Simulation and Analysis of Linear Permanent Magnet Vernier Motors for Direct Drive Systems

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1 Available online at vol. 3, no. 8, December 07, pp DOI: /ijpe.7.08.p.3043 Simulation and Analyi of Linear Permanent Magnet Vernier Motor for Direct Drive Sytem Mingjie Wang a, Yanyan Li b, Hongbo Qiu a, Cunxiang Yang a,*, Conghan Li a a School of Electrical & Information Engineering, Zhengzhou Univerity of Light Indutry, Zhengzhou 45000, China b School of Mechanical & Electrical Engineering, Zhengzhou Univerity of Light Indutry, Zhengzhou 45000, China Abtract In order to keep the motor volume and lot number unchanged a well a reduce the motor peed, a new type of linear permanent magnet vernier motor (LVM) i dicued. The characteritic of LVM are imple tructure, low peed, and reduced thrut ripple. According to the air-gap permeance about lot only on the tator and the formula of flux denity with no-load EMF, the thrut are analyzed, and the motor tructure i given. It teady performance, compared with the traditional permanent magnet linear ynchronou motor (LSM), are imulated by uing the finite element method (FEM) a compared with the traditional permanent magnet linear ynchronou motor (LSM). The reult how that it ha a good performance in a low peed, epecially ince the detent force i very mall, o it i uitable for the low-peed direct-drive ytem. Keyword: air-gap permeance; flux modulation; finite element method (FEM); low-peed (Submitted on July 5, 07; Revied on Augut 30, 07; Accepted on September 5, 07) (Thi paper wa preented at the Third International Sympoium on Sytem and Software Reliability.) 07 Totem Publiher, Inc. All right reerved.. Introduction Permanent magnet linear ynchronou motor (LSM) i getting more and more attention becaue of it high thrut, fat repone, high efficiency, etc., and are applied to modern indutry [4,]. The LSM alo ha ome diadvantage uch a being difficult to reduce the peed in the indutrial frequency power condition, mainly becaue it i required to increae the motor pole pair and decreae pole pitch. At preent, in order to get lower peed, we uually ue the frequency converter to reduce power frequency, but the performance of LSM become poor. In order to keep the motor volume and lot number unchanged a well a reduce the motor peed, improve performance, and get a low peed and high thrut at higher frequency, the tructure of the motor can be improved. In recent year, ome new type of low-peed permanent magnet vernier motor (VM) ued for electromobile and wind power generation are propoed in order to get high torque [7,8]. The working principle of VM i baed on the magnetic field modulation theory. The teeth are flux modulation pole, which can produce pecial pace harmonic, o that the rotor can rotate at low peed efficiently; when rotor rotate a mall angle, the flux rotate a large angle at the ame time [6,0]. It ha many advantage uch a imple tructure, low peed and high thrut denity. The tructure of LVM difference from VM are cut-open magnetic circuit and large air-gap. In [], a novel linear tator permanent magnet vernier motor ued for wave energy converion wa propoed; the mover with alient teeth have no which are mounted on the urface of the tator teeth. The thrut denity i very high and the detent force i very mall relative to the normal thrut. A new form of linear hybrid ynchronou motor with a egmented mover i propoed []. The number of egmented mover and tator lot hould be reaonable; otherwie the detent force will be * Correponding author. addre: motormag@63.com

2 Simulation and Analyi of Linear Permanent Magnet Vernier Motor for Direct Drive Sytem 305 large. In [], a LVM with improved force denity i preented. Both the tator and mover are lotted; the vertically and horizontally magnetized are inerted into armature lot. For eliminating the end cogging force, a new topology of LVM compoed of three mover i propoed [3], but the manufacture and intallation greatly impact the detent force. Eentially, the above-mentioned linear motor integrate a conventional LSM with a magnetic gear; the are uually mounted on the flux modulation pole. A new type LVM i dicued in thi paper, which can be ued for low peed and high thrut application. Baed on the magnetic gear effect, the motor utilize the lot effect to modulate the magnetic field in the airgap. Thi paper adopt airgap permeance to dicu the magnetic field of and armature winding, a imple tructure of it i given to analyze. The correponding magnetic flux denity, harmonic pectra, thrut, and detent force are imulated by uing the FEM. It teady performance compared with the traditional LSM are analyzed; the reult how that it ha a good performance at a low peed.. Theory analyi.. Magnetic field produced by If only tator lotted, mover i mooth, the air-gap permeance i expreed a below ( ) 0 k k co kz () 0 Where,, i air gap length, 0 k k number, i the angular diplacement of the air gap poition, i air gap coefficient that conider the tator lot effect, k i the k order harmonic of the air-gap permeance. z i tator lot If the magnetization direction of the are placed alternately along the direction of motion, the MMF of the i given by [5] F FP (, t) co[ vp ( t )] v v v,3,5 () Where, F i the amplitude of fundamental magnetic potential of, p i pole pair of. If tator lotted and on mover, neglecting the higher order component, the flux denity produced by i expreed a below B (, t) F (, t) ( ) F co[ p ( t )] ( co z ) P 0 F F 0co p ( t ) co[( z p ) p t] (3) In order to generate the ynchronou thrut force, the pole pair of tator winding p mut be equal to the pole pair of the p w w, o z p p,, w i angular frequency, the mover peed i, The mover peed i z p p p n=60f/ p, the ratio of tator magnetic field ynchronou peed and mover peed i r.. Magnetic field produced by armature winding The magnetic potential of armature winding i given by G n / n p / p z / p. v F (, t) F co( wt vp ) a mv v,3,5 (4)

3 306 Mingjie Wang, Yanyan Li, Hongbo Qiu, Cunxiang Yang, and Conghan Li Where, i the mover angular diplacement, neglecting the higher order component, the flux denity produced by armature winding i expreed a below Ba (, t) Fm co( wt p ) ( ) Fm F (5) m Fm 0 co( wt p ) co[ wt ( z p) ] co[ wt ( z p) ].3. Flux denity comparion F (, t) F co( wt p ), the armature magnetic potential rotate in the poitive direction, the poitive equence If a m current i in the winding, we compare the flux denity produced by armature winding and by a follow The flux denity of armature winding i given by B (, t) B co( wt p ) B co[ wt ( z p) ] B co[ wt ( z p ) ] (6) a a ah ah The flux denity of i given by B (, t) B [ p t co( z p ) ] B co p ( t ) (7) h Where, B a F m 0 i the fundamental amplitude of armature flux denity, m ah ah amplitude of armature flux denity, than the harmonic amplitude of it. B Bah B F Ba > the harmonic amplitude of flux denity, harmonic amplitude of it..4. Parameter calculation.4.. Speed calculation ah B F B i the harmonic, the fundamental amplitude of armature flux denity i greater i the fundamental amplitude of flux denity, h 0 B < B h The ynchronou peed of armature magnetic field i given by B F i, the fundamental amplitude of flux denity i le than the v f G v / v p / p z / p r (8) So (9) can be derived from (8). v v / G p f / p lf / p f r v v / G v / ( z / p ) r (9) Where, v i mover peed,, i mechanical angular velocity of the tator and mover repectively, i the winding pole pitch, l i the mover length,.4.. No-load EMF calculation The air-gap flux produced by can be expreed a follow i the pole pitch, o the mover peed i related to the pole pitch.

4 Simulation and Analyi of Linear Permanent Magnet Vernier Motor for Direct Drive Sytem 307 pl 0 p h p B (, t) d [ B co( wt p ) B co( wt p )] d l Bh p [ B in( )]co wt p / p p (0) p If in( ) p implified a follow i elected, the no-load flux i maximum, then the thrut i maximum. The no-load flux can be l B ( B )co wt ( )co wt co wt h 0 m mh m Gr () motor. l l, Bh m B, mh, G where, m m mh So the no-load emf can be expreed a below r l i the length of tranvere direction of the d l N k w B e N k ( B )in wt E in wt 0 w h w 0 dt Gr () Where, E l N k w Bh ( B ) G w 0 r (3).4.3. Thrut calculation The electromagnetic power i given by P 3E I co (4) e 0 Where, i the inner power factor angle, I i the RMS of the tator current. The thrut i i given by f x P e v (5) w Subtituting (3) (4) and v into the (5), the thrut i derived P 3E I co 3wN k I p p B f co 3 N k I l ( B )co v v G p p p e 0 w m h x w / r vp / (6) 3. FEM analyi According to the theoretical analyi, thi paper adopt the tructure of the lotted tator, the mooth mover, and on the mover. Fig. (a) how the tructure of the LVM. The tator with a three phae winding i infinitely long and the mover equipped with NdFeB magnet i finitely long. =, =0, p=, f=50hz, and the mover peed i 0.6m/. Fig. (b) z p how the tructure of the LSM. It baic pecification i the ame a the LVM to allow a fair comparion. Mover length, material and the peed are the ame a the LVM, p=.

5 308 Mingjie Wang, Yanyan Li, Hongbo Qiu, Cunxiang Yang, and Conghan Li (a) Figure. (a) Structure of the LVM; (b) Structure of the LSM (b) 3.. Air-gap magnetic field analyi of LVM D FEM i ued to calculate the magnetic field. The characteritic equation for FE analyi can be expreed a follow A A 0 : J J x y : A 0 J A : Ht n p M 0 p (7) J Where, 0 i the olving region, A i the magnetic vector potential, i the permeability, i the armature current denity, repectively, repectively. H t 0 i the air permeability, J p and M are the equivalent magnetizing current denity and magnetization intenity of i the tangential component of the flux intenity., are the firt and econd boundary condition Fig. how the air-gap flux denity of armature winding and repectively along the y direction. It can be een that along the mover length, the armature winding pole pair are and pole pair are 0, which are obviouly the 5th order harmonic in. The flux ditribution i aymmetric becaue of the two end. Figure. Air-gap flux denity of By The Fourier analyi reult of B and B a along the y direction are hown in Fig. 3. It can be een that the amplitude of the 5th harmonic produced by i greater than the fundamental wave and the other harmonic. But, the amplitude of the fundamental wave i greater than the 5th harmonic produced by armature winding. Both of them are greater than the other harmonic, which agree with the theoretical analyi.

6 Simulation and Analyi of Linear Permanent Magnet Vernier Motor for Direct Drive Sytem No-load EMF analyi of LVM (a) (b) Figure 3. (a) Harmonic ditribution of ; (b) Harmonic ditribution of armature winding The no-load EMF i a critical parameter for the analye of the motor performance. It can be calculated by FEM when the ' peed i 0.6m/, and there i no current in the olving region. That i to ay, the current denity of the armature winding J =0. The no-load EMF waveform given in Fig. 4 are imulated by FEM; it can be een that the waveform are inuoidal and the amplitude of each phae are accordant Thrut comparion Figure 4. No-load EMF veru time The force i computed by uing Maxwell' tre tenor. The thrut F x i calculated a follow [9] x [( ) ] x y x x y y 0 F B B n B B n d (8) Where, S i the urface of integration, detent force. n x, n y are the unit vector, If J =0, only acting on the motor, the force i The thrut veru time i hown in Fig. 5 when AC current i in the armature winding, the mover peed i 0.6m/ in the teady operation. It i hown that the table thrut i derived. The average maximum of the propoed motor i 54.N, the thrut ripple i about 3N becaue of the detent force, the average maximum of the LSM i 35N, and the thrut ripple i about 75N.

7 30 Mingjie Wang, Yanyan Li, Hongbo Qiu, Cunxiang Yang, and Conghan Li 3.4. Detent force comparion Figure 5. Maximum thrut veru time Fig. 6 how the detent force veru time. The amplitude of the propoed motor i about N, the period of it i a tooth pitch becaue the i the mover which i finitely long, and the amplitude of the LSM i 80N. The maximum thrut of LVM i decreaed about 98N compared with LSM if the volume of the are the ame, but the thrut of LVM i alo very large. The thrut ripple of LVM i about 4.7% and the thrut ripple of LSM i about.7% o the thrut ripple of LVM i very low. 4. Concluion Figure 6. Detent force veru time The machine configuration and working principle of a novel LVM have been dicued. Thi paper ha analyzed magnetic field according to air-gap permeance baed on the motor tructure. Thi paper ha alo dicued the relationhip of the tructure parameter, whoe characteritic are analyzed by FEM. Compared with the LSM, the thrut ripple of the propoed LVM i very mall in a low peed, o it can be ued in low-peed direct-drive ytem. Acknowledgement Thi work i upported by the Key S&T Special Project of Henan Province (600600), the Key Scientific Reearch Project of Henan Higher Education Intitution (8A470007), and the Science Foundation for Doctorate Reearch of the Zhengzhou Univerity of Light Indutry (06BSJJ005). Reference. Y. Du, K. T. Chau, M. Cheng, Y. Fan, A Linear Stator Permanent Magnet Vernier HTS Machine for Wave Energy Converion, IEEE Tran. on Appl. Supercon., vol., no. 3, pp.50505, June 0.. J. D. Edward, S.J.O. Proverb, Theory and Performance of Segmental Secondary Linear Hybrid Synchronou Motor, IET Electr. Power Appl., vol. 4, I. 7, pp , July Y. Gao, R. Qu, D. Li, F. Che, Force Ripple Minimization of a Linear Vernier Permanent Magnet Machine for Direct-Drive Servo Application, IEEE Tran. on Magn., vol. 53, no. 6, pp , Jun. 07.

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