含时滞反馈控制的直齿圆柱齿轮主共振分析

Primary resonance analysis for a spur gear system with time delay feedback control

为了减小直齿圆柱齿轮系统由于外载荷波动和时变啮合刚度引起的振动,建立了直齿圆柱齿轮的时滞反馈减振动力学模型,并利用多尺度法对时滞反馈齿轮传动系统进行求解,获得了齿轮系统主共振频率响应方程,通过分析比较载荷波动、啮合刚度波动和时滞反馈控制参数对主共振的影响,可以得出:齿轮系统存在的载荷波动和啮合刚度波动都会导致齿轮系统主共振不稳定;合理匹配的时滞控制参数能够使主共振快速收敛到稳定解,反之可能导致系统振动加剧,使系统稳定性变差。

In order to reduce vibration of a spur gear system caused by external load fluctuation and time-varying meshing stiffness one, its dynamical model with time delay feedback control was established. The multi-scale method was applied to solve this system, and obtain its primary resonance frequency equation. Effects of load fluctuation, mesh stiffness one and time delay feedback control parameters on the system’s primary resonance were analyzed contrastively. The results showed that the load fluctuation and gear meshing stiffness one can cause the system main resonance unstable;time delay control parameters should be matched reasonably to make the primary resonance quickly converge to the stable solution, otherwise, the system vibration may be intensified to cause the system’s stability worse.