基于相對運動理論的球度誤差矩陣尋優算法
徐永祥， 崔昭霞， 韓  峰， 劉  珍
（內蒙古工業大學機械學院，內蒙古 呼和浩特 010051）
摘  要：針對目前球度誤差計算多采用復雜尋優算法的現狀，根據球度誤差最小包容區域的特點，給出球度誤差計算的目標函數，提出一種簡化的球度誤差矩陣尋優算法。依據相對運動理論，將擬合球面的球心設定在三維直角坐標系的原點上，利用矩陣變換整體平移被測球面上各測點，使之快速趨近于球度誤差最小包容區域的目標位置。實例證明該方法具有易于使用和快速高效的特點。該思想同樣適用于其他形狀誤差的評定計算，為形狀誤差的統一求解提供一種新思路。
關鍵詞：球度誤差；矩陣變換；擬合球面；最小包容區域
中圖分類號：TG8；TB92；TH161+.12；TM930.115      文獻標志碼：A      文章編號：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