基于相对运动理论的球度误差矩阵寻优算法
徐永祥， 崔昭霞， 韩  峰， 刘  珍
（内蒙古工业大学机械学院，内蒙古 呼和浩特 010051）
摘  要：针对目前球度误差计算多采用复杂寻优算法的现状，根据球度误差最小包容区域的特点，给出球度误差计算的目标函数，提出一种简化的球度误差矩阵寻优算法。依据相对运动理论，将拟合球面的球心设定在三维直角坐标系的原点上，利用矩阵变换整体平移被测球面上各测点，使之快速趋近于球度误差最小包容区域的目标位置。实例证明该方法具有易于使用和快速高效的特点。该思想同样适用于其他形状误差的评定计算，为形状误差的统一求解提供一种新思路。
关键词：球度误差；矩阵变换；拟合球面；最小包容区域
中图分类号：TG8；TB92；TH161+.12；TM930.115      文献标志码：A      文章编号：1674-5124（2013）03-0017-03
Matrix optimization method for calculating sphericity error
base on relative motion theory
XU Yong-xiang， CUI Zhao-xia， HAN Feng， LIU Zhen
（Mechanical College，Inner Mongolia University of Technology，Huhhot 010051，China）
Abstract: For resolving the problem that the sphericity errors are calculated mostly with complex optimization algorithms， a simplified matrix optimization method for calculating the sphericity error was proposed. Its objective function of calculating the sphericity error was given according to the features of sphericity error minimum zone. According to the relative motion theory， firstly， the center of fitting sphere was set on the coordinate origin of 3D rectangular coordinates. Then， all measuring points on the sphere to be measured were translated through appropriate matrix transformations. At last， the algorithm makes it rapidly tend to the objective location of sphericity error minimum zone. It is proved by actual measurements that the method is simple and efficient. This method also can be used to calculate other form errors and it provides a new and unified way for calculating form errors.
Key words: sphericity error； matrix transformation； fitting sphere； minimum zone