Calculation Method for Natural Frequencies of Stator of Permanent Magnet Synchronous Motors Based on Three-Dimensional Elastic Theory

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.