Dynamic Analysis of Planetary Gears With Bearing Clearance

Abstract

This study investigates the dynamics of planetary gears where nonlinearity is induced by bearing clearance. Lumped-parameter and finite element models with bearing clearance, tooth separation, and gear mesh stiffness variation are developed. The harmonic balance method with arc length continuation is applied to the lumped-parameter model to obtain the dynamic response. Solution stability is analyzed using Floquet theory. Rich nonlinear behavior is exhibited, consisting of nonlinear jumps, a hardening effect induced by the transition from no bearing contact to contact, and softening induced by tooth separation. Bearings of the central members (sun, carrier, and ring) impact against the bearing races near resonances, which leads to coexisting solutions in wide speed ranges, grazing bifurcation, and chaos. Secondary Hopf and period-doubling bifurcations are the routes to chaos. Input torque can suppress some of the nonlinear effects caused by bearing clearance.