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A study of the electrical effects of armature eccentricity in a four-pole, lap-wound D.C. machine Smith, Donald Sinclair 1933

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STUDY OF THE ELECTRICAL EFFECTS OF AmUTUKS ECCEITTRICITY IB A 3?Oim-POIS, IAP-WOUHD D. C. HfcGHIKS by Donald S i n c l a i r Siaith xx CXJO A Thesis submitted f o r the Degree of : ~ 7-IASTER OF APPLIED SCIENCE i n the Department of ELECTRICAL ENGINEERING XX, THE UNIVERSITY OF BRITISH COLUMBIA September 1933 P R E ] ? A G E The w r i t e r wishes to acknowledge the h e l p f u l advice and encouragement o f f e r e d during the course of h i s work by Dr. H. V i c k e r s , head of the Department of Mechanical and E l e c t r i c a l Engineering. He a l s o wishes', to thank Mr* C o u l t h a r d f o r the l a r g e amount of time he g a v e , . p a r t i c u l a r l y .in helping w i t h the o s c i l -lograph- wo^k*. September 1933 "vanecuver, B. C. Donald S. Smith L S T U 3 D Y jEE E L E C T R I C A L E F F E C T S OF ARKATUKE ECCEKTPJGITY I K A FOUR-POLE, LAP-WOUIID D. C. MACHIHS One of the disadvantages of the lap-wound B. G. machine i s due to the f a c t that each of the p a r a l l e l armature paths i s unuer the i n f l u e n c e of only two adjacent poles. Thus, i f f o r any reason the f l u x i s not the same f o r a l l • tke^po-ibeB*- the -E. M. F.•s of the p a r a l l e l paths w i l l not he equal, and t h i s leads to c i r c u l a t i n g c u r r e n t s through the brushes,. I n the wave-wound machine there i s no such d i f f i c u l t y as each p a r a l l e l path i s subjected to the i n f l u e n c e of a l l the po l e s . For many types of machines, however, the lap-winding i s more s u i t a b l e , ' and i t s use has been made p o s s i b l e l a r g e l y as a r e s u l t of the i n t r o d u c t i o n of e q u a l i z i n g connections. These are connections between p o i n t s on the armature which should be at the same p o t e n t i a l , and they were developed by D r . B . G. Lamme• The a c t i o n of the c u r r e n t s which f l o w i n these connections i s s i m i l a r to th a t of the c u r r e n t s c i r c u l a t i n g through the armatures of a l t e r n a t o r s running i n p a r a l l e l > they set up M. II. F. s which, tend to e q u a l i z e the p o l a r f l u x e s * I n e q u a l i t y of the main pole f l u x e s may be due to s e v e r a l causes,, most important of which i s unequal air-gap lengths. As the reluctance of the magnetic c i r c u i t i s l a r g e l y concen-t r a t e d i n the a i r - g a p , and i n any ca.se the l a t t e r i s very s h o r t , i t takes but l i t t l e e c c e n t r i c i t y of the armature to cause con-siderable magnetic unbalance. Perfect balance i s not l i k e l y to be r e a l i z e d as there i s always the p o s s i b i l i t y of s l i g h t im-perfections i n the castings. Even i f a machine when new operates s a t i s f a c t o r i l y there i s the wear i n the bearings which, though s l i g h t , may be s u f f i c i e n t to cause bad c i r c u l a t i n g cur-rents. What has been s a i d rege.rding the use of equalizing con-nections applies to lap-windings i n general, but i t was pointed out some years ago by I>r. W. Lulofs that the four-pole machine offered a special case, and he argued that f o r i t no such con-nections were necessary. I t has been the object of t h i s thesis further to study the operation of a four-pole machine both with and without equalizing connections. Although some information regarding the action of equalizing connections on machines with a larger number of poles than four may be obtained, the general case could be studied to much better advantage on a machine with six or more poles. The machine used was a 3 K. V/. 250 v o l t , d i r e c t current generator s p e c i a l l y b u i l t f o r experimental work. On the .shaft,, and at that end remote from the commutator, are f i f t e e n s l i p -rings which are connected to tapping points on the'armature back connections. Eight of the s l i p - r i n g s are connected to four pairs of diametrically opposite points equally spaced around the armature. The four equalizing connections can then be completed by connecting appropriate contacts which bear on the s l i p - r i n g s , and meters or oscillograph shunts can he introduced ••as- desired» Besides the provision f o r studying equalizing currents, the machine provides f a c i l i t i e s f o r investigating commutation. Three c o i l - s i d e s from one s l o t and one c o i l - a i d e from an ad-jacent s l o t have i n each case one of t h e i r turns opened at the hack of the armature and leads are taken to s l i p - r i n g s so i t v / i l l he possible to complete the connections through o s c i l l o -graph shunts. with a view to simulating the conditions which obtain when the bearings of a machine become worn, the test machine was b u i l t so that the gap length could be varied. For this purpose outboard bearings were provided i n place o f end-bells', and t o vary the gap i t is•merely necessary to i n s e r t shims o f varying thickness between the pole-frame and the "bed-plate. As a r e s u l t of early tests with, four equalizing connections i t was thought advisable to make provision f o r other s i m i l a r connections i n order to extend the study somewhat. F i n a l l y , provision was made f o r eight more equalizers by tapping the back connections i n sixteen places; a larg e r number was considered, but the increased complexity of connections would not have been warranted. For these new connections well insulated leads were taken from the tapping points to terminals spaced around, the outer rim of a f i b r e disc, immediately behind the back con-nections. Then insulated connectors were made to j o i n up • opposite terminals, and thus the equalizing connections could be Inserted or removed at w i l l . Although i t would have been preferable to so space these new equalizing connections that the t o t a l of twelve would have been exactly evenly d i s t r i b u t e d about the armature winding, i t was decided that this would be extremely d i f f i c u l t , due to the necessity i n such case of tapping conductors near the bottom of the s l o t s . Instead, a nearly even spacing was used i n which the conductor tapped was that one leading d i r e c t l y to a com-mutator segment; t h i s made more r e a d i l y possible the l o c a t i o n of the-proper conductors, though even so t h i s proved a, r e a l d i f f i c u l t y . Due to the small s i z e of the conductors and t h e i r consequent crossing of one another i n the s l o t s ^ the only method of lo c a t i n g the correct ones was by the use of a duetor* Using s p e c i a l l y developed sharp'points that would not damage the cotton covering of the conductors*, and setting-one set of points on the appropriate commutator bar the resistances were .measured to locate the desired conductor.. The spacing of these connections and the arrangement of the removable equalizers i s shown i n the appendix A* • ' - :-The p o s s i b i l i t y of introducing the equalizing connections at the commutator end was considered, but as the four o r i g i n a l connections were at the back t h i s idea was discarded. The f i r s t step i n the experimental work was to compare the general operation of the machine on varying loads with d i f f e r e n t numbers of equalizing connections. In order to render con-dit i o n s as severe as possible the pole frame was shimmed up f o r most of the tests to give the maximum e c c e n t r i c i t y possible, within l i m i t s of safety. The normal air-gap as measured with -f e e l e r s (not that given i n the s p e c i f i c a t i o n s ) was 0.068 inches, and with maximum e c c e n t r i c i t y the average length of two top gaps was 0.096 Inches and that of the two bottom gaps 0.040 inches* - Without any shims the magnetic balance of the machine was very good; i n f a c t the maximum •circulating current through the brushes was 0.08 ampe., which i s n e g l i g i b l y small compared to the f u l l load current of the machine of 16 amps. This was when-,no.-equalizers.- were used. For a l l the tests the machine was driven as a generator and separately excited from the.. 250 v o l t b a t t e r i e s . For the f i r s t tests. the. Sciirage motor was used and i t proved to be i d e a l f o r the purpose because of i t s speed, range; for most of the tests, however, a three phase induction motor had to be used,.and consequently there was a small drop i n speed as the generator load was increased. 'This drop was not s u f f i c i e n t to a f f e c t the r e s u l t s appreciably so no correction f o r i t i s made In the calculations* Considerable d i f f i c u l t y was encountered at times due to sudden fluctuations i n the supply voltage and frequency, and c e r t a i n of the inconsistant readings may be attributed to this cause. Loading of the generator was done by means of loading rheostats, and besides the ammeter .in the load c i r c u i t ammeters were placed i n each of the connections between • brushes of l i k e p o l a r i t y . From these readings can be calculated the c i r c u l a t i n g currents, these being the useless currents which f l e w through the brushes and brush connections. ISumexxeally-they are h a l f the d i f f e r e n c e of the c u r r e n t s s u p p l i e d by p a i r s of brushes.of l i k e p o l a r i t y . The accompanying graphs show the v a r i a t i o n i n the two c i r c u l a t i n g c u r r e n t s on a base of l o a d c u r r e n t , using d i f f e r e n t numbers of e q u a l i z i n g connections. T y p i c a l sheets of t e s t r e -s u l t s from which these curves have been p l o t t e d are shown i n appendix B. The f i r s t s e t of curves covers t h r e e c a s e s ; f i r s t l y , t h a t i n which no e q u a l i z i n g connections are used, secondly,- that i n which there are f o u r such connections, and l a s t l y , t hat i n which there tire twelve. The r e s u l t s are i n t e r -e s t i n g as they i n d i c a t e poorer operation w i t h f o u r connections than w i t h none at a l l . On the other hand there seems l i t t l e to choose between the use of twelve connections and o p e r a t i o n without any, a t ' l e a s t as regards the c i r c u l a t i n g c u r r e n t s . On l i g h t loads these c u r r e n t s a r e c o n s i d e r a b l y smaller'when using the twelve connections than when they are dispensed-withy but i n the v i c i n i t y of f u l l : l o a d the opposite i s t r u e . The second set of curves a f f o r d s a comparison of the c i r c u l a t i n g c u r rents when using ten and twelve connections, and i n t h i s case there i s not much d i f f e r e n c e i n favour of the l a r g e r number. With only ten connections, the spacing i s n e c e s s a r i l y r a t h e r uneven. I t would appear from these c o n s i d e r a t i o n s that a f u r t h e r i n -crease i n the number of e q u a l i z e r s beyond twelve would improve operation somewhat, though probably not to any great extent. I n any case the values of c i r c u l a t i n g c u r r e n t s are not exces-s i v e l y l a r g e comparing them w i t h the f u l l load current of the machine of 16 amps. Perhaps i t would have been b e t t e r to p l o t the curves on a base of the normal load c u r r e n t per brush, or h a l f the load c u r r e n t , as t h i s presents the case i n a t r u e r .light.., C e r t a i n i t i s that a study of these curves convinces one tha t there i s a marked d i f f e r e n c e between the four-pole machine and those w i t h s i x or more p o l e s , f o r w i t h these l a t t e r , the In t r o d u c t i o n of e q u a l i z i n g connections I n v a r i a b l e improves operation. I.t would appear th a t i t i s unnecessary and inad-v i s a b l e to use e q u a l i z i n g connections on a normally c o n s t r u c t -ed four-pole machine. While the values of the c i r c u l a t i n g c u r r ents are q u i t e a p p r e c i a b l e , i t must be remembered that the case s t u d i e d i s an extreme one and c e r t a i n l y not ofte n l i k e l y to be p a r a l l e l e d .in practice. I t w i l l be n o t i c e d that, i n the case i n which no equal-izers, are used, there i s not much v a r i a t i o n i n the, values of the two c i r c u l a t i n g c u r r e n t s as the load i s v a r i e d . This i s explained by the f a c t that the r e s i s t a n c e of the. armature to the c i r c u l a t i n g c u r rents i s not a f f e c t e d by changing values of load current. In any path i n the armature taken by a c i r -c u l a t i n g c u r r e n t , the r e s i s t a n c e drop i n one h a l f due to load c u r r e n t i s i n the opposite d i r e c t i o n to that i n the other h a l f , so the net e f f e c t I s zero. The f a c t that there i s some v a r i a t i o n in the c i r c u l a t i n g c u r r e n t s i s probably due to both a change i n brush contact r e s i s t a n c e and a change i n the p o l a r f l u x e s as a r e s u l t of the or d i n a r y armature r e a c t i o n e f f e c t ; The question of the e f f e c t on the c i r c u l a t i n g c u r r e n t s of an incres.se i n the r e s i s t a n c e of the e q u a l i z i n g connections was only considered f o r the ease i n which f o u r connections wer used. With a 0.2 ohm. e x t e r n a l r e s i s t a n c e i n each e q u a l i z e r there was not much d i f f e r e n c e i n the c i r c u l a t i n g c u r r e n t s , and i f anything, there was a s l i g h t Improvement i n tha t regard. The e q u a l i z i n g c u r r e n t s themselves dropped only about b% although the r e s i s t a n c e added was l a r g e ; the t o t a l armature r e s i s t a n c e i s only 0.4 ohm. The e q u a l i z i n g currents must be l i m i t e d l a r g e l y by inductance, and hence the s i z e of the con-nections i s probably not very important, though of course, they must be of s u f f i c i e n t cross s e c t i o n to prevent over-h e a t i n g . Considerable d i f f i c u l t y was encountered i n the t e s t s due to the conta c t drop between the contacts and the s l i p - r i n g s , and at t h i s j u n c t u r e i t might be w e l l to go i n t o t h i s matter with a view to showing to what an extent i t may a f f e c t the value of the r e s u l t s . Although the contact drop i s not normal-l y l a r g e i t may beeorae appr e c i a b l e when sparking occurs; and there i s not only the i n c r e a s e d r e s i s t a n c e of the e q u a l i z i n g connections to consider but a l s o , and what i s probably more-important, the a d d i t i o n a l unbalance of the armature c i r c u i t . The l a t t e r i s due to the f a c t that three o r e v e n , a l l . f o u r . o f the opened c o i l s are i n one p a r a l l e l path of the armature, so that p r a c t i c a l l y a l l the Increased r e s i s t a n c e i s i n that one path* This must l e a d to a f u r t h e r change i n the: c u r r e n t d i s -t r i b u t i o n , w i t h the path of i n c r e a s e d r e s i s t a n c e . s h i r k i n g i t s share of the l o a d . In view of t h i s , i t was f i n a l l y decided to make s o l i d connections between s l i p - r i n g s when p o s s i b l e and thus a v o i d the contact drop completely. For t a k i n g o s c i l l o g r a m s , however, i t was necessary to use c e r t a i n of the c o n t a c t s , and f o r the osc i l l o g r a m s to be of any value the contact drop had to be low. The machine was o r i g i n -a l l y -equipped w i t h s o f t copper contacts to run on the brass s l i p - r i n g s . The contact f i n g e r s were of r a t h e r s o f t brass and consequently no great pressure, was p o s s i b l e ; moreover, any attempt to change the pressure by t u r n i n g the h o l d e r f o r the contact f i n g e r s r e s u l t e d i n the contacts r i d i n g on one edge-only. With t h i s arrangement sparking was very common. In order to increase the contact pressure:, w i t h the i d e a of reducing the contact drop, e x t r a pieces of s p r i n g phosphor bronze were made to r e i n f o r c e the contact f i n g e r s . The i n -creased pressure d i d improve the contact t e m p o r a r i l y , but a f t e r a s h o r t run the contact became blackened and sparking was as bad as ever. The bla c k e n i n g was due to copper dust and .vaseline, the l a t t e r b eing necessary to keep down the tempera-ture a t the contact. The next attempt a t improving the contacts was with the use of carbon brushes but these proved u n s a t i s f a c t o r y . They have the great advantage t h a t they q u i c k l y wear to the shape of the B l i p - r i n g s , and moreover they are s e l f - l u b r i c a t i n g , but the contact drop i s normally s e v e r a l times that £or a copper brush. The carbon used was r a t h e r s o f t and i t may be tha t a somewhat harder carbon or a mixture of carbon and copper would prove c o n s i d e r a b l y b e t t e r . The best r e s u l t s were obtained w i t h brass c o n t a c t s . The contact piece i t s e l f was about h a l f an i n c h long, three-, eighths wide and one-eighth t h i c k . This was soldered to a very f l e x i b l e s t r i p of shim brass which merely h e l d i t i n p o s i t i o n . The pressure at the contact came from a piece of s p r i n g phosphor bronze place d behind the t h i n contact f i n g e r and b e a r i n g on the middle of the contact p i e c e . The reason f o r t h i s arrangement was that the t h i n s t r i p s upporting the contact piece would a l l o w i t to l i e f l a t a g a i n s t the s l i p - r i n g , no matter how the support f o r the contacts was turned to change the pressure. The s l i p - r i n g s were given a t h i n c o a t i n g of v a s e l i n e which, even w i t h l a r g e pressure, kept down the tem-perature to a reasonable v a l u e . With t h i s arrangement the machine could be operated f o r q u i t e a time without the contacts blackening and consequent s p a r k i n g . I n order to g a i n an i d e a of the a c t u a l contact drop , one of the s l i p - r i n g s was f u r n i s h e d w i t h a. second brush, s u i t a b l y I n s u l a t e d , and a d i r e c t c u r r e n t c i r c u i t completed through the the two. With the machine d r i v e n at normal., speed.,* and of course unexcited, simultaneous readings of current and voltage were taken. The contact drop f o r the two brushes was of the - 13 -order of 0*3 v o l t s * v a r y i n g from 0.24 w i t h 1.2 amps»> f l o w i n g to 0.34 wi t h 7*0 amps. Thus, assuming the drop at each contact to he the same, we have a v a r i a t i o n of the- contact drop from 0.12 v o l t s to 0.17 v o l t s w i t h a c u r r e n t v a r i a t i o n from 1.2 to 7.0 amps. This i s s t i l l r a t h e r more than was hoped f o r . hut i t was found t h a t by e x e r t i n g e x t r a pressure, say w i t h a p e n c i l h e l d behind the contact, the voltage drop, was reduced to 0.01 v o l t . This provides an easy way of o b t a i n i n g accuracy i n the •oscillograms as t h i s e x t r a pressure i s r e a d i l y a p p l i e d w h i l e .they are being taken. The b i g decrease i n the contact drop w i t h i n c r e a s e d pressure would seem to i n d i c a t e that the f i l m o r d i n a r i l y e x i s t i n g i s broken down. Before going on to an examination of the oscillograms., we w i l l proceed w i t h a study of the case In which no e q u a l i z i n g connections are used, i n l i g h t of the theory of Dr. L u l o f s . I n the f i r s t p l a c e , and i n as b r i e f a manner as p o s s i b l e , h i s •general expressions f o r brush c i r c u l a t i n g c u r r e n t s w i l l be developed, and then an attempt w i l l be made to apply these to the case we are i n v e s t i g a t i n g . Consider the e f f e c t of an armature e c c e n t r i c i t y which makes a l l the gaps unequal.. We. w i l l not be very f a r wrong i f we assume that the increase i n f l u x from H x over i t s normal value and the decrease from IT, are equal, although due to the s a t u r a t i o n of the i r o n t h i s w i l l not be e n t i r e l y t r u e . The same holds f o r the f l u x e s i n S, and S^. BIAGRAMATIC REPRESEKTATIOIT <&, TYPICAL L&S-SflKDIHG. (Armature back connections ..shown dotted.) "Making use of t h i s assumption we may then c o n s i d e r the f l u x d i s t r i b u t i o n the same as w i t h equal gaps, except that we now have two superimposed f l u x e s n x n, and s, as w e l l as the normal p o l a r f l u x e s , \7ith the top gaps longer than the lower ones, as shown, n l n, must be d i r e c t e d from to IT, so as to strengthen H z by the same amount as IT, i s weakened; s i m i l a r , c o n s i d e r a t i o n s show that s t s, must go from S x to S, . The armature i s then not only r o t a t i n g i n i t s normal f i e l d , but a l s o i n the two f i e l d s n x n, and s L s, . Consider f i r s t the e f f e c t of n x n, ; as the armature conductors r o t a t e i n t h i s f i e l d there are 21. II, F.s induced i n them which are down under 17 v and up under U r. As a r e s u l t , c u r r e n t s flow through the ,.two p a r a l l e l paths i n the armature., and the c i r c u i t i s com-p l e t e d through the brushes B and B and the brush connection. The d i r e c t i o n of the cur r e n t s i s down under II, , up under 1^ and both up and down under the south, poles; t h i s l a s t i s apparent i f we f o l l o w the winding through from one p o s i t i v e brush to the other. JTow examine the armature r e a c t i o n e f f e c t of these c u r r e n t s ; o b v i o u s l y there i s an II. l\. F. s e t up i n the d i r e c t i o n S, S L and., f o r the present n e g l e c t i n g the. cross f l u x s x , t h i s would produce a f l u x i n the same d i r e c t i o n as the M. H* ,F. ••• But the •armature i s r o t a t i n g I n t h i s f i e l d s e t up by I t s •••.own ampere-turns* and E:» l . . J , s are induced- which are down under S z and up under 3,. As be f o r e , c u r r e n t s flow down under S-x* up under B| and In both d i r e c t i o n s under the other two poles. The M. II. F. due to these c u r r e n t s i s i n the opposite d i r e c t i o n to n^n,', so that due to the unequal air-gaps c i r c u l a t i n g -c u r r e n t s f l o w , which tend p a r t i a l l y to wipe out the e f f e c t which caused them. Let us now consider the combined e f f e c t of the two cross f i e l d s . Having gone thus f a r , i t . is•• apparent t h a t f o r the pur-pose of determining the vo l t a g e s generated between brushes of l i k e p o l a r i t y . , i t i s simply necessary to consider the machine as two separate two-pole machines. I f then 0, i s the r e s u l t a n t f l u x i n the d i r e c t i o n of 3J X IT, the'Ii. If. F. i s : ' ' • •-'•16'. - • P M 5 0 s ir • B ~ 'I™-~^ «««-~--s — — s i n c e p-s.a«2 a 60 x 10 8 60 x 10s How l e t I , be the c i r c u l a t i n g c u r r e n t i n the armature which flows down under IT , and up under H z, and 1 ^  he the c i r c u l a t i n g c u r r e n t which flows down under S x and up under S,. The net . f l u x i n the d i r e c t i o n of the n o r t h poles (from 12 x to IT, ) i s ; M*. 11. F . ' due to 1'j.; reluctance of f l u x path n ^ n r — — n, n,-H, .being- the reluctance of a path through two opposite p o l e s , the armature,and yoke. The reason f o r using f i s apparent i f we consider the d i r e c t i o n s of the c i r c u l a t i n g c u r r e n t s i n a lap-winding* Hue to the f a c t t h a t currents, equal t o - I z flow i n both d i r e c t i o n s under !•!, and IT x the II* E. F.s due to these p a r t s of the winding wipe each other out. S i m i l a r l y , the net 0.4 ir H I . f l u x from S , to S x i s *. Hence 3, r ( n ^ , - R t J s o T l o ' 10 8r, where r ( i s the re s i s t a n c e ' to 1, of the path through the armature, brushes, and brush connections. 60 x 10 s r^ 'This gives us simultaneous equations from which I , and I may be calculated. On solving we get: Ri n,. n, + 0.1 z M s 2. s, I - 2 60 x 1 0 6 r * -I - .^ntrrvmUHUAU a MnOTwH ]»»'•»«• Wi»^«mir.)*]ii>.M^^ i w - m r - ^ . . • • . n r . - n . i j - "m,.Int., - n. -,-mf m 60 x 10 s r-« R. + (.0,1 K 2 1 H 80 x 10 s R x r a <L'l-^ 2.. K tlx n, And I , - ^ ^ - ^ .—.. _ _ . .. 60 x 10 6 II•>.... «, l O . l * 9 ) x ¥ 2 X K 60 x 10 6 Ri x, These are the expressions developed by Dr. Lul'ofs though not in quite the same form as he gave them; he used the., quantity which he c a l l e d magnetic resistance, but magnetic re-luctance has been used here as i t is. now commonly used, i n h i s o r i g i n a l papers Br. L u l o f s discussed a numerical example of e c c e n t r i c i t y i n the d i r e c t i o n of one p a i r of opposite poles, but our case of e c c e n t r i c i t y along a neutral axis introduces new d i f f i c u l t i e s . I n the f i r s t place the cross f i e l d s n 1 n, and s L S | must be calculated,and then we w i l l proceed to deter-mine values of the reluctances R, and R z and. the resistances r , and x^. The f i n a l step w i l l be a substitution of these values In the expressions f o r 11 and I^. In the c a l c u l a t i o n of the cross f i e l d s we w i l l assume them equal, as this Is t h e o r e t i c a l l y the oase when the pole frame i s raised v e r t i c a l l y . itx s S3 i _ | 18 Suppose <j>, i s the f l u x i n the two top p o l e s and 0z the f l u x i n the two "bottom p o l e s , w i t h the r e l u c t -ances as shown I n the sketch, f i g * 2 . R" I s the reluctance of each of the top gaps and R f the r e l u c t -ance of each of the bottom gaps... 2?ig. i2. DIAGRAM SHOWING KAGHBT1C R3SLUC TAKGES Then ijfc jv 2 (H' * Rs) (See Appendix 0 Also,, assi imlng a l i n e a r open c i r c u i t c h a r a c t e r i s t i c , , we have — 0 where p i s the normal f l u x per pole of the m^achine-;:- • How i n order to determine the values of the rel u c t a n c e s of, the va r i o u s parfes of the magnetic c i r c u i t we make use of the open c i r c u i t c h a r a c t e r i s t i c of the machine. For the .machine . i n q u e s t i o n the f i e l d - c u r r e n t i s 0...99 amps* w i t h an open c i r c u i t - voltage of 250 v o l t s at 1200 R*P,.Lt. There are 1950 f i e l d turns per p o l e , so the number of ampere-turns p e r pole i s 1930,.. Mith a l l the gaps on the machine equal we have the-normal f l u x per pole • 4 from t h e -general K^ M,.!?*. ;equation;; P _60_ X T 10 ** 20 — ." d.765 x 10 6 /lines,. 0,4 IT I , iLt « Q.4 ^ x • 1950 .we have toes 4 <+ K «t R^ + 4 0.785 x 1 0 6 = 3170 x 1 0 u n i t s of reluctance I t i s now necessary to separate out the var i o u s terms of t h i s expression. The r e l u c t a n c e l\ of the gap i s e a s i l y obtained from the gap dimensions. R " T s 0.063 x 2.54 • A • ' 18.3 " x 2.54 i s 14G3 x 1 0 ^ In t h i s . e a s e A i s the e f f e c t i v e a i r-gap area and i t i s obtained from the apparent a i r - g a p area w i t h the use of Car t e r * s f a c t o r . : Y/~e have now* f * * f + R 3 B 1707 x 10"fe' VJe proceed to c a l c u l a t e the value of B 3 , the reluctance of a p o l e . .The r a d i a l - l e n g t h of the pole i s 3*92 inches and the c r o s s area 11.55 square Inches. Hence the normal f l u x d e n s i t y , n e g l e c t i n g leakage i s : ft The name of t h i s u n i t was formerly the oersted but the I n t e r -n a t i o n a l E l e c t r o t e c h n i c a l Commission i n 1930 adopted oe r s t e d f o r the u n i t of magnetizing f o r c e , l e a v i n g the u n i t of magnetic reluctance nameless. - 21 -.. • s S J J Z § § - J L J £ 6 l i n e s per square i n c h 11.56 s 1G.25 kilO'-lines per square cm. Prom the magnetisation curve f o r commercial sheet s t e e l the ampere-turns per cm. at t h i s f l u x d e n s i t y are 4.1; .this gives a t o t a l of 4.1 x 3.92 x 2*54 s 40.3 ampere-turns per po l e . Hence K 3 - of765 x i o ? 5 3 * 5 - 1 0 _ b . This makes f ^ * f 2 1654 x l(T f c '^ e can now go hack to our determination of the values of 0, and 0X i i n the f i r s t place we w i l l assume that the r e l u c t -ances R'&nd Ru are i n the same p r o p o r t i o n to R as are the cor-responding l e n g t h s of the gaps. I t would be p o s s i b l e to de-termine them more accurately bymaking use of Ga r t e r ' s f a c t o r , as was done i n c a l c u l a t i n g the e f f e c t i v e gap area w i t h no e c c e n t r i c i t y , but the refinement would probably not be i n keeping with the r e s t of the c a l c u l a t i o n . Taking the average l e n g t h of each of the upper gaps as 0.096 inches and that of each of the lower as 0*04 Inches the values of R* and R" are: R' • 0-040 x 1463 x 10"6 = 860. x 10"fe . ..• 0.068 . H " " 0.068 x 1 4 6 3 x 1 0 ^ ~ 2066. x 10"b H E N C A 4L, S 4 x 1654 * 2(860 * 55) s ,4221 '07. 4 x 1654 t 2(2066 + 53} 5427 but ^ 0.765 x 10fe 22 —1 This gives 0, s 0.669 x 10 6 , fc- 0.-861 x 10fe whence n z n, =. o^ s, 0.096 x 10 f alines. I t might appear that In - these c a l c u l a t i o n s the question of leakage flux, was neglected completely hut this i s not the case. Since we are working from the 0. C. C. the value o£ w i l l a c t u a l l y include leakage paths,as well as the paths through the yoke* There appear to he two simple means by which we can check experimentally this t h e o r e t i c a l l y determined value of the cross f l u x , and thus get some idea of how f a r from the truth our assumptions have lead us. The most obvious and simple deter-mination of the cross-flux i s by means of the open-circuit voltages between brushes of l i k e p o l a r i t y . The readings should be. talien with the f i e l d excited by the normal no-load f i e l d current, and not when a voltmeter across the terminals of the machine r e g i s t e r s normal voltage. This l a t t e r i s no c r i t e r i o n , as with the connections between brushes of l i k e p o l a r i t y broken there are four d i f f e r e n t voltages between various sets of posi-t i v e and negative brushes. A c t u a l l y upon measurement, the voltages between brushes of l i k e p o l a r i t y , with 0.96 amps, i n the f i e l d , were 29.5 vo l t s from A to C and 29.8 v o l t s from D to B. This shows' a d i f f e r -ence of only about 1% i n the cross fluxes and f o r our purposes we w i l l take the average, 29.65 v o l t s . How substituting t h i s value i n our genera,! E. !£. J?. equation we w i l l get the value of the cross-flux: a 60 x 10 s 0 = 2 29.65 x 60 x .108 2 1632 x 1200 * 0.0908 x 10 6 l i n e s . This cheoks reasonably well with the previously determined value n2 n, s s x s, s 0.096 x 10 f elines. A second check on the value of the c r o s s - f i e l d should he possible by moans of an oscillogram of generated c o l l voltage. V/ith the brushes l i f t e d or the connections between brushes of l i k e p o l a r i t y broken, there w i l l be no' currents flowing i n the armature, provided, of course, that there are no equalizing connections. Hence i f an oscillogram can be taken of the v o l t -age generated i n one conductor the ordlnates should represent not only voltage but also f l u x density to a d i f f e r e n t scale. But the i n t e g r a l of f l u x density over the ISO e l e c t r i c a l degrees between brushes gives the t o t a l f l u x from any pole. Hence the r a t i o of the areas under two parts of the generated voltage oscillogram, corresponding to a top and bottom pole should be the same as the r a t i o of the fluxes i n those poles. Bue to the small scale of the oscillograms taken, i t was rather d i f f i c u l t to measure the areas accurately, but a value of the ra t i o of 1.33 was obtained which i s probably f a i r l y good. That Is J ~ - = 1-33 . . • ' ' • - 24. »• . But as "before •» . Cik .„ o.765 x 10 fc From these two we get <jh = 0.874 x 10 4 0.657 x 10fe and hence n , •= s t e, «. 0.108 x 10'lines This value i s high but the error i s not more than might be ex-pected considering the small areas which had to bo measured. We can now go on to a determination of the reluctances R, and R x. Considering f i r s t the reluctance of a c r o s s - f l u x path when there are no other fluxes present, we see that i t i s equal to 2 E 3 + U " + R T) + i\+ r (See f i g . 2 . ) or since R" + R' » 2 B R^.2"" H,* SR *'B #* T ' v:-With the machine f u l l y excited this, expression Involves an ^approximation. due to the saturation of the iron,, but we w i l l use I t f o r want of a better. Substituting actual values we get: R , sr R x a 2x53xl0" 6 + 2x1463x10"" 4- 4xl654xl0" f e = 9648xl0"fc How l e t us proceed with a determination of r , and r x , keeping i n mind that they were defined as the resistances to I, and ! L of the paths through the armature, brushes, and brush connections. I f a?* i s the -aaanaiaia?© -reeiS'tance. as.:-measured i n the usual way* the resistance of each quarter of the armature Is 4 ra- - Then, i f r i s the brush resistance, the t o t a l re-sistance to a c i r c u l a t i n g current I i n the brushes w i l l be 4 r + 2 r . . Hence the resistance to a current I i n each branch w i l l he 8 r ^ + 4 -. From actual measurement r ^  s 0.40 ohms.,, hut a suit a b l e value of r ^ Is not so e a s i l y obtain-a b l e . However we w i l l not be f a r wrong i f we assume a one v o l t drop at each brush contact which, f o r a c u r r e n t of say 2 amps., gi v e s a value of r ^ of 0.5 ohms. Hence r, s r z - 8 x 0.4 + 4 x 0.5 •s 5.2 ohms. How su b s t i t u t i n g i n the expression f o r I, we get 9648 x 10~fex 0.096 x 1Q6 + 0.1 x 1632 x 1200 x 0.096 x 10* I - -1632 60 X 1 0 a X 5.2 60 x 10* x 5.2 x 9648 x, 10'^ ( Q U ^ x (1632) 1x 1200 • Tl632) i X 1200 60 x 10'x 9648 x 1 0 x 5.2 « p.,566 +1.893 - 2.16 amps. 0.094 + 1.043 A i q o T r lr895 -,0.566 . 1 . 1 7 amps. A L J O A i 0.094 * 1.043 These are the c i r c u l a t i n g currents i n the armature conductors; the corresponding currents i n the brushes and brush connectors w i l l bo 4.32 and 2.34 amps. These values do not agree very well with the experimentally determined values of 2.16 and 1.40 amps, though they are of the same order. Looking f o r a possible cause of t h i s discrepancy we na t u r a l l y question the value of resistance used, but an examination of the expressions f o r I, and I z reveals the f a c t that an error i n the value of the re-sistance w i l l not r e s u l t i n anything but a s m a l l e r r o r i n the currents. This i s due to the f a c t that the resistance appears to the same power i n the more s i g n i f i c a n t terms of both numer-ator and denominator. The other quantity which could cause - 28 -trouble i s the reluctance.of the cross path, and an error i n this case- w i l l r e s u l t In a large error i n the f i n a l r e s u l t . • looking further to more general causes of possible error wo have to examine the e f f e c t of saturation on the r e s u l t s . The simplest way to do t h i s i s by-means of a h a l f voltage test, f o r at h a l f voltage we are working on the st r a i g h t part of the open c i r c u i t c h a r a c t e r i s t i c . The.calculations are sim i l a r to those f o r f u l l e x c i t a t i o n so w i l l be omitted. ITew values of the cross f l u x and also of magnetic reluctance and of r e s i s t -ance arc determined, and then substituted i n the general ex-pressions f o r I, and I x . The r e s u l t i n g values are: ••!,.••••« 1.07 amps* I j . " - 0.54' amps. The brush c i r c u l a t i n g currents are then 2.14 and 1.08 amps, as compared with experimentally determined values of 1.15 and 0.86 amps. Again there i s rather poor agreement, and i n fac t there Is much the same discrepancy as there was with f u l l e x c i t a t i o n . "This would seem to indicate that saturation did not, play an im-portant r o l e , at lea s t at no-load. 'As the machine i s loaded up, of course, the values of the c i r c u l a t i n g currents change somewhat,, due to the saturation of the pole at the leading edge. So f a r no mention has been made of the interpoles and t h e i r possible effects In general, when there i s no load cur-rent flowing, there are two ways i n which the presence of: interpoles might a f f e c t the r e s u l t s ; f i r s t l y due to the arm-ature EJCPS under, the interpoles, and secondly due to the leak-age f l u x from the main poles through the interpoles changing the main pole f l u x d i s t r i b u t i o n . The f i r s t need h a r d l y be considered as the interpole f l u x i s not only s m a l l , but i s l i m i t e d to the commutation sone. The second e f f e c t would also appear to be small as, even with the armature eccentric, there w i l l never be anything but a small I I . I f . F* along the i n t e r -poles. This Is more obvious i f we consider f i r s t the case of equal gaps where the• M* IS* I?.*- tending to produce leakage f l u x through the interpoles I s t h e o r e t i c a l l y aero, due to the f a c t t h a t each main pole f i e l d c a r r i e s .just s u f f i c i e n t ampere-turns to take the f l u x h a l f way round a f l u x path. S7e come now to the question of the value of Dr. Lulof s' theory. In the f i r s t place i t does not In our case give re-s u l t s i n close agreement w i t h experimental r e s u l t s , but i t may be that the writer has not applied the theory to the best advantage. On the other hand i t gives a good picture of what a c t u a l l y takes place, and f o r t h i s reason alone i s valuable. As to the p o s s i b i l i t y of using a graphical method of deter-mining c i r c u l a t i n g c u r r e n t s , beginning w i t h the open c i r c u i t . characteristic,,... i t i s evident; t h a t i t would e n t a i l a•• process of successive approximations. This, because we are dealing with two interdependent quantities, namely f l u x and current. The merit of L u l o f s ' method l i e s i n the use of simultaneous equa-tions, the only way of avoiding approximations of t h i s kind. Thus f a r we have not examined the part played by equal-i z i n g connections i n a four-pole machine. Unlike the machine with s i x or more poles i n which these connections are respons-i b l e e n t i r e l y f o r correcting the f l u x d i s t r i b u t i o n * the four-pole machine bas the two e f f e c t s acting together. The best method of studying these e f f e c t s both s i n g l y and together i s by means of oscillograms showing the f l u x d i s t r i b u t i o n around the armature under d i f f e r e n t , c o n d i t i o n s . Since the S, IT. IP. generated i n a conductor as i t revolves with too armature i s proportional to the f l u x density, an oscillogram of 3. II. E . would give to another scale the f l u x d i s t r i b u t i o n i n the gaps.; . At of Irs t the use of .a -search c o i l was considered^but not only would i t have been d i f f i c u l t to i n -troduce another conductor i n the s l o t s , but the E,- F. around the c o i l would be the summation of two E* 11, F.s out of phase, and these would have to be separated out. Instead, a single conductor of the armature winding was u t i l i z e d ; f o r the purpose one was selected which connected d i r e c t l y from a commutator segment to one of the s l i p - r i n g s at the back of the armature. Then the commutator segment was grounded to the shaft by an e a s i l y removable connection and a contact f i n g e r placed to bear d i r e c t l y on the shaft.. To. get oscillograms of voltage i t was then only necessary to connect the two contact fingers, one from e i t h e r end of the conductor, to a h i g h resistance element of the oscillograph. As a precaution a second contact f i n g e r was provided on the s l i p - r i n g so t h a t the oscillograph current was not drawn from the same contact as the load current. Evidently the oscillograms w i l l not represent absolutely accurately the f l u x d i s t r i b u t i o n for there are errors involved. In the case i n which there are no currents flowing i n the arm-ature the only error i s that due to the drop at the contacts, and i t has been shown previously that by taking proper pre-cautions at the time of photographing, t h i s w i l l be n e g l i g i b l e . When there are armature currents flowing,. however, there i s the effect of resistance drop and i n some cases inductance drop to consider. Now the generated E. M . F. per conductor i s approx-imately 0.6 vo l t s 'and the resistance drop along the conductor with a current of 4 amps. flowing i s only of the order of 0.015 vol t s so this e f f e c t may be neglected. Further, when no equal-i z e r s are u t i l i z e d the conductor current i s p r a c t i c a l l y ; o f con-stant value between commutation periods, so the effect of s e l f and mutual inductance need not.be considered. When using equal-i z e r s , on the other hand, the armature currents are far from constant and as a re s u l t the voltage wave of the oscillogram w i l l be i n error. From an examination of actual oscillograms such as no. 6, i t i s evident that the eff e c t i s not very large and f o r our purposes may be neglected. The f l u x d i s t r i b u t i o n i n the gaps due so l e l y to the f i e l d windings i s shown by oscillogram no. 9, which was taken with the brushes l i f t e d and no equalizing connections i n c i r c u i t . Under these conditions no currents can flow i n the armature; that t h i s i s true i s evident i f we remember that the t o t a l f l u x leaving the armature i s the same as that entering, and hence the summation of the E. M. F.s around the armature w i l l be zero at - 30 -any i n s t a n t . Oscillogram 9 was the one used p r e v i o u s l y f o r a c a l c u l a t i o n of the r a t i o of the p o l a r f l u x e s hut as was pointed out the s c a l e i s s m a l l , w i t h the r e s u l t that the measurement of area i s not very accurate. I t would appear that enlargement wit h an o r d i n a r y p r o j e c t o r would o f f e r the best means of obtain-i n g dependable r e s u l t s . Due to the e c c e n t r i c i t y of the arma-ture the f l u x i s not only d i f f e r e n t under the top and bottom p o l e s , but there i s a v a r i a t i o n i n f l u x d e n s i t y under i n d i v i d -u a l p o l e s , and t h i s shows up c l e a r l y i n the o s c i l l o g r a m . 6 8 Voltage per conductor w i t h no e q u a l i z i n g connect-ions and at no l o a d . 7 C o i l current w i t h no e q u a l i z i n g connections and at no l o a d . 9 Voltage per conductor w i t h brushes l i f t e d and no e q u a l i z i n g connections. The two p o r t i o n s of the wave corresponding to the two s h o r t e r gaps have t h e i r maximum ordlnates adjacent to the n e u t r a l a x i s between these poles, as would be expected. F u r t h e r , the tooth harmonic or r i p p l e on the c r e s t s of the waves i s more pro-nounced f o r the short gaps than f o r the long ones. How l e t us examine the e f f e c t of brush c i r c u l a t i n g cur-rents on the wave form; i n t h i s case no e q u a l i z i n g connections are used but the cu r r e n t s I, and Ix w i l l c i r c u l a t e through the ax-mature, brushes, and brush connections. Oscillogram no. 8 represents these c o n d i t i o n s on no l o a d . I n the f i r s t place i t w i l l be n o t i c e d t h a t the p o l a r f l u x e s are now much more n e a r l y equal than i n the previous case; a c t u a l l y the r a t i o i s of the. order of 1.05 to 1, though an accurate determination has not been made* Ho. 8 i s s i m i l a r to no. 9 i n that the slopes of the wave tops are much the same, due to the f a c t that the armature K. M. i s more or l e s s evenly d i s t r i b u t e d over each pole. The r a t h e r l a r g e S. K. F,s i n the i n t e r p o l e zones w i l l be due to the commutation of the c i r c u l a t i n g c u r r e n t s ; o s c i l l o g r a m no. 9 shows that the leakage f l u x through the i n t e r p o l e s i s n e g l i -g i b l y s m a l l . O s c i l l o g r a m no. 7 i s one of current I n an arma-ture c o i l and was taken a t the same time as no. 3; the currents • are a c t u a l l y the sum or d i f f e r e n c e of 1 1 and 1 x and of course are more or l e s s constant under any one pole. U n f o r t u n a t e l y there i s no record of the commutation p e r i o d . The e f f e c t of e q u a l i z i n g connections on the main pole f l u x e s I s shown by o s c i l l o g r a m s no. 4 and no. 17; the f i r s t of these was taken w i t h a l l twelve e q u a l i z i n g connections i n c i r c u i t and the second w i t h only f o u r . For these o s c i l l o g r a m s - 32 -the brushes were l i f t e d so that the only c u r r e n t s flowing were e q u a l i z i n g c u r r e n t s . With only f o u r connections i n c i r c u i t the e q u a l i z a t i o n of f l u x i s marked, but i t i s somewhat l e s s than t h a t due to the brush c i r c u l a t i n g c u r r e n t s ; w i t h twelve e q u a l i z e r s the f l u x i s very n e a r l y the same f o r a l l f o u r p o l e s . 2 Voltage per conductor w i t h 12 e q u a l i z e r s and at no l o a d . 3 C o i l c u r r e n t w i t h brushes l i f t e d and 12 e q u a l i z e r s i n c i r c u i t . 4 Voltage per conductor w i t h brushes l i f t e d and 12 equal-i z e r s i n c i r c u i t . T h i s e q u a l i z a t i o n of f l u x due s o l e l y to the e q u a l i z i n g c u r r e n t s , i s of utmost importance f o r a machine w i t h s i x o r more p o l e s , and has i n the past been st u d i e d mathematically. Recently R. M. Baker, i n a paper e n t i t l e d " E q u a l i z i n g Currents i n the Armature of a D. C. Machine" presented a t an A. I. 1. B. 1? Voltage per conductor with brushes l i f t e d and with 4 equalizers. 13 Voltage per conductor at no load and with 4 equalizers. 12 C o i l current at no load and with 4 equalizers. convention, attached the prob 1 era i n r a t h e r a d i f f e r e n t way, using f o r h i s t e s t s a f o u r - p o l e machine, w i t h a la r g e number of e q u a l i z i n g connections. S t a r t i n g w i t h an o s c i l l o g r a m of arma-ture c u r r e n t taken w i t h a l l brushes l i f t e d he i n t e g r a t e d to get the r e s u l t i n g c o r r e c t i v e M. M. P., and showed how the i n -e q u a l i t i e s of s a i n pole f l u x were thus smoothed out. His treatment i s a p p l i c a b l e , of course, only when a comparatively large number of connections i s used, as he takes the o s c i l -logram of c u r r e n t i n one c o i l as i t r o t a t e s w i t h the armature, -.34 -and treats i t as a steady space d i s t r i b u t i o n of current i n the form of a c u r r e n t sheet. l o r our case, that Is with a small number of connections, t h i s treatment i s hardly a p p l i c a b l e as the space d i s t r i b u t i o n of. c u r r e n t i s not constant, w i t h r e -spect to the armature, the wave I s a r e c t a n g u l a r one with changes i n ordlnates a t each e q u a l i s i n g point; f u r t h e r , the ordinate at any point i e c o n s t a n t l y v a r y i n g . With respect to the f i e l d poles we have then a s e r i e s of rectangular, p u l s a t i n g waves t r a v e l l i n g at the speed of the armature. From t h i s , i t would appear that the c o r r e c t i v e II. IS. 3P. would also vary to some extent. I t might i n our case be possible to arrive at a wave of average current d i s t r i b u t i o n around the armature, and use t h i s to f i n d the c o r r e c t i v e M.. M. F. but the process would be tedious and of doubtful value. To.go f u r t h e r back,we might from p u r e l y t h e o r e t i c a l con-siderations determine the f i n a l f l u x d i s t r i b u t i o n due to a c e r t a i n i n i t i a l unbalance. The process would be as follows: f i r s t , assuming sinusoidal d i s t r i b u t i o n of f l u x i n the gap,, we would get expressions f o r the currents i n a l l sections of the armature. Then f o r each section another general expression could he obtained by simple integration, g i v i n g the average value of current a t any point. Inserting numerical values and evaluating these l a s t expressions f o r a number of p o i n t s , a wave could be plotted g i v i n g the average current d i s t r i b u t i o n . The next step v/ould be the integration of the current wave to give the corrective 15. II. F. from which we would proceed to f i n d t h e new d i s t r i b u t i o n o f f l u x . B u t t h i s l a s t g i v e s o n l y a f i r s t a p p r o x i m a t i o n ^ a n d I t would p r o b a b l y be n e c e s s a r y to r e -p e a t t h e p r o c e s s s e v e r a l t i m e s b e f o r e good r e s u l t s would be o b t a i n e d . The w r i t e r a t t e m p t e d a s o l u t i o n a l o n g t h e s e l i n e s , n e g l e c t i n g m u t u a l i n d u c t a n c e e f f e c t s and. a l s o the r e s i s t a n c e and I n d u c t a n c e o f the e q u a l i z i n g c o n n e c t i o n s t h e m s e l v e s , b u t even w i t h t h e s e s i m p l i f i c a t i o n s a* s a t i s f a c t o r y s o l u t i o n was n o t o b t a i n e d . Bo f a r i n o u r c o n s i d e r a t i o n o f the o s c i l l o g r a m s , we have examined s e p a r a t e l y the c o r r e c t i v e e f f e c t s o f c i r c u l a t i n g c u r -r e n t s a n d of e q u a l i z i n g c u r r e n t s . 3?or n o r m a l o p e r a t i o n w i t h any-number of e q u a l i s i n g c o n n e c t i o n s " t h e c o r r e c t i v e M. M- f . I s due t o b o t h t h e s e c u r r e n t s . O s c i l l o g r a m s n o . 2 and n o . 13 were t a k e n w i t h t w e l v e a n d f o u r c o n n e c t i o n s r e s p e c t i v e l y , and i n b o t h c a s e s c u r r e n t s were c i r c u l a t i n g t h r o u g h the b r u s h e s and b r u s h c o n n e c t i o n s , b u t t h e machine was n o t l o a d e d . I t i s to be n o t i c e d t h a t I n the case o f f o u r c o n n e c t i o n s the c o r r e c t i o n o f t h e p o l e f l u x e s i s a p p a r e n t l y l e s s t h a n when no b r u s h c i r c u l a t i n g c u r r e n t s were f l o w i n g ; with, the twelve c o n n e c t i o n s i t i s d i f f i c u l t to say what the d i f f e r e n c e i s , f o r b o t h w i t h and w i t h o u t b r u s h c i r c u l a t i n g c u r r e n t s , the c o r r e c t i o n i s f a i r l y c o m p l e t e . The e f f e c t o f the l o a d c u r r e n t i s shown i n o s c i l l o g r a m no. 6 w h i c h was t a k e n w i t h t w e l v e e q u a l i z i n g c o n n e c t i o n s i n , and a t f u l l l o a d . The f l u x p e r p o l e s t i l l r e m a i n s n e a r l y e q u a l f o r - 36 -a l l poles as i n the previous case, the only point of i n t e r e s t attached to the o s c i l l o g r a m being the change i n slope of the wave c r e s t f o r two of the po l e s . This i s due to the ordinary armature r e a c t i o n e f f e c t which i s cross magnetizing. 6 Voltage per conductor w i t h 12 connections and at f u l l l o a d . 5 C o i l c u r r e n t w i t h 12 e q u a l i z i n g connections and a t f u l l l o a d . 16 C o i l c u r r e n t w i t h 4 e q u a l i z i n g connections and w i t h brushes l i f t e d . The foregoing a n a l y s i s of the voltage oscillograms has been almost p u r e l y a q u a l i t a t i v e one, and could p o s s i b l y be c a r r i e d f u r t h e r w i t h the a i d of other o s c i l l o g r a m s . However, i t serves to show i n a simple manner how the f l u x d i s t r i b u t i o n i s changed by v a r y i n g c o n d i t i o n s . I t had o r i g i n a l l y been one of the aims of t h i s t h e s i s to s t u d y c o m m u t a t i o n w i t h r e f e r e n c e to the e f f e c t o f b r u s h c i r -c u l a t i n g c u r r e n t s and e q u a l i z i n g c u r r e n t s . W i t h " a "view to t h i s . , o s c i l l o g r a m s o f c o i l c u r r e n t u n d e r d i f f e r e n t c o n d i t i o n s were tolcen on the We3tinghouse m u l t i - e l e m e n t o s c i l l o g r a p h . U n f o r t u n a t e l y a l l the o s c i l l o g r a m s were u n s a t i s f a c t o r y , as no r e c o r d c o u l d he o b t a i n e d o f the commutation p e r i o d . T h i s i s due t o t h e r a p i d change o f c u r r e n t , and t h e c o n s e q u e n t h i g h s p e e d o f t h e s p o t o f l i g h t i n the o s c i l l o g r a p h . U r i th s u c h •speeds p h o t o g r a p h i c f i lm a p p e a r s t o be n o t s u f f i c i e n t l y s e n s i -t i v e t o p r o d u c e a r e c o r d . T h e r e might be an improvement i f the o s c i l l o g r a p h lamp v/ere o p e r a t e d a t a s l i g h t l y . h i g h e r peak v o l t a g e , b u t much b e t t e r r e s u l t s c o u l d be o b t a i n e d w i t h t h e use', off-the c a t h o d e r a y o s c i l l o g r a p h . I t w o u l d b e n e c e s s a r y to a m p l i f y c o n s i d e r a b l y I n s u c h c a s e , b u t t h i s c o u l d be a c h i e v e d s a t i s f a c t o r i l y with a r e s i s t a n c e c o u p l e d a m p l i f i e r . O s c i l l o g r a m s n o s . 5,. 7, a n d 12 a r e t y p i c a l c o i l c u r r e n t o s c i l l o g r a m s a n d i l l u s t r a t e the d i f f i c u l t y e n c o u n t e r e d . I n n o . 5 , w h i c h was t a k e n w i t h twelve e q u a l i z i n g c o n n e c t i o n s and w i t h t h e machine f u l l y l o a d e d , t h e r e i s a f a i n t t r a c e i n t h e commutation . p e r i o d w h i c h seems to i n d i c a t e s a t i s f a c t o r y com-. m u t a t i o n , b u t t h a t i s a l l w h i c h c a n be s a i d . I t would be n e c e s s a r y t o open out the waves c o n s i d e r a b l y b y i n c r e a s i n g f i l m s p e e d b e f o r e much i n f o r m a t i o n c o u l d be g a i n e d . O s c i l l o -gram n o , 7, w h i c h has,, a l r e a d y -been d i s c u s s e d , g i v e s no r e c o r d •whatever o f c o m m u t a t i o n , and n o . 12, w h i c h was t a k e n w i t h f o u r e q u a l i z i n g c o n n e c t i o n s , and a t no l o a d , i s l i t t l e b e t t e r . I t .38 ' i s n o t even p o s s i b l e to t e l l whether o r n o t o v e r - c o m m u t a t i o n t a k e s p l a c e . ' From the r e s u l t s o f the o r d i n a r y t e s t s I t i s p o s s i b l e to make some o b s e r v a t i o n s on commutation i n g e n e r a l . I n the f i r s t p l a c e , even w i t h t h e a r m a t u r e e c c e n t r i c i t y a maximum,, t h e r e was no c a s e o f s p a r k i n g a t t h e b r u s h e s , p r o v i d e d the l a t t e r were r i d i n g s m o o t h l y on t h e commutator. T h i s I n i t s e l f i s p r o o f t h a t commutation i s n e v e r v e r y b a d . On the o t h e r h a n d , com-m u t a t i o n c a n n o t h e l p b u t be a d v e r s e l y a f f e c t e d when the mag-n e t i c b a l a n c e I s p o o r ? a s the I n t e r - p o l e e f f e c t r e m a i n s d e p e n -d e n t upon the l o a d c u r r e n t and i s n o t a f f e c t e d b y c i r c u l a t i n g c u r r e n t s . F u r t h e r , any e c c e n t r i c i t y o f the a r m a t u r e w i l l change the f l u x f r o m the' i n t e r - p o l e s , due t o the change i n l e n g t h o f t h e i n t e r - p o l e g a p s . T h i s t h e s i s i s i n no way a c o m p l e t e a n a l y s i s of even one phase o f t h e s u b j e c t o f m a g n e t i c i m b a l a n c e and I t s c o r r e c t i o n , a n d I s t o q u i t e a n e x t e n t an a b s t r a c t d i s c u s s i o n . I t has aimed to d i f f e r e n t i a t e between t h e f o u r - p o l e machine and one w i t h s i x o r more p o l e s , and to. examine to some e x t e n t the two c o r r e c t i v e e f f e c t s i n the c a s e o f the f o r m e r . The d i s c u s s i o n p o i n t s to t h e c o n c l u s i o n t h a t the p e r f o r m a n c e of a f o u r - p o l e l a p - w o u n d machine w i t h e q u a l i z i n g c o n n e c t i o n s does n o t w a r r a n t the com-p l i c a t i n g o f the machine w i t h t h e s e c o n n e c t i o n s . T h i s c o n f i r m s the c o n c l u s i o n o f I ' r . L u l o f s w i t h r e s p e c t to the f o u r - p o l e m a c h i n e . C e r t a i n d e t a i l s have been i n c l u d e d i n t h i s p r e s e n -t a t i o n w h i c h , though n o t a l t o g e t h e r e s s e n t i a l , might p o s s i b l y •'- 39 -• be h e l p f u l to anyone el s e w o o i n g along p a r a l l e l l i n e s on t h e same machine* • BIBLIOGRAPHY (1) "Armature Reaction i n a D . G-* Lap Wound Machine" \T. i,ulofs,. Electrician,, 1912 (2) " E q u a l l i n g Currents In t h e A r m a t u r e of a 33.-G-. Machine1* R* If. Baker,'A. 1* B» B, paper Ho. '§2-5 (3) - '"The Development of the D . 0, Generator i n A m e r i c a " 3 . G . Lamme, E l e c . Jour., Yol»XEl -(40) (41) Arrangement o f E q u a l i s i n g C o n n e c t i o n s The f o l l o w i n g t a b l e shows t h e arrangement o f e q u a l i z i n g c o n n e c t i o n s on the m a c h i n e . Bumbers i n the f i r s t column r e f e r to commutator segments, a n d t h e s e c o n d column g i v e s the s l i p -r i n g o r t e r m i n a l t o w h i c h t h e commutator segments a r e j o i n e d by a s i n g l e a r m a t u r e c o n d u c t o r . n u m b e r i n g o f t h e . c o m m u t a t o r s e g -ments i s a s shown I n f i g . 3 , a n d f o r l o c a t i o n on the machine s e q u e n t n o . 66 has a d r i l l h o l e on the e n d . I T h i s was u s e d for g r o u n d i n g o f the segment t o t h e s h a f t when t a k i n g v o l t a g e oscj3 -'lograms^T F i g * - 4 shows t h e numbering' o f t e r m i n a l s p l a c e d on t h e f i b r e d i s c , and i n t h i s e a s e , nos.. 12 and 13 a r e c l o s e l y s p a c e d , and t h u s c a n be l o c a t e d * O G ^ o o c o r - i o t n e -* # C v c O 3 H O 5 C 5 C 0 £ > - C D H H H H O O O O O H H CM. w to K l <^ w in CM CM 02 CM OJ CM C2 CM OJ OraOHI^-EOOOS-O CD LO ^  02 OJ CO CQ tO • # • • • * ' * • » • . * • • tt O.i 0.2 CM CM H H H H H W (35 W H » W W O O) to tO 10 CO CD Ci H H -•f * ' * * • > •#- *' ,-• ^ <tf tO lO o w o a o to 10 w ^ O tO CO CD O CQ. Ol sji H O H O l t O ^ t D ^ - C Q J f CO 1£> CD tO CO CO H '-O C M Hsl**>-OHHiOlOl>-02 tO ^ « CD 2> CO OJ O H • H H O C G O t Q t O t O l O i O O ^tOt>-COCO2>CO3>C0 H CM tO ^ » lO CO C- CO OS O C D O t O L O t O i O t O O -,4' * • • * *« ^ in t- co to t- co z> cb H 02 tQ "sfi lO CQ 2> CO 05 CO tO sJJ 02 lO tO 05 tO to HOCM^LO-^IO^IO »* *-' «• ft * * . • - * O l O O H C M t O s H l O C O I I " # 0 3 C Q l O O O C Q t Q l O * * * - » « » » * » ^ CO H C3'£-'tQ O CQ tO H H W tO tO ^ I S : ' . • t - CO H 02 tO 05 O VO C D 0 3 0 0 0 0 0 H H .• » • • . * - * • « 'A O O H H ' r f H H H H to O 00 B LO co to o *' # * #' « • * * - ^ 1 LO £-£-0>tt> CM tO £-CQCOCQCOCOCOfc-S-E-t o o i o t o t o o o t o O lO O ^ t ^ t O r i O M O O M l O C - O H ' v H c D G O • • - r-l rH H r-1 o'ri'o co a to o p • * # « » <* fc {*-=»' « O O O O C O f f l t O ^ K ) H 02 01 tO -tf.tfl CO t> O O O O O O O O O tfJlOlOlOtOlOiOtOlO CM 02 02 CM 01 02-02 Ol CM o o o o o o o o p M K H O O H D O C R ^ (?2 W W W OJ K H H H H H H H r i r t H H H (42a) tOHCQCOCMCD^lOCS <t! 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CD jC tO ^  02 to CD t> t - E -CO «H t> SO i> 1Q J>- © G5 6 «T-M. -sP tQ OS Z> ,o to tO K) f-t **£ -<r * •*• H 03. tO-^ji IO ra H O O O O CO CO LO O -•» *•»•»-^j i IO CD £-02 riOO o o co co to o tO CO JO H tO to CD 05 CO LO % • • • - # * CO © O H M ' -H r-t t—i * • * •* * # m <sf tO JN tO C0-£-.l>:C0 p • •H . •P o o tO Z> CO H O O O H -. *>' -«•; * •-H r-t r i H I 02 O - 1=02 CP . 0 CO CD -a o •H -p O o o o •If -H •H: H KS P Ol Q> id 10 « o to 02 H O 02 tQ CQ 05 H 02 bO 03 * G5 bO O CO O O O JO O C-, » * « » • C M ^ CO!> rH r-i H - r l O tQ O CO > * • » * CO CO s f o •stfiO CD C~ O O O O \Q IO l O IO 03 TO 03 0 2 O O O IO O CT> 05 CO K H H H H H H H (42T>) 02 CD 05 tO 02 LQ <X> C rH CO 05 tO iO C- 00 - 9 ' «t - r« * O O O O O H H H H o o ^ t o r - c o t o o o c Q 02 CX> O to -sP to tO CO O r-i 0.2 02 02 Ol 02 02 < "vP ^  02 CO O tO O IO IO t O tO O tO 05 CO H IO CQ O • • .»••.-»-.*.. « • . • • • O O O rH r-t OJ i>0 tO tO C D C O C O - v P C D H O H L O Q i L O s P O C i £ - C 5 t D C D C D CQ O "4] *tf ^ W C O C D C F S ^ O O O l O O tO CO 0J t - 02 O 03 Oi _>* * - # . #. • # » .« O O r-i SO !> CT5 0> O - • - H CO tO 2S b0 H 0-2 O 03 O W O tO H 'sf' "vf1 r-i CO CO Q O O O r I K CO-IO =115 CQ=-02 ^ ^ r l ^ l O O I f l O o o 0 5 0 5 co m co to to Q r l r i K CO ^ l O .CO'£>-m ^ ^ H ^ i o o L O o * *--«-•-#•*.- *' -» • •* 0 0 0 5 0 co to«co-to to• - • I t-i H 0J t0 IO CD £-CO IO w t- c- to o to LO 02 ^  "vti O HI tQ t- -vs' ^ « « « ' * • * * * * ' • O 02 CO CO Oi O H i — \ Hi 0 J o •H O! CJ § o o 'si •H N : •H1 H P a CD a !> H (!) 'tew *^ (r» to t - CO H CO 1 0 to p o CQ OOOCO t-t-.t-.B-.CO CO L0 l o 0 0 0 0 0 0 0 0 o tO LO © ^ O ^N 1 O LO 05 C Q K H H H W W N ^ LO LO CD I - « - . » . » • * » » • • » • j> Q r H H H r - i H H i H H H r-i O 1' 0J IO 02 02 CO r-i Z> O O <0 2>- l> CO IO LQ ^  02 H * . • ' . • • • . • . * .» «—) rH rH r-i r-i r-i HI r-i «H H O H C 0 C B O G 5 0 5 O O CO to to to ce co co 0 H to * . 18 •.» * *. •* * • * „ « 02 OJ 02 02 OJ C\2 tO tO tO CD LO tO CO 02 C- H LO IO C-00 O 051- CO 00 tO IO Ol Q O O O HI Csv> bO LO CO 2> LO tO 00 LO O 5- 05 LO LQ Hoa5to03a5**t- - to - * . H « - * * " rH CO! 02 tO IO CO 05 CO o H 0 5 t O U 3 l O C O L O t O L O b O • -a • • * • • • * • •H CO 05 O 3> LO LO OS CD rH 02 ^ IO CD CD t O C O O D O O t O C Q O O O O l f f l r o O O O O O r i -# * * • * * e O O O H H H H r l r l tO CO H LO CO O ^ O i.O W tO LO CO CD 05 O Ol tO CO CO CD CD CD CD t - t> Z-02 O O 00 IO O 10 LO O ^P CO OJ LO C- 00 02 02 « • • * • • . * O OJ ^  t - 05 H ^ CO CO HI r-i r-i rH 0 £ - Ol CO 'tOO 0 2 O O .« « ( S » * * OCTJG5COa3s>05LOI^) - H 02- tO ^  IO CD 2> O O O O O O O O O LO LO IO tO tO IO IO 1 0 to Qi 02 02 Ol C\2 02 02 CM Oi LO O LO O ' - O l O l f l O O 03 02 H rH O 05 CO CO 05 02 02 02 02 02 H H H H H r i r i r i r i r i r l r i r l PI O HI •P a? +> -H Ol HI jd1 0 1 P o 0). Pi o o b£ S3 •H • N v! H CJ P o l 0 ; O £3i C D O L 0 0 0 5 C O C O I O L O to CO CQ CD 7$ t<0 tO C- CTS CD * 4 - • • •• •» * » • « -»-O H 02 tO LO CD 2>QQ • 05 CO O W O 0> CO COLO 10 to * » ' * « • * fe CO CO CD tO tO J>'C55"'^ P :CD H 02 tO sP IO CO 1> CO CS5 LO CO O L O O CO O tO SO CD •H CttrCD'tO-tQ 02 CD•!>- C\2 tO H O O H 02 CO siMOcD 2>-1" r LO GO O LO O O O LO IO to H Ol CD t tO 02 CO t - Ol H H.O2-t0 •sP-'-lO'CO I 1 to 05 H 02 02 02 tO <tf LO CD b0 ^ P ^ ! ^  ^' ^ O O O O O O O O O O' tO P^ CO O O CO tQ O LO -NP • *- * ; * «' -*"• * ' * ' t0C~-s>-«>C0C0 05 OC75 O ©I' 02 OJ 02 02 0 i 02.LO 02 tO L O t O C O O t O C T i O C CO IO H W OJ O LO 2> O O H LO O H t O l O £ > 0 5 0 2 * ^ i O CO H ' H ' H H O fcOC- CO O tO O CD tO -a • . * « «:»'•»•*.« « O fr- ^ O CO t ~ CO CO 0 2 OJ • H 02 Ol tO -NP -LO' CD i n i o i o i n i O L O i o i o i O L O (.'.'? Gv2 CQ 02 Ol Oi OJ 02 OJ Oi rA f~U-^ r-i r-^ r~\ r-\ rH r-i - LO IO LO LO IO lO LO O O LO H H'H H H O f f l O O O 02 02 02 OJ K M r l H w w H r i H H H H H H H H (43a) T r e a t m e n t o f F l u x D i s t r i b u t i o n by means o f S o l u t i o n s o f I E l e c t r i c C i r c u i t F o r t h e p u r p o s e o f d e t e r m i n i n g flux d i s t r i b u t i o n m toe .magnetic c i r c u i t " u n d e r s t a t i c c o n d i t i o n s , t h e following metnod S S ^ o p t e d . : R a t h e r t h a n ^ i t o ^ e q u a t i o n s ^ f ^ ^ ^ ^ ^ h and r e l u c t a n c e s , a n analagous e l e c t r i c ° f : t h l s method h a s no p a r t i c u l a r m e r i t , the two. .djdgiara^ox i x g . 5 , shov t h e m a g n e t i c c i r c u i t I n w h i c h we a r e i n t e r e s t e d a n d a l s o the e l e c t r i c c i r c u i t which tie w i l l s o l v e . F~IG. 5 ID i ag i-am of h^lagrtefic R eluctancess Analogous EI <3ct ric Circuit 2B * (?^ + H 2E - (R* + B 2B = (R„ t- R 23 - (R* + H1 H 4 f o l l o w i n g e q u a t i o n s a r e t r u e A-+ r + JR x ) i | + Kx i¥ - 3? Iff +• r + Ko.) ix + R i is + r if R , i , + r + Ri.) i 3 + - r i-r + Hi U •(» r +* iij.) i<t i^ L ii ••+: r is- R'x I3 R^ 12. + xi ^  I3 — "Li* « 0 1. - i i + la - = 0 (2) . . . ( 4) ' -ft •» * « .'» (5) Hon vie w i l l assume t h a t i , ^ I s and 1* =. 6. T h i s i s n o t e x a c t l y t r u e b u t a g e n e r a l s o l u t i o n o f the f i v e o r i g i n a l e q u a t i o n s shows t h a t the a s s u m p t i o n i s w a r r a n t e d i n our c a s e . (43b) We have then:. 2E - (R^ + R'x+r * Rj.)!, «*• R^ i ¥ + R x i f c - (6) 2E ~ ( R , •+ R»+r + R i j i j . 4 R , i , + R z i , (7) T h e s e t h r e e may be s o l v e d b y d e t e r m i n a n t s and we g e t : i n i ) ,.23£ ( B ^ . R a . ^ r * ft?-. ) i . = .RJ + 3R^R 1+ 2 r R* + + 3R..RV 4 3 r R'x+ 3 r R x + r*• 2B {R* - Rx 4 r * 3 R ' i 1 3,2 s I > - ' - " where D sta,nds f o r t h e d e n o m i n a t o r o f the e x p r e s s i o n f o r i k» E e n c e we can p r o c e e d t o f i n d the r a t i o o f i , <+ i ^ t o i 5 + i ^ i i * ix ^ i> * i * . ~ R ^ ^ R ^ t xtm+ R'J. » R » » RT.+ r 4- 3R'^ i-5 * iif. 1, 4 LA R,+ r ••+- R ' i +- R.+ 3R,-v r - R ' z R* ,* r . •t.-^Rji: R^ + r 4 2R2. How g o i n g b a c k a n d a p p l y i n g t h i s r e s u l t to o u r m a g n e t i c c i r c u i t w gelt/ • 4SJ U«:i.±..X ftjB , (R',4 .R?,! + r + 2 (R t R 3 , 

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