The magnetic field and torque of permanent-magnetic spherical motor (PMSpM) are difficult to analyze due to the complicated structure, and therefore are often analyzed by the finite-element method (FEM) or Lorentz force method, with large amount of calculation and time consumption. This paper firstestablishes a three-dimensional (3-D) magnetic field analytical model of a spherical motor with permanent magnets (PMs) by the equivalent surface current method. Secondly, through the Lorentz force spatial integration of energized stator coil, a torque analytical model is established. Thirdly, in order to avoid repeated integration operation, a torque interpolation model based on torque Map is established. Both magnetic field and torque analytical models are verified by comparing with FEM and the experiment respectively. It is shown that the method proposed not only ensures the modeling accuracy but also significantly speeds up the analysis.

中文翻译：

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基于洛伦兹力法的转矩图的永磁球形电动机转矩分析模型的研究

永磁球形电动机（PMSpM）的磁场和转矩由于结构复杂而难以分析，因此通常采用有限元法（FEM）或洛伦兹力法进行分析，计算量大，时间长消费。本文首先通过等效表面电流法建立了带有永磁体（PMs）的球形电动机的三维（3-D）磁场分析模型。其次，通过励磁定子线圈的洛伦兹力空间积分，建立了转矩分析模型。第三，为避免重复积分操作，建立了基于扭矩图的扭矩插补模型。通过分别与有限元法和实验比较，验证了磁场和转矩分析模型。