Electromagnetic Design and Experiment of Halbach Array Based Permanent Magnet Fault-Tolerant Motors

Transcription

1 Intrnational Confrnc on Mchatronics, Elctronic, Industrial and Control Enginring (MEIC 05) Elctromagntic Dsign and Exprimnt of albach Array Basd Prmannt Magnt Fault-Tolrant Motors Chng Ying School of Elctrical Enginring Nantong Univrsity Nantong, China Mao Jingfng * School of Elctrical Enginring Nantong Univrsity Nantong, China mail:mao.jf@ntu.du.cn Wu Aihua School of Elctrical and Information Enginring Jiangsu Univrsity Zhnjiang, China mail:wu.ah@ntu.du.cn * Corrsponding Author Wu Guoqing School of Elctrical Enginring Nantong Univrsity Nantong, China mail:wgq@ntu.du.cn Abstract In ordr to mt high rliability application rquirmnts of modrn lctric driv systm, a kind of albach array basd prmannt magnt fault-tolrant motors (PMFTM) is studid in this papr. Firstly, th structur, charactristics and fault-tolrant working principl of PMFTM ar analyzd. Scondly, according to th lctromagntism thorm and Maxwll's quation, th lctromagntic paramtrs calculation quations ar drivd, and thn th ky paramtrs of KW four-phas six-pol albach array basd PMFTM ar workd out. Thirdly, a PMFTM prototyp is built and tstd, and th xprimnt on this rsarchd motor has provd that th rationality and accuracy of this motor. Ky words-prmannt magnt fault-tolrant motors; albach array; motor dsign; lctromagntic analysis I. INTRODUCTION With th rapid dvlopmnt of rar arth prmannt magntic matrials, prmannt magnt motor is gtting mor and mor widly utilization in th lctric driv systm with its advantags lik high ficincy, high torqu inrtia ratio, high nrgy dnsity and so on. In som high rliability of lctric driv application dmand situations, w oftn us th backup rdundancy tchnology, which conncts lots of indpndnt motor systms togthr in th way of sris or paralll, and through switching th working way of hot and cold standby to improv th ability of continuous work of whol machin whn machin is at th stat of mchanical or lctrical parts fault[,]. This fault-tolrant mthod has clar principl and simpl control, but it still has som waknsss, lik larg volum, a lot of parts and low utilization rat. In ordr to ovrcom ths shortcomings, basd on th mind of backup fault-tolrant tchnology, rsarching on th prmannt magnt motor with high rliability is gradually bcoming a hot issu in th study of modrn lctric driv systm[3,4]. Prmannt magnt fault-tolrant motor (PMFTM) is a nw typ of prmannt magnt brushlss motor which dvlopd in rcnt yars, this kind of motor can also us th phas sgrgation and rdundant capacity mthod to mak th rst of fault phas continu running aftr on phas or numbr phass of motor having a failur occurs, in addition to th gnral advantags of traditional prmannt magnt motor. At prsnt, th rsarch of prmannt magnt motor on th aspcts of motor structur, fault-tolrant control stratgy ar still in th initial stag. Litratur[5,6] rspctivly usd th prmannt magnt fault-tolrant motor as th driv motor in lctric ful pump systm of lctric or ovrall-lctrical plan, and dsignd thm as th lctric actuator of lctric string gar systm to mak th plan has strongr rliability and scurity. Litratur[7] applid prmannt magnt fault-tolrant motor into driving systm of lctric vhicl, and took it as xcution motor of wir control string dvic to furthr improv th car driving safty prformanc. Litratur[8] studid th dirct torqu control and th optimal currnt control stratgy of multiphas prmannt magnt fault-tolrant motor. Litratur[9] proposd th fault tolrant control stratgy with singl-phas opn circuit which is basd on two driving topological structur of -bridg and star typ. In this papr, a four-phas six-pol prmannt magnt fault-tolrant motor is our rsarch targt. This motor has combind with th advantags of albach prmannt magnt array structur in th aspct of sinusoidal in unilatral magntic fild and th aspct of magntic shilding. According to th analysis of working principl 05. Th authors - Publishd by Atlantis Prss 08

2 of th motor, w dtrmind th phas numbr, pols numbr, and th shap of stator slot and rotor magnt stl. Basd on th arrangmnts of rotor magnt stl and th arrangmnts of winding, and th paramtrs calculation of magntic circuit, w obtaind th structur paramtrs of motor with albach array, which can mak th motor has a small torqu rippl and th no-load countr lctromotiv forc has a high sin dgr. II. STRUCTURE PARAMETERS DESIGN OF PERMANENT MAGNET FAULT-TOLERANT MOTOR Bcaus of th diffrnt structur, compard prmannt magnt fault-tolrant motor with th traditional prmannt magnt synchronous motor, thr ar many diffrncs in trms of paramtr dsign. In this sction, w us a four-phas six-pol prmannt magnt fault-tolrant motor as an xampl, and rsarch th dsign of motor structur and lctromagntic paramtrs. Th main prformanc paramtrs of this motor ar as follows: ratd powr P N =KW, ratd voltag U N =36V, ratd spd n N =00rpm, numbr of th stator N s =8, rotor pol pairs p=3, numbr of phas m=4, ratd ficincy η N =90%, th ratd powr factor cosψ N =0.8. A. Dsign of stator innr diamtr and cor lngth Th main dimnsions of th prmannt magnt fault-tolrant motor ar spcifid th insid diamtr and th fctiv axial lngth of stator cor which can b dtrmind according to th nd of imum torqu and dynamic rspons indication [0]. Whn th biggst lctromagntic torqu of motor is T m (N. m), thn th rlationship btwn main dimnsions and lctromagntic loads is: 4 Tm B L D A0 i () 4 whr B is th flux dnsity of fundamntal amplitud (T), A is th stator lctric load valid valu (A/CM). Obtaind th rlationship btwn th main dimnsions of motor and th lctromagntic loads according to formula (): D i L 4 Tm 0 () B A mnik dp A (3) p whr m is th motor phas, N is th winding turns, I is th stator currnt, p is th rotor pol pairs, K dp is th winding factor, τ is th motor pol pitch. r w tak powr load A=50A/cm, th flux dnsity of fundamntal amplitud B δ =0.8T. Bcaus th dynamic rspons prformanc indx of a prmannt magnt fault-tolrant motor mainly rrs to th motor that undr th fct of imum lctromagntic torqu T m can acclrat linarly from rst to turning spd ω b during tim of t b, that is: J Jb Tm (4) pt pt b whr J is th rotor and load inrtia (kg. m ). Thror, according to formula (4) w can obtain th ratio of imum lctromagntic torqu to th momnt of inrtia is: Tm b (5) J ptb Th momnt of inrtia of th motor rotor can approach to: Di 4 7 J FL ( ) 0 (6) whr ρ F is th mass dnsity of th rotor matrial iron (g/cm 3 ). W tak formula () and formula (6) into quation (5), can obtain th stator innr diamtr D i (cm) is: D i 8 ptbb A (7) 3 0 Thn according to quation (), w can obtain th fctiv axial lngth of th stator cor L (cm) is: L b F b F (8) B A 4 Tm 0 0T m Di B A 4ptb B. Dsign of groov paramtrs Fig. shows th block diagram of stator slots of prmannt magnt fault-tolrant motor aftr straightning. From Fig., w can know that th paramtrs which nd b calculatd includ: notch thicknss, slot width B, stator tooth width B t and stator tooth hight s. Firstly, according to th magntic saturation constraint conditions of th stator tth, w obtaind th tooth hight and th tooth width. Scondly, according to th dsign rquirmnts of slot lakag inductanc, w drivd th notch hight and width. Finally, in accordanc with th rquirmnts of intrnal winding currnt dnsity of stator slot, w calculatd th othr paramtrs, lik th width of th groov bottom B s and th width of th groov top B s. sy Bt Bs s Bs B Figur. An alvolar structur of stator ry hm bm Figur. Th rotor yok structur s 083

3 ) Paramtr calculation of stator tth Assuming all of th air-gap magntic flux through th main stator tth, so th stator tooth width is obtaind as follows: B i Bt (9) b whr B δ is magntic load, α i is calculatd pol arc coficint. Bcaus whn frromagntic matrial undr normal circumstancs, th imum magntic flux dnsity of th stator tth b t qual to.4~.6t, thror, this articl slctd b t =.5T, and according to formula (9) can driv th stator tooth width B t. Gnrally, th hight and width ratio of th stator tth is btwn.5 and 3. Bcaus, if th ratio is small, th stator slot is vry shallow, this may caus vry high currnt dnsity that through th innr winding. But if th ratio is larg, thn th stator slot is vry dp, th stator yok is asy to rach saturation, and th lctromagntic torqu may rduc. So in this papr, w tak th valu of, and th stator tooth hight is: s B t (0) ) Calculation of notch paramtr In ordr to rduc th saturation dgr of th stator tooth tip imum xtnt, at th sam tim to improv th slot lakag inductanc L σ, th notch thicknss gnrally takn to b (0.35~0.5)B t, this articl is takn as 0.4 tims, that is: Slot lakag inductanc L σ is: t 0. 4B t () 0N ( B )( L B ) L () B Bcaus th notch width B is much smallr than th fctiv axial lngth of stator cor L, thror, formula () can b simplifid as: 0N ( B ) L L (3) B Rarranging slot width B is: N L (4) 0 B L 0N L whr th slot lakag inductanc L δ takn as 0.33 tims of th coil inductanc L s, and has th following formulas: E0 E0 Ls (5) I f I I s P N (6) mu N N cos N whr E 0 is th motor back lctromotiv forc (V), ω is th lctrical angular frquncy (rad/s), I s is th stady-stat short-circuit currnt (A), I is th motor ratd currnt (A), f is th ratd synchronization frquncy (z). 3) Calculation of armatur winding turns and coil diamtr Th dinition of motor no-load back lctromotiv forc(emf) is: E f Nkw 0 (7) whr f is th ratd synchronization frquncy(z), k w is th winding factor, Φ 0 is th fundamntal magntic flux air gap(wb), and has th following formulas: 4 i 0 ( sin B ) L (8) So th numbr of turns of th armatur winding N is: 0.8E0 p N (9) f k B D L sin( ) w i According to th dimnsions of slot form, w can gt th ara of stator slots A s is: ( Bs Bs ) s sin As (0) whr θ is th mchanical angl that rlativ to th cntrlin of th pol (rad), and: Width of th top slot is: ( Di ) Bs Bt () Q Width of th bottom slot is: id ( s s Bs ) Q i B t () whr Q is th numbr of stator slots, in ordr to rduc th dgr of magntic saturation of tooth boots, s gnrally takn as 0.5~mm. 4) Calculation of stator and rotor yok portion thicknss Th thicknss of th yok of stator and rotor nds to mt th constraints of magntic saturation, for th four-phas six-pol prmannt magnt fault-tolrant motor in this articl, th imum valu of yok flux dnsity is.6~.8t, which is slightly largr than th imum limit valu of flux dnsity in tooth portion, in this papr th valu is.6t. Thn th thicknss of th stator yok portion sy is: b m i sy (3) b Th thicknss of th rotor yok is: sy B p ry (4) bry whr b sy is th flux dnsity of stator yok portion (T), b ry is th flux dnsity of rotor yok portion (T). C. Magntic circuit dsign Magntic circuit dsign includs th dtrmination of ovrall structur, th dtrmination of sizing and th slction of matrial, which focuss on th work of choosing prmannt magntic matrials and dsigning th oprating point. 084

4 ) Prmannt magnt matrial slction In this papr, w chos NdFB N38 as th prmannt magnt matrial, th rmannc dnsity B r0 is.3t, th tmpratur coficint α Br is 0. %/, th irrvrsibl dmagntization loss IL is 0.7%, th calculatd corciv forc of prmannt magnt c0 is 899kA/m. W can obtain following rsults according to th slction of NdFB N38: ()Rmannt flux dnsity during th oprating tmpratur: B [ ( t 0) /00] [ IL /00] B r Br r0.8t ()Calculatd corciv forc during th oprating tmpratur: ( t 0) /00] [ IL/00] c [ Br c ka/ m (3)Rlativ prmability of th prmannt magnt: Br 0 r c0 whr 0 is vacuum prmability, 0 =40-7 /m. ) Dtrmin th shap of prmannt magnt Surfac magntic pol structur can improv th ability of isolation btwn th windings, in this articl w us th surfac-typ til-shapd magntic pols in th prmannt magnt fault tolrant motor, shown in Fig.3. Th structur of prmannt magnt contacting th air gap dirctly is asy procssing and installation. And uss a concntric til-shapd magntic pols, i.., th outr diamtr and th intr diamtr of th prmannt magnts hav a common cntr, it shown as in th Fig.4. Th width of prmannt magnt b M is: b p (6) M whr μ r is th rlativ prmability of frromagntic matrial; δ i is th calculating air gap lngth of motor(cm); B r is th rsidual magntic induction intnsity of prmannt magnt (T); B δ is th magntic load (T); α p is th prcntag of pol mbrac. Gnrally B r /B δ qual to.~.35. 4) Prmannt magnt magntization way of dsign In this papr, th arrangmnt of prmannt magnt is in th way of albach array [], this kind of arrangmnt can not only nhanc th air gap flux of motor, but also can wakn th magntic flux of rotor yok, which is particularly suitabl for th rotor structur of using surfac-mountd prmannt magnt. albach array is a novl magntic structur array that combins radial array with tangntial array, as Fig.5(a) shows, so that w can mak th magntic fild in on sid of prmannt magnt strngthning and th othr sid wakning. Th rational dsign of albach array can mak th air-gap flux dnsity and th no-load back lctromotiv forc having good sinusoidal. (a) albach array structur diagram (b) Th distribution of magntic forc lins Figur 3. Surfac tils pol Figur 4. Concntric magntic tils 3) Calculat th siz of prmannt magnt Th main siz paramtrs of prmannt magnt part includ th thicknss and th width of prmannt magnt, and can b dtrmind by th following formula: Th thicknss of prmannt magnt h M is: h o r M i (5) Br B Figur 5. Magntic fild distribution of albach array structur Fig.5 (b) shows th distribution of magntic quipotntial lin of th prmannt magnt motor with albach array which is calculatd by th ANOSOFT which is on of th finit lmnt analysis softwar. As w can s, aftr using albach array, th magntic flux of rotor yok significantly rducd, whil th magntic flux that across air gap into th stator significantly incrasd, which incrass th magntic load of prmannt magnt motor and th dnsity of forc and nrgy, so albach array is vry suitabl for th idal for th prmannt magnt fault-tolrant motor with th intr rotor structur of prmannt magnt postd outsid. 085

5 TABLE Ⅰ. PARAMETERS OF KW FOUR-PASE SIX-POLE PERMANENT MAGNET FAULT-TOLERANT MOTOR Ratd voltag/v 36 Ratd spd/r.min - 00 NdF Stator and rotor DW30- Magnt Matrial N38 matrial 35 Outsid stator Insid stator diamtr/mm diamtr/mm Stator tooth.4 Stator yok thick/mm 5.4 width/mm Fig.7 is an actual masurd wavorm of on phas no-load back lctromotiv forc. From this figur, w can know that th sinusoidal of this wavorm displayd vry wll, so th motor dsign is rasonably and accurat which laid a good foundation for th control rsarch of fault-tolrant motor. Insid rotor diamtr/mm 64 Rotor yok thick/mm.5 Magnt thicknss/mm 8.7 Stator cor lngth/mm 39.3 Notch thicknss/mm 4.6 Prcntag of pol mbrac 0.64 Gap lngth/mm 0.8 Winding turns of pr phas 36 Figur 7. On phas no-load back lctromotiv forc wavorm Through th simulation of ANSOFT softwar, w dtrmind to us th albach array with two pics of prmannt magnt pr pol, and th radian numbrs of ths two pics of prmannt magnt ar 35 and 5. Bcaus w can gt th highst sinusoidal wavorm of no-load back lctromotiv forc with this radian. According to th dsign rsults of this motor, w got th paramtrs of this KW four-phas six-pol structur prmannt magnt fault-tolrant motor that listd in Tabl. III. EXPERIMENTAL TESTING OF TIS MOTOR Basd on th prmannts of motor siz that dsignd bor, W manufacturd a KW xprimntal prototyp of this four-phas six-pol prmannt magnt fault-tolrant motor. Th xtrnal apparanc is shown in Fig.6. IV. CONCLUSION In this papr, for th rquirmnt of powr-drivn applications with high-rliability, w hav rsarchd and dsignd on kind of prmannt magnt motor of four-phas six-pol structur with albach array. Basd on th charactristics of th motor structur and th analysis of fault-tolrant mchanism, and combind with th principls of lctromagntism and dsign mthod of albach array, w calculatd th main dimnsions and th lctromagntic paramtrs of th KW prmannt magnt fault-tolrant motor. And through th xprimntal tsting of this motor, w also vrifid th corrctnss and rationality of this motor dsign procss. ACKNOWLEDGMENT Th prsnt papr has bn financd by th National Natural Scinc Foundation of China ( , 6735), Natural Scinc Foundation of Jiangsu Provinc (BK0438), Qing Lan Projct of Jiangsu Provinc, and Postgraduat Rsarch Innovation Program of Jiangsu Provinc(CXLX3_68). (a) Extrnal apparanc of motor (b) Rotor of motor Figur 6. A KW four-phas six-pol prmannt magnt fault-tolrant motor REFERENCES [] R. R. Errablli, P. Mutschlr. A fault tolrant digital controllr for powr lctronic applications[c]. 3th Europ Confrnc on Powr Elctron Applications, 009: -0. [] Niu Xumi, Gao Guoqin, Liu Xinjun,t al. Dynamics modling and xprimnts of 3-DOF paralll mchanism with actuation rdundancy[j]. Transactions of th Chins Socity of Agricultural Enginring, 03,9(6):3-4. [3] A.M. El-Rai. Fault-tolrant prmannt magnt machins: a rviw[j]. IET Elctronics Powr Applications, 0,5(): [4] Ji Jinghua, Sun Yukun, Zhu Jihong, t al. Dsign, analysis and xprimntal validation of a modular prmannt-magnt machin[j]. Transaction of China Elctrotchnical Socity, 00,5(): -9. [5] B. C. Mcrow, A. G. Jack. Dsign and tsting of a four-phas fault-tolrant prmannt-magnt machin for an ngin ful pump[j]. IEEE Transactions on Enrgy Convrsion, 004, 9(): [6] ao Z Y, u Y W. Dsign and xprimntal analysis on th control systm of high rliability fault tolrant prmannt magnt motor 086

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