@prefix vivo: . @prefix edm: . @prefix ns0: . @prefix dcterms: . @prefix skos: . vivo:departmentOrSchool "Applied Science, Faculty of"@en, "Electrical and Computer Engineering, Department of"@en ; edm:dataProvider "DSpace"@en ; ns0:degreeCampus "UBCV"@en ; dcterms:creator "Smith, Donald Sinclair"@en ; dcterms:issued "2011-10-25T22:48:27Z"@en, "1933"@en ; vivo:relatedDegree "Master of Applied Science - MASc"@en ; ns0:degreeGrantor "University of British Columbia"@en ; dcterms:description "[No abstract available]"@en ; edm:aggregatedCHO "https://circle.library.ubc.ca/rest/handle/2429/38267?expand=metadata"@en ; skos:note "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 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 , 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 •» . 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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 - ' - \" 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 , "@en ; edm:hasType "Thesis/Dissertation"@en ; edm:isShownAt "10.14288/1.0105041"@en ; dcterms:language "eng"@en ; ns0:degreeDiscipline "Electrical and Computer Engineering"@en ; edm:provider "Vancouver : University of British Columbia Library"@en ; dcterms:publisher "University of British Columbia"@en ; dcterms:rights "For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use."@en ; ns0:scholarLevel "Graduate"@en ; dcterms:title "A study of the electrical effects of armature eccentricity in a four-pole, lap-wound D.C. machine"@en ; dcterms:type "Text"@en ; ns0:identifierURI "http://hdl.handle.net/2429/38267"@en .