基于区间分析的平面尺寸链求解实例研究

Case Study of Plane Dimensional Chain Calculation Based on Interval Analysis

针对极值法求解尺寸链过于保守、统计法求解尺寸链需知晓各环的概率分布等问题,研究了用区间分析方法来计算复杂平面尺寸链方程组的原理和方法。首先,将尺寸链中的各环尺寸及其偏差以区间数的形式来表示,构建区间参数方程组;其次,利用Krawczyk算子及INTLAB工具箱编写了求解区间参数方程组的应用程序,并引入区间截断法;最后,对机枪机心结构尺寸链实例分别进行了区间分析计算和CE/TOL6σ软件计算,并进行对比和分析研究。研究结果表明采用区间分析求解平面尺寸链的计算结果优于极值法,并能弥补RSS统计法的固有缺陷。

Aiming at the problems that worst-case method is too conservative when solving dimensional chain and statistical method needs to know the probability distribution of each loop, the principle and method of calculating the complex dimensional chain equations with interval analysis method are studied. Firstly, the size and deviation of each loop in the dimension chain are expressed in the form of interval number. Secondly, Krawczyk operator and INTLAB toolbox are used to write an application program for solving interval parameter equations, and interval truncation method is introduced. Finally, the interval analysis calculation and CE/TOL6σ software calculation are respectively carried out for the example of machine gun core dimension chain, and the comparison and analysis are conducted. The results show that the interval analysis method is superior to the worst case method and can make up the inherent defects of the RSS statistical method.