Sensitivity analysis of surface contour error to geometric errors for four-axis ultra-precision machine tools

This study first proposes a novel model that mathematically maps the geometric errors of machine tools to freeform surface contour errors. Specifically, leveraging a kinematics-based geometric error model, the actual tool path for machining a freeform surface can be obtained, which deviates from the tool position surface (TPS) based on Non-Uniform B-Spline (NUBS) surface interpolation. The shortest distance from the center point of the tool nose arc to the tool position surface is then used to derive the contour error distribution of the TPS. Then, using this model, the sensitivity of freeform surface contour errors to geometric errors, for different freeform surfaces and machine tool configuration parameters, is calculated through global sensitivity analysis. The results reveal that as the surface slope increases, the number of sensitive geometric error terms rises. Additionally, the more pronounced the non-rotating characteristics of the surface, the higher the sensitivity of ${\theta }_{\mathrm{zc}}$. Moreover, the tool's position on the rotating B-axis influences the B-axis positioning error ${\theta }_{\mathrm{yb}}$. Finally, the compensation experiments based on sensitivity analyses show that the proposed method can significantly decrease the contour error of freeform surfaces by approximately 30.85 %, demonstrating its feasibility and effectiveness in compensating for the sensitive geometric errors identified by the proposed model.