Abstract：The air-gap magnetic field distribution of an eccentric harmonic magnetic gear is analyzed by applying the fractional linear transformation method. Two eccentric circles in the z-plane are mapped on two concentric circles in the w-plane. The Laplace field equation in the concentric annular is easily solved by assuming unit difference in magnetic potential between two circles. After the field expressions are mapped back into the z-plane the relative permeance functions due to the rotor eccentricity can then be obtained. The magnetic field distribution can be estimated by modulating the field distribution in the air gap without rotor eccentricity by the relative permeance function. The resultant air-gap magnetic fields can be obtained by superposition of the stator and rotor field components with rotor eccentricity. When the radial and tangential components of flux densities are calculated, the electromagnetic torque of the magnetic harmonic gear is determined by the Maxwell stress tensor. Finite element results confirm the validity of the analytical prediction.
章跃进, 章君达. 偏心式谐波磁力齿轮气隙磁场分式线性变换解析模型[J]. 电工技术学报, 2018, 33(15): 3572-3577.
Zhang Yuejin, Zhang Junda. Analytical Model of Magnetic Field of Eccentric Harmonic Magnetic Gear Using Fractional Linear Transformation Method. Transactions of China Electrotechnical Society, 2018, 33(15): 3572-3577.
[1] 付兴贺, 王标, 林明耀. 磁力齿轮发展综述[J]. 电工技术学报, 2016, 31(18): 1-12. Fu Xinghe, Wang Biao, Lin Mingyao.Overview and recent developments of magnetic gears[J]. Transactions of China Electrotechnical Society, 2016, 31(18): 1-12. [2] Atallah K, Howe D.A novel high-performance magnetic gear[J]. IEEE Transactions on Magnetics, 2001, 37(4): 2844-2846. [3] 李祥林, 程明, 邹国棠, 等. 聚磁式场调制永磁风力发电机工作原理与静态特性[J]. 电工技术学报, 2014, 29(11): 1-9. Li Xianglin, Cheng Ming, Zou Guotang, et al.Principle and analysis of a new flux-concentrating field-modulated permanent-magnet wind power generator[J]. Transactions of China Electrotechnical Society, 2014, 29(11): 1-9. [4] Rens J, Clark R, Calveriey S, et al.Design, analysis and realization of a novel magnetic harmonic magnetic gear[C]//18th International Conference on Electrical Machines, Vilamoura, 2008: 1-4. [5] Rens J, Atallah K, Caverly S D, et al.A novel magnetic harmonic gear[J]. IEEE Transactions on Industry Applications, 2010, 46(1): 206-212. [6] Li Kang, Bird J, Kadel J, et al.A flux-focusing cycloidal magnetic gearbox[J]. IEEE Transactions on Magnetics, 2015, 51(11): 2025-2027, 2015. [7] Kim U, Lieu D K.Magnetic field calculation in permanent magnet motors with rotor eccentricity: without slotting effect[J]. IEEE Transactions on Magnetics, 1998, 34(4): 2243-2252. [8] Kim U, Lieu D K.Magnetic field calculation in permanent magnet motors with rotor eccentricity: with slotting effect considered[J]. IEEE Transactions on Magnetics, 1998, 34(4): 2253-2266. [9] 仇志坚, 李琛, 周晓燕, 等. 表贴式永磁电机转子偏心空载气隙磁场解析[J]. 电工技术学报, 2013, 28(3): 114-121. Qiu Zhijian, Li Chen, Zhou Xiaoyan, et al.Analytical calculation of no-load air-gap magnetic field in surface-mounted permanent magnet motors with rotor eccentricity[J]. Transactions of China Electrotechnical Society, 2013, 28(3): 114-121. [10] 刘蓉晖, 章跃进, 李琛, 等. 永磁电动机转子偏心空载气隙磁场矢量位解析法[J]. 微特电机,2013, 41(6): 6-9. Liu Ronghui, Zhang Yuejin, Li Chen, et al.Analytical method with vector magnetic potential for open-circuit air-gap magnetic field computation in permanent magnet motors with rotor eccentricity[J]. Micro Motors, 2013, 41(6): 6-9. [11] 周晓燕, 李琛, 仇志坚, 等. 基于摄动法的交替极永磁电机偏心磁场解析计算[J]. 电工技术学报, 2013, 28(9): 321-331. Zhou Xiaoyan, Li Chen, Qiu Zhijian, et al.Magnetic field calculation for consequent-pole motor with rotor eccentricity based on perturbation method[J]. Transactions of China Electrotechnical Society, 2013, 28(9): 321-331. [12] 刘蓉晖, 李琛, 章跃进. 偏心式谐波磁力齿轮气隙磁场解析模型[J]. 中国电机工程学报,2013, 33(36): 126-133. Liu Ronghui, Li Chen, Zhang Yuejin.Analytical model for air-gap magnetic field calculation in an eccentric magnetic harmonic gear[J]. Proceedings of the CSEE, 2013, 33(36): 126-133. [13] 藉勇亮. 电磁场边值问题的解析法研究[D]. 重庆: 重庆师范大学, 2007. [14] 雷银照. 关于电磁场解析方法的一些认识[J]. 电工技术学报, 2016, 31(19): 11-25. Lei Yinzhao.Reviews of analytical methods for electromagneitc fields[J]. Transactions of China Electrotechnical Society, 2016, 31(19): 11-25. [15] Zhu Z D, Howe D, Bolte E, et al.Instantaneous magnetic field distribution in permanent magnet brushless DC motors, part I: open circuit field[J]. IEEE Transactions on Magnetics, 1993, 29(1): 124-135. [16] Zhu Z Q, Howe D, Bolte E, et al.Instantaneous magnetic field distribution in brushless permanent magnet DC motors, part Ⅲ: effect of stator slotting[J]. IEEE Transactions on Magnetics, 1993, 29(1): 143-151. [17] Zarko D, Ban D, Lipo T A.Analytical calculation of magnetic field distribution in the slotted air gap of a surface permanent-magnet motor using complex relative air-gap permeance[J]. IEEE Transactions on Magnetics, 2006, 42(7): 1828-1837. [18] Li J T, Liu Z J, Nay L H A. Effect of radial magnetic forces in permanent magnet motors with rotor eccentricity[J]. IEEE Transactions on Magnetics, 2007, 43(6): 2025-2027.
2018, Vol. 33 
