Application of the adaptive Monte Carlo method in a five-axis machine tool calibration uncertainty estimation including the thermal behavior

Calibration of the geometry of five-axis machine tools needs to be performed periodically since the machine accuracy has a direct impact on machined parts. Because mechanical adjustment and a software correction may be done using calibration results, the measurement results must be evaluated. In this paper, the scale and master ball artefact (SAMBA) method is evaluated through the estimation of the uncertainty of the identified machine geometric error parameters. This approach has the multi-input multi-output (MIMO) model and an iterative solution that makes it challenging to apply commonly used uncertainty calculation methods The Guide to the Expression of Uncertainty in Measurement Supplement 2 (GUM S2) gives the opportunity to estimate the uncertainty of a MIMO model through the adaptive Monte Carlo method (MCM). In order to include all the uncertainty sources, the input uncertainty is estimated from the repeated calibration tests performed in different thermal conditions (with and without the warm-up cycle). The uncertainty is calculated for each of the identified machine geometric error parameters along with their covariance. The correlation between the output variables and the impact of the machine state, before and during the repeated calibration, are analyzed. The results demonstrate that the machine tool geometry variations occur even without the warm-up cycle performed before the calibration. Moreover, machine performance has an impact the calibration results.