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from the machine, this excitation must be increased to 37,000
ampere-turns to give the same terminal voltage under full-load
conditions (80 per cent, power factor). If then, we can calculate
the voltage, with this greater field excitation, when the load is
thrown off, the inherent regulation can be predetermined, and,
incidentally, we shall obtain a point on the open-circuit charac-
teristic corresponding to a fairly high value of the excitation.

The required flux curve, marked A , has been plotted in Fig.
141. It is derived, like any other flux curve, from the m.m.f.
curve M of Fig. 142, by using the saturation curves of Fig. 139
which must be extended beyond the limits of the diagram in
order to read the flux values for the higher degrees of excitation.
Careful measurements of the flux curve A give an area over the
pole pitch of 129 sq. cm., and if we assume the form factor of
the resulting e.m.f. wave (not plotted) to be the same as for the
open-circuit curve at normal voltage, i.e., 1.11, the voltage cor-
responding to the flux Ao will be

3,810 X 119
106.3

where 106.3 is the previously measured area of flux curve A.
The inherent regulation at 80 per cent, power factor is therefore

4,625 - 3,810

3,810 =21.4 per cent.

This is well within the specified limit of 25 per cent, which
again points to the fact that a somewhat smaller air gap, or a
lower flux density in the rotor teeth would have been permissible.

It should be pointed out here that the external power factor
corresponding to the flux distribution curve C of Fig. 141 is not
necessarily exactly 0.8; because the method of determining the

23

354 PRINCIPLES OF ELECTRICAL DESIGN

angle /3 = 54 degrees (Figs. 137 and 142) was based on certain
conditions that may not actually be fulfilled. A closer determina-
tion of the external power factor corresponding to the conditions
that have been studied is easily made as follows.

The angle a of Fig. 137 was determined on page 349 and found
to be 11 degrees. The angle \f/ f is therefore a = 54 11 =
43 degrees, instead of the previously obtained value of 40 40'
(see calculations Under items (52) to (54)). The vector OE' g is
known, and its value is 4,000 volts, since this is the e.m.f. devel-
oped by the flux distribution C of Fig. 141. In order to obtain
the corrected values for the angle 6 and the length of the vector
OE t in Fig. 137, we have:

OB = OE' g cos ^' = 4,000 cos 43

= 2,925

whence OA = 2,917

Also, BE' g = OE' g sin V = 4,000 sin 43

= 2,725
whence AE t = 2,419

Thus, tan 6 = ~r= = 0.83, which corresponds to = 39 40'.

The external power factor is therefore cos = 0.77 and the

terminal voltage = \/3 ^-^ = - (JTT~ " = 6)57 *

Thus, the condition that has actually been worked out by
graphical methods corresponds to a terminal voltage of 6,570 with
full-load current on an external power factor of 0.77. This is
sufficiently close to the specified condition with figures 6,600 and
0.8 to show that the machine will comply with the requirements.
Applying these corrections to the regulation, we have:

on an external power factor of 0.77

_ A/3 X 4625 - 6570

~ 6570
= 22 per cent.

Item (71). On the assumption that the inductance of the
armature windings can be correctly calculated, the short-circuit
current corresponding to any given field excitation can readily be
determined by the method described in Art. 107. The- curve
marked volts in Fig. 146 is the open-circuit characteristic of the
machine, the scale of ordinates being on the left-hand side of the
diagram. The construction shows that, in order to develop the

EXAMPLE OF ALTERNATOR DESIGN

355

flux necessary to produce full-load current (700 amp.) in the
short-circuited windings, 1,900 ampere-turns per pole are re-
quired. This is the excitation which will develop an " apparent "
e.m.f. equal to the sum of items (37) and (38); the effect of the
IR drop being negligible. The armature m.m.f. is almost directly
demagnetizing, and the ampere-turns per pole must, therefore, be
1,900 + 11,340 == 13,240. The current curve, within the range
of the diagram, will be a straight line, and with the full-load ex-
citation of 37,000 ampere-turns, the short-circuit current will be
1,950 amp., or 2.8 times normal. This is the steady value which
the short-circuit current would attain if the field excitation were
gradually brought up to full-load value; but at the instant of the
occurrence of a short-circuit with full-load excitation, the current

Volts per Phase Winding

2000 2
1800 g
1600 ^
1400 1
1200 tj
1000
800 1
6000
400J
200W

^

^

^

^

^^

/

_,

^

/

,'

,*

^

^

^

^

<

!?

^

^

/

/

^

^

/

y

^

/

/

/

ff ^

^

/

/

^

^

/

^

s"

v\

^C-,

_L

_L

4000 8000 12000 16000 20000 24000 28000 82000 36000 40000
Ampere Turns per Pole

Fio. 146. Curves of open-circuit voltage and short-circuit current 8000
k.v.a. turbo-generator.

would be limited only by the impedance of the stator windings
which must set up a flux of self-induction equal to the total flux.
If we neglect the effect of iron saturation and the changes in the
paths of the flux leakage lines, the momentary current might be

4 000
700 X ~OC" = 9,150 amp., or 13 times normal-load current.

It might even be greater than this, depending upon the instan-
taneous value of the generated e.m.f. when the short-circuit oc-
curs, and the windings should be arranged if possible to with-
stand without injury the mechanical forces exerted on the coils
under this condition. If this cannot be done, reactance coils
external to the machine must be provided; but the tendency
to-day is to design machines, even of the largest sizes, with suffi-

356 PRINCIPLES OF ELECTRICAL DESIGN

cient internal magnetic leakage to prevent mechanical injury
due to excessive magnetic forces on short-circuit.

Items (72) and (73). Seeing that the calculation of efficiency
when working out the example in dynamo design, it will not be
necessary to cover the same ground a second time. We shall,
therefore, determine the full-load efficiency only (item (73)).

The windage and bearing friction loss is very difficult to esti-
mate; but some approximate figures were given in Art. 111. We
shall assume 1.1 per cent, of the total k.v.a. output for the loss
due (mainly) to the friction of the air passing through the axial
ducts, and also to friction in the outside bearing. It is assumed
that the losses in the bearing on the side of the prime mover are
included in the steam-turbine efficiency. The power necessary
to drive the blower is not included in the above estimate of the
windage and friction loss.

For the correct calculation of iron losses, the reader is referred
to Art. 60, Chap. IX where the method of determining the tooth
losses was explained ; but since the maximum tooth density under
full-load conditions, as indicated by curve C of Fig. 141 does not
differ appreciably from the maximum of the open-circuit curve
(A), we shall not trouble to correct the tooth losses as previously
calculated.

With reference to the iron in the body of the stator, the flux
indicated by the area of the load flux curve C of Fig. 141 does
not all enter the core below the slots, because this total flux in-
cludes the slot-leakage flux, as explained in Art. 95. The posi-
tion of the conductors carrying the maximum current coincides
with the zero point on the armature m.m.f. curve. This is the
position 17 degrees in Figs. 141 and 142; and the current in the con-
ductor will be approximately 700 X cos 53 = 420 amp. The slot-
leakage flux corresponding to this particular current the total
not the ''equivalent" flux can be calculated as explained in
Art. 96, Chap. XIII, when deriving formula (104) which, how-
ever, gives the " equivalent" and not the total slot leakage flux.
If \$> s is the calculated slot flux, and \$ is the total flux per pole
in the air gap, then the flux actually carried by the section of

<i>
the armature iron below the slots is ^ \$ This correction

is a refinement which need not be applied in the case of a turbo-
alternator, in which the pole pitch is always large, causing <,

EXAMPLE OF ALTERNATOR DESIGN 357

to be small in relation to \$; but in machines with a small pole
pitch especially if there is only one slot per pole per phase

The full-load flux per pole is 65.2 X 10 6 maxwells (item (40)),
as against 62.2 X 10 8 (item (17)) on open circuit. With the in-
crease of flux density, the loss per pound of iron will be about
3.5 instead of 3.2 watts, and the full-load iron loss will, therefore,
be 0.3 X 28,000 = 8.4 kw. more than on open circuit; thus
bringing the total iron loss up to (say) 130 kw.

The loss at the slip rings may be calculated by the approximate
formula given in Art. 111. The diameter of the slip rings will
probably not be less than 15 in., so that the rubbing velocity

will be , -^ X 1,800 = 7,100 ft. per minute. The contact
l

area of the two sets of brushes (to carry 514 amp.) might be 5

7 100 X 5
sq. in., making the loss from this cause "'"I"" = 355 watts,

which is negligible in comparison with the other losses.
Adding up the separate losses, we have:

Windage and friction ................................. 88 kw.

Stator iron ......... . 130 kw.

Stator copper ......... 21 kw.

Rotor copper .................... ...... 66 kw.

Total 305 kw.

The kw. output is 0.8 X 8,000 = 6,400 and the efficiency, ex-
cluding losses in exciter and in air blower external to the gener-

ator, is therefore ^^SOS = ' 955 -

Items (74) and (75). On the basis of 290 kw. to be carried
away by the circulating air with a mean increase of temperature
of about 20C., the quantity of air required will be 29,000 cu. ft.
per minute. The cross-section of the ducts (item (69)) is 6.6 sq.
ft., and the average velocity in the ducts (item (75)) is, therefore,

' = 4,400 ft! per minute.

In the design of large generators there are many matters of
detail to be considered which have received but little attention
here. The question of temperature rise, for instance, is one that
would receive more attention from the practical designer than
we have given it here. It is usually permissible to assume that,
if the difference in temperature between ingoing and outgoing air

358 PRINCIPLES OF ELECTRICAL DESIGN

is 20C., the actual temperature rise of the heated surfaces as
measured by thermometer, will not exceed 40 to 50C.; but,
unless every part of the machine is carefully designed, excessive
local heating may result. The temperature of the copper in the
slots might ordinarily be from 15 to 25C. higher than that of
the iron from which it is separated by layers of insulating material ;
but should this insulation be very thick, and the cooling ducts
of insufficient section or improperly located, very much higher
internal temperatures may be reached.

INDEX

Acyclic D. C. generators, reference

to, 83

Air-gap, density (see Flux density),
"equivalent," 117, 212, 337
length of, 119, 252, 325, 337
permeance, 116, 272, 336
Alternator, design sheets for 8,000

k.v.a., 322

three phase, output of, 247
Alternators, classification of, 238

single-phase, 280, 321
Amortisseur windings (see Pole-face

windings).
Ampere-conductors per inch (see

Ampere-turns, calculation of, on

horseshoe magnet, 60
in dynamo field coils, 139, 187
in series winding (dynamo), 190
on armature (of dynamo), 78, 136

(of alternator), 249, 278, 345
on interpoles, calculation of, 174
per unit length in air, 21
"Apparent" developed voltage

(A.C.), 287, 334

Armature ampere-turns (see Ampere-
turns).

coils, length of, 97, 261
conductors, current density in, 97,

259

insulation of (see Insulation),
losses in, 318
number of, 206
core, flux densities in, 104, 210,

266, 330

losses in, 100, 104, 266, 331, 356
net and gross length of, 103, 326
current, effect of, on flux distri-
bution, 135

diameter (how determined), 77,
205

Armature, m.m.f., 136, 274, 278

in single-phase alternators, 280
reactance and reaction, 304
teeth (see Teeth),
windings, concentrated (.A.C.), 242
distributed (A.C.), 242
double layer (A.C.), 255
duplex, 86
full pitch, 85
inductance of, 263
insulation of (see Insulation),
losses in, 99
multiple or lap, 86
multiplex, 86
resistance of, 97, 209, 260
series or wave, 86
short pitch (chorded), 85, 160
simplex, 86

single layer (A.C.), 255
single-, two-, and three-phase,

240
spread of (A.C.), 257; in single

phase, 258

Armatures, drum-wound, 84
ring-wound, 84

temperature rise of, 107, 111, 267
ventilation of, 105, 261, 351
AKNOLD, DR. E., referred to, 141
Asynchronous A.C. generators re-
ferred to, 237

B

Balancing coils (see Pole-face wind-
ings).

BEHREND, B. A., referred to, 307
B-H curves, 16, 17, 18, 215
Brown and Sharp gage, 34, 36
Brush contact resistance, 179, 226
effect of, on commutation,

147, 175

pressure, usual, 179
width, as affecting commutation,
157, 162

359

360

INDEX

Brush, width, usual limits, 178
Brushes, current density at contact
surface of, 178, 180

friction losses at, 182, 227, 318

PR losses at, 181

Calorie, definition of, 47
CARTER, F. W., referred to, 116
Chorded armature windings, 85, 160
Circular lifting magnet, design of, 64
mils, definition 35, conversion

factor, 36
per ampere, conversion factor,

41

CLAYTON, A. E., referred to, 309
Clutch, magnetic, 50
Coefficient (see Cooling, Friction,

Leakage, coefficient).
Commutating poles (see Interpoles).
Commutation, effect of brush re-
sistance on, 147, 175
of end flux on, 151
of field distortion on, 169
of slot leakage on, 149
ideal, or "straight line," 148
mechanical details affecting, 178
selective, 88
sparking limits, 175
theory of, 142
time of, 140, 162
Commutator, 180, 184
diameter of, 181
peripheral velocity of, 184
segments, number of, 90, 93, 223

volts between, 94
temperature rise of, 181
Compensating windings (see Pole-
face windings).

Concentrated windings (see Arma-
ture windings).

Conductors (see Armature conduc-
tors).

Conical pole faces, magnets with, 31
Cooling coefficient (magnet coils), 45

(dynamo field coils), 194
of armatures, etc. (see Tempera-
ture rise).

Copper wire, properties of, 33
resistance of, 36
tables, 34, 35, 38
weight of, 36, 47
Core (see Armature core).
Cost, important factor in design, 6

of electromagnets, 49, 69
Critical speed of rotor, 327
Cultural subjects, value of study

of, 8
Current density at brush contact

surface, 178, 180
in armature conductors, 96,

259, 328

in coils of horseshoe magnet, 56
usual, in magnet windings, 41

Damping grids (see Pole-face wind-
ings).

ings, 90

Density (see Flux, Current, density).

Distributed armature windings (see

Armature),
field windings, 270, 335

Distribution factor, 243

Diverter, 193, 233, for interpoles,
168

Dynamo, design sheets for 75
kw., 201

A-connection, 244

E

Eddy-current losses (see Losses).
Efficiency of dynamo, 195, 197, 233

of alternator, 317, 357
Electromagnets, circular type, 64
cost of, 49, 69
design of, 48, 53
short stroke plunger type, 64

developed in alternator armatures,
242, 261, 291
in dynamo armatures, 72, 138
by cutting of end flux (commu-
tation), 159

INDEX

361

E.m.f., instantaneous value of de-
veloped (alternator), 293
virtual, or effective, value of, 294,

346
wave form, 291, 346

Empirical formulas, impossible to
avoid, 3

Enamelled wires, 38

End connections (armature), length
of, 98

End flux cut by commutated coil,
155

English language, importance of
thorough knowledge of, 5

Equalizing connections for dyna-
mos, 90

Equivalent sine waves, 295, 348
slot flux, 161, 164, 285

ESTERLINE, PROP. J. W. f referred
to, 101

Excitation (see Ampere-turns).

Exciting current, usual values of
(dynamos), 192

Face conductors (definition), 72 (see

also Armature conductors).
Factor of safety, calculation of, in

magnet design, 63

Fans, power required to drive venti-
lating, 107, 318

FIELD, PROP. A. B., referred to, 319
Field distortion in relation to com-
mutation, 169

magnet design, 185, 228, 299
with distributed windings, 270

272, 335
rheostat, 191
windings, design of, 191, 231, 299,

351
FLEMING AND JOHNSON, referred to,

192
Flux density (definition), 13

in air gap of alternators, 251,

325

of dynamos, 75, 132
of magnets, 50, 54, 63, 65
in armature cores. 104, 210, 266,
330

Flux density in armature teeth, 102,
104, 119, 122, 197, 209, 214, 251,

266
in commutating zone, 165, 167,

224

in pole core, 213
in rotor teeth, 335
distribution, effect of armature

current on, 135
effect of neighboring poles on,

126, 130

effect of tooth saturation on, 132
over armature surface, 124, 129,

213, 221, 342
leakage (see Leakage).
Form factor, 294
Frequency of alternators, 238

of D.C. dynamos, 78
Friction coefficient (between met-
als), 52

of brushes, 182
losses (alternators), 317
(brushes), 181, 227, 318
(dynamos), 196

Gauss (definition), 13
Generator (see Alternator; dynamo).
Gilbert, 11; definition, 12
GRAY, PROF. A., referred to, 309

HAWKINS AND WALLIS, referred to, 99
HAY, DR. A., referred to, 116, 132
Heating coefficient (see Cooling

coefficient).

intermittent, of magnet coils, 46
of armatures, coils, etc. (see'

Temperature rise).
HELE-SHAW, H. S., referred to, 116
HOBART AND PUNGA, referred to, 307
Homopolar machines (reference

only), 83

Horsepower transmitted by mag-
netic clutch, 52

Horseshoe lifting magnet, design of
53

362

INDEX

Hysteresis losses in armature stamp-
ings, 102
teeth, 196

Imagination, value of, to the de-
signer, 7

Inclined surfaces, effect of, on mag-
netic pull, 30

Inductance of A.C. armature wind-
ings, 263, 288

of armature end connections, 304
of slot windings (turbo-alternator),
329

Armature conductors).

Inherent regulation (definition), 252

Insulating materials, 37, 95

Insulation, breakdown voltages, 40
of armatures, 91, 96, 207, 258, 329
maximum allowable temperatures

for, 108
thickness of, on magnet spools, 41

Intensity of magnetic field (defini-
tion), 12

Intermittent heating of magnet
coils, 46

Interpole design (numerical exam-
ple), 171

calculation of ampere-turns re-
quired on, 174

K

KAPP, DR. G., referred to, 110
L

LAMME, B. G., referred to, 141
Language, importance of thorough

study of, 5

Lap, or multiple, armature wind-
ing, 86

Leakage factor (definition), 28
in alternators, 300
in dynamos, 187

Leakage of commutating poles, 167,

174
Leakage flux, 21

effect of, in saturation under-
in armature slots, 149, 281

calculation of, 160, 284
in circular lifting magnet, 67
in horseshoe magnet, 57
in multipolar dynamo, 187
in similar designs, 27
in turbo-alternators, 349
paths, permeance of, in air, 22
LEHMANN, DR., referred to, 124
Lifting magnets (see Electromag-
nets).

LISTER, G. A., referred to, 46
Losses at brush contact surface, 181,

182, 227, 318
in armature conductors, 318

stampings, 101, 104, 266, 331,

356

teeth, 102, 196, 211, 233, 318,
331

M

McCoRMiCK, B. T., referred to, 307
Magnetic circuit, 10; fundamental

equation, 14
of alternator, 299
of dynamo, 185, 228
circuits in parallel, 18
clutch, design of, 50
flux, 11; definition, 13
force (H), definition of, 12
leakage (see Leakage flux),
pull (formulas), 29
Magnetization curves for iron, 16,

17, 18, 215

Magnetizing force (H), 12
Magnetomotive force (m.m.f.), 11;

definition, 12

distribution of, over armature
periphery, 128, 134, 342, 344
Magnets (see Electromagnets).
Magnet windings, calculation of, 41,

61, 66

Materials used in magnets and
dynamos, 32

INDEX

363

Maxwell, 11; definition, 13
MENGES, C. L. R. E., referred to, 155
Mesh connection, 244
Mica, commutator, thickness of, 94,

177
MOORE, PROP. C. R., referred to,

101, 132
MORDEY flat coil alternator referred

to, 239

MORTENSEN, S. H., referred to, 307
Moss, E. W., referred to, 84
Motors, continuous current, 70, 235
MOULD, J., referred to, 84
Multiple, or lap, winding, 86
Multiplex armature windings, 86

Neutral field, or zone (definition),

146, 283
NOEGQBRATH, J. E., referred to, 84

O

Oersted (definition), 13
Open-circuit characteristic curve

(see Saturation curve).
Output formula for D.C. dynamos,
73,76

of three-phase generator, 247

PARSE ALL AND HOB ART, referred to,

101

PELTON water-wheel, referred to, 241
ing).

velocity of alternator rotors, 238
of commutators, 184
of dynamo armatures, 77
Permeability, 11, 15; definition, 13
Permeance, 11; definition, 13
between concentric cylinders, 26
flat surfaces, 24
parallel cylinders, 27
curve, 123, 130
of air gap (slotted armatures),

116, 272

of leakage paths (formulas), 23
Phases, number of, 239

Plunger magnet, 49

Polar coordinates, use of, for plot-
ting irregular waves, 294, 347

Pole arc, 74, 76, 204, 249

Pole-face windings, 170, 279, 322,
336

Pole, length of, 186, 227

Pole pitch (definition), 74; usual

values, 80

factors determining width of,
78, 248

Pole shoes, 188, 269

Poles, number of, 80, 204, 241

POWELL, P. H., referred to, 116

Pressure rise when switching off
magnet coil, 33

Pressures, usual, in commercial
designs, 33, 248

Properties of materials, 32

Pull exerted by magnets, 29, 50

Quantity of air required with

forced ventilation, 112
of electricity, 70

R

Reactance, armature, 304

coils, use of, 355
Reactive voltage drop (slots), 288;

(ends), 266, 304, 332
Regulation, effect of flux distribu-
tion on, 311

inherent (definition), 252
of alternators, 252, 301, 312, 352
on any power factor, 309
on zero power factor, 305
Reluctance, magnetic, 1 1 ; definition,

13

Resistance of armature windings, 97
of copper wires, 36
variation of, with temperature, 36
Rheostat, shunt field, 191
Rise of pressure on switching-off coil,

33
of temperature (see Temperature

rise).

Rotor of turbo-alternators, 270, 272,
335

364

INDEX

Saturation curve for alternator, 302,

306, 310, 340, 355
for dynamo, 189, 190, 228
Self-induction, not different from

other induction, 155
Series field winding, 190, 192, 231

or wave, winding, 86
Short-circuit current of alternators,

252, 308, 354
Short pitch armature windings, 85,

160

Shunt winding calculation (dyna-
mos), 191, 231
with two sizes of wire, 42
Simplex armature windings, 86
SIMPSON'S rule, 122, 217
Single-phase alternators, 280, 321
Size of wire, calculation of, in mag-
net coils, 41

Sketches, importance of neat, 4
" Skull cracker," 64
Slot, dimensions of, in alternator,

259

in dynamo, 92, 93, 207
insulation (see Insulation of arma-

tures).
leakage flux, calculation of, 160,

284
effect of, on commutation,

149

"equivalent," 161, 164, 285
in alternators, 281
pitch (definition), 92
Slots, number of, 93, 260
Space factor (definition), 39;

(values), 40
Sparking at brushes, prevention of,

175, 225

Specific heat, 47

values for alternators, 250, 325

for dynamos, 76

Speeds, usual (dynamos), 81; (alter-
nators), 241
Star connection, 244
STEINMETZ, DR. C. P., referred to,
141

S.W.G. wire table, 35
Symbols, list of, xi

use of, 2
Synchronous A.C. generators (see

Alternators).

Teeth, dimensions of (dynamos), 92,

208; (alternators), 259
flux density in, 104, 119, 122, 197,

209
losses in, 102, 196, 211, 233, 318,

331

number of, 93, 260
strength of rotor, 336
taper, losses in, 196

m.m.f. calculations for, 122
Temperature, internal, of magnet

coils, 45

rise of alternator field coils, 300
of armatures, 107, 112, 212,

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