1 2 Z θ. 1 T z = 3 mm (b) 轴向气隙磁密 2 Fig. 2 Air gap flux density when rotor aligns with stator with trapezoidal P

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1 212 ELECTRI C MACHINES AND CONTROL Vol. 1 No. May 212 11 TM 31 A 1-9X 212 - - Influence of structure of taper permanent magnet motor on performance parameters LIU Wei-liang CHAI Feng PEI Yu-long CHENG Shu-kang CHEN Qing-quan School of Electrical Engineering and Automation Harbin Institute of Technology Harbin 11 China Abstract Taper permanent magnet motor has a structure different from universal permanent magnet motor. Analysis and calculation of taper permanent magnet motor is special and the reduced form method would lead to some inaccurate understanding. In this paper the 3D finite element method was adopted to analyze the magnetic field of the taper permanent magnet motor under different structure parameters and the results indicated that the distribution of magnetic field along axial direction in taper permanent magnet motor is fairly uniform and the air gap field will decrease linearly when the axial displacement of rotor increases. Then the influence of structure parameters such as taper angle axial displacement of rotor shape of permanent magnet on d-axis and q-axis inductances as well as torque was studied. It shows that the d-axis and q-axis inductances have different variation trends with axial displacement of rotor under different permanent magnet shapes and taper angle affects the variation magnitude of the d-axis and q- axis inductances. Torque will decrease when the axial displacement of rotor increases. The validity of calculation and analysis is verified by experiment results of prototype. Key words taper permanent magnet motor 3D finite element method taper angle inductances torque 211-12 - 21 123 HIT. ICRST. 2113 HIT. NSRIF. 2939 1982 193 199 19 193

1 2 Z θ. 1 T z = 3 mm 1-2 3 3-8 - 9 1. 28 1-1. 1 1. 1 9 1-28 (b) 轴向气隙磁密 2 Fig. 2 Air gap flux density when rotor aligns with stator with trapezoidal PM 1. 1. 2 9.2 -.2 (a) 径向气隙磁密 -28 28-1. 9 3 Fig. 3-28 z = 3 mm Radial flux density at z = 3 mm 31 z = 1. 2 T z = 3 mm 1 1 T Fig. 1 Sketch of conical PM rotor iron 2 3

2 1. 1 T L q = ψ q /i q ψ pm z = α =. 9 T z = 3 mm. T 1. 1. 31-28 1 2 3 Fig. Air gap flux density of pole center with different axial displacement of rotor 11-13 3 - - -2 2 i d%/a (a) 直轴电感 空载反电势 /V 空载反电势 /V 2-2 -..1.1.2 2 2 1 1 t/s (a) 定转子对齐时的空载反电势 2 i d > 2. 1 i d = - A L d = ψ d - ψ pm /i d i d = A... - - -2 2 Fig. 啄 =.3mm 啄 =.mm i d%/a (b) 交轴电感 啄 =.mm 啄 =.8mm 啄 =.mm 啄 =.9mm 啄 =.mm 啄 =1mm α = The d-axis and q-axis inductances with different air-gap length at α = 2. 2 1 2 3 α (b) 转子在不同轴向位置时的空载反电势 Fig. No-load EMF of PM motor with conical rotor α

3. 1 mh α > i d = A α = z > 2 mm z = 3 mm α > 8 z > 1. mm.8...2.8. 1 1. 2 2. 3 (a) 直轴电感 (i d=a) z > 2. mm 8... 3.. 1 1. 2 2. 3 (b) 直轴电感 (i d=a).. 1 1. 2 2. 3 (a) 直轴电感 (i d=a).....2.8. 1 1. 2 2. 3 (c) 交轴电感 (i q=a) 琢 = 琢 =1 琢 =2 琢 =3 琢 = 琢 = 琢 =. 琢 = 3.. 1 1. 2 2. 3 (b) 直轴电感 (i d=a) 8.. Fig.. 1 1. 2 2. 3 The d-axis and q-axis inductances at different taper angle with trapezoidal PM (c) 交轴电感 (i q=a) 琢 = 琢 = 8 Fig. 8 The d-axis and q-axis inductances at different taper angle with parallelogram PM 琢 = 琢 =1 琢 =2 琢 =. 琢 =3 琢 =

1-9 z=mm z=2mm z=3mm -11-12 9 1 1-1 9 1 i q = A Fig. 1 Torque with trapezoidal PM i q = A Fig. 9... 3. 3-8 - 8... i d%/a (a)l d. -8-8 9 i q%/a (b)l q Inductances when rotor aligns with stator 3 12 i = A Fig. 12 Torque with trapezoidal PM i = A 1 11 i q = A 11 1 α = 2 z = 3 mm. 2 N m 转矩 /(N m) 转矩 /(N m) 11 Fig. 11-1 z=1mm -13 2 3 - -8-1 z=mm z=1mm z=2mm z=3mm 琢 /( ) -12 1 2 3 琢 /( ) i q = A Torque with trapezoidal PM i q = A 12 转矩 /(N m) 12 9 3 18 13 9.8 1. 2. 3.2

3 8 CHENG Shukang LIU Weiliang CHAI Feng et al. Magnetic field analysis and inductances calculation of taper permanent magnet motor J. Proceedings of the CSEE 21 3 1 -. 3 DORRELL D. Modelling of non-uniform rotor eccentricity and calculation of unbalanced magnetic pull in a 3-phase cage induction motor C / /International Conference on Electrical Machines August 28-3 2 Espoo Finland. 2 182-182. TOLIYAT H A AL-NUAIM N A. Simulation and detection of dynamic air-gap eccentricity in salient-pole synchronous machines mania. 211 1 -. in Electrical Engineering May 12-1 211 Bucharest Ro- J. IEEE Transactions on Industry Applications 1999 3 1 12 GHITA C TRIFU I. Linearization of aeolian synchronous generator with conical rotor C / /The th International Symposium on. 22-221. Advanced Topics in Electrical Engineering May 12-1 211 J. 28 28 Bucharest Romania. 211 1 -. 3 8-89. 13 KASCAK P. JANSEN R DEVER T et al. Motoring performance of a conical pole-pair separated bearingless electric machine ZHANG Zhuoran YAN Yangguang SU Kaicheng. Magnetic circuit calculation and 3-dimensional field analysis of IPM hybrid excitation synchronous machine under no-load condition J. Pro- USA. 211 1 - C / /211 IEEE Energytech May 2-2 211 Cleveland. ceedings of the CSEE 28 28 3 8-89. 1 38-2. LI Weili SONG Chengyu CAO Junci et al. Numerical analysis of axial-radial flux type fully superconducting synchronous motor C / /The 1th Biennial IEEE Conference on Electromagnetic Field Computation May 9-12 21 Chicago USA. 21 1.. J. 2 2 21 13-18. XIE Dexin YAN Xiuke ZHANG Yihuang et al. Three dimensional finite element analysis of winding magnetic flux linkage in rotary electric machines J. Proceedings of the CSEE 2 2 21 13-18. 1. M. 9. 199 1 -. J. 2 1 1 21-2. 2. REN Lei CUI Ruihua WANG Zongpei et al. Saturation effect of J. 21 3 1 -. PMSM windings inductance J. Transactions of China Electrotechnical Society 2 1 1 21-2. 1 DEMERDASH N A NEHL T W. Electric machinery parameters and torques by current and energy perturbations from field computations. II. Applications and results J. IEEE Transactions on Energy Conversion 1999 1 11-122. 11 GHITA C TRIFU I. Aeolian synchronous generator with conical rotor C / /The th International Symposium on Advanced Topics 1 DUTTA R RAHMAN M F. A comparative analysis of two test. methods of measuring d-and q-axes inductances of interior permanent-magnet machine J. IEEE Transactions on Magnetics J. 22 22 1 38-2. WANG Qunjing MA Fei LI guoli et al. The analysis and calculations on 3-dimensional field and inductance of a claw-pole alterna- 1 WENTZLOFF D. Experimental characterization of an integrated 2 2 11 312-318 tor under no-load condition J. Proceedings of the CSEE 22 22 starter /generator D. Cambridge Massachusetts Institute of Technology 22 8-3.

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