A novel sensitivity analysis method for geometric errors in precision lathes based on variance decomposition and partial derivative integration

Precision machine tools are influenced by geometric errors during the machining process, making the accurate identification of key geometric error terms essential for effective workpiece compensation and improved machining accuracy. However, current sensitivity analysis methods often overlook the interactions between high-order error terms, leading to inadequate efficiency and accuracy in error compensation. To address this issue, this paper proposes the VPM sensitivity analysis method, which is based on variance decomposition and partial derivative integration, considering the coupling effects of high-order geometric error terms. First, the volumetric error model of the tool-workpiece system in precision lathes was established using multi-body system theory and homogeneous coordinate transformation. Then, the VPM sensitivity analysis method was introduced, and a new sensitivity index N_i was defined. Based on the volumetric error model, Sobol and VPM sensitivity analysis were performed in different directions. Taking a cylindrical workpiece as an example, a turning test was carried out on a precision lathe. The results demonstrate that, compared to the traditional Sobol sensitivity analysis method, the proposed VPM sensitivity analysis method achieves superior convergence accuracy and enhances the roundness of the workpiece by 36.7 %, thus verifying the effectiveness of the method.