Alfred Still.

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PRINCIPLES OF
ELECTRICAL DESIGN



McGraw-Hill BookCompany



Electrical World The Engineering and Mining Journal
Engineering Record Engineering News

Railway Age Gazette American Machinist

Signal E,ngin<?9r American Engineer

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Metallurgical and Chemical Engineering P o we r



PRINCIPLES

OF

ELECTRICAL DESIGN

D. C. AND A. C. GENERATORS



BY
ALFRED STILL

PROFESSOR OF ELECTRICAL DESIGN, PURDUE UNIVERSITY; FELLOW AMERICAN INSTITUTE
OF ELECTRICAL ENGINEERS; MEMBER INSTITUTION OF CIVIL ENGINEERS; MEMBER
INSTITUTION OF ELECTMCAL ENGINEERS. AUTHOR OF "OVERHEAD ELEC-
TRIC POWER TRANSMISSION," "POLYPHASE CURRENTS," ETC.



Fr<is7



McGRAW-HILL BOOK COMPANY, INC.
239 WEST 39TH STREET. NEW YORK



LONDON: HILL PUBLISHING CO., LTD.

6 A 8 BOUVERIE ST., E. C.

1916



58



COPYRIGHT, 1916, BY THE
McGRAW-HiLL BOOK COMPANY, INC.



THB. MAPLE. PRESS. YORK. PA



PREFACE

This book is intended mainly for the use of students following
courses in Electrical Engineering, and for this reason emphasis is
laid on fundamentals and principles of general application, while
but little attention is paid to the needs of the practical designer,
who may be trusted to devise his own time-saving methods of
calculation, provided always that he has a thorough understand-
ing of the essentials governing all electrical design.

The writer is a firm believer in the advantage of having a
concrete mental conception of the hidden actions which produce
visible or measurable results, and in studying the electromotive
forces developed in the windings of electric generators, he con-
sistently represents the effects as being due to the cutting by the
conductors of imaginary magnetic lines.

No attempt has been made to deal adequately with the me-
chanical principles involved in the design of electrical machinery.
Thus as a reference book for the designer, this text is admittedly
incomplete. It is incomplete also as a means of giving the stu-
dent what he is supposed to get from a course in electrical design,
for the simple reason that no art can be mastered by the mere
reading of a book. In this as in every other study, all that is
worth having the student must himself acquire by giving his
mind to the business on hand and taking pains. The book cannot
do more than serve as a reference text or the basis for a course
of lectures; and for every hour of book study, four to six hours
should be spent in the actual working out of practical designs.

The writer has ventured to express some views regarding the
qualifications of the successful designer in an introductory chap-
ter where he believes they are less likely to remain permanently
buried than if embodied in a preface of unconventional length.
At the same time he does not claim that the procedure here
adopted is such as will meet the requirements of the professional
designer; but in criticising the book, it is important to bear in
mind that its main object is to illustrate the logical application
of known fundamental principles, and so help the reader to
realize the practical value of theoretical knowledge. It is not to

338041



vi PREFACE

be supposed for a moment that an experienced designer can afford
the time required to work through the detailed design sheets as
here given in connection with the numerical examples ; but, apart
from the fact that he generally makes use of existing patterns
and stampings, in connection with which he has at hand a vast
amount of accumulated data, he is in a position to apply short-
cut methods to his work. This is not readily done by the student,
who usually lacks the experience, judgment, and sense of propor-
tion, without which "rule of thumb" methods and rough ap-
proximations cannot be applied intelligently.

Portions of the material here presented have appeared recently
in articles and papers contributed by the writer to the "Elec-
trical World," the Journal of the Franklin Institute, and the
Journal of the Institution of Electrical Engineers; but what has
been borrowed from these publications has to a large extent been
rewritten.

The thanks of the writer are also due to Mr. D. L. Curtner,
not only for assistance in reading and correcting proofs; but
also for valuable suggestions and helpful criticism.

LAFAYETTE, IND.,
June, 1916.



CONTENTS

PREFACE v

LIST OF SYMBOLS xi

CHAPTER I

INTRODUCTORY 1

CHAPTER II

THE MAGNETIC CIRCUIT ELECTROMAGNETS
ART. PAGE

1. The magnetic circuit 10

2. Definitions 12

3. Effect of iron in the magnetic circuit 15

4. Magnetic circuits in parallel 18

5. Calculation of leakage paths 22

6. Flux leakage in similar designs 27

7. Leakage coefficient 28

8. Tractive force 29

9. Materials Wire and insulation 32

10. Calculation of magnet windings 41

11. Heat dissipation Temperature rise 44

12. Intermittent heating 46

CHAPTER III
THE DESIGN OF ELECTROMAGNETS

13. Introductory 48

14. Short stroke tractive magnet 49

15. Magnetic clutch 50

16. Horseshoe lifting magnet (Numerical example) 53

17. Circular lifting magnet (Numerical example) 64

CONTINUOUS CURRENT GENERATORS
CHAPTER IV

DYNAMO DESIGN FUNDAMENTAL CONSIDERATIONS BRIEF OUTLINE OF

PROBLEM

18. Generation of e.m.f 70

19. The output formuU 72

20. Number of poles Pole pitch Frequency 78

vii



viii CONTENTS

CHAPTER V

ARMATURE WINDINGS AND SLOT INSULATION
ART. PAGE

21. Introductory 83

22. Ring- and drum-wound armatures 84

23. Multiple and series windings 84

24. Equalizing connections for multiple-wound armatures 90

25. Insulation of armature windings 91

26. Number of teeth on armature 93

27. Number of commutator segments Potential difference between

segments 93

28. Nature and thickness of slot insulation 94

29. Current density in armature conductors 96

30. Length and resistance of armature winding 97

CHAPTER VI

LOSSES IN ARMATURES -VENTILATION TEMPERATURE RISE

31. Hysteresis and eddy-current losses in armature stampings ... 100

32. Usual densities and losses in armature cores 104

33. Ventilation of armatures 105

34. Cooling surfaces and temperature rise of armature 107

35. Summary, and syllabus of following chapters 113

CHAPTER VII
FLUX DISTRIBUTION OVER ARMATURE SURFACE

36. Air-gap flux distribution with toothed armatures 115

37. Actual tooth density in terms of air-gap density 119

38. Correction for taper of tooth 121

39. Variation of permeance over pole pitch Permeance curve . . .123

40. Open-circuit flux distribution and m.m.f. curves 128

41. Practical method of predetermining flux distribution 129

42. Open-circuit flux distribution curves as influenced by tooth satura-

tion 132

43. Effect of armature current in modifying flux distribution . . . .135

CHAPTER VIII
COMMUTATION

44. Introductory . 140

45. Theory of commutation 142

46. Effect of slot flux . . . ...... ..... . '" '. ... ,.:..- . 149

47. Effect of end flux . . . J , '.'.. , .Jh 151

48. Calculation of end flux 155

49. Calculation of slot flux cut by coil during commutation 160

50. Commutating interpoles 165

51. Example of interpole design 171



CONTENTS ix

ART. PAGE

52. Prevention of sparking Practical considerations 175

53. Mechanical details affecting commutation 178

54. Heating of commutator Temperature rise 181

CHAPTER IX

THE MAGNETIC CIRCUIT DESIGN OF FIELD MAGNETS EFFICIENCY

55. The magnetic circuit of the dynamo 185

56. Leakage factor in multipolar dynamos 186

57. Calculation of total ampere-turns required on field magnets ... 187

58. Arrangement and calculation of field windings 190

59. Temperature rise of field coils 193

60. Efficiency 195

CHAPTER X
DESIGN OF A CONTINUOUS CURRENT DYNAMO NUMERICAL EXAMPLE

61. Introductory 199

62. Design sheets for 75-kw. multipolar dynamo 200

63. Numerical example Calculations 204

64. Design of continuous current motors 235

ALTERNATING-CURRENT GENERATORS

CHAPTER XI
DESIGN OF ALTERNATORS FUNDAMENTAL CONSIDERATIONS

65. Introductory 237

66. Classification of synchronous generators 238

67. Number of phases 239

68. Number of poles Frequency 241

69. Usual speeds of A.C. generators 241

70. E.m.f. developed in windings 242

71. Star and mesh connections 244

72. Power output of three-phase generators 247

73. Usual voltages 248

74. Pole pitch and pole arc 248

75. Specific loading 250

76. Flux density in air gap 251

77. Length of air gap Inherent regulation 252

CHAPTER XII
ARMATURE WINDINGS LOSSES AND TEMPERATURE RISE

78. Types of windings 255

79. Spread of winding 257

80. Insulation of armature windings 258

81. Current density in armature conductors . . . 259



x CONTENTS

AKT. PAGE

2. Tooth and slot proportions 259

83. Length and resistance of armature winding 260

84. Ventilation 261

85. Full load developed voltage 261

86. Inductance of A.C. armature windings 263

87. Calculation of armature inductance 264

88. Total losses to be radiated from armature core 266

89. Temperature rise of armature 267

CHAPTER XIII
AIR-GAP FLUX DISTRIBUTION WAVE SHAPES

90. Shape of pole face 269

91. Variation of permeance over pole pitch (Salient pole machines) . .271

92. M.m.f. and flux distribution on open circuit (Salient pole machines) 272

93. Special case of cylindrical field magnet with distributed winding . 272

94. Armature m.m.f in alternating-current generators 274

95. Slot leakage flux 281

96. Calculation of slot leakage flux 284

97. Effect of slot leakage on full-load air-gap flux 286

98. Method of determining position of armature m.m.f 288

99. Air-gap flux distribution under load 290

100. Form of developed e.m.f. wave 291

101. Form factor 294

102. Equivalent sine waves 295

CHAPTER XIV
REGULATION AND EFFICIENCY OF ALTERNATORS

103. The magnetic circuit 299

104. Regulation 301

105. Factors influencing the inherent regulation of alternators .... 303

106. Regulation on zero power factor 305

107. Short-circuit current 308

108. Regulation on any power factor 309

109. Influence of flux distribution on regulation 311

110. Outline of procedure in calculating regulation from study of e.m.f.

waves 312

111. Efficiency 317

CHAPTER XV
EXAMPLE OF ALTERNATOR DESIGN

112. Introductory > . 320

113. Single-phase alternators 321

114. Design sheets for 8000-kw. turbo-alternator 322

115. Numerical example Calculations 324

INDEX . 359



LIST OF SYMBOLS

A = area of cross-section ; area of surface.

A = area of one lobe of periodic wave plotted to polar coordinates.

A c = ampere-conductors in pole pitch.

a = coefficient in resistance-temperature formulas.

B = magnetic flux density (gauss).
/? or B" = magnetic flux density (maxwells per square inch).

B a = instantaneous average value of air-gap density over the arma-
ture conductors of one phase.

B c = average air-gap density in zone of commutation.
B c = average or equivalent flux density in pole cores.
Bg = flux density in air gap (gausses).
B g = average air-gap density over tooth pitch.
B p = average air-gap density under commutating pole.
B t = actual flux density in teeth.
B. & S. = Brown and Sharpe wire gage.
6 = number of brush sets.

C = electrostatic capacity (farads).
c coefficient of friction.
c = length of pole (radial).

D = diameter of armature core (including teeth).
D e = diameter of commutator (inches).

d = diameter of magnet core.

d inside diameter of armature core.

d = maximum value of equivalent sine-wave.

d = depth of armature 'slot (length of tooth).
d, = equivalent length of tooth.

E = electromotive force (e.m.f.); difference of potential (volt).
E a = volts per phase in armature winding.
EC = volts per conductor.
E e = e.m.f. generated in end connections of short-circuited coil

during commutation (volts).
E m = mean or average value of e.m.f.
Eo = terminal voltage when load is thrown off.
E, = reactance voltage drop per phase (slot leakage only).
E t = terminal voltage.
e = instantaneous value of e.m.f. (volts).
e e = instantaneous e.m.f. per armature inductor,
e.m.f. = electromotive force.

/ = frequency (cycles per second).

xi



xii LIST OF SYMBOLS

H = intensity of magnetic field; magnetizing force (gilberts per

centimeter; or gauss).
hp. = horsepower.

/ = current, amperes.
7 = current per phase (or per conductor) in alternator armature

winding.

I c = current per conductor in armature.
I m = mean or average value of current.
i = instantaneous value of current.

i s = instantaneous value of current in armature conductor (for slot
leakage calculations).

k.v.a. = kilovolt-amperes.
k.w. = kilowatts.

k = a constant; any whole number.

k = cooling coefficient.

k = distribution factor (A.C. armature windings).

pole arc.
10 armature core length.

permissible current density at brush tip.
average current density over brush contact surface.

L = inductance; coefficient of self-induction (henry).
L c = length of cylindrical surface of commutator (inches).

I = a length, usually expressed in centimeters.

I = %l e (commutation).
I' = axial projection of armature end connections beyond slot (A.C.

generator).

I" = a length expressed in inches.
l a = gross length of armature core.
l c = total axial length of brush contact surface.
l e = length of end portions of armature coil.
If. = leakage factor.

In = net length of iron in armature core (usually inches).
IP = axial length of commutating pole face.
l v total axial length taken up by vent ducts.

M = thickness of commutator mica.
(M ) = circular mils per ampere.
(m) = circular mils,
m.m.f. = magnetomotive force (gilbert).

TV = number of revolutions per minute.
N, = number of revolutions per second.
n = number of radial air ducts in armature core.
n = number of slots per pole.
n s = number of slots per pole per phase.



LIST OF SYMBOLS xiii

P = power; watts.
P = permeance.

P = pressure, pounds per square inch.
p = number of poles.
Pi = number of electrical paths in parallel in armature, winding.

Q = quantity of electricity.

q = specific loading of armature periphery (ampere-conductors per
inch).

R = resistance (ohm).

R - resistance of armature coil undergoing commutation.

R = magnetic reluctance (oersted).
R" = resistance between opposite faces of an inch cube of copper

(ohm).

Re brush contact resistance per square inch of contact surface.
Rd = radial depth of armature stampings below slots.
jRo = resistance at temperature zero degrees.
Rt = resistance at temperature t degrees.

pole arc.
r = ratio -

pole pitch.

r = length of radius vector.

S = number of turns in a coil of wire.
iS> = brush contact surface.
s = slot width,
a/. = space factor.
SI = ampere turns.

(SI) a = armature ampere-turns per pole.
(SI)g = ampere-turns for air gap.

T = temperature rise in degrees Centigrade.
T = number of turns in armature coil.

T e = number of turns in armature coil between tappings to com-
mutator bars.
T. = number of inductors in one slot.

t = interval of time.

t = temperature (degrees Centigrade).

t = thickness of magnet winding.

t = width of tooth.
te = time of commutation.
tr = width of rotor tooth.



V = peripheral velocity of armature centimeters per second.
V e = surface velocity of commutator centimeters per second.

v = peripheral velocity feet per minute.

v e = peripheral velocity of commutator surface feet per minute.
v* = average velocity of air in ventilating ducts feet per minute.



xiv LIST OF SYMBOLS

W = power watts.
W = width of brush (circumferential).
W a = brush width (arc) referred to armature periphery.
w = a portion of the total (circumferential) width of brush.



cooling coefficients (armature temperature).

X = reactance (ohm).

Z = impedance (ohm).

Z = number of inductors in series per phase (A.C. generator).
Z = number of inductors on armature (D.C. generator).
Z' = total number of inductors (A.C. generator).

a = angle denoting slope of coil side in end connections of armature

winding.
a = angle of phase displacement of developed e.m.f. due to armature

cross magnetization.

/3 = angle of lag of current behind phase of open-circuit e.m.f.
A = current density; amperes per square inch.
A w = maximum current density over contact surface of brush.
5 = clearance between coil sides in end connections of armature

windings.

5 = length of actual air gap tooth top to pole face.

be = length of equivalent air gap in machines with toothed armatures.
8 S = deflection of shaft (inches).

6 = an angle.

6 = angle of lag (cos 6 = power factor).

X = slot pitch.

n = permeability = B/H^

n- = 3.1416 approximately.

T = pole pitch (usually in inches).

$ = magnetic flux (maxwell).

<l> = total flux entering armature from each pole face.
$ = flux per pole actually cut by armature conductors.
$> c = total flux entering teeth comprised in commutating zone.
&d = flux entering armature core through roots of teeth (commuta-
tion).

$ e = total flux cut by one end of armature coil during commutation.
3> e = total flux cut by end connections (both ends) of polyphase

armature winding.
3> s = "equivalent" slot leakage flux (magnetic circuit closed through

roots of teeth).

>' ts = "equivalent" slot flux (magnetic circuit closed through tops of
teeth).

$i = leakage flux (maxwells).

$, = total slot leakage flux.

<l>x = flux entering armature in space of one tooth pitch.

^ = internal power-factor angle.
^ = "apparent" internal power-factor angle.

co = 2*f



PRINCIPLES
OF ELECTRICAL DESIGN



CHAPTER I
INTRODUCTORY

By devoting a whole chapter to introductory remarks and
generalities which are rarely given a prominent place in modern
technical literature, the author hopes not only to explain the
scheme and purpose of this book, but to show what may be
gained by an intelligent study of the conditions to be met, and
the difficulties to be overcome, by the designer of electrical
machinery.

The knowledge required of the reader includes elementary
mathematics, the use of vectors for representing alternating
quantities, the principles of electricity and magnetism, and
some familiarity with electrical apparatus and machinery,
such as may be acquired in the laboratories of teaching institu-
tions equipped for the training of electrical engineers, or in the
handling and operation of electrical plant in manufacturing
works and power stations. The principles of the magnetic
circuit will be explained here in some detail, because the whole
subject of generator design from the electrical standpoint is
little more than a practical application of the known laws of
the electric and magnetic circuits; but a fair knowledge of the
physics underlying the action of electromagnetic apparatus is
presupposed.

The conception of the magnetic circuit consisting of closed
lines or tubes qf induction linked with the electric circuit
involving the cutting of these magnetic lines by the conductors
in which an e.m.f. is generated is unquestionably a useful one
for the practical engineer; and the student should endeavor to
form a mental picture of these imaginary magnetic lines in
connection with every piece of electrical apparatus or machinery
which he desires to understand thoroughly.

1



2 PRINCIPLES OF ELECTRICAL DESIGN

Having clearly realized the general shape and distribution
of the magnetic field surrounding a conductor or linked with a
coil of wire carrying an electric current, the next step is to cal-
culate with sufficient accuracy for practical purposes the quantity
of magnetic flux produced by a given current; or the e.m.f.
developed by the cutting of a known magnetic field. This leads
to the consideration of units of measurement.

The practical units of the C.G.S. system will be used so far as
possible; but since engineers of English-speaking countries still
prefer the foot and inch for the measurement of length, there
must necessarily be a certain amount of conversion from centi-
meter to inch units, and vice versa. This may, at first sight,
appear objectionable; but, in the opinion of the writer, there is
something to be gained by having to transform results from one
system of units to another. The process helps to counteract
the tendency of mathematically trained minds to lay hold of
symbols and formulas and treat them as realities, instead of
striving always to visualize the physical (or natural) reality
which these symbols stand for. The same may be said of such
alphabetical letters as are in general use to denote certain physical
quantities or coefficients; as /* for permeability, and L for the
coefficient of self-induction. Familiarity with these symbols
tends to obscure the physical meaning of the things they stand
for; and although uniformity in the use of symbols in technical
literature cannot be otherwise than advantageous, 1 the use of
unconventional symbols involves their correct definition, and
for this reason their occasional appearance in writings that are
professedly of an instructional nature should not be condemned.
This point is made here to emphasize the writer's 'conviction
that the student should endeavor to regard symbols and mathe-
matical analysis as convenient means to attain a desired end;
and that he should cultivate the habit of forming a concept or
mental image of the physical factors involved in every problem,
even during the intermediate processes of a calculation, if this
can be done.

By way of illustrating the application of fundamental magnetic
principles, the design of electromagnets will be taken up before
considering the magnetic field of dynamos. This preliminary
study should be very helpful in paving the way to the main
subject; and the chapter on magnet design has been written with

1 A list of the symbols used will be found at the beginning of this book.



INTRODUCTORY 3

this end in view : it does not treat of coreless solenoids or magnetic
mechanisms with relatively long air gaps; because the air clear-
ance is always small in dynamo-electric machinery.

In the method of design as followed in this book, an attempt is
made to base all arguments on scientific facts, and build up a
design in a logical manner from known fundamental principles.
This is admittedly different from the method followed by the
practical designer, who uses empirical formulas and " short
cuts," justified only by experience and practical knowledge.
It must not, however, be supposed that a commercial machine
can be designed without the aid of some rules and formulas
which have not been developed from first principles, for the
simple reason that the factors involved are either so numerous
or so abstruse that they cannot all be taken into account when
deriving the final formula or equation. In any case the con-
stants used in all formulas, even when developed on strictly
scientific lines, are invariably the result of observations made on
actual tests; and many of them, such as the coefficients of fric-
tion, magnetic reluctance, and eddy-current loss, are subject to
variation under conditions which it is difficult to determine.
The formulas used in design are therefore frequently empirical,
and they yield results that are often approximations only; but
an effort will be made to explain, whenever possible, the scientific
basis underlying all formulas used in this book.

A perception of the fitness of a thing to fulfil a given purpose
and of the relative importance of the several factors entering
into a problem, is essential to the successful designer. This
quality, which may be referred to as engineering judgment, is
not easily taught; it grows with practice, and is strengthened by
the experience gained sometimes through repeated failures;
but it is necessary to success in engineering work, whether this
is of the nature of invention and designing, or the surmounting
of such obstacles and difficulties as will arise in every branch of
progressive engineering. All the conditions and governing factors
are not accurately known at the outset, and a good designer is
able to make a close estimate or a shrewd guess which, in nine
cases out of ten, will give him the required proportion or dimen-
sion; he will then apply tests based upon established scientific
principles in order to check his estimate, and so satisfy himself
that his machine will conform with the specified requirements.



4 PRINCIPLES OF ELECTRICAL DESIGN

A knowledge of the theory and practice of design, the thorough-
ness of which must depend upon the line of work to be ultimately
followed, would seem to be of great importance to every engineer.
It may not be of great benefit to all men in the matter of forming



Online LibraryAlfred StillPrinciples of electrical design; d. c. and a. c. generators → online text (page 1 of 30)