Kinematics and error modeling for micro-structure grinding on cylindrical-coordinate TTG

The fabrication of micro-structures on complex surfaces requires multi-axis linkage with continuously varying tool posture, making the machining accuracy highly sensitive to geometric error propagation. Such challenges become more significant in cylindrical-coordinate machine tools with rotation-dominated kinematic structures due to the strong coupling among rotational axes, translational axes, and posture-dependent error amplification. To address these challenges, this study establishes an integrated framework combining actual kinematic modeling, geometric error propagation, global sensitivity evaluation, and experimental validation using a twin-turret generator (TTG) machine tool. Based on the nominal kinematic model of the TTG, an actual kinematic model considering geometric error sources is established to analyze the trajectory-dependent propagation of geometric errors during micro-grinding processes, while a Sobol-sequence-based global sensitivity analysis is employed to quantify the influence of individual geometric error sources. The results reveal that geometric error sensitivity is governed not only by the workspace position but also by the selected machining configuration. For the same micro-structure array, different inverse kinematic solutions produce distinct coordinated axis motions, resulting in different geometric error propagation paths, dominant error contributors, and sensitivity distributions. These findings demonstrate that machining configuration provides an additional degree of freedom for geometric error control. Micro-grinding experiments on planar and spherical micro-structured surfaces show good agreement between the predicted spatial error distributions and the experimentally observed machining characteristics, with the coefficient of determination (R²) of the machining accuracy prediction model improving from 0.148 to 0.491 after incorporating geometric errors. The proposed framework provides an effective tool for configuration-aware machining accuracy evaluation and offers practical guidance for machining configuration selection, machine calibration, and precision-oriented process planning in cylindrical-coordinate machine tools.