永磁球形电动机空芯定子线圈磁场的解析分析
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摘要
永磁球形电机定子线圈呈空芯圆柱形结构,由多匝导线缠绕在柱状铝芯上,离散分布在定子球壳内壁不同经、纬度线交叉点处.针对采用集中绕制方式的定子线圈的结构特点,基于毕奥-萨伐尔定律,并考虑球形电机定子线圈在定子坐标系中的位置关系对问题分析复杂性的影响,首先推导得到了任意位置单匝线圈在空间任意点处的磁场分布,并与现有文献进行了比较验证.其次将单匝线圈推广到多层多匝线圈,求解得到了任意位置多层多匝定子线圈在空间任意点处的磁场分布解析表达式.最后就定子线圈在不同路径上的磁场分布情况,与有限元法所得结果进行了比较,证明了该解析表达式的有效性.
Permanent magnet spherical motor stator coils are of hollow cylindrical structure.Stator coils are formed by multiple wires wrapping cylindrical aluminum core and distributed independently on the intersection of longitude line and latitude line on the inner wall of the stator spherical shell.In view of the centralized winding structure characteristics of the stator coils,based on Biot-Savart law,and given the influence of the actual position relationship between spherical motor stator coils and stator coordinate system on the complexity of problem analysis,the magnetic field distribution of single turn coil at any position in any space is obtained in this paper and it is verified by comparing with the existing literature.Then,single turn coil is extended to multilayer turns coil and the magnetic field distribution of multilayer turns coil at any position in any space is obtained.Finally,the analytical method in this paper is compared with finite element method in terms of magnetic field distribution on different paths to verify the effectiveness of the proposed analytical method.
Permanent magnet spherical motor stator coils are of hollow cylindrical structure.Stator coils are formed by multiple wires wrapping cylindrical aluminum core and distributed independently on the intersection of longitude line and latitude line on the inner wall of the stator spherical shell.In view of the centralized winding structure characteristics of the stator coils,based on Biot-Savart law,and given the influence of the actual position relationship between spherical motor stator coils and stator coordinate system on the complexity of problem analysis,the magnetic field distribution of single turn coil at any position in any space is obtained in this paper and it is verified by comparing with the existing literature.Then,single turn coil is extended to multilayer turns coil and the magnetic field distribution of multilayer turns coil at any position in any space is obtained.Finally,the analytical method in this paper is compared with finite element method in terms of magnetic field distribution on different paths to verify the effectiveness of the proposed analytical method.
引文
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[16]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(in Chinese).
[17]祝胜涛.基于有限元法的永磁球形电动机暂态特性分析[D].天津:天津大学电气与自动化工程学院,2012.Zhu Shengtao.Transient characteristic analysis of the permanent magnet spherical motor based on finite element method[D].Tianjin:School of Electrical Engineering and Automation,Tianjin University,2012(in Chinese).
[18]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 magnet model and magnetic field analysis of the permanent magnet spherical motor stator windings[J].Journal of Tianjin University,2012,45(11):1024-1029(in Chinese).
[19]李洪凤,沈彦波.永磁球形电动机永磁体涡流损耗分析[J].电工技术学报,2015,30(12):268-275.Li Hongfeng,Shen Yanbo.Permanent magnet eddy current loss analysis of the permanent magnet spherical motor[J].Transactions of CES,2015,30(12):268-275(in Chinese).
[20]朱平.圆电流空间磁场分布[J].大学物理,2005,24(9):13-17.Zhu Ping.Space magnetic field distribution of circular current[J].University Physics,2005,24(9):13-17(in Chinese).
[21]张德根,张波.圆电流和亥姆霍兹线圈磁场的数值模拟[J].皖西学院学报,2014,30(2):39-44.Zhang Degen,Zhang Bo.The numerical simulation of magnetic field of circular current and Helmholtz coil[J].Journal of West Anhui University,2014,30(2):39-44(in Chinese).
[22]曾令宏,张之翔.圆环电流的磁场以及两共轴圆环电流之间的相互作用力[J].大学物理,2002,21(9):14-16.Zeng Linghong,Zhang Zhixiang.The interaction force between magnetic field generated by ring current and two coaxial ring current[J].University Physics,2002,21(9):14-16(in Chinese).
[23]向裕民.圆环电流磁场的普遍分布[J].大学物理,1999,18(1):14-17.Xiang Yumin.The widespread distribution of the ring current magnetic field[J].University Physics,1999,18(1):14-17(in Chinese).
[24]张星辉.圆电流磁感线的分布及磁感应强度的函数表达式[J].大学物理,2006,25(1):32-37.Zhang Xinghui.Distribution of circular current magnetic induction line and function expression of the magnetic induction intensity[J].University Physics,2006,25(1):32-37(in Chinese).
[25]邰显康,云月厚,李国栋.用级数拟合求圆电流磁场解析解[J].大学物理,2003,21(3):6-8.Tai Xiankang,Yun Yuehou,Li Guodong.Circular current magnetic field analytical solution based on series fitting[J].University Physics,2003,21(3):6-8(in Chinese).
[2]Wang L,Zhang L,Xu M.Simulation analysis on the influence of magnetic field distribution caused by motor spindle air-gap[C]//International Conference on Electronic and Mechanical Engineering and Information Technology.Harbin,China,2011:215-218.
[3]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.
[4]Kajikawa K,Uchida Y,Nakamura T,et al.Development of stator windings for fully superconducting motor with Mg B2 wires[J].IEEE Transactions on Applied Superconductivity,2013,23(3):5201604-5201604.
[5]Li L,Cao J,Kou B,et al.Design of the HTS permanent magnet motor with superconducting armature winding[J].IEEE Transactions on Applied Superconductivity,2012,22(22):5200704-5200704.
[6]Zhao J,Shi G,Du L.Miniaturized air-driven planar magnetic generators[J].Energies,2015,8(10):11755-11769.
[7]Cukovic J P,Klop?i?B,Dolinar D.Analysis of stator winding tester for AC machines[J].Przeglad Elektrotechniczny,2012,88(7):16-19.
[8]Lemmens J,Mulier K,Driesen J,et al.Efficiency improvement of a high dynamic BLDC linear motor by multiphase control[C]//IEEE Energy Conversion Congress and Exposition.Denver,USA,2013:1191-1196.
[9]Xu J,Ma W,Lu J,et al.Analysis of magnetic field distribution and parameter calculation of linear induction motor with novel winding construction[C]//XIX International Conference on Electrical Machines(ICEM).Rome,Italy,2010:1-6.
[10]Wu L J,Zhu Z Q,Staton D,et al.Analytical model for predicting magnet loss of surface-mounted permanent magnet machines accounting for slotting effect and load[J].IEEE Transactions on Magnetics,2012,48(1):107-117.
[11]Han S H,Jahns T M,Zhu Z Q.Analysis of rotor core eddy-current losses in interior permanent magnet synchronous machines[J].IEEE Transactions on Industry Applications,2010,46(1):196-205.
[12]Wu L J,Zhu Z Q,Staton D,et al.Analytical modeling and analysis of open-circuit magnet loss in surfacemounted permanent-magnet machines[J].IEEE Transactions on Magnetics,2012,48(3):1234-1247.
[13]Wu L J,Zhu Z Q,Staton D,et al.Analytical model for predicting magnet loss of surface-mounted permanent magnet machines accounting for slotting effect and load[J].IEEE Transactions on Magnetics,2012,48(1):107-117.
[14]Ishak D,Zhu Z Q,Howe D.Eddy-current loss in the rotor magnets of permanent-magnet brushless machines having a fractional number of slots per pole[J].IEEE Transactions on Magnetics,2005,41(9):2462-2469.
[15]Zhao N,Zhu Z Q,Liu W.Rotor eddy current loss calculation and thermal analysis of permanent magnet motor and generator[J].IEEE Transactions on Magnetics,2011,47(10):4199-4202.
[16]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(in Chinese).
[17]祝胜涛.基于有限元法的永磁球形电动机暂态特性分析[D].天津:天津大学电气与自动化工程学院,2012.Zhu Shengtao.Transient characteristic analysis of the permanent magnet spherical motor based on finite element method[D].Tianjin:School of Electrical Engineering and Automation,Tianjin University,2012(in Chinese).
[18]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 magnet model and magnetic field analysis of the permanent magnet spherical motor stator windings[J].Journal of Tianjin University,2012,45(11):1024-1029(in Chinese).
[19]李洪凤,沈彦波.永磁球形电动机永磁体涡流损耗分析[J].电工技术学报,2015,30(12):268-275.Li Hongfeng,Shen Yanbo.Permanent magnet eddy current loss analysis of the permanent magnet spherical motor[J].Transactions of CES,2015,30(12):268-275(in Chinese).
[20]朱平.圆电流空间磁场分布[J].大学物理,2005,24(9):13-17.Zhu Ping.Space magnetic field distribution of circular current[J].University Physics,2005,24(9):13-17(in Chinese).
[21]张德根,张波.圆电流和亥姆霍兹线圈磁场的数值模拟[J].皖西学院学报,2014,30(2):39-44.Zhang Degen,Zhang Bo.The numerical simulation of magnetic field of circular current and Helmholtz coil[J].Journal of West Anhui University,2014,30(2):39-44(in Chinese).
[22]曾令宏,张之翔.圆环电流的磁场以及两共轴圆环电流之间的相互作用力[J].大学物理,2002,21(9):14-16.Zeng Linghong,Zhang Zhixiang.The interaction force between magnetic field generated by ring current and two coaxial ring current[J].University Physics,2002,21(9):14-16(in Chinese).
[23]向裕民.圆环电流磁场的普遍分布[J].大学物理,1999,18(1):14-17.Xiang Yumin.The widespread distribution of the ring current magnetic field[J].University Physics,1999,18(1):14-17(in Chinese).
[24]张星辉.圆电流磁感线的分布及磁感应强度的函数表达式[J].大学物理,2006,25(1):32-37.Zhang Xinghui.Distribution of circular current magnetic induction line and function expression of the magnetic induction intensity[J].University Physics,2006,25(1):32-37(in Chinese).
[25]邰显康,云月厚,李国栋.用级数拟合求圆电流磁场解析解[J].大学物理,2003,21(3):6-8.Tai Xiankang,Yun Yuehou,Li Guodong.Circular current magnetic field analytical solution based on series fitting[J].University Physics,2003,21(3):6-8(in Chinese).