Estimation and correction of geometric errors of two-dimensional moving structures of coordinate measuring machines

This study presents a novel approach for the estimation and correction of geometric errors in twodimensional motion systems of coordinate measuring machines using the principles of differential geometry. Geometric errors are understood as the result of coordinate transformations between machine-measured (digital) and actual coordinates, described by the Jacobian matrix. The proposed method involves determining the components of the Jacobian matrix based on positional errors, deviations from straightness, angular deviations, and deviations from the mutual perpendicularity of the axes, measured using a Renishaw XL-80 laser interferometer. The correction model integrates error maps, numerical derivatives and integrals, and a moving average filter to minimize random noise. This method was experimentally validated on a computerized universal measuring microscope (UIM-21). The results of the end measure of length measurements before and after correction revealed significant reductions in data dispersion and the elimination of outliers, confirming improved measurement reliability. The approach offers practical advantages, including reduced calibration time, lower costs, and adaptability to various coordinate measuring machines configurations. The developed model enhances in-plane measurement accuracy and provides a foundation for applying differential geometry-based corrections to more complex multi-axis measuring systems.

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