尺寸链的计算机数值解法

在直线尺寸链问题中,封闭环尺寸是组成环尺寸的线性函数,因而用解析公式计算封闭环极限尺寸和公差比较方便,在平面尺寸链和空间尺寸链中,封闭环与组成环的函数关系较为复杂,用解析公式计算封闭环极限尺寸、公差较为困难,有时甚至无法求解,本文提出了尺寸链的计算机数值解法,论述了常见的和复杂的尺寸链方程的一般形式及其解法,以及极值法、概率统计法、统计试验法求解封闭环公差及极限偏差的方法,该方法适用于计算机计算,不仅能求解常用的也能求解复杂的尺寸链问题。

Computer-Based Numerical Solving Process of the Dimensional Chain Equations

In linear dimesional chain, the dimension ofclosing link is the linear function of the component link. It isfairly convenient to calculate the closing link tolerances withthe analytic equations. However, if the dimensional chain to bedealt with is planar or spacial, the functional relation betweenthe closing link and the component links will be rather complic-ated so that it will be rather difficult or even impossible toobtain the component link tolerances with analytic equations.In this article, a sort of computer--based numerical solvingprvecss of dimensional chain is presented. The general formsand their solving Processes of the common as well as the compli-cated dimensional chain equations are discussed. The way ofusing the extremum method, probabilistic method and statisticaltrial method to calculate the closing link tolerancesand the li-mit errors are also given.This method is suitable for the calcu-lations on computers. It can be used for solving problems of bothcommon and complicated dimensional chain.