Modeling and Bifurcation Characteristics of Double Stage Planetary Gear Train with Multiple Clearances

This paper proposes a new non-linear transverse-torsional coupled model for double stage planetary gear train, and gear's geometric eccentricity error, synthetical transmission error, time-varying meshing stiffness, sun-planet and planet-ring gear pair's backlashes and sun gear's bearing clearance are taken into account. The differential governing equations of motion are derived and solved by applying variable step-size Runge-Kutta numerical integration method. The system motion state is investigated systematically and qualitatively, and exhibits diverse bifurcation and chaos characteristics under different bifurcation parameters including meshing frequency, sun planet backlash and planet ring backlash. Analysis results showed that the increasing damping could suppress the region of chaotic motion and improve the system's stability significantly; the route of period-doubling to chaotic motion was observed for both first and second stage's motion state under the bifurcation parameter of meshing frequency; The routes of period doubling and crisis to chaos were identified under the bifurcation parameter of sun planet backlash; Besides, the increasing damping ratio could split the bifurcation diagram window into different sections and strong coupling effects are generated to second stage's motion. Several different types of routes to chaos were observed under the bifurcation parameter of planet-ring backlash including period doubling and 3T-periodic channel; Besides, it concluded that planet-ring backlash could generate a strong coupling effect to both stage's nonlinear behavior.