Nonlinear Dynamic Analysis of Ravigneaux Planetary Gear Transmission System

To enhance the transmission stability during vehicle gearbox operation, this paper analyzed the nonlinear vibration characteristics of the Ravigneaux planetary gear transmission system in the transmission, and established a dynamic model of the Ravigneaux planetary gear transmission system including a variety of nonlinear factors. The model comprehensively considers nonlinear factors such as time-varying meshing stiffness, time-varying meshing damping, comprehensive transmission error, dynamic meshing force and time-varying friction force. Based on Newton’s second law, the nonlinear dynamic differential equations of the system were derived, and the Runge-Kutta numerical integration method was used to iteratively solve the differential equations of the system to obtain the dynamic response characteristics of the system under different external excitation frequencies. To investigate the impact of different excitation frequencies on the vibration displacement of the front and rear sun gear pairs, this study constructed time history diagrams, frequency spectra, phase portraits, and Poincare maps. The analysis shows that the vibration displacement evolution law of the two gear pairs is consistent. In order to further reveal the evolution law of the nonlinear response of the system, the bifurcation diagram and the spatial waterfall diagram were used to analyze the influence of the external excitation frequency on the nonlinear behavior of the system and reveal its evolution process. The results show that vibration displacement of the dual gear pairs undergoes a nonlinear evolution path along with variations in external excitation frequency: transitioning from chaotic motion through period-doubling bifurcation, and ultimately converging to periodic motion. By reasonably adjusting the external excitation frequency, unsteady vibrations can be effectively suppressed throughout the system, transient impact loads reduced, thereby enhancing operational stability and extending gear transmission service life. This research provides both theoretical foundations and engineering references for designing and optimizing high-performance, highly-reliable transmissions for new energy vehicles.