高速列车齿轮传动系统参数振动稳定性

Stability Analysis of Parametric Vibration for Gear Transmission System in High-Speed Train

为了准确表达参数激励下高速列车齿轮系统振动的稳定性,利用有限元方法得到高速列车齿轮系统时变啮合刚度,并用傅里叶级数展开进行拟合.考虑齿轮啮合误差,建立了高速列车齿轮传动系统扭转振动模型.结合多尺度近似解析方法,推导了参激振动下高速列车齿轮系统的近似解析解,得到了系统的稳定性边界曲线,并分析了影响齿轮传动系统稳定性的相关因素.研究结果表明:齿轮系统的不稳定性区域随着列车运行的速度降低总体呈减小趋势,但是在发生参数共振速度处存在明显不稳定区域;增大阻尼有利于系统的稳定性,当阻尼系数从0.01增加到0.05时,处于稳定区域的刚度波动幅值从5%增加至20%;增加齿轮的重合度可以减小啮合刚度的谐波特性,从而增强系统的稳定性.

In order to study the stability of the gear transmission system in high-speed trains, a dynamic model describing the torsional vibration behaviors of the gear system was developed. In this model, the time-varying mesh stiffness of meshing teeth pairs was calculated through finite element analysis, and the mesh stiffness and transmission error were expanded using the technique of Fourier series. Based on this model, the multiple scales method was used to solve the nonlinear differential equations of gear systems, and the approximate analytical solution and transition curves that separate stable from unstable regions were obtained. In addition, the main factors that influence the stability were discussed. The results show that the unstable regions decrease with the decrease of the train＇s running speed, but an unstable region always exists at the speed where parametric resonance occurs; increasing the damping is effective to reduce the unstable regions ： as the damping increases from 0.01 to 0.05, the amplitude of mesh stiffness fluctuation in stable regions increases from 5% to 20% ; and, an increase in the contact ratio can help suppress the harmonic characteristics of mesh stiffness so as to improve the stability of system.