Abstract:

This study aims to improve the transmission stability of vehicle gearboxes during operation by focusing on the Ravigneaux planetary gear system. A comprehensive analysis of the nonlinear vibration characteristics of the Ravigneaux planetary gear transmission is conducted, and a dynamic model incorporating multiple coupled nonlinear factors is established. The model accounts for time-varying mesh stiffness, backlash, comprehensive transmission error, dynamic meshing force, and time-varying friction. Based on this, a set of nonlinear dynamic differential equations is derived, which are solved iteratively using the Runge-Kutta numerical integration method to obtain the system's dynamic response under varying external excitation frequencies. The system's complex nonlinear dynamic behavior is revealed through time history diagrams, spectrum diagram, phase diagram and Poincaré diagram. Furthermore, with other system parameters held constant, bifurcation diagrams and three-dimensional waterfall plots are employed to analyze the influence of excitation frequency on the vibration response. The results show that as the excitation frequency changes, the system’s vibration response evolves from chaotic states to periodic bifurcations, and eventually transitions to a stable single-period motion. This research provides a theoretical basis and engineering reference for adjusting excitation parameters to suppress non-steady-state vibrations and enhance the operational stability of the transmission system.

Key words: ravigneaux planetary gear, nonlinear systems, dynamic response, bifurcation and chaos