两级定轴齿轮分岔与混沌特性研究

Bifurcation and Chaos Characteristics of Two-stage Gear Train Sets

为研究两级定轴齿轮传动系统的混沌振动控制,建立了包含时变啮合刚度、齿侧间隙和综合啮合误差等非线性因素的两级齿轮无量纲动力学方程,利用数值方法进行求解,获得系统的分岔图及Poincáre截面,研究系统随激励频率变化的过渡过程,并分析啮合阻尼比对系统分岔与混沌特性的影响。结果表明:两级齿轮系统的过渡过程表现为激变过渡及阵发周期过渡,阻尼的大小会改变混沌区域的大小,两级齿轮在运动过程中同时发生激变,二级齿轮在分岔点的激变相对平稳。

In order to investigate the chaos vibration control of a two-stage gear train, a nonlinear dynamics dimensionless equation of a two-stage gear train with time varying meshing stiffness, errors of transmission and backlashes was established and solved with the numerical method. The influences of excitation frequency and damping coefficient on the bifurcation and chaos properties of the system were analyzed with bifurcation diagram and Poincare section. The study result shows that the system＇s motion state would change into chaos in the way of crisis or intermittency, the damping coefficient would influence the region of bifurcation; the two-stage gears would germinate crisis in the process of movement at the same time, while the second gear remained relatively stable at the bifurcation point.