Sphericity measurement through a new minimum zone algorithm with error compensation of point coordinates

摘要

Sphericity is a relevant tolerance of form in many fields of engineering. Measuring sphericity is frequently accomplished through the fitting of the point coordinates obtained from coordinate measuring machines (CMMs) to a substitution sphere. This paper presents a new algorithm for sphericity of minimum zone tolerance. It faces its resolution through the flatness problem associated with the implicit formulation of the polar plane of the sphere. The polarity transformation allows the iterative resolution of the minimum zone sphericity through a simpler flatness problem. Its accuracy is compared with the least-squares solution and some well-known minimum zone algorithms from literature. Its performance reaches or surpasses them. Next, a new error compensation model of point coordinates for sphericity is developed. A model based on the regression of the error by each CMM axis is incorporated into the sphericity measurement model. The explained error propagated allows correcting the sphericity calculated by the CMM indication, but also facilitates the uncertainty estimation by the propagation of the unexplained residual error in the regression through the measurement model. The experimental verification by the Monte Carlo Method shows efficient results. The jointly proposed method of a new algorithm with error compensation and uncertainty estimation can effectively contribute to the improvement of sphericity measurement from point coordinates in precision and accuracy. (C) 2019 Elsevier Ltd. All rights reserved.