基于球谐函数的动量球定子磁场分析
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摘要
提出一种新的圆柱形定子线圈空间磁场解析法。在双多面体结构动量球中,缠绕成圆柱形的空心定子线圈按照一定规律分布在定子球壳的表面。首先,将通电线圈等效为圆柱形永磁体,进而利用尺寸等效获得圆锥形永磁体模型,并获得线圈电流与永磁体剩余磁化强度之间的关系。然后,通过求解气隙中标量磁位满足的拉普拉斯方程,得到气隙中磁场的球谐函数描述。最后,通过分析有限元仿真结果和实验结果,可知径向磁通密度解析结果在表达定子磁场方面的准确性较高。
This paper presents a new spatial magnetic field(MF) analysis method of cylindrical stator coil. In the double polyhedral structure reaction sphere(RS), air-cored stator coils formed into a cylindrical shape are distributed on the surface of the stator shell in accordance with a certain rule. First, the energized coil is equivalent to a cylindrical permanent magnet, the conical permanent magnet model is obtained using the size equivalent, and the relationship between the coil current and the residual magnetization of the PM is obtained. Then, the spherical harmonics description of the air gap magnetic field is obtained by solving the Laplace equation with the air gap scalar magnetic field. Finally, by analyzing the finite element simulation results and experimental results, it can be seen that the radial magnetic density analytical expression has a good accuracy in fitting the stator MF.
This paper presents a new spatial magnetic field(MF) analysis method of cylindrical stator coil. In the double polyhedral structure reaction sphere(RS), air-cored stator coils formed into a cylindrical shape are distributed on the surface of the stator shell in accordance with a certain rule. First, the energized coil is equivalent to a cylindrical permanent magnet, the conical permanent magnet model is obtained using the size equivalent, and the relationship between the coil current and the residual magnetization of the PM is obtained. Then, the spherical harmonics description of the air gap magnetic field is obtained by solving the Laplace equation with the air gap scalar magnetic field. Finally, by analyzing the finite element simulation results and experimental results, it can be seen that the radial magnetic density analytical expression has a good accuracy in fitting the stator MF.
引文
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[12]Yan Liang,Liu Delong,Jiao Zongxia,et al.Magnetic field modeling based on geometrical equivalence principle for spherical actuator with cylindrical shaped magnet poles[J].Aerospace Science and Technology,2016,49:17-25.
[13]Yan Liang,Chen I-Ming,Yang Guilin,et al.Analytical and experimental investigation on the magnetic field and torque of a permanent magnet spherical actuator[J].IEEE/ASME Transactions on Mechatronics,2006,11(4):409-419.
[14]Xin Jianguo,Xia Changliang,Li Hongfeng,et al.Anovel orientation measurement using optical sensor for spherical motor[J].Science China Technological Sciences,2013,56(6):1330-1339.
[2]Li Bin,Yu Rujian,Li Hongfeng,et al.Modeling and analysis of a 3-DOF spherical momentum exchange actuator for spacecraft attitude maneuver[J].Journal of Aerospace Engineering,2015,28(6):1-9.
[3]信建国,夏长亮,李洪凤,等.基于解析模型的永磁球形电机永磁体优化设计[J].电工技术学报,2013,28(7):87-95.Xin Jianguo,Xia Changliang,Li Hongfeng,et al.Optimization design of permanent magnet array for spherical motor based on analytical model[J].Transactions of China Electrotechnical Society,2013,28(7):87-95.
[4]鞠鲁峰,王群京,李国丽,等.永磁球形电机的支持向量机模型的参数寻优[J].电工技术学报,2014,29(1):85-90.Ju Lufeng,Wang Qunjing,Li Guoli,et al.Parameter optimization for support vector machine model of permanent magnet spherical motors[J].Transactions of China Electrotechnical Society,2014,29(1):85-90.
[5]吴立建,王群京,杜世俊,等.磁场积分法在永磁步进球形电动机场分析中的应用[J].中国电机工程学报,2004,24(9):192-197.Wu Lijian,Wang Qunjing,Du Shijun,et al.Application of magnetic field integral method in the analysis of permanent magnet stepping spherical motor[J].Proceedings of the CSEE,2004,24(9):192-197.
[6]Kok-Meng L,Son H.Equivalent voice-coil models for real-time computation in electromagnetic actuation and sensor applications[C]//2007 IEEE/ASMEInternational Conference on Advanced Intelligent Mechatronics,Zurich,Switzerland,2007:1-6.
[7]李洪凤,李天梦,韩冰.永磁球形电动机空芯定子线圈磁场的解析分析[J].天津大学学报(自然科学与工程技术版),2015,229(1):64-72.Li Hongfeng,Li Tianmeng,Han Bing.Magnetic field analysis of the hollow stator coil in permanent magnet spherical motor[J].Journal of Tianjin University(Science and Technology),2018,229(1):64-72.
[8]Yan Liang,Wu Zewu,Jiao Zongxia,et al.Equivalent energized coil model for magnetic field of permanentmagnet spherical actuators[J].Sensors and Actuators A:Physical,2015,229:68-76.
[9]李斌,刘超,李洪凤,等.永磁球形电机定子绕组的永磁体模型及磁场分析[J].天津大学学报,2012,45(11):1024-1029.Li Bin,Liu Chao,Li Hongfeng,et al.Permanent magnetic model and magnetic field analysis for stator coil of permanent magnetic spherical motor[J].Journal of Tianjin University,2012,45(11):1024-1029.
[10]李斌,翟雪冰,李桂丹,等.永磁球形电机定子磁场的球谐波分析[J].电工技术学报,2013,28(1):302-306.Li Bin,Zhai Xuebing,Li Guidan,et al.The spherical harmonics analysis for the stator magnetic field of permanent magnetic spherical motor[J].Transactions of China Electrotechnical Society,2013,28(1):302-306.
[11]Li Bin,Li Zhitian,Li Guidan.Magnetic field model for permanent magnet spherical motor with double polyhedron structure[J].IEEE Transactions on Magnetics,2017,53(12):1-5.
[12]Yan Liang,Liu Delong,Jiao Zongxia,et al.Magnetic field modeling based on geometrical equivalence principle for spherical actuator with cylindrical shaped magnet poles[J].Aerospace Science and Technology,2016,49:17-25.
[13]Yan Liang,Chen I-Ming,Yang Guilin,et al.Analytical and experimental investigation on the magnetic field and torque of a permanent magnet spherical actuator[J].IEEE/ASME Transactions on Mechatronics,2006,11(4):409-419.
[14]Xin Jianguo,Xia Changliang,Li Hongfeng,et al.Anovel orientation measurement using optical sensor for spherical motor[J].Science China Technological Sciences,2013,56(6):1330-1339.