A full-covariance uncertainty assessment in on-machine probing

Abstract

Despite the growing use of machine tools for in-process measurement, the uncertainty evaluation of on-machine probing has mostly remained limited to the method specifically developed in ISO 15530-3 for coordinate-measuring machines. These methods reduce the on-machine measurement problem to a single-output system, so that the law of propagation of uncertainty becomes applicable, which excludes any covariance effect between the input quantities. This study proposes a methodology that inclusively estimates the uncertainty associated with any probing within the working space of a five-axis machine tool. Defined by the machine's forward kinematic model, the on-machine measurement function receives the machine geometric errors and the axis positions for a probed point set, and estimates its compensated position in the workpiece frame. The proposed uncertainty estimator assembles the covariance matrices associated with these input quantities and evaluates the measurement uncertainty through an adaptive Monte Carlo method. Unlike the task-specific method given by ISO 15530-3, this scheme eliminates the need for any part's calibrated counterpart and involves the covariance between the input quantities. The experimental verification of the new method includes the on-machine measurement of the length of a gauge block and the diameter and sphericity of a precision sphere through highly diverse axis positions of a five-axis machine tool. Over the 225 possible combinations of 15 point sets (each of size 2) probed on the gauge block, the coverage probability of the expanded uncertainty (for a coverage factor of 2) estimated for the gauge's length is 90%. Then, 10 point sets (each of size 25) collected on the sphere create 10 accumulated pools, and from each, 200 randomly drawn samples estimate the sphere's diameter. The coverage probabilities of the expanded uncertainty estimated for the pools built of up to 7 point sets remain above 94%. These levels of confidence are comparable to the theoretical level (95%).