Assessing Circularity in Three Dimensions1

Abstract

This research resolves an inconsistency problem that arises from assessing circularity of workpiece measured by coordinate measuring machines (CMMs). Although the notion of circularity is employed to constrain two-dimensional circular features, in practice the measured points are obtained in a three-dimensional space and are in general not in the same plane, let alone being in a “perpendicular” cross-section. All of the algorithms currently used for assessing circularity deal with data in a single plane that is perpendicular to the axis of a cylindrical feature from which the circular feature is extracted. This discrepancy causes the assessed circularity significantly departing from the actual circularity and resulting in rejection of in-tolerance parts. This research designs a compensation procedure for deriving two-dimensional data from three-dimensional biased measured points. The circularity is assessed based on the compensated two-dimensional data points. The assessment results with the compensation are compared with those without compensation. A program containing a variety of implementations of form fitting algorithms is developed and used to illustrate the improvement on the accuracy of assessment.