基于相對(duì)運(yùn)動(dòng)理論的球度誤差矩陣尋優(yōu)算法
中國(guó)測(cè)試雜志
基于相對(duì)運(yùn)動(dòng)理論的球度誤差矩陣尋優(yōu)算法
徐永祥， 崔昭霞， 韓 峰， 劉 珍
（內(nèi)蒙古工業(yè)大學(xué)機(jī)械學(xué)院，內(nèi)蒙古 呼和浩特 010051）
摘 要：針對(duì)目前球度誤差計(jì)算多采用復(fù)雜尋優(yōu)算法的現(xiàn)狀，根據(jù)球度誤差最小包容區(qū)域的特點(diǎn)，給出球度誤差計(jì)算的目標(biāo)函數(shù)，提出一種簡(jiǎn)化的球度誤差矩陣尋優(yōu)算法。依據(jù)相對(duì)運(yùn)動(dòng)理論，將擬合球面的球心設(shè)定在三維直角坐標(biāo)系的原點(diǎn)上，利用矩陣變換整體平移被測(cè)球面上各測(cè)點(diǎn)，使之快速趨近于球度誤差最小包容區(qū)域的目標(biāo)位置。實(shí)例證明該方法具有易于使用和快速高效的特點(diǎn)。該思想同樣適用于其他形狀誤差的評(píng)定計(jì)算，為形狀誤差的統(tǒng)一求解提供一種新思路。
關(guān)鍵詞：球度誤差；矩陣變換；擬合球面；最小包容區(qū)域
中圖分類號(hào)：TG8；TB92；TH161+.12；TM930.115 文獻(xiàn)標(biāo)志碼：A 文章編號(hào)：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
