Alfred Still.

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displacement referred to therefore corresponds, in a four-pole
machine, to a movement of 2 to 2J actual space degrees.

In connection with Fig. 85, it should be observed that it is
only in the case of a full-pitch winding that both coil-sides will
be moving through a field of the same density at the same
instant of time. In the design under consideration the pole
pitch is equal to 11J4 times the slot pitch, while the two sides
of the coil would probably be spaced exactly 11 slot pitches
apart. This is very little short of a full-pitch winding, and the
flux cut by the two sides of the coil is very nearly the same
at any given instant; but the method illustrated by Fig. 85 can,
of course, be used for determining the proper brush position with
short-pitch as well as with full-pitch windings.

Item (108) : Brush Pressure. Refer Arts. 53 and 54. Assume
Ij-^ lb. per square inch.

Items (109) to (112): Brush Resistance and Losses. Refer
Arts. 53 and 54. From Fig. 68 (page 179) we find the
surface resistance of hard carbon brushes to be about 0.025 ohms
per square inch fora current density of 36.2 (item (93)). The
area of all brushes of the same sign is 9 sq. in. (item (94)) ; and the
total brush resistance is therefore

- 2 9 5 X 2 = 0.00556 ohm.

The calculated IR drop is 0.00556 X 326 = 1.81 volts, which
should be increased by about 25 per cent, as suggested on page
181, making this item 2.25 volts. The PR loss is 326 X 2.25 =
730 watts. In these, and some previous, calculations, the value
of the line current (item (12)) has been used in place of the total
current passing through the armature windings. It is true
that an allowance should have been made for the shunt exciting

PROCEDURE IN DESIGN OF D.C. GENERATOR 227

current; but this is usually an unnecessary refinement; and when
calculating brush losses, great accuracy in results is not attainable
because the resistance at the brush-contact surface is always a
quantity of rather doubtful value.

Item (113): Brush-friction Loss. Refer Art. 54. Assuming a
coefficient of friction of 0.25, the brush-friction loss by formula
(89) is

0.25 X 1.5 X 18 X 600 X 13.5 X TT X 746

Wf - "i2X3pOO~ = 324 WattS '

Items (115) and (116): Cooling Surface and Temperature Rise
of Commutator. Refer Art. 54 and Fig. 70, page 183. The radial
height of the risers will be about 2 in., making D r = 17% in.
The radial depth of the exposed ends of the copper bars might
amount to % in., making D e = 12 in.; and the total cooling
surface considered, worked out as explained on page 182, amounts
to 492 sq. in.

The radiating coefficient, as given in formula (90), is

2 130
- 25 + - ' 0463 '

whence T = 400 y n Vufis = 46.3C., which is permissible.

Had this calculated temperature rise exceeded 50, it might
have been necessary to increase the axial length of the com-
mutator, or reduce the losses by using a soft quality of carbon
brush and perhaps a lighter pressure at the contact surface.
In some cases special ventilating ducts are provided inside the
commutator; but these should not be necessary in a machine of
the type and size considered.

Item (117): Leakage Coefficient. Refer Art. 56, page 186.
The value of this item was estimated at 1.2 in connection with
the shaping of the pole shoe (item (68)).

Items (118) to (121): Flux Density in Pole Core. A cylindrical
pole core 10 in. in diameter has been decided upon (item (68)).
The area of cross-section is therefore 78.54 sq. in., and the
full-load flux density in the pole core near the yoke ring is

6,970,000 X 1.2
78.54 X 6.45 = 16 ' 50 gausses *

Item (122): Radial Length of Pole. Refer Art. 55, page 186.
The full-load ampere-turns per pole for air gap, teeth and slots
amount to about 6,000 (see Fig. 83). Then, by formula (91),

228

PRINCIPLES OF ELECTRICAL DESIGN

the length of winding space should be c =

6,000

875

6.85 in.

Let us make the cylindrical pole core 7 in. long, which will de-
termine the inside diameter of the yoke ring. This will have
to be about 38 in. as shown in Fig. 86.

Items (123) to (127): Dimensions of Yoke Ring. Assuming a
density of 15,000 gausses in the cast-steel yoke ring, the cross-
section will be

6,970,000 X 1.2
2 X 15,000 X 6.45 "

The dimensions can now be determined, and the lengths of the
flux paths obtained from Fig. 86.

FIG. 86. Magnetic circuit of four-pole dynamo.

Item (128): Open-circuit Saturation Curve. Refer Chap. IX,
Arts. 55, 56, and 57. Also Art. 16 of Chap. III. The calcula-
tions of the total ampere-turns on each pole of the machine, to
develop on open circuit a given voltage, are shown in the accom-
panying table. Suitable values of terminal voltage are selected
to obtain points on the saturation curve. One of the values
should be slightly higher than the developed e.m.f. under full-
load conditions. It is not necessary to make the calculations
for very low voltages because the reluctance of the iron parts
of the magnetic circuit is then negligible. For each selected
value of the developed e.m.f., the ampere-turns for the com-
plete magnetic circuit are calculated exactly as explained in

PROCEDURE IN DESIGN OF D.C. GENERATOR 229

Chap. Ill, Art. 16, in connection with the horseshoe lifting mag-
net. The useful flux entering the armature must be multiplied
by the leakage factor to obtain the total flux in the yoke ring;
and, in the case of the pole cores, the approximation suggested
in Art. 16 (page 60) may be used. The average value of the
pole-core density, for use in calculating the ampere-turns required,

s

In this instance B y = 1.2B P ', whence B c = 1.133B P , the mean-
ing of which is that the density in the pole core is calculated
on the assumption that the leakage factor is 1.133 instead of
1.2, as used for estimating the flux in the frame.

OPEN-CIRCUIT SATURATION
(Table for Calculating Ampere-turns per Pole for Total Magnetic Circuit)

Flux entering armature per pole

(maxwells)

245
7,160,000

230

6,725,000

210

6,140,000

190
5,560,000

Flux density (lines
per square inch)

Armature core (36 sq. in.)
Air gap (maximum value)
Pole core (78.54 sq. in.)
Yoke ring (43.2 sq. in.)

99,400
56,100
103,400
99,400

93,400
52,600
97,100
93,400

85,250
48,000
88,700
85,250

77,250
43,400
80,300
77,250

a

Armature

80

42

20

11

!l

Pole core

104

64

26

14

<D "-

Yoke

80

42

20

11

i

Armature (o = 5.1)

408

214

102

56

l

Pole core (c 8)

832

512

208

112

g|

3*

Yoke (y = 15)

1,200

630

300

165

Air gap and teeth

5,750

5,300

4,800

4 250

Total ampere-turns

8,190

6,656

5,410

4,583

230

PRINCIPLES OF ELECTRICAL DESIGN

The ampere-turns per inch are read off the upper curve of
Fig. 3 (page 17), and the lengths of the various parts of the
magnetic circuit are taken from Figo 86. The length of the
iron path in the armature core is taken as one-third of the pole
pitch, as suggested in Art. 57. The ampere-turns for the air
gap, teeth and slots are read directly off the curve a, b, c, d t
e, /, of Fig. 82 (page 219), for the density corresponding to the
maximum value of the flux curve A of. Fig. 84. It is assumed that

wo

240
230
220
210
200
190
180
>170
160
150
140
130
120

^

^

**

G

/

/"

F

^

/f

/,

'

/

/
/
/

/

j

/

/
/

/

/
/

/

/

/
/

/
/

/

/

Sh

unt.

Open

Oirc

iit^

->

*ti

)isto

tion

S

mnt.

Full

Loac

Se:

ies

110

3000

4000

8000

9000

5000 6000 7000

Ampere -Turns per Pole

FIG. 87. Open-circuit saturation curve (numerical example).

the shape of this curve remains unaltered, and that the maximum
ordinate is directly proportional to the developed voltage.

The curve, Fig. 87, is plotted from the results of these calcu-
lations. It shows the connection between developed e.m.f. (or
open-circuit terminal voltage) and the corresponding ampere-
turns of excitation per pole. The shunt ampere-turns on open

230
circuit are 5,930, and at full load, 5,930 X 220 = 6,200. The

ampere-turns in the series winding are 7,850 6,200 = 1,650,
which includes the ampere-turns to compensate for armature

PROCEDURE IN DESIGN OF D.C. GENERATOR 231

demagnetization and distortion. This correction, amounting to
400 ampere-turns, is obtained from Fig. 82, where this number
of ampere-turns is seen to be necessary to raise the flux density
under the center of the pole from 7,260 to 7,800 gausses, as
explained on page 222.

Items (133) to (137) : Shunt Field Winding. Refer Art. 58,
Chap. IX, and Art. 10, Chap. II. The length of winding space
for the shunt may be determined by dividing the total length
available for the windings in the proportion of the ampere-
turns in shunt and series coils respectively. The length of the

6 200
cylindrical core is 7 in., and 7 X ^ = 5,53. Some allowance

should be made for external insulation, and the net length of
winding space for the shunt coils might be, say, 5 in. Let us
assume the total thickness of winding to be 2 in. The inside
diameter of the winding might be 10)^ in., making the average
diameter 1234 in., and the mean length per turn, 38.5 in. We
shall suppose that the shunt rheostat absorbs 15 per cent, of
the voltage on open circuit; which leaves 187 volts across the
s,hunt winding. By formula (26) on page 42, we have:

38.5 X 5,930 X 4
(ro) = ~ - = 4 > 880

Referring to the wire table on page 34, the standard size of
wire of cross-section nearest to this calculated value is No.
13 B. & S. gage. This can be used if the rheostat is arranged to
reduce the voltage across the winding in the proper proportion.
The number of turns per inch is 11.8, from which it is seen that
1,360 turns can be wound in the space available.
The resistance of all the four coils in series is

38.5 X 1,360 X 4 X 2.328

12 X 1,000 l0 ' 5 hmS) at

The current, under open-circuit conditions, is .,' ^ = 4.36

230
amp., and at full load (item (136)) it is 4.36 X 220= 4.56 amp.

This is only 1.4 per cent, of the line current; a low value, which
might perhaps be increased in order to reduce the amount of
copper in the field coils if the temperature rise is not excessive.
Items (139) to (142): Series Field Coils. Refer Art. 58, page
192. The series turns may be placed at either end of the pole,

232 PRINCIPLES OF ELECTRICAL DESIGN

preferably near the pole shoe. The space available in a radial
direction is about 7 5J = 1% in. The number of turns

per pole is ' = 5.06. Let us put 5^ turns on each pole, and

make the final adjustment by means of a diverter. The current

1 650

through the series winding will therefore be ' , = 300 amp.

o.o

The total depth of winding might be about the same as for the
shunt coils, i.e., 2 in. The mean length per turn would then be
38.5 in., and the total length, 4 X 5.5 X 38.5 = 847 or, with an
allowance for connections, say, 890 in. Assuming a current
density of 1,200 amp. per square inch, the cross-section would be

OQA

^ 2QQ = 0.25 sq. in. This winding may consist of flat copper

strip wound on edge, or of any other shape of conductor of this
cross-section. If preferred, two or more conductors of some stock
size can be connected in parallel to make up a total cross-section
of about 0.25 sq. in. The space available is more than sufficient,
and we shall assume for the present that the cross-section is
exactly 0.25 sq. in., or 318,000 circular mils. The resistance, at

890
60C., will then be Q1Qnnn = 0.0028 ohm. The drop in volts in

the series winding is therefore 0.0028 X 300 = 0.84, which, being
very small, may be increased if it is found that the temperature
rise is appreciably below the specified limit.

Items (143) and (144) : Temperature Rise of Field Coils. Refer
Art. 59, Chap. IX. The area of the two cylindrical surfaces is
approximately 7 X 7r(10 -f 14) = 528 sq. in. The area of the

two ends is 2 X j (14 - To ) = 151 sq. in. The total cooling

surface of all the field windings is therefore 679 X 4 = 2,720 sq.
in., approximately.

The PR loss at full load in the shunt winding is (4.56) 2 X 38.4
= 800 watts; and the PR loss in the series coils is (300) 2 X
0.0028 = 252 watts, making a total loss of 1,052 watts.

The cooling coefficient, as given by curve A of Fig. 76 (page
194), is 0.009, and the temperature rise will therefore be

1,052
0.009 X 2,720

This is a little higher than the specified limit of 40, and if the
cooling coefficient could be relied upon for the accurate prede-

PROCEDURE IN DESIGN OF D.C. GENERATOR 233

termination of the temperature rise, it would be necessary either
to increase the weight of copper in the coils, or to sectionalize
the windings so as to improve the ventilation. The latter course
would be the right one in this case since the copper loss is not by
any means excessive, and it would be desirable to reduce rather
than increase the amount of copper in the field windings.

Items (145) and (146): Resistance of Diverter. Assuming the
"long shunt" connection, the series current passing through the
diverter will be 30.56 amp., and the resistance of the diverter
must therefore be

son

0.0028 X qTTKA = - 0275 ohm -

OO.OD

A resistance slightly greater than this should be provided, of a
material and cross-section capable of carrying at least 40 amp.
when the machine is on the test floor.

Item (147): New Calculation of Losses in Teeth. Refer Art. 60,
Chap. IX. The maximum value of the air-gap density under
full-load conditions may be read off curve C of Fig. 84 (page 221)
where it is seen to be 10,800 gausses. The corresponding tooth
density, as read off Fig. 81 (page 216), is 23,100. This is the
density at the narrowest part of the tooth. On the assumption
that flux neither enters nor leaves the tooth up to a distance d e
from the bottom of the slot (see Fig. 38, page 122), the tooth
densities at the three sections considered are B w = 18,870, B m =
21,000, and B n = 23,100 gausses. Referring to Fig. 34 (page
102), we find the watts per pound corresponding to these den-
sities to be 4.1, 4.8, and 5.5, respectively, the mean value being
4.8. The total weight of iron in the teeth (item (57)) is 75 lb., and
the corrected total loss in the teeth is 75 X 4.8 = 360 watts.

Items (148) and (149): Efficiency at Any Output. Refer Art.
60, Chap. IX. The efficiency table on page 235 requires but
little explanation. Each column stands for a particular output,
expressed as a fraction of rated full load. The terminal voltage
is calculated on the assumption that it conforms to a straight-

The windage and friction loss is taken as 1.8 per cent, of the

The core loss which includes the corrected tooth loss is the
calculated full-load value. It will actually vary somewhat with

234

PRINCIPLES OF ELECTRICAL DESIGN

the load (and developed voltage), but for practical purposes may
be assumed constant.

The constant losses are made up as follows:

Windage and bearing friction = 0.018 X 75,000 = 1,350 watts.

Brush friction (item (113)) = 324 watts.

Iron loss in core and teeth (item 60) = 1,644 watts.

Total = 3,318 watts.

The full-load current in the armature is the line current plus
the shunt current (item (136)), and since the armature resistance

i.o

g.7

.6

20 40 60 80 100

Output _ ( Percentage of Full Load )

FIG. 88. Efficiency curve.

120

140

is known (item (44)), the PR loss in the armature at different loads

The brush-contact PR loss is obtained by referring to Fig. 69
(page 179) and adding 25 per cent, to the calculated losses.

We shall assume the "long shunt" connection, which means
that the series winding and diverter will, together, carry the full
armature current, and the series field PR losses will therefore be
directly proportional to the copper losses in the armature.

Fig. 88 is the efficiency curve plotted from the figures in the
table. The full-load efficiency is 0.915, and judging by the shape

PROCEDURE IN DESIGN OF D.C. GENERATOR 235

of the curve, the maximum efficiency of 0.92 will probably be

EFFICIENCY TABLE

M

H

M

1

IK

Terminal voltage

220

222.5

225

227.5

230

232.5

Line current

84.3

167

247

326

403

Constant power loss. .

3,318

3,318

3,318

3,318

3,318

3,318

Armature I 2 R loss

111

419

897

1,540

2,342

Brush-contact I*R loss

152

322

528

744

964

Series field and diverter

20

76

162

278

423

Shunt field and rheostat

960

980

1,000

1,025

1,050

1,070

Total loss

4,278

4,582

5,135

5,930

6,930

8,117

Output (watts)

18,750

37,500

56,250

75,000

93,750

Input (watts)

4,278

23,332

42,635

62,180

81,930

101,867

Efficiency (per cent.)

80.3

87.8

90.5

91.5

92

Referring to the usual efficiencies of commercial machines as
given on page 197, it is seen that the calculated value of 91.5
compares favorably with the average value of 91.2 for a 75-kw.
dynamo.

64. Design of Continuous-current Motors. The dynamo
being a reversible machine, may be used as a generator to
convert mechanical into electrical energy, or as a motor to convert
electrical into mechanical energy. If the machine is to be used
as a motor, the efficiency should first be estimated by referring
to the figures on page 197. This efficiency, in the case of a

. ,, ,. output
motor, is the ratio - -, whence

Kw. =

horsepower X 746

efficiency X 1,000

and the design may be proceeded with exactly as if the machine
were to be used as a generator to give this particular kilowatt
output at the specified speed.

It is even more important in a motor than in a generator
that the machine should work sparklessly at all loads without
change of the brush position. The specification usually calls for
operation without destructive sparking from zero load to 25
per cent, overload, with the brushes in a fixed position. If the
direction of revolution of the motor is to be reversible, it is neces-
sary for the brushes to be on the geometric neutral line, a con-
dition which is usually met by providing commutating interpoles.

236 PRINCIPLES OF ELECTRICAL DESIGN

On account of the conditions under which they have to operate,
dynamo machines when used as motors are more often totally
enclosed than when used as generators. In the case of the larger
units forced ventilation would then be resorted to, but the
smaller sizes may be self-cooling. The temperature rise is then
largely equalized throughout the machine, and somewhat higher
surface temperatures are allowable than in the case of open-type
machines. A temperature rise of 60, by thermometer, is allow-
able inside the machine but this means that the temperature
rise of the enclosing case must be considerably less than this, say
35 or 40C.

In the absence of data on the particular type of enclosed motor
under consideration, a cooling coefficient of 0.008 to 0.01 may
be used. This figure denotes the number of watts that can be
square inch of the entire external surface of the enclosed motor.

CHAPTER XI

DESIGN OF ALTERNATORS FUNDAMENTAL
CONSIDERATIONS

65. Introductory. In the continuous-current dynamo the func-
tion of the commutator is merely to rectify the armature cur-
rents in order that a machine with alternating e.m.fs. generated
in its windings shall deliver unidirectional currents at the ter-
minals. It may therefore be argued that the design of alter-
nating-current generators should be taken up before that of D.C.
dynamos, the changes caused by the addition of the commutator
being considered in the second place. There are, however, many
matters of importance to be considered in connection with an
alternating-current generator, which have no part in the design of
a continuous-current dynamo. Among these may be mentioned
the effects due to changes in wave shapes of e.m.f. and current; the
importance of the inductance, not only of the armature itself, but
also of the circuit external to the generator; and the fact that the
voltage regulation depends not only on the IR drop, but also on
the power factor of the load, i.e., on the phase displacement of the
current relatively to the e.m.f. The problems to be solved being
somewhat less simple than those connected with continuous-current
machines, the writer believes that the arrangement of the subject
as followed in this book is justified.

It is proposed to treat the design of A.C. machines as nearly
as possible on the lines followed in the D.C. designs. In order
to avoid unnecessary repetitions, references will be made to pre-
vious chapters and stress will be laid on the essentials only,
particular attention being paid to the points of difference between
A.C. and D.C. machinery.

The design of asynchronous generators will not be touched
upon. This type of machine is essentially an induction motor
reversed, the rotor, with its short-circuited windings, being me-
chanically driven. The writer has explained elsewhere the prin-
ciples underlying the working of these machines, 1 and since they

1 ALFRED STILL: "Polyphase Currents," WHITTAKER & Co.

237

238 PRINCIPLES OF ELECTRICAL DESIGN

are of a type not commonly met with, they will not again be
referred to.

The remainder of this book will be devoted to a study of the
synchronous alternating-current generator, and since multipolar
polyphase generators with stationary armatures are more com-
mon than any other type, they will receive more attention than
the less frequently seen designs; but the case of the high-speed,
steam-turbine-driven units, with a small number of poles and
distributed field windings, will also be considered.

Apart from the absence of commutator, the chief point of dif-
ference between an A.C. and D.C. generator is that the frequency
of the former is specified, whereas, in the latter, this is a matter
which concerns the manufacturer only. It follows that, for a
given speed, the number of poles is determined by the frequency
requirements, and this fact necessarily influences the design. In
Europe a frequency of 50 cycles per second is common, the idea
being that this is high enough for lighting purposes while being
sufficiently low to allow of the same circuits being used occasion-
ally for power purposes also. A lower frequency is usually to be
preferred for power schemes, and the standards in America are
25 cycles for power purposes and 60 cycles for lighting.

66. Classification of Synchronous Generators. It is well to
distinguish between two classes of alternators:

1. Machines with salient poles, driven at moderate speeds by
belt, or direct-connected to reciprocating steam, gas, or oil
engines, or to water turbines. The peripheral speed of the ro-
tating part (usually the field magnets) will generally lie between
the limits of 3,000 and 8,000 ft. per minute.

2. Machines direct-coupled to high-speed steam turbines, in
which the peripheral velocity usually exceeds 12,000 ft. per min-
ute, is commonly about 18,000, and may attain 24,000 ft. per min-
ute. In these machines the field system is always the part that
rotates; the number of poles is small, and although salient poles
are sometimes used on the lower speeds, the cylindrical field
magnet with distributed windings is more common. The me-
chanical problems encountered in the design of these high-speed
machines are relatively of greater importance than the electrical
problems; but since these are beyond the scope of this book,
they will not be considered in detail. Such differences as occur
in the electrical calculations will be pointed out as the work
proceeds.

DESIGN OF ALTERNATORS 239

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