In the research of torque ripple of permanent magnet toroidal motor (PMTM), the planet gears are affected by the end-effect force during its rotation due to the special structure of the central worm stator. The existence of the end-effect force will cause vibration and noise, which will lead to poor operation accuracy of the planet gears. In view of the above problems, the formation mechanism of the torque ripple is analyzed. We point out that the sudden change in the magnetic induction intensity at the end of the central worm stator is the main source of the end-effect force. The Schwarz–Christoffel transformation method is used to analyze the magnetic field distribution at the end of the stator. The mathematical model of the end-effect force of PMTM is derived by applying Maxwell stress tensor method. The influence of the structural parameters on the end-effect force of PMTM is analyzed by finite-element simulation. The results show that the output fluctuation of PMTM can be effectively reduced by choosing the optimal wrap angle of the central worm stator by calculating. In addition, choosing the appropriate polar arc coefficient of the planet gears can further reduce the influence of the end-effect force. These research results can provide important reference for the structural optimization of PMTM.

中文翻译：

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永磁环形电机端部作用力分析及弱化方法

在永磁环形电机(PMTM)转矩脉动研究中，由于中心蜗轮定子的特殊结构，行星齿轮在旋转过程中受到端部效应力的影响。末端作用力的存在会引起振动和噪声，从而导致行星齿轮运转精度差。针对上述问题，分析了转矩脉动的形成机理。我们指出，中心蜗杆定子端部磁感应强度的突变是端部效应力的主要来源。Schwarz-Christoffel 变换方法用于分析定子端部的磁场分布。应用麦克斯韦应力张量方法推导出PMTM端效力的数学模型。通过有限元仿真分析了结构参数对PMTM端效力的影响。结果表明，通过计算选择中心蜗轮定子的最佳包角可以有效降低PMTM的输出波动。此外，选择合适的行星齿轮极弧系数可以进一步降低端效力的影响。这些研究成果可为PMTM的结构优化提供重要参考。选择合适的行星齿轮极弧系数可以进一步降低端效力的影响。这些研究成果可为PMTM的结构优化提供重要参考。选择合适的行星齿轮极弧系数可以进一步降低端效力的影响。这些研究成果可为PMTM的结构优化提供重要参考。