The variable-speed permanent magnet synchronous motors (PMSMs) have high harmonic contents in the current and wide variable speed range, which results in a wide frequency range of electromagnetic force waves and their frequencies change with the speed. Accurate calculation of the natural frequencies of the stator is an important premise for improving electromagnetic vibration and noise. In order to improve the calculation accuracy of the natural frequencies of the stator, the influences of the tooth feet and tooth shoulders are fully considered, the stator core and enclosure are regarded as cylindrical shells with axial ribs attached inside and outside the shells, respectively. Considering the moment of inertia and the transverse shear deformation of the cylindrical shells, the vibration displacement of the continuous system is dispersed by Galerkin dispersion and Rayleigh-Ritz method, the characteristic equations of the stator under free vibration are derived based on the three-dimensional shell theory, and the natural frequencies of the stator with anisotropic material are obtained. In addition, the calculation method of stator natural frequencies under different boundary conditions is given. Further, the natural frequencies of the end cover and the entire motor are analyzed. In order to verify the accuracy of the calculation method, the natural frequencies of a stator are calculated by the finite element method (FEM) and the hammering method. The results obtained by the calculation method in this paper are in good agreement with the experimental results, which proves the effectiveness of the calculation method.

中文翻译：

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基于三维弹性理论的永磁同步电动机定子固有频率计算方法

变速永磁同步电动机（PMSM）在电流中具有较高的谐波含量，并且在较宽的变速范围内，导致电磁力波的频率范围较宽，并且它们的频率随速度而变化。定子固有频率的准确计算是改善电磁振动和噪声的重要前提。为了提高定子固有频率的计算精度，充分考虑了齿脚和齿肩的影响，将定子铁心和壳体视为圆柱壳，并在壳体的内部和外部分别附有轴向肋。考虑到圆柱壳的惯性矩和横向剪切变形，利用Galerkin法和Rayleigh-Ritz法对连续系统的振动位移进行分散，基于三维壳理论推导了自由振动状态下定子的特征方程，得到了具有各向异性材料的定子固有频率。 。另外，给出了不同边界条件下定子固有频率的计算方法。此外，分析了端盖和整个电动机的固有频率。为了验证该计算方法的准确性，通过有限元方法（FEM）和锤击方法来计算定子的固有频率。本文计算方法得到的结果与实验结果吻合良好，证明了该方法的有效性。