轮轨黏着下计及齿轮啮合特性的机车驱动系统主共振

Main resonance of a locomotive driving system considering mesh characteristics of gears under wheel-rail adhesion

针对机车驱动系统的振动问题,考虑了内部齿轮啮合的静传递误差、时变啮合刚度和齿侧间隙,建立了内部齿轮啮合动态激励和外部轮轨黏着力激励共同作用下机车驱动系统的动力学模型及方程,采用多尺度法进行求解,获得了系统主共振的频率响应方程,并开展实例研究,仿真分析了系统参数变化对频率响应曲线的影响以及轮轨黏着力变化对驱动系统主共振响应的影响。研究结果表明:轮轨黏着力的动态变化值会影响系统主共振发生的频率和幅值;系统的非线性特性使得主共振的频响曲线产生多值情况,误差速度项激励的系数F_3、误差谐波项的幅值e_r、一次谐波刚度的比值k_(e1)的减小或系统阻尼的增大有利于减小多值区域的产生,同时,F_3、e_r、k_(e1)的减小对振幅有一定的抑制作用。此外,主共振时(不计齿轮啮合阻尼),在无量纲时间[2 000~2 500]范围内,当静平衡位置处蠕滑率s_0=0.012,考虑轮轨黏着力的动态变化时位移的最大值较轮轨黏着力为恒值时减小了约35.35%;当s_0=0.035,考虑轮轨黏着力的动态变化时位移的最大值较轮轨黏着力为恒值时增大了约115.55%;且两种情况下,考虑轮轨黏着力的动态变化与否对系统振动的相轨迹和频谱图具有较大影响。

Aiming at vibration problems of a locomotive driving system,its dynamic model and corresponding equations under internal gears meshing dynamic excitation and external wheel-rail adhesion excitation were established considering static transmission error,time-varying mesh stiffness and backlash due to inside gears meshing. The main resonance frequency equation of the system was derived using the multi-scale method. Case studies were done. The influences of the system’s parameters on its frequency response curve were analyzed. The effects of wheel-rail adhesion force changes on the system’s main resonance response were simulated. The results showed that dynamic changes of wheel-rail adhesion force can affect the system’s main resonance frequency and amplitude; the nonlinear characteristics of the system can lead to multi-value phenomena of the main resonance ’s frequency response curve; decrease in the coefficient of error velocity term F3,the amplitude of error harmonic term er,and the ratio of the first harmonic stiffness ke1 or increase in the system ’s damping can reduce multi-value regions; meanwhile,decrease in F3,er and ke1 can suppress the main resonance amplitude to a certain extent; when the main resonance occurs not considering gears mesh damping within the dimensionless time range of 2 000—2 500 and the creep rate at static equilibrium position s0= 0. 012,the maximum displacement considering dynamic change of wheel-rail adhesion force decreases by about 35. 35% compared with that considering constant wheel-rail adhesion force; when s0 is 0. 035,the maximum displacement considering dynamic change of wheel-rail adhesion force increases by about 115. 55% compared with that considering constant wheel-rail adhesion force; in the above two cases,considering dynamic change of wheel-rail adhesion force or not can greatly affect frequency spectrum and phase trajectory of the system’s vibration.