This paper presented a novel analytical method for calculating magnetic field in the slotted air gap of spoke-type permanent-magnet machines using conformal mapping. Firstly, flux density without slots and complex relative air-gap permeance of slotted air gap are derived from conformal transformation separately. Secondly, they are combined in order to obtain normalized flux density taking account into the slots effect. The finite element (FE) results confirmed the validity of the analytical method for predicting magnetic field and back electromotive force (BEMF) in the slotted air gap of spoke-type permanent-magnet machines. In comparison with FE result, the analytical solution yields higher peak value of cogging torque.

中文翻译：

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基于保角映射的轮辐式永磁电机缝隙气隙中磁场的新型解析计算

本文提出了一种利用保角映射计算轮辐式永磁电机缝隙气隙中磁场的新颖分析方法。首先，分别从共形变换推导了无狭缝的磁通密度和狭缝气隙的相对气隙磁导率。其次，将它们组合在一起以获得考虑到缝隙效应的归一化通量密度。有限元（FE）的结果证实了用于预测辐条型永磁电机的缝隙气隙中的磁场和反电动势（BEMF）的分析方法的有效性。与有限元分析结果相比，解析解产生的齿槽转矩峰值更高。