F ROM -TH E - LI BRARY- OF WILLIAM -A HILLEBRAND ELECTRICAL MACHINE DESIGN McGraw-Hill BookComparry PwSfisfiers ofBoo/br Electrical World The Engineering and Mining Journal Engineering Record Engineering News Kailway Age Gazette American Machinist Signal E,ngi noer American Engineer Electric Railway Journal Coal Age Metallurgical and Chemical Engineering P o we r ELECTRICAL MACHINE DESIGN THE DESIGN AND SPECIFICATION OF DIRECT AND ALTERNATING CURRENT MACHINERY BY ALEXANDER GRAY, Whit. Sch., B. Sc. (Edin. and McGill) ELECTRICAL ENGINEERING, MCGILL UNIVERSITY MONTREAL, CANADA McGRAW-HILL BOOK COMPANY 239 WEST 39TH STREET, NEW YORK 6 BOUVERIE STREET, LOND.ON, E. G. 1913 COPYRIGHT, 1913, BY THE McGRAW-HiLL BOOK COMPANY 1HE. MAPLE. PRESS. YORK. PA PREFACE The following work was compiled as a course of lectures on Electrical Machine Design delivered at McGill University. Since the design of electrical machinery is as much an art as a science no list of formulae or collection of data is sufficient to enable one to become a successful designer. There is a certain amount of data, however, sifted from the mass of material on the subject, which every designer finds convenient to compile for ready reference. This work contains data that the author found necessary to tabulate during several years of experience as a designer of electrical apparatus. A study of design is of the utmost importance to all students, because only by such a study can a knowledge of the limitations of machines be acquired. The machines discussed are those which have become more or less standard, namely, direct-cur- rent generators and motors, alternating current generators, syn- chronous motors, polyphase induction motors, and transformers; other apparatus seldom offers an electrical problem that is not discussed under one or more of the above headings. The principle followed throughout the work is to build up the design for the given rating by the use of a few fundamental formulae and design constants, the meaning and limits of which are discussed thoroughly, and the same procedure has been followed for the several pieces of apparatus. The author wishes to acknowledge his indebtedness to Mr. B. A. Behrend, under whom he learned the first principles of electrical design and whose influence will be seen throughout the work; to the engineers of the Allis-Chalmers-Bullock Company of Montreal, Canada, and particularly to Mr. Bradley T. Mc- Cormick, Mr. G. P. Cole and Mr. H. F. Eilers; to Mr. A. Mc- N aught on of McGill University for criticism of the arrangement of the work and to Mr. A. M. S. Boyd for assistance in the proof- reading. McGiLL UNIVERSITY, September 2, 1912. 99588 CONTENTS SECTION I DIRECT-CURRENT MACHINERY CHAPTER I PAGE MAGNETIC INDUCTION .1 Lines of Force Direction of an Electric Current Magnetic Field Surrounding a Conductor Magneto Induction Direction of the Generated E. M. F. Magnetomotive Force. CHAPTER II ARMATURE WINDING 7 Gramme Winding Re-entrancy Objections to the Gramme Winding Drum Winding E.M.F. Equation Multipolar Ma- chines Equalizer Connections Short Pitch Windings Mul- tiple Windings Series Windings Lap and Wave Windings Shop Instructions Several Coils in a Slot Number of Slots Odd Windings. CHAPTER III CONSTRUCTION OF MACHINES 24 Armature Poles Yoke Co mmutator B earings Slide Rails Large Machines. CHAPTER IV INSULATION 30 Materials Thickness Heat and Vibration Grounds and Short- circuits Slot Insulation Puncture Test End Connection Insula- tion Surface Leakage Several Coils in a Slot Examples of Armature and Field Coil Insulation. CHAPTER V THE MAGNETIC CIRCUIT 42 Leakage Factor Magnetic Areas Fringing Constant Flux Densities Calculation of the No-load Saturation Curve and of the Leakage Factor. , CHAPTER VI ARMATURE REACTION 54 Armature Reaction Flux Distribution in the Air Gap Armature Reaction when the Brushes are Shifted Full Load Saturation Curve Relative Strength of Field and Armature. vii viii CONTENTS CHAPTER VII PAGE DESIGN OF THE MAGNETIC CIRCUIT 62 Field Coil Heating Size of Field Wire-^-Length of Field Coils- Weight of Field Coils Design of the Field System for a Given Armature. CHAPTER VIII COMMUTATION 72 Resistance Commutation Effect of the Self-induction of the Coils Current Density in the Brush Reactance Voltage Brush Con- tact Resistance Energy at the Brush Contact Reactance Voltage for Full Pitch Multiple, Short Pitch Multiple and Series Windings. CHAPTER IX COMMUTATION (Continued) 85 Sparking Voltage Minimum Number of Slots per Pole Brush Arc Limits of Reactance Voltage Limit of Armature Loading Interpole Machines Interpole Dimensions Flashing Over. CHAPTER X EFFICIENCY AND LOSSES . 97 Efficiency Bearing Friction Brush Friction Windage Loss Iron Losses Armature Copper Loss Field Copper Loss Brush Contact Resistance Loss. CHAPTER XI HEATING 104 Temperature Rise Maximum Safe Temperature Temperature Gradient in the Core Limiting Values of Flux Density Heating of Winding Temperature Gradient in the Conductors Commu- tator Heating Application of the Heating Constants. CHAPTER XII PROCEDURE IN ARMATURE DESIGN . 114 The Output Equation Relation Between Diameter and Length of the Armature Magnetic and Electric Loading Formulae for Armature Design Examples of Armature Design. CHAPTER XIII MOTOR DESIGN AND RATINGS 127 Procedure in Design Ratings for Different Voltages and Speeds Enclosed Motor Possible Ratings for a Given Armature. CHAPTER XIV LIMITATIONS IN DESIGN 138 Reactance Voltage and Average Voltage per Bar High Voltage CONTENTS ix PAGE Large Current Best Winding for Commutation Limits of Out- put in Non-interpole, Interpole, and Turbo Generators. CHAPTER XV DESIGN OF INTERPOLE MACHINES 146 Preliminary Design Design of Armature, Commutator and Field System Example. CHAPTER XVI SPECIFICATIONS 153 Example Points to be Observed Effect of Voltage and Speed on Efficiency. SECTION II ALTERNATORS AND SYNCHRONOUS MOTORS CHAPTER XVII ALTERNATOR WINDINGS 160 Fundamental Diagrams Y and A Connection Several Con- ductors per Slot Chain, Double-layer and Wave Windings Several Circuits per Phase. CHAPTER XVIII THE GENERATED ELECTRO-MOTIVE FORCE 178, Form Factor Wave Form Harmonics and Methods of Eliminat- ing Them Y and A Connection Harmonics Due to Armature Slots Effect of the Number of Slots on the Voltage Rating Effect of the Number of Phases on the Rating General E. M. F. Equation. CHAPTER XIX CONSTRUCTION OF ALTERNATORS 191 Stator Poles Field Ring. CHAPTER XX INSULATION 195 Definitions Insulators in Series Air Films Thickness of Insula- tion Potential Gradient Time of Application of the Strain* Examples of Alternator Insulation. CHAPTER XXI ARMATURE REACTION 208 Armature Fields Vector Diagram Full Load Saturation Curves Synchronous Reactance Calculation of the Demagnetizing Ampere-turns per Pole and of the Leakage Reactance End Con- nection, Slot and Tooth Tip Reactance Variation of Armature x CONTENTS PAGE Reactance and Armature Reaction with Power Factor Full Load Saturation Curves at any Power Factor Regulation Effect of Pole Saturation on the Regulation Relation Between the M. M. FS. of Field and Armature Single Phase Machines Comparison Between Single and Polyphase Alternators. CHAPTER XXII DESIGN OF THE REVOLVING FIELD SYSTEM 237 Field Excitation Procedure in Design Calculation of the Satura- tion Curves. CHAPTER XXIII LOSSES, EFFICIENCY AND HEATING 247 Bearing Friction Brush Friction Windage Loss Iron Loss Copper Loss Eddy Current Losses in the Conductors Efficiency Heating Internal Temperature of High Voltage Machines. CHAPTER XXIV PROCEDURE IN DESIGN 255 The Output Equation Relation Between Diameter and Length of the Armature Effect of the Number of Poles on this Relation Variation of Armature Length with a Given Diameter Windings for Different Voltages Examples of Alternator Design. CHAPTER XXV HIGH SPEED ALTERNATORS 272 Alternators Built for an Overspeed Turbo Alternators Rotor Construction and Stresses Diameter of Shaft Critical Speed Heating of Turbo Alternators Current on an Instantaneous Short- circuit Gap Density Demagnetizing Ampere-turns per Pole Relation Between the M. M. FS. of Field and Armature Pro- cedure in the Design of Turbo Alternators Limitations Due to Low Voltage Single Phase Turbo Alternators. CHAPTER XXVI SPECIAL PROBLEMS ON ALTERNATORS 297 Flywheel Design Design of Dampers Synchronous Motors for Power Factor Correction Design of Synchronous Motors Self- starting Synchronous Motors. CHAPTER XXVII ALTERNATOR SPECIFICATIONS 312 Example Notes on Alternator Specifications Effect of Voltage and Speed on the Efficiency. CONTENTS xi SECTION III POLYPHASE INDUCTION MOTORS CHAPTER XXVIII PAGE ELEMENTARY THEORY OF OPERATION 319 Revolving Field Multipolar Motors Windings Rotor Current and Voltage Starting Torque Running Conditions Vector Diagrams. CHAPTER XXIX GRAPHICAL TREATMENT OF THE INDUCTION MOTOR 332 Current Relations in Rotor and Stator Revolving Fields of Rotor and Stator Flux Diagram Proof of the Circle Law No Load and Short-circuit Points Representation of the Losses Relation Between Rotor Loss and Slip Interpretation of the Circle Diagram. CHAPTER XXX CONSTRUCTION OF THE CIRCLE DIAGRAM FROM TEST RESULTS .... 342 No Load Saturation Curve Short-circuit Curve Construction of the Diagram. CHAPTER XXXI CONSTRUCTION OF INDUCTION MOTORS 348 Stator Rotor. CHAPTER XXXII MAGNETIZING CURRENT AND NO-LOAD LOSSES 352 E. M. F. Equation Magnetizing Current Friction Loss Iron Loss Rotor Slot Design Calculation of the No-load Losses. CHAPTER XXXIII LEAKAGE REACTANCE 360 Leakage Fields Zig-zag Reactance Complete Formula Belt Leakage Approximate Formula for Preliminary Design. CHAPTER XXXIV COPPER LOSSES 371 Loss in the Conductors Loss in the End- connectors. CHAPTER XXXV HEATING OF INDUCTION MOTORS 375 Heating and Cooling Curves Intermittent Ratings Heating at Starting Stator and Rotor Heating Effect of Construction Enclosed and Semi-enclosed Motors. xii CONTENTS CHAPTER XXXVI PAGE NOISE AND DEAD POINTS IN INDUCTION MOTORS 385 Windage Noise Pulsations of the Main Field Vibration of the Tooth Tips Variations in the Leakage Field Dead Points at Starting. CHAPTER XXXVII PROCEDURE IN DESIGN 391 The Output Equation Relation Between Diameter and Length of the Stator Preliminary Design Detailed Design Design of Wound Rotor Motors Variation of the Stator Length with a Given Diameter Windings for Different Voltages Examples of Induction Motor Design. CHAPTER XXXVIII SPECIAL PROBLEMS ON INDUCTION MOTORS 409 Slow Speed Motors Closed Slots High Speed Motors Two- pole Motors Effect of Variations in Voltage and Frequency on the Operation. CHAPTER XXXIX INDUCTION MOTOR SPECIFICATIONS 422 Example Effect of Voltage and Speed on the Characteristics Specifications for Wound Rotor Motors. SECTION IV TRANSFORMERS CHAPTER XL OPERATION OF TRANSFORMERS 427 No-load Full Load Short Circuit Regulation. CHAPTER XLI CONSTRUCTION OF TRANSFORMERS 433 Small Core Type Large Shell Type. CHAPTER XLII MAGNETIZING CURRENT AND IRON Loss 439 E. M. F. Equation No-load Losses Exciting Current. CHAPTER XLIII LEAKAGE REACTANCE 445 Core Type with Two Coils per Leg Core Type with Split Secondary Windings Shell Type. CONTENTS xiii CHAPTER XLIV PAGE TRANSFORMER INSULATION 449 Transformer Oil Surface Leakage Bushings Coil Insulation Extra Insulation on the End Turns Insulation Between the Windings and Core. CHAPTER XLV LOSSES, EFFICIENCY AND HEATING 461 Iron Loss Copper Loss Eddy Current Loss in the Winding Efficiency Temperature Gradient in the Oil Temperature Gra- dient in Core and in Shell Type Transformers Temperature of the Oil Air Blast Transformers Water Cooled Transformers Heating Constants Effect of Oil Ducts Maximum Temperature in the Windings Section of Wire in the Coils. CHAPTER XL VI PROCEDURE IN DESIGN 476 The Output Equation Core Type Transformers Design of a Distributing Transformer Shell Type Transformers Design of a 110, 000- volt Power Transformer. CHAPTER XL VII SPECIAL PROBLEMS IN TRANSFORMERS 487 Comparison Between Core and Shell Type Transformers Three Phase Transformers Operation on Different Frequencies. CHAPTER XL VIII TRANSFORMER SPECIFICATIONS '. . . 494 Example for Distributing Transformers Effect of Voltage on the Characteristics. CHAPTER XLIX MECHANICAL DESIGN 499 Fundamental Principles Yokes Rotors and Spiders Commuta- tors Unbalanced Magnetic Pull Bearings Shafts Pulleys Brush Holders. WIRE TABLE . 508 TABLES OF SYMBOLS 512 INDEX . . 513 ELECTRICAL MACHINE DESIGN CHAPTER I \ i:\ji V MAGNETIC INDUCTIO^ ] ;;, ; i / ' \ ^ ' ; 1. Lines of Force. A magnetic field is represented by lines of force. These are continuous lines whose direction at any point is that of the force acting on a north pole placed at the point, therefore, as shown in Fig.l, lines of force always leave a north pole and enter a south pole. FIG. 1. Direction of lines of force. 2. Direction of an Electric Current. P and Q, Fig. 2, are two conductors carrying current. The current is going down in conductor P and coming up in conductor Q. If the direction of o Q Up FIG. 2. Direction of an electric current. the current be represented by an arrow, then in conductor P the tail of the arrow will be seen and this is represented by a cross; in conductor Q the point of the arrow will be seen and this is represented by a point or dot. 1 2 ELECTRICAL MACHINE DESIGN 3. Magnetic Field Surrounding a Conductor Which is Carrying Current. In conductor P, Fig. 3, an electric current is passing downward. It has been found by experiment that in such a case the conductor is surrounded by a whirl of magnetic lines in the direction shown. This direction can be found by the following rule: "If a corkscrew be screwed into the conductor in the direction of the current then the head of the corkscrew will travel in 1 the direction of; the lines of force." ' 4. Magneto' Induction. Faraday's experiments showed that .when /the. magnetic 'flux threading a coil changes, an e.m.f. is generated 'in tire' coil, and that this e.m.f. is proportional to the rate of change of flux in the coil. FIG. 3. Magnetic field surrounding a conductor. The unit of e.m.f. is so chosen that one unit of e.m.f. is gener- ated in a coil of one turn when the rate of change of flux in the coil is one line per second. This is called the c.g.s. unit; the practical unit, called the volt, is 10 8 c.g.s. units. 5. Direction of the Generated E.M.F. N and S, Fig. 4, are the north and south poles of a magnet, is the total number of lines of force passing from the north to the south pole, A is a coil of one turn. When the coil A is moved from position 1, where the number of lines threading the coil is , to position 2, where the number of lines threading the coil is zero, in a time of t seconds, then the average e.m.f. generated in the coil = ylO~ 8 volts; or at any ( t instant the e.m.f. = -^10~ 8 volts. at MAGNETIC INDUCTION 3 The quantity ~ is the rate at which conductor xy, Fig. 4, is cutting lines of force, so that the voltage generated by a conductor which is cutting lines of force is equal to (the lines cut per second) X 10~ 8 . The direction of this e.m.f. is found by Fleming's Rule which states that " If the thumb, forefinger and middle finger of the right hand are all set perpendicular to one another so as to represent three co-ordinates in space, the thumb pointed in the direction of motion of the conductor relative to the magnetic FIG. 4. Direction of the generated e.m.f. field, and the forefinger in the direction of the lines of force, then the middle finger will point in the direction in which the generated e.m.f. tends to send the current of electiicity." The direction of the e.m.f. in Fig. 4 is found by Fleming's three- finger rule, and the current due to this e.m.f. is in such a direction as to tend to maintain the flux threading the coil, or, as stated by the very general law known as Lenz's Law, "the generated e.m.f. always tends to send a current in such a direction as to oppose the change of flux which produces it." The complete 4 ELECTRICAL MACHINE DESIGN statement of the e.m.f. equation is, therefore, that the e.m.f. at any instant = -^~10~ 8 volts. 6. Magnetomotive Force. In Fig. 5 the current 7 passes through the T turns of the coil C which is wound on an iron core, and a magnetic flux is set up in the magnetic circuit. This flux is found to depend on the number of ampere-turns TI, and, corresponding to Ohm's law for the electric circuit, there is a law for the magnetic circuit namely, m.m.f. =(f>R, where m.m.f. is the magnetomotive force and depends on TI, is the flux threading the magnetic circuit, R is the reluctance of the magnetic circuit. The most convenient unit of m.m.f. would have been the ampere-turn, but in order to conform to the definition of potential as used in hydraulic and electric circuits, another unit has to be adopted. The difference of potential in centimeters between two points in a hydraulic circuit is the work done in ergs in moving unit mass of water from one point to the other, and the difference of mag- netic potential (m.m.f.) between two points in a magnetic circuit is the work done in ergs in moving a unit pole from one point to the other. Let a unit pole, which has 4n lines of force, be moved through the electro-magnet from A to B in a time of t seconds, then an e.m.f. E= Tx~j- c.g.s. units will be generated between a and b. In order to maintain the current 7 constant against this e.m.f. an amount of work =EI ergs per second must be done; so that the m.m.f. between A and B = EIt ergs, It ergs, ergs when 7 is in c.g.s. units, = j~ 77 ergs when 7 is in amperes, therefore the unit of m.m.f. is not the ampere-turn, but is equal to -^ ampere-turns. It must be understood that this m.m.f. is what might be called the generated m.m.f., thus in the electro-magnet shown MAGNETIC INDUCTION 5 in Fig. 5 the generated m.m.f. is equal to y~ TI, but the effective m.m.f. between A and B is equal to this generated m.m.f. minus the m.m.f. necessary to send the magnetic flux round the iron part of the magnetic circuit. Take for example the extreme case shown in Fig. 6, where the core is bent round to form a complete annular ring. The generated m.m.f. between the points A and B = Tr> TI, but A is the same point as B so that there can be no difference of magnetic potential between them, therefore all the generated m.m.f. is used up in sending the FIG. 5. Magnetic circuit. FIG. 6. Closed magnetic circuit. flux (f> through the ring itself. By means of such a ring the magnetic materials used in electrical machinery are tested; the cross-section S of the ring arid also the mean length I are known, and for a given generated m.m.f. the flux (f> can be measured. Then since m.m.f. = ~^ = lu o , from which k can be found. B is the flux density or number of lines per square centimeter, k is the specific reluctance and = 1 for air, I is in centimeters. For an air path, B, the flux density in lines per square centi- meter = ~--) where I is in centimeters. When inch units are 6 ELECTRICAL MACHINE DESIGN used, so that I is in inches, and the flux density is in lines per square inch, then TI B, the flux density in lines per square inch = 3. 2-p* (1) For materials like iron, k, the specific reluctance, is much less than 1, and the value of k varies with the flux density. For practical work the value of k is never plotted; it is more con- venient to use curves of the type shown in Fig. 42, page 47, which curves are determined by testing rings of the particular TI material and plotting B in lines per square inch against -j-> where I is in inches. CHAPTER II ARMATURE WINDING 7. Definition of Armature Winding. In Fig. 7 the armature A of a generator is revolving in the magnetic field NS in the direction of the arrow. The directions of the e.m.fs. which are generated in the conductors of the armature are found by the three-finger rule and shown in the usual way by crosses and dots. The principal purpose of the armature winding is to connect the armature conductors together in such a way that a desired resultant e.m.f. can be maintained between two points which are connected to an external circuit. The conductors and their interconnections taken together form the winding. FIG. 7. Direction of current in a D.-C. generator. FIG. 8. Two-pole simplex Gramme winding. 8. Gramme Ring Winding. This type of winding, which is shown diagrammatically in Fig. 8, was one of the first to be used. Although the winding is now practically obsolete it is mentioned because of its simplicity, and because it shows more clearly than does any other type of winding the meaning of the different terms used in the system of nomenclature. 1 The two-pole winding shown in Fig. 8 is the simplest type of Gramme winding; it has only two paths between the + and the brush and is called the simplex winding to distinguish it from 1 The system of nomenclature adopted in this chapter is that of Parshall and Hobart. 7 8 ELECTRICAL MACHINE DESIGN the other two fundamental Gramme windings, shown in Figs. 9 and 10. Inspection of these latter figures shows that in each of these cases there are four paths between the + and the - brush, or twice as many as in the case of the simplex winding; for this reason they are called duplex windings. There is, however, an essential difference between the two duplex windings and to distinguish between them it is necessary to define the term re-entrancy. 9. Re-entrancy. -If the winding shown in Fig. 8 be followed round the machine starting at any point b, it will be found that the winding returns to the starting-point, or is re-entrant, and that before it becomes re-entrant every conductor has been taken in once and only once; such a winding is called a singly re-entrant winding. FIG. 9. Doubly re-entrant duplex winding. FIG. 10. Singly re-entrant duplex winding. If the winding shown in Fig. 9 be followed round the machine starting at any point b, it will be found to be re-entrant when only half of the conductors have been taken; in fact the winding is simply two singly re-entrant windings put on the same core, and is called a doubly re-entrant duplex winding. If, on the other hand, the winding shown in Fig. 10 be followed round the machine starting at any point 6, it will be found that it' does not become re-entrant until every conductor has been taken in once and only once; it is therefore a singly re-entrant duplex winding. It is evidently possible to carry this process of increasing the number of paths through the winding much further so as to get multiplex multiply re-entrant, multiplex singly re-entrant, and many other combinations; but such windings are rarely to be found in modern machines, in fact even duplex windings are ARMATURE WINDING seldom used except for large-current low-voltage machines. In such machines the large current entering the brush is divided up and passes through the several paths, so that during commu- tation the current which is being commutated is only half of what it would have been had a simplex winding been used. This is shown at the positive brush, Fig. 10, where it will be seen that only the current in coil 5, or half of the total current, is being commutated at that instant. In the case of a duplex winding the brush must be wide enough to cover two segments in order to collect current from all four paths. 10. Objections to the Gramme Winding. In the case of small machines it is difficult to find space below the core for the return part of the winding without making the diameter of the machine unnecessarily large; while in the case of large machines, where the winding is made of heavy strip copper, it is difficult to remove and replace damaged coils. The number of coils and commutator segments is twice that required for a machine of the same voltage and with the other type of winding, namely the drum winding. FIG. 11. Coil for drum winding. In many cases the active part of a coil is only a small portion of the total coil since the side and return connections do not cut lines of force. Since the whole winding lies close to the iron of the core the coefficient of self-induction of the coils is large and the machine on that account is liable to spark. 11. Drum Winding. This winding was developed to over- come the objections to the Gramme winding. In the simplest 10 ELECTRICAL MACHINE DESIGN case two conductors are joined together to form a coil of the shape shown in Fig. 11. This coil is placed on the machine in such a way that when one side a of the coil is under a north pole, the other side b is under the adj acent south pole, therefore both sides of the coil are active and the e.m.fs. generated in the two sides act in the same direction round the coil. Since each coil consists of at least two conductors, the total number of con- ductors for a drum winding must be even. Fig. 12 shows a two-pole simplex singly re-entrant drum winding with 16 conductors. It might seem that conductors FIG. 12. Two-pole simplex singly re-entrant drum winding. which are exactly opposite to one another should be connected in series to form a coil, so that conductor 1 should be connected to conductor 9 and then back to conductor 2, but a few trials will show that in order to get a singly re-entrant winding it is necessary to make the even conductors the returns for the odd. Starting then at conductor 1 the winding goes to the nearest even conductor to that which is exactly opposite, namely conductor 8, then returning back to the south pole the next odd conductor is number 3, which again is connected to conductor 10, and so on; so that the complete winding can be represented by the following table: l-8_3-10_5-12_7-14_9-16_ll-2_13-4_15-6_l, which shows clearly that the winding is re-entrant, and also that every conductor has been taken in once and only once. ARMATURE WINDING 11 The connections of this winding to the commutator are shown in Fig. 12. Fig. 13 is another method adopted to show the connections of the same winding and is obtained by splitting Fig. 12 at xy and opening it out on to a plane. This gives what is called the developed winding and shows clearly the shape of the coil which is used. If Fig. 13 be cut out and bent around a drum it will give the best possible representation of a drum winding. Inspection of Figs. 12 and 13 shows that, just as in the case of the simplex Gramme winding, there are two paths between the + and the brush. 1 14 12 11 10 9 8 , ^ 7 6 ( \ ,1 5 > 4 3 , 2 1 i N I S FIG. 13. B- B-f -Developed two-pole simplex singly re-entrant drum winding. 12. The E.M.F. Equation. If (f) a is the flux per pole which is cut by the armature conductors, p is the number of poles, Pi is the number of paths through the armature, Z is the total number of face conductors on the armature surface, r.p.m. is the speed of the armature in revolutions per minute, then one conductor cuts (f> a p lines per revolution or, . r.p.m.

tr /? C\ \ ' 12 ELECTRICAL MACHINE DESIGN The number of poles and paths is determined by the designer of the machine. 13. Multipolar Machines. One of the easiest ways by which to get several paths through the winding is to build multipolar FIG. 14. Six-pole simplex singly re-entrant multiple drum winding. I FIG. 15. Part of a six-pole simplex singly re-entrant multiple drum winding. machines, thus Fig. 14 shows a six-pole drum winding which has six paths in parallel between the + and the terminals. There are three + and three brushes and like brushes are connected together outside of the machine at T+ and T- . The ARMATURE WINDING 13 diagram which is used in this case is a slight modification of the developed diagram and gets over the difficulty of splitting the winding. Fig. 14 is rather complicated and will be explained in detail. Figure 15 shows the armature conductors, the poles and the commutator of the same machine. There are two conductors in each slot so that a section through one of the slots is as shown at S, Fig. 15; the winding lies in two layers and is called a double layer winding. In Fig. 14 there are 24 slots and 48 conductors; a conductor in the top half of a slot is an odd-numbered conductor and that in the bottom half of a slot is an even-numbered con- ductor, so that, since the even conductors are the returns for the odd, each coil has one side in the top of one slot and the other side in the bottom of the slot which is one pole pitch further over. The coils are all alike and are made on the same former; a few of the coils are shown in place in Fig. 15, where conductors that are in the top layer are represented by heavy lines while those in the bottom layer are represented by dotted lines. 14. Equalizer Connections. In the winding shown in Fig. 14 there are six paths in parallel between the + and the terminals, and it is necessary that the voltages in all six paths be equal, otherwise circulating currents will flow through the machine. In Fig. 16, for example, is shown a case where, due to wear in the bearings, the armature is not central with the poles, and there- fore the flux density in the air gap under poles A is greater than that in the air gap under poles B, so that the conductors under poles A will have higher voltages generated in them than those that are under poles B, and the voltage between brushes c and d will be greater than that between brushes/ and g. Since c and/ are connected together, as also are d and g, a circulating current will flow from c to /, through the winding to g, then to d and back through the winding to c, as shown diagrammatically at C, Fig. 16. Since the circulating currents pass through the brushes, some of the brushes will have to carry more current than they were designed for, and sparking will result. To prevent the circulating current from having any large value it is necessary to prevent unequal flux distribution in the air gaps under the poles. This can be done by setting up the machine carefully, taking off the outside connections T+ and T_ between the brushes, and adj ust- ing the thickness of the air gaps under the different poles until 14 ELECTRICAL MACHINE DESIGN the voltages between + and brushes are all equal, the machine being fully excited and running at full speed and no load. It is impossible, to eliminate entirely this circulating current, but its effect must be minimized. This is done by providing a low resistance path of copper between the points c and / and also between d and g, inside of the brushes, so that the circulating current will pass around this low-resistance path rather than through the brushes. It must be understood that the equal- izer connections, as these low-resistance paths are called, do not eliminate the circulating current, but merely prevent it / 9 C FIG. 16. Machine with unequal air-gaps to show the action of equalizer connections. from passing through the brushes. When the armature in Fig. 16 revolves into another position a different set of conductors have to be supplied with equalizers, and in order that the machine may be properly equalized in all positions of the arma- ture, all points which ought to be at the same potential at any instant must be connected together. Figure 14 is the complete diagram showing all the windings and also the equalizers. It is not necessary to equalize all the coils, because when, as in Fig. 14, the brush is on a coil which is not directly connected to an equalizer, there is still a path of lower resistance than that through the brushes, namely round one turn of the winding and then through the equalizer connec- tion. It is usual in practice to put in about 30 per cent, of the maximum possible number of equalizer connections. ARMATURE WINDING 15 The developed diagram corresponding to that of Fig. 14 is shown in Fig. 17; the only change that has been made is that the equalizer connections have been put at the back of the machine where they can be easily got at for repair. When these connec- tions are placed behind the commutator it is impossible to get at them for repair without disconnecting the commutator from the armature winding. When an armature is supplied with equalizer connections each brush will carry its proper share of the total current, because at . + * + II FIG. 17. Six-pole simplex singly re-entrant drum winding. one side the brushes are all connected together through the terminal connections and at the other side through the equalizer connections, so that the voltage drop across each brush is the same, and since the brushes are all made of the same material they must have the same current density. 15. Short Pitch Windings. In Fig. 14 the two sides of each coil are exactly one pole pitch apart; such a winding is said to be full pitch. In Fig. 18 is shown a winding in which the two sides of each coil are less than one pole pitch apart; such a winding is said to be short pitch. Fig. 19 shows the developed diagram for this short-pitch winding at the instant when the coils in the neutral zone are short-circuited. It will be seen that the effective width of the neutral zone has been reduced by the angle a; this disadvantage, however, is compensated for by the fact that the conductors of the coils which are short-circuited at any instant are not in the same slot. This, as shown in Art. 67 page 82, lessens the mutual induction between the short-circuited coils and tends to improve commutation. Shortening the pitch by more than one slot decreases the neutral zone but does not 16 ELECTRICAL MACHINE DESIGN further decrease the mutual induction, so that there is no advantage in shortening the coil pitch more than one slot, but rather the reverse. Since there are seldom less than 12 slots per pole the effect of the shortening of the pitch on the generated voltage and on the armature reaction can be neglected. FIG. 18. Six-pole simplex singly re-entrant short-pitch multiple drum winding. FIG. 19. Corresponding developed drum winding. 16. Multiple Windings. The windings shown in Figs. 14 and 18 have the same number of circuits through the armature as there are poles. Had they been duplex windings they would have had twice as many circuits. When the winding has a number of circuits which is a multiple of the number of poles ARMATURE WINDING 17 it is called a multiple winding to distinguish it from that described in the next article which is called a series winding. Since windings that are not simplex and singly re-entrant are very rare, these two terms are generally left out, so that, unless it is actually stated to the contrary, all windings are assumed to be simplex singly re-entrant, and the windings shown in Figs. 14 and 18 would be called six-pole multiple drum windings. FIG. 20. Six-pole series progressive drum winding. FIG. 21. Small part of the above winding. 17. Series Windings. It is possible to wind multipolar machines so that there are only two paths through the armature winding. Such windings are called series windings and an example of one is shown in Fig. 20 for a six-pole machine; in Fig. 21 a small portion of the winding is shown to make the complete diagram clearer. 18 ELECTRICAL MACHINE DESIGN If the winding be followed through, starting from the brush, it will be seen that there are only two circuits through the armature, and that only two brushes are required. At the instant shown in Fig. 21 the - brush is short-circuiting two commutator segments and in so doing short circuits three coils. Since the points a, b and c are all at the same poten- tial it is possible to put brushes at each of these points, so that the current will not be collected from one set of brushes but from three; this will allow the use of a commutator of 1/3 of the length of that required when only one set of positive and one set of negative brushes are used. A machine with a series winding will therefore have in most cases the same number of brush sets as there are poles. FIG. 22. Six-pole series retrogressive drum winding. It may be seen from Fig. 21 that the number of commutator segments must not be a multiple of the number of poles otherwise the winding would close in one turn round the machine; to be singly re-entrant the winding must progress by one commutator segment, as shown in Fig. 20, or retrogress by one commutator segment, as shown in Fig. 22, each time it passes once round the armature, the condition for this is that $, the number of commutator segments, =&~+l, where k is a whole number Zj and p the number of poles. When the sign is used the winding is progressive, as in Fig. 20, where the number of commutator ARMATURE WINDING 19 segments is 23, and when the + sign is used the winding is retro- gressive, as in Fig. 22, where the number of commutator segments is 25. The paragraph in Art. 14, page 15, on the division of the total current of the machine, holds to a certain extent for the series winding also; the one side of all the brushes are connected together through the short-circuited coils, as shown in Fig. 21, while the other side of the same brushes are con- nected together through the terminal connections. It is im- portant to notice, however, that since the number of com- T) mutator segments S is not a multiple of ~> the number of pairs i of poles, and since the brushes of like polarity are spaced two pole pitches apart, a kind of selective commutation will take place, thus when, as shown in Fig. 21, brush a is short-circuiting a set of three coils in series, brush 6 has just begun to short-circuit an entirely different set of three coils in series and brush c has nearly finished short-circuiting still another set of three coils in series. The series winding has the great advantage that equalizers are not required, since, as shown in Fig. 21, the winding is already equalized by the coils themselves, so that there can be no circu- lating current passing through the brushes; further 'there can FIG. 23. Coils with several turns. be no circulating current in the machine due to such causes as unequal air gaps because each circuit of the winding is made up of conductors in series from under all the poles. On account of this fact, and also because of the property that only two sets of brushes are required, the series winding is used for D.-C. railway motors, because in a four-pole railway motor the two brushes can be set 90 degrees apart so as to have both sets of brushes above the commutator, where they can be easily inspected from the car. 20 ELECTRICAL MACHINE DESIGN 18. Lap and Wave Windings. From the appearance of the individual coils of the two windings, Figs. 14 and 20, the former is sometimes called a lap winding and the latter *a wave winding. It must be understood, however, that each of the coils shown in these diagrams may consist of more than one turn of wire, thus Fig. 23 shows both a lap and a wave coil with several turns per coil, so that the terms lap and wave apply only to the connec- tions to the commutator and not to the shape of the coil itself; the terms multiple and series are more generally used. 19. Shop Instructions. It would be a mistake to send winding diagrams such as those described in this chapter into the shop and expect the men in the winding room to connect up a machine properly from the information given there; the instructions must be given in much simpler form. For a winding such as that shown in Fig. 17 the shop instructions would read: "Put the coil in slots 1 and 5 and the commutator connections in segments 1 and 2," where the position of segment 1 relative to that of slot 1 is fixed by the shape of the end of the coil. All the coils are made on formers and are exactly alike, so that, having the first coil in place, the workman can go straight ahead and put in the other coils in a similar manner. In the case of a winding such as that shown in Fig. 20, the instructions would read: " Put the coil in slots 1 and 5 and the commutator connections in segments 1 and 9," where the position of segment 1 relative to that of slot 1 is again fixed by the shape of the coil. 20. Duplex Multipolar Windings. The multipolar windings discussed so far have all been simplex and singly re-entrant. It is evident that both multiple and series windings can be made duplex if necessary; such windings can easily be drawn from the information already given in this chapter and no special discussion of them is necessary. 21. Windings with Several Coil Sides in One Slot. There are generally more coils than there are slots. Fig. 24 shows part of the winding diagram for a machine which has a multiple wind- ing with four coil sides in each slot and two turns per coil, and Fig. 25 shows part of the winding diagram for a series wound machine also with four coil sides in each slot and two turns per coil. A section through one slot in each case is shown in Fig. 26; there are eight conductors per slot and conductors are numbered similarly in Figs. 25 and 26. In each case there are ARMATURE WINDING 21 FIG. 24. Multiple winding with four coil sides per slot and two turns per coil. 345 J 1 1 1 1 1 L FIG 25. Series winding with four coil sides per slot and two turns per coil. 1256 3478 FIG. 26. Section through one slot of the above windings. 22 ELECTRICAL MACHINE DESIGN two commutator segments to a slot since the number of commuta- tor segments is always the same as the number of coils, in fact a coil may be denned as the winding element between two commutator segments. 22. Number of Slots and Odd Windings. For series or wave windings the number of coils = S, the number of commutator segments, = k^+l, therefore the number of coils must always be u odd, and the number of slots should also be odd. Even when an odd number of slots is used it is not always possible to get a wave winding without some modification. Suppose, for example, that a 110-volt four-pole machine has 49 slots and two conductors per slot, then the number of coils = 49 = 24^ + 1, which will give a satisfactory winding; when wound for 220 volts the machine requires twice the number of conductors, or four conductors per slot, so that the number of coils = 98 = 49^ + which will not give 2i a wave winding. In such a case, however, the winding can be made wave by cutting out one coil so that the machine has really 97 coils instead of 98, and has also 97 commutator seg- ments; the extra coil is put into the machine for the sake of appearance but is not connected up, its two ends are taped so as to completely insulate the coil, and it is called a dead coil. When the armature is large in diameter it is built in segments as described in Art. 28, page 28. In such a case it is difficult to get an odd number of slots on the armature; indeed, it can only be done when the number of segments that make up one complete ring of the armature and also the number of slots per segment are both odd numbers; however, for reasons to be discussed under commutation, series or wave windings are seldom found in large machines. For multiple or lap windings the number of slots must be multiple of half the number of poles if equalizers are to be used; this can be ascertained from Fig. 16, where it is seen that in the case of a six-pole machine the equalizers must each connect together three points on the armature exactly two pole pitches apart from one another. It is found, however, that small four-pole machines with multiple windings run sparklessly without equalizers, and since the only condition that limits a multiple winding without equalizers is that the number of con- ARMATURE WINDING 23 ductors be even, for such small machines the same punching is used as for the machine with the series winding, namely, a punch- ing having an odd number of slots; the number of conductors will be even since the winding is double layer, and has therefore a multiple of two conductors per slot. By the use of the same punching for both multiple and series windings, a smaller stock of standard parts needs to be kept, quicker shipment can be made, and lower selling prices given for small motors, than if different punchings were used. In the case of large machines it is best to make the winding such that equalizers can be used, because the sparking caused by the want of equalizers becomes worse as the number of poles and as the output of the machine increases. CHAPTER III CONSTRUCTION OF MACHINES The construction of electrical machinery is really a branch of mechanical engineering but it is one which requires considerable knowledge of electrical phenomena. Figure 27 shows the type of construction that is generally adopted for D.-C. machines of outputs up to 100 h.p. at 600 r.p.m. 23. The Armature. M, the armature core, is built up of laminations of sheet steel 0.014 in. thick, the thinner the lamina- tions the lower the eddy current loss in the core, but sheets thinner than 0.014 in. are flimsy and difficult to handle. The laminations are insulated from one another by a layer of varnish and are mounted directly on the shaft of the machine and held there by means of a key, as shown at K. It will be noticed that in the key-way K there is a small notch, called a marking notch, the object of which is to ensure that the burrs on the punchings all lie the same way; it is impossible to punch out slots and holes without burring over the edge, and unless these burrs all lie in the same direction a loose core is produced. The laminations are punched on the outer periphery with slots F which carry the armature coils G. The type of slot shown is that which is in general use and is called the open slot. The other type which is sometimes used is closed at the top; the coils in this case have to be pushed in from the ends. The open slot has the advantage that the armature coils can be fully insu- lated before being put into the machine, and that the coils can be taken out, repaired, and replaced, in the case of a break- down, more easily than if the closed type of slot had been adopted. The armature core is divided into blocks by means of brass vent segments, shown at P\ the object of the vent ducts so produced is to allow free circulation of air through the machine to keep it cool; they divide the core into blocks less than 3 in. thick and are approximately 3/8 in. wide; narrower ducts are 24 CONSTRUCTION OF MACHINES 25 not very effective and are easily blocked up, while wider ducts do not give increased cooling effect and take up space which might be filled with iron. The vent segments are mounted directly on the shaft, and, along with the laminations of the core, are clamped between two cast-iron end heads N. These end heads carry the coil supports L which are attached by arms shaped so as to act as fans and maintain a circulation of air through the machine. The armature coils are held against centrifugal force by steel band wires, five sets of which are shown. 24. Poles and Yoke. The armature revolves in the magnetic field produced by the exciting coils A which are wound on and insulated from the poles B. In Fig. 27 the poles are of circular cross-section so as to give the required area for the flux with the minimum length of mean turn of the field coil. They are made of forged steel and, attached to them by means of screws, there is a laminated pole face E made of sheet steel 0.025 in. thick, to prevent, as far as possible, eddy currents in the pole faces. The pole face laminations are stacked up to give the neces- sary axial lejigth and are held together by four rivets. In Fig. 27 it will be seen that each end lamination has a projection on it for the purpose of supporting the field coil. The axial length of the pole in the machine shown is 3/8 in. shorter than the axial length of the armature core. This is done to enable the revolving part of the machine to oscillate axially and so prevent the journals and bearings from wearing in grooves. In order that the armature may oscillate freely it is necessary that the reluctance of the air gap does not change between the two extreme positions, the condition for which is that the armature core be longer or shorter axially than the pole face by the amount to be allowed for oscillation, which is usually 3/8 in. for motors up to 50 h. p. at 900 r.p.m., and 1/2 in. for larger machines. The poles are attached to the yoke C by means of screws, the yoke also carries the bearing housings D which stiffen the whole machine so that the yoke need not have a section greater than that necessary to carry the flux. The housings and yoke are clamped together by means of through bolts, and the construction must be such that the housings are capable of rotation relative to the yoke through 26 ELECTRICAL MACHINE DESIGN CONSTRUCTION OF MACHINES 27 90 or 180 degrees in order that the machine, usually a small motor, may be mounted on the wall or on the ceiling. This rotation of the bearings is necessary in such cases because, since the machines are lubricated by means of oil rings, the oil wells must be always below the shaft. 25. Commutator. The commutator is built up of segments J of hard drawn copper insulated from one another by mica which varies in thickness from 0.02 to 0.06 in., depending on the diameter of the commutator and the thickness. of the segment. The mica used for this purpose must be one of the soft varieties, such as amber mica, so that it will wear equally with the copper segments. The segments of mica and copper are clamped between two cast-iron V-clamps S and insulated therefrom by cones of micanite 1/16 in. thick. The commutator shell, as the clamps and their supports are called, is provided with air passages R which help to keep the machine cool. The commutator segments are connected to the armature winding by necks or risers H which, in all modern machines, have air spaces between them as shown, so that air will be drawn across the commutator surface and between the risers by the fanning effect of the armature. This air is very' effective in cooling the commutator. 26. Bearings. The construction of a typical bearing is shown in detail and is self-explanatory. The points of interest are: the projection T on the oil-hole cover, the object of which is to keep the oil ring from rising and resting on the bushing; the oil slingers on the shaft, which prevent the oil from creeping along the shaft and leaving the bearing dry; the bearing construction with a liner of special bearing metal, which is a snug fit in the bearing shell and which can readily be removed and replaced when worn; the method adopted for draining the oil back into the oil well. The level of the oil is shown and it will be seen that it is in contact with a large portion of the bearing shell and is therefore well cooled. The oil may be drained out when old and dirty by taking out the plug shown at the bottom. There is a small overflow at U which prevents the bearing from being filled too full. The brushes are carried on studs which are insulated from the rocker arm V. The rocker arm is carried on a turned seat on the bearing and can be clamped in a definite position. 28 ELECTRICAL MACHINE DESIGN 27. Slide Rails. When the machine has to drive or be driven by a belt, the feet of the yoke are slotted as shown, so that it can be mounted on rails and a belt-tightening device supplied. 28. Large Machines. For large machines the type of con- struction is somewhat different from that already described; Fig. 28 shows the type of construction generally adopted for large direct-connected engine units. When the armature diameter is larger than 30 in., so that the punchings can no longer be made in one ring, the armature core is built up of segments which are carried by dovetails on the spider; the segments of alternate layers overlap one another so as to break joint and give a solid core. FIG. 28. Engine type D.-C. generator. The vent ducts in this machine are obtained by setting strips of sheet steel on edge as shown at V', these strips are carried up to support the teeth and are held in position by projections punched in the lamination adjoining the vent duct. Vent ducts are placed at the ends of the core, partly for ventilation but principally to support the teeth. The poles are of rectangular cross-section and are built up of laminations of the shape shown at P. The laminations are CONSTRUCTION OF MACHINES 29 0.025 in. thick and are assembled so that the cutaway pole tips of adjacent laminations point in opposite directions. A satu- rated pole tip is therefore produced, which is an aid to commutation. The laminations are riveted together to form a pole which is then fastened to the yoke by screws. The shaft, bearings, and base of such a machine are generally supplied by the engine builder. The bearings are similar to those shown in Fig. 27 except that the bushing is generally made of babbitt metal, which is cast and expanded into a cast- iron shell. One oil ring is put in for each 8-in. length of the bearing bushing. Since the shaft is supplied by the engine builder it is necessary to support the commutator from the armature spider, and one way of doing this is shown in Fig. 28. The brush rigging must also be supported from the machine in some way and is generally carried from the yoke as shown. Brushes of like polarity are joined together by copper rings R which carry the total current of the machine to the terminals. The yoke of a large D.-C. generator is always split so that, should the armature become damaged, the top half of the yoke can be lifted away and repairs done without removing the armature. CHAPTER IV INSULATION 29. Properties desired in Insulating Materials. A good in- sulator for electrical machinery must have high dielectric strength and high electrical resistance, should be- tough and flexible, and should not be affected by heat, vibration, or other operating conditions. The material is generally used in sheets and its dielectric strength is measured by placing a sheet of the material 0.01 in. thick between two flat circular electrodes and gradually raising the voltage between these electrodes until the material breaks down. To get consistent results the same electrodes and 'the same pressure between electrodes should be used for all comparative tests; a size of 2 in. diameter, with the corners rounded to a radius of 0.2 in., and a pressure of 1.5 lb. per square inch, have been found satisfactory. The value of the dielectric strength is defined as the highest effective alternating voltage that 1 mil will withstand for 1 minute without breaking down. The material should be tested over the range of temperature through which it may have to be used, and all the conditions of the test and of the material should be noted; for example, the dielectric strength depends largely on the amount of moisture which the material contains and is generally highest when the material has been baked and the free moisture expelled. The flexibility is measured by the number of times the material will bend backward and forward through 90 degrees over a sharp corner without the fibers of the material breaking or the dielectric strength becoming seriously lessened. Materials which are quite flexible under ordinary conditions often become brittle when baked so as to expel moisture. 30. Materials in General Use. For the insulation of windings the choice is limited to the following materials. Micanite, mica, varnished cloth, paper, cotton, various gums and varnishes. Cotton tape which is generally 0.006 in. thick and 0.75 in. wide is put on coils in the way shown in Fig. 29, which is called half-lap taping. Such a layer of tape will withstand about 250 30 INSULATION 31 volts when dry. When the tape is impregnated with a suitable compound so as to fill up the air spaces between the fibers of the cotton such a half-lap layer will withstand about 1000 volts. Cotton Covering. Small wires are insulated by spinning over them a number of layers of cotton floss; the wire generally used for armature and field windings is insulated with two layers of cotton and is called double cotton covered (d.c.c.) wire. FIG. 29. Half -lap taping. Single cotton-covered wire is sometimes used for field windings, and for very small wires silk is used instead of cotton because it can be put on in thinner layers. The thickness of the covering varies with the size of the wire which it covers, and its value may be found from the table on page 508. A double layer, with a total thickness for the two layers of 0.007 in., will withstand about 150 volts. When impregnated with a suitable compound' it will withstand about 600 volts. Micanite, as used for coil and commutator insulation, is made of thin flakes of mica which are stuck together with a flexible varnish. The resultant sheet is then baked while under pressure to expel any excess of varnish and is afterwards milled to a standard thickness, usually 0.01 or 0.02 in. It is a very reliable insulator and, if carefully made, is very uniform in quality. It can be bent over a sharp corner without injury because the individual flakes of mica slide over one another. To make this possible the varnish has to be very flexible. Being easily bruised, it must be carefully handled, and when put in position on the coil, must be protected by some tougher material. The dielectric strength of micanite is about 800 volts per mil on a 10-mil sample, and is not seriously lessened by heat up to 150 C., but long-continued exposure to a temperature greater 32 ELECTRICAL MACHINE DESIGN than 100 C. causes the sticking varnish to loose its flexibility. Micanite does not absorb moisture readily, but its dielectric strength is reduced by contact with machine oil. Varnished Cloth. Cloth which has been treated with varnish is sold under different trade names. Empire cloth for example, is a cambric cloth treated with linseed oil. It is very uniform in qual- ity, has a dielectric strength of about 750 volts per mil on a 10-mil sample, and will bend over a sharp corner without cracking. It must be carefully handled so as to prevent the oil film, on which the dielectric strength largely depends, from becoming cracked or scraped. Various Papers. These go under different trade names, such as fish 'paper, rope paper, horn fiber, leatheroid, etc. When dry, they have a dielectric strength of about 250 volts per mil on a 10-mil sample. They are chosen principally for toughness and, after having been baked long enough to expel all moisture, should bend over a sharp corner without cracking. The presence of moisture in a paper greatly reduces its dielectric strength and generally increases its flexibility; all papers absorb moisture from the air. It is good practice to mould the paper to the required shape while it is damp, then bake it to expel moisture and impregnate it before it has time to absorb moisture again. Impregnating Compound. The compound which has been referred to is usually made with an asphaltum or a paraffin base, which is dissolved in a thinning material. It should have as little chemical action as possible on copper, iron, and in- sulating materials. It should be fluid when applied; must be used at temperatures below the break-down temperature of cotton, namely 120 C. ; should be solid at all temperatures below 100 C., and should not contract in changing from the fluid to the solid state. Elastic Finishing Varnish. This is usually an air-drying varnish and is put on the outside of insulated coils. It should be oil-, water-, acid- and alkali-proof, should dry quickly, and have a hard surface when dry. 31. Thickness of Insulating Materials. It is not generally advisable to use material which is thicker than 0.02 in., because if there is any flaw in the material that flaw generally goes through the whole thickness, whereas if several thin sheets are used the flaws will rarely overlap; thick sheets also are not so flexible as are thin sheets. For these reasons it is better to use several INSULATION 33 layers of thin material to give the desired thickness rather than a single layer of thick material. 32. Effect of Heat and Vibration. It is not advisable to allow the temperature of the insulating materials mentioned in Art. 30 to exceed 85 C. because, while at that temperature the dielectric strength is not much affected, long exposure to such a temperature makes the materials dry and brittle so that they readily pulverize under vibration. It must be understood that the final test of an insulating material is the way it stands up in service when subjected to wide variations in voltage and temperature and to moisture, vibration, and other operating conditions found in practice. 33. Grounds and Short-circuits. If one of the conductors of an armature winding touch the core, the potential of the core becomes that of the winding at the point of contact, and if the frame (yoke, housings and base) of the machine be insulated from the ground, a dangerous difference of potential may be FIG. 30. Winding with grounds. established between the frame and the ground. For safety it is advisable to ground the frame of the machine, and then the potential of the winding at the point of contact with the core will always be the ground potential. If the winding be grounded at two points a short-circuit is produced and a large current flows through the short-circuit, this will burn the windings before the circuit-breakers can open and put the machine out of operation. If, for example, the winding shown in Fig. 30 becomes grounded at the point a, the difference of potential between the point b and the ground changes from \E t to E t , but no short circuit is produced unless there exists another ground in the 34 ELECTRICAL MACHINE DESIGN winding at some point d, or in the system at some point e. If the machine were a motor, a short-circuit would open the circuit- breakers, but not before some damage had been done. If the machine were a generator, and a short-circuit took place between points a and d,the circuit-breakers would not open unless power could come over the line from some other source, such as another generator operating in parallel with the machine in question, or from motors which are driven as generators by the inertia of their load. 34. Slot Insulation and Puncture Test. As shown in the preceding article, the insulation between the conductors and a core which is grounded may, under certain circumstances, be subjected to a difference of potential equal to the terminal voltage of the machine. Due to operating causes still greater differences of potential are liable to occur. To make sure that there is enough insulation between the conductors and the core, and that this insulation has not been damaged in handling, all new machines are subjected to a puncture test before they are shipped; that is, a high voltage is applied between the conductors and the core for 1 minute. If the insulation does not break down during this test it is assumed to be ample. The value of the puncture voltage is got from the following table which is taken from the standardization rules of the A. I. E. E. Rated terminal voltage of circuit Rated output Testing voltage Not exceeding 400 volts Under 10 kw 1000 volts Not exceeding 400 volts 10 kw. and over. . . 1500 volts 400 and over, but less than 800 volts. . . Under 10 kw 1500 volts 400 and over, but less than 800 volts.. . 10 kw. and over. . . 2000 volts 800 and over, but less than 1200 volts. . . Any 3500 volts 1200 and over, but less than 2500 volts. . . Any 5000 volts 2500 and over Any Double nor- mal rated voltage 35. Insulation of End Connections. Examination of Fig. 30 will show that the voltage between two end connections which cross one another may be, as at point /, almost equal to E t} the terminal voltage. The end connections must therefore be insulated for this voltage. 36. Surface Leakage. If the end connections had only sufficient insulation to withstand the voltage E t this insulation would break down during the puncture test due to what is INSULATION 35 called surface leakage. Fig. 31 shows part of a motor winding and the insulation at the point where the winding leaves the slot. The slot insulation is sufficient to withstand the puncture test and is continued beyond the slot for a distance ef. When a high voltage is applied between the winding and the core the stress in the air at b may be sufficient to ionize it, then the air be- tween e and/ becomes a conductor, the drop of potential between e and/ becomes small, and the voltage across the end-connection insulation at /, which equals the puncture voltage minus the FIG. 31. Insulation where coil leaves slot. drop between e and /, becomes high. To prevent break-down of the end-connection insulation due to this cause the distance efis made as large as possible without increasing the 'total length of the machine to an unreasonable extent, and the end-connection insulation is made strong enough to withstand the full puncture voltage but with a lower factor of safety than that used for the slot insulation. Suitable values of ef, taken from practice, are given in the following table. Rated terminal voltage of circuit Length Not exceeding 800 volts . 75 in. 800 volts and over, but less than 2500 volts 1 . 25 in. 2500 volts and over, but less than 5000 volts 2.0 in. 5000 volts and over, but less than 7500 volts 3.0 in. 7500 volts and over, but less than 11000 volts 4.5 in. 37. Several Coil Sides in One Slot. In Fig. 25, page 21, is shown part of the winding diagram for a machine with four coil sides in each slot and two turns per coil, and Fig. 26 shows a section through one of the slots of the machine. This latter figure is duplicated and shown in greater detail in Fig. 34. Since the voltage between two adjacent commutator segments seldom exceeds 20 volts and is more often of the order of 5 volts, 36 ELECTRICAL MACHINE DESIGN the amount of insulation between adjacent conductors need not be large, thus the conductors shown are insulated from one another by one layer of tape on each conductor and the group of conductors is then insulated more fully from the core. The completely insulated group of coils is shown in Fig. 32, and Fig. 33 shows the same group of coils before they are insulated. When the individual coils are made up of a number of turns of d.c.c. round wire it is advisable to put a layer of paper between FIG. 32. FIG. 33. Coil for double layer winding with two turns per coil and 8 cond. per slot. them, as shown at a, Fig. 35, because the cotton covering may become damaged when the coils are squeezed together to get them into the slot. The voltage between adjacent turns of the same coil is so low that the cotton covering on the conductor is ample for insulating purposes. 38. Examples of Armature Insulation. The methods adopted in insulating coils, and the reasons for the various operations, can best be understood by the detailed description of some actual examples. Example 1. The insulation for the winding of a 240-volt D.-C. generator. The winding is a double-layer multiple one INSULATION 37 with two turns per coil and four coil sides or eight conductors per slot; the conductors are of strip copper wound on edge. A section through the slot and insulation is shown in Fig. 34 and the various operations are as follows: (a) After the copper has been bent to shape, tape it all over with one layer of half-lap cotton tape 0.006 in. thick. This forms the insulation between adjacent conductors in the same slot. (6) Tape together the two coils that form one group with one layer of half-lap cotton tape 0.006 in. thick all round the coils. This forms the end connection insulation and also part of the slot insulation. (c) Bake the coil in a vacuum tank at 100 C. so as to expel all moisture, then dip it into a tank of impregnating compound at 120 C. and leave it there long enough to become saturated with the compound. (d) Put one turn of empire cloth 0.01 in. thick on the slot part of the coil and lap it over as shown at d. This empire cloth is 1^ in. longer than the core so that it sticks out f in. from each end. (e) Put one turn of paper 0.01 in. thick on the slot part of the coil and lap it over as shown at e. This paper also is 1^ in. longer than the core; it is not put on for insulating purposes but to protect the other insulation which is liable otherwise to be- come damaged when the coils are being placed in the slots. (/) Heat the coil to 100 C. and then press the slot part to shape while hot. The heat softens the compound and the press- ing forces out all excess of compound. The coil is allowed to cool while under pressure and comes out of the press with such a shape and size that it slips easily into the slot. (g) Dip the ends of the coil into elastic finishing varnish. Example 2. The insulation for the winding of a 10 h.p. 500- volt motor with a double layer winding having five turns per coil and thirty conductors per slot. The conductors are of double cotton-covered wire. (a) Put one turn of paper 0.005 in. thick round the slot part of two of the groups of conductors that form the individual coils. This paper is 1? in. longer than the core and forms part of the insulation between individual coils in the same slot and also part of the insulation from winding to core. (b) Put one turn of empire cloth 0.01 in. thick round the three 38 ELECTRICAL MACHINE DESIGN coils that form one group and lap it over as shown at 6. This empire cloth is 1^ in. longer than the core. (c) Put one turn of paper 0.005 in. thick on the slot part of the coil, make it also 1^ in. longer than the core, and lap it on the top. (d) Tape the ends of the group of three coils with one layer of half-lap cotton tape 0.006 in. thick and carry this tape on to the paper of the slot insulation for a distance of i in. so as to seal the coil. (e) Wind the machine with these coil groups putting a lining of paper 0.01 in. thick in the slot and a strip of fiber 1/16 in. thick on the top of the coils and then hold the coils down with band wires. e 0.01 Paper. C?0.01 // Empire 6 H' Lap Tape a H Lap Tape FIG. 34. FIG. 35. Armature slot insulation. (/) Place the armature in a vacuum tank and bake it at 100 C. to expel moisture, then force impregnating compound into the tank at a pressure of 60 Ib. per square inch and maintain this pressure for several hours until the winding has been thor- oughly impregnated. (g) Rotate the armature, while it is still hot, at a high speed so as to get rid of the excess of compound which will otherwise come out some day when the machine is carrying a heavy load. INSULATION 39 (h) Paint the end connections with elastic finishing varnish taking care to get into all the corners. 39. Total Thickness and Apparent Strength of Slot Insulation. Example 1, Fig. 34. Width, inches Depth, inches Volts Tape on conductor 1,000 Tape on group of coils Empire cloth 0.024 02 0.024 03 1,000 7,500 Paper . . . 02 03 2,500 Total .... 064 084 12,000 In the above table under the heading of width is given the space taken up in the width of the slot by the different layers of insulation. The tape on the conductor has not been added because it is a variable quantity and depends on the number of conductors per slot. Under the heading of depth is given the space taken up in the depth of half a slot by the different layers of insulation; here also the tape on the individual conductors has not been added since it varies with the number of conductors which are vertically above one another in the slot. The apparent strength of the above insulation is 12,000 volts and the required puncture test is 1500 volts so that there is a factor of safety of 8. Example 2, Fig. 35. Width, inches Depth, inches Volts Dec on wire 600 Paper on coils Empire cloth 0.03 02 . 0.01 03 1,250 7,500 Paper 01 015 1,250 Paper '. 0.02 0.005 2,500 Total 08 06 13,100 The puncture voltage is 2000 and the factor of safety =6.5. 40 ELECTRICAL MACHINE DESIGN -2 Layers O.Ol"Paper. - Via Cardboard. -2 Layers 0.006"Tape. 0.006 Tape. 0.03 "Paper. 0.03"Canvas. 0.025"Steel. 0.03"Canvas. FIG. 36. Field coil insulation. /Tape Wood FIG. 37. Ventilated field coils. INSULATION 41 40. Field Coil Insulation. Two examples of field coil insula- tion are shown in Fig. 36. Diagram A shows an example of a coil which is carried in a cardboard spool while diagram B shows an example of a coil which is carried in an insulated metal spool. In both cases the coils, after being wound in the spool and taped up, are baked in a vacuum and then impregnated with compound. This compound is a better insulator than the air which it replaces it is also a better conductor of heat. Figure 37 shows the type of coil which is used to a large extent on machines the armature diameter of which is greater than 20 in. The shunt coils are made of d.c.c. wire, wound in layers; the individual shunt coils are 1 in. thick and are separated by ventilating spaces 1/2 in. wide. The insulation is carried out entirely by wooden spacing blocks so that there is a large radi- ating surface, and also little insulation to keep in the heat. The coils are made self-supporting by being impregnated with a solid compound at about 120 C. The insulation on the individual turns of the series coil con- sists of one layer of cotton tape 0.006 in. .thick and half lapped; this coil, when made of strip copper as shown, is not impregnated but is dipped in finishing varnish. CHAPTER V THE MAGNETIC CIRCUIT 41. The Magnetic Path. Fig. 38 shows two poles of a multi- polar D.-C. generator, each pole of which has an exciting coil of Tf turns through which a current // flows. Due to this excita- tion a magnetic flux is produced and the mean path of this flux is shown by the dotted lines. This magnetic flux consists of two parts, one, e , which does not cross the air gap and is called the leakage flux. FIG. 38. The paths of the~main and of the leakage fluxes. 42. The Leakage Factor. The total flux which passes through the yoke and enters the pole = rL c . A ag = the actual gap area per pole =-^r where C is a constant greater than 1, called the Carter coefficient. This constant takes into account the effect of the slots in reducing the air-gap area. N A t = the tooth area per pole = tL n ; only those teeth which are under the poles are effective. A c = the area of the armature core =d a L n . A p = the pole area =W P L P when the pole is solid; when built up of laminations the pole area =(W P L P X const.) where the const, is a stacking factor and = 0.95 approximately: A y = the yoke area. 44. The Carter Coefficient. l Fig. 39 shows the path of the magnetic flux across the air gap. If it were not for the armature slots and vent ducts the air-gap area per pole would be ^rl/ c which is called the apparent gap area. The actual gap area per (T* \ Ji -, u rf \ X H t-+ -fs-> f _ ^*v 1 ^^ ^^ 2 ^^^_ / + fs "^*" 111 ^ - "*^, -^ ** ^ ~ ^. ^== Values of -f- n FIG. 40. The Carter fringing constant. ISGsq.in. ' Slots 200-0.43 xl.6 Coils 400 Winding 1 Turn Mult. Z. 800 Poles 10 ' K.W. 400 Volts no load 240 Volts full load 240 .R.P.M. 200 FIG. 41. Magnetic circuit. THE MAGNETIC CIRCUIT 45 It is required to find the value of the Carter coefficient for the machine drawn to scale in Fig. 41. s =0.43 in. / -0.48 in. 8 =0.3 in. 1-1.44 / =0.78 from Fig. 40 = 0.48 + 0.43 0.48 + 0.78X0.43 There is a small amount of fringing at the pole tips which tends to increase the air-gap area, but its effect is counter- balanced by the fact that at the pole tips, d, the thickness of the air gap, is increased. . The Carter coefficient for the vent ducts can be found in the same way as for the slots, but since its value is nearly always = 1 the calculation is seldom made. 45. The Flux Densities. The flux in the different parts of the magnetic circuit is shown in Fig. 38, then: B g = the apparent flux density in the air gap = ^- A Q B ag = the actual flux density in the air g&p = CB g . B t = the apparent flux density in the teeth = ^- At B c = the flux density in the armature core^T^-- ZA C Bp = the flux density in the pole = -^- Ap By = the flux density in the yoke = ^j ZAy The flux density in the teeth at normal voltage is generally about 150,000 lines per square inch, and at such densities the permeability of the iron in the teeth becomes comparable with that of air, so that a considerable amount of flux passes down the slots, vent ducts, and the air spaces between the laminations. .If the assumption is made that the teeth have no taper, and that the lines of force are parallel both in the teeth and in the air paths, and if B at = the actual flux density in the teeth, B s = the flux density in the air path consisting of the slots, vent ducts, and air spaces between laminations, B't = the apparent flux density in the teeth, then 46 ELECTRICAL MACHINE DESIGN a across the air gap of the machine shown in Fig. 38. The m.m.f. between points a and b is Tflf ampere-turns and this must be equal to AT y + AT p + AT g + AT t + AT C , where AT y is the ampere-turns necessary to send the flux %(j> m through the length l y of the yoke. The value of B y is known and the corresponding number of ampere-turns required for each inch of the yoke path is found from Fig. 42. This value of ampere-turns per inch multiplied by the length l y gives the value of ATu. THE MAGNETIC CIRCUIT 47 170 x 10 3 S"g j^t* .x-^ - 8 I? 1 "! in x-* 1 -** a d" 16 3 w ^x- --* m ^ x^ x Q a 150 X m ^ ^ C J x^ g g EC -MA ^ ^ ^ *^^ 75 ^ iX^* i x"* ^ CQ 130 ** ,^ J190 / CO / 'K. OL S( K) 10 JO VI 00 14 00 1G JO ISi >0 20 W) 22 00 24 00 2tt DO 110 -.. / 2( / xT mr er 3 1 uri 1ST ^ - or ^,.1^ 111 ^ ch ^^> -- fin ** ion ^w et b^ e^V *^* ^^ .-*- ^*** i"" ^" ^. ^-> . TO ^ \ ^ en r *S on / ' x *" ( > fc ^ ^-^ / / r^ 0^ ,^ **** ** 2 4Q go I/ f c >* b . 1 / ^ ^ 3 ri 10 70 1 / ^ / 20 fiO / \ y I 10 50 20 40 60 80 100 120 140 160 180 200 Ampere Turns per Inch FIG. 42. Magnetization curves. 170 xlO 3 160 150 .5 140 ^c .-S 130 120 110 4=2 __=2.5 _=3 110 120 130 140 150 160 170 180* 10 3 Apparent Density in Lines per Sq Jn. FIG. 43. Densities in armature teeth. 48 ELECTRICAL MACHINE DESIGN AT P is the ampere-turns necessary to send the flux (f> m through the length l p of the pole and is found in a similar manner. AT ' g is the ampere-turns necessary to send the flux c/> a across one air gap. To find this value it is necessary to find first of all the value of C, the Carter coefficient, and then the actual flux density in the air gap, namely B ag CB g . AT Bag lines per square inch =3. 2 r-^ (3) where d is the air gap thickness in inches. AT t is the ampere-turns necessary to send the flux (j> a through the length d of the tooth. The value of B t , the apparent tooth 160xlO 70 20 40 60 80 100 120 140 160 180 200 Amoere Turns per In. FIG. 44. Magnetization curves for sheet steel. density, is readily found, and the value of B at , the actual flux density, can be found by the use of the curves in Fig. 43. The value of ampere-turns per inch corresponding to this actual density can then be taken from Fig. 42. This latter quantity when multiplied by d gives the value of AT t . When the teeth are tapered as shown in Fig. 44, so that the flux density is not uniform through the total depth of the tooth, THE MAGNETIC CIRCUIT 49 the problem becomes more difficult. It is necessary to divide the tooth length d into a number of small parts, find the average flux density in each of these parts and the corresponding value of ampere-turns per inch; the average value of these latter quantities multiplied by d gives the value of ATt. This process is slow, but in Fig. 44 is plotted a series of curves whereby, if the actual flux density at the top and bottom of the tooth is known, the average ampere-turns per inch can be found directly. AT C is the ampere-turns necessary to send the flux J< a through the length l c of the core and is found by the use of the curves in Fig. 42. Example. Fig. 41 shows a dimensioned sketch of a 10-pole, 400-kw., 240- volt, 200 r. p. m. generator; it is required to draw the no-load saturation curve for this machine. r.p.m. poles ., = ^ 240X60X10X10 8 therefore e = ei + e2 + e 3 + e4, where (j>ei= the leakage flux in paths 1, between the inner faces of the pole shoes. (j) 62 = the leakage flux in paths 2, between the flanks of the pole shoes. es = the leakage flux in paths 3, between the inner faces of the poles. f < "is > .-"' VN -~ .-a). -"I h s^ ZH ^i-H_ F--Ci> I 1 "0 FIG. 46. The leakage paths. and (f) e2 = l9(AT g+t )h s Iog 10 1-4 - l 1 1 l 1 1 1 1 1 I / I \ since there are four paths 2, per pole. The m.m.f. across the paths 3 and 4 varies from zero at the bottom of the poles to 2(AT g+t ) at the shoe, and the average value is taken as AT g+t ampere-turns, so that and THE MAGNETIC CIRCUIT 53 Given the complete data on a magnetic circuit, the value of AT g+t , the ampere-turns to send the flux e =

ez + e can be obtained by substitution in the above formulae. The leakage f actor = r^p^- 9a It is required to find the leakage factor for the machine shown in Fig. 41. h 8 = 1.5 in. L 8 = 11.5 in. ifj = 6 in. W 8 = 12.7 in. h p = 13.5 in. L p = 11. 5 in. = 12.5 in. W p = 10.5 in. then ei i*rir ^ / L5xll - 5 \ -37(4r,+ ( ) 10 (/!../ g+t) \ Q / *, "1 Q f A rji i A 1 > lr\rr /'IL " 1 -18(4^+,) iy^Yi.f fir+ &io V 1 > ox/ J ^ X O / A-. ^VAT.^ /13.5X11.6\ RO(AT~,A v , ,- 7rXl0.5\ ,) 13.5 tog,. (1+^1^5) and e = 181 X 8280 = 1,500,000 and a the flux per pole which crosses the gap = 9. OX 10 6 from the table on page 51 ; therefore the leakage f actor =. _ 9,000,000 + 1,500,000 9,000,000 = 1.16 For a first approximation the following values of the leakage factor may be used: Four-pole machines up to 10-in. armature diameter 1.25 Multipolar machines between 10 and 30-in. diameter 1.2 between 30 and 60-in. diameter 1.18 greater than 60-in. diameter 1.15 These values apply to the type of machine shown in Fig. 28. CHAPTER VI ARMATURE REACTION 48. Armature Reaction. In Fig. 47, A shows the magnetic field that is produced in the air gap of a two-pole machine by the m.m.f. of the main exciting coils. x y Distribution of Flux due to m.m.f . of Main_Field. Distribution of Flux due to m.m.f. of Armature. D Distribution of Flux uirder Load Conditions. FIG. 47. Flux distribution curves. B shows the armature carrying current and the magnetic field produced thereby when the brushes are in the neutral 54 ARMATURE REACTION 55 position and the main field is not excited. The m.m.f. between a and b, called the cross-magnetizing ampere-turns per pair of poles, due to the current I c in each of the Z conductors = J ZI C ampere-turns, and that between c and d and also that between g and h = $ ZI c ampere-turns. Half of this latter m.m.f. acts across the path ce and the other half across the path fd since the reluctances of the paths ef and cd are so low that they may be neglected. Therefore, the cross-magnetizing effect at each pole 17 tip = J I c for any number of poles (4) C shows the resultant magnetic field when, as under operating conditions, both the main and the armature m.m.fs. exist to- gether. The flux density, compared with the value shown at A, is increased at the pole tips d and g and decreased at the pole tips c and h. A convenient method of showing the flux distribution in the air gap is shown in diagrams D, E and F, Fig. 47, which are obtained by assuming that the diagrams A } B and C are split at xy and opened out on to a plane, and that the flux density at the different points is plotted vertically. D shows the flux distribution due to the main m.m.f. acting alone. E shows the flux distribution due to the armature m.m.f. acting alone. F shows the resultant distribution when both the main and the armature m.m.fs. exist together and is obtained by adding the ordinates of curves D and E. It is permissible to add these ordinates of flux density together provided that the paths df and gk do not in the meantime become highly saturated. These paths, however, include the gap and teeth, and the flux density in the teeth due to the main field is about 150,000 lines per square inch at normal voltage, which is well above the point of saturation, so that an increase in m.m.f., such as that at / due to the armature m.m.f., will produce an increase in flux density at pole tip/ of only a small amount; while a decrease in m.m.f. of the same value at pole tip e will produce a decrease in flux density at that pole tip of a much larger amount; thus the total flux per pole will be decreased. It is usual to consider the effect of armature reaction as being due to a number of lines of force acting in the direction shown in diagram B, Fig. 47, and this diagram shows that the same 56 ELECTRICAL MACHINE DESIGN number of lines is added at the one pole tip as is subtracted at the other pole tip. A truer representation is that shown in Fig. 48. Since the lines of force of armature reaction meet a high reluc- tance at d some of them take the easier path through hmc. These latter lines are in the opposite direction to those of the main field and are, therefore, demagnetizing. FIG. 48. Demagnetizing effect of armature reaction with the brushes at the neutral point. 49. Distribution of Flux in the Air Gap at Full Load. 1 Fig. 49 is part of the development of a multipolar machine with p poles, and curve D shows the flux distribution in the air gap due to the main m.m.f. acting alone. The armature m.m.fs. across df and 17 ce each = J ^ I c ampere-turns and curve G shows the distribu- tion of the armature m.m.f. Curve 1, Fig. 50, is the no-load saturation curve of the machine and curve 2 is that part of this saturation curve for the tooth, gap and pole face, so that if oy is the ampere-turns per pole required to send the no-load flux through the magnetic circuit of the machine then ox is that necessary to send this same flux through the length of one gap, one tooth and one pol eface. Across np, Fig. 49, the m.m.f. at full-load is the same as at 1 The method adopted in this article is a slight modification of that pro posed by S. P. Thompson, Chapter XVII, Dynamo Electric Machinery, Vol. I. ARMATURE REACTION 57 FIG. 49. Flux distribution at full-load. Flux per Pole Ampere Turns per Pole FIG. 50. No-load saturation curves. 58 ELECTRICAL MACHINE DESIGN no-load and therefore the flux density in the air gap at n is unchanged. Across df the m.m.f. at full-load is no longer ox, Fig. 50, but 2 = ox l , where xx l = ^ 7 c = the m.m.f. across df due to the armature; therefore the flux density in the air gap at d at full-load is increased over its value at no-load in the ratio ^ *-j sx Fig. 50, and is so plotted at dw, Fig. 49. Across ce the m.m.f. at full-load is no longer ox, Fig. 50, but Z ox 2 , where xx 2 ~%<{> I c , and therefore the flux density in the air gap at c at full-load is less than that at no-load in the 'ijnf* ratio -; Fig. 50, and is so plotted at cz, Fig. 49. sx Thus, in Fig. 49, curve D shows the distribution of the flux in the air gap at no-load and curve F that at full-load. The total flux per pole is less at full-load than at no-load in the ratio of the area enclosed by curve F to that enclosed by curve D, which ratio is practically the same as area 2 ; 1 > Fig. 50. Y FIG. 51. FIG. 52. Demagnetizing and cross magnetizing effect of the armature. 50. Armature Reaction when the Brushes are Shifted. Fig. 51 shows the armature carrying current and the magnetic field produced thereby when the brushes are shifted through an angle so as to improve the commutation. The armature field is no longer at right angles to the main field and the easiest way in which to consider its effect is to assume that it is the resultant of two components, one in the direction OY which is ARMATURE REACTION 59 called the cross-magnetizing component, the effect of which has already been discussed, and another in the direction OX which is called the demagnetizing component because it is directly opposed to the main field. Fig. 52 shows the armature divided up so as to produce these two components, and it will be seen that the demagnetizing ampere-turns per pair of poles or the demagnetizing ampere-turns per pole i z 2d : V 180 The angle 6 for preliminary calculations is usually taken as 18 26 electrical degrees so that ^7, = 0.2. loU 51. The Full Load Saturation Curve. It is required to draw this curve for the machine which is drawn to scale in Fig. 41 and to which the following data applies. Rating: 400 kw., 240 volts, 1670 amp., 200 r.p.m. Poles ............................................ 10 Coils ............................................ 400 Winding ............................... . . one turn multiple Total conductors ................................. 800 Current per conductor ............................. 167 Per cent, pole enclosure ............................ 0.7 Volts drop at full-load across armature, brushes and series field ..................................... 8.7 6, the angle of advance of the brushes ............... 18 degrees 800X167 Armature ampere- turns per pole = - ^ .......... 6700 2i X 10 (800 - X . 2 X 167) = 1340 (800 -jQ- X0.7 X 167) =4700 Curve 1, Fig. 53, the no-load saturation curve, is taken directly from Fig. 45. Curve 2, Fig. 53, that part of the saturation curve for the tooth and gap, is plotted from the figures in the table on page 51. The m.m.f. required to send the no-load flux through the magnetic circuit is 9990 ampere-turns, of which 8280 ampere- turns are required for the gap and tooth. The voltage generated due to this flux is 240. 60 ELECTRICAL MACHINE DESIGN At full load the m.m.f. at one pole tip = 8280+4700 = 12980 ampere-turns, and that at the other pole tip = 8280 - 4700 = 3 580 ampere-turns. The flux crossing the air gap is reduced in the ratio Fig. 53, and, due to this reduction in flux, the voltage generated is reduced from 240 to 235.5. 2a4 6 8 10 12 d 14.xl0 3 Ampere Turns per Pole FIG. 53. No-load and full-load saturation curves. To maintain the generated voltage at this reduced value of 235.5 volts it is necessary to increase the no-load field excitation of 9990 ampere-turns by 1340, the demagnetizing ampere-turns per pole. The terminal voltage is less than the generated voltage of 235.5 by 8.7, the voltage required to send the full-load current through the armature, brushes and series field. The full load saturation curve is drawn parallel to the no-load saturation curve through the point g so found. ARMATURE REACTION 61 In order to get the same flux across the air gap at full-load as at no-load the field excitation has to be increased over its no-load value so as to counteract the effect of the m.m.f. of the armature. Due to this increase in excitation the leakage flux is increased, so that the leakage factor is greater at full-load than at no-load, and still more excitation is required on account of the resulting increase in the pole and yoke densities. This latter increase in excitation, however, cannot readily be calculated. 52. Relative Strength of Field and Armature M.M.FS. Inspec- tion of Fig. 49 will show that if the armature current be increased to such a value that the cross-magnetizing ampere-turns of the 2? armature at the pole tips, namely \ <[>-I c ampere-turns, becomes equal to the ampere-turns for the tooth and gap due to the main field excitation, then the flux density will be zero under the pole tip toward which the brushes have been shifted in order to help commutation, so that to obtain a reversing field it is necessary that the ampere-turns of the main field for gap and tooth be greater 17 than J -I c . To get a reasonably strong field for commutating purposes, experience shows that the above value at full load should not be less than 1.7, and the higher the value the better the commuta- tion, other things being equal, but at the same time the more expensive the machine due to the extra field copper required. y The quantity \ <1>I C is equal to $ (armature ampere-turns per ampere-turns of main field for gap and tooth armature ampere-turns per pole at full load = 1.2 ............................................ (6) a formula which is greatly used in dynamo design. In deriving this formula it is assumed that the m.m.f of the series field is just able to counteract the demagnetizing effect of the armature m.m.f. In the case of a shunt motor, where there is no series winding, and where the shunt excitation is constant, the ampere- turns of the main field for the gap and tooth =1.2 (armature ampere-turns per pole) + the demagnetizing ampere-turns. CHAPTER VII DESIGN OF THE MAGNETIC CIRCUIT The problem to be solved in this chapter is, given the armature of a machine and also its rating to design the poles, yoke, and field coils. 53. Field Coil Heating. 1 Fig. 54 shows one of the poles of a D. C. machine with its field coil. The exciting current // passes through this coil and gradually raises its temperature until the point is reached where the rate at which heat is dissipated by the coil is equal to the rate at which it is generated in the coil. <-d f FIG. 54. D.-C. field coil. The hottest part of the coil is at A, and the heat has to be carried from this point to the radiating surfaces B, C, D and E, so that there must be a temperature gradient between A and the radiating surface of the coil; Fig. 55 shows the temperature at different points in the thickness of a field coil. The maximum temperature of the coil limits the amount of current that it can carry without injury, but this temperature is difficult to measure. The external temperature of the coil can be taken by means of a thermometer, and the mean tempera- *A good summary, with complete references, of the work published on field coil heating will be found in a paper by Lister: Journal of the Institution of Electrical Engineers, Dec., 1906. 62 DESIGN OF MAGNETIC CIRCUIT 63 ture can be found by the increase in resistance of the coil, since the resistance of copper at any temperature t = R t = R (l + 0.004 t) where R is the resistance at C. and t is in centigrade degrees. It is found that the ratio between the maximum and the mean temperature seldom exceeds 1.2, while that between the mean and the external surface temperature varies from about 1.4 to 3. The latter figure is found in some of the early machines whose field coils were covered with tape and rope. When the coil is insulated as shown in Fig. 36 the ratio of the mean temperature to that of the external surface will be approximately 1.5 if the 100 X ^^ ^ -~^ ""X Degrees Cent. Rise 8 fe / X s. / \ \ s 05 Q \ a I rn I FIG. 55. Temperature gradient in field coils. external surface is left bare except for the d.c.c. on the wire, the whole coil impregnated with compound, and the coil about 2 in. thick; the compound is a better conductor of heat than the air which it replaces and is also a better insulator. If two layers of half-lapped tape be put on the external surface of the coil the ratio will increase to about 1.7 and if in addition a layer of cardboard 1/16 in. thick be put on the external surface, as was formerly done to protect the coil, the ratio will exceed 2. These are average figures and may vary considerably since they are affected by the fanning action of the armature, the kind of compound used, the thickness of the insulation on the wire, the radiating power of the poles and yoke on which depends the radiating power of the surface D. The heating constants for field coils are figured in many differ- ent ways, depending on what is taken for the radiating surface. While it is true that all the surfaces^ B, C, D and E, are active in radiating heat, yet they are not all equally effective, and for that 64 ELECTRICAL MACHINE DESIGN reason, and also for convenience, the radiating surface is taken as the external surface B. For impregnated coils without any insulating material on the external surface other than that on the wire itself, the watts that can be radiated per square inch of the external surface for a temperature rise of 40 C. on that surface, which corre- sponds to an average temperature rise of 60 C. and a maximum temperature rise of 70 C., varies from 0.5 to 1.0 depending on the length of the coil and also on the peripheral velocity of the arma- ture. The effect of the fanning action of the armature can readily be understood so that the slope of the curves in Fig. 56 needs no explanation. It will be seen from this diagram that a short coil is more effective than a long one because the ratio of the total radiating surface B, C, D and E } to the external surface B on which the constants are based, is greater in the short than in the long coil, and also because only that portion of the long coil which is near the armature is affected by the armature fanning. 1.2 0.8 - wo 0.4 $ 1 2 3 4 5 6xlO~ 3 Peripheral Velocity of the Armature in Ft. per Min. FIG. 56. Field coil heating constant. The radiating surface of a coil is often increased by putting in ventilating openings as shown in Fig. 37; this method would seem to double the radiating surface, but the sides of the venti- lating opening are not so effective as either the inner or the outer surface of the coil. For this type of field coil, where the individual coils are 1 in. thick and spaced i in. apart, the watts per square inch of external surface can be increased 50 per cent, over the values given in Fig. 56. DESIGN OF MAGNETIC CIRCUIT 54. The Size of Wire for Field Coils : If Ef is the voltage across each field coil, // is the current in the coil, Tf is the number of turns in the coil, MT is the length of the mean turn of the coil in inches, M is the section of the wire used in circular mils. 65 then the resistance of the coil EMTxT- since the resistance of copper is approximately 1 ohm per circular mil per inch length, and (7) so that for a given machine the size of field wire is fixed as soon as the ampere-turns and the voltage per coil are known. U.i 1 o- 1 \ -> -ay? *^L -D- \ S -t \ > N S T ^ ^^ \ \ \, \ ' \ 2 6 8 10 12 14 16 18 20 22 Z B. & S. Gage FIG. 57. Space factor for wire. 55. The Length L f of the Field Coil. The watts radiated from the coil shown in Fig. 54 = external surf ace X watts per square inch. The total section of copper in the coil = dj xLf Xsf square inch, where s/., the space factor of the wire, is the section of the wire divided by the space that the wire takes up in the coil and is got from Fig. 57. The section of the wire in the coil = ^L square inches dfXLjXs/X 1,270,000 . ^ - circular mils. 1 f -AT 66 ELECTRICAL MACHINE DESIGN M TX T-r The watts loss per coil = - l Xlf 2 and, substituting for M, dfXLfXsfX 1,270,000 The watts loss per coil also = external surface of coil X watts per square inch. = external periphery of coilx/X watts per square inch. Therefore, equating these two values together, mean tumX(IfT f ) 2 L'/- ext. periphery X watts per sq. in. XdfXsfX 1,270,000 j T _ IfTf I mean turn ,~. 1 = 1000 \ ext. periphery X watts per sq. in. Xd/Xs/X 1.27 In order to have an idea as to the value of I/ found from the above equation assume the following average values: sfj the space factor =0.6 df, the coil depth =2.0 in. watts per square inch =0.6. external periphery = 1 . 2 X mean turn. T T 7 then Lf, the radial length of coil space, =~n approxi- mately. 56. Weight and Depth of Field Coils. The weight of the field coil = 0.32 XMTxLfXdfXsf. pounds, where 0.32 is the weight of a cubic inch of copper, _ IfTf I mean turn ' 1000 \ ext. periphery X watts per sq. in. XdfXsfXl.27 a constant =IfTf - = approximately, for a given machine, therefore the weight of the field coil / = a constant Vo/ for a given machine. This may be interpreted as follows: the larger the value of df, the shorter the length L/, the smaller the radiating surface, and therefore the lower the value of permissible loss per coil, Since the section of the field coil wire is fixed, because, as shown in Art. 54, it depends only on the. ampere-turns and the voltage per coil, a lower permissible loss can only be ob- DESIGN OF MAGNETIC CIRCUIT 67 tained by a smaller value of // and therefore by a larger value of Tf and a more expensive coil. It would seem then that the thinner the field coil the cheaper the machine, but it must not be overlooked that, as the value of df becomes less, and therefore the cost of the field copper decreases, the value of Z// increases and therefore the cost of the poles and yoke also increases. The value of df for minimum cost of field system must take this into account and can readily be determined by trial; an average value for df is 2 in. 57. Procedure in the Design of the Field System for a Given Armature. (1) Find the air gap clearance as follows: AT 'g +tj the ampere-turns per pole for gap and teeth, = 1.2 (armature AT per pole) for generators, = 1.2 (armature AT per pole) + demagnetizing AT per pole, for shunt motors; see page 61. From the armature data, AT t , the ampere-turns per pole for the teeth, can be found: B XCX<10 8 a ~ 800X200~~ = 9X10 6 200 minimum tooth area per pole = . 43 X -^- X . 7 X 9 . 45 = 57 sq. in. 9X 10 8 maximum tooth density = -== o = 158,000 lines per square anch, apparent. = 150,000 lines per square inch, actual, from Fig. 43. tooth taper = A; = 1.1 2 ampere-turns per pole for the teeth = 1300X 1.6, from Fig. 44. = 2080 Ampere-turns per pole for the gap = 8100 2080 = 6020 , .. 9X10 6 Apparent gap density = 18 2XO 7xl2 = 59,000 lines per square inch. _ 3.2X6020 ~~6pOO~~ = 0.328 therefore C =1.12 from Fig. 40, page 44, and d =0.29 (make gap clearance =0.3 in.) (2) Draw the saturation curves. No-load excitation =1.25X8100 = 10,100 amp.-turns approximately. 10,100 ' = = m> a PP roximatel y- Allow 30 per cent, more for the series coil, so that the coil space = 13 in. 70 ELECTRICAL MACHINE DESIGN 9X10 6 X1.18 The pole area = -^^- I The yoke area = 95,000 = 112 sq. in. approximately. 9X10 3 X1.18 2X40,000 = 132 sq. in. approximately. From the dimensions found above the magnetic circuit is drawn to scale and the no-load and full-load saturation curves are determined. For the machine in question the curves are shown in Fig. 53. (3) Design the shunt coil. The no-load excitation =9990 amp.-turns E f , the volts per coil = 240 ^ - 8 =19 MT, the mean turn =53 in. External periphery of the coil =61 in. QQQfl V ^ Size of shunt coil wire = "*= 28,000 circular mils; iy use No. 5| B & S. gauge, a special size between No. 5 and No. 6, which has a section of 29,500 circular mils and a diameter when insulated with d.c.c. of 0.19 in. Where such odd sizes are not available the coil can be made up of the proper number of turns of No. 5 wire in series with the proper number of turns of No. 6, so as to have the same resistance as that of a coil made with wire of a section of 28,000 circular mils. L/ = 10.5 in. assuming that d/ = 2 in. s/=0.65 watts per sq. in. =0.6 o The number of layers of wire in a depth of 2 in. =^---Q = 10. * \) . j.y The number of turns per layer in a length of 10.5 in. = ^-=55. u.iy The number of turns per coil =10X55 = 550. 9990 The shunt current = =18.2 amp. ooO 29 500 The current density in the field coil wire = ^-5-0" = 1600 c i r - m ^ s P er amp. lo>2 (4) Design the series coil. The excitation at full-load and normal voltage =12,800 amp.-turns. The shunt excitation at normal voltage = 9,990 amp.-turns. Therefore the series ampere-turns at full load = 2810 The series turns =2.5 The series current =^~~ = 1 120 2.5 The current in the series shunt =1670 1120 = 550 amperes i Ano The current density in the series coil =^r-s- = 1330 circular mils per amp. 1 .2 The size of the series coil wire = 1 330 X 1120 = 1,500,000 circular mils = 1.2 sq. in. DESIGN OF MAGNETIC CIRCUIT 71 The resistance of 2.5 turns of this wire The voltage drop in one series coil = 8.8X 10~ 5 X 1120 = 0.1 volts The loss in one series coil =0.1 X 1120 = 112 watts The permissible watts per square inch external surface =0.6X 1.2 = 0.72. 112 The necessary radiating surf ace = TT^S = 155 sq. in. U. I i The external periphery of the coil =61 in. approximately The length L/ of the series coil= -^- =2.5 in. _ . , ., . section of wire The thickness of the series field coil wire = ^ Lf 1.2 2.5 = 0.5 in. The section of the wire is made up of four strips in parallel each 0.125X2.5 section so that the coil may be readily bent to shape. CHAPTER VIII COMMUTATION The direction of the current in the conductors of a D.-C. machine at any instant is shown in Fig. 59; therefore, as the armature revolves and conductors pass from one side of the neutral line to the other, the current in these conductors must be reversed from a value I c to a value 7 C , where 7 C is the current in each conductor. FIG. 59. Direction of current in a D.-C. armature. Figure 61 shows part of a full-pitch double-layer multiple winding with two conductors per slot and with the coils M undergoing commutation, and Fig. 60 shows part of the corre- sponding ring winding. It may be seen from diagrams A and E that the current in coils M is reversed as the armature moves so that the brushes change from commutator segments 1 and 5 to segments 2 and 6. 58. Resistance Commutation. Let the coils M be in such a position between the poles TV and S that, during commutation, they are not cutting any lines of force due to the m.m.f. of the field and armature, and let the contact resistances r l and r 2 , diagram B, between the brush and segments 5 and 6, be so large 72 COMMUTATION N S 73 FIG. 60. FIG. 61. Stages in the process of commutation. 74 ELECTRICAL MACHINE DESIGN that the effect of the resistance and self induction of the coils M may be neglected. In the position shown in diagram B the contact area between the brush and segment 5 is large while that between the brush and segment 6 is small, and the current 2I C} which passes through the brush, divides up into two parts which are proportional to the areas of contact between the brush and segments 5 and 6 respectively, and are equal to I e +i and I c i. In the position shown in diagram C the two contact areas are equal and there is no tendency for current to flow round the coil M. In the position shown in diagram D the contact area between the brush and segment 5 is small while that between the brush and segment 6 is large, and the current 21 c which passes through the brush divides up into two parts as shown in the diagram; the current i in coil M now passes in a direction opposite to that which it had in diagram A. As the contact area with seg- ment 5 decreases, the value of the current i which passes round coil M increases until, at the instant shown in diagram E, this current is equal to I c . By this action of the brush the current in the coil M is reversed or commutated while the armature moves through the distance of the brush width, and the variation of current with time is plotted in curve 1, Fig. 62, and follows a straight line law. 59. Effect of the Self-induction of the Coil. The resistance of the coil undergoing commutation is generally so low that its effect can be neglected, but the effect of self-induction must be considered. The current i in the coils M sets up lines of force which link these coils. As this current reverses the lines of force also reverse, as shown in diagrams B and D, and the change of flux generates an e.m.f. in each coil M which is generally called its e.m.f. of self-induction. It is important to notice however that part of the flux which links one of the coils, say M, is due to current in the coil Af x on one side and to current in the coil M 2 on the other side, so that this generated e.m.f. is really an e.m.f. of self and mutual induction. The e.m.f. of self and mutual induction opposes the change of current which produces it, so that at the end of half of the period of commutation the current in the coils M has not be- come zero but has still the value cd, curves 2, 3 and 4, Fig. 62; COMMUTATION 75 these curves show the variation of current with time for differ- ent values of the ratio -= = where: L + M R is the resistance of the total brush contact in ohms, T c is the time of commutation in seconds, L is the coefficient of self-induction of one coil M in henries, M is the coefficient of mutual induction between coil M and coils M! and M 2 in henries. The equation from which these curves were plotted is derived as follows: The difference of potential between a and b, diagram B, Fig. 61, (Ic+i)?! (I c i)r 2 and this must be equal and opposite to the generated voltage (L + M) -=- or (I n +i) ri -(I c -i)r 2 If now R and T c have the values already mentioned, and t is the time measured from the start of commutation therefore (I e +i)R (7^7) +(L + M) ~-(I c -i)R (^) =0 \J- C "' (*" , di I RT C \ (I c +i Ic-i and -jT= ( T . *,) 1 ~ t r~ at \L + M] \l c t t The results from this equation are plotted in Fig. 62 for 7? / 7 7 different values of the ratio /r ' (L+M) 60. Current Density in the Brush. By the use of the values of i plotted in Fig. 62 the value of the current I c +i flowing from the brush to segment 5 can be determined, and from it the cur- rent density in the brush tip s at any instant can be obtained. This quantity is plotted against time in Fig. 63, and it will be 7P7 1 seen that, for values of T .Z* less than 1, the current density in the brush tip s becomes infinite, and due to the concentration of energy at this tip sparking takes place. The criterion for sparkless commutation then is that L+M 1 For the solution of this equation see Reid on Direct Current Commuta- tion. Trans, of A. I. E. E., Vol. 24, 1905. 76 ELECTRICAL MACHINE DESIGN be greater than 1, and perfect commutation is denned as such a change of current in the coil being commutated that the current density over the contact surface between the brush and the commutator segment is constant and uniform. i X \\ \v 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Time from Start of Commutation FIG. 62. 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 T c Time from Start of Commutation FIG. 63. RT, Curve l,- r+M - Curve 2. =- j^ = RT C Curve 3. L + M Curve 4. =5^5= infinity. 1.0 0.5 Current in the short-circuited coil and current density at the brush tip. 61. The Reactance Voltage. The above criterion for sparkless commutation is used in practice in a slightly different form for, 7PT 7 if ,. c must be greater than 1 then R must be greater than ^ and 21 C R greater than 21 This latter quantity is called the average reactance voltage, and is the e.m.f. of self and mutual induction of the coil being commutated on the assumption that the current varies from I c to 7 C according to a straight line law. This average reactance voltage then should always be less than 2I C R the voltage drop across one brush contact. 62. Brush Contact Resistance. Curve 1, Fig. 64, shows the COMMUTATION 77 value of the resistance of unit section of brush contact plotted against current density in that contact; the resistance decreases as the current density increases and for higher values than 35 amperes per square inch it varies almost inversely as the current density and the voltage drop across the contact becomes prac tically constant, as shown in curve 2, Fig. 64. Such curves of brush resistance are obtained by testing the brushes on a revolving collector ring and allowing sufficient time to elapse between readings to let the conditions become stationary. i.o 0.8 0.6 0.4 > 0.2 \ .06 .04 .02 10 20 30 40 50 60 70 80 90 100 Amperes per Sq. Inch FIG. 64. Brush-contact resistance curves. The resistance from ring to brush is generally greater than that from brush to ring by an amount which varies with the material of the brush. It would seem that, by neglecting the effect of the variation of contact resistance with current density, as was done in Art. 59, the results there obtained would be rendered of little practical im- portance, it is found, however, that the variation in resistance is largely a temperature effect and that at constant temperature the contact resistance does not vary through such extreme limits, also that, due to the thermal conductivity of carbon, the temperature difference between two points on a brush contact is not very great. Suppose that, having reached the value of 10 amperes per square inch, and the resistance having become stationary at 0.06 ohms per square inch, see Fig. 64, the current density were 78 ELECTRICAL MACHINE DESIGN suddenly increased to 40 amperes per square inch; the re- sistance in ohms per square inch would not fall suddenly to 0.023 but would have a value of about 0.06 and this would gradually decrease until, after about 20 minutes, the resistance would have reached the value of 0.023, the value which it ought to have according to curve 1, Fig. 64. This explains why a machine will stand a considerable overload for a short time without sparking, whereas if the overload be maintained the machine will begin to spark as the brush temperature increases and the contact resistance decreases. Sparking is cumulative in its effect because slight sparking raises the temperature of the brush contact, which reduces the contact resistance and causes the operation to become worse. 63. Brush Pressure. The brush contact resistance is found to decrease as the brush pressure increases and as the rubbing velocity decreases, but these effects can be neglected in any study of commutation since the change due to rubbing velocity is small, while the biush pressure is fixed by the service and is made as small as possible. The brush pressure is seldom less than 1.5 Ib. per square inch of contact surface because at lower pressures the brushes are liable to chatter, while if the pressure be too great the brushes cut the commutator if they are hard or wear down and smear the commutator if they are soft. A brush pres- sure greater than 2 Ib. per square inch is seldom exceeded except for street car motors, in which case the vibration of the machine itself is excessive, and pressures as high as 5 Ib. per square inch have to be used to prevent undue chattering of the brushes. 64. Energy at the Brush Contact. The criterion for sparkless commutation is that the energy at the brush tip, which is pro- portional to the current density in that tip, shall not become infinite. The average energy expended at the brush contact must also be limited as may be seen from the following table: Kind of brush 1 Current density Volts across one contact Very soft carbon 50 70 amp per so in 6-0 4 Soft carbon 4065 amp. per sq. in 7-0 55 Fairly hard carbon Very hard carbon 30-45 amp. per sq. in 25-40 amp. per sq. in 1.1-0.9 1.5-1.2 Arnold, Die Gleichstrom-machine, Vol. 1, page 351. COMMUTATION 79 The product of amperes per square inch and volts drop across one contact has an average value of 35 watts per square inch. It must be understood that these figures are for machines which operate without sparking and without shifting of the brushes from no load to 25 per cent, overload, but have not necessarily what was defined in Art. 60, page 76, as perfect commutation. The better the commutation the more nearly uniform the current density in the brush contact and the higher the average current density that can be used without trouble developing. 65. Calculation of the Reactance Voltage for Machines with Full-pitch Multiple Windings. Consider first the case where there are T turns per coil and the brush covers only one segment, as shown in Fig. 65. The winding is of the double layer type and has two coil sides per slot; a section through one slot is shown at S, Fig. 65, for the case where 7" = 6. i) I . I FIG. 65. Flux circling a full-pitch multiple coil during short-circuit. Let (f> s be the number of lines of force that circle 1 in. length of the slot part of the coil M for each ampere conductor in the group of conductors that are simultaneously under- going commutation. and (j) e the number of lines of force that circle 1 in. length of the end connections of the coil M for each ampere conductor in the group of end connections that are simultaneously undergoing commutation. In one of the slots A there are 2T conductors, each carrying a current i, so that the flux that circles one side of coil M = 8 X L c x2Txi lines. In one of the groups of end connections, as at X, Fig. 65, there are T conductors, each carrying a current i, so 80 ELECTRICAL MACHINE DESIGN that the flux that circles one group of end connections of length L e = (j) e XL e xTxi lines. The total flux that circles the coil M due to the current i in the coil = c = 2Ti and (L + M)=XW~ 8 henry = 2 T 2 (2 s L c + e L e } XlO- 8 henry T c , the time of commutation, is the time taken by the commuta- tor to move through the distance of the brush width and is equal 60 segments covered by the brush t/o x ' r.p.m. total number of commutator segments 60 segments covered by the brush X r.p.m. S therefore, when the brush covers only one segment, the average 27* reactance volt age = ^= _ 97 60 66. The Effect of Wide Slots and Brushes. Neglect for the present the effect of the end connection flux, which is small com- pared with the slot flux, and compare the four cases shown in Fig. 66. A shows part of a winding which has 6 coil sides per slot and a brush which covers 1 commutator segment. B shows part of a winding which has 2 coil sides per slot and a brush which covers 1 commutator segment. C shows part of a winding which has 6 coil sides per slot and a brush which covers 3 commutator segments. D shows part of a winding which has 2 coil sides per slot and a brush which covers 3 commutator segments. The slots in cases A and C are three times as wide as those in B and D and the coils shown black are those which are under- going commutation. In B the time of commutation is the same as in A, but the flux a is three times as large since the reluctance of its path is proportional to the ratio - 1 - ^rr, the reluctance of the iron slot width' part of the path being neglected. The reactance voltage is therefore three times as large. COMMUTATION 81 In C the time of commutation is three times as long as in A, and the flux (f> s also is three times as large since there are three times as many conductors undergoing commutation at the same instant. The reactance voltage is therefore the same in each case. In D the time of commutation is the same as in C and so also is the flux (f> s , since the reluctance of three short paths in series is the same as that of a single path three times as long. The reactance voltage is therefore the same in D as it is in C or A. in 1-1 1 FIG. 66. Effect of slot and brush width on the reactance voltage. From the above discussion the following conclusions can be drawn namely, that when the brush covers one commutator segment only, the reactance voltage is greater the narrower the slot; compare for example, cases A and B' } also that an increase in the brush width has no effect on the reactance voltage as long as the group of conductors simultaneously commutated is not greater than the total number of conductors per slot (compare A and C), but decreases the reactance voltage if the group of 82 ELECTRICAL MACHINE DESIGN conductors simultaneously commutated is greater than the total number of conductors per slot (compare B and D) . The method for determining the brush width is taken up in Art. 72; it is pointed out here, however, that the brush generally covers more than one commutator segment, and under these conditions the case of a very narrow slot with the brush covering one commutator segment, namely case 5, Fig. 66, can be neglected; with this restriction the formula for reactance voltage on page 80 can be used for all slot and brush widths. x lt has been found experimentally that, for the shape of coil in general use in D.-C. machines and for slots which have the slot depth , . . , . . . . ratio -, : ^ru = 3.5, a value which is seldom exceeded in non- slot width interpole machines, the value of (f> s may be taken as 10 lines per ampere conductor per inch length of core, and (f) e may be taken as 2 lines per ampere conductor per inch length of end connection. By substituting the above values in the formula for reactance voltage on page 80, the following result is obtained for the reactance voltage of a full pitch double layer multiple winding namely: Average reactance voltage (9) 60 = 1.33xXr.p.m.X/ c XT 2 (L c +0.1Le)10 - 8 1,1,1 FIG. 67. Flux circling a short-pitch multiple coil during short-circuit. 67. Short Pitch Multiple Windings. It was pointed out in Art. 15, page 15, that, when a short-pitch winding is used, the con- ductors of the coils which are short circuited at any instant are not in the same slot, thus Fig. 67 shows the short pitch diagram 1 Hobart, Continuous Current Dynamo Design, page 108. COMMUTATION 83 which corresponds to the full-pitch one shown in Fig. 65, and it will be seen that, while the end connection flux is the same in each case, the slot flux < s has only half the value for a short- pitch winding that it has for a full-pitch winding so long as the pitch is short enough to prevent the conductors which are short- circuited at any instant from lying in the top and bottom of the same slot. For a short -pitch double-layer multiple winding the value of the average reactance voltage . (10) FIG. 68. Coils in a series winding that are short-circuited by one brush. 68. Calculation of the Reactance Voltage for Machines with Series or Two Circuit Windings. Fig. 68, which is a reproduction of Fig. 21, shows that when only one + and one brush are used each brush short circuits ^ coils in series, so that the average reactance voltage in such a case When, however, the same number of sets of brushes are used as there are poles, so that brushes are also placed at b and c, there is a short commutation path round one coil which is short-circuited by two brushes at the same potential, in addition to the long path around ~ coils in series and, so far as this short path alone is concerned, the average reactance voltage = 1.33 xXr.p.m.X/ c xr 2 (L c + 0.1 L e )10- 8 . 84 ELECTRICAL MACHINE DESIGN The value of the reactance voltage that should be used as a criterion for commutation is somewhere between these two values, and the results are still further complicated by what is known as selective commutation which was described in Art. 17, page 19, so that in practice it is usual to use the former of the two equations, which is pessimistic; the commutation will gener- ally be about 20 per cent, better than that indicated by the value of reactance voltage so found. 69. Formulae for Reactance Voltage. Collecting together the results obtained in Arts. 66, 67 and 68, the following formulae are obtained: The average reactance voltage = 1.33xSXr.p.m.X/ c xr 2 (Z/ c + 0.1 L e )10~ 8 for full-pitch mul- tiple windings = 1.33 XSXr.p.m.X/ c X T 2 (^ + 0.1 L e ) 10~ 8 for short-pitch mul- tiple windings = 1.33 X/SXr.p.m. X / c X T 2 (L c + 0.1 L e ) | X 10~ 8 for series windings. It is pointed out in Art. 99, page 117, that, in order to have an economical machine, the core length L c should lie between the values (0.9 to 0.6) X[pole pitch]. The length L e of the end connections is directly proportional to the pole pitch and =1.4 (pole pitch) approximately, so that L e has a value between (1.6 and 2.4) X[L C ] and an average value = 2L C . Substituting this average value in the above formula for react- ance voltage the following approximate formula is obtained: The average reactance voltage 10~ 8 (12) where S = the number of commutator segments r.p.m. =the speed of the machine in revolutions per minute 7 c = the current in each armature conductor jT = the number of turns per coil L c = the frame length in inches = 1 for multiple and = ^ for series windings paths 2 A; = 1.6 for series and full-pitch multiple windings = 0.93 for short-pitch multiple windings. CHAPTER IX COMMUTATION (Continued) 70. The Sparking Voltage. Down to this point it has been assumed that the coils in which the current is being commutated are in such a position between the poles that, during commuta- tion, they are not cutting any lines of force due to the m.m.f. of the field and the armature. Under these conditions the value of the reactance voltage when sparking begins is called the sparking voltage, and depends on the brush resistance, as shown in Art. 61, page 76. In practice the brushes are generally shifted from the above neutral position in such a direction that the coils which are undergoing commutation are in a magnetic field, and an e.m.f. E s is generated in them, due to the cutting of this field, which opposes the e.m.f. of self and mutual induction and so causes the commutation to be more nearly perfect. In such cases the value of the resultant of this generated voltage and of the react- ance voltage, when sparking begins, is called the sparking voltage. As the load on a machine increases the reactance voltage jncreases with it, and in order that the commutation may be perfect at all loads the voltage E s must increase at the same rate; this can only be the case if the distance the brushes are shifted from the neutral varies with the load. Suppose that the brushes are in such a position that commuta- tion is perfect at 50 per cent, overload, and that they are fixed there; then at no-load there will be no reactance voltage to counteract, but there will be a large generated voltage E s which will cause a circulating current to flow in the short-circuited coil, and sparking will take place if E s is larger than the sparking voltage. Modern D.-C. machines are expected to carry any load from no-load up to 25 per cent, overload without sparking and also without shifting of the brushes during operation. To accom- plish this result the brushes are shifted from the neutral position, in such a direction as to help commutation when the machine is loaded, until the machine is about to spark at no-load; the voltage E S) which is generated in the short-circuited coil, will then 85 86 ELECTRICAL MACHINE DESIGN be a little less than the sparking voltage. When the machine is carrying 25 per cent, overload the reactance voltage will be greater than the generated voltage E s by an amount which is just a little less than the sparking voltage, and half way between Volts Shunt Volts Curve Compound Load Volts B Load Over Compound FIG. 69. Variation of the voltage in the short-circuited coil with load. these two points E s will be equal and opposite to the reactance voltage and the commutation will be perfect. From the above it would seem that the reactance voltage at 25 per cent, overload could have a value equal to about twice the sparking voltage, but in obtaining this result it has been assumed COMMUTATION 87 that the generated voltage E 8 remains constant at all loads; as a matter of fact, it decreases with increase of load due to the cross- magnetizing effect of the armature, as pointed out in Art. 48, page 54. To prevent this decrease in the value of E 8 from becoming too large, the relation between the field and armature strengths is fixed by making the field ampere-turns per pole for gap and tooth greater than 1.2 (the armature ampere-turns per pole) + the demagnetizing ampere-turns per pole; see Art. 52, page 61. The diagrams in Fig. 69 show the variation of E 8 and of the reactance voltage with load. Curve 1 shows the relation between E 8 and the load, and curve 2 shows that between the reactance voltage and load. The brushes are shifted until the value of E s at no-load is equal to the sparking voltage; at load B the com- mutation is perfect, and at load C the reactance voltage is greater than E 8 by the sparking voltage. These curves show clearly the superiority of the overcompound machine as far as commu- tation is concerned. 71. Minimum Number of Slots per Pole. Fig. 70 shows three of the stages in the commutation of the current in a machine which has six coil sides per slot. The commutator segments are evenly spaced, while the coils, being in slots, are not. It will be seen that, between the instant when the brush breaks contact with coil A and the instant when it breaks contact with coil C, the slot in which these coils lie has moved through the distance x, so that, if the magnetic field in which the coils undergo com- mutation is just right for coil A, it will be a little too strong for coil J5, and much too strong for coil C; this latter coil will there- fore be so badly commutated that sparking will result and will show up on the commutator in the blackening of every third commutator segment due to the poor commutation of the coil to which it is connected. The distance x = the slot pitch width of one commutator segment. The distance through which a slot moves while the conductors which it carries are undergoing commutation is limited by making the number of slots per pole such that there are not less than 3.5 slots in the space between the poles; this space is generally 30 per cent, of the pole pitch, so that the number of slots per pole, corresponding to 3.5 slots in the space between poles, is 12, and is the smallest number of slots per pole that should be used. For large machines there are seldom less than 14 slots per pole. 88 ELECTRICAL MACHINE DESIGN 72. The Brush Width. It was pointed out in Art. 66, page 82, that the brush width has very little effect on the reactance voltage because, while the number of adjacent coils that are simultaneously undergoing commutation increases with the brush width, the time of commutation also increases at the same rate. Figure 71 shows the distribution of the magnetic field in the space between the poles of a loaded D.-C. generator and also the u FIG. 70. Variation of the position of the short-circuited coil when there are several coils per slot. position of a wide brush. It will be seen that, in order to keep the tip a of the brush from under the pole, where the magnetic field is too strong , the tip b has to be in a magnetic field which is not a reversing field, so that at the start of commutation in any coil the current in that coil will increase, as shown in Fig. 72, and the effective time of commutation will be less than the COMMUTATION 89 cd apparent time in the ratio To limit this effect the brush ce should not cover more than 28 per cent, of the space between poles or 0.28X0.3 times the pole pitch. The brush arc measured on the armature surface should there- FIG. 71. Flux distribution at full-load in the space between poles. e d c FIG. 72. Variation of the current in the short-circuited coil when the biush is too wide. pole pitch fore not be greater than - ^^ or > measured on the commu- tator surface, should not be greater than pole pitch dia. commutator 12 X dia. armature There is still another limit to the brush arc. When the brushes are shifted from the neutral position in order to help commutation under load there is an e.m.f. generated in the short-circuited coils, namely E s . Thus, in the case shown in Fig. 73, where the brush covers five segments, the voltage generated between a and b is that of five coils in series and the resistance of the path to the 90 ELECTRICAL MACHINE DESIGN circulating current that will flow is comparatively low, being that of one coil and two contacts. To prevent trouble due to this circulating current it is necessary to limit the brush arc so that it shall not cover more than three commutator segments. 73. Limits of the Reactance Voltage. In the discussion in Art. 61, page 76, it is shown that the reactance voltage should not exceed the voltage drop across one brush contact when the brushes are in such a position that the short-circuited coil is not FIG. 73. Circulating currents at no-load in a wide brush. cutting any lines of force due to the m.m.f. of the field and armature, and the discussion in Art. 70, page 85, shows that higher values may be used when the brushes are shifted forward so as to help commutation. Experiment shows that higher values of the reactance voltage may be used than the limits indicated by theory and the follow- ing, found from experience, may be used in design work. For machines which must operate without destructive sparking at all loads from no-load to 25 per cent, overload with brushes in a fixed position, the reactance voltage at full load should not exceed 0.7 (volts drop per pair of brushes) with the brushes on the neutral position, nor should it exceed the volts drop per pair of brushes for machines with the brushes shifted so as to help commutation. These figures apply to machines which are built so that: The number of slots per pole is greater than 12; COMMUTATION 91 The brush arc covers less than 1/12 of the pole pitch when measured on the armature surface> and also does not cover more than three commutator segments; The pole arc is not greater than 70 per cent, of the pole pitch; ATg + t is greater than 1.2 (armature AT per pole) + the demag- netizing AT per pole. These figures are intimately connected with one another and also with the reactance voltage; for example, the brushes may be made wider and the main field weaker than indicated, but in such cases the reactance voltage must also be decreased otherwise trouble will develop. In addition it must be noted that, as pointed out in Art. 68, page 84, the commutation of a machine with a series winding is about 20 per cent, better than represented by the value of the reactance voltage obtained from the formula. For machines with short-pitch windings on the other hand, the operation is about 30 per cent, worse than represented by the value of the reactance voltage obtained from the formula, because, as shown in Art. 15, page 15, the effective width of the space between poles is less than the actual width by the distance of one slot pitch. FIG. 74. Field due to the armature m.m.f. 74. Limit of Armature Loading. Fig. 74 shows part of a multipolar machine; the current in the armature conductors is represented by crosses and dots and the lines of force of armature reaction are also shown. As the number of armature ampere- turns per pole increases the field ampere-turns per pole must also be increased so as to prevent too great a distortion of the main field and consequently poor commutation. There is, however, one part of the armature field which is not counteracted by the main field, namely, the field out on the end connections; this is stationary in space and therefore cut by the coils which are undergoing commutation. The e.m.f. due to the cutting of this field acts in such a direction as to oppose commuta- tion, and in order to prevent this voltage from having such a 92 ELECTRICAL MACHINE DESIGN value as to cause trouble it is advisable to limit the number of armature ampere-turns per pole to about 7500; a higher value than this must be accompanied by a low reactance voltage otherwise trouble will develop. 75. Interpole Machines. -It was pointed out in Art. 70, page 85, that commutation can be helped by shifting the brushes so that the short-circuited coils are in a magnetic field, and it was also shown that, if the e.m.f. generated due to this field was to be equal and opposite at all times to the reactance voltage, the strength of the field should be proportional to the load. FIG. 75. Magnetic circuit of a four-pole interpole machine. Figure 75 shows an interpole generator diagrammatically; n and s are auxiliary poles which have a series winding, so that their strength increases as the load increases. In a generator the brushes would be shifted forward in the direction of motion so that B + would come under the tip of the N pole and B_ under the tip of the S pole; instead of that, in the interpole machine, the auxiliary n pole is brought to the brush B + and the auxiliary s pole to the brush #_. Before the interpole can send a flux across the air gap in such a direction as to help commutation it must have a m.m.f. equal to that of the cross magnetizing effect of the armature which r7 = J / C ampere-turns, see Art. 48, page 55, = the armature ampere-turns per pole, COMMUTATION 93 and in addition a m.m.f. to send a flux across the air gap large enough to generate an e.m.f. in the short-circuited coil which shall be equal and opposite to the e.m.f. of self and mutual induction and to that generated due to cutting the magnetic field out on the end connections. In order that the flux produced by the interpole may be always proportional to the load, it is necessary that the interpole magnetic circuit do not become saturated. 76. Interpole Dimensions. Wt p , the interpole arc, should be such that, while the current in a conductor is being commu- tated, the slot in which that conductor lies is under the interpole. FIG. 76. Dimensions of interpole. The distance moved by the coil A, Fig. 70, while it is short- circuited by the brush, is equal to the brush arc referred to armature diameter the armature surf ace = brush arc X - p ; commutator diameter' the total arc which must be under the influence of the interpole is greater than this by the distance x which, as pointed out in Art. 71 , page 87, =the slot pitch -- the width of one commutator segment referred to the armature surface. As shown in Fig. 76, the flux fringes out from either side of the interpole by a distance which is approximately equal to the air-gap clearance, so that the effective interpole arc = Wi p + 2d; this arc must be equal to the slot pitch + brush arc segment width, all referred to the armature surface. This arc must also be such that the reluctance of the gap under the interpole shall vary as little as possible for different positions of the armature, otherwise the interpole field will be a pulsating one; if, for example, the arc were equal to the width of one tooth, then- the interpole air-gap reluctance would vary from a maximum when a tooth was under the pole to a minimum when a slot was under the pole. If the interpole effective arc be a multiple of the slot pitch, as in Fig. 76, where it is equal to twice the slot pitch, the reluctance of the gap will 94 ELECTRICAL MACHINE DESIGN be practically constant, because, as one tooth moves from under the pole another comes under its influence. As a general rule the effective interpole arc is about 15 per cent of the pole pitch and is adjusted so as to be approximately a multiple of the slot pitch; the brush arc is then made to suit the interpole arc so found. To allow space for the interpole and to prevent the interpole leakage flux from being too large, the arc of the main pole is kept down to about 65 per cent of the pole pitch. The axial length of the interpole, Li p ,is found as follows: If Bi is the average interpole gap density, then the voltage gene- rated in each coil while under the interpole = the lines cut per second XlO~ 8 = 2 and this should equal the reactance voltage, which, for a full pitch winding, the type used on interpole machines, = 1.6xSXr.p.m. X/ c Xl/ c X r 2 XlO~ 8 volts per coil; therefore, equating these two values together and simplifying = ampere conductors per inch X L c X 48 r , /ampere conductor per inch\ and Li = L c I- -\ X 48 The value of Bi is generally chosen about 45,000 lines per square inch at full load, for which value the interpole circuit does not become saturated up to 50 per cent, overload. The value of ampere conductors per inch seldom exceeds 900; for this value, and for the value of interpole gap density given above The interpole excitation is not figured out accurately; the usual practice is to put on each interpole a number of ampere-turns which at full load =1.5 (armature AT per pole) = 1.5 such a value is sufficient to overcome the armature m.m.f. and also to send sufficient flux across the interpole gap to allow the neces- sary voltage to be generated. This value of m.m.f. is generally COMMUTATION 95 too large and the final adjustment is made by means of a shunt after the machine has been erected. 77. Flashing Over. If the voltage between adjacent commu- tator segments becomes too high the machine is liable to flash over on the commutator from brush to brush, particularly if the commutator is dirty. The voltage between two adjacent bars should not if possible exceed 40; turbo generators have been built in which this value was greater than 60, but such machines are sensitive to changes of load and liable to flash over unless supplied with compensating windings. It must be clearly under- stood that there is considerable difference between the maximum voltage between commutator bars and the average value, this can be seen from Fig. 49, which shows that when the machine is loaded the flux density in the air gap at point d is much higher than the average gap density; at this point the highest voltage per coil will be generated. A B FIG. 77. Armature field with and without compensating windings. Flashing over is generally caused by a sudden change of load, the reason being as follows: Fig. 77, diagram A, shows the arma- ture cross field when the machine is loaded; a sudden change in load causes the value of this field to change and a voltage is generated in the armature coils which is proportional to the rate of change of flux and is a maximum in the coil a. This voltage increases or decreases that which already exists between adja- cent commutator segments and the increase may be sufficient to cause the voltage between adjacent commutator segments to become too high and the machine to flash over. When the load is very fluctuating in character, such as the load on a motor driving a reversing rolling mill at the instant of reversal of the rolls, at which instant the current changes from 96 ELECTRICAL MACHINE DESIGN less than full-load current to about three times full-load current in the opposite direction, the average voltage between commuta- tor bars should not exceed 15, or it will be necessary to supply the machine with a compensating winding to prevent flashing over. Fig. 78 shows such a machine. The poles carry a winding on the pole face which is connected in series with the FIG. 78. Yoke of machine with interpoles and compensating windings. armature and which has the same number of ampere-turns per pole as there are on the armature. The current in the pole-face conductors passes in the opposite direction to that in the arma- ture conductors under the same pole, so that the armature field is completely neutralized, as shown in Fig. 77, diagram B; there is no crowding of the lines into one pole tip as shown in Fig. 49, and there is no sudden change of armature field with load and therefore no tendency to flash over. CHAPTER X EFFICIENCY AND LOSSES _ , ^^ . . output output 78. The Efficiency of a generator = -T input output + losses , output input -losses , and that of a motor = ^ = where the losses input input are: Mechanical losses windage, brush and bearing friction. Iron losses hysteresis and eddy current losses. Copper losses in field and armature coils. Commutator contact resistance loss. 79. Bearing Friction. In a high speed bearing with ring lubrication there is always a film of oil between the shaft and the bushing; bearing friction is therefore an example of fluid friction and the tangential force at the rubbing surface in such a case = kAbVb n lb., where A; is a constant which depends on the vis- cosity of the oil and is found by experiment to be =0.036 for bearings with ring lubrication using light machine oil. Ab is the projected area of the bearing in square inches = (the bearing diameter db in inches X the bearing length lb in inches); Vb is the rubbing velocity of the bearing in feet per minute; n is found experimentally to vary from 1 for low values of Vb to for very high values and is approximately 0.5 for bearing speeds from 100 to 1000 ft. per minute. For moderate speed bearings with ring lubrication and with light machine oil the force of friction = 0.036 A b V b * pounds and the friction loss = 0.036AbVb* ft. lb. per minute = 0. 81 dblb~ watts. (13) It is important to notice that this loss is independent of the bearing pressure and is therefore independent of the load. As the pressure on the bearing increases the thickness of the oil film decreases and at a certain limiting pressure it breaks down and the bearing seizes. For electrical machinery the 7 97 98 ELECTRICAL MACHINE DESIGN bearing load . . . bearing pressure = f- > should not exceed 80 Ib. per -Aft square inch when the machine is carrying full load, such a bearing will carry 100 per cent, overload without breakdown. The bearing loss increases rapidly with the rubbing velocity and after a certain velocity has been reached the bearings are no longer large enough to be' self-cooling. For self-cooling bearings the rubbing velocity should not exceed 1000 ft. per minute unless the bearing is specially designed to get rid of the heat, and even this value should only be used for machines which are built so that a large supply of cool air passes continuously over the external surface of the bearing. The bearings of totally enclosed motors for example are poorly ventilated and should not be run with a rubbing velocity greater than about 800 ft. per minute. The thickness of the oil film in a bearing varies inversely as the temperature of the oil, and this temperature should not exceed 70 C. when measured by a thermometer in the oil well. 80. Brush Friction. If H is the coefficient of friction; P the brush pressure in pounds per square inch; A the total brush rubbing surface in square inches; V r the rubbing velocity in feet per minute; then the friction loss =/j.PAV r ft. Ib. per minute. Approximate, values found in practice are: fji = 0.28 and P =2 Ib. per square inch, for which values the friction loss = 1.25 A^. watts. (14) 81. Windage Loss. It is difficult to predetermine this loss, but, up to peripheral velocities of 6000 ft. per minute, it is so small that it may be neglected. Fig. 79 shows the windage and bearing friction loss of a motor which has an armature diameter of 100 in. and three bearings each 10 in. by 30 in. The circles show the actual test points and the curve shows the value of the bearing friction loss calculated from the formula, friction loss =3X0.81 X d b X h * watts. At a speed of 230 r.p.m. the peripheral velocity of the armature is 6000 ft. per minute, up to which speed the windage loss can be neglected; at higher speeds it becomes large because it is proportional to the (peripheral velocity). 3 EFFICIENCY AND LOSSES Few electrical machines except turbo generators are run at peripheral speeds greater than 6000 ft. per minute, because the cost increases very rapidly for higher speeds on account of the 30 20 M 100 200 300 400 R.P.M. FIG. 79. Windage and friction loss in a large motor. special construction required to hold the coils against centrif- ugal force. 82. Iron Losses. It may be seen from Fig. 80 that the flux in FIG. 80. Distribution of flux in the armature. any portion of the armature of a D. C. machine goes through one cycle while the armature moves through the distance of two pole pitches; that is, the flux in any portion of the armature 100 ELECTRICAL MACHINE DESIGN passes through ^ cycles per revolution, or through ^X Zi Z OU cycles per second. The iron losses consist of the hysteresis loss which =KB r *fW watts, and the eddy current loss which = K e (Bft) 2 W watts where K is the hysteresis constant and varies with the grade of iron; K e is a constant which is inversely proportional to the electrical resistance of the iron; B is the maximum flux density in lines per square inch; / is the frequency in cycles per second; W is the weight of the iron in pounds; t is the thickness of the core laminations in inches. The eddy current loss can be reduced by the use of iron which has a high electrical resistance. At present, however, most of the grades of very high resistance iron have a lower permeability than those of lower electrical resistance; they also cost more and are more brittle; machines built with such iron are liable to have the teeth break off due to vibration. The reduction in the total loss by the use of high resistance iron is not so great as one would expect, because a large part of the loss is due to losses discussed in the next article and these are not greatly affected by the grade of iron used. The eddy current loss can be reduced by a reduction in t, the thickness of the laminations; this value is generally about 0.014 in.; thinner iron is difficult to handle. 83. Additional Iron Losses. Besides the ordinary hysteresis and eddy current loss already mentioned there are additional losses which cannot be calculated, due to the following causes: (a) Loss due to filing of the slots. When the laminations that form the core have been assembled it will be found that in most cases the slots are rough and must be filed smooth in order that the slot insulation may not be cut. This filing burrs the laminations over on one another and provides a low resistance path through which eddy currents can flow; that is, it tends to defeat the result to be obtained by laminating the core. (6) Losses in the spider and end heads due to the leakage flux which gets into these parts of the machine; these losses may be large because the material is not laminated. (c) Loss due to non-uniform distribution of flux in the arma- EFFICIENCY AND LOSSES 101 ture core. When calculating the value of B c , the flux density in the core, page 45, it is assumed that the flux ia uniformly spread over the core area. This however is not tife'QEfogantL the actual flux distribution is shown in Fig. 80; the lines -of force take the path of least reluctance and there'! 9T3 - crowd in behind the teeth until that part of the core becomes saturated, then they spread further out. Due to this concentration of flux, the core loss, which is approximately proportional to (flux density), 2 is greater than that got by assuming that the flux distribution is uniform through the whole depth of the core. It is sometimes possible to increase the core depth so as to keep the apparent flux density in the core low and yet make no perceptible reduction in the core loss, because the increased depth of core does not carry its proper share of the flux; for this reason there is seldom much to be gained by making the value of B c less than 80,000 lines per square inch, which is near the point at which saturation begins and the flux tends to become uniform. (d) Pole face losses. Fig. 39 shows the distribution of flux in the air gap of a D. C. machine and, as the armature revolves and the teeth move past the pole face, e.m.fs. will be induced which will cause currents to flow across the pole face. Experi- ment shows that when solid pole faces are used the loss due to these currents increases very rapidly as the slot opening becomes greater than twice the length of the air gap; when the slot open- ings are wider than this the pole face must be laminated. (e) Variation of the iron loss with load. It is shown in Fig. 49 that, when the machine is loaded, the flux density is not uniform in all the teeth under the pole but is stronger at one pole tip than at the other. The effect of the increase of flux density in the teeth under one pole tip in increasing the iron loss is greater than the effect of the decrease of flux density in the teeth under the other tip in reducing the iron loss. 84. Calculation of Core Loss. Due to the additional losses it is impossible to predetermine the total core loss by the use of fundamental formulae; core loss calculations for new designs aie based on the results obtained from tests on similar machines built under the same conditions. Such test results are plotted in Fig. 81 for machines built with ordinary iron .of a thickness of 0.014 in., the slots being made with notching dies so that a certain amount of filing has to be done. 102 ELECTRICAL MACHINE DESIGN Example of calculation: For the machine shown in Fig. 41 the value of B at the actual flux density in the teeth and B c the average flux density in the bore are given in Art. 46, page 49. $at ISO'jGOO lines per square inch; Bf <=84,OQO lines per square inch; Wt, Sthe to&tr* weight of the armature teeth = 385 lb.; W c , the total weight of the armature core = 2300 lb. ; The frequency = 16.6 cycles per second; The loss per pound for the teeth = 6 watts, from Fig. 81; The loss per pound for the core = 1.8 watts, from Fig. 81; The total loss = 385X6 + 2300X1. 8 = 6450 watts. 1015 20 25 30 Cycles per Second 40 50 50 100 10 15 35 40 20 25 3 "V/atts-per Lb. FIG. 81. Iron loss curves for revolving machinery. 45 50 85. Armature Copper Loss. The resistance of copper at the normal operating temperature of an electric machine is approxi- mately 1 ohm per circular mil cross-section per inch length, so that if Z is the total number of conductors; Lb is the length of one conductor in inches; M is the cross-section of each conductor in circular mils; 7 C is the current in each conductor in amperes; ^r^ M then the resistance of one conductor in the loss in one conductor in watts =irx/c 2 M EFFICIENCY AND LOSSES 103 and the total copper loss in the armature in watts = Z-^/ c 2 (15) The value of L& = 1.35 (pole pitch) + 2 (armature axial length) + 3 in. approximately for the type of coil shown in Fig. 33, page 36. 86. Shunt Field Copper Loss. This loss, which = E t l f watts, where jE^is the terminal voltage of the machine and // is the current in the shunt coil, is made up of the loss in the field coils and the loss in the field rheostat; the latter for a generator is about 20 per cent, of the total shunt field loss. 87. Series Field Copper Loss. This loss =I a 2 R s watts, where R s is the resistance of the series field in ohms and I a the total armature current. When a series shunt is used, so that part of the current I a passes through the series field and the remainder passes through the shunt, the resistance R s is the combined resist- ance of the series field and the series shunt in parallel. 88. Brush Contact Resistance Loss. This loss has already been discussed in Art. 62, page 76, and =EbI a watts, where Eb is the voltage drop per pair of brushes and I a is the armature current. The volts drop per pair of brushes is approximately constant over a wide range of current, as shown in Fig. 64. CHAPTER XI r T HEATING 89. Cause of Temperature Rise. The losses in an electrical machine are transformed into heat; part of this heat is dissipated by the machine and the remainder, being absorbed, causes the temperature of the machine to increase. The temperature becomes stationary when the heat absorption becomes zero, that is when the point is reached where the rate at which heat is generated in the machine is equal to the rate at which it is dissipated. 90. Maximum Safe Operating Temperature. The highest safe temperature at which an electrical machine can be operated continuously is about 85 C. with the present practice in insu- lating, because, if subjected to that temperature for any length of time, the paper and cloth which are used for coil insulation become brittle, and pulverize due to vibration. The usual heating guarantee is that the machine shall carry full load con- - tinuously with a temperature rise of not more than 40 C. This is a con- servative guarantee and allows the machine to carry 25 per cent, overload without injury if the air temperature does not exceed 25 C. If the air temperature is greater than 25 C. a lower temperature rise must FIG. 82. The heat paths be allowed in order that the final tem . in an armature core. , ,, . , perature shall not be excessive. 91. Temperature Gradient in the Core of an Electrical Machine. Fig. 82 shows an iron core built up of laminations that are separated from one another by varnish. In this core there is an alternating magnetic flux and the loss in the core for different flux densities and for different frequencies can be found by the help of the curves in Fig. 81, page 102. 104 B HEATING 105 The hottest part of the core is at A and the heat in the center of the core has to be conducted to and dissipated by the surfaces B and C. In order to have an idea as to the relative heat resistances of the paths from A to the surfaces B and C, consider the following propositions. (a) Assume that all the heat passes in the direction Y, then the watts crossing 1 sq. in. of the core at y = (watts per cubic inch) X y and since the difference in temperature between two faces a distance dy apart (watts per cubic inch)?/ dy 1.5 degrees centigrade, where 1.5 is the thermal conductivity of iron in watts per 1-in. cube per 1 C. difference in temperature, therefore, the difference in temperature between A and surface B Temp. Temp. V = 1000 Ft. per Min. V = 10,000 Ft. per Min. FIG. 83. Temperatures in an iron core. Y = T ab = (watts per cubic inch)?/ dy 1.5 Y 2 = (watts per cubic inch) -=- deg. C. o (6) If the heat were all conducted in the direction X then, since the conductivity of a core along the laminations is approxi- mately fifty-six times as great as that across the laminations and layers of varnish, the difference in temperature between A and surface C would be r / V2 = T ac = (watts per cubic inch) = deg. C. Example; when the frequency is 60 cycles and the flux density is 75,000 lines per square inch then the watts per cubic inch = 2.3 and 106 ELECTRICAL MACHINE DESIGN = 0.8F 2 deg.C. . C. The fact that the conductivity along the laminations is so much better than that across the laminations would indicate that axial ventilation, whereby air is blown across the ends of the laminations, is the most effective. In practice, however, nearly all electrical machines are cooled by means of radial vent ducts, and, in order to discuss intelligently the effect of such ducts, it is necessary to find out the heat resistance between the surfaces B, C and the air. When air is blown across the surface of an iron core at V ft. per minute, the watts dissipated per square inch of radiating surface for 1 C. rise of the surface temperature is found by ex- periment to be = 0.0245(1 +0.00127 7). 1 If then, as in case (a), all the heat in the core has to be dis- sipated by surface B, the difference in temperature between sur- face B and the air = T b _ watts per square inch on surface B 00245(1 + 0.00127 V) _ (watts per cubic inch) F 0.0245(1 + 0.00127 7) Similarly in case (b), where it is assumed that all the heat is dissipated by surface C, the difference in temperature between surface C and the air T e _ (watts per cubic inch) X 0.0245(1 + 0.00127 7) Where X=1.5 in., and for a value of 1 watt per cubic inch, the following table shows the values of T a b, T ac , T b and T c for dif- ferent values of Y and of V. 7 = 10,000 T b T c 4.5 4.5 9.0 4.5 18.0 4.5 These results are plotted in Fig. 83 and from them the follow- ing general conclusions may be drawn: As the core depth Y increases, the path from A to B becomes long compared with that from A to C and, therefore, T & becomes comparable with T ac in spite of the relatively high conductivity along the laminations. 1 Ott, Electrician, March 7, 1907. 7 = 1000 X F T ac Tab T b T c 1.5 1.5 42 0.75 27 27 1.5 3.0 42 3.0 54 27 1.5 6.0 42 12.0 108 27 HEATING 107 The area C increases with the core depth while area B remains constant so that the deeper the core the larger the part of the total heat which is conducted across the laminations and dissipated from the surface of the vent ducts. 92. Limiting Values of Flux Density. The peripheral velocity of a machine 7tD a = Xr.p.m. _7iD a pXr.p.m. p X 12 = 10XTX/ ft. per minute (16) therefore, for a given frequency, the peripheral velocity of a machine is proportional to its pole pitch. For a given axial length of core, the longer the pole pitch the greater the flux per pole, and the deeper the core to carry this flux. Where the peripheral velocity of a machine is low, the core is shallow, the vent ducts have little effect on account of their small radiating surface, and the ventilation is poor; the loss, however, is small because there is not much iron in the core. Where the peripheral velocity is high the core is deep, the vent ducts are very effective on account of their large radiating surface, and the ventilation is good; the loss, however, is large since much iron is used in the core. For a given frequency the same flux densities can be used for all peripheral velocities. The following flux densities may be used for D. C. machines with a temperature rise of 40 C., built with iron 0.014 in. thick, the relation between core loss and flux density being as- shown in Fig. 81 : Frequency (cycles per second) Flux density in teeth (lines per square inch) Flux density in core (lines per square inch) 30 40 60 150,000 140,000 125,000 100,000 85,000 75,000 Core densities higher than 85,000 lines per square inch are seldom used, even for frequencies that are lower than 40 cycles, because at these densities the core becomes saturated and the 108 ELECTRICAL MACHINE DESIGN cost of the extra field copper required to send the flux through a saturated core is greater than the cost of the extra iron required to keep the core density below the saturation point. There is no such objection, however, to high-tooth densities because a machine with saturated teeth and a short air gap is just as effective in preventing field distortion as a machine with un- saturated teeth and a long air gap; see Art. 52, page 61, and does not require any more excitation. 93. Heating of the End Connections of the Winding. The end connection heating must be taken up separately from that of the II II Length of End Connections in Inches S 8 g / v> / / / <> ^ / ~jr ^ ^ -^ 5 10 15 20 25 30 Pole Pitch in Inches FIG. 84. Dimensions of coils. core because the kind of radiating surface is different and also the manner in which it is cooled. Since the resistance of copper is 1 ohm per circular mil per inch the copper loss in the end connections of one conductor = ^T l 2d + s *"O003' where 0.003 is the thermal conductivity of ordinary paper and cloth insulation in watts per inch cube per 1 C. difference in temperature, and 2d + s is the area of the path per 1 in. axial length of slot. Take for example the following figures : Ampere conductors per inch = 760 Slot pitch =0.88 in. Ampere conductors per slot =760X0.88 = 670 Circular mils per ampere = 560 d =1.6 in. s =0.43 in. Thickness of insulation =0.07 in., including clearance Temperature difference between inner and outer layers of insulation 670 0.07 1 560 A 3.63 A 0.003 = 8 deg. C. 95. Commutator Heating. The modern D. C. armature is constructed as shown in Fig. 27; the commutator is smaller in diameter than the armature core, and the commutator necks which join the armature winding to the commutator are separated from one another by air spaces, so that when the armature re- volves an air circulation is set up as shown by the arrows in Fig. 87, and cool air is drawn over the commutator surface. The relation between permissible watts per square inch of commutator surface and commutator peripheral velocity, ob- tained from tests on non-interpole machines, is shown in Fig. 87. The radiating surface is taken as nD c F. It would seem that the radiating surface ought to include that of the commutator necks. It is found, however, that a considerable portion of the commutator neck, such as from a to b, can be closed up without 112 ELECTRICAL MACHINE DESIGN affecting the commutator ventilation or temperature to any great extent; just how much of the surface of the necks should be considered as radiating surface has not yet been determined experimentally. The heat to be dissipated is assumed to be due to the brush friction and contact resistance losses. There are also losses which cannot be measured, due to poor commutation and to brush chattering. If the commutation is poor and the brushes 0,5 1.0 1.5 2.0 2.5 3.0 3.5 xlO 3 Peripheral Velocity of the Commutator in Ft. per Mm. FIG. 87. Temperature rise of commutators. chatter badly the temperature rise may be higher than that obtained by the use of the curve in Fig. 87, while in cases where the commutation is exceedingly good and where there is no chattering the temperature rise may be lower. 96. Application of Heating Constants. When designing a new D. C. machine for a guaranteed temperature rise of 40 C. the core heating is limited by keeping the flux densities below the values given in Art. 92, page 107, and the end connection heating amp. cond. per in. . is limited by keeping the ratio cir mils per amp ; below the values given in Fig. 85, page 109. The approximate increase in temperature of the copper at the center of the core over the temperatures of the iron and of the end connections is found by HEATING 113 the use of the formulae in Art. 94. The design is then compared with designs on similar machines which have already been tested and the densities modified accordingly. The results of careful tests on similar machines should always take precedence over results obtained from average curves and these curves should always be changing as improvements are made in the methods of ventilation. CHAPTER XII PROCEDURE IN ARMATURE DESIGN 97. The Output Equation 10- 8 volts, Formula 2, page 11 and paths xD a 10-' "60" and watts 60.8 X10 7 nm The value of B g , the apparent average gap density, is limited by the permissible value of Bt, the maximum tooth density, which value, as shown in Art. 92, page 107, is about FIG. 88. Effect of the armature diameter on the tooth taper. 150,000 lines per square inch for frequencies up to 30 cycles. That B g also depends on the diameter of the machine may be seen from Fig. 88; the smaller the diameter the greater the tooth taper and therefore the lower the gap density for a given density at the bottom of the teeth. 114 PROCEDURE IN ARMATURE DESIGN 115 Fig. 89 shows the relation between B g and D a for average machines; in cases where the frequency is greater than 30 cycles per second slightly lower values of B g must be used. The value of q, the ampere conductors per inch, is limited partly by heating and partly by commutation. Suppose that 70 x 1C 3 20 40 60 80 100 Armature Diameter in Inches Ampere Conductors per Inch ,--- . . J5, ^ ** / / / f . ^ -^ / / / A 20 40 60 80 NX B 230 400 600 800 100 Kilowatts Fio. F 90. FIG. 89. FiG.^90. C B -A fi |_ / to ox CT> oo Watts per Sq.lnch for 40Cent. "Rise 3.0 x 10 1.0 1 2.0 0.8 1 S 0.6 0.3 a 1.0 0.4 0.2 a i 0.2 0.1 ^ mp.Cond. per Inch { ^ 2.0 9 2 L6 a 1.2 S0.8 a ^ M 1 Y\. / . v M ? s / ^ ^ ^ X C, / s* / / / < *v> / f^T ' /^ ^ / / *^ ^~ ^*~ ^\^ ^' /, / ^ x / X no a p rheratl electric loading = ZT C PROCEDURE IN ARMATURE DESIGN 117 ZI C = B 9 L C 2 and therefore depends largely on the frame length L c , which quantity is limited in the following way: Figure 93 shows one field and one armature coil for a D. C. machine. A pole of circular section is the most economical so far as the field system is concerned because it has the largest area for the shortest mean turn of field coil. If the pole be rectan- gular in section then that with a square section has the largest area for the shortest mean turn. It will generally be found that the ratio j-*- -rr- lies between the values 1.1 and 1.7. frame length FIG. 93. Shape of field and armature coils. The pole pitch is limited by armature reaction; thus in Art. 74, page 91, it was shown that the armature ampere-turns per pole should not exceed 7500. Further, as pointed out in Art. 74, the . field ampere-turns per pole (gap + tooth) . ratio - i is seldom less than armature ampere-turns per pole 1.2. An increase in the armature m.m.f. per pole, therefore, requires a corresponding increase in the m.m.f. of the main field and an increase in the radial length of the poles. Rather than allow the armature ampere-turns per pole to exceed 7500, it will generally be found economical to increase the number of poles, so that they may not have too great a radial length. For 7500 armature ampere-turns per pole, and 900 ampere conductors per inch, the pole pitch is approximately 118 ELECTRICAL MACHINE DESIGN ^7500X2 900 -17 in. L c therefore, as pointed out above, should not exceed ^pr = 15 in., except in the special case where the peripheral velocity is al- ready so high that the diameter cannot be increased and the rating can only be obtained by the use of an extra long armature. If L c , the frame length, =15 in. B g , the average gap density, =60,000 lines per square inch (/>, the pole enclosure, =0.7 g, the ampere conductors per inch, =900 . magnetic loading then A;, the ratio--,- ? -^-^ T^- =700. electric loading For a machine with a small armature diameter the most economical frame length will be less than 15 in.; for example, a machine 5 in. in diameter and 15 in. long would be more expen- sive and would give more trouble than one which had the same value of D a 2 L C) but a diameter of 9 in. and a frame length of 4.5 in., so that, since k depends largely on the length L c its value varies with the diameter of the machine. Now watts .. i v 1 = electric loading X magnetic loading X AAN/in8 r.p.m. ou/\iu = k (electric loading) 2 X a constant (21) TTTQ 'j"i'Q and for each value of - - there is a value of k, and there- r.p.m. fore of electric loading (Z/ c ), which gives the most economical machine. Fig. 91 shows the relation between these two quanti- ties for a line of non-interpole machines, and this curve may be used for preliminary design. It must be understood, and will be seen from the examples given later, that the value of k may vary over a considerable range without affecting the cost of the machine to any consid- erable extent. The value of k is also affected by the cost of labor and therefore varies under different conditions of manufacture. 100. Formulae for Armature Design. A = ^electricloading) 2 Xaconstant,formula21, page 118. where electric loading = (Z/ c ) . PROCEDURE IN ARMATURE DESIGN 119 watts 60.8X10 7 -D a *L c = x formula 19, page 114. ~E = Z a x s X10- formula 2, page 11. - Coils = k | + 1 for a series winding Art. 22, page 22. Slots = k oil for a series winding Art. 22, page 22. = k for a multiple winding with equalizers Art. 22, page 22. F Slots per pole should be greater than 12 for small machines greater than 14 for large machines Art. 71, page 87. G -Reactance voltage = k X S Xr.p.m. X/ C XL C X T 2 X (formula 12, page 84.) where k = 1.6 for series and full-pitch multiple windings ; = 0.93 for short-pitch multiple windings. H Reactance voltage = 0.7 (volts per pair of brushes) when the brushes are on the neutral ; = 1.0 (volts per pair of brushes) when the brushes are shifted from the neutral; Art. 73, page 90. The reactance voltage may be 20 per cent, greater than this for machines with series windings and must be 30 per cent. less for those with short-pitch multiple windings. ZI J Armature ampere-turns per pole = ^- and should be less than 7,500 Art. 74, page 91. maximum tooth width . . K -- ^7 .,., = 1.1 for large machines; slot width = 1.0 for small machines; these are approximate values found from practice L Flux density is taken from the following table 120 ELECTRICAL MACHINE DESIGN Cycles per second Tooth-density lines per square inch Core-density lines per square inch 30 40 60 150,000 140,000 125,000 100,000 85,000 75,000 Art. 92, page 107. M Commutator dia. =0.6 armature dia. for large machines; = 0.75 armature dia. for small machines. These are values taken from practice. Except in the case of turbo generators the peripheral velocity of the commutator should not, if possible, exceed 3500 ft. per minute. To keep below this peripheral velocity it may be necessary to use smaller values for the diameter than those given above. N - Wearing depth of the commutator, namely, the amount that can be turned of the radius without making the com- mutator too weak mechanically varies from 0.5 in. on a 5-in. commutator to 1.0 in. on a 50-in. commutator. P Brush arc should be less than pole pitch comm. dia. X . j " 12 s arm. dia. and should not cover more than 3 segments Art. 72, page 89. Q -Watts per square inch brush contact = 35 approximately Art. 64, page 78. V r R Brush friction =1.25 A 100 watts formula 14, page 98. 10 1. Preliminary Design. To simplify the work of prelimi- nary design the necessary formulae and curves are gathered together above and the method of procedure is as follows: Find the electric loading ZI C for the given rating, from Fig. 91. 71 Find g = -^ from Fig. 90. 7lU a From these two quantities find D a the armature diameter. Tabulate three preliminary designs; one for a diameter 20 per cent, larger than that already found and the other 20 per cent, smaller. Find B g , the apparent gap density, from Fig. 89. PROCEDURE IN ARMATURE DESIGN 121 Find I/c, the frame length, from formula B, page 119. Find p, the number of poles, which should have such a value that ~ ^TT; lies between the values 1.1 and 1.7. Art. 99, frame length page 117. Find a , the flux per pole, = B g (/>rL c where ^ = 0.7 approx. Find Z, the number of armature face conductors, from for- mula D. Choose the cheapest winding that will give a reactance voltage below the desired limit; a series winding is generally the cheapest because it requires the smallest number of coils and commutator segments. Find S, the number of commutator segments, from the value of Z and the type of winding used. Make D c , the commutator diameter, = (0.6 to 0.75) X (armature diameter) for a first approximation. Find the brush arc from formula P. Find the commutator length so that the watts per square inch brush contact shall not exceed 35. Choose between the different designs. Example. Determine approximately the dimensions of a D.-C. generator of the following rating: 400 kw., 240 volts, 1670 amperes, 200 r.p.m. The work is carried out in tabular form as follows: Ampere conductors 1.33X 10 8 , from Fig. 91 Ampere conductors per ii Armature diameter Apparent gap density . . . Frame length Poles nch. . . '.B g ..L C v .733, froir . .58 in. 58,000 12 in. 10 L Fig. 90 45 in. 56,500 20.5 in 8 70 in. 59,000, from Fig. 89 8 in., formula B 16, formula C Pole pitch . i 18.2 in. 17.6 ir L. 13. 8 in. Flux per pole Total face conductors . . . Winding. . .(f)a .Z 8.8X10 6 820 , . one-turn 14. 3X 505 multiple, 10 6 4.55X10 6 1590; formula D short-pitch Commutator segments . . , Reactance voltage ..S . .RV. 410 1.5 252 2.0 795 1 . 2, formula G Commutator diameter . . . Brush arc . . ..D C 35 in. .0.91 in. 27 in. 0.88 in 42 in., formula M . 69 in., formula P Brush length .10.5 in. 13.5 in 8. 5 in. Amperes per square inch brush contact of 35 35 35 Magnetic loading a p 640 1090 440 Electric loading Zl c 122 ELECTRICAL MACHINE DESIGN The second machine, which has an armature diameter of 45 in., has the largest flux per pole and therefore the deepest core and the heaviest yoke. It is the longest machine and therefore the most expensive in core assembly. It has the smallest number of coils and commutator segments and is therefore cheapest in winding and commutator assembly. The third machine, which has an armature diameter of 70 in., has the smallest flux per pole and therefore the shallowest core and the lightest yoke. It is the shortest machine and therefore the cheapest in core assembly. It has the largest number of coils and commutator segments and is therefore the most expensive in winding and commutator assembly. The first machine probably costs less than either of the other two; it has also a comparatively low reactance voltage and should commutate satisfactorily. Before completing the design with the 58 in. diameter it is advisable to design the machine roughly with different numbers of poles in the following way: Poles 8 10 12 Armature diameter 58 in. Frame length 12 in. Apparent gap density 58,000 Pole pitch 22.8 in. 18.2 in. 15.2 in. Flux per pole 11 .OX 10 6 8.8X 10 6 7.4X 10 6 Total face conductors 658 820 975 Winding one-turn multiple, short-pitch Reactan.ce voltage 1.5 1.5 1.5 Armature ampere-turns per pole. 8550 6900 5700 Commutator diameter 35 in. 35 in. 35 in. Brush arc 1.14 in. 0.91 in. 0.76 in. Brush length 10 . 5 in. 10 . 5 in. 10 . 5 in. The first machine is most expensive in material due to the large flux per pole and therefore the deep core and the large section of yoke. The third machine is most expensive in labor due to the number of coils and commutator segments that are required. The reactance voltage is the same in each case but the armature ampere-turns per pole is greatest in the first machine and least in the last, so that, so far as commutation is concerned, the last machine is to be preferred, and the first one should not be used if possible. Armature Design. Having determined the approximate PROCEDURE IN ARMATURE DESIGN 123 dimensions of the machine, it is now necessary to design the armature in detail, which is done in tabular form in the following way: Choose the 10-pole design as the most suitable, then External diameter of armature 58 in. from preliminary design Frame length 12 in. from preliminary design Center vent ducts 3 . 5 in. wide Gross iron in frame length 10. 5 in. Net iron in frame length 9 . 45 in. Poles 10 Pole pitch 18.2 in. Probable flux per pole 8.8X 10 6 from preliminary design Probable number of face conductors .... 820 from preliminary design Winding. The minimum number of slots per pole = 14, formula F, therefore the minimum number of total slots =140, and the nearest suitable number is 200 Conductors per slot = 4 Coils =400 Commutator segments =400 Winding = one turn multiple, short pitch Reactance voltage =1.5, formula G 167x800 Ampere conductors per inch = q = -^ = 730 7C /\ OO Amp. cond. per inch -f~^ -, = 1.3 for 40 C. rise, from Fig. 92 Cir. mils per amp. Circular mils per ampere 560 Amperes per conductor at full load 167 Section of conductor =167X560 =93.500 circular mils = 0.073 sq. in. =0.91 in. 91 Probable slot width = ~ =0.43 in., formula K 0.43 assumed slot width . 064 width of slot insulation, see page 39 . 04 clearance between coil and core . 326 available width for copper and insulation on conductors. Use strip copper in the slot as shown in Fig. 34 and put two conductors in the width of the slot; make the strip 0.14 in. wide and insulate it with half lapped cotton tape 0.006 in. thick. Depth of conductor = -^T- = 0.52 in.; increase this to 0.55 in. to allow for rounding of the corners. Slot depth is found as follows : 124 ELECTRICAL MACHINE DESIGN . 55 depth of each conductor . 024 insulation thickness on each conductor 0.084 depth of slot insulation, see page 39. . 658 depth of each insulated coil 2 number of coils in depth of slot 1.316 depth of coil space . 2 thickness of stick in top of slot 1.516 necessary depth of slot; make it 1.6 in. deep. Diameter at bottom of slot ..... . ...... 54.8 in. Slot pitch at bottom of slot ........... 0.86 in. Minimum tooth width ................ . 0.43 in. 900 Tooth area per pole = X 0.7X0.43X9.45 = 57 sq. in. Flux per pole with 800 conductors ........ 9X 10 6 for 240 volts, formula D- Maximum tooth density ................... 158,000 lines per square inch. this density is not too high so that the core does not need to be length- ened. Flux density in the core, assumed ............ 85,000 lines per square inch 9X 10 6 Core area - 2X8OO .............. '- . , ,, core area Core depth = : --- ................ 5.6 in. net iron Internal diameter of armature .......... 43.6 in. The above data is now filled in on the armature design sheet shown on page 125. Commutator Design. Commutator diameter, assumed to be 0.6 (armature diameter) =35 in. Number of commutator segments ...... 400 Width of one segment and mica 71 = 0.275 in. 400 Brush arc ........................... 0.91 in., formula P. Use a brush 0.75 in. thick set at an angle of 30, so that the brush arc = 0.87 in. Segments covered by brush ........... .3.1 Amperes per set of brushes = X 2 = 334 poles Amperes per square inch of brush contact, 35 assumed Necessary brush length ................ 11 in. Brushes per stud, use 6 brushes, each 0.75 in. X 1.75 in. Commutator length = 6(1. 75 + 0.25) + 1 = 13 in. allow 0.25 in. between brushes and 1 in. additional clearance Peripheral velocity of commutator ...... 1830 ft. per minute. Total brush contact area = 10X6X 1.75X0.87 = 91 sq. in. Commutator friction loss .............. 2100 formula R. Volts drop per pair of brushes .......... 2.5 formula H. PROCEDURE IN ARMATURE DESIGN 125 Contact resistance loss = 2. 5 X 1670 = 4200 watts Watts per square inch of commutator surface = 4200 + 2100 7TX35X13 = 4.4 Probable temperature rise on commutator =40 C., from Fig. 92. Had the commutator temperature rise come out too high, it would have been necessary to have used brushes with lower contact resistance, which might cause the commutation to be poor, or else to have increased the com- mutator radiating surface. The above data is now filled in on the design sheet shown below. 102. Armature and Commutator Design Sheet. Armature External diameter 58 in. Internal diameter ^3.5 in. Frame length 12 in. End ducts 2-1/2 in. Center ducts 3-1/2 in. Gross iron 10.5 in. Net iron 9.45 in. Slots, number 200. size 0.43 in. XI. 6 in. Cond. per slot, number 4. size. . .0.14 in. X 0.55 in. Coils 400. Turns per coil 1. Total conductors 800. Winding, type multiple. pitch 1-20. Slot pitch 0.91 in. -0.86 in. Tooth width 0.48 in. -0.43 in. Max. tooth width ....1.11. .5.65 in. ..18.2 in. 0.7. 57 sq. in. Slot width Core depth Pole pitch Per cent, enclosure .... Min. tooth area per pole Core area per pole 53 sq. in. Apparent gap area per pole 153 sq. in. Densities, Iron loss, Excitation Flux per pole, no-load 9X 10 6 . Maximum tooth density (apparent), 158,000 lines per square inch. Maximum tooth density (actual), 150,000 lines per square inch. Core density, 85,000 lines per square inch. 35 in. 13 in. 400. 0.275 in. 0.03 in. 1 in. 0.87 in. 10. " X If")- Commutator Diameter Face Bars Bar and mica Mica Wearing depth Brush arc Brush studs Brushes per stud 6 (f Amperes per square inch contact . 37. Peripheral velocity ft. per min., 1830. Friction loss, watts, 2100 Volts per pair of brushes, 2.5. Contact resistance loss, watts,. 4200. Watts per 'square inch surf ace. .4.4. Temperature rise, deg. C 40. Average volts per bar 6. Cross-connect every fourth coil. Size of cross-connectors; half the conductor section. Copper loss, Commutation Amp. cond. per inch 730. Circular mils per ampere 560. Length of conductor 42 in. Copper loss 10 kw. Volts drop in armature =-p- = 6 (formula 15, page 103). Armature AT. per pole 6700. ^ AT (gap + tooth) J-tcitlO A m *~~ arm. AT. per pole 1 . 24. Reactance voltage 1.5. 126 ELCTRICAL MACHINE DESIGN Gap density (apparent), 59,000 lines per square inch. Weight teeth 385 Ib. core 2300 Ib. Frequency, eye. per second, .... 16.6. Iron loss, 6450 watts (Art. 84, page 102). Air gap clearance 0.3 in. Carter coefficient 1.12. AT. gap, Art. 46 6200. AT. tooth, Art. 46 2080. Rating Kilowatt 400. Volts no-load 240. Volts full-load 240. Amperes 1670. R. p. m 200. Magnetic loading Electric loading Output f actor = = 5 ' CHAPTER XIII MOTOR DESIGN AND RATINGS 103. Procedure in Design. The design of a D.-C. motor is carried out in exactly the same way as that of a D.-C. generator. Example. Determine approximately the dimensions of a D.-C. shunt motor of the following rating: 30 h.p., 120 volts, 900 r.p.m. Probable efficiency . =90 per cent. Full- load current =208 amperes. Kilowatt input =25. Ampere conductors =0.19X10 5 , from Fig. 91. Ampere conductors per inch =480, from Fig. 90. Armature diameter = 12.5 in. Apparent gap density, B g =44,000, from Fig. 89. Frame length, L c =7.3, from formula B, page 119. Poles =4, from formula C. Pole pitch =9.8 in. Flux per pole =2.2X 10 6 = 5^L C . Total face conductors =364 for multiple winding. = 182 for series winding, formula D. Reactance voltage =1.0 for a full- pitch multiple winding with one turn per coil, = 2 . for the same winding with two turns per coil, = 2.0 for a series winding with one turn per coil, formula G. Winding: The series winding is the cheapest since it requires half as many coils and commutator bars as are required for the one-turn multiple winding, and it does not require equalizers as in the case of the two-turn multiple winding. Commutator diameter = 0. 75 X Armature diameter =9.5 in., formula M. Brush arc =0.61 in. Brush length =5.0 in. Amperes per square inch of brush contact =35. While working on the preliminary design it is desirable to find the probable pole area and see if a circular section is suit- able for the particular diameter and frame length that have been chosen. Flux in pole = .\ ^ Bai iating Surfac ) T^) (? ^ I 2 3 4xl0 3 Armature Peripheral Velocity in. Ft. per Min. FIG. 94. Heating curve for enclosed motors. In order to lower the temperature rise it is necessary to lower the rating so as to cut down the losses. The horse-power is reduced so as to cut down the current, and the speed is increased so as to cut down the flux and, therefore, the core loss and the excitation loss. In the machine under discussion let the horse-power be reduced 30 per cent, and the speed be increased 20 per cent., the losses will then be changed as follows: Excitation loss is proportional to the ampere-turns and this will be reduced about 20 per cent., due to the decrease in flux. Iron loss is found by the use of the curves in Fig. 81 for 20 per cent, lower densities and 20 per cent, higher frequency. Armature copper loss is proportional to the (current) 2 and is MOTOR DESIGN AND RATINGS 135 therefore reduced to ^-^of its original value, due to the de- crease in horse-power. Brush friction loss will be reduced 30 per cent, because less brush area is required and will be increased 20 per cent, because of the increase in speed. Contact resistance loss will be proportional to the current since the current density in the brush is kept constant and the volts drop per pair of brushes is unchanged. The losses then will be as follows: 30 h.p. 900 r.p.m. 23 h.p. 1080 r.p.m". Excitation loss 350 290 Iron loss 630 580 Armature copper loss 1070 630 Commutator friction loss 340 315 Contact resistance loss 416 320 Total loss, 2806 2135 Watts per square inch for 1 C. rise =0.0105 0.0118, from Fig. 94. Square inch radiating surface 3340 3340 Watts per square inch . 84 . 64 Probable temperature rise 80 C. 55 C. 108. Possible Ratings for a given Armature. The following ratings are generally recognized by manufacturers of small motors and are given to show approximately what a motor can do under different conditions of operation. Continuous Duty, Constant Speed, Open Shunt Motors. For such machines the usual temperature guarantee is that the temperature rise shall not exceed 40 C. by thermometer after a continuous full-load run, nor shall it exceed 55 C. after 2 hours at 25 per cent, overload immediately following the full- load run. The guarantee for commutation is that the machine shall operate over the whole range from no-load to 25 per cent, over- load without destructive sparking and without shifting of the brushes. Continuous Duty, Constant Speed, Screen-covered Shunt Motors. Due to the resistance of the perforated sheet metal that is used to close up all the openings in the machine to the free circulation of air, the temperature rise will be about 20 per cent, higher than that for the same machine operating as an open motor. 136 ELECTRICAL MACHINE DESIGN Continuous Duty, Constant Speed, Enclosed Shunt Motors. For such machines the temperature guarantee is that the tem- perature rise inside of the machine shall not exceed 65 C. by thermometer after a continuous full-load run. An overload tem- perature guarantee is seldom made. To keep within this guarantee the standard open motor is generally given a 30 per cent, lower horse-power rating so as to reduce the armature current, and is run at 20 per cent, higher speed so as to reduce the flux per pole and therefore the iron loss and the excitation loss. Elevator Rating, Open Compound Motor. For such service the usual temperature guarantee is that the temperature rise shall not exceed 45 C. after a full-load run for 1 hour and that, immediately after the full-load run, the machine shall carry 50 per cent, overload for 1 minute without injury. To obtain this rating the standard open motor is rated up about 20 per cent. The compound field is generally made about 30 per cent, of the total field excitation at full-load so that the starting current will be less than it would be with a shunt motor of the same rating. For elevator service the brushes must be on the neutral position so that the motor can operate equally well in both directions. Crane Rating, Totally Enclosed Series Motor. For such serv- ice the usual temperature guarantee is that the temperature rise inside of the machine shall not exceed 55 C. after a full- load run for half an hour, the machine shall also carry 50 per cent, overload for 1 minute, immediately following the full-load run, without injury. To obtain this rating the standard open motor is given about twice its normal rating. A crane motor is operated with brushes on the neutral position. Hoisting Rating, Open Series Motor. For such service the usual temperature guarantee is that the temperature rise shall not exceed 55 C. after a full-load run for 1 hour, the machine shall also carry 50 per cent, overload for 1 minute, immediately following the full-load run, without injury. To obtain this rating the standard open motor is given about twice its normal rating. A hoist motor is operated with the brushes on the neutral position. Variable Speed Motors for Machine Tools. The size of such a MOTOR DESIGN AND RATINGS 137 machine depends on the minimum speed at which it is necessary to give the rated power because a machine tool such as a lathe takes a constant horse-power at all speeds, since the cutting speed of the tool is practically constant. After the minimum speed has been fixed the maximum speed is that at which the peripheral velocity or the reactance voltage becomes too high. If the limit of speed due to reactance voltage is reached before the peripheral velocity of the machine has become dangerous then higher speeds can be obtained, and therefore the speed range of the machine increased, by the use of interpoles. CHAPTER XIV LIMITATIONS IN DESIGN 109. Relation between Reactance Voltage and Average Volts per Bar. The voltage between brushes = Z6 a T -~^ X -- ^- 10~ 8 60 paths o and the number of commutator segments between brushes = for both series and multiple windings, therefore, the average voltage between adjacent commutator segments paths fcL ot" 1 * Thereactance voltage = -2TSCB fcL -P.m. poles vP oles xlO- Vot" 1 *) 60 XX ~ patns where k 0.93 for short-pitch multiple windings, Art. 69, page 84. = 1.6 for series and for full-pitch multiple windings, therefore avera g e volts P er segment = 2B g pr reactance voltage 60kSI c T 60/cg (22) 110. Limitation Due to High Voltage. A given frame, includ- ing yoke, poles and armature parts, has to be wound for different voltages but for the same speed, it is required to find out if there is any upper limit to the voltage for which the machine may be wound. Since, as shown in Art. 109, average volts per segment B Q (b rr- - = T^T = a constant, approx. reactance voltage I5qk therefore, for the same reactance voltage in each case, the average volts per segment must be constant and the number of commu- tator segments must increase directly as the terminal voltage. As the number of commutator segments increases the thickness of each decreases and the commutator becomes expensive and 138 LIMITATIONS IN DESIGN 139 is liable to develop high bars, since the probability of such trouble increases with the number of segments. When the point is reached beyond which it is not considered advisable to increase the number of commutator segments, higher terminal voltages must be obtained by an increase in the number of turns per coil or by a decrease in the number of paths through the winding since = a constant X TT for a given frame and speed, patns ST = a constant X TT~ for a given frame and speed. paths In either case the average volts per bar is increased and so also is the reactance voltage; a point will finally be reached beyond which the reactance voltage becomes so high that good commuta- tion is impossible without the use of interpoles. When interpoles are supplied the voltage between commutator segments may have any value up to about 30 if the load is fairly steady, but when such a value is reached the machine becomes sensitive to changes of load and liable to flash over; the limit can be extended a little further by the use of com- pensating windings as described in Art. 77, page 95, but very little is known regarding the operation of D.-C. machines under such extreme conditions. 111. Limitation due to Large Current. When the voltage for which a machine is wound is lowered, the current taken from the machine increases and to carry this current increased brush contact surface must be supplied. When the brushes are shifted forward so as to help commuta- pole pitch commutator dia. tion the maximum brush arc = ~ -- X -~r- -- and 12 armature dia. when this value of brush arc has been reached increased current can be collected from the machine only by increasing the axial length of the brushes and commutator. The commutator bars are subject to expansion and to con- traction as the load, and therefore their temperature, varies, and the difficulty in keeping a commutator true increases with its length. The limit of commutator length must be left to the judgment of the designer since it varies with the type of con- struction used and with the class of labor available. The type 140 ELECTRICAL MACHINE DESIGN of commutator shown in Fig. 28 is seldom made longer than 24 in.; longer commutators have been made by putting two such commutators on the same shaft and connecting the cor- responding bars on each with flexible links so as to form an equivalent single bar of twice the length. The brush arc can be increased about 20 per cent, over the value given in the above formula if the brushes are in the neutral position, and low resistance brushes may be used, but neither of these changes can be made unless the reactance voltage of the machine is low or interpoles are supplied to take care of the commutation; such low resistance brushes, as pointed out in Art. 64, page 78, have a larger current carrying capacity than have brushes of higher contact resistance. 112. The Best Winding for Commutation. E, the generated volt age = Z^, a r patns r.p. 1(f)a 60 and the reactance voltage _ r.p.m. poles 1(f)a 60 paths X paths where /c = 1.6 for series and full-pitch multiple windings = 0.93 for short-pitch multiple windings therefore the reactance voltage = k (SX TX r.p.m. X^^-XlO" 8 ) I C L C T pains ^ kT X paths For a given frame and a given output aj L c and Exl a are all constant and under these conditions A: X turns per coil Reactance voltage = a constant X - -rr~ paths therefore the multiple winding is better than the series winding since it has the larger number of paths; the multiple winding with one turn per coil is the best type of full-pitch winding; and the short-pitch multiple winding is better than the full-pitch multiple winding because it has a lower value of k. LIMITATIONS IN DESIGN 141 The best winding that can be used in any case is therefore the short-pitch, one-turn multiple winding. 113. . Limitations due to Speed in Non-interpole Machines. The best winding that can be used in such a machine is the short- pitch, one-turn multiple winding for which the reactance voltage -0.93 S r.p.m. I C L C IQ- 8 and I a =I c X paths _ _ RV 0.93XSXr.p.m.XL c XlO- 8Xpa = 2 S(Bg(/frL c ) ':!'Q 'XlO~ 8 - for a one-turn short-pitch multiple winding, since poles = paths. therefore 9 XD a . since pT = xD a y watts X 9 . . u ,,. , and D a = r> T / p v , f r a short-pitch, one-turn multiple K V /\ -D g X Y winding. For sparkless commutation from no-load to 25 per cent. overload, with brushes shifted from the neutral and clamped, the reactance voltage at full-load for a short-pitch multiple winding should not exceed 0.75 (volts drop per pair of brushes), formula H, page 119, and the volts drop per pair of brushes should not exceed 3, otherwise it will be difficult to keep the commutator cool, therefore the highest value for RV in the above formula is 0.75 X 3 = 2.25 volts; for this value the armature diameter watts D -=5p the difference in the constant being due to the fact that k for a short-pitch winding = 0.93 whereas k for a full-pitch winding = 1.6. For an interpole machine the reactance voltage should not exceed 15 and the pole enclosure should be about 0.65; for these values _ watts XI. 6 Taking this value of D a , a peripherial velocity of 6000 ft. per minute, and the relation between D a and B g shown in Fig. 89 : the maximum output that can be obtained for a given speed is figured out and plotted in curve 3, Fig. 95. 116. Limit of Output for Turbo Generators. The only differ- ence between turbo generators, and the ordinary interpole machine discussed in the last article, is that the construction of 144 ELECTRICAL MACHINE DESIGN the former is made such that it can be run at peripheral velocities of the order of 15,000 ft. per minute. For this peripheral velocity and for a reactance voltage of 15, the maximum output that can be obtained for a given speed is figured out and plotted in curve 1, Fig. 96. Curve 2, Fig. 96, gives the usual speed of steam turbines for different outputs, and it may be seen that for outputs greater than 1000 kw., it is difficult to build generators that can be direct connected to steam turbines, because speeds lower than those in curve 2 can be obtained only by a sacrifice of efficiency. The output for a given speed can be increased over the value given in curve l,Fig. 96, by the use of peripheral velocities 3000 2000 1000 1000 2000 3000 4000 5000 6000 R.P.M. FIG. 96. Limits of output for D.-C. turbo-generators. higher than 15,000 ft. per minute and by the use of a higher value of the average volts per bar. To increase that value over 30 volts will probably require the use of compensating windings in addition to interpoles and machines have been built in which this value was as high as 60 but such machines are very sensitive to changes in load and to changes in the interpole field. For such a high value of average volts per bar the reactance voltage will probably be about 30 volts and the interpole difficult to adjust and further, any lag of the interpole field behind the inter- pole current, when the load and therefore the current changes, will lead to trouble in commutation. One must be careful in the interpretation of the curves shown LIMITATIONS IN DESIGN 145 in Figs. 95 and 96. They are derived on the assumption that the machine is limited only by commutation. For many of the out- puts within the range of the different curves the voltage or current limitation might be reached before the output limit is reached due to speed. Some of the ratings also would probably require a machine with forced ventilation. 10 CHAPTER XV DESIGN OF INTERPOLE MACHINES 117. Preliminary Design. The preliminary design work on an interpole machine, whereby the principal dimensions are determined approximately, is carried out in the same way as that on the non-interpole machine discussed in Art. 101, page 120, but some slight modifications are made on the constants used. It was pointed out in Art. 66, page 80, that, the deeper the slots in a D.-C. machine, the greater the slot leakage flux, and therefore the greater the reactance voltage; because of this the slots in non-interpole machines have to be limited in depth so that the value of q, the ampere conductors per inch, cannot greatly exceed that given in Fig. 90. When interpoles are supplied the reactance voltage becomes of less importance and it is possible to use deep slots without the risk of trouble due to poor commutation; with such deep slots a large amount of copper can be put on each inch of the armature periphery, so that the value of q may be made larger than in the case of the non-inter- pole machine, and is usually about 20 per cent, larger than that given in Fig. 90, page 115. field amp. -turns per pole for tooth and gap . , . The ratio - -^r- - is seldom armature ampere-turns per pole less that 1.2 for machines without interpoles, in order that the magnetic field under the pole tip toward which the brushes are shifted to help commutation may not be too weak. When inter- poles are supplied such a commutating field is no longer necessary, and a weaker main field is generally used. Inspection of Fig. 49, page 57, will show that if the cross-magnetizing ampere-turns % at the pole tips, namely J^ I C} becomes equal to the ampere- turns per pole for tooth and gap due to the main field excita- tion, then the effective m.m.f . across the gap and tooth under one pole tip will be zero while that under the other pole tip ha\e twice the no-load value; the field will therefore be greatly distorted. On account of the saturation of the teeth under this latter pole tip the flux density will not be proportional to the m.m.f. and, as pointed out in Art. 48, the total flux per 146 DESIGN OF INTERPOLE MACHINES 147 pole will be reduced. Due to the high flux density under the one pole tip, the armature core loss, which depends on the maximum density in the core, will be higher at full-load than at no-load, and the tendency to flash over, which, as pointed out in Art. 77, page 95, depends principally on the voltage between adjacent commutator segments at any point, will also be greater. , . field amp. -turns per pole for tooth and gap . The ratio - '- is found armature cross ampere-turns at the pole tips in practice to have a value of about 1.2 for interpole machines and, taking the value of the pole enclosure = 0.65, the ratio field amp. -turns per pole for gap and tooth armature ampere-turns per pole = 0.8 approx. As the armature ampere-turns per pole is increased the field ampere-turns must increase in the same ratio, and the pole length must also increase in order to carry this excitation. When the armature strength reaches the value of 10,000 ampere-turns per pole it will generally be found that an increase in the number of poles, and therefore a decrease in the armature strength per pole and in the length of poles, will give a more economical machine. , . magnetic loading B g L c The ratio r^^ i 3-=- = , Art. 99, page 116, and electric loading q for interpole machines is generally about 10 per cent, smaller than for machines without interpoles; in the above equation

/N (volts per cond.) 2 total copper section = a const ant XT- ~r- total copper section for a given frame, rating and speed. Except in the case of very small machines, the same amount of copper can be got into a machine at any voltage up to 600, so that over this range the higher the voltage the higher the effi- ciency, on account of the considerable reduction in the commuta- tor loss. 124. Effect of Speed on the Efficiency. As shown in Art, 97, page 114, = a constant X D a 2 L c XB g X X q = a constant X B g X q for a given frame. If then a given machine is increased in speed the frequency will increase, and therefore the flux per pole, and B g , the average flux density in the air gap, must be decreased, as shown in Art. 92, page 107, while, due to the better ventilation, the value of q must be increased for the same rise in temperature. Over a considerable range of speed the product of B g and q is approxi- mately constant and therefore the watts output is approximately directly proportional to the r.p.m. With regard to the losses; the 158 ELECTRICAL MACHINE DESIGN field excitation loss is proportional to the field excitation and, therefore, as shown in Art. 52, page 61, is directly proportional to , . , Z/ c pole-pitch the armature ampere-turns per pole, which =-5 =g 2p 2 If then and so for a given machine, is directly proportional to q. q increases, the excitation loss also increases. The total armature and commutator loss will increase with the speed because, for the same temperature rise, the permissible loss in the revolving part of a given machine = (A + 5Xr.p.m.) where A is the loss that is dissipated by radiation and is in- dependent of the speed. Thus in a given machine, when the speed is increased, the output is directly proportional to the speed, the excitation loss is increased slightly, and part of the armature and commutator loss is directly proportional to the speed, therefore, the losses do not R.P.M. Percent Efficiency ^ 3^ ~z=~- TT \ X _ -&. 200 400 600 800 1000 Kilowatts FIG. 98. Efficiency curves for 550- volt D.-C. generators. increase as rapidly as the output does and the higher the speed the higher the efficiency until the speed is reached at which a radical change in the design is necessary, such as the addition of interpoles or of compensating windings, when a slight drop is efficiency generally takes place due to the extra loss in these additional parts. If now the case be taken of two machines which have the same axial length and the same pole-pitch but a different number of poles, and the speed in r. p.m. is made inversely as the number of poles so that the peripheral velocity and the frequency is the SPECIFICATIONS 159 same in each case, then each pole, with the corresponding part of the armature, may be considered as one unit. The output, excitation loss, armature and commutator loss will all be proportional to the number of poles, so that, for an increase in the watts output with a proportional decrease in the speed, the efficiency is unchanged over a considerable range in speed. Curves 1 and 2, Fig. 98, show the efficiencies that may be expected from a line of 550 volt D.-C. generators at speeds 95 w I 90 ' 85 1000 500 20 40 60 80 100 Horsepower FIG. 99. Efficiency curves for 220-volt D.-C. motors. given in the corresponding speed curves 1 and 2; the slow speed machines are direct connected engine type units and the efficiency does not include the windage and bearing friction losses; the high-speed machines are belted units. Figure 99 shows a similar set of curves for a line of 220 volt D.-C. motors. CHAPTER XVII ALTERNATOR WINDINGS 125. Single-phase Fundamental Winding Diagram. Diagram A, Fig. 100, shows the essential parts of a single-phase alternator which has one armature conductor per pole. The direction of motion of the armature conductors relative to the magnetic \ ^y o \ s J, ^ y B N N FIG. 100. Fundamental single-phase winding diagram. field is shown by the arrow, and the direction of the generated e.m.f. in each conductor is found by Fleming's three-finger rule and is indicated in the usual way by crosses and dots. The conductors a, 6, c and d are connected in series so that their voltages add up and the method of connection is indicated 160 ALTERNATOR WINDINGS 161 in diagram A. Such a connection diagram, however, becomes exceedingly complicated for the windings that are used in practice and a simpler diagram is that shown at C, Fig. 100, which is got by splitting diagram A at xy and opening it out on to a plane. FIG. 101. Fundamental two-phase winding diagram. FIG. 102. Fundamental three-phase winding diagram. F l n\ F. FIG. 103. Fundamental three-phase Y-connected winding. Diagram C may be called the fundamental single-phase wind- ing diagram because on it all other single-phase diagrams are based. The letters S and F stand for the start and finish of the winding respectively. 126. The Frequency Equation. The voltage generated in 11 162 ELECTRICAL MACHINE DESIGN any one conductor goes through one cycle while the conductor moves relative *to the magnetic field through the distance of two-pole pitches, so that one cycle of e.m.f. is completed per pair of poles; /Y\ the cycles completed per revolution = y the cycles completed per second =^ X ']?' > 2* oU Ph. 1 Ph. 2 Ph. 3 A FIG. 104. Currents in the three phases. therefore /, the frequency in cycles per second 120 (23) 127. Electrical Degrees. The e.m.f. wave of an alternator is represented by a harmonic curve and therefore completes one cycle in 2n or 360 degrees; as shown above, the e.m.f. of an Si FIG. 105. Voltage vector diagram for a Y-connected winding. alternator completes one cycle while the armature moves, relative to the poles, through the distance of two-pole pitches; it is very convenient to call this distance 360 electrical degrees. 128. Two- and Three-phase Fundamental Winding Diagrams. Fig. 101 shows the fundamental winding diagram for a two-phase machine. A two-phase winding consists of two single-phase windings which are spaced 90 electrical degrees apart so that the ALTERNATOR WINDINGS 163 e.m.fs. generated in them will be out of phase with one another by 90 degrees. Figure 102 shows the fundamental winding diagram for a three-phase machine. A three-phase winding consists of three single-phase windings which are spaced 120 electrical degrees apart so that the e.m.fs. generated in them will be out of phase with one another by 120 degrees. FIG. 106. Fundamental three-phase A-connected winding. 129. Y and A Connection. It will be seen from Fig. 102 that a three-phase winding requires six leads, two for each phase. It is usual, however, to connect certain of these leads together so that only three have to be brought out from the machine and connected to the load. Ph. 1 Ph. 2 V /\ FIG. 107. E.M.FS. in the three phases. Figure 103 shows the Y connection used for this purpose. The three finishes of the winding are connected together to form a resultant lead n and the current in this lead at any instant is the sum of the currents in the three phases. The current in each of the three phases at any instant may be found from the curves in 164 ELECTRICAL MACHINE DESIGN Fig. 104 from which curves it may be seen that at any instant the sum of the currents in the three phases is zero, so that the lead n may be dispensed with and the machine run with the three leads S lt S 2 , and S 3 . Figure 105 shows the voltage vector diagram for a Y-connected winding and from the shape of this diagram the connection takes its name. Figure 106 shows the A connection. The winding is connected to form a closed circuit according to the following table: S, to F 2 5 2 to F s 5 3 to F! It would seem that, since the windings form a closed circuit, the e.m.fs. of the three phases would cause a circulating current to flow FIG. 108. Voltage vector diagram for a A -connected winding. in this circuit; however, the three e.m.fs. are 120 degrees out of phase with one another and an inspection of Fig. 107 will show that the resultant of three such e.m.fs. in series is zero at any instant. Fig. 108 shows the voltage vector diagram for a A -connected winding, the phase relation of the three voltages is the same as in Fig. 105. 130. Voltage, Current and Power Relations in Y- and A -Con- nected Windings. Let M and N, Fig. 109, represent two phases of a three-phase winding, the voltages generated therein are out of phase with one another by 120 degrees and are represented by vectors in diagram B. If the phases are connected in series, so that F 2 is connected to S lf then the voltage, between F 1 and S 2 = the voltage from F! to S + the voltage from F 2 to S 2 = E r , diagram C, and is equal to E, the voltage per phase. ALTERNATOR WINDINGS 165 M N I Si -F 2 S z A 3?, \ . FIG. 109. Voltage relations in three-phase windings. M N '* FIG. 110. Current relations in three-phase windings. 166 ELECTRICAL MACHINE DESIGN If, however, as in a Y-connected winding, F 2 is connected to FU then the voltage between S t and S 2 = the voltage from S 1 to F 4- the voltage from F 2 to S 2 = E r , diagram Z>, which is equal to 1.73 E. In a Y-connected machine therefore, the voltage between j- 1 f . \ r ""} C s 'j {< 90 * 1 A "'wo-phase f ^ j i 1 > 1! :' i 1 k . _1 k r /L J -j- A ^ J c t -2 j ^ T ^ ^ \ "1"T: .J 1 ^2 F t i z? u m .m l< 12Q >j< 12Q 2 -- Three-phase s, C D FIG. 111. Four-pole chain winding. terminals is 1.73 times the voltage per phase, while the current in each line is the same as the current per phase. Let M and N } Fig. 110, represent two phases of a three-phase winding, the currents therein are out of phase with one another by 120 degrees and are represented by vectors in diagram B. ALTERNA TOR^W IN DINGS 167 If the two phases are connectecfin parallel, so that F 2 is con- nected to F lt then the current in the line connected to F^F 2 = the current from F l to S^ + the current from F 2 to S 2 = 7 r , diagram C, and is equal to I, the current per phase. If, however, as in a A -connected winding, S is connected to jP then the current in the line connected to S = the current FIG. 112. Three-phase chain winding with one slot per phase per pole. from /Sj to F + the current from F 2 to >S 2 , which is equal to the current from F 2 to S 2 - the current from F^ to S 1 = I r , diagram D, =-1.737. In a A -connected machine therefore, the current in each line is 1.73 times the current in each phase while the voltage between terminals is the same as the voltage per phase. 168 ELECTRICAL MACHINE DESIGN LL.JLJ - LL j I I j i F,\ Two Phase Three Phase, one phase shown FIG. 113. Four-pole double layer winding. ALTERNATOR WINDINGS 169 The power delivered by a three-phase alternator = 3 E I cos 6 = 1.73 E t fi cos 6 for either Y- or A -connected machines where E is the voltage per phase, / is the current per phase, E t is the voltage between terminals, Ii is the current in each line, is the phase angle between E and /. 131. Windings with Several Conductors per Slot. When there are more than one conductor per slot a slight modification must be made on the fundamental winding diagrams. Consider for example the case where there are four conductors per slot. FIG. 114. Coil for a double layer winding. One method of connecting up the winding is shown in Fig. Ill, which shows the two- and three-phase diagrams. Each coil m consists of four turns of wire as shown in diagram C; these wires are insulated from one another and are then insulated in a group from the core so that a section through one slot and coil is as shown in diagram D. On account of its appearance this type of winding is called the Chain Winding. Figure 112 shows part of a machine, which is wound according to diagram B, Fig. Ill; the method whereby one coil is made to jump over the other is clearly shown. Another method of connecting up the winding is shown in Fig. 113, which shows the two- and three-phase diagrams. Each 170 ELECTRICAL MACHINE DESIGN coil n consists of two turns of wire as shown in diagram C; these wires are insulated from one another and are also insulated from the core so that a section through one slot and coil is as shown in diagram D. The coils are shaped as shown in Fig. 114; one side of each coil, represented in the winding diagrams by a heavy line, lies in the top of a slot, while the other side, represented by a light line, lies in the bottom of a slot about a pole-pitch further over on the armature. The whole winding lies in two layers and is therefore called the Double-Layer Winding. 132. Comparison between Chain and Double-Layer Windings. Chain The number of conductors per slot may be any number. The number of coils is half of the number of slots. There are several shapes of coil, therefore a large outlay is neces- sary for winding tools, and a large number of spare coils must be kept in case of breakdown. The end connections of the winding are separated by large air spaces. Double-layer The number of conductors per slot must be a multiple of two. The number of coils is the same as the number of slots. The coils are all alike, therefore the number of winding tools is a min- imum and so also is the number of spare coils that must be kept. The end connections are all close together and therefore more liable to breakdown between phases than in the chain winding. The chain winding is the easier to repair because, in order to get a damaged coil out of a machine, fewer good coils have to be removed than in the case of the double layer winding; this may be seen from the chain winding and the corresponding double- layer winding shown in Figs. 118 and 119. The chain winding requires the larger initial outlay for tools but the winding itself is the cheaper because there are not so many coils to be formed and insulated. The amount of the slot section that is taken up by insulation is less with the chain than with the double-layer winding, as may be seen by comparing diagrams D, Figs. Ill and 113. 133. Wave Windings. The connections from coil to coil, marked/ in diagram A, Fig. 113, and called jumpers, must have the same section as the conductors in the winding. When there are only two conductors per slot the conductors are large in section and the jumpers become expensive; in such a case the wave winding is generally used because it requires very few ALTERNATOR WINDINGS 171 jumpers. Such a winding is shown in Fig. 115, which shows the two- and three-phase diagrams. 134. Windings with Several Slots per Phase per Pole. Modern alternators have seldom less than two slots per phase per pole. The principle advantages of the distributed winding are that the wave form is improved and the total radiating surface of the coils increased; the self-induction of the winding is reduced but that, as shown in Art. 209, page 282, is in some cases a disadvantage. Two Phase Three Phase FIG. 115. Four-pole wave winding. 135. Windings With Several Circuits per Phase. The windings shown down to this point have all been single-circuit windings, that is, windings in which all the conductors of one phase are connected in series with one another. It is, however, often necessary to use more than one circuit. Suppose, for example, that a large number of small alternators are to be built for stock, the winding used would be such that by 172 ELECTRICAL MACHINE DESIGN a slight change in the connections, it could be made suitable for a number of standard voltages. FIG. 116. Two circuit windings. FIG. 117. Alternator with an eccentric rotor. Figure 116 shows the winding diagram for one phase of an eight- pole three-phase machine with two slots per phase per pole. ALTERNATOR WINDINGS 173 Diagram A shows a single circuit connection. Diagrams B, C and D show possible two circuit connections. When a winding is divided up into a number of circuits in parallel it is necessary, in order to prevent circulating currents, Two Circuit , FIG. 118. Four-pole, two-phase, chain winding with eight slots per pole. \ \ 1 1 2 f IK $ m Two Circuit Si FIG. 119. Four-pole, two-phase, double layer winding with eight slots per pole, one phase shown. that the voltages in the different circuits in parallel be equal to and in phase with one another. Diagram B does not meet this condition because the voltages in the two circuits shown, while of equal value, are out of phase 174 ELECTRICAL MACHINE DESIGN --">"" ^ 1 f 7-- flit; Lj_j_j_ J i i 1 I \ M n _, ,_ -3j~T ~ ^ ^_ _ ~ T't: I i i 1 i A > ^ "\ n (\\ 1 \f T & Is IT s, One Circuit 1 1 1 1 F l 3 ! k 1^0 5, One Circuit T Two Circuit Zik 1^ i l J LJ i i u t ( i k 1 i 4- -r~ ^ s, Two Circuit Y FIG. 120. ^Four-pole, three-phase, chain winding with nine slots per pole. ALTERNATOR WINDINGS 175 | pOOf XOO- T jU^u^f-^ ' rvu s 'u'> 1 1 J 1 1 J M 1 | 1 US F l | IF. One Circuit y\ ^ 1 rt n ^ rf- 1OA ^ < laU > < (j > o o 3 02 * 1 \ 1 1 1 I 1 |F 2 F l \&\ One Circuit Y \ c o 1*^3 2 II II II II II r V^ ^ ^^ Y^ ^^ ^^ ^<7^'U V T p I [^ ') *> '*! & w ' ! L ! ffe I Si #1 ? 'o" 2 \ s "^ 15^3 1 F ~ F * 1 -j ]5s \ r f I r ' j I i 1 & !j d k *; i i F 1 i s* Two Circuit Y FIG. 121. Four-pole, three-phase, double layer winding with nine slots per pole. 176 ELECTRICAL MACHINE DESIGN with one another by the angle corresponding to one slot-pitch, namely, by 30 degrees. The winding shown in diagram D is to be preferred to that in diagram C for the following reason. Fig. 117 shows an eight-pole machine the field and armature of which are eccentric due to poor workmanship in erection. The voltage generated in a circuit made up of conductors in slots a, b, c and d is smaller than that LL r I .,,, i, . . 1 i j 1 1 1 i ! I 1 i L _|_ 1 1 1 J L ,.l** FIG. 122. Six-pole, three-phase, chain winding with three slots per pole. generated in a similar circuit wound in slots e, /, g and h, so that if these two circuits be put in parallel a circulating current will flow. Diagram C, Fig. 116, shows an example of such a winding. In diagram D the connection is such that each of the two circuits takes in conductors from under all of the poles so that, no matter how different the air gaps become, the voltages in the two circuits are always equal. L_ -| > 1 1 i i - j i L- -\ . 1 " 1 1 FIG. 123. Three-phase chain winding with coils all alike. 136. Examples of Winding Diagrams. Figs. 118, 119, 120 and 121 show typical alternator winding diagrams and should be carefully studied. Many other examples might have been shown but the subject is too wide to take up in greater detail. When the number of groups of coils is odd in a machine with a chain winding, it is impossible to have the same number of groups of long as of short coils, and one group must be put into the machine the coils of which have one side long and the other ALTERNATOR WINDINGS 177 side short; such a winding is shown in Fig. 122 for a six-pole machine with three phases, one slot per phase per pole, and one coil per group. By the use of specially shaped coils, as shown in Fig. 123, it is possible to reduce the number of coil shapes that are re- quired for a chain winding. In the particular case shown the coils are all alike. Double Layer Winding FIG. 124. Four-pole, single-phase winding with four active slots per pole. In a single-phase machine it is generally advisable, for the reason explained in Art. 145, page 187, to make the winding cover not more than two-thirds of the pole-pitch. Such a winding is shown in Fig. 124 for a machine with six slots per pole, of which only four are used. 12 CHAPTER XVIII THE GENERATED ELECTRO -MOTIVE FORCE 137. The Form Factor and the E.M.F. per Conductor. If (f> a is the flux per pole and p the number of poles then one armature conductor cuts (f> a p lines of force per revolution . r.p.m. r or (f> a p * lines per second and the average e.m.f. in one conductor = (f) a p -jr^ : 10~ 8 volts. The form factor of an e.m.f. wave is denned as the ratio effective voltage . . \/2 r and for a sine wave of e.m.f. this value = 7 average voltage 2 71 1.11 The effective e.m.f. per conductor = < a p ''' 10~ 8 X form factor .m.f. (24) , r.p.m. = 1.11 < p ^ 10~ 8 for sine wave e.m.f. , , , . since /, the frequency = 138. The Wave Form. Fig. 125 shows the shape of pole face that is in general use and curve A shows the distribution of flux in the air gap under such a pole face. , The e.m.f. in a conductor is proportional to the rate of cutting lines of force and has therefore a wave form of the same shape as the curve of flux distribution. Curve A is not a sine wave but can be considered as the resultant of a number of sine waves consisting of a fundamental and harmonics. The frequency and magnitude of these har- monics depend principally on the ratio of pole arc to pole-pitch. In Fig. 125 this ratio is 0.65 and the fundamental and harmonics which go to make up the flux distribution curve are shown to scale, higher harmonics than the seventh being neglected. 178 THE GENERATED ELECTRO-MOTIVE FORCE 179 139. Trouble due to Harmonics. The fundamental and har- monics that go to make up an e.m.f. wave act as if each had a separate existence. If the circuit to which this e.m.f. is ap- plied consists of an inductance L in series with a capacity C so that the impedence of the circuit then the current in this circuit consists of _ _ a fundamental = 1 ~2*AC E n and harmonics of the form ^ f T 1 nL< where E n is the effective value of the nth harmonic. If now, f n has such a value that 2xf n L = so that the circuit is FIG. 125. E. M. F. wave of an alternator. in reasonance at this frequency, then the nth harmonic of cur- rent will be infinite, and the nth harmonic of e.m.f. across L and C individually will also be infinite. The above is an ideal case; in ordinary circuits the current cannot reach infinity on account of the resistance that is always present, nevertheless, if the circuit is in resonance at the fre- quency of the fundamental or of any of the harmonics, danger- ously high voltages will be produced between different points in the circuit. The constants of a circuit are seldom such as to 180 ELECTRICAL MACHINE DESIGN give trouble at the fundamental frequency, trouble is generally due to high frequency harmonics. It is desirable then to elimi- nate harmonics from the e.m.f. wave of a generator as far as possible and several of the methods adopted are described below. 140. Shape of Pole Face. The pole face is sometimes shaped as shown in Fig. 126, that is, the air gap is varied from a minimum FIG. 126. Pole face shaped to give a sine wave e. m. f. under the center of the pole to a maximum at the pole tip, so as to make the flux distribution curve approximately a sine curve; then the e.m.f. wave from each conductor will be approxi- mately a sine wave. 141. Use of Several Slots per Phase per Pole. Fig. 127 shows part of a three-phase machine which has six slots per pole or o o o A B o o o o FIG. 127. E. M. F. wave of a three-phase alternator with two slots per phase per pole. two slots per phase per pole. The e.m.f. generated in a conductor in slot A is represented at any instant by curve A, and that in a conductor in slot B by curve B, which is out of phase with curve A by the angle corresponding to one slot-pitch, or 30 degrees. When the conductors in slots A and B are connected in series so that their e.m.f s. add up, the resultant e.m.f. at any instant is given by curve C, which is got by adding together the ordinates of curves A and B. C is more nearly a sine curve than either A or B. -\ If the fundamental and harmonics that go to make up curves THE GENERATED ELECTRO-MOTIVE FORCE 181 A and B are known, then those which go to make up curve C can be readily found as follows: The fundamental of the resultant wave C is the vector sum of the fundamentals of A and B, which are 6 electrical degrees apart, and the nth harmonic of C is the vector sum of the nth harmonics of A and B which are (nX#) FIG. 128. The vector diagram for the fundamental and the harmonics. electrical degrees apart. For example, curves A and B, Fig. 128 are 30 degrees out of phase with one another and each consists of a fundamental and a third harmonic as shown. Cj is the re- sultant of the fundamentals A l and B 1 and C 3 , the third har- monic of curve C, is the resultant of the two third harmonics A 3 and B~. FIG. 129. Short-pitch coil. 142. Use of Short -pitch Windings. Fig. 129 shows a short- pitch coil. The e.m.f. waves in the conductors A and B are out of phase with one another by 6 degrees, but each has the same shape as the curve of flux distribution. The problem of finding the resultant e.m.f. wave is therefore the same as that discussed in the last article. 182 ELECTRICAL MACHINE DESIGN If n6, the phase angle between the nth harmonics of curves A and B, becomes equal to 180 degrees, then the corresponding harmonic is eliminated from the resultant curve C since the two FIG. 130. Elimination of harmonics from the e. m. f . wave. FIG. 131. Unsymmetrical waves due to even harmonics. harmonics which go to make it up are equal and opposite. If, for example, there are 9 slots per pole and the coil is one slot short, then the angle 6 is 20 electrical degrees, and the 9th harmonic is eliminated from the voltage wave of the coil; in general, if the THE GENERATED ELECTRO-MOTIVE FORCE 183 pitch of the coil be shortened by of the pole-pitch then, as shown in Fig. 130, the nth harmonic will be eliminated It may be pointed out here that an even harmonic is seldom found in the e.m.f . wave of an alternator, because the resultant of a fundamental and an even harmonic gives an unsymmetrical curve, as shown in Fig. 131, where the resultant curve is made up D FIG. 132. Effect of the Y- and A -connection on the third harmonic. of a fundamental and a second harmonic. If then the e.m.f. wave is symmetrical it may be assumed that no even harmonics are present. 143. Effect of the Y- and A -Connection on the Harmonics. The fundamentals of the three e.m.fs. are 120 degrees out of phase with one another and are represented by vectors in dia- gram A, Fig. 132. The nth harmonics are (nXl20) degrees out of phase with one another. When the -phases are Y-connected the terminal F 2 is brought to the potential of terminal F^ and the resultant fundamental 184 ELECTRICAL MACHINE DESIGN between S l and S 2 is represented by the vector S S 2 and =1.73 times the fundamental in one phase. In the case of the third harmonic the e.m.fs. are (3 X 120) = 360 degrees out of phase with one another and are represented by vectors in diagram B; the resultant third harmonic between S l and S 2 is zero so that, in a Y-connected alternator, no third harmonic, nor any harmonic which is a multiple of three, is found in the terminal voltage wave. When the phases are A -connected, any harmonic in the voltage wave of one phase will also be found in that of the terminal volt- age; a greater objection to the use of this connection for alterna- tors is that the harmonics cause circulating currents to flow in the closed circuit produced by the A -connection. Diagram C shows the voltage vector diagram for the fundamentals in the e.m.f. wave of each phase; the three vectors are 120 degrees out of phase with one another and the resultant voltage in the closed circuit due to the fundamentals is zero. Diagram D shows the voltage vector diagram for the third harmonic in the e.m.f. wave of each phase, the three vectors are 360 -degrees out of phase with one another and the resultant voltage in the closed circuit due to the third harmonics is three times the value of the third harmonic in one phase. A circulat- ing current will flow in the closed circuit, of triple frequency and < zj7 of a value =-= -, where E 3 is the effective value of the third <3z 3 harmonic in each phase and 2 3 is the impedence per phase to the third harmonic. 144. Harmonics Produced by Armature Slots. Fig. 133 shows two positions of the pole of an alternator relative to the armature. In position A the air gap reluctance is a minimum and in position B is a maximum. The flux per pole pulsates, due to this change in reluctance, once in the distance of a slot-pitch, or 2 a times in the distance of two pole-pitches, where a = slots per pole, and the e.m.f. generated in each coil by the main field goes through one cycle while the pole moves, relative to the armature, through the distance of two pole-pitches, therefore the frequency of the flux pulsation 2 a/. The flux per pole then consists of a constant value (f> a , and a superimposed alternating flux which has a frequency of 2a times the fundamental frequency of the machine, or at any instant the flux per pole THE GENERATED ELECTRO-MOTIVE FORCE 185 i cos 2a6 where (f> a +4>i is the maximum value of the pulsating flux and 6 is the angle moved through from position A, Fig. 133, in elec- trical degrees; therefore the flux threading coil C } which is a full-pitch coil, ^^a +0i when the coil is in position A = [0a + 0i cos 2a#]cos when the coil has moved through 6 electric degrees relative to the pole, and the e.m.f. in coil C at any instant B FIG. 133. Variation of the air gap reluctance. 0i cos 2a0)cps0 ~~ i cos 2a6)cos9 dO 27r/[-sin 0(^+^008 2ad}-cosd(2a^) 1 sin 2aO}]T sin 6 + ^sm cos 2a6 + 2a a , through a distance y relative to the armature, one of these constant progressive fields moves through a distance 2ay relative to the pole, or through a distance (2a + l)y relative to the armature, while the other moves through a dis- tance 2 ay relative to the poles, or through a distance (2a l)y THE GENERATED ELECTRO-MOTIVE FORCE 187 relative to the armature. If then the fundamental frequency of the generated e.m.f. is /, the two other fields will generate e.m.fs. of frequencies = (2a + I)/ and (2a I)/ respectively. To keep down the value of these harmonics the reluctance of the air gap under the poles should be made as nearly constant as possible for all positions of the pole relative to the armature. 145. Effect of the Number of Slots on the Terminal E.M.F. Fig. 135 shows the winding diagrams for an alternator with A- Three Phase 1 1 ' 1 1 1 A B III] ^\ , N^ * B-Two Phase C- Single Phase A B C D \ D - Single Phace FIG. 135. Effect of the distribution of the winding on the terminal voltage. six slots per pole and wound for single, two- and three-phase respectively, the same punching being used in each case. The e.m.fs. in the conductors in adjacent slots are out of phase with 180 one another by the angle corresponding to one slot-pitch ^- = 30 electrical degrees. In the three-phase winding the conductors in slots A and B are connected in series so that their voltages act in the same direction; the resultant voltage E r , diagram E } is not equal to 188 ELECTRICAL MACHINE DESIGN 2e, where e is the voltage per conductor, but is the resultant of two e.m.fs. e which are 30 degrees out of phase with one another and = 2e X 0.96. In the case of the two-phase winding the conductors A, B and C are connected so that their voltages add up and the resultant voltage E r = 3e X 0.91. In the case of the single-phase winding where all the con- ductors are used the resultant voltage E r = $e X 0.64, while if only four of the six slots per pole are used, as shown in diagram D, the resultant voltage E r = 4e X 0.84, which is only 10 per cent, lower than that obtained when all six slots are used. A gain of 10 per cent, in voltage is not worth the cost of the 50 per cent, increase in armature copper that is required, so that single- phase machines are generally wound as shown in diagram D. 146. Rating of Alternators. The maximum voltage that an alternator can give continuously is limited by the permissible value of the flux per pole, and the maximum current is limited by the armature copper loss which, along with the core loss, heats the machine. When the value of volts and amperes is fixed, the kilowatt rating depends only on the power factor of the load. The r power factor is a variable quantity, and one over which the builder of the machine has no control, so that an alternator is generally rated by giving the product of volts and amperes, which is called the volt ampere rating, and this quantity divided by 1000 gives the rating in k.v.a. (kilovolt amperes). 147. Effect of the Number of Phases on the Rating. Consider the four machines whose winding diagrams are shown in Fig. 135, and let the number of conductors per slot be the same in each, then the voltage per phase is given in the following table : Number of phases Voltage per phase Single-phase (all slots used) constant X 6e X 0.64. Single-phase (2/3 of slots used) constant X4e X0.84. Two-phase constant X 3e X0.91. Three-phase constant X 2e X0.96. Since there are the same number of conductors per slot* these conductors have the same section and therefore carry the same current I c ; the volt ampere rating, which equals volts per phase X current per phase X number of phases, is given in the following table: THE GENERATED ELECTRO-MOTIVE FORCE 189 Number of phases Volt ampere rating Single-phase (all slots used) constant X 6e X 0.64 X 1 X / c . Single-phase (2/3 of slots used) constant X4eX0.84X lX/c- Two-phase constant X3eX0.9lX2X/ c . Three-phase constant X 2eX 0.96X3 X/r. = a constant X 0.64. = a constant X0.56. = a constant X0.91. = a constant X 0.96. In practice the machine is given the same rating for both two- and three-phase windings, although the three-phase machine is the better, and is given 65 per cent, of this rating when wound for single-phase operation. 148. The General E.M.F. Equation. It is shown in Art. 145 that, when the winding of an alternator is distributed, the terminal voltage is less than ZXe where Z = conductors in series per phase e = volts per conductor and is equal to kZe where k is the distribution factor and is found from the following table, which is worked up by the method explained in Art. 145: Slots per phase Distribution factor per pole Two-phase Three-phase 1 1.0 1.0 2 0.924 ,0.966 3 0.911 0.96 4 0.906 0.958 6 0.903 0.956 The single phase results are not tabulated since they depend on the number of slots that are used by the winding. When a short-pitch is used, as is often done with double layer windings, then, as shown in Fig. 136, which shows part of a three- phase double layer winding with three slots per phase per pole, the two adjacent belts A and B are out of phase with one another by 6 degrees, and, as shown in Fig. 137, the resultant voltage, when these two belts are put in series, is equal to twice f\ the voltage in one belt multiplied by cos ^. It was shown in Art. 137 that the effective e.m.f. per con- ductor = 2.22 (f> a f 10~ 8 volts. 190 ELECTRICAL MACHINE DESIGN If the winding is full-pitch and is not distributed then the voltage per phase = 2.22 Z

a flQ- 8 cos (26) CHAPTER XIX CONSTRUCTION OF ALTERNATORS Figure 138 shows the type of construction that is generally used for alternators; it is known as the revolving field type. 149. The Stator. In the revolving field type of machine the stator is the armature. B, the stator core, is built up of lamina- FIG. 138. Revolving field alternator. tions of sheet steel 0.014 in. thick, which are insulated from one another by layers of varnish and are then mounted in a self- supporting cast-iron yoke A. These laminations are punched on the inner periphery with slots C which carry the stator coils D. The type of slot shown is the open slot; it has the advan- tage over the closed slot that the coils can be fully insulated be- 191 192 ELECTRICAL MACHINE DESIGN fore being put into the machine and can also be more easily repaired. The stator core is divided into blocks by means of vent seg- ments of cast brass, and the duels thereby provided allow air to circulate freely through the machine to keep it cool. The vent ducts are spaced about 3 in. apart and are half an inch wide. The stator laminations and vent segments are clamped between two cast-steel end heads E. When the teeth are long they are supported by strong finger supports placed at F } be- tween the end heads and the end punchings of the core. FIG. 139. Poles and field coil. When the external diameter of the stator core is less than 30 in. the core punching is generally made in a complete ring; when this diameter is greater than 30 in. the core is generally built up in segments which, as shown in Fig. 138, are fixed to the yoke by means of dovetails; the segments of adjacent layers of laminations break joint with one another so as to overlap and produce a solid core. 150. Poles and Field Ring. Inside of the stator revolves the rotor or revolving field system. The poles G carry the exciting CONSTRUCTION OF ALTERNATORS 193 coils H and are excited by direct current from some external source. The excitation voltage is independent of the terminal voltage of the machine and is generally chosen low, so that for a given excitation the field current will be comparatively large and the field coils will have few turns. For the usual excitation voltage of 120 it will generally be possible, except on the smaller machines, to use the type of field winding shown in Fig. 139, which is made by bending strip copper on edge; the layers of strip copper are insulated from one another by layers of paper about 0.01 in. thick, and the whole field coil is supported by and insulated from the poles and field ring as shown at A, Fig. 140. For small machines the excitation loss is com- 3 Turns 0.015 Paper. X'"Brass Collar. ^"Fiber Collar, . ,, 3 Turns O.Ol&Taper. M"Fiber Collar. FIG. 140. Alternator field coils. paratively low, and with an excitation voltage of 120 the section of the wire is too small and the number of turns required too large to allow the use of a strip copper coil; in such cases double cotton- covered square wire is used as shown at B, Fig. 140; the coils are tapered so as to allow free circulation of air around them. Since the number of poles in an alternator is fixed by the speed and the frequency, it rarely happens that this number is such as to allow the use of a pole of circular section; the pole is generally rectangular in section and, as shown in Fig. 139, is built up of punchings of sheet steel 0.025 in. thick which are riveted together between two cast-steel end plates. The poles are generally attached to the field ring by means of bolts as shown at K, Fig. 138, or by means of dovetails and tapered keys as shown at L; two tapered keys are used which are driven in from opposite ends. 13 194 ELECTRICAL MACHINE DESIGN The exciting current is led into the revolving field system by means of brushes which bear on cast-iron or cast-bras^ slip rings; the slip rings are carried by and insulated from the shaft as shown at M; the brushes are generally of soft self -lubricating carbon and carry about 75 amperes per square inch. FIG. 141. Revolving field alternator. The stator of an alternator is seldom split except in the case of very large machines where it is done for convenience in ship- ment. In order that the stator windings can be examined and easily repaired it is advisable to arrange that the whole stator slide axially on the base, and the key shown at N is for the pur- pose of keeping the alignment correct. Fig. 141 shows a 1000-k.v.a. water-wheel driven alternator of the type described in this chapter. CHAPTER XX INSULATION The insulation of low-voltage machines has been discussed in Chapter IV and presents no particular difficulty, since insu- lation which is strong enough mechanically is generally ample for electrical purppses up to 600 volts. For higher voltages, how- ever, the thickness of insulation required to prevent breakdown is great compared with that required for mechanical strength and, unless such insulation is carefully designed, trouble is liable to develop. 151. Definitions. If a difference of electric potential be A FIG. 142. Distribution of the dielectric flux. established between two electrodes a and 6, Fig. 142, which are separated by an insulating material or dielectric, a molecular strain will be set up in the dielectric. This molecular strain is conveniently represented by lines of dielectric flux, and the number of lines per unit area, which is called the Dielectric Flux Density, is taken as a measure of the strain. When the dielectric flux density reaches a certain critical value 195 196 ELECTRICAL MACHINE DESIGN the material is disrupted and loses its insulating properties; this critical value depends on the nature, thickness and condition of the material. The distribution of dielectric flux depends largely on the shape of the electrodes, as shown in diagrams A and B, Fig. 142. When an insulating material of uniform thickness t is placed between two parallel plates and subjected to a voltage E } the dielectric flux density or molecular strain is uniform through the total thickness of the material and is conveniently represented by the E ratio > the volts per unit thickness, Under such conditions of t test, the highest effective alternating voltage that } mil (0.001 in.) thickness of the material will withstand for 1 minute is generally called its Dielectric Strength. FIG. 143. Potential gradient at a slot corner. When the dielectric flux density is not uniform throughout Tfl the total thickness of the material, the ratio-,-, the volts per L unit thickness, has little meaning. In Fig. 143 for example, which shows the dielectric flux distribution at the corner of a slot, it will be seen that the dielectric flux density, or molecular strain, is greatest at the surface of the conductor and decreases as the lines spread out. Under such conditions the strain at any point is conveniently expressed by what is known as the Potential Gradient at the point, where this quantity is the volts per unit thickness that would be required to set up the same dielectric INSULATION 197 flux density as that at the point in question if the material were of uniform thickness and tested between two parallel plates. The potential gradient across ab is given by curve A. 152. Insulators in Series. If an air film be placed between two electrodes and subjected to a difference of potential, a certain dielectric flux density will be produced in the air. If now the air be replaced by mica, a greater dielectric flux density will be produced for the same difference of potential. The Specific Inductive Capacity of an insulating material is defined as the dielectric flux density in the material the dielectric flux density in air for the same value of volts per mil. Figure 144 shows two cases of dielectric subjected to a difference of electric potential between electrodes of the same size and the same distance apart. In A the dielectric is air, and in B is made up of air and mica in series. Since the specific inductive capacity of mica is greater than that of the air which it replaces, FIG. 144. Effect of the specific inductive capacity of the dielectric on the dielectric flux density. being about 6, the dielectric flux density is greater in B than in A for the same difference of potential between the electrodes, and the air in B is subjected to a greater strain than that in A, so that it will break down at a lower value of voltage between the terminals, although at the same value of volts per mil. Since in B the two materials, air and mica, are in series, the dielectric flux density is the same in each and therefore, from the definition of specific inductive- capacity, the volts per mil thickness in the mica_ 1 the volts per mil thickness in the air ~sp. ind. cap of mica = - approximately The greater the thickness of mica in the total thickness be- tween electrodes the larger will be the dielectric flux density 198 ELECTRICAL MACHINE DESIGN and the greater therefore the value of volts per mil thickness in the air for a given voltage between the electrodes. 153. Effect of Air Films in Insulation. From the above discussion it will be seen that, should there be an air film in the thickness of a solid dielectric, then, for a perfectly conservative value of volts per mil of total thickness of the dielectric, the volts per mil across the air film may be sufficient to disrupt it if the solid dielectric have a specific inductive capacity greater than one. When air is disrupted ozone and oxides of nitrogen are formed, these oxidize nearly- all the insulators used for electrical ma- chinery except mica and thereby seriously impair their in- sulating properties. 154. The Design of Insulation. The voltage that a given insulation will stand depends on FIG. 145. Effect of the voltage on the thickness of the slot insulation. The thickness of the insulation; The dielectric strength of the material; The potential gradient across the material; The length of time that the voltage is applied. 155. The Thickness of the Insulation. Fig. 145 shows the slot of an alternator insulated in the one case for high voltage and in the other case for low voltage. If the space occupied by insulation could be filled with copper the output of the machine could be considerably increased, so that the solution of high voltage insulation problems is not solved economically by indefinitely increasing the thickness of the dielectric with increasing voltage, but by the selection and proper use of the most suitable materials. 156. The Potential Gradient. Insulating materials break down wherever they are overstressed, and if the stress is not uniform INSULATION 199 they break down first at the point of highest stress; it is therefore necessary to make a study of the distribution of stress, or of the potential gradient in the material. Consider the case of the slot corner shown in Fig. 143, the lines of dielectric^ flux pass radially from the conductor to the side of the slot, so that the dielectric flux density is a maximum at the surface of the conductor and a minimum at the surface of the slot and the potential gradient curve, if the dielectric is of the same material throughout, is as shown in diagram A. The inner layers of the insulation therefore carry more than their share of the voltage, and these layers break down long before the stress in the outer layers reaches the break- down point. FIG. 146. Potential gradient with graded insulation. It is possible to make the outer layers carry their share of the total voltage by grading the insulation in the following way: Materials having different specific inductive capacities are used and put on in layers in such a way that the lower the specific inductive capacity the further away is the material from the conductor. This relieves the strain on the inner layers because, as pointed out in the discussion of insulators in series, the voltage required to send a given dielectric flux through a layer of insulat- ing material is inversely as the specific inductive capacity of the material, so that the higher the specific inductive capacity of the inner layers the lower the voltage drop across these layers and the higher therefore the voltage drop across the outer layers. 200 ELECTRICAL MACHINE DESIGN The potential gradient for such insulation, made up in three layers, is shown in diagram J5, Fig. 146. The potential gradient can be controlled in many cases by a slight alteration in the shape of the surfaces to be insulated from one another. Fig. 147 shows three cases of slot insulation, and it is evident that the potential gradient is more uniform in case B than in case A, while case C is the best of the three because of the extra thickness of the dielectric at the corner; in this last case the insulation generally punctures between the parallel sides of FIG. 147. Effect of the shape of the surfaces to be insulated on the distribution of dielectric flux. the slot and conductor, and not at the corner. Since the stress is uniform through the thickness of the insulation when it is between two parallel surfaces, grading of the insulation has no advantages for machines whose slots have square corners. 157. Time of Application of Electric Strain. 1 That the voltage at which an insulating material will puncture depends on the Time FIG. 148. Effect of time on the puncture voltage. length of time that this voltage is applied is shown by the curve in Fig. 148. E is the maximum voltage that the material will withstand for an infinite length of time without deterioration due to heating and consequent puncture. If air films are present in the insulation then a lower voltage than E will cause puncture if applied for some time, but the action in this case is a secondary one. Fleming and Johnson, Journal of the Institution of Elect. Eng., Vol. 47, page 530. INSULATION 201 In Art. 152, page 197, it was pointed out that the stress on an air film bedded in a material of specific inductive capacity greater than one is very high, and that the film may become ruptured and ozone and oxides of nitrogen be produced which attack the other insulation causing deterioration and consequent puncture. The amount of these gases produced by the rupture of a thin air film is not enough to do much harm unless there is a constant supply of air to the film. When an electrical machine is started up its coils become heated and, since the gases in the film expand, some of them are expelled. When the machine is shut down the coils cool off, the gases in the film contract, and a fresh supply of air is drawn in. This action is known as the breathing action of the coils. Trouble due to this breathing action takes months to develop and usually shows up as a breakdown between adjacent turns; the insulation between these turns having become brittle due to oxidization, readily pulverizes due to vibration. The trouble can be eliminated by constructing the coils so that they contain no air pockets, and in the endeavor to do this various methods have been adopted for impregnating the coils and sealing their ends. The compounds generally used for impregnating purposes are made fluid by heating to a temperature of about 100 C., and in cooling to normal temperatures most of them contract about 10 per cent, and this 10 per cent, becomes filled with air. Since, with the present methods of insulating, it may be con- sidered impossible to eliminate all the air pockets from a coil, it is necessary to keep the stress in the air films below that value at which they will rupture. This can be done by increasing the total thickness of the insulation and also by the use of material which has a low specific inductive capacity. It is unfortunate that mica, which is one of the most reliable of insulators, has a high specific inductive capacity; a good composite insulator can be made up of mica paper, which consists of a layer of mica backed by a layer of paper; the specific inductive capacity of the former is about six, and of the latter is about two, while the combination has a value between these two figures. Such an insulation is described fully on page 205 and may be expected to withstand 45 volts per mil indefinitely without trouble due to the breakdown of air films. For such insulation then the minimum thickness in mils between the conductor and 202 ELECTRICAL MACHINE DESIGN the side of the slot = volts from cond. to ground 45 If the in- sulation were made up entirely of mica a greater total thickness would be required on account of the high specific inductive capacity of the mica, while if made up entirely of paper a smaller total thickness would be required so far as the breakdown of the air film is concerned, but paper is not reliable as an insulator when used alone. 158. Design of Slot Insulation. The following points are taken up fully in Chapter IV: The materials in general use are; micanite and empire cloth, which are used principally on account of their dielectric strength; ooo OOP 000 OOP Q @ oo o@ o@ 00 oo oo A B FIG. 149. Insulation between layers of conductors. tape, which is used principally to bind the conductors together; paper, which is used to protect the other insulation. The puncture test recommended by the American Institute of Electrical Engineers is given in the table on page 34. The end connections should be insulated for the full voltage between the terminals. To minimize surface leakage the slot insulation should be carried beyond the core for a distance which depends on the voltage and which is found from the table on page 35. 159. Insulation between Conductors in the Same Slot. In high-voltage alternators the number of turns per coil is large and the size of the wire comparatively small. Fig. 149 shows sections through two alternator slots; in A the winding is double layer and in B is chain; the conductors are numbered in the order in which they are wound. INSULATION 203 Between conductors 1 and 2, 2 and 3, 3 and 4, etc., there is the voltage of only one turn or of two conductors, be- tween 2 and 5 there is the voltage of six conductors and between 1 and 6 the voltage of ten conductors. These con- ductors are usually of double cotton-covered wire, and it has been found advisable to increase this insulation, by putting in layers of empire cloth as shown, when the voltage between adjacent conductors exceeds 25 volts, because the impregnation of the cotton may not be thorough, and the cotton covering may become damaged when the conductors are squeezed together. 160. Examples of Alternator and Induction Motor Insulation. Example i. Insulation for a 440- volt induction motor with a wire- wound coil and a double layer winding. A section through the slot and insulation is shown in Fig. 150, and the insulation consists of: (a) Double cotton covering on the conductors. (b) A layer of empire cloth 0.006 in. thick between horizontal layers of conductors. (c) One turn of paper 0.01 in. thick on the slot part of the coil to hold the conductors in layers. (d) One layer of half-lapped empire cloth tape 0.006 in. thick all round the coil. (e) One turn of paper 0.01 in. thick on the slot part of the coil to protect the empire cloth. (f) One layer of half-lapped cotton tape 0.006 in. thick on the end con- nections to protect the empire cloth. The coil is baked and impregnated before the paper and cotton tape are put on, and is dipped in finishing varnish after they are put on to make it water- and oil-proof. The thickness of the slot insulation and the apparent dielec- tric strength are given in the table below: Width Depth Voltage D C C on wire 53 600 Paper Empire cloth . 0.02 o 024 0.03 0.024 2,500 4,500 Paper 0.02 0.03 2,500 0.064 0.084 10,100 204 ELECTRICAL MACHINE DESIGN In the above table, under heading of width, is given the space taken up in the width of the slot by the different layers of insulation. The insulation on the conductors has not been added since it varies with the number of conductors per slot. Under the heading of depth is .given the space taken up in the depth of half a slot by the different layers of insulation. Under the heading of voltage is given the apparent dielectric strength of the insulation; the figures used for the different materials are taken from Chapter IV. The puncture test voltage is 2000; therefore the factor of safety is 5.0. FIG. 150. 440 volt slot insulation. FIG. 151. 2200 volt slot insulation. Example 2. Insulation for a 2200-volt induction motor with a strip copper coil and a double-layer winding. A section through the slot and insulation is shown in Fig. 151 and the insulation consists of: (a) One layer of half-lapped cotton tape 0.006 in. thick on each con- ductor to form the insulation between conductors. (b) One layer of half -lapped cotton tape 0.006 in. thick all round the coil to bind the conductors together. (c) One turn of micanite 0.02 in. thick on the slot part of the coil. (d) Two layers of half-lapped empire cloth 0.006 in. thick all round the coil. (e) One turn of paper 0.01 in. thick on the slot part of the coil to protect the empire cloth. (f) One layer of half-lapped cotton tape 0.006 in. thick on the end con- nections to protect the empire cloth. INSULATION 205 The coil is baked and impregnated before the paper and last taping of cotton tape are put on. After they are on, the slot part of the coil is hot pressed and then allowed to cool under pres- sure, after which the coil is dipped in finishing varnish to make it water- and oil-proof. The thickness of the insulation and the apparent dielectric strength are given in the table below. Width Depth Voltage Tape on conductor 1 000 Tape on coil Micanite Empire cloth 0.024 0.04 048 0.024 0.06 048 1,000 16,000 9 000 Paper 0.02 0.03* 2,500 0.132 0.162 29,500 The puncture test voltage is 5000; therefore the factor of safety is 5.8. Example 3. Insulation for a 11, 000- volt alternator with a strip copper coil and a chain winding. A section through the slot and insulation is shown in Fig. 152 and the insulation consists of : (a) One layer of half-lapped cotton tape 0.006 in. thick on each con- ductor to form the insulation between adjacent conductors. (b) One layer of micanite 0.02 in. thick between vertical layers of con- ductors, all round the coil. (c) Two layers of half-lapped empire cloth 0.006 in. thick on each of the two sections of the coil, this empire cloth to go on both slot part and end connections of the coil. (d) One layer of cotton tape 0.006 in. thick, half-lapped on the ends and taped with a butt joint on the slot part of the coil. This tape is to bind the two sections of the coil firmly together. (e) Three turns of mica paper, made of 5 mil paper and 7 mil mica, on the slot part of the coil. (f) One layer of cotton tape 0.006 in. thick, half lapped on the ends and butt joint on the slot part of the coil. (g) Bake and impregnate the coil. (h) Three layers of half-lapped empire cloth 0.006 in. thick all round the coil. (j) Three turns of mica paper on the slot part of the coil. (k) One layer of cotton tape 0.006 in. thick, half-lapped on the ends and butt joint on the slot part of the coil. 206 ELECTRICAL MACHINE DESIGN (1) Two layers of half-lapped empire cloth 0.006 in. thick all round the coil. (m) Three turns of mica paper on the slot part of the coil. (n) Three layers of half-lapped empire cloth 0.006 in. thick all round the coil. (o) One layer of cotton tape 0.006 in. thick, half -lapped on the ends and butt joint on the slot part of the coil. (p) Bake and impregnate the coil. (q) One turn of paper 0.015 in. thick on the slot part of the coil. (r) Hot press the slot part of the coil and allow it to cool while under pressure. FIG. 152. 11,000 volt slot insulation. The thickness of the insulation and its apparent dielectric strength are given in the table below. Width Depth Voltage (a) Tape on conductor 1 000 (b) Micanite between layers (c) Empire cloth on each section . (d) Cotton tape 0.02 0.096 012 0.048 0.012 9,000 (e) Mica paper 0.084 0.072 20,550 (f ) Cotton tape (h) Empire cloth 0.012 072 0.012 072 13 500 (j) Mica paper (k) Cotton tape 0.084 012 0.072 012 20,550 (1) Empire cloth (m) Mica paper (n) Empire clotji 0.048 0.084 072 0.048 0.072 072 9,000 20,550 13,500 (o) Cotton tape 0.012 0.012 (q) Paper 0.045 0.045 3,750 0.653 0.549 111,400 INSULATION 207 The minimum thickness of insulation between copper and iron = 279 mils, therefore the volts per mil at normal voltage =40. The puncture test voltage for this insulation is 22 ; 000 volts, therefore the factor of safety is 5.1. The insulation on each end connection consists of: 10 layers of half-lapped empire cloth 5 layers of half -lapped cotton tape; this insulation, along with the air space between coils, is ample. CHAPTER XXI ARMATURE REACTIONS IN ALTERNATORS POLYPHASE MACHINES 161. The Armature Fields. a and 6, Fig. 153, are two con- ductors of one phase of a polyphase alternator. When current flows in these conductors they become encircled by lines of force. These lines may be divided into two groups; r , the lines which pass through the magnetic circuit and whose effect is called armature reaction, and (/> x , called leakage lines, which do not pass through the magnetic circuit. 162. Armature Reaction. Diagram A, Fig. 154, shows an end view of part of a three-phase alternator which has six slots per pole. The starts of the three windings are spaced 120 electrical FIG. 153. The armature fields. degrees apart and are marked u $ 2 , 3 . The armature moves relative to the poles in the direction of the arrow and the e.m.f . in each phase at any instant is given by the curves in diagram F. In diagram A is shown the relative position of the armature and poles, and also the direction of the e.m.f. in each conductor, at instant 1, diagram F, at which instant the e.m.f. in phase 1 is a maximum. Let the current be in phase with the generated e.m.f., then diagram G shows the current in each phase at any instant, and the three diagrams, B, C and D, show the direction of the current in each conductor and also the relative position of the poles and armature at the three instants 1, 2 and 3. It may be seen from these diagrams that the currents in the three phases produce a resultant armature m.m.f. which moves in the same direction as the poles and at the same speed. Since the armature resultant 208 ARMATURE REACTIONS IN ALTERNATORS 209 m.m.f . is added to that of the main field at one pole tip, and sub- tracted from it at the other tip of the same pole, the resultant effect is cross-magnetizing. Let the current lag the generated e.m.f. by 90 degrees, then diagram H shows the current in each phase at any instant, and Ph.l Ph.2 Ph.3 (oWT) (*) >) O N S N Direction of Generated E.M.F. \/ Ph.3 Armature M.M.F. when Current is in Phase with Generated E.M.F. = -0.86 J TO = 0.86/ m \ A Ph.1 Ph.2 Armature M.M.F. when Current TLags the Generated E.M.F. by 90 Degrees. FIG. 154. The armature m.m.f. of a three phase alternator. diagram E shows the direction of the current in each conductor and also the relative position of the poles and armature at instant 1. The resultant m.m.f. of the armature has the same value as before and moves at the same speed and in the same direction, but has now a different position relative to the poles and is demag- netizing in effect. 14 210 ELECTRICAL MACHINE DESIGN If the current lead the generated e.m.f. by 90 degrees; then it can be shown in a similar way that the resultant armature m.m.f. has the same magnitude, speed and direction as before, but is magnetizing in effect. 163. The Alternator Vector Diagram. On no-load the current in the windings of an alternator is zero and the only m.m.f. which is acting across the air gap is F , that due to the main field; F Q sends a constant flux cf> a across the gap. This flux moves rela- tive to the armature surface so that the flux which, due to the m.m.f. F , threads the windings of one phase of the armature is alternating and has a maximum value = (j> a . The voltage generated in a coil lags the flux which threads the coil, and whose change produces the voltage, by 90 degrees; thus, in Fig. 155, the flux threading coil a is a maximum but the voltage a b a b O O FIG. 155. The generated e.m.f. in a coil. in that coil is zero, while the total flux threading the coil 6 is zero and the voltage in that coil is a maximum; that is, the voltage is in phase with the flux which the coil cuts, but lags the flux which threads the coil by 90 degrees. The vector diagram for one phase of a polyphase alternator is shown in Fig. 156. On no-load, F 0f the m.m.f. of the main field referred to the armature, produces an alternating flux in the windings of each phase, and E , the voltage generated in each phase by that flux, lags F Q by 90 degrees. When the alternator is loaded the currents in the armature produce a m.m.f. F a of armature reaction which, if acting alone, produces a field (j) r of constant strength which moves in the same direction and at the same speed as the main field. In Fig. 154, diagram B, it may be seen that when the current in phase 1 is a maximum the flux which threads the windings of that phase is also a maximum; in diagram C the current in phase 2 is zero and the flux which threads the windings of that phase is also zero. In general it may be shown that the flux which, due to the revolving field (f> r , threads the winding of one phase of the armature is an alternating flux which has a maximum value = r and is in phase with the current in that winding. ARMATURE REACTIONS IN ALTERNATORS 211 If the alternator is loaded and I, Fig. 156, is the current per phase, then F g , the resultant of the m.m.fs. .F and F a , will produce a resultant magnetic flux a which is alternating with respect to the armature windings, and E g , the voltage per phase due to the flux g , will lag it by 90 degrees. In addition to the m.m.f. of armature reaction the current in the windings of one phase sets up an alternating magnetic flux cf) x which, as shown in Fig. 153, circles these windings but does not link the magnetic circuit; this flux is in phase with the current in the windings and is proportional to that current since its magnetic circuit is not saturated at normal tooth densities. FIG. 156. The vector diagram for an alternator. In Fig. 156 F is the m.m.f. due to the field excitation referred to one phase of the armature. E is the voltage per phase which would be generated by the flux produced by F . I is the current per phase. F a is the m.m.f. of armature reaction referred to one phase of the armature and, as pointed out above, is in phase with /. F g is the resultant of the two m.m.fs. F and F a . (f> g is the flux that threads the windings of one phase due to F g . Eg is the voltage generated in that phase by (f> g . (f) x is the armature leakage flux per phase produced by 7. E x is the voltage per phase generated by the flux x and is called the leakage reactance voltage. E X =IX where X is the leakage reactance per phase. E E t is the resultant of E g and E 3 is the terminal voltage per phase and = E-IR taken as vectors, where R is the effective resistance per phase. 212 ELECTRICAL MACHINE DESIGN Figure 157 shows the above diagram for the particular case where the power factor is approximately zero and the current lags the generated voltage by 90 degrees. In this case the m.m.f. of armature reaction is subtracted directly from that of FIG. 157. The vector diagram for an alternator on zero power factor. the main field to give the resultant m.m.f., and the leakage reactance voltage is subtracted directly from the generated voltage Eg to give the terminal voltage. The resistance drop O Ampere Turns per Pole 9 FIG. 153. The saturation curves of an alternator. can be neglected in this case since its phase relation is such that it has little effect on the value of the terminal voltage. 164. Full -load Saturation Curve at Zero Power Factor with Lagging Current. Curve 1, Fig. 158, shows the no-load satura- ARMATURE REACTIONS IN ALTERNATORS 213 tion curve of an alternator. When the machine is loaded, the power factor of the load zero, and the current lagging, the m.m.f. of armature reaction is directly demagnetizing, and to overcome its effect and maintain the flux <> a which crosses the air gap constant, a number of ampere-turns per pole equal to the arma- ture demagnetizing ampere-turns per pole must be added to the main field excitation. Under these conditions the increase in the field excitation causes the leakage flux (j> e , Fig. 159, to increase to the value. 0/ e , where A T.g +t + demagnetizing AT. per pole\ without increasing the value of ^ 1 h-J f \ [-.- - FIG. 159. The main field and the pole leakage. Curve 2, Fig. 158, is a new no-load saturation curve which is calculated with the value of the leakage factor corresponding to full-load, zero power factor and lagging current. To maintain the flux crossing the air gap constant and = a a number of ampere- turns per pole, ab, equal to the armature demagnetizing ampere-turns per pole, must be added to the value obtained from curve 2. The terminal voltage is less than that generated due to the flux e = the lines of force that circle 1 in. length of the belt of end connections for each ampere conductor in that belt, 216 ELECTRICAL MACHINE DESIGN j=the lines of force that cross the tooth tips and circle 1 in. length of the phase belt of conductors for each ampere conductor in that belt, 6 = conductors per slot, c = slots per phase per pole, then the total flux that links the coils shown the coefficient of self-induction of these coils = : 1 ~ 8 henry i = b 2 c 2 [0 e X2L e + (0s +(f)t) X2L c ]XlO~ 8 henry the reactance of these coils in ohms - 2nfb 2 c 2 [ e X 2L e + (0. + 00 X 2L C ] X 10~ 8 since there are p/2 of these groups of coils per phase the reactance of one phase in ohms = 2;r/p6 2 c 2 [0 e L e + (0. + 00 X L c ] X 10" 8 (28) For a double layer winding a slight modification is required in the above formula. Figure 162 shows part of the winding of one phase of a poly- phase alternator which has a double layer winding. be The number of turns in the coils shown =-=- the total flux that links these coils = 0C . bXc the coefficient of self-induction of these coils henry -* henry ARMATURE REACTIONS IN ALTERNATORS 217 the reactance of these coils in ohms since there are p of these groups of coils per phase, the reactance of one phase (29) which differs from the formula for the chain winding in that the end connection reactance is reduced to half the value. V 2 b c Cond. FIG. 162. The armature leakage fields with a double layer winding. 168. End -connection Reactance. e depends principally on 20 16 12 8 12 16 20 24 28 Pole Pitch in Inches FIG. 163. The end connection leakage flux. the length of the end-connection leakage path, namely, the length around the belt of end connections, which, as may be seen 218 ELECTRICAL MACHINE DESIGN from Figs. 161 and 162, is directly proportional to the pole-pitch and inversely proportional to the number of the phases, and (f> e decreases as this length increases, so that is approxi- TL i mately proportional to for any number of phases. pole pitch L e , the length of the end connections, increases with the pole- pitch as may be seen from Figs. 161 and 162, and in Fig. 163 - is plotted against pole-pitch from test results. ^, **- - e ^ ,/ m d, FIG. 164. The slot leakage flux. 169. Slot Reactance. Fig. 164 shows part of one phase of an alternator which has a chain winding. The m.m.f. between m and n = b X cXi X^r ampere-turns, therefore the leakage a -t flux d(j> 2.5 all in inch units cs the reluctance of the iron part of the leakage path is neglected since it is small compared with that of the air path across the slots. ARMATURE REACTIONS IN ALTERNATORS 219 This flux d per 1 in. length of core 4:7i dy = 10^- X2.54 all in inch units dy and the total tooth-tip leakage flux that links one phase belt per 1 in. length of core f = 3.26ci I Jo dy ARMATURE REACTIONS IN ALTERNATORS 221 - 2.35 to log,. (l+ 1) therefore t a, the lines of force that cross the tooth tips and circle 1 in. length of the phase belt of conductors for each ampere conductor in that belt, when the belt lies between the poles, B shows the case where there are two slots per phase per pole and it may be seen that in such a case . -2.JWJ log, C shows the case where there are three slots per phase per pole and it may be seen that in such a case the flux 2.35 Iog l0 1 1 + * 1 circles the total belt while the flux Iog 10 ( 1 H (is produced by, and circles 1 /3 of 6 \ w/ the total belt. This latter flux is equivalent to a flux -^ log 10 ( 1 + ) circling y \ w/ the whole belt, + + therefore fc. - 2.35 logl +3 + log,, l + D shows the tooth-tip leakage path round the coils of one phase of a machine with 1 slot per phase per pole, when the winding of that phase lies under the poles. In this case ta while the conductors are in the belt hk = t p while the conductors are in the belt kl FIG. 166. Variation of the current in the phase belt at zero power factor with the position of the belt relative to the poles. On zero power factor the current in a conductor is a maximum when the e.m.f. generated in that conductor is zero, that is when the conductor is between the poles. As the conductor moves relative to the poles the current in the conductor varies accord- ing to a sine law as shown in Fig. 166, therefore, since the tooth- tip reactance per phase = 27ifb 2 c 2 ptaL c ^O~ 8 when the cond. are in the belt hk and = 27r/6 2 c 2 pi p L c 10~ 8 when the cond. are in the belt kl the effective voltage per phase on zero power factor due to tooth- tip leakage = 27r/6 2 c 2 p<^ a L c 10~ 8 X effective current between h and k, while they are in this belt and =2nfb 2 c 2 p(j> t pL c lO~ s X effective current between k and I, while they are in this latter belt ARMATURE REACTIONS IN ALTERNATORS 223 and from formula 28, page 216, the effective voltage per phase due to tooth-tip leakage therefore , is approximately ./i=# " \ 1 1 < effect, current in belt hk effect, current in belt kl As a general rule, (ft, the pole enclosure = 0.6 and for this value 1

e L e may be found from Fig. 163 = ^/^ d 2d^ d 4 c 3s s s + w w > fa = 2.35 Iog 10 ( 1 -\ J for 1 slot per phase per pole = 2.35 Iog 10 ( 1 +-^r-. ) for 2 slots per phase per pole - for 3 slots per phase per pole 224 ELECTRICAL MACHINE DESIGN txC for 1 or 2 slots per phase per pole 10 = 3.2 XTT X^ -s for 3 slots per phase per pole f= frequency in cycles per second 6 = cond. per slot c = slots per phase per pole p = poles n = phases L c = frame length in inches t = width of tooth at the tip C = Carter coefficient found from Fig. 40, page 44. slot dimensions are given in Figs. 164 and 165. Example of Calculation. The armature reaction and armature reactance can be checked approximately by the no-load satura- tion and the short-circuit curves of an alternator. Fig. 167 shows the actual test curves on a small alternator which was built as follows: Poles, 6 Pole enclosure, . 6 Pole pitch, 10.5 in. Air gap clearance, 0.2 in. Slots per pole, 6 Conductors per slot, 12 Size of slot, . 75 X 1 . 75 in. , open Tooth width, 1 . in. Carter coefficient, 1 . 2 Frame length, 6.5 in. Winding, double layer Y-connected Turns per field coil, 420 Rating, 65 k.v.a., 600 volts, three-phase, 60 cycles. To send full-load current through the machine on short-circuit requires an excitation of 4.8 amperes. Now the power factor during this test is zero since the machine is carrying no-load, and the terminal voltage is zero since the machine is short-circuited, therefore m is- a point on the full-load saturation curve at zero power factor, the resistance drop being neglected. The demagnetizing ampere-turns per pole = 0.35Xcond. per poleX/ c -0.35X12X6X62.5 = 1580 ampere-turns per pole the corresponding field current ARMATURE REACTIONS IN ALTERNATORS 225 _ demagnetizing ampere- turns per pole field-turns per pole 1580 420 = 3.75 700 600 500 400 g etf Jsoo 200 100 amperes | Armature Current , ^ X T 1 * *y / / // ' 1 / / / & / S -/ 4 V / J 5 / 4 4 < y Full Load Curre Qt b / ! // n 4 m - 8 12 16 20 Field Current FIG. 167. No-load saturation and short circuit curves on a, 65 k.v.a three-phase alternator. The reactance per phase c 10- 8 ohms. where ~ = 5Xn from Fig. 163, since the pole-pitch =10.5 in. = 15 3.2/ 1.5 .25 =2.35 log (l+^Xl ) .0.82 15 226 ELECTRICAL MACHINE DESIGN 4>t =0.52X0.82+0.42X9.6=4.4 and reactance per phase = 2 X?r X60 X12 2 X2 2 X 6(15. + (1.6 +4.4)6.5) X10~ 8 = 0.7 ohms. The voltage drop per phase = 0.7X62. 5 = 44 volts and the voltage drop at the terminals =1.73x44 = 76 volts since the winding is Y-connected. These two figures, 3.75 field amperes 76 terminal volts are the only ones required for the construction of triangle abm, Fig. 167, and it may be seen that the calculated results check the test results very closely. 172. Variation of Armature Reaction and Armature Reactance with Power Factor. When an alternator is carrying a load whose power factor is zero, the current in the conductors reaches r , due to the armature m.m.f., goes through half a cycle relative to the armature coils, while relative to the poles it changes from a maximum in diagram A to zero in diagram B and back to a maximum in diagram C, and so, as shown in curve a, diagram E, is pulsating relative to the poles with double normal frequency. The poles are surrounded by the field coils, which are short- circuited through the exciter, and any pulsating flux in the poles induces a current in these coils which, according to Lenz's law, tends to wipe out the flux; thus the pulsation becomes 232 ELECTRICAL MACHINE DESIGN dampened out, as shown in curve 6, diagram E. The armature field is therefore equivalent in effect to a constant field, which is fixed relative to the poles and has a value of half the max mum value which it would have if the pulsation were not dampened out. Another way to look at the above subject is as follows: The armature field is stationary in space and is alternating. Such a field, as pointed out in Art. 144, page 184, can be exactly rep- resented by two progressive fields of constant value which move in opposite directions through the distance of two pole-pitches while the alternating field goes through one cycle. Consider these two fields to exist separately, then one moves in the same direction and at the same speed as the poles while the other moves at the same speed but in the opposite direction to the poles. The former is therefore stationary with regard to the poles and may be treated in exactly the same way as the armature field in a polyphase machine; the latter field revolves at the same speed as the main poles but in the opposite direction and so causes a double frequency pulsation of flux in these poles which pulsa- tion induces currents in the field windings that tend to wipe out the flux, so that the effect of this latter field can be neglected in a discussion of armature reaction. A flux of double frequency in the poles will produce a third harmonic of e.m.f. in the armature, as shown in Art. 144, page 184; a third harmonic of current in the armature will produce a fourth harmonic oi flux in the poles and so on; however, high frequency harmonics in the poles are so well dampened out that those higher than the third can be neglected. The demagnetizing ampere-turns per pole and the leakage reactance are worked out below for a particular case; the method is quite general, but since the result depends on the per cent, of the pole-pitch that is covered by the winding, no general formula is deduced. 178. The Demagnetizing Ampere-turns per Pole at Zero Power Factor. Fig. 173 shows the distribution of the m.m.f. of arma- ture reaction for a machine with b conductors per slot, and six slots per pole, of which four are used, at the instant when the current has its maximum value. If the pole arc =0.6 times the pole-pitch then the average value of that part of the maximum m.m.f. which is effective X3.6^ ARMATURE REACTIONS IN ALTERNATORS 233 = area of cross-hatched curve in Fig. 173 The constant field which is fixed relative to the poles, and which is the only one that need be considered in calculations, has a value of half the above maximum value, therefore, the average value of the part of this constant field which is effective =AT av is such that FIG. 173. The maximum m.m.f. of a single-phase alternator on zero power factor. and AT av =0.92 bl m = 1.3 bl c where I c is the effective current effective slots per pole = 0.32Xcond. per poleX/ c . (30) 179. The Leakage Reactance. As in the case of the polyphase machine this consists of end connection, slot and tooth-tip reactance. The end-connection reactance =2xfpb 2 c 2 ((f> e Le) 10~ 8 for a machine with a chain winding, and half of this value for a ma- chine with a double-layer winding; where c is the effective number of slots per pole or the number which carry conductors. (j) e L e is found from Fig. 163, but it must be noted that for the type of winding shown in Fig. 174, (f> e links the coils of four slots and the length of the end-connection leakage patl} is two-thirds of the value which it would have if all the slots were used; the value of (f> e Le is therefore 3/2 times that found from Fig. 163. The slot reactance = 234 ELECTRICAL MACHINE DESIGN , 3.2 /^ d 2 2d 3 d\ ,. where $ s = (~-\ -+ - + : the slot dimensions are c \3s s s + w w/' given in Fig. 164, page 218, and c is the effective number of slots per pole. I I I I FIG. 174. The end connection leakage path in single-phase alternators. im FIG. 175. The positions of maximum and minimum tooth tip leakage. The tooth-tip reactance varies from a maximum, when the conductors are in position A, Fig. 175, to a minimum, when they are in position B. In the former position it may be seen ARMATURE REACTIONS IN ALTERNATORS 235 that three only of the slots lie under the pole at any time, while in the latter position it may be assumed that three only of the slots are effective since the leakage lines which link all the slots have to pass through the field windings and are therefore dampened out. An approximate solution for the case of a machine with six slots per pole of which four are used, and which has a pole arc = 0.6 times the pole-pitch, is tooth-tip reactance = 2nfb 2 c 2 pL c X (f>t X 10~ 8 where t =0.52X0.75+0.42x10.7-4.9 reactance per phase = {2X7rX60Xl2 2 X4 2 X6 (7.5+0.8x6.5) 10~ 8 } + {2X7rX60Xl2 2 x3 2 X6 (4.9X6.5) lO" 8 } = 1.6 ohms the voltage drop per phase = 1.6X62. 5 = 100 volts. with this value and with the demagnetizing effect = 2. 3 amp. the triangle abn, shown dotted in Fig. 167, is drawn in and it may be seen that the calculated results check the test results very closely. 180. Regulation of Single -Phase and Three -Phase Alternators. In the machine whose test results are shown in Fig. 167 the out- put at full-load = 1.73X600X62.5 = 65 k.v.a. for the three-phase rating = 600 X62.5 =37.5 k.v.a. for the single-phase rating or the single-phase output is about 60 per cent, of the three- phase output. For this ratio, n is a point on the full-load saturation curve of the single-phase machine and m a point on that of the three-phase machine, and, as may be seen, the former machine has the better regulation. For the same regu- lation in each case the single phase machine may be given 65 per cent, of the three-phase rating. CHAPTER XXII DESIGN OF A REVOLVING FIELD SYSTEM The problem to be solved in this chapter is, given the arma- ture of an alternator and also its rating to design the whole revolving field system. 2 3 4. 5^ w 6 e 7 8 9 Q 10 Z 11 w 12 x 10 3 Ampere Turns per Pole FIG. 176. Saturation curves for a 400 k.v.a. 2400- volt, 3-phase, 60-cycle, 600 r.p.m. alternator. 181. Field Excitation. Fig. 176 shows several of the satura- tion curves of an alternator: the excitation required for normal voltage = on at no-load = oe at full-load and unity power factor = og at full-load and 85 per cent, power factor = ol at full-load and zero power factor 237 238 ELECTRICAL MACHINE DESIGN ... exciter voltage the maximum exciting current = t r-r ..,., TT- and not resistance ot field coils the maximum excitation = max. exciting current X field- turns per pole The radiating surface of the field coils should be large enough to keep the temperature rise with the excitation og below that guaranteed, which is generally 40 C. The maximum excitation om should be large enough to enable the alternator to give normal voltage on all loads and power factors to be met in practice. If the maximum excitation is equal to ol, and, therefore, large enough to maintain normal voltage at full-load and zero power factor, it will generally be found ample for all ordinary overloads and power factors. The field resistance should have such a value that the max- imum excitation om may be obtained with the normal exciter voltage. The ratio - is about 1.25 for normal machines, so that if og the temperature rise with excitation og is 40 C. that with exci- tation om will be 40X1.25 2 or 62 C. It is therefore usual to design the field coils for an excitation om and for a temperature rise of 65 C. 182. Procedure in the Design of a Revolving Field System. (a.) Find AT max , the maximum excitation = 3 (armature AT. per pole) for a first approximation, see Art. 176, page 230. (6.) Find M, the section of the field coil wire from the formula T... A T max X mean turn M = -^j Formula 7, page 65. volts per coil ,, ., exciter voltage where the volts per coil= , - and the mean turn is poles found as follows: (f> a =ihe flux per pole crossing the gap= 2 22kZf Formula 25, page 190. If.j the leakage factor, is assumed to be 1.2 for a first approximation. Pole area = r-^i ., where the pole density at normal pole density voltage and frequency and at no-load is taken as 95,000 lines per square inch, which is about the point of saturation. The pole area also = 0.95 XL P XW P . DESIGN OF A REVOLVING FIELD SYSTEM 239 L p , the axial length of the pole, is made 0.5 in. shorter than the frame length so that the rotor can oscillate f reejy. The value of W p , the pole waist, and of MT, the mean turn of the coil, can then be found approximately. (c) Find Lf, the radial length of the field coil, from the formula j _ AT max r~ mean turn 1000 \ext. periphery X watts per sq. in. Xd f Xsf XI. 27 Formula 8, page 66, where: external periphery is found approximately from the pole dimensions; 23456 Peripheral Velocity of Rotor in Ft. per Min. 8xl0 3 FIG. 177. Heating curves for the field coils of revolving field alternators. watts per square inch is found from Fig. 177 which gives the results of tests on machines similar in construction to that shown in Fig. 138, and with the type of field coil shown in Fig. 140; df, the winding depth, is chosen so as to give the most econom- ical field structure. It was shown in Art. 56, page 66, that the smaller the value of df the lower the cost of the field cop- per but the longer and more expensive the poles. The most 240 ELECTRICAL MACHINE DESIGN economical depth can be found by trial but the following values may be used as a first approximation: Depth of field coil 60-cycle 25-cycle 5 in 6 in. 10 in 0.75 in. 1.0 in. 15 in 1.0 in. 1.25 in. 20 in 1.5 in. 30 in 2.0 in. 40 in 2.5 in. For a given pole-pitch the 60-cycle machine runs at a higher peripheral velocity than the 25-cycle machine, it therefore requires less radiating surface for the same excitation and the poles become very short unless the value of df is decreased below that which is found best for 25-cycle machines. The above figures are for strip copper field windings; when d.c.c. wire is used the above depth should be increased about 20 per cent, because of the poorer space factor of this type of winding, and the coils should be tapered, if necessary, as shown in Fig. 140. (d) Tf is the number of field-turns that will fill up the space dfLf, the size of wire being fixed. 183. Calculation of the Saturation Curves. It is necessary first of all to find the air gap clearance, which is done as follows: The approximate number of ampere-turns per pole required for the air gap at no-load and normal voltage, namely oq, Fig. 176 = o? Iq and is approximately = A T max -l. 5 (armature AT. per pole). Since the flux per pole and also the dimensions of the machine are given, the apparent gap density and, therefore, the air gap clearance required, can be found from the formulae flux per pole crossing the gap Apparent gap density = apparent gap density Air gap ampere-turns = Formula 3, page 48. DESIGN OF A REVOLVING FIELD SYSTEM 241 The magnetic circuit is now drawn in to scale and the leakage factor and the no-load saturation curves calculated by the method explained in Arts. 46 and 47, page 46. The leakage factor at full-load and zero power factor = l + 0m /^g+< + demagnetizing AT. per po \ ATg + t 212, where l.m is the no-load leakage factor, and the demagnetizing AT. per pole = 0.35Xcond. per poleX/ c . A new no-load saturation curve is calculated using the above full-load leakage factor and plotted as shown in the dotted curve in Fig. 176. The reactance per phase is determined from the formulae on page 223 and the triangle pqr and the full-load saturation curve at zero power factor are then drawn in. The full-load saturation curves at other power factors are calculated by the use of the diagram shown in Fig. 169, and from these curves the regulation at the different power factors is determined. If the regulation found from the curves is equal to or slightly better than the regulation required, then the field design is complete. If the regulation found is considerably better than that re- quired, then the machine is unnecessarily expensive and the following changes may be made: a. The air gap may be made smaller so that less excitation is required and the cost of the field copper is reduced; the effect of such a reduction in air gap is explained in Art. 176, page 229. b. The armature can be redesigned and the value of g, the ampere conductors per inch, increased. If the total number of conductors is increased, the flux per pole is decreased, and for the same tooth density and a reduced value of flux per pole the diameter or frame length or both must be reduced; in order to carry the increased number of ampere conductors on each inch of the periphery, deeper slots must be supplied. These changes will increase both the armature reaction and the armature reactance and tend to make the regulation worse, but will make the machine cheaper. If the regulation found from the curves is worse than that required, then the following changes may be made on the machine to improve it: 16 242 ELECTRICAL MACHINE DESIGN c. The air gap may be increased so that more excitation is re- quired and the cost of the field copper is increased, the effect of such an increase in air gap is explained in Art. 176, page 229. d. The air gap may be decreased and the pole section reduced so as to increase the pole density and bend over the saturation curve as shown in Fig. 170; this, however, is a risky expedient unless all the material that goes into the machine is carefully tested for permeability and rejected if not up to standard. If the permeability of the material put into the machine is lower than was expected then the chances are that the machine will not be able to give its voltage on low power factor loads. e. The armature can be redesigned and the value of q, the ampere conductors per inch, decreased, this will have an effect opposite to that discussed in section b and will require a more expensive machine but will give better regulation. Example. The armature of a 400-kv.a., 2400-volt, 96-amp., 3-phase, 60-cycle, 600-r.p.m. revolving field alternator is built as follows: Poles, 12 Internal diameter, 43 in. Frame length, 12.25 in. Center vent ducts, 3 0.5 in. Slots per pole, number, 6 open type Slots per pole, size, . 75 X 2 . in. Conductors per slot, 12 Connection, Y Exciter voltage, 120 It is required to design the revolving field system: The armature ampere-turns per pole cond. per slot . = slots per pole X ~ X /c = 6X6X96 = 3450 ampere-turns. A T m ax = the maximum excitation = 3 X 3450 = 10,400 ampere-turns, approxi- mately. 2400 E = the voltage per phase == ^r~^ since the connection is Y 1 . 10 = 1380 1380X10 8 a = the flux per pole =2.22 X 0.96 X 72 X 12X60 3 = 3.8X10 6 If = the leakage factor, is assumed to be =1.2. DESIGN OF A REVOLVING FIELD SYSTEM 243 = 48 sq. in. L p = the axial length of the pole, is made . 5 in. shorter than the frame length and =11.75 in. m 48 sq. in. W p = the pole waist -L.- = 4.25 in. df, the depth of the field coil =0.75 in. from the table on page 240. MT = the mean turn = 2(11.75 + 4. 25) + ?rX 1.25 = 36 in. External periphery of field coil =38 in. ,, ,, , c , , 10,400X36 M, the section of field wire = - ^ = 37,500 circular mils = 0.03 sq. in. = 0.04 X 0.75 (strip copper wound on edge) Watts per square inch for 65 C. rise =6.3 from Fig. 177, page 239. 04 sf. the space factor = 77- 0.04 + thickness of insulation = 0.8 using paper which is 0.01 in. thick T xi j- i i ^u * u M 10,400 / 36 L/> the radial length of field coil = -*j^fr 38X6.3X0.75X0.8X1.27 = 4.75 in. 4 75 T 7 /, the number of turns per pole = - ' 0.05 = 95 turns. The maximum exciting current = A T max ~w~ 10,400 95 = 110 amperes Maximum output from exciter =120X110 = 13 kw. = 3.25 per cent, of the volt ampere rating. AT g , the gap ampere-turns per pole at normal voltage and no-load, = AT max 1.5X armature AT. per pole, approximately = 10,400-1.5X3450 = 5200 ampere-turns. ^, the pole enclosure, is taken as 0.65 which is an average value; if the pole arc be made too large, the pole leakage becomes excessive and the leakage factor high. 3.8X10 6 B a , the apparent gap density n . 25x p.65X 12.25 = 42,500 lines per square inch. 5200X3.2 X C = 42500 0.39 in. 244 ELECTRICAL MACHINE DESIGN C = the Carter coefficient =1.12 from Fig. 40, page 44 d = the air gap in inches =0.35 Calculation of the leakage factor: In Fig. 178 h 8 = 1. in. L 8 =11.75 in. l^ = 3.8 in. W 8 = 7.0 in. h p = 5.25 in. L p =11.75 in. Z 3 = 5.2 in. W p = 4.25 in. and FIG. 178. The pole dimensions. 1X11.75 (" X 7 \ 1+ 2 J X3^/ 5.25X11.75 and e = the total leakage flux per pole = 40 = 11 AT g+t = 77 ATg+t - 18AT g + t = 146 ATg+t The value of AT g +t =5200 ampere-turns approximately, since the tooth densities in alternators are so low that the ampere-turns for the teeth can be neglected here, therefore e = 146 X 5200 = 760,000 3.8X10 6 + 760000 and the no-load leakage factor = g 8xlQg = 1.20 The full-load leakage factor, at zero power factor, 5200 + 0.35X6X12X96^ 200 = 1.3 DESIGN OF A REVOLVING FIELD SYSTEM 245 The magnetic areas: r = the pole -pitch (/> = the per cent, enclosure L g = the gross iron L n = the net iron A g = the apparent gap area C = the Carter coefficient At = minimum tooth area per pole = 11. 25 in. = 0.65 = 10.75 in. = 9.6 in. = 90 sq. in. = 1.12, already found. = 6X0.65X1.13X9.6. = 42.3 sq. in. No-load voltage Flux per pole Leakage factor 2400 3 . 8 X 10 6 1.2 2700 4.28X10 6 1.2 3000 4.75X10 6 1.2 Length Area Density AT. Density AT. Density AT. Air gap 0.35 90 1.12 42,500 5200 5850 6500 Teeth Pole Total amp.-turn 2.0 6.0 s per pole 42.3 90,000 47 . 5 j 96,000 50 325 101,000 108,000 100 960 112,000 120,000 220 2280 5575 6910 9000 To get the figures for the no-load saturation curve with the full -load leakage factor it is necessary to recalculate the excita- tion for the poles, using a leakage factor of 1.3; the air gap and teeth are not affected. Pole 6.0 47.5 105,000 770 119,000 2220 132,000 5200 Total amp. -turns per pole 6020 8170 11,920 From the former set of values the no-load saturation curve in Fig. 176 is plotted and from the latter set the dotted curve, which is the no-load saturation curve with the full-load leakage factor, is plotted. In the above calculation the core and revolving field ring have been neglected since the flux density is very low in the case of the core to keep down the temperature of the iron and in the case of the field ring to give the necessary mechanical strength and rigidity. The reactance per phase is found by the method shown on page 224, as follows: 246 ELECTRICAL MACHINE DESIGN = 5.3X3 from Fig. 163-16 3.2/ 1.75 0.25 1.13X1.12 -- <, -0.52X0.87+0.42X5.8-2.9 Reactance per phase -2X 7iX60 X12 2 X2 2 X 12(16 + (1.7 +2.9) X 12.25) 10- 8 = 1.88 ohms The voltage drop per phase = 1. 88 X 96 -180 volts The voltage drop at the terminals - 1 .73 X 180 310 volts since the winding is Y-connected 12.9 per cent, of normal voltage The demagnetizing ampere-turns per pole 0.35X6X12x96 -2420 and the corresponding field current .. , , , field-turns per pole 25.5 amperes. The full-load saturation curve at zero power factor and lagging current can now be drawn in and is shown in Fig. 176. The curves at unity power factor and at 85 per cent, power factor are also drawn in and the regulation as determined from these curves 9 per cent, at unity power factor = 21 per cent, at 85 per cent, power factor = 26 per cent, at zero power factor. CHAPTER XXIII LOSSES, EFFICIENCY AND HEATING Many of the losses in an alternator are similar to and are figured out in the same way as those in a D.-C. machine. / y, \ 3 184. Bearing Friction Loss = Q.Sldl(~ ) ] 2 watts where d = the bearing diameter in inches, l=the bearing length in inches, F&=the rubbing velocity of the bearing in feet per minute. 185. Brush Friction. This loss is small since there are few brushes and the rubbing velocity is low; y the loss = 1.25 A - watts where A is the total brush rubbing surface in square inches, V r is the rubbing velocity in feet per minute. 186. Windage Loss. This loss cannot be separated out from the bearing friction loss so that its value is not known and, except in the case of turbo generators, it can be neglected since it is comparatively small. 187. Iron or Core Losses. As in the case of the D.-C. machine these include the hysteresis and eddy current losses; additional core loss due to filing, to leakage flux in the yoke and end heads, and to non-uniform distribution of flux in the core; losses in the pole face. The total core loss is figured out by the use of the curves in Fig. 81, page 102, which curves are found to apply to alternators as well as to D.-C. machines. 188. Excitation Loss. The field excitation and therefore the field excitation loss vary with the power factor, as shown in Fig. 176. The loss = amperes in the field X voltage at the field terminals; for separately excited machines the rheostat is not considered as part of the machine. 247 248 ELECTRICAL MACHINE DESIGN 189. Armature Copper Loss. L b The resistance of one conductor = ohms M and the loss in one conductor = \* watts M where L& is the length of one conductor in inches, 7 c is the current in each conductor, M is the section of each conductor in cir. mils. The total armature copper loss = Z m flQ- 8 volts the resistance of this loop 1X2L C - -- ohms the eddy current in the loop _ effective e.m.f. resistance 250 ELECTRICAL MACHINE DESIGN 4.44 X l.7 X6/ X; 700 ' 8 " 0.003 = 29C. In such a case a large part of the copper loss will be conducted to and dissipated by the end connections, and in order that these may .. amp.cond.per inch remain cool the value of the ratio . ., must be err. mils per amp. taken lower than that given in Fig. 181, and the temperature rise on the end connections must be limited to about 30 C. at normal load in order that the copper in the center of the machine may not get too hot and char the insulation. CHAPTER XXIV PROCEDURE IN DESIGN 193. The Output Equation. E = 2.22 kZ(j> a f X 10~ 8 formula 25, page 190. and q 2.l2xZx(B g (fn:XL e )X- ^ "XlO" 8 taking k = 0.96 nZI c therefore nEI = the output in watts ,2.12X7T 2 X10- 8 v 12Q - XBrfLc r.p.m. gZV and ft' r _ volt amperes 5.7 X10 8 Hf^mT" ^B,^T The value of 5^ ; the apparent gap density, is limited by the permissible value of B t , the maximum stator tooth density which, as pointed out in Art. 191, page 252, is approximately 90,000 lines per square inch at 60 cycles 110,000 lines per square inch at 25. cycles for open slot machines. Now (f) a = B t and is therefore B g = B t X-, X^ A L/C The ratio y^ is approximately equal to 0.75 taking the vent J^c ducts and the insulation between the laminations into account. The ratio - varies with the slot pitch. Suppose, for example, 6 255 256 ELECTRICAL MACHINE DESIGN that in a given alternator the number of slots is halved; since the same total number of conductors is required in each case, the total space required for copper remains constant, but the space required for slot insulation is approximately proportional to the number of slots since its thickness is unchanged, so that when the number of slots is halved the slot may be less than twice the width of the original one; the ratio therefore increases as the slot pitch increases. The slot pitch is seldom made greater than 2.75 in. because the section of the copper in a coil for such a slot is large compared with the radiating surface of the coil and it becomes difficult to keep the windings cool. Figure 182, which shows the relation between - = and slot pitch found in practice for open slot machines, may be used in preliminary design. B g is found from the formula given above and is plotted against pole-pitch in Fig. 183, a reasonable value for the slot pitch being assumed. The value of B g for alternators is considerably less than that found for D.-C. machines because of the lower tooth density in the former type of machine due to the fact that its armature is stationary while that of the D.-C. machine is revolving. For a given output and speed, therefore, the value of D 2 a L c is greater for alternators than for D.-C. machines. The value of q is limited partly by heating but principally by the regulation expected. Suppose for example that for a given rating the value of q is increased, which can be done by increasing the number of conductors in the machine or decreasing the diame- ter. In the former case the armature reaction will be increased since it is proportional to the number of conductors per pole and the armature reactance will be increased since it is proportional to the square of the number of conductors per slot. In the latter case the frame length must increase as the diameter is decreased in order to carry the flux per pole and the slots must be made deeper in order to carry the larger number of ampere conductors on each inch of the periphery, both of which changes increase the armature reactance; the armature reaction, since it depends on the conductors per pole, being equal to 0.35 X cond. per pole X I c , is unchanged. PROCEDURE IN DESIGN 257 The value of q given in Fig. 184 may be used for a first approximation in preliminary design and will give reasonably good regulation if the ratio of field excitation at full-load and zero power factor to armature ampere-turns per pole be not less than three, and the pole density at no-load and normal voltage be about 95,000 lines per square inch. g 60x10-1 50 3 40 Hi a 5 30 20 10 Slot Slot Width in Inches p r r .^ CT 01 c 32 X X* ^ f.\ N V S ^ X* 1 ^ x" t\v. ^ >=* -- *^*^ ft 1 ot * - * ^~ + ,- x*" ^ 800 400 200 0.5 1.0 1.5 2.0 2.5 ff 3.0 Slot Pitch in Inches FIG. 182. 1 i C <.:h / or yvh / ^^ / x* 5 10 - 15 20 25 3( Pole Pitch in Inches FIG. 183. 2.0 51.5 1.0 20 40 60 80 100 A 200 400 600 800 1000 B 2000 4000 6000 8000 10000 C K.V. A. Output FIG. 184. \ \ \ X *-- . ~ ~ 4 8 12 16 20 24 Poles FIG. 185. Curves used in preliminary design. 194. The Relation between D a and L c . There is no simple method whereby D a 2 L c can be separated into its two components so as to give the best machine. In the case of the D.-C. machine the ratio between the magnetic and the electric loading was used in order to determine D a and L c and then the number of poles was chosen so as to give an economical shape of coil. The number of poles in an alternator is fixed by the speed and the frequency, and the diameter and length of the machine has to be chosen so as to give an economical shape of coil. If for 17 258 ELECTRICAL MACHINE DESIGN example the number of poles on a given diameter be increased, the pole-pitch will be reduced, the field coil will become more and more flattened out, and a point will finally be reached at which it would be more economical to increase the diameter and shorten the length of the machine than to keep the diameter constant. Pole -pitch 195. Effect of the Number of Poles on the Ratio - . Frame length Figure 186 shows part of two machines which are duplicates of one another so far as the pole unit is concerned; that is, they have B FIG. 186. Effect of the number of poles on the length of field coils. the same pole-pitch, air gap, armature ampere-turns per pole and field ampere-turns per pole; but the total number of poles is small in machine A and large in machine B. It may be seen that in the former machine there is not room for the field coils because of the large angle between the poles. In order to get the field coils on to the poles it is necessary to increase the diameter of the machine without increasing the radial length of the field coil, that is without increasing the armature ampere-turns per pole, on which this length principally depends, so that the same number of armature ampere-turns per pole must now be put on a larger pole-pitch and the value of q, the ampere conductors per inch, thereby reduced. Although the diameter of the machine is increased, the flux per pole must be kept constant otherwise the pole waist will increase; the pole arc will generally PROCEDURE IN DESIGN 259 be unchanged and the ratio p ?f n will decrease as the di- ameter is increased, and in four- and six-pole machines will have a value of about 0.6. The above difficulty, due to a small number of poles, is more apparent in machines of low than in those of high fre- quency, because in the former the output per pole is generally larger, for example a 400-k.v.a., 514-r.p.m., 60-cycle machine has 14 poles and an output of 28.5 k.v.a. per pole; a 400-k.v.a., 500-r.p.m., 25-cycle machine has 6 poles and an output of 67 k.v.a. per pole; a 6 pole, 60-cycle alternator with an output of 67 k.v.a. per pole would have a rating of 400 k.v.a. at 1200 r.p.m., which would be as difficult to build as the above 25-cycle machine but is such an unusual rating that the difficulty seldom occurs. The value of q in Fig. 184 applies to machines which have more than 10 poles; for machines with four poles this value should be reduced 30 per cent, for a first approximation, and for a machine with six poles should be reduced about 20 per cent. Figure 185 shows the value of the ratio ~~^ ~ -^ generally frame length ' found in revolving field machines when the diameter is not limited by peripheral velocity, and may be used in preliminary design; the reason for the increase in the ratio as the number of poles decreases has been pointed out above. 196. Procedure in Design. volt amperes 5.7X10 8 , DaLc= ~^mT" -^ formula 32, page 255 and frame length = a constant > found from Fig. 185, page 257, , pole-pitch therefore L c = a constant pXa constant , n 3 _volt amperes 5.7 Xl0 8 XpX a constant ~~r^m7~ *XB a XfXq from which D a may be found approximately since Eg can be found approximately from Fig. 183, q can be found from Fig. 184, is assumed to be =0.65 for a first approximation, 260 ELECTRICAL MACHINE DESIGN the constant = the ratio J- - T- rr from Fig. 185. frame length Tabulate three preliminary designs, one for a diameter 20 per cent, larger than that already found and the other 20 per cent. smaller. Find the probable total number of conductors - = - and LC assume that the winding to be used is single circuit, and Y connected if three-phase, so that I c the full-load line current. Find the number of slots; there should be at least two slots per pole, if possible, in order to get the advantages of the distrib- uted winding, see Art. 141, page 180, but the slot pitch should not exceed 2.75 in.; Art. 193, page 256. -,.,,, T , , probable total conductors Find the conductors per slot = r -- e i . : take number of slots the nearest number that will give a suitable winding. Find the corresponding total number of conductors. Find (/) a from the formula E = 2.22 kZ$ a f 10~ 8 formula 25, page 190. Find the actual frame length as follows: . a slot P ltch = total slots 5 divide this into s + t by the use of Fig. 182, page 257; the minimum tooth area required = - " , - r max. tooth density where the max. tooth density =90,000 lines per square inch for 60 cycles 110,000 lines per square inch for 25 cycles for open slot machines, and is 15 per cent, larger for machines with partially closed slots; the tooth area per pole = slots per pole XXtXL n , from which L n can be found L c =L g + (ihe center vent ducts), where these ducts are 0.5 in. wide and are spaced 3 in. apart. Find d, the air gap clearance, as follows: ATX3.2 " * Q PROCEDURE IN DESIGN 261 where AT g is taken as 1.5 (armature ampere-turns per pole) for a first approximation. The field is now designed roughly as explained in Art. 182, page 238, and the machine drawn out to scale, after which the saturation curves are calculated, drawn in, and the regulation determined. If the regulation is better or worse than that desired from the machine then the design must be changed as explained in Art. 183, page 241. Example. Determine approximately the dimensions of an alternator of the following rating: 400 k.v.a., 2400 volts, 3-phase, 60 cycle, 96 amperes, 600 r.p.m. The work is carried out in tabular form as follows: Apparent gap density, Amp. cond. per inch, Per cent, enclosure, Pole pitch B g =42,000, from Fig. 183. q =614, from Fig. 184. (j> =0.65 assumed. = 0.95, from Fig. 185. ,-, , ,, a constant -t rame length Poles, p =12 for 600 r.p.m. at 60 cycles. Armature diameter, D a =43 in., from formula 33, page 259. Take a larger and a smaller diameter so that Armature diameter, D a =43 in. Total conductors, probable, Z c =865 Pole-pitch, t=11.3in. Slots per pole =6 Total slots =72 Cond. per slot =12 Connection =Y Total conductors, actual, Z c =864 Flux per pole, a =3.8 X 10 6 Slot pitch, A =1.88 in. Slot width, s =0.75 in. Minimum tooth width, t =1.13 in. Tooth area per pole required =42.3 sq. in. Net axial length of iron, L n =9.6 in. Gross length, L g =10.6 in. Center vent ducts =3-05 in. Frame length, L c =12.10 in. Apparent gap density, B g =42,800 Armature AT. per pole =3450 A T g assumed =5200 8C =0.39 Field system: Maximum AT. per pole, AT max =10,400 Leakage factor, assumed Pole area required Axial length of pole, Pole waist, Depth of field coil, Mean turn, External periphery Exciter voltage Section of wire, = 1.2 =48 sq. in. L p =11.6 in. W p =4.25 in. df =0.75 in. MT=37 in. =39 in. = 120 M =38,500 -0.04X0.75 in. 36 in. 725 9.4 in. 72 10 Y 720 4.56 X10 6 1.57 in. 0.67 in. 0.9 in. 51 sq. in. 14.5 in. 16.1 in. 5-0.5 in. 18.6 in. 40,200 2880 4300 0.34 8,600 1.2 58 sq. in. 18 in. 3.4 in. 0.75 in. 47 in. 49 in. 120 40,500 0.04X0.8 in. 52 in. 1050 13.6 in. 6 72 14 Y 1008 3.25 X10 6 2.27 in. 0.85 in., Fig. 182 1.42 in. 36 sq. in. 6.5 in. 7.2 in. 2-0.5 in. 8.2 in. 44,800 4050 6100 0.44 12,200 1.2 41 sq. in. 7.7 in. 5.6 in. 0.85 in. 32 in. 34 in. 120 39,000 0.04X0.8 in. 262 ELECTRICAL MACHINE DESIGN Watts per square inch =6.0 5.5 , 6.5 page 239 Space factor, s/=0.8 0.8 0.8 Radial length of field coil, Lf =4.7 in. 4.0 in. '5.2 in. The three machines are now drawn in to scale as shown in Fig. 187. The 36-in. machine is expensive in core assembly while the 52-in. machine is expensive in inactive material, such as the material in the yoke. So far as operation is concerned there is little to choose be- tween the machines. The armature ampere-turns per pole is the same fraction of the field ampere-turns per pole in each case, the voltage drop due to armature reactance is also about the same for each design. In the 36-in. machine the air gap is small and the length L c is large which tend to make the reactance large, but there are only 10 conductors per slot, whereas in the 52-in. machine, while the air gap is larger and the frame length shorter, the number of conductors per slot is 14; the reactance is proportional to the square of the number of conductors per slot. The 36-in. machine is rather long for the diameter and would be difficult to ventilate properly, in fact it would probably re- quire fans. Assume that, after careful consideration of the weights of the three machines and of the probable cost of the labor, which latter quantity varies with the size of the factory and its organization, the 43-in. machine is chosen as the most satisfactory; it is now necessary to complete the design of this machine. Winding 96x864 Amp. oo nd. per men = ^- = 614 Amp. cond. per in. n . F ., =1.05 from Fig. 181 Cir. mils per amp. Cir. mils per amp. =600 Amp. per cond. at full load =96 < Section of conductor =58,000 cir. mils = 0.046 sq. in. 0.75 slot width 0.132 width of slot insulation, see page 205. 0.04 clearance between coil and core 0.578 availaible width for copper and insulation on conductor. Use strip copper 0.07 in. wide and arrange the conductors six wide in the slot, each conductor to be taped with half-lapped cotton tape 0.006 in. thick. PROCEDURE IN DESIGN 263 36 in. FIG. 187. Comparative designs for a 400 k.v.a., 60-cycle, 600 r.p.m. alternator. 264 ELECTRICAL MACHINE DESIGN section of cond. 0.046 Depth of conductor width of cond. 0.07 = 0.65 in. In order that there may be no trouble due to eddy current loss caused by the slot leakage flux, the conductor is divided into two strips each 0.325 in. deep. Slot depth is found as follows: 0.325 depth of each conductor 0.024 insulation thickness on each conductor 0.70 depth of two insulated conductors 0.162 depth of slot insulation on each coil 0.862 depth of each insulated coil 2 number of coils in depth of the slot 1.72 depth of coil space 0.20 thickness of stick in top of slot 2.0 depth of slot. Flux density in the core =45,000 assumed Core area =53 s is the same in each case since the slots are unchanged, (fit is the same in each case since the teeth and air gap are unchanged. The armature reactance drop is therefore proportional to (cond. per slot) 2 X current X (A + BL C ) or to (cond. per slot) (A + BL C ) or to - j - i where A and B are constants, L>c so that the longer the machine the lower is its reactance drop and the better the regulation, other things being unchanged. The pole leakage flux consists of flank leakage which is constant and pole-face leakage which is proportional to the frame length; <$> a , the flux per pole, is directly proportional to the frame length; the leakage factor =^ a ^ e = c where C, D and F are con- 9a fJLtc stants and so is smallest for the longest machine that is built on a given diameter. A machine cannot be lengthened indefinitely, however, because a point is finally reached at which it becomes impossible to cool the center of the core without a considerable modification in the type of construction and the addition of fans, and still further, as the length increases the pole section departs more and more from the square section. 199. Windings for Different Voltages. The armature of a 400-k.v.a., 2400-volt, 96-ampere, 3-phase, 60-cycle, 600-r.p.m. alternator is built as follows: Internal diameter, 43 in. Frame length, 12.25 in. Slots, number, 72 Slots, size, 0.75 in. X 2.0 in. Conductors per slot, number, 12 Conductors per slot, size, 2(0.07 in. X 0.325 in.) Connection, Y It is required to design armature windings for the following voltages : PROCEDURE IN DESIGN 267 600 volts, 3-phase, 60 cycles, 2400 volts, 2-phase, 60 cycles. To find the Conductors per Slot. E = 2.22kZ a flO-* = a constant X & X cond. per slot X phases cond. per slot . . .. = a constant X k X - r^ for a given frame and phases frequency. For the machine in question k = 0.966 for a 3-phase winding = 0.911 for a 2-phase winding volts per phase X phases and the constant = A; X cond. per slot 2400 X 3 1.73 Xd 0.966X12 = 360 For the 600-volt, 3-phase winding volts per phaseX phases cond. per slot = -f- A; X a constant 600X3 0.966X360 = 5.2, or say 5, if 600 is the voltage per phase, that is if the winding is A connected 600 1.73 and X3 0.966X360 f*r\(\ = 3.0 if Y^T^ is the voltage per phase, that is if 1.7o the winding is Y connected. The Y connected winding is the better of the two because with such a connection any third harmonic in the e.m.f. wave is elimi- nated, whereas in the case of a A connected winding the third harmonics cause a circulating current to flow in the closed circuit of the delta. Since the winding is double layer, the number of conductors per slot must be a multiple of two, so that the winding actually used will have six conductors per slot and will be connected two circuit. For the 2400-volt, 2-phase winding 268 ELECTRICAL MACHINE DESIGN volts per phaseX phases cond. per slot= -f- #Xa constant 2400X2 0.911X360 = 14.7 In order to use 15 conductors per slot it will be necessary, if the winding is double layer, to use 30 conductors per slot and connect the winding two circuit, and the size of each conductor will be small; it will be preferable to use 14 conductors per slot, for which number the flux density in the machine is 5 per cent, higher than for the original 2400-volt, 3-phase winding. To find the Size of Conductor. In order that the stator loss and stator heating be the same in each case it is necessary to keep the ,. amp. cond. per inch , . ratio -. -, - constant; the work is carried out in cir mils per amp. tabular form as follows: rt a g ft 8 1 "d & * d "5 if I <3 c 8 aS d O O C o c 1| * l Hi a N j-S O fl Bl < CO 400 2400 3 96 Y 96 12 2(0.07X0.325 in.) 614 600 400 600 3 384 YY 192 6 4(0.07X0.325 in.) 614 600 400 2400 2 83 1 circuit 83 14 2(0.055X0.325 in.) 620 550 It may be seen from the value of circular mils per ampere that the two-phase machine will get about 10 per cent, hotter than the three-phase machines because it is not possible to get sufficient copper into the slot for this rating. This trouble is inherent to the two-phase machine because, for a given frame, rating and terminal voltage cond. per slot 2 phase _ E t X 2 X 1 .73 X 0.966 cond. per slot 3 ph. Y.~ 1 0.911X^X3 current per cond. 2 phase_k.w. 1. current per cond. 3 ph.Y. 2E t k.w. = 1.22 1.16 that is to say, the number of conductors per slot for the two-phase rating is 22 per cent, greater than that for the three-phase rating, while the current per conductor is reduced only 16 per cent. 200. Example of a Machine with Field Coils of D. C. C. Wire. The following is a preliminary design for a 75-k.v.a.. 2400-volt, 3-phase, 18-ampere, 60-cycle, 1200-r.p.m. alternator. PROCEDURE IN DESIGN 269 Apparent gap density, B g = 42,000, from Fig. 183 Amp. cond. per inch, = 2.0X 10 6 Slot pitch, ^ = 1.83 Slot width, s = 0.75, from Fig. 182 Minimum tooth width, / = 1.08 Tooth area per pole required =22.2 sq. in. Net axial length of iron, L n = 5.3 in. Gross length, Z/ g = 5.9 in. Center vent ducts =1-0. 5 in. Frame length, L c = 6.4in. Apparent gap density, .60 = 43,600 Armature AT. per pole =2480 AT g assumed =3700 dC =0.27 in. Field system. Maximum AT per pole, AT ma x = 7500 Leakage factor assumed =1.2 Pole area =25.5 sq. in. Axial length of pole, Z/ p =6.0in. Pole waist, TF P = 4.5 in. Depth of field coil, d/ = 1.0 in., assumed Mean turn =25 in. External periphery =29 in. Exciter voltage =120 Section of field wire =9500 cir. mils. Use No. 11 square B. & S. gauge which has a section of 10,500 cir. mils. Watts per square inch =4.7, page 239. Space factor =0.86 Radial length of field coils, L/ = 3.25 in. The field coil as designed with a uniform thickness of 1 in. is shown dotted in Fig. 188, the actual shape of coil used is shown by heavy lines. 270 ELECTRICAL MACHINE DESIGN 201. Design of a 25 -cycle Alternator. Two designs are given below for an alternator of the following rating; 400 k. v. a. ; 2400 volts, 3 phase, 96 amperes, 25 cycle, 500 r.p.m. In the first design the value of ampere conductors per inch is taken from Fig. 184, in the second design a value 20 per 'cent, lower is used and the per cent, enclosure is also reduced. FIG. 188. Field system of a 75 k.v.a., 60-cycle, 1200 r.p.m. alternator. Apparent gap density, y Amp. cond. per inch, * g=614 Per cent, enclosure, ^ = 0.65 Pole pitch TV = a constant =1.6 Frame length Poles, p = 6 Armature .diameter, D a = 41 in. Probable total conductors, Z c = 820 Pole-pitch, T = 21.5in. Slots per pole =9 Total slots =54 Cond. per slot =15 Connection =Y Total conductors, Z c = 810 Flux per pole, a = 9.7 X 10 6 Slot pitch, X = 2.39 in. Slot width, s = 0.9in. Minimum tooth width, / = 1.49 in. Tooth area required per pole = 88 sq. in. Net axial length of iron, L n = 10 in. Gross iron, L g = ll in. Center vent ducts =3-0.5 in. Frame length, L c = 12.5 in. Apparent gap density, B g = 55, 000 Armature AT per pole =6500 A T g assumed =9750 C =0.57 52,000 510 0.6 1.6 6 44 in. 730 23 in. 9 54 13 Y 702 11.2X10 6 2.56 in. 0.9 in. 1.66 in. 102 sq. in. 11. 4 in. 12.7 in. 3-0.5 in. 14.2 in. 57,000 5600 8400 0.47 PROCEDURE IN DESIGN 271 Field system. Maximum AT. per pole Leakage factor assumed Pole area Axial length of pole, Pole waist, Depth of field coil, Mean turn External periphery Section of wire = 19,500 = 1.2 = 120 sq. in. = 12in. = 50 in. = 55 in. = 49,000. = 0.026in.X 1.5 in. 16,800 1.2 142 sq. in. 13.7 in. 11 in. 1.5 in. 55 in. 60 in. 46,000. 0.024 in. X 1.5 in. This wire is difficult to bend, therefore use a double layer winding and conductors of section 0.052 in. X 0.75 in. 0.048 in. X 0.75 in. Watts per square inch =4.6. 4.2, page 239 Space factor =0.86. 0.86. Radial depth of field coil =7.3 in. 6.1 in. Part of each machine is drawn to scale in Fig. 189 and it may be seen that the first design is an impossible one unless modified; the field coils may be made shorter but then the radiating surface will be reduced and the temperature rise of the field coils be too great or they may be made of d.c.c. wire and tapered off as shown in Fig. 188. FIG. 189. Field system of a 400 k.v.a., 25-cycle, 500 r.p.m. alternator. It must not be imagined that the designs which have been worked out in this chapter are the only possible ones that might have been used. If the regulation expected from the ma- chine differs from that obtained from the particular design which has been worked out then a radical change in that design will be necessary, but when one design has been worked out completely and its characteristics determined the changes necessary to meet certain requirements can readily be determined. CHAPTER XXV HIGH-SPEED ALTERNATORS 202. Alternators Built for an Overspeed. A typical example of such a machine is an alternator which is direct connected to a water-wheel. The peripheral velocity of a water-wheel is less than the velocity of the operating water; if the load on such a machine be suddenly removed, and the governor does not operate rapidly enough, then the machine will accelerate until it runs with a peripheral velocity which is approximately equal to the velocity of the water and is from 60 to 100 per cent, above normal, de- pending on the type of wheel used. An alternator which is direct connected to a water-wheel must have a diameter small enough to allow the machine to run at the above overspeed without the stresses due to centrifugal force becoming dangerous. When this diameter has been reached, the output for a given speed can be increased only by increasing the length of the machine, and after a certain length has been reached it becomes impossible to keep the center of the machine cool without the use of special methods of ventilation. Example. Determine approximately the dimensions of an alternator of the following rating : 2750 k.v.a., 2400 volts, three phase, 660 amperes, 60 cycles, 600 r.p.m.; the machine has to run at an overspeed of 75 per cent. If the design were carried out in the usual way then the following would be the result. Apparent gap density, = 43,000. Amp. cond. per inch, q = 72Q. Per cent, enclosure, ^=0.7. Pole-pitch T- =a constant =0.95. Frame length Poles, p = 12. Armature diameter, D a = 76 in. With this diameter the peripheral velocity at 600 r.p.m. would be 12,000 ft. per minute and the peripheral velocity at 272 HIGH SPEED ALTERNATORS 273 the overspeed would be 21,000 ft. per minute. At such a speed the stresses due to centrifugal force are so large that it is difficult to build a safe rotor. With the type of construction shown in Fig. 190, a safe and comparatively cheap machine can be built with a peripheral velocity of 17,500 ft. per minute, which corresponds to a pe- ripheral velocity of 10,000 ft. per minute under normal running conditions, and a maximum diameter of 64 in. for the machine in question. The design can now be continued as follows: Armature diameter, D a = 64in. Total conductors (probable) Z c = 220. Pole-pitch, T = 16.8 in. Slots per pole = 6. Total slots = 72. Conductors per slot =3.0; use 6 cond. per slot and connect the winding two circuit Y. Total conductors (actual), Z c = 216. Flux per pole, < a = 15.2 X 10 6 . Slot pitch, A = 2.8 in. Slot width, s = 0.95 in. Tooth width, / = 1.85 in. Tooth area required per pole =169 sq. in. Net axial length of iron, Z/ n = 21.7in. Gross length of iron, L g = 24.25 in. Center vent ducts =9-0.5 in. Frame length, L c = 28,75 in. The remainder of the design is carried out in the usual way and the machine is then drawn to scale as shown in Fig. 190, which shows the kind of ventilation required to keep the center of the machine cool. Fans are placed at the ends of the rotor to create an air pressure and so force air out across the back of the punchings and also through the vent ducts. Coil retainers are put at A to prevent the rotor coils from bulging out due to centrifugal force. 203. Turbo Alternators. Alternators which are direct con- nected to steam tubines run at a high speed and have therefore few poles, even for large ratings. It was pointed out in Art. 195, page 258, that when the number of poles is small it becomes difficult to find space for the necessary field copper, but that this difficulty could be overcome by increasing the diameter of the machine and lowering the value of q, the ampere conductors per inch. 18 274 ELECTRICAL MACHINE DESIGN In the case of the turbo alternator the diameter cannot be increased beyond the value at which the stresses in the machine due to centrifiugal force reach their safe limit, and some other method of solving the difficulty must be found. The number of ampere-turns per pole on the field may be reduced below that desired, without changing the armature design, but this, as pointed out in Art. 176, page 229, will cause the regulation of the machine to be poor. FIG. 190. Outline of a 2750 k.v.a., 600 r.p.m., 60-cycle, water wheel driven alternator, to run at 75 per cent, overspeed. The number of ampere-turns per pole may be reduced below the value desired, on both field and armature; then the regulation may be good, but, since the number of conductors is reduced, the flux per pole will be increased for the same rating, the machine must therefore be lengthened to keep down the flux density and so will be expensive. The number of ampere-turns per pole on both armature and field may be left as desired and the field coils, allowed to run hot; then the regulation may be good and the machine not too expensive, but it will be necessary to use materials such as mica and asbestos for the field insulation so that it will not deteriorate due to the high temperature. With such insulation it is usual to design the field coils for a temperature rise by resistance of 100 C. at the maximum field excitation; this corresponds to an increase in resistance of about 40 per cent. HIGH SPEED ALTERNATORS 275 204. Rotor Construction for Turbo Alternators. Due to the high peripheral velocities required for turbo alternators the centrifugal force acting on a body at the rotor surface of such a machine is very large, for example, a weight of 1 Ib. revolving at 1800 r.p.m. with a peripheral velocity of 20,000 ft. per minute is acted on by a centrifugal force of 2000 Ib. It is, therefore, necessary to adopt a strong type of construction; one which can be well balanced and which will stay in good balance indefi- nitely; that is, the rotor windings must be rigidly held so that they cannot move. The type of construction shown in Fig. 191 fulfills the above conditions and has also the additional advan- tage that since there are no projections on the rotor surface the windage loss and the noise due to stirring up of the air are a minimum. 205. Stresses in Turbo Rotors. The electrical and mechanical design of a turbo rotor must be carried out together, because the space available for field copper cannot be determined until the section of steel below the rotor coils, required for mechanical strength, has been fixed. The most important of the stresses in the type of rotor shown in Fig. 191 are determined approximately as follows: Stress at the Bottom of a Rotor Tooth. Assume that one tooth carries the centrifugal force due to its own weight and to that of the contents of one slot, and also that the total weight of copper, insulation and wedge in a slot is the same as that of an equal volume of steel. Consider one inch in axial length of the rotor, then in Fig. 192, where all the dimensions are in inches, dw = 2xr ^^.XdrXQ.28 Ib. = weight of the cross-hatched piece oDU v = 12 x 60~ =tne P er iP neral velocity of this piece; , ., dwXv 2 Xl2 the centrifugal force due to dw=-~ 9 X r the total centrifugal force carried by a rotor tooth 21.5X10 276 ELECTRICAL MACHINE DESIGN HIGH SPEED ALTERNATORS 277 centrifugal force the stress at the bottom of a rotor tooth = (r^-r^r.p.m. 2 t (34) Stress in the Disc. The centrifugal force of the section of the rotor enclosed in i a (r^ r^r.p.m. 2 8 the angle /? = 2L V X iV ~ lb " the vertical component of this force ''.p.m.^ 21.5X10" Part of Wedse FIG. 192. the total vertical component due to half the rotor e average value of sin 21 5X10 6 1.9X10 5 / /v 3 ^_ > A 3"\ ^ />^ -oo^ 2 the stress in the section d r l (35) 3.8Xd r Xl0 5 Stress in the Wedge. The total force acting upward on the wedge is the centrifugal force of the contents of the slot J = sXdrX0.3X .p.m.V 60 / X 12 gxr 278 ELECTRICAL MACHINE DESIGN = (r 1 2 -r 2 2 )XsXr.p.m 2 2.3 XlO 5 = P p the stress at section ab due to shear = - ^ =S the stress at point 6 dud to bending = -r- p = B ry I r>2 the maximum stress in the wedge = -^ + \-j- + *S 2 206. Diameter of the Shaft. Every shaft deflects due to the weight which it carries so that as it revolves it is bent to and fro once in a revolution. If the speed at which the shaft revolves is such that the frequency of this bending is the same as the natural frequency of vibration of the shaft laterally between its bearings then the equilibrium becomes unstable, the vibration excessive, and the shaft liable to break unless very stiff. The speed at which this takes place is called the critical speed and should not be within 20 per cent, of the actual running speed. VP T where E = Youngs modulus for the shaft material 7 = the moment of inertia of the shaft section about a diameter = ^rd s 4 DTC weight of rotor M = the mass of the revolving part = 2L = the distance between the bearings, see Fig. 191 Hhe const ant = 75 for turbo rotors if inch and Ib. units are used / 28 X 10 6 therefore the critical speed = 100 Xd s 2 \- ' . ,. ^ (36) ^ rotor weight XL 3 If, instead of vibrating as a whole, the shaft vibrates in two halves with a node in the middle, then the frequency of this harmonic is got by substituting for L in the above equation the value Z//2 and is equal to = the fundamental frequency X2 3 ; 2 = 2.8 times the fundamental frequency. It is found in practice that this harmonic has a value which varies from about 2.4 to 2.6 times the fundamental frequency. The deflection of the shaft is generally limited to 5 per cent. 1 Behrend, Elect. Rev., N. Y., 1904, page 375. HIGH SPEED ALTERNATORS 279 of the air-gap clearance so that 'there shall not be any trouble due to magnetic unbalancing, therefore TFv deflection-- ~~ = 0.05d inches where TF = the weight of the rotor + the unbalanced magnetic pull inlb.; see Art. 346. The stress in the shaft is determined as follows: WL. Mb, the bending moment at the center of the shaft = ^pinch Ib. z/ watts input 33000 Mt, the twisting moment = -- ,_., Xx Xl2 74o 2;rr.p.m. watts input r . , .. -X 85 inch Ib. r.p.nr i x u ,r M e , the equivalent bending moment = = stress Xd s 3 (37) Oa 207. Heating of Turbo Rotors. The assumption made in the following discussion is that all the heat generated in the part abed of the rotor, Fig. 191, is dissipated from the surface nD r l, so that each part of the rotor gets rid of its own heat and there is no conduction axially along the winding. The difference in temperature between the rotor copper and the air which enters the machine the difference in temperature from copper to iron + the difference in temperature between the iron and the air at the rotor surface + the difference in temperature between the air at the rotor surface and that entering the machine, which value may be taken as 15 C. It was shown in Art. 94, page 109, that in any slot the difference in temperature between the copper and the iron _amp. cond. per slot thickness of insulation 1 cir. mils per amp. 2d + s 0.003 amp. cond. per pole X 33 1 X slots per poleX cir mils per amp. (2d) taking the thickness of slot insulation and the slot clearance to be 0.1 in. and neglecting s for the case of strip copper laid flat in the slot, because the heat will not travel down through the layers of insulation. 280 ELECTRICAL MACHINE DESIGN The difference in temperature between the rotor surface and the air surrounding it is found as follows : The resistance of a conductor of M cir. mils section, I in. long =s ohm - II 2 The loss in this conductor =^- watts. M The total loss in section abcd = ^r- cond. per slot X slots per amp. cond. per pole poleXpoles. = ^- -^ -XpXl cir. mils per amp. The watts per square inch of radiating surface _amp. cond. per pole pXl cir. mils per amp. xD r l _ amp. cond. per pole 1 cir. mils per amp. r ' The temperature rise of this surface above that of the air which surrounds it is 10 C. per watt per square inch when the peripheral velocity is 20,000 ft. per minute. This is a lower value than that which would have been obtained by the use of the curves in Fig. 177, page 239, but these curves were based on the results obtained from tests on definite pole machines which stir up the air much better than does the cylindrical type of rotor, and further, the radiating surface was assumed to be the external surface of the coils, whereas it should include the surface of the poles and field ring to be on the same basis as the above figure for cylindrical rotors. The temperature rise of the rotor surface above that of the surrounding air is therefore _ amp. cond. per pole 10 cir. mils per amp. pole-pitch* The temperature rise of the rotor copper above that of the air entering the power-house in C _ amp. cond. per pole/ 10 33 ^ i * cir. mils per amp. ypole-pitch slots per pole (2d)/ and for a temperature rise of 100 C. cir. mils per amp. = amp. cond. per pole/ 10 33 \ ,, 85 ~\ pole-pitch + slots per pole (2d))" ( ' HIGH SPEED ALTERNATORS 281 208. Heating of Turbo Stators. For its output, the radiating surface of a turbo alternator is generally small, and it is advisable to cool such machines by forced ventilation. At present most turbos are self-contained and have fans attached to the rotor to move the necessary volume of air; these fans are very ineffi- cient, and, in passing through them, the air is heated and raised in temperature from 5 to 10 C. In the machine shown in Fig. 191 the air is supplied by an external fan and is filtered before it enters the generator. If, in a machine which is cooled by forced ventilation, ti= the temperature of the air at the inlet in deg. C., =the average temperature of the air at the outlet in deg. C., then each pound of air passing through the machine per minute takes with it 0.238( tj) Ib. calories per minute or 7.5( ti) watts and each cubic foot of air per minute takes 0.5360 -^) watts since the specific heat of air at constant pressure = 0.238 and the volume of 1 Ib. of air is approximately 14 cu. ft. If 100 cu. ft. of air per minute are supplied for each kilowatt loss in the machine then the average rise in temperature of the air will be 19 C. When air is blown across the surface of an iron core at V ft per minute the watts dissipated per square inch for 1 C rise of the surface = 0.0245(1 +0.00127 V). It is not generally advisable to use velocities higher than 6000 ft. per minute, because for higher velocities the air friction loss is large and the air is heated up due to this loss. For this air velocity the watts per square inch for 1 C. rise = 0.21. The watts per square inch of vent duct surface = watts per cubic inchX^, Fig. 82, page 104, where .XT = half the distance between vent ducts. For 2-in. blocks of iron, a velocity of 6000 ft. per minute and a difference in temperature between the iron and the air of 10 C. watts per cubic inch =0.21 X 10 = 2.1 and the watts per pound = 7. 5 which, as may be seen from Fig. 81, page 102, corresponds to a value of flux density of 282 ELECTRICAL MACHINE DESIGN 75,000 lines per square inch at 60 cycles and 120,000 lines per square inch at 25 cycles. As a matter of fact the iron loss in turbo generators is about 0.7 times the value found from the curves in Fig. 81 because the bulk of this loss is in the core behind the teeth and is therefore not affected by filing of the slots; the pole face loss in a turbo generator is also small because the air gap is long and so prevents tufting of the flux. In a long machine like a turbo generator most of the heat due to stator copper loss has to be conducted through the slot in- sulation and dissipated from the sides of the vent ducts, and this counteracts the effect of the reduced core loss so far as core heating is concerned. For a new machine the following values of flux density should not be exceeded unless there is considerable information obtained from tests on other machines which would justify the use of higher values. Maximum tooth Maximum core Frequency density, lines per density, lines per square inch square inch 25 cycles 120,000 85,000 60 cycles 100,000 65,000 for ordinary iron 0.014 in. thick. 209. Short-circuits. When an alternator running at normal speed is short-circuited and the field excitation gradually increased, the current which flows for any field excitation can be found from a short-circuit curve such as that in Fig. 167, page 225, and at the excitation for normal voltage and no-load the armature current on short-circuit will seldom exceed three times full-load current. The terminal voltage and the power factor are both zero on short-circuit, and the voltage drop, as shown in diagram A, Fig. 193, is made up of the drop E E g due to armature reaction, and of the armature reactance drop IX. When an alternator, running at normal speed, no-load and excited for normal voltage, is suddenly short-circuited, the arma- ture current increases and tends to demagnetize the poles. Now the flux in the poles cannot change suddenly because the poles are surrounded by the field coils, which are short-circuited through the exciter, so that any decrease in the flux in the poles causes a current to flow round the field coils in such a direction as to HIGH SPEED ALTERNATORS 283 maintain the flux. The armature reaction is therefore not instan- taneous in action and at the first instant after the short-circuit the current in the armature is limited only by the armature reactance. The operation of an alternator on a sudden short-circuit is shown in diagram B, Fig. 193. The maximum value of the current depends on the value of the voltage at the instant of the short-circuit; in Fig. 194, curve 1 gives the value of the generated e.m.f. at any instant, and curve 2 the value of the reactance voltage at any instant during the first few cycles after the short-circuit; the terminal voltage is zero, the armature reaction is dampened out by the field winding, and the reactance voltage is equal and opposite to the generated e.m.f. E< Y/^T A 'IX B FIG. 193. Vector diagram for an alternator on short circuit. The reactance voltage is produced by the change in the short- circuit current and, according to Lenz's law, acts in such a direction as to oppose this change. If then, as in diagram A, Fig. 194, the short-circuit takes place at the instant a, when the generated voltage is a maximum, then between a and b the re- actance voltage is negative and must therefore be opposing a growth of current while between 6 and c the reactance voltage is positive and must be opposing a decay of current. At the instant of short-circuit the current is zero, and curve 3 is the current curve which meets these conditions. If, as in diagram B, Fig. 194, the short-circuit takes place at the instant /, when the generated voltage is zero, then between / and g the reactance voltage is positive and must therefore be opposing a decay of current while between g and h the reactance 284 ELECTRICAL MACHINE DESIGN voltage is negative and must be opposing a growth of current. At the instant of short-circuit the current is zero and curve 3 is that current curve which meets these conditions. Neglecting the leakage reactance of the rotor, the current in the case represented by diagram A ; Fig. 194, has an effective FIG. 194. Effect on the value of the current of the point of the e.m.f. wave at which the short circuit occurs. generated voltage per phase value = , , while in the case repre- reactance per phase sented by diagram B the maximum current is twice as large. 210. Probable Value of the Current on an Instantaneous Short- circuit.^ It was shown in the last article that the effective current under the most favorable conditions generated voltage per phase = --, and therefore reactance per phase HIGH SPEED ALTERNATORS 285 current on instantaneous short-circuit _ generated voltage full-load current reactance voltage* The generated voltage per phase = 2.22 X&XZ0 a /10- 8 formula 25, page 190 = 2.12(6cp) X(B^rL c )/10- 8 taking k = 0.96; the reactance voltage per phase = 2nfb 2 c 2 p[ s +(i>t)L c ]lO- 8 Xl for a chain winding; formula 28, page 223. = 2rfb 2 c 2 p - + (0 s + ia Ct = 3.2 ^ for machines with cylindrical rotors, the type generally used for turbo generators. In order that the regulation of the machine may have a reasonable value, d, the air-gap, is fixed by the value of the armature ampere-turns per pole and is approximately proportional to the pole-pitch, therefore t is approximately inversely propor- tional to the pole-pitch. , ,. reactance voltage 3q [(f) e L c s +t] f u The ratio- =%-^r r V + -^ for a chain generated voltage B g ((>[nL c n winding = -=-^- %- + for a double layer winding, B g \2nL c n \ s and (f> t are plotted in Fig. 195 for average machines which have not less than two slots per phase per pole 286 ELECTRICAL MACHINE DESIGN nor a larger slot pitch than 2.75 in., and for machines with open slots and laminated rotors. Example. Determine approximately the per cent, reactance drop at full-load in the following machine: Normal output in k.v.a 6250 Normal voltage at terminals 2400 Number of phases 3 Current per phase 1500 R.p.m 1800 Frequency 60 cycle Internal diameter of armature 45 in Pole-pitch 35.5 in. Frame length 51 in. Average gap density 30,000 lines per square inch Per cent, enclosure 1.0 Ampere conductors per inch 635 Winding Double layer, Y-connected 10 20 30 Pole Eitch in Inches Definite Poles Cylindrical Rotors FIG. 195. Values of the leakage fluxes. 40 3X635/ 17 = 30, 000 Reactance voltage Generated voltage When a solid pole face is used, as in most turbo alternators with cylindrical rotors, the value of

m = + (f> e and this remains constant during the first few cycles after an instantaneous short-circuit. In order that (f> m remain constant a current must flow in the rotor winding in such a direction as to oppose HIGH SPEED ALTERNATORS 287 the demagnetizing effect of the armature reaction. This current is large, so that the m.m.f. between the poles and, therefore, the leakage flux (f> e are much larger immediately after a sudden short-circuit than at no-load. If (j) eo =ihQ pole leakage flux at no-load and (f> es =the pole leakage flux immediately after a short-circuit, then the generated voltage in the machine, which is produced by the flux a , is less immediately after a short-circuit than it was immediately before in the ratio ^ ~1 and this tends m s +<< the term - . n Use a laminated rotor if possible. Use a cylindrical rotor rather than one of the definite pole type, because of the larger value of (f> t , as may be seen from Fig. 195. All the above changes are made to increase the reactance of the machine and, therefore, tend to make the regulation poor. The value of the instantaneous short-circuit current can be reduced by making the pole leakage factor large and this will not affect the regulation seriously if the pole pieces are unsaturated at normal voltage. 211. Supports for Stator End Connections. The large current due to an instantaneous short-circuit takes several seconds to get down to the value which it would have on a gradual short- circuit, and during this time the force of attraction between adjacent conductors of the same phase is very large and tends 288 ELECTRICAL MACHINE DESIGN to bunch the end connections of each phase together. The force between the groups of end connections of adjacent phases is also very large and, when the currents in these phases are in opposite directions, this force tends to separate the phase groups of end connections. To prevent any movement of the coils due to this effect it is necessary to brace them thoroughly in some such way as that shown in Fig. 191. 212. The Gap Density. For the type of rotor shown in Fig. 191 the distribution of flux in the air gap is given by the heavy line curve in Fig. 196; if two more slots per pole are added, as !. L -< 8 v FIG. 196. Flux distribution in the air gap of a turbo alternator. shown dotted in Fig. 196, the flux will be increased by the amount enclosed by the dotted curve and, for a considerable increase in rotor copper and rotor loss, only a small increase in the flux per pole will be obtained. The angle ft is therefore seldom made less than 30 electrical degrees and for this value the maximum gap density = the average gap density X 1.5 approximately. The maximum gap density depends on the peimissible value of the maximum tooth density since - *-* g max J - J tmax^j ) } the blocks of iron in the core are about 2 in. thick, the vent ducts 0.625 in. wide and the stacking factor = 0.9, therefore ^ = 0.68; HIGH SPEED ALTERNATORS 289 an average value for - = 1.5 for turbos, since the slot pitch is 6 generally large and B t max = 100,000 lines per square inch for 60 cycles = 120,000 lines per square inch for 25 cycles therefore Bg m ax= 45,000 lines per square inch for 60 cycles = 54,000 lines per square inch for 25 cycles 213. The Demagnetizing Ampere -turns per Pole at Zero Power Factor. The distribution of the m.m.f. of armature reaction at two different instants is shown in Fig. 160, page 214, for a machine with six slots per pole and b conductors per slot. In the case of a definite pole machine the portion of this diagram which is cross hatched is effective in demagnetizing the poles, whereas in the type of machine with a cylindrical rotor the whole armature m.m.f. is effective and for this case A T av X 6 A = area of diagram A = area of diagram B .8666/ m X2/1 = 6.9667 OT ^ the average value from diagrams A and B therefore AT av = l.WbI m = 1.646/ c where I c is the effective current per conductor /slots per pole N = 1.6467 C ,- = 0.275 Xcond. per poleX/ c The maximum m.m.f. of the field windings is that at the center of the poles and is equal to the ampere-turns per pole. The average m.m.f. when /?, Fig. 196, is 30 electrical degrees maximum m.m.f. 1 K - approximately i.o _the ampere-turns per pole 1.5 19 290 ELECTRICAL MACHINE DESIGN therefore the ampere turns per pole required on the field to overcome the demagnetizing effect of the armature = 1. 5 X 0.275 X cond. per poleX/ c = 0.41 X cond. per pole X I c (40) 214. Relation between the Ampere -turns per pole on Field and Armature. For definite pole machines the value of the ampere- turns for the gap on no-load and normal voltage = AT g = 1,5 times the armature ampere-turns per pole for a first approximation, see Art. 183, page 240. It may be seen by a comparison of formulae 27 and 40, pages 215 and 290, that, for a machine with a cylindrical rotor, a larger number of field ampere-turns are required to overcome the demagnetizing effect of the armature than for a definite pole machine; and further, it will be seen from the example in Art. 215 that the air gap of a turbo alternator is very long and the number of ampere-turns used up in sending the flux through the poles is, therefore, very small compared with that required for the gap, so that the saturation curve does not bend over and the advantage of a saturated pole, pointed out in Art. 175, page 228, cannot readily be obtained. For these two reasons it is necessary, in order to get reasonably good regulation from a turbo alternator, to make A T g = 1.75 (armature ampere-turns per pole at full-load) for a first approximation, a value which is about 25 per cent, larger than for a definite pole machine. 215. Procedure in Turbo Design. The method whereby the preliminary design of a turbo alternator is worked out can best be seen from the following example. Work out the preliminary design for a 5000 kw. 2400 volt, three-phase, 1500 ampere, 60 cycle, 1800 r.p.m. machine, to operate at 80 per cent, power factor. Maximum peripheral velocity, 20,000 ft. per minute assumed Rotor diameter, Z) r = 42.5in. Rotor pole pitch, r = 33.5 in. Amp. cond. per inch, q = 600, see Art. 195, page 258 Armature amp. -turn per pole, = = 10,000 pr . 2 AT g =1.75X1 0,000 for a first approxi- mation = 17,500 HIGH SPEED ALTERNATORS 291 Probable value of Cd C may be taken Internal diameter of stator, Total conductors (probable) , Pole pitch, Slots per pole Total slots Conductors per slot Total conductors (actual), Flux per pole, Slot pitch, Slot width, Tooth width, Tooth area required per pole Net length of iron in the core, Gross length of iron in the core, Center vent ducts Frame length, Average gap density, = 3.2xAT g t>g max = 1.25. in. . =1.0 for such a large air gap Z> =45 in. Z c = qX * Da = 57 Ic r = 35.5. in. =15 = 60 = 1 Z c = 60 < a = 54.5X 10 6 A =2.36 in. s=0.8in. / = 1.56 in. av = 820sq. in. 1.5 L n = 35 in. L^ = 39 in. = 19-0.625 in. Lc = 51 in. a v=^ =30,000 lines per square inch. The machine is now drawn approximately to scale and the distance between bearings determined; this distance =140 in. Rotor Design. = ^X42.5 2 X5lX0.2s) 1.5 = 30,000 lb.; the multiplier 1.5 is used to take ac- count of end connections, coil retainers. etc. =16 in. the stress in the shaft =2600 lb. per sq. in. and the shaft deflection =0 018 in. neglecting the unbalanced magnetic pull. Probable rotor weight Shaft diameter and Depth below slots = d . . . x , Rotor slot depth VOQ y 1 A6 30,000 X7Q 3 formula 36 > 278 = 1340 r.p.m. = 2.4 X 1340 = 3240 r.p.m. (21 25 3 _ 8 3 }1800 2 = 3. 8x i 4; ooo x iQ^ formula 35, page 277 = 5.5 in. (42.5 -16-11) = 292 ELECTRICAL MACHINE DESIGN Probable depth of wedge Available slot depth Armature amp. -turns per pole Max. field amp.-turns per pole Probable mean turn Section of rotor conductor Cir mils per ampere Maximum exciting current Ampere conductors per slot Conductors per slot = 7.75 in. = 1.25; should be checked after the slot width has been determined = 6.5 in. = 11,250 = 3.25X11,250 assumed = 37,000 = 156 in. from scale drawing 37,000X156 formula 7, page 65 for 30 120 volt excitation = 193,000; this value should be increased 10 per cent, because of the high tem- perature at which the field will be run, therefore, = 210,000 cir mils. 2X37,000 / 10. 33 \ formula 38, 85 \33.5 + 6X13/ page 280 = 640 with 6 slots per pole. A smaller conductor could be used if the rotor were made with 8 slots per pole and the two rotors should be worked out together to determine which will be the cheaper, total cir mil section of conductor 210,000 640 = 328 amp. 37,000X2 6 = 12,300 12,300 ~ 328 amp. = 38 cir mil per ampere The winding to be of strip copper laid flat in the slot; the available depth for copper and insulation = 6. 5, of which 0.2 is used for slot insulation; the available depth for 38 conductors and the insulation between them = 6. 3 in. = 0.15, and of insulation 0.015 = 210,000 cir mils. = 0.165 sq. in. = 1.1 in. = 1.3 in., allowing 0.1 in. per side for in sulation and clearance = / where (21.25 3 -13.5 3 )1800 2 X 360 t + s 21.5X10 6 X2^X13.5 " X t formula 34, page 277 = 0.65 in. Thickness of conductor Section of conductor Width of conductor Width of slot Width of tooth at the root Tooth stress 14,000 From which t HIGH SPEED ALTERNATORS 293 Stator Core Design. Conductors per slot = 1 Ampere cond. per slot =1500 Ampere cond. per inch =630 Cir mils per ampere =800; assumed for a first approximation Cir mils per conductor =800X 1500 = 1,200,000 Section of conductor =0.95 sq. in. = 0.55 in. X 1.75 in. = 20 strips each = 0.11 in. X 0.45 in. ; 5 wide and 4 deep in the slot. Slot depth is found as follows . 45 depth of each strip 0.024 insulation on each strip 1 . 9 depth of conductors and conductor insulation 0. 16 depth of slot insulation . 25 depth of wedge 2 . 3 depth of slot. Temperature difference copper to iron amp. cond. per slot insul. thickness 1 .. = cir. mils per amp. 2d + s ~ O003 f rmula 18 ' page U1 _. 1500 1(0.8-0.55) ~ 800 > ~~ 574 =15 C. This figure is probably pessimistic because it neglects the heat that is conducted axially along the copper and dissipated at the end connections, it also neglects the effect of the vent ducts; it does indicate, however, that the section of copper chosen is not too large because, according to the assumptions made in this chapter, the temperature rise of the air = 19 C. for 100 cu. ft. per minute per kilowatt loss, the temperature difference from stator iron to air in ducts = 10 C. with a core density of 65,000 lines per square inch, the temperature difference from copper to iron = 15 C. If lower temperatures are desired it is necessary to use a larger supply of air, lower core densities, or lower copper densities. rni_ j xi_ e u i_- j xu i j. flux per pole The depth of iron behind the slots = = nr^ ~^r- 2 X 65000 X net iron 54000000 "2X65000X35 = 12 in. Volume of Air required. It is difficult to predetermine the losses in a turbo with any degree of accuracy; the PR loss in 294 ELECTRICAL MACHINE DESIGN the field and armature can be determined accurately, but the iron loss, the windage loss due to air friction in the ducts, and the load loss which is large in turbo generators, cannot be determined accurately without considerable data on machines previously built and tested. For preliminary design-work Fig. 208, page 318, may be used, which shows that the effi- ciency of a 5000-kw. turbo at 1800 r.p.m. is approximately 95 per cent., neglecting the bearing loss, which is charged to the turbine; therefore the loss in the machine =250 kw. and the volume of air required =25,000 cu. ft. per minute. The area of the vent duct section = number of ducts X duct width X core depth = 19 X 0.5 X 12 square inches = 0.8 sq. ft. the vent segments are 0.625 in. thick but the available space for air is only 0.5 in. As shown in Fig. 191, there are ten air paths through the machine, so that the air velocity 25000 10X0.8 = 3200 ft. per minute; it will be necessary to' use a higher air velocity than 3200 ft. per minute in order to cool the core; this may be obtained by cutting down the number of paths through the machine without changing the total volume of air but may be better obtained by increasing the volume of air passing through the machine. 216. Limitations in Design due to Low Voltage. The larger the flux per pole in a machine the smaller the number of conductors required for a given voltage since E = a constant X Z X < a X/ and for large low-voltage machines it is sometimes difficult to find a suitable winding without considerable change in the machine; for example, in the turbo designed in the last article: For 2400 volts, three phase, the winding has 60 conductors, 60 slots and 1 conductor per slot Y-connected. For 600 volts, three phase, the same punching may be used with 1 conductor per slot connected YYYY. HIGH SPEED ALTERNATORS 295 For 500 volts, three phase, a total of 12.5 conductors are required in series and a new punching is needed with 48 slots, 1 conductor per slot connected YYYY. 217. Single-phase Turbo Generators. In the design of this type of machine a new difficulty presents itself. It was shown in Art 177, page 231, that the armature reaction in a single-phase alternator is pulsating and causes a double frequency pulsation of flux in the poles, and, therefore, a large eddy current and hysteresis loss therein. These pulsations are dampened out somewhat by the eddy currents, but an eddy-current path in iron is a high-resistance path and the eddy-current loss is, therefore, large. In order to dampen out the flux pulsations with a minimum loss it has been found necessary to surround the rotor with a squirrel- cage winding of copper in which eddy currents will be induced tending to wipe out the pulsating effect of armature reaction, and since the resistance of this squirrel cage can be made low its loss can be small. A suitable squirrel cage may be made by using copper for the slot wedges shown in Fig. 192, dove- tailing similar wedges into the pole face, and connecting them all together at the ends by copper rings. The following figures 1 show how necessary these dampers are: A 1000-k.v.a., 2-pole, 25-cycle turbo alternator was tested three- phase; one phase was then opened and the machine run with two phases in series, which gave a single-phase winding with 2/3 of the total conductors, see Fig. 124, page 177. The same flux per pole and the same current per conductor were used in each case with the following result: HEAT RUNS ON FULL-LOAD Three phase Single phase Single phase no dampers no dampers with dampers 31 122 37 Temperature rise in deg. C. In the three-phase machine the armature reaction is constant in value and revolves at the same speed and in the same direction as the poles so that dampers are not required. The pulsating field of armature reaction, as pointed out in Art. 177, page 231, is equivalent to two revolving fields, one of which revolves in the same direction and at the same speed as 1 Waters, Trans, of Amer. Ihst. of Elect. Eng., Vol. 29, page 1069. 296 ELECTRICAL MACHINE DESIGN the poles, while the other, which causes the trouble, revolves at the same speed but in the opposite direction. The e.m.f. induced in an eddy-current path depends on the rate at which the lines of force of this latter field are cut and has a large value in a high-speed turbo alternator but causes little trouble in moderate- speed machines. CHAPTER XXVI SPECIAL PROBLEMS ON ALTERNATORS 218. Flywheel Design for Engine-driven Alternators. W hen two alternators are operating properly in parallel the currents flow as shown in diagram A, Fig. 197, and the operation is represented by diagram B. The e.m.fs. P and Q are equal and opposite with respect to the closed circuit consisting of the two armatures and the lines connecting them, and there is, therefore, no current circulating between the machines. Should one of the machines, say Q, slow down for an instant the currents will flow as shown in diagram C, and the operation is represented by diagram D when machine Q lags behind machine P by electrical degrees. The two e.m.fs. are no longer opposed to one another and there is a resultant e.m.f. E r which sends a circulating current round the closed circuit. While this cir- culating current has no separate existence, because it combines with the current which each machine supplies to the load to give the resultant current in the machine, yet it is convenient to consider its effect separately. ET This circulating current == ^=- and lags E r by 90, Xp+Xg where X p =the synchronous reactance of machine P Xq=the synchronous reactance of machine Q; the resistances of the armatures and the resistance and reactance of the line are all small compared with the above reactances and so can be neglected. It may be seen from diagram C that this circulating current is in the same direction as the e.m.f. in P, it therefore acts as an additional load on that machine and causes it to slow down; being opposed to the e.m.f. in Q it, therefore, lightens the load on that machine and causes it to speed up; therefore, the two machines tend to come together, until they are in the position shown in diagram B, where the machines are in step and the circulating current is zero. Due, however, to 297 298 ELECTRICAL MACHINE DESIGN the inertia of the machines, they will swing beyond the position of no circulating current which current will then be reversed and tend to pull the machines together again. The frequency of this swinging will be that of the natural vibration of the machines; the swinging will gradually die down due to the dampening effect of eddy currents in the pole faces, field coils and dampers. w W c * D FIG. 197. Diagrammatic representation of two alternators in parallel. If one of the machines is direct-connected to an engine whose torque is pulsating, forced oscillations will be impressed on the machine; if their period of vibration is within 20 per cent, of the natural period of vibration, cumulative oscillation will take place and the machines be thrown out of step unless they are powerfully dampened. It is, therefore, of extreme importance to study the natural period of vibration of alternators. 219. Two Like Machines Equally Excited. When swinging takes place between two such machines they move in opposite directions with the same frequency, so that if Fig. 198 shows the vector diagram of the two machines referred to the closed circuit, then SPECIAL PROBLEMS ON ALTERNATORS 299 6 = the angle of displacement between the two machines; r\ a. =the angle of displacement of one machine from the 2j position of zero circulating current or mean position. n E r =2E sin- TyT I, the circulating current = -=^ where X is the synchronous 2X reactance of each machine ~ A = I where I sc is the short-circuit current at the excitation required at no-load for voltage E and may be found from a short-circuit curve such as that in Fig. 200. I sc is generally about 2.5 times full-load current. FIG. 198. Vector diagram for two like machines in parallel. The synchronising power, or power transferred from one machine to the other, in watts 6 = nEI cos = nE(I 8C sin sin . 0\ e m TT 1 cos 2 1 L 300 ELECTRICAL MACHINE DESIGN r\ = nEI sc for small oscillations, where 6 is the angular dis- placement between the machines in electrical radians; = nEI sc a where a is the angular displacement of one ma- chine from its mean position in electrical radians; 7) = nEI sc a ( - where a is the same angular displacement a in mechanical radians. The torque corresponding to the above power transfer _ lb . at ! ft. radius = nEI sc ^ X 3. 5 a r.p.m. = Ka that is to say, the torque is directly proportional to the displace- ment and therefore the equation for the small displacements is Wr 2 d 2 a = ~ ^rT2~ from which the time of oscillation in seconds = 2.T, TFr 2 X r.p.m. watts XA^XpX 2.9 where TFr 2 =the moment of inertia of one machine in lb. ft. 2 , r.p.m. =the speed of the machine in revolutions per minute, watts = the normal output of the machine at unity power factor, ,. short-circuit current ., ,. k<=the ratio c -^r - at the excitation full-load current corresponding to voltage E at no-load, p = ih.Q number of poles. 220. One Small Machine in Parallel with Several Large Units. In this case, if the small machine is driven by an engine, it will swing about its mean position but will not be able to make the large units with which it is in parallel swing in the opposite SPECIAL PROBLEMS ON ALTERNATORS 301 direction, so that if Fig. 199 shows the vector diagram of the two machines referred to the closed circuit then a=the angle of displacement between the small machine and the others with which it is in parallel, and is also the angle of displacement of the small machine from its mean position E r =2Esm~ I, the circulating current = -^ where X is the synchronous X reactance of the small machine; the reactance of all the other machines in parallel is very small compared with this value and may be neglected, _a E sin 2 A / /"' a I = 21 sc sin ~2 the synchronising power in watts a = nEI cos -^ = nEx2I sc sin ^ cos ~ 2 = n]EI 8C a this is the same value as that obtained for FIG. 199. Vector two like machines so that the time of oscilla- diagram for a small tion will be the same as for two like machine in P arallel . . with a large station, machines. Example. 1 Cross compound engines running at 83 revolutions per minute, with a flywheel effect of 8.5X10 6 Ib. ft. 2 , driving three-phase alternators of 2100 k.v.a. output at 50 cycles, were found to hunt with the periodicity of the revolution. The short- circuit current of the machine for different excitations varied between 2.3 and 3.3 times full-load current. In such a case there is an impulse impressed on the system every stroke or four impulses per revolution; if any one of these impulses differs in magnitude from the others, due to unequal steam distribution, there will also be a forced oscillation with the periodicity of the revolution. 1 Rosenberg, Journal of the Inst. of Elect. Eng., Vol. 42, page 549. 302 ELECTRICAL MACHINE DESIGN For the machine in question the time of one cycle of natural J8.5X 10 6 "X83~ acy ^2100 X 1000X [2.31 X 72 poles X 2.9 L3.3J = 0.7 to 0.84 seconds. The number of forced oscillations per minute due to unequal steam distribution is 83 and the corresponding period of vibration is, therefore, =ff = 0.72 seconds, which corresponds very closely with that of the natural frequency. It was found possible to maintain parallel operation long enough to allow tests to be made by carefully equalizing the steam distribution so as to eliminate this low frequency forced oscillation. / 9 Excitation FIG. 200. Variation of the natural frequency of oscillation with excitation. It is advisable to design the flywheel so that the natural frequency of vibration of the machine is lower than that of the lowest forced oscillation; this will sometimes require the use of an enormous wheel; as, for example, in the case of alternators operating in parallel" and driven by large slow-speed gas engines. Gas engines are generally of the four-cycle type; that is, there is an explosion once in two revolutions. If the engine is of the four-cycle, double-acting, cross-tandem type there are four explosions to the revolution and the forced frequencies in such a case are: SPECIAL PROBLEMS ON ALTERNATORS 303 One impulse every two revolutions due to an unequal distribution of gas making one explosion always more powerful than the others; this is not a desirable condition of operation but one that must be provided for. One impulse per revolution due to the want of perfect balance of the reciprocating parts. One impulse per quarter revolution due to the four explosions in each revolution. In order that the natural frequency of oscillation of the alternator be below the frequency of the lowest impulse a very heavy and expensive flywheel is required, so that the wheel is often made with a moment of inertia of such a value that, over the whole range of operation, the natural frequency of the alter- nator is more than 20 per cent, higher than that of the lowest impulse and more than 20 per cent, lower than that of the impulse of next higher frequency. For example, in Fig. 200 the excitation during operation may vary from of to og and the value of the short-circuit current from I t to 7 2 . The natural frequency of oscillation is directly proportional to the square root of the short-circuit current, and for the value of W 2 r chosen is not within 20 per cent, of the frequency of either of the two lowest impulses for any excitation between of and og. 221. Use of Dampers. For gas-engine driven alternators m End Ring. Cast Steel End Plate. Laminations. FIG. 201. Alternator dampers. powerful dampers are supplied because the applied torque varies so much during each revolution. The type of damper shown in Fig. 201 is that generally used, it consists of a complete squirrel cage around the machine and acts as follows: The damper rods are embedded in the pole face and so do not cut the main field, therefore any damping effect is due to cut- ting of the armature field. If the armature field revolves at synchronous speed with a uniform angular velocity then, due to 304 ELECTRICAL MACHINE DESIGN the impulses of the engine, the poles oscillate about the position of uniform angular velocity and cut this field. The curve in Fig. 202 shows the distribution of the armature field; the poles move relative to it in the direction of the arrow and e.m.fs. are induced in the rotor bars in the direction shown by the dots and crosses. The frequency of these e.m.fs. is that of the oscillation of the machine and is of the order of two cycles per second, so that the reactance of the damper bars can be neglected compared with their resistance if the slots in which they lie are open at the top as shown in Fig. 201. The currents in the bars are, therefore, in phase with the e.m.fs. and so are also represented by the same crosses and dots; it may be seen that the direction Damper Torque Dam P er Tor 1 ue FIG. 202. Operation of dampers. of these currents is such that the force exerted on them by the armature field tends to prevent the relative motion of the arma- ture and the damper rods. The e.m.f. in a damper rod at any instant = B ga XL c XV c X 10~ 8 volts. Where B ga = the gap density at that part of the field which is being cut at the particular instant L c =the frame length y c =the velocity of the damper rod relative to the armature field in inches per second. ,, displacement from mean position the average value of V c = time of l/^ - 180 where /? = the maximum displacement of the poles, in electrical degrees, from the position of uniform angular velocity and / n =the frequency of oscillation; therefore the effective voltage in a damper rod is approximately = l.lXB a xL c X ga volts. SPECIAL PROBLEMS ON ALTERNATORS 305 The resistance of a damper rod of copper = - ohms the effective current in a damper rod = B ga X ^ T X4.4/ n XMXlO- 8 the current density in circular mils per ampere 10 8 X180 The dampening effect depends on the value of the total damper current, which, for a given machine, depends on the number of damper rods and on their section. If the section of these rods be increased they will carry a larger current, will have a greater dampening effect and the angle of swing will be reduced so that the larger this section the lower the current density because of the reduction in the value of /?. It is of interest to know the order of magnitude of this current density; for example, assume that J30a=25 ; 000 lines per square inch /?= + 5 electrical degrees which will give a circulating cur- rent of about 25 per cent, of full-load current T=10 in., for which the peripheral velocity is 6000 ft. per minute at 60 cycles / n = two cycles per second. , , ., 10 S X180 then the current density = 25;0 oo x5x io x4 .4x2 = 1640 circular mils per ampere. This value is pessimistic in that it neglects the resistance of the end connectors. It was pointed out above that the dampening effect depends on the total damper section. For gas-engine alternators it is usual to put into the dampers about 25 per cent, of the section of copper that is put into the stator and then, if the damping is not sufficient, or if the dampers get too hot, to look for the cause of the trouble in the governor, flywheel, or load on the system; a pulsating load is equivalent as far as hunting is concerned to a pulsating torque in the engine. One cause of damper heating must be carefully guarded against. If the dampers are spaced as in Fig. 203, then, when in position A, the flux threading between two adjacent dampers is large, while in position B this flux is small, so that every time a stator tooth is passed the flux threading between two 20 306 ELECTRICAL MACHINE DESIGN damper rods goes through one cycle and the frequency of the current which the induced e.m.f. sends round the closed circuit = the number of stator slots X the revolutions per second. This current is not a damping current and is liable to cause excessive heating and, to prevent the flux pulsation which produces it, the distance between damper rods should be a multiple of the stator slot pitch, as shown at C. For steam-engine driven alternators the strong damping effect of the squirrel cage is seldom required and a cheaper form of L U L T HJ LJ O O D FIG. 203. Spacing of dampers. damper is made by surrounding the poles with brass collars as shown in Fig. 140, page 193, where the edges of these collars act exactly like rods threaded across the pole face except that the effect is not so powerful, because they are shielded by the pole tips so that the flux cut is comparatively small. 222. Synchronous Motors for Power-factor Correction. Con- sider a synchronous motor running with constant load and constant applied voltage. If the field excitation of the motor be increased its back e.m.f. tends to increase, but this cannot increase much because the applied voltage is constant so that a demagnetiz- ing current must flow in the motor armature to counteract the effect of the increased field excitation; this current must be wattless because the load is constant and to be demagnetizing SPECIAL PROBLEMS ON ALTERNATORS 307 it must lag the back generated e.m.f. of the motor and, there- fore, lead the applied e.m.f. of the generator. If on the other hand, the field excitation of the motor be decreased its back e.m.f. tends to diminish and a wattless and magnetizing current must flow in the motor armature; to be magnetizing this current must lead the back generated e.m.f. of the motor and, therefore, lag the applied e.m.f. of the generator. The size of motor required for a given power-factor correction may be found from a diagram such as Fig. 204 where E is the voltage of the power station 7, the total station current per phase, lags E by 6 degrees, and the power factor is 70 per cent. E Percent Power Factor 100 95 90 80 70 FIG. 204. Size of motor for power factor correction. FIG. 205. Size of motor for power factor correction. To raise the power factor of this station to 100 per cent, the synchronous motor must draw a leading current =ab and nxExab . ., ,, the motor input must be= . in nri k.v.a. if the motor is jLUUU running light and the efficiency is 100 per cent. It may be seen from Fig. 204 that to raise the power factor of the system from 70 to 80 per cent, requires a wattless current ac per phase, 70 to 90 per cent, requires a wattless current ae per phase, 70 to 95 per cent, requires a wattless current af per phase, 70 to 100 per cent, requires a wattless current ab per phase. 308 ELECTRICAL MACHINE DESIGN The improvement in power factor from 95 to 100 per cent, is, therefore, obtained at a considerable cost. When synchronous motors are used for power-factor correction it is advisable to arrange that some of the load on the system is carried by these machines; for example, if ab, Fig. 205, is the wattless current per phase required for power factor correc- tion, then in order to carry a mechanical load of the same value in k.v.a. the rating of the motor would not be doubled but increased by only 41 per cent.; or for the case shown by triangle abd, with an increase in current of 12 per cent, over the value required for the mechanical load a power-factor correction effect of 50 per cent, may be obtained. 223. Design of Synchronous Motors. Diagram A, Fig. 206, shows some of the saturation curves of an alternator taken at constant current and varying power factor. If this machine were used as a synchronous motor then for the maximum power-factor, correction effect the power factor of the motor would be zero and the excitation = o/ for zero power-factor correction effect the power factor of the motor would be 100 per cent, and the excitation = og for 80 per cent, load and 60 per cent, power-factor correction effect the excitation would be = oh. Synchronous motors are generally high-speed machines and have, therefore, few poles, so that, as pointed out in Art. 195, page 258, they will be troubled with field heating if designed in the same way as synchronous generators, because for power- factor correction work they are operated with large excita- tion. In a synchronous motor, however, close regulation is not required so that for these machines the value of q, the ampere conductors per inch, may be run about 20 per cent, higher than the value given in Fig. 184 and the ratio maximum field excitation , , . , . _ - may be made less than 3, which value armature AT. per pole was suggested as a first approximation for synchronous generators in Art. 176, page 229. Diagram B, Fig. 206, shows saturation curves for a synchronous motor of the same rating as that of the generator whose curves are given in diagram A. Since the flywheel effect of a synchronous motor is generally small, no extra flywheel being supplied, its natural frequency of vibration will generally be comparatively high and the machine therefore liable to be set in violent oscillation by some of the SPECIAL PROBLEMS ON ALTERNATORS 309 forced frequencies on the system, for that reason synchronous motors are generally supplied with dampers. 224. Self-starting Synchronous Motors.- These are polyphase machines which are used for motor generator sets and for driving 9 h Excitation A Excitation B FIG. 206. Saturation curves of an alternator. apparatus which requires a small starting torque, when a special starting motor is not desired. They are built exactly like gas- engine alternators and consist of a standard synchronous motor supplied with a squirrel-cage winding on the poles. The method whereby this squirrel cage is calculated so as to meet the required starting conditions will be understood after a study of the induc- tion motor; the following points of importance, however, must be noted here: Polyphase currents in the armature winding produce a revolv- 310 ELECTRICAL MACHINE DESIGN ing field which tends to pull the squirrel cage round with it. In order that e.m.fs. may be induced in the squirrel cage by the revolving field the flux must enter the poles, therefore the poles should be laminated and, during the starting period, the field coils should be open circuited. The pole enclosure must be such that the; air-gap under the pole has a constant reluctance for all positions bf the pole relative to the armature. If the pole were made as shown in Fig. 207 then in position 4 the air-gap reluctance would be a minimum and in position B would be a maximum; in such a case the machine would lock in position A and would require a large force to move it out of this locking position. In Art. 283 on the induction motor, it is shown that if the rotor slot pitch is a multiple of that of the stator, locking will take L FIG. 207. Effect of the pole arc on the air gap reluctance. place due to the leakage fields and that in order to prevent this locking the rotor slot pitch must differ from that of the stator. It was pointed out in Art. 221 that to prevent useless circulating currents the rotor slot pitch should be a multiple of that of the stator, so that a compromise must be made and the rods spaced as shown in diagram D, Fig. 203, where t r , the rotor tooth, is made equal to the stator slot pitch, for which value it will be found that the air-gap reluctance under a rotor tooth, which is proportional to a + 6, is constant in all positions of the rotor. Since the frequency of the flux which, due to the revolving field, passes through the poles, is very high at starting, being equal to the frequency of the applied e.m.f., there will be high voltages SPECIAL PROBLEMS ON ALTERNATORS 311 generated in the field coils because the number of turns per coil is large, so that for self-starting synchronous motors the excitation voltage should be as low as possible so as to keep down the number of turns per pole and the field coils must be better insulated than for ordinary synchronous machines; in the case of machines with a large total flux it is sometimes advisable to supply a break-up switch which will open up the field circuit in several places at starting so that the starting e.m.fs. in the different poles will not add up. When the motor is nearly up to speed the field circuit is closed and a small excitation applied which tends to bring the motor into synchronism and ensures that it comes into step with the proper polarity. CHAPTER XXVII SPECIFICATIONS 225. The following is a typical specification for an alternator. SPECIFICATION FOR AN ALTERNATING CURRENT GENERATOR Rating. Rated capacity in kilo volt-amperes .... 400 Power factor 100 per cent. Normal terminal voltage 2,400 Phases 3 Amperes per terminal 96 Frequency in cycles per second 60 Speed in revolutions per minute 600 Construction. The generator is for direct connection to a horizontal type of water-wheel and shall be of the internal revolving field type, supplied with base, two pedestal bearings bolted to the base, and a horizontal shaft extended for a flange coupling. The machine must be so constructed that the stator can be shifted sideways to give access to both armature and field coils. Stator. The stator coils must be insulated complete before being put into the slots, shall be thoroughly impregnated with compound, and must be readily removable for repairs. Shields must be supplied to protect the coils where they project beyond the core. Bidders must state the type of slot to be used whether open, partially closed, or completely closed. Rotor.- The rotor must be strong mechanically and able to run at 75 per cent, overspeed with safety. Any fans or projecting parts on the rotor must be screened in such a way that a person working around the machine is not liable to be hurt. Workmanship and Finish. The workmanship shall be first class, all parts shall be made to standard gauge and interchange- able, and all surfaces not machined are to be dressed, filled, and rubbed down to present a smooth finished appearance. Exciter.- The alternator shall be separately excited and the exciter, which must be direct-connected, is described in a separate specification. 312 SPECIFICATIONS 313 Rheostat. A suitable field rheostat with face plate and sprocket wheel for distance control is to be supplied. Foundation bolts will not be furnished. Coupling. This is to be supplied by the builder of the water- wheel who shall send one-half to the alternator builder to be pressed on the alternator shaft. General. Bidders shall furnish plans or cuts with descriptive matter from which a clear idea of the construction may be ob- tained; they shall also furnish the following information: Stator net weight, Rotor net weight, Net weight of base and pedestals, Shipping weight, Efficiency at J, J, f , full- and 1J non-inductive load, Regulation at normal output, at 100 per cent, and also at 85 per cent, power factor, Exciting current, at normal voltage and speed, for normal k.v.a. output, at 100 per cent, and at 85 per cent, power factor. The exciter voltage is 120. Efficiency. The losses in the machine shall be taken as : Windage, friction, and core loss, which shall be determined by driving the machine by an independent D.-C. motor, the output of which may be suitably determined, the alternator being run at normal speed and excited for normal voltage at no-load. Field loss, which shall be taken as the exciting current corre- sponding to the different loads multiplied by the corresponding voltage at the field terminals, the field coils being at their full- load temperature. The armature PR loss; the armature resistance being meas- ured immediately after the full-load heat run. The load loss, which is determined from a short-circuit core loss test, the machine being short-circuited through an ammeter, run at normal speed, and the field excitation adjusted to send the currents corresponding to the different loads through the arma- ture. One-third of the difference between the loss so found and the PR loss for the same current, shall be taken as the load loss. Regulation. This shall be taken as the per cent, increase in terminal voltage when the load at which the guarantee is made is reduced to zero, the speed and excitation being kept constant. It shall be found by assuming the synchronous impedence constant for a given excitation, this impedence to be determined 314 ELECTRICAL MACHINE DESIGN from saturation curves at no-load and also at full-load and zero power factor. Temperature. The machine shall carry its normal load in k.v.a., at normal voltage and speed and at 100 per cent, power factor, continuously, with a temperature rise that shall not exceed 40 C. by thermometer t on any part of the machine, and, immediately after the full-load heat run, shall carry 25 per cent, overload for 2 hours, at the same voltage, speed and power factor, with a temperature rise that shall not exceed 55 C. by thermometer on any part of the machine. The temperature rise of the bearings shall not exceed 40 C. as measured by a thermometer in the oil well, either at normal load or at the overload. No compromise heat run, other than one at normal voltage, zero power factor, and with the armature current for which the guarantee is made, will be accepted. If the manufacturer cannot load the machine, a heat run will be made within 3 months after its erection to find out if it meets the heating guarantee; the test to be made by the alternator builder who shall supply the necessary men and instruments. Overload Capacity. The machine must be able to carry at least 50 per cent, overload at 80 per cent, power factor with the normal exciter voltage of 120. The machine shall be capable of standing an instantaneous short-circuit when operating at normal voltage, normal speed, and no-load, and must be able to carry this short-circuit for 10 seconds without injury. Insulation. The machine shall stand the puncture test recommended in the standardization rules of the American Institute of Electrical Engineers (latest edition) and the insula- tion resistance of the armature and field windings shall each be greater than one megohm. Testing Facilities. The builder shall provide the necessary- facilities and labor for testing the machine in accordance with this specification. 226. Notes on Alternator Specifications. The builder of the al- ternator generally inserts the following clause in the specification. "We guarantee successful parallel operation between our generators, without racing, hunting, or pumping, whether driven by water-wheels or steam engines, provided that the variation of the angular velocity of the prime movers does not produce SPECIFICATIONS 315 between two generators operating in parallel a displacement of more than five (5) electrical degrees (2^ on either side of the mean position), one electrical degree being equal to one mechanical degree divided by half the number of poles." This clause is inserted to ensure that the engine builder shall supply such a flywheel and governor that the variation of the angular velocity of the engine during one revolution shall be within reasonable limits. As shown in Art 218, however, hunt- ing may take place if the natural period of oscillation of the machine is approximately the same as that of any of the forced oscillations on the system. In practically every case the burden of proof when hunting takes place is put on to the alternator builder. In the case of alternators for direct connection to gas engines it is often advisable for the alternator builder to check up the size of the proposed flywheel and make sure that it is not such as shall cause resonance. Wave Form. It is often specified that the e.m.f. when plotted on a polar diagram, shall not deviate radially more than 5 per cent, from a circle; it must be remembered, however, that -the serious trouble, due to a bad wave form, is generally due to the higher harmonics and these harmonics are usually well within the 5 per cent, specified. Temperature Rise. In turbo generators the temperature rise by thermometer is misleading, particularly in the case of the rotor, and specifications for these machines should call for the temperature rise to be determined by the increase in elec- trical resistance; a convenient figure to remember is that 10 per cent, increase in the resistance of copper is equivalent approx- imately to 25 per cent, increase in temperature. In high voltage machines the stator temperature should be determined from resistance measurements, and in the case of large and important machines it is sometimes specified that the internal temperature of the machine at the hottest part shall be measured by a thermo-couple built into a coil or by the increase in resistance of a number of turns of fine wire wound round a coil before it is insulated; this coil is placed as near the neutral of the machine as possible. 227. Effect of Voltage on the Efficiency. Consider the case of two machines built on the same frame and for the same output and speed but for different voltages. 316 ELECTRICAL MACHINE DESIGN The windage and friction loss is independent of the voltage since it depends on the speed, which is constant. The excitation loss and the iron loss are independent of the voltage, the winding being made so that the flux per pole is the same for all voltages. In order to have the same flux per pole the total number of conductors must be directly proportional to the voltage, and if the total amount of copper in the machine is kept constant the size of the conductor will be inversely proportional to the voltage and therefore directly proportional to the current, so that the current density in the conductors, and therefore the copper loss, is independent of the voltage. If, however, as is generally the case, the total amount of armature copper decreases as the voltage increases, on account of the space taken up by insulation, then in order to keep the copper loss constant the current rating must decrease more rapidly than the voltage increases and the output become less the higher the voltage. If then the total section of copper is constant at all voltages, the losses, output and efficiency will be independent of the voltage; but if the total section of copper decreases as the voltage increases then, while the losses remain constant, the output and the efficiency decrease with increase of voltage. 228. Effect of Speed on the Efficiency. Consider two machines built for the same kw. output, one of which runs at twice the speed of the other, and assume that kw. y 7T~2T~ = a constant also that j-r- ^r- = a constant frame length both of which are approximately true for machines which have more than 10 poles, then the relative dimensions of the two machines are given in the following table: Machine A Machine B Output kw. kw. Speed r.p.m. 2(r.p.m.) Poles p 1/2 (p) Internal diameter of armature D a y-^ Frame length L c 1.25(L C ) Pole-pitch T 1.25 (T) Core depth d a 1.25 d a SPECIFICATIONS 317 Core Loss.- The core weight is approx. = a const. XD a xL c Xd a and is the same for each machine, so that for the same flux density in the core the core loss is independent of the speed. ^ nZI c 2 Lh H- Copper loss = n =- where !!/&= (L c + 1.5r) approx. cir. mil per cond. _amp. cond. per inch i X 7T D d (jLj c ~i~l.OT) cir. mils per ampere , ,. amp. cond. per. inch .,..,-,,,,. The ratio -T-* ~ - is limited by heating as shown in cir. mils per ampere Fig. 181, page 253, and since the peripheral velocity is only 25 per cent, higher in machine B than in machine A, it may be assumed that this ratio has approximately the same value in the two machines and the copper loss is therefore a const. XD a (L c + 1.5r) in machine A D a and a const. X^- (1.25L c + 1.9r) in machine B l.o = a const. XDo(0.80L c + 1.2T) so that the higher the speed for a given output the lower is the copper loss. Windage Loss is approximately proportional to the surface of the rotor multiplied by the (peripheral velocity) 3 . The peri- pheral velocity of machine B is 25 per cent, greater than that of machine A, and the windage loss is greater for the high-speed than for the low-speed machine. Bearing Friction Loss. = a constant XdXlX(Vb)%, formula 13, page 97. Since the torque on the shaft of machine B is approxi- mately half that on machine A, and the projected area of the bearing = dXl is directly proportional to this torque, therefore, the bearing friction loss = a const. XdXlX (Vb)% in machine A = a const. X p X(x/2.V&)$ in machine B -a const. XdXlX(V b }% X0.85 in machine B so that the higher the speed, the lower the bearing friction loss. Excitation Loss. The radiating surface of the field coil is approx- imately = 2 (pole waist + frame length) X radial length of field coil. Machine B has 25 per cent, greater pole waist, 25 per cent, longer frame length, and 10 per cent, longer poles radially than has machine A, but it has also half the number of poles and, therefore, 0.7 times the radiating surface. The permissible watts per square inch in machine B is approxi- 318 ELECTRICAL MACHINE DESIGN mately 25 per cent, greater than in machine A, therefore, if the total permissible watts excitation loss in machine A = W the permissible excitation loss in machine B = IF X 0.7 X 1.25 = 0.88 W therefore the higher the speed, the lower the field excitation loss. 100 95 3 90 R.P.M. 720 200 1800 1000 2000 3000 Eilo-volt Amperes 4000 5000 FIG. 208. Efficiency curves for 2400 volt alternators. It may therefore be stated as a general rule, that the higher the speed of a machine for a given rating in kilowatts the lower are the losses and the higher the efficiency. Fig. 208 shows curves of efficiency for polyphase alternators wound for 2400 volts. CHAPTER XXVIII ELEMENTARY THEORY OF OPERATION 229. The Revolving Field. P, Fig. 209, shows the essential parts of a two-pole two-phase induction motor. The stator or stationary part carries two windings M and JV spaced 90 electrical degrees apart. These windings are connected to a two-phase alternator and the currents which flow at any instant in the coils M and N are given by the curves in diagram Q ; at instant A for example, the current in phase l=-\-I m while that in phase 2 = zero. The windings of each phase are marked S and F at the termi- nals and these letters stand for start and finish respectively; a + current is one that goes in at S, and a current one that goes in at F. The resultant magnetic field produced by the windings M and N at instants A, B, C and D is shown in diagram R from which it may be seen that, although the windings are stationary, a revolving field is produced which is of constant strength and which moves through the distance of two pole-pitches while the current in one phase passes through one cycle. To reverse the direction of rotation of this field it is necessary to reverse the connections of one phase. P, Fig. 210, shows the winding for a two-pole three-phase motor; M, N and Q, the windings of the three phases, are spaced 120 electrical degrees apart. These windings are con- nected to a three-phase alternator and the currents which flow at any instant in the coils M, N and Q are given by the curves in diagram R. The resultant magnetic field that is produced by the windings at instants A, B, C and D is shown in diagram S from which it may be seen that, just as in the case of the two-phase machine, a revolving field is produced which is of constant strength and which moves through the distance of two pole-pitches while the current in one phase passes through one cycle. To reverse the direction of rotation of this field it is necessary 319 320 ELECTRICAL MACHINE DESIGN to interchange the connections of two of the phases; for example, to connect phase 2 of the motor to phase 3 of the alternator and phase 3 of the motor to phase 2 of the alternator. FIG. 209. The revolving field of a two-pole two-phase induction motor. 230. Multipolar Motors. Fig. 211 shows the winding for a four-pole, two-phase motor and also the resultant magnetic field at the instants A and B, Fig. 209. The field moves through the distance of 1/2 (pole-pitch) while the current in one phase passes through 1/4 (cycle). ELEMENTARY THEORY OF OPERATION 321 Fig. 212 shows the winding for a four-pole, three-phase motor and also the resultant magnetic field at the instants A and B, Fig. 210. In this case the field moves through the distance of A B C D A Ii- Im h=-y 2 im I s =- l /2lm 7 3 =-/w & FIG. 210. The revolving field of a two-pole three-phase induction motor. 1/3 (pole-pitch) while the current in one phase passes through l/6(cycle). In general the field moves through the distance of two pole- 21 322 ELECTRICAL MACHINE DESIGN pitches or through - of a revolution while the current in one phase passes through one cycle, therefore, the speed of the revolving field ==- X/ revolutions per second 120X/ P revolutions per minute (42) this is called the synchronous speed. Diagrammatic Representation of a 4 Pole 2 Phase Induction Motor FIG. 211. The revolving field of a four-pole two-phase induction motor. 231. Induction Motor Windings. The conditions to be fulfilled by these windings are that the phases should be wound alike, should have the same number of turns, and should be spaced 90 electrical degrees apart in the case of a two-phase winding and 120 electrical degrees apart in the case of a three-phase winding. The above are the conditions that have to be fulfilled by alternator windings so that the diagrams developed in Chapter XVII apply to induction motors as well as to alternators. ELEMENTARY THEORY OF OPERATION 323 Fig. 213 shows an actual stator with its windings arranged in phase belts. The ends of the coils are bent back so that the rotating part of the machine, called the rotor, can readily be put in position. The type of rotor which is in most general use is shown in Fig. 214 and is called the squirrel-cage type. It consists of an iron core slotted to carry the copper rotor bars; these bars are Diagrammatic Representation of a 4 Pole 3 Phase Induction Motor FIG. 212. The revolving field of a four-pole three-phase induction motor. joined together at the ends by brass end connectors so as to form a closed winding. 232. Rotor Voltage and Current at Standstill. The actions and reactions of the stator and rotor will be taken up later; it is neces- sary, however, to point out here that, since the applied voltage per phase is constant, the back voltage per phase must be approxi- mately constant at all loads. This back voltage is produced by the revolving field, therefore, the actions and reactions of the 324 ELECTRICAL MACHINE DESIGN stator and rotor must be such as to keep the revolving field approximately constant at all loads. Let the revolving field be represented by a revolving north and south pole as shown in diagram A, Fig. 215, and then for convenience let this figure be split at xy and opened out on to a plane; the result will be diagram B, of which a plan is shown in diagram D. FIG. 213. Stator of an induction motor. The distribution of flux on the rotor surface due to the revolv- ing field is given by the curve in diagram B at a certain instant. The field is moving in the direction of the arrow; it therefore cuts the rotor bars and generates in them, e.m.fs. which are shown in magnitude at the same instant in diagram D. Since the rotor ELEMENTARY THEORY OF OPERATION 325 circuit is closed these e.m.fs. will cause currents to flow in the rotor bars. The frequency of the e.m.fs. in the rotor bars at standstill ' - cycles per second = the frequency of the stator applied e.m.f., so that the frequency of the rotor currents is high, and the reactance of the rotor, which is proportional to this fre- quency, is large compared with its resistance; the rotor current FIG. 214. Squirrel cage rotor. therefore lags considerably behind the rotor voltage as shown by the curve in diagram D and also by crosses and dots in dia- gram C. The value of this current at standstill _ rotor voltage at standstill rotor impedance at standstill and this is usually about 5.5 times the full-load rotor current. 233. Starting Torque. As shown in diagrams C and D the rotor bars are carrying current and are in a magnetic field so that a force is exerted tending to move them ; this force when multiplied by the radius of the rotor gives the torque. The relative torque at different points on the rotor surface is given by the curve in diagram D, which is got by multiplying the value of flux density 326 ELECTRICAL MACHINE DESIGN at different points on the rotpr surface by the value of the current in the rotor bar at these, points. It may be seen from this curve, and also from diagram C, that at some points on the rotor sur- face the torque is in one direction and at other points is in the opposite direction so that the resultant torque is quite small. N ooooooooooooo \\1 --- Torque Rotor Voltage Rotor Current FIG. 215. Production of torque in an induction motor. As a rule the starting torque of a squirrel-cage motor is about 1.5 times full-load torque when the rotor current is about 5.5 times the full-load rotor current. Diagram C shows that the resultant torque is in such a direction as to tend to make the rotor follow up the revolving field. ELEMENTARY THEORY OF OPERATION 327 The starting torque can be increased for a given current if that current be brought more in phase with the voltage, this can read- ily be seen from the curves in Fig. 215. The angle of lag of the rotor current can be decreased by increasing the rotor resistance, and sufficient resistance is generally put in the rotor circuit to bring the current down to its full-load value; the angle of lag is thSn so small that full-load torque is developed. When a motor is running under load a large rotor resistance is undesirable because it causes large loss, low efficiency, and 1"' 15 1U>. TV ft-; K" KOTOH. FIG. 216. Wound rotor type of induction motor. excessive heating. To get over this difficulty the wound rotor motor was developed. This type of motor has the same stator as that used for the squirrel-cage machine but its rotor is as shown in Fig. 216; the rotor bars are connected together to form a winding, but this winding is not closed on itself as in the squirrel- cage machine, it is left open at three points which are connected to three slip rings, and the winding is closed outside of the ma- chine through resistances which can be adjusted. The winding is finally short circuited at the slip rings when the motor is up 328 ELECTRICAL MACHINE DESIGN to speed. In this way it is possible to have the advantage of high rotor resistance for starting and low rotor resistance when the motor is running at full speed. 234. Running Conditions. It was pointed out in the last arti- cle that the resultant torque is in such a direction as to make the rotor follow up the revolving field. When the motor is not carrying any load the rotor will revolve at practically synchro- nous speed, that is, at the speed of the revolving field. If the motor is then loaded it will slow down and slip through the revolv- ing field, the rotor bars will cut lines of force, the e.m.fs. generated in these bars will cause currents to flow in them and a torque will be produced. The rotor will slow up until the point is reached at which the torque developed by the rotor is equal to the torque exerted by the load. rp, ,. syn. r.p.m. r. p.m. of rotor . The ratio - - is called the per cent, syn. r.p.m. slip and is represented by the symbol s, its value at full-load is generally about 4 per cent. 400 800 1000 1200 1400 R.P.M. FIG. 217. Characteristics of a 25-h.p., 440-volt, 3-phase, 60-cycle, 1200 syn. r.p.m. induction motor. As the load is increased the rotor drops in speed and the slip, rotor current, frequency and lag of rotor current all increase. The torque developed by the rotor tends to increase due to the increase in rotor current and to decrease due to the increase in current lag. Up to a certain point, called the break-down point or point of maximum torque, the effect of the current is greater ELEMENTARY THEORY OF OPERATION 329 than that of the current lag, beyond that point the effect of the current lag is the greater, so that after the break-down point is passed the torque actually decreases even although the current is increasing. The relation between speed, torque, and current is shown in Fig. 217 fora 25-h. p., 440-volt, three-phase, 60-cycle, 1200-syn. r.p.m. induction motor. 235. Vector Diagram at No-load. At no-load a motor runs at synchronous speed so that the slip, rotor voltage and rotor cur- rent are all zero. Consider the winding S 1 F 1 of one phase of the stator as shown in Fig. 209 or 210. The voltage E l applied to this phase causes a current 7 , called the magnetizing current, to flow in the winding. This current, along with the magnetizing currents in the other phases, produces a revolving field / is of constant strength the flux (/) g which threads the winding S l F l is an alternating flux and is a maximum and = (/>/ when the magnetizing current in the winding S L F l is a maximum; this can be ascertained. by exami- nation of diagram R, Fig. 209 and of diagram S, Fig. 210, so that the flux which threads the winding $,1^ is in phase with the magnetizing current 7 in that winding. The alternating flux g by 90. This T7I voltage causes a current 7 2 = ~- to flow in the closed rotor circuit; ^2 sX 7 2 lags the voltage E 2 by an angle whose tangent = -=-*, H 2 where Z 2 is the rotor impedance at full-load, X 2 is the rotor reactance per phase at standstill, R 2 is the rotor resistance per phase, s, the per cent, slip, is approximately = 4 per cent., E E l FIG. 218. No-load vector diagram. FIG. 219. Vector diagram at full load. with this value of s the angle of lag of the rotor current at full load seldom exceeds 20. In Fig. 219 / is the magnetizing current, which has the same value as in Fig. 218, g is the flux per pole threading one phase of both rotor and stator windings, ELEMENTARY THEORY OF OPERATION 331 E^b is the back e.m.f. of the stator, E 2 is the e.m.f. generated in one phase of the rotor by flux g , 7 2 is the current in that phase, E^ is the component of the applied e.m.f. which is equal and opposite to EL&., Now E lf the applied voltage, is constant and is the resultant of 7? u and 7^; this latter quantity is comparatively small even at full-load, so that it may be assumed that E n has the same value at full-load as at no-load and therefore E^, which is equal and opposite to E ll and (j) g which produces E^, are approxi- mately constant at all loads, so that the resultant magnetiz- ing effect of the stator and rotor currents must be equal to the magnetizing effect of the current I . The stator current may therefore be divided into two components, one of which 7 U has a m.m.f. equal and opposite to that of the rotor current 7 2 ; the other component of stator current must be I , because this is the necessary condition for a constant value of $ g and of E^', therefore, in Fig. 219, 7 U is a component of primary current whose m.m.f. is equal and opposite to that of 7 2 . 7, is the primary current and is the resultant of I and 7 U . E { is the applied voltage and is the resultant of E l} and 7 t Z r CHAPTER XXIX GRAPHICAL TREATMENT OF THE INDUCTION MOTOR 237. Current Relations in Rotor and Stator. It is shown in Art. 236 that the m.m.f. of the rotor opposes that of the stator, and that the resultant m.m.f., namely, that of the magnetiz- ing current, is just sufficient to produce the constant revolving field f . Fig. 220 shows the position of the windings of one phase of both rotor and stator, and also the direction of the currents in these Staler Rotor FIG. 220. The magnetic fields in an induction motor. windings, at the instant that the rotor and stator m.m.f s. are directly opposing one another. As the rotor revolves relative to the stator there will be positions on either side of that shown in Fig. 220, in which the rotor and stator m.m.fs. do not quite oppose one another; two such positions are shown in Fig. 221; this overlapping of the phases is called the belt effect and is dis- cussed more fully in Chap. 33. Due to the revolving field (j>f an alternating flux g threads one phase of both rotor and stator windings. It is shown in Fig. 220 that, in addition to the flux $ g which crosses the air-gap, there is a leakage flux (f> t i which links the stator coils but does not cross the air-gap; 0^ is proportional to the current I t which produces it. There is also a leakage flux (f> 2 i which links the rotor 332 GRAPHICAL TREATMENT 333 coils but does not cross the air-gap; 2 i is proportional to the current 7 2 which produces it. 238. The Stator and Rotor Revolving Fields. If /! =the frequency of the stator current, s =the per cent, slip, r.p.m. 1 =the synchronous speed, X FIG. 221. Overlapping of the phases. then/ 2 , the frequency of the rotor current = s/ 1? see Art. 236, and (1 s)r.p.m. 1 = the rotor speed. The stator current acting alone produces a field which revolves at synchronous speed, namely r.p.m.j; the rotor current acting alone produces a field which revolves at a speed of s(r.p.m. 1 ) relative to the rotor surface or at sCr.p.m.J + (1 -s)r.p.m. 1 = r.p.m.! relative to the stator surface; that is, the two fields revolve at the same speed in space and so can be represented on the same diagram. 239. The Voltage and Current Diagram. Fig. 224 shows the voltage and current relations in an induction motor. EI =the voltage per phase applied to the stator windings, /!=the stator current per phase, and lags E^ by 6 degrees; the locus of /! is a circle. 240. The Flux Diagram. Consider the stator current acting alone, then in Fig. 222: 334 ELECTRICAL MACHINE DESIGN i which crosses the gap and threads one phase of the rotor = v^. Consider the rotor current 7 2 acting alone, then: 2 =the flux per pole threading one phase of the rotor, cp 2 i =the rotor leakage flux per phase per pole, (j) 2g =that part of 2 which crosses the garj and threads one phase of the stator = v 2 ^f) 2 . Under load conditions, when both 1^ and 7 2 are acting, ls =the actual flux per pole threading one phase of the stator, (j) 2r =the actual flux per pole threading one phase of the rotor, g E^i =I^X 1} generated by the flux^z E 2g = the. rotor e.m.f. per phase generated by g . This e.m.f. sends a current 7 2 through the rotor winding which pro- duces the leakage flux 2 i and generates the e.m.f. E 2 i = I 2 X 2 in that winding. E 2g , therefore, consists of two components, namely, E 2r to overcome the resistance per phase and a voltage equal and opposite to E 2 i to overcome the reactance per pha&e. Since E 2r is in phase with 7 2 and therefore with 2 , the angle aoh = angle oab = 90. The applied voltage must be equal and opposite to E^ if the stator resistance per phase and therefore the voltage I l R l is sufficiently small to be neglected. Since E l is constant, therefore E^b, and the flux is which produces E^, must be constant in magnitude. 241. Geometrical Proof of the Circle Law. In Fig. 222 draw dk perpendicular to fd so as to cut the line of produced at k. In triangles aob and fdk, angle oab ;= angle fdk = 90, angle oba= angle dfk t fk fd fd fd therefore, f = 7 = j- = ~^r r ob ab ac cb ohcb GRAPHICAL TREATMENT 335 and oh-cb (v 1 Xof)(v 2 Xoh) oh(l v^Vz) = a constant, since v 1} v 2 , and of are all constant. Since fk is constant and angle fdk is an angle of 90, the locus of d, or of 0j, is a circle whose center is on the line ok and whose diameter =fk. If the magnetic circuit be not saturated, and this is the case at the actual flux densities due to 18 and 2r , the actual fluxes in the machine, then Fig. 222 may be transformed into Fig. 223, FIG. 222. Voltage and flux diagram. pro- which is a m.m.f. and voltage diagram, by making njb portional to <^ and njb 2 cJ 2 proportional to 2 . Fig. 223 may be transformed into a voltage and current dia- gram as shown in Fig. 224, and in this form, with a slight modi- fication, it is generally used. 242. Special Cases. 1. The motor is running without load and, therefore, at synchronous speed, so that the rotor e.m.f. and the rotor current are zero. Under these conditions Fig. 224 becomes Fig. 225. 336 ELECTRICAL MACHINE DESIGN 2. The motor is at standstill and the rotor resistance is assumed to be zero. Under these conditions Figs. 222 and 224 give Fig. 227. Since R 2 is zero therefore E 2r and 2r are both zero, and E 2g must be equal and opposite to E 2 i and therefore equal to I 2 X 2 . Now E lb =E ig +E l i FIG. 223. Voltage and m.m.f. diagram. HE> FIG. 224. Voltage and current diagram and ^^ since they are produced by the same flux E 2 g therefore E^ 22 Y ^ GRAPHICAL TREATMENT 337 (43) the value of I t in this case is Id the maximum current, Fig. 224. 243. Representation of the Losses on the Circle Diagram. The losses in an induction motor are: Mechanical losses windage and friction loss. Constant losses Iron or core loss hysteresis and eddy -current loss. f Stator copper loss. Variable losses | Rotor copper loss. [ Load losses. No-load conditions. Constant Losses. As a motor is loaded, the rotor drops in speed and the slip and therefore the frequency of the flux in the rotor core increases. Due to the drop in speed the windage and friction loss decrease and due to the increase in frequency of the rotor flux 'the iron loss in the rotor core increase?, so that it is reasonable to assume that the sum of these two losses is constant at all speeds. To overcome the constant loss a stator current I wo is required, in phase with the applied voltage and of such a value that n^EJ wo = the constant loss in watts. To take account of this in the circle diagram the no-load conditions have to be changed from those of Fig. 225 to those of Fig. 226. Variable Losses. These are nJ 2 Jt^ and n 2 I 2 2 R 2 . In Fig. 224 the stator current = 7 t and the corresponding rotor current = / 2 =/ 11 X X 1 * 1 n 2 b 2 c 2 338 ELECTRICAL MACHINE DESIGN The Rotor Copper Loss. This loss = n 2 I 2 2 R 2 watts T n 2 b 2 c 2 = / 2 u Xa constant. \ Fig. 224 Now = xD; where D is a constant therefore the rotor loss = x(a constant). To allow for the rotor loss on the circle diagram take any stator current I lt find the corresponding rotor current 7 2 and the rotor copper loss n 2 P 2 R 2 in watts; set up from the base line c k E 2 FIG. 227. Conditions at standstill with zero rotor and stator resistance. old a current I rw as shown in Fig. 224, in phase with E lt such that n i E l I rw = the rotor copper loss in watts. Draw a straight line through I and I rw . The vertical distance from the base to this line is proportional to x and is a measure of the rotor loss. The Stator Copper Loss. This Ioss = n 1 / 2 1 # 1 watts. I\ is assumed to be = / 2 +/ 2 u ; the error due to this assumption is comparatively small. The part of the copper loss n l P R l is added to the constant losses, the other part n l P ll R L is propor- tional to x just as in the case of the *otor loss. To allow for the stator loss on the circle diagram take any stator current / l; find the corresponding stator copper loss n^P^R^ in watts; set up from the line/w, Fig. 224, a current I 8W in phase with E 17 such that n 1 ' 1 / sw = the stator copper loss in watts. Draw a straight line through I and I sw . GRAPHICAL TREATMENT 339 Load Losses. These consist of various eddy-current losses which cannot be accurately predetermined and which are* made as small as possible by careful design; they are usually allowed for by increasing the variable losses by a certain percentage found from tests on similar machines. 244. Relation Between Rotor Loss and Slip. Let the curve in Fig. 228 represent the distribution of the actual rotor revolving field (j) r corresponding to the alternating flux 2r , Fig. 222. FIG. 228. Torque on a rotor conductor. The e.m.f. generated in a rotor conductor by this flux -2.22 r2 10- 8 volts -2.22 5 rw rL c (s/J 10 ~ 8 volts and is in phase with the flux density. It is shown in Fig. 222 that 7 2 is in phase with the voltage E 2r so that the loss per conductor = E 2r Xl 2 watts -2.22 B r m 2 TL c s/;/ 2 10- 8 watts. 71 Since 7 2 is in phase with E 2r it is also in phase with the flux density so that the average force on a rotor conductor = B r eff c dynes, where B r and L c are in centimeter units and the work done by this conductor in ergs is therefore = B r e ffX j^Xl/cXcond. velocity in centimeters per second 340 ELECTRICAL MACHINE DESIGN B r m 7 = T=- |Y) XL c Xn (rotor diameter X revolutions per second) or in watts rotor loss therefore, - rotor output 1 s , rotor input 1 and - ~T = ^ rotor output 1 s _ synchronous speed actual speed 245. The Final Form of the Circle Diagram. Fig. 229 shows the form in which the circle diagram is generally used. FIG. 229. The circle diagram. For a stator current 7 1 =oc = full-load current gc =the power component of the primary current fg =that part of gc required to overcome the constant losses ef =that part of gc required to overcome the stator copper loss de =that part of gc required to overcome the rotor copper loss cd =that part of gc required to overcome the mechanical load - =the power factor eg oc cd eg dc ce de ce the efficiency rotor output rotor input rotor loss actual speed synchronous speed rotor input = s = per cent, slip the h. p. output = 746 GRAPHICAL TREATMENT 341 ,. _, ^. 33000 the corresponding torque, ^ "^74^ X~ -- lb. at 1 ft. radius. At synchronous speed this same torque would produce .i , - horse-power . . ., . = 74.fi" norse -P ower ;' this is called the Synchronous Horse-power due to full-load torque. At standstill the synchronous horse-power due to the starting n+E.(lm) the rotor copper loss in watts torque = - JS_ The maximum horse-power output of the motor _n l E l (maximum value of dc) 746 The maximum torque is that which gives a synchronous horse- n.E* (maximum value of ce\ power = - JW - The use of this circle diagram is shown by an example which is worked out fully in the next chapter. CHAPTER XXX CONSTRUCTION OF THE CIRCLE DIAGRAM FROM TESTS The no-load saturation and the short-circuit tests are those that are usually made on an induction motor in order to de- termine its characteristics. 246. The No-load Saturation Curve. The figures necessary for the construction of this curve are got by running the motor at normal frequency and without load. Starting at 50 per cent, above normal voltage, the voltage is gradually reduced until the motor begins to drop in speed and simultaneous readings are taken of voltage, current and- total watts input. The results of such a test on a 50 h. p., 440-volt, three-phase, 60-cycle, eight-pole, Y-connected motor are given below. NO-LOAD SATURATION I E t II P Terminal volts Line current Watts input 600 32.3 2,940 562 29.0 2,650 521 25.9 2,350 470 22.6 2,100 422 19.8 1,860 375 17.0 1,650 318 14.2 1,450 275 12.5 1,300 222 10.5 1,150 175 8.9 1,080 120 7.5 960 In Fig. 230:- The relation between E t and // is shown. in curve 1, The relation between E t and P is shown in curve 2, The straight line, curve 3, shows the relation between E t and that part of the exciting current which is required to send the magnetic flux across the air gap; this curve is calculated by 342 CONSTRUCTION OF THE CIRCLE DIAGRAM 343 the method explained in Chap. XXXII. At normal voltage the exciting current is 21 amperes, the magnetizing current required to send the magnetic flux across the air-gap is 17.6 amperes, and 21 the ratio -~ -^ =l.2Q = 17. b which is called the iron factor. Curve 1 is not tangent to curve 3 because, in addition to the true magnetizing current, the exciting current contains the power Terminal Volts =Et / ? X / g g i Values of / wsc P r f* C7< CT / /i 9 X 3/ / ~" 77 """ r "~ ^ . y / X It X x^ ^ it , 2 x ^ ^ ^ r^^ /} i I x x ^ -^ ^^ , - "** / / ^ ^ ^ ^ G i 'I ^ X r ^^ ^ -^ ^ 1 ft ^ ^ ^ 1^ ^ ^ ; -M- > 0.5 1.0 1.5 2.0 2.5 3.0 Kilowatts at No Load=P 10 20 30 40 Amperes at No Load = I e 50 100 150 200 250 300 350 Amperes on Short Circuit -I S c 400 Curve 1. Curve 2. Curve 4. Curve 5. current. Terminal volts and exciting current. Terminal volts and no-load loss. Terminal volts and short-circuit current. Short-circuit current and power component of short-circuit . Curve 6. Short-circuit current and FIG. 230 torque in ft.-lbs. terminal volts. Test curves on a 50-h.p., 440-volt, 3-ph., 60-cycle, 900-syn. r.p.m. induction motor. component I wo which is required to overcome the losses P. I wo is quite large at low voltages; for example, at 120 volts I e =7.2 amperes P =960 watts 960 I =v7.2 2 4.6 2 = 5.6 amperes = the true magnetizing cur- rent. The difference between I and I e is comparatively small at normal voltage, for example, at 440 volts 344 ELECTRICAL MACHINE DESIGN I e = 21 amperes P =1950 watts I wo =2.54 amperes I =\/21 2 -2.54 2 = 20.8 amperes P contains the windage and friction loss, the core loss, and the small stator copper loss due to the current I e . If curve 2 be produced so as to cut the axis as shown, then the watts loss at zero voltage = 800 watts, must be the windage and friction loss since the flux, and therefore the core loss, is zero and the stator copper loss can be neglected. 247. The Short-circuit Curve. This curve shows the relation between stator voltage and current, the rotor being at stand- still. The figures necessary for its construction are obtained by blocking the rotor so that it cannot revolve and applying voltage to the stator windings at normal frequency; the rotor is sometimes held by means of a prony brake so that readings of starting torque may also be taken. The applied voltage is gradually raised from zero to a value that will send about twice full-load current through the motor, and simultaneous readings are taken of voltage, current, total watts input, and torque. The results of such a test on the 50 h. p. motor on which the saturation test was made are given below. SHORT CIRCUIT E\ I.c P * wsc T T Et Terminal volts Line current Watts input Torque in pounds at 1 ft. radius 222 185 3,000 78 155 .7 201 165 2,400 69 122 .61 178 143 1,820 59 94 .53 162 127 1,420 51 71 .44 138 109 990 41 51 .37 120 88 680 33 35 .29 101 72 440 25 23 .23 80 58 270 20 14 .18 58 42 140 14 7 .12 38 27 60 9 CONSTRUCTION OF THE CIRCLE DIAGRAM 345 E t On short-circuit I sc = r. - r 2 X. + XJ^ )-5i formula 43, page 337, so \ 2 C 2/ U 2 that theoretically the relation between E t and I sc in the above table should be represented by a straight line. The actual relation is shown in curve 4, Fig. 230; the curve gradually bends away from the straight line due to the gradual saturation of the iron part of the leakage path. The watts input on short-circuit =1.73E t I wsc ,it is also = kl sc 2 , because it is all expended in copper loss, and since E t is proportional to I sc , see curve 4, therefore I wsc also is propor- tional to I sc and the relation is plotted, for the tests in the above table, in curve 5. In Art. 245, it was shown that the starting torque is propor- tional to n 2 I? 2 R 2 , the rotor copper loss, where 7 2 is the rotor cur- rent on short-circuit, and since 7 2 is proportional to 7 SC which is , .. starting torque . . , proportional to E t therefore - -% - is proportional to tit I sc and the relation is plotted, for the tests in the above table, in curve 6. Curves 4, 5 and 6 are produced as shown, so that the probable values at normal voltage of 7 SC , I wsc , and ^ may be deter- mined; at 440-volts I sc =370 amperes 7 WSC = 150 amperes torque in Ib. ft. . iT~ \2t volts torque in pounds at 1 ft. radius =1.2X440 = 528, 528X2^X900 torque in synchronous horse-power = -- ^7^ -- = 90 248. Construction of the Circle Diagram. The results ob- tained from the curves in Fig. 230 are to be used in order to construct the circle diagram, Fig. 231, from which the charac- teristics of the motor will be determined. 1. Locate the short-circuit point. With o as center and radius 7 SC =370 amperes describe the arc of a circle; of the total current 7 SC the power component 7 w;sc = 150 amperes. These two values of current give I, the short-circuit point. 2. Locate the no-load point. At 440 volts the exciting current = 7 e =21 amperes and the value of P at the same voltage = 1950 watts, so that the power component of the exciting current 346 ELECTRICAL MACHINE DESIGN 1950 = == -7-7.^ = 2.54 amperes. These two values of current give 1. /o X 44U the point I e , the no-load point. 3. Draw the circle. The circle must pass through the two points I and I e and must have its center on the constant loss line. 4. Find the stator and rotor copper losses. Of the total copper loss represented by Ip the part mp represents the stator copper loss and is determined as follows: The resistance of the stator winding from terminal to neutral, measured by direct current = 0.112 ohms, so that the stator copper loss on short-circuit = 370 2 X 0.1 12X3 =46000 watts, and the corresponding power corn- 50 100 150 200 250 Line Current in Amperes FIG. 231. Circle diagram for a 50-h.p., 440- volt. 3-ph., 60-cycle, 900-syn. r.p.m. induction motor. 46000 ponent of current = ^TO ~/Mn~^0 amperes =mp. 1. /o X 44U For any stator current oc the constant loss = pnX 1.73X440 watts the stator copper loss = fe X 1.73 X440 watts the rotor copper loss deX 1.73 X 440 watts the mechanical output = cdX 1.73X440 watts 249. To Find the Characteristics at Full-load. The full-load = 50 h. p. and the value of cd corresponding to this output = 50 X 746 - = 49 amperes; the point c on the circle is then found JL. i o X 44U to suit and the following values scaled off ce =.51 amp. eg =55 amp. oc =62 amp; CONSTRUCTION OF THE CIRCLE DIAGRAM 347 cd 49 from which the efficiency = = ^-_ = 89 per cent. eg 55 the power f actor = = =89 per cent. cd 49 the actual speed = syn. speed X =900Xvr = 865 r.p.m. C@ O-L r de 2 the slip= = ^j =4 per cent. The maximum value of cd = 120 amperes so that the maximum 120X1.73X440 horse-power = TA " - = 122. The maximum value of ce = 160 amperes so that the maximum 160X1.73X440 torque in synchronous horse-power = =164 = about 3.25 times full-load torque. The value of ml = 87. 5 amperes so that the starting torque 87.5X1.73X440 in synchronous horse-power = - 74fi~~ = or a " ou * 1.8 times full-load torque, which checks closely, with the value found by brake readings. In plotting test results it is advisable to plot line current and terminal volts rather than current per phase and voltage per phase, because then the diagram becomes independent of the connection, since three-phase power = 1.73 Editor either Y or A connection, and two-phase power = 2E t Ii for either star or ring connection. CHAPTER XXXI CONSTRUCTION OF INDUCTION MOTORS 250. Fig. 232 shows the type of construction that is generally adopted for motors up to 200 horse-power at 600 r.p.m. The particular machine shown is a squirrel-cage motor. 251. The Stator. B, the stator core, is built up of laminations of sheet steel 0.014 in. thick which are separated from one another by layers of varnish and have slots E punched on their inner periphery to carry the stator coils D. FIG. 232. Small squirrel-cage induction motor. Two kinds of slot are in general use and both are shown in Fig. 233. The partially closed slot is used for all rotors and has the advantage that it causes only a small reduction in the air- gap area; the open slot is generally used for stators because the stator coils are subject to comparatively high voltages, and the open slot construction allows the coils to be fully insulated 348 CONSTRUCTION OF INDUCTION MOTORS 349 before they are put into the machine, it also allows the coils to be easily and quickly repaired in case of breakdown. The core is built up with ventilating segments spaced about Vent Segment Open Slot Partially Closed Slot FIG. 233. Slots and vent segments. FIG. 234. Parts of an Allis Chalmers Bullock squirrel-cage induction motor. 3 in. apart; one segment is shown at F, Fig. 232, and in greater detail in Fig. 233, and consists of a light brass casting which is riveted to the adjacent lamination of the core; the 350 ELECTRICAL MACHINE DESIGN lamination for this purpose is usually made of 0.025 in. steel. The laminations are clamped tightly between two cast-iron end heads C, and in order to prevent the core from spreading out on the inner periphery, tooth supports G, of strong brass, are often placed between the end heads and the core. The stator yoke A carries the stator core and the bearing hous- ings N. When the motor has to be mounted on a wall, or on a ceiling, the housings N must be rotated through 90 or 180 respectively; this is necessary because ring oiling is always used for motor bearings, and the oil well L must always be below the shaft. The bearing housings help to stiffen the whole machine and allow the use of a fairly light yoke. The shape of the hous- ings, as may be seen from Fig. 234, is such that it is a simple matter to close the openings between the arms with perforated sheet metal so as to form a semi-enclosed motor, or all the openings in the machine with sheet metal so as to form a totally enclosed motor. 252. The Rotor.' The rotor core also is built up of laminations of sheet steel, which are usually 0.025 in. thick; the use of such thick sheets is permissible because the frequency of the magnetic flux in the rotor is low and the rotor core loss is small. The core with its vent ducts is clamped between two end heads and mounted on a spider K, Fig. 232. In the case of squirrel-cage rotors the depth of the rotor slot is usually so small that a tooth support is not required. The rotor bars are carried in partially closed slots and are connected together at the ends by rings P called end connectors; these rings are usually supported on fan blades which are carried by the end heads. The shaft M is extra stiff because the clearance between the stator and rotor is very small, and the bearings H are extra large so as to give a reasonably long life to the wearing surface. The whole machine is carried on slide rails Q, which are rigidly fixed to the foundation and by sliding the motor along the rails the belt may be tightened or slackened. Slide rails are not used for geared or direct-connected motors. 253. Large Motors. Fig. 235 shows the type of construction for large motors. Pedestal bearings are used, so that the yoke has to be extra stiff in order to be self-supporting. The stator coils are tied to a wooden coil support ring R which is carried by brackets attached to the end heads; coil supports should be used CONSTRUCTION OF INDUCTION MOTORS 351 even on small motors if the coils are flimsy and liable to move due to vibration. Both squirrel-cage and wound-rotor constructions are shown in Fig. 235 and it may be seen that the same spider U can be used in either case; the two rotors differ in the number and size of slots and in the shape of the end head. S is a band of steel FIG. 235. Large induction motor; both squirrel-cage and wound-rotor construction shown. wire used to bind down the rotor coils of the wound-rotor machine on to the coil support T which is carried by the end heads; this coil support acts as a fan and helps to keep the machine cool. When the rotor diameter is greater than '30 in. the rotor core is generally built up of segments which are carried by dovetails on the rotor spider. CHAPTER XXXII MAGNETIZING CURRENT AND NO-LOAD LOSSES 254. The E.M.F. Equation. The revolving field generates e.m.fs. in the stator windings which are equal and opposite to those applied, therefore, as shown in Art. 148, page 189, #=2.22 kZ a = the flux per pole of the revolving field "'/= the frequency of the applied e.m.f. so that, if the winding of an induction motor and also its operating voltage and frequency are known, the value of the revolving field can be found from the above equation. 255. The Magnetizing Current. Diagram A, Fig. 236, shows an end view of part of the stator of a three-phase induction motor which has twelve slots per pole. The starts of the windings of the three phases are spaced 120 electrical degrees apart and are marked S lt S 2 and S 3 . Diagram B shows the value of the current in each phase at any instant. Diagram C shows the direction of the current in each conductor at the instant F and the corresponding distribution of m.m.f. Diagram D shows the direction of the current in each con- ductor at the instant G and the corresponding distribution of m.m.f. It will be seen that the revolving field is not quite constant in value but varies between the two limits shown in diagrams C and D. The. average m.m.f., AT av , is found as follows: Xl2A= area of curve in diagram C = 4.06/ IB X * 3.567 m X2/l 3.0?>/ m X2/l 2.5&/ m x2A 28 6/ m A 352 MAGNETIZING CURRENT AND NO-LOAD LOSSES 353 UOOOOOOOOOOOOOO FIG. 236, The revolving field. 354 ELECTRICAL MACHINE DESIGN also AT av Xl2^ area of curve in diagram D - 4.0X0.8666/ m X5/l 3.0X0.866 6/ m X2/l 2.0X0.866 67 W X2A 1.0X0.866 6/ TO X2A 27.7 bl m l therefore, taking the mean of these two values A T a X 12;. = 27.85 bI m X and AT av = 2.32 6/ w since there are 12 slots per pole = 0.273 (cond. per pole) I e The value of AT av can be found in a similar way for any number of slots per pole and for both two- and three-phase windings and varies slightly from the above figure for different cases, but in general the value of AT av used for all polyphase windings = 0.273 (cond. per pole) I c . The relation between the flux per pole and the magnetizing current per phase is found from the formula -0.87 (cond. per pole) I e rL dC or/ = 7^ -rtX-T^XaC (44) 0.87 (cond. per pole) rL g where I = the magnetizing current per phase (effective value) s = the lines of force that cross the slots and circle 1 in. length of the phase belt of conductors for each ampere conductor in that belt. < z = the lines of force -that zig-zag along the air-gap and circle 1 in. length of the phase belt of conductors for each ampere conductor in that belt. 360 LEAKAGE REACTANCE 361 then, just as in the case of the alternator, the stator reactance per phase in ohms = 2xfb 2 c 2 p[(j)eL e + ( 8 +(f) z )Lg]lO~ s for a chain winding = 27r/6 2 c 2 p[% r ^4- (0 + z I o o / "i where r = 3.2 1 ^ 364 ELECTRICAL MACHINE DESIGN the end-connection reactance in formula 45 is the equivalent reactance of both rotor and stator. For squirrel-cage motors the end-connection reactance of the rotor may be neglected and the curve for- - in Fig. 244 used directly. For wound-rotor IV motors on the other hand it might seem at first that this value should be doubled, but it must be remembered that the m.m.fs. of rotor and stator are opposing and the leakage flux has to get through the space Vj Fig. 235, between the two layers of wind- ings, so that the closer together these windings are the more restricted is the space V and the smaller the leakage flux; for ordinary motors it is satisfactory to use the value for -- in Fig. 244 and increase it by 35 per cent. Example of Calculation. Find the maximum current Id for the following machine. Rating. 50 h. p., 440 volts, three-phase, 60 cycle, 900 syn. r.p.m. The construction of the machine is as follows: Stator Rotor External diameter .......... 25 in. 18.91 in. Internal diameter ........... 19 in. 15.5 in. Frame length ............... 6.375 in. 6.375 in. Vent ducts ................. 1-3/8 in. 1-3/8 in. Gross iron ................. 6 in. 6 in. Slots, number .............. 96 79 Slots, size ................. 0.32 in. XI. 5 in. 0.45 in. X 0.4 in. Cond. per slot, number ...... 6 1 Cond. per slot, size .......... 0.14 in. X 0.2 in. 0.4 in. X 0.35 in. Connection ................. Y Squirrel cage Winding .................... Double layer Air-gap clearance ........... 0.03 in. A stator and a rotor slot are shown to scale in Fig. 242. The calculation is carried out in the following way: pole-pitch =7.5 in. ^p = 4.3 from Fig. 244 = 0.622 (7, = 1.52 ,-1.03 n lP ~96_ \3X0 = [6.3 + 2.1] for the stator 1-3 , - 2 \ , Q 26- 62 V l 1 l 0.32 + 0.32/+ '0.03 1.52 + 1.03 LEAKAGE REACTANCE 365 0-26 0^03 \L52 + UM~ l ) J l fc 0/0.40 2X0.07 79 3X0.45 ^ = r [3.2 + 2.6] for the rotor = 0.415(0.54 + 0.96) = 0.62 ohms 440 The voltage per phase =^-^ = 254 since the connection is Y and the maxi- 254 mum current per phase = ^^ = 410 amperes. < 6.32^ L0.03 FIG. 242. Stator and rotor slot for a 50-h.p 900-syn. r.p.m. induction motor. 265. Belt Leakage. 1 In addition to the end connection, slot, and zig-zag leakage, there is another which enters into the react- ance formula for a wound -rotor motor, namely, the belt leakage. In developing the formula on page 363 it was assumed that the m.m.f. of the rotor was equal and opposite to that of the stator at every instant. This cannot be the case in a wound- rotor machine because, as shown in Fig. 221, the winding is arranged in phase belts and the stator and rotor belts sometimes overlap one another. When the stator and rotor are in the relative position shown in diagram A, Fig. 243, the currents in the stator phase belts are 1 Adams, Trans, of International Electrical Congress, 1904, Vol. 1, page 706. 366 ELECTRICAL MACHINE DESIGN exactly opposed by those in the rotor phase belts. The starts of the windings of the three phases are spaced 120 electrical degrees apart, and it may be seen from diagram A, that the cur- rents in the three stator belts S 1} S 2 and S 3 , and also in the three rotor belts R 1} R ? and R 3 are out of phase with one another by 60 degrees; they are represented by vectors in diagram B. When the stator and rotor are in the relative position shown in diagram C the currents in the belts have the phase relation shewn in diagram D. s\ s. fr"^* nnonoooOQI FIG. 243. Belt leakage in 3-phase machines. Part of diagram C is shown to a large scale in diagram E where it may be seen that belt R 3 overlaps belt S 3 by a distance fg and belt S 2 by a distance gh. In the belt fg the current in the stator conductors is S' 3 , diagram D, and that in the rotor conductors is R ? , of which the component om opposes the stator current; mn, the remaining part of the stator current, is not opposed by an equivalent rotor current and is represented by crosses in diagram E. In the belt gh the current in the stator conductors is S 2 , dia- LEAKAGE REACTANCE 367 gram D, and that in the rotor conductors is R 3 , of which the component op opposes the stator current; pq, the remaining part of the stator current, is not opposed by an equivalent rotor cur- rent and is represented by dots in diagram E. The currents represented by crosses and dots in diagram E set up the flux (f>b, which is in phase with the belt of conductors which it links and is therefore the same in effect as a leakage flux; it is called the belt leakage. & varies through one cycle while the rotor moves, relative to the stator, through the dis- tance of one-phase belt, and this belt flux is the cause of the variation in short-circuit current with constant applied voltage that is found in wound rotor motors, when the rotor is moved relative to the stator. The belt flux per ampere conductor in the phase belt and per inch axial length of core depends on the reluctance of the belt- leakage path and is directly proportional to the pole-pitch, in- inversely proportional to the air-gap clearance and to the Carter fringing constant, and is the greater the smaller the number of phases and therefore the wider the phase belt, so that the average value of the belt leakage that circles 1 in. length of the phase belt per ampere conductor in that belt, = a const. X and the average belt reactance per phase which must be added to formula 45, page 363, in the case of wound-rotor motors const. X (46) In addition to varying with the number of phases, the constant depends on the number of slots per phase per pole because, as shown in diagram E, the belt flux which links conductors a and b is smaller than if these conductors were concentrated in slot c. The value of the constant, which is found theoretically, is given in the following table: Stator slots per pole Two-phase motors Three-phase motors 6 0.0052X3 0.00107X3 12 XI. 5 XI. 5 18 XI. 25 Xl-25 24 XI. 15 XI. 15 30 X 1 . 10 X 1 . 1 Infinity. Xl.O Xl.O 368 ELECTRICAL MACHINE DESIGN For motors which have two-phase stators and three-phase rotors a mean value should be used. 266. Approximate Values for the Leakage Reactance. For a machine with a double-layer winding the equivalent reactance per phase -' from for- mula 45, page 363, where 6 L ~ varies with the pole-pitch as shown in Fig. 244. 2.0 4 6 8 10 12 Pole Pitch in Inches FIG. 244. Leakage constants. smce 14 16 18 ' the total slot width per pole, is proportional to the pole-pitch, therefore is approximately inversely proportional to the pole-pitch. = ~~ " ^ s approximately LEAKAGE REACTANCE 369 constant, the maximum value being limited by humming as shown in Art. 282, page 387, and that being the case the Carter fringing constants C l and C 2 are also approximately constant. The number of slots per pole =nXc is approx- imately proportional to the pole-pitch, therefore is approximately inversely proportional to pole-pitch. The reactance per phase then = 27rfb 2 c 2 pn(K l + K 2 L g )W- s (47) where K^ and K 2 are plotted in Fig. 244 against pole-pitch, from the results of tests on a large number of machines with open 16 14 12 10 12345678 Values of L g in Inches FIG. 245. Variation of the leakage flux with frame length. stator slots, partially closed rotor flots, and double-layer wind- ings. The reason for the large value for wound-rotor motors compared with that for squirrel-cage machines is that in the former there is the additional end-connection leakage of the rotor, the belt leakage, and the larger rotor-slot leakage due to the deep slots required to accommodate the rotor conductors and insulation. The method whereby these constants were determined may be understood from the following example. ^ 24 370 ELECTRICAL MACHINE DESIGN Three machines were built as follows: A B C Terminal voltage 440 440 440 Phases 3 3 3 Cycles 60 60 60 Poles 8 8 8 Stator internal diameter . 19 in. 19 in. 19 in Pole-pitch 7.5 in. 7.5 in. 7.5 in. Gross iron . 4.5 in. 6 in. 7.75 in. Slots per pole 12 12 12 Conductors per slot . . 8 6 8 Connection Y Y A Maximum current Id ^v*. a tc-oc... 270 400 575 The results are worked up as follows: Voltage per phase 254 254 440 Current per phase . 270 400 334 Reactance per phase 0.94 0.63 1.32 K +K L .10.2 12.2 14.2 These results are plotted against the values of L g in Fig. 245 from which it may be seen that K l} the part which is independent of the frame length, =4.2 while K 2 = 1.30; these values check closely with the curves in Fig. 244. CHAPTER XXXIV THE COPPER LOSSES 267. Copper Losses in the Conductors. If L&^the length of a stator conductor in inches 7 ci = the effective current per conductor M\ = the section of each conductor in cir. mils then the resistance of one conductor = -~ ohms; IvL j the loss in one conductor and the total stator copper loss = M WattS total cond. X L bl X / 2 C1 = l watts (48) Similarly the total rotor copper loss = 2 2 * 2 - watts (49) M 2 268. The Rotor End -connector Loss. Fig. 246 shows the distribution of current in part of the rotor of a squirrel-cage induction motor. FIG. 246. Current distribution in the rotor end connectors. The effective current in each rotor bar =/ C2 The average current in each rotor bar T^V The current in the ring at A = the maximum current in the ring = average current per cond. Xl/2 (cond. per pole) 2p 371 372 ELECTRICAL MACHINE DESIGN The effective current in each ring =^-^T 1.11 , . , , , . nD r Xk r The resistance of each ring == ^ x 1270000 where D r = the mean diameter of the ring in inches A r = the area of the ring in square inches A r X 1,270,000 = the area of the ring in cir. mils _ the specific resistance of the ring material the specific resistance of copper ' The loss in two rings =3X jx x In addition to the above copper losses there are eddy-current losses in the conductors due to the leakage flux which crosses the slot horizontally, as described in Art. 189, page 248. To prevent these losses from having a large value it is necessary to laminate the conductors horizontally. When the rotor is running at full speed the eddy-current loss in the rotor bars is small, because the rotor frequency is low; even at standstill, when the rotor frequency is the same as that of the stator, the eddy-current loss in the rotor bars is still low because the conductors are not very deep. Such eddy-current loss at standstill causes an increase in the starting torque without a sacrifice of the running efficiency, since the frequency is low and the eddy current loss negligible at full- load speed. A number of patents have been taken out on different methods of exaggerating this eddy-current loss in the rotor, but motors built under these patents have not come into general use. * EXAMPLE OF COPPER Loss CALCULATION A 50-h. p., 440-volt, 3-phase, 60-cycle, 900-syn. r.p.m. induc- tion motor is built as follows: Stator Rotor External diameter .......... 25 in. 18.94 in. Internal diameter ........... 19 in. 15.5 in. Frame length ............... 6 . 375 in. 6 . 375 in. Slots, number .............. 96 79 THE COPPER LOSSES 373 Slots, size . 32 in. X 1 . 5 in. . 45 in. X 0.4 in. Cond. per slot, number 6 1 size 0. 14 in. X 0.2 in. 0.4 in. X 0.35 in. Connection Y Squirrel cage Section of each end ring, A f . . . 75 sq. in. Mean diameter of end rings . .17.5 in. Resistance of end-ring material is 5 times that of copper. The circle diagram for the machine is shown in Fig. 247; it is required to draw in the copper loss lines. FIG. 247. Calculated circle diagram for a 50-h.p., 440-volt, 3-phase, 60- cycle, 900-syn. r.p.m. induction motor. L&! the length of stator conductor Lfo the length of rotor conductor The maximum stator current per cond. The maximum rotor current per conductor = (415 21) X = 20.5 in,, from Fig. 84 = frame length + 4 in. = 10.5 in. = the maximum current in the line, since the connection is Y = 415 amp. 96X6 79 = 394X 96X6 The maximum stator cond. loss The maximum rotor cond. loss The maximum rotor ring loss 79 2880 amp. 96X6X20.5X415 2 0.14X0.2X1270000" From formula 48. 57 kw. 79X1X10.5X2880 2 0.4X0.35X1270000 From formula 49. 39 kw. 9X2880\2 17.5X5 1000X8 / ' x 0.76" From formula 50 . = 47 kw. -fi 374 ELECTRICAL MACHINE DESIGN Therefore in Fig. 247 1. 73 X 440 Xab= 57,000 and a& = 75 amp. 1. 73 X 440 X 6c = 39,000 and be = 51 amp. 1. 73 X 440 Xcd = 47,000 and cd = Q2 amp. From these figures the loss lines can readily be drawn in. The final circle compares closely with that found from test and plotted in Fig. 231. CHAPTER XXXV HEATING OF INDUCTION MOTORS 269. Heating and Cooling Curves. The losses in an electrical machine are transformed into heat; part of this heat is dissipated by the machine and the remainder, being absorbed, causes the temperature of the machine to increase. The temperature becomes stationary when the heat absorption becomes zero, that is, when the point is reached where the rate at which heat is generated in the machine is equal to the rate at which it is dissipated by the machine. A \ -de Time in Seconds FIG. 248. Heating and cooling curves. The rate at which heat is dissipated by any machine depends on 8, the difference between the temperature of the machine and that of the surrounding air. During the first interval after a machine has been started up, S is small, very little of the generated heat is dissipated, therefore a large part is absorbed and the temperature rises rapidly. As the temperature increases, that part of the heat which is dissipated increases, therefore the part which is absorbed decreases and the temperature rises more slowly. The relation between temperature rise and time is shown in Fig. 248. The equation to this curve is derived as follows : 375 376 ELECTRICAL MACHINE DESIGN In a given machine let d8 be the increase in temperature in the time dt. The heat generated during this time =QXdt Ib. calories where Q = 0.53(kw. loss) The heat absorbed by the machine =WXsXd8 Ib. calories where W is the weight of the active part of the machine in pounds and Sj its specific heat =0.1 approximately The heat dissipated =A(a + bV)8xdt Ib. calories where A is the radiating surface of the machine V is the peripheral velocity a and b are constants. The heat generated = the heat dissipated + the heat absorbed or and the temperature rise is a maximum and = 8 m when the heat absorbed is zero or when Qdt=A(a+bV)8 m dt therefore A(a+bV)8 m dt=A(a+bV)8dt + Wsd8 Wsd8 and >- f o Jo t i.- v. - Ws from which A(a+bV) and s^8 = e ~ A ~^^~ therefore 8 = 8 m 1 1 e W^ = 8 m (l-e-T) (51) , Ws where T = A(a+bV} Ws8 m A(a+bV)6, Q or QT = Ws8 m (52) HEATING OF INDUCTION MOTORS 377 Therefore T is the time that would be taken to raise the tem- perature of the machine 6 m deg. if all the heat were absorbed. The cooling curve is the reciprocal of the heating curve and its equation is derived as follows: if the temperature falls d deg. in dt seconds then the heat dissipated = - WXsXdS = A(a + bV)S Xdt Ws dS therefore dt= A(a+bV) 8 and from which 6 = 9 m e~~ (53) If the motor is standing still while cooling the temperature drops much more slowly, as shown in Fig. 249. Consider the following example: An induction motor is run at full load and the final temperature rise =45 C. The current density in the stator cond. =480 cir. mils per ampere The iron loss at no-load and normal voltage = 1000 watts The weight of iron in the stator =115 Ib. The iron loss per pound =8.7 watts It is required to find the time constant T. The resistance of a copper wire L in. long and M cir. mils section = 1 r- r ohms. M The loss in this wire due to a current / = -Tur watts M = X5.3X10" 4 Ib. calories per second. The weight of this wire = LxMx2.5XlO~ 7 Ib. The specific heat of copper =0.09. Since QT = WsS m therefore X5.3X10 ~ 4 X T = LXMx2.5XlO - ? X0.09X TO M S m 2.3 XlO 4 and -rfr = 7- -- M ^ deg. Cent, rise per second. T (cir. mils per amp.) 2 378 ELECTRICAL MACHINE DESIGN In the given problem M = 480 and 6> m = 45 C. therefore T for the coils =450 seconds. Consider now the iron loss: The loss per pound of iron =P watts = PX5.3X10~ 4 Ib. calories second The specific heat of iron =0.1 approximately Since QT = Ws0 m therefore PX5.3X 10~ 4 X T = l XO.l X 9 m per ~ = T7 deg. Cent, rise per second. and In the given problem P = 8.7 watts per pound and $ m = therefore T for the iron of the stator =1000 seconds. C. 20 40 GO D 100 120 140 160 180 200 Time in Minutes FIG. 249. Heating and cooling curves. For the value of T found for the copper, and for $ w = 47 C., the relation between temperature and time is plotted in Fig. 249, and it will be seen that the calculated curve differs consider- ably from that found from test. The actual temperature rise in a given time is less than that calculated because: a. It has been assumed that all the iron loss is in the stator whereas a portion of it which cannot readily be separated out is due to rotor pulsation loss. b. Part of the heat developed in the active part of the machine is conducted to and absorbed by the frame. HEATING OF INDUCTION MOTORS 379 c. The temperature of the copper rises more rapidly than that of the iron and there is. a transfer of heat which tends to bring them to the same temperature. d. The thermal capacity of the insulation has been neglected. 270. Time to Reach the Final Temperature. Due to the chances of error pointed out above it is difficult to predetermine the rate of increase of temperature. It may be seen from formula 51 that the larger the value of T, which is called the time constant, the smaller is the rate of increase of temperature. T is the time that would be taken to raise the temperature of the machine to its final value if all the heat were absorbed, so that the lower the copper and iron densities the larger the value of T and the smaller the rate of increase of temperature. Slow-speed machines have poor ventilation and therefore low copper densities so that for such machines the rate of increase of temperature is comparatively small. Low-frequency machines, in which the flux density in the core is limited by permeability rather than by the iron loss, have the loss per pound of iron low and the rate of increase of temperature comparatively small. The current density in the field coils of D.-C. machines is usually of the order of 1200 cir. mils per ampere so that such coils heat up slowly. 271. Intermittent Ratings. Suppose that a motor is operating on a continuous cycle, X seconds loaded and Y seconds without load, the final temperature will vary, during each cycle, between 9 X and S yj Fig. 248, where these temperatures are such that the temperature increase in time X is equal to the temperature decrease in time Y. Under such conditions of service therefore Syj the highest temperature, is lower than &,, the maximum temperature which would be obtained on continuous operation under load. For such service, therefore, a motor may have higher copper and iron densities than it would have if designed for the same load but for continuous operation. 272 Heating of Squirrel -cage Motors at Starting. The loss in a squirrel-cage rotor at starting is very large and equals the full-load output of the machine X the per cent, of full-load torque required to start the load. Thus, if a 20 h. p. squirrel-cage motor has to develop full-load torque at starting the rotor loss under these conditions must be 20 h. p. This loss, in the form of heat, 380 ELECTRICAL MACHINE DESIGN has to be absorbed by the rotor copper, and the temperature rises rapidly unless there is sufficient body of copper to absorb this heat during the starting period. The stator current also is large at starting; an average squirrel- cage motor with normal voltage applied to the terminals develops about 1.5 times full-load torque and takes about 5.5 times full- load current; when started on reduced voltage it develops full- load torque with about 4.5 times full-load current, since the starting torque is proportional to the rotor loss and therefore to the square of the current. As shown in Art. 269, the temperature rise when the heat is all absorbed may be found from the following formula. 2.3 XlO 4 Degrees Cent, rise per sec. =. -- ^ = for copper wire (cir. mils per amp.) 2 watts per Ib. . . , ,. 1 q - for iron bodies watts per Ib. . ,. y^x - for copper bodies. An average value for the cir. mils per ampere at full-load is 500, for both rotor and stator. The starting current in the motor for full-load torque is about 4.5 times full-load current, the corresponding value of cir. mils per ampere is 110, and the tem- perature rise 1.9 C. per second. The proper weight of end connector to be used in any par- ticular case depends on the starting torque required and the time needed to bring the motor up to full speed. For motors from 5 h. p. to 100 h. p. the loss per pound of end connector is generally taken about 1 kw. and, corresponding to this loss, the temperature rise of the end connectors 1000 = 6 C. per second approximately. 273. Stator Heating. The temperature rise of the stator of an induction motor is fixed in the same way as that of the armature of a D.-C. machine. For induction motors built with iron of the same grade as used in D.-C. machines and of a thickness of 0.014 in., so that the iron loss curves are as shown in Fig. 81, the following flux densities HEATING OF INDUCTION MOTORS 381 may be used for a machine whose temperature rise at normal load must not exceed 40 C. Maximum tooth density Maximum core density in frequency . ,. . ,. in lines per sq. in. lines per sq. in. 60 cycles 85,000 65,000 25 cycles 100,000 85,000 These figures represent standard practice for machines with open stator slots and partially closed rotor slots when the rotor slot is designed as pointed out in Art. 257, page 356, for minimum pulsation loss. When both stator and rotor slots are partially closed these densities may safely be increased 15 per cent. The end connection heating is limited by keeping the value of . amp. cond. per inch . . the ratio ^- ^ below that given in Fig. 250, cir. mils per amp. which curve applies to wound-rotor motors, and to squirrel-cage motors with less than 4 per cent, slip, of the type shown in Figs. 232 and 235. 274. Rotor Heating. At full-load and normal speed the fre- quency of the flux in the rotor is very low so that comparatively high flux densities may be used. The rotor tooth density is not carried above 120,000 lines per square inch if possible, because, for greater values, the m.m.f. required to send the flux through these teeth becomes large and causes the power factor to be low; for the same reason the rotor core density is seldom carried above the point of saturation, namely about 85,000 lines per square inch. So far as heating is concerned the rotor core loss is so small that it may be neglected. The rotor copper loss is limited by making the ratio amp. cond. per inch e . . . ~ ^ - the same for the rotor as for the stator, and cir. mils per amp. then, if the motor is of the squirrel-cage type, any additional rotor resistance that is required to give the necessary starting torque is put in the end connectors, which are easily cooled. Since the rotor ventilation is better than that of the stator, because it is revolving, the rotor temperature is generally lower than that of the stator and is not calculated. 275. Effect of Rotor Loss on Stator Heating. The heating of the rotor causes the air which blows on the stator to be hotter than the surrounding air. The heating curve in Fig. 250 applies to squirrel-cage motors with about 4 per cent, slip or 4 per cent. 382 ELECTRICAL MACHINE DESIGN rotor loss, and for the type of construction shown in Figs. 232 and 235. When greater rotor loss than this is required, as in the case of squirrel-cage motors for operating certain classes of cement machinery, then the air blowing on the stator will be hotter than usual and the stator temperature will be higher than the value got from Fig. 250. On account of this extra rotor loss such high torque squirrel-cage motors are built on frames that are about 20 per cent, larger than standard. l.Z i 1.0 S S 0.8 3 i o 0.6 a d o.4 ^ H CD 0.2 O / / / / / / / / x^ 1 2 3 4 5 6xlO ; Peripheral Velocity of Rotor in Ft. per Min. FIG. 250. Heating of the stator end connections. 276. Effect of Construction on Heating. Fig. 251 shows the relative proportions of a 25-cycle and of a 60-cycle motor of the same horse-power and speed and therefore with the same size of bearings. In the case of the 25-cycle machine the bearing blocks up the air inlet, and in such a case the temperature rise should be figured conservatively until the first machine has been tested and accurate data obtained. Another objection to the 25-cycle motor is that the coils stick out a considerable distance from the iron of the core and there is a tendency for the cooling air to circulate as shown by the arrows and not to pass out of the machine; in such a case it may be necessary to put in a baffle, as indicated by the dotted line A, to deflect the air stream in the proper direction. 277. Heating of Enclosed Motors. Experiment shows that in the case of a totally enclosed motor the temperature rise of the coils and core of the machine is proportional to the total loss HEATING OF INDUCTION MOTORS 383 (neglecting bearing friction) and is independent of the distribu- tion of this loss, is inversely proportional to the external radiating surface and depends on the peripheral velocity of the rotor in the way shown in Fig. 94. FIG. 251. Motors built for the same output and speed but for different frequencies. 278. Heating of Semi -enclosed Motors. When the openings in the frame of a motor are blocked up with perforated sheet metal the machine is said to be semi-enclosed. The perfo- rated metal acts as a baffle, prevents the free circulation of air through the machine, and causes the temperature to rise, on an average, about 25 per cent, higher than it would for the same machine operating at the same load but as an open motor. The effect of enclosing a motor may be seen from the following table which gives the results of a series of heat runs made on a motor similar to that shown in Fig. 232 and constructed as follows: Internal dia. of stator Frame length Peripheral velocity of rotor . . Stator copper loss Rotor copper loss Iron loss Total loss External radiating surface . . . . . .20 in. . . .5.5 in. . . . 4730 ft. per minute . . .0.77 kw. . . .0.9 kw. . .0.77kw. . . .2.44 kw. . . . 3260 sq. in. 384 ELECTRICAL MACHINE DESIGN Opening in housings Openings in Openings in closed with housings housings perforated closed with closed with Parts of motor Open motor sheet metal f-in. holes on sheet metal sheet metal f-in. centers Yoke open- Yoke open- Yoke open- ings open ings open ings closed Stator coils 18.5 22 46 74 Stator iron 18.5 20 48 71 Rotor cond 15 21 46 71 Hotor ring 14 21 44 69 Rotor iron 14 20 41 61 Oil in bearings 14 24 39 57 Outside of yoke 30 The temperature rise is given in deg. cent. The first machine of a new type that is built is generally very liberally designed, the copper and iron densities are low. If this machine runs cool in test it may get a higher rating than that for which it was originally built, and, based on the results of the tests on this machine, the next is designed more closely. Electrical design is not an exact science but is always changing to suit the requirements of the customer, the accumulating experience of the designer, and the competition of other manufacturers. CHAPTER XXXVI NOISE AND DEAD POINTS IN INDUCTION MOTORS 279. Noise due to Windage. Fig. 252 shows the standard construction used for induction motors. As the rotor revolves air currents are set up in the direction shown by the arrows, and it may be seen from diagram A that a puff of air will pass through the stator, between the stator coils, every time a rotor tooth comes opposite a stator tooth, so that the machine acts as a siren. FIG. 252. Windage in induction motors. The intensity of the note emitted depends on the peripheral velocity of the rotor, while its pitch or frequency = the number of puffs per second = the number of rotor slots X revolutions per second _ peripheral vel. of rotoran ft. per min. 5 X rotor slot pitch in inches (54) The higher the pitch of the note the more objectionable it becomes, and a note with a frequency greater than 1560 cycles per second, which is the high G of a soprano, is very objectionable if loud and long sustained. For a peripheral velocity of 8000 ft. per minute and a rotor slot pitch of 1 in., the frequency of the windage note is 1600 cycles per second. Noise due to windage can be lowered in intensity by blocking up the rotor vent ducts; if the motor then runs hot due to poor ventilation, some other method of cooling must be adopted such as blowing air across the external surface of the punchings, 25 385 386 ELECTRICAL MACHINE DESIGN or the motor may be totally enclosed and cooled by forced ventilation. The intensity of the note can be greatly reduced by staggering the vent ducts as shown in Fig. 253, and since the air-gap clearance is large in high-speed machines, which are the only ones that are noisy due to windage, the ventilation of such machines will not be seriously affected. It should also be noted that for high-speed machines a large number of narrow ducts will give quieter operation than a smaller number of wide ducts, because the velocity of the air through each duct will be reduced. 280. Noise due to Pulsations of the Main Flux. In Fig. 237, page 356, A shows part of a machine which has a large number of rotor slots. The flux in a rotor tooth pulsates from a maximum when the tooth is in position x, to a minimum when the tooth is in position y, and the frequency of this pulsation is equal to I FIG. 253. Motor with staggered vent ducts. A B FIG. 254. Variation of the force of magnetic attraction on the rotor tooth tips. the number of stator teeth X revolutions per second. This pulsation of flux causes a noise which varies in intensity with the voltage. To minimize this noise the machine should be designed so as to have a minimum pulsation loss, the condition for which, as shown in Art. 257, page 356, is that the rotor tooth shall be equal to the stator slot pitch, and the rotor slit shall be narrow. The noise due to pulsation of the main flux may be minimized by stacking the rotor tightly. 281. Noise due to Vibration of the Rotor Tooth Tips. Fig. 254 shows several of the slots of the stator and rotor of an induction motor. When the rotor tips are in the position shown at A there is a force of attraction between the stator tooth and the rotor tooth tip, while in position B this force is zero; the rotor tooth tip will therefore be set in vibration with a frequency equal NOISE AND DEAD POINTS 387 to the number of stator teeth X revolutions per second. This noise cannot be minimized by making the core tight and must be provided against by having the root y sufficiently thick to prevent bending and by the use of a moderate air-gap clearance. Noise due to this cause is rarely found in conservatively designed machines; it has been found in machines which are built with a small air-gap so as to lower the magnetizing current, and those built with a very thin rotor tooth tip so as to lower the reactance. 282. Noise due to Leakage Flux. The principal cause of noise in induction motors is the variation in the reluctance of the zig-zag leakage path. When the stator and rotor slots are in the relative position shown in B, Fig. 254, the zig-zag leakage flux is a minimum, and when in the relative position shown in A, is a maximum/ so that there is a pulsation of flux in the tooth tips and two notes are emitted which have frequencies equal to the number of rotor slots X revolutions per second and the number of stator slots X revolutions per second respectively. To ensure that the noise thus produced will not be objection- able it is necessary to make the variation in the zig-zag leakage flux a minimum, and the most satisfactory way to do this is to make the zig-zag leakage as small as possible. This leakage flux is directly proportional to the ampere cond. per slot and inversely proportional to the air-gap clearance, and it has been found from experience that in order to prevent excessive noise up to 25 per cent, overload the ratio amp. cond. per slot at full-load , . . -4 ~- -. 7 - should not exceed 14X10 3 for air-gap clearance in inches machines with open stator and partially closed rotor slots, or 12X10 3 for machines with partially closed slots for both stator and rotor. It is also found that, as the frequencies of the two notes pro- duced by zig-zag leakage approach one another in value, the noise becomes more and more objectionable, and that, for even , ., ,. amp. cond. per slot at full-load lower values of the ratio -. -. : -, - than air-gap clearance in inches those given above, the noise will be objectionable if the number of rotor slots is within 20 per cent, of the number of stator slots. The cause of the noise in any given case can readily be deter- mined. Run the motor on normal voltage and no-load and, if it is noisy, the trouble is due to windage, pulsation of the main field, or weak rotor tooth tips; then open the circuit, and if the 388 ELECTRICAL MACHINE DESIGN motor is still noisy the trouble is due to windage. If the motor is quiet on no-load but noisy when loaded the trouble is due to the zig-zag leakage flux. 283. Dead Points at Starting. It was shown in Art. 245, page 341, that the starting torque in synchronous horse-power is equal to the rotor loss at starting. If the rotor is not properly designed this torque may not all be available. Distance moved by Rotor B FIG. 255. Variation in the starting torque. In the case of a squirrel-cage motor at standstill, the applied voltage is low and the main flux therefore small, but the starting current is several times full-load current and therefore the zig-zag leakage flux is large. This flux is a maximum when the stator and rotor slots have the relative position shown in diagram A, Fig. 254, and a minimum when they have the position shown in B, so that there is a tendency for the rotor to lock in position A, the position of minimum reluctance. If the force tending to NOISE AND DEAD POINTS 389 rotate the rotor is less than that tending to hold the rotor locked, then the rotor will not start up. A, Fig. 255, shows several slots of a machine which has five stator slots for every four rotor slots, so that when the available torque is a minimum every fourth rotor slot is in the locked position. Diagram B shows the result of a test made on this machine, the torque being measured by a brake for different positions of the rotor relative to the stator; it may be seen that there are five positions of minimum torque in the distance of a rotor slot pitch. In order that the variation in starting torque may be a mini- mum it is necessary to make the number of locking points small. If the number of rotor slots is equal to the number of stator slots then, when the starting torque is a minimum, each rotor slot will be in the locked position; if there are four rotor to every five stator slots then the number of locking points will be one- fourth of the total number of rotor slots; if the number of rotor and of stator slots are prime to one another then only one rotor slot can be in the locked position at any instant and the best conditions for starting are obtained. It has been found by experience that the starting torque for a squirrel-cage motor will be practically constant, if not more than one-sixth of the total number of rotor slots are in the locked position at any instant. Wound-rotor motors have a regular phase winding and, in order that this winding may be balanced, the number of rotor slots as well as the number of stator slots must be a multiple of the ,. stator slots number of poles and of the number of phases; the ratio p stator slots per phase per pole , must therefore = - ,- -~r~ - T -and, since the rotor slots per phase per pole number of rotor slots per phase per pole is often three or four, it might be expected that such machines would not have good starting torque because of dead points. This is not the case however because, at .starting, wound-rotor motors have a large resistance in the rotor circuit, and full-load torque tending to cause rotation is obtained with full-load current, therefore the zig-zag leakage at starting is much smaller than in squirrel-cage machines and the force tending to cause locking is small. If a wound-rotor motor be taken which has not more than 30 per cent, of the rotor slots in the locking position at any instant, and full voltage be applied to the stator while the rotor circuit is 390 ELECTRICAL MACHINE DESIGN open, then the main flux will have its normal value; it will be found that the rotor can readily be rotated by hand, which shows that dead points are not, as generally stated, due to variations in the reluctance of the air-gap to the main field. If now this same motor be short-circuited at the rotor terminals, so that it is equiva- lent to a squirrel-cage motor with low rotor resistance, it will be found impossible in most cases to get the motor to start up even without load, because of the locking effect of the leakage flux. If resistance be inserted in the rotor circuit it will be found that, as the rotor resistance increases, the variation in the starting torque becomes less and less, and that when this resist- ance is such that full-load torque is developed with normal volt- age and full-load current, the variation in starting torque due to leakage flux is so small that it can be neglected. CHAPTER XXXVII PROCEDURE IN DESIGN 284. The Output Equation. # = 2.22 kZ^flQ- 8 volts. See page 352. = 2.22 kZ(B g rL a }(^^J^~ IIO' 8 volts _2.22/clQ- 8 120 nZI volts -I i ,)/ \ y " v . - - j.- - - 77 and = 7T.D, therefore nE'/ = n ( y 20 j ZB g 7iD a L g r.p.m. ( ~rJ^ L \ / J \ 7?r and = 2.35 X lO~ 12 B g q cosd XyX r.p.m. X D a 2 L g taking k= 0.96 from which D a 2 L & =^^- ogvx p 10 !".^/^.. (55) The value of B^, the apparent average gap density, is limited by the permissible value of B t) the maximum stator tooth density, since where the iron insulation factor =^- = 0.9 L 9 the permissible value of B t = 85,000 lines per square inch for 60 cycles = 100,000 lines per square inch for 25 cycles and y=2.1 approximately, being slightly larger for machines of h small pole-pitch therefore, for machines jvith a pole-pitch greater than 7 in., 391 392 ELECTRICAL MACHINE DESIGN 11 J9MOJ % PROCEDURE IN DESIGN 393 #0=23,000 lines per square inch for 60 cycles, approximately = 27,000 lines per square inch for 25 cycles, approximately. The Values of cos and y. The values that may be expected from a line of 60-cycle motors with open stator slots and par- tially closed rotor slots are given in Fig. 256, diagram A, and corresponding curves for a line of 25-cycle motors are given in diagram B. Two power factor curves a and b are given for the 60-cycle machines; these correspond to the two speed curves a and 6. The power factor increases very slowly for speeds above a but drops very rapidly for speeds below b. GOO 400 200 20 200 40 60 400 600 Brake Horsepower 800 100 1000 FIG. 257. Curve to be used in preliminary design for frequencies between 25 and 60 cycles. The power factor and efficiency can be improved by the use of partially closed slots for both stator and rotor. 285. The Relation between D a and L g . There is no simple method whereby D a 2 L g can be separated into its two components in such a way as to give the best machine, the only satisfactory method is to assume different sets of values, work out the design roughly for each case, and pick out that which will give good operation at a reasonable cost. To simplify this work the following equations are developed. I = the magnetizing current per phase (7) _ = 0.87 cond. per pole X TL7 X<5XCXL2 ' page 354 ' . . cond. per pole XB a Xd 394 ELECTRICAL MACHINE DESIGN taking C = 1.5, an average value for machines with open stator slots and partially closed rotor slots. therefore -j =ihe per cent, magnetizing current = cond. per pole X/ xB Xd = 2.05 *X^ (56) The minimum permissible air-gap clearance is fixed by me- chanical considerations and should increase as the diameter, frame length and peripheral velocity increase; its value should not be smaller than that given by the following empirical formula: d = 0.005 +0.00035Z> a + 0.001L0 +0.0037 (57) where $ = the air-gap clearance in inches D a =the stator internal diameter in inches L0 = the gross iron in the frame length in inches F=the peripheral velocity of the rotor in 1000s of feet per minute. The ratio -j- is found as follows: where E = 2.22kZcj) a fW- 8 volts, formula 25, page 190. = 2.22kZ(B g rL g )flQ- 8 volts and X eq = 2nfb 2 c 2 pn(K l + K 2 Lg) 10 ~ 8 ohms, formula 47, page 369. -* ohms P , I d 2.22X0.96 / B g rL therefore -j- -^ >x- (58) q Ki+K 2 L g The Value of q. From formulae 55, 56, and 58 it may be seen that the larger the value of q the smaller the value of D a 2 L g , the smaller the per cent, magnetizing current, and the smaller the circle diameter and therefore the overload capacity. Since the ,. amp. cond. per inch , copper heating depends on the ratio ^- TJ , the cir. mils, per amp. ; larger the value of q, the greater the amount of copper required to PROCEDURE IN DESIGN 395 keep the temperature rise within reasonable limits and therefore the deeper the slots and the larger the slot reactance. Fig. 257 gives average values of q for 25- and 60-cycle induction motors and this curve may be used for a first approximation. 286. Desirable Values for I and I d . Fig. 258 shows the circle diagram for a reasonably good induction motor: The power factor at full-load The starting torque The maximum torque The maximum output = 90 per cent = 1.5 times full-load torque = 2.7 times full-load torque = 2.2 times full-load To obtain such characteristics the magnetizing current should not exceed one-third of full-load current, nor should the maximum current Id be less than six times full-load current. FIG. 258. Circle diagram for an average induction motor. 287. Example of Preliminary Design. To simplify the work the necessary formulae are gathered together below. JMX 10" r.p.m. 2.35B g q cos >05^ - B a . Ln where , r K i +K 2 L g D a = the internal diameter of the stator in inches L0 = the axial length of the gross iron in inches B g is taken as 23,000 for 60 cycles 27,000 for 25 cycles q is found from Fig. 257 396 ELECTRICAL MACHINE DESIGN cos 6 and TJ are found from Fig. 256 d = 0.005 + 0.00035D a + O.OOIZ^ + 0.0037 where 7 = the peripheral velocity of the rotor in 1000s of feet per minute. K l and KJL g are found by the use of the curves in Fig. 244. The work is carried out in tabular form as shown below, where the figures are given for a 50 h. p., 60-cycle 7 900 r.p.m. motor. PRELIMINARY DESIGN SHEET 50 h. p., squirrel cage, 60 cycles, 900 r. p. m. 50 = 23,000, 5 = 600, cos < ?= 89 per cent, r?=8< ) per cent., D a z L g = 2150 D. L g T V d J ^ + K 2 Li i 7 la I Id I 15 9.5 5.9 3.5 0.03 3 ,7 + 14 .(> = 18. 3 0.4 6.7 17 7.5 6.7 4.0 0.03 4. + 10. 8 = 14 .8 0.35 6.5 19 6.0 7.5 4.5 0.031 4. 3+ 8. I = 12 .4 0.32 6.2 21 5.0 8.2 4.9 0.032 4. 5+ 6. 1 = 10. 9 0.31 5.9 23 4.0 9.0 5.4 0.033 4. 7+ 4. 8 = 9. 5 0.29 5.4 So far as operation is concerned the 19-in. diameter machine is probably the best all-round machine. The 15-in. machine has the largest magnetizing current and therefore the lowest power factor while the 23-in. machine has the smallest circle diameter and therefore the smallest overload capacity. The shop conditions must be known before the costs of the above machines can be intelligently compared. The cost of yoke, spider and housings is greatest for the 23-in. machine, and the cost of assembling the cores is greatest for the 15-in. ma- chine; the total cost is probably least for the 19-in. machine, but will not vary very much over the range of machines shown. 288. Detailed Design. The work of completing the 50 h. p., 60-cycle, 900 r.p.m. design is carried out in tabular form for the 440-volt, three-phase rating as follows : Stator design /X120 Poles = =8 r.p.m. Internal diameter of stator = 19 in. from preliminary design Gross iron = 6 in. from preliminary design Vent ducts = 1 - 0.375 in. Net iron = 0.9 X gross iron =5.4 in. Pole-pitch = 7.46 in. Slots per pole =12, to be suitable for two and three phase PROCEDURE IN DESIGN 397 if chosen . =6, the machine would be noisy, see Art. 282 if chosen = 18, the slots would be very narrow. Slot-pitch = P le -P itch =0.622 in. slots per pole Slot width =0.311 =half the slot pitch for a first approximation Ampere conductors per inch =600 from preliminary design Ampere conductors per slot =374 = Ampere cond. per inch X slot pitch Full-load current =62 amp. taking cos = 0.89 and r?=0.89 amp. cond. per slot Conductors per slot =8= . ,, , ^ full-load current Connection =Y, because the current in each conductor was taken equal to the line current Amp. cond. per inch n ^ ., =1.0 from Fig. 250 Cir. mils per amp. Circular mils per ampere =600 required Circular mils per conductor = 600 X full-load current = 37,200 Size of conductor =0.029 sq. in. Size of slot and section of conductor are worked out in tabular form thus: 0.311 in. = assumed slot width 0.064 in. = width of slot insulation, see page 203 0.04 in. = necessary clearance 0.207 in. = available width for copper and insulation on conductors Use copper strip 0.2 in. wide insulated with double cotton Covering and change the slot width to 0.32 for a second approximation, therefore the size of conductor = 0.14 in. X0.2 in. 0.14 in. = depth of each conductor 0.015 in. = thickness of the cotton covering 0.155 in. = depth of each conductor and its insulation 0.465 in. = depth of three cond. and their insulation 0.084 in. = depth of slot insulation on each coil, see page 203. 0.549 in. = depth of insulated coil 1.098 in. = depth of two insulated coils 0.1 in. = thickness of stick in top of slot 1.198 in. = necessary depth of slot. Before fixing the slot depth the windings for all the probable ratings to be built on this frame should be worked out and the slot made deep enough for the worst. In this case a suitable slot depth is 1.5 in. 440 Voltage per phase ~ = 2 ^' since the connection is Y per pole =1,040,000, from formula 25, page 190 Minimum tooth width =0.302 in., taking slot width =0.32 in. Minimum tooth area per pole = minimum tooth width X slots per pole X net iron 398 ELECTRICAL MACHINE DESIGN = 19.6 sq. in. ., . flux per pole TT Maximum tooth density = : r~X~ mm. tooth area per pole 2 = 83,000 lines per square inch. Had this density come out too high it would have been necessary to have increased the length of the machine or decreased the slot width. Maximum core density =65,000 lines per square inch, assumed flux per pole ~2Xcore depth X net iron Core depth = 1.48 in. ; use 1.5 to give an even figure for the stator external diameter. The above data is now filled in on the design sheet shown on page 402. Rotor design Air-gap clearance =0.03 in. from preliminary design External diameter =18. 94 in. Gross iron = 6 in. Vent ducts =10.5 in.; slightly wider than for stator Net iron =5.4 in. stator slots , Number of slots -- for quiet operation, Art. 282 page 387. With this number = 80 there would be 5 rotor slots for every 6 stator slots and the starting torque would not be uniform, see Art. 283, page 388; use therefore 79 slots. Rotor current per cond. at full load -I,, (Fig. 224)x totalstator conductors total rotor conductors where I u is taken equal to 0.85 X / for a first approximation, a value which must be checked after the data for the circle diagram has been calculated and the circle drawn. = 385 amperes 385X79 Ampere conductors per inch = = 510 Amp. cond. per inch n =1.0approx., the same as for the stator Cir. mils per amp. Circular mils per ampere =510 desired Size of conductor =510X385 = 195,000 circular mils = 0.15 sq. in. approximately. Size of slot must be chosen so that the flux density at the bottom of the rotor tooth shall not exceed 120,000 lines per square inch and the work is carried out as follows: PROCEDURE IN DESIGN 399 Assumed copper section, 0.2 in. X 0.75 in. 0.3 in. X0.5 in. 0.4 in. X0.35 in. Slot section to allow for insulation and clearance, 0.25 in. X 0.8 in. 0.35 in. X 0.55 in. 0.45 in. X 0.4 in. Rotor diameter at bottom of slot, 17.14 in. 17.64 in. 17.94 in. Minimum slot pitch, 0.68 in. 0.70 in. 0.72 in. Minimum rotor tooth, 0.43 in. 0.35 in. 0.27 in. Minimum tooth area per pole, 23 sq. in. 18.7 sq. in. 14.4 sq. in. Flux per pole, 1.04X10 6 1.04X10 6 1.04X10 6 Maximum tooth density; lines per square inch, 71,000 87,000 114,000 The wider and shallower the slot the lower is the rotor reactance so that the last of the three is chosen, namely, 0.45 in. X 0.4 in. The necessary data for the circle .diagram is now calculated. The magnetizing current =21 amperes, from Art. 259, page 357. The no-load loss =1680 watts iron loss + 810 watts bearing friction, from Art. 259. The maximum stator current =415 amperes, from Art. 264, page 364. The circle is then drawn to scale as in Fig. 247. The section of the rotor ring is found as follows: The maximum stator conductor loss = 57 kw. Art. 268, page 373. therefore in Fig. 247, ab =75 amperes The maximum rotor conductor loss =39 kw. Art. 268 therefore be =51 amperes The maximum starting torque de- . , =90 syn. h. p. sired J therefore Im : 67 syn. kw. 67X1000 1.73X440 = 88 amperes and bd =113 amperes For full-load torque at starting the rotor loss = 50 syn. h. p. = 37 syn. kw. of which the loss in the rings ^^^M = 20 k Wi The weight of the end rings =1 Ib. per kw. loss, Art. 272, page 379 = 201b. The mean diameter of end ring =17.5 in. approximately The section of each end ring =0.57 sq. in. The resistance factor for the ring material is found from formula 50, namely, C /N 67 \2 2) r k r loss in two rings =0.5 ( ^nL ) X -^ where /c 2 = the maximum rotor current = (4 15 21) = 2880 amperes and the corresponding ring loss = 1.73X440Xcd = 1.73X440X62 =47,000 watts 400 ELECTRICAL MACHINE DESIGN therefore 47,000 = 0.5 (^ X ^ from which k r = 3.8 Certain standard compositions are used for the end-ring mate- rial, and in this case a composition which had five times the resist- ance of copper was used, and the ring section increased to 0.75 sq. in. to keep the loss the same. The design is now complete and the data should be gathered together in convenient form on a design sheet similar to that on page 402. 289. Design of a Wound -rotor Machine. It. is desired to design a rotor of the wound type for the 50-h. p., 440-volt, 3-phase, 60-cycle, 900-r.p.m. motor of which the stator data is tabulated on page 402. The work is carried out in a similar way to that adopted for the squirrel-cage design. Air-gap clearance External diameter Gross iron Vent ducts Net iron Number of slots Conductors per slot Current per conductor at full-load Terminal voltage at standstill = 0.03 in. the same as for the squirrel- cage motor = 18.94 in. = 6 in. = 1-0.5 in. = 5.4 in. stator slots .. =~2 -- for quiet operation = 80; use 72 or 9 slots per pole = 2, assumed; this number gives the simplest winding = 210 amperes -nox 72x2 JX 96X6 = 110 The brushes and slip rings will be cheaper and easier cooled if the winding is made with 4 conductors per slot, Y-connected; then = 105 amperes = 220 = 510 = 1.0, the same as for the stator = 510 = 510X105 = 53,500 cir. mils = 0.042 sq. in. Current per conductor at full-load Terminal voltage at standstill Amp. cond. per inch Amp. cond. per inch Cir. mils per amp. Circular mils per ampere desired Size of conductor PROCEDURE IN DESIGN 401 Size of slot is found in the same way as for the squirrel-cage machine and that chosen in this case = 0.42 in. X 1.0 in. Size of conductor =0.12 in. X 0.35 in. arranged 2 wide and 2 deep. The magnetizing current =21 amperes, the same as for the squirrel-cage machine The iron loss =1,680 watts The bearing friction loss =810 watts The maximum stator current is worked out in a similar way to that for the squirrel-cage machine, see Art. 264, page 364; thus for a wound-rotor machine the reactance per phase where T = 7. 5 in. ^^ = 4.3 from Fig. 244 ^ = 0.622 in. = 0.03 in. C1 it 1 2 = 1.16 =m&-< A 2 = 0.83 + z= 1 [.> / 1.0' 0.1 2X0.07 0.03\ n 2 p ~72[ \3X0.42 + 0.42 + 0.42 + 0.1 + ~07T/ = [5.1 + 2.8] const. = 1 . 5 X 0. 00 1 07, from page 367. 0.00107X1.5X ) ^ = 0.415X[0. 72+ (0.088 + 0.11 + 0.032)6] = 0.87 254 Max. current per phase = ^= = 300 amp. as against 415 for the squirrel- cage motor. 290. Induction Motor Design Sheet. All dimensions in inch units. 26 402 ELECTRICAL MACHINE DESIGN Stator Squirrel cage Wound rotor External diameter, Internal diameter, Frame length, End ducts, Center ducts, Gross iron, Net iron, Slots, number, size, Cond. per slot, number, size, Winding, type, connection, Minimum slot pitch, Minimum tooth width, Core depth, Pole-pitch, Minimum tooth area per pole, Core area, Apparent gap area per pole, Flux per pole, Maximum tooth density, Maximum core density, Ampere conductors per inch, Circular mils per ampere, Length of conductors, Maximum current per conductor, Maximum conductor loss, Section of each end connector, Resistance factor, Maximum ring loss, Apparent gap density, Air-gap clearance, Carter coefficient, Magnetizing current, gap, total, Reactance per phase, Maximum line current Id, Rating Horse-power, Terminal voltage, Amperes, full-load, Phases, Frequency, Syn. r.p.m., Poles, 25 18.94 18.94 19 15.5 14.5 6.375 6.5 6.5 none none none 1-0.375 1-0.5 1-0.5 6 6 6 5.4 5.4 5.4 96 79 72 0.32X1.5 0.45X0.4 0.42X1.0 6 1 4 0.14X0.2 0.4X0.35 0.12X0.35 double-layer squirrel-cage double-layer Y Y 0.622 0.72 0.73 0.302 0.27 0.31 1.5 1.22 1.12 7.46 19.6 14.4 15 8.1 6.6 6.0 45 1.04X10 6 1.04X10 6 1.04X10 6 83,000 114,000 110,000 64,000 79,000 86,000 600 510 510 570 460 510 20.5 10.5 19 415 2,880 560 57 kw. 39 kw. 32 kw. 0.75 5.0 47 kw. 23,000 0.03 1.52 1.03 1.03 17.6 21 12 16.75 stator 0.62 0.87 stator 415 2,880 300 stator 50 440 62 385 105 3 60 900 8 PROCEDURE IN DESIGN 403 V 13 13 10.2 2.55 15 9.75 11.8 2.95 17 7.6 13.3 3.34 19 6.1 14.9 3.74 21 5.0 16.5 4.12 K +KL ^ Id I I 5. + 14. 4 = 19 .4 0. 27 10 .2 5. 4 + 10. = 15 .4 0. 23 9 .0 5, ,7+ 7. 2 = 12 .9 0. 19 9 .0 6, 0+ 5. 4 = 11 .4 0. 18 8 .1 6. 4+ 4. 2 = 10 .6 0. 17 7 .2 291. Design of a 25-cycle Motor. It is required to design a motor of the following rating: 50 h. p., 440 volts, 3-phase, 25-cycle, 750 r.p.m., squirrel cage. = 27,000; g=600; cos = 90 per cent.; r?=89 per cent.; D a 2 L g = d 0.30 0.29 0.28 0.29 0.30 Any one of these machines would be satisfactory as far as magnetizing current and overload capacity are concerned. The 13-in. machine, however, is long and difficult to ventilate prop- erly so that it need not be considered. Of the others, the machine with the smallest diameter will generally be the cheapest so that the choice lies between the 15- and the 17-in. machine; there will be very little difference in cost between the two, but the 17-in. machine will be the easier to ventilate properly and will have the better appearance. Detailed Design for the 17-in. Machine. Since the per cent, magnetizing current is small it will be advisable to increase the air-gap over the minimum value of 0.029 in.; it may be taken =0.04 in. without making the magnetizing current too large or the power factor at full-load too low. Poles, Internal diameter of stator, Gross iron, Vent ducts, Net iron, Slots per pole, slot pitch amp. cond. per slot amp, cond. per slot air-gap clearance Slots per pole, Pole-pitch, Slot pitch, Slot width, Ampere conductors per inch, Amperes conductors per slot, = 4 = 17 in. = 7. 5 in. = 2-0.5 in. = 6. 8 in. = 12 or = 1.12 in. = 670 = 17X10 3 Noisy 18 0.74 in. 445 11 X10 3 Quiet, see Art. 282, page 387 = 18, suitable for both two- and three-phase = 13. 4 in. =0.74 in. = 0.37 in. = 600 from preliminary design = 445 404 ELECTRICAL MACHINE DESIGN Full-load current, =61 Conductors per slot, = 7 . 3 if Y-connected = 1 2 . 6 if A -conne cted Amp. cpnd. per inch, ^r. TJ = U . o & Cir. mils per amp. Ampere conductors per inch for 12 A winding. =570 Circular mils per ampere, = 700 Amperes per conductor, =35 for a delta-connected winding Circular mils per conductor, =25,000 Section of conductors, =0.02 square inch. = 0.08X0. 25 in. Size of slot, =0.37 XI. 75 in. Voltage per phase, =440 since connection is A Flux per pole, = 2, 900, 000 Minimum tooth width, =0.37 in. Minimum tooth area per pole, =45. 5 square inch. Maximum tooth density, = 100,000 lines per square inch. The rotor of this machine may be designed by the same method as that adopted for the 60-cycle machine in Art. 288; the probable number of slots = 59. It might seem that, since the overload capacity is more than sufficient for all ordinary purposes, a value of q higher than 600 might have been used. This would have allowed the use of a slightly shorter machine, as may be seen from formula 55, page 391, but would have necessitated a larger section of copper to keep the heating within reasonable limits, and a larger number of conductors per slot. It is probable that the small decrease in length of the machine would have been more than compensated for in price by the increased amount of copper required for both stator and rotor. 292. Variation in the Length of a Machine for a Given Diameter. In order to save on the original outlay for the tools required to build a line of induction motors it is advisable to design at least two lengths of machine for each diameter. In the case of small factories, where the total output is not very large, three different frame lengths may be used for each diameter. The principal dimensions of three squirrel-cage machines built on a 19-in. diameter for 8 poles, 60 cycles and 900 r.p.m. are tabulated below. External diameter of stator, 25 in. 25 in. 25 in. Internal diameter of stator, 19 in. 19 in. 19 in. Frame length, 4. 5 in. 6.375 in. 8.125 in. PROCEDURE IN DESIGN 405 Center ducts, none 1-0.375 in. 1-0.375 in. Gross iron, 4. 5 in. 6 in. 7.75 in. Net iron, 4.05 in. 5.4 in. 7.0 in. Slots, 96 96 96 Size of slot, .32 in. XI. 5 in . .32 in. XI. 5 in. .32 in. XI. 5 in. Conductor per slot, 8 6 8 Size of conductor, 0.1in.X0.2in. 0.14in.X0.2in. 0.1 in. X 0.2 in. Connection, Y Y A Ampere conductors per inch, 580 600 600 Circular mils per ampere, 560 580 600 Amperes per conductor, 45 62 46.5 Amperes per terminal, 45 62 80 Terminal voltage, 440 440 440 Phases, 3 3 3 Output, 35 h. p. 50 h. p. 65 h. p. Air gap clearance, 0.03 in. 0.03 in. 0.03 in. Magnetizing current, 16 amp. 21 amp. 27 amp. K l actual, see Fig. 245, page 369, 4.30 4.30 4.30 K 2 L g actual, 5.90 7.90 9.90 Reactance per phase in ohms, 0.92 0.62 1.27 Maximum current in line, 275 amp. 410 amp. 600 amp. Magnetizing current, 35 per cent. 34 per cent. 34 per cent. Maximum current, 6.1 full-load 6.6 full-load 7.5 full-load. The above machines are discussed under the following heads: Conductors per Slot. Since the same stator punchings are used in each case, the number of slots is fixed, and for the same flux density in the different machines the flux per pole must be directly proportional to the net iron. Now the voltage per conductor is proportional to the flux per pole, so that the number of conductors in series, for the same voltage per phase, must be inversely proportional to the flux per pole and therefore inversely proportional to the net iron in the frame length. Size of Conductor. This is inversely proportional to the number of conductors per slot for the same total copper section per slot. Current Rating. For the same current density in the conduc- tors, the current in each conductor must be proportional to the conductor section. If the connection is Y, the current rating is the same as the current per conductor; if the con- nection is A, the current rating =1.73 times the current per conductor. Output. For the same total section of copper, the output of the machine is proportional to the net iron in the frame length, 406 ELECTRICAL MACHINE DESIGN because output = a const. X phases X volts per phase X current per phase = a const. X n X Z(j> a Xl c = a const. XnZI c X a = a const. X total copper section XL n Magnetizing Current = ?r ^ r r XB g XXC, and 0.87 X cond. per pole since B g , d and C are all constant, the magnetizing current is inversely proportional to the number of cond. per pole and therefore to the number of conductors per slot. Maximum Current. The leakage flux per phase is made up of two parts, the end-connection leakage which is independent of the frame length, and the slot and zig-zag leakages which are directly proportional to the frame length. The reactance per phase =2nfb 2 c 2 pn(K 1 +K 2 L g )W~ 8 = a const. Xb 2 (K l + K 2 L g ) for machines built with the same punchings. From the data in the table it may be seen that, so far as magnetizing current and overload capacity are concerned, the longest machine is the best; but a machine cannot be lengthened indefinitely because a point is finally reached at which it becomes impossible to cool the center of the core properly, without con- siderable modification in the type of construction. Even before this point is reached it will generally be found economical to increase the diameter rather than keep on increasing the length because, since the output is proportional to D a 2 L g , an increase in diameter of 10 per cent, is equivalent to an increase in frame length of 22 per cent. 293. Windings for Different Voltages. The stator of a 35-h. p., 440-volt, 3-phase, 45-ampere, 60-cycle, 900-r.p.m. induction motor is constructed as follows : Internal diameter of stator 19 in. Frame length 4 . 5 in. Slots, number 96 Slots, size . 32 X 1 . 5 in. Conductors per slot, number 8 size 0.1X0.2 Connection Y It is required to design windings for the following voltages: 220 volts, 3 phase, 60 cycles 550 volts, 3 phase, 60 cycles PROCEDURE IN DESIGN 407 250 volts, 3 phase, 60 cycles 550 volts, 2 phase, 60 cycles. Conductors per slot. E = 2.22kZfi a flQ- 8 volts 7 cond. per slot , .. , , = a const. X&X r^ for a given frame and frequency, phases For the machine in question A; = 0.956 for three-phase windings . =0.908 for two-phase windings volts per phase X phases and the constant = j-f ^ f-r A; X cond. per slot 440 0.956X8 = 100 The windings for the different voltages may be tabulated thus: Term, voltage Phases Volts per phase Conductors per slot Connec- tion 440 3 254 8 Y 220 3 127 4 Y Use 8 conductors per slot con- nected YY. 550 3 320 10 Y 250 3 144 4.55 Y An impossible winding. 250 8 A Use instead of the one above. 550 2 550 12.2 Single Use 12 conductors per slot. circuit Size of Conductor. This must be chosen so that the stator copper loss and copper heating are the same for each voltage; that this may be the case it is necessary to keep the ratio amp. cond. per inch . . , r^ TJ - constant. The work is carried out in cir. mils per amp. tabular form thus: -j I* a . S3 i* J2 d | ll 1 +3 .s S "o 1 o o S a ' S o A 0} *H 0) O rt ^ a . T3 H CM 3 -2 3 6 p, O ft I ^ O 440 3 45 45 8 Y 580 560 0.1X0.2 in. 220 3 90 45 8 YY 580 560 0.1X0.2 in. 550 3 36 36 10 Y 580 560 0.08X0.2 in. 250 3 80 46 8 A 600 600 0.11X0. 2 in. 550 2 31 31 12 1 circuit 600 610 0.075X0.2 in. 408 ELECTRICAL MACHINE DESIGN The rotor winding is the same for all stator voltages and phases, because the only connection between the stator and rotor is the flux in the air-gap, and this is kept constant by the use of the proper number of stator conductors per slot. It is therefore possible to build motors for stock, complete except for the stator winding, which winding can be specified when the voltage and number of phases on which the machine will operate are known. It must not be imagined that the designs which have been worked out in this chapter are the only ones that could have been used. Electrical design is very flexible and different values for flux density and ampere conductors per inch might have been used to give a satisfactory machine, and perhaps a cheaper one. Where labor is cheap it will often pay to use closed stator slots, fans, forced ventilation or other means to reduce the size of the machine for a given output. When one design for a given rating is worked out completely, the designer has to go over it and try the effect of changing the different quantities until he is satisfied that, for the shop in which machines of his design will be built, the final design will give the most satisfactory machine both as regards manufacturing cost and reliability when in service. CHAPTER XXXVIII SPECIAL PROBLEMS IN INDUCTION MOTOR DESIGN 294. Slow Speed Motors. Since y = 2.05^ formula 56, page 394 and ^ = 0.337 J 3 ^ T -r formula 58, page 394 -- therefore ~ = a const. &fv , *? (59) and the ratio T depends largely on the ratio -- 1 o '. la 6 full-load current In moderate speed machines 7-= r r>, r r^~rfi , =18. I 0.33 full-load current In high speed machines the dimensions are small and the pe- ripheral velocity high, so that the ratio -^ is generally large, since the value of r is directly proportional to the peripheral velocity and the value of d increases with the dimensions of the machine. Such machines therefore have a large value of Id and a large overload capacity, they have also a small value of I and a high power factor. In the case of slow speed machines the dimensions are large so as to get the necessary radiating surface, and the peripheral velocity is generally low because of the large number of poles. Because of the small pole-pitch the ratio -^ is small, and the LO characteristics of the machine are small overload capacity, large magnetizing current and low power factor. Compare for example the preliminary designs for machines of 300-h. p. output, 60 cycles and 720 and 300 r.p.m. respectively. Horse-power, 300 300 Frequency, 60 60 r.p.m., 720 300 409 410 ELECTRICAL MACHINE DESIGN B g , 23,000 23,000 q, 730 730 cos 6, assumed, 91 per cent. 84 per cent. t) assumed 91 per cent. 90 per cent. Da z L g , 12,700 33,500 D a , 36 in. 65 in. L g , 10 in. 8 in. r, 11. 3 in. 8. 5 in. V, in 1000s of ft. per min., 6.8 5.1 d, 0.048 in. 0.051 in. K v 5.3 4.5 K 2 L g , 10.5 10 , 15.8 14.5 0.275 0.39 6.7 5.9 These two machines are shown to scale in Fig. 259. The above figures show that, the higher the speed for a given horse-power, the smaller is the magnetizing current and the larger the overload capacity; this is a characteristic property which cannot be changed except by the use of air-gaps on the slow speed machines which are not large enough for mechanical purposes. For slow speed motors the use of 25 cycles offers considerable advantage over the use of 60 cycles because, for the same r.p.m., the number of poles is the smaller in the case of the 25-cycle motor and therefore the pole-pitch and the ratio ^ are the larger. LO Compare for example the preliminary designs for machines of 300 h. p. at 300 r.p.m., for 25- and 60-cycle operation respectively. Horse-power, 300 300 Frequency, 60 25 r.p.m., 300 300 Poles, 24 10 B g , 23,000 27,000 q, 730 730 cos 6, assumed, 84 per cent. 90 per cent. r), assumed, 90 per cent. 90 per cent D2/v\2^i 1 ' ^ ^e . /* + e , * + Z\T ,]io- Zxjb c p n \j} n iP \ KlP i I *^i n 2 p / where for machine A 2% 0/1.3 [ 0.2 \ n 2 p 0-05 1 r / 0.45 2X0.07 0.03 \3X0.55 0.55+0.07 0.07 5.25 : 220 7.56 288 SPECIAL PROBLEMS Reactance per phase = 2;: X 60 X 2 2 X 4 2 X 24 2 X 3 \~ + ( ^^ \_ Z \ zoo 413 = 0.256 Voltage per phase = 440 for A connection Max. current per phase = = 1720 amp. Max. line current = 1 720 X 1 . 73 = 3000 amp. For machine B eL e _ . 2 2n n 2 p '288 10.5 : 288 7.0 220 1.5 2X0.07 0.03 3X0.31 0.31 +0.1 . O.I OJ62/J_ 1 \ 0.05 \1-04 1.02 / ' 45 I 2X - 07 l ' 03 ^ IQ26 ' 81 / 1 3X0.45 " r 0.45 + 0.07 0.07/ n 0.05 \1. 04 Reactance per phase =2?rX60Xl 2 X4 2 X24 2 x3 = 0.09 440 Voltage per phase = ^_ =254 for a Y-connection l.Yo Max. current per phase = Q QQ = 2800 = maximum line current. The points of importance in the above designs are: Open slot Flux density, stator teeth ............ 85,000 Flux density, stator core ............. 59,000 Core depth ......................... 2 . in. Carter coefficient ................... 1.4 Conductors per slot ................. 2A =1.16Y Internal diameter of stator ........... 65 in. Flux per pole ....................... 1.8X10 6 Magnetizing current ................. 175 amp. Maximum current ................. . 3,000 Closed slot 97,000 82,000 1 . 4 in. 1 . 04 2YY = 1Y 57 in. 2.08X10 6 168 amp. 16.4 2,800 When closed slots are used the flux density may be high, since the pulsation loss is almost entirely eliminated. The value of the Carter fringing coefficient is decreased and 414 ELECTRICAL MACHINE DESIGN therefore the magnetizing current is reduced for the same winding or, as in the above machines, the number of conductors is reduced for the same magnetizing current. Because of the reduction in the number of conductors the stator internal diameter is decreased for the same value of q, the ampere conductors per inch. Because of the reduced number of conductors the reactance of the winding is decreased, and because of the increase in the slot and the zig-zag leakage, due to the closing of the slot, the reactance is increased. The final result is that the closed slot machine is smaller and cheaper than the open slot machine, especially if, as in Europe, the cost of winding labor is cheap; it has the same characteristics as the open slot machine. If the closed slot machine were made on the same diameter as the open slot machine it would have the better characteristics. 296. High-speed Motors. The number of speeds in the useful range for small belted motors is smaller for 25 than for 60 cycles, as may be seen from the following table: Revolutions per minute .roles 60 cycles 25 cycles 2 3,600 1,500 4 1,800 750 6 1,200 500 8 900 375 10 720 300 for that reason, and also because they are cheaper than 25-cycle motors of the same speed, 60-cycle motors should be used where most of the driven machines are moderate speed belted machines. Compare for example the preliminary design for a 300 h. p., 60 cycle, 720 r.p.m., machine with that for a 300 h. p., 25 cycle. 750 r.p.m. machine. Horse-power, Frequency, R.p.m., Poles 300 60 720 10 300 25 750 4 SPECIAL PROBLEMS 415 cos 6, assumed, T), assumed, D* a Lg, D a L ff , V, in 1000s of ft. per min. 9, K^L g , Io I' Id 23,000 730 91 per cent. 91 per cent. 12,700 36 in. 10 in. 11. 3 in. 6.8 0.048 in. 5.3 10.5 15.8 0.275 6.7 27,000 730 92 per cent. 91 per cent. 10,300 27 in. Min. 2JL in. 5.3 0.045 in. 7 10.2 17.2 0.16 10.2 These two machines are shown to scale in Fig. 259. Since the magnetizing current of the 25-cycle machine is so small, it will be advisable to increase the air-gap clearance and thereby have less chance of mechanical trouble. Because the 25-cycle machine has the smaller diameter it must not be imagined that it is the cheaper machine. It has the smaller number of poles, the larger flux per pole and, there- fore, the deeper core. Due to the large pole-pitch the end con- nections are long, and due to the lower peripheral velocity and the greater difficulty in cooling the long machine, a large section of copper and deep slots are necessary. These facts are shown by the following table : Horse-power, 300 300 R.p.m., 720 750 Poles, 10 4 Pole-pitch, 11. 3 in. 21 in. Gross iron, 10 in. 14 in. Flux per pole =B g rL g , 2.6X10 6 8.0X10 6 Stator core density, assumed, 65,000 85,000 Necessary core area, 20 sq. in. 47 sq. in. Core depth, 2 . 25 in. 3 . 75 in. Rotor core density, assumed, 85,000 85,000 Necessary core area, 15 sq. in. 47 sq. in. Core depth, 1 . 7 in. 3 . 75 in. Length of stator conductor 30 in. 48 in. from Fig. 84. A section through the two machines is shown to scale in Fig. 259, from which it may be seen that the 25-cycle motor has the 416 ELECTRICAL MACHINE DESIGN larger amount of material in it, and will probably be the more expensive machine. In the case of large high-speed motors, such as those for direct connection to centrifugal pumps or for motor generator sets, care must be taken in the design to ensure that the machines will be quiet in operation. Consider for example, the design of a direct-connected wound- rotor motor of the following rating: 1000 h. p., 60 cycles, 900 r.p.m. 5g = 24,000, 2=800, cos = 92 per cent., i? = 92 per cent., D a 2 ff = 29,000 D a L g T V d K l -{-K 2 L g Io I Id I 32 28. 5 12.6 7. 55 0.067 7.5 + 36 = 43 .5 0.33 6.6 36 22. 5 14.1 8. 45 0.065 7.7 + 27 = 34 .7 0.28 6.6 40 18, 15.7 9. 40 0.065 8.3 + 20. 5 = 28, .8 0.26 6.3 44 15. 17.2 10. 3 0.066 8.6 + 17 = 25 ,6 0.24 6.0 When using the curves in Fig. 244 to determine K 1 and K 2 it should be noted that, for wound-rotor machines, the values of K l found from the curve must be multiplied by 4/3, and the values of K 2 must be taken from the upper curve. In order that the noise of the machine be not objectionable at no-load, the peripheral velocity should, if possible, be less than 8000 ft. per min. and the pitch of the windage note should be kept below 1400 cycles per second. The number of rotor slots per pole to satisfy this latter condition may be found from formula 54, page 385, namely: frequency of windage note = rotor slots X revolutions per second = 1440 if 12 slots per pole are used. For quiet operation at full-load, the number of slots per pole for the stator should exceed that for the rotor by about 20 per cent.; see Art. 282, page 387. For machines with 15 slots per pole, the values of the stator slot pitch = Q ~, of the ampere conductors per slot = q X h, and o X 1& . amp. cond. per slot , . , ,, . , . n , , of the ratio ^- - on which the noise at full-load air-gap clearance largely depends, are given in the following table: SPECIAL PROBLEMS 417 The last of these machines is close to the noise limit, and the first is too long to ventilate properly, so that the choice lies Amp. cond. ^ amp. cond. per slot per slot d 32 0.84 670 0.067 10.0 36 0.94 750 0.065 11.5 40 1.05 840 0.065 12.8 44 1.15 920 0.066 13.8 between a machine of 36-in. and one of 40-in. diameter. If the designer has been troubled with noisy machines he will probably choose that with the smaller diameter, because it will have the lower peripheral velocity, and, therefore, the lower intensity of windage note. If he is satisfied, from experience with other high-speed machines which have been built and tested, that the 40-in. motor will not be noisy, then it will probably be chosen because it is shorter and easier to ventilate. The rating of 1000 h. p. is about the highest that can safely be built at 900 r.p.m. with the open type of construction, since a machine of larger diameter is liable to give trouble due to noise, and a longer machine is liable to get hot at the centre of the core. A larger diameter and a higher peripheral velocity may be used if the motor is partially enclosed, so as to muffle the noise, and then cooled by forced ventilation. 297. Two-pole Motors. Since, for induction motors operating on 25 cycles, there is no available speed between 1500 and 750 r.p.m., the former speed is largely used for motors that are direct- connected to centrifugal pumps, and would also be largely used for small belted motors were it not that the cost of a 1500-r.p.m. motor is seldom less than that of a 750-r.p.m. machine of the same horse-power. Consider for example, comparative designs for a 300-h. p. 25-cycle induction motor at 1500 and at 750 r.p.m. respectively. Horse-power, R.p.m., Poles, cos d, assumed, 27 300 750 4 27,000 730 92 300 1,500 2 27,000 730 93 418 ELECTRICAL MACHINE DESIGN i), assumed, D a *Lg, D a> g , , V, in 1000s of ft. per min. d K lt K 2 L g , Flux per pole, Core density; lines per sq. in. Core area, Core depth, Length of stator conductor, 91 10,300 27 in. 14 in. 21 in. 5.3 0.045 in. 7 10.2 17.2 0.16 10.2 8.0X10 6 85,000 47 sq. in. 3. 75 in. 48 in. 90 5,100 18 in. 16 in. 28 in. 7.0 0.048 in. 8 9.3 17.3 0.13 11.5 12.0X10 6 85,000 71 sq. in. 5 in. 62 in. Some idea as to the relative proportions of these two machines may be obtained from Fig. 259. When full-pitch windings are used for induction-motor stators, the revolving field consists of a fundamental and harmonics. If there is a pronounced nth harmonic, the resultant revolving field may be considered as the resultant of a fundamental which revolves at synchronous speed, and of a harmonic which revolves at n times synchronous speed; if these fields move in the same direction the resultant torque curve will be curve 3, Fig. 260, which is made up of curves 1 and 2, due to the fundamental and the harmonic respectively. One of the characteristics of the two-pole motor, and particularly of the two-pole 25-cycle motor, is its large pole-pitch and consequent large overload capacity, so that for such machines, when of the squirrel-cage type and designed with small slip in order to obtain high efficiency, the overload torque ab of the harmonic may become compar- able with the normal torque of the fundamental, and in such a case the motor will run at a speed ra, which is approximately -th of synchronous speed, and is called a sub-synchronous speed. IV This sub-synchronous locking speed may be eliminated by the use of a high-resistance rotor, which raises the part cd of curve 1 without affecting the overload torque; an extreme case of a high-resistance rotor is a rotor of the wound type. Another way to eliminate these locking speeds is to eliminate the harmonics SPECIAL PROBLEMS 419 by the use of a short-pitch winding in the stator. Fig. 261 shows the flux distribution curve for a machine with a large number of stator slots; in diagram A a full-pitch winding is used, while in diagram B the winding is made 2-/3 of full-pitch; it may be seen that in the latter case a nearer approach to a sine wave is 300 H. P. 720 R. P. M. 60 Cycle 300 H. P. 300 R. P. M. 60 Cycle 300 H. P. 750 R. P. M. 25 Cycle 300 H. P. 1500 R. P. M. 25 Cycle FIG. 259. 300 h.p. induction motors for different speeds and frequencies. obtained than in the former. The short-pitch winding has the additional advantage that it reduces the length of end connec- tions considerably and for that reason is useful for both two- and four-pole machines. Against this advantage there is the dis- advantage that, since E = 2.22kZ n flQ-* cos- 2i where 6 is the angle in electrical degrees by which the pitch is 420 ELECTRICAL MACHINE DESIGN shortened, therefore, for the same flux per pole, a larger number of conductors is required with a short than with a full pitch winding. 1 \\7 T* FIG. 260. Speed torque curve for a motor with harmonics in the wave of flux distribution. 298. Effect of Variations in Voltage and Frequency on the Operation. For a given machine E = & const. 7 = a const. X eq = a, const. X/ Tjl Id = Y^~ = a const. X(j> X cq If the voltage applied to the motor terminals is reduced, the value of = a const. X - 2 Since the windings for different voltages are chosen so as to keep the value of B g constant, the per cent, magnetizing current de- pends largely on the value of q. It was pointed out above that, if wound for high voltage, the rating of a given machine has to be reduced below the value which it would have if wound for low voltage. Now the number of conductors is directly propor- tional to the voltage, and, so long as the output is constant and the current inversely proportional to the voltage, the product of current X conductors is constant, and the per cent. magnetizing current and the power factor are independent of the voltage. If the current drops faster than the voltage increases, then the value of the product of conductors X current will decrease and the per cent, magnetizing current increase, thereby causing the power factor to be poorer, the higher the voltage. 426 ELECTRICAL MACHINE DESIGN 301. Effect of Speed on the Characteristics. The effect of speed on the efficiency is the same as for alternators and has been studied in Art. 228, page 316; the higher the speed for a given rat- ing, the higher is the efficiency. The effect of speed on the power factor and overload capacity has been discussed fully in the last chapter; the result of an increase in speed for a given horse-power is to improve the power factor and increase the overload capacity. 302. Specifications for Wound -rotor Machines. For such motors the same style of specification may be used as for the squirrel-cage machine, with the following modifications: No potential starter is required; in its place a resistance starter is supplied which has several starting notches. The type of service should be stated; a starter to be used for variable- speed work must be large because it absorbs a large amount of energy while in operation, for example, if a motor has to operate at half speed the amount of heat to be dissipated by the starter is approximately equal to the output of the motor; a starter that is built only for starting duty would burn up in a short time if used for variable-speed service. The starting torque can be made anything from zero to the pull-out torque by the variation of the external resistance of the rotor. The temperature guarantee is made for the maximum speed. A motor with a temperature rise of 40 deg. cent, at full load and maximum speed can generally operate continuously at half speed with full-load torque without injury. When a wound-rotor motor is operating at reduced speed, but with constant stator current, the iron loss of the stator remains constant, while that of the rotor increases because of the increase in slip and, therefore, of rotor frequency; the copper losses also remain constant, so that the heating increases as the speed de- creases; the horse-power is not constant but is proportional to the speed. CHAPTER XL OPERATION OF TRANSFORMERS 303. No-load Conditions. Fig. 262 shows a transformer diagrammatically; the two windings, which have T l and T 2 turns respectively, are wound on an iron core C. An alternating voltage E lt applied to the primary coil T lt causes a current I e , called the exciting current, to flow in the coil; c, CVx* V Is y 2 3> c ^ > c r \>c 'f ^ t ' _L , c Ti -V J ^ *. \J X ^\ C ( V $ J V i Core Type Shell Type A B FIG. 262. Diagrammalic representation of transformers. this current produces in the core an alternating flux, (f> co . The flux co is the flux in the core, I m is the magnetizing current, or that part of I e which is in phase with CO , I w , the component of I e which is in phase with the applied e.m.f., is required to overcome the no-load losses, E 2 , the e.m.f. generated in the secondary winding, lags co , and since E i = E lb} therefore f 2 =5 2 (60) E l T l 304. Full-load Conditions. When the secondary of a trans- former is connected to a load, a current 7 2 flows in the secondary winding; the phase relation between E 2 and 7 2 depends on the power factor of the load. The fluxes which are present in a transformer core at full- load are shown in Fig. 262. The m.m.f . between a and b = T l l l ampere-turns, where 7 t is the full-load current, and due to this m.m.f. a flux 0^ is produced which threads the primary winding but does not thread the secondary; ^ 1? is called the primary leakage flux and is in phase with the current 7 t . The m.m.f. between c and d = T 2 I 2 ampere-turns, where 7 2 is the full-load secondary current, and due to this m.m.f. the secondary leakage flux 2 z is produced which threads the secondary winding but does not thread the primary. In Fig. 264 7 2 is the current in the secondary winding, (f> 2 i, the secondary leakage flux, is in phase with 7 2 , (f> c , the flux in the core, threads both primary and secondary windings, 2 is the actual flux threading the secondary winding, E 2 is the e.m.f. generated in the secondary winding by 2 , E 2t , the secondary terminal e.m.f., is less than E 2 by I 2 R 2} the e.m.f. required to overcome the resistance of the secondary winding, OPERATION OF TRANSFORMERS 429 /! is the current in the primary winding, fa, the primary leakage flux, is in phase with I 1} $! is the actual flux threading the primary winding, E lb is the e.m.f. generated in the primary winding by lf E lt the primary applied e.m.f., is made up of a component equal and opposite to E^, and a component 7^ to overcome the primary resistance. FIG. 264. Vector diagram at full load. FIG. 265. Vector diagram at full load. The applied voltage E i is constant, and I 1 R 1 is comparatively small even at full-load, so that it may be assumed that E^ is equal to E ly and that lt which produces E^, is approxi- mately constant at all loads; the resultant of the m.m.fs. of the primary and secondary windings at full-load must, therefore, as far as the primary is concerned, be equal in effect to the m.m.f. of the exciting current I e , so that the primary current may be divided up into two components, one of which has a m.m.f. 430 ELECTRICAL MACHINE DESIGN equal and opposite to that of the secondary winding, while the other is equal to I e . It is usual to consider that the primary and secondary leakage fluxes have an existence separate from that of the core flux c ,- so that in Fig. 265 2 consists of two components (j> c and (j> 2 i, E 2 consists of two components; E 2C due to ^ c , and E 2 i due to $ 2 i, E 2 i lags (f> 2 i and therefore 7 2 by 90, it is also proportional to 7 2 , so that it acts exactly like a reactance and I 2 X 2 , where X 2 is the secondary leakage reactance, < t consists of two components c and 0^, E n consists of two components E IC and E^ which latter = I l X l the primary leakage-reactance drop. 305. Conditions on Short-circuit. On short-circuit the termi- nal voltage of the secondary is zero; the diagram representing FIG. 266. Vector diagram on short circuit. the operation is shown in Fig. 266 when the transformer is short- circuited and a primary e.m.f. applied which is large enough to circulate full-load current through the transformer. Since the applied e.m.f., and therefore the primary flux, is small, the exciting current may be neglected and TJ[^ and T 2 I 2 will then be equal and opposite. #i= where ab = OPERATION OF TRANSFORMERS 431 therefore R. _L i -t T l where jR e g and X e9 are the equivalent primary resistance and reactance respectively. 306. Regulation. Fig. 267 shows the vector diagram at full- load with the primary voltages expressed in terms of the secondary and the magnetizing current neglected. *3> c FIG. 267. Vector diagram on full load with primary voltages expressed in terms of the secondary. The regulation of constant potential transformers is defined as the per cent, increase of secondary terminal voltage from full- load to no-load ; the primary applied voltage being constant. In Fig. 267 the rise in secondary voltage from full-load to no-load =fc = I 2 R e cos 0+I 2 X e sin d + bc where R e and X e are the equivalent secondary resistance and reactance respectively and bcX2ab= (bd) 2 or bc = (bd) 2 2ab (I 2 X e cos 6-I 2 R e smdy 2(E 20 -bc) (I 2 X e cos 6-I 2 R e sinfl) 2 approximately. 432 ELECTRICAL MACHINE DESIGN The per cent, regulation \Q/C =ioo/ \ ac , // X \ 2 =-100 ^ + i ( - ) at 100 per cent, power factor. - - - V approximately at 80 per cent. power factor, lagging current. (61) CHAPTER XLI CONSTRUCTION OF TRANSFORMERS 307. Small Core -type Distributing Transformers. Figs. 268 and 269 show the various parts of such a transformer. The core A is built of L-shaped punchings, insulated from one another by varnish, and stacked to give a circuit with only two joints; FIG. 268. Core of a small distributing transformer. the joints are made by interleaving the punchings so as to keep the total reluctance of the magnetic circuit small. The core is assembled through the coils and is then clamped together 28 433 434 ELECTRICAL MACHINE DESIGN at the ends by brackets B and C; the limbs of the core are held tight to prevent vibration and humming by wooden spacers D which are put in between the core and low-tension winding. The coils are wound on formers and are impregnated with special compound. In the example shown the low-voltage FIG. 269. Small core-type transformer. winding has two half coils F and G on each leg, and a high- voltage coil H sandwiched between them; the object of this construction is to keep the reactance low. Wooden spacers are CONSTRUCTION OF TRANSFORMERS 435 used to separate the windings from one another and from the core so as to allow the oil in which the transformer is placed to cir- culate freely and thereby keep the coils and the core cool. There are two primary and two secondary coils, and the leads from each coil are brought up through an insulated board on which is mounted a porcelain block M for the high -voltage leads; by means of connectors the high-voltage coils may be put in I) FIG. 270. Large shell-type transformer. series or in parallel. The four low-voltage leads and the two leads from the high-voltage terminal board are brought out of the transformer tank through porcelain bushings which are cemented in. The tank is filled with a special mineral oil above the level of the windings, this oil acts as an insulator and also helps to keep 436 ELECTRICAL MACHINE DESIGN the transformer cool by circulating inside of the tank and carrying the heat from the transformer where it is generated, to the tank where it is dissipated. 308. Large Shell-type Power Transformers. Figs. 270, 271 and 272 show the various parts of such a transformer. The core FIG. 271. Shell-type transformer in process of construction. A is built up of punchings which are insulated from one another by varnish and are put together as shown in Fig. 273, with the joints overlapped so as to keep the total reluctance of the mag- CONSTRUCTION OF TRANSFORMERS 437 netic circuit small. The core is assembled around the coils and is then clamped between two end supports B and C; the bottom one is supplied with legs to support the whole transformer, while the top one carries the two terminal boards D and E, the former for the high-voltage leads and the latter for those of the f =' FIG. 272. Pancake coils for a shell- type transformer. low-voltage winding. The core is sometimes supplied with horizontal ducts which are obtained by building the core up with spacers; these ducts add to the radiating surface of the core and help to cool it but were not necessary in the transformer shown. 438 ELECTRICAL MACHINE DESIGN The coils are wound on formers and are then taped up indi- vidually, after which they are gathered together with the neces- sary insulation between them and insulated in a group; around these coils the core is built as shown in Fig. 271. The high- and low-voltage coils are sandwiched as shown in Fig. 272 to keep the reactance small; this latter illustration also shows the method of insulating the high- and low-voltage windings from one another by pressboard washers F, and the two adjacent high- L/ FIG. 273. Method of stacking the punchings of a shell-type transformer. voltage coils by a similar but smaller washer G. The winding is well supplied with ducts through which the oil can circulate. For large power transformers a tank such as that in Fig. 269 has not sufficient radiating surface and it is necessary to use corrugated tanks or tanks with extra cooling surface such as those shown in Fig. 298 or else to cool the transformer by forced draft as shown in Fig. 299 or by water coils as shown in Fig. 300.. In all cases the eye bolts which are used for lifting the tanks should extend to the bottom to prevent straining of the tank while it is being lifted. CHAPTER XLII MAGNETIZING CURRENT AND IRON LOSS 309. The E.M.F. Equation. If in a transformer (j> a is the maximum flux threading the windings at no-load, T is the number of turns in the winding, / is the frequency of the applied e.m.f ., then the flux threading the windings changes from (> a to (j) a in the time of half a cycle, or the average rate of change of flux = 2 (j> a X 2/ and the average voltage in the coil = 4 T a flQ ~ 8 For a sine wave of e.m.f., the form factor = 1.11 and E eff = 4A4:T(t> a fW ~ s volts (62) 310. The No-load Losses. The losses in a transformer at no- load are the hysteresis and eddy-current losses in the active iron, and the small eddy-current losses due to stray flux in the iron brackets and supports; these latter losses may be neglected if care is taken to keep the brackets away from stray fields. The hysteresis loss = KB^fW watts, and the eddy-current loss = K e (BftyW watts, where K is the hysteresis constant and varies with the grade of iron, K e is a constant which is inversely proportional to the electrical resistance of the iron, B is the maximum flux density in lines per square inch, / is the frequency in cycles per second, t is the thickness of the laminations in inches, W is the weight of the iron in pounds. The eddy-current loss = i 2 r, where r is the resistance of the eddy-current path and i, the eddy-current = - therefore the eddy- e 2 current loss = , where e, the voltage producing the eddy-cur- rent, is proportional to the flux density, the frequency, and the thickness of the iron. 439 440 ELECTRICAL MACHINE DESIGN The eddy-current loss may be reduced by a reduction in t } the thickness of the laminations, but this reduction cannot be carried to extreme because, for a given volume of core, the space taken up by the insulation on the laminations depends on their thick- ness; as they become thinner the amount of iron in the core decreases, the flux density for a given total flux increases, and finally a value is reached at which the amount of iron in the core is so small that the increase in flux density, and therefore in iron loss, more than compensates for the reduction in the eddy- current loss due to the reduction in the value of t. The iron which is used for other electrical machinery and is 0.014 in. thick is also that in most general use for transformers up to frequencies of 60 cycles. Special alloyed iron is largely used for 60-cycle transformers because it can be obtained with a high electrical resistance and, therefore, low eddy-current loss, it has also a small hysteresis constant; since it costs more and has lower permeability than ordinary iron, it is seldom used for 25-cycle transformers in which the core density is generally limited by magnetizing cur- rent and not by iron loss. When iron under pressure, as in the core of a transformer or other electrical machine, is subjected to a temperature of over 80 C. for a period of the order of six months, it will be found that the hysteresis loss has increased from 10 to 20 per cent, due to what is known as ageing. This ageing causes the iron loss and the temperature of a transformer to increase and the efficiency to decrease, but is not of importance in revolving machinery, because in such machines the hysteresis loss is only a small part of the total iron loss. Special alloyed iron shows very little ageing. The hysteresis loss in a transformer is affected by the wave form of the applied e.m.f. because, as shown by the equation # = 4xform f actor X TfaflQ- 8 for a given voltage, the higher the form factor, the lower the flux, the lower the flux density and, therefore, the lower the hysteresis loss. A wave with a high form factor is peaked, so that the advantage of low hysteresis loss is counteracted by the fact that the peaked e.m.f. has the greater tendency to puncture the insula- tion; a sine wave is the best for all conditions of operation. 311. The Exciting Current. Assume first that the maximum MAGNETIZING CURRENT AND IRON LOSS 441 flux density in the transformer core is below the point of satura- tion, so that the magnetizing current is directly proportional to the flux; then, if the flux varies according to a sine law, the mag- netizing current also follows a sine law, as shown in diagram A ; Fig. 274. For the given value of B m , the corresponding maximum ampere-turns per inch of core may be found from Fig. 42, page 47, and the effective magnetizing current I m max. amp. turns per inch X length of magnetic path n FIG. 274. Curves of flux and magnetizing current. or \/2/ w T = max. amp. turns per in. XL^ now E = 4A4Tcl> a flQ-* = 4MTB m A c flQ~ 8 , where A c is the core area in square inches therefore EI m = & const. XB m X amp. -turns per in. xA c L m Xf = a const. X function of B m X core weight Xf; 442 ELECTRICAL MACHINE DESIGN 8 10 12 - 14 16 18 20 22 24 26 28 Exciting Volt Amperes per Pound 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 Watts per Pound FIG. 275. Iron loss and exciting current in transformers. MAGNETIZING CURRENT AND IRON LOSS 443 since amp.-turns per inch depends on B m and A c L mj the core volume, is proportional to the core weight; therefore FT -^^r = the magnetizing volt amperes per pound = a function of B m Xf When the core is saturated at the higher densities, the curve of magnetizing current is no longer a sine curve but is peaked, as shown in diagram B, Fig. 274, because, as the points of high density are reached, the current increases faster than the flux on account of saturation, so that it is not possible to use the curves in Fig. 42 directly, a correction factor must be applied because of the form of the wave; in practice a different method is followed which allows the effect of joints, saturation and losses all to be taken into account. It was shown that the magnetizing volt amperes per pound = & function of B m Xf the iron loss per pound =KfB l ' 6 + K e (Btf) 2 = a function of B m for a given thickness and frequency, therefore the exciting volt amperes per pound = \/ (magnetizing volt amp. per pound) 2 + (iron loss per pound) 2 = a function of B m for a given thickness and frequency. If then a small test transformer be made of the material to be used for a line of transformers, and tested at no-load for exciting current and iron loss, the results may be plotted against maximum flux density as shown in Fig. 275, where test results are given for ordinary iron and for special alloyed iron at 25 and at 60 cycles; these curves may then be used for other transformers. Example. A transformer is constructed as follows: Weight of core, 1,760 Ib. alloyed iron Turns of primary winding, 526 Output, 300 k.v.a. Primary voltage, 12,000 Frequency, 60 cycles Core section, 122 sq. in. FIG. 277. FIG. 278. FIGS. 277 and 278. Leakage paths in core-type transformers. The m.m.fs. of the two coils, as shown in Fig. 264, are equal and opposite, and the currents are shown at one instant by crosses and dots. The leakage flux passes between the coils 445 446 ELECTRICAL MACHINE DESIGN and returns by way of the core on one side, and through the air on the other side; the space S is like the center of a long thin solenoid, and the return path of the leakage flux that links the primary coil has an infinite section so that its reluctance may be neglected; the return path for the flux that links the secondary coil is through the iron core, and its reluctance may also be neglected. The m.m.f. between the top and bottom of the coils for dif- ferent depths y is given by curve 1, the m.m.f. at depth y = T 2 I 2 xjr ampere-turns, <*2 therefore the flux d = 3.2 T 2 7 2 f- X 2nr * dy all in inch units. $2 Li This flux links T.^ turns of the secondary coil, and the interlinkages per unit current = 3. 2 ( T 2 y } X^^Xdy; \ d 2 ] L the coefficient of self-induction of the secondary coil due to the leakage flux which passes through the coil = 3.2X r~XT f*d z ' 2 I y* d y *L^ henry The m.m.f. along the space between coils = TJi = T 2 I 2 ampere-turns, therefore the flux which passes between the coils = 3. 2 X r -~ X T 2 I 2 ; since half of this flux may Li be assumed to link the primary and the other half the second- ary coil, the coefficient of self-induction of the secondary coil due to this flux henry; i the total coefficient of self-induction of the secondary coil = 3.2X 2 * r x7VXlO- 8 (| + |) henry; the leakage reactance of each secondary coil LEAKAGE REACTANCE 447 similarly the leakage reactance of each primary coil and X e , the equivalent secondary reactance -* (63) also the equivalent primary reactance If the coils on the two legs are connected in series the total reactance will have double the above value, and if connected in parallel will have half the value. 313. Core -type Transformers with Split Secondary Coils. Fig. 278 shows the leakage paths for one leg of such a transformer. The m.m.f. between the top and bottom of the coils for dif- ferent depths of winding space is given by curve 1, and the dis- tribution of leakage flux is symmetrical about the line ab. Consider coil 2 and half of coil 1, the equivalent primary reactance and, similarly, for coil 3 and the other half of coil 1, the equivalent primary reactance has the same value, therefore the total equivalent primary reactance <>- (64) which is between half and quarter of the value given in formula 63, for the case where the coils are not split up. 314. Shell-type Transformers. The coils of such a trans- former are generally arranged as shown in Fig. 272; the same arrangement is shown diagrammatically in Fig. 279, which also shows the distribution of leakage flux. The distribution of leakage flux is symmetrical about the 448 ELECTRICAL MACHINE DESIGN lines a, b, and c, and for one primary and one secondary coil the equivalent primary reactance (65) \ f \ / \ S \ /^ * 1 . i ( X Fx^ i r 1 P * * i [ X px" * 1 i > I- i L i 2 1 x ;x x\ y j| k *" ^ fr V ^_ [. . \ t: r x jt i y \ / v J V l\s V a b * \ T( turns FIG. 279. Leakage paths in shell- type transformers. where MT is the mean turn of coil; the total equivalent primary reactance when the primary coils are all in series = 27r/X3.2xr i 2 X^(^+| 1 +| 2 )lO- 8 X number of primary coils. This gives a value which is low; the error, however, seldom exceeds 6 per cent. CHAPTER XLIV TRANSFORMER INSULATION The insulation of transformers differs from that of the machines previously discussed in that it is submerged in oil. 315. Transformer Oil. Oil has the following properties which make it valuable for high-voltage insulation: It fills up all the spaces in the windings; it is a better insulator than air at normal pressure; it can be set in rapid circulation so as to carry heat from the small surface of the transformer to the large surface of the tank; it has a fairly high specific heat, and will allow the trans- former immersed in it to carry a heavy overload for a short time without excessive temperature rise; it will quench an arc. To be suitable for transformer insulation and cooling the oil should be light over the range of temperature through which the transformer may have to operate, because the ability of the oil to carry heat readily from the transformer to the case or cooling coils depends on its viscosity; it must be free from moisture, acid, alkali, sulphur, or other materials which might impair the insulation of the transformer; it must have as high a flash point as is consistent with low viscosity and must evaporate very slowly up to temperatures of 100 C. The oil largely used is a mineral oil which begins to burn at 149 C., has a flash point of 139 C., a specific gravity of 0.83, and a dielectric strength greater than 40,000 volts when tested between 1/2-in. spheres spaced 0.2 in. apart. The dielectric strength is greatly reduced by the additidn of moisture; 0.04 per cent, of moisture will reduce the dielectric strength about 50 per cent. This moisture may be removed by filtering the oil under pressure through dry blotting paper, or, if a filter press is not available, by boiling it at 110 C. until the dielectric strength has reached its proper value. When a transformer is in operation the oil may be sampled by drawing some off from the bottom of the tank through a tap provided for the purpose; the bulk of the moisture settles to the bottom. Only materials which are not attacked by nor are soluble in transformer oil should be used for transformer insulation; the 29 449 450 ELECTRICAL MACHINE DESIGN materials generally used are cotton, paper, wood and special varnishes. Wood, which is largely used for spacers, must be free from knots, and, in the case of maple, must also be free from sugar. Maple and ash are largely used, and, to ensure that they are free from moisture, they are baked and then impregnated with compound, or are boiled for about 24 hours in transformer oil at 110 C. Fullerboard and pressboard are largely used for spacers in transformers; the latter material has a laminated structure, so that impurities seldom go through the total thickness of the piece, it also bends readily, so that there is no objection to its use in sheets 1/16 in. thick. When baked and then allowed to soak in transformer oil 1/16- in. pressboard will withstand about 30,000 volts. Only varnishes which are specially made for transformer work should be used for im- pregnating coils, other varnishes may be soluble in hot transformer oil. 316. Surface Leakage. Fig. 280 shows two electrodes in air with pressboard be- tween them. When the difference of poten- tial between the two electrodes is increased, streamers will creep along the surface of the pressboard and finally form a short-circuit between the electrodes. The distribution of the dielectric flux is shown in the two cases and in diagram A the stress around the electrodes is much larger than in diagram B. The mechanism of the breakdown due to surface leakage is not definitely known; creepage takes place under oil as well as in air, but the creepage distance under oil is only about one-third of that in air for the same test conditions. The following tests 1 were made on a sheet of pressboard which was dried and then boiled in transformer oil : Tested as in diagram A: L = 6 in.; = 0.095 in.; creepage dis- tance =12. 095 in.; voltage to cause arcing across the surface = 40,000 volts. 1 A. B. Hendricks, Transactions of A. I. E. E., Vol. 30, page 295. .A FIG. 280. Surface leakage. TRANSFORMER INSULATION 451 Tested as in diagram B: L = 3 in. = the creepage distance; voltage to cause arcing across the surface = 50,000 volts. Fig 281 shows the results of similar tests made under oil, different thicknesses of pressboard being obtained by increasing the number of sheets; it may be seen from the curves that an increase in the thickness of the insulation has little effect on the creepage distance between two electrodes that are on the same side of the sheet, but has a large effect on the creepage distance around the end, the reason being that in the former case, shown in diagram B, the distribution of stress around the electrode 160 140 120 100 : 80 I 60 40 Terminals an opposite 12345 Total Arcing Distance - Inches FIG. 281. Creepage voltage on oiled pressboard. Conditions of test; Pressboard 0.095 in. thick, boiled in transformer oil, then tested under oil for creepage voltage with the electrodes first on the same side of the pressboard and then on opposite sides. is almost independent of the thickness of the material on which the electrodes rest, while in diagram A the dielectric flux passing through the material is inversely proportional to the thickness between electrodes, so that the greater the thickness the lower the stress around the electrodes. Trouble due to surface leakage is often eliminated more economically by an increase in the thick- ness of the dielectric than by an increase in the creepage length. 317. Transformer Bushings. 1 The terminals of the high- and low-voltage windings have to be brought out of the tank through 1 A. B. Reynders, Transactions of A. I. E. E , Vol. 28, page 209. 452 ELECTRICAL MACHINE DESIGN bushings. For voltages up to about 40,000 above ground, bushings made of porcelain or of composition are used. These bushings extend below the surface of the oil at one end; the other end is carried above the tank to a height sufficient to prevent breakdown due to surface leakage. Fig. 282 shows a bushing built to withstand a puncture test of 200,000 volts to ground for one minute. Diagram B shows the distribution of dielectric flux across a section of the bushing at xy, and since the strain in the material is proportional to the dielectric flux density, this strain is a maximum at the surface 1 FIG. 282. Solid bushing to withstand a puncture test of 200,000 volts for one minute. of the conductor and a minimum at the outer surface of the bushing; the strain at any point is proportional to the poten- tial gradient at the point, the curve of which is shown. To reduce the maximum value of the potential gradient it is necessary to reduce the dielectric flux density at the surface of the conductor, which may be done by increasing the diameter of the conductor without reducing the thickness of the bushing, or by increasing the thickness of the bushing. In order to make the outer layers of the bushing carry their TRANSFORMER INSULATION 453 proper share of the voltage, the condenser type of bushing shown in Fig. 283 was designed. It consists of a number of concentric condensers of tin-foil and paper in series between the center conductor and the cover of the tank. When condensers are put in series, the voltage drop across each is inversely proportional to its electric capacity so that, in the condenser type of bushing, if each concentric condenser have the same thickness and the \ FIG. 283. Diagrammatic representation of a condenser bushing. same capacity, the voltages across the different layers will all be equal and the strain will be uniform through the thickness of the bushing. The capacity of such condensers is proportional to area of plates thickness of dielectric so that, if the thickness of the different layers of dielectric, and also the area nDL of the different layers of tin-foil, be kept con- 454 ELECTRICAL MACHINE DESIGN stant, the voltage across each thickness of insulation will be equal to the total voltage divided by the number of layers. A bushing built with equal areas of plate and equal thicknesses of dielectric has the shape shown in diagram B; in such a case the voltages across the different layers are all equal, but the distance between two adjacent layers of tin-foil at a is greater than at b, so that the bushing is not economically designed for surface leakage. Condenser bushings are generally constructed as shown in diagram A; the surface distance between layers of tin- D C FIG. 284. Oil filled bushing. foil is constant, and the creepage distance under oil is con- siderably less than in air. When such a bushing is in operation, lines of dielectric flux pass through the air as shown in diagram B, and since the edge of the tin-foil is thin, the stress in the air at that edge is large and the air breaks down there, forming a corona. The corona contains ozone and oxides of nitrogen which attack the adjoining insulation and finally cause breakdown of the bushing. To prevent the corona from forming it is necessary to eliminate the air from around the bushing, and for this purpose TRANSFORMER INSULATION 455 the bushing is surrounded by a cylinder of fiber shown at C, which is then filled up with compound. Another type of bushing which is largely used for high-voltage work is the compound filled bushing of which a section is shown in Fig. 284. This type of bushing is built up of composition rings which are carefully fitted into one another and then clamped between two metal heads by a bolt C which acts as the conductor. ff~T .L. ^__i. Solid. Condenser. Oil Filled. FIG. 285. Bushings built to withstand 200,000 volts for one minute. The creepage distance is obtained by building rings B of com- position into the bushing. The whole center of the bushing is filled with compound or thick oil into which baffles of pressboard are placed as shown at D to prevent lining up of impurities in the compound along the lines of stress. Fig. 285 shows a solid bushing, a condenser bushing, and an oil filled bushing, all able to withstand a puncture test of 200,000 volts for 1 minute. 318. Insulation of Coils. : In most high-voltage shell-type transformers of moderate output, and in all core-type trans- formers, the high -volt age coils have several turns per layer, and the voltage between end turns of adj acent layers, which is equal to the volts per turn multiplied by twice the turns per layer, may 456 ELECTRICAL MACHINE DESIGN become high, so that, while the cotton coveiing on the wire is generally sufficient for the insulation of adjacent conductors in the same layer, it is necessary to supply additional insulation between adjacent layers of the coils. It is also necessary to provide sufficient creepage distance, which is done, where the space is available, by making the insulation between layers extend beyond the winding as shown in Fig. 288. Where the space is not available, as in the coils for shell-type transformers, the con- struction shown in diagram A, Fig. 287, is often adopted; one turn of cord is placed at each end of each layer and the insulation between layers is carried out to cover the cord; this construction lessens the chance of damage to the coil while being handled. For high-voltage transformers it is advisable to make the high- voltage winding of a number of coils in series with ample creepage distance and ample insulation between them, and to limit the voltage per coil to about 5000. The voltage between layers should not, if possible, exceed 350 volts. 319. Extra Insulation on the End Turns of the High-voltage Winding. *A condenser consists of two conductors with dielectric between, so that the high- and low-voltage windings of a trans- former, with the oil between, form a condenser; so also is there an electrostatic capacity between the high-voltage winding and the tank and between the low-voltage winding and the tank. A transformer may therefore be represented diagrammatically by a distributed inductance and capacity as shown in Fig. 286. Suppose that the transformer is disconnected from the line and all at the ground potential. If the potential of one end A of the high-voltage winding be suddenly raised to a value E, the potential of the whole high-voltage winding will gradually rise to the same value. The potential cannot rise instantaneously; the voltage at B for example, cannot reach the value E until the condensers at that point have been charged to a value Q = idt = CE, where C is the electro-static capacity between point B and the ground. The charging current i has to flow through the winding to B, and this takes a definite, though very short, time. The condensers near A will be charged first and the potential above ground of each point in the high-voltage winding is given by curves 1, 2 and 3 at successive instants. At the instant after switching represented by curve 1, the difference of potential between two points A and D, that is, 1 Walter S. Moody, Transactions of A. I. E. E., Vol. 26, page 1173. TRANSFORMER INSULATION 457 across the first few turns of the winding, =E 1} which is almost equal to the full potential E; because of this high voltage between turns, it is necessary to insulate the end turns from one 1 JLI-L1J. JLJL.L-L1-L-L-L-L 1 Low Voltage Winding Voltage nding TTTTTTTTTTTTTTTTT FIG. 286. The potential of transformer coils immediately after switching. 0.02 Fuller-board- 0.014"Fuller-board^ 0. QQI'F u 1 1 e r- boa rd ^ Cord D.C.C. Square Wire V 2 Lap Tape s i urn i an 0.014 Fuller-board Wire with Two Wrappings of Empire Cloth Tape Wire with One Wrapping of Tape 0.007"Fuller-board l / 2 L a P Tape A B FIG. 287. Insulation of the end turns of a 12,000 volt transformer coil, another for a voltage between turns of many times the normal value. Any sudden change in the potential of a transformer terminal. 458 ELECTRICAL MACHINE DESIGN such as that due to switching or to grounding of a line, will produce this high voltage between end turns. Diagram A, Fig. 287, shows a method of insulating the end turns of a coil for a shell-type transformer, when the coil is of wire wound in layers, and diagram B, for a coil wound with strip HV. sUl.c.c. wire =.014 'Fuller-board between Layers 0.02 Micanite 0.10'fcress- board }4 Lap Cotton Tape Coils are Impregnated FIG. 288. Insulation for a 2200/220 volt transformer. copper. This extra insulation is put on each end of the high- voltage winding for a distance of about 75 ft., and then any taps that are required for the purpose of changing the transformer ratio are connected to the inside of the winding, so that the extra insulation is always on the end turns. TRANSFORMER INSULATION 459 r^f fc P?-| M^ sO -*s*--> --. : '- { "'"-' ^^ t L^ kk , ^ j FIG. 289. Insulation for a shell-type transformer. 140 120 100 &GO 40 20 7 '/ 12345 Values from Curves 1 and 2 in Inches 5 10 15 Values from Curve 3 in Tnches FIG. 290. Spacings for the coils of shell-type transformers. 460 ELECTRICAL MACHINE DESIGN 320. Insulation between the Windings and Core. Fig. 288 shows the method of insulating a small core-type distributing transformer wound for 2200/220 volts. Fig. 289 shows an example of a shell-type transformer wound for moderate voltage, an illustration of such a winding and insulation is shown in Figs. 271 and 272. The various spacings used for different voltages are given in Fig. 290, where curve 1 gives the distance between high- and low-voltage windings and also between the high-voltage winding and the core; curve 2 gives '// \ Pressboard L.Y Coils \ H.V. Coils Insulation FIG. 291. Insulation for 110,000 volts. the total thickness of the pressboard in this distance; curve 3 gives the distance X between the high-voltage coil and the iron at the top and bottom of the core. Fig. 291 shows an example of a shell-type transformer wound for 63,500/13,200 volts for operation in a Y-connected bank on 110,000 volts; the insulation to ground, and also from high- to low-voltage winding, is the same as that for a 110,000-volt transformer. One-quarter of the total winding is shown in plan; there are 12 high-voltage coils, so that the voltage per coil = 5300. CHAPTER XLY LOSSES, EFFICIENCY AND HEATING 321. The Losses. The losses in a transformer are: the iron loss, the loss in the dielectric, and the copper loss. The iron loss has already been discussed in Art. 310, page 439. The loss in the dielectric, about which very little is known, causes the material to heat up and its dielectric strength to decrease. The loss is kept small by the use of ample distances between points at different potential, and the heating is kept small by a liberal supply of oil ducts through the insulation; the layers of solid insulation should not be thicker than 0.25 in. 322. The Copper Loss. If MT is the mean turn of a transformer coil in inches, M is the section of the wire in the coil in circular mils, I is the effective current in each turn of the coil, MT then the resistance of each turn = -^- ohms M MTxP and the loss per coil in watts = -^ X turns (65) In addition to the above copper loss there is the eddy-current loss in the conductors, which may be large if the conductors are not properly laminated or arranged so that the leakage flux cuts their narrow sides. Diagram B, Fig. 292, shows part of the winding of a core-type transformer and the direction of the alter- nating leakage flux at one instant. If the coils are wound of strip copper on edge as shown at E, then eddy currents will flow in the direction shown by the crosses and dots, and the loss will be much larger than if the coils are wound with flat strip as shown at A. Diagram D, Fig 292, shows part of the winding of a shell-type transformer, and the direction of the leakage flux and the eddy currents at one instant. If such a coil is laminated in the direc- tion of the leakage lines it will be weakened mechanically; for that reason it is not advisable to laminate the conductors unless 461 462 ELECTRICAL MACHINE DESIGN they are wider than 0.5 in. for 60 cycles, or 0.75 in. for 25 cycles, for which values, and for ordinary current densities, the eddy- current loss will be about 20 per cent, of the calculated PR loss. Even after the conductors of a core-type transformer have been laminated, considerable eddy-current loss may under certain circumstances be found in the windings; for example, A, Fig. 292, shows part of the winding of a low-voltage large-current transformer where the coil is made up of four wires in parallel; eddy currents tend to flow in the direction represented at one FIG. 292. Eddy currents in transformer coils. instant by the crosses and dots, and since the parallel wires are all connected together at the ends, the current will flow down one wire a, cross through the soldered joint at the end to wire b, up which it will pass and then return by the other soldered joint to conductor a, so that if the coil is developed on to a plane the currents will flow as shown in diagram C. To eliminate this circulating current the bunch of wires is given a half twist, as shown at F, so that in any one strip there are two e.m.fs., produced by the leakage flux, which are equal and opposite, the resultant e.m.f. is therefore zero and no circulating current will flow. LOSSES, EFFICIENCY AND HEATING 463 323. The Efficiency. If C.L. is the iron or core loss in watts, PR the copper loss in watts, El the output of. the transformer in watts, . output then, in, the efficiency = -* output + losses El EI+PR+C.L. The efficiency is a maximum when or (EI + PR + C.L.)E-EI(E + 2IR)=Q or PR = C.L. that is, when the copper loss is equal to the core loss. The all-day efficiency, which is of importance in distributing transformers, is defined by the following equation: EIXX all-day efficiency = where X is the number of hours during which the transformer is loaded each day, and 24 is the number of hours during which the iron loss is supplied. Distributing transformers should therefore be designed to have as small a core loss as possible, because this loss has to be supplied continuously. 324. Heating of Transformers. Since nearly all except instru- ment transformers are oil immersed, the subject of cooling by natural draft is not of importance and shall not be discussed. When a transformer is in operation under oil the heat generated in the core and windings has to be carried to the tank, from the external surface of which it is dissipated to the air. When the oil in contact with the transformer surface is heated, it be- comes lighter and rises, and cool oil flows in from the bottom of the tank to take its place, so that a circulation of oil is set up, as shown in Fig. 293. That it may circulate freely the oil should have a low viscosity, and the lighter the oil the better it is as a cooling medium for transformers. 325. The Temperature Gradient in the Oil. Fig. 293 shows a core-type transformer and also shows the temperature of the oil at different points along its surface. At the bottom of the tank the oil temperature is T^; the oil moves along the circulation path and its temperature rises and reaches a maximum value T t 464 ELECTRICAL MACHINE DESIGN at the top of the transformer, it then passes to the tank and, as it moves downward, the heat is gradually given up to the tank. After a number of hours, during which the whole body of the transformer and the oil are absorbing heat and being raised in temperature, conditions become fixed, the oil circulation and its temperature cycle become definite, and the different points of the transformer have their maximum temperature. 326. The Temperature Gradient in a Core-type Transformer. Consider the core of the transformer shown in Fig. 293. Iron is a good conductor of heat along the laminations, so that the difference in temperature between the points A and B of the FIG. 293. Temperature gradient in a core-type transformer. core cannot be great, and the difference in temperature between the core and the adjacent oil must be greater at the bottom of the core than at the top; because of this, much of the heat generated in the top part of the core is conducted downward and dissipated from the surface at the bottom, that is, the bottom part of the core surface is more active than the top part in dissipating the heat due to the iron losses. The conditions are different for the windings. These are formed of insulated wire wound in layers, and, because of the LOSSES, EFFICIENCY AND HEATING 465 number of layers of insulation in the length of the coil, very little of the heat generated in the top turns will be conducted downward through the winding. Most of the heat generated at any point in the winding will be conducted to and dissipated from the nearest coil surface, so that the watts dissipated per unit area of coil surface, and therefore the temperature difference between the coil surface and the adjacent oil, will be approxi- Oil Level B FIG. 294. Shell-type transformer in tank. mately constant at all points, and the temperature of the surface of the coil will be a maximum at the top of the transformer. The hottest part of the whole winding will be at C. Measurement of the temperature rise by resistance gives little information as to the temperature of the hottest part of the coil of a core-type transformer, because the temperature so found is the average temperature and may be less than that of the oil measured at the top of the transformer. 327. The Temperature Gradient in a Shell -type Transformer. Fig. 294 shows such a transformer. Since the core is laminated horizontally, and since iron is a poor conductor of heat across the laminations, most of the heat generated at any point in the core is conducted to and dissipated from the nearest core surface, so that each part of the core surface is equally active in dissipating 30 466 ELECTRICAL MACHINE DESIGN heat, and the temperature of the core is a maximum at the top and a minimum at the bottom. The conditions are different for the windings. These are made up of what are known as pancake coils, which are thin and have a large radiating surface. Since the top layers of the winding at A are connected directly to the bottom layers at B by a short length of copper, the temperature difference between o.i 0.2 0.3 Watts per Sq. In. Barrel Surface FIG. 295. Heating curves for transformer tanks. A and B cannot be very great, and the difference in temperature between the winding and the adjacent oil must be greater at the bottom than at the top. Because of this much of the heat generated in the top part of the winding is conducted downward and dissipated from the winding surface at the bottom of the coil. The temperature of the winding is more uniform throughout than in a core type transformer, and resistance measurements are of more value. 328. The Temperature of the Oil. The rise in temperature of LOSSES, EFFICIENCY AND HEATING 467 the oil over that of the external air depends principally on the loss to be dissipated, and on the external surface of the tank. The heat in the oil is transmitted through the tank and dissipated from its external surface. Part of this heat is dissi- pated by direct radiation, and part by convection currents which flow up the sides of the tank. For a plain boiler-plate tank, without ribs or corrugations, the highest temperature rise of the FIG. 296. Corrugated tank. oil is plotted against watts per square inch external surface in Fig. 295, for a tank which is round in section, and which has a height of approximately 1.5 times the diameter. This tempera- ture rise is made up principally of the temperature difference between the air and the tank, and that between the tank and the oil; the former is about three times as large as the latter. The temperature rise of the oil may be reduced by increasing 468 ELECTRICAL MACHINE DESIGN the surface of the tank which is readily done by making it corrugated, as shown in Fig. 296. This increase in surface does not increase the direct radiation from the tank, because only that component of surface which is perpendicular to a radius is effective; for this reason the watts per square inch for a given temperature rise does not increase directly as the increase in surface. Consider the curve in Fig. 295 for corrugations 3 in. deep and spaced 1 in. apart; the external surface of the tank is Pipe Surface 7500 sq. in, Tank Surface 4100 sq. in 0.3 0.4 0.5 0.6 Watts per Sq. Inch FIG. 297. Heating curves for transformer tanks. increased about six and one-half times, while the watts per square inch for a given temperature rise is only increased about 60 per cent, over the value for a plain boiler-plate tank. Fig. 297 shows the results of tests on a boiler-plate tank with external pipes added to improve the circulation. It will be seen from curves 1 and 2 that the watts per square inch of total surface for a given temperature rise is almost as large in LOSSES, EFFICIENCY AND HEATING 469 the special tank as in the plain boiler-plate tank or, comparing curves 1 and 3, the surface of the special tank is 2.8 times that of the plain boiler-plate tank, while the watts per square inch for a given temperature rise is increased about 2.5 times. Fig. 298 shows a tank built so as to present three cooling surfaces to the air. Oil Level FIG. 298. Tank with large cooling surface. 329. Air-blast Transformers. Fig. 299 shows such a trans- former. The problem in this case is like that discussed fully on page 281 on the heating of turbo generators; 150 cu. ft. of air is supplied per minute per k.w. loss, and the average temper- ature of the air increases about 12 deg. cent, between the inlet and outlet. The temperature of the coils and core is kept within reasonable values by providing the necessary radiating surface, using the formula, watts per square inch for 1 deg. cent, rise = 0.0245(1 +0.00127 7), where the temperature rise is measured on the surface and V is the velocity of the air across the surface in feet per minute. In the case of vent ducts, and surfaces which are facing one another, it must be noted that there can be no radiation term 470 ELECTRICAL MACHINE DESIGN because the surfaces are at the same temperature and in such cases, watts per square inch for 1 deg. cent, rise =0.0245(0.001277). The air used should be filtered, otherwise the ducts will become clogged up with dust and the transformer get hot. Dampers are usually supplied at the top of the case so that the distribution of the air through the core and coils may be controlled. FIG. 299. Air blast transformer. 330. Water-cooled Transformers. If coils of copper pipe carrying water be placed at the top of the case as shown in Fig. 300, then the oil which is heated by contact with the transformer will rise and carry the heat to the cooling coils. If ti is the inlet temperature of the water, t is that at the outlet, then each pound of water passing through the coils per minute takes with it (t ti) Ib. calories per minute or 32(t -ti) watts. With 2.5 Ib. of water per minute per kilowatt loss the average temperature rise of the water will be 12.5 deg. cent. LOSSES, EFFICIENCY AND HEATING 471 It is advisable in water-cooled transformers to immerse the whole of the cooling coil, otherwise, due to the low temperature of the water passing through, moisture will deposit on the coil and get into the oil. The coil should be of seamless copper tube about 11/4 in. external diameter, and the drain tap should be FIG. 300. Water cooled transformer. at the bottom of the spiral so that, when not in operation, the spiral will be empty and therefore will not burst in frosty weather. 331. Heating Constants used in Practice. The calculation of the temperature rise of a transformer is so complicated by the oil circulation, and by the temperature gradient in the oil, coils and 472 ELECTRICAL MACHINE DESIGN core that, until the results of a complete investigation of the subject are available, empirical constants will have to be used. The necessary tank surface for a given loss is found from Fig. 295. The watts per square inch coil surface = 0.35 for self-cooled shell-type coils wound with small wire = 0.4 for self-cooled shell-type coils wound with strip copper = 0.35 for small core-type transformers; these figures may be increased 20 per cent, for trans- formers which are water cooled or I & cooled by forced draft. The watts per square inch iron surface = 1.0 for both core and shell type; the area of cooling surface is taken as the edge surface and half of that part of the flat surface which is ex- posed to the oil circulation, see Art. 332. The watts per square inch water pipe surface = 1.0, for a 1.25-in. pipe, the sup- ply being 2.5 Ib. per minute per k.w. loss. 332. Effect of Ducts. It is difficult to determine how effective the ducts are in keeping a transformer core cool. Fig. 301 shows a block of iron which is laminated vertically. The hottest part of the iron is at A and the temperature difference from A to B. *Tf i I C i t A FIG. 301. Heat paths in a transformer core. j. = (watts per cu. in.) -5- deg. cent; page 105 o that between A and C = T ac = (watts per cu. in.) - deg. cent. o The temperature difference between surface B and the oil = (watts per cu. in.) Y X 16 since the temperature difference between the iron and the adjoin- LOSSES, EFFICIENCY AND HEATING 473 ing oil is 16 deg. cent, per watt per square inch. The tempera- ture difference between surface C and the oil = (watts per cu. in.)XXl6 The relative heat resistance of the two paths may be taken approximately as pathB If the ducts are spaced 2 in. apart, so that X = 1.0 in., then for different values of Y the relative heat resistance may be found from the following table: RELATIVE HEAT RESISTANCE X Y Along laminations Across laminations 1 in. 1 in. 0.48 1.0 1 in. 2 in. 1.0 1.0 1 in. Sin. 1.5 1.0 1 in. 4 in. 2.0 1.0 that is, for the particular values taken, the duct surface is half as effective as that of the edge, if it is as well supplied with cool oil, that is, if the ducts are vertical and of sufficient width to allow free circulation. 333. The Maximum Temperature in the Coils. Although the maximum temperature in the coils of a transformer cannot readily be determined, it is necessary to find out on what it depends and what its probable value may be. In Fig. 302, which shows part of the coil of a transformer, let the thickness of the coil be small compared with the mean turn MT, and assume that the heat passes in both directions from the center line L. If, of the thickness x, the part kx is insulation and (1 k) x is copper then the current in the section xy = xy(l-k) X amperes per square inch sq. n. per amp. xy (l-fc)X 1.27X10 6 cir. mils per amp. 474 ELECTRICAL MACHINE DESIGN The resistance of a ring of length MT and section z?/(l-A;) sq. in. = MT. ~xy (l-/b)Xl.27xl0 6 the loss in this ring = current 2 X resistance (xy (1-&)X1.27X10 6 ) 2 XM'T. xy (l-fc)Xl.27xl0 8 (cir. mils per amp.) 2 = MTX xy (1 - k) X 1.2.7 X 10 6 (cir. mils per amp.) 2 The heat due to this loss crosses the section of thickness dx, of which A; X da; is insulation, and since the specific conductivity of \dx A B FIG. 302. Part of a transformer coil showing insulation between layers. insulating material = 0.003, in watts per inch cube per deg. cent, difference in temperature, therefore the difference in tempera- ture between the center and the surface -Jr-J: M Txxy(l - k] X 1.27X 10 6 kXdx_ /N TI *- rrt v , *?\ (cir. mils per amp.) 2.1 XlO 8 k(l-k)X 2 0.003 (66) (cir. mils per amp.) 2 Consider the following example: A core-type transformer with the windings insulated as in Fig. 288, has the high-tension winding made with No. 12 square d. c. c. wire. The high- voltage winding is 1 in. thick, the current- density is 1600 cir. mils per ampere, and there is one thickness of 0.007 in. fullerboard between layers; LOSSES, EFFICIENCY AND HEATING 475 it is required to find the maximum difference in temperature between the inner and outer layers of the winding. Thickness of wire = . 0808 Thickness of cotton covering =0.01 Thickness of fuller-board = . 007 Value of* Value of l-k -0.89 ,.~ 2.1X10 8 XO. 174X0.89 Temperature difference = Ignn2 JLoUU = 13 deg. cent. If round wire is used instead of square, then the contact area between adjacent layers is greatly reduced, and the tempera- ture difference increased. It is advisable for such coils as that discussed above to use square or rectangular wire and to limit the thickness of the coil to 1 in., and the current density to about 1600 cir. mils per ampere. 334. The Section of the Wire in the Coils. Diagram A, Fig. 302, shows part of a coil of a shell-type transformer, and B shows part of a coil of a core type transformer. The loss in one layer of the winding, as may be seen from the last Art. MTx2Xy(l - fe) X 1.27X 10 6 6 ttg (cir. mils per amp.) 2 the corresponding radiating surface =MTXr sq. in. therefore the watts per sq. in. = - . , 2X (cir. mils per amp.) 2 and cir. mils per amp. = 8XlOaJ 2X < l ~ k ^ (67) \watts per sq. in. = 1350^2^(1 -k) 2 when watts per sq. in. -0.35 = 1260\/2X(1-A;) 2 when watts per sq. in. = 0.4 CHAPTER XL VI PROCEDURE IN DESIGN 335. The Output Equation. # = 4.447Y a /10- 8 , formula 62, page 439; and El = the watts output 4A a 2 / -irk 7 0a magnetic loading = 4.44 v y^-X/XlO~ 8 where k t = ^, = -^-^, T ^ kt TI electric loading The volts per turn of coil = V t = 4.44< a /10~ 8 so that, for a given voltage, the lower the frequency the larger the product (f> a XT. If a transformer is built with a large number of turns, so that fcj = ~ is small, then the copper loss is large because of the large number of turns, and the core loss is small because of the low frequency; such a transformer would therefore have its maximum efficiency at a fraction of full-load; see page 463. In order that the efficiency may be a maximum at or near full-load, the full load copper and the core loss must be ap- proximately equal and the flux must increase as the frequency decreases; it is found in practice that the value of k t =^ is approximately inversely proportional to the frequency, or that k t f is approximately constant, therefore volts per turn, V t = B, const. X \/watts (68) where the following average values of the constant are found in practice; for core-type distributing transformers oU ^ for core-type power transformers o(J ^ for shell-type power transformers. 4d The constant for the distributing transformer is less than that 476 PROCEDURE IN DESIGN 477 for the power transformer because, while in the latter the highest efficiency is desired around full-load, in the former a small core loss and a high all day efficiency is desired. To obtain a small core loss it is necessary to keep the value of k t = small, and therefore the constant in formula 68 must be small. The constant is different for core- and for shell-type trans- formers because of the difference in construction. Fig. 303 shows the ordinary proportions of a core-type transformer; the J L J L A FIG. 303. Core-type transformer. FIG. 304. Shell-type transformer. distance a is generally about 1.5X6 so as to keep the ratio of X to Y within reasonable limits, and prevent the use of a thin wide tank. If the coil on limb B of the transformer in Fig. 303 be placed on limb A, and limb B then split up the center and one-half bent over to give Fig. 304, a shell-type transformer is produced which has the same amount of copper and iron as the corresponding core-type transformer. The resulting shell-type transformer is flat and low, so that the tank required to hold it takes up con- 478 ELECTRICAL MACHINE DESIGN siderable floor space; the proportions are therefore changed so as to give the ordinary shape shown in Fig. 305, and for a given rating it will be found that the ratio ~y is about four times as large for the transformer in Fig. 305 as it is for that in Figs. 303 or 304; that is, the shell-type transformer has generally twice the flux and half the number of turns that the core-type trans- former has for the same rating. The distance a is generally about QXb to give a reasonable shape of core. FIG. 305. Shell-type transformer. 336. Procedure in the Design of Core -type Transformers. 1 The volts per turn = ^V watts for power transformers 1 = orA/watts for distributing transformers. oU The number of coils is chosen so as to keep the voltage per coil less than 5000, but there should not be less than two high-voltage and two low-voltage coils; the number of turns per coil is equal to _^ terminal voltage volts per turn X number of coils The depth of the coil measured from the nearest oil duct should not be greater than 1.0 in., except in the case of small distributing PROCEDURE IN DESIGN 479 transformers insulated as shown in Fig. 288 which have no oil duct between the low voltage winding and the core. In such a case the depth from the core to the oil may be 2 in., the reason being that the heat in the inner layers of the winding is con- ducted through the insulation into the core and dissipated by the core surface. The section of the wire in circular mils is found from formula 67, page 475, namely, cir. mils per amp. = 1350\/(1 k) 2 x2X where X= the greatest depth from the inside of the winding to the nearest oil or core surface, (1 k) 2 = per cent, copper in the vertical layers of the winding X that in the horizontal layers and the area of the wire is the product of the full-load current in the winding and the circular mils per ampere. The section of wire should be chosen so that it is not thicker than 0.125 in., and the wire should be wound flat as shown at A, Fig. 292. The number of layers in the winding is the same as the number of wires in the assumed depth of the coil; the number of conduc- tors per layer is the total number of turns per coil divided by the number of layers, and the height of the winding is the number of turns per layer multiplied by the width of the wire in the direc- tion parallel to the limbs of the core. The flux in the core is found from formula 62, page 439; namely, E = 4.44 X turns X flux X frequency XlO~ 8 flux in core , , ,, and the core area = - 5 rr , where the value of the core core density density is taken for a first approximation, = 65,000 lines per square inch 60-cycle distributing transformers = 75,000 lines per square inch 25-cycle distributing transformers = 90,000 lines per square inch 60-cycle power transformers = 80,000 lines per square inch 25-cycle power transformers alloyed iron being used for 60-cycle transformers, to keep down the loss in the distributing transformer so as to have a high all- day efficiency, and to keep down the heating in the power trans- formers. Ordinary iron is used for 25-cycle transformers, be- cause, due to the low frequency, the loss is generally small, while the densities have to be kept low in order that the magnetizing current will not be too large a per cent, of the full-load current. The core and windings are drawn in to scale; the losses, magnetizing current, resistance and reactance drops are deter- 480 ELECTRICAL MACHINE DESIGN mined, and the size of the tank is fixed. If the transformer as designed does not meet the guarantees then certain changes must be made. If the core loss is too high, either the core density must' be reduced, which will increase the size of the transformer, or the total flux must be reduced, which will require an increase in the number of turns for the same voltage, and, therefore, an increase in the copper loss. The resistance and the reactance drops may both be reduced by a reduction in the number of turns, because the resistance is directly proportional to the number of turns, while the reactance is proportional to the square of the number of turns. Example. Design and determine the characteristics of a 15- k. v. a., 2200- to 220-volt, 60-cycle distributing transformer. Design of the High-voltage Winding Volts per turn =1.52 Total number of turns = 1440 Coils = 2; one on each leg Turns per coil = 720 Total depth of winding =2.0 in., assumed Cir. mils per ampere = 1350 X \/ 2 X - 9 X 0.8 = 1620 Full-load current =6.8 amp. Section of wire =11,000 cir. mils; use no. 10 square B. & S. = 0.1019 in. X0.1019 in. which has a section of 13,000 cir. mils, not allowing for rounding of the corners Insulation =0.01 in. double cotton-covering, 0.014 in. fullerboard between layers /I 7N 0.1019 - ' (1-fc) vertical = o7Tl9 Number of layers (1-&) horizontal = 0.1019 + 0.01 + 0.014 = 8 Turns per layer =90 Height of winding = 90 X (0.1019 + 0.01) = 10 in. Height of opening =11.75 in. ; see Fig. 288 Design of the Low-voltage Winding Total number of turns = 1440 X ratio of transformation = 144 PROCEDURE IN DESIGN 481 Turns per coil = 72 Circular mils per amperes =1620; the same as for the high- voltage coil Section of wire =110,000 circular mils = 0.087 sq. in. = 0.11 in. X0.8 in.; this will be difficult to wind on a small transformer because of its width, therefore, change the winding as follows: Turns per coil = 72 ; number of coils = 4 connected two in parallel ; size of wire = 0.11 in. X 0.4 in. Insulation =0.015 in. cotton covering 0.014 in. fullerboard between layers winding height Turns per layer = width of wire -iM ~0.415 = 24 72 Number of layers per coil = = 3 Number of layers per leg =6, because there are two coils per leg Depth of winding = (0.11 in. +0.015 in. +0.014 in.) 6 = 0.83 in. Thickness of insulation between the high- and low- voltage coils = 0.12 in. Design of Core Flux =5.72X10 5 Core density, assumed =65,000 lines per square inch Necessary core section =8.8 sq. in Actual section adopted =2.5X4 and stacking factor =0.9 Width of opening =4.5 in., to allow a little clearance between coils on different legs ; see Fig. 288. Calculation of the Losses and the Magnetizing Current Mean turn of low- voltage coil = 16.6 in. 144X16.6 Resistance of secondary winding = 2X0.11X0.4X1.27X10 6 = 0.021 ohms Mean turn of high- voltage coil =24 in. 1440X24 Resistance of primary winding = 13000 = 2.6 ohms Loss in primary winding =2.6X6.8 2 = 120 watts 31 482 ELECTRICAL MACHINE DESIGN Loss in secondary winding =0.021 X68 2 = 97 watts Weight of core =1101b. Actual core density =63,500 lines per square inch Core loss in watts (alloyed iron) =110x0.9; from Fig. 275, page 442. = 99 watts Volt amperes excitation =110X5 = 550 Per cent, exciting current =3.3 Calculation of the Regulation Equivalent primary reactance = 2 TT/X 3. 2 T^X. ' ( + +s) 10~ 8 X2 L \3 3 / where / =60 T, =720 16.6 + 24 .. . X eq of primary = 27rX60X3.2x720 2 X - - -+0.12 X10~ 8 X2 = 20.3 in. L =10 in. d l =1.0 in. d 2 =0.83 in. S =0.12 in. coils = 2 20.4/1.0 + 0.83 (- 10 \ 3 = 18.6 ohms The reactance drop referred to the primary =18.6X6.8 = 126 volts = 5.8 per cent. The primary resistance drop =2.6x6.8 = 17.6 volts The secondary resistance drop =0.021 X 68 = 1.43 volts The resistance drop referred to the primary = 17.6 + 1. 43 X = 31.9 volts = 1.44 per cent. Design of the Tank The total losses at full-load are: Iron loss, 99 watts Primary copper loss, 120 watts Secondary copper loss, 97 watts Total loss, 316 watts The watts per square inch for 35 deg. cent, rise of the oil = 0.225, therefore the tank surface in contact with the oil _ 316 ~ 0.225 = 1400 sq. in. PROCEDURE IN DESIGN 483 337. Procedure in the Design of a Shell -type Transformer. The work is carried out in exactly the same way as for a core-type transformer except that the width of the coil is seldom made greater than about 0.5 in., so as to provide ample radiating sur- face and allow the use of comparatively high copper densities. The number of coils is again chosen so as to keep the voltage per coil less than 5000; still further subdivision of the winding may be required in some cases to reduce the reactance. Example. Design a 1500 - k.v.a., 63,500- to 13,200-volts, 25- cycle power transformer for operation in a three-phase bank on a 110,000 volt line. Dssign of the High-voltage Winding Volts per turn = 49 Total number of turns = 1300 Coils =12 Turns per coil =108 average; use 10 coils with 113 turns and 2 end coils with 85 turns Width of coil, assumed =0.4 in. Because of the high voltage the distance x, Fig. 291, will be large, and there will be little iron saved by making the strip wider than 0.4 in. with the idea of keeping the distance x small. Circular mils per ampere = 1260 X \/0.4X0.6 where (1-&) 2 is assumed to be = 0.6 = 615. Section of wire =14,500 circular mils = 0.0285X0.4 in. Insulation =0.015 in. cotton covering 0.014 in. fullerboard ,. 0.0285 Under ordinary circumstances the calculation for the size of conductor would be repeated using the correct value for (l-k) to find the value of the circular mils per ampere. In a very high voltage transformer, however, the amount of copper is small compared with the amount of iron and insulation, so that it is not advisable to run the chance of high temperature rise for a small gain in the amount of copper used. The conductor chosen for this transformer is therefore 0.03X0.4 in. Height of winding = turns X thickness of insulated wire = 113 X (0.03 + 0.015 + 0.014) = 6.7 in. = 7 in. to allow for bulging Space between winding and core =4.5 in., from Fig. 290. Width of opening = 7 + (2 X 4 . 5) = 16 in. 484 ELECTRICAL MACHINE DESIGN The arrangement of the winding must now be decided on and several possible methods are shown in Fig. 306. A would give a very long core and take up a large floor space, it would also have a large core loss and magnetiz- ing current because of the large amount of iron in the magnetic circuit, but of the three shown it would have the lowest reactance. B would have a lower magnetizing current and a lower core loss than A, it would also be considerably cheaper, but would have a larger reactance. C will have values of core loss, magnetizing current and reactance be- tween these of A and B, and the design will be completed for this arrange- ment to find its characteristics. FIG. 306. Arrangement of coils in a 110,000-volt shell-type transformer. Design of the Low-voltage Winding Total number of turns Coils Turns per coil Width of copper assumed Circular mils per ampere Section of wire = 270 = 6 = 45 = 0.4 in. = 1260 X\/0-4X 0.9 where (1-&) 2 is assumed to be = 0.9 = 755 = 86,000 circular mills = 0.17 in. X 0.4 in. use 2 X (0.085 in. X 0.4 in.) with a strip of fuller-board between PROCEDURE IN DESIGN 485 Insulation =0.007 fullerboard between wires 0.024 half lap cotton tape 0.014 fullerboard between layers Thickness of insulated strip =0.215 in. Height of winding =0.215X45 = 9.7 in. = 10.2 in. to allow for bulging. This allows ample clearance between the winding and the core, in fact the winding could be made narrower and higher because 0.75 in. would be ample spacing for 13,200 volts, but it is advisable to use the larger spacing, where it is available without any sacrifice of space or material. The coils with the insulation are now drawn to scale as shown in Fig. 291, and the length of the opening determined; this value is 43 in. Design of the Core Flux =44X10 Core density, assumed = 80,000 lines per square inch Necessary core section =550 sq. in. Actual section adopted = 14 X 43. 5 in. Calculation of the Losses and the Magnetizing Current Mean turn of the low- voltage winding = 170 in. .., , . ,. 6X45X170 Resistance of the low-voltage winding 0.17 X 0.4 X 1.27 X10 6 = 0.53 ohms Mean turn of high- voltage winding = 190 in. ... , u . ,. 1300X190 Resistance of high- voltage winding = 0.03 x 0.4 X 1.27 X 10 6 = 16.2 ohms Loss in the high- voltage winding = 16.2 X 23.6 2 = 9000 watts Loss in the low- voltage winding =0.53 X 114 2 = 6900 watts Weight of core =22,000 Ib. Core loss in watts (ordinary iron) =22000X0.9; from Fig. 275. = 20,000 watts Total loss at full-load = 35,900 watts Efficiency =97.7 per cent. Volt amperes excitation = 22000 X 5.4 = 119,000 = 8 per cent. The equivalent primary reactance = 2;r/X 3. 2 X ZV ^ (^ + ^ + S \ X 10 X coil groups where MT. =180 in. L = 16 in. d, = 1.3 in. See Figs. 279 and 291. d 2 = 0.4in. 5 = 4.5 in. 486 ELECTRICAL MACHINE DESIGN coil groups =6; diagram C, Fig. 306 Equivalent primary reactance =2^X25x3.2x216 2 X^ (~ + 4:.5\ 10~ 8 X6 = 80 ohms The reactance drop referred to the primary =80X23.6 = 1900 volts = 3.0 per cent. The primary resistance drop =380 The secondary resistance drop referred to the primary = 60 X ^j = 290 The resistance drop referred to the primary = 670 = 1.05 per cent. The tank is made round in section and clears the core by 2 in. at the corners. The total loss =35,900 watts The water-pipe surface required =35,000 sq. in. = 750 ft. of 1 1/4-in. pipe. CHAPTER XL VII SPECIAL PROBLEMS IN TRANSFORMER DESIGN 338. Comparison between Core- and Shell-type Transformers. Figs. 303 and 305 show the two types built for the same output and drawn to the same scale. It was shown in Art. 335, page 476, that, due to the difference in the construction, the volts per turn has twice the value for shell-type that it has for core-type trans- formers, in fact volts per t urn = - ^/ watts for shell-type power transformers Zo = \/watts for core-type power transformers ol) so that the number of turns for a given voltage is the smaller for transformers of the shell type. The essential differences between the two types are: For the- same voltage and output the shell type has half as many turns as the core type, it has also the longer mean turn of coil, but the smaller total amount of copper. The shell type, since it has half as many turns, must have twice the flux of the core type and, because of that, must have twice the core section; but the mean length of magnetic path is shorter and the total weight of iron only slightly greater. Since, as shown on page 443, the magnetizing current and the iron loss are proportional to the weight of the core for a given frequency and density, transformers of the core type can more readily be designed for small iron loss and small exciting current than can those of the shell type, and for that reason are generally used for distributing transformers, since these are built with a small iron loss so as to have a high all-day efficiency. It must, of course, be understood that by changing the proportions some- what, shell-type transformers can also be built suitable for dis- tributing service, but the fact that the core type is the one gener- ally used would indicate that for such service it is the cheaper to construct. For very high-voltage service the losses are not of so much 487 488 ELECTRICAL MACHINE DESIGN importance as reliability in operation. Fig. 307 shows the relative proportions of a high-voltage core and of a high voltage shell type transformer; the coils of such transformers are not easily braced and supported if the core-type of construction is used, and the forces due to short-circuits are more liable to destroy the winding than in the case of shell-type transformers, in which the coils are braced in such a way that these forces cannot bend them out of shape. FIG. 307. High voltage core, and shell-type transformers. terminal voltage The current on a dead short-circuit = impedence of winding and may reach, in power transformers, a value of 50 times full- load current. In the case of an instantaneous short-circuit the current may reach still greater values depending, as shown in Art. 209, page 284, on the point of the voltage wave at which the short-circuit takes place. Since the forces tending to separate the high- and low-voltage windings, and to pull together the turns of windings of the same coil, are proportional to the square of the SPECIAL PROBLEMS IN TRANSFORMER DESIGN 489 current, they may reach very large values on short-circuit and may destroy the winding. Of the two types of transformer, the shell-type is the better able to resist such forces. The winding of a transformer is divided up into a number of coils in series, and the voltage per coil should not exceed about 5000 volts. It will generally be found that the distance X, over which this voltage is acting, is less in the core- than in the shell- type transformer. The reactance of a transformer depends on the square of the number of turns, and on the way in which the winding is sub- divided. Due to the large space required between the high- and low-voltage coils it is not practicable to subdivide the winding of a core-type transformer more than is shown in Fig. 307, while the shell type winding can be well subdivided before the length Y is greater than that required for a cylindrical tank. Because of this, and also because it has the smaller total number of turns, the reactance of a shell-type transformer can readily be kept within reasonable limits while that of a core type cannot, in- deed, it is principally because certain regulation guarantees are demanded that the shell type has to be used, although it is doubtful if good regulation and the consequent large short- circuit current is as desirable for power transformers as poorer regulation and a smaller current on short-circuit. So far as the coils themselves are concerned the shell type of transformer, in large sizes, has the advantage that strip copper wound in one turn per layer may be used; this gives a stiff coil and one not liable to break down. For outputs up to 500 k. v.a. at 110,000 volts the core type will probably be the cheaper, and for outputs greater than 1000 k.v.a. the shell type must be used to keep the reactance drop within reasonable limits; between these two outputs the type to be used depends largely on the previous experience of the designer. The core-type transformer has the great advantage that it can be easily repaired, especially if built with butt joints so that the top limb may be removed and the windings and insula- tion lifted off. 339. Three-phase Transformers. Diagram A, Fig. 308, shows a single-phase transformer with all the windings gathered to- gether on one leg, and diagram B shows three such transformers with the idle legs gathered together to form a resultant magnetic return path. The flux in that return path is the sum of three 490 ELECTRICAL MACHINE DESIGN B D E F FIG. 308. Development of the three-phase core-type transformer. SPECIAL PROBLEMS IN TRANSFORMER DESIGN 491 fluxes which are 120 electrical degrees out of phase with one another and is therefore zero, the center path may therefore be dispensed with. In diagram B the flux in a yoke is the same as that in a core, the yoke and core have therefore the same area. If the three cores are connected together at the top and bottom as shown in diagram C, then the three yokes form a delta connection, and, as shown by the vector diagram D, the flux in the yoke is less than that in the core in the ratio =* and the yoke section may be less than v 3 that of the core. The bank of transformers may be still further simplified by operating it with a V or open delta-connected magnetic circuit as shown in diagram E, and this latter trans- former, when developed on to a plane as shown in diagram F, gives the three-phase core type that is generally used. There is FIG. 309. Three phase shell-type transformer. a considerable reduction in material between three transformers, such as that in diagram A, and the single transformer in diagram F, so that the three-phase transformer is cheaper, has less mate- rial, greater efficiency, and takes up less room than three single- phase transformers of the same total output. So far as the design is concerned there is no new problem; each leg is treated as if it belonged to a separate single-phase transformer. Diagram A, Fig. 309, shows a single-phase shell-type trans- former, and diagram B shows three such transformers set one above the other to form a three-phase bank. If the three coils 492 ELECTRICAL MACHINE DESIGN were all wound and connected in the same direction, as in the case of the three-phase core-type transformer, then the flux in the core at M would be produced by three m.m.fs., 120 degrees out of phase with one another, and would be zero, because at any instant the m.m.f. of one phase would be equal and oppo- site to the sum of the m.m.fs. of the other two phases.i The center coil is connected backward and the direction of the flux in the Section of the iron core. FIG. 310. Three-phase shell- type transformer. cores and cross pieces at one instant is shown by the arrows. The total flux in one of the cross pieces, say A, is the sum of the fluxes in cores 1 and 2, and the value may be found from dia gram C. A very economical type of three-phase transformer is shown in Fig. 310; it is almost circular in section and may be used in a cylindrical tank. SPECIAL PROBLEMS IN TRANSFORMER DESIGN 493 340. Operation of a Transformer at Different Frequencies. The e.m.f. =E -4.44 = 4.44!T m A c /10- 8 = a const. X-BmX/for a given transformer; the iron losses = hysteresis loss + eddy-current loss = KB m 1 '*+K e B m 22 for a iven transfor *f+K e B m 2 f 2 for a given transformer E 1 ' 9 = a const. X-7 6 + a const. X E 2 so that, for a given voltage, as the frequency increases the hysteresis loss decreases, while the eddy-current loss remains constant. A standard transformer, designed for a definite frequency, may operate at frequencies which are considerably higher or lower than that for which the transformer was designed; if the transformer is designed so that at normal frequency and full- load the copper and iron losses are equal and the efficiency a maximum, then at lower frequencies the iron loss will be larger than the copper loss, and at higher frequencies the copper loss will be the greater. In order that a low-frequency transformer may have approxi- mately the same core loss and copper loss at full-load, the section of the iron in the core must be increased over that required for a transformer of the same rating but of higher frequency, in order to lower the densites and reduce the core loss, so that, for the same rating and efficiency, the lower the frequency, the larger the amount of iron, and the heavier the transformer. CHAPTER XLVIII SPECIFICATIONS 341. The following specification is intended to cover a line of transformers for lighting and power service and for sizes up to 50 k.v.a. STANDARD SPECIFICATION FOR OIL-IMMERSED, SELF-COOLED TRANSFORMERS Rating. Rated capacity in kilovolt amperes 1 to 50 Normal high voltage 2200 and 1100 Normal low voltage at no-load 220 and 110 Phases 1 Frequency in cycles per second 60 Construction. The transformers are for combined lighting and power service. The windings shall be so arranged that with either 2200 or 1100 volts on the primary side the secondary volt- age may be either 110 or 220; taps must also be supplied so that if desired the secondary voltage may be raised 5 or 10 per cent, with normal applied high voltage. The tanks must be of cast iron or sheet iron of approved shape and construction, must be im- pervious to oil and water, and have covers supplied with gaskets. Eye bolts or hooks must be supplied for the lifting of the tank with the transformer and oil. With transformers larger than 5 k.v.a. output, oil plugs must be supplied at the bottom of the tank for the removal of the oil. Four secondary leads and two primary leads shall be brought out of the tank through porcelain bushings properly cemented in. The transformer itself shall be properly anchored in the tank to prevent movement. Core. This shall be of non-ageing steel assembled tightly so as to prevent buzzing during operation. Windings. The high- and low-voltage coils must be insulated from one another by a shield of ample dielectric strength. The coils, when wound, shall be baked in a vacuum and then impreg- nated with a compound which is waterproof and is not acted on by transformer oil over the range of temperature through which the transformer may have to operate. 494 SPECIFIC A TIONS 495 Oil. The oil supplied with the transformer shall be a mineral oil suitable for transformer insulation, and must be free from moisture, acid, alkali, sulphur or other materials which might impair the insulation of the transformer. It should have a flash- point higher than 139 deg. cent, and a dielectric strength greater than 40,000 volts when tested between half inch spheres spaced 0.2 in. apart. Sufficient oil must be contained in the tank to submerge the windings and the core at all temperatures from to 80 deg. cent. Cut Outs. Two plug cut outs shall be supplied for the high- voltage side of the transformer for operation up to 2500 volts. Workmanship and Finish. The workmanship shall be first class and the materials used in the construction of the highest grade. The tank shall be thoroughly painted with a black waterproof paint. General. Bidders shall furnish cuts with descriptive matter from which a clear idea of the construction may be obtained. They shall also state the following: Net weight of transformer. Net weight of case. Net weight of oil. Shipping weight. Dimensions of the tank. Core loss. Copper loss at full-load. Regulation at 100 per cent, and at 80 per cent, power factor. Exciting current at normal voltage and at 20 per cent, over normal voltage. The core loss shall be taken as the electrical input determined by wattmeter readings, the transformer operating at no-load, on normal voltage and frequency, and with a sine wave of applied e.m.f. The copper loss shall be taken as the electrical input deter- mined by wattmeter readings, the transformer being short- circuited and full-load current flowing in the high-voltage coils; measurements to be made on the high-voltage side. The regulation shall be calculated by the use of the following formulae; the per cent, regulation = 100 t"~(~r) a ^ 100 per cent, power factor L E 2\ E j j /0.8/E+0.6/Z\ = 100 ( - ~~E^ ~ J at 80 P er cent - P ower 496 ELECTRICAL MACHINE DESIGN where E is the normal secondary voltage at no-load I is the full-load secondary current IR is the resistance drop in terms of the secondary IX is the reactance drop 'in terms of the secondary. These two latter values are to be found by short-circuiting the secondary winding and measuring the applied voltage and the watts input required to send full-load current through the primary winding. watts input secondary full-load current IZ = the impedence drop in terms of the secondary 220 = the short-circuit voltage X 7^ IX = V(IZ) 2 -(IRY 2 Temperature. The transformer shall carry the rated capacity at normal voltage and frequency and with a sine wave of applied e.m.f . for 24 hours, with a temperature rise that shall not exceed 45 deg. cent, by resistance or thermometer on any part of the windings, core or oil, and, immediately after the full-load run, shall carry 25 per cent, overload at the same voltage and fre- quency for two hours, with a temperature rise that shall not exceed 55 deg. cent, by resistance or thermometer on any part. The temperature rise shall be referred to a room temperature of 25. deg. cent. Insulation. The transformers shall withstand a puncture test of 10,000 volts for one minute between the high-voltage winding and the core, tank, and low-voltage winding; also a puncture test of 2500 volts for one minute between the low- voltage winding and the core and tank. The transformer shall operate without trouble for five minutes at double normal voltage and no-load; the frequency may be in- creased during this test if desired. These insulation tests shall be made -immediately after the heat run. 342. Effect of Voltage on the Characteristics. The effect of high voltage in a transformer is that large spacings are required between the high- and low-voltage coils and also between the high-voltage coils and the core, so that the higher the voltage the longer the magnetic path and also the mean turn of the coils. Because of the large spacings, the reactance of high-voltage transformers is greater than of those of lower voltage, and the SPECIFICATIONS 497 i-l O O O OOOO5 Oi l> l> O CO CO CO CO CO CO CO COiOTf CO CO O Ci TJH O5 CO 00 CO 00 O i I 00000000 OOOii-i(M 000000 OOOO o^ o^ OOOOOOOO lO CO O i-l CO 00 1C CO l> Oi (N IO O i-H CO 00 (N (N O TH i-l i-l (N -H(M(M(N COCOCO^H r^ 1C CO (N O>OOO i I -^ CO (M i I O O (N C^llNiOTfri l>OS C^-^I>T}H CDCOCDO i IrHrHCO COCO&OCO 1>OOO- rH CS O T I CO d lO t^ Ol T I TH 00 OQ 00 CO *O l>- CO C^l CO OOOrH r- 1 i I . Q5 rH T I O^ t^* rH 00 T I t>- i I 05 COi liOC^Oi O5 CO CO. 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I 510 ELECTRICAL MACHINE DESIGN d to i> co rH CO rH IO 00 '' r ~' _ co T-H to oo O5 (M 00 O5 (N CO CO O 00 CO 8 i iO t^ O5 rH t> 00 O5 rH TH CO 00 O5 CO 00 CO to 00 C^ CO rH i-H TH CS Cl l> O5 rH CO O5 C^ 00 t> 00 CO CO CO rH to t^ i co to oo TH CO 00 to 00 O O 00 rH O5 CO o o CO to O O5 CO CO rH CO O O O O rH CO CO T-H O CO CO O O5 CO T-H CO CO 00 (N T-H i 1 rH rH CQ 1>- O 00 to l>- Csj CO CO rH CO ti 1 d ^ ao 02 (M (M d "^ 11 (N rH O CO rH 00 CO CO rH CO CO CO rH 00 CO rH C^J CO (M (N (N (M rH 00 (M CO O O 00 1> to rH (M rH i-H TH rH ^ 1*1 53 02 a O t^ CO (N (N co to T-H oq t> 00 O5 tO !> rH t^ to co o o CO CO O to CO cr 1 g T-H O TH CO to 00 (M t^ (N 00 to CO O 00 | 00 t^ CO to rH CO CO Cq C^ rH rH rH TH S3 o t-, 02 rH rH CO OO O !> 0<0^ CO l>* CO CO OO l5 2 r^H CO T-H O5 O rH IO 00 O5 00 O5 CD I> CO ^ fl 00 rH rH CO CO CO r|H CO O to O CO CO CO CO rH h. IO 00 CO CO O5 CO 00 CO CO 00 O QQ CO 00 rH rH to (M O 00 CO S rS CO CO TH rH iO 00 iO (M CO 00 00 (M (M O O5 O5 C^ to O5 CO rH (M 00 00 rH O CO . O rH 00 T-H 00 rH O CO . 1> CO to to rH rH rH CO CO S s S 02 d | O (N 00 rH O t^ "* to CO T-H CO (N (M (N 00 O5 O i I ri a ^ T5 o s . o MECHANICAL DESIGN 511 t- l>- 00 CM CO TjH rH rH O5 CO CO rH CO "^ CO *O CO ^ CO 00 CO CO t > 00 Oi 01 rH Tf 00 CO O5 00 - CO C5 C5 rH rH rH CM CM CO *O !> OS rH 1C O ^ rH rH (N (N 00 00 t^* b* OS 00 O^ CO ^O ^1 ^^ 00 O5 OOOC^IOCO *OCOOCO^tn (Nl^-iOiO IOT^OOSCO oo-^c^coio -HHOOI^OO 1>-O5C^OOS r^ OS C^J t>* rH (N(N(N(N(N (MrHrHrHO OOOO rHrHrHOO OOOOO OOOO t^ l^- O5 C^ 00 C^ 00 ^ C^l C^ CO CO C^ rH 00 CO *O CO C^l C^l CO>OTjHCO(N (NrHrHOO OOOO lOrHCOOOO OiCOOOOi C^00l>00 1 I rH CO OO CO *O TjH CO C^l rH rH rH CO CO CO CO TflTflCOCOfN X " o 2 a b 3 O) s ^ II rHcNCO'^lO COt^OO CO Tj< (N e = end connection leakage constant 79, 215, 360 (f> m total flux per pole 42 < 8 = slot leakage constant 79, 216, 360 (f) t = tooth tip leakage constant 216 ta = tooth tip leakage constant 221 tp = tooth tip leakage constant 221 ( j )z = zig zag leakage constant 360 (f> = per cent, pole enclosure 42 INDEX Ageing of iron, 440 Air blast for cooling, 281, 469 ducts, armature, 24, 28, 192, 349 field coils, 40 films in insulation, 198, 201 gap, area, 43 clearance, 67, 69, 229, 240, 243, 260, 394, 403 flux density in, 45, 94, 114, 256, 288, 393 distribution in, 44, 54-58, 209, 288, 358 fringing constant, 43 Alloyed iron, 100, 440 Alternating and rotating fields, 186 Alternator, construction, 191 current density, 252, 253, 262, 293 field system design, 237 flux densities, 229, 245, 252, 257, 282, 289 generated e.m.f., 178 heating, 239, 252-254, 279-282 insulation, 193, 203-207 losses, 247-251 procedure in design, 255 ratings, 188, 236 reactance of armature, 215-226, 233-236, 285 reactions of armature, 208-236, 289 slots, 180, 256, 260, 262 specifications, 312 turbo, 273 vector diagrams, 210-212 windings, 160 Amortisseurs, 295, 303 Ampere conductors, 115 conductors per inch, 109, 115, 146, 241, 256, 258, 381, 394 turns, 4 Ampere turns per pole, armature, 61, 91, 147, 230, 290 cross magnetizing, 55-61, 146, 209 demagnetizing, 59, 149, 209,. 214, 232, 289 field excitation, 46-51, 67, 237, 238, 290, 308 interpole field, 92, 94, 151 series field, 68 Areas, magnetic, 42, 359 Armature, D.-C., construction, 24, 153 current density, 109-111, 123, 131 flux densities, 45, 107, 1.14 generated e.m.f., 11 heating, 104 insulation, 36 losses, 97 peripheral velocity, 142, 144 procedure in design, 114, 147 reaction, 54 resistance, 102 slots, 24, 87, 123 strength relative to field, 61, 87 91, 146 winding, 7 Asbestos, 274 Average volts per bar, 95, 138, 143 Back e.m.f., 323 Bearing, construction, 27, 29 design: 97, 504 friction, 97, 344, 357 housings, 25, 350 oil temperature, 98, 314 Belt leakage, 332, 365 Blackening of commutator seg- ments, 87 Break down point, 328 Breathing of coils, 201 517 518 INDEX Brush, arc, 9, 80, 88, 91, 94, 148 contact resistance, 76 current density, 75, 78, 194 friction, 98 holders, 506 number of sets, 12, 18 pressure, 78 Bushings, transformer, 435, 451 Carter fringing constant, 43 Cast iron, magnetic properties, 47 stresses in, 500 steel, magnetic properties, 47 stresses in, 500 Centrifugal force of turbo rotors, 275 Chain windings, 169 Characteristics, 424 and frequency, 392, 410, 420, 493 and speed, 157, 316, 392, 409, 426 and voltage, 156, 315, 420, 424, 425, 496 Circle diagrams, 333-347 Cir. mils per ampere, 109-111, 123, 252, 293, 380, 381, 475 Circulating current in brushes, 13, 90 in windings, 13, 19, 164, 173, 184, 297 Closed slots, 24, 348, 411 Coils, armature, 22, 36-39, 108, 153, 203-207, 250 field, 40, 62, 68, 193 groups, 36 transformer, 434, 438, 455, 461 Commutation, best winding for sparkless, 140 guarantee, 155 perfect, 76 selective, 19 theory, 72 with duplex windings, 9 interpoles, 92 series windings, 19, 83 short pitch windings, 15, 82 Commutator, construction, 27, 153 sign, 121, 124, 148 Commutator, diameter, 120 heating, 111 insulation, 27 length, 139, 148 losses, 98, 103 mechanical design, 501 number of segments, 18, 138 peripheral velocity, 120 ventilation, 27, 111 voltage between segments, 138, 143 wearing depth, 120 Compensating fields coils, 96, 144 Condenser bushings, 453 Conductors, current density in, 109- 111,123,252,293,380,381, 475 eddy currents in, 248, 372, 461 lamination of, 248, 249, 461 number of, 121, 127, 130, 260, 267, 397, 407 Construction of alternators, 191, 272, 312 D.-C. machines, 24, 153 induction motors, 323, 348, 422 transformers, 433, 494 Contact resistance, 76 Cooling. See Heating, by convection, 106 Copper loss, armatures, 102, 248 field coils, 103, 247 induction motors, 371 transformers, 461, 481 resistance of, 102 Core, flux density in alternator, 252, 282 in D.-C. armature, 45, 107 in induction motor, 358, 381 in transformer, 479 or iron loss, 99, 355, 439, 442, 443 type transformers, construction, 433 heating, 464 insulation, 458 procedure in design, 478 reactance, 445, 482 three-phase, 490 INDEX 519 Corrugated tanks, 467 Cotton, 30 covering for wire, 31, 508 Creepage, surface, 34, 450, 454, 455, 456 Critical speed of turbo rotors, 278 Cross magnetizing ampere turns, 55-61, 146, 209 Current density in alternator wind- ings, 252, 253, 262, 293 in brush contacts, 75, 78, 194 in D.-C. armatures, 109-111, 123, 131 in field coils, 69, 70, 151, 379 in induction motors, 380, 381, 397, 407 in transformers, 475 direction, 1 maximum in induction motors, 337, 363, 394, 395, relations in induction motors, 323, 331, 335 in transformers, 429 Curves of amp. cond. per inch, 115, 257, 393 of armature and stator heating, 115, 253, 382 of efficiency, 158, 159, 318, 392 of field coil heating, 64, 239 of gap density, 115, 257 of iron loss, 102, 442 of magnetization, 47, 48, 442 of power factor, 392 of saturation, 50, 60, 237, 309, 343 of short circuit, 225, 343 of space factor, 65 of transformer heating, 466. 468 D 2 L, 114, 255, 391 Dampers, 295, 303 Dead coils, 22, 130 points at starting, 310, 388 Delta connection, 163, 407 and harmonics, 183 Demagnetizing ampere turns, 59, 149, 209, 214, 232, 289 Density of current in alternator windings, 252, 253, 262, 293 in brush contacts, 75, 78, 194 in D.-C. armatures, 109-111, 123, 131 in field coils, 69, 70, 151, 379 in induction motors, 380, 381, 397,- 407 in transformers. 475 of flux, and m.m.f., 5 in air gap, 45, 94. 114, 256, 288, 393 in armature and stator cores, 45, 107, 252, 282, 358, 381 in pole cores, 45, 67, 229 in rotor cores, 381 in teeth, 45, 46, 107, 252, 282, 358, 381 in transformer cores, 479 in yoke, 45, 67 Design procedure for alternators, 255 for d.-c. generators, 114 for d.-c. motors, 127 for field system, 62, 237 for induction motors, 391 for interpole machines, 146 for synchronous motors, 308 for transformers, 476 for turbo alternators, 290 Diameter of armature or stator, 116, 120, 141, 143, 257, 259, 393 Dielectric flux, 195 strength, 30, 196 of cotton, 30 of empire cloth, 32 of micanite, 31 of oil, 449 of paper, 32 Dimensions and frequency, 415, 493 and output, 114, 255, 391 Direction of current, 1 of e.m.f., 3 of magnetic lines, 1, 2 Distributed windings, 171, 180, 187 Distributing transformer, 433, 463, 476, 487 520 INDEX Distribution factor, 189 of magnetic field, gap, 44, 54- 58, 209, 288, 358 core, 101, 358 Double frequency harmonics, 231 layer windings, 13, 170 Doubly re-entrant windings, 8 Dovetails, 28, 192, 193, 351, 500 Drum windings, 9 Ducts in armature and stator cores, 24, 28, 192, 349 in field coils, 40 in transformer, 435, 472 Duplex windings, 8, 20 Eddy currents in armature and stator cores, 100, in conductors, 248, 372, 461 in pole shoes, 101, 295 in transformer cores, 439, 444 Efficiency, effect of speed, 157, 316, 392, 426 of voltage, 156, 315, 420, 425, 496 of alternators, 251, 313, 318 of d.-c. machines, 97, 132, 158, 159 of induction motors, 392, 423 of transformers, 463, 497 Electric loading, 116, 147, 476 Electrical degrees, 162 Electromotive force, 2 direction of, 3 in alternators, 178, 189 in d.-c. machines, 11 in induction motors, 352 in transformers, 439 Empire cloth, 32 Enclosed machines, 350 heating of, 134, 383 rating of, 133 End connection heating, 108, 252, 254, 381 Insulation, 34, 207 leakage, 217 length, 108 supports, 287, 350 play for shafts, 25 End rings, loss in induction motor, 371 section, 399 turns, insulation of transformer, 456 Equalizer connections, 13, 22 Equivalent reactance, induction mo- tor, 337, 363 transformer, 431, 447 resistance, 431 Even harmonics, 183 Excitation, calculation of no-load, 46, 242 of full load, 59, 246 of induction motor, 357 of transformer, 440, 481, 485 effect of power factor, 237 for joints, 444 synchronous motor, 306 Exciter, 193, 311, 312 Exciting coils, 25, 193 current, 352, 357, 394, 440, 481, 485 Fans, 25, 252, 273, 351 Field coils, compensating, 96, 144 construction, 40, 68, 193 design procedure, 62, 237 heating, 62, 239 insulation, 40. 193 interpole, 150 losses, 103, 133, 237, 247 ventilation, 40, 64, 193 magnetic, distribution in gap, 44, 54-58, 209, 288, 358 in core, 101, 358 leakage between poles, 42, 51, 213 in alternators, 215, 233 in induction motors, 360 in transformers, 445 relation between main and armature, 61, 229, 290 magnets, construction, 25, 192 dimensions, 25, 65, 67, 238 flux density, 45, 67, 229 turbo, 275 Flashing over, 95 INDEX 521 Fleming's rule, 3 Flux distribution in air gap, 44, 54- 58, 209, 288, 358 in armature core, 101, 358 density, and m.m.f., 5 in air gap, 45, 94, 114, 256, 288, 393 in armature and stator cores, 45, 107, 252, 282, 358, 381 in pole cores, 45, 67, 229 in rotor cores, 381 in teeth, 45, 46, 107, 252, 282, 358, 381 in transformer cores, 479 in yoke, 45, 67 pulsations, 184, 386 Flywheels, 297-303, 315 Forced draft, 281, 469 oscillations, 298, 302 Form factor, 178, 439, 440 Fractional pitch winding, 15, 82, 181, 189, 419 Frequency and characteristics, 392, 410, 420, 493 and dimensions, '41 5, 493 speed and poles, 162, 322 Friction in bearings, 97, 344, 357 in brushes, 98 Fringing of flux, 43 Full-load saturation, 59, 212, 227, 237, 309 Fullerboard, 450, 457, 458 Gap. See Air gap. Grading of insulation, 199 Gramme ring winding, 7, 9 Grounds, 33 Guarantees, commutation, 135, 155 efficiency, 154, 313, 423, 495 overload capacity, 135, 155, 314, 424 power factor, 392, 423 temperature, 133, 155, 314, 424, 496 regulation, 313, 495 Harmonics in the e.m.f. wave, 178 Harmonics, in the magnetic field, 184, 231, 295, 418 Heat, effect on insulation, 31, 33, 104 Heating and cooling curves, 375 and construction, 252, 382 of alternator rotors, 239 stators, 252 of commutators, 111 of dampers, 305 of d.-c. armatures, 104 of enclosed machines, 134, 382 of field coils, 62, 239 of high voltage coils, 109, 250, 253 of induction motors, 375 of oil in bearings, 98, 314 of semi-enclosed machines, 383 of transformers, 463 of turbos, 274, 279, 295 High speed alternators, 272 induction motors, 414 limitations in design, 141, 417 torque ratings, 382 voltage insulation for alterna- tors, 201, 205 for transformers, 459, 488 limitations in design, 138, 488 due to harmonics, 179 Horn fibre, 32 Housings, 25, 350 Humming, 385, 416, 434 Hunting of alternators, 298, 314 of synchronous motors, 308 Hysteresis loss, 100, 439, 440 Impedence of windings. See React- ance. Impregnating compound, 31, 32, 201, 450 Induction motor, construction, 348 current density, 380, 381 excitation, 352, 357 flux densities, 358, 381, 393 generated e.m.f., 352 heating, 375 insulation, 203 losses, 355, 371 noise, 385 522 INDEX Induction motor, peripheral velocity, 416 procedure in design, 391 reactance, 360 slots, 356, 386, 387, 389, 391, 397, 398, 416 specifications, 422 starting torque, 388 theory of operation, 319 vector diagrams, 329, 333 windings, 322 Insulating materials, canvas, 40 cotton, 30, 31 empire cloth, 32 fibre, 32 fullerboard, 450, 457, 458 impregnating compound, 31, 32, 201, 450 micanite, 31 mica paper. 201 oil, 449 paper, 32 pressboard, 450 silk, 31 tape, 30 varnish, 32, 450 wood, 450 Insulation, air films in, 198, 201 chemical effects in high volt- age, 201 condenser type, 453 creepage across, 34, 450, 454, 455, 456 dielectric strength, 30, 196 effect of heat, 31, 33, 104 of moisture, 30, 32, 449 of time, 200 of vibration, 33 grading of, 199 potential gradient, 196, 198, 200, 452 puncture test, 30, 34, 424, 496 specific inductive capacity, 197, 198, 201 thickness of, 32, 39, 101, 203, 205, 206, 459 Insulation of armature and stator coils, 36, 203 Insulation of commutators, 27 of end connections, 34, 207 of field coils, 40, 193 of rotor bars, 411, 424 of transformers, 438, 449 of turbo rotors, 274 Intermittent ratings, 379 Interpole ampere turns per pole, 92, 94, 151 dimensions, 93, 150 field system design, 149 machines, 92, 137, 140 limit of output, 142 procedure in design, 146 Iron, ageing of, 440 alloyed, 100, 440 losses. 99, 355, 439, 442, 443 magnetization curves, 47, 48, 442 thickness of laminations, 100, 191, 348, 350, 440 Joints in magnetic circuit, 433, 436, 444 Jumpers, 170 Kilo volt amperes, 188 Lag of current in induction motors, 325, 327 synchronous motors, 306, 307 Lamination of conductors, 248, 249, 461 of core bodies, 24, 28, 100, 191, 348, 350, 440 of pole faces, 25, 101 Laminations, thickness of, 100, 191, 348, 350, 440 Lap windings, 20 Lead of current in synchronous motors, 306, 307 Leakage factor, no-load, 42, 51, 53, 244 full-load, 213, 244 field, belt, 332, 365 end connection, 215, 217 pole, 42, 51, 213 slot, 215, 218 INDEX 523 Leakage field, tooth tip, 216, 220 transformer coils, 428, 445 zig zag, 361, 387 reactance in alternators, 215, 233, 285 in induction motors, 360 in transformers, 445, 482 Length and diameter of armatures, 11.6, 257, 264, 393, 404 of air gap, 67, 69, 229, 240, 243, 260, 394, 403 of armature coils, 108 Limitations in design, high voltage, 138, 488 large current, 139 low voltage, 294 speed, 141, 272, 417 Lines of force, 1 Loading, electric and magnetic, 116, 147, 476 Locking points at starting, 310, 388 Losses, constant, 337 copper, 102, 248, 338, 371, 461 contact resistance, 103 eddy currents in conductors, 248, 372 field coils, 103, 247 friction, 97, 98 in alternators, 247 in d.-c. machines, 97 in induction motors, 355, 371 in transformers, 439, 461 iron, 99, 355, 439 load, 251 pulsation, 355 rotor end ring, 371 windage, 98 Low voltage limitations in design, 139, 294 Magnet coils. See Field Coils. Magnetic areas, 42, 359 circuit, example of calculation, 42 field, distribution in gap, 44, 54- 58, 209, 288, 358 in core, 101, 358 Magnetic field, leakage between poles, 42, 51, 213 in alternators, 215, 233 in induction motors, 360 in transformers, 445 relation between main and armature, 61, 229, 290 Magnetic loading, 116, 147, 476 potential, 4 pull, unbalanced, 501 Magnetization curves, 47, 48, 442 Magnetizing current in induction motors, 352, 357, 394 in transformers, 440, 481, 485 Magnetomotive force, 4 Maximum current in induction motors, 337, 363, 394, 395 output, 341, 347, 409, 424 temperature rise, 62, 104, 464, 473 torque, 328, 341, 347 Mechanical design, 499 Mica for commutators, 27 Micanite, 31 Mica paper, 201 Moisture and insulation, 30, 32, 449 Motors, d.-c., procedure in design, 127 ratings, 129, 133, 135 Motors. See Induction and Syn- chronous. Multiple windings, 16, 21, 79, 140 Multiplex windings, 8 Natural frequency of alternators, 298, 303 Nickel steel, 500 Noise in induction motors, 385, 416 in transformers, 434 No-load current. See Magnetizing Current, saturation curve, 46, 240, 342 Oil for transformers, 449 Output and dimensions, 114, 255, 391 limits, high voltage, 138, 488 large current, 139 524 INDEX Output limits, low voltage, 294 , speed, 141, 272, 417 " maximum, 341, 347, 409, 424 of three-phase alternators, 169 Over excitation of synchronous motors, 306 Overload capacity, 78, 135, 155, 314, 424 Overspeed requirements. 272 Pancake coils, 466 Paper, 32 Parallel operation of alternators, 297 Peripheral velocity of armatures, 142, 144 of commutators, 120 of rotors, 272, 275, 290, 416 Pitch of poles, 42, 117, 258 of slots, 43, 87, 123, 256, 357, 386, 389, 391 of windings, 15, 20 Pole arc and harmonics, 178 construction, 25, 28, 101, 192, 275 dimensions, 25, 65, 67, 238 enclosure, 42, 49, 91. 259 face and wave form, 180 flux density, 45, 67, 229 number of, 117, 162, 322 pitch, 42 pitch and characteristics, 409, 410 Potential gradient, 196, 198, 200, 452 starter, 423 Power factor and armature reaction, 208, 226 and excitation, 237 and frequency, 392, 410. 420 and speed, 392, 409, 426 and voltage, 420, 425 correction by synchronous motors, 306 in three-phase machines, 169 Pressboard, 450 Pressure on bearings, 504 on brushes, 78 Procedure in design of alternators, 255 Procedure in design of d.-c. genera- tors, 114 motors, 127 field system, 62, 237 induction motors, 391 interpole machines, 146 synchronous motors, 308 transformers, 476 turbo alternators, 290 Progressive windings, 18 Pulley design, 504 Pulsations of magnetic field, 184, 386 Puncture tests, 30, 34, 424, 496 Ratings, d.-c. motors, 129, 133, 135 high torque induction motors, 382 intermittent, 379 single and polyphase alterna- tors, 188, 236 Ratio of transformation, 428 Reactance of alternators, 215, 233, 285 of induction motors, 360 of transformers, 445, 482 synchronous, 213 voltage, limits, 90, 138, 143, 146 of interpole machines, 149 of non-interpole machines, 79 Reaction, armature, in d.-c. ma- chines, 54 in polyphase alternators, 208, 289 in single phase alternators, 231 Re-entrant windings, 8 Regulation, and size of machine, 241 effect of air gap on, 229 of pole saturation on, 228 of power factor on, 246 in synchronous motors, 308 of alternators, 228, 236, 313 of transformers, 431, 489, 495 Resistance of alternator and stator' windings, 102, 248 of brush contacts, 76 of copper, 102 of field coils, 65 of induction motor rotor, 371 INDEX 525 Resistance of transformer, 461 starting in induction motors, 327, 382 Resonance between machines hunt- ing, 315 in electric circuits, 179 Retrogressive windings, 19 Reversing of induction motors, 319 Revolving field in induction motors, 319, 333 type of alternator, 191 Ring winding, 7, 9 Rocker arm, 27 Rotating and alternating fields, 186 Rotor of alternator, construction, 192, 275 current density, 238, 243 flux density, 229, 245 heating, 239, 274, 279 insulation, 193, 274 losses, 247 peripheral velocity, 272, 275, 290 procedure in design, 237, 291 strength relative to armature, 230, 290 turbo, 275 of induction motor, construc- tion, 323, 350, 422 current density, 380, 381 effect of resistance, 327, 382 flux density, 358, 381 heating, 381 insulation, 411,. 424 losses, 355, 371 peripheral velocity, 416 procedure in design, 398, 400 slip, 328, 339 slots, 356, 386, 387, 389, 398 voltage, 400, 411 winding, 323, 327, 408 Sandwiched coils for transformers, 434, 438, 484 Saturation curves, no-load, 46, 240, 342 full-load, 59, 212, 227, 237, 309 Screen covered motors, 135, 350, 383 Segmental punchings for armatures, 22, 28, 192, 351 Segments of commutator, number, 18, 138 Selective commutation, 19 Self induction of windings. See Reactance and Reactance Voltage. Semi-enclosed motors, 135, 350, 383 Series field design, 68 windings, 17, 21 commutation with, 19, 83 Shafts, 278, 504 Shell type transformers, construc- tion, 436 heating, 465 insulation, 459 procedure in design, 483 reactance. 447, 485, 489 three-phase, 491 Short circuit, 33 sudden, 282, 314, 488 test on alternators, 224 on induction motors, 344 on transformers, 430, 495, 496 pitch windings, 15, 82, 181, 189, 419 Silk covering for wires, 31 Simplex windings, 7 Single-phase alternators, armature reaction, 231 turbos, 295 windings, 160, 177, 188 Singly re-entrant windings, 8 Size of machine and frequency, 415, 493 and output, 114, 255, 391 and regulation, 241 Skew coils, 176 Slip, 328, 339 rings, 194, 327 Slots, dimensions, 80, 123, 131, 146, 256, 260, 262, 397, 398 effect on wave form, 180 insulation, 36, 203, 411 number, 22, 87, 180, 260, 396, 398, 416 526 INDEX Slots, open and closed, 24, 252, 349, 356, 381, 411 space factor, 132 Slow speed motors, 409 Space factor in slots, 132 of field coils, 65, 243 Speed and characteristics, 157, 316, 392, 409, 426 and torque curves, 328, 420 frequency and poles, 162, 322 limitations in design, 141, 272, 417 peripheral of armatures, 142, 144 of commutators, 120 of rotors, 272, 275, 290, 416 synchronous, 322 Sparking, cause, 75 criteria, 75, 90 prevention, 76, 85, 87, 90, 91 voltage, 85 Spiders, 350,. 500 Specifications, 153, 312, 422, 494 Starting current, 325, 424 torque, and rotor loss, 325, 341 372 dead points, 310, 388 in two pole motors, 418 synchronous horse-power, 341, 345, 347 sychronous motors, 309 Squirrel cage dampers, 295, 303 rotors, construction, 323, 350, 422 current density, 380, 381 flux density, 358, 381 heating at starting, 379 losses, 355, 371 procedure in design, 398 Stator, construction, 197, 348, 499 current density, 253, 262, 293, 380 flux density, 252, 282, 358, 381 generated e.m.f., 178, 352 heating, 252, 281, 380 insulation, 203 losses, 247, 355, 371 procedure in design, 255, 391 Stator reactance, 215, 233, 285, 360 resistance, 248 slots, 180, 256, 260, 262, 396, 398, 416 strength relative to field, 229, 290 windings, 160, 322 Steel. See Iron and Cast Steel. Strength of main and armature fields, 61, 229, 290 Surface creepage, 34, 450, 454, 455, 456 Sub-synchronous speed, 418 Synchronous motor design, 308 excitation, 306 power factor correction effect, 306 size, 307 starting torque, 309 Tanks for transformers, 466, 482, 486, 494 Tape, 30 Teeth, dimensions, 80, 123, 131, 146, 256, 260, 262, 397, 398 effect on wave form, 180 flux density, 45, 46, 107, 252, 282, 358, 381 Temperature rise, by resistance, 63, 465, 466 guarantees, 133, 155, 314, 424, 496 maximum, 62, 104, 464, 473 of alternator rotors, 239 stators, 252 of commutators, 111 of d.-c. armatures, 104 of enclosed machines, 134, 382 of field coils, 62, 239 of high voltage coils, 109, 250, 253 of induction motors, 375 of oil in bearings, 98, 314 of semi-enclosed machines, 383 of transformers, 463 of turbos, 274, 279, 295, 315 Tests for efficiency, 154, 313, 423, 495 INDEX 527 Tests for saturation, 342 for short circuit, 344 Theory of operation of alternator, 208 of induction motor, 319 of transformer, 427 Thickness of core laminations, 100, 191, 348, 350, 440 of insulating materials, 32, 201, 461 of mica in commutators, 27 of slot insulation, 39, 201, 203, 205, 206 Third harmonic and connection of winding, 183 Three-finger rule, 3 Three-phase power, 169 transformers, 489 windings, 162 Torque and speed curves, 328, 420 in synchronous horse-power, 341, 345, 347 maximum, 328, 341, 347 starting, in induction motors, 325, 341, 372, 388, 418 in synchronous motors, 309 Transformers, construction, 433, 494 current density, 475 excitation, 440, 481, 485 flux density, 479 generated e.m.f., 439 heating, 463 insulation, 438, 449 losses, 439, 461 procedure in design, 476 reactance, 445, 482 theory of operation, 427 vector diagrams, 427 Turbo d.-c. machines, 143 Turbo alternators, construction, 275 flux densities, 282 heating, 274, 279, 295 procedure in design, 290 reactance of armature, 285 reactions of armature, 289 shaft, 278 single-phase, 295 stresses, 275 Two-phase windings, 162 Two-pole motor, 418 Unbalanced magnetic pull, 501 Variable speed motor, 136, 426 Varnish, 32, 450 Vector diagrams, alternator, 210 induction motor, 329, 333 transformer, 427 Vent ducts, in armature and stator cores, 24, 28, 192, 349 in field coils, 40 Ventilation of air blast transform- ers, 469 of commutators, 27, 111 of d.-c. armatures, 24, 28, 109 of field coils, 40 of induction motors, 349, 382 of power house, 252 of turbo alternators, 281 Vibration and insulation, 33 Volt ampere rating, 188 Voltage and characteristics, 156, 315, 420, 424, 425, 496 between adjacent commutator segments, 95, 138, 143 limitations in design, 138, 294, 488 per turn in transformers, 476 Water cooled transformer, 470 wheel driven alternators, 252, 272 Wave form, 178, 315 windings, 20, 170 Windage, 98, 385 Winding, choice of, 123, 127, 128, 140, 260, 397 for different voltages, 130, 267, 407 pitch, 15, 20 Windings, A.-C., chain, 169 distributed, 171, 180, 187 double layer, 170 odd number of coil groups, 176 several circuits, 171 528 INDEX Windings, A. C., short pitch, 181, 189, 419 single-phase, 160, 177, 188 three-phase, 162 two-phase, 162 wave, 170 Y and A-connected, 163, 183, 407 D.-C., compensating, 96 dead coils, 22, 130 double layer, 13 doubly re-entrant, 8 drum, 9 duplex, 8, 20 equalizers, 13, 19, 22 Gramme ring, 7, 9 lap, 20 multiple, 16, 21, 79, 140 progressive, 18 re-entrant, 8 retrogressive, 19 Windings, D.-C., series, 17, 19, 21, 83 short pitch, 15, 82 simplex, 7 wave, 20 Wire table, 508 size for field coils, 65 size for transformer coils, 475 Wood, 450 Wound rotor motor, construction, 327, 351 procedure in design, 400 rotor voltage, 400, 411 theory, 327 Y-connection, 163, 260 and harmonics, 183 Yoke construction, 25, 29, 191, 350, 499 flux density, 45, 67 Zig zag leakage, 361, 387 THIS BOOK IS DUB ON THE LAST DATE STAMPED BELOW AN INITIAL FINE OF 25 CENTS WILL BE ASSESSED FOR FAILURE TO RETURN THIS BOOK ON THE DATE DUE. THE PENALTY WILL INCREASE TO SO CENTS ON THE FOURTH DAY AND TO $1.OO ON THE SEVENTH DAY OVERDUE. 81 194! Itfft NOV .10 1941 M. AUG 37 1Q44 JAN 111947 DEC 4 1940M . LD 21-100m-7,'39(402s) TU 995887 THE UNIVERSITY OF CALIFORNIA LIBRARY