LINEAR SYNCHRONOUS MOTOR WITH TRAVELLING WAVE-EXCITATION

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1 LINEAR SYNCHRONOUS MOTOR WITH TRAVELLING WAVE-EXCITATION () Dr. Frnc Tóth, () Norbrt Szabó (), () Univrsity of Miskolc, Dpartmnt of Elctrical and Elctronic Enginring () () Univrsity of Miskolc, H 55 Miskolc-Egytmvaros (), () Phon: / 59Fax: mail: () lktoth@gold.uni-miskolc.hu, () lkszabo@gold.uni-miskolc.hu Ky-words: Linar synchronous machin, finit lmnt mthod.introduction Drivation Of Th Linar Machins is usually carrid out from th construction of convntional rotary machins. Accordingly if a convntional rotary machin is cut by a radial plan to th axis and unrolld w can obtain an lctrical machin with two paralll plan surfacs sparatd by airspac. In this way, a numbr of diffrnt typ of linar machins can b dvlopd dpnding on th typ of th initial rotary machin, w can spak about linar induction motor (LIMs), linar synchronous motors (LSMs), and dirct-currnt linar motors (DCLMs). Th rsult is a flat linar motor that producs linar forc. Trms usd at th rotary machins stator and rotor at th linar machins corrspond to th primary and scondary, rspctivly. It is clar that wr motion ovr a considrabl distanc is rquird with a constant powr, ithr th primary or th scondary mmbr must b longatd. Such longation lads to th major classs of linar machins which may b dsignatd as short primary and short scondary. Th altrnating currnt linar synchronous motor can b obtaind, if a woundrotor induction motor is cut by a radial plan and unrolld. (It is considrd as a doubl -sidd stator configuration without scondary part.) Th arrangmnt dscribd abov assumd that both parts consist of lctrical conductors in slots in a laminatd stl cor, which is th usual arrangmnt in a rotary machin. If th primary windings and th scondary windings ar xitd from th sam supply thn two moving magntic filds ar producd, undr propr circumstancs, in sam dirction. If th scondary can mov, thn a forc is stablishd, that is put th scondary in motion and th pols of th two parts will b positiond opposing on anothr (this is th synchronous standing stat). In th cas if, for xampl, th frquncy of th supply in scondary part is changd and th frquncy of th supply in primary part rmains constant, in this momnt a forc will b dvlopd and th scondary will mov with a vlocity dtrmind by th diffrnc btwn th frquncis. As this kind of arrangmnt and supply of linar machins cannot b found in th tchnical litratur th mthod is patntd. []. Basic connction in Finit-lmnt calculating mthod W dtrminat th motor important paramtr with th hlp of finit lmnt mthod. Th allottd task solution did in th following stps with th finit-lmnt mthod. First of all th xamin pic, or spatial- (two dimnsion cas plan) partial, dissociation to rang-part so-calld finitlmnt. Finit-lmnt intrfac, rspctivly sign significant point insid so-calld nod, whr w took som nodal paramtr. Th nodal paramtr in most cass th rplacmnt valu was th task typical function in th nods. Th typical function approximat in partly (rang-part). Th approximat functions wr polynomial mostly, which com about th natur of th task nd to satisfaction th conditions. Tak approximat function in vry rang-part finit lmnt intrfac nod paramtr us intrconnct. Th substitution of approaching concrn th whol body into th givn function of th typical function, transform th functiond function into nod paramtrs function.. Th linar algbraic quation systm solution givs th valu of th nod paramtrs.

2 Knowldg of nod paramtrs us lmntary approximat polynomial any points of th body dtrminabl th charactristic function, rspctivly th driv quantity (. magntic inductio n). [, ] Linar synchronous motor with travlling wav-xcitation two dimnsion calculation modl accordingly abov numratd principl th. figur show dissociation of th rang and trminal priod. In th. figur w not that what kind of margin condition considr th xtrnal rim of th whol rang. Insid th rang th Ω is th ithr dxcitation, Ω is th othr dxcitation, whil th Ω is th airspac btwn th two part, th n vctor is surfac normal of this rang.. figur. Btwn th Ω and th Ω rang th following quations ar valid: Insid th Ω rang ar: rot H = J ( vagy ) () div B = 0 () H = ν( B )B () rot H = 0 (4) div B = 0 (5) H = ν 0 B (6) whr ν = / µ th magntic rluctanc. Th formulas blow ar availabl in th Γ margin transition: Similarly th Γ margin transition ar: Figur. show margin fac: n ( H H ) = 0 (7) n ( B B ) = 0 (8) n J = 0 (9) n ( H H ) = 0 (0) n( B B ) = 0 () n J = 0 () n B = 0 in th Γ B at margin () n H = 0 in th Γ H at margin(4) Magntic vctor potntial as usual to choos in two dimnsion tasks for th typical function of th nod paramtrs.

3 As known with th hlp of th vctor potntial rprsnt magntic induction, rot A = B (5) With knowldg of th known vctor-transformations using th (5) and th() th() can b xprssd in th following way: rot ( ν rota) = grad( ν) rota+ ν grad( diva) ν A= J( or) (6) Apply th (6) quation to on lmnt of th xamind domain, it is possibl that insid th lmnt th, ν rluctanc valu is prmannt, furthrmor with th Coulomb masur ( div A = 0 ) th (6) bcom simpl considrably:: ν A = J ( or ) (7) Th (7) is th xprssion of th Poisson quation solution by givn limit can b rducd to a variabl problm solution. In cas of plan-problm th ν I = A J A dω AJ Γ Ω rot Γ dl min w look for th valu of A vctor-potntial blong to intgral xtrm of [4]. Examining two dimnsion cas w hav to considr only th z dirction componnts of th vctorpotntial and th currnt dnsity, so th(7) is rducd to th following scalar quation: ν A = J (9) If w xam th(8) quation with Dirichlt typ limit-condition, thn on th limit-surfac th A tangnt componnt is prscrib, and if it zro, thn on th right sid of th (8) quation found scond intgral is zro, so (0) intgral xprssd to on finit-lmnt ν I = ( grad A) JA min dx dy (0) has got xtrm, if th along th curv bordr th Ω surfac th A varis as it is prscribd (In th appndix w introduc th connction btwn nrgy-procss and th nrgy-functional in th currnt-machins.) Th (0) quation has got xtrm valu, whn its first variation is zro. Constitut (0) th drivativ as (A) of magntic vctor-potntial, w can writ on th i th nod of lmnt: (8) I A i = ν ( grad A) A i JA dxdy = ν A A A A A ( ) + ( ) J dxdy = 0 x Ai x y Ai y Ai () Whr th A can b obtaind from A i vctor-potntial valus, which ar in th nod of th vctorpotntial lmnt. By th task, which is dlinatd, w dividd th xamind quadrangular domains to finit- lmnts, by which in a quadrangular lmnt th vctor-potntial valu can b xprssd from th gomtric masurs and th vctor-potntial valus of nods: [ N]{ A} A( ζ, η) = Ni ( ζ, η) Ai + N j ( ζ, η) Aj + Nk ( ζ, η) Ak + Nl ( ζ, η) Al = () whr N i, j,k l, is form-factor connctd with gomtric masurs and position of finit- lmnt [5], A i, j,k,l is th valu of vctor-potntial in th summit of quadrangular substituting () for (), thn doing th pointd driving and intgrating, w gt to an algbraic quation systm, which usually is givn in matrix form. [ ] { A} { C} K = () whr, { A} is th pillar matrix of magntic vctor-potntial valus of nods connctd with lmnt, [ K] is th factor matrix, which contains th gomtric masurs btwn nods and th valus, which dtrmin th position of nod, { } C is th pillar matrix of currnt-dnsity valus connctd nods.

Solvd th () quation by all lmnt of th xamination Ω domain, w gt in th nods of domain th valus of magntic vctor-potntial, so w can considr mor spac-dscription valus.

figur mntiond task ralization in ESTAR program, th finit lmnt distribution and th bordr conditions ar shown by. figur.

4 Solvd th () quation by all lmnt of th xamination Ω domain, w gt in th nods of domain th valus of magntic vctor-potntial, so w can considr mor spac-dscription valus. W usd th COSMOS/M ESTAR program packag to th solution th task abov mntiond, by which on th.figur mntiond task ralization in ESTAR program, th finit lmnt distribution and th bordr conditions ar shown by. figur.. figur Two dimnsion modl with quadrangular formd finit-lmnt distribution By th calculation w considrd th non-linarity of iron componnts in th Ω and Ω domains. In. figur w can s th B-H magntic curv of th iron, which has bn takn into th program as data.. Introduction of calculatd rsults. figur Th curv of iron B-H applid in th program Th calculations wr run with transint analysis program, w supposd, that th xcitation of long armatur (th Ω domain) - as th 4. figur shows - is altrnating currnt. Th plac valus of calculatd rsults w introduc in two typical status of synch opration, nutral opration status in a clos status, and th maximum load in clos status. (Th clos attribut rfr to th valus, w got btwn th nutral and th maximum load and w hav possibility to introduc thm) Th 4a shows th plac-valus of calculatd valus: magntic vctor-potntial, magntic induction, hauling powr and attractiv powr. At first w introduc thos rsults, which shows th valus clos to th synch status. Th 4. figur shows th gomtric arrangmnt of takn ngin-modl, if th long vrtical-part has got A.C. xcitation. 4. figur Gomtric arrangmnt of ngin modl takn to calculation 4

. Th rsults of th procding wav xcitation ngin.

stat of ngin (a, figurs), in th maximum hauling powr stat (b,

figur Th valu of th magntic vctor-potntial in nod of

figur Th valu of th magntic induction in nod of finit-lmnt: a)

figur Th valus in nod of hauling powr actd on th long car-cas:

5 . Th rsults of th procding wav xcitation ngin. Th changs of mor important typical of plac-valus in th nutral stat of ngin (a, figurs), in th maximum hauling powr stat (b, figurs) 5. figur Th valu of th magntic vctor-potntial in nod of finit-lmnt: a) nutral, b) status clos to dump point 6. figur Th valu of th magntic induction in nod of finit-lmnt: a) nutral, b) status clos to dump point 7. figur Th valus in nod of hauling powr actd on th long car-cas: a) in status clos to nutral, b) status clos to dump point 8. figur Th valus in nod of attractiv powr actd on th long car cas: a) nutral, b) status clos to dump point 5

Th calculation whr run with transint analysis program lik arlir from th output fil w can know th avrag hauling powr valus. Ths valus was drawn with MATLAB program.

6 Th calculation whr run with transint analysis program lik arlir from th output fil w can know th avrag hauling powr valus. Ths valus was drawn with MATLAB program. Th avrag valu of hauling powr is shown in 9.a figur, 9.b figur nar angular variation, whil th attractiv powr avrag valu is shown in 9.b. figur. 9. figur Th avrag a) hauling powr, b) attractiv powr on m wid ngin dtrmind with calculation.4 Supporting of calculatd rsults with xprimnt W usd th 9 laboratory modl shown in 0. figur to th masurmnt, whr w usd cross linar ngin. W fixd th first ngin, whil th scond can mov on whl. Th two on-sidd inductor was addd up to atomic battry, thn masurd from synchronous point 6 N. If now w bind th on inductor from powr supply and w clos th battry sho short (additional winding with linar induction motor),th valu of hauling powr in this status N. Th ratio of th masurd valus is 7,.. figur Laboratory masuring station W had to mak th ngin modl with windd scondary part to compar th ratio of calculatd rsults. Unfortunatly bcaus of th boundd amount of our program w couldn t mak th finit lmnt calculating modl of ral laboratory modl, only th induction ngin modl as th 4. figur shows. Th. figur shows th gomtric arrangmnt of windd scondary linar induction motor. 6

. figur Th gomtric arrangmnt of th induction ngin Th 5. Figur shows th hauling powr of th windd scondary induction ngin in standing position. figur and th travlling-wav xcitd induction ngin 4. figur. W gt nar th calculatd valus th following ratio: 74,4 N/4 N= 8,6.

7 . figur Th gomtric arrangmnt of th induction ngin Th 5. Figur shows th hauling powr of th windd scondary induction ngin in standing position. figur and th travlling-wav xcitd induction ngin 4. figur. W gt nar th calculatd valus th following ratio: 74,4 N/4 N= 8,6. In spit of th fact, that th paramtrs of th ngin- to th masuring and calculation- ar diffrnt, th rations givs vry similar valus, which justify th simulation rsults.. Conclusion 5. figur. Th comparing of th avrag hauling powr of mtr wind ngins In this articl w introduc by a small spd ( or middl spd ) linar synch ngin a xcitation mthod and arrangmnt that hasn t bn xamind xcpt th author in th bibliography by linar ngin. Th author calld this ngin arrangmnt: travlling-wav ngin. If w compar th travlling-wav ngin with th linar induction ngin which has got similar paramtrs, thn th travlling-wav ngin has got many advantag opposit th induction ngin: it originat much biggr hauling-powr, th longitudinal dirction final-ffct, th cross dirction final-ffct is similar by th rotating machins, th magntic air-gap smallr than by th induction ngins. So th fficincy, th prformanc-factor. Th variation of th ngin-spd and dirction can b simply solvd, at braking th nrgy gt back to th ntwork. It s disadvantag against th induction ngin is that th whol path-lngth must b mad windd and a on windd part must b fd from variabl frquncy invrtr. But th mntiond disadvantags apply onc at th invstmnt.. Rfrnc. Tóth Frnc: Linar synchronous motor with travlling wav-xcitation, (patnt pnding ). Editd by John R. Braur: What vry nginr should know about FINITE ELEMENT ANALYSIS, Marcll Dkkr, Inc Sivstr P.P. &. Frrari R.L. : Finit Elmnts for Elctrical Enginrs.,Cambridg Uni. Prss, Pi-bai Zhou: Numrical Analysis of lctromagntic Filds, Springr-Vrlag Brlin, Frnc Tóth, Tihamér Ádám: Comparison of Diffrnt Typ of Linar Synchronous Machins Using Finit-Elmnt Analysis. 9 th Int. Conf. on Powr Elctronic and Motion Control EPE-PEMC 000 Kosic, pp

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