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Font size magnetic circuit is readily calculated if the leakage factor can
be estimated; but the length of tne pole core (the dimension c
in Fig. 71) will depend upon the number of ampere-turns re-
quired, and therefore on the length of the air gap, which must be
decided upon at an early stage in the design (see end of Art. 36,
page 119).

Let (SI)gt be the ampere-turns required at full load for the
air gap, teeth, and slots; then, if we assume a depth of winding
on the field coils of 1% in., a winding space factor of 0.5, and a
current density 'of 1,000 amp. per square inch of copper cross-
section, the length of the winding space (which is approximately
equal to the length of c of Fig. 71) would be:

(SI) at

' 875

If, now, we make the further assumptions that (SI) g t is 50
per cent, greater than the ampere-turns necessary to overcome
the reluctance of the actual air clearance of length d in., and
that the air-gap density B = 8,000 gausses, we may write:

2^fl^ = X 2.54 X 8,000

J. .O

and, putting 875c in place of (SI) gt , we get the relation

2.54 X 8,000 X 1.5

0.4*- X 875
= 285 (approximately) (92)

For a preliminary calculation of the ampere-turns required
for the complete magnetic circuit, a value of c (the length of the
pole) rather greater than as calculated by formula (91) or (92)
may be selected. This dimension will be subject to modifica-
tion if it is afterward found that the cooling surface of the field
windings is insufficient to prevent an excessive rise of temperature.

56. Leakage Factor in Multipolar Dynamos. Apart from the
useful flux entering the armature core, there will, be in every

THE MAGNETIC CIRCUIT

187

design of dynamo, some leakage flux between pole shoes and
between pole cores which, in a plane normal to the axis of
rotation, will follow paths somewhat as indicated in Fig. 72.
The amount of this leakage flux is not easily calculated; but it
can be approximately predetermined by applying the conven-
tional formulas of Art. 5, Chap. II, or by the graphical method
as outlined in Art. 39, Chap. VII. Other approximate graphical
methods are used by designers 1 and, in the case of radical de-
partures from standard types, some such method of estimating
the leakage flux must be adopted. It will, however, be found

FIG. 72. Leakage flux in multipolar dynamo.

that the leakage factor does not vary appreciably in modern
designs of multipolar dynamos, and the following values may be
adopted for the purpose of determining the necessary cross-
sections of the pole cores and frame.

Kw. output of dynamo

20 to 50

50 to 150

150 to 250

250 to 400

500 and larger

Leakage coefficient

1.15 to 1.3
1.14 to 1.26
1 . 13 to 1 . 23
1.11 to 1.19
1 . 10 to 1 . 16

57. Calculation of Total Ampere-turns Required on Field
Magnets. The maximum values of the m.m.f. curves obtained
by the method followed in Chap. VII (see Arts. 40 and 43)
give the ampere-turns per pole required to overcome the re-
luctance of the air gap, teeth and slots. The balance of the
total ampere-turns is easily calculated since the lengths and
cross-sections of the various parts of the magnetic circuit are

1 See p. 326 of WALKER'S "Specification and Design of Dynamo-
electric Machinery."

188 PRINCIPLES OF ELECTRICAL DESIGN

known, and a suitable leakage factor may be selected from the
table in the preceding article. The method of procedure is
exactly as explained in connection with the design of a horseshoe
lifting magnet (see Art. 16, page 52), and it will be again fol-
lowed in detail when working out a numerical example of con-
tinuous-current generator design. The flux path of average
length is indicated in Fig. 71. There may be some doubt as to
what is the proper value to take for the length of the path a in
the armature core below the teeth, because the flux density will
be less uniform in this part of the magnetic circuit than in the
poles and yoke. As a matter of fact, the ampere-turns neces-
sary to overcome the reluctance of the armature core (apart
from the teeth) are but a small percentage of the total, because
the flux density must necessarily be low to avoid large losses
due to the reversals of magnetic flux. It is, therefore, something
of a refinement to take account of the unequal distribution of
the flux in the armature core; but if the length of the path a
of Fig. 71 be taken as one-third of the pole pitch r, a more
accurate value for the ampere-turns will be obtained than if
the length were measured along the curved path shown in the
illustration. It is, of course, understood that the density to be
used in the calculation is the maximum flux density at the
section midway between the poles, on the assumption that the
flux is uniformly distributed over this section. Thus, if \$
is the useful flux per pole entering the armature core, and Rd

is the radial depth of stampings below the teeth, the maximum

\$
density in armature core to be used in the calculations is op 7

ZK din

where l n stands, as before, for the net axial length of the
armature.

Solid-pole shoes are rarely used in connection with armatures
having open slots. With semi-closed slots, or even with open
slots if the air gap is large, the eddy-current losses in solid-pole
shoes may be very small, but laminated pole pieces are now the
rule rather than the exception. The thickness of the steel
sheets used to build up the pole pieces is usually greater than
that of the armature punchings, a thickness of 0.025 in. being
fairly common. In small machines it is sometimes economical
to construct the complete pole of sheet-steel stampings, as this
dispenses with the labor cost of fitting a separate built-up pole
piece on the solid pole core.

THE MAGNETIC CIRCUIT

189

Referring to Fig. 49 on page 133, the curve (a) was plotted
by assuming different values of air-gap density; it shows the
relation between the ampere-turns required for air gap, teeth
and slots, and the air-gap density over the slot pitch at the
center of the pole face. We are now in a position to plot an
open-circuit saturation curve which shall include the ampere-
turns necessary to overcome the reluctance of all parts of the
magnetic circuit; but instead of giving the relation between total
ampere-turns per pole and the air-gap density, it will be more
convenient to plot a curve connecting field ampere-turns and
e.m.f. generated in the armature. This can easily be done since
we know the total flux per pole and the generated e.m.f. corre-
sponding to the value B a of the maximum air-gap density (Fig.
49). Thus, in Fig. 73 the distance OP a is the same as in Fig.
49, but the vertical scale has been altered so that the correspond-
ing value Eo as read off the dotted curve of Fig. 73 now stand for
the volts developed in the armature by the cutting of the flux,
instead of the air-gap density under the center of the pole face.
The full-line curve of Fig. 73 is the open-circuit characteristic
of the whole machine. It gives
the connection between field am-
pere-turns per pole and the termi-
nal voltage on open circuit, on the
understanding that the speed is
turns required to overcome the
reluctance of the field poles, yoke,
and armature core, account for the p
space between the full-line and c
uration curve for the complete
machine has been re-drawn in Fig. 74.

Ampere Turns per Pole
FIG. 73.

Here OE is the termi-
nal voltage on open circuit; OE t is the terminal voltage at full
load (the machine is assumed to be over-compounded) ; and OEd
is the necessary developed voltage at full load, i.e., the voltage
that must be generated in the armature conductors by the
cutting of the flux in order that the terminal voltage at full
load shall be OE t .

Draw a straight line connecting the origin, 0, of the curve and
the point F corresponding to the no-load voltage, and produce
this to G where it meets the horizontal line representing full-

190

PRINCIPLES OF ELECTRICAL DESIGN

load terminal voltage. Then, since the ampere-turns on the
shunt at no load are OA, they will obviously have increased to
OB at full load on account of the higher terminal voltage (the
"long shunt" connection is here assumed). The ampere-turns
necessary to produce the required full-load flux will be OC;
but the field excitation must be greater than this in order to
balance the distortional and demagnetizing effects of the arma-
ture current. It was found that the ampere-turns necessary
to counteract the effects of the armature current were repre-
sented by the distance P b P a in Fig. 49 (Art. 42, page 133) . These

E d

Shunt (Full Load) < Series _^

D

O ABC

Ampere Turns per Pole

FIG. 74. Open-circuit saturation curve of dynamo.

SI to Compensate
for Demagnetising
aaid Distortional
Effect of
Armature

ampere-turns had to be put on the field poles, not to increase
the air-gap flux and thus develop a higher voltage, but merely
to counteract the effects of the armature current and restore
the air-gap flux to its original value on open circuit. It is
therefore correct to say that additional ampere-turns approxi-
mately equal to this amount must be added to the field wind-
ings in order that the necessary flux shall be cut by the armature
conductors. This addition is shown in Fig. 74, where the
distance CD has the same value as PbP a in Fig. 49. It follows
that OD represents the total ampere-turns required per pole
at full load. Of this total amount, OB will be due to the shunt
winding, and the balance, BD, must be provided by the series
winding.

58. Arrangement and Calculation of Field Windings. Since
the ampere-turns required in the shunt winding have now been

THE MAGNETIC CIRCUIT 191

determined, the calculation of the size of wire for a given voltage
may be proceeded with exactly as explained in connection with
the winding, of magnet coils (see Art. 10, Chap. II). The allow-
able cooling surface is not quite the same as for the coils of lifting
magnets, because the fanning effect of the rotating armature is
to some extent beneficial; but it will be convenient to consider
the heating effects of the shunt and series coils together, and
the question of cooling coefficients for use in predetermining
temperature rise will therefore be taken up later.

Shunt Field Rheostat. Even when the machine is compounded
by the addition of a series winding, it is usual to provide an
adjustable resistance in series with the shunt winding. This
field rheostat allows of the excitation being kept constant not-
withstanding the fact that the shunt winding will not have the
the same resistance when cold as it will have when a continuous
run of several hours' duration has raised the temperature of
the coils. The rheostat also allows of final adjustments being
made after the machine has been built and tested.

In compound-wound generators it is customary to allow a
voltage drop in the rheostat amounting to 15 or 20 per cent,
of the total terminal pressure; and a sufficient number of con-
tacts should be provided to avoid a variation of more than %
to 1 per cent, change of voltage when cutting in or out sections
of the rheostat.

The size of wire for the shunt field coils should therefore be
calculated on the assumption that the impressed voltage is 15
to 20 per cent, less than the terminal voltage of the machine.
It will generally be found desirable to connect the windings on
all the poles in series. With shunt-wound dynamos, the field
rheostat plays a more important part: it must be designed to
give the required variation in field strength between no load and
full load, at constant speed, or, in the case of a motor, to provide
for the required speed variation. The amount by which the
excitation has to be varied apart from the requirements to
compensate for the effects of temperature changes may be
determined by reference to the saturation curve as drawn in
Fig. 74.

In a well-designed machine, the PR losses in the shunt field
winding should not greatly exceed the values given below, where
the loss is expressed as a percentage of the rated output of the
dynamo :

192 PRINCIPLES OF ELECTRICAL DESIGN

Output of machine, kilowatts Exciting current, percentage of

of total current

10 3.5

20 3.0

50 2.4

100 2.0

200 1.7

300 1.6

500 1.5

1,000 and larger 1 . 3 to 1 .

Series Windings. The series winding on the field magnets
carries the main current from the machine and thus adds to the
constant excitation of the shunt coils a number of ampere-turns
generally in accordance with the demand for a stronger field.
It is not usual to wind the series turns on the outside of the
shunt wire; but this may be done in small machines. The series
turns are usually placed at one end of the pole, either up against
the pole shoe, or more commonly near the yoke ring. Space
must, therefore, be left for the series winding at the time when
the dimensions of the shunt coil are decided upon. The total
winding space available may be divided in proportion to the
ampere-turns required on the shunt and series coils respectively.
The coils near the yoke ring, in a machine with revolving arma-
ture, are frequently made to project from the pole core farther
than the coils near the pole shoe, partly because the space
available between the poles increases with the radial distance
from the center, but also because the cooling effect of the air
thrown from the rotating armature will be greater if the field
windings are stepped out in this manner.

The construction and insulation of field windings deserves
careful attention; but for details of this nature, the designer
must rely largely upon the practice of manufacturing firms and
his own common sense. The pressures to be considered in
D.C. designs are not high, and the chief points requiring atten-
tion are the proper arrangement and the insulation of the start-
ing and finishing ends of the coils. 1

The size of conductors for use in the series winding may be
determined by considerations of permissible voltage drop, or,
if this is unimportant, the temperature rise will be the determin-

1 Much useful information regarding the insulation of windings will be
found in Chap. IV of "Insulation and Design of Electrical Windings," by
A. P. M. FLEMING and R. JOHNSON (LONGMANS & Co.).

THE MAGNETIC CIRCUIT

193

ing factor. In the latter case, the allowable current density
will be about the same as in the shunt coils, unless the series
turns are next to the pole shoe, in which case a slightly higher
density would be permissible because of the better ventilation.
If the current to be carried exceeds 100 amp., the coils may be
made of flat copper strip wound edgewise by means of a special
machine. For smaller currents, cotton-covered wires of square
or rectangular section are commonly used; the round wire being
rarely employed, unless the diameter is less than that of No. 8
B. & S. gage.

On account of the method of connecting the series coils be-
tween adjacent poles on a multipolar dynamo, there will be an
odd number of turns per pair of poles, or a whole number plus
a half turn on each pole. This will easily be understood by re-
ferring to Fig. 75 which is supposed to show a portion of the

FIG. 75. Diagram of series field winding.

crown of poles, looking down through the yoke ring onto the
cylindrical surface of the armature. The number of ampere-
turns required per pole being known, the number of turns in
the series winding can easily be calculated. It may not be
possible to put this exact number on the pole, and a slightly
greater number of turns is, therefore, provided, the excess of
current being shunted through a diverter. This is merely a re-
sistance connected as a shunt to the series winding. Thus if the
required series ampere-turns per pole are 2,000, and the current
300 amp., the calculated number of turns per pole is 6.66.
Since 6j- turns will not be sufficient, the winding may consist
of 7H turns, and the current required through the coils is, there-
fore, 2,000/7.5 = 267 amp. The balance of 33 amp. must be
shunted through the diverter, the resistance of which is easily
calculated after determining the resistance of the series coils
from the known cross-section and computed length of the winding.
69. Temperature Rise of Field Coils. On account of the
proximity of the shunt and series windings, it is advisable to

13

194

PRINCIPLES OF ELECTRICAL DESIGN

consider the joint losses in connection with the entire cooling
surface. The reader is referred to Art. 11, Chap. II, where the
heating of magnet coils was discussed. The problem of keeping
the temperature, rise of field coils within safe limits (40 to 45C.)
is complicated by the fact that the fanning action of the rotating
armature will have an effect upon the cooling coefficient; but
this has been taken into account in the curves of Fig. 76. The

0.011

0.009

? 0.007

1

'8

0.006

l

0.005

cT

1000 2000 3000 4000 5000

Peripheral Speed of Armature -Feet per Minute

FIG. 76. Cooling coefficients for field coils of dynamos.

curve marked A applies to machines with wide spacing between
poles, and good ventilation, while the curve B should be used
when the main poles are close together, or when commutating
poles interfere with the free circulation of air round the main
windings. The coefficient obtained from the curves, being
watts per square inch per degree rise, is the reciprocal of the coef-
ficient k used in the chapter on magnet design; but the cooling
surface considered is the same, namely, the total external surface
of the winding, including the two ends and also the inner surface

THE MAGNETIC CIRCUIT 195

near the iron pole core. The cooling coefficient will necessarily
depend upon the type and size of the machine, and it should, if
possible, be determined from tests made on machines generally
similar to the one being designed. The modern tendency in
design is all toward increased output by improvements in the
qualities of materials and in methods of ventilation. Field
coils are now frequently built with seetionalized windings so
arranged that the air has free access, not only between the sub-
divisions of the winding, but also between the inside of the coils
and the pole core. The gain is not always proportionate to the
total cost and space required; but the cooling coefficients given
in Fig. 76 would not be applicable to such designs without modi-
fication. Each manufacturer has his own data to guide him in
his calculation of new designs; but even if such data were
available for publication, it would be of little value without the
experience which enables the designer to apply it intelligently
to a practical case.

60. Efficiency. The efficiency of a dynamo is the ratio of
power output to power input, or,

_ output

Efficiency == output + losses

In computing the total losses, an estimate has to be made
of the power lost through windage and bearing friction. It is
almost impossible to predetermine these quantities accurately.
The loss due to air friction will depend upon the design of the
armature and arrangement of poles and frame, apart from the
actual surface velocity; while the bearing friction will depend
upon the number and size of the bearings, the method of lubri-
cation, the weight of the rotating parts, and the method of
coupling to the prime mover. The factors to be taken into
account are so numerous and so difficult to determine that, in
the case of new designs or departures from standard types, it is
usual to group these losses together and make a reasonable
allowance for them in the calculations of efficiency. The fric-
tion losses will increase with the surface velocities; but since
the volume, and therefore the weight, of the rotating armature
of a machine of given output will decrease with increase of speed,
it is found that the total friction losses may be expressed as a
percentage of the total output, and this percentage will not
vary greatly in machines of different outputs and speeds. The

196 PRINCIPLES OF ELECTRICAL DESIGN

following figures indicate approximately the losses due to wind-
age and bearing friction in modern types of dynamos.

Rated kw. output Friction losses (per cent.)

10 3.0

30 2.5

60 2.0

100 1.5

200 1.0

500 0.75

Large machines . 6

Closer Estimate of Hysteresis and Eddy-current Losses in
Armature Teeth. For the purpose of calculating the armature
losses with sufficient accuracy to determine whether or not the
temperature rise is likely to be excessive, it was suggested in
Art. 31 (page 103), that the average value of the apparent tooth
density be used in calculating the iron loss in the teeth. When
the tooth density is very high, or the taper of the tooth consider-
able, this method will not yield very accurate results. It is the
actual tooth density which, together with the frequency, will
determine the losses per pound in a given quality of steel punch-
ings; and this actual tooth density may be read off a curve plotted
from the formulas derived in Art. 37, Chap. VII.

The tooth density with which we are concerned in the calcu-
lations of power losses, is obviously the maximum density, and
this will occur when the tooth is in the zone of maximum air
gap density, the value of which can be read off the full-load
flux distribution curve, C, derived as explained in Art. 43,
Chap. VII.

When the tooth is not of the same cross-section throughout
its length, the question arises as to what particular value of the
actual tooth density should be taken for the purpose of calcu-
lating the iron losses. The tooth might be divided into a
number of imaginary sections concentric with the shaft, and the
watts lost in the elemental sections could be calculated and
totalled; but this would be a lengthy and tedious process, and
the following approximation will usually give results of suffi-
cient accuracy for practical purposes.

First calculate the actual flux density at the root of the tooth
(see Art. 37, page. 119), and then again, at two other sections,
namely, near the top where the circumference of the " equivalent"

THE MAGNETIC CIRCUIT 197

smooth core armature would cut through the tooth, and also at
a point midway between these two extremes. These sections
are shown in Fig. 38, page 122; and if the assumption is made that
no flux lines either enter or leave the sides of the tooth, the densi-
ties at the middle and top of the tooth can readily be expressed
in terms of the root density since they will vary inversely as the
cross-section of the tooth. If, now, the iron loss in watts per
pound is read off the curves of Fig. 34, page 102, for the three
selected values of the tooth density, the average loss per pound
multiplied by the total weight of iron in the teeth, will represent,
within a reasonable degree of accuracy, the total loss in the
teeth of the machine.

A high tooth density is an advantage from the point of view
of field distortion. It can easily be understood that a high flux
density, by saturating the teeth, will have a tendency to resist
the changes in the air-gap flux distribution, brought about by
the cross-magnetizing effect of the armature currents; and it is
therefore advisable to check the approximate estimate of tooth
losses with the results obtained by the more exact method of
calculation.

In predetermining the efficiency, it is important that all the
power losses in the machine be taken into account. These must
include the losses in rheostats or diverters, which may be con-
sidered as part of the machine. A complete list of the losses to
be evaluated when predetermining the efficiency will be found
in the following chapter, where a numerical example will illus-
trate in detail the steps to be followed in designing a dynamo.

As a check on calculations, the efficiencies in the following
tables may be referred to. They represent a fair average of
what may be expected in a machine of modern design.

Kw. output Efficiency, per cent.

10 86.0

20 87.6

30 88.8

40 89.7

50 90.3

75 91.2

100 91.6

200 92.0

500 and larger 93 to 95

198 PRINCIPLES OF ELECTRICAL DESI N

EFFICIENCIES OF DYNAMOS WHEN NOT DELIVERING FULL-LOAD CURRENT

Output as fraction of full load

Size of machine (Rated kw. output)

10 kw.

200 kw.

y

70.0 per cent.
80.0 " "
84.5 " "
86.0 " "

86 per cent.

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