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General Forms of Periodical Solutions to Nonlinear Dynamics of a Spur Gear Pair

机译：正齿轮对非线性动力学的一般形式

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In this paper the Incremental Harmonic Balance Method (IHBM) is extended to analyse the nonlinear dynamics of a spur gear pair and some new results are obtained. At first the dynamical model of a spur gear pair is established, where the backlash, time-varying stiffness and static transmission error are all included. Here the time-varying stiffness and static transmission error are represented by the multi-order harmonic series through Fourier expansion. Based on the IHBM, the general forms of the periodic solutions to this system are derived, which is useful to obtain the solutions with arbitrary precision. And the difference between the frequency-response to the multi-order and single-order harmonic is analysed. Then the effects of the multi-order harmonic on the kinds of the periodic solutions are also investigated by IHBM, and the comparison with the numerical solutions shows the validity of the proposed method. At last the influence of the damping ratio and the excitation amplitude on frequency-response curves is researched, which presents some useful information to analyse and/or control the dynamics of gear system.
机译：在本文中，增量谐波平衡方法（IHBM）扩展以分析正齿轮对的非线性动力学，并获得一些新结果。首先，建立了正齿轮对的动态模型，其中包括间隙，时变刚度和静态传输误差。这里，时变刚度和静态传输误差由傅里叶扩展的多阶谐波串表示。基于IHBM，推导出对该系统的一般形式的定期解决方案，这对于获得具有任意精度的解决方案是有用的。分析了对多阶和单阶谐波的频率响应之间的差异。然后，IHBM还研究了多阶谐波对周期性溶液种类的影响，与数值解决方案的比较显示了所提出的方法的有效性。最后，研究了阻尼比和激发幅度对频率响应曲线的影响，这提出了一些有用的信息来分析和/或控制齿轮系统的动态。

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