Identification of inherent position-independent geometric errors for three-axis machine tools using a double ballbar with an extension fixture

This paper presents a double ballbar method with an extension fixture to identify the position-independent geometric errors of three-axis machine tools with respect to their entire workspace by conducting face- and body-diagonal length tests. To extend the length of the double ballbar to the required nominal length in the face- and body-diagonal directions, an extension fixture is designed and manufactured using a fused-deposition-modeling 3D printer to ensure that it is lightweight. Inherent position-independent geometric errors can be calculated from measured lengths by using homogeneous transformation matrices, which are multiplied under the assumption of small values, to determine the volumetric error produced by a machine tool. The relationships between the position-independent geometric errors, roll-pitch-yaw errors, and measured lengths can be derived according to the definition of the straightness errors, based on the end-point of the reference straight line. Finally, the position-independent geometric errors, with analysis of measurement uncertainties, can be identified by substituting the values of the roll-pitch-yaw errors, measured by a multi-axis calibrator, into the derived relations. The results can then be validated by re-measuring the face- and body-diagonal lengths with error compensation. The main advantage of the proposed approach is that it can be used to identify the inherent position-independent geometric errors of machine tool workspaces. This could contribute to reducing volumetric errors in machine-tool workspaces by allowing compensation for measurement errors, thus making machine tools more effective.