Generalized kinematic modeling of wall thickness error in mirror milling considering mirror geometric constraints based on screw theory

Abstract

The mirror milling system ensures wall thickness accuracy by synchronously coordinating the movements of both the milling and support sides, along with precise control of their relative distance. However, the ideal mirror geometric constraints cannot be consistently maintained by the tool and support head due to various errors. Therefore, the wall thickness error model for mirror milling is crucial for controlling the precision of wall thickness. In this study, a generalized kinematic model of wall thickness error in mirror milling based on screw theory was established. The constraints of mirror milling and errors in the motion axes were analyzed. The motion chains of both the milling and support sides were described based on the screw theory. The kinematic models of nominal and actual wall thickness were established respectively. The generalized kinematic wall thickness error model was obtained by subtracting the above two models. The model’s validity was verified through a horizontal dual four-axis MMS and a hybrid vertical dual five-axis MMS. The key errors were calculated using the Sobol sensitivity analysis method. Finally, the application prospects of the generalized kinematic model in improving the machining accuracy of thin-walled parts were discussed.