Dimensional Measurement Data Analysis, Part 1: A Zone Fitting Algorithm

Measured data taken from Coordinate Measuring Machines (CMMs) are in the form of Cartesian coordinates of points from a part surface. In order to interpret the data, a numerical analysis must be performed on them. Currently, data fitting techniques such as a least squares fit or a min-max fit are employed to compare the measured points to the design model. As the objectives of the various techniques differ, they often yield conflicting results. Since this discrepancy may lead to a different conclusions in the process dimensional inspection, it is critical that inspection procedures are based on well defined criteria that employ the appropriate technique to achieve the desired inspection goals. If tolerances are represented by tolerance zones, a zone fitting algorithm, introduced in this paper, provides a more consistent means of verify conformance to the tolerance zone. It determines whether a set of measured points fits into a specified tolerance zone. If the point set can fit into the zone, a rigid body transformation placing the points inside the zone is returned. The algorithm is numerically stable and addresses a general type of tolerance zone. The examples demonstrate that the zone fitting algorithm is more consistent compared to the least squares fit and the min-max fit in tolerance zone conformance verification. A subsequent paper (Part 2) addresses the determination of a minimum zone that extends inspection from a pass/fail mode to a quality analysis operation.