Translation torsion coupling dynamic modeling and nonlinearities investigation of non-circular planetary gear systems

This paper addresses the challenging issues of transmission quality degradation and difficulty in obtaining dynamic response characteristics caused by the nonlinear behavior of non-circular planetary gear systems (NPG). A dynamic model for NPG was developed, encompassing axial elastic displacement, backlash, tooth surface friction, time-varying meshing stiffness, and viscoelastic damping. Fourier fitting matrices for time-varying mesh stiffness and polynomial models for dynamic backlash in non-circular gears were acquired to enhance model precision. Various analysis techniques including phase trajectory diagrams, bifurcation diagrams, time history diagrams, Poincaré mapping diagrams, and phase amplitude frequency characteristic curves were used to evaluate the nonlinear behavior of NPGs. Research results indicate that increasing the damping ratio benefits frequency response bandwidth, reduces phase lag, and improves system stability. The friction coefficient on the surface of non-circular gears also plays a role in ensuring the stability and phase consistency of NGP, although excessive coefficients can induce chaos. The output solar gear is more sensitive to internal excitation, with higher internal excitation leading to stronger system chaos.