Geometric Error Calibration in Machine Tools: Error Separation Using Data Redundancy and Numerical Optimization

Abstract

Despite the high level of sophistication of machine tools, they are still subject to geometric errors arising from various sources, which directly affect the dimensional accuracy of machined parts. Given the limitations of traditional calibration methods, such as high cost, time consumption, and complexity, this study proposes and applies an alternative method based on error separation for geometric evaluation in a three-axis CNC machining center, demonstrating its practical feasibility. Using a slender 1045 steel artifact and a pair of LVDT sensors with a resolution of 0.0001 mm, measurements were performed in six different setups, with the instruments and artifact fixed to the machine structure. The mathematical model developed has a sparse matrix structure and was solved numerically using the LSQR algorithm, reaching satisfactory convergence in 130 iterations. The straightness profiles obtained through the proposed method were compared to measurements taken with a CMM, showing agreement. The analysis of angular and linear errors allowed the identification of a critical region at 320 mm along the y-axis, where the largest deviations occur, indicating points for applying numerical compensation or mechanical adjustments. The method stood out for enabling the mathematical removal of errors and reconstruction of the artifact's profile, as well as for its ability to locate and quantify geometric errors in regions crucial for defining the cutting height of the tool. The modeling and algorithm used allow for precise results with low computational cost. Thus, the study presents significant potential for calibration and predictive maintenance of machine tools, providing technical information for decisions on error compensation and quality improvement in the machining process.