Torsional dynamics and parametric instability in integrated electric drive systems with PMSM and gear train

This study investigates the vibrational stability and torsional vibration characteristics of an integrated electric drive system composed of a permanent magnet synchronous motor (PMSM) and a two-stage gear pair under parametric excitation. An electromechanically coupled nonlinear torsional dynamic model is established, incorporating electromagnetic effects and time-varying mesh stiffness. The method of multiple scales is employed to analyze the parametric excitation-induced vibrational stability of the system, and the Runge-Kutta method is used to solve the vibrational differential equations and examine the dynamic response characteristics. The results indicate that the system exhibits significant coupled vibrational behavior: the spectrum of the dynamic meshing force contains not only the meshing frequency of the current gear pair but also the system’s natural frequencies and meshing frequency components from other gear stages. Under conditions without external excitation, the system is found to exhibit not only primary resonance responses due to time-varying mesh stiffness excitation but also various nonlinear vibrational phenomena such as subharmonic resonance, superharmonic resonance, and combination resonance. The response is particularly pronounced near twice the first-order natural frequency.