LASSO based compensation method for geometric errors of large coordinate measuring machine

Abstract

The quasi-rigid body model is the relationship model between the volume error and the geometric error of the CMM under the consideration of simple deformation. The quasi-rigid body model reflects the comprehensive influence of all geometric errors and ensures the calibration accuracy of geometric errors. However, the geometric error solution based on the quasi-rigid body model has the problem of multicollinearity. To solve this problem, in this study, the geometric errors of CMM are compensated using laser tracing multistation measurement technology and the LASSO (Least absolute shrinkage and selection operator, LASSO) algorithm. First, a laser tracing multi-station measurement model is established, and then the coordinates of the laser tracer station are obtained by solving the redundant equations provided by the laser tracer multi-station measurement system using the L-M (Levenberg Marquardt) algorithm. The global positioning system localization principle combined with the L-M algorithm is used to determine the actual position of the CMM measurement point. Then, the volume error is determined by calculating the difference between the actual position of the measurement point and the planned position. A mathematical model of the volumetric and geometric errors is obtained from the CMM quasi-rigid body model, and the LASSO algorithm is used to solve the model to obtain the 17 geometric errors of the CMM. Using the relationship between the volume error and the uniaxial geometric error, the 4 rotational errors are solved of εz (x), εx- (z), εv (z), εz (z). To verify the measurement accuracy of the compensated CMM, the compensation effect is verified by using the XL80 interferometer with the measuring block. The experimental results indicate that when error compensation is performed, the measurement accuracy of the CMM is improved by >50% compared to the initial state, and no mechanical processing is involved.