Accuracy improvement of volumetric error modeling in CNC machine tools

Three-axis structures are widely used as the main body of multi-axis CNC machine tools and coordinate measuring machines. As an open-loop mechanism, the cumulative effects of position-dependent/position-independent geometric errors of the moving axes cause significant volumetric deviation of the functional point. Such effect is more tangible for angular error motions, where they can considerably be magnified by long Abbe offsets. An appropriate volumetric error modeling approach should estimate the total effect of individual error motions accurately. Accuracy of the model depends on applied error propagation scheme and correctness of the error identification procedure. In this paper, both issues are investigated in order to enhance the practical validity of the model in presence of rigid-body and steady thermal assumptions. Regarding mechanical design of the sliding system, the linear axes are categorized in two different extruding type and sliding type with different error-mapping functions. Based on the homogeneous transformation matrix method, the overall consequence of error motions of each axis is calculated separately within entire working volume. The new approach explicitly contributes the axis design and structural configuration in error propagation procedure and facilitates the root cause identification for volumetric deviations of the functional point. The modeling scheme is verified experimentally on a three-axis CNC machine tool via comparison of the estimations with measured error values on circular and diagonal tool paths.