The Minimum Zone Evaluation for Sphericity Error Based on the Dichotomy Approximating

Abstract:

A new algorithm which is “the minimum zone evaluation for sphericity error based on the dichotomy approximating” has been presented with the geometric characteristics and research situation of sphericity error and through the understanding of the definition and the evaluation problem of the sphericity. The principle of the algorithm is that based on finding the initial point of the ball as the base, around which the side decorates cube by certain length, calculating the distance of the points on the sphere to the cube measuring points of the eight vertex and the initial point, by comparing and judging to find a new beginning starting point, and arrange new cube repeatedly until meets the requirement. The sphericity error value of corresponding evaluation method (Minimum Zone Sphere method (MZS)) was obtained according to that. The mathematical formula、program flowchart and example verification were given. The example verification results show that the sphericity error can be evaluated effectively and exactly with this algorithm.

• Periodical: Applied Mechanics and Materials (Volumes 105-107)
• Pages: 1975-1979
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.105-107.1975
• Online since: September 2011
• Authors: Xian Qing Lei, Hong Wei Song, Jia Zhou
• Keywords: Dichotomy Approximating Algorithm, Error Evaluation, Minimum Zone, Sphericity

References

[1] C.K. Chen, C.H. Liu. A study on analyzing the problem of the spherical form error [J]. Precision Engineering. 2000,24:119-126.

DOI: 10.1016/s0141-6359(99)00035-5

[2] K.C. Fan, J.C. Lee. Analysis of minimum zone sphericity error using minimum potential energy theory[J]. Precision Engineering,1999,23:65-72.

DOI: 10.1016/s0141-6359(98)00024-5

[3] G.L. Samuel, M.S. Shunmugam. Evaluation of sphericity error from coordinate measurement data using computational geometric techniques[J]. Computer Methods in Applied Mechanics and Engineering. 2001,190:6765-6781.

DOI: 10.1016/s0045-7825(01)00220-1

[4] F. Liu, X.N. Peng. Evaluation of sphericity error by using minimum circumscribed sphere [J]. Journal of Mechanical Engineering. 2009,45( 9):243-248.(In Chinese).

DOI: 10.3901/jme.2009.09.243

[5] X. Yu, M.F. Huang, P. Xia, et, al. Sphericity error evaluation based on an improved particle swarm optimization[J]. Computer Systems and Applications.2009,18(12):201-203. (In Chinese).

[6] X.L. Wen, A.G. Song. An immune evolutionary algorithm for sphericity error evaluation [J]. International Journal of Machine Tools and Manufacture, 2004,44:1077-1084.

DOI: 10.1016/j.ijmachtools.2004.02.018

[7] Kanada T. Evaluation of spherical from errors –computation of sphericity by means of minimum zone method and some examinations with using simulated data [J]. Prec Eng, 1995,17(4):281-289.

DOI: 10.1016/0141-6359(95)00017-8

[8] G.L. Samuel, M.S. Shunmugam. Evaluation of sphericity error from data using computational geometric techniques [J]. International Journal of Machine Tools and Manufacture. 2002,42:405-416.

DOI: 10.1016/s0890-6955(01)00124-9

[9] H.P. Zeng, F.W. Wang, Hui Zhang, et, al. New method of pneumatic measurement for sphere Diameter and sphericity-errors [J]. Metrology and Measurement Technique. 2010,30:32-33. (In Chinese).

[10] X.G. Yang, Y.M. Huang. Study on Assessing Criteria and High-Precision Evaluating Method of Detection Errors for 3D Probe [J]. Acta Metrologica Sinlca.2008,7,29(3):207-210. (In Chinese).