齿轮传动系统的参数稳定性及振动特性分析

PARAMETER STABILITY AND VIBRATION CHARACTERISTICS ANALYSIS OF GEAR TRANSMISSION SYSTEM

考虑齿轮时变啮合刚度与齿侧间隙,建立齿轮副系统动力学模型。利用Floquet理论推导了参数激励作用下齿轮系统的近似解析解,得到了系统的稳定性边界曲线。采用Newmark-β数值求解法对齿轮系统进行动力学仿真,研究了时变刚度、齿侧间隙、啮合阻尼对齿轮传动系统动力学特性的影响。研究结果表明:当参数激励的频率等于派生系统自由振动周期的2/n倍时,系统可能产生参数共振,随着参数激励频率的增加不稳定区域逐渐增大;齿侧间隙的存在则导致齿轮系统产生多值解和幅值跳跃等典型的非线性动力学特征;随着外部激励幅值和阻尼比增大及内部激励幅值的减小,齿轮系统的非线性振动特征逐渐减弱。

Considering the time-varying meshing stiffness and gear backlash,a dynamic model of gear transmission system is established.The Floquet theory is used to obtain the approximate analytic solution and the stability boundary curve of the transmission system.The Newmark-βnumerical simulation method was used to simulate dynamic characteristics of gear system.The effect of time-varying mesh stiffness,backlash and damping effect on dynamic characteristics are studied.The results show that the system may generate parametric resonance when the frequency of parameter excitation is equal to 2/n of the free vibration period of the derived system;The gear backlash leads to multi-value properties and amplitude jump phenomena;The nonlinear vibration response of the system will be decreased with the increasing of the external excitation amplitude,damping ratio and the decreasing of the internal excitation amplitude.