Probability-Theoretical Model for Estimating Measurement Errors of Coordinate Measuring Machines

One of the parameters for determining the quality of manufacturing of coordinate measuring machines (CMM) is the measurement error achieved by using these machines. Obtaining an estimate of measurement error based on practical experiments is a complex task. In this paper, we present a mathematical model of the measurement process on a coordinate measuring machine. The model is implemented on the basis of a dimensional chain and takes into account the influence of the main sources of systematic errors of CMM. Multiple modeling of the measurement process with the reproduction of the probabilistic nature of the errors of CMM forms a cloud of possible measurement results used to obtain the required estimate of the measurement error. The carried out experimental researches have shown influence of such sources of errors on the accuracy of the coordinate measuring machine operation as positioning errors along the measuring axes, their curvature and mutual non-perpendicularity, and the deflection of the measuring probe. The proposed model for estimating the measurement error can be used to select the layout of the measuring machine, which has the best accuracy at a given cost.