用于磨损仿真的空间啮合曲面离散化方法

Dispersion Method of Space Contact Tooth Surface for Wearing Imitation

提出了一种磨损齿面的描述方法 ,给出了双三次样条曲面中角点信息方阵的构造和求解方法·讨论了用该方法逼近齿廓曲面的可行性 :型值点在齿面上 ;二阶偏导数连续·解决了用样条函数研究图形的几何性质时其表示方法缺乏几何不变性的不方便之处 ;型值点均匀 ,因而曲面光顺 ;边界条件不难确定·以具体算例验证了这种方法的计算精度 ,与齿廓曲面方程计算的结果比较 ,型值点处 ,前 15位有效数值相同 ,最大误差在两型值点的中点附近 ,随网格加密而减小·精度足以满足磨损计算的要求 ,从而为磨损过程的计算机仿真奠定了基础·

A method for describing the worn tooth profile was presented. A method was develeped for structuring and calculating apex information matrix of double cube parameter spline surface. The feasibility of using it to approach gear profile was discussed: the shape value point at tooth surface; quadric partial derivative continuum; when the spline function is used to study the geometing property of a surface,its expression method is short of geometric fixdness. The new method overcomes this shortage; since the shape value points are uniformity, the surface is lubricity; the determination boundary conditions is easy. The calculating precision was validated by an example. Compared with the calculating result by tooth profile equation, the value in first fifteen is same. The maximum value of error is at the midpoint of two shape value points and minishes with gridding increasing. This method is accurate enough to meet the requirement of wearing calculation. Therefore it establishes a foundation on wearing tooth surface description and wearing imitation.