基于分割球面逼近和差分进化的复杂曲面轮廓度误差评定

中国机械工程 ›› 2014, Vol. 25 ›› Issue (2): 152-156.

基于分割球面逼近和差分进化的复杂曲面轮廓度误差评定

何改云;刘欣;刘佩佩;郭龙真

天津大学机构理论与装备设计教育部重点实验室,天津,300072

出版日期:2014-01-25 发布日期:2014-02-19
基金资助:
国家自然科学基金资助项目(50975200)

Evaluation of Complex Surface Profile Errors Based on Subdivision and Sphere Approximation Method and Differential Evolution Algorithm

He Gaiyun;Liu Xin;Liu Peipei;Guo Longzhen

Key Laboratory of Mechanism Theory and Equipment Design of Ministry of Education,Tianjin University,Tianjin,300072

Online:2014-01-25 Published:2014-02-19
Supported by:
National Natural Science Foundation of China（No. 50975200）

摘要/Abstract

摘要：

为了评定复杂曲面轮廓度误差,提出了一种快速简便的分割球面逼近方法。该方法用球面逐步逼近测点垂足所在的曲面片来求得测点到设计曲面的最短距离,然后利用差分进化算法优化测点位置，结合分割球面逼近方法最终求得复杂曲面轮廓度误差值。将分割球面逼近方法和差分进化算法相结合，用于计算蜗杆齿面的轮廓度误差，仿真结果表明，该方法计算精度高于最小二乘法，能满足高精度误差评定的需求。

关键词: 最短距离, 分割球面逼近, 轮廓度误差, 差分进化算法

Abstract: In order to evaluate the profile errors of complex surface,a subdivision and sphere approximation method, fast and convenient, was firstly presented. Approximating the surface patch containing the perpendicular foot of measuring point by a sphere, the shortest distance between a measuring point and surface was obtained. Secondly, a differential evolution algorithm was selected to optimize the position of measuring points. Finally, the evaluation of complex surface profile errors was realized by using subdivision and sphere approximation method combined with differential evolution algorithm. The proposed method was used to evaluate worm tooth-surface profile errors and the simulation results show that the method can obtain higher calculation accuracy compared with least square method and can satisfy the requirements of high-precision error evaluation.

Key words: shortest distance, subdivision and sphere approximation, profile error, differential evolution algorithm

中图分类号:

TH161

何改云, 刘欣, 刘佩佩, 郭龙真. 基于分割球面逼近和差分进化的复杂曲面轮廓度误差评定[J]. 中国机械工程, 2014, 25(2): 152-156.

He Gaiyun, Liu Xin, Liu Peipei, Guo Longzhen. Evaluation of Complex Surface Profile Errors Based on Subdivision and Sphere Approximation Method and Differential Evolution Algorithm[J]. China Mechanical Engineering, 2014, 25(2): 152-156.

参考文献

[1]丁汉,朱利民,熊振华.复杂曲面快速测量、建模及基于测量点云的RP和NC加工[J].机械工程学报,2003,39(11):28-37.
Ding Han,Zhu Limin,Xiong Zhenhua.Survey on Coordinate Measurement,Geometric Modeling and RP or NC Code Generation from Measured Data Points[J].Journal of Mechanical Engineering,2003,39(11):28-37.
[2]王伯平,曾建潮.一种自调整的空间面轮廓度误差的评定方法[J].计量学报,2002,23(2):106-108.
Wang Boping,Zeng Jianchao.An Automatic Adjustment Method for Evaluation of Space Surface Profile Error[J].Acta Metrologica Sinica,2002,23(2):106-108.
[3]王林艳,王建华.基于坐标法的复杂曲面轮廓度的误差评定[J].西安工业学院学报,2006,26(3):228-232.
Wang Linyan,Wang Jianhua.Evaluation of Profile Error of Complex Surface by Coordinate Method[J].Journal of Xi’an Technological University,2006,26(3):228-232.
[4]郭慧,林大钧.基于微粒群算法的复杂曲面轮廓度误差计算[J].东华大学学报(自然科学版),2008,34(3):274-277.
Guo Hui,Lin Dajun.Profile Error Computation of Complicated Surface Based on Particle Swarm Optimization[J].Journal of Donghua University(Natural Science),2008,34(3):274-277.
[5]廖平.基于遗传算法和分割逼近法精确计算复杂曲面轮廓度误差[J].机械工程学报,2010,46(10):2-6.
Liao Ping.Calculating of Complex Surface Profile Error Based on Subdivision Approach Algorithm and Genetic Algorithm[J]. Journal of Mechanical Engineering,2010,46(10):2-6.
[6]廖平.基于粒子群算法和分割逼近法的复杂曲面轮廓度误差计算[J].中国机械工程,2010,21(2):201-205.
Liao Ping.Calculation of Complex Surface Profile Errors Based on Hybrid Particle Swarm Optimization Algorithm[J].China Mechanical Engineering,2010,21(2):201-205.
[7]Piegl L.On NURBS:a Survey[J].IEEE Computer Graphics and Application,1991,11(1):55-71.
[8]Piegl L,Tiller W.The NURBS Book[M].2nd ed.Berlin:Springer,1997.
[9]Storn R,Price K.Differential Evolution—a Simple and Efficient Heuristic for Global Optimization over Continuous Spaces[J]. Journal of Global Optimization,1997,11:341-359.
[10]王俊,蔡兴国.基于差分进化算法的动态可用输电能力计算研究[J].电力系统保护与控制,2010,38(4):39-44.
Wang Jun,Cai Xingguo.Study of Calculating the Dynamic Available Transfer Capability with the Differential Evolution Algorithm[J].Power System Protection and Contro,2010,38(4):39-44.
[11]He Gaiyun,Zhang Song,Ding Baihui,et al.The Study of Error Evaluation Strategy of Complex Surface in On-machine Verification System[J].Advanced Science Letters,2011,4:2996-3001.