多边形转子磁轭永磁同步电机空载气隙磁场解析计算
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摘要
该文利用分区域方法对多边形转子磁轭永磁同步电机的空载气隙磁场进行了解析推导。该方法基于磁场连续性定理,将磁场的边界条件和交界条件相结合,在忽略磁饱和的条件下,利用不规则磁轭半径函数和偏心永磁体半径函数求解空载气隙磁场。将该方法的计算结果与有限元计算结果相对比,两者吻合较好,证明了该方法可以准确有效地计算多边形转子磁轭永磁同步电机的空载气隙磁场。
This paper presents an analytical method on the calculation of no-load air-gap magnetic fields in a permanent magnet synchronous motor with polygonal rotor magnetic yoke by the use of dividing the region into parts. This method is based on the continuity theorem of magnetic flux, and under the condition of neglecting magnetic saturation. The irregular radius function of rotor magnetic yoke and the radius function of the eccentric permanent magnet were used to solve the calculation of no-load air-gap magnetic fields through combing the boundary conditions with the interface conditions of magnetic fields. Compared to the calculation results of finite element analysis(FEA), this method can agree well with FEA, which verifies that this method is capable to calculate no-load air-gap magnetic fields in a permanent magnet synchronous motor with polygonal rotor magnetic yoke accurately and effectively.
This paper presents an analytical method on the calculation of no-load air-gap magnetic fields in a permanent magnet synchronous motor with polygonal rotor magnetic yoke by the use of dividing the region into parts. This method is based on the continuity theorem of magnetic flux, and under the condition of neglecting magnetic saturation. The irregular radius function of rotor magnetic yoke and the radius function of the eccentric permanent magnet were used to solve the calculation of no-load air-gap magnetic fields through combing the boundary conditions with the interface conditions of magnetic fields. Compared to the calculation results of finite element analysis(FEA), this method can agree well with FEA, which verifies that this method is capable to calculate no-load air-gap magnetic fields in a permanent magnet synchronous motor with polygonal rotor magnetic yoke accurately and effectively.
引文
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[16]王强,王友仁,孔德明,等.隐极式无刷直流电机转子初始位置估计[J].中国电机工程学报,2012,32(33):105-110,182.Wang Qiang,Wang Youren,Kong Deming,et al.Initial rotor position estimation for Non-salient pole brushless DC motors[J].Proceedings of the CSEE,2012,32(33):105-110,182(in Chinese).
[17]薛志强,周羽,李槐树.考虑定转子双边开槽时表贴式永磁电机空载磁场解析计算[J].中国电机工程学报,2016,37(8):2399-2408.Xue Zhiqiang,Zhou Yu,Li Huaishu.Analytical calculation of Open-circuit field in Surface-mounted Permanent-magnet machines accounting for slots in stator and rotor[J].Proceedings of the CSEE,2016,37(8):2399-2408(in Chinese).
[18]Zhu Z Q,Howe D,Chan C C.Improved analytical model for predicting the magnetic field distribution in brushless permanent-magnet machines[J].IEEE Transactions on Magnetics,2002,38(1):229-238.
[19]曹永娟,黄允凯,金龙,等.磁极组合型轴向磁场无铁心永磁电机的设计与分析[J].中国电机工程学报,2014,34(6):903-909.Cao Yongjuan,Huang Yunkai,Jin Long,et al.Design and analysis of a stator coreless Axial-flux permanent magnet machine with module poles[J].Proceedings of the CSEE,2014,34(6):903-909(in Chinese).
[20]夏加宽,沈丽,彭兵,等.齿槽效应对永磁直线伺服电机法向力波动的影响[J].中国电机工程学报,2015,35(11):2847-2853.Xia Jiakuan,Shen Li,Peng Bing,et al.Influences of cogging effects on normal force ripple in permanent magnet linear servo motors[J].Proceedings of the CSEE,2015,35(11):2847-2853(in Chinese).
[21]陈云云,全力,朱孝勇,等.双凸极永磁双转子电机优化设计与电磁特性分析[J].中国电机工程学报,2014,34(12):1912-1921.Chen Yunyun,Quan Li,Zhu Xiaoyong,et al.Optimal design and electromagnetic performance analysis of Double-salient Permanent-magnet double-rotor motors[J].Proceedings of the CSEE,2014,34(12):1912-1921(in Chinese).
[22]黄允凯,周涛,董剑宁,等.轴向永磁电机及其研究发展综述[J].中国电机工程学报,2015,35(1):192-205.Huang Yunkai,Zhou Tao,Dong Jianning,et al.An overview on developments and researches of axial flux permanent magnet machines[J].Proceedings of the CSEE,2015,35(1):192-205(in Chinese).
[2]董剑宁,黄允凯,金龙,等.高速永磁电机设计与分析技术综述[J].中国电机工程学报,2014,34(27):4640-4653.Dong Jianning,Huang Yunkai,Jin Long,et al.Review on high speed permanent magnet machines including design and analysis technologies[J].Proceedings of the CSEE,2014,34(27):4640-4653(in Chinese).
[3]卢琴芬,程传莹,叶云岳,等.每极分数槽永磁直线电机的槽极数配合研究[J].中国电机工程学报,2012,32(36):68-74.Lu Qinfen,Cheng Chuanying,Ye Yunyue,et al.Slot/Pole number combination research of PM linear motors with fractional slots per pole[J].Proceedings of CSEE,2012,32(36):68-74(in Chinese).
[4]郭思源,周理兵.表面埋入式永磁电机磁场解析[J].中国电机工程学报,2015,35(3):710-718.Guo Siyuan,Zhou Libing.Analytical solution of magnetic field in Surface-inset permanent magnet machines[J].Proceedings of the CSEE,2015,35(3):710-718(in Chinese).
[5]杨玉波,王秀和,丁婷婷,等.极弧系数组合优化的永磁电机齿槽转矩削弱方法[J].中国电机工程学报,2007,27(6):7-11.Yang Yubo,Wang Xiuhe,Ding Tingting,et al.Analysis of the optimization of the pole arc combination to reduce the cogging torque in PM motors[J].Proceedings of the CSEE,2007,27(6):7-11(in Chinese).
[6]张鑫,王秀和,杨玉波.基于改进磁场分割法的开关磁阻电机径向力波抑制能力解析计算[J].电工技术学报,2015,30(22):9-18.Zhang Xin,Wang Xiuhe,Yang Yubo.The computation of vibration reduction capacity for switched reluctance motor based on improved magnetic field partition method[J].Transactions of China Electrotechnical Society,2015,30(22):9-18(in Chinese).
[7]杨浩东,陈阳生.分数槽永磁同步电机电磁振动的分析与抑制[J].中国电机工程学报,2011,31(24):83-89.Yang Haodong,Chen Yangsheng.Electromagnetic vibration analysis and suppression of permanent magnet synchronous motor with fractional slot combination[J].Proceeding of the CSEE,2011,31(24):83-89(in Chinese).
[8]Zhu Z Q,Howe D,Bolte E,et al.Instantaneous magnetic field distribution in brushless permanent magnet DC motors.I.Open-circuit field[J].IEEETransactions on Magnetics,1993,29(1):124-135.
[9]Zhu Z Q,Howe D.Instantaneous magnetic field distribution in brushless permanent magnet DCmotors.III.Effect of stator slotting[J].IEEE Transactions on Magnetics,1993,29(1):143-151.
[10]Zhu Z Q,Wu L J,Xia Z P.An accurate subdomain model for magnetic field computation in slotted Surface-mounted Permanent-magnet machines[J].IEEETransactions on Magnetics,2010,46(4):1100-1115.
[11]Wu L J,Zhu Z Q,Staton D,et al.An improved subdomain model for predicting magnetic field of Surface-mounted permanent magnet machines accounting for Tooth-tips[J].IEEE Transactions on Magnetics,2011,47(6):1693-1704.
[12]Wu L J,Zhu Z Q,Chen J T,et al.An analytical model of unbalanced magnetic force in Fractional-slot Surface-mounted permanent magnet machines[J].IEEETransactions on Magnetics,2010,46(7):2686-2700.
[13]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.
[14]于吉坤,李立毅,张江鹏,等.定子开槽永磁同步电机气隙比磁导解析计算[J].电工技术学报,2016,31(S1):45-52.Yu Jikun,Li Liyi,Zhang Jiangpeng,et al.Analytical calculation of Air-gap relative permeance in slotted permanent magnet synchronous motor[J].Transactions of China Electrotechnical Society,2016,31(S1):45-52(in Chinese).
[15]周羽,李槐树,周石,等.考虑开槽时永磁无刷直流电机气隙磁场的解析计算[J].中国电机工程学报,2014,34(S1):182-188.Zhou Yu,Li Huaishu,Zhou Shi,et al.Analytical method for calculating Air-gap magnetic field of brushless DCmotor accounting for slots[J].Proceedings of the CSEE,2014,34(S1):182-188(in Chinese).
[16]王强,王友仁,孔德明,等.隐极式无刷直流电机转子初始位置估计[J].中国电机工程学报,2012,32(33):105-110,182.Wang Qiang,Wang Youren,Kong Deming,et al.Initial rotor position estimation for Non-salient pole brushless DC motors[J].Proceedings of the CSEE,2012,32(33):105-110,182(in Chinese).
[17]薛志强,周羽,李槐树.考虑定转子双边开槽时表贴式永磁电机空载磁场解析计算[J].中国电机工程学报,2016,37(8):2399-2408.Xue Zhiqiang,Zhou Yu,Li Huaishu.Analytical calculation of Open-circuit field in Surface-mounted Permanent-magnet machines accounting for slots in stator and rotor[J].Proceedings of the CSEE,2016,37(8):2399-2408(in Chinese).
[18]Zhu Z Q,Howe D,Chan C C.Improved analytical model for predicting the magnetic field distribution in brushless permanent-magnet machines[J].IEEE Transactions on Magnetics,2002,38(1):229-238.
[19]曹永娟,黄允凯,金龙,等.磁极组合型轴向磁场无铁心永磁电机的设计与分析[J].中国电机工程学报,2014,34(6):903-909.Cao Yongjuan,Huang Yunkai,Jin Long,et al.Design and analysis of a stator coreless Axial-flux permanent magnet machine with module poles[J].Proceedings of the CSEE,2014,34(6):903-909(in Chinese).
[20]夏加宽,沈丽,彭兵,等.齿槽效应对永磁直线伺服电机法向力波动的影响[J].中国电机工程学报,2015,35(11):2847-2853.Xia Jiakuan,Shen Li,Peng Bing,et al.Influences of cogging effects on normal force ripple in permanent magnet linear servo motors[J].Proceedings of the CSEE,2015,35(11):2847-2853(in Chinese).
[21]陈云云,全力,朱孝勇,等.双凸极永磁双转子电机优化设计与电磁特性分析[J].中国电机工程学报,2014,34(12):1912-1921.Chen Yunyun,Quan Li,Zhu Xiaoyong,et al.Optimal design and electromagnetic performance analysis of Double-salient Permanent-magnet double-rotor motors[J].Proceedings of the CSEE,2014,34(12):1912-1921(in Chinese).
[22]黄允凯,周涛,董剑宁,等.轴向永磁电机及其研究发展综述[J].中国电机工程学报,2015,35(1):192-205.Huang Yunkai,Zhou Tao,Dong Jianning,et al.An overview on developments and researches of axial flux permanent magnet machines[J].Proceedings of the CSEE,2015,35(1):192-205(in Chinese).