两极平行充磁环形永磁体磁场解析计算
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摘要
针对内装不导磁心轴的两极平行充磁环形永磁体,在极坐标系下推导了当它置于定子腔和空气中两种情形下产生的磁场解析计算公式。根据材料和结构特点,将整个求解场域划分为不同的区域,分别用对应的控制函数来表达,通过求解拉普拉斯方程或泊松方程获得各区域的矢量磁位通解,利用边界条件和接口条件求解通解中的相关系数,得到各区域磁场分布的解析模型。以一台内装不导磁心轴的2极24槽平行充磁环形永磁同步电机(RSPMSM)为例,将磁场分布的解析计算结果与有限元计算结果进行对比,验证了解析模型的正确性。基于该解析模型讨论了转子尺寸对径向磁密的影响。利用该解析模型可以在该类永磁同步电机初始设计前期快速且精确地计算开路静磁场,还可以评估该类永磁转子的充磁结果。
Two-pole parallel magnetised ring-shaped permanent magnets( RSPMs) with non-magnetic conductive shafts were taken as the study objects. The analytical formulas of the magnetic fields produced by the RSPMs placed in the stator bore and air were deduced in the polar coordinate system. According to the material and structural characteristics,the whole solution field domain were divided into different regions which are expressed by the corresponding governing functions respectively. The general solution of vector magnetic potential for each region was obtained by solving the Laplace's equation or Poisson equation. The relevant coefficients in the general solutions were obtained using the boundary conditions and interface conditions and then the analytical model of the magnetic field distribution of each region. Taking a 2 pole-24 slot parallel magnetised ring-shaped permanent magnet synchronous motor( RSPMSM) with a non-magnetic conductive shaft as example,the magnetic field distributions obtained by the analytical model were compared with those by the finite element method,which verifies the correctness of the analytical model. In addition,the effects of rotor dimensions on radial flux density were discussed on the basis of the analytical models. By using the analytical models,the open-circuit magnetostatic field can be quickly and precisely calculated during early stage of the initial design of permanent magnet synchronous motors of this kind and the magnetisation results of the permanent magnet rotors of this kind can be evaluated.
Two-pole parallel magnetised ring-shaped permanent magnets( RSPMs) with non-magnetic conductive shafts were taken as the study objects. The analytical formulas of the magnetic fields produced by the RSPMs placed in the stator bore and air were deduced in the polar coordinate system. According to the material and structural characteristics,the whole solution field domain were divided into different regions which are expressed by the corresponding governing functions respectively. The general solution of vector magnetic potential for each region was obtained by solving the Laplace's equation or Poisson equation. The relevant coefficients in the general solutions were obtained using the boundary conditions and interface conditions and then the analytical model of the magnetic field distribution of each region. Taking a 2 pole-24 slot parallel magnetised ring-shaped permanent magnet synchronous motor( RSPMSM) with a non-magnetic conductive shaft as example,the magnetic field distributions obtained by the analytical model were compared with those by the finite element method,which verifies the correctness of the analytical model. In addition,the effects of rotor dimensions on radial flux density were discussed on the basis of the analytical models. By using the analytical models,the open-circuit magnetostatic field can be quickly and precisely calculated during early stage of the initial design of permanent magnet synchronous motors of this kind and the magnetisation results of the permanent magnet rotors of this kind can be evaluated.
引文
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[9]黄克峰,王金全,徐晔,等.径向充磁永磁同步电机空载气隙磁场研究[J].防爆电机,2015,50(3):1-5.
[10] Zhu Z Q,Ng K,Howe D. Design and analysis of high-speed brushless permanent magnet motors[C]//International Conference on Electrical Machines and Drives. 1997:381-385.
[11]沈建新,陈利根.永磁无刷电机中平行充磁2极气隙磁场的解析计算[J].电机与控制应用,2006,33(1):7-10.
[12] Cheng W J,Sun Y H,Yu L,et al. Analytical solution to magnetic field distribution of a parallel magnetised rotor with cylindrical or ring-type permanent magnet[J]. IET Electric Power Applications,2015,9(6):429-437.
[13] Zhu Z Q,Howe D. Instantaneous magnetic field distribution in brushless permanent magnet dc motors,partⅢ:effect of stator slotting[J]. IEEE Transactions on Magnetics,1993,29(1):143-151.
[2] Boules N. Prediction of no-load flux density distribution in permanent magnet machines[J]. IEEE Transactions on Industry Applications,1985,21(4):633-643.
[3] Gu Q S,Gao H Z. Air gap field for pm electric machines[J]. Electric Machines and Power Systems,1985,10(5-6):459-470.
[4] Zhu Z Q,Howe D,Bolte E,et al. Instantaneous magnetic field distribution in brushless permanent magnet dc motors,partⅠ:opencircuit field[J]. IEEE Transactions on Magnetics,1993,29(1):124-135.
[5]王兴华,励庆孚,王曙鸿.永磁无刷直流电机磁阻转矩的解析计算方法[J].中国电机工程学报,2002,22(10):104-108.
[6] Selvaggi J P,Salon S,Kwon O M,et al. Computation of the threedimensional magnetic field from solid permanent-magnet bipolar cylinders by employing toroidal harmonics[J]. IEEE Transactions on Magnetics,2007,43(10):3833-3839.
[7] Rahideh A,Korakianitis T. Analytical calculation of open-circuit magnetic field distribution of slotless brushless PM machines[J].International Journal of Electrical Power and Energy Systems,2013,44(1):99-114.
[8]李界华,胡佳,文泽军.考虑磁钢磁化方式的永磁电机空载气隙磁场性能分析[J].湘潭大学自然科学学报,2015,37(3):35-42.
[9]黄克峰,王金全,徐晔,等.径向充磁永磁同步电机空载气隙磁场研究[J].防爆电机,2015,50(3):1-5.
[10] Zhu Z Q,Ng K,Howe D. Design and analysis of high-speed brushless permanent magnet motors[C]//International Conference on Electrical Machines and Drives. 1997:381-385.
[11]沈建新,陈利根.永磁无刷电机中平行充磁2极气隙磁场的解析计算[J].电机与控制应用,2006,33(1):7-10.
[12] Cheng W J,Sun Y H,Yu L,et al. Analytical solution to magnetic field distribution of a parallel magnetised rotor with cylindrical or ring-type permanent magnet[J]. IET Electric Power Applications,2015,9(6):429-437.
[13] Zhu Z Q,Howe D. Instantaneous magnetic field distribution in brushless permanent magnet dc motors,partⅢ:effect of stator slotting[J]. IEEE Transactions on Magnetics,1993,29(1):143-151.