The accurate estimation of the geometric deviations is not possible only by manipulating the Euclidian distances of the discrete measured points from substitute geometry. The real geometric deviations of a measured surface need to be calculated based on the desired tolerance zone of the surface. This fact is usually neglected in common practices in the coordinate metrology of surfaces. The importance of considering the desired tolerance zone in estimation of the optimum deviation zone is demonstrated in this paper. Then a best fit method is presented which complies with the tolerance requirements of the designed surface. The developed fitting methodology constructs a substitute geometry to minimizes the residual deviations corresponding to the given tolerance zone and the needs of down-stream operations that use the results of the inspection process. It is shown how the developed objective function can be adopted for a case of closed-loop manufacturing process, when the under-cut residual deviations of the manufactured part can be corrected by a down-stream operation. In order to validate the proposed methodology, experiments are conducted. The results show a significant reduction of uncertainties in coordinate metrology of geometric surfaces. Implementation of this method directly results in increasing the accuracy of the entire tolerance evaluation process, and less uncertainty in quality control of the manufactured parts.
Composite mirror shape deviations due to temperature changes