Thermal errors significantly affect the accurate performance of computer numerical control (CNC) machine tools. In this paper, an improved robust thermal error prediction approach is proposed for CNC machine tools based on the adaptive Least Absolute Shrinkage and Selection Operator (LASSO) and eXtreme Gradient Boosting (XGBoost) algorithms. Specifically, the adaptive LASSO method enjoys the oracle property of selecting temperature-sensitive variables. After the temperature-sensitive variable selection, the XGBoost algorithm is further adopted to model and predict thermal errors. Since the XGBoost algorithm is decision tree based, it has natural advantages to address the multicollinearity and provide interpretable results. Furthermore, based on the experimental data from the Vcenter-55 type 3-axis vertical machining center, the proposed algorithm is compared with benchmark methods to demonstrate its superior performance on prediction accuracy with 7.05 $\mathsf{\mu }\mathrm{m}$ (over 14.5% improvement), robustness with 5.61 $\mathsf{\mu }\mathrm{m}$ (over 12.9% improvement), worst-case scenario predictions with 16.49 $\mathsf{\mu }\mathrm{m}$ (over 25.0% improvement), and percentage errors with 13.33% (over 10.7% improvement). Finally, the real-world applicability of the proposed model is verified through thermal error compensation experiments.

Establishing a mathematical model to predict and compensate for the thermal error of CNC machine tools is a commonly used approach. Most existing methods, especially those based on deep learning algorithms, have complicated models that need huge amounts of training data and lack interpretability. Therefore, this paper proposes a regularized regression algorithm for thermal error modeling, which has a simple structure that can be easily implemented in practice and has good interpretability. In addition, automatic temperature-sensitive variable selection is realized. Specifically, the least absolute regression method combined with two regularization techniques is used to establish the thermal error prediction model. The prediction effects are compared with state-of-the-art algorithms, including deep-learning-based algorithms. Comparison of the results shows that the proposed method has the best prediction accuracy and robustness. Finally, compensation experiments with the established model are conducted and prove the effectiveness of the proposed modeling method.

The modeling and compensation method is a common method for reducing the influence of thermal error on the accuracy of machine tools. The prediction accuracy and robustness of the thermal error model are two key performance measures for evaluating the compensation effect. However, it is difficult to maintain the prediction accuracy and robustness at the desired level when the ambient temperature exhibits strong seasonal variations. Therefore, a year-round thermal error modeling and compensation method for the spindle of machine tools based on ambient temperature intervals (ATIs) is proposed in this paper. First, the ATIs applicable to the thermal error prediction models (TEPMs) under different ambient temperatures are investigated, where the C-Means clustering algorithm is utilized to determine ATIs. Furthermore, the prediction effect of different numbers of ATIs is analyzed to obtain the optimal number of ATIs. Then, the TEPMs corresponding to different ATIs in the annual ambient temperature range are established. Finally, the established TEPMs of ATIs are used to predict the experimental data of the entire year, and the prediction accuracy and robustness of the proposed ATI model are analyzed and compared with those of the low and high ambient temperature models. The prediction accuracies of the ATI model are 20.6% and 41.7% higher than those of the low and high ambient temperature models, respectively, and the robustness is improved by 48.8% and 62.0%, respectively. This indicates that the proposed ATI method can achieve high prediction accuracy and robustness regardless of the seasonal temperature variations throughout the year.