Use of a Virtual Polyhedron for Interim Checking of the Volumetric and Geometric Errors of Machine Tools

Volumetric and geometric errors should be periodically checked to ensure that the accuracy of machine tools remains within the tolerable range. However, existing methods require complex devices, and are thus unsuitable for cost-effective interim error checks. We present a simple, rapid and cost-effective method for interim error checks. The measurement paths are constructed using a virtual polyhedron; volumetric errors are checked by calculating the coordinates of the vertices using the measured side lengths. The tool is sequentially moved to each vertex, and the side lengths are measured using a double ball-bar. As the virtual polyhedron is composed of virtual regular tetrahedrons, the relationships between the coordinates of the vertices and side lengths are unique. Linear scale and squareness errors are measured using an error synthesis model with a least-squares approach. The method was applied to a real machine tool, and performance was verified by confirming that the maximum L² norm of volumetric error is improved from 57.6 to 32.8 μm after compensating for the measured geometric errors. Thus, the validity of the proposed method was confirmed by an improvement of 43% in volumetric error. The measurement results were confirmed by the circular tests of ISO 230-4; the peak-to-valley radial deviation improved from 16.0 to 11.2 μm after compensation, and the proposed method contributed to a 30% improvement in the radial deviation.