Compared with single-stage transmission, multi-stage planetary gear transmission has higher efficiency, but its structure is more complex. Multi stage planetary gear train has more complex dynamic characteristics, so there are many researches on multi-stage planetary gear train.
Sheng et al. Analyzed the static and dynamic load sharing coefficient of the two-stage planetary gear transmission system and the operation law of the central gear, and carried out experimental verification; Wang et al. Studied the influence of electromechanical characteristics on the mechanical performance of the multi-stage planetary system; sun et al The natural frequency and coupling model of the multi-stage planetary gear system are analyzed; Li Sheng et al. Establish the pure torsional dynamic model of the two-stage planetary gear system, study the way of the system into chaos and the influence of meshing damping ratio on the nonlinear characteristics of the system; Chen Liang et al. Establish the dynamic model of the three-stage planetary gear system, study the dynamic characteristics of the system; Qin Datong et al The relationship between vibration and internal and external excitation of multi-stage planetary gear system was studied; Chen Fu considered various factors to establish torsion model of multi-stage planetary gear system, and studied the way to chaos; Li Siqian et al.  studied the load sharing characteristics of two-stage planetary gear system under the influence of various nonlinear factors.
At present, there is no quantitative analysis on the nonlinear characteristics of two-stage planetary gear system. In this paper, the two-stage planetary gear transmission system is taken as the research object. The nonlinear factors such as time-varying meshing stiffness, backlash and meshing error are introduced. The system dynamics equations are established by dimensionless treatment. The numerical method is used to solve the equations. The bifurcation diagram, phase space trajectory and Poincare section are analyzed qualitatively Based on the quantitative analysis of Lyapunov exponent and correlation dimension, the influence of excitation frequency and backlash on the chaotic state of the system is studied, which provides a theoretical basis for the fault mechanism research and vibration analysis of multi-stage planetary system.