Alfred Still.

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

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known, the correct flux-distribution curves can readily be plotted.
Let the curve of Fig. 50 represent the distribution of the re-
sultant field m.m.f. on open circuit obtained as explained in Art.
40 (Fig. 44) ; then, at any point such as e, the m.m.f. is given by
the length of the ordinate ee'. Find this value on the horizontal
scale of Fig. 49, and the height of the ordinate at this point,
where it meets curve e (which is not drawn in Fig. 49), is the
flux density, which can be plotted as ee' in Fig. 51. In this
manner the flux curve A of Fig. 51 is obtained. The area
of this curve, taken between any given points on the armature
periphery, is obviously a measure of the total flux entering the
armature between those points. The required flux per pole is



FLUX DISTRIBUTION



135



usually known. The average density over the pole pitch, r,
as explained in Art. 41, is

3>

B g (average) = ^r

where l a is the gross length of armature. 1 By drawing the dotted
rectangle of height B g ( average) as shown in Fig. 51, its area can
be compared with that of curve A by measuring with a planim-
eter. If these areas are not equal, the ampere-turns per field
pole, as represented by the curve of Fig. 50, must be altered
and a new flux curve plotted, of which the area must indicate the
required flux.




FIG. 51. Open-circuit flux distribution.

43. Effect of Armature Current in Modifying Flux Distribution.

The distribution of m.m.f. over armature surface when the

field poles are acting alone has already been calculated and

plotted in Fig. 50, and the effect of the armature current in

modifying this distribution may be ascertained by noting that

the armature ampere-turns between any two points such as d

and d' on the armature circumference (see Fig. 52) are q(b a),

where q stands for the specific loading or the ampere-conductors

per unit length of armature circumference.

Let p = number of poles,

Z = total number of conductors on armature surface,
I c = current in each conductor,
T = pole pitch,

ZI e

then q = -
pr

1 The gross length l a of the armature core usually exceeds the axial length
of the pole shoe by an amount equal to twice the air gap, 5. Thus, by as-
suming the flux distribution as given by curve A of Fig. 51 to extend to the
extreme ends of the armature, a practical allowance is made for the fringe
of flux which enters the corners and ends of the armature core.



136



PRINCIPLES OF ELECTRICAL DESIGN



and the armature m.m.f. tending to modify the flux due to the
field poles alone is

ZI e (b - a)



0.4



pr



between the points d and d'.

In order that a curve may be plotted on the same basis as the
resultant field m.m.f. curve, it is necessary to know the armature
m.m.f. per pole at all points. Let the distance between the
points d and d' be equal to the pitch r\ then the effect of the arma-
ture m.m.f. at d f upon the pole S will be exactly the same as



S




N




S


I


^ d' \-


^ d \^




FIG. 52. Magnetizing effect of armature inductors.

the effect of the armature m.m.f. at d upon the pole N, and
the m.m.f. per pole at the point d may be expressed as

0.47rZJ c (b -a)



(Armature m.m.f.)^ =



(65)



Its maximum value which always occurs in the zone of com-
mutation is



Armature m.m.f. per pole =



(66)



The combination of this armature m.m.f. with the m.m.f. due
to the field coils only, as represented by Fig. 50, is carried out
graphically in Fig. 53. The curves F and A represent field and
armature ampere-turns (or m.m.f. in gilberts, if preferred).
These are the two components of a resultant m.m.f. curve, R,
the ordinates of which are a measure of the tendency to send flux
between any point on the armature surface and the pole shoe N.
The actual value of the flux density at the various armature
points under load conditions can therefore be obtained by using



FLUX DISTRIBUTION



137



the curves of Fig. 49 and plotting the values of air-gap density
corresponding to the ampere-turns read off the curve R of Fig. 53.
The procedure is exactly the same as when obtaining the open-
circuit flux curve (Fig. 51) by using the values of Figs. 49 and
50, but the new curve of flux distribution which may be called
curve B, to distinguish it from the open-circuit flux curve A
gives the distribution over armature surface for a given brush
position and a specified output. The difference in area of
curves A and B is a measure of the flux lost through armature
reaction; it includes not only direct demagnetization, but also
cross-magnetization which by producing distortion of the flux

Max.Field S7 per Pole

'Resultant M.M.F.under
Load ConditoDB




Max. Armature 57
per Pole

I

sh Shift

FIG. 53. Addition of field and armature m.m.fs.

distribution leads sometimes to local concentration of high
densities and reduction of total flux owing to saturation of| the
iron in the armature teeth.

The final flux curve for the loaded machine is generally similar
to curve B, except that its area must be such as to indicate that
the desired voltage will be generated. This increased area is, of
course, obtained by increasing the field ampere-turns. In other
words, the curve F of Fig. 53 has to be replaced by a new open-
circuit m.m.f. curve such that the new R curve resulting from its
combination with the existing curve A will produce a new flux curve
similar to B, but of the required area. This new flux-distribution
curve may be called curve C, to distinguish it from the open-
circuit curve A and also from the flux curve B, which, although a
load curve, has too small an area to generate the required volt-
age. The amount by which the ordinates of curve F should be
increased may be found by trial, but it is generally possible to
estimate the necessary correction to give the required result.



138 PRINCIPLES OF ELECTRICAL DESIGN

The added field ampere-turns may be thought of as compensat-
ing for two distinct effects :

1. The loss of pressure due to armature reaction.

2. The loss of pressure due to IR drop in armature, brush
contacts, and series field windings.

The correction for (1) consists in bringing the total flux up
to its value on open circuit. It is the ampere-turns necessary to
raise the air-gap density from its average value over curve B to
its average value over curve A. An approximate method of mak-
ing this correction is to find on curve (a) of Fig. 49 (i.e., the curve
corresponding to point a at center of pole) the ampere-turns
PbP a required to produce the difference of flux density BbB a
when OB b = average flux density over curve B, and OB a =
average flux density over curve A. The correction for (2)
consists in increasing the flux per pole to such an extent that it
will generate the increased voltage. This is the correction for
compounding; it compensates for all internal loss of pressure,
and must include over-compounding if this is called for.

If E' = required full-load developed volts, and

E = open-circuit terminal volts (being also the no-load
developed volts), then,

Area of flux curve C _ E'
Area of flux curve A "" E

In this manner the required area of curve C is obtained. The
average flux density must be increased in this proportion, and
the necessary additional ampere-turns for this correction are
arrived at approximately by making P a P c (as indicated on
Fig. 49) such as to increase the air-gap density in the ratio of
E' to E.

The area of the final curve C, which should be measured for
the purpose of checking with the required area, is that com-
prised between the points on the armature surface which corre-
spond with the position of the brushes on the commutator,
portions of the flux curve measured below the datum line being
considered negative, and deducted from the area measured
above the datum line.

The amount by which the area of the full-load flux curve C
must exceed the area of the open-circuit flux curve A may be
determined approximately by estimating the probable voltage
drop in the series winding (if any) and at the brush-contact



FLUX DISTRIBUTION 139

surfaces. In the case of compound-wound machines, it will
be known at the outset whether the dynamo is to be flat-com-
pounded or over-compounded. Over-compounding is resorted
to when the drop in the circuit fed by the machine is likely to
be high. The terminal voltage may then be 5 per cent., or even
10 per cent., higher at full load than on open circuit. The balance
of the e.m.f. to be developed at full load consists of:

1. The IR drop in armature winding.

2. The IR drop in series field (if any).

3. The IR drop in interpole winding (if any).

4. The IR drop at brush-contact surface.

Item (1) can readily be calculated since the armature winding
has been designed. Item (2) may be estimated at from one-
fourth to one-half the armature drop. Item (3) may be esti-
mated at from one-fourth to one-half the armature drop. Item
(4) will be discussed later, but it may be estimated at 2 volts,
and is practically constant for machines of widely different
voltages and outputs.

By totalling these items of internal loss of pressure, and
adding thereto the required difference between the terminal
volts at full load and at no load, the full-load developed voltage
E' is obtained, and the required area of curve C is therefore:

E f
Area of open-circuit flux curve A X -j*

where E is the open-circuit terminal voltage as previously
defined.

The ampere-turns necessary to produce the curve C of this
particular area will not be far short of the total ampere-turns
on the field coils at full load, because the air gap, teeth and slots
have considerably greater reluctance than the remainder of the
magnetic circuit. The extra ampere-turns required to over-
come the reluctance of the armature core, magnet limbs and
frame will be considered later when dealing with the magnetic
circuit as a whole and the field-magnet windings.



CHAPTER VIII
COMMUTATION

44. Introductory. A continuous-current dynamo is pro-
vided with a commutator in order that unidirectional currents
may be drawn from armature windings in which the current
actually alternates in direction as the conductors pass successively
under poles of opposite kind.

As each coil in turn passes through the zone of commutation,
it is short-circuited by the brush, and during the short lapse of.
time between the closing and the opening of this short-circuit
the current in the coil must change from a steady value of -f-7 c
to a steady value of I c .

Let W = surface width of brush (brush arc) in centimeters.
M = thickness of insulating mica in centimeters.
V c = surface velocity of commutator in centimeters per
second.

The time of commutation, in seconds, may then be written,

W - M






V c



Since M is usually small with reference to W, it is generally

W

possible to express the time of commutation as t c = ^ that is

r C

to say, the time taken by any point on the commutator surface
to pass under the brush is approximately the same as the dura-
tion of the short-circuit. It is during this time, t c , that the
current in the commutated coil must pass through zero value
in changing from the full armature current of value +/ c to the
full armature current of value 7 C . If R is the resistance of
the short-circuited coil, and if any possible disturbing effect of
brush-contact resistance be neglected, it is evident that the
e.m.f. in the coil should be e I c X R at the commencement of
commutation. At the instant of time when the current is
changing its direction i.e., when no current is flowing in the
coil the e.m.f. is e = X R = 0. At the end of the time

140



COMMUTATION 141

t c , when the coil is just about to be thrown in series with the
other coils of the armature winding carrying a current of I e
amp., the e.m.f. in the coil should be e = I C R. It is when the
e.m.f. in the coil has some value other than this theoretical value
that sparking is liable to occur.

The theoretical investigation of commutation phenomena is
admittedly difficult, because it is almost impossible to take
account of the many causes which lead to sparking at the brushes.
Some of the problems to be dealt with are of a purely mechanical
nature, and it is necessary to make certain assumptions and to
disregard certain influencing factors in order that the essential
features of the problem of commutation may be studied. The
writer has deliberately departed from the usual method of
treating this subject because he believes that it is possible to
put the fundamental principles involved into a somewhat simpler
form than they are likely to assume when clothed in mathe-
matical symbolism. An attempt will be made to obtain a
clear conception of the physical phenomena involved in the
theory of commutation.

Before the publication of MR. LAMME'S paper 1 the methods
of DR. STEiNMETz 2 and DR. E. ARNOLD' formed the nucleus around
which the bulk of our commutation literature clung. MR.
LAMME'S paper has the great merit of putting the more or less
familiar problems of commutation in a new light. The end he
attains is approximately, the same as that attained by any
other reasonably accurate method of analysis, provided all
factors of importance are included, and the difficulties he en-
counters are of the same order and magnitude as those en-
countered by other investigators; but, by getting nearer to the
true physical conditions in the zone of commutation, he saves
us from drifting, sometimes aimlessly, on a sea of abstract specu-
lation. Although the presentation of the subject as given in
this chapter has undoubtedly been suggested by the reading of
MR. LAMME'S paper, yet its aim is not so much to furnish addi-
tional material for the designer as to give the student a clear
conception of the phenomena of commutation. The writer's
end is simplicity or clearness, even if the less important factors

1 B. G. LAMME: "A Theory of Commutation and Its Application to
Interpole Machines," Trans. A. I. E. E., vol. XXX, pp. 2359-2404.

2 "Theoretical Elements of Electrical Engineering."
8 "Die Gleichstrom-Maschine."



142 PRINCIPLES OF ELECTRICAL DESIGN

are entirely ignored, while, in MR. LAMME'S own words, his
method of analysis, including as it does more conditions than
are usually included, " instead of making the problem appear
simpler than formerly . . . makes the problem appear more
complex." 1

In the first place, it may be stated that considerations of a
mechanical nature, such as vibration, uneven or oily commutator
surface, insufficient or excessive brush pressure, etc., cannot be
dwelt upon here, and, in the second place, ideal or " straight-
line" commutation will be assumed, and the conditions neces-
sary to produce this generally desirable result investigated,
in order that a multitude of more or less arbitrary assumptions
may not obscure the problem in its early stages. By working
from the simplest possible case to the more complex it is thought
that the object in view a physical conception of commutation
phenomena leading to practical ends will best be served, and
influencing factors of relatively small practical importance will
be either disregarded or but briefly referred to.

45. Theory of Commutation. Consider a closed coil of wire
of T c turns moving in a magnetic field. At the instant of time
t = the total flux of induction passing through the coil is
+ $o maxwells, and at the instant of time t = t c sec. the total
flux through the coil is + $ t maxwells. Then on the assumption
that the flux links equally with every turn in the coil, the average
value of the e.m.f. developed in the coil during the interval of
time t c is

($ f - $,)
Em= -



If R is the ohmic resistance of the coil and e is any instantaneous
value of the e.m.f. produced by the cutting of the actual magnetic
field in the neighborhood of the wire, the instantaneous value

p

of the current in the coil is i = g, because e is the only e.m.f.

in the circuit tending to produce flow of current. The usual
conception of a distinct flux due to the current i producing a
certain flux linkage known as the self-inductance of the circuit
is avoided; but its equivalent has not been overlooked, seeing
that the magnetomotive force due to the current in the coil is
a factor in the production of the flux actually linked with this
current at the instant of time considered. It is not suggested

1 Reply to discussion, Trans. A. I. E. E., vol. XXX, p. 2426 (1911).



COMMUTATION 143

that the orthodox method of introducing self-induction and
mutual induction as separate entities endowed with certain prop-
erties peculiarly their own is not without advantages in the
solution of many problems, especially when mathematical analysis
is resorted to, but it tends to obscure the issue when seeking a
clear understanding of the physical aspects of commutation.
The splitting up of the magnetic induction resulting from dif-
ferent causes into several components is frequently convenient
and should not be condemned except in certain cases when iron
is present in the magnetic circuit. It cannot, however, be de-
nied that self-induction and mutual induction are frequently
thought of as different from other kinds of induction. We are
indebted for this state of things to some writers whose familiarity
with mathematical methods renders a clear physical conception
of complicated phenomena unnecessary, but the practical engi-
neer or designer who produces the best work, especially in de-
partures from standard practice, is usually he who has the clearest
vision of the physical facts involved in the problem under con-
sideration. If the term self-induction calls up a mental picture
of magnetic lines, being a certain component expressed in
maxwells of the total or resultant flux of induction in a circuit,
this does not prevent our speaking of flux linkage per ampere
of current as inductance expressed in henrys and using the

formula e = L -j. to calculate that component of the total e.m.f.

in a circuit which would have a real existence if the field due to
the current i in the wire were alone to be considered.

Following the lead of MR. LAMME, the wires in the coil under-
going commutation will be thought of as cutting through a total
flux of induction, expressed in magnetic lines or maxwells, this
flux being the result of the magnetizing forces of field coils and
armature windings combined.

In Fig. 54 the thick-line rectangle represents a full-pitch
armature coil of T turns undergoing commutation. The dotted
rectangles show the position of two consecutive field poles, and
the shaded curve represents the ascertained or calculated flux
distribution over the armature surface. The ordinates of this
curve indicate at any point on the periphery the density of the
flux entering the armature core. The direction of slope of
the shading lines indicates whether the flux is positive or
negative. A method that may be followed in predetermining



144



PRINCIPLES OF ELECTRICAL DESIGN



the flux distribution over the armature surface, including the
interpolar space, was outlined in Chap. VII (refer to Art. 41,
42 and 43) , and the flux-distribution curves of Fig. 54 might have
been obtained in the same manner as the flux curve C referred to
in Art. 43. The coil of Fig. 54 is supposed to be moving from
left to right, and measurements on the horizontal axis XX may
represent either distance travelled or lapse of time, since the arma-
ture is revolving at a uniform speed. The case considered is
that of a ' dynamo without commutating poles, with brushes
moved forward from the geometric neutral or no-load com-
mutation position until a neutral commutating zone is again




FIG. 54. Diagram showing ideal armature coil in commutating zone.

found. The flux curves as drawn are the result of the combined
m.m.fs. of field coils and armature windings. During the time
of commutation, t c , which, if we neglect the effect of mica thick-
ness, is the time taken by a point on the commutator to pass
under the brush of width W, the conductors on the right-hand
side of the short-circuited coil have been moved through the
neutral zone from a weak field of positive polarity into a weak
field of negative polarity, while the conductors on the left-hand
side of the coil have moved from a weak field of negative polarity
into a weak field of positive polarity. Owing to the symmetry
of the fields under the poles of opposite kind (i.e., the similarity
in shape and equality in magnitude of the shaded flux curves),
and the fact that the small portions of the flux curves near the



COMMUTATION 145

neutral point may be considered as straight lines, the resultant
flux cut by the two coil-sides joined in series by the end con-
nections may be represented by the shaded area in Fig. 55,
where positive values are measured above, and negative values
below, the horizontal axis. Intervals of time are measured
horizontally from left to right, and the straight line BE' rep-
resents the flux distribution in the commutating zone. The
direction of this flux is such as to develop in the short-circuited
coil, at every instant of time during the period of commutation,
an e.m.f. tending to produce a current in the required direction;
that is to say, from the commencement of short-circuit, when

+

*^J >^t

t-t e




!

FIG. 55. Flux distribution in commutating zone of ideal armature coil.

t = 0, until the middle of the commutation period, when both
flux and current are of zero value, the small amount of flux cut
by the short-circuited conductors is of the same kind as that
previously cut by the conductors, while from the time t = t c /2
until the end of commutation (t t r ) the flux is of the opposite
kind, being such as will cause the current to flow in the oppo-
site direction. The amount of the flux required to bring about
this condition is only a small percentage 1 of the flux cut by a coil
under the main poles in the same interval of time, because the
resistance of the armature windings is always low in comparison
with the resistance of the external circuit, and, as a matter of
fact, it is the average value of the flux entering the armature
over the commutating zone with which the designer is usually
concerned. If the brushes are so placed as to bring the short-
circuited conductors in a neutral field, satisfactory commutation
will result.

1 The flux density where the coil-side enters or leaves the commutating
zone (the positions t = and t = k of Fig. 55) would be about 2.5 per cent,
of the average density under the main poles, because this is the ratio of the
armature IR drop to the developed voltage in a well-designed dynamo of
moderate size say, 50 to 100 kw.
10



146



PRINCIPLES OF ELECTRICAL DESIGN



Returning to a consideration of the case represented by Fig.
54, it must not be overlooked that the armature coil there shown
is not of a practical shape, the end connections are shown parallel
to the direction of travel of the coil, and the cutting of fluxes by
these end portions of the coil has not been considered. When
we consider the end fluxes, or the effect of commutating inter-
poles, especially when these are not equal in number to the main
poles or do not extend the full length of the armature core, then
the flux cut by the short-circuited conductors at any given part
of their total length such as the center of the " active" portion,
whether on a smooth core or in slots may have an appreci-
able value; but if we consider the total flux cut by all parts of
the wire forming the commutated coil, when the current i in this
coil is passing through zero value, it is most emphatically true
that the coil as a whole is moving in a " neutral field," i.e., a
resultant field which is either of zero value (when the sum of all
its components is correctly taken) or of which the direction is
parallel to the direction of travel of the conductors.




FIG. 56. Diagram of coil and commutator during commutation.



At the beginning and end of the commutation period the
field in which the coil moves should be such as to produce an
e.m.f. in the short-circuited coil of the value e = I C R, where I c
is the value of the current per path of the armature circuit and
R is the resistance of the short-circuited coil. On the assumption
of a uniform current density over the surface of the brush, the
brush contact resistance need not be taken into account, as
will be clear from the following considerations. Fig. 56 shows a
brush of width W covering several segments of the commutator.
The total current entering the brush is 2/ c , and since the density



Online LibraryAlfred StillPrinciples of electrical design; d. c. and a. c. generators → online text (page 12 of 30)