Key geometric error identification method for ultra precision machine tool based on error-position-dependent sensitivity analysis

The geometric errors of ultra-precision machine tools have a significant impact on the contour accuracy and surface quality of optical components. Due to the diversity and coupling of geometric error sources, the decoupling and propagation mechanisms of the comprehensive errors become highly complex. Sensitivity analysis (SA) is a widely adopted quantitative tool for evaluating the relative contributions of error sources and identifying the key errors. However, conventional SA methods typically assume a constant error range across the entire workspace, thereby neglecting the position-dependent characteristics of specific geometric errors. To fill this gap, this study proposes a key geometric error identification method based on an error-position-dependent sensitivity analysis (EPDSA), which dynamically adjusts the input ranges of geometric errors according to their positions and calculates sensitivity indices across the entire workspace. The experimental results demonstrate that the proposed method effectively captures pronounced spatial variations in sensitivity indices, leading to distinct key error identifications compared with conventional methods. The key error ratio (KER) further indicates that the key errors identified by EPDSA account for a larger proportion of the total error, 0.55 compared with 0.39 for the conventional method, thereby enabling more accurate and reliable sensitivity evaluation and offering targeted guidance for error compensation in ultra-precision machine tools.