate the three descriptions of losses from each other. 195. Although, as we have seen, the hysteretic loss increases with the i. 6th power of the intensity of flux, yet it is stated to have been found experimentally, that when a mass of iron, such as an armature, is rotated in a sufficiently powerful magnetic 178 ELECTRO-DYNAMIC MACHINERY. field, the hysteretic loss entirely disappears, owing to the sup- posed rotation of all the elementary molecular magnets about their axes during the rotation of the armature without losing parallelism, and, consequently, without any molecular oscil- lation and expenditure of magnetic energy as heat. So far as experiments have yet shown, this critical intensity in the iron is above that which ordinary dynamo or motor armatures attain, so that under practical conditions, the i.6th power of the maximum intensity determines the hysteretic loss. 196. From an examination of the formula expressing the hysteretic activity in the armature, it is evident that the activity might be decreased by a decrease either in the number of poles, the speed of revolution, the flux density, or the hys- teretic coefficient. Since, however, in any machine the first three factors are practically fixed, it is important that the remaining factor, or hysteretic coefficient, should be kept as low as is commercially possible. For this reason, whenever the hysteretic loss is a considerable item in the total losses of the generator, care is taken to select the magnetically softest iron commercially available, in which the hysteretic coefficient is a minimum. 197. We have already referred to the increase in tempera- ture of the edges of the field-magnet poles during the operation of a dynamo armature, and have ascribed the cause of such heating to the development of eddy currents locally produced there. It is to be remarked, however, that some of the heat in such cases may usually be ascribed to true hysteretic changes in magnetization. CHAPTER XVIII. ARMATURE REACTION AND SPARKING AT COMMUTATORS. 198. In the operation of a dynamo-electric generator, con- siderable difficulty is frequently experienced from the sparking which occurs at the commutator, that is to say, instead of the current being quietly carried off from the armature to the external circuit, a destructive arc, which produces burning, occurs between the ends of the brushes and the commutator segments. The tendency of this sparking, unless promptly checked, is to grow more and more marked from the mechani- cal irregularities produced by the pitting and uneven erosion FIG. 149. GRAMME-RING ARMATURE IN BIPOLAR FIELD ON OPEN CIRCUIT. of the commutator segments. It becomes, therefore, a matter of considerable practical importance to discuss the causes of sparking at the commutator, and the means which have been proposed, and are in use, to overcome the difficulty. Ipp. When a Gramme-ring armature, such as that shown in Fig. 149, is rotated on open circuit, in a uniform bipolar field, the brushes, when placed on the commutator, must be kept at diametrically opposite points corresponding to the line n n. If applied to the commutator at any other points, sparking will probably occur, although the armature is on open circuit. The reason for this is seen by an examination of the figure, which represents a pair of coils C, C, about to undergo com- 179 i8o ELECTRO-DYNAMIC MACHINERY. mutation ; i. e., about to be transferred by the rotation of the armature from one side of the brush to the other, and being short circuited by the brushes, as they bridge over the adjacent segments of the commutator to which their ends are connected. Since the coils C, C', in the position shown, embrace the maximum amount of flux passing through the armature, there will be no E. M. F. induced in them, and, consequently, there will be no current set up during the time of short circuit under the brushes. In other words, the prime condition for non- sparking at the commutator is that the coils shall be short FIG. 150. GRAMME-RING ARMATURE WITH BRUSHES DISPLACED FROM NEUTRAL LINE. circuited only at the time, and in the position, where no E. M. Fs. are being generated in them. 200. If the brushes be advanced into a position such as that represented in Fig. 150, so that the diameter of commutation : i. e., the diameter of the commutator on which the brushes rest, is shifted from B, B ', to a new position, powerful sparking will, probably, be set up, for the reason that in this position the rate of change, in the flux linked with these coils, is consider- able, and, consequently, there is a considerable E. M. F. induced in them, so that, when they are short circuited by the brushes, heavy currents tend to be produced in the circuit of these coils according to Ohm's law. If, for example, a bipolar Gramme-ring armature gives passage to a total useful flux of i megaweber, and there are 1,000 turns on the armature, and 50 segments in the commutator, then, if the speed of rota- tion be 10 revolutions per second, the E. M. F. set up between the brushes will be 10 X 1,000 x 1,000,000 100,000,000 = IOO volts, ARMATURE REACTION. l8r and, since there are 25 commutator bars on each side of the diameter of commutation, there will be an average of four volts per coil of 20 turns. If the resistance of each coil be o.oi ohm, the current which tends to be set up in a short- circuited coil having the average E. M. F. is 4 = 400 amperes. o.oi 201. It now remains to be explained how the existence of a powerful current in the short-circuited coil will produce violent sparking at the commutator. It is well known that the presence of a spark indicates a higher E. M. F. than the four volts, which we have assumed in this case is to be gen- erated in the short-circuited coil. The increase in the voltage at the moment of sparking is due to what is called the induct- ance of the coil. At the moment of short circuiting the coil by the bridging of the brushes across the two adjacent commutator segments, a powerful magnetic flux is set up in the coil, owing to its M. M. F. This flux is so directed through the coil as to set up in it an E. M. F. which opposes the development of the current. On the cessation of the current, owing to the breaking of the coil's circuit at the commutator, the coil is rapidly emptied of flux, and a powerful E. M. F. is set up in the same direction as the current, sufficiently powerful to produce sparking between the brush and the edge of the segment it is leaving. The E. M. F. so generated during the filling or emptying of the loop by its own flux is called the E. M. F. of self-induction. f=j 202. Fig. 151 diagrammatically represents the flux produced in the short-circuited coils C', C, by the M. M. F. of the current produced during the short circuit. This flux passes princi- pally through the air-gap and neighboring pole face, a small portion passing through the air in the interior of the armature between the core and the shaft. The greater the flux produced by the coil, the greater will be the E. M. F. developed in the coil, when the flux is suddenly withdrawn. The capability of a conducting loop or turn for producing E. M. F. by self- induction is called its inductance, and may be measured by the linkage of flux with the turn per ampere of the current it carries, that is, by the amount of flux passing through it. 1 82 ELECTRO-DYNAMIC MACHINERY. 203. We have thus far considered the coils C, C ', as being composed of a single turn. If, however, each of these coils is composed of two turns, and the same current strength passes through each of these turns, then the M. M. F. of the coil will be doubled, and, if the iron in the armature core and pole face, is far from being saturated, the amount of flux passing through the two turns will be twice as great as that which pre- viously passed through one. When this flux is introduced or removed it will generate E. M. F. in both turns, and, conse- quently, will induce twice as much E. M. F. in the two turns together as in a single turn. The inductance of the* coil, or its capacity for developing E. M. F. by self-induction, is thus four times as great with two turns as with one, because there is FIG. 151. DIAGRAMMATIC REPRESENTATION OF FLUX IN MAGNETIC CIRCUIT OF SHORT-CIRCUITED COIL. double the amount of flux, and double the number of turns receiving that flux. 204. It is evident, therefore, that the inductance of a coil increases rapidly with the number of its turns, and although not quite proportionally to the square of the number, since, with a large number of turns, although the M. M. F. is in- creased in proportion to the number, yet the amount of flux passing through each of the turns, owing to leakage, is not the same. The E. M. F. of self-induction generated in each coil depends: (i.) Upon the E. M. F. induced in the coil by the revolution of the armature. (2.) Upon the resistance of the coil, or its capability for allowing a large current to flow through it. (3.) Upon the inductance of the coil, or its capability for ARMATURE REACTION. 183 permitting that current to induce a powerful E. M. F. when the circuit is made or broken. The E. M. F. induced on making the circuit at the commu- tator is advantageous, since it checks the development of the current ; the E. M. F. induced on breaking the circuit is harmful, since it enables a spark to follow the brush. If, therefore, no sparking is to occur in a dynamo-electric machine at no load, the brushes must rest on segments, con- nected with coils in which no E. M. F. is being generated. 205. If the external circuit of the armature be closed through a resistance, so that current flows through the arma- ture coils and brushes into the external circuit, the preceding conditions become considerably modified. Fig. 152 represents the condition of affairs in which a current FIG. 152. DIAGRAMMATIC REPRESENTATION OF MAGNETIC CIRCUIT OF ARMATURE. is flowing through the armature coils, and the brushes are resting on the commutator, with the diameter of commutation at the neutral points, or in a plane at right angles to the polar axis. In this figure the direction of the armature rotation is the same as shown in previous figures; namely, counter-clockwise. Here the flux produced by the M. M. F. of the armature coils takes place in the circuits digrammatically indicated by the curved arrows. The magnetization, therefore, produced by the current circulating in the armature turns, is a cross mag- netization^ or a magnetization at right angles to the magnetiza- tion set up by the field flux. The field flux through the poles and armature is diagrammatically indicated in Fig. 153, where the north pole is assumed to be situated at the left-hand side 1 84 ELECTRO-D YNAMIC MA CHINER Y. of the figure, and the average direction of the field flux is at right angles to the average' direction of the armature flux. An inspection of Figs. 152 and 153 will show that at the leading edges of the pole-piece, Z, Z', that is, at those edges of the pole- piece which the armature is approaching, the direction of the flux produced by the armature is opposite to that of the FIG. 153. DIAGRAMMATIC REPRESENTATION OF FIELD FLUX PASSING THROUGH ARMATURE. flux produced by the field, and that, consequently, the effect of superposing these fluxes is to weaken the flux at the leading edge as is shown in Fig. 154. On the contrary, at \h^ following edges F' and F t of the pole-pieces, the direction of the armature FIG. 154. EFFECT OF SUPERPOSING ARMATURE FLUX ON FIELD FLUX. flux coincides with the direction of the field flux, and the super- position of these two fluxes will have the effect of intensifying the flux at the following edges. Consequently, the neutral line in the armature, or the line symmetrically disposed as regards the entering and leaving flux, will no longer occupy the posi- tion N, N, at right angles to the polar axis, but will occupy a position n n' ; therefore, in order to set the brushes so that they may rest upon commutator segments connected with coils ARMATURE REACTION. 185 having no E. M. F. generated in them, it is necessary to bring the diameter of commutation into coincidence with the neutral line, or to give the. brushes a lead; i. e., a forward motion, or in the direction in which the armature is rotating. 206. This, however, will not in itself, as a rule, prevent sparking, for the reason that induced E. M. Fs. are produced in the coil under commutation at load, even although, the coil being commuted has no resultant E. M. F. set up by rotation. This induced E. M. F. is due to the inductance of the coil and FIG. 155. REVERSAL OF CURRENT IN ARMATURE COILS DURING COM- MUTATION. to the load current which it carries. An inspection of Fig. 155 will show that as the coil C, approaches the brush B, the current in the coil, as shown by the arrows, is directed upward on the side facing the observer; while on leaving the brush, after having undergone commutation, the current in the coil will be flowing in the opposite direction or downward. The sudden reversal of the current in the coil under commutation produces a sudden reversal of the magnetic flux linked with the local magnetic circuit of that coil, and this sudden change in the magnetic flux through the coil induces in it a powerful E. M. F., causing a spark to follow the brush. In order that no spark shall be produced from this cause, it is necessary that before the brush leaves the segment the cur- rent in the coil shall have become reversed, and will therefore be flowing in the same direction as that which will pass through it during its passage before the pole face N. In order to effect this it is necessary to bring the coil that is being commutated into a field of sufficient intensity to induce in it, while short circuited, a current strength equal and opposite to that which 186 ELECTRO-DYNAMIC MACHINERY. passes when it first becomes short circuited by the brush. It is not, therefore, usually possible to keep the brushes on the neutral line as shown in Fig. 154, at n n', but their lead must be increased, until the coil under commutation is in a sufficiently powerful field beneath the pole face to produce, or nearly pro- duce, this reversal of current. The amount of lead necessary to give to the brushes in order to effect this will depend upon the inductance of the coils, and also on the strength of the current in the armature. 207. The lead of the brushes, besides tending to reduce sparking at the commutator, tends to diminish the E. M. F. generated by the armature, for two distinct reasons : First, because it connects in series armature windings in which the E. M. Fs. are in opposition, as will be seen from an examina- tion of Fig. 156; and second, because the M. M. F. of the armature coils over which the lead has extended exerts a C. M. M. F. in the main magnetic circuit of the field coils, thereby tending to reduce the useful flux passing through the armature. This effect is called the back-magnetization of the armature. Cross-magnetization, therefore, exists in every armature as soon as it generates a current, but back-mag- netization only exists when a current is generated in the arma- ture, and the diameter of commutation is shifted from the neutral points. 208. The conditions which favor marked sparking at the commutator of a generator are, therefore, as follows; namely, (i.) A powerful current in the armature; /. ^., the sparking increases with the load. (2.) A large number of turns in each coil connected to the commutator; i. e., the sparking increases with the inductance. (3.) A great distortion of the neutral line through the armature, or a powerful armature reaction. (4.) A high speed of rotation of the armature, since the current in the coil has less time in which to be reversed during the period of short circuiting. (5.) A nearly closed magnetic circuit for each coil; /. e., a small reluctance in the magnetic circuit of each coil, whereby the inductance of the coil is increased. ARMATURE REACTION. 187 The conditions which favor quiet commutation, or the absence of sparking, are as follows; namely, (i.) A small number of turns in each commuted coil, or a large number of commutator bars. (2.) Decrease of current strength through the armature. (3.) A lead of the brushes. (4.) A powerful field, or a high magnetic intensity in the entrefer, due to the M. M. F. of the field magnets. (5.) A large reluctance in the magnetic circuit of each coil. 209. An inspection of Figs. 152-154 will render it evident that the effect of superposition of the armature M. M. F. upon the M. M. F. of the field magnets, is to weaken the intensity of the field flux at the leading edges of the pole- pieces, and to strengthen the intensity at the following edges of the pole-pieces. At the same time, it is necessary to advance the brushes; /. e., the diameter of commutation, so as to bring the commuted coils under the- leading edges of the pole-pieces, in order that they may receive a sufficiently powerful intensity of field flux to enable the armature current to be reversed in the coil under the brushes, and sparkless commutation thus to be effected. If, however, the number of ampere-turns on the armature; i. e., its M. M. F. at a given load, be sufficiently great, the field flux at the leading edges of the poles will be so far weakened, that the intensity left there will be insufficient to effect sparkless commutation, no matter how great the lead may be. In other words, the flux from the armature will overpower the field flux, in any position of the brushes. This will take place when the M. M. F. due to half the turns of active conductor on the armature, covered by the pole face, is equal to the drop of magnetic potential in the field flux through the entrefer. 210. The magnetic intensity under the edge of the lead- ing pole-piece will be zero, when the magnetic difference of potential between this polar edge and the armature core, immediately beneath, is zero. The magnetic difference of po- tential across the gap at this point due to the field flux alone, will be the magnetic drop in the entrefer, or ($>d, where (E, is the field intensity in the gap with no current in the armature, 188 ELECTRO-DYNAMIC MACHINERY, and d, the length of the entrefer in cms. The total M. M. F. of the armature, along the arc of one pole, will be -- wp, where wp is the number of turns covered by the pole, and this will be the total difference of potential in the magnetic circuit of the armature. Assuming that the armature is not operated near the intensity of magnetic saturation, almost the entire reluctance in the armature circuit will be in the entrefer. Fig. 156 represents diagrammatically the magnetic circuit of a Gramme-ring armature. The reluctance between be and cd, in the field pole, also between ef and fa, in the armature, will be comparatively small, so that the total magnetic difference of potential developed by the armature will be expended in the two air-gaps ab and de, half the M. M. F. of the turns beneath the pole face being expended in each air-gap. Strictly speak- FIG. 156. MAGNETIC CIRCUITS OF GRAMME-RING ARMATURE DUE TO ITS" OWN M. M. F. ing, the magnetic flux produced by the armature will not be confined to the paths indicated by the dotted arrows, but will pass across the air-gap at all points not situated on the neutral line cf. The above principles may be relied upon, however, to a first approximation. 211. In order, therefore, that a smooth-core armature should be capable of sparkless commutation, the M. M. F. of the turns on its surface, covered by each pole, should be somewhat less than the drop of magnetic potential in each air-gap, so as to leave a residual flux from the field in which to reverse the armature current in the coil under commutation. For example, if each air-gap or entrefer has a length of 2 cms., and the intensity in the air is 3,000 gausses, the drop of potential in the air will be 6,000 gilberts. If the number of ARMATURE REACTION. 189 Gramme-ring armature turns, covered by one pole-piece, is 200, then a current of 80 amperes from the armature will repre- sent 40 amperes on each side, and the M. M. F., produced by this current will be - - x 40 X 200 = 10,056 gilberts, and half of this amount, or 5,028, being less than the drop of field flux in the gap, should leave a margin for sparkless commu- tation. 212. Although the preceding rule enables the limit of current for sparkless commutation, on a smooth-core armature, to be predicted under the conditions described, yet it by no means follows that sparkless commutation must necessarily be obtained if the M. M. F. of the armature lies within this limit. If, for example, the number of commutator segments is very small, the inductance of each segment may be considerable, and a powerful flux intensity may be required to reverse the current under the brush in the presence of such inductance. No exact rules have yet been formulated for the determina- tion of the inductance in a coil with which a given current strength, speed of rotation, and field intensity, shall render sparkless commutation possible. 213. The methods in general use for the suppression of sparking may be classified as follows: (i.) Those which aim at the reduction of inductance in the commuted coils. (2. ) Those which aim at the reduction of the current strength passing through the coil during its short circuit by the brush, and, therefore, at the reduction of the current strength which must be reversed before the short circuit is over. (3.) Those which aim at the reduction of the armature reac- tion, so as to reduce its influence in weakening the field in- tensity in which the coil is commuted. 214. There are two methods for reducing the inductance of the armature coils. The first is to employ a great number of commutator seg- ments, thus decreasing the number of turns in each coil under commutation. It is evident that an indefinitely great number *9 ELECTRO-DYNAMIC MACHINERY. of commutator segments would absolutely prevent sparking. A great number of commutator segments 'is, however, both troublesome and expensive, so that in practice a reasonable maximum cannot be exceeded. The second method for lessening the inductance of the arma- ture coils differs from the preceding only in the method of connection. It consists in providing two separate windings- or sets of coils ; or, as it is sometimes called, in double -winding the armature. The two separate windings are insulated from each other, but are connected to the commutator at alternate segments, so that the brush rests coincidently upon segments- that are connected with each winding. Each winding there- fore, furnishes half the current strength, and the effect of the inductance in each coil is reduced. 215. When the brushes are not so shifted as to bring the diameter of commutation into coincidence with, or even in ad- vance of, the neutral point, the coil under commutation will be situated in a magnetic flux in the wrong direction; /'. X 160 > ^ / ^ B , f 130 / 120 / / j * 90 / " 80 // ~j i / si / It m A/l / / / / P 7 10 2 30 40 60 J50 70 80 90 .100 UO 120 130 14 VO.LTS ON FIELD FIG. 168. CHARACTERISTIC CURVE OF SHUNT-WOUND DYNAMO. 185 volts, with 140 volts on the magnets. Here also the E. M. F., , may be expressed by the Frolich equation, E = - : - , e being the pressure on the field magnets; taking x -j- yc the two observations, 120 = and 174 = we ^+ I20/ find x = 0.43 and jy = 0.0022, from which the general equation becomes, ^ e E = 0.43 -j- 0.0022 e volts. REGULA TION OF D YNAMOS. 2 1 3 The locus of this equation is represented by the dotted line, which practically coincides with the full line A B C t of observation. 253. When, therefore, two reliable observations have been made of the E. M. F. generated by an armature, at observed exciting current strengths, or pressures, situated not too closely together, it is possible to construct the characteristic curve throughout to a degree of accuracy sufficient for all practical purposes. The Frolich equation, by which this is possible, is a con- sequence of the fact that the reluctance of the air paths in the magnetic circuit of a generator is. constant, while the reluc- tivity of the iron in the circuit is everywhere capable of being expressed by the formula v = a -J- b OC (Par. 59) ; and, consequently, the total apparent reluctance of the armature takes the form x -\-y&, and the useful flux passing through or the armature $ = , &, being the magnetomo- x ~r y v tive force in gilberts, but F, may be expressed in ampere- turns, in amperes or in volts applied to the coils. 254. When the characteristic curves of a shunt machine have been obtained, it is a simple matter to determine what the series winding must be in order to properly compound it, either for the drop in the armature, or for the drop in any given portion of the external circuit as well. Thus, suppose it be required to determine the series winding for the machine whose characteristic curve is represented in Fig. 168. If the E. M. F. required at the terminals of the machine be 120 volts at all loads, and if the drop in the armature, due to its resistance at full load, as well as the resistance of its series coil, and to any shifting of the brushes that may be necessary, amounts in all to 10 volts, then the full-load current must supply the M. M. F. necessary to carry the E. M. F. from 120 to 130 volts, equivalent to raising the pressure by 8 volts from. 70 to 78 volts on the shunt winding. The increase in current strength from the shunt winding represented by these eight volts multiplied by the number of turns in the shunt winding, gives the M. M. F. required, and the full-load current must 214 ELECTRO-DYNAMIC MACHINERY. pass through a sufficient number of turns to supply this M. M. F. in its series coil. 255- I n a ^ commercial circuits, electro-receptive devices require to be operated either at Constant current or at constant pressure. The majority of such devices are designed for con- stant pressure; such, for example, are parallel or multiple- connected incandescent lamps and motors. Some devices, however, require to be operated by a constant current. Of these, the arc lamp is, perhaps, the most important. Series- FIG. 169. SHUNT FIELD AND RHEOSTAT. connected incandescent lamps, and a few forms of motors, also belong to this class. 256. In order to maintain a constant pressure at the ter- minals of a motor with a varying load, it is necessary, in order to compensate for the drop of pressure in supply con- ductors, that the pressure at the generator terminals either be kept constant, or slightly raised as the load increases. With shunt-wound machines this regulation requires to be carried out by hand, a rheostat being inserted between the field and the armature, as shown in Fig. 169. 257. Various forms are given to rheostats for such purposes. They consist, however, essentially of coils of wire, usually iron wire, so arranged as to expose a sufficiently large surface to the surrounding air, as to enable them to keep within safe limits of temperature under all conditions of use. The resist- ance is divided into a number of separate coils and the ter- minals of these are connected to brass plates usually arranged REGULATION- OF DYNAMOS. 215 in circles, upon the external surface of a plate of slate, wood or other non-conducting material, so that, by the aid of a handle, a contact strip can be brought into connection with any one of them. The coils being arranged in series, the movement of the handle in one direction adds resistance to the field circuit, and in the opposite direction, cuts resistance out FIGS. 170 AND 171. FORMS OF FIELD RHEOSTAT. of the circuit. Figs. 170 and 171 show different forms of field rheostats, with wheel controlling handles. In some rheostats the resistance wire is embedded in an enamel, which is caused to adhere to a plate of cast iron. This gives a very compact form of resistance ; for, the intimate contact of the wire with the iron plate, together with the large free surface of the plate, enables the heat to be readily dissipated and prevents any great elevation of temperature from being attained. Two of such rheostats are shown in Fig. 172. 258. Compound-wound machines can be made to regulate automatically, and do not require to have their E. M. F. 2i6 ELECTRO-DYNAMIC MACHINERY. adjusted by the aid of a field rheostat. For this reason they are very extensively used in the operation of electric motors. Series-wound machines are invariably used for operating arc lamps in series. Since the load they have to maintain is apt to be variable, such machines must possess the power of vary- ing their E. M. F. within wide limits. Two methods are in use for maintaining constant the strength of current. That in most general use is to shift the position of the collecting brushes on the commutator so as to take off a higher or lower E. M. F. according as the load in the external circuit increases or de- creases. The effect of this shifting will be evident from an inspection of Fig. 156 ; for, if the diameter of commutation be FIG. 172. ENAMEL RHEOSTATS. shifted to the right or left, the E. M. F. in some of the coils- will be opposed to that in the remainder, the difference only being delivered at the brushes. In practice, the diameter of commutation would never reach the position of maximum E. M. F. represented in Fig. 156, and might, on the other hand, rotate through a sufficiently large angle to produce only a small fraction of the total E. M. F. - 259. In all cases where the brushes are shifted through a considerable range over the commutator, care has to be taken to avoid the sparking that is likely to ensue if a certain balance is not maintained between the M. M. F. of the armature and the magnetic intensity in the air-gap. The fact that the current strength through the armature coils is practically constant at REGULATION OF DYNAMOS. 217 all loads, enables this balance to be effectually maintained, when once it has been reached at any load. 260. Series-wound arc-light generators have their armatures wound in two ways ; namely, closed-coil armatures, and open-coil armatures. In the former, all the armature coils are constantly in the circuit, while in the latter, some of the coils are cut out of the circuit by the commutator, during a portion of the revo- lution. The ordinary continuous-current generator for pro- ducing constant pressure is, therefore, a closed-coil armature. Fig. 173 represents diagrammatically a form of open-coil arma- ture winding. The three coils shown are ooanected to a com- FIG. 173. OPEN COIL-WINDING. mon or neutral point o. In the position represented, the coil A, is disconnected from the circuits, the coils B and C, remain- ing in the circuit of the brushes b b' . 261. In closed-coil, series-wound, arc-light generators, the brushes are given a forward lead ; i. e., a lead in the direction of the rotation of the armature. The amount of this lead controls the E. M. F. produced between the brushes. It is essential, in order to prevent violent sparking, that the coil under commuta- tion should be running through an intensity sufficient to nearly reverse the current in the commuted coil during the time of its short circuiting. Since the current strength in the field, and also in the armature, is maintained constant at all loads, it is necessary that the intensity of flux, through which the com- muted coils run, should be uniform, or nearly uniform, at all loads and of the proper degree to effect current reversal. The 2l8 ELECTRO-D YNAMIC MA CHINER Y. M. M. F. of the field magnet, is constant and the M. M F. of the armature is also constant, but the flux produced by the M. M. F. of the armature varies with the position of the brushes and the number of active turns that exist in that portion of the arma- ture which is covered by the pole-piece, on each side of the diam- eter of commutation. The pole-pieces are usually so shaped that as the number of active turns in the armature covered by each pole increase ; /. e., as the load and E. M. F. of the machine increase, the trailing pole corners become more nearly saturated, and by their increasing reluctance check the tendency to increase the flux from the armature, so that an approximate balance between the field flux and the armature flux is main- .FIG. 174. DIAGRAM OF AUTOMATIC REGULATOR CONNECTIONS. tained at all loads. The armature flux always opposes the field flux at the diameter of commutation. The magnetic circuit, therefore, has to be so designed that the armature flux shall never quite neutralize the field flux at this point, but shall always leave a small residual field flux for the purpose of obtain- ing sparkless commutation. 262. The other method, which is employed for maintaining the current strength constant, introduces a variable shunt around the terminals of the field coil, in such a manner that when the current through the circuit becomes excessive, the shunt is lowered in resistance, and diverts a sufficiently large amount of current from the field magnets to lower their M. M F. to the required value. In order, however, to avoid the necessity for making this regulation by hand, it may be effected REGULATION 'OF DYNAMOS. 219 automatically as follows : namely, an electromagnet, situated in the main circuit, is caused by the attraction of its armature, on an increase in the main current strength, to bring pressure upon a pile of carbon discs. This pile of discs offers a certain resistance to the passage of a current, the resistance of the pile diminishing as the pressure upon it increases. The pile is placed as a shunt around the field magnet, so as to divert from the magnet a portion of the main current strength. When the attraction on the armature of the electromagnet increases the pressure on the pile, the resistance of the shunt path is dimin- ished, and less current flows through the field magnets, as represented in Fig. 174, where -S", is the series winding, shunted by the carbon pile P, and M t is the controlling magnet inserted in the main circuit. 263. Both the above methods are capable of compensating not only for variations in the resistance, or C. E. M. F. of the circuit, but also for variations in the speed of driving. In this respect the compensation is more nearly complete than that of constant pressure machines; for, compound-wound gener- tors can maintain a constant pressure under variations of load, but not under variations of speed. CHAPTER XXI. COMBINATIONS OF DYNAMOS IN SERIES OR IN PARALLEL. 264. When a system of electric conductors is supplied from a central station, it is evident, that if the load on the system was constant, a single large generator unit would be the simplest and cheapest source of electric supply, except, per- haps, on the score of reserve, in case of, accidental breakdown. In practice, however, the load is never constant, and, there- fore, the capacity of the generating unit is always consider- ably less than the total activity that has to be supplied at the busiest time. Moreover, engines and generators are neces- sarily so constructed, that while they may be comparatively very efficient when working at full load, they are far less effi- cient when working at a small fraction of their load, so that it is desirable to maintain such units as are in use, at full load under all circumstances. This consideration of wasted power, in operating large units at light loads, applies with less force to plants operated by water power, but, even in this case, it is usually found uneconomical to operate a large generator, for many hours of a day, when a smaller one would be quite com- petent to supply the load. 265. The generating units in a central station are, there- fore, so arranged that they may be individually called upon at any time to add their activity to the output of the station. Electrically, these generators must be connected either in separate circuits, or in series or in parallel in the same circuit. The method of connecting dynamos in series, so far as con- tinuous-current circuits are concerned, is only employed for arc lamps operated in series. When a great number of arc lamps have to be supplied over a given district, they are usu- ally arranged in different circuits, each circuit containing ap- proximately the same number of lamps. Each such circuit is then connected, as a full load, to a single arc-light generator. DYNAMOS IN SERIES OR IN PARALLEL. 221 When, however, owing to some failure of continuity in a cir- cuit, it is found impossible to operate two circuits independ- ently, it is sometimes desirable to connect the two circuits to- gether at some point outside the station, and to operate the increased load of lamps by two or more dynamos connected in series. 266. Generators are also connected in series when it is de- sired to employ, on the external circuits, the sum of the pres- sures of those generators. For example, in cases of the trans- mission of power to considerable distances, a high pressure in the conducting circuit is economically necessary. Whenever this pressure is greater than that which can be readily obtained from a single continuous-current generator, it is possible to connect two or more generators in series, so as to obtain the sum of their pressures. Thus, five generators, each supplying 500 volts pressure, will, when connected in series, supply a total pressure of 2,500 volts. The plan is rarely followed. 267. As a modification of the above plan, which is rarely adopted, five-wire, and three-wire systems, employing respec- tively four and two generators in series, are in use. The five- wire system, although employed in Europe, has not found favor in the United States. The three-wire system, however, is extensively employed. In this system, two generators of equal voltage, say 125 volts, are connected in series so as to supply a total pressure of 250 volts. Such a pressure is cap- able of operating incandescent lamps in series of two. To enable single lamps, however, to be operated independently, a third or neutral wire is carried through the system from the common connection point of the two generators, and the dis- tribution of lamps, on the two sides of the system, is so arranged that the equalizing current, passing through the neutral wire, is small, and nearly as many lamps are operated at any one time on the positive, as on the negative side of the system. A pair of generators connected for three-wire service, therefore, con- stitutes a generating unit in a three-wire central station. 268. Series-generators are never, in practice, connected in parallel. Shunt-wound and compound-wound machines are capable of being connected in parallel, and most central sta- 222 ELECTRO-DYNAMIC MACHINERY. tions arrange the generators in such a manner that they may be connected to, or disconnected from, the mains according to the requirements of the load. 269. Central stations, supplying incandescent lamps in par- allel, usually employ shunt-wound generators, for the reason that the efficient and economic operation of the lamps requires a nearly uniform pressure at all lamp terminals. Not only does the uniformity in the amount of illumination from an incandescent lamp depend upon the uniformity of the pressure supplied at its terminals, very small variations in the pressure markedly varying the intensity of light, but also such variations of pressure materially affect the life of the lamp. Thus a 5o-watt, 16 candle-power, incandescent lamp, intended to- be operated at a pressure of 115 volts, would have its probable life reduced by about 15 per cent., if operated steadily at 116 volts, and reduced by about 30 per cent, if operated steadily at 117 volts pressure. For this reason the pressure in the street mains supplying the lamps requires constant careful at- tention. Since it would be impossible to obtain at the mains a sufficient uniformity of pressure, under all conditions of load, by compound winding, and hand regulation would still be re- quired, there is an advantage in dispensing altogether with, compound winding, and resorting to hand regulation, with shunt winding, for the entire adjustment. 270. When two or more generators are connected in parallel, it becomes necessary that the electromotive forces they supply shall be equal, within certain limits. If, for example, two- generators are connected in parallel, each working at half load, then if the drop of pressure in each generator armature at full load is two per cent, of its total E. M. F., it is evident that it is only necessary to increase the pressure of one generator twa per cent, above that of the other, in order that the pressure at the brushes of the first shall be equal to the E. M. F. generated in the armature of the second. Under these circumstances na current will flow through the armature of the second machine, and all the load will be thrown on the first machine. If the E. M. F. of the first machine be still further raised, the pres- sure at its brush-es-will be greater than the E. M. F. in the DYNAMOS IN SERIES OR IN armature in the second, and a current will pass through the second armature in a direction opposite to that which it tends to produce, and, therefore, in a direction tending to rotate the second generator as a motor. In other words, the control of pressure between the two machines must be within closer limits than two per cent. Early in the history of central station practice, difficulties were experienced in controlling the pressure of multiple-connected dynamos within limits nec- essary to avoid this unequalizing action, but at the present time, the governing of the engines and the control of the field magnets are so reliable, that this difficulty has practically dis- appeared. It is important to remember, however, that the larger the generator unit employed, and the smaller the drop in pressure taking place at full load through its armature, the narrower is the limit of speed or regulation, in which inde- pendent units will equalize their load, although as a counter- acting tendency, the larger will be the amount of power which, in case of disequalizing, will be thrown upon the leading ma- chine tending to check its acceleration. 271. Compound-wound generators are almost invariably em- ployed for supplying electric currents to street railway sys- tems. This is principally for the reason that the load in a street railway system is necessarily liable to sudden and marked fluctuations, and these fluctuations would be liable to produce marked variations in the pressure at the generator terminals, if the machines were merely shunt wound. Such generators are operated in parallel units. Here, as in the case of shunt- wound machines, it is necessary that the E. M. F. generated by each machine should be nearly the same, in order that the load should be equally distributed; but instability of control is greater in the case of compound-wound machines than in the case of shunt machines, for the reason that when one of a number of parallel-connected shunt-wound machines acceler- ates, and thereby rises in E. M. F., so as to assume an undue share of the load, the drop in the armature thereby increases, and tends to diminish the irregularity, so that not only does the greater load tend to retard the engine connected to the leading machine, but also the drop in its armature aids in equalizing the distribution. 224 ELECTRO-D Y NAM 1C MA CHINER Y. In the case of compound-wound machines in parallel, any acceleration tends, as before, to increase the E. M. F. of the generator and, therefore, its share of the load, but the series coil of the compound winding being excited by the additional load, tends to increase the output of the machine, and, there- fore, the governing of the engine has to be entirely depended on to prevent disequalization. Of recent years, however, the plan has been widely adopted of employing an equalizing bar between compound-wound generating units operated in par- f 1 B B FIG. 175. PARALLEL CONNECTION OF COMPOUND-WOUND GENERATORS. allel. The connections of an equalizing bar are shown in Fig. .175. Here the two compound-wound generators are connected to the positive and negative omnibus bars, or bus bars, as they are generally termed, AA and BB, while the series coils are connected together in parallel by the equalizing bar QQ. It is evident that the equalizing bar connects all series coils of the different dynamos in parallel, so that any excess of current, supplied by the armature. of one machine, must necessarily ex- cite all the generators to the same extent. 272. When a number of compound-wound generators are running in parallel, and the load increases, so that it is desired to add another unit to the generating battery of dynamos, the engine connected with the new unit is brought up to speed, and the shunt field excited. This brings the E. M. F. of the DYNAMOS IN SERIES OR IN PARALLEL. 225 machine up to nearly 500 volts. Its series winding is then connected in parallel with the series winding of the neighbor- ing machines, by the switch on the equalizing bar, so that its excitation is then equal to that of all the other machines. The E. M. F. of the machine is then brought up slightly in excess of the station pressure by the aid of the field rheostat, and, as soon as this is accomplished, the main armature switch is closed, thus connecting the armature with the bus bars. The load of the machine is finally adjusted by increasing the shunt excita- tion, with the aid of the rheostat, until the ammeter connected with the machine shows that its load is approximately equal to that of the neighboring generators. The same steps are taken in reverse order to remove a generator from the circuit. 273. Fig. 176 is a diagram of a street-railway switchboard for two generators. It is customary, both for convenience and simplicity, to erect switchboards in panels, one for each generating unit, so that each panel controls a separate unit, and is in immediate connection with its neighbors. In the figure, the two panels are designated by dotted lines, the one on the left, active, and the one on the right, out of use. On each panel there are two main switches, P and JV, for the posi- tive and negative armature terminals. A smaller switch, not shown, is usually located on the right of each panel, and is for lighting up the station lamps from any panel and its connected machines, at will. R, is a shunt rheostat, placed at the back of the panel, with its handle extending through to the front, and S, is a small switch for opening and closing the shunt circuit of the field coils through the rheostat, 1?. A, is the generator ammeter, brought into use by the switches P and JV, and T, is the automatic circuit-breaker for the panel. This electro- magnetic circuit-breaker, opens the circuit of the machine when the current strength, owing to a short circuit or other abnormal condition, becomes dangerously great, thereby reliev- ing the generator of the strain. The switch connected to the equalizing bar E is not placed in this instance, on the panel, but is mounted close to the generator with the object of diminishing the amount of copper conductor required. Each panel is also provided with a voltmeter connection and lightning arrester, which have been omitted here for the sake of simplicity. 226 EL E C TR 0-D YNA MIC MA CHINER Y. 274. The operations for introducing a unit into the battery of generators in this case, is as follows : the generator is brought up to speed, the equalizing switch is closed, % thus connecting the series coils of the machines in parallel with the machines in use. The positive main switch P, is next closed, connecting V EQUALIZING BUS FIG. 176. DIAGRAM OF SWITCHBOARD CONNECTIONS FOR TWO COMPOUND- WOUND GENERATORS. one side of the armature to ground and to return track feeders. The field switch S, is next closed, and the E. M. F. of the machine brought up to slightly above station pressure by the aid of the rheostat R ; finally, the negative main switch N, is closed, throwing the armature into the battery, and the load is DYNAMOS IN SERIES OR IN PARALLEL. 22^ adjusted by the rheostat R, in accordance with the indications of the ammeter A. 275 Another arrangement for railway switchboards consists in mounting the three switches, in close proximity to each other and attaching a single handle to the three blades, so that the three connections may be made or broken by a single operation. When the railway mains are connected with the station by several feeders, it is customary to add another section to the switchboard where switches and ammeters are provided for handling the various feeders. CHAPTER XXII. DISC ARMATURES AND SINGLE-FIELD-COIL MACHINES. 276. Before leaving the subject of generators, it may be well to discuss a few types of generators that do not fall under the 4 FIG. 177. DISC-ARMATURE GENERATOR. types already discussed, and which are occasionally met with in practice. These may be described as ; (i.) Disc-armature machines. (2.) Single-field-coil machines. 228 FIG. 178. DISC ARMATURE. 230 ELECTRO-DYNAMIC MACHINERY, (3.) Unipolar machines, or commutatorless continuous- current machines. 277. Generators employing disc armatures are frequently used in Europe, and although they are very seldom employed in the United States, yet it is proper to describe them as being types of machines capable of efficient use. In one form of disc-armature generator, the armature is devoid of iron, and is built of conducting spokes like a wheel, which revolves in a vertical plane between opposite field-magnet poles. Such a ,. FIG. 179. DIAGRAM OF DISC-ARMATURE WINDING. disc-armature machine is shown in Fig. 177. It is to be observed that the entire machine is practically encased in iron, and is provided with three windows on the vertical face; through these windows the brushes, BB, rest on the commu- tator which is placed on the periphery of the disc, resembling in this respect the generator in Fig. 103. The armature of this machine is shown in Fig. 178 mounted on a suitable support. The radial spokes are of soft iron, and are connected into loops by the copper strips leading to the commutator segments on the periphery. The object of employing iron spokes is to diminish the reluctance of the air-gap. The field poles face DISC ARMATURES. 231 each other, being separated by the disc armature, which revolves between them. Such an armature is evidently capa- ble of being operated at an abnormally high temperature without danger, being constructed of practically fireproof materials. The electric connections of an octopolar machine are represented diagrammatically in Fig. 179. The brushes, it will be observed, are applied at the centres of any adjacent FIG. ISO. DISC-ARMATURE GENERATOR. pair of poles. Another form of the machine is represented in Fig. 1 80. 278. An example of a single-field-coil multipolar dynamo is shown in Fig. 181. This is a quadripolar generator with four sets of brushes. The interior of the field frame, with its pro- jecting pole-pieces and exciting coil, is shown in Fig. 182. It will be seen that the field frame is made in halves, FIG, l8l. COMPOUND-WOUND GENERATOR WITH SINGLE FIELD COIL. FIG. 182. DETAILS OF MAGNET, SINGLE-FIELD-COIL GENERATOR. SINGLE-FIELD- COIL MA CHINES. 233 between which are enclosed the armature and the single field magnetizing coil. Four projections N, N, and S y S, form the pole-pieces of the quadripolar field; that is to say, the magnetic FIG. 183. ARMATURE OF QUADRIPOLAR, SINGLE-FIELD-COIL MACHINE. flux produced by the M. M. F. of the. single coil C C, passes through the field frame into the two pole faces JV and JV, in parallel through the armature into the adjacent pole faces S, S, thus completing the circuit through the field frame. The drum-wound, toothed-core armature, is shown in Fig. 183. CHAPTER XXIII. COMMUTATORLESS CONTINUOUS-CURRENT GENERATORS. 279. Commutatorless continuous-current dynamos are sometimes called unipolar dynamos, although erroneously. It is impossible to produce a single magnetic pole in a magnet,^ since all mag- netic flux is necessarily circuital, and must produce poles, both where it enters and where it leaves a magnet. The fact that these machines are capable of furnishing a continuous current without the aid of a commutator, at one time caused consider- able study to be given to them in the hope of rendering them FIG. 184. FARADAY DISC. commercially practicable. The maximum E. M. F. which they have been constructed to produce, appears, however, to have been about six volts, and, consequently, they have practically fallen out of use, although they have been commercially employed for electroplating. 280. Fig. 184 represents what is known as a Faraday disc. This was, in fact, the earliest dynamo ever produced, and was of the so-called unipolar type; for here, a copper disc D, rotated, by mechanical force, about an axis parallel to the direction of the magnetic flux, supplied by a permanent horse- shoe magnet M M, continuously cuts magnetic flux in the same CONTINUOUS-CURRENT GENERATORS. 235 direction, and, consequently, furnishes a continuous E. M. F. between the terminals S, S', without the use of a commutator. 281. The portion of the disc lying between the poles is caused to rotate in a nearly uniform magnetic flux, and with a velocity which depends upon the radius of the disc at the point con- sidered, as well as on the angular speed of rotation. The di- rection of the E. M. F. induced will be radially downward from the axis to the periphery, and, if connection be secured between the axis as one terminal, and the rotating contact or brush as the other terminal, an E. M. F. will be continuously produced in that portion of the disc which lies beneath the poles; or, more strictly, in that portion of the disc which passes through the flux between them and around their edges. If, however, as in Fig. 185, the disc be completely covered by the pole faces, a FIG. 185. FARADAY DISC. radial system of E. M. Fs. will be induced outward in the direc- tions indicated by the arrows, or inward, if the direction of rotation be reversed. If no contacts are applied to the disc, these E. M. Fs. will supply no current, and will do no work. If brushes are applied at the axis, and at any or all parts of the periphery, the E. M. F. can be led off to the external circuit. 282. The value of the E. M. F. will depend upon the angular speed of rotation, the intensity of the magnetic flux, and the radius of the disc. The intensity of the magnetic flux can usually be made much greater by the use of a soft-iron disc instead of a copper disc, thereby practically reducing the reluctance of the magnetic circuit between the poles to that of two clearance films of air, since the reluctance of the iron disc will be negligibly small. 283. If we consider any small length of radius d /, Fig. 186, situated ,at a distance /, from the axis.of the disc, the E. M. F. 236 ELECTRO-DYNAMIC MACHINERY. generated in this element of the disc will be the product of the intensity, the length of the element, and its velocity across the flux. The element will be moving across the magnetic flux of uniform intensity, (B gausses, at a velocity / co centimetres per second, where GO, is the angular velocity of the disc in radians per second. Consequently, the E. M. F. in this element will be: de I &o . dr . B C. G. S. units of E. M. F. The total E. M. F. will be the sum of the elementary E. M. Fs. included in the radius taken from / = 0, to / = Z, the radius of the disc, or the integral of de, in the above equation between Z a the limits / = o, and / = L. This integral is GO (& = e. The E. M. F. from such a disc, therefore, increases as the FIG. i 86 square of the radius of the disc, directly as the speed, and directly as the uniform intensity of the magnetic flux. The same result can be obtained in a slightly different expression, since G? = 2 n , where , is the number of revolutions of the Z 8 disc in a second, e . 27rn(& = 7rZ,' t n(&=:Sn($> where 2 S, is the active surface of the disc. This will also be true if the surface S, instead of extending over the entire face of the disc, extends only from the periphery to some intermediate radius. From this point of view the E. M. F. of the disc is equal to the product of the intensity in which it runs, the number of revolutions it makes per second, and its active sur- face in square centimetres. To reduce this E. M. F. to volts, we have to divide by 100,000,000. 284. There are two recognized types of commutatorless continuous-current dynamos; namely, the disc type and the cylinder type. The outlines of a particular form of the disc type are represented in Fig. 187. Here the shaft S S, usually hori- CONTINUOUS-CURRENT GENERATORS. 237 zontal, carries a concentric, perpendicular disc of copper or iron, rotating in a vertical plane, in the ring-shaped magnetic frame, in a circular groove, through the flux produced by two coils of wire. The general direction of the magnetic flux, through the field frame and disc, is represented by the curved arrows. It will be observed that the magnetic flux will be uniformly distributed so as to pass through the rotating disc at right angles. Brushes rest on the periphery, and on the shaft, of the disc. Inasmuch as the E. M. F. in the disc is radially directed at all points, the brushes for carrying off the current may be as numerous as is desired. These brushes are FIG. 187. DISC TYPE OF COMMUTATORLESS DIRECT-CURRENT GENERATOR. marked b, b, in the figure. A and B, are the main terminals -of the machine, and/, /', the field terminals. 285. If we suppose that the intensity &, is 12,000 gausses, that the radius of the disc is i foot, or 30.48 centimetres, that the active surface on each side of the disc is 2,500 square cen- timetres, and that the speed of rotation is 2,400 revolutions per minute, or 40 revolutions per second, then the E. M. F. obtain- able from the machine will be : 2,500 X 100,000,000 In order to produce an E. M. F. of say 140 volts, such as would be required for continuous-current central-station gen- 238 ELECTRO-DYNAMIC MACHINERY. erators, it would be necessary either to connect a number of such machines in series, or to increase the diameter of the disc, or to increase the speed of rotation. It would, probably, be unsafe to run the disc at a peripheral speed exceeding 200 miles per hour, owing to the dangerously powerful mechanical stresses that would be developed in it by centrifugal force. This important mechanical consideration imposes a limit of speed of rotation and diameter of the disc, taken conjointly. By increasing, however, the active surface of the disc, and, at the same time, working at a safe peripheral velocity, it would FIG. l88. DIAGRAM SHOWING FLUX DENSITY THROUGH DISC ALONG A RADIUS. be possible to construct large disc generators of this type for an E. M. F. of 100 or 150 volts. 286. It should be borne in mind that although such machines- would be capable of producing continuous currents without the use of a commutator, yet the necessity of maintaining efficient rubbing contacts on the periphery of the rapidly-revolving disc introduces a difficulty and waste of power which has hitherto prevented the development of this system, and, probably, accounts for the fact that large machines of this type do not exist. 287. Irregularities in the distribution of magnetic flux over the surface of the disc may give rise to strong eddy currents and waste of power in the same. If the flux be variable along any radius of the disc O B, as represented in Fig. 188, so that the intensity (B, is no't uniform along these lines, this irregu- larity will not produce eddy currents in the disc unless the dis- tribution is different along different radii. In other words, if CONTINUOUS-CURRENT GENERA TORS. 2 39 the distribution of magnetic flux and intensity are symmetrical about the axis of rotation of the disc, the irregularities which exist will only alter the intensity of E. M. F. in different elements of a radius. In Fig. 188, the intensity, instead of being uniform from centre to edge, as indicated by the straight line da c, increases toward the edge, following the line o a b. FIG. 189. CYLINDER TYPE OF COMMUTATORLESS CONTINUOUS-CURRENT GENERATOR. The formula for determining the E. M. F. of the disc is in such case rendered somewhat more complex. 288. If, however, the curve o a b, of flux intensity along different radii is different, so that the distribution of magnetic intensity is not symmetrical about the axis of rotation, then eddy currents will tend to form, the amount of power so wasted depending upon the amount of irregularity, the resis- tivity of the material in the disc, and the load on the machine. FIG. 190. INDICATING DIRECTION OF E. M. F. INDUCED IN REVOLVING CYLINDER. 289. Fig. 189 represents the outlines of a particular form of the second, or cylindrical type of commutatorless continuous- current generator. Here a metallic conducting cylinder cccc, revolves concentrically upon the shaft S S, through the uniform magnetic flux, produced by the field frame surrounding it. Here, however, two sets of brushes bb, b'b ', have to be applied to the edges of the cylinder in order to supply the main ter- Xl* OF TH E MBNIVERSIT ^S 2 40 ELECTRO-DYNAMIC MACHINERY. minals A and B. The terminals of the four circular coils con- stituting the field winding are shown at/, /'. 290. If the magnetic intensity produced by the field is uniform, the E. M. F. will be generated in lines along the sur- face of the cylinder parallel to its axis, as represented in Fig. 190. If v, be the peripheral velocity of the cylinder in centi- metres per second, /, the length of the cylinder in centimetres, and (R the uniform intensity, in gausses, the E. M. F. generated by the machine will be: v /(B e = volts. 100,000,000 Machines of the cylindrical type have been constructed and used for electrolytic apparatus, and give very powerful cur- rents, as compared with ordinary generators of the same dimensions employing commutators. Unsatisfactory as these unipolar machines have so far proved, except in special cases, they are, nevertheless, the only dynamos which have yet been successfully constructed for furnishing continuous currents without the use of a commutator. CHAPTER XXIV. ELECTRO-DYNAMIC FORCE. 291. In discussing the magnetic flux surrounding an active conductor, we have observed in Par. 34, that it is distributed in concentric cylinders around the conductor, as shown in Figs. 27 and 28. It is evident that if a straight conducting FIG. igi. STRAIGHT CONDUCTOR IN UNIFORM MAGNETIC FLUX. wire A B, say / cms. in length, as shown in Fig. 191, be situated in the uniform magnetic flux represented by the arrows, the flux will exert no mechanical influence upon the wire. If, how- ever, the wire carries a uniform current in the direction from t FIG. 192. MAGNETIC FLUX SURROUNDING ACTIVE CONDUCTOR. A to B, then, as is represented diagrammatically in Fig. 192, the system of concentric circular flux, indicated by a single circle of arrows, will be established around the wire, appearing clockwise to an observer looking from A, along the direction in which the current flows, and, as has already been pointed out, this circular magnetic flux will have an intensity propor- tional to the current strength. 241 242 ELECTRO-D YNAMIC MA CHINER Y. 292. If such a conductor be introduced into a uniform mag- netic flux, as is represented in Fig. 193, it is evident that above the wire at C, the direction of the flux produced by the current is the same as that of the field, while below the wire at D y the direction of the flux from the current is opposite to that from the field. Consequently, the flux above the wire is denser, FIG. 193. DIAGRAM SHOWING DIRECTION IN ELECTRO-DYNAMIC FORCE. and that below the wire is weaker, or less dense, than that of the rest of the field. The effect of this dissymmetrical distri- bution of the flux density in the immediate neighborhood of the wire, is to produce a mechanical force exerted upon the substance of the wire, called the electro-dynamic force, tending to move it from the region of densest flux toward the region of weakest flux; or, in the case of Fig. 193, vertically down- FIG. 194. DIAGRAM SHOWING DIRECTION IN ELECTRO-DYNAMIC FORCE. ward, as indicated by the large arrow. If, however, the direc- tion of the current in the wire be reversed, as shown in Fig. 194, and that of the external field remain unchanged, the flux will be densest beneath the wire and weakest above it, so that the electro-dynamic force will now be exerted in the opposite direction, or vertically upward, as shown by the large arrows. ELECTRO-DYNAMIC FORCE. 243 293. If the direction both of the current in the wire and the flux in the external field be reversed, the direction of the electro-dynamic force will not be changed, as is represented in Fig. 195, where the direction of the electro-dynamic force is downward as in Fig. 193, though the direction of the current and the direction of the magnetic field are both reversed. 294. A convenient rule for remembering the direction of the motion is known as Fleming's hand rule. It is, in gen- eral, the same as that already given for dynamos in Par. 81, except that in applying it, the left hand must be used instead of the right. For example, if the hand be held as in the rule for dynamos, if the/orefinger of the left hand shows the direc- tion of the/" lux, and the middle finger the direction of the cur- FIG. 195. DIAGRAM SHOWING DIRECTION IN ELECTRO-DYNAMIC FORCE. rent, then the thumb will show the direction of the motion. It must be remembered, that in applying Fleming's rule, the right hand is used for dynamos in determining the direction of the induced E. M. F., and the left hand for motors in deter- mining the direction of motion. 295. We shall now determine the value of the electro- dynamic force in any given case, on the doctrine of the con- servation of energy. To do this, we may consider the ideal apparatus, represented in Fig. 196, where a horizontal con- ductor E F, moves without friction against two vertical metallic uprights A B, and CD. This conductor is supported by a weightless thread, passing over two frictionless pulleys P, P, and bearing a weight W. If now a current enters the upright A B, and, passing through the sliding conductor E F y leaves the 244 ELECTRO-D YNA MIC MA CHINER Y. upright CD, at C, then, in accordance with the preceding principles, under the influence of the uniform magnetic flux passing horizontally across the bar in the direction of the arrows, an electro-dynamic force will act vertically downwards upon the rod. If this electro-dynamic force is sufficiently powerful to raise the weight W, it will evidently do work on such weight, as soon as it causes the bar to move. Let us suppose that it produces a steady velocity of the bar E F, of v cms. per second, in a downward direction. Then if /, be the FIG. 196. IDEAL ELECTRO-DYNAMIC MOTOR. electro-dynamic force in dynes exerted on the bar, the activity exerted will be, v f centimetre-dynes-per-second, or ergs-per- second. Since 10,000,000 ergs make one joule, this will be an activity of vf 10,000,000 joules-per-second, or watts. This activity will be expended in raising the weight W, assuming the absence of friction. As in all cases of work expended, the requisite activity to perform such work must be drawn from some source, and in this case the source is the electric circuit. 296. When the bar of length / cms. moves with the velocity of v centimetres-per-second, through the uniform flux of den- ELECTRO-DYNAMIC FORCE. 245 sity (&, it must generate an E. M. F. as stated in Par. 82, of e (& / v t C. G. S. units, or &/v volts. 100,000,000 This E. M. F. is always directed against the current in the wire, and is, therefore, always a C. E. M. F. in the circuit. The current of / amperes passing through the rod will, there- fore, do work upon this C. E. M. F. with an activity of e i watts - / watts. 100,000,000 This activity must be equal to the activity exerted mechan- ically by the system, so that we have the equation, vf (B Iv i 10,000,000 100,000,000 From which, . 7 / / - pounds weight. " 10 x 981 X 453-6 If, for example, the rod shown in Fig. 196 had a length of one metre, or 100 centimetres, and moved in the earth's flux whose horizontal component = 0.2 gauss, then if supplied with a uniform current of 1,000 amperes, it would exert a downward force of 0.2 x 100 X = 2,000 dynes; or ap- 10 proximately, 2 grammes weight. 246 ELECTRO-DYNAMIC MACHINERY. 297. We have heretofore considered the wire as lying at right angles to the flux through which it is moved. If, how- ever, the wire A B, lies obliquely to the flux, at an angle ft, as is represented in Fig. 197, then the effective length of the wire, or the projected length of AB, at right angles to the flux will be a b. In symbols this will be / sin /?, and the electro- dynamic force will be / = & / sin /3 dynes. 298. Although such a machine as is represented in Fig. 196 is capable of performing mechanical work, and might be, therefore, regarded as a form of electro -dynamic motor, yet all FIG. 197. WIRE LYING OBLIQUE TO MAGNETIC FLUX. practical electro-dynamic motors are operated by means of conducting loops, capable of rotating about an axis. We shall, therefore, now consider such forms of conductor. 299. If the rectangular loop a a" a'" a"", Fig. 198, placed in a horizontal plane, in a uniform magnetic flux, be capable of rotation about the axis oo, then if a current of i amperes be caused to flow through the loop in the direction a' a" a'" a"", electro-dynamic forces will be set up, according to the preced- ing principles, upon the sides a' a", and a'" a"", but there will be no electro-dynamic force upon the remaining two sides. Under the influence of these electro-dynamic forces, the side a' a", will tend to move upwards, and the side a'" a"", down- wards. The loop, therefore, if free to move, will rotate, and will occupy the successive positions , c and d. At the last named position, the plane of the loop being vertical, although the electro-dynamic force will still exist, tending to move the the side a' a", downwards, and the side a'" a"", upwards, yet ELECTRO-DYNAMIC FORCE. 247 these forces can produce no motion, being in opposite direc- tions and in the same plane as the axis; or, in other words, the loop considered as a rotatable system is at a dead point. 300. It is clear, from what has been already explained, that if the direction of the current in the loop had been reversed while the direction of the field flux remained the same ; or, if the direction of the field flux be reversed with the direction of current remaining the same, that the direction of the electro- dynamic forces would have been changed, tending to move the side a 1 a", upwards and the side a'" a"", downwards, so that the loop would have rotated in the opposite direction until it reached the vertical plane. Consequently, when a loop, lying FIG. 198. LOOP OF ACTIVE CONDUCTOR IN MAGNETIC FLUX. in the plane of the magnetic flux, receives an electric current it tends to rotate, and, if free, will rotate until it stands at right angles to the magnetic flux. 301. An inspection of the figure will show that when the loop is in the plane of magnetic flux, that is to say, when the rotary electro-dynamic force is a maximum, the loop contains no magnetic flux passing through it, while when the loop is in the vertical position, and the rotary power of the electro- dynamic force is zero, it has the maximum amount of flux passing through it. The effect of the electro-dynamic force, therefore, has been to move the conducting loop out of the position in which no flux passes through it, into the position in which the maximum possible amount of flux passes through it, under the given conditions. 248 ELECTRO-D YNAMIC MA CHINER Y. 302. When an active conductor is bent in the form of a loop r such, for example, as is shown in Fig. 199, all the flux pro- duced by the loop will thread or pass through the loop in the same direction, and this direction will depend upon the direc- tion of the current around the loop. If, for example, we con- sider the loop a 1 a" 2 a 3 a\ independently of the magnetic flux into which it is introduced, and send a current of / amperes, in the same direction as before around the loop, the general dis- tribution of the flux around the sides of the loop is represented FIG. 199. DIAGRAM SHOWING COINCIDENCE IN DIRECTION OF FLUX PATHS AROUND A LOOP OF ACTIVE CONDUCTOR. by the circular arrows, from which it will be seen that all the flux passes downward through the loop as represented by the large arrow. If this loop be now introduced into the external magnetic flux, as shown in Fig. 192, it will tend to rotate, until the external magnetic flux passes through it in the same direc- tion as the flux produced by its own current. Generally, therefore, it may be stated that when an active conducting loop is brought into a magnetic field, the electro-dynamic force tends to move the loop until its flux coincides in direc- tion with that of the field. 303. During the rotation of the loop as shown in Fig. 198 from the position a, to the position d, the loop will embrace a certain amount of flux, say webers, from the external field. In other words, in the position d, the loop holds $ webers more flux than in the position a. If the current / amperes, passing through the loop be uniform during the ELECTRO-DYNAMIC FORCE. 249 rotation, then it can readily be shown that the amount of work performed by the loop during this motion is, , * # W := ergs, but this motion comprises only one quarter of a complete revolution. At the same rate the work done in one revolu- tion would be, 4 * $ 4 / $ ergs - ioules. 10 10 x 10,000,000 304. In a bipolar motor with a drum-wound armature on which there are w wires, counted once completely around the periphery, or loops over the surface, there will be ~- times as much work performed in one revolution as though a single loop existed on the surface; the work-per-revolution will, therefore, be 4 / $ w joules. 100, 000,OOO '2 If now the motor makes n revolutions per second, the work performed will be n times this number of joules in a second, or 4 / > n w 2 i $ n w watts. = watts. 100,000,000 *2 100,000,000 Then, as will be shown hereafter, the current supplied at the brushes of the motor will be / = 2 i amperes, if /, be the cur- rent through each loop, so that the activity absorbed by the motor will be, / $ n w watts. 100,000,000 We know that the E. M. F. of a rotating armature is ^) 72 2/ e = volts (see par. 132), 100,000,000 so that we have simply, that the activity absorbed by the motor armature available for mechanical work is e I watts, and this must be true under all conditions, in every motor. When an E. M. F. of E volts acts in the same direction as a current 7 amperes; /. e., drives the current, it does work on the current with an activity of E I watts, the activity being expended by the source of E. M. F. On the other hand, when an E. M. F. of E volts acts in the opposite direction to 250 ELECTRO-DYNAMIC MACHINERY. a current of / amperes, and therefore opposes it, or is a C. E. M. F. to the current, the current does work on the C. E. M. F. with an activity of E I watts, and this activity appears at the source of C. E. M. F. If the C. E. M. F. be merely apparent in a conductor containing a resistance R ohms, as a drop I R volts, the activity E I I* R, and is expended in the resistance as heat. If the C. E. M. F. be caused by electro-magnetic induction, as in a revolving motor armature, the activity E /, is expended in mechanical work, including frictions of every kind. CHAPTER XXV. MOTOR TORQUE. 305. We now proceed to determine the values of the rotary effort of a loop at different positions around the axis. This rotary effort is called the torque. Torque may be defined as the moment of a force about an axis of rotation. The torque is measured by the product of a force and the radius at which it acts. Thus, if in Fig. 200, a weight of /*, pounds, be sus- pended from the pulley F, and, therefore, acts at a radius / feet, the torque exerted by the weight about the axis will be P I pounds-feet. If JP, be expressed in grammes, and /, in centimetres, the torque will be expressed in gramme-centi- metres; and if P, be in dynes and /, in centimetres, the torque 100 LB& FIG. 200. DIAGRAM ILLUSTRATING NATURE AND AMOUNT OF TORQUE. will be expressed in dyne-centimetres. Thus, at A, Fig. 200, the torque about the axis of the pulley Y, is 400 pounds-feet. At B, it is 800 pounds-feet. At C y it is 400 pounds-feet. As an example of the practical application of torque in electric motors, let us suppose that the pulley JP 9 is attached to the armature shaft of a motor, and that the motor succeeds in raising the weight J/", by the cord over the periphery of the pulley, then the motor will exert a torque at the pulley of M I pounds-feet. Thus, if the pulley be 12 inches in diameter = 0.5 foot in radius, and the weight be 100 pounds, then if the thickness of the cord be neglected, the torque 251 252 ELECTRO-DYNAMIC MACHINERY. exerted by the motor will be 100 x 0.5 = 50 pounds-feet, about the shaft, at the pulley. 306. The work done by the torque which produces rotation through an angle /?, expressed in radians, is the product of the torque and the angle. Thus, if the torque r, rotates the sys- tem through unit angle about an axis, the torque does an amount of work = r. If the torque be expressed in pounds- feet, this amount of work will be in foot-pounds. If the torque be expressed in gm.-cms., the work will be expressed in cm.- gms., and finally, if the torque be expressed in dyne-cms, the work will be expressed in cm. -dynes, or ergs. Since there are 2 7t radians in one complete revolution, the amount of work done by a torque r, in one complete revolution will be 2 n r units of work. For example, the motor in the last paragraph, which produced a torque of 50 pounds-feet, would, in one revolution, do an amount of work represented by 50 X 2 TT = 314. 16 foot- pounds. It is evident, in fact, that since the diameter of the pulley is one foot, one complete revolution will lift the weight M, through 3.1416 feet, and the work done in raising a loo-pound weight through this distance will be 314.16 foot- pounds. Similarly, if &?, expressed in radians per second, be the angular velocity produced by the torque, then the activity of this torque will be r GO units of work per second. For example, a motor making 1,200 revolutions per minute, or 20 revolutions per second, has an angular velocity of 20 x 27T = 125.7 radians per second. If the torque of this motor be 10,000 dyne-cms., the activity of this torque; /. ^., of the motor, will be 10,000 X 125.7 = 1,257,000 ergs per second* = 0.1257 watt. 307. A torque must necessarily be independent of the radius at which it is measured. Thus, if a motor shaft is capable of lifting a pound weight at a radius of one foot; /. e., of exerting a torque of one pound-foot, then it will evidently be capable of supporting half a pound at a radius of two feet, or one third of a pound at a radius of three feet, etc. In each case the torque will be the same; /. e., one pound-foot. 308. The torque produced by a loop, situated in a uniform magnetic flux, varies with the angular position of the loop. MOTOR TORQUE. 253 For example, returning to Fig. 198, the torque of the active loop is zero in the position d y and is a maximum in the position a. The electro-dynamic force exerted by the side a' a" will be (B / dynes, and, if the radius at which this acts 10 about the axis /. ^., half the length of the side a' a"", be a cms., then torque exerted by this side will be - - dyne-cms. Similarly, the torque exerted in the same direction around the FIG. 201. DIAGRAM SHOWING SMALL ANGULAR DISPLACEMENT ABOUT ITS AXIS, OF A LOOP IN UNIFORM MAGNETIC FLUX IN ITS PLANE. axis by the side a'" a'", will be also dyne-cms., so that 2 ($> 1 1 a the total torque around the axis will be dyne-cms. If the loop moves under the influence of this torque through a very small angle dp, the work done will be i: d ft = ' - dp, but a d fi = ds, the small arc moved through, as shown in Fie:. 201, so that the work done will be . The 10 amount of flux linked with the loop during this small movement will be 2 (B ds I = d <, so that the work done becomes d #, or I d where I, stands for the current strength in C. G. S. units of ten amperes each. Consequently, in any small excur- sion of the loop, the work done will always be the product of 254 ELECTRO-DYNAMIC MACHINERY. the current strength and the increase of flux therewith enclosed. It is evident that the amount of flux which is brought within the loop by a given small excursion, varies with the position of the loop; that is to say, a small excursion through the arc ds, at the position represented both in plane and isometric projection, where the plane of the loop coin- cides with the direction of the flux, in Fig. 201, will introduce an amount of flux = / (B ds. But the same small excursion in FIG. 202. SMALL ANGULAR DISPLACEMENT OF A LOOP IN UNIFORM MAG- NETIC FLUX PERPENDICULAR TO ITS PLANE. the position represented in Fig. 202 /. ^., where the plane of the loop is perpendicular to the flux will introduce practi- cally no additional flux into the loop. At any intermediate position, it will be evident that the flux introduced by a small excursion of arc ds, will be / ds ($> cos /?, where /?, is the angle included between the plane of the loop and the direction of magnetic flux. The torque exerted by the loop, therefore, varies as the cosine of the angle between the plane of the loop and the direction of the external flux. 309. Let us now consider the application of the foregoing principles to the simplest form of electro-magnetic motor. For this purpose we will consider a smooth-core armature A, Fig. 203, situated in a bipolar field. We will suppose that the total magnetic flux passing through the loop of the wire in the position shown, from the north pole N, to the south pole S, is $ webers, and that a steady current of* amperes, is maintained through the loop of wire attached to the armature core. In the position of the loop as shown in Fig. 203, there will be no- MOTOR TORQUE. 255 rotary electro-dynamic force exerted upon the wire, and the armature will be at a dead point. If, however, the armature be moved from this position into that shown in Fig. 204, so that it enters the magnetic flux, assumed to be uniformly dis- tributed over the surface of the poles and armature core, then a rotary electro-dynamic force is set up on the wire, and com- FIG. 2O3. DRUM ARMATURE WITH SINGLE TURN OF ACTIVE CONDUCTORS AT DEAD POINT. municated from the wire to the armature core on which it is / d 4> secured. The torque being . dyne-cms., where/, is the d 3> current strength in amperes, and - the rate at which flux en- closed by the loop is altered per unit angle of displacement. If, for example, the total flux $ = i megaweber, and the polar FIG. 204. ACTIVE CONDUCTOR ENTERING POLAR FLUX. angle over which we assume that this flux is uniformly dis- tributed is 120, or = radians, then the rate of emptying flux from the loop during its passage through the polar arc will be - - = 9 - webers-per-radian, and if the strength T of current in the loop be maintained at 20 amperes, the torque exerted by the electro-dynamic forces around the armature shaft 20 1,500,000 will be X - - = 955,000 dyne-cms. Since a torque TO 7t 256 ELECTRO-DYNAMIC MACHINERY, of i pound-foot = 13,550,000 dyne-cms., this torque would be represented by = 0.0705 pound-foot, or 0.0705 i3,55> 000 pound at one foot radius. The armature will continue to move under this torque, if free to do so, until the position of Fig. 205 is reached, where FIG. 205. ACTIVE CONDUCTOR LEAVING POLAR FLUX. it is evident that a still further displacement will not increase the amount of flux threaded through the loop. The amount of work which will have been performed by the electro-dynamic forces during this angular displacement of 120 or - radians, will have been t ft 955,000 X = 2,000,000 o 5 / 20 ergs, or, simply $ = x 1,000,000 = 2,000,000 ergs = 0.2 joule. 310. The armature may continue by its momentum to move past the position of Fig. 205, to that of Fig. 206. As soon as it FIG. 206. ACTIVE CONDUCTOR RE-ENTERING POLAR FLUX, AND ACTED ON BY OPPOSING ELECTRO-DYNAMIC FORCE. reaches the latter position, a counter electro-dynamic force will be exerted upon it, tending to arrest and reverse its motion. Consequently, if the electro-dynamic force is to produce a con- tinuous rotation, it is necessary that the direction of the cur- rent through the coil be reversed at this point; /. ^., commuted, or the direction of the field be reversed as soon as this point is MOTOR TORQUE. 257 reached. As it is not usually practicable to reverse the field, the direction of current through the coil is reversed by means of a commutator, so that when the position of Fig. 206 is reached, the current is passing through the wire in the opposite direction to that as shown by the arrow. Under these circum- stances, the electro-dynamic force and torque continue in the same direction around the axis of the armature and expend another 0.2 joule upon the armature in its rotation to the original position shown in Fig. 203. It is to be remembered that the representation of the flux in Figs. 203-206 is diagrammatic, since the flux in the entrefer is rarely uniform, never terminates abruptly at the polar* edges, and is, moreover, affected by the flux produced around the active conductor. 311. The total amount of work done in one complete revolu- .tion of the armature upon a single turn of active conductor is, , 2 i $ 2 i therefore, - ergs, or - joules. 10 100,000,000 If the load on the motor be small, so that the momentum of the armature can be depended upon to carry it past the dead- points which occur twice in each complete revolution, the armature will make, say n, revolutions per second, and the amount of work absorbed by the armature loop in this time n i $ n will be - joules in a second, or an activity of 100,000,000 2 * $ n watts. 100,000,000 The E. M. F. generated by the rotation of this loop through ft tyy the magnetic field, by dynamo action, will be - 100,000,000 volts, (Par. 132) where w, in this case is 2, since there are two conductors upon the surface of the armature, counting once completely around. The C. E. M. F. will, therefore, be 2 $ n volts, and the activity of the electric current 100,000,000 upon this C. E. M. F. will be - watts, as above. 100,000,000 Hence it appears that in this, as in every case, the torque and work produced by an electro-magnetic motor depends upon the C. E. M. F. it can exert as a dynamo. 258 ELECTRO-DYNAMIC MACHINERY. 312. Fig. 207 represents a Gramme-ring armature, carrying a single turn of conductor, situated in a bipolar field. If the total useful flux through the armature is $ webers, as before, $ half of this amount will pass through the turn, or webers, since the flux divides itself into two equal portions, as repre- sented in the figure. It will be evident, as before, that start- ing at the position of Fig. 207, there will be no rotary electro- dynamic force exerted upon the loop, until it enters the flux, FIG. 2O7. GRAMME-RING ARMATURE WITH SINGLE TURN OF ACTIVE CON- DUCTOR AT DEAD POINT. assumed to commence beneath the edge of the pole-piece, and / d the torque will then be uniform at the value - 7j dyne- 10 d ft centimetres, until the turn emerges from beneath the pole-piece / # at Z. The work done in this passage will have been . 10 2 ergs, and this work will have been taken from the circuit, and,, therefore, from the source of E. M. F. driving the current i, and will be liberated as mechanical work (including frictions). If, by the aid of the commutator, the direction of the current around the loop be reversed, the turn, when caused, either by momentum or by direct displacement, to enter the field at , Fig. 208, will again receive a rotary electro-dynamic force whose torque is ^- until the angle /?, has been again 10 d ft i & passed, when the work performed will be * ergs, as be- fore. The total work done upon the armature in one revolu- / ^ i $ tion will, therefore, be '2 x X = ergs, and if the IO 2 IO armature make n revolutions per second, the activity expended / n i $ n upon it will be ergs per second = watts but 10 100,000,000 MOTOR TORQUE. 259 considering the rotating armature in this case, as a dynamo n armature, its E. M. F. will average volts, since 100,000,000 there is only one turn of the wire upon its surface, and, consequently, the activity expended on the armature will i.Q'n be e i = watts. 100,000,000 313. We have hitherto considered that the armature, whether of the Gramme-ring or drum type, possessed only a single C ' FIG. 208. GRAMME-RING ARMATURE WITH SINGLE TURN OF ACTIVE CON- DUCTOR. turn. As a consequence the torque exerted by a constant cur- rent in the armature will vary between a certain maximum and zero, that is to say, the motor will possess dead-points. If, however, a number of turns be uniformly wound upon the arma- ture, as in the dynamos already considered, it will be evident that the same number of turns will always be situated in the magnetic flux beneath the poles and in the air space beyond them, in all positions of the armature, and that, consequently, the torque exerted upon the armature will be constant when the magnetic flux and the current strength are constant. The torque exerted by the armature with w wires upon its surface, / w counted once completely around, will be dyne-cms., 10 2 7t whether for a Gramme-ring or a drum armature, and this whether the armature be smooth-core or toothed-core. That this is the case will be evident from the following con- sideration. The work done on a single wire in one complete t revolution is ergs, and if there are w wires on the surface 10 of the armature, the total work done by electro-dynamic forces in one revolution will be ergs. But the work done by a TO 2 60 ELECTRO-D YNA MIC MA CHINER V. torque T dyne-cms, exerted through an angle of ft radians is r fi cm. -dynes or ergs, and since one revolution is 2 n radians, the work done by the torque will be 2 n T ergs. Therefore, 2 n t = , or r = dyne-cms. 10 10 2 n For example, if a Gramme-ring armature has 200 turns of wire, counted once all round the surface, and the current strength supplied to the armature from the external circuit to the brushes is 50 amperes, while the total useful flux passing from one pole through the armature across to the other pole is 5,000,000 wejpers, or 5 megawebers, then the torque exerted by the armature under these conditions will be, 50 500,000,000 x 200 795,800,000 x - = 795, 800,000 dyne-cms. = 10 * 27T 13,550,000 pounds-feet = 58.73 pounds-feet. 314. The torque produced by multipolar continuous-current motors is independent of the number of poles, if the armature winding be of the multiple-connected type ; i. e., if there are as many complete circuits through the armature as there are poles in the field. In every such case, if >, be the useful flux in webers passing from one pole into the armature, /, the total current strength delivered to the armature in amperes, and w, the number of armature conductors counted once completely around its surface, the torque will be, centimetre-dynes, or pounds-feet. 20 7t i $ w 20 n x 13,550,000 If, however, the armature be series-connected, so that there are only two circuits through it, and there are/, poles in the field frame, the torque will be P i $w , " pounds-feet. 2 20 n X 13,550,000 315. In a smooth-core armature, the electro-dynamic force, and, therefore, the torque, is exerted upon the active con- ductors, that is to say, the force which rotates the armature acts on the conductors which draw the armature around with MOTOR TORQUE. 261 them. Consequently, a necessity exists in this type of motor to attach the wires securely to the surface of the core in order to prevent mechanical displacement. 316. In a toothed-core armature, where the wires are so deeply embedded in the surface of the core as to be practically surrounded by iron, the electro-dynamic force or torque is ex- erted on the mass of the iron itself, and not on the wire. That is to say, the armature current magnetizes the core, and the mag- netized core is then acted upon by the field flux. As soon as the iron of the armature core becomes nearly saturated by the flux passing through it, the electro-dynamic force will be exerted in a greater degree upon the embedded conductors, but, under ordinary conditions, the electro-dynamic force which they re- ceive is comparatively small. A toothed-core armature, there- fore, not only serves to protect its conductors from injury, since they are embedded in its mass, but also prevents their receiving severe electro-dynamic stresses. It is not surprising, therefore, that the tendency of modern dynamo construction is almost entirely in the direction of toothed-core armatures. 317. It might be supposed that the preceding rule for cal- culating the value of the torque in a motor, whether running or at rest, would only hold true where there existed a fairly uniform distribution of the field flux, such as would be the case where there was no marked armature reaction. Observations appear to show, however, that if we take into consideration the actual resultant useful flux which enters the armature from any pole, the torque will always be correctly given by the pre- ceding rule, even when the armature reaction is very marked. That is to say if $, be the total useful flux passing through i $ w the armature from one field pole, the torque will be - 20 7t dyne-centimetres, no matter how much flux may be produced independently by the M. M. F. of the armature. 318. We have hitherto studied the fundamental rules for calculating the torque in the case of any continuous-current motor, whether bipolar or multipolar. It is well to observe that in practice the torque available from a motor at full load 262 ELECTRO-DYNAMIC MACHINERY. can be determined without reference to either the amount of useful flux passing through the armature, or to the amount of full-load current strength. 'For, if the full-load output of a motor be P watts, and the speed at which it runs be ;; revolu- tions per second, then the work done per second will be 10,000,000 P ergs. The angular velocity of the shaft will be 2 n n radians, and the torque, will, therefore be, 10,000,000 P r - dyne-centimetres. 2 n n 10,000,000 P t pounds-feet. I 355 ) 00 2 TT p r = 0.1174 pounds-feet. For example, if a motor gives six horse-power output at full load, and makes 600 revolutions per minute, required its torque. Here the output, />, = 4,476 watts, the speed in revolutions p per second n = 10, = 447.6, and the torque exerted by the motor at full load will be, t 0.1174 x 4,476 = 52.55 pounds-feet. If the amount of torque which the motor has to exert in order to start the load connected with it never exceeds the torque when running at full load, then the current which will be re- quired to pass through the armature in order to start it will not exceed the full load current. 319. It is sometimes required to determine what amount of torque must be developed by a motor armature in order to operate a machine under given conditions. For example, if a machine has to be driven with an activity of ten horse-power, at a speed of 300 revolutions per minute, what will be the torque exerted by the motor running at 900 revolutions per minute, suitable countershafting being employed between machine and motor to maintain these speeds ? If we employ the formula in the preceding paragraph, we find for the power P = 10 x 746 = 7,460 watts. The speed ;/ = -= = 5 revolutions per 60 MOTOR TORQUE. 263 second, so that the torque exerted at the shaft of the machine is r 0.1174 -- =0.1174 x - = 175.1 pounds-feet. The velocity-ratio of motor to machine is - = 3, so that the 300 torque exerted by the motor, neglecting friction-torque in the countershafting will be ^- = 58.37 pounds-feet or 58.37 o pounds at i foot radius. Or, we might consider that the motor would, neglecting frictional waste of energy in countershafting, be exerting a power P of 10 x 746 = 7,460 watts at a speed of n = ~ = 15 revolutions per second. Its torque would then be, by the same P 0.1174 X 7,460 formula, r = 0.1174 = - ' - = 58.37 pounds-feet. 320. In some cases it is necessary to determine the torque which must be exerted by a street-car motor at maximum load. It is not sufficient that the motor shall be able to exert a maxi- mum activity of say 20 H. P. It is necessary that it shall be able to exert the given maximum torque at a definite maximum speed of rotation, and, therefore, the given maximum activity of 20 H. P. Otherwise, the motor might be of 40 H. P. capacity, and, yet by failing to exert the required torque, might be unable to start the car, or, in other words, the motor would have too high a speed. For example, required the torque to be exerted by each of two single-reduction motors in order to start a car with 30" wheels weighing 6 short tons light, and loaded with 100 passengers, up a ten per cent, grade, the gearing ratio of armature to car wheel being 3 to i. Here 100 passengers may be taken as weighing 15,000 Ibs. or 7^ short tons. The total weight of the car is therefore 27,000 Ibs. The frictional pull required to start a car from rest on level rails, under average commercial conditions, is about 1.8 per cent, of the weight, or, in this case, 486 Ibs. weight. The pull exerted against gravity is also 2,700 Ibs., making the total pull 3,186 Ibs. weight. The radius of the car wheel being = 1.25 feet, the torque at the car 2 4 264 ELECTRO-DYNAMIC MACHINERY. wheel axle is 3,186 x 1.25 = 3,983 pounds-feet. The torque at the motor shafts is therefore 3>9 3 = 1,328 pounds-feet, and each motor must therefore exert I ^- = 664 pounds-feet. If the motors make 600 revolutions per minute or 10 revolu- tions per second, exerting this torque, their activity will be 664 x 10 x 2 TT X 1.355 = 5 6 >53 watts, = 56.53 KW, and their combined activity 113.1 KW, neglecting gear frictions. 321. Considering the case of a motor armature in rotation, the speed of its rotation for a given E. M. F. applied to its armature terminals will depend upon three things : viz., (i.) The load imposed upon the armature, or the torque it has to exert. (2.) The electric resistance of the armature in ohms. (3.) Its dynamo-power ; i. e., its power of producing C. E. M. F., or the number of volts it will produce per revolution per second. If , be the E. M. F. in volts applied to the armature termi- nals, T, the torque, which the motor has to exert, including the torque of frictions, in megadyne-decimetres (dyne-cms. X io~ 7 ) r, the resistance of the motor armature in ohms, and e, the C. E. M. F. produced in volts per revolution per second of the armature. Then n e, will be the total C. E. M. F. . ~-^- will be the current strength received by the armature according to Ohm's law. The activity of this current expended upon ' 9 //* ^2 P the C. E. M. F. will be their product, or n e x - watts, and this must be equal to the total rate of working, or / n e\ 2 7t n T, = consequently, n e f J = 2 n n t and E r-c n 2 it r revolutions per second. For example, if a motor armature, whose resistance is 2 ohms, has a uniformly excited field, which may be either of the bipolar or multipolar type, and is supplied with 500 volts at its terminals ; and if the C. E. M. F. it produces by revolution in the field is 40 volts per-revolution-per-second, then the speed MOTOR TORQUE. 265 at which the motor will rotate, when exerting a torque, including all frictions, of 100 pounds-feet (100 x 13,550,000 dyne-centi- metres, = 135.5 megadyne-decimetres) will be 500 27T X 2X 135-5 n = - = 12.5 i. 06 = 11.44 revolutions- 40 1,600 per-second. 322. It will be observed from the above formula that if either the torque be zero, or the resistance of the armature is Tf zero, the speed of the motor will simply be revolutions-per- second. Or, in other words, that the armature will run at such a speed that its C. E. M. F. shall just equal the E. M. F. applied to the armature ; **. e. without drop of pressure in the armature. If the torque could be made zero, the motor would do no work and would require no current to be supplied to it, so that no matter what the resistance of the armature might be, the drop in the armature would be zero. All motors necessarily have to exert some torque in order to over- come various frictions, but on light load their speed approxi- mates to the value revolutions-per-second. If the resistance of the motor is very small, which is approximately true in the case of a large motor, the second term ^ , in the formula, becomes small, and the diminution in speed due to load is, therefore, also small. In other words, the drop which takes place in the armature due to its resistance is correspond- ingly reduced, permitting the motor to maintain its speed and C. E. M. F. of rotation. Fig. 209 represents diagrammati- cally a motor armature revolving in a suitably excited magnetic field, and supplied from a pair of mains, J/, M, with a steady pressure of 500 volts. The resistance of the arma- ture is represented as being collected in the coil r, while the C. E. M. F. of the motor is indicated as opposing the passage of the current from the mains. The drop in the resistance is represented as being 40 volts, while the C. E. M. F. is 500 40, or 460 volts. 323. The E. M. F. applied to the terminals of a motor armature, therefore, has to be met by an equal and opposite or 266 ELECTRO-D YNAMIC MA CHINEX Y. C. E. M. F. in the armature, which is composed of two parts, that due to rotation in the magnetic flux, or to dynamo- electric action, and that apparent C. E. M. F. which is entirely due to drop of pressure in the resistance of the arma- ture, considered as an equivalent length of wire. The activity expended against the C. E. M. F. of rotation is activity expended in producing torque, and, therefore, almost all available for producing useful work, while the activity expended against the C. E. M. F. of drop is entirely expended in heating the wire. As the load on the motor is increased, the current FIG. 209. DIAGRAM REPRESENTING RESISTANCE AND C. E. M. F. IN A REVOLVING MOTOR-ARMATURE. which must be supplied to the motor to overcome the addi- tional load or torque increases the drop in the armature, and, therefore, diminishes the C. E. M. F. which has to be made up by rotation, and the speed falls, or tends to fall, in proportion. 324. When a motor armature is at rest, its C. E. M. F. of rotation is zero, and the C. E. M. F. which it can produce under these conditions must be entirely composed of drop of pressure. In other words, the current which will pass through it is limited entirely by the ohmic resistance of the circuit. If /, be the current strength in amperes supplied to a motor armature at a pressure of E volts, the activity expended in the armature will be E i watts. The activity expended in produc- MOTOR TORQUE. 267 ing torque will be // e i watts, so that disregarding mechanical and electro-magnetic frictions, the efficiency of the motor will be -y^-r = -=-, or simply the ratio of the C. E. M. F. of rota- & l Jc, tion to the impressed E. M. F. This is a maximum at no load ; /. e., when the motor does no work, and is zero when the motor is at rest. The value of e, the volts-per-revolution-per-second, is in all cases of multiple-connected armatures equal to w x I0 ~ 8 , where $, is the number of webers of flux passing usefully into the armature from any one pole, and /, is the number of turns of conductor counted once around its periphery. 325. The speed of a motor, therefore, varies, to the first ap- proximation, inversely as the useful magnetic flux, and in- versely as the number of armature conductors. A slow-speed motor, other things being equal, is a motor of large flux, or large number of turns, or both, and, as will afterward be shown, in order to decrease the speed at which the motor is running, it is only necessary to increase, by any suitable means, the use- ful flux passing through its armature. 326. Just as in the case of a generator armature, whose maximum output is obtained when the drop in its armature is equal to half its terminal E. M. F. (Par. 9), so in the case of the motor, the" output is a maximum (neglecting frictions), when the drop in the armature is half the E. M. F. applied at TT> the armature terminals, or, in symbols, when n e = ; the 2 speed of the motor being then half its theoretical maximum speed, assuming no friction. Similarly, just as it is impracticable to operate a generator of any size at its maximum theoretical output, since the activity expended within it would be so great as probably to destroy it, being equal to its external activity, so no motor of any size can be operated so as to give the maximum theoretical output of work, since the activity expended in heating the machine, being equal to its output, would, probably, cause its destruc- tion. CHAPTER XXVI. EFFICIENCY OF MOTORS. 327. As in the case of generators, the commercial efficiency of the electric motor is the ratio of the output to the intake: that is, Output EfficienC ^ : Intake- ' Since the output must be equal to the intake after subtracting the loss taking place in the machine, the above may be expressed as follows: Intake Losses Efficiency = - Intake 328. The losses which occur in a motor are of the same nature as those already pointed out in Par. 224, in connection with a generator. This is evident from the fact that a motor is but a generator in reversed action; so that any dynamo is capable of being operated, either as a generator or as a motor, according as the driving power is applied to it mechanically or electrically. There is this difference, however, between the two cases, that a very small dynamo-electric machine may be capable of acting as a motor, while it is not capable of acting as a dynamo, owing to the fact that it is not able, unaided, to excite its own field magnets, its residual magnetism being insufficient for this purpose. On this account, motors can be constructed of much smaller sizes than self-exciting generators. 329. If the losses which occur in a dynamo-electric machine, acting as a generator, have been determined, we can then closely estimate what these losses will be when the machine is operated as a motor, and, consequently, the efficiency of the machine as a motor can be arrived at. 330. There is this difference between a dynamo and a motor as regards the output; viz., in the dynamo, the energy lost is EFFICIENCY OF MOTORS. 269 derived from the driving source, while in the motor the energy lost is'derived electrically from the circuit; but the output of .a dynamo-electric machine is almost invariably determined by the electric activity in its armature circuit; that is to say, the .armature is limited to a certain number of amperes received or delivered at a certain number of volts pressure, so that since this load is the output, when the machine is a generator, and the intake, when the machine is a motor, it is evident that .after the losses as a motor have been subtracted, the mechani- cal output will be less than the electrical output which the machine produces as a generator. 331. For example, let us suppose that a certain machine, -acting as a series-wound generator, is capable of delivering 10 .amperes at a pressure of 100 volts, so that its output is i KW. Let us also suppose that when acting as a generator, a loss of 250 watts occurs, in friction, hysteresis, eddy currents and PR losses, both in the armature and in the field; then the mechanical intake of the machine will be 1,250 watts, and its commercial efficiency, = 0.8, or 80 per cent. When, however, the machine is operated as a motor, the armature is limited to the same current strength of 10 amperes, and the pressure at the machine terminals can only be slightly in excess of the 100 volts previously delivered. Let us suppose that this is no volts. Then the intake of the machine will be 1,100 watts. Assuming the same losses as before; namely, 250 watts, the output would be only 850 watts, and the efficiency, therefore, - - = 0.772, or about 2^ per cent, less than in the preceding case. It is clear, therefore, that while the output of the machine was 1,000 watts when acting as a generator, it was limited to 850 watts 'when acting as a motor, assuming that the same limiting armature temperature and same liability to sparking were accepted in each case. 332. The difference above pointed out between the output of a machine acting as a generator and as a motor, diminishes with an increase in the size of the machine. Thus, while a j-KW generator is usually only a i-H. P. motor (or has an out- 270 ELECTRO-D YNAMIC MA CHINER Y. put of say 750 watts), a generator of 200 KW would, probably,. be a motor of 185 H. P. ; so that in the case of very large machines, the difference between the outputs in the two cases would be practically negligible. 333. The curve in the accompanying Fig. 210, approximately represents the efficiency which may be expected at full load 4 100 95 5 Li. U. ? 65 / ^ as MMER DIALJ FFICjj NOY_ - / 25 50 75 100 125 1 '-- IOI ftWATTR OUTPUT jO 175 20( KILOWATTS OUTPUT FIG. 210. COMMERCIAL EFFICIENCY CURVE OF MOTORS AT FULL LOAD. from motors of varying capacity up to 200 KW. This curve has been plotted from a number of actual observations with machines constructed in the United States. 334. It is to be remembered, however, that the full load efficiency of a motor is not always the criterion upon which its suitability for economically performing a given service is to be determined. It not infrequently happens that the character of the work which a motor has to perform is necessarily exceed- ingly variable, so that the average load might not be half the full load of the machine. Under such conditions, the average efficiency is of more importance than the full-load* efficiency. Were the efficiency curve of all motors in relation. EFFICIENCY OF MOTORS. 271 to their load of the same general outline, the average efficiency would be, approximately, the same in all motors having the same full-load efficiency. As a matter of fact, however, the efficiency curves of different machines may be very different. Thus one machine may have its maximum efficiency at half load, and behave at full load, in regard to its efficiency, as though it were actually overloaded, while another machine, with the same full-load efficiency, may show a lower efficiency at half load. Obviously the first machine would be preferred for variable work, other things being equal 335. Similar considerations apply to electric generators. The full-load efficiency is not in every case the ultimate criterion of economical delivery of work, but it generally happens that generators are installed in such a manner, and under such conditions, that a nearer approach to their full load is attained, so that ordinarily the shape of the efficiency curve of a generator is not of such great importance as that of a motor. Fig. 211 represents the efficiency curves of two motors, each having a full-load efficiency of 78 per cent. One of these machines has an efficiency, at about two-thirds load, of 84 per cent., but at overloads is inefficient, while the other becomes more efficient at slight overloads. 336. In order to produce a motor of given full-load efficiency with comparatively small loss at moderate loads, and, there- fore, a comparatively heavy loss at heavy loads, we may em- ploy a slow-speed motor, or a motor which shall generate the necessary C. E. M. F. at a comparatively low speed. Such a machine will probably have a small loss in mechanical friction, because of its lower speed of revolution. It will, similarly, have, probably, a small loss in hysteresis and eddy currents for the same reason, but a slow speed motor will probably have a greater number of armature turns in order to com- pensate for the smaller rate of revolution, and the I*R loss in the armature is, therefore, likely to be greater at full load. In such a machine, the loss at full load is principally due to PR; and, since this loss decreases rapidly with 7, it will evidently have a small loss at moderate loads. 272 ELECTRO-DYNAMIC MACHINERY. 337; The speed at which a motor will run in performing a given amount of work varies considerably with different types of motors. For example, of two motors of 20 KW capacity, one may run at 400 revolutions-per-minute, and the other at 1,000 revolutions-per-minute. It is evident that the first machine will have two and a half times the full-load torque of the second. The lower speed is, however, generally speaking, only to be obtained at the expense of additional copper and iron ; that is to say, the cost of material in a slow-speed machine will, probably, be greater than the cost of material 100 It PROPORTION OF LOAD g FIG. 211. EFFICIENCY CURVES OF TWO DIFFERENT MOTORS HAVING SAME FULL-LOAD EFFICIENCY. in a high-speed machine of the same output and relative excel- lence of design. It becomes, therefore, a question as to the relative commercial advantage of slow speed versus high speed in a motor. 338. Motors are generally installed to drive machinery either by belts or' gears, and the belt speed or the gear speed of machinery is, in practice, a comparatively fixed quantity. If, EFFICIENCY OF MOTORS. 273 therefore, the speed of the motor be greater than the speed of the main driving wheel of the machines with which the motor is connected, intermediate reducing gear or countershafting has to be installed. This adds to the expense of installation, not only in first cost, but also in maintenance, lubrication, and the continuous loss of power it introduces through friction. The result is, that up to a certain point, slow-speed motors are economically preferable, and the tendency of recent years has been toward the production of slower speed dynamo machinery. In comparing, therefore, the prices of two motors of equal output, the speed at which they run has to be taken into account, as well as the efficiency at which they will operate. It is to be remembered that any means in the design which will enable a motor to supply its output at a slower speed, are -equivalent to means which will enable a motor of the higher speed to supply a greater output. 339. The weight of.a motor is a matter of considerable im- portance in cases of loco motors / /'. e., of travelling motors, as in the case of electric locomotives, street-car motors or launch motors, but in the case of stationary motors, their weight is of less consequence, since, after freight has been once paid for their shipment, no extra expense is entailed by reason of their increased mass when in operation. Indeed, weight is often a -desirable quality for a motor to possess in order to ensure steadiness of driving, although undue weight in the armature is apt to produce frictional loss, and diminished efficiency. 340. In comparing the relative weights of motors, two cri- teria may be established; namely, (i) In regard to torque, and (2) in regard to activity. In some cases, the work required from the motor is such that the pull or torque which must be given in reference to its weight is the main consideration, while in other cases it is not the torque, but the output per-pound of weight, which must be considered. 341. The torque-per-pound, in the case of street-car motors, where lightness is an important factor, has been increased to 274 ELECTRO-DYNAMIC MACHINERY. 133,000 centimetre-dynes per-ampere, per-kilogramme of weight; or, 0.0045 pound-foot per-ampere per-pound of total motor weight, exclusive of gears, so that a 5oo-volt street-car motor, weighing 223 pounds, and supplied with one ampere of current, would exert a torque of one pound-foot. In stationary motors, the torque is usually only o.ooi to 0.0015 pound-foot per-ampere per-pound of .weight, or about four times less than with street-car motors. This is owing to the fact that cast iron is more largely employed in stationary motors, owing to its lesser cost. The output per-pound of weight in motors varies from 5 watts per pound to 15 watts per pound, according to the size and speed of the motor. 342. We may now allude to the theoretical conditions which must be complied with in order to obtain the maximum amount of torque in a motor for a given mass of material. It must be carefully remembered, however, that these theoretical conditions require both modification and amplification, when applied to practice, so that the practical problem is the theo- retical problem combined with the problem of mechanical construction. / ^ iu 343. The torque of a motor armature being - cm.- dynes, we require to make this expression a maximum for a given mass of copper wire in the armature and in the field magnets, neglecting at present all considerations of structural strength. ^ w The torque-per-ampere will be cm. -dynes. 2O 7t In order to make this a maximum, both # and w, should be as great as possible. 344. It is evident that if we simply desired a motor of power- ful torque-per-ampere, regardless of its weight, we should employ as much useful iron as possible, so as to obtain as great a useful magnetic flux #, through the armature, as possible, and we should employ as many turns of wire upon the surface of the armature as could be obtained without mak- EFFICIENCY OF MOTORS. 275 ing the armature reaction excessive, or without introducing too high a resistance, and too much expenditure of energy in the armature winding. Such a motor would essentially be a heavy motor, so that the requirements of a motor with power- ful torque-per-ampere would simply be met by a motor of great useful weight, and this, indeed, would be obvious without any arithmetical reasoning. 345. When, however, the torque-per-ampere per-pound-of- weight has to be a maximum, the best means of attacking the problem is to consider a given total weight of copper and iron in the armature, and examine by what means this total weight can be most effectually employed for producing dynamo-power; i, , excited by the current passing through the field coils. If the circuit of the field coils should accidentally become broken, the magnet Z>, will release its armature, which will release the detent, which will allow the handle H, with its contact bars B, B, to return to the " off " position, under the action of the spiral spring; or, should the armature current become excessively strong, thereby endanger- ing the armature, the relay magnet will attract its armature, which will thereby short-circuit the detent magnet, and the same result will follow. The armature will, therefore, be stopped by any overload, and will be cut out of circuit by any accidental cessation of the current in the field. By means of a push-button circuit, the armature can be brought to rest, by pressing a push button placed at any distance from the machine. 383. All the phenomena of armature reaction which we have traced in connection with dynamos in Pars. 198 to 223 are pre- STARTING AND REVERSING OF MOTORS, 303 sented by motors, with the exception that the direction of the M. M. F. of the armature, relatively to the field magnets, is reversed; that is to say, a motor runs so that the magnetic flux produced by its armature tends to pass through the pole which the armature approaches; /. to o % d V ~" J3 rt 3 C o- H o ^ -^ i tn o H 1 3 i W H fi o-S 0.083 0.417 0.0417 50 33 83 0.083 0.0083 0.033 0.0413 0-55 0-55 i 0.125 o.8 7 s 0.0875 so 75 125 0.125 0.0125 0.075 0.0875 1-25 0.625 2 0.208 1.792 0.1792 So 158 208 0.208 0.0208 0.158 0.179 2.633 0.658 3 0.292 2.708 0.2708 SO 242 292 0.292 0.0292 0.242 0.271 4-03 0.667 4 0-375 3-625 0.3625 50 3 2 5 375 0-375 0.0375 0.325 0.3625 5-42 0.678 S 0-459 4-541 0.4541 .SO 409 459 0-459 0.0459 0.409 0-454 6.82 0.682 10 0.876 9.124 0.9124 50 826 876 0.876 0.0876 1 0.826 0.913 18-97 0.689 406. It is, therefore, evident that a motor armature, with constant field excitation, can develop a speed closely propor- tional to the pressure at its terminals, and, therefore, serve as a motor-meter, if the retarding torque be small and constant, or, if it be partly small and constant, and partly proportional to the speed. 407. One of the most important recent applications of motors is their distributed application to machine tools in large factories. Instead of employing long lines of counter- shafting, which must necessarily be constantly driven during working hours, a separate electric motor is applied directly to each machine, so that each machine is started and stopped according to its own requirements. Moreover, the range of regulation of speed, which is obtainable from a common coun- tershafting, is necessarily more limited in degree than that which can be effected by the use of independent motors. ME TER- MO TORS. 3 I ^ 408. By the use of individual electric motors, not only is each tool capable of ^operation at its best speeds, and under com- plete control, but also the friction of long lines of counter- shafting is eliminated. The economy is greatest where the nature of the work in the machine shop is such that the average power supplied to the tools is much less than the maximum power, or the ratio of average to maximum power; /". ^., the load factor is small, since the motors, when completely dis- connected from a circuit, take no power, whereas, the countershafting consumes, practically, the same amount of power friction, whether the tools be active or idle. CHAPTER XXX. MOTOR DYNAMOS. 409. The consideration of dynamos and motors naturally leads to that of a third class of apparatus, which partakes of the nature of each; namely, motor- dynamos, or, as they are sometimes called, dyna-motors. It is evident that if a motor be rigidly connected to a dynamo, either by a belt or by a coupling, that we obtain a means whereby electric power can be transformed through the intermediary of mechanical power. Thus, the motor may be operated from a high-tension circuit, while the dynamo .operates a low-tension circuit, Or vice versa ; but, neglecting losses taking place in the two machines, the amount of electric energy absorbed and delivered in the re- spective circuits will be the same, the combination being utilized for the purpose of transforming the pressure and cur- rent strength. For this reason a motor-dynamo is commonly called a rotary transformer, in order to distinguish it from an ordinary alternating-current transformer, which always remains at rest. 410. Instead of rigidly connecting together two separate machines; /'. w m x io~ 8 . The generated secondary E. M. F. will be ;/ 3>w f IV X io- 8 volts = ( t I I r t ) *. WHI The pressure at the secondary terminals will be further re- duced by the drop in the secondary winding; or E* = (A ~ A >\) ~ ^ >V l ' W m Tf the weight of copper in the two windings is equal, 7 2 ;- 2 , will T V *i$) practically be equal to - ! -, so that Wm The machine, therefore, acts as though it were a dynamo of E. M. F. !-2L E with an internal resistance of zr , or twice that w m of the secondary winding. 416. In all motor dynamos, having a field magnet common to both armatures, the ratio of transformation, neglecting ar- mature drop, is constant, no matter how the field excitation is varied. Motor-generators are often employed for raising or lowering the pressure of continuous-current circuits. Thus electroplating E. M. Fs. of, say 6 volts, are obtainable in this manner from circuits of no, 220 or 500 volts pressure. Simi- larly, pressure of 150 volts are obtainable from a few storage batteries by such apparatus. 417. In central stations for low-pressure distribution, say at 220 volts, by a three-wire system, some of the feeders have to be maintained at a higher pressure than others, in order that all the feeding points, or points of connection between feeders and the mains, should have the same pressure. This is ac- complished either by employing separate dynamos, operated at slightly different pressures, or by introducing at the central station motor-dynamos having their dynamos in circuit with the feeders. Such motor-dynamos are frequently called boosters. The motor-dynamo for this purpose requires that means should be provided for regulating the E. M. F. which is to be added to the feeder circuit. This can only be done by employing separate field magnets for the motor and generator armatures. OF THE NIVERSITY) N. OF . jr MOTOR DYNAMOS. 323 Fig. 232 represents a practical form of booster employed in a three-wire central station. The middle machine is a motor operated at central-station pressure of, perhaps, 250 volts; the others are generators, having their armatures coupled to the same shaft as that of the motor armature. One dynamo is FIG. 232. BOOSTER IN THREE-WIRE CENTRAL STATION. connected in circuit with the positive conductor of the feeder whose pressure is to be raised, and the other is connected in the circuit of the negative conductor. Since these feeders carry heavy currents and require to be of very low resistance, the necessity for the massive copper brushes and connections of the dynamos will be evident. The amount of E. M. F. which will be generated in these armatures will be determined by the excitation of their field magnets. THE END. INDEX. Active Conductor, Magnetic Flux of, 37 Aero-Ferric Magnetic Circuits, 68-73 Air-Gap, Magnetic, 57 Air-Path, Alternative Magnetic, 42 Aligned M. M. F., 56 Alternating-Current Dynamos, 17 Alternative Magnetic Air-Path, 52 Alternators, 17 Multiphase, 25 Uniphase, 26 Ampere, Definition of, 49 Ampere-Hour Meter, 313 Ampere-Turn, Definition of, 40 Anomalous Magnet, 47 Arc-Light Dynamos, 26 Armature, Back Magnetization of, 1 86 Cores, Cross-Sections of, 126 , Core Discs for, 152 Core, Lamination of, 105 , Cylinder or Drum, 23 Disc, 23 Double Winding of, 190 Gramme-Ring, 23 PR, Loss in, 200 Iron-Clad, Definition of, 24 Journal Bearings, 159-163 of Machine, 9 Neutral Line of, 184 Pole, 110-116 Radial, no Reaction and Sparking at Com- mutators, 179-198 Ring, 23 , Smooth-Core, 23, 152 Definition of, 24 Toothed-Core, 152 , Definition of, 24 1 23 Turns, Effect of, on E. M. F., 3 Winding, Closed-Coil, no , Disc, 230 , Dissymmetry of, 125 , Inter-Connected, 145 Space, 275 Wire, Effective Length of, 246 Armatures, Closed-Coil, 217 , Gramme-R.ing, 117-127 , Lap Winding for, 155 , Open-Coil, 217 , Wave- Winding for, 155 Attractions and Repulsions, Laws of Magnetic, 33 Automatic Regulation of Dyna- mos, 218 Average Efficiency of Motor, 279 Back Magnetization of Armature, 1 86 Balancing Coil of Armature, 194 Bar, Equalizing, 224 Bars, Bus, 224 , Omnibus, 224 Bearings, Self-Oiling, 161 Belt-Driven Dynamos, 18, 135 Bipolar Dynamo, 16 Boosters, 322, 323 Box, Field-Regulating, for Dy- namo, 14 Brush, Dynamo, 124 Brushes, Forward Lead of, 217 , Lead of, 185 of Dynamo, 9 of Motor, Lag of, 303 Bus Bars, 224 Calculation of Gramme-Ring Dy- namo Windings, 128-134 Capability, Electric, of Dynamo, 126 , Electric, of Dynamo-Electric Machine, 4 Car Motor, 277 Characteristic Curve of Dynamos, 210 External, of Series- Wound Dy- namo, 210 Internal, of Series- Wound Dy- namo, 210 of Shunt- Wound Dynamo, 212 Circuit, Magnetic, 48 Return, for Track Feeders, 226 Circuits, Ferric-Magnetic, 55-67 , Magnetic, Non-Ferric, 48-54 325 326 INDEX. Circuit, Transmission, Definition of, i Circular Distribution of Magnetic Flux Around Conductor, 37 , Magnetic Flux, Assumed Di- rection of, 39 Closed Circular Solenoid, 50 Coil Armature Winding, no Armatures, 217 Coefficient, Hysteretic, 174 Coil, Balancing, of Armature, 194 , Inductance, 301 , of, 181 , Starting, 301 Combinations of Dynamos in Se- ries or in Parallel, 220-227 Commercial Efficiency of Dyna- mo, 5 of Dynamos, Circumstances Affecting, 7 of Motor, 268 Commutation, Definition of, 180 , Diameter of, 180 , Quiet, Circumstances Favor- ing, 187 , Sparkless, Circumstances Fa- voring, 1 86 Commutator, Circumstances Fa- voring Sparking at, 186 , Forms of, 123 of Dynamo, 9 Commutatorless, Continuous-Cur- rent Dynamo, Disc Type of, 236 Dynamos, 234 Generators, 234-240 Commutators, Sparking at, 179- 198 Compound Magnets, 105 Winding of Dynamos, 208 Compound- Wound Dynamos, 14 , Uses for, 209- Conductor, Active, Magnetic Flux of, 37 Consequent Poles of Dynamo, 22 Constant-Current Dynamos, 10 Constant-Potential Dynamos, 10 Constants, Reluctivity, Table of, 65 Continuous-Current Commutator- less Dynamos, 28, 234 , Cylinder Type of, 236 Dynamo, 20 Generators, 234-240 Generator, Limitations to Output of, 203 Convention as to Direction of Cir- cular Magnetic Flux, 39 Converging Magnetic Flux, 35 Core Discs for Armatures, 152 Core, Effect of Lamination on Eddy Currents, 166 Coulomb Meter, 313 Counter Electro-Dynamic Force, 256 Cross Magnetization, 183 Currents, Eddy, 164-171 , Eddy, Definition of, 164 , , Effect of Lamination of Core on, 166 , , Origin of, 165 Curves, Characteristic of Dyna- mos, 210 of Reluctivity in Relation to Flux Density, 66 Cutting Process vs. Enclosing of Magnetic Flux, 82 Cycles of Magnetization, 174 Cylinder or Drum Armature, 23 Type of Commutatorless Con- tinuous-Current Dynamos, 236 Decipolar Dynamos, 17 Density, Flux, 34 , Prime Flux, 54 Devices, Receptive, Definition of, i Diameter of Commutation, 180 Diffusion, Magnetic, 52, 53 Diphase Dynamo, 27 Direct-Driven Dynamos, 135 Disc Armature, 23 Armature Winding, 230 Armatures and Single Field- coil Machines, 228-233 , Faraday's, 234 Type of Commutatorless Con- tinuous-Current Dynamos, 236 Dissymmetry, Magnetic, 124 of Armature Winding, 125 Distribution of Magnetic Field, 41 -47 of Magnetic Flux, 31 of Magnetic Flux of Conductor, Diverging Magnetic Flux, 35 Double Circuit, Bipolar Dynamo, 16 Double Winding of Armature, 190 Drum Armatures, 152 or Cylinder Armatures, 23 Dynamo Armatures, Electro-Dy- namic Induction in, 90-102 , Bipolar, 16 Brush, 124 Brushes of, 9 , Commercial Efficiency of, 5 Commutator, 9 , Consequent Poles of, 22 INDEX. 3 2 7 Dynamo, Continuous-Current, 20 , Biphase, 27 , Double-Circuit, Bipolar, 16 , Electric Capability of, 126 , Efficiency of, 5 Dynamo-Electric Generator, 2 Machine, Electric Capability of, 5 Dynamo Field-Regulating Box, 14 Intake, 5 Load of, 15 Magneto-Electric, n Output of, 5 Plating, 26 Dynamo-Power of Motor, 266 Dynamo Relation between Output and Resistance, 6 , Self-Excited, 12 , , Compound-Wound, 13 , Separately Excited, 12 , Single-Circuit, Bipolar, 16 , Telegraphic, 26 Dynamos, Alternating-Current, 17 , Arc-Light, 26 , Automatic Regulation of, 218 , Belt-Driven, 18 . Characteristic Curves of, 210 , Circumstances Influencing Electric and Commercial Effi- ciency of, 7 , Combination of, in Series or Parallel, 220-227 , Commutatorless Continuous- Current, 28, 234 , Compound- Wound, 14 , , Uses for, 209 , Constant-Current, 10 , Constant-Potential, 10 , Decipolar, 17 , Direct-Driven, 135 , Heating of, 199-205 , Incandescent Light, 26 , Inductor, 25 , Multipolar, 16 , Multipolar, Gramme-Ring, 135 -151 , Octopolar, 17 , Over-Compounded, 209 , Quadripolar, 17 , Regulation of, 206-219 , Self -Excited, Series- Wound, 13 , Series-Wound, Uses for, 209 , Sextipolar, 17 , Shunt-Wound, Uses for, 209 , Simple Magnetic Circuits, 22 , Single-Field-Coil, Multipolar, 28 , Single-Phase, 27 , Three-Phase, 27 Dynamos, Triphase, 27 , Two-Phase, 27 , Unipolar, 28 Dynamotors, 317 Dyne, Definition of ,'69 E. M. P., Effect of Number of Armature Turns on, 3 , Effect of Speed of Revolution on, 3 , Induced by Magneto Genera- tors, 103-109 , Induced in Loop, Rule for Direction of, 94 , of Electro-Dynamic Induction, Value of , 75-82 , of Self-induction, 181 , of Self-induction, Circum- stances Affecting Value of, 182 , Produced by Cutting Earth's Flux, 90 Earth's Flux, E. M. F. Produced by Cutting, 90 Eddy Currents, 164-171 , Definition of, 164 , Effect of Lamination of Core on, 166 , Formation of, in Pole-pieces, 169 , Origin of, 165 Edges, Leading, of Pole-pieces, 184 Efficiency, Average, of Motor, 270 , Full Load of Motor, 270 of Motors, 268-279 Electric Capability of Dynamo, 126 of Dynamo-Electric Ma- chine, 5 Efficiency of Dynamos, Circum- stances Affecting, 7 Flux, Unit of, 49 Electro-Dynamic Force, 241-249 Induction, 75-82 in Dynamo Armature, 90-102 , Laws of, 74-89 Machinery, i Machinery, Classification of, i Enameled Rheostats, 216 Entrefer, 105 Equalizing Bar, 224 Ether, Assumed Properties of, 29 Ether Path of Reluctivity, 60 External Characteristic of Series- Wound Dynamo, 210 Factor, Leakage, 132 , Load, 317 Faraday's Disc, 234 Feeders for Return Track, 226 328 INDEX. Eeedin 3 Points, 322 Ferric Magnetic Circuits, 55-67 : Path of Metallic Reluctivity, 60 Field Magnet of Machine, 9 , Magnetic, 32 Magnets, I s R Losses in, 199 Poles, Eddy-Current Losses in, 200 Regulating Box for Dynamo, 14 Rheostats, 215 Fleming's Hand Rule for Dyna- mos, 74 Motors, 243 Flux, Circular Magnetic, Conven- tion as to Direction of, 39 , Converging Magnetic, 35 Density, 34 , Diverging Magnetic, 35 , Magnetic, Unit of, 49 Density, Prime, 54 , Prime, 56 , Magnetic, 29 , , Distribution of, 31 , , Irregular, 35 , , Variations of, 33 Paths, Magnetic, 2 Following Edges of Pole-Pieces, 184 Force, M. M., Induced, 56 Electro-Dynamic, 241-249 Lines of Magnetic, 34 Magnetic, Tubes, 35 Magnetizing, 53 Magnetomotive, 31 , Prime, 56 Forces, Electromotive, Methods for Increasing, 3 French Measures, Table of, 8 Friction Losses in Bearings and Brushes, 201 , Magnetic, 174 Full-Load Efficiency of Motor, 270 Gap, Magnetic Air, 57 Gauss, Definition of, 35 Generator Armature, Limiting Temperature of, 203 , Dynamo-Electric, 2 Generators, Commutatorless Con- tinuous-Current,234~24o , Definition of, i Gilbert, Definition of, 40 Gramme-Ring Armature, 23 Armatures, 117-127 Dynamos, Multipolar, 135-151 Hand Rule, Fleming's, for Dyna* mos, 74 Heating of Dynamos, 199-205 Hysteretic Activity, Table of, 175 Losses in Armature and Field Poles, 200 Loss, 174 Coefficient, 174 Hysteresis, Magnetic, 172-178 , , Definition of, 172 Incandescent Light Dynamos, 26 Individual Electric Motors, 317 Idle Wire on Armature, 100 Inductance Coil, 301 of Coil, 181 Induction, Electro-Dynamic, 75-82 , , Laws of, 74-89 in Dynamo Armature, 90-102 , Self, E. M. F. of, 181 Inductor Dynamos, 25 Intake of Dynamo, Definition of, 5 Inter-Connected Armature Wind- ing, 145 Internal Characteristics of Series- Wound Dynamo, 210 Iron-Clad Armature, 24 Irregular Magnetic Flux, 35 Joint Reluctivity, 60 Journal Bearings for Armatures, 159-163 Lag of Motor Brushes, 303 Lamination of Armature Core, 105 Lamp, Pilot, Definition of, 12 Lap Winding for Armatures, 155 Laws of Electro-Dynamic Induc- tion, 74-89 Magnetic Attractions and Repulsions, 33 Lead, Forward, of Dynamo Brushes, 217 of Brushes, 195 Leading Edges of Pole-pieces, 184 Pole of Motor, 303 Leakage Factor, 132 , Magnetic, 52, 53 Length, Effective, of Armature Wire, 246 Limitation to Output of Continu- ous-Current Generator, 203 Limiting Temperature of Genera- tor Armature, 203 Line, Neutral, of Armature, 194 Lines of Magnetic Force, 34 , Stream, 30 Load Factor, 317 of Dynamo, 15 Locomotors, 273 INDEX. 329 Loss by Eddy Currents in Arma- ture and Field Poles, 200 , Hysteretic, 174 , , in Armature and Field Poles, 200 Losses, I 2 R, in Field Magnets, 199 in Armature, I 2 R, 200 Produced by Air-Churning, 201 Friction in Bearings and Brushes, 201 M M. F., Aligned, 56 Induced, 56 Methods of Producing, 38 Prime, 56 Structural, 56 Unit of, 40 Machine, Armature of, 9 Circumstances Influencing Electric Efficiency of Dyna- mos, 7 , Field Magnet of, 9 , Magnetic Flux Produced by, 9 Machinery, Electro-Dynamic, i , , Classification of, i Machines, Disc Armature and Single Field-Coil, 228-233 Magnet, Anomalous, 47 , Mechanical Analogue of, 30 , North-Seeking Pole of, 29 Magnets, Compound, 105 , Molecular, 56 Magnetic Air-Gap, 57 Air Path, Alternative, 52 Attractions and Repulsions, Laws of , 33 Circuit, 48 Circuit, Application of Ohm's Law to, 49 Circuits, Aero-Ferric, 68-73 Diffusion, 52, 53 Field, 32 Dissymmetry, 124 Field, Distribution of, 41-47 , Method of Mapping, 32 , Negatives of, 32 , Photographic Positives of, 32 Flux, 29 , Converging, 35 , Cutting Process, Enclos- ing, 82 Density, 34 , Diverging, 35 , Effect of, on C. E. M. F., 58 , Irregular, 35 of Dynamo, 9 , Uniform, 35 , Unit of, 49 , Unit of Intensity of, 35 Magnetic Flux, Variations of, 33 Force, Tubes of, 35 Friction, 174 Hysteresis, 172-178 , Definition of, 172 Intensity, 34 Leakage, 52, 53 Permeability, 55 , Definition of, 3 Potential, Fall of, 53 Reluctance, 48 Magnetism, Definition of, 29 , Molecular, 56 , Residual, 55, 173 , Streaming-Ether Theory of, 29 Magnetization, Back, of Arma- ture, 1 86 , Cross, 183 , Cycles of, 174 Magnetizing Force, 53 in Relation to Reluctivity, 59 Magneto-Electric Dynamo, n Magneto Generators, E. M. F. Induced by, 103-109 Magnetomotive Force, 31 Mapping of Magnetic Field, 32 Mechanical Analogue of Mag- net, 30 Meter Motors, 309-317 Methods for Suppressing Spark- ing, 189 Molecular Magnetism, 56 Magnets, 56 Motor, Average Efficiency of, 270 , Commercial Efficiency of, 268 , Dynamo-Power of, 264 Dynamos, 318-323 , Definition of, 318 , Full-Load Efficiency of, 270 , Leading Pole of, 303 Torque, 251-267 , Trailing Pole of, 303 Motors, Efficiency of, 268-279 , Fleming's Hand Rule for, 243 for Street Car, 277 , Individual Electric, 217 , Regulation of, 280-296 , Slow Speed, 271 , Starting and Reversing of, 291 -308 , Stationary, 273 , Traveling, 273 Multiphase Alternators, 26 Multipolar Dynamos, 16 , Single-Field-Coil, 28 Gramme-Ring Dynamos, 135- 151 33 INDEX. Negatives of Magnetic Fields, 32 Neutral Line of Armature, 184 Wire of Three-Wire System, 221 Non-Ferric Magnetic Circuits, 48-54 North-Seeking Pole of Magnet, 29 Octopolar Dynamos, 17 Oersted, Definition of, 49 Ohm, Definition of, 49 Ohm's Law, 49 Applied to Magnetic Cir- cuit, 49 Oilers, Sight-Feeding, 160 Omnibus Bars, 224 Open-Coil Armatures, 217 Over-Compounded Dynamos, 209 Output and Dimensions of Dyna- mos, Relation Between, 136 of Dynamo, Definition of, 5 , Relation Between and Re- sistance, 6 Permeability, Magnetic, 55 , , Definition of, 3 Photographic Positives of Mag- netic Fields, 32 Pilot Lamp, Definition of, 12 Plating Dynamo, 26 Points, Feeding, 322 Pole Armature, 25 Armatures, 110-116 , Leading, of Motor, 303 , North-Seeking of Magnet, 29 , South-Seeking, 29 , Trailing, of Motor, 303 Pole-Pieces, Following Edges of, 184 , Formation of Eddy Currents in, 169 , Leading Edges of, 184 Poles, Consequent, of Dynamo, 22 Potential, Magnetic, Fall of, 53 Prime Flux, 56 Flux Density, 54 M. M. F.,56 Properties, Assumed, of Ether, 29 Buadripolar Dynamos, 17 uiet Commutation, Circumstan- ces Favoring, 187 Radial Armature, no Ratio of Transformation, 321 Receptive Devices, Definition of, i Regulation of Dynamos, 206-219 of Motors, 280-296 Reluctance, 48 , Magnetic, 48 Reluctance, Unit of, 49 Reluctivity, 48 , Constants, Table of, 65 Curves in Relation to Flux Density, 66 , Ether Path of, 60 in Relation to Magnetizing Force, 59 , Joint, 60 , Metallic, Ferric Path of, 60 Residual Magnetism, 55, 173 Resistivity, 48 Return Track Feeders, 226 Reversing and Starting of Motors,. 291-308 Rheostats, Enameled, 216 , Field, 215 , Starting, 298 Ring Armature, 23 Ring Armatures, Gramme, 117- 127 Rotary Transformers, 318 Rule, Fleming Hand, for Motors,. 243 for Direction of E. M. F. In- duced in Loop, 94 Self-Excited Compound- Wound Dynamo, 13 Dynamo, 12 Series-Wound Dynamos, 13 Self-Induction, E. M. F., of, 181 E. M. F., of, Circumstances Af- fecting Value of, 182 Self-Oiling Bearings, 161 Separately-Excited Dynamo, 12 Series or Parallel Combinations of Dynamos, 220-227. Winding of Dynamos, 206 Series- Wound Dynamo, External Characteristic of, 210 Dynamo, Internal Character- istic of, 210 Sextipolar Dynamo, 17 Shunt Winding of Dynamos, 207 Shunt-Wound Dynamo, Charac- teristic of, 212 Dynamos, Uses for, 209 Sight-Feeding Oilers, 160 Simple Magnetic Circuit Dyna- mos, 22 Single-Circuit Bipolar Dynamo, 16 Single Field-Coil Multipolar Dy- namos, 28 Single-Phase Dynamos, 27 Slow Speed Motor, 271 Smooth-Core Armature, 23 Armatures, 152 INDEX. 33 1 Smooth-core Armature, Definition of, 24 Solenoid, Closed Circular, 50 Sources, Electromotive, 2 South-Seeking Pole, 29 Space for Armature Winding, 275 Sparking and Armature Reaction, 179-198 at Commutator, Circumstances Favoring, 186 , Definition of, iSo , Methods for Suppressing, 189 Sparkless Commutation, Circum- stances Favoring, 186 Specific Resistance, 48 Speed of Revolution, Effect of, on E.M.F.,3 Starting and Reversing of Motors, 291-308 Coil, 301 Rheostats, 298 Stationary Motors, 273 Step-Down Transformers, 319 Step-Up Transformers, 319 Stream Lines, 30 Streaming-Ether Theory of Mag- netism, 29 Structural M. M. F., 56 System, Three-Wire, 221 Table of French Measures, 8 of Hysteretic Activity, 175 of Reluctivity Constants, 65 Telegraphic Dynamo, 26 Thermal Losses, 204 Three-Phase Dynamos, 27 Three Phasers, 27 Three- Wire System, 221 , Neutral Wire of, 221 Toothed-Core Armature, 23 , Definition of, 24 Armatures, 152 Torque, Definition of, 251 , Motor, 251-267 Transformation, Ratio of, 321 Transformers, Rotary, 318 , Step-Down, 319 * , Step-Up, 319 Transmission Circuits, Definition of, i Travelling Motors, 273 Triphase Dynamos, 27 Triphasers, 27 Tubes of Magnetic Force, 35 Turns, Armature, Effect of, on E. M. F., 3 Two-Phase Dynamos, 27 Two Phasers, 27 Uniform Magnetic Flux, 35 Uniphase Alternators, 26 Unipolar Dynamos, 28, 234 Unit of Electric Flux, 49 Force, in C. G. S. System, 68 M. M. F., 40 Magnetic Flux, 49 Intensity, 35 Reluctance, 49 Variations of Magnetic Flux, 33 Volt, Definition of, 49 Voltaic Analogue of Aero-Ferric Circuit, 69 Simple Ferric Circuit, 69 Circuit, Magnetic Analogue of, 53 Wattmeter, 313 Wave Winding for Armatures, 155 Weber, Definition of, 49 Winding, Closed-Coil Armature, no , Compound, of Dynamos, 208 , Disc Armature, 230 for Armature, Inter-Connected, 145 Armatures, Lap, 155 Armature, Wave, 155 of Gramme-Ring Dynamo, Cal- culations of, 128-134 , Shunt, of Dynamos, 207 , Space, for Armature, 275 Wire, Armature, Effective Length of, 246 , Idle, on Armature, 100 , Neutral, of Three-wire System, 221 f^ OF THE (XTNIVERSITT RETURN TO the circulation desk of any University of California Library or to the NORTHERN REGIONAL LIBRARY FACILITY Bldg. 400, Richmond Field Station University of California Richmond, CA 94804-4698 ALL BOOKS MAY BE RECALLED AFTER 7 DAYS 2-month loans may be renewed by calling (415) 642-6753 1-year loans may be recharged by bringing books to NRLF Renewals and recharges may be made 4 days prior to due date DUE AS STAMPED BELOW 41992 65032 THE UNIVERSITY OF CALIFORNIA LIBRARY