凸轮廓面特性自适应分析的共轭曲面离散解析原理

Discretization and Analysis Principle of Conjugating Surfaces for Contours Adaptive Analyzing of Cams

目前，凸轮ＣＡＤ／ＣＡＭ系统中廓面分析的数学模型是刚性的，这从根本上制约了凸轮ＣＡＤ／ＣＡＭ系统的柔性。本文将廓面分析建立在共轭曲面理论的基础上，提出了共轭曲面分析的离散解析原理。从共轭曲面的生成过程出发，认为轮廓曲面Σ１是从动曲面Σ２以及相对运动共同作用的结果，通过对从动曲面Σ２和相对运动的分析，获得轮廓曲面Σ１上相应点的特征。作者推导了由从动曲面Σ２及相对运动获得轮廓曲面Σ１特性的公式，从数学模型上将离散运算和共轭曲面解析处理结合起来。“离散解析原理”使得计算机智能化、自适应处理解析的共轭曲面问题成为可能。这为构建高柔性凸轮ＣＡＤ／ＣＡＭ系统奠定了坚实的理论基础，并提供了有效的实现方法。

At present the CAD/CAM software system is lowly flexible due to the mathematical models of contours design being stiff.To overcome the shortcoming,the discretization and analysis principle for conjugating surfaces adaptive analyzing founded on the theory of conjugating surfaces is proposed in this paper.The surface Σ 1 has been regarded,taking the generating process of conjugating surfaces into account,as the resultant of the interaction between surface Σ 2 and the relative motion between surface Σ 1 and surface Σ 2.So the characteristics of surface Σ 1 could be decided through analyzing the characteristics of surface Σ 2 and the relative motion and the authors have derived the formula of surface Σ 1s characteristics in the form of surface Σ 2 and parameter of the relative motion,the mathematical forms of which is suitable for the combination of the computers discrete calculation and the analytical solutions of conjugating surfaces.This method makes the solutions of conjugating surfaces intelligent and automatic and the highly adaptive analysis of cams contours possible and is helpful to construct highly flexible CAD/CAM software system of cams design.