Assessing circularity in three dimensions

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 spare and are in general nor in the same plane, let alone bein g in a "perpendicular" cross-section. All of the algorithms currently used for assessing circularity deal with data in a single plane that is perpendi cular to the axis of a cylindrical feature from which the circular feature is extracted. This discrepancy causes the assessed circularity significantl y departing from the actual circularity and resulting in rejection of in-to lerance parts. This research designs a compensation procedure for deriving two-dimensional data from three-dimensional biased measured points. The cir cularity is assessed based on the compensated two-dimensional data points. The assessment results with the compensation are compared with those withou t compensation. A program containing a variety of implementations of form f itting algorithms is developed and used to illustrate the improvement on th e accuracy of assessment.