Design and analysis of moving magnet synchronous surface motor with linear halbach array

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1 Available olie at Proedia Egieerig 16 (2011 ) Iteratioal Workshop o Automobile, Power ad Eergy Egieerig Desig ad aalysis of movig maget syhroous surfae motor with liear halbah array Xiaohog Hao Peghu Xig Li Bai Shool of Mehatrois Egieerig, Uiversity of Eletrois Siee ad Tehology, Chegdu , Chia Abstrat To solve the diffiulty of lower speed ad preisio of ovetioal stage, a movig maget type syhroous surfae motor (MMSSM) with slotless iro yoke ad Halbah array is desiged, where the stator ad mover are omposed of four eletromageti oils ad four Halbah arrays respetively. The mageti field distributios are derived aalytially i terms of mageti salar potetial with the method of separatio of variables. O the basis of the aalytial field, the expressios of the flux likage, bak-eletromotive fore (EMF) ad thrust fore are aquired ad examied, the hief desig parameters, suh as air gap legth, pole umber, maget thikess ad oil thikess, are optimized to maximize the thrust fore of the MMSSM. A ompariso betwee the results of the proposed method ad fiite elemet aalysis verifies the feasibility ad redibility, whih failitates the haraterizatio of MMSSM ad provides a basis for system dyami modelig ad simulatio ad servo otrol developmet Published by Elsevier Ltd. Ope aess uder CC BY-NC-ND liese. Seletio ad/or peer-review uder resposibility of Soiety for Automobile, Power ad Eergy Egieerig Keywords: Movig maget; Surfae motor; Liear Halbah array; Thrust fore aalysis. 1. Itrodutio I may high tehology fields, the requiremet of two dimesioal high preisio positioig devie is ireasig, suh as itegrated-iruit photolithography (stepper ad repeat positioig), material siee (saig tuelig mirosopy), mediie ad biology (ell biology researh), ad so o. Traditioal twodimesioal positioig devies use two staked liear motors as atuator of high preisio positioig system. Thus, positio preisio ad respose speed of the positioig devies are limited. Moreover, it has disadvatage of high maufaturig ost, ompliated struture of otroller ad omplexity of the alibratio test, et. Therefore, the diret drive surfae motor has bee suggested to replae above method. Nowadays, may types of surfae motors have bee proposed [1] [2] [3] [4]. Aordig to their workig priiples, most Published by Elsevier Ltd. doi: /j.proeg Ope aess uder CC BY-NC-ND liese.

2 Xiaohog Hao et al. / Proedia Egieerig 16 ( 2011 ) of the plaar motors a be lassified ito three types, i.e., variable relutae plaar motor, idutio plaar motor ad syhroous permaet maget plaar motor. Amog them, syhroous surfae motor attrated more ad more attetio of the aademi ad idustrial field. This is due to the fat that they have several advatages: high fore desity, exellet servo harateristis ad high effiiet [5]. However, urret syhroous surfae motors have some shortomigs. First, they have slot or without iro ore, whih produe a udesirable destabilizig tooth ripple oggig fore [6] [7]. For the syhroous surfae motor without iro ore, the mageti iruit of the maget array is ope to the air gap ad therefore flux desity i the air gap is dereased seriously [8]. Seod, the movig parts osist of may eletromaget widigs ad the statioery part is omposed of permaet magets array [9]. Thus, the movig able ot oly dereases the reliability, but also limits the mover s movemet. I this paper, a movig maget syhroous surfae motor (MMSSM) with slotless stator iro ore is proposed. Its drivig harateristis are predited aordig to desig parameters suh as maget thikess, air gap legth, oil thikess, ad pole pairs. Thus, we a better uderstad the workig priiple of the MMSSM. Furthermore, it a be used to develop otroller of the MMSSM. 2. Struture of the MMSSM 2.1 Struture Fig.1 shows the fudametal struture of the MMSSM. Ad its drivig method is the same as i the ase of a ordiary three-phase syhroous permaet maget rotary motor. The MMSSM otais mahie frame, stator iro ore, X ad Y thrust fore widigs, Halbah array ad stage. X ad Y thrust fore widigs are oetrated full-pith widig havig three isolated phase sets. Two X thrust fore widigs are used for drivig i the X-diretio ad two Y thrust fore widigs for Y-diretio. Four liear Halbah array are attahed uder the stage. To prevet ifluees from fritio, ompressed air is poured from the holes of the bottom of the stator iro ore to keep a gap floatig the mover (stage ad Halbah array). By swithig off the urret value i the three-phase widigs appropriately, the mover a move quikly i the plae surfae. (a) (b) Fig.1 MMSSM with slotless iro ore. (a) MMSSM, (b) Halbah array ad stage Compared to the ovetioal syhroous surfae motor, the MMSSM has the followig distitive features. Firstly, the stator ore is made of iro material, ad there is o slot o the iro ore. Thus, it elimiates the tooth ripple oggig effet, ad thereby improves the dyami performae ad servo harateristis.

3 110 Xiaohog Hao et al. / Proedia Egieerig 16 ( 2011 ) Seodly, Halbah array is used i the surfae motor, thus, mageti flux desity exposed to oil beomes deser tha ovetioal mageti array [10]. The more mageti flux is exposed to the thrust fore widig, the more thrust fore is produed by Loretz fore. Fially, the surfae motor is a movig maget type. I the ase of the movig maget surfae motor, the movig part is the maget ad the statioary part is the widigs. Cosequetly, the mover is free of the wire ad a rotate itself i additio to performig motios i two diretios o the plae by meas of the appropriate exitatio of the widigs. 2.2 Permaet maget material The material of the permaet maget is a importat fator to the suess of the proposed MMSSM. These permaet magets, suh as AlNiCo magets have low oerivity, Ferrite magets have low remaee, Samarium magets are quite expesive at preset. Advaed rare earth NdFeB magets have high residual stregth whih ehae the mageti fores, ad strog oerive fore whih lower a demagetizig effet ad are very stable uder higher workig temperatures. Therefore, the NdFeB permaet maget is deemed as the best hoie. I the desig aalyzed here, the NdFeB permaet maget have the followig harateristis: residual idutio B r =1.24~1.26T; oerive fore H =920~960 KA m -1 ; maximum eergy produt BH max =295~303 KJ m -3. These harateristis miimize the eergy required ad maximize the flux, ad thus high ratio of thrust fore to permaet maget volume may be ahieved. 3. Mageti field aalysis I order to desig the MMSSM preisely, it is eessary to aalyze mageti field i the whole aalysis regio iludig air gap ad oil area. As oe of the umerial methods i mageti field aalysis, the FEM is kow to allow a aurate aalysis of eletrial mahies ad a osider geometri details ad the oliearity of the mageti material [19]. However, FEM requires log omputatio time partiularly at the iitial desig stage. Therefore, the aalyti tehique that solved the mageti salar potetials is used for the alulatio of mageti field distributio. 3.1 Mageti field by Halbah array A: aalys is model Fig. 2 shows mageti field aalysis model by Halbah array. The motor is idealized as a 2-D struture. Ad followigs are assumed i order to solve the mageti salar potetial equatios. 1) The motor has the periodiity i the x diretio. 2) The magetizatio value of permaet maget is ostat. 3) The relative permeability of the iro ore is ifiity. B: Mageti Equatios The mageti field distributio was obtaied aalytially by solvig the equatios of the mageti salar potetial. 1) I the air gap The mageti salar potetial1 satisfies the followig Laplae equatio x z (1)

4 Xiaohog Hao et al. / Proedia Egieerig 16 ( 2011 ) Let H1 ad B 1 deote the mageti field stregth ad mageti flux desity i the air gap, respetively. The, the followig equatios are satisfied 2) I the permaet magets H B (2) 1 1 H (3) The mageti salar potetial 2 i the permaet magets satisfies the followig equatio x M z Where is the relative reoil permeability of the permaet magets ad M is the remaet m magetizatio. For a permaet maget havig a liear demagetizatio harateristi, is ostat ad the magetizatio M is related to the remaee B r by M Br 0. As M 0 i the maget, the equatio of2 a be dedued, i.e., x z m 0 Let H 2 ad B 2 deote the maget field stregth ad maget flux desity i the permaet maget, respetively. The, the followig equatios are satisfied H 2 0 r 2 m (4) (5) (6) B ( H M) (7) C: Boudary Coditio Equatios (1) ad (4) a be solved usig the followig boudary oditios. H1( x,0) z0 0 H2 ( x, d g) zdg0 H1( x, g) zg H2( x, g) zg B1( x, g) B2( x, g) D: solvig equatios The magetizatio layer of the Halbah array is of thikess d, ad withi this layer the maget array is represeted by a ifiite Fourier series i horizotal ( x -direted) ad vertial ( z -direted) magetizatio ompoets through terms Mz x ad Mx x Mz( x) M A os x M si os os os x (9) Mx( x) M B si x M si os os si x (10) Where is the wavelegth of the Halbah array. A is the is the th harmoi amplitude of x th harmoi amplitude of Mz (8) x, ad B M x. From (9) ad (10), it follows that A B 0 for 0, 2i,

5 112 Xiaohog Hao et al. / Proedia Egieerig 16 ( 2011 ) A B for 4i 1. By applyig the above boudary oditios to the iterfaes betwee differet material regios, ad the the mageti field stregth ad mageti flux desity i the air gap are give by 2 2 d z 2 H1x MA1e e si x 1,5,9,13...(4i1)... (11) 2 2 d z 2 H1z MA1e e os x 1,5,9,13...(4i1)... (12) 2 2 d z 2 B1x 0H1x 0MA1e e si x 1,5,9,13...(4i1)... (13) 2 2 d z 2 B1z 0H1z 0MA1e e os x 1,5,9,13...(4i1)... (14) Where subsript x ad z deote x -diretio ad z -diretio, respetively. z is the distae from widig surfae to the Halbah array uderside. follows: Aordig to (14), the first harmoi of the mageti flux desity futio 2 2 d z z r 1 1 os m os B x B A e e x B x Bz x is expressed as 2 2 d z Where Bm Br 1e e is the peak mageti flux desity. Aordig to the aalysis as metioed above, the mageti field geerated by Halbah array is obtaied. Z (15) Air gap Maget array d Air gap O Stator yoke FE regio g X 3.2 Mageti field by stator widig urret : Magetizatio diretio Fig.2 Mageti field aalysis model by Halbah array The mageti field aalysis model by stator widig urret is show i Fig. 3. I otrast with the mover, the stator is log eough to be assumed that it is ifiitely log. Therefore, usig the mageti salar potetial equatio (16), the mageti fields a be solved i similar way 0Jx (16) x z Where J(x) is armature urret desity. The mageti field due to stator widig urret is

6 Xiaohog Hao et al. / Proedia Egieerig 16 ( 2011 ) sih s k h d b Bz 0 1 osh kz os kx 1,3,.. sih kh k (17) Where K is As metioed above, total mageti field is superpositio of the field due to Halbah array ad stator widig urret. Z Air gap Widig Stator yoke O h X FE regio Fig.3 Mageti field aalysis model by widig urret 4. Bak EMF ad Thrust Fore The symbols used for alulatio of the mageti flux likage are show i Fig. 4. The referee frame XYZ is fixed o the stator. Iitially, oe of oil of phase A x -widig are fixed o the positio x, y. The mageti flux likage of a widig a be derived by itegratig three isolated areas of retagle area ABDEA, ar area BCDB, ad ar area AEFA. Ad the equatio for alulatig the flux likage of phase A x -widig is expressed as follows: where N is turs of eah oil, x NN B x ds NN B 2 x fa ds AD BD AE x z x m os (18) s s N x is the umber of series turs phase A of x - widig. AD AE are the fluxes through the faes ABDEA, BCDB, ad AEFA, respetively. BD AD NB l N B xdxdy x l l x y x y 2 2 m y lx l os si os x ly m x y, BD, ad (19) l l x y lx x y 2 x NBmlx lx lx l os si os x ly m x y 2 4 N B dxdy x (20) AE (21) Cosequetly, the total mageti flux likage of phase A x -widig is expressed as follows Bl m y 2 si l os x NN B l si l os x l 2 4 x x m x x x fa x Whe the mover is movig alog the x -diretio, the mageti field is movig whilst the stator is stati; hee, the distributio of the air gap mageti field varies with the positio of mover. So, the flux oupled with eah widig is variat with time. The bak EMF of eah phase a be writte as BD (22)

7 114 Xiaohog Hao et al. / Proedia Egieerig 16 ( 2011 ) d d dx d E v (23) dt dx dt dx Thus, bak EMF is give by the produt of veloity v ad the rate of hage i flux likage with respet to positio. Hee, the bak EMF of phase A, whih results from relative motio betwee the stator ad mover, is obtaied as x x dfa dfa lx 2x lx lx 2 lx Ea v2nsnbm si si os si x v dt dx 2 2 ly 4 (24) where v is the motor veloity alog the x -diretio. For the fully-pith widig, the distributio of eah phase of the three phase widig over a third of the pole pith. The, the mageti flux likage of phase B ad phase C are obtaied from (22) 2 4 substitutig x with x ad x respetively. 3 3 Cosequetly, the bak EMF of phase B ad C are obtaied as 2 Eb Eax (25) 3 Where E b ad E Eax 4 3 E are phase B ad C bak EMF, respetively. The thrust fore that is exerted o the mover i the surfae motor, resultig from the iteratio betwee the widig urret ad the permaet maget field, is give by Ea 2 4 F EaIaEbIbEI v IaIbx Ix v 3 3 Where I a, I b, ad I are urret vetors of phase A, phase B, ad phase C, respetively. D C Y L x /2 B (26) (27) L y (X, Y ) X L x E A Fig. 4 Widig shape ad symbols for flux alulatio of mageti flux ligkage 5. Thrust fore aalysis aordig to desig parameters A: Thrust fore aalysis aordig to air gap legth F

8 Xiaohog Hao et al. / Proedia Egieerig 16 ( 2011 ) First, this paper examied the effet of air gap legth o the thrust fore for differet pole umbers with the maget array size fixed. Fig. 5 shows thrust fore urves atig o the mover alog the air gap legth with pole umbers equal to 1, 2.5, 4 ad 5.5. It a be see that the more pole umbers irease, the more variatio of thrust fore is greatly affeted by air gap legth. I ase of air gap<0.4mm, 1 poles is superior to the others for thrust harateristis aordig to air gap legth, but if air gap legth beomes short, it is diffiult to maitai fixed air gap. I ase of air gap>0.63mm, 5.5 poles is superior to the others for thrust harateristis aordig to air gap legth, but air gap legth is too log to produe high thrust. Therefore, these aalyses make us hoose 2.5 poles for values of various air gap legths, uder ostrait oditio fixed other parameters. Thrust fore (N) 1. 1 pole poles 3. 4 poles poles Air gap legth (mm) Fig.5 Thrust fore urves for differet pole pairs B: Thrust fore aalysis aordig to maget thikess Next, this paper examied the effet of maget array thikess o the thrust fore with the air gap legth fixed. Fig. 6(a) shows thrust fore urves atig o the mover versus maget array thikess for differet pole umbers. It a be disovered that thrust fore ireases with ireasig poles umbers. I ase of pole umbers >2.5, the ireasig rate slightly dereases. I additioally, It a also be observed that for the differet pole umbers, thrust fore variatio aordig to maget array thikess, as the value of maget array thikess is 12mm or more, seldom hage. So, for a fixed air gap legth, maget array thikess a be hose as 12mm. This paper otiued this ivestigatio of maget array thikess o the thrust fore for differet pole pith with the air gap legth ad pole umbers fixed. Fig. 6(b) shows thrust fore variatios atig o the mover versus maget array thikess for differet values of pole pith. It a be see that the more values of maget array thikess irease, the more thrust fore ireases ad the more values of pole pith irease, the more differee of thrust fore variatios are slowed dow. I partiular, it a be observed that thrust variatio aordig to maget thikess i ase of the value of pole pith=8mm is almost twie as muh as that i ase of the value of pole pith=4mm, whereas thrust fore variatio aordig to maget array thikess i ase of the value of pole pith=8mm makes little differee that i

9 116 Xiaohog Hao et al. / Proedia Egieerig 16 ( 2011 ) ase of the value of pole pith=16mm. So, for a fixed air gap legth, proper maget pole pith 8mm a be determied from these results Thrust fore (N) pole poles 3. 4 poles poles Thrust fore (N) pole pith=4mm 2. pole pith=8mm 3. pole pith=12mm 4. pole pith=16mm Maget array thikess (mm) Maget array thikess (mm) (a) (b) Fig. 6 Thrust fore urves. (a) for differet pole pairs, (b) for differet pole pith C: Thrust fore aalysis aordig to widig thikess Fially, this paper ivestigated the effet of the widig thikess o the thrust with the air gap legth ad maget array size fixed. Fig. 7(a) shows the variatio of the urret desity i the stator widigs with the thikess of the widigs uder the ostrait of ostat ohmi power dissipatio i the stator widigs. Plotted i Fig. 7(b) is the thrust fore per urret desity i the widigs, whih is the itegral of the z -ompoet of the o-load air gap mageti flux desity over the volume oupied by the stator widigs. The produt of the Fig. 7(a) ad (b), show i Fig. 7(), idiated that there is a optimal thikess of stator widigs (i this ase 6mm) for highest motor thrust fore. 6. Desig results The speifiatio of the MMSSM from the desig proess is show i Table I. Ad the result of thrust fore omputatio orrespodig to a series of load urret values are show i F ig.8. It a be see that the thrust fore ripple every 60 0 is geerated. This is beause of the mismathig of the urret ad the mageti field. Ad also the thrust fore by FEM is somewhat less tha that aalytial method. The reaso is that the oliear harateristi of permeability i iro ore is osidered i the FEM. Maximum thrust fore of above 30N is got while the exited urret is 2A. 7. Colusios A movig maget syhroous surfae motor (MMSSM) with slotless iro ore has bee proposed. It has higher fore desity ompared to the oreless MMSSM. Two sets of widigs for geeratig x -diretio thrust fore ad y -diretio thrust fore is perpediularly fixed i the x -diretio ad y -diretio of the stator iro ore, respetively. For the MMSSM, mageti field distributio has a very sigifiat effet o the drivig harateristi. By usig the method of separatio of variables, Aalytial solutios of mageti field distributio are derived, ad the results are verified agaist the 2-D FEM.

10 Xiaohog Hao et al. / Proedia Egieerig 16 ( 2011 ) (a) (b) Fig.7 Optimal thikess of widigs for high thrust fore (a) Curret desity i widigs uder ostat ohmi power dissipatio, (b) Thrust fore per ohmi power dissipatio, () Optimal thikess of stator widigs. The shape of oils ad Halbah array has sigifiat effet o the thrust fore. This paper, therefore, ivestigated the effet uder ostat MMF. Ad thrust fore ripple takig ito aout drivig maer is also aalyzed that is geerated by mismathig the urret ad mageti field. The desig results are useful i developig the otrol system of the MMSSM. Copyright: All authors must sig the Trasfer of Copyright agreemet before the artile a be published. This trasfer agreemet eables Elsevier to protet the opyrighted material for the authors, but does ot reliquish the authors' proprietary rights. The opyright trasfer overs the exlusive rights to reprodue ad distribute the artile, iludig reprits, photographi reprodutios, mirofilm or ay other reprodutios of similar ature ad traslatios. Authors are resposible for obtaiig from the opyright holder permissio to reprodue ay figures for whih opyright exists. Akowledgemets: This work was supported by the Fudametal Researh Fuds for the Cetral Uiversities(Grat Number: ZYGX2009J080) ()

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