星形齿轮传动系统分岔与混沌的研究

迄今，未有文献详细研究复杂齿轮系统在强非线性因素激励下的混沌与分岔性态。建立了星形齿轮传动的间隙型非线性动力学模型并用数值解法进行了求解。研究了系统在改变激振频率或者齿轮副啮合阻尼比时产生的种类分岔以及通向混沌的途径。利用Poincare映射和分岔图详细描述了系统在倍周期分岔和拟周期分岔道路上吸引子由规则运动到混沌运动深化过程。发现了因变化阻尼比引起的周期倍化道路上存在的吸引子突变现象。从而首次从理论上揭示了星形齿轮系统非线性动力学行为的复杂性态。

BIFURCATIONS AND CHAOS OF STAR GEAR SYSTEM

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.