Standardization of CMM fitting algorithms and development of inspection maps for use in Statistical Process Control

The choice of fitting algorithm in CMM metrology has often been based on mathematical convenience rather than the fundamental GD&T principles dictated by the ASME Y14.5 standard. Algorithms based on the least squares technique are mostly used for GD&T inspection and this wrong choice of fitting algorithm results in errors that are often overlooked and leads to deficiency in the inspection process. The efforts by organizations such as NIST and NPL and many other researchers to evaluate commercial CMM software were concerned with the mathematical correctness of the algorithms and developing efficient and intelligent methods to overcome the inherent difficulties associated with the mathematics of these algorithms. None of these works evaluate the ramifications of the choice of a particular fitting algorithm for a particular tolerance type. To illustrate the errors that can arise out of a wrong choice of fitting algorithm, a case study was done on a simple prismatic part with intentional variations and the algorithms that were employed in the software were reverse engineered. Based on the results of the experiments, a standardization of fitting algorithms is proposed in light of the definition provided in the standard and an interpretation of manual inspection methods. The standardized fitting algorithms developed for substitute feature fitting are then used to develop Inspection maps (i-Maps) for size, orientation and form tolerances that apply to planar feature types. A methodology for Statistical Process Control (SPC) using these i-Maps is developed by fitting the i-Maps for a batch of parts into the parent Tolerance Maps (T-Maps).Different methods of computing the i-Maps for a batch are explored such as the mean, standard deviations, computing the convex hull and doing a principal component analysis of the distribution of the individual parts. The control limits for the process and the SPC and process capability metrics are computed from inspection samples and the resulting i-Maps. Thus, a framework for statistical control of the manufacturing process is developed.