单自由度齿轮系统的周期运动和混沌运动

建立了综合考虑齿侧间隙、时变啮合刚度、综合啮合误差等因素下的定轴直齿圆柱轮副的单自由度非线性动力学模型,利用变步长Runge-Kutta法对单自由度运动微分方程进行数值求解.结合系统的分岔图、相图和Poincaré映射图,对系统随频率变化时的动力学特性进行分析.结果表明:齿轮啮合频率的变化导致系统发生连续倍周期分岔,从而产生混沌运动.另外,由于齿轮间隙非线性的影响,系统还存在擦切分岔等非光滑分岔现象.

Periodic motions and chaotic motion in single-degree -of-freedom spur gear pair system

The nonlinear dynamic model for a spur gear pair system was established when the dynamical parameters as backlashes,bearing clearances,time-varying meshing stiffness and so on were considered.The nonlinear single-degree-of-freedom equations were solved by employing variable step size Runge-Kutta integration method.The nonlinear dynamic characteristics of the system was discussed for the varying of the frequency based on bifurcation diagrams,phase portraits and diagrams of Poincaré mapping.The sequence of doubling bifurcation,grazing bifurcation and chaotic motion was obtained.The research of chaos and bifurcation is helpful to dynamic optimize design.