曲面综合法复杂齿面啮合仿真分析方法研究

Research on Meshing Simulation Analysis Method for Complex Flanks Based on Surface Synthesis Method

根据空间曲面啮合原理,构建共轭曲面的数理综合模型;基于该模型坐标变换,求得弧齿锥齿轮大、小轮齿面的数理解;基于曲面综合,给出齿面修形梯度曲面(简称Ease-off曲面)的构建方法;以齿面的旋转投影平面为坐标平面划分网格,计算了小轮修形齿面与共轭齿面的法向修形量,得到弧齿锥齿轮Ease-off曲面;通过解析Ease-off曲面,获得了完整的齿面接触形态:差曲线、接触路径、传动误差等,与齿面实际接触斑点形态高度一致。为复杂齿面的拓扑设计、啮合形态仿真提供了一种准确可行的手段。

According to the space meshing theory,the mathematics model of conjugate surfaces is con⁃structed.Based on the coordinate transformation of this model,the mathematical solution of the wheel and pinion tooth surfaces is obtained.On the basis of surface synthesis,the construction method of gradient surface(Ease off)for tooth modification is given.Taking the rotating projection plane of the tooth surface as the coordinate plane,the normal deviation of the modified tooth surface from the conjugate tooth surfaces for pinions is calculat⁃ed,and the Ease-off surface of the spiral bevel gear is obtained.Based on analysis of the Ease-off surface,the complete contact morphological characteristics of tooth surface are obtained:the contact line-off,contact path,transmission error,etc.,which are highly consistent with the actual contact pattern of the tooth surface.The above findings provide an accurate and feasible method for the topology design and meshing simulation of com⁃plex tooth surfaces.