Evaluation of measurement uncertainty in H-drive stage during high acceleration based on Monte Carlo method

• An error propagation model is proposed to estimate uncertainty of H-drive stage.
• Monte Carlo method is used to analyze uncertainty of H-drive stage.
• The error propagation model can be used in error budget and compensation.

This paper presents an integrated error propagation analysis method to estimate the measurement uncertainty using Monte Carlo method in order to analyze the measurement accuracy of an H-drive stage with air bearing during high acceleration subjected to the influence of a variety of errors, including straightness errors, thermal errors, deformation errors and air bearing gap change errors caused by acceleration force. Firstly, the integrated error propagation model of an H-drive stage is built combined with the effects of the various error sources based on the multi-body system and instrument precision theory. Then these errors are identified by experiments and finite element analysis and the influence of each error in six degrees of freedom displacement is obtained. Finally, the displacement measurement uncertainty of the stage in the reference coordinate system is evaluated by Monte Carlo method, within 95% probability, the displacement measurement results and the expanded uncertainty in x and y directions are calculated x=(165.000±0.064) mm and y=(195.000±0.054) mm respectively. The proposed method can be used in the error budget of precise machine design and applied in error compensation to improve the measurement and control accuracy of precise machine workpiece stage.