Comparative study of roundness evaluation algorithms for coordinate measurement and form data

Abstract

Roundness error is one of the significant parameters used in quality analysis and control of circular or cylindrical components. In both laboratories and industries, direct estimation of roundness error is predominantly obtained using the coordinate measuring machine and form testing device. The literature is copiously supplied with different approaches/algorithms for the implementation of the reference circles that are used to quantify roundness error. A test for their relative performance is of relevance in order to make a decision about which approach is to be used for the execution of a given reference circle. This paper replicates and compares a few selected benchmark algorithms from literature to make recommendations for the optimum choice of execution methods for Minimum Circumscribed Circle (MCC), Maximum Inscribed Circle (MIC) and Minimum Zone Circle (MZC) that are used to compute roundness error. A new computational geometric concept using reflection mapping technique was formulated to assess roundness using MIC and MZC, which has also been used in the comparison. All the algorithms were tested using the same ten sets of coordinate/profile data to establish their relative efficacy in roundness error computation. It was found that no single computation concept consistently gave the best results for all the three reference circles simultaneously. Thus, the three reference circles have been independently analyzed, and recommendations for the algorithm to be used for each of them have been presented individually.