Year-Round Thermal Error Modeling and Compensation for the Spindle of Machine Tools Based on Ambient Temperature Intervals

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.