Rigid-flexible coupling error modeling of large gantry machine tools based on potential energy analysis

A B S T R A C T Large gantry machine tools exhibit large dimensions, large mass, and high structural flexibility and are typically equipped with mechanically coupled dual-axis drive systems. During kinematic calibration, geometric errors and gravity-induced deformation are strongly coupled, limiting further improvement in absolute accuracy. This study proposes a rigid-flexible modeling method for large gantry machine tools. Based on mechanical analysis and error theory, the coupling relationship between the gravity-induced deformation errors and internal stress deformation under statically indeterminate conditions is derived, and a rigid-flexible coupling model (RFCM) is established. Kinematic calibration experiments using an XM-60 laser interferometer demonstrate a 50%–70% improvement in body diagonal positional accuracy. Moreover, the average positioning error after compensation decreases from 0.022–0.037 mm to 0.002–0.010 mm, the maximum error reduces from 0.024–0.044 mm to 0.0057–0.017 mm, and the root mean square error reduces from 0.032 mm to 0.007 mm, thereby verifying the effectiveness of the proposed method.