Thermal error robust modeling method for CNC machine tools based on a split unbiased estimation algorithm

In the thermal error compensation technology of CNC machine tools, the core issue is to establish a mathematical model of thermal error with high prediction accuracy and strong robustness. The prerequisite for the mathematical model is choosing optimum temperature sensitive points for modeling. Currently, there are many methods that prioritize reducing the collinearity between temperature sensitive points first before considering the influence weights of temperature sensitive points on thermal error. In this paper, we determined that these methods are unable to ensure that all the temperature sensitive points have high influence weights on thermal error through experimental analysis of the thermal error of Leaderway-V450 CNC machine tools in an idle state. This causes volatility in the temperature sensitive points and decreases the prediction accuracy and robustness of the model. In this regard, we present a new thermal error modeling method called the “Gray relation − Split Unbiased Estimation thermal error robust modeling method”, or the “GR-SUE method”. In the “GR-SUE method”, several temperature sensitive points with the highest influence weights on thermal error are selected directly using the gray relation algorithm. However, the gray relation algorithm causes a significant collinearity problem between temperature sensitive points. Therefore, we improve the multiple linear regression algorithm and propose a split unbiased estimation modeling algorithm to inhibit the influence of collinearity on the prediction accuracy and robustness of the model. Finally, the “GR-SUE method” is verified using numerous thermal error experiments of Leaderway-V450 CNC machine tools at an idle state under different rotation speeds and ambient temperatures. The experimental results show that the “GR-SUE method” can significantly reduce the volatility of temperature sensitive points and improve the prediction accuracy and robustness of the model.