Abstract:

In order to investigate the influences of the backlash and other nonlinear factors on the system, a nonlinear dynamics model for a single-stage spur gear pair system with three degree-of-freedom was established wherein the backlash, the time-varying stiffness, the torsion motion and the transmission error were considered. The nonlinear three-degree-of-freedom equations were solved by employing variable step size Runge-Kutta integration method and the bifurcation diagrams were obtained. The nonlinear dynamics characteristics of the system were discussed for the varying of the exciting frequency and classified based on bifurcation diagrams, phase portraits, Poincaré maps and FFT spectrum. The Hopf bifurcation, torus doubling bifurcation, grazing bifurcation and doubling bifurcation are found in the different values of the exciting frequency and their bifurcation points are given. There are two routes from periodic motion to chaos motion.

Key words: nonlinear dynamics, chaos, bifurcation, gear, Hopf

摘要：

为研究齿轮传动系统中齿侧间隙等非线性因素对系统振动特性的影响，综合考虑齿侧间隙、时变啮合刚度、综合啮合误差和轴承纵向响应，建立了三自由度单级直齿轮副传动系统的扭转振动非线性动力学模型;采用变步长4-5阶Runge-Kutta法，对系统运动的状态方程进行了数值求解;构建了系统的Poincaré截面，得到了系统的分岔图。结合系统相图、Poincaré映射图及FFT频谱图，分析了系统在激励频率变化时的动力学特性，发现系统在不同激励频率下会发生Hopf分岔、环面倍化、擦切分岔及倍化分岔。

关键词: 非线性动力学, 混沌, 分岔, 齿轮, Hopf