关键词: 非线性动力学, 分岔, 混沌, 星形齿轮传动系统

Abstract: Up to now, there are no literatures including the reports on the bifurcation and chaos of the complex gearing system with the clearance-type non-linearity. The nonlinear dynamic model of star gear system is established and a numerical method to solve the governed differential equations is developed. Two typical routes to chaos by period – doubling route or quasi-periodic route with changing either meshing damping ratio or frequency of excitation are studied and discussed. The evolutions of system dynamic responses are demonstrated in detail; by Poincare maps when the system undergoes a sequence of period-doubling or quasi-periodic bifurcations to chaos. The jump discontinuity is observed on the condition of the occurrence of period-doubling routes to chaos by changing damping ratio. The complicated nonlinear dynamic behaviors of star gear system are theoretically analyzed for the first time.

Key words: Bifurcation, Chaos, Nonlinear dynamics, Star gear system