A Best-Fit Method to Maximize Conformance to Tolerance in Surface Coordinate Metrology

Abstract

This article discusses that the deviation zone of a profile cannot be computed only by using the Euclidian distances of the discrete measured points from substitute geometry and without considering the desired tolerance zone of the profile. The importance of considering the desired tolerance zone in estimating the optimum deviation zone is demonstrated, and a best-fit method is presented which complies with the tolerance requirements of the designed surface. A customized version of this fitting method is presented, which constructs a substitute geometry to minimize the residual deviations corresponding to the given tolerance zone and the need for additional manufacturing operations to correct the measured surface. It is shown how the developed objective function can be adopted in the case of a closed-loop manufacturing process, when the undercut residual deviations of the manufactured part can be corrected by a downstream operation. To validate the proposed methodology, a variety of experiments are conducted, the results of which show a significant reduction of uncertainties in coordinate metrology of geometric surfaces. Implementation of this method results in the increased accuracy of the entire tolerance-evaluation (Equation 1) The difference between the two points inside the norm bracket indicates the Euclidian distance from the point p′ and the substitute geometry, G′′. The corresponding point, p′′, is the point on the substitute geometry with a minimum Euclidian distance