基于势能原理的铰接支撑齿条-齿轮时变啮合刚度解析计算

Analytical Calculation for Time-varying Mesh Stiffness of Articulated Supported Rack-Gear Based on Potential Energy Principle

齿轮齿条传动是一种重要的机械传动方式,其内部时变啮合刚度是一种主要的激励源,对系统振动噪声水平有着重要影响。针对齿轮齿条时变啮合刚度高效、准确的解析计算问题,提出了一种基于势能原理的铰接支撑齿条与齿轮啮合刚度解析计算方法,计算获得了不同参数下的齿轮齿条时变啮合刚度,并利用有限元法验证了建立的解析计算模型的正确性。同时,利用建立的解析计算方法分析了垂向间隙、压力角、齿条长度等参数对齿轮齿条时变啮合刚度的影响规律。结果表明,建立的解析计算方法能够准确计算齿轮齿条时变啮合刚度,为齿轮齿条传动系统动态特性分析提供了理论支撑。

Gear-rack transmission is an important mechanical transmission mode and the time-varying mesh stiffness of gear-rack is one of the main excitation sources, which has an important effect on the vibration and noise level of the mechanical system. An analytical calculation method for time-varying mesh stiffness of articulated supported rack-gear transmission is proposed based on the potential energy principle, which aims to solve the problem of efficient and accurate analytical calculation for gear-rack mesh stiffness. Then, the time-varying mesh stiffness of a gear-rack transmission with different parameters is calculated using this method. By comparing the calculated results with that derived from the finite element model, the correctness of the established analytical calculation model is verified. In addition, the effect of the vertical clearance, pressure angle and rack length on the time-varying mesh stiffness of gear-rack is analyzed using this analytical calculation model. The results indicate that the analytical calculation model can accurately calculate the time-varying mesh stiffness of the gear-rack transmission, and it can provide theoretical support for the dynamic analysis of gear-rack transmission system.