考虑温度效应的斜齿轮时变啮合刚度解析算法

林腾蛟　赵子瑞　江飞洋　陈兵奎

摘   要：以斜齿轮副为研究对象，基于切片法和积分思想，计入齿面接触温度变化引起的齿廓形变，结合轮齿接触、弯曲、剪切、轴向压缩及基体弹性变形，提出了考虑温度效应的斜齿轮啮合刚度解析算法，并通过有限元法验证了算法的准确性. 分析了不同摩擦因数、输入转矩、输入转速等工况参数对斜齿轮啮合刚度的影响规律. 结果表明，考虑齿轮温升影响后，轮齿从啮入到啮出整个过程的啮合刚度均有所增大;随着摩擦因数、输入转矩和输入转速的增大，斜齿轮本体温度及啮合齿面瞬时闪温升高，单齿啮合刚度和综合啮合刚度均值呈增大趋势. 研究结果可为高速重载齿轮系统准确高效的动力学分析提供理论依据.

关键词：斜齿轮;温度效应;时变啮合刚度;势能法

中图分类号：TH132.41                  文献标志码：A

Abstract：Taking a helical gear pair as the research object，the analytic algorithm of time-varying mesh stiffness of helical gears with temperature was proposed based on slicing method and integral thought. In this algorithm，the tooth profile deformation caused by change of tooth contact temperature，elastic deformation of tooth contact，bending，shear，axial compression and the wheel were taken into account. The accuracy of the algorithm was verified by using finite element method. Then the influence of working parameters，such as friction coefficient，input torque and input speed，on the mesh stiffness of gears was analyzed. The results show that the mesh stiffness of teeth increases in the whole meshing process after considering the influence of temperature. Besides，the body temperature and instantaneous flash temperature of helical gears increase with the increase of friction coefficient，input torque and input speed，so the single mesh stiffness and the mean of total mesh stiffness increase. The research results can provide a theoretical basis for accurate and efficient dynamic analysis of the high-speed and heavy-duty gear system.

Key words：helical gears;temperature effect;time-varing mesh stiffness;potential energy method

齒轮系统作为机械装置中最为广泛的动力和运动传递形式，正朝着大功率、高转速、低噪声和轻量化方向发展. 在高速重载工况下，由于啮合齿面相对滑动速度大，瞬时温升高，直接影响齿轮系统内部的温度分布，引起结构热应力及热变形，进而对齿轮啮合刚度产生较大影响，而准确高效的啮合刚度计算方法又是齿轮系统动力学分析的关键. 因此，综合考虑温度影响，开展斜齿轮时变啮合刚度解析算法研究，对高速重载齿轮系统动力学设计有着重要的工程意义.

近年来，对于齿轮系统时变啮合刚度的……