外部动态激励作用下齿轮系统非线性动力学特性

Non-Linear Dynamics of Spur Gear Pair under External Periodic Excitation

为了研究外部动态激励作用下齿轮系统非线性动力学特性,建立了考虑周期时变刚度、齿侧间隙、黏弹性阻尼和外部动态激励的单自由度直齿轮副系统动力学模型。针对外部动态激励作用下的周期时变刚度、齿侧间隙、激励幅值和阻尼比对齿轮副系统动力学特性的影响,采用增量谐波平衡法来求解齿轮副系统的稳态周期响应,并采用四阶变步长Runge-Kutta数值方法进行了验证。研究结果表明,增量谐波平衡法求解结果与数值仿真结果吻合得较好,齿轮系统在外部动态激励作用下会引起参数共振、多值解和幅值跳跃等非线性动力学行为,增大激励幅值和阻尼比等参数,能够有效控制齿轮系统的非线性振动响应。

Under external periodic excitation, the dynamic model of a single-degree-of-freedom spur gear pair with periodic time-varying stiffness, backlash and viscous damping is established. The incremental harmonic balance method （IHBM） is applied to analyze the dynamic responses of the gear pair system. A comparison with Runge-Kutta integration results shows the accuracy and authority of IHBM. The effects of the periodic time-varying stiffness, backlash, excitation amplitude and viscous damping ratio on the dynamic characteristics of gear pair system are investigated. It indicates that the time-varying factors and backlash under periodic excitation usually lead to parametric resonance, multi-valued properties and amplitude jump phenomena. The enhanced excitation amplitude and the damping ratio facilitate controlling the nonlinear vibration.