Baseline Uncertainty in Geometric Tolerance Inspection by Coordinate Measuring Machines: the Case of Position Tolerance with Maximum Material Condition

The paper concerns the analysis and the design of the measurement process by which position tolerances on mechanical parts are checked by Coordinate Measuring Machines (CMM). This measurement process is widely used in industry and conditions the good functioning of millions of components, assemblies and systems. CMMs inspect parts by exploring their surface at a small number of points and return the point Cartesian coordinates. Then data are numerically elaborated to estimate the position error. The analysis aims to evaluate measurement uncertainty as generated by two sources: the random error related to coordinate retrieval and the sampling error inherent to the way CMMs operate. By simulating random error via computer, the measurement process is fully recreated by a simulation model. Then an extensive computer experimentation, combining Montecarlo simulation and DOE, is performed. The study has revealed interesting statistical properties of the two-dimensional position error, which have useful practical implications. Another contribution of the paper is the use of the uncertainty analysis to design an efficient measurement process, namely one that attains a good trade-off between cost and accuracy. For a given total number of measurement points, their optimal allocation on the different part surfaces is provided.