Rigid–flexible coupled vibration response of electric drive systems considering gear eccentricity errors

To investigate the influence of gear eccentricity errors on the vibration characteristics, this paper focuses on a centralized electric drive system as the research object, an electromagnetic model of the permanent magnet synchronous motor (PMSM) and a rigid–flexible coupled dynamic model of a multistage gear transmission system that accounts for shaft flexibility, dynamic transmission error, and time-varying meshing stiffness were established respectively. The electromagnetic torque exerted by PMSM on gear transmission systems was calculated with the Maxwell stress tensor formulation. Subsequently, the nonlinear mechanical excitation from the gearbox is extracted and applied to the motor model, thereby achieving bidirectional coupling involving both the PMSM and the gear-driven transmission system. Building upon the above, the electric drive system’s dynamic responses were analyzed under typical operating conditions with a motor speed of 15,000 rpm and a 55 Nm torque, including vibration acceleration and vibration displacement. Through simulations at different rotational speeds, the precision of the gearbox was further validated. The results show that when the shaft’s flexibility is taken into account, the fluctuation amplitude of the vibration acceleration increases by a factor of 4.39. As the gear eccentricity increases, the periodic fluctuations in meshing force, meshing stiffness, and transmission error become increasingly pronounced, resulting in a 16.9% increase in the X-direction fluctuation amplitude and a 6.9% increase in the Y-direction fluctuation amplitude of the intermediate shaft track trajectory. Additionally, gear eccentricity errors increased the fluctuation amplitude of electromagnetic torque by 3.81%. This research provides theoretical guidance for vibration suppression in electric drive systems.