Assessing Circularity in Three Dimensions¹

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.