考虑延长啮合时齿轮参数振动稳定性研究

Parametric stability for spur gear pair system considering effect of extended tooth contact

考虑因轮齿受载弹性变形引起的轮齿延长啮合效应时,将使得啮合刚度随时间变化形式发生改变,而这一变化对于系统的动态特性产生重要影响。在考虑轮齿延长啮合时齿轮参数振动稳定性的变化情况,首先建立齿轮副参数振动分析模型,进而研究了系统稳定性分析方法,主要是状态转移矩阵的确定和稳定性判据;在此基础上,以实际应用的高速重载齿轮副为例讨论了延长啮合与否系统稳定区间的变化情况,同时还考虑了系统阻尼的影响。研究结果表明:轮齿延长啮合作用使得低转速和高转速范围内的各不稳定区减小,而对于中等转速范围内,考虑延长啮合使得不稳定区变大。

In view of extended tooth contact due to the tooth deformation under load, the time-varying pattern of mesh stiffness model would change and further influence the parametric stability of geared system significantly. Therefore, research on parametric stability for spur-gear-pair system considering effect of extended tooth contact is carried out in this paper. Firstly, a torsional parametric vibration model for spur-gear-pair system is established. Then, the method for stability analysis, including two key elements （one is the derivation of state transition matrix for the system taking into account the effect of extended tooth contact; the other is the stability criterion for parametric vibration system） is presented in detail. In order to illustrate the effect of extended tooth contact the stability of geared system, stable and unstable regions of a practically used high-speed and heavy load spur-gear-pair with and without the effect of extended tooth contact are respectively determined. In addition, different operating torques and mesh dampings of the gear pair are also discussed for their influences upon stable regions in the analysis. The results show that due to the extended tooth contact the unstable regions in small and high speed ranges are reduced, while the unstable regions in middling speed range are larger as the effect of extended tooth contact.