Halbach阵列盘式永磁电机的解析计算
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摘要
以一台Halbach阵列盘式永磁电机为对象,采用精确子域法,在直角坐标系下推导该电机空载气隙磁场的解析计算方法。该方法通过分离Halbach永磁体,得到各永磁体的磁化强度,通过叠加法合成最终磁化强度,根据边界条件求解电机的磁场,继而获得相关电磁性能。将有限元计算结果和实验结果分别与解析计算结果进行对比,结果表明所推导的解析方法具有较高的精度。该文所述模型可推广至绝大部分Halbach阵列结构,对该类型电机的快速计算具有一定的指导意义。
In this paper, an axial flux permanent magnet(AFPM) machine with Halbach array was taken as a research object. Based on the sub-domain(SD) technique, the analytical model for calculating no-load flux density was derived under the Cartesian coordinate system. The magnetization of permanent magnets was calculated separately and the final magnetization was obtained using the superposition method. Afterwards, the magnetic field of subdomains was solved according to boundary conditions and interface conditions. Based on the previous results, the magnetic characteristics such as flux linkage and cogging torque, were calculated. The results obtained from the analytical model are verified by the finite element model to validate the proposed method. The analysis method can be applied to most surface-mounted axial flux permanent magnet machines with Halbach arrays, this method has certain guiding significance for the fast calculation of this kind of machines.
In this paper, an axial flux permanent magnet(AFPM) machine with Halbach array was taken as a research object. Based on the sub-domain(SD) technique, the analytical model for calculating no-load flux density was derived under the Cartesian coordinate system. The magnetization of permanent magnets was calculated separately and the final magnetization was obtained using the superposition method. Afterwards, the magnetic field of subdomains was solved according to boundary conditions and interface conditions. Based on the previous results, the magnetic characteristics such as flux linkage and cogging torque, were calculated. The results obtained from the analytical model are verified by the finite element model to validate the proposed method. The analysis method can be applied to most surface-mounted axial flux permanent magnet machines with Halbach arrays, this method has certain guiding significance for the fast calculation of this kind of machines.
引文
[1]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]Gieras J F,Wang R J,Kamper M J.Axial flux permanent magnet brushless machines[M].2nd edition.New York:Springer,2008:281-282..
[3]Nguyen T D,Tseng KJ,Zhang S.A novel axial flux permanent-magnet machine for flywheel energy storage system:design and analysis[J].IEEE Transactions on Industrial Electronics,2011,58(9):3784-3794.
[4]Kumar S,Lipo T A,Kwon B I.A 32,000 rev/min axial flux permanent magnet machine for energy storage with mechanical stress analysis[J].IEEE Transactions on Magnetics,2016,PP(99):1-1.
[5]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).
[6]Ajily E,Abbaszadeh K,Ardebili M.Three-dimensional field reconstruction method for modeling axial flux permanent magnet machines[J].IEEE Transactions on Energy Conversion,2015,30(1):199-207.
[7]Ajily E,Ardebili M,Abbaszadeh K.Magnet defect and rotor eccentricity modeling in axial-flux permanentmagnet machines via 3-D field reconstruction method[J].IEEE Transactions on Energy Conversion,2015,PP(99):1-10.
[8]Marignetti F,Vahedi A,Mirimani S M.An analytical approach to eccentricity in axial flux permanent magnet synchronous generators for wind turbines[J].Electric Power Components and Systems,2015,43(8-10):1039-1250.
[9]Hemeida A,Sergeant P.Analytical modeling of surface PMSM using a combined solution of Maxwell’s equations and magnetic equivalent circuit[J].IEEE Transactions on Magnetics,2014,50(12):1-13.
[10]Bellara A,Tiegna H,Amara Y.On load analytical modelling of the magnetic field for axial flux surface-inset permanent magnet machines with semi-closed slots[C]//2010 XIX International Conference onElectrical Machines(ICEM).IEEE,2012:2852-2858.
[11]Tiegna H,Bellara A,Amara Y.Analytical modeling of the open-circuit magnetic field in axial flux permanentmagnet machines with semi-closed slots[J].IEEETransactions on Magnetics,2012,48(3):1212-1226.
[12]黄允凯,周涛.基于等效磁路法的轴向永磁电机效率优化设计[J].电工技术学报,2015,30(2):73-79.Huang Yunkai,Zhou Tao.Efficiency optimization design of axial flux permanent magnet machines using magnetic equivalent circuit[J].Transactions of China Electrotechnical Society,2015,30(2):73-79(in Chinese).
[13]董剑宁,黄允凯,金龙,等.定子无铁心轴向磁场永磁电机的解析设计[J].电工技术学报,2013,28(3):43-49.Dong Jianning,Huang Yunkai,Jin Long,et al.Analytical design method of stator-coreless axial flux permanent magnet machines[J].Transactions of China Electrotechnical Society,2013,28(3):43-49(in Chinese).
[14]范坚坚,吴建华.计及齿槽极间隔断Halbach型磁钢的PMSM气隙磁场解析分析[J].中国电机工程学报,2010,30(12):98-105.Fan Jianjian,Wu Jianhua.Analytical solution and analysis of airgap magnetic field of PMSM with Partition-betweenpoles Halbach magnet considering effect of slotting[J].Proceedings of the CSEE,2010,30(12):98-105(in Chinese).
[15]范坚坚,吴建华,李创平,等.分块式Halbach型磁钢的永磁同步电机解析[J].电工技术学报,2013,28(3):35-42.Fan Jianjian,Wu Jianhua.Li Chuangping,et al.Solution of permanent magnet synchronous motors with partition between poles Halbach magnet[J].Transactions of China Electrotechnical Society,2013,28(3):35-42(in Chinese).
[16]梁京辉,张晓锋,乔鸣忠,等.离散式任意充磁角度Halbach永磁电机解析模型研究[J].物理学报,2013(15):39-47.Liang Jinghui,Zhang Xiaofeng,Qiao Mingzhong,et al.Analytic model of discrete random magnetizing Halbach PM motor[J].Acta Physica Sinica,2013(15):39-47(in Chinese).
[17]李琛,章跃进,井立兵.Halbach阵列半闭口槽永磁电机全局解析法研究[J].中国电机工程学报,2013,33(33):85-94.Li Chen,Zhang Yuejin,Jing Libing.Researches on an exact analytical method of Halbach-array permanentmagnet motors with semi-closed slots[J].Proceedings of the CSEE,2013,33(33):85-94(in Chinese).
[18]Shen Y.Novel permanent magnet brushless machines having segmented Halbach array[D].Sheffield:University of Sheffield,2013.
[19]李桂丹,于海峰,王晓远,等.基于Halbach阵列的盘式无铁心永磁同步电机磁钢优化[J].微电机,2015(2):1-6.Li Guidan,Yu Haifeng,Wang Xiaoyuan,et al.Magnet optimization of disc coreless permanent magnet synchronous motor based on Halbach[J].Micromotors,2015(2):1-6(in Chinese).
[20]陈殷,张昆仑,胡巧琳.基于盘式Halbach永磁阵列的重力平衡装置电磁力计算[J].电工技术学报,2014,29(5):36-42.Chen Yin,Zhang Kunlun,Hu Qiaolin.Calculating electromagnetic force created by gravity balance device based on discal Halbach permanent magnet array[J].Transactions of China Electrotechnical Society,2014,29(5):36-42(in Chinese).
[21]Huang Y,Guo B,Guo Y,et al.Analytical modeling of axial flux PM machines with eccentricities[J].International Journal of Applied Electromagnetics and Mechanics,2017,53(4):757-777.
[22]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).
[23]Shen Y,Zhu Z Q.Investigation of permanent magnet brushless machines having unequal-magnet height pole[J].IEEE Transactions on Magnetics,2012,48(12):4815-4830.
[2]Gieras J F,Wang R J,Kamper M J.Axial flux permanent magnet brushless machines[M].2nd edition.New York:Springer,2008:281-282..
[3]Nguyen T D,Tseng KJ,Zhang S.A novel axial flux permanent-magnet machine for flywheel energy storage system:design and analysis[J].IEEE Transactions on Industrial Electronics,2011,58(9):3784-3794.
[4]Kumar S,Lipo T A,Kwon B I.A 32,000 rev/min axial flux permanent magnet machine for energy storage with mechanical stress analysis[J].IEEE Transactions on Magnetics,2016,PP(99):1-1.
[5]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).
[6]Ajily E,Abbaszadeh K,Ardebili M.Three-dimensional field reconstruction method for modeling axial flux permanent magnet machines[J].IEEE Transactions on Energy Conversion,2015,30(1):199-207.
[7]Ajily E,Ardebili M,Abbaszadeh K.Magnet defect and rotor eccentricity modeling in axial-flux permanentmagnet machines via 3-D field reconstruction method[J].IEEE Transactions on Energy Conversion,2015,PP(99):1-10.
[8]Marignetti F,Vahedi A,Mirimani S M.An analytical approach to eccentricity in axial flux permanent magnet synchronous generators for wind turbines[J].Electric Power Components and Systems,2015,43(8-10):1039-1250.
[9]Hemeida A,Sergeant P.Analytical modeling of surface PMSM using a combined solution of Maxwell’s equations and magnetic equivalent circuit[J].IEEE Transactions on Magnetics,2014,50(12):1-13.
[10]Bellara A,Tiegna H,Amara Y.On load analytical modelling of the magnetic field for axial flux surface-inset permanent magnet machines with semi-closed slots[C]//2010 XIX International Conference onElectrical Machines(ICEM).IEEE,2012:2852-2858.
[11]Tiegna H,Bellara A,Amara Y.Analytical modeling of the open-circuit magnetic field in axial flux permanentmagnet machines with semi-closed slots[J].IEEETransactions on Magnetics,2012,48(3):1212-1226.
[12]黄允凯,周涛.基于等效磁路法的轴向永磁电机效率优化设计[J].电工技术学报,2015,30(2):73-79.Huang Yunkai,Zhou Tao.Efficiency optimization design of axial flux permanent magnet machines using magnetic equivalent circuit[J].Transactions of China Electrotechnical Society,2015,30(2):73-79(in Chinese).
[13]董剑宁,黄允凯,金龙,等.定子无铁心轴向磁场永磁电机的解析设计[J].电工技术学报,2013,28(3):43-49.Dong Jianning,Huang Yunkai,Jin Long,et al.Analytical design method of stator-coreless axial flux permanent magnet machines[J].Transactions of China Electrotechnical Society,2013,28(3):43-49(in Chinese).
[14]范坚坚,吴建华.计及齿槽极间隔断Halbach型磁钢的PMSM气隙磁场解析分析[J].中国电机工程学报,2010,30(12):98-105.Fan Jianjian,Wu Jianhua.Analytical solution and analysis of airgap magnetic field of PMSM with Partition-betweenpoles Halbach magnet considering effect of slotting[J].Proceedings of the CSEE,2010,30(12):98-105(in Chinese).
[15]范坚坚,吴建华,李创平,等.分块式Halbach型磁钢的永磁同步电机解析[J].电工技术学报,2013,28(3):35-42.Fan Jianjian,Wu Jianhua.Li Chuangping,et al.Solution of permanent magnet synchronous motors with partition between poles Halbach magnet[J].Transactions of China Electrotechnical Society,2013,28(3):35-42(in Chinese).
[16]梁京辉,张晓锋,乔鸣忠,等.离散式任意充磁角度Halbach永磁电机解析模型研究[J].物理学报,2013(15):39-47.Liang Jinghui,Zhang Xiaofeng,Qiao Mingzhong,et al.Analytic model of discrete random magnetizing Halbach PM motor[J].Acta Physica Sinica,2013(15):39-47(in Chinese).
[17]李琛,章跃进,井立兵.Halbach阵列半闭口槽永磁电机全局解析法研究[J].中国电机工程学报,2013,33(33):85-94.Li Chen,Zhang Yuejin,Jing Libing.Researches on an exact analytical method of Halbach-array permanentmagnet motors with semi-closed slots[J].Proceedings of the CSEE,2013,33(33):85-94(in Chinese).
[18]Shen Y.Novel permanent magnet brushless machines having segmented Halbach array[D].Sheffield:University of Sheffield,2013.
[19]李桂丹,于海峰,王晓远,等.基于Halbach阵列的盘式无铁心永磁同步电机磁钢优化[J].微电机,2015(2):1-6.Li Guidan,Yu Haifeng,Wang Xiaoyuan,et al.Magnet optimization of disc coreless permanent magnet synchronous motor based on Halbach[J].Micromotors,2015(2):1-6(in Chinese).
[20]陈殷,张昆仑,胡巧琳.基于盘式Halbach永磁阵列的重力平衡装置电磁力计算[J].电工技术学报,2014,29(5):36-42.Chen Yin,Zhang Kunlun,Hu Qiaolin.Calculating electromagnetic force created by gravity balance device based on discal Halbach permanent magnet array[J].Transactions of China Electrotechnical Society,2014,29(5):36-42(in Chinese).
[21]Huang Y,Guo B,Guo Y,et al.Analytical modeling of axial flux PM machines with eccentricities[J].International Journal of Applied Electromagnetics and Mechanics,2017,53(4):757-777.
[22]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).
[23]Shen Y,Zhu Z Q.Investigation of permanent magnet brushless machines having unequal-magnet height pole[J].IEEE Transactions on Magnetics,2012,48(12):4815-4830.