Fast calculation of the multi-speed vibration characteristics of PMSMs considering tangential force and modal participation factor

This paper addresses the multi-physical field coupling problem of electromagnetic vibration in permanent magnet synchronous motors (PMSMs), and presents a fast calculation method for multi-harmonic decoupling of electromagnetic forces based on subdomain analysis and an equivalent ring model. This method breaks through the simplifying assumptions of traditional models regarding the non-uniform distribution of tangential electromagnetic forces and high-frequency nonlinear effects. By introducing a modified modal participation factor and an orthogonal anisotropic stiffness superposition criterion, it achieves a low-order modal frequency error of <7% for the stator-winding system and constructs a nonlinear mapping model between tangential forces and high-frequency vibrations. Compared with existing studies that neglect the non-uniform distribution of tooth surface forces and end constraint effects, the proposed method exhibits spectral localization accuracy better than 5% in the low-frequency band (<3 kHz) and improves computational efficiency by 80%. It significantly alleviates the modeling complexity of traditional finite element methods under multi-speed conditions and high-frequency prediction deviations. Experimental verification shows that this method can accurately characterize the electromagnetic vibration characteristics of motors, providing an effective technical approach for the early suppression of motor vibration and noise.