|
|

 
  
    
 

II

|

HNN

|
|

it

ANALYTICAL STUDY
OF D. C. COMMUTATION

Thesis for Degree of E. E,
Harold L. Smith

ae
THES!S

 
THESIS

 

 
The €uegect netter for this thesis on
commutation is iér,el) @ awsveloypireit cr tie Writers
Perierce in the jesion of b, C. notorse end .sncretois
Gur tie, ti.e Last Séverel ears. Conciucréer. de aate wee
E

Ortéineu thre the drpvee
trotclur di: certain mec. s fre
led néturalily to further tiecret=
ruer to udeternmine the nmeturs of
Vlhat chances to reels.

The writer vec fortunete In havi cher
of tie develor;ment of a line cf U.C. notorse, reten
we Prescs meximun, also « line of ceries crane
intermittently reted. In tidis work certain uitficulties
were encourtered on éeccount of tie greater output fer unit
hel bt of material whict. rede itt necsssery to rescert te
@ mumcer olf refinements in calculatvicn in order to
prscdict tee performerce viti a eufficisnt decree of
accuracy).

C
ct
OQ
rx
«9

It as le G@im to uctermins @€ ieaeri
ae Poeelicle thc actual ccorditions durin. corrutetion,
ani the various fectors in their prc} ler “reletion. in
severél césce the ti:cOry Lécores other: CUnversore Lut
etill is celicvesd to ce werthy of consideretion, in ti.et
it may lead to « tLstter unuerstenaging of corditions and
suerd the detioner fren « construction vhich ney leas
1 5

DD

trouclae. are £ nwincer of mit..cads cf caelculceticn
for determin

Los a... .. ~ y- Lg:
Me 6G 6 COMrm UtLatieon Cleéerecte

Wore or less practice] velus Vier 2) 3

typee It Le not tig weiters ahterntion to attenpt a@ ugve-
lojpwent of en entireiy met reti.cu of ceolculsetion, cue
Piaticr LO léhe Vwett mas proves co1 volose Prop ola. eticcds
emu cor.cine with trem feverel reidtierne: te Widct. me o1
mes not ve uSeu, depeurnal:.,, u,ow toe completeness of the
a:.e1° ‘ Sie deklirci.

1OGTS5
L-4

co

“.

tn

I

4

he

-
pw
+

e

C

t
Cc
Cc
r
C
c*
5
oC
~~

{

bey
bwe

fra yew. a 4 : '
Ee uULY Cae ls ive ~l ke

' - / a ~4 a we . a e . toa et
L G&G — Vaules Cla w2.brusar 2 Lure

an eo ye ey Rs a :
2wCO. Cl Leda ECace
\. et Vor 4 sti.) , ’ ‘ 2
siOe CL CCM ULE > dies, Caer

on “ mysey- r 4 we = ey gs
ree Ca CONnsuUtEtor eLre

.QOe CL turns Or COMmuUuCci Ors

eeptl. of cenauctcre an ise

Cn

be

t-t>

C eR Dyed tee oY eG Spee
an L Na 2 Ne Jot 3V Oolutions ko ° SECOClMaG

Seen dt a ae ty bee ee . $4-,.
Pla GErser OL arn uvure 2:1 Lie:

~ + - 7 _* ae . 4 ove, >, agar “ . + i
TLezetin of érréture core C2.

wiec

-4

Cloth of Conswute

7 ob tat, = ; ter 4 ft.
»auidi. Ou CO, Putetire cle

e . . 2 a ; _. oe
eyuavalsit air man tok, ota.
¢
B =

—_
— —_

a.

Vv. —
h

TH
i J —
a ”

a A
° —_
Ly —_

° asc we su. 13 ~

v lux Lei 2liicd

ry .- . « e - . -.
Plus acrcdty in lisies Ber os

-_—
»
is
’ t
ony
r4
e 2
r.

Slum gerne

PerBReeéai.c

r

Lovell cecsductors on toe

f,ypory 7
ual ooheu.

4 : .
vlube&

rp, . dyn, . ~~ 2 bt, ° .
fiery turne excitation

— 4 - ro 4 aie 4 ne
co Joeery ota. Ca o21.% Stréd -.t bert
CHAPTER I
LOAD CURRENT RELATIONS IN THE COIL

A A y MULT VI TG
InapD.C. armature winding the current enters
at the positive brush and divides half going each way
around the armature to the negative brush, or adjacent
negative brushes if it be a multipolar machine. Fig. I
shows part of a multiple winding. Let I equal the total
current entering the brush. Assumeing that the contact
resistance is uniform over the entire face of the brush
it is evident that the current entering any commutator bar
will be proportional to the contact area. Since the
current divides evenly any coil out away from the influence
of the brush will have 2/2 amps. flowing in it. For
example, coil (L) and coil (Q) will have */2 amps flowing,
but in opposite directions. The current in coil (L)
comes from two sources, part from_the brush to bar #4, and
the rest from around coil (M). amps enter bar #4
from the brush, .thus the current in coil (M) equals;-
; x'._ I x’. —~ be
We dw pl = B-pl = -
Likewise the current in coil (N) is that in coil(M) less
that entering bar #3, equals;-

é : "Oy! ‘ _ b-2 =) "

iet,- Ri= ptr - Ri = Spares 1
oxea) y — (b-2x-2a)T _ (b-x-8

i= 1, _{b-x-8) I: Dp" —_ (oox-e)T

ay (be Bx-2al-2vs2xe2d) = _ 4

Coil (Q) is thr last coil effected by the brush
on the other side, and according to the first assumption,
that the current divides equally, the current in this coil
should be7/z but in the opposite directiom. The equasion
bears this out, the negative sign showing the direction.

It is chiefly of interest to trace the change in tke
current during commutation, for one coil, from If2 in one
direction to I/2 in the other. Consider coil (M) fig. I
(a) and (b). In (a) it was found that the current equaled;-

i,= (ope )T

It is evident that the coil will start to commutate when
the brush edge first starts on bar #4 or when x=0. and
will finish when the other edge leaves bar #3 or x'=b

Fig. 1 (b) shows the position of the brush when the coil

(M) has nearly finished commutating. Summing the current for
each coil as before gives as follows;-

I
~ 1-{2 =27-2a-2pe2ae2z)I — — +
i, = i, Cu-gez)L = (p-2 ?

This checkes out the same as before so it may be assumed
that the law is general, Considering coil (M) alone;-

4
— = = a
iy = put, atz'=x'

In this way a general expression is optained for
the current in any céil, in terms of the width of the brush
and the distance traveled.

i= ne = [1 - 2] +

b=Width of the brush.
x'=Distance traveled.
I =Current per brush
For convenience let the distance b and x be
measured in bars, thus;

x=ar

12 fi-2] 4
b=Width of brush in bars

x=Distance traveled in bars.

The above also shows that the time required for
one coil to completely commutate, is the time required for
b bars to pass under the brush. The commutating zone of
the coil may thus be said to be »b bars wide. During this
time the current changes from I/2 in one direction to I/2
in the other acording to the law as stated abuve. This is
the equasion of a straight line starting with x=0; izsI/2
and ending with x=b; i=-I/2 (see Fig@.2)

The abéve is a proof of the well known law of
current reversal ina coil, for ideal commutation where the
short circuit current is not considered. The law holds for
& two circuit winding only when one set of brushes are used.

The effect of more brushes will be considered below .

Where ;5-

bag

Where ;5-
i

 

 

 

 

 

 

[1 | *e “EY ~s [o2 ]* |
Er _*
) (A)
["o [=5 _———
. ( Pn
2 Pn (B)
x's
 

 

Fig 2

COMMUTATION OF A SINGLE COIL ( TWO CIRCUIT WINDING)

In general the commutation of a single coil in
a@ two circuit winding is similar to that in a multiple
winding. The action is exactly the same when only one set
of brushes is used. Consider a six pole machine as in
Fig. 3 with only one posative brush; brush #1. Instead of
cOil (M) alone commutating, the current must go clear around
the machine and back to bar b. Thus for brush #1 the current
in coil (M) will reverse the same as in @ multiple winding,
and the commutating zone will be equal th the brush width b
bars. When brushes #2 and #3 are also used each adds
its current to the coil, but begins to commutate p/p bars
later. This means that the actual curremt in coil (M) at
any instant is the resultant of the currents in the coil, as
commutated by the separate like brush arms. Or to obtain
the actual reverseing wave of the current the sum of 1 - p/p
separate curves ( as in Fig.2) each added p/p bars out of
phase giveing a reversing . wave as in Fig.4. This gives
@ commutating zone (1 - p/p ) bars longer than for a
multiple winding, or a series with only two brush arms.

The actual commutating zone thus equals;-

Y
Zone one coil = (b+1-4) Two circuit
" " " = b Multiple

In a paltiple winding the number of circuits
p' equals the number of poles p therefore 1 - p/p=0

thus a general expression can be obtained for both typea of
winding.

4

Zone for one coil = 1 -+; D

p
 

Fig. 3

 

 

 

 

 

alb
wy +

4

'
——

 

ZZ

 

 

 

a

bars

&#
=

ae

 

 

 

 

Ie

:

{00

200-—
COMMUTATION OF THE TOP AND BOTTOM CONDUCTORS IN THE SLOT
The discussion so far has considered the change
in current in a single coid. It is obvious that the slot
reactance voltage of any coil is proportional to the rate
of whange of the slot amp. turns. The rate of change of
the slot amp. turns is proportional to the combined rate of
change of current in the separate conductors. The simp-
lest case is that
of one coil per slot
as in fig 5A. The

 

 

 

 

 

 

 

 

 

 

—TIeel lms! © Inre Blot flux which
\N NY causes the reactance
\N N NSS is due to the combined
N SS KS N M.M.F. of the top
N NNi and bottom conductor
AL Bk C ‘thus it is necessary
to fimd the rate of
Fig. 5 change in current of

poth the top and
bottom conductor and add them at their proper phase relation
The rate of change of the current in the top conductor
has been determined and found to be a straight line function
for a multiple winding, and a broken line for the series
Winding ( Fig.4 ) It is evident that the bottom conductor
is part of another similar coil, thus will have the same
current reversal curve, but may not commutate in phase.
Fig.6 represents a developed two circuit winding
Coil (M) will commutate in (b+1- p/p ) bars, and
will start when bar #2 first enters under brush #1. Similarly
coil (N) will start when bar #6 enters under brush #2.
Cond. #(l¢y) is a bottom conductor, and a part of coil (M).
The top conductor directly above it is cond. #y Thus
any top conductor is connected to commutator bar # (C+1)/2
where C is the number of the conductor. :
For example ;-
Cond #1 connected to bar # Aft = 1

"5 wo we Sh _
rr ee 2

For both conductors to commutate in phase, bar #2
and bar #6 must both enter under brushes #1 and #2 at the
same time. This is only possible when the pitch from bar #1
to bar # (y¢#1)/2 equals a brush pitch.

The pitch from bar #1 to bar # (y#1)/2 equals;-

(y#1) _ — (y-1
wp -1 =

The brush pitch in bars equals B/p
 
oD Ww dolor dof WT a
co} Val lo} fo} Lo} Pal [o

/
Si /
eine /

~
~ Z
~
>

 

 

ol7l[el9 [elu l[elsefawtos[e [|

 

 

¥3 ¥4.

 

 

 

 

 

 

 

 

 

 

 

 

 

Two Cirevit Progressive 4 Pole.
Fig. GA
 

 

ad
De lan | ele De se |

 

 

 

 

 

 

 

 

 

#4 i #2
wien >
| P , |
i (y-1) —>i

2
Fig. 6B

The difference in phase between the two conductors is the
difference in the two pitches.

B . (yy. = $0 +22 - 9)
p 2 a 2 Pp
A multiple winding will wind with any number of
slots. It is nearly always necessary to use equalizer
connections, thus inorder to have symmétrical taps, the number
of slots must be evenly divisable by the number of pairs of
poles. The slots may or may not be divisible by the number
of poles, and still wind correctly, the only difference being
that the coil throw will be full pitch in one case and chorded
+ slot in the other. It is evident that for full pitch the
top and bottom conductors will commutate in phase. In any
case the phase difference works out to be the same as for the
two circuit whnding, in exactly the same way. See fig. 6B.
This value may be simplified by substituting as
follows;
y = Throw of coil in conductors

y = 1 +(2m, Throw in slots)

Therefore;
rat ( t+ 25 - 7 - 2m,Throw in slots )

== -(msthrow in slots)
This figure shows
@ combination of the
curves found in Fig.
4 i, for a complete
top coil. In this
figure the two such
waves are combined
W bars out of phase
i, for the top coil
and ij for the bottom
coil giving , ly for

the wave of the
13 bars combined currents.

 

 

        
    
    
 

 

Yo \

¢

(~

I
~-4t°--------

(

\

’

 

a
<— b+1- £+¥.
3
4
r Fig.7
But: B = Theoretical. throw for full pitch, in slots
a mp

Therefore ;
m
VY =_ mp ~™x Thtow in slots
( Throw full pitch ~ Actual throw )
f Ww =m ( Slots chorded )

The total commutating zone for one coil per slot is thus
increased by Y bars, The total woll be;

—_ p!
Zone = b+t+1 ->+V

The current reversal curve for this condition
is shown in Fig 7.
SEVERAL COILS PER SLOT
When there is more than one coil per slot, as in
Fig. 5B and 5C, each set of conductors ( top and bottom )
must be taken into account separately. In Fig.8 the cond #y'
and #(lty'), parts of coils (M) and (U), are considered ;
together, as having the sum of their amp. turns changing
acording to the law as determined above for one coil as per
Fig. 7. Conductors #(y't2) and #(y'+#3). coils (N) and (V)
will have the same current reversal curve, but will start One
bar later, and so on for each set of conductors in the saot.
Thus after the rate of change of the amp. turns for one
set has been obtained, inorder to obtain the change of the
entire slot amp.turns. it will be necessary to add "m"
current reversal curves as found for one set(Fig.7) each one
bar out of phase with the proceeding. This will increase
the total commutating zone by (m-1) bars, and give a curve
as shown in Fig.9.
The analysis was carried thru in the same general
manner for the muktiple winding, and the same result obtained.
Taking account of all the factors involved inthe
usual types of windings i.e. multiple and two circuit; a
complete reversai of the slot amp.turns will take place while
Z bars are passing under the brush, or the commutating zone
in bars may be said to be Z bars wide.

   

 

eer Bo fk
2|3|4|s]o|7| 8] 9 J10[1 {12| 13[ 14] 05] 16] 12 [28] 19 [20 [a1 |22|23|24|2s|26|27|26| 24/30]
t 2 +3

Fig, 8

 

 

 
 

 

 

 

bars

6

 

 

 

 

 

 

i]
Za[b+X-E+¥ +( mz )] vars = (b+ PemeY)

Z=(v-Lemey)

Where;

Width of brush in bars.

No. of circuits on the armatures.

No. of main poles.

No. of bars per slot, or coils per slot.

m No. of slots chorded. #(1- (2B)/p-y' )
No. of commutator bars.

Conductor pitch 1 - 2mN

=Throv of the coil

you Ww Wilt ul

a4 WEB oO

The discussion so far has deat with the change of
current in the coil due to the main load current, neglecting
tha short circuit current that might be present. This is
the ideal condition and is never obtained, there being a
certain amount of short circuit current even with the best
of compensation. However it is logical to approach the
actual conditions in this way, inorder to determine the various
facgors involved causing, this short circuit currert. |

The Blot amp.turn reversal curve was plotted for a
1a4rse number of conditions, that is various combinations or
brush width, number of poles, chording, and ebt.,and in
general the shape of the curve was found to very closely
resemble a cosine wave, for one half cycle. The error is so
Slight that it is thot advisable to use the cosine law in
part of the analysis to follow.

12
CHAPTER II

GENERATION OF REACRANCE VOLTAGE

The short circuit current in the brushes of a comnut-
atyp machine, is a function of the reactance voltage in the
coil from bar to bar, and the resistance of the short circuit

In considering the reactance voltage it is feasable to
divide it into several parts.

1 Slot reactance.

2 Tooth tip leakage.

3 Zig zag leakage.

4 Interpolay leakage.
5 End winding leakage.

The separate parts as listed above will be considered
separately, and to considerable detail.

SLOT REACTANCE

It is very evident that when the current in a coil
changes there is generated a reactance voltage in that part
of the coil which lies in the slot, proportional to the
square of the number of conductors per coil, the current,
and a constant depending ipon the shape of the slot. If
other coils lie in the same slot there will be a mutual
inductance, i.e. a voltage induced in coil #1 due to any
change of current in coil #2. This voltage will be propor-
tional to the product of the turns in each coil, and the
current in coil #2 multiplied by a slot constant. The turns
in coil #2, the current, the rate of change, or the phase
relation may or may not be the same as for coil #1. The
different types of windings, and coil combinations determine
the current relations in the different coils in the slot,
so it is necessary to consider some of the combinations
separately.

Before taking up the séparate cases, let us first
derive the various slot constants. These constants have
been derived for A.C. practice and are in general use, in
the form as shown on Curve #91471. Our present case differs
nowever in that all conductors in the slot do not carry .
Currents in the same phase. It is the usual practice in D.C.
commutation to use the average change of current per conductor
for all the conductors in the slot, which makes it possible
to use the A.C. constant. This is the practical way of
Ssolviing: the problem, and this method will be used in the
final analysis. However it is interesting to derive the
separate constants for the different conductors, and study
ent effect on the voltages.
 

Pica Pe On) ae

 

 

 

 

 

 

 

curve =4141l

Corrie yA rae eee fer i ee a eT Pe
ad ihe pet | ta’ Ca slot

u ahora kale ees
ae

ra Te Phd eed aad falar ee

 

S,
S. Cae

FIRE eS a re

Curve 12-34-47
te ya :

ee
Fig.10 shows a sample arrangement of conductors
in a slot for a two layer winding, one coil per slot.
Consider the effect of a changéng current in the tpp

conductor and the reactance voltage generated in it due to
this change.
Let ;- T= No. of cond. per coil

t= * " " in the coil below position x

= Total flux across the slot
d@ = Differential flux across the slot at x

Other symbols as per figure 10c

(1) 6 = t. . 10°" For any position x
But ;- t — 2 Therefore; t = 2Tx.

T V V
(2) ag — 3.19 t ai L ax

8

8 6
Also 6. 2 i— e2tT at

f= kab = 2nabe
(3) ag — 3.19 2T Lidi x dx

Vs at

(4) e = 3.19 4T L di x*dx

Vs 10 at

Equasion 4 gives the voltage generated in all the
conductors t'up to position x, due to the change in dg the
differential flux atnposition x. The total voltage is the
summation of all the conductors as cut by all the flux.

. 0
(5) EW 3.194 Lai | 2 3,19TL V . di
— “V's 1o8at je aX = ae Tae - 6s * at

2.

The flux across the top of the slot over length c
encircles all the conductors thus;-

(6) E— 3.19TL ,o , ai
108 s "dt
Thus the total voltage per slot equals;-
(7) E=3.19TL ,K , di x -~{Vae
108 at 6s 8

Equation 7 shows that the reactance voltage in the
top coil in the slot is determined by a constant for the
Blot shape, and varies as the rate of change in current in
that coil. From our assumption of simple commutation of
 

’
een
Sal

ey

2

. .
-
— : a ae
:
:
a | ff
oom =

 

 

 
the coil, the current reverses acording to a linear function
in a time required for the commutator to move a distance of
tb-1-p/p) bars, or a time;

t= =e

di ft BRI
dt — ¢t >

Therefore; 3.19 B Rel 72
t= 10°. -b “AKI

In a similar way the slot constants may be i
determined for the other conditions as shown in Figs. 10c to
10f. In these figures at the right side are shown values
of flux density acréss the slot. The first diagram shows the
actual flux density across the slot, and the area the total
flux. The second diagram represents the effective flux which
is effective in produceing a voltage in the conductors. fhe
area of this curve represents the effective flux which would
encircle all the conductors in the coil and give the correct
voltage.

| Fig. 11 shows the space current curve and the
self induced voltage curve for any conductor, over a pole
pitch, or from brush to brush. Over the greater portion of
the space the current remains constant and no voltage is
generated. With a straight line corrent change, the voltage
jumps immediately to full value and remains at that value
overthe commutating zone for that conductor, as shown in the
figure.
CASE I. Fig. 12 shows a multiple winding full pithh one
coil per slot. We are interested in d&termining the reactance
voltage generated in the coil (M) ( cond.#1 and comd. #(y#1))
due to self induction and due to the mutual induction of coil
(A) and (3%). An inspection of the position of the brushes
with respect to the bars connected to the three coils, shows
that they all commutate at the same time, thus the currents
all reverse in the phase, as shown in Fig l2a, and are of
equal value.( assumeing equal brush area and contact reststance)

Cond.#1 is in the pop of the slot, thus its voltage comes’ |
under Fig.10c, and has a small value; cond.#(y+t1) in the
bottom of the slot acording to Fig.10d has the largest value.

The effect of cond#2 on #1, and of cond.#y on #y+1) follow
acording to Figs. 10e and 10f respectively. These voltages
are plotteai in Fig.12b showing a sudden rise in value, the
instant bars#l and #2 are shortcircuited, and fall to zero
&8 soon as the leave the brush.

17
 

 

 

 

Bet

.
“a, ,

5

 

 
W
7
x

 

as

 

 

A p

fe ha a

| ca} “
Dt Geer 1
7. 5
5 teat

es
Sua
"hates
Pee

 

 

 

 

 

 

 

 

ieee

 

Pit,
Ve
ee
pene
nim a

-

 

PIE =
hn!
ea
> ye Se
 

 

tee

 

 

 

  

Magpie Beg, agen ee, a Eee ie

'
ws

   

     

wit gone

eee
\odeal

LM

 

  

 

            

WW
SS
SS

  

 
CASE LIL Fig. 13 shows a multiple winding, one coil per
slot, but with a short throw. The reactance voltage of self-
induction in the coil (M) is the same as in Case I. Due to
the chording of the winding, coil (A) commutates before coil
(M),and coil (X) later. Thus the currents in cond.#2 starts

vars before cond.#1 and generates a voltage in #1 as
sHown in Fig.l13a. The voltage in cond.#(y+1) due to cond #y
starts 2°Y bars later. Fig.13b shows the summation or the
total voltage wave in coil (M). It will be noted that in
this case the wave has the same maximum value, but is spread
out and stepped so there is not such a sudden change. fhe
voltage wave is wider than the short circuit zone of the coil
so there is a certain definite voltage in the coil when the
short circuit condition begins and when it ends.

CASE II = IV’. A multiple winding with several coils per slot
full pitch, and chorded. These two conditions are much
@like and can be treated together. Fig. 14 shows a winding
@eccording to case IV. Consideration of coils (A), (M) and (X)
show a case II relation, and from Fig.13 will give voltages in
coil (M) as shown in 14a. Coils (B), (N) and (Y) have the
same relation, but in each instanee commutate one bar later
thus giging a voltage relation as shown in 14b. Cond #1
and #3 are located in slot #1 side by side, so that the#flux
across the slot due to either cond.will cut similar portions
of the other, thus generateing the same voltage in each.

The above applies also to cond.#(y+1l) and #(y+3). The
flux due to cond #4 cuts cond #1 in the same manner as it
does cond #2, thus the voltage in either coil (M) or (N) is
equal to the sum of l4a and 14b giving a voltage wave as
shown in l4c. Note that coil (M) has a low voltage at the
start of the short circuit zone, and high at Bhe end. The
reverse is true for coil (N).

CASE V Two circuit winding one coil per slot. The conditions
with a two circuit winding are much more complicated than

for a multiple type. Let us consider first the slot reactance
voltage for one coil, say coil (M) Fig. 15. This coil bears

on brush #1 and #3, which are at the same potential and are
connected so it is possible for a short circuit to flow.

The current from brush #1 reversing in the circuit thru
coils (M) and (Y), causes a current reversal curve as shown
in 15a ( use this phase position as a reference.) This
current flowing thru (M) generates a voltage in cond. #1 and
#(Y41) by self induction as shown in e, Fig 15e. Brush #3
also feeds in the cuirraht which flows thru coil (M); this
current is (1-2W) bars ahead of that from brush #1, and

enerates the voltage e, in the conds. #1 and #(y+1). Brush
4 feeds in current in coil (A) and coil (R) which current
in cond #y generates es in cond.#(y}1). This voltage is
(1-3Y) bars earlier than brush #1. Brush #4 also feeds coil
(B) cond.#2 and generates eq, in cond.#1, which is 3W later
than the reference

2/
 

 

 

 

              

7 |
Pe ee

j

A

we eG | Ree) za rare | rr) eae

Ne ee

 

fig 15

 

 

 

 

 

 

 

Sean ae de

 

’
~
|

ei me

 

 

orn y

 

 
 

 

 

t

if

2 i
A
be i

aa Short ate y oe

 

 
The summation ofm these individual voltages, as shown in

15f gives the total fof the coil (M). Brush #2 alsé feeds

coil (R) and (B), conds. #(y¢1l) and #2, thus generating: a
voltage in cond #(y#1) and #1. This voltage isWbars later
than the reference and is shown in 15c as esThe reactance
voatage in coil (M) between brushes #1 and #3 is thus the
sum as shown in 15f. The total voltage from bar #1 thru
coil (M) and (Y) to bar #2, may be obtatned by adding the
voltage of the two coils in their correct phase relation, in
this case 2Wbars as shown in Fig.16. It will be noted
that this gives an unsymetrical voltage wave shape due to
the different voltage values for the conductors in the top
and in the bottom of the slots.

We have shown in Case V the general method of
obtaining the voltage wave for a two circuit winding. The
case of several coils pgr slot, or a larger number of poles
complicates the analysis still more, and will not be given
here. The method of analysis outlined above is interesting
in so far as it shows the actual voltages per bar, and the
relative size of the steps in the wave. From the work so far
we may conclude that any increase in the circuits, as for
several coils per slot, or more poles and brushes, will :
increase the number of steps in the wave and the relative
size of the steps is of less importance. On account of the
complication a simpler method will now be developed, one that
may easily be applied in every day design calculations.

Let us start with the assumption that all cond.
in the slot, hold the same position, i.e. each one occupies the
whole copper space in the slot, but carries its own current.

This assumption allows the use of the standard A.C. slot
constants as given on curve #91471, in our voltage formula,
and obtain the average voltage for the different positions.

We have previously determined the rate of change of the
total amp. turns in the slot ( Fig.9 ). The voltage generated
in the conductors is thus preportional to the differential
of this curve, and the conductors in series. An easier
way to arrive at the same curve is to build it up separately
step by step first obtaining the voltage per step by;-

_ 3.19 B Rs L Tr,
z= “Tor tr & I

_--#dg.19 gshogs the steps to be followed, and is of a purely
general nature. It is well to choose some some scale and
lay off the first wave,,the height proportional to the
voltage induced by the current in one conductor, from one
brush. Fig. 17A illustrates this case for a two circuit
winding four pole with four brush arms, with current from two
erushessn feeding into the shaded conductor

24
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 
 

 

 

 

sas Ud A le

ewe Wave
Pa 0

Te ae ee sat

tte Cond (y+) a

 

 

for Cond * rs PDE Se £

 

ia Cond be 0) “ae |

 

‘ 2
Ls

 

Nr Vewetinec icon a
wave Afton bar] te
bar * 2 eM oe

 
 

 

 

 

 
Fig. 17 B shows a similar condition for the adjacent
conductor, which however starts one bar later. 17C shows
A and B combined giving the voltage zenerated in one conductor
due to the current in both top conductors. D shows a similar
wave for the two bottom conductors, note the phase difference
is W bars later. The voltage in one conductor due to the
combined current in the slot is given in Fig.17E. This
voltage is generated in each circuit in the slot.
The voltage per coil is made up of that for several
conductors in series, depending upon the type of winding.
Refering to the multiple type Fig 12 and 13, the voltage in
Coil (M) is the sum of that for conds. #1 and #(y41). Altho
these conductors are in separate slots, they will have equal
voltages generated in them, but not necessarily in phase,
Inspection of Fig.12 shows that slot #1 and #X commutate
in phase, so the total voltage per coil is double that for
one conductor, as determined acording to the method outlined in
Fig.17. With a chorded winding as in Fig. 13 slot #X
commutates py bars later so it is necessary to combine two
voltages as' obtained for ons slot YW bars apart in phase.
In the two circuit winding as shown in Fig. 15
the voltage per bar is the summation of the waves for conds.
#1; #ly¢i); #2(y+1); #2(y41)41 and #3(y41)42, each ina
separate slot and each commutating YW bars apart. It is thus |
necessary to combine p separate voltage waves as obtained
in Fig.17 each Y bars apart giving a resultant wave as in
Fig. 18. |
According to the usual types of windings with
several coils fer stot, the conductors in the same sircuit
hold similar positions in the slots. Since all conductors in
the same slot have the same voittage, it follows that there
m. circuits having the same voltage in each, not only in
respect to shape and magnitude but also in phase. However
their short circuit periods are not the same, there being
respectively one bar apart. This point will be teken up more
in detail later on. .
It is well to note at this time that chording has
the effect of lengthening out the commutating zone, giving a
broader and flater wave shape, also more nearly a sine shape
if it is not carried to the extreme.
A large number of cases were pdtotted varying the
different factors, and it was found that for the practical
limits ‘the variation from a sine was not very great/

 

% The writer knows of only two cases, which are ex
exceptions. one a special D.C. winding for a large generator,
and an experimental A.C. serités railway motor. These windinge
had special cross connections from front to rear, and gave
twice as many circuits as poles. or + turn per bar.
TOOTH TIP LEAKACH

There is unotner leskage flux to be considered,
and thst is the fringing “lux over the tooth tips from
slot to slot ¢s shown ia ig. 19. This flux is produced
by the slot cmp. turns, that is the same excitation which
produces the slot flux, in fact, this part may be consi-
dered &s an edditioneal slot flux, for the nert of the in-
terpoler space not under the interpole. From Fis. 19 it
will be seen thet, there cre two peths for the flux to
follow, one part from tip to tip and down into the iron,
end another entirely through the air, the division de-
pending upon the reletive reluctance of the peths. The
flux méy be approximately calculated by assuming semi-
ecirculer flux peths as in Sig. 20. When the psth down
into the next tootr hecomes longer than,the peth stréight
across, the flux vill continue in the sir gep. This
point is reached when:-

t
Tete tet e
t

Ore FT Fa

It is thus necessary to determine the flux
separetely for each path.

d
df= 2.19 mI L pepe

7
= d
f = 3.19 mI %, L | fhe

 

 

Oo
3.19 mI Ye L (3
w= a @ m Lo x loge a
WT
or f = 2£.564 mI tL y, log (-t)
S
ALlEOo- ax
d = 2,19 mIT, L
fr C wx + 5S +i
Pp Pe
t
26.38 mI TT, L dx

 

+ Wx*+ees + Tt

2 £207 tt }
Y} - 628m IT, loge (E07 tts)

 

28
 

 

 

 

 
 

)
P 24.68 mITEL log (ec - #)

Trere fore p + PD = p

I S_
p = 3.19m IT, L x .732 [roe = + 2 log (2-3)

 

G

X =20f a)
10 «I

.
ao 2 R +(e
a £0.02 f _ To L x 73] 108 a + z lor (2 =)
LO
The ebove form is r-ther cumbersome, so by

plotting the curve for velues of rE over the usual r-nge,

it wes found th-t ea simpler form could be used which is
very nearly equivalent, being about 6{: higher, or:-

P
73 | 10@ ct + 2 108 (2 - $)]- sol

“hus

L P |
so x /at-F il

 

* We have the ecuesiogs in the usual form for re-
naetance. So we may sevarate - 1 and use it es e part
of the slot constant. for non-interpolar muchines this

may be directly incorporéeted in the slot constént, before
plotting the slot voltage curves.

Mor ioterpolar mechines, it aprlies only to the
part of the ermature not covered by the interpole co had
better be calculated seperetely.

* This tooth tip leakage apzears also on 4.C. Gener-

ators incressing the slot reectence in the interpoler space.

The writer hes used this constant successfully on these types
of méchines.

30
 

ZIG GAG LAAKAGE

Thisleskereis only found in Comnutating pole
muchines «nd is, in fact, 2 modification of the tooth tip
leakage. The effect of having a commutating pole, is to
reduce the reluctance of the tooth tip path, and allow
more flux. This circuit can be sonsidered as shown in
Wig. 21, with the equivalent air pap under the commutating
pole, and the slots closed.

Sor any slot, the flux can thus pass into the
pole on one side, as &rea x Sig. 21, and return through
the area P-x. Tne Permeance of the circuit considering .
air path only is thus:-

P = O19 la = 3,19 (Px-x* ) Lg
Golo + ps] Fe

ror the flux encirclins the slot

P = 3.19 mIT, ly L{ex-x* )

PG

 

According to tne eyuasion for Permeance, the flux
wave will be zero under each tip of the Aux. pole, end a maxi-
mum at the center. The Permeance curve is shown in Pig. 224.
It will be noted et once that the shape is similar to a sine
curve, comps&rison shows about 5% variation. We my thus
assume a Sine shape over the entire comnutsting zone, to take
care of fringing; having a maximum:

PL
max = 3.19 rt. = SP he
© = .8P Le Sine
Ge

It has been determined above that the slot amp.
turns, very approximetely &s a eosine wave over the zone.

Thus :-

ITTtTenmil1iT cos ©

Therefore:

Pp = ~8 Pp IT, m Ly sin O Cos O
Ge

 
 
 

ieee ae cechomma:
VSP PEE een tienen

\
RS ee Ge RR eee
-

 

N Aw

 

AAO eid Lk hed
.

‘

ee Le hd

SMALL EA

 

 

BRC ES

 

 

 

 

 

 

 

 

 

 

 

 
 
 

 

 

 

 

 

ve therefore lieve « flux wave of double the cur-
rent frequency having @ complete cycle over the connutating
zone.

To d(¢, Sin 2 ut)

 

 

 

 

 

 

e€ —&

108 dt

_ 2 4 P Imig hs , 2w(- Cos 2 ot)

108 Se

But w ¢ 21 f = £& T Bis
Zz Z
C3 - £€.5 P Im r L
bse Cc ~a Cos 2 Bhg t
8
10 GC, Zz

n T
4 ex = -~ £.5 P mM C Lia I

 

6
10° G,

“ig. ££) shows the final voltage wave over the
commutating zone, the full lines are the mathematical val-
ues. However, there is considerable fringing flux so the
curves will be modified more nearly like the dotted curves.

A voltage of the value ss just determined, will
be generated in each coil in the slot. The total voltage
per bar may be determined by adiing the voltages for each
conductor in the circuit, at its proper amplitude end nhase
relation, as has been discussed under slot voltage.

The above investigation of the dig dag leakage
Shows thst the commnutsting pole air gap is the governing
factor. In order to make this leakage small, tne sir gep
should be large. Practice has snown that it is necessary
to have large Aux.pole gaps and 4 stiff field for success-

ful commutation. In fact, this investig: tion wes proceeded

33
by the writer's attempts to build mchines vith very small
interpole gaps, which resulted in bad commutetion even with
careful adjustment of the excitation. This applies more
especially to mchines ébove 75 H.?P.

TNPUUPOLAR RLUA

In non-conmmutating pole machines and in the inter-
polar space not covered by interpoles, there is e certain
amount of fringing flux from the main poles and the yoke, as
Shown in Tis. f3a.

* The flux over the commutsting zone is due mainly
to the armsture excitation which mgnitizes salons the inter-
polar axis. Usually this flux is small on account of the
high reluctance of the path, however, it is lerge enough to
necessitate calculating.

Pig. 23B csiuows the man and armature fields plotted
seperately for a pole pitch. The effect of the high reluct-
ance of the interpolar peth is at once evident due to the
smell flux densely at the cammutating zone. Fig. 23C Shows
the total interpolar flux for both fields. The best wy to
obtain values for this field, is to plot the complete full
load field form the s: me as for the saturation curve plotting
armature surface to flux deity in the air gap. From this
field form can be obtsined the correct shifting of the
brushes for & non-comnutating pole machine, and the inter-
polar voltage for the space not occupied by the commutating
pole.

The voltage may be obtained for the various positions

by:-
ee TD Rg L, Te 10° @
There D = «.rmature Diameter. -
L,«s length of arm:ture not covered by the
intervole. |
Q - *lux density in lines per 5g. inch.

“In &. C. comuutetes motors, Hepulsion #ad Compensated
series tyres, the interpobar flux path hes & low reluctsnce and,
if proper cire is not tered in adjusting the compons: ting fields
and choosing the arm:.ture wiading combinetiouc co es to comnen-
sate at this point, & prohibitative internolar flux will result,
eceoucing bead comsutation due to its ovn mesnitude.

34
 

 

 

 

Mees?

EY

  

a

   

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

a) te A a Pl
Cou cd abe

 

 
*his voltege should be celculated for ell the conductors
in the circuit under considerétion, end comtined in their

recpective phése positions.
Mud COTS RACTALCS VOLTAGS.

The armature end windings are carrying current
and produce a field having sir paths somewhat similar to
the main armature field. Fig. £44, shows a sketch of the
end windings, full pitch, of a D.Q.arnature. The shaded
coils represent thors vhich ere commutating, the ones in
which we wish to determine the voltage.

In order to determine the field through which
these coils are passing, let us assume the winding to be
spread out so 6s to five & continuous current sheet, as
represented in Fig. 245. First consider the straight part
of the coil a or 5 in which the throw is the same as in the
core. The current shea is in the form of a rectangular
wave one cycle per pair of poles, thus-.--

i= f(d+e)

Taking XX' as a reference plane, consider the
flux at point Z2Z' « distance d& sway. The point ZzZ' is
acted upon by 411 the current elements over several nole
pitches. The current element 2 causes a field at Z pro-
vortional to the current and the nermeance. ‘The flux
Qirectly at 4 depends upon the'summationof all the cur-
rent elements.

Let 1 = Current rer inch.
K w Ratio of inches to Sadians.
d9 - Increment of anguler dist&nces.
Kd 9 = " " line&r " °
1kd Oe " " current = di
I = Maximum current rer inch.

~ Of

(dr0)do

 

_ 3 2 ~ (oust f'(440) K d@ TF
(3, ~ 27T Ke Werke 2

JtPrt 3) tf

From the Yourier wveries ve my obtain the evcuesion .
for & rectangular wave, or, -

f'(4+0) - 4 [ in (Avo) +S sin 3 (a4+6) + F ~inos(ar@)...|

36
 

Pers;

ae. Ae

‘

 

 

.

ed

 

 

o-

 

 

   

 

 

 

 

 

 

 

 

 

 
 

Thnerefore:- - 0 ~
| El} sink Cos@dO 4yCosd win dO 4

 

 

 

 

GQ = 97 =
* of +00
— oo . |
Cin 3a Cos 26d38 + Cos Sin 26 d38 - ----
3 30 z= 5°
+ of ~
(3 =e2tl ( Cos d+ 1/3 Cos Sh 41/5 Cos 5¢@ + ------- )

This equation fives a rather neaked flux density dis-
tribution, over as pole pitch &s sho.n in fig. €4C. tnis
curve is with the Sssumption of instant&neous current rever-
sal at the commutation zone, as per the solid lines while
actusl conditions are more nearl7 &S shovn by the dotted
lines. ‘This will also change the flux density et thet
point, by cutting off the peak of the wave, making it more
nearly triangular in sheve. The mex density over the short
circuited coil is thus vhen

d- O or:-

(3, = 4 I approx.

tne voltsxce ror the streight nert or tue coil ecusls:-
-8

s # 47 bp ig (atE) 10 Tol

“or the Slant néart of the coil, the winiine my be
considered s&s being chorded, tie throw varying from full pitch
<=t the straight pert to zero pitch ét tne tips. The field
strength will decretzse towards the tip of tne coil, upproxi-
mately in s direct prorortion the field form becoming flet
topnved, &@Ss shown in Tig. £40 (a bc & d ). The short circuited
coil M is chorded towards the tip so cuts a different pert of
the field for successive positions away from the core. ‘hus
the voltege generated in the slant part of the coil will vary

from that for tie straight part, to zero, ena the averc:o¢g will
1)

rz
eC
ab

ake
be for & Length @ h, or the totel voltage for tle corlete eid
Tine ings both clues «o* tir © te will be,
v° ty 2 -6 4
Ye 4T7Dig (At+Bth) 10 os I
This voltage may be considered as nraectically constant over

the commutetion zone and my be now added to the other nerts
es found ebove.

By tne formula and methods outlined above, it is possi-
ble to obtsin « feir ide of the reactance voltage per bar and
the variations over @ cycle. In & commutating pole machine,
this volt:ge is not a@véiluble to drive snort circuit current
through the brusn, for the commutating nole is placed et such
& position as to produce a field which will generate in this
Circuit a counter voltige which will just belénce or kill the
rea etéuce voltage. “or tne study of this circuit see Unenter

Oe

33
Wry rs

CrP pte dust due

C C Oi US £V1 Lay G P be C I2.CU [2 e

A¥ter having determined the shape end value of
the re&ctance voltafre wave, the next step is to find the
correct shape and value of "the comautating nole flux which
will generete s counter voltere, in the short circuited
coil. Knoving the Bu... per bar, the «ux pole flux den-
sity equals:-

a - x 10°
x |

TDR. To le &

 

when wpe weaictéice volts per bur.
oer ho can oF &ux pole.

g= no sux poles aifecting the circuit.
a. aux pole air Gen Den.

whe above formulé applies strictly only where the
vindinge is full pitch und Woe. O, &nd the aumber aux poles
equals the number main poles. In this case the aux,pole
compensating volteges generated in each conductor under the
successive aux poles,wili Le in phase, und the aux, pole flux
for any one pole need. generate & compensating voltage only
for the conductors under it. From this it is evident, that

it is only necessary to obtain the reactance voltage wave E
per conductor inste@d of per circuit, or:

B= z, 108
~ TD ks tq deg

 

The same generel reasoning is true for a chorded winding,
(See Fig. 26). where the conductors cutting the succesive
AUX. pole fields do not do so in phase. The compensating
wave is the sum of the several compenset ing voltages per
conductor, combined in their proper phese relations. as
with a full pitch, winding it is not necessery to determine
the complete voltage weve per circuit, for, if this is done,
the Aux, field form so obtsined must be separated into the
individual pole values which, when combined, will give this
resultant field.

we thus find thet we cén short circuit some of
our work in determining the Aux flux for the cases where
the sux poles equél the méin poles, either multiple or two-
circuit winding.

40
 

 

 

 

 

 

 
 

 

 

 

The method, &s outlined &bove, has been in use
for sometime and hes been very successful. Hovever, it has
also been spnlied incorrectly to the cases where the Aux
poles equals helf tne number of main poles and the winding
Chorded. The writer found considerable vsriation and un-
looked for results in these cases, so the following theory
was developed.

It is clearly evident that for a full nitch wind-
ing, the reactance voltége rer bur zone is no wider than for
One conductor, but has twice the emplitude, so the first
method may be used end tne resulting flux doubled. Fig. 27
Shows the case of & multiple winding cnorded. Here the vol-
tages for the two conductors ere out of phase and the reac-
tance voltage wave per har hés @ zoneW bars wider than for
the single conductor. Yor correct compensation, this must
be neutralized at all positions, so the one aux field must
be wide enough and strong enough to generéte this compen-
sating voltage in the one conductor. according to this, tke
Aux field must be wider than for & single conductor, or:-

Qa. = 4, 108
* ip ts Te La

 

Thus, for the same ermture winding, the Aux pole must not

only carry double the flux but must also be thicker to give
@ wider field.

The two circuit winding is very similar and is shown
in Fig. 28. Coils Mand Y each have a commutating pole so each
will be compensated separately, thus, for determining the Aux
flux, only one coil need be considered. In this respect the
total reactance voltage wave for the two conductors should be

found and a aux pole field form found to compensate for this
shape.

There is one other case that might be mentioned ,and,
that is, where one auxpole can be used for a two circuit wind-
ing with one set of brushes end any number of main poles. With
this arrangement, the one Aux pole must compensate for the conm-
plete circuit from brush to brush. Knowing the required Aux
field, the next step is to determine the correct shape of pole
to give that field or @s close as possible.

Probably the best method is to assume several pole
bevels and air gaps and ptot a field form and compare its shape
with the required field form. In this way a close approximate-
ion can easily be obtained. kKnowins the recuired Maximum flux

density and the equivalent air gap at thet point, the gep amp.
turns can be obtained.

I T O13 (2. max CG.

42.
- ll -

Obtaining the averege flux density under the Aux pole,and
thé gap &rea, the total useful aux flux can be obtained.

Fig £9 & and B, show the Aux pole field form and
pole bevel. or successful operations, there must be no sat-
uration in eny of the iron parts at this point, so the method
outlined above is correct. fig. £9 E, shows slso the fring-
ing of the main field. This combines with the sux field
and distorts it to the shape &s shown in Pig. 29 ©. It will
be seen that one pert of the Aux field is now reversed and
will generate a voltege in the short circuited coil in the
same direction as the reactance voltage instead of opnosing
it. The other side of the field will be too strong and cause
Girculating currents in the opposite direction. The dotted
curve in Fig. 29 c shows the required field for correct com-
pensation they should coincide, this is not possible so the
best compromise must found, which is when

(3, = Os. °

This brings out &n important consideration in bevel-
ing the aux pole. It is not always best to try and mke the
aux field elone, &s shown in B, conform to the required shape,
for with a strong main field, Q, may be too large and if the
Aux field is strengthened to decrease it, (3, Will be increased
beyond the limits. In this case it is better to use a wider
pole with a field form considerably wider than that required.
This will decrease (3, and will increase (3, , but not in so great
a proportion, but that the maximum value of (3 or Q, c&n be
decreased and made more nearly equal.

sometimes it is elso better to increase the total
iux field strength, so that @. is *oo strong, also, by; so do-
ing @, m&y be decreased to within, the limits.

This effect of distortion of the aux field by the
main field is very mrked, in practice. The writer first
noticed it when building a 200 KW 230 Volt 900 RPM Generator.
The Aux poles were first beveled to fit the required field
form, but the machine would not cammutate with any adjustment
of the aux field strength. afterwards, new poles were made
with very little bevel aid commutation was very satisfactory.

The writer also has noticed that adjustable speed
motors, that would commutate well at high speed, say 1600 NPM,
with &@ very weak main field, would not commutate et low speed
400 RPM, even with boosted aux field. This is clearly a case
of aux field distortion, for the distortion is only present
to any extent at low speed. It is at once evident that con-
dition could be bettered ty beveling the aux pole different
on each side, as shown in Pig. 30 & Fig. 30 c, shows that
Q,» and >, c&n be greetly reduced.
 

 

 

 

      

 

See hee

Petey SS. Sh a

 

 

 

 

 

eld,

nis es
ot) aaa]

a
‘4
'

 

 

 

 

 

 
The writer knows of one machine in which this vas
done, @ lerge high speed generator, which could be made to
commutate in no other wey. Tnis is not general practice
and is not very practical, for the nmAachine is no longer re-
versibdle.

anotiner metrod of bettering conditions end decreas-
ing (2, , would be to shift the brushes, slightly, so us to suke
the required commiteting field more nearly coincide with the
actual field. as before, cure must be exercised so as not to

unduely increuse (3,.

The space between the min pole tips end the aux
pole is usuelly sm&ll and since the exciting amp. turns on
the aux pole is slso large, there will be considerable leak-
age, to the aux pole from the tips. It is important to de-
termine this leekage flux to some degree of accuracy, how-
ever, it is not importent enough to warrant detailed calcu-
lations. An aprproximite vélue can be obtained by consider-
ing the aux excitations elone, &s show in tig. 31. Assume
the Aux amp. turns about 50% stronger then the armature amp

turns.

Approx. = 1.5 x _W x I per Cond.
p

With this value for excitation, the leakage flux
may be determined for tie paths, as shown in “ig. G1. ‘lost
of tire leukége is ¢t tre tins, &S shown,although there is a
Gert&in emount frea weia weole te auc gobs Obi the
VO wie Yo..c, hovever, it decreuses fest, for the excitstion
is decreasing and the reluctance incressing. To the useful
Ux flux must be now cdded tre aux leske ze Tlux und the
saturation for the eux pole calculeted for their scum. In
designing © new vechine it is importént to m&ke this calcu-
lation, for tne Sux pole must not be saturated for success-
ful overation, the ux density should be kept well below
the knee of the curve. The leakage flux y%,° in average
machines will run. from 200%. to 300% or gy , and increases
towerds the yoke, so the pole may be good for the flux near
the armature, tut not «t the yoke. This point should alweys

be checxed.

Voy becu

In practice, the pole is often made larger near the
yoke, to decresse saturation, end the aux coil as near the
arm ture &S nossible, to decretse letkere. This is the prec-
tice in roteries, aul in some high voltege generators, built
to withstand short circuit.

tne writer also used « tapered sux pole on & Series

Crane motor vhere the m teri&l was worked very herd. The
general idea is shown in Fig. Se.

4S
 

 

 

   

ee ee

 

CO ar a en eer er ee
’

ar rt ei

 

a ae
Ps i Paty a %
vee 6 ek Pi

       
 

- a
i oo

 

 

 

 
~13-

Hhéeving ané&lyzed tie re th of the Interpole flux
for the teeth, «ir gap and tne Interpole itself, we find
that there is still enother rert of the circuit, the yoke.
Besides carrying the interpolar flux ga. end Interpole
leakage Qi. , it also cerries the m:in flux, which great-
ly complicates the anslysis. Let us first consider the
Simplest case tiat of the séme number of main and inter-
polar, as showvm in Fig. 83. In the figure, the exciting
amp turns and the several flux petns are shown in anproxi-
mately the correct relstions. It will be noted that the
different parts of the yoke carry different values of
flux, the interpolér flux tending to increase or reduce
the magnetic density. With €@ shunt machine, it is thus
evident that the yoke carries & uniform flux ena R= Ge ; ;
under load the interpole flux will @imwide approximately,
half going each wey, which mexes @Q > q, or

p, - P, = f. +4.

In order to determine the extra excitation to put on the
interpole, let us plot the curve 2s in Vig. 34 for the
yoke circuit from X to Y' or # pole pitch. Plot the
curve total 1T for this section against total flux in
this section. or tne interpole circuig&, the path is each
way, XYX' and xXY'X', Sip. 34 gives us the condition
for half of this circuit, so we need to combine the amp
turns for two sections at there corresponding flux values
On essumption thst half the interpole flux goes each way,
measure on the curve the point Po + Y,. which is the
yoke flux with no main field. Assuming
again that the min flux divides nei? eéch wey, it is
noted that the flux in section XYf' is increased sn amount
+ J. giving a flux @% as shown on the curve, requiring
— Bg 1T, to produce it. In section Y'X' the
main flux is in opposition to the interpole flux énd is
larger, so the direction is actuzlly changed; this is
shown on the curve, giving # as the flux in the section
requiring lily in the orposite direction. The curve shows
that in section X Y', due to the mein flux 1T, , more is
required in order to get @ed, trough the cirauit, while
for circuit Z'X' the flux ¢?, is in the reverse direction,
and relative to the entire circuit 2 Y' X'; the amp turns
1T> are not s megnetic drop with respect to Ga Feu , thus
the total drop in the circuit xX Y'X' is the difference
1T, - 1%g. This excitation must be pléced upon the inter-
poles in order to force the flux through.

It is easily seen tnat when the yoke cirzuit is
not satureted, there are no internole emp turns to be added.

In this line it is well to mention, et thic time,
the effect of the interpolar flux on the miin pole saturation.
 

 
 

#

=

Tl aac oe

o
2

.
5

SS a.
“=

bs

a

  

om Bie

 

 
     

ae
> ~

Raat sort yremec)

3 <

     

 

mR gu Mz
ie ui

|

SeLaeiiiintiednacene imaabeneiiea

  

)

 

“Date ot ee”

™
This ecireuvit is Y xX ¥', we use the seme seturetion curye as
for the interpole cirmit; «sscume the min flux QyrtG% to
divide ecuelly and 187 off the position Gn + D, and pro-
ceed ins similar mnner as above to 2 increz.se
reth X Y' and decreese rath X YY @. emount equel to o, ¢
which gives the position Q, and @,vhich coincide 2
with the values found from tne internole circuit analyses.
From the curve it wes found treat with no interpolar flux 1T
amp turns are required per nalf circuit and the circuits are
ecuel. Thus, the iU.L. main field &mp turn required ¢re ¢€ 17s.
Hovever, for full internole field, een circuit reyuires é
different émount, or &@ totsl of LT, +r lte. tre amount of
increaced excitation recuired is tnus:-

1T = 1T,+i1te - 2 1Ts,

GQ)

Cc.

Tie armature core part of tne circuit holds & simi-
ler relation to tiet of the yoke except tir t it does not
carry the leakage fluxes. Tre excitstion for the core can
thus be trested in the s&me manner €s outlined above, except

uniting leakége fluxes.

mrs

wre y Nv TTS se) _ rN ™ _" . a - ; 7 pe: .- MAT.
Oi Cm td tots TaaiG + QL. ~ tat PL. Ik O - T

4
ae ew hat on Sod

The more common practice on sm&ll motors is to use
half &s meay commuteting poles as min poles, this case,
makes the distribution of the main and comnut: ting pole flux-
es much more complicated.

Sie. 35, shows &n aprroximte distribution of these
fluxes. The first importeat differeuce is that it is no long-
er correct to essume that Pra +d, geoes in each yoke ré€tn,
for there is seturstion L due to the intermole (tlux
in one peth and not in the other. Ey a more or less eut fund
ry method this distribution can be determined. Drew the
saturation curve for the joke, Fig. 36, in © similsr mnuaer
to “ig. 34. -.Siume tnat Dr + does go ecually in exch
Side ofthe ore, and 1lsy & off tris roint on tne
curve which gives 17,.. “@ xnow that circuit Y X'Y"' does
carry more flux, so a@s:ume a certeéin increése ind ley off the
flux giving qm énd 1lTy amp turns corresponding. Aow in or-
der tiret Ard, renéin consteat the path Y X I' must Lave
less flux, so reduce this €n euyuel velue so that this circuit

 

has aneverage of QO +H . Using this value of ‘lux_as
= sterting point, “ circuit & “£' carries +
«15090, s9 snould be incressed this ainount 2

x ff should

giving thus d, ana 1t,. In the sume menner circuit X
be redueed « like «mount fivineg P, End 1Te . ‘the drop euch
weg must be tne same from f£ to £'. ‘Vie sterted witn the drop
Lor Pp, equcel to eg lity , tuus the dropfor the otuer circuit
~

4

comes 1m

.

a ae
= +,
RRL en

ee Tae in

rs

cA

<

ae
ie

 
must be tie ¢fmne, or:

17, + 1%, «c € td or the constructirn ‘may be

done frunniely as shorn. If tunis is not true the original
ASE Sumptions were. inept rast and must be modified to give
ditferent values th, , and q. ° “rom the deta now at

nend it is nogsible to en&lyce tne other virts of tne cir-
cuits comuon to both fluxes.

b+ = &+9,
Pu. * p, N+ Pe
~ -h= Arh.

P+ —$n,+ In 4 f= + ds +q,

similsrity to tne first case, it is found to re-

 

quire:
Aux Pole ivy = if, - lt,
iwi: in Lkole 1f -

 

1, + If — 1%,
&

“he agnélysis for the srusture core follows in the sume way,
omitting the le kages.

with the érranrement, eos per Sig. 35, the &ux flux
has to return through the teeth méin Sir gép and wwin poles,
so extra excitetion is required to drive the flux through at
the higher density.

Fig. 57, Shows tie saturation curve for the main
air gap and teeth, also the full load tooth curve, te king
account of distortion. leke GY, on tne tgoth curve giving
LT, the full load amp turns required for %,witn no &ux poles.
The aux flux y, divides nalf going to e&ch pole m&king the
flux in e&ch nole resnectively $,, and d,. requiring liy,a4-.d

“10g. |
the Aux nole thus recuires:-

iT =- (it.

,
id) Ila
toe Iiisin vole recuires:-

1T = lin, + itm, se LTm On each nole.,

 

o
oe
[It will te noted that for the ~-n ond teeth, the
lesxége fluxes were not considered for they do not so through
This pert of the circuit.

S/
The mia pole seturetion is to be considered in
the séme ménner, hovever, in tnis case Loth leakege fluxes
Should be used.

neving determined the excitation required to
Grive the 4ux flux 4 end the leskaere, GY, Ground the aux
circuit, the next step is to determine the €ctual amp turns
necessary for the aux Coil. Compérison of Fig. 25 Gad 2d
shows that the sux flux must be in the opnosite direction
to the armsture cross field, as shown in fig. 23b. It is
thus necesssry to have sufficient emp. turns on the aux
pole to neutreé lize the armature excitation at this point,
plus enoush to drive the recuired flux around the magnet io
circuit.

Pig. 26 chows the ¢«rmature emp. turns which must
be neutrelized. Tnus tre total amp. turns on the Aux pole
must be:-

1T -% I, x % of full piteh + IT for Aux Saturation.
Ep
where:- Wy = Tot cond. on armature.
I, = Current per cond.

Prom the required aux excitation, the actual number
of turns for the pole can easily be détermined, «nd the coils
designed.

by earrying through tre above calculation for sever-
al values of @& , an @ux pole saturation curve can be plotted
2s shown in Fig. 39. Like all s&turation curves, the flux
does not increase directly with the excitation, while the re-
actance voltage is &@ direct function of the load, (See dotted
line Fig. 39). In order to obtain the best averege condition,
it i8 necessary to over compensate at light losds, and under
compensate on overloads.

It is very luportent in the design of the aux magne-
tic circuit to keen free from saturetion or so «s to make the
ux saturation curve aes straignt as possible. It is sSometi:es
very difficult to obtain good conditions, esnecielly, on ad-
justable speed motors with @& wide speed range, for the aux
Saturation is different for the different speeds while excita-
tion remains ti.e sé&me.

52
 

 

\ P ’ Fd l
Po aT Tea a Ae OF Correct aT Teta Le

ae
Pa are are obtawed mi ‘oe

Nees

eZ
= .

eet ct

i

a

 

 

 

 

 

 
* The field should be cdjusted for fo00d comnensa-
tion et high speed where the rate of cutting is high, and
the field is weak and easily effected by shorteircuitcrcurirent
For this position tha main field is small and the common
parts of the circuit uassturated, sco the yoke excitation
required for the aux pole vill be small. However, et low
speed and full field, the yoke excitation required will
be lerge and the field will not be strong enough to pro-
duce the correct amount of flux, so the machize will be
undercompensated.

as would be expected this condition is much more
pronounced where tne aux poles equals half the main poles,
in fact, it is the practice to use the lerge number of Aux
poles for adjustable speed motors with a speed range of
over two to one. The writer tried to build three to one
and four to one ratings with four main poles and two Aux
poles but with no great success; commutation was bad, at

certain speeds &nd the speed regulation poor.

wome difficulty w&és also encountered in building
series wound crane motors, to mke them commutate on over
loads. witn the series type, the field becomes stronger
with the load wrich increases tne Aux excitation required
for the yoke very ranidly, maxing the aux saturation curves
nearly flet for over lo&éds.

The writer kas 6lso encountered seemly contradic-
tory results where the machine was over compensated at low
speed. this was finslly traced to en entirely ditferent
reason. ihe méchine had four main end aux poles end the
yoke unsaturated even at full field. .owever, the sux pole
itself wes smé&ll end the mein poles and maih pole tips pret-
ty well saturated. iat high speed the Aux pole leukege was
very high, sufficient to saturate the Aux pole body itself,
and limit the useful aux flux. «at slow sneed and full
field the méin pole snd pole tins, © rert of the Aux leék-
age path, were seturated soes to cut dom the Aux leakage
flux and sllow the correct sux useful flux.

pee wpeed herulétion of adjustable speed iotors,
by writer, slect. Journel, 1°16.

sds
1 -¢, 4 Spot
diovan LOM a wd
. c: - “ay c
: ) . ST 4 ' ’
ke Ue wi. ¥ L\ Ae ch

4 - “se
Sul Lou
' an 1it¢
ew Wi. we &

beter at fevers

Lic bluba. COLibact

Cyin,, the tisory for comutetion
ra} ter siréile te Pind
t

cr ct
' free
mn
pes
c
ae

o3
CO

a DOs.
PCs
cexs,ditiocne,
ruck, Lut
tidt tire

-

tJ.

~ .
ha Lal ‘

obey 0D
fe
MOORS
mr

c

tate
tc * ct oct

b
c
~
t
4
an
C

2 : 71-5 - . - , te - .
LELE Lit pet cured: t..c volt
7 .
abe

dojo tyes bruss shunt ond Ctl or
ctor at tne gia oF tig Urucsy, tie

‘to oarep Fron corautater to the: truc: ,
Ube Of tie Current ceéreiiy in tiie
pueciyvouit Curroi.t couesin, an

c.
sae . 4a aug. 4,8 , 4 - . 2 tf aA, . + 4 .
Curve wvVirsGilb Gere lle yvall bes 6 -€2} 2UU1 Ci Om Oj Li.u Cle VEC
4+, 0.28 - 2G.
c&Lil: VCE 2
rn, > + a o- at + . ° a e : . = 4 ' +
~ Ul ce Ren eae ay VU a Lae & 2 ue CC Le bow. ont ‘ do eiad 9
2 yp et ye aa ” - pa - Ls ’ ’ ’
Su TA Cehsao aur : Liye 4u > © Lod L dpote ve biituals yy a Lie tks
Loon Bye 4 Le tees hos eG “4 8 4 aaa ye
f2.Gedil ob. i Gls e201 Cis heed Gala SNCL Ect... turns;
. co . - . . 4 4 —— aun. 8 4. \ooncuee wey 7
pdb ef@eyn Leg evel Og hart Ci tis VLlilGl..w y vl-8 Gey CCid:
ae . Lom Prot - -~ 3 4. ae - yous ga
are tos c1ertecirciéite: coils Picts Okeke Whiucr ti.6 corrute
4 . . —— 4 4 ¢ 2 -. eae - -~5 ND . ’ c ° 4
. cleus e:faal Cleculi: waahs £ ld eee ] ix ghise asrhyo. all

c*
t
p-40

r
qu
te

c ot vo" 8 A {

ebad id ‘> @ ‘£ “eS
~ pe Sa BON -

L CG Ll \. sa Opwas aS )

+ a ft: ” ; -

or A 4S

Ail gle. 4x,

hesusd £0 ties
Ul. emcees of
tan PerccCtencse

tL, te

c..0P.-Circul

rex tds $4 7 1
veiliojsu Lticald, 81.5
Cluri wha c 1.6 Gna a eran

i
Tarecettos Of
C

Clis
. a - i v7 7 sor a
Ccoutect urcy. o aco ggvel ter tre
s a ~ . . ‘ 77 .
- - -_ @ “x ‘oe ~~" ¢ ‘ os a4 wh ( . a uv C4. vy a.

fy +. FY

“Ca. ie
relicerai voltaic will prow

. - | oe . aay . + 5 - * . 7 og s »
mn t:.6¢ €4206 : orver €c¢ tice rese

7 7 7. ner <4 > of 5 4 2 -s f' a we oes
’ . af ry. : te rol ’ > c f
OYrrcvyv&e f2.CW Lic UaPocer_icikt o Ll GES
tic ¢ + eo \ 4 ‘ ‘ C “~~ T 1 >
GC Cl bw lL u. 9 cl. A - L ) e “3 VY NM ~ + C ' t i to
~~ ~, e . e - . a . A> f oc 4 i A 4 ee ue
C Oailn 1 sac. aee - as ° Spl VY wih dba or Na . Vion

i. necuel Curpent

i
+ _, @ “ae Le CEL ,
cerntect i

Or
 

 

D
=

      

yale
P Diff erence
eet aa le

on ra th mami
se

!
}
{
1
i
t
ea
i
1
1
|

So]

*

     

| SS FR CR BS Os Se

rs ee

ors

   

oa
!
I
y
!
!
/
}
I
!

Ma

C7

 

 

a Sark Sa Pe See
¥ :

 

 

 

el Teme TL ae

Sy
x
a)
4A
s
ed
.
a

 

ameunt remrred

f)

 

 
Ss bn ~ ~~ »

zt
"4

42

ror

on

aa
.
at ot

.

ri

Ue

(CWis

we

yy
4s

Back.

welues
Oy

~. O1

”

t: >
~ de VY

one
for

vow OY

Co wla

“ss
wedi

LW
al
Lis

°

colu
LO

c
Cc.

ws

rrezmt
L

L

C

in

wer
tile

Ati

Lo
he

-
bows
Cr
wb.

Yo.’

(yg ts

a

elt
r

1

2
o~

—_

ta

iL,

fours
Cert

we
‘Ss

aH

+
r

Sy:
J ae
ro
Lu

a
“Yet
i

LE’

: é aa & ) oe 4
qi ww V 3 u aos i O u GS
at

a ..

MooLar
yh.
CURVY
> .
of da

LIC
wot

io
os

Toe
vi
A

‘le
ber
CULV

1

Q

- oy
bats fe

wh
a

istr

be
ws

S71

nM ke
Sel @1

Cc:
e €¢
yor ey
oe
r.ot.

Vis
Poe

aiPoCt

mh ew

ii?

GL

cl

wf

1 wre 4
fOV-COn
7
LEVGL tu:
ares

Cc *

“

(bo wae

Tor

~

‘ oT
nN 4 Cc oe
£.. ©
Nake
a

«4

€

CYoernrce:
CO

or
ettad
CUulVv
Ls

Lope
ws a
4

la CG

ri.
iO’

rosy

“ .
te La 4

COliu.
 
 

 

 

 
  

e belween eee
Baw Me-
ou ma

2 =,

 

 

 

 

ee

 

 

 

 

 

 
 
“
art

« 4
“2
ct.

 

°
7
*
, wf _*
n,
>
ae ,
a / a

ROOM U

Cr

aa
) =

ONLY

 

   
 
 

wi
* rs
ate oe
tty a
“tk vx :
at,

Hye

 

 
ar > 220-0
rae Srey - ey
Nee os ooo SREP BIS Cea

= ~
SEEMS SCS Dae “i mM ‘ "te roar
ts SRecihs aise: : Paes fae
+e.

oe rere _ =
p z Hy Pope

ou preomege ger we

Pete

we tsaee Rostra vared bled woes we: :
iva weneie m : bess: iit igi eos a meen rim rime EIT FLEUR,

C4 Wt dy POPS DE:

 

°

eters
er rere wares
» Pia eee eases

Sat bale hard

ae
no 4 @
+o ae

Py

 
 

- vod : ‘ ‘ : - ' :f a aye iy! : : bg , .
ta : cota eee he Bhi : tonvattr hy at :
pbibwenr end tt ‘ 1 ‘

 

eigen

: : poi a Eke ie atticid a ES
oua$ Seek gorse root spre ‘ a4 : . vee ‘ :

Perth le and

 

-

 

a fle Fes 7
ne FF Re a ae oe ee Pee Bie .
ork mad # Bm ae f Haiee # ners bf

 

 

 

 

 

 

- — . -
“
at + .
e
(
i )
1
a
«
. . ;
-
r
t
Mes
a “a
Oz
e
é
-
*
eo gee |
s c . 4
“ t
a
t
heed |
|
Lok
. , o
. < ’
ie
woe,

 
 

 

     

 

 

 

ere - en
tee rea
ra
ease PS
, : rs *
wale (APES eee SSM Me SL SSPE Meer) 5s) oS
peng ech Sac Pept AE IIe rieretaege ton 3
ad Moda d ead 34.

 

- .
rw Prine a5

i ; oe ee pp oar
{EE RHR AEP Beptig wes se EE PPS EST) ee ee EE wo NES

  

Ute amy Beat

iy xa
STs es ne E 2B,

 

 

Boite sii wane EH

ite

    

      

 

   

  

    

ak
5S Ra oe § Pega rs. na pose starr eemerte “oe ee Fe eb S43 welt
— eee oe : n vice : Diol. ee gree pores
Papeete 0-2 3 ee OTe xctene- 137 rehire *: on see qa Po) hiseele ay . Dae eee ae age reed 4x4 a5 Fe MELEE ye PE pte yee pt ag!
-satatall ie ube mpc or SE er . Bas ‘

 

 

vEMesEFOKTs oY: aot FF TP} SEB ees meres re epee rene

—e-ialtal