永磁球形电动机永磁体涡流损耗分析
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摘要
永磁球形电动机的磁极呈球面锥体结构,各定子线圈相互独立分布于定子球壳内表面,针对这些特性,提出了一种计算永磁球形电动机永磁体涡流损耗的三维解析模型。该模型将双重傅里叶级数法与矢量磁位解析法相结合,首先利用双重傅里叶级数法求得定子内径处电流密度分布,继而将其作为边界条件,借助三维拉普拉斯方程,获得了矢量磁位的特解,最后推导得到了永磁球形电动机永磁体涡流损耗的解析表达式。该模型充分考虑到了时间谐波与空间谐波对涡流损耗的影响,并分析了不同的电机结构参数对永磁体涡流损耗的影响。将解析法与有限元法所得结果进行了比较,结果一致,证明了该解析模型的有效性。
The rotor magnets of the permanent magnet spherical motor(PMSM) have a structure of spherical cone, and all of the stator coils are distributed on the inner surface of the stator shell independently of each other. In view of these characteristics, a three-dimensional(3-D) analytical model is presented to study the eddy current loss of magnets in the PMSM. And this model combines the double Fourier series decomposition and the magnetic vector potential method. First, the current density distribution at the inner diameter of the stator is described by employing the double Fourier series decomposition. With the current density distribution and other boundary conditions, the unique solution of magnetic vector potential is obtained by solving 3-D Laplace's equations. Further, the analytic expression of PM eddy current loss in the PMSM is derived. This model considers the effect of harmonics, and the influence of different motor parameters on the eddy current loss has been analyzed. The results of analytical method and finite element method(FEM) are compared, proving the effectiveness of the proposed analytical model.
The rotor magnets of the permanent magnet spherical motor(PMSM) have a structure of spherical cone, and all of the stator coils are distributed on the inner surface of the stator shell independently of each other. In view of these characteristics, a three-dimensional(3-D) analytical model is presented to study the eddy current loss of magnets in the PMSM. And this model combines the double Fourier series decomposition and the magnetic vector potential method. First, the current density distribution at the inner diameter of the stator is described by employing the double Fourier series decomposition. With the current density distribution and other boundary conditions, the unique solution of magnetic vector potential is obtained by solving 3-D Laplace's equations. Further, the analytic expression of PM eddy current loss in the PMSM is derived. This model considers the effect of harmonics, and the influence of different motor parameters on the eddy current loss has been analyzed. The results of analytical method and finite element method(FEM) are compared, proving the effectiveness of the proposed analytical model.
引文
[1]Li H F,Xia C L,Shi T N.Spherical Harmonic Analysis of a Novel Halbach Array PM Spherical Motor[C].IEEE International Conference on Robotics and Biomimetics,2007:2085-2089.
[2]Xia C L,Li H F,Shi T N.3-D Magnetic Field and Torque Analysis of a Novel Halbach Array PermanentMagnet Spherical Motor[J].IEEE Transactions on Magnetics,2008,44(8):2016-2020.
[3]Li H F,Xia C L,Song P,et al.Magnetic Field Analysis of A Halbach Array PM Spherical Motor[C].IEEE International Conference on Automation and Logistics,2007:2019-2023.
[4]李洪凤.Halbach阵列永磁球形电动机三维磁场分析[D].天津:天津大学,2008.Li H F.3-D Magnetic Field Analysis of a Halbach Array PM Spherical Motor[D].Tianjin:Tianjin University,2008.
[5]Xia C L,Song P,Li H F,Li B and Shi T N.Research on Torque Calculation Method of Permanent-magnet Spherical Motor Based on the Finite-Element Method[J].IEEE Transactions on Magnetics.2009,45(4):2015-2022.
[6]Yan L,Chen I M,Lee K M,et al.Modeling and Iron-Effect Analysis on Magnetic Field and Torque Output of Electromagnetic Spherical Actuators With Iron Stator,IEEE/ASME Transactions on Mechatronics[J],2012,17(6):1080-1087.
[7]Xin J G,XIA C L,Li H F,Shi T N.A novel orientation measurement using optical sensor for spherical motor[J].Science China,2013,56(6):1330-1339.
[8]信建国,夏长亮,李洪凤,史婷娜.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,Shi Tingna.Optimization design of permanent magnet array for spherical motor based on analytical model[J].Transactions of China Electrotechnical Society,2013,28(7):87-95.
[9]鞠鲁峰,王群京,李国丽.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.Parameter optimization for support vector machine model of permanent magnet spherical motors[J].Transactions of China Electrotechnical Society,2014,29(1):85-90.
[10]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.
[11]Norio Takahashi,Hirofumi Shinagawa,Daisuke Miyagi.Analysis of Eddy Current Losses of Segmented Nd-Fe-B Sintered Magnets Considering Contact Resistance[J].IEEE Transactions on Magnetics,2009,45(3):1234-1237.
[12]Seok-Myeong Jang,Hyun-Kyu Kim,Jang-Young Choi.Analysis and comparison for rotor eddy current losses of permanent magnet synchronous generator according to dc and ac load conditions[C].Journal of applied physics,2009:300-303.
[13]Nannan Zhao,Z.Q.Zhu,Weiguo Liu.Rotor Eddy Current Loss Calculation and Thermal Analysis of Permanent Magnet Motor and Generator[J].IEEE Transactions on Magnetics,2011,47(10):4199-4202.
[14]李伟力,孙佳慧,孙红丽.汽轮发电机稳态与负序工况下转子涡流损耗计算和温度场分析[J].电工技术学报,2012,27(9):174-182.Li Weili,Sun Jiahui,Sun Hongli.Calculation and analysis of eddy loss and temperature field in rotor of synchronous generator under steady state and negative sequence[J].Transactions of China Electrotechnical Society,2012,27(9):174-182.
[15]解恩,刘卫国,罗玲,王璞.PWM调制对无刷直流电机转子涡流损耗的影响[J].电工技术学报,2013,28(2):117-125.Xie En,Liu Weiguo,Luo Ling,Wang Pu.Influence of PWM on rotor eddy-current losses in brushless DC motor[J].Transactions of China Electrotechnical Society,2013,28(2):117-125.
[16]H.Domeki,Y.Ishihara,C.Kaido,Y.Kawase,S.Kitamura,T.Shimomura,N.Takahashi,T.Yamada,and K.Yamazaki.Investigation of benchmark model for estimating iron loss in rotating machine[J].IEEE Trans.on Magn.,2004,40(2):794–797.
[2]Xia C L,Li H F,Shi T N.3-D Magnetic Field and Torque Analysis of a Novel Halbach Array PermanentMagnet Spherical Motor[J].IEEE Transactions on Magnetics,2008,44(8):2016-2020.
[3]Li H F,Xia C L,Song P,et al.Magnetic Field Analysis of A Halbach Array PM Spherical Motor[C].IEEE International Conference on Automation and Logistics,2007:2019-2023.
[4]李洪凤.Halbach阵列永磁球形电动机三维磁场分析[D].天津:天津大学,2008.Li H F.3-D Magnetic Field Analysis of a Halbach Array PM Spherical Motor[D].Tianjin:Tianjin University,2008.
[5]Xia C L,Song P,Li H F,Li B and Shi T N.Research on Torque Calculation Method of Permanent-magnet Spherical Motor Based on the Finite-Element Method[J].IEEE Transactions on Magnetics.2009,45(4):2015-2022.
[6]Yan L,Chen I M,Lee K M,et al.Modeling and Iron-Effect Analysis on Magnetic Field and Torque Output of Electromagnetic Spherical Actuators With Iron Stator,IEEE/ASME Transactions on Mechatronics[J],2012,17(6):1080-1087.
[7]Xin J G,XIA C L,Li H F,Shi T N.A novel orientation measurement using optical sensor for spherical motor[J].Science China,2013,56(6):1330-1339.
[8]信建国,夏长亮,李洪凤,史婷娜.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,Shi Tingna.Optimization design of permanent magnet array for spherical motor based on analytical model[J].Transactions of China Electrotechnical Society,2013,28(7):87-95.
[9]鞠鲁峰,王群京,李国丽.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.Parameter optimization for support vector machine model of permanent magnet spherical motors[J].Transactions of China Electrotechnical Society,2014,29(1):85-90.
[10]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.
[11]Norio Takahashi,Hirofumi Shinagawa,Daisuke Miyagi.Analysis of Eddy Current Losses of Segmented Nd-Fe-B Sintered Magnets Considering Contact Resistance[J].IEEE Transactions on Magnetics,2009,45(3):1234-1237.
[12]Seok-Myeong Jang,Hyun-Kyu Kim,Jang-Young Choi.Analysis and comparison for rotor eddy current losses of permanent magnet synchronous generator according to dc and ac load conditions[C].Journal of applied physics,2009:300-303.
[13]Nannan Zhao,Z.Q.Zhu,Weiguo Liu.Rotor Eddy Current Loss Calculation and Thermal Analysis of Permanent Magnet Motor and Generator[J].IEEE Transactions on Magnetics,2011,47(10):4199-4202.
[14]李伟力,孙佳慧,孙红丽.汽轮发电机稳态与负序工况下转子涡流损耗计算和温度场分析[J].电工技术学报,2012,27(9):174-182.Li Weili,Sun Jiahui,Sun Hongli.Calculation and analysis of eddy loss and temperature field in rotor of synchronous generator under steady state and negative sequence[J].Transactions of China Electrotechnical Society,2012,27(9):174-182.
[15]解恩,刘卫国,罗玲,王璞.PWM调制对无刷直流电机转子涡流损耗的影响[J].电工技术学报,2013,28(2):117-125.Xie En,Liu Weiguo,Luo Ling,Wang Pu.Influence of PWM on rotor eddy-current losses in brushless DC motor[J].Transactions of China Electrotechnical Society,2013,28(2):117-125.
[16]H.Domeki,Y.Ishihara,C.Kaido,Y.Kawase,S.Kitamura,T.Shimomura,N.Takahashi,T.Yamada,and K.Yamazaki.Investigation of benchmark model for estimating iron loss in rotating machine[J].IEEE Trans.on Magn.,2004,40(2):794–797.