Simple and efficient algorithms for roundness evaluation from the coordinate measurement data

Abstract A common problem of quality control and inspection of circular parts is the measurement of their roundness. Recently, the coordinate measuring machines (CMMs) have been used to measure roundness errors by collecting a large number of points from the profile of the rounded parts to meet the international standards. Direct evaluation of roundness from this large number of pointes is complex and time consuming. Therefore, efficient algorithms should be designed to meet the standards and to simplify and accelerate the computation process. This paper introduces simple and efficient algorithms to evaluate the roundness error from the large number of points obtained by CMMs using three internationally defined methods: Minimum Circumscribed Circle (MCC), Maximum Inscribed Circle (MIC) and Minimum Zone Circles (MZC). A software has been developed using C++ to apply these algorithms on the data obtained by CMMs. The developed algorithms were verified by comparing their results with the results obtained by a commercial instrument and the maximum variation between the two results did not exceed than ±2.27%. The efficiency of the introduced algorithms was verified in terms of computation time and the results proved the efficiency of the developed algorithms.

[1]  H. Ding,et al.  A unified approach for circularity and spatial straightness evaluation using semi-definite programming , 2007 .

[2]  F. P. Preparata,et al.  Convex hulls of finite sets of points in two and three dimensions , 1977, CACM.

[3]  M. S. Shunmugam,et al.  Evaluation of form data using computational geometric techniques—Part I: Circularity error , 2007 .

[4]  Jyunping Huang,et al.  A new strategy for circularity problems , 2001 .

[5]  Utpal Roy,et al.  Establishment of a pair of concentric circles with the minimum radial separation for assessing roundness error , 1992, Comput. Aided Des..

[6]  D G Chetwynd,et al.  Applications of Linear Programming to Engineering Metrology , 1985 .

[7]  H. Chang,et al.  Evaluation of circularity tolerance using Monte Carlo simulation for coordinate measuring machine , 1993 .

[8]  T.S.R. Murthy,et al.  Minimum zone evaluation of surfaces , 1980 .

[9]  M. S. Shunmugam,et al.  Evaluation of circularity from coordinate and form data using computational geometric techniques , 2000 .

[10]  Ronald L. Graham,et al.  An Efficient Algorithm for Determining the Convex Hull of a Finite Planar Set , 1972, Inf. Process. Lett..

[11]  M. S. Shunmugam,et al.  Evaluation of circularity and sphericity from coordinate measurement data , 2003 .

[12]  Xiulan Wen,et al.  An effective genetic algorithm for circularity error unified evaluation , 2006 .

[13]  Hsien-Yu Tseng,et al.  A stochastic optimization approach for roundness measurement , 1999, Pattern Recognit. Lett..

[14]  M. S. Shunmugam,et al.  Criteria for Computer-Aided Form Evaluation , 1991 .

[15]  Wen-Yuh Jywe,et al.  The min–max problem for evaluating the form error of a circle , 1999 .

[16]  Shi Zhaoyao,et al.  Development and application of convex hull in the assessment of roundness error , 2008 .

[17]  Jyunping Huang,et al.  An exact solution for the roundness evaluation problems , 1999 .

[18]  Utpal Roy,et al.  Development and application of Voronoi diagrams in the assessment of roundness error in an industrial environment , 1994 .

[19]  P. B. Dhanish,et al.  A simple algorithm for evaluation of minimum zone circularity error from coordinate data , 2002 .

[20]  M. S. Shunmugam,et al.  On assessment of geometric errors , 1986 .

[21]  O. Novaski,et al.  Utilization of voronoi diagrams for circularity algorithms , 1997 .