Effective Design Parameters on the End Effect in Single-Sided Linear Induction Motors

Transcription

1 World Acady of Scnc, Engnrng and Tchnology ntrnatonal Journal of Elctrcal and Coputr Engnrng Vol:4, No:4, 00 Effctv Dgn Paratr on th End Effct n Sngl-Sdd Lnar nducton Motor A. Zar Bazghalh, M. R. Naghahan, H. Mahoudanh, M. R. Mhkatoddn ntrnatonal Scnc ndx, Elctrcal and Coputr Engnrng Vol:4, No:4, 00 wat.org/publcaton/086 Abtract Lnar nducton otor ar ud n varou ndutr but thy hav o pcfc phnona whch ar th cau for o probl. Th ot portant phnonon calld nd ffct. End ffct dcra ffcncy, powr factor and output forc and unbalanc th pha currnt. Th phnonon or portant n du and hgh pd achn. n th papr a factor, EEF, obtand by an accurat quvalnt crcut odl, to dtrn th nd ffct ntnty. n th way, all of ffctv dgn paratr on nd ffct dcrbd. Accuracy of th quvalnt crcut odl valuatd by two dnonal fnt-lnt analy ung ANSYS. Th rult how th accuracy of th quvalnt crcut odl. Kyword Lnar nducton otor, nd ffct, quvalnt crcut odl, fnt-lnt thod.. NTRODUCTON OWADAYS th applcaton of lnar otor (LM) ar N wdly xtndd. [],[]. LM can provd lnar oton drctly. Thu thr no nd to whl, gar or any typ of rotary to lnar oton convrtor. Thank to abnc of chancal convrtor, th typ of otor ha good prforanc and hgh rlablty [3]. Fro dffrnt typ of LM th lnar nducton otor (LM) ar ud or, pcally, n th for of ngl-dd lnar nducton otor (SLM). n o applcaton of SLM, th condary cag-typ or woundd [4]. But by ung of a hgh conductng plat Backd by a frroagntc atral (Back ron), ntad of cag or woundd typ of condary, th tructur of SLM wll b or and or plfd. Th bcau of wdly uag of SLM. Svral dffrnt thod hav bn prntd for analy of LM, uch a quvalnt crcut odl (ECM), -D and -D lctroagntc fld analy and nurcal thod ncludng fnt-lnt (FEM) and fnt-dffrnc (FDM) thod [5]-[9]. End ffct of LM ha bn o far tudd n vral rarch, n whch dffrnt purpo hav bn condrd. N. Fuj and T. Harada hav tudd nd ffct n SLM wth laddr typ condary. Thy prntd t p t a a factor to aur th dgr of nd ffct [0]. Whr n whch t p pang duraton of prary cor at a condary pont and t half-prod of lp frquncy. n anothr papr th nd ffct ha bn nvtgatd copltly by ung of FEM []. Th phnonon banful and affct th output of otor thu t a good da to copnat th phnonon n LM []. But t a bttr da to dgn a achn wth lowr dgr of nd ffct. To achv th purpo t ncary to rconnotr all of ffctv dgn paratr on nd ffct. n a rarch, o of th paratr ar ntroducd by hlp of -D lctroagntc fld analy [3]. n th papr all of ffctv dgn paratr wll b dcrbd. n ordr to prfor th da, a utabl ECM wll b ntroducd. Th odl obtand by odfyng th Duncan odl. Th rultant ECM nclud nd ffct, truly. By hlp of th ECM a factor wll b obtand whch dcrb th nd ffct ntnty. Thn th ffct of dgn paratr on th nd ffct wll b nvtgatd through approprat 3-plot by hlp of MATLAB. Fnally, th -D t tppng nonlnar FEM carrd out by hlp of ANSYS to valuat th proffrd ECM.. ECM OF SLMS CONSDERS END EFFECT Th rlatv oton btwn hort prary and long condary, cau to nd ffct. Th ffct lad to brakng forc and addtonal lo that ar producd by ddy currnt at th ntry and xt ral a t can b n n Fg. [4]. A. Zar Bazghalh, Powr and Watr Unvrty of Tchnology, Thran, ran (corrpondng author to provd phon: ; -al: ar.zarbazghalh7@gal.co). M. R. Naghahan, Powr and Watr Unvrty of Tchnology, Thran, ran. (-al: naghahan@yahoo.co). H. Mahoudanh, Claud Brnard Lyon Unvrty, Lyon, Franc (al: ahoudanh@yahoo.co). M. R. Mhkatoddn, Powr and Watr Unvrty of Tchnology, Thran, ran (-al: hkatoddn@.org). Fg. Eddy currnt gnraton at th ntry and xt ral A t can b n n Fg., by nglctng nd ffct, th ECM of SLM co to ECM of rotary nducton otor (RM) []. ntrnatonal Scholarly and Scntfc Rarch & nnovaton 4(4) cholar.wat.org/ /086

2 World Acady of Scnc, Engnrng and Tchnology ntrnatonal Journal of Elctrcal and Coputr Engnrng Vol:4, No:4, 00 ntrnatonal Scnc ndx, Elctrcal and Coputr Engnrng Vol:4, No:4, 00 wat.org/publcaton/086 V Ph R Fg. ECM of SLM by nglctng nd ffct On of th bt ECM that ncludd nd ffct th ECM uggtd by Duncan [5]. n th cton Duncan ECM ha bn dcrbd and odfd to achv th utabl ECM, for a fat and accurat tudy on SLM. Th r and dcay of condary ddy currnt ar controlld by th condary lakag t contant Tlr = Llr R and total condary t contant Tr = Lr R, rpctvly. Notng that th ntry ddy currnt caud by ntry nd ffct dcay wth th t contant T r, th avrag valu of ntry ddy currnt ε ovr th otor lngth gvn by: ε T Z υ t Tr = dt T /. () υ 0 Whr T v th t that th otor nd to ovrpa a pont. Motor can tranvr a dtanc qual to v. Tr ovr th t duraton T r. Thu, th otor lngth can b noralzd by v. Tr uch that [5]: ls R = () ( L + L ) v By th way, th noralzd otor lngth dpnd on vlocty. Ung (), quaton (), bco: x ε =. dx = (3) 0 Thu, th agntzng currnt rduc a followng: ε = (4) Th rducton n th agntzng currnt wll b accountd n ECM by odfyng th agntzng nductanc a followng: L = L ( ) (5) But that wll not b all. Bcau, whn nducd ddy currnt crculat n condary plat, t cau to ohc lo. Th lo wll b producd by R.Th ffctv valu of ddy currnt ovr th otor lngth can b valuatd a: / / x ε r = = dx (6) 0 Thrfor, th valu of ohc lo du to ntry ddy currnt can b obtand by: Pntry = ε rr =. R (7) Th total ddy currnt n th ar gap can b obtand fro (3) a ( ). To atfy th tady tat condton n th ar gap, ddy currnt ut b vanhd at xt ral durng th t T v. Thrfor, th ohc lo caud by xt ddy currnt ay b valuatd by: Lr ( ) ( ) Pxt = = (8) Tυ Thu, fro (7) and (8), th total ohc lo du to ddy currnt n th condary wll b: xp( ) Pddy = R (9) A t can b n n quaton (9), th ohc powr lo can b rprntd by a rtor whch connctd n r to th agntzng nductanc. A t can b n n Fg.3, th dffrnc btwn Duncan odl and convntonal quvalnt crcut of RM th chang n th agntzng branch du to th nd ffct []. V Ph R R Fg. 3 ECM uggtd by Duncan n Duncan odl Th ECM paratr ar obtand by th tandard opn and hort crcut tt, but, bcau of th pcfc phnona n LM, th ECM paratr chang wth lp and cannot b obtand by tandard tt [3]. Th bt way to obtan ECM paratr of SLM, ung analytcal quaton [6],[7]. Z W L c R + = J c N ph (0) σ cu N ph μ W = ω 3 λ λd λ lc () p p q Z ( ) = ( jωμ o K ) [ tanh( K d) ] () K W τ Z (4) F tr ( jωμ K )[ tanh( K d ] ( ) = ) = K tr F W τ F F ron [ 4 μ o f ( N phk w π p] Wτ g ) (3) Th condary cor n SLM ad of old ron or tl, o, aturaton occur n o opraton condton. n ordr to ntrnatonal Scholarly and Scntfc Rarch & nnovaton 4(4) cholar.wat.org/ /086

3 World Acady of Scnc, Engnrng and Tchnology ntrnatonal Journal of Elctrcal and Coputr Engnrng Vol:4, No:4, 00 ntrnatonal Scnc ndx, Elctrcal and Coputr Engnrng Vol:4, No:4, 00 wat.org/publcaton/086 tak th ffct nto account, th aturaton coffcnt, K, ha bn dfnd and cau to ncra n ar gap lngth. g = K K ( + K )( g d) (5) l c + Th aturaton coffcnt for th condary back ron, K, th rato of back ron rluctanc to th u of conductor and th ar gap rluctanc. Condrng th avrag lngth of old back ron flux path to b / β and th dpth of fld pntraton n th ron a δ, th aturaton factor tak th for []: μ K = (6) μ δ ( g + d K β 0 ) 0.5 [ ( β jωμ σ ) ] c δ = R + (7) Th avrag prablty of back ron can b coputd durng an tratv procdur [8]. n ordr to obtan th goal frt t ncary to calculat th approxat valu of flux dnty n th ar gap []. B = jj μ g β ( + jg ) (8) ag [ ] 0 J = N ph K w pτ (9) Aung an xponntal for for th fld dtrbuton n th back ron th flux dnty at th urfac of th back ron tak th for []: B = B ag δ β (0) Th condary of SLM ha no pcfc path for nducd currnt. Th phnonon cau to ncra n quvalnt condary rtanc. Th ffct known a th tranvr dg ffct and hould b condrd by utabl coffcnt []. σ = σ f k f () σ = σ k () A raltc ar gap flux dnty lowr than 0.4T, lad to odrat flux dnt n th prary cor ron, and thu cor lo can b nglctd and th propulon forc, th powr factor, and th ffcncy can b obtand fro [8]: = 3 R (3) F x co ϕ = Fx fτ + 3 R + 3 R 3V (4) η = F fτ (5) ( ) F f + R + R x τ 3 3 x. END EFFECT NTENSTY Two ECM ar dcrbd n lat cton. Th frt on (Fg.) do not condr nd ffct but th cond on (Fg.3) condr th addtonal lo n th ntry and xt ral and rducton of forc caud by nd ffct. Thrfor, th ar gap powr whch calculatd by th frt ECM at contant currnt, P ag(n), for a SLM whch ha no nd ffct, But th ar gap powr whch calculatd by th cond ECM, P ag(w), contan th addtonal lo and forc rducton caud by nd ffct. Thu, nd ffct ntnty, EEF, can b aurd by th followng quaton: n) w) w) EEF = = (6) n) n) EEF vru otor pd hown n Fg.4. Fg. 4 EEF vru otor pd V. EFFECTVE DESGN PARAMETERS TABLE MAN DESGN PARAMETERS OF CASE STUDY SLM Sybol Valu Nubr of pol 4 Nubr of lot pr pol pr pha Nonal pd (/) 0 Nonal currnt (A) 00 Pol ptch () 0.8 Frquncy (Hz) 60 Prary wdth () 0.36 Currnt dnty (A/ ) 6.5 Slp 0.3 Ar gap lngth () 3 Conductng plat thckn () Conductng plat rtvty to alunu 0.6 rtvty rato Th EEF can b ud to dcovr th ffctv dgn paratr on th nd ffct ntnty. n th cton th nflunc of dgn paratr on nd ffct ntnty wll b dcrbd. To achv th goal th dcrbd ECM wll b ud. Th ca tudy achn ulaton dtal ha bn dcrbd n Tabl. Chang n th ar gap lngth can affct th flux dtrbuton n th ar gap and condary. By th way, an ncra n th ar gap lngth ncra th lo n th xt and ntry ara of ral. Alo, n th ca of nonfrrou conductng plat, f th conductng plat thckn ncra, th condary t contant ncra that lad to nd ffct travllng wav of allr agntud. A t can b n n Fg.5, EEF ncra by ncrang th ar gap lngth and dcrang th condary conductng plat thckn. Varaton of nd ffct ntnty, wth th condary conductng plat rtvty and lot ptch to lot wdth rato (SPSW), jutfabl by th t contant of condary, too. A conductng plat wth largr rtvty caud to allr condary t contant. t lad to a or ntnv nd ffct. Varaton n th tator cor dgn can affct th nd ffct ntnty, too. Largr aount of SPSW (allr tooth ntrnatonal Scholarly and Scntfc Rarch & nnovaton 4(4) cholar.wat.org/ /086

4 World Acady of Scnc, Engnrng and Tchnology ntrnatonal Journal of Elctrcal and Coputr Engnrng Vol:4, No:4, 00 wdth) cau to largr condary lakag ractanc and largr condary t contant. Fnally, t rult nd ffct travllng wav of allr agntud. Fg.6 how th varaton of EEF rlatd to SPSW and conductng plat rtvty to alunu rtvty rato (CRAR). Th EEF varaton rlatd to th frquncy and dgn currnt dnty ar hown n fg.8. At a contant lp for a contant chancal pd th dcra n frquncy wll ncra th pol ptch. Th cau to a largr condary t contant and allr nd ffct. Th dgn currnt dnty ha no ntv ffct on nd ffct ntnty. Bcau n th papr chang n dgn currnt dnty only chang th lot dpth and ha no ffct on lot wdth and tooth wdth. ntrnatonal Scnc ndx, Elctrcal and Coputr Engnrng Vol:4, No:4, 00 wat.org/publcaton/086 Fg. 5 End ffct ntnty vru ar gap lngth and conductng plat thckn Fg. 6 End ffct ntnty vru lot ptch to lot wdth rato and conductng plat rtvty to alunu rtvty rato Fg.7 how th varaton of EEF rlatd to th nubr of pol par (NP) and nubr of lot pr pol pr pha (NSPP). Th dcra n th EEF wth ncra n NP caud by th fact, or pol tnd to har th contant nd ffct lo btwn th. t n that NSPP ha no nbl ffct on th EEF, but largr NSPP can odrat th pha unbalanc du to nd ffct. Fg. 7 End ffct ntnty vru nubr of pol par and nubr of lot pr pol pr pha Fg. 8 End ffct ntnty vru frquncy and currnt dnty Fg.9 how th varaton of EEF by chang n th valu of lp and prary wdth to pol ptch rato. A th lp ncra, th nd ffct ntnty wll dcra. For a contant frquncy to achv a partcular pd lp rducton cau to pol ptch rducton and th dcra th condary t contant whch lad to a or ntnv nd ffct. Fg. 9 End ffct ntnty vru lp and prary wdth to pol ptch rato V. VALDATON STAGE Th tudy carrd out bad on a nw quvalnt crcut odl. Thrfor, valdty of th rult anly dpnd on th accuracy of th crcut odl. Thu -D t tppng FEM ud to valuat th rult. Fg.0 how th coparon of rult fro ECM and FEM. t can b n that ECM rult ar clo nough to th FEM rult. Fg., how th flux dnty dtrbuton, and flux ln, n th SLM rpctvly. A th prary of th SLM ov to rght, th flux dnty rducd n th front of SLM and rflctd bhnd th SLM. ntrnatonal Scholarly and Scntfc Rarch & nnovaton 4(4) cholar.wat.org/ /086

5 World Acady of Scnc, Engnrng and Tchnology ntrnatonal Journal of Elctrcal and Coputr Engnrng Vol:4, No:4, 00 Fg.3 how th flux dnty dtrbuton n th ar gap. t can b n that th flux dnty of ar gap l than 0.T, thu th prary cor lo nglgbl. V. CONCLUSON Th papr prnt a thod to tudy th nflunc of dgn paratr on th nd ffct ntnty n SLM. n ordr to obtan th purpo, a quck quvalnt crcut odl, wa ntroducd. Th odl condrd th pcfc phnona n SLM, uch a tranvr dg ffct and aturaton ffct, by an of o propr factor. Th longtudnal nd ffct wa alo condrd by odfyng Duncan quvalnt crcut odl. For th purpo of aurng th nd ffct ntnty a nw factor, EEF, wa ntroducd. At th nd of ulaton, th accuracy of uggtd ECM wa valuatd by -D t tppng FEM analy that pl th good accuracy of th thod. Fg. 0 Forc vru pd APPEND ntrnatonal Scnc ndx, Elctrcal and Coputr Engnrng Vol:4, No:4, 00 wat.org/publcaton/086 Fg. - Flux dnty dtrbuton n SLM Fg. Flux ln n th SLM Fg. 3 Flux dnty dtrbuton n th conductng plat Sybol SYMBOLS uantty W l c Stator wdth and nd conncton lngth P,τ Nubr of pol and pol ptch q Nubr of lot pr pol pr pha R, Prary rtanc and ractanc Magntzng ractanc N ph Nubr of turn pr pha g, d Ar gap lngth and conductng plat thckn K Conductng plat coffcnt k Conductng plat coffcnt du to dg ffct K F Back ron coffcnt k f Back ron coffcnt du to dg ffct K tr Prary to condary rato K w Wndng factor K c, K l Cartr coffcnt and lakag factor σ, σ f Conductng plat and back ron conductvty REFERENCES [] J. F. Gra, Lnar nducton Drv. Oxford, U.K.: Nw Clarndon Pr, 994. [] M. Mral, A. Doroud,; J.S. Moghan, Obtanng th opratng charactrtc of lnar nducton otor: a nw approach EEE Tran. Magn. Vol.38, pp: u:, March 00. [3] J. F. Eatha, Novl ynchronou achn: Lnar and dc, Proc. nt. Elct. Enrg., vol. 37, pp , Jan [4] T. Kok, S. Son, nvtgaton of condary lot ptch of a cagtyp lnar nducton otor, EEE Tran. Magn., vol. 9, no. 6, pp , Nov [5] W. u, G. Sun, Y, L,; Rarch on Prforanc Charactrtc of Lnar nducton Motor EEE ndutral lctronc and applcaton conf. 007 pp [6] R.C. Crpp, J.A.C. Ulon, J.F. Rodrgu,; nflunc of Dgn Paratr on Lnar nducton Motor End Effct EEE Tran. Enr.Conv.vol.3 no. pp , Jun [7] K. dr, G.E. Dawon, A. R. Eatha; Modlng and Prforanc of Lnar nducton Motor wth Saturabl Prary EEE Tran. ndu. vol.9, no.6, pp. 3-8, Nov [8] T. Yaaguch, Y. Kawa, M. Yohda, Y. Sato; Ohdach, Y.; 3-D Fnt Elnt Analy of a Lnar nducton Motor EEE Tran. Magn. vol.37, no.5, pp: Sp 00. ntrnatonal Scholarly and Scntfc Rarch & nnovaton 4(4) cholar.wat.org/ /086

6 World Acady of Scnc, Engnrng and Tchnology ntrnatonal Journal of Elctrcal and Coputr Engnrng Vol:4, No:4, 00 ntrnatonal Scnc ndx, Elctrcal and Coputr Engnrng Vol:4, No:4, 00 wat.org/publcaton/086 [9] Y. Nozak, T. Kok, E. Maada; Analy of Lnar nducton Motor for HSST and Lnar Mtro ung Fnt Dffrnc Mthod Proc. of th 5th ntrnatonal Sypou on Lnar Drv for ndutry Applcaton, pp: 68-7, LDA005. [0] N. Fuj, T. Harada, A Nw Vwpont of End Effct of Lnar nducton Motor fro Scondary Sd n Laddr Typ Modl EEE Tran. Magn., vol. 35, no. 5, pp , Sp [] A. H. Slçuk, H. Kürü, nvtgaton of End Effct n Lnar nducton Motor by Ung th Fnt-Elnt Mthod EEE Tran. Magn., vol. 44, no. 7, pp , July [] N. Fuj, T. Kayauga, T. Hoh, Spl End Effct Copnator for Lnar nducton Motor EEE Tran. Magn., vol. 38, no. 5, pp , Sp. 00. [3] R. C. Crpp, J. A. C. Ulon, J. F. Rodrgu, nflunc of Dgn Paratr on Lnar nducton Motor End Effct EEE Enrgy Conv. Magn., vol. 3, no., pp , Jun [4] J.H. Sung, K. Na, A Nw Approach to Vctor Control for a Lnar nducton Motor Condrng End Effct, EEE AS annual tng, pp.84-89, 999. [5] J. Duncan, Lnar nducton otor Equvalnt crcut odl, Proc. nt. Elc. Eng., pt. B, vol. 30, no., 983. [6] J. Faz, H. Jafar; Accurat Modlng of Sngl-Sdd Lnar nducton Motor Condr End Effct and Equvalnt Thckn EEE Tran. Magn. vol.36, no.5, pp: , Sp 000. [7]. Bolda and S. A. Naar, Lnar Elctroagntc Dvc. Nw York: Taylor & Franc, 00. [8] R. M. Pa,. Bolda, and S. A. Naar, A coplt quvalnt crcut of a lnar nducton otor wth ht condary, EEE Tran. Magn., vol. 4, pp , Jan ntrnatonal Scholarly and Scntfc Rarch & nnovaton 4(4) cholar.wat.org/ /086