Allocation of geometrical errors for developing precision measurement machine

A high-precision measurement machine tool faces the challenge of correlating the overall motion accuracy with the components form and positional accuracy. This study presents an innovative method for addressing this issue in ultra-precision measuring machines. A geometric error model based on multibody theory, and a weight model are established to predict measurement results and correlate overall motion accuracy with individual component accuracy. To validate the model, a target overall motion accuracy of 100 nm is set and the all the individual components accuracy is calculated by the geometric error weights derived from the proposed model. By fabricating a critical component, the linear guideway, to meet specific individual accuracies and incorporating it in an ultra-precise measurement machine, the study demonstrates achieving the individual accuracies with the magnetorheological polishing. Finally, the overall motion accuracy is validated by a cross test among the designed machine, DUI profilometer, and Zygo interferometer. By measuring a same optical surface, the measurement results show the surface PV differences better than 100 nm. The results demonstrate the validation of the correlation between overall motion accuracy and component accuracy established by the method described in this paper. In conclusion, this study offers an accurate design solution for determining overall motion and individual accuracies, enabling high accuracy in intelligent manufacturing equipment.