结合有限元法和接触理论的内齿轮副啮合刚度计算方法  

A Method for Determining the Mesh Stiffness of Internal Gear by Combining Finite Element Method and Contact Theory

作　　者：常乐浩[1] 田宏炜 贺朝霞[1] 刘更[2] Chang Lehao;Tian Hongwei;He Zhaoxia;Liu Geng(Key Laboratory of Road Construction Technology and Equipment of Ministry of Education,Chang＇an University,Xi＇an 710064,China;Shaanxi Engineering Laboratory for Transmissions and Controls,Northwestern Polytechnical University,Xi＇an 710072,China)

机构地区：[1]长安大学道路施工技术与装备教育部重点实验室,陕西西安710064 [2]西北工业大学陕西省机电传动与控制工程实验室,陕西西安710072

出　　处：《机械传动》2018年第8期61-64,79,共5页Journal of Mechanical Transmission

基　　金：国家自然科学基金(51605040;51535009);中央高校基本科研业务费资助项目(310825171009)

摘　　要：提出了一种将有限元方法和接触理论相结合的内啮合齿轮副啮合刚度计算方法。该方法通过齿轮整体和局部有限元模型分离出啮合点宏观变形,利用线接触变形解析公式计算啮合点接触变形,求解非线性啮合平衡方程后得到齿轮副时变啮合刚度和载荷分布。该方法相比一般有限元法具有更高的计算效率和稳定性,同时克服了解析方法难以考虑斜齿轮和不同齿圈结构影响的缺点。最后,分析了内齿圈不同支撑数目和齿圈厚度对啮合刚度的影响。该方法可为内齿轮副强度及动态特性设计提供有效指导。A method for determining the mesh stiffness of internal gears is proposed by using a combination of finite element method and the contact theory. The global deformation of contact point is separated by a full finite element model and a partial one. The local contact deformation is calculated by using the analytical formula for a line contact problem. The mesh stiffness and load distribution can be obtained after solving the nonlinear contact equilibrium equations. Compared with the conventional finite element method,the proposed method has higher computational efficiency and stability. And it also overcomes the disadvantage that the analytical method is difficult to consider helical gears and different gear ring structures. Then the influences of constraints number and thickness of ring gears on the mesh stiffness are analyzed. This method can provide effective guidance for the design of the strength and dynamic characteristics of the internal gears.

关 键 词：内齿轮 啮合刚度 有限元法 接触理论 

分 类 号：TH132.41[机械工程—机械制造及自动化]