Abstract: 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 fre-quency, 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.

Key words: Bifurcation structure, Gear system, Parameter plane, Point of crisis, Stable domain