Development of a library of feature fitting algorithms for CMMs

Abstract

Conformance of a manufactured feature to the applied geometric tolerances is done by analyzing the point cloud that is measured on the feature. To that end, a geometric feature is fitted to the point cloud and the results are assessed to see whether the fitted feature lies within the specified tolerance limits or not. Coordinate Measuring Machines (CMMs) use feature fitting algorithms that incorporate least square estimates as a basis for obtaining minimum, maximum, and zone fits. However, it is well known that results obtained from different vendors for the same data set often do not agree. This may be because of different interpretations of the GD&T standards, or the use of least squares algorithms as the basis for all fitting. Therefore, a reference or normative comprehensive library of algorithms addressing the fitting procedure (all datums, targets) for every tolerance class is needed. The library is specific to feature fitting for tolerance verification. This paper addresses linear, planar, circular, and cylindrical features only. This set of algorithms described conforms to the international Standards for GD&T. In order to reduce the number of points to be analyzed, and to identify the possible candidate points for linear, circular and planar features, 2D and 3D convex hulls are used. For minimum, maximum, and Chebyshev cylinders, geometric search algorithms are used. Algorithms are divided into three major categories: least square, unconstrained, and constrained fits.