一类单自由度齿轮系统动力学特性分析

Analysis of the nonlinear dynamic characteristics of a single-degree-of-freedom spur gear pair system

建立了考虑齿侧间隙、时变啮合刚度等因素下的单自由度齿轮系统非线性动力学模型,采用变步长Runge-Kutta法对系统运动微分方程进行数值求解.结合系统的分岔图、Lyapunov指数图、相图、庞加莱映射图、时间相应图,分析系统随阻尼比变化时的动力学特性和啮合刚度对系统的影响,得到系统的混沌运动形成过程.结果表明,随着阻尼比变化,系统表现出丰富的动力学特性,同时啮合刚度影响系统的分岔点位置.

A nonlinear dynamic model for a spur gear pair system was established wherein the backlash and mesh stiffness were considered. The nonlinearsingle degree - of - freedom equations were solved by employing the variable step - size Runge - Kutta integration method. The nonlinear dynamic characteristics of the system were discussed concerning different damping ratios based on bifurcation diagrams, Lyapunov exponents andphase portraits, Poincare maps ,the time response figure, and mesh stiffness＇s effect on the system. The result has showed that along with the changed damping ratio, the system has showed abundant dynamic characteristics, and its mesh stiffness has affected the location of the bifurcation point of the system.