齿轮系统参数平面内的分岔结构

基于含有间隙和时变啮合刚度的非线性单级齿轮系统动力学模型,对参数平面内周期运动和混沌运动的分岔结构进行了研究。通过分岔计算得到了啮合刚度的波动幅值、激励频率、激励力的波动幅值以及平均激励力分别与阻尼比构成的参数平面内的域界;通过多项式曲线拟合,得出了相应的域界方程;并由拟合方程确定了周期运动的稳定参数域和混沌吸引子的激变点。结果表明,通过对参数平面内分岔结构的研究,稳定参数域可以为非线性齿轮系统的分析和设计提供依据;混沌吸引子的激变点有助于确定不稳定周期轨道,以便于控制混沌。

BIFURCATION STRUCTURE IN PARAMETER PLANE OF GEAR SYSTEM

Based on the dynamical model of nonlinear system of a gear pair with backlash and time-varying mesh stiffness, the bifurcation structure of periodic motion and chaotic motion in parameter plane is studied. In the parameter planes of damping ratio to fluctuating coefficient of mesh stiffness, exciting frequency, fluctuating amplitude of exciting force and average exciting force respectively, the boundaries of domain are obtained. Then by means of the polynomial curve fit, the corresponding equations describing the boundaries of domain are established. And based on the fit equations, the stable parameter domains and the points of crisis are obtained. Results show that by researching bifurcation structure in parameter plane, the stable parameter domain can provide helps for analyzing and designing the nonlinear gear system, and the point of crisis of chaotic attractor is helpful to obtain the unstable periodic orbit and control chaos.