第21卷第5期 2013年5月
文章编号
1004-924X(2013)05-131206
光学精密工程
Optics and Precision Engineering
评定平面度误差的几何搜索逼近算法
雷贤卿1*，李飞，涂鲜萍，王世锋”
（1.河南科技大学机电工程学院，河南洛阳471003； 2.洛阳轴研科技股份有限公司，河南洛阳471003)
Vol.21No.5
May2013
摘要：为了快速准确地评定机械零件的平面度误差，提出了基于几何搜索逼近的平面度误差最小区域评定算法。闹述了利用几何优化搜索算法求解平面度误差的过程和步骤，给出了数学计算公式。首先选择被测平面的3个边缘点为参考
极差；通过比较判断及改变参考点，构造新的辅助点、参考平面和辅助平面，最终实现平面度误差的最小区域评定。用提出的方法对一组测量数据进行了处理。结果表明，在终止搜索的条件为0.00001mm时，几何搜索逼近评定算法的结果分别比凸包法、计算几何法、最小二乘法、遗传算法和进化策略计算的结果减小了17.1、7.3、18.03、6.13和0.3μm，得到的数据显示该算法不仅能准确地得到最小区域解，面且计算结果有良好的稳定性，适合在平面度误差测量仪器和三坐标测量机上使用。
键词：平面度误差；误差评定；几何搜索逼近；最小区域关
中图分类号：TH161.1
文献标识码：A
doi;10.3788/OPE,20132105.1312
Geometry searching approximation algorithm for
flatnesserrorevaluation
LEI Xian-qing'', LI Fei',TU Xian-ping', WANG Shi-feng
(l.SchoolofMechatronicsEngineering，HenanUniversityofScienceand
Technology，Luoyang471003,China;
2.LuoyangBearingScience&Technology Co.,Ltd.,Luoyang471003,China)
*Correspondingauthor，E-mail:ly-lxq@163.com
Abstract: To evaluate the flatness errors of mechanical parts accurately and rapidly, an algorithm u sing geometry searching approximation to evaluate the flatness error minimum zone was presented. The principle and steps of the algorithm to solve the flatness error was described in detail and the mathematical formulas were given, First, the three edge points of the measured plane were selected as reference points, and the auxiliary points, reference plane and auxiliary planes were constructed based on the reference points. Then, the distance differences of all measurement points to the supposed ideal planes were calculated by taking the reference plane and auxiliary planes as supposed ideal planes. The reference points, auxiliary points, reference plane and auxiliary planes were reconstructed by compa ring the distance differences. Finally, by repeating this processes, the minimum zone evaluation for flatness error was implemented. The method was used to process a group of metrical data, and the re
收稿日期：2013-01-18；修订日期：2013-02-27
基金项目：国家自然科学基金资助项目（No,50875076)；河南省基础与前沿技术研究计划资助项目（No.122300410114；
No.,122300413209)