曲线齿面齿轮的参数化建模与时变啮合刚度计算

Exploring Parametric Modeling and Time-varying Mesh Stiffness of Face Gear with Curved Tooth

以曲线齿面齿轮传动系统为研究对象，对小模数曲线齿面齿轮与渐开线圆柱蜗杆传动系统进行了齿面方程求解、几何模型建立及啮合接触分析。主要包含以下内容：依据齿轮几何学与啮合理论，分别推导出渐开线圆柱蜗杆与曲线齿面齿轮的齿面方程，基于此利用参数化建模的方法建立了准确的几何装配模型，并在其整体装配模型基础上建立了五齿啮合模型；阐述了一种基于有限元分析的时变啮合刚度算法，建立了曲线齿面齿轮啮合接触分析的有限元模型，并基于此对其啮合过程中不同接触位置的传动应力以及时变啮合刚度进行分析，获得了其时变啮合刚度的变化规律与传动应力的变化情况。

A small module face gear with curved tooth and an involute cylindrical worm transmission system have been studied with the finite element analysis. The calculation models of time-varying mesh stiffness and stress of face gear with curved tooth are established. Firstly, some existing mesh stiffness calculation methods are introduced, and their disadvantages are analyzed. Based on the gear geometry and the gear formation theory, this paper derives the mathematical models for the involute cylindrical worm and the face gear with curved tooth and obtains the discrete coordinates on the tooth surface. On this basis, the paper establishes the geometrical model and the assembly model and then develops the model of face gear with five teeth. Then it elaborates the time-varying mesh stiffness calculation method based on the finite element analysis. The accuracy of this method is verified with an example of straight tooth column gear. Through the contrast with available literatures, the calculation method in this paper is checked. Finally, the finite element model of the face gear with curved tooth is created with the ANSYS software. Then the paper applies the finite element model to analyzing the gears in several different meshing positions during the transmission.