CMM Influence Factors and Uncertainty Associated with Length Measurement

This paper is concerned with coordinate measuring machine (CMM) uncertainty evaluation, in particular, the uncertainties associated with point clouds and distances derived from the point cloud. The uncertainty evaluation approach is model-based following the principles of the Guide to the Expression of Uncertainty in Measurement and the law of the propagation of uncertainty. The paper considers a range of CMM influence factors and derives an explicit dependence for the point cloud data coordinates on the influence factors, allowing uncertainties associated with the influence factors to be propagated through to point cloud uncertainties. The paper describes the use of Gaussian processes to model kinematic and probing errors using a small number of statistical hyper-parameters. These models permit an explicit statement of the uncertainty associated with point clouds and length measurement, enabling the latter to be compared directly with a statement of the maximum permissible error in length measurement. The uncertainty evaluation methodology is direct in that it requires no optimisation nor Monte Carlo simulations.