Nonlinear Vibration Analysis of a Planetary Gear Set in an In-wheel Powertrain Considering Torque Ripple Effects

As electric vehicles shift from centralized to distributed drive architectures, reducer-integrated in-wheel powertrain has become a mainstream wheel-end solution. However, the compact integration of the permanent magnet synchronous motor and planetary gear set introduces strong electromechanical coupling, leading to complex torsional vibration responses. To reveal this vibration mechanism, this study first validates a theoretical model of electromagnetic torque ripple against finite element simulations. Subsequently, a pure torsional nonlinear dynamic model of the planetary gear set is proposed, which incorporates time-varying mesh stiffness, gear backlash, transmission error, and tooth surface friction. The electromagnetic torque ripple is introduced as an external excitation into the dynamic model. The vibration response characteristics of the system under both constant and dynamic torque excitations are investigated, with a focus on how torque ripple parameters govern bifurcation behavior. The results demonstrate that introducing realistic electromagnetic torque pulsations significantly intensifies the nonlinear response within the low-frequency excitation range. The bifurcation results show that a larger torque ripple amplitude increases the amplitude of periodic motion. It also generates multiple sideband frequency components through nonlinear coupling. A distinct critical threshold for the average torque is identified as 36.5 Nm, which strictly governs the system’s transition from chaos to stable periodic motion. This study provides theoretical insight into the vibration mechanisms of in-wheel powertrains and supports their dynamic performance optimization.