基于刀具基本齿廓，根据齿廓法线法求得柔轮齿廓，再通过包络理论求解出与其共轭的刚轮齿廓。利用Matlab软件的数据处理和绘制图形功能，编程显示出刚柔轮齿廓的参数及形状，并进行新齿形啮合性能的判断，计算出理论啮合弧长及同时啮合的齿对数。对柔轮齿廓上每个点在啮入过程中与刚轮齿廓的侧隙值进行求解，找出最小侧隙值并进行规律分析，验证刚柔轮不发生啮合干涉。分析柔轮变形引起的轮齿偏斜现象，针对此现象引起的刚柔轮啮合问题，采用修改变位系数的方法，在不改变柔轮齿廓参数的条件下，设计刚轮的三维齿廓来避免啮合干涉。

Based on the basic profile of the tool, according to the tooth profile normal method to obtain the flexible gear tooth profile, then the conjugated rigid wheel profile is solved by the envelope theory. Using the data processing ability and graphics display function of the Matlab software, the parameters and shape of the flexion wheel tooth profile is displayed by programming, and the new tooth profile meshing performance is judged, the theoretical meshing arc length and the number of pairs of tooth meshing at the same time are calculated. The backlash value of every point in the flexible gear profile to rigid wheel tooth profile is solved, then the minimum backlash value is found out and rule analysis is carried out, the rigid flexible wheel does not engage in meshing interference is verified. The deflection of the gear teeth caused by the flexible wheel deformation is analyzed, and using the method of modifying displacement coefficient to solve the meshing problem caused by the flexible wheel deformation, and the three-dimensional tooth profile of the rigid wheel is designed to avoid meshing interference without changing the parameters of the flexible wheel tooth profile.