基于多项式的等高齿锥齿轮时变啮合刚度建模

Modelling of high-spiral bevel gear mesh stiffness based on polynomial

针对某型雷达装置的等高齿锥齿轮在啮合时的时变啮合刚度,提出一种多项式函数展开的时变啮合刚度新模型。通过转速、负载扭矩、阻尼因子系数分析,构建了多项式函数展开的时变啮合刚度模型,建立了等高齿锥齿轮的非线性动力学方程。将本文建立的时变啮合刚度模型与传统的多阶简谐波叠加形式的时变啮合刚度模型以及综合刚度参考数据模型进行分析对比,发现在小阻尼、重载工况下这种多项式形式的时变啮合刚度模型能更贴近于时变啮合刚度的实际特性,该模型为齿轮传动的减振、降噪、平稳传动等方面的动力学研究打下基础。

We present a new time-varying mesh stiffness model using polynomial function with regard to the time-varying mesh stiffness of the high-bevel gear of a radar device. By analyzing the revolution speed, load torque and damping factor, we build the mesh stiffness model and the nonlinear dynamic equations of the high-bevel gear. We compare the proposed mesh stiffness model with traditional rime- varying mesh stiffness model of multi-order harmonic superposition and reference data model of time- varying comprehensive stiffness. It is shown that, with small damping and overload, the proposed model is much closer to the actual characteristics of the time-varying stiffness. This model lays a foundation to study the gear transmission dynamics, such as vibration damping, noise reduction, smooth transmission and other aspects with small damping and overload.