Development of a Novel Vernier Permanent Magnet Machine Shuangxia Niu 1, S. L. Ho 1, W. N. Fu 1, and L. L. Wang 2 1 The Hong Kong Polytechnic Univerity, Hung Hom, Kowloon, Hong Kong 2 Zhejiang Univerity, Hangzhou 310027, China In thi paper, a novel direct-drive double rotor Vernier permanent magnet (DR-VPM) machine i propoed and analyzed. The key i to incorporate two concentric rotor and the Vernier tructure within one PM machine, while keeping the machine volume and lot number not increaing. The main merit of thi propoed machine are it compact tructure, improved torque denity, reduced tator end winding length, and hence reduced copper lo. The operating principle of the machine i dicued and it teady and tranient performance are analyzed uing circuit-fie-motion coupled time-tepping finite element method (CFM-TS-FEM). A dual-excitation PM Vernier (DE-VPM) machine and a ingle outer rotor PM Vernier (SR-VPM) machine are deigned and compared with thi propoed Vernier PM machine with CFM-TS-FEM. FEM Comparion reult verify the advantageou performance of the propoed machine. Index Term CFM-TS-FEM, gearing effect, permanent magnet, Vernier machine. H I. INTRODUCTION IGH TORQUE, low peed permanent magnet (PM) machine are deirable for the direct-drive ytem. Since thee machine need to operate at low peed, they uually have a large pole number, lot number and a bulky ize. In order to reduce the volume and improve the torque denity, many tructure of PM machine have been tudie, uch a double tator PM machine, double rotor PM machine, multi-tator multi-rotor PM machine [1-2]. If the pole number i kept unchanged, fractional lot concentrated winding tructure can be adopted to reduce the lot number [3]. In fractional-lot concentrated winding, each coil i wound on one tooth and lot number per pole per phae i le than one. Compared with integer lot winding, the end winding i hortened and copper utilization i reduced. If higher torque i required to be induced at low peed, the Vernier tructure of tator i preferred to implify the machine tructure and reduce the lot number [4]. Baed on the magnetic gear effect the Vernier PM machine can produce pecific pace harmonic in the airgap magnetic fie with low armature pole pair and lot number. Hence, manufacture cot i aving and copper lo i further reduced. In thi paper, the DR-VPM machine adopting open lot tructure of tator and drum winding i propoed. Firtly, the compact double rotor tructure can fully utilize the limited pace within the PM machine. Secondly, with the drum winding, in which the coil are wound around the tator core, one et of tator winding can effectively hared by the inner and outer rotor and epecially, the end winding can be deigned very hort to reduce the copper loe. Finally, thi Vernier tructure of machine can produce a high torque with le lot at a very low peed, baed on the magnetic gear effect. Hence it i very uitable for the low peed, high torque direct-drive ytem. The performance of the machine i compared with it counterpart, namely, a dual-excitation Vernier PM (DE-VPM) machine and a ingle outer rotor Vernier PM (SR-VPM) machine with the CFM-TS-FEM. Comparion reult verify the advantageou performance of thi propoed machine. II. MACHINE STRUCTURE Fig. 1 give the configuration of the propoed DR-VPM machine. Thi machine i deigned with 17 pole-pair PM mounted on the urface of the inner and outer rotor, 1 polepair three phae drum winding in the open tator lot. There are totally two airgap and 18 lot on each ide of tator in the machine. Vernier machine i deigned baed on the magnetic gear effect. In the magnetic gear, the torque tranmiion i dependent on the modulation of magnetic filed uing ferromagnetic pole piece between the outer tator and the high peed rotor. According to [5], the number of pole-pair in the pace harmonic of the flux denity ditribution and the peed of the pace harmonic produced by either the high or low peed rotor PM, i given by p m, k = mp + kn (1) ω m, k = mp ωr mp + kn (2) where, m = 1,3,5, L,, k = 0, ± 1, ± 2, L, ± ; p i the pole-pair number of the inner rotor; n i the number of the ferromagnetic pole piece and ω r i the inner rotor peed of the machine. In order to tranmit torque at different peed, the pole pair of the outer PM mut be equal to. When p m, k m = 1, k = 1, the larget pace harmonic component i obtained.
Baed on the ame principle, for the Vernier machine, the fundamental rule i, P1, 1 = p N (3) where, N i the flux-modulation pole on the tator urface, alo named tator teeth; P 1, 1 i the PM pair and p i the winding pole pair. For thi propoed PM Vernier machine, the parameter are P 1, 1 = 17, N = 18, and p = 1. Then, baed on magnetic gear effect, the flux-modulation pole can modulate the low harmonic component of the airgap magnetic fie to the pecific high harmonic component and the armature fundamental fie rotate at N / p time of the rotor peed, but in an oppoite direction. Fig. 1. The DR-VPM machine. Machine tructure. Front view. The advantage of thi propoed DR-VPM machine are ditinct: (1) The compact double rotor tructure can fully utilize the limited pace within the outer rotor. The whole volume of machine i reduced and there are two airgap to produce the electromagnetic torque, and hence the torque denity i improved. (2) The open tator lot tructure implifie the tator tructure, and effectively utilize the inner tator pace and then further improve the torque denity. (3) Compared with the conventional tator winding, the drum winding tructure can effectively reduce the end winding length and reduce the copper loe. In the double rotor tructure, the two rotor hare the ame et of tator winding and induce the electromagnetic torque, o the tructure i implified. (4) The modulation pole can modulate the low harmonic component, namely fundamental pace harmonic, to the high harmonic component, namely 17 th pace harmonic, in the airgap magnetic fie with low armature pole pair pace harmonic and le tator lot. III. CFM-TS-FEM ANALYSIS There are two airgap and two rotating bodie in thi propoed machine. The circuit-fie-motion coupled timetepping finite element method (CFM-TS-FEM) i newly employed to analyze the teady and tranient performance of thi DR-VPM machine. A. CFM-TS-FEM In thi paper, the propoed CFM-TS-FEM i adopted to a 2- D problem defined in the x-y plane. The 2-D fie equation in air, iron and current denity region i [6]: ( ν A) σ = J (4) where, A i the z-component of the magnetic vector potential, ν i the reluctivity of the material, σ i the conductivity and J i the current denity. In region of PM, and in winding, which erve a coupling port to the external electric circuit, the baic equation of the tranient magnetic fie-circuit coupled problem can be ummarized a: M y M ( ) 0 x lp ν A lpσ + i + i = lp ad w ν μ Sa Sa x y and an additional equation d Ω + Rdciad = 0 Sa Ω together with an electric circuit branch equation Ω Rdciw = uw Sa d (7) Ω where; d p i the polarity (+1 or 1) to repreent, repectively, the forward path or return path; S i the total cro-ectional area of the region occupied by the winding in the olution domain; N i the total conductor number of thi winding; a i the number of parallel branche in the winding; R dc i the d.c. reitance of the winding; i w and u w are the branch current and voltage of the winding, repectively; i ad i the additional current introduced to enure the lat coefficient matrix of the ytem equation i ymmetrical; μ 0 i the magnetic permeability in vacuum; M x and M y are, repectively, the x- and y- component of the magnetization vector (ampere/ meter) in PM. (5) (6)
Simulating the rotation of the two rotor i realized uing matching boundary technique. Three mehe, aociated with one tator and two rotor, are generated eparately. The mehe of the rotor do not really rotate; only the relation of the node on the moving interface are changed according to the rotor poition. The Maxwell tenor (force on a urface with unit area) i given by r 1 1 2 2 r BnH tt + Bn μht n (11) 2 μ where; t r and n r are the unit vector tangential and normal to the urface, repectively; B n and H t are normal component of the magnetic flux denity and tangential component of the magnetic fie intenity, repectively. By integrating the Maxwell tenor on the liding urface between the tator meh and the rotor meh, the force vector F r can be obtained. r r r The electromagnetic torque i T = R F, where T r i the rigid lever arm from the rotation anchor to the liding urface. B. FEM Analyi Reult For the propoed DR-VPM machine, the rated peed of the machine i deigned a 300 rpm. The rated current i 4.4 A. The rated torque i 22.5 Nm. The outer and inner airgap length i et a 0.6 mm and 0.4 mm repectively. The material of permanent magnet i NdFeB ( Br = 1.23T, H c = 8.9e5 Unit of Hc???). Baed on the above deign data, the magnetic fie ditribution at the full load i computed, a hown in Fig. 2. The reult how that the magnetic fie in the tator core and rotor core i reaonable, namely below 1.3 T. It i alo hown that the majority of magnetic flux line can uccefully pa through thee two airgap and realize the torque tranmiion and power converion. The thickne of the inner and outer PM i deigned a 2 mm and the correponding radial flux denity waveform in the outer and inner airgap at no load are hown in Fig. 3. Fig. 4 how the back EMF waveform at the rated peed of 300 rpm. It i hown that three phae voltage i ymmetrical. When, thi DR-VPM machine i fed with threephae rated current at the rated peed, the correponding output torque at the outer rotor and the inner rotor i 14.5 Nm and 8 Nm, repectively, and the total output torque i 22.5 Nm. Fig. 2. Magnetic flux ditribution at full load. Magnetic flux line. Magnetic flux denity. Fig. 3. Flux denity in the airgap. In the outer airgap. In the inner airgap. Fig. 4. Back-EMF waveform. Fig. 5. Torque waveform. C. Comparion Analyi In order to verify the advantageou performance of the propoed DR-VPM machine, two of it counterpart, namely dual excitation Vernier (DE-VPM) machine and ingle-rotor Vernier (SD-VPM) machine are eparately deigned and analyzed with CFM-TS-FEM. The configuration and magnetic flux ditribution are hown in Fig. 6 and Fig. 7, repectively. Thee two VPM machine are deigned with the ame peripheral dimenion. The deign data of thee three VPM machine are ummarized a hown in Table I. TABLE I DESIGN DATA Item DR-VPM DE-VPM SR-VPM Number of phae 3 3 3 Rated current 4.4 A 4.4 A 4.4 A Rated frequency 85 Hz 85 Hz 85 Hz Rated peed 300 rpm 300 rpm 300 rpm Rated Torque 22.5 Nm 20.1 Nm 15.0 Nm Number of tator lot 18*2 18*2 18 Number of PM pole pair 17*2 17*2 17 Outer lot depth 4.6 mm 6.0 mm 7.2 mm Inner lot depth 3.6 mm 5.0 mm NA
Outer rotor outer radiu 68.0 mm NA 68.0 mm Outer tator outer radiu NA 65.0 mm NA Outer PM outer radiu 58.0 mm 48.4 mm 58.0 mm Outer PM inner radiu 56.0 mm 46.4 mm 56.0 mm Inner PM outer radiu 32.9 mm 39.4 mm NA Inner PM inner radiu 32.6 mm 37.4 mm NA Outer airgap length 0.6 mm 0.6 mm 0.6 mm Inner airgap length 0.4 mm 0.4 mm NA Axial length 60 mm 60 mm 60 mm Outer tator winding turn 26 26 26 Inner tator winding turn NA 18 NA Remanence of PM 1.23 T 1.23 T 1.23 T For the DE-VPM machine, there are two concentric tator and each one i fed with one et of three-phae drum winding current. Two et of 17 pole-pair PM are repectively mounted on the inner and outer urface of the rotor. The main advantage of thi machine i that the output torque or power can be imultaneouly produced by current in both the inner and outer tator. Beide, two independent et of tator winding can be flexibly controlled or connected to obtain the required performance of machine. Both DR-VPM and DE- VPM have two airgap. Compared with the DE-VPM, in the propoed DR-VPM machine, the end winding of tator are greatly reduced and copper material i fully utilized. Baed on the calculation reult, copper lo i reduced nearly 40.9%. For the SR-VPM machine, only outer rotor i adopted and the tator winding arrangement i totally the ame with the propoed DR-VPM machine. Compared with the dual airgap tructure, the torque output capability of the SR-VPM machine i obviouly lower. With CFM-TS-FEM, the output torque at the full load i hown in Fig. 8. It i hown that the DR-VPM can improve the output torque nearly 11.9% compared with DE-VPM machine and nearly 50% compared with the SR-VPM. Since the volume of machine i the ame, the torque denity of thi propoed DR-VPM i much larger than it counterpart. The tatic torque veru angle curve, a hown in Fig. 9, can alo verify thee ame reult. The core lo curve of the machine are compared in Fig. 10. It i hown that, in the SR-VPM machine, the core loe are the mallet. Thi i due to the double airgap tructure will reult in increaed harmonic pace component in the tator and rotor core. Fig. 7. Single outer rotor Vernier PM machine. Configuration. Magnetic flux ditribution at full load. Torque (Nm) 25 20 15 10 5 0 0 10 20 30 40 50 Fig. 8. Full load torque waveform. Time (m) Fig. 9. Torque angle relationhip waveform. DR-VPM DE-VPM SR-VPM Lo (W) Fig. 10. The core lo curve veru time at full-load operation. Fig.6. Dual-excitation Vernier PM machine. Configuration. Magnetic flux ditribution at full load. IV. CONCLUSION A novel DR-VPM machine i deigned and analyzed uing circuit-fie-motion coupled TS-FEM. The integrated deign can effectively improve the torque denity and implify the
machine tructure. The teady and tranient performance of machine i compared with a DE-VPM machine and a SR- VPM machine, which are deigned with the ame peripheral dimenion. Comparion reult verify the advantageou performance of the propoed DR-VPM machine. ACKNOWLEDGMENT Thi work wa upported in part by The Hong Kong Polytechnic Univerity under Grant 1BBZ7 and B-Q18X. REFERENCES [1] R. Qu, and T.A. Lipo, Dual-rotor, radial-flux, toroidally wound, permanent-magnet machine, IEEE Tranaction on Inductry Application, vol. 39, no. 6, Nov./Dec. 2003, pp. 1665-1673. [2] S. Niu, K.T. Chau and Chuang Yu, Quantitative comparion of doubletator and traditional permanent magnet bruhle machine, Journal of Applied Phyic, vol.105, no. 7, Feb. 2009, pp. 07F105-07F105-3. [3] A.M. El-Refaie, and T.M. Jahn, Optimal flux-weakening in urface PM machine uing concentrated winding, IEEE Tranaction on Indutry Appllication, vol. 41, no. 3, May/Jun. 2005, pp. 790-800. [4] A. Toba and T.A. Lipo, Novel dual-excitation permanent magnet vernier machine, Proceeding of IEEE Indutry Application Society Annual Meeting, vol. 4, Oct. 1999, pp. 2539-2544. [5] K. Atallah, D. Howe. A novel high-performance magnetic gear, IEEE Tran. Magn., vol. 37, no. 4, July 2001, pp. 2844-2846. [6] W. N. Fu, P. Zhou, D. Lin, S. Stanton and Z. J. Cende, Modeling of olid conductor in two-dimenional tranient finite-element analyi and it application to electric machine, IEEE Tran. Magn., vol. 40, no. 2, March 2004, pp. 426-434.