基于增量谐波平衡法的星型齿轮传动非线性动力学分析

建立了两级星型齿轮传动系统的非线性动力学分析模型,模型中考虑了系统的综合啮合误差、时变啮合刚度以及齿侧间隙。推导了多自由度多间隙系统的增量谐波平衡法计算公式,利用上述方法求解了系统非线性微分方程组,得到了两级星型齿轮传动的非线性频响特性。分析了阻尼系数、时变啮合刚度以及误差等参数对系统动态特性的影响。分析结果表明:间隙会使两级星型齿轮传动系统中出现多值解及跳跃现象的典型非线性特征;增大系统阻尼系数可以抑制系统的共振幅值;增大时变刚度幅值使得齿轮副传动误差的幅值增大;增大激励误差的幅值,使得系统各构件的振动幅值增大;多级星型齿轮传动系统有着比单级传动更丰富的非线性动态特性。

Nonlinear Dynamic Analysis of a 2-Stage Star Gear Train Based on Incremental Harmonic Balance Method

A dynamic analysis model in which the gear error and the time-varying stiffness and backlash are included is established for a 2-stage star gear train.Incremental harmonic balance method(IHBM) formulations are derived for multiple degrees of freedom nonlinear dynamic equations of the 2-stage star gear train with backlash.The nonlinear frequency response characteristics of the system are obtained by using the IHBM.The influence of the damping ratio and the time-varying stiffness and backlash on the system dynamic characteristic is analyzed.Analysis results show that (1) backlash is the cause of the typical nonlinear dynamic characteristic of the 2-stage star gear train;(2) the resonance amplitude of the system decreases with the increase of the damping ratio;(3) the amplitude of transmission error increases with the increase of the amplitude of the time-varying stiffness;(4) the resonance amplitude of the system increases with the increase of the gear errors.