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

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.