Robustness of thermal error compensation modeling models of CNC machine tools

In order to achieve effective control of thermal error compensation of computer numerical control (CNC) machine tools, the prediction accuracy and robustness of the compensation model is particularly important. In this paper, the temperature of sensitive points and thermal error of the spindle in Z direction are measured. Using a combination of fuzzy clustering analysis and gray correlation method to select temperature-sensitive points and then using multiple linear regression of least squares and least absolute estimation methods, distributed lag model, and support vector regression machine to establish prediction models of the relationship between temperature of sensitive points and the thermal error. Also, the temperature values of sensitive points and the thermal error in the experimental conditions of different ambient temperatures and different spindle speeds are measured. By comparing the prediction accuracy of various prediction models under different experimental conditions verify the robustness of the models. Experimental results show that when the modeling data are less, the prediction accuracy of multiple linear regression of least squares and least absolute estimation methods and distributed lag model is declined, and their robustness are poor, while support vector regression model has good prediction accuracy and its robustness remains strong when changing the experimental conditions. However, when modeling data are rich, the prediction accuracy of various algorithms is improved, but the robustness of support vector regression model is volatile. The robustness analysis of different models provides a useful reference for the thermal error compensation model, selection of CNC machine tools, and has good engineering applications.