关键词: Lyapunov指数, Poincaré映射, 多自由度非线性模型, 分岔特性分析, 轿车转向系

Abstract: Severe shimmy of a car’s front wheel occurs when it runs at 80 km•h–1 or higher speed. In allusion to this shimmy problem, a 4 degrees of freedom nonlinear dynamic model of automotive steering is established. During modeling, the elastic function of steering link rod is taken over and the link rod is looked at spring-damper unit. Nonlinear factors including lateral force of tire, clearance of steering link rod, coulomb friction of the pin etc. are added to this model. Under the condition that unbalance mass exists in the wheel, the nonlinear dynamic characteristics of steering system are analyzed. Bifurcation rules of the steering system are obtained by using the method of Poincaré mapping and frequency chart analysis. The Lyapunov exponent spectrum is calculated by Schmidt method. Unstable areas are divided and movement status is made certain. All the numerical results can provide the theoretical support for design or optimization of steering system dynamic parameters and active or passive control of nonlinear shimmy.

Key words: Bifurcation characteristics analysis, Lyapunov exponents, Multi-degree nonlinear model, Poincaré mapping, Steering system of a car