考虑不确定参数的齿轮副非线性动态特性分析

摘要

The nonlinear dynamic model of a gear pair with backlash and time-varying mesh stiffness was developed to investigate the effects of uncertain dynamic parameters on dynamic characteristics of the system.The interval harmonic balance method based on the harmonic balance method and the Chebyshev inclusion function was presented.The amplitude frequency responses in two different damping cases were compared.The results show that:in the weak damping case (ζ1 ),the system has obvious nonlinear jumping phenomenon.In addition,the dynamic characteristics of the system are sensitive to the variabilities of the excitation parameters and backlash,and insensitive to the variabilities of the stiffness and damping parameters.The jumping phenomenon will disappear and the amplitudes will decrease when the damping ratio is equal to 0.1.Furthermore,the variabilities of the stiffness parameter,excitation parameters and backlash have significant effects on dynamic responses of the system.The influence of uncertain damping on the dynamic response focuses upon the resonance region.%为分析系统动力学参数的不确定性对齿轮副动态响应的影响情况，建立含齿侧间隙和时变啮合刚度的齿轮副动力学模型，并运用区间谐波平衡法分析了考虑区间系统参数的齿轮副非线性系统动态响应。区间谐波平衡法主要是将谐波平衡法与 Chebyshev 区间包含函数相结合，通过该方法对比分析了两种不同阻尼情况下的齿轮系统频域响应情况。结果表明：在弱阻尼（ζ）情况下，系统存在明显的非线性跳跃现象，而且系统频域响应对刚度参数和阻尼参数的波动性不敏感，而对激励参数和齿侧间隙的波动性敏感。而当ζ＝0．1时，系统响应的非线性跳跃现象消失，系统响应幅值降低。刚度参数、载荷参数和齿侧间隙的波动性对所分析区域内的系统响应均有明显影响。阻尼参数的波动性对系统响应的影响则集中于主共振区域。