Nonlinear Dynamics of Ravigneaux Planetary Gearset in Automobile Transmission Systems

Due to the unique structure and transmission ratio of the Ravigneaux planetary gearset, this paper investigates the nonlinear vibration characteristics of the Ravigneaux planetary gearset transmission systems. First, a dynamic model of the Ravigneaux planetary gearset transmission systems is established, considering nonlinear factors such as time-varying meshing stiffness, comprehensive equivalent errors, tooth clearance, and time-varying friction. Next, the dynamic equations are formulated and solved. The nonlinear behavior of the system is characterized through phase diagrams, Poincaré diagrams, time-domain plots, and frequency-domain plots. The bifurcation diagram and three-dimensional spectrum diagram illustrate how different external load excitation frequencies affect the system’s nonlinear behavior. The results indicate that as the external load excitation changes, the system’s motion state transits from chaotic to bifurcation and ultimately to periodic motion. Finally, the multiscale method is employed to examine the effects of various parameters on the main resonance characteristics of the system, determining the stability conditions for the primary resonance. The principal resonance analysis reveals that increasing damping, stiffness, and fluctuations in the external load can enhance the system’s stability.