Alfred Still.

# Principles of electrical design; d. c. and a. c. generators online

. (page 15 of 30)
Online LibraryAlfred StillPrinciples of electrical design; d. c. and a. c. generators → online text (page 15 of 30)
Font size ductors in the slot affected are not all carrying the full armature
current. This will be seen by reference to Fig. 65, where coil
A (consisting of two turns) is just about to be short-circuited by
the brush. At this instant the current in the coil-sides B and D

is i = 27 C X 5-? = 0.572/c as indicated by the diagram sketched

o.O

on the brush of width W covering three and one-half bars, the

.

1
1

j

!

i
1

"i

fft Q ~ "~ 7

j /\ 4 t

FIG. 65. Illustrating example of interpole design.

straight-line law of current variation being assumed. At the end
of commutation, when the position of the affected slot relatively
to brush and interpole is as indicated by the dotted lines, the
current in all four coil-sides is 7 C . We may, therefore, assume
the slot flux to be produced by a current of which the average

3 + 572
value is not I c = 76 amp., but I c X ~r~ - = 68 amp. The

slot flux \$ es in formula (85), which is the " equivalent" value as-

COMMUTATION

173

suming the total slot flux to pass outward from the armature core
through the teeth, is, therefore, by formula (77),

l&vd

whence,

TI e

1.6* X 1.5X4X68X11 X 2.54

3 X 0.39
= 49,000 maxwells,

this being the equivalent slot flux taken over the full length of
the armature.

Turning now to the flux leaving the armature in that part of
the commutating belt which is not covered by the interpole, let
the curve Fig. 66 represent the full-load flux distribution over

FIG. 66. Flux curve showing density on geometric neutral line,
lated without interpoles.)

(Calcu-

armature surface, calculated on the assumption that there are
no interpoles. This is the flux curve C, derived in the manner
outlined in Art. 43, Chap. VII, but with the brushes left in the
no-load position. There will be no directly demagnetizing effect
due to brush lead since the brushes will remain on the geometric
neutral line. The flux density at a point midway between the
two poles has the value B, which for the purpose of this example
may be assumed to be 1,500 gausses.

If lp = axial length of interpole (not yet determined), the total
flux which must pass from interpole into armature teeth is

\$c = \$e + \$Ja + BW a (l a ~ lp)

174 PRINCIPLES OF ELECTRICAL DESIGN

which is simply formula (85) with the armature flux per centi-
meter of length expressed as BW a instead of \$ a - The axial
length lp of the interpole face can, therefore, be determined if a
suitable value for the average air-gap density under full-load con-
ditions is assumed. Let B p stand for this value; then

B p l p W a = Qe^esla + BW a (l a ~ l p )

whence

lp = " e W a (B p +B) (86)

If the flux densities are expressed in gausses, the dimensions must
be in centimeters, and if B p is taken as 4,500 gausses, the length
l p is found, by formula (86), to be 12.4 cm. or, say, 5 in.
The total flux in the interpole air gap at full load is then,

\$ c = 64,800 + 49,000 + 1,500 X 6.45 X 1.375(11 - 5)
= 193,600 maxwells.

Assuming a leakage factor of 1.9 and a cross-section under
interpole winding of (5 X 1J^) sq. in., the full-load density in the
core of the interpole would be 7,600 gausses.

Calculation of Ampere-turns Required on Interpole. Referring
to Fig. 65, it will be seen that when the coil A is about to be short-
circuited, the interpole flux enters the armature through the
teeth 1 and 2. At the end of commutation this flux enters the
teeth 3 and 4. The permanence of the air gap of length d may
vary slightly with the change in the position of the armature
teeth; it may be calculated by any of the approximate methods. 1
Assuming an actual air gap J4 in- long, the equivalent air gap
might be 0.3 in. The full-load ampere-turns required to over-
come air-gap reluctance will therefore be
0.3 X 2.54 X 4,500

f\ A ) i \J

To this must be added the ampere-turns to oppose the armature
m.m.f. If the reduction of current in the short-circuited coils is
neglected, the armature ampere-turns per pole are

IZ/c = (120 X 8) X 76

2 p 2X6

= 6,080

If we neglect the very small m.m.f. required to overcome the re-
luctance of the interpole core, the total ampere-turns on each
1 See Art. 36, p. 115.

COMMUTATION

175

interpole should be 2,720 + 6,080 = 8,800 at full load. The
full-load current of the machine is 200,000 -f- 440 = 455 amp.,
and the required number of turns is 8,800 4- 455 = 19.35. In
practice about 21 turns would be put on the interpole of this
machine, and if necessary a diverter would be provided to adjust
the current in accordance with results obtained on test.

52. Prevention of Sparking Practical Considerations. It is
not suggested that the method of considering commutation phe-
nomena as outlined above covers the subject completely. The
designer aims at obtaining " ideal" commutation under certain
load conditions, knowing well that, even when series-wound corn-
mutating poles are used, the required conditions cannot be ex-
actly fulfilled at other loads. He relies on the resistance of the

FIG. 67. Armature coil near end of commutation period.

carbon brush to give sparkless commutation even when the con-
ditions depart appreciably from those of "ideal" commutation.
The extent to which the ideal condition can be departed from
without producing destructive sparking is not easily determined
except by experimental means.

In Art. 45, page 146 the effect of the brush-contact resistance
was considered, and it was seen that the value of this resistance
has no effect on the problem of commutation provided the change
of current in the short-circuited coil takes place in accordance
with the "ideal" or straight-line law. The reason is that, when
" straight-line " commutation is obtained, the distribution of the
current over the contact surface of a brush of rectangular section
is necessarily uniform. If, now, we wish to examine the condi-
tions of commutation when the changes of current do not follow
the ideal straight-line law, it is necessary to consider the effect of
the brush-contact resistance when the current density is no longer
uniform^over the entire surface. The diagram, Fig. 67, is gener-

176 PRINCIPLES OF ELECTRICAL DESIGN

ally similar to Fig. 56, except that the coil connecting segments
A and B has moved nearer to the edge of the commutation zone.
The distance, in inches, still to be travelled before the removal of
the short-circuit is w, which is supposed to be only a small per-
centage of the total brush arc W.

Let R be the resistance, in ohms, of the coil connecting the
commutator segments A and B.

R c = the contact resistance of the brushes per square inch of
area.

l c = the total length, in inches, of the set of brushes measured
parallel to the axis of rotation.

A = the average current density, in amperes per square inch,
over the brush-contact surface. It will also be, approxi-
mately, the density over the surface Sb of the segment
B (Fig. 67).

AU, = the maximum permissible current density over the sur-
face of the brush tip of width w.

Summing up the e.m.fs. and potential differences in the path
of the short-circuit (the resistance of the material in the body of
the brush being neglected), we can write, for the value of the
volts developed in the short-circuited coil at the instant con-
sidered,

e = iR + A# c - & W R C
But

i = I c ia

wherein the meaning of the symbols will be evident from an in-
spection of Fig. 67. This last equation may be written,

i = I c &wl c w
Substituting in the previous equation, we get,

e = I C R - &J e wR - Rc(& w - A)

If, now, we imagine w to become smaller and smaller as it ap-
proaches zero value, the second term on the right-hand side of
the equation becomes of relatively less and less importance, and
we may therefore write,

e = I C R - R c (k w - A)

which gives an approximate value for the permissible e.m.f. in
the short-circuited coil at the end of the commutation period.
If preferred, this equation may be put in the form

e = I C R - R c &(k - 1) (87)

COMMUTATION 177

wherein k is the ratio of the permissible density at brush tip to
the average density over brush-contact surface.

For values of A above 30 amp. to the square inch, the voltage
drop R<A, with carbon brushes, is usually about 1 volt. It fol-
lows that, if the value of k may be as high as 2.5, the actual e.m.f .
in the short-circuited coil may differ from the ideal e.m.f. by
about 1.5 volts. This is, however, a case for experimental
determination ; but once a safe value for k or for A w has been
determined, the allowable variation in the commutating flux
\$ c as given by formulas 82, page 164, and 85, page 167 may
readily be calculated. If the assumed value of 1.5 volts varia-
tion is permissible, it follows that the amount by which the flux
entering the teeth in the commutating zone may differ from the
ideal value is

^ 1.5J C X10 8

* = ~^TT

3l e X 10 8
= 2 JP maxwells (88)

4 L c

wherein t c is the time of commutation in seconds, and T c is the
number of turns in the short-circuited coil.

Apart from all considerations of a mechanical nature, commu-
tation can be improved by increasing the thickness of insulation
between commutator bars. This might in many cases be made
considerably thicker than the usual ^2 m - with advantage in
the matter of sparking; but it is not always easy to obtain large
spacing between bars, and thick mica insulation is otherwise
objectionable.

When calculating the equivalent slot flux, the assumption
made virtually supposes the slot to contain a large number of
small wires all connected in series. With solid conductors of
large cross-section, the local currents in the copper would alter
the distribution of the slot flux and call for a reversing field
differing slightly from the field calculated by the aid of the
formulas given in this chapter. Again, the field due to the
armature m.m.f. is usually assumed to be stationary in space.
This is practically true when the number of teeth is large and
the brush arc is a multiple of the bar pitch. With few teeth
and a brush covering a fractional number of bars, the oscilla-
tions of the armature field (of small magnitude but high fre-
quency) may have some slight effect on commutation; but with
12

178 PRINCIPLES OF ELECTRICAL DESIGN

a better understanding of the main principles underlying commu-
tation phenomena these and similar modifying factors of
secondary importance tend to assume a less formidable aspect.
The designer, who must of necesssity be an engineer, desires
to see clearly what he is doing. If he uses formulas of which
he does not know the derivation or physical significance, he is
working in the dark. In general, he asks for more physics and
less mathematics. If he can picture the short-circuited coil
cutting through the various components of the flux in the
commutating zone, and understand how these flux components
may be calculated within limits of accuracy that are generally
satisfactory in practice, he will have a working knowledge of
the phenomena of commutation which should be especially
valuable in cases where test data cannot be relied upon.

53. Mechanical Details Affecting Commutation. The quality
of the carbon used for the brushes, together with the pressure
between brush and commutator surface, will determine the heat-
ing due to friction, and therefore, to some extent, the dimensions
and proportions of the commutator. The pressure between
brush and commutator is usually adjusted by springs so that it
shall be from 1 to 2 Ib. per square inch of contact surface. In
order to avoid excessive temperature rise, the current density
is rarely allowed to exceed 30 or 40 amp. per square inch of
brush-contact surface. A sufficient cooling surface is thus
provided from which the heat developed through friction and
PR loss may be radiated. The width of brush (brush arc)
should lie within the limits of 1J4 and 3^ commutator bars;
and as a further check on the desirable dimensions, the width
should not exceed J^2 of the pole pitch referred to the
commutator surface. Having determined the width of the
brush, and decided upon a suitable current density, the total
axial length per brush set may be calculated, and the length of
the commutator decided upon.

The individual brush rarely exceeds 2 in., measured parallel to
the axis of rotation, and when a greater length of contact surface
is required, several brush holders are provided on the one spindle
or brush arm. Even in small machines, the number of brushes
per set should not be less than two, so as to allow of examination
and adjustment while running. The final check in the matter
of commutator design is the probable temperature rise; but this
will be again referred to when considering losses and efficiency.

COMMUTATION

179

The curvv Figs. 68 and 69, give respectively the contact re-
sistance and tu ^ of potential for different current densities.
Two curves are pic -d in each case: the one referring to a hard

20 30 40 50 CO

Current Density- Amperes per Square Inch

FIG. 68. Contact resistance, carbon brushes.

10

. Carbon

20 30 40 50 60

Current Density Amperes per Square Inch

70

SO

FIG. 69. Pressure drop at contact surfaces, carbon brushes.

quality of carbon, and the other to the much softer electro-
graphitic carbon which has a lower resistance and may be worked
at a higher current density. An average pressure of 1.5 Ib.

180 PRINCIPLES OF ELECTRICAL DESIGN

per square inch between contact surfaces has b f 2 assumed in
order to avoid the plotting of a large numb'- ui curves. For
high-voltage machines, the harder qualit-" JL ' carbon will gener-
ally be found most suitable. For low ._ _ jltages, economy may
frequently be effected by using the graphitic brushes with cur-
rent densities as high as 60 amp. to the square inch of contact
surface. It is an interesting, but not very clearly explained,
fact that the temperature ris'j of the negative brushes is greater
than that of the positive brushes. In other words, the watts
lost are greater when the current flow according to the popular
conception is from carbon to copper, than when it is from
copper to carbon. Tne resistances given in Fig. 68 have been
averaged for the + and brushes.

On low-voltagj dynamos, when the current to be collected is
very large, copper brushes must be used. The resistance of
the contact between brush and commutator is then much lower
than with carbon brushes and the current density may be as
high as 200 amp. per square inch of contact surface. The con-
tact-surface resistance may be anything between 0.0007 and
0.0028 ohm per square inch, a safe figure for the purpose of
calculating the brush losses being 0.002 ohm. If the current
density at the contact surface is 150 amp. per square inch (a
very common value), the total loss of pressure at the brushes
will be 0.004 X 150 = 0.6 volts, instead of about 2 volts, which
is usual with carbon brushes.

The degree of hardness of the copper used for the commutator
segments is a matter of importance; an occasional soft bar will
invariably lead to sparking troubles because of unequal wear.
A perfectly true cylindrical commutator surface is essential
to sparkless running. The different sets of brushes should be
"st'aggered" in order to cover the whole surface of the commu-
tator and so prevent the formation of grooves. For the same
reason, and also to ensure more even wear of the journals and
bearings, some end play should be allowed to the shaft. In
large machines it is not uncommon to provide some device, in
the form of an electromagnet with automatically controlled
exciting coil, to ensure that the desirable longitudinal motion
of the rotating parts shall be obtained

Owing to the hardness of the mica insulation relatively to that
of the copper bars, there is a tendency for the mica to project
slightly above the surface of the copper. This naturally leads

COMMUTATION 181

to sparking troubles, and it is not uncommon to groove the
commutator between bars, cutting down the mica about ^ in.
below the surface, leaving an air space as the insulation between
the bars. This undercutting process may have to be repeated
as the commutator wears down in use.

As the effects of any irregularities on the commutator suiface
are accentuated by high speeds, it is usual to limit the surface
velocity of the commutator to about 3,000 ft. per minute when
possible. . The diameter of the commutator in large machines
is generally about 60 per cent, of the armature diameter, while,
in small machines, this ratio may be as high as 0.75.

The design of brushes and holders is a matter of great im-
portance; as a general rule, it may be said that the lighter the
moving parts of brush and holder, the better the conditions in
regard to sparking when the surface of the commutator is not
absolutely true.

54. Heating of Commutator Temperature Rise. In some
cases it is necessary to provide special means of ventilation to
keep the temperature of the commutator within reasonable
limits; but as a rule a sufficiently large cooling surface may be
obtained without unduly increasing the size and cost of the
commutator.

The losses to be dissipated consist of:

1. The PR loss at brush-contact surface.

2. The loss due to friction of the brushes on commutator
surface.

The PR loss in the commutator segments is relatively small
and can usually be neglected.

The watts lost under item (1) are approximately 2/, where I
is the total current taken from the machine. This assumes an
average value of 2 volts for the total potential drop between
commutator and carbon brushes. For a more exact determina-
tion of this electrical loss, the curves of Fig. 69 can be used. As
the current passing into all the positive brushes includes the
shunt exciting current, an allowance should be made for this.
Moreover, the assumed condition of uniform current density
over brush-contact surface will not be fulfilled in practice. The
uneven distribution of current density will increase the losses,
of voltage drop as read off the curves of Fig. 69.

The losses under item (2) are less easily calculated because

182 PRINCIPLES OF ELECTRICAL DESIGN

the coefficient of friction will depend not only upon the quality
of the carbon brush but also on the condition of the commutator
surface.

Let P = the pressure of the brush on the commutator, in
pounds per square inch of contact surface (usually
from 1 to 1% Ib.) ;
c = the coefficient of friction;
A = the total area of brush contact surface (square

inches) ;

v c = the peripheral velocity of the commutator in feet
per minute;

then the friction loss is cPAv c foot-pounds per minute.

If DC is the diameter of the commutator in inches, and N is
the number of revolutions per minute,

The friction loss, expressed in watts, is

cPAND* X 746
12 X 33,000

The value of c for a good quality of carbon brush of medium
hardness may lie between 0.2 and 0.3; but this coefficient is
not reliable as it depends upon many factors which cannot
easily be accounted for.

The watts that can be dissipated per square inch of commu-
tator surface will depend on many factors which cannot be
embodied in a formula. The peripheral velocity of the com-
mutator surface will undoubtedly have an effect upon the cool-
ing coefficient; but the influence of high speeds on the cooling
of revolving cylindrical surfaces is not so great as might be
expected. The design of the risers i.e., the copper connections
between the commutator bars and the armature windings
has much to do with the effective cooling of small commutators;
but this factor is of less importance when the axial length of the
commutator is considerable.

Some designers consider only the outside cylindrical surface
of the commutator when calculating temperature rise; but this
leads to unsatisfactory results in the case of short commutators.
In the formula here proposed, it is assumed that the risers add
to the effective cooling surface up to a limiting radial distance

COMMUTATION

183

of 2 in.; that is to say, if the risers are longer than 2 in., the area
beyond this distance will be considered ineffective in the matter
of dissipating heat losses occurring at the commutator surface.
The external surface of the carbon-brush holders is helpful in
keeping down the temperature and it will be taken into account
by assuming that the cooling surface of the commutator is in-
creased by an amount equal to 2l c b sq. in.; where l e is the total
axial length of one set of brushes, and b is the total number of
brush sets.

FIG. 70. Cooling surface of commutator.

The cooling area, as indicated in Fig. 70, will therefore con-
sist of the cylindrical surface TrDcL e ', the surface of the risers

(D r 2 - D c 2 ); the surface of the exposed ends (if any) of the

copper bars, of value - (D c 2 D 2 ); and the allowance of

2l c b for the brush holders.

The empirical formula here proposed for calculating the tem-
perature rise of the commutator is

At V

(90)

where W = the total watts to be dissipated.

A = the cooling area computed as above (square inches).
v c = the peripheral velocity of the cylindrical surface of

the commutator in feet per minute.
T = the temperature rise in degrees Centigrade.

184 PRINCIPLES OF ELECTRICAL DESIGN

The allowable temperature rise, i.e., the limiting value of T
in formula (90) is 45 to 50C.

The mechanical construction of the commutator is a matter
of great importance, and when the peripheral velocity exceeds
4,000 ft. per minute, special means may have to be adopted
to ensure satisfactory operation. For instance, if the axial
length is great, it may be necessary to provide one or more
steel rings which can be slipped over the surface of the bars and
shrunk on, to prevent displacement of the bars or loosening of
the mica insulation owing to vibration or centrifugal action.
These mechanical details must, however, be studied elsewhere
as their discussion is not included in the scope of this book. A
sufficient radial depth of commutator bar must be provided in
order that the strength and stiffness may be sufficient to resist
the effects of centrifugal force. This dimension of the copper
segments should include an allowance of % to % in. for wear,
as the commutator must be large enough in diameter to allow
of its being turned down occasionally without reducing the
cross-section of the segments to a dangerous extent. The
mechanical considerations are the controlling factors in this
connection, as the cross-section is usually ample to carry the
required current. The pitch of the bars at the commutator
surface should not be less than 0.2 in., because, with the mica
of the usual thickness (0.03 to 0.035 in.) the bar would be
mechanically unsatisfactory if the thickness were reduced below
this limit.

CHAPTER IX

THE MAGNETIC CIRCUIT DESIGN OF FIELD
MAGNETS EFFICIENCY

55. The Magnetic Circuit of the Dynamo. Once the total
flux per pole necessary to develop the required voltage is known,
it is an easy matter to design the complete magnetic circuit and
provide it with a suitable winding in order that the required
flux shall enter the armature. -The method of procedure is
similar to that adopted in the design of a horseshoe lifting magnet
(see Art. 16, Chap. Ill), and for this reason the subject will be
dealt with very briefly in this chapter.

SECTION THROUGH

A-B

FIG. 71. Magnetic circuit of multipolar dynamo.

Fig. 71 shows the flux paths in a multipolar dynamo. If we
know the flux density in the iron at all parts of the magnetic
circuit and the average lengths, y, c, and a, of the flux paths per
pole in the yoke, pole cores, and armature, respectively, we can,
by referring to the B-H curves of the materials used in the con-
struction, easily calculate the ampere-turns necessary to over-
come the reluctance of these portions of the magnetic circuit.
The greatest part of the total reluctance is in the air gap and

185

186 PRINCIPLES OF ELECTRICAL DESIGN

teeth; but the amount of excitation required to send the flux
through air gap, teeth, and slots, has already been calculated,
and may be read off the. curve a of Fig. 49, page 133. The air-
gap density to be used in obtaining this component of the total
field ampere-turns will be the maximum value of the air-gap
density as obtained from the flux curve A of Fig. 51 (for open-
circuit conditions).

The necessary cross-section of iron in the various parts of the

Online LibraryAlfred StillPrinciples of electrical design; d. c. and a. c. generators → online text (page 15 of 30)