|
|
|
| Minimum Zone Evaluating for Sphericity Error Based on Geometry Search Approaching Method |
| LEI Xian-qing,GAO Zuo-bin,MA Wen-suo,DUAN Ming-de |
| Department of Machatronics Engineering, Henan University of Science & Technology, Luoyang, Henan 471003, China |
|
|
|
|
Abstract According to geometric definition of the sphericity, a novel evaluation method which named as geometry search approaching method for sphericity error is presented. Firstly, an initial reference point is taken as a datum point and built a regular hexahedron and established an auxiliary points. Secondly, the each auxiliary points and the datum point are used as the centre of the measured sphere to calculate the radius of all measured points. And then modify the side length of the hexahedron or the position of the reference point by comparing these radius extreme differences. Finally, by repeating this process, the minimum zone containing all measurement points is obtained and the minimum zone evaluation for the measured spherical surface is implemented. The method is used to process a group of metrical data, and the results indicate that the sphericity error value from this algorithm can be reduced by 0.6μm as compared with least square method, and are consistent with the results obtained by the analytic method and evolutionary computation method. The results show that the algorithm can get not only the minimum zone solution accurately but also has good stability.
|
|
Received: 18 September 2014
Published: 27 January 2016
|
|
|
|
|
|
［1］Danish P B, Shunmugam M S. Algorithm for form error evaluation using the theory of discrete and linear Chebyshev approximation［J］. Computer Methods in Applied Mechanics and Engineering, 1991,92(3): 309-324.
［2］Kanad T. Evaluation of spherical form errors computation of sphericity by means of minimum zone method and some examinations with using simulated data［J］. Precision Engineering, 1995, 17(4): 281-289.
［3］刘文文,邓善熙,聂恒敬. 球度误差包容评定的高精度实现方法［J］. 计量学报,2000,21(2):100-105.
［4］Chen C K, Liu C H. Study on analyzing the problem of the spherical form error. Precision Engineering, 2000,24 (2):119-126.
［5］Cui C C, Che R S,Ye D, et al. Sphericity error evaluation using the genetic algorithm［J］. Optics and Precision Engineering, 2002,10 (4): 333-339.
［6］Wen X L, Song A G. An immune evolutionary algorithm for sphericity error evaluation［J］. International Journal of Machine Tools and Manufacture, 2004,44 (10): 1077-1084.
［7］温秀兰, 宋爱国. 基于免疫进化计算的球度误差评定［J］. 计量学报,2005,26(1):12-15.
［8］Fan K C, Lee J C. Analysis of minimum zone sphericity error using minimum potential energy theory［J］. Precision Engineering, 1999,23 (2): 65-72.
［9］Samuel G L, Shunmugam M S. Evaluation of sphericity error from form data using computational geometric techniques［J］. International Journal of Machine Tools and Manufacture, 2002,42 (3):405-416.
［10］雷贤卿,宋红卫,薛玉君,等. 球度误差的网格搜索算法［J］.农业机械学报, 2012,43(5):222-225.
［11］刘飞,彭晓楠. 最小外接球法球度误差评价与实现［J］. 机械工程学报,2009,45(9):243-248. |
|
|
|
2016, Vol. 37 
