Simulative methods are nowadays frequently used in metrology for the simulation of measurement uncertainty and the prediction of errors that may occur during measurements. In coordinate metrology, such methods are primarily used with the typical three-axis Coordinate Measuring Machines (CMMs), and lately, also with mobile measuring systems. However, no similar simulative models have been developed for five-axis systems in spite of their growing popularity in recent years. This paper presents the numerical model of probe head errors for probe heads that are used in five-axis coordinate systems. The model is based on measurements of material standards (standard ring) and the use of the Monte Carlo method combined with select interpolation methods. The developed model may be used in conjunction with one of the known models of CMM kinematic errors to form a virtual model of a five-axis coordinate system. In addition, the developed methodology allows for the correction of identified probe head errors, thus improving measurement accuracy. Subsequent verification tests prove the correct functioning of the presented model.

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Five-axis measuring systems (i.e. coordinate measuring machines equipped with articulated probe heads capable of continuous indexation or five-axis machine tools with inspection probe mounted on a tilt and swivel head) are becoming more and more popular, especially in industrial applications, since their usage speeds up the measurement process without significant loss in accuracy. Widespread adoption of these systems necessitates development of viable and easy-to-use measurement uncertainty estimation methods. This paper describes the experiments required for identification of errors of five-axis measuring systems based on usage of LasrTracer system and measurements of ring standard. It also expounds the methodology for implementation of virtual CMM-based simulation model for these systems giving the explanation on all input quantities used in the model along with detailed mathematical explanations on uncertainty propagation procedure. Eventually, it presents the validation methodology and the results of validation measurements performed in order to prove the correct functioning of developed model. Basing on these results, the main conclusion drawn in the paper is that presented virtual model should be regarded as working properly and producing metrologically correct values of measurement uncertainty for common metrological tasks known from GD&T framework.

The following article examines the methodology of identifying and modeling kinematic errors of coordinate measuring machines with the use of a modern and precise interferometric system-the LaserTracer. Since the kinematic errors of coordinate measuring machines (CMMs) are by far the most prevalent factor in measurement uncertainty, a specially developed model could be used for efficient uncertainty evaluation as an additional module of the virtual measuring machine responsible for simulation of the CMM kinematic errors. The model could also be of use for determining optimal measurement strategy, and would potentially improve the uncertainty of measurements performed.