Adaptive thermal error prediction for CNC machine tool spindle using online measurement and an improved recursive least square algorithm

Abstract

Establishing models for predicting and compensating for spindle thermal errors is cost-effective and necessary to improve the accuracy of machine tools for smart manufacturing. However, the prediction performance of existing methods deteriorates significantly with dynamic working conditions of machine tools because training from static conditions leads to the inability to adapt to dynamic conditions. Therefore, an adaptive thermal error modeling method using online measurement and an improved recursive least square algorithm is proposed to fill this research gap, which updates the thermal error model adaptively to ensure that dynamic working conditions are learned in real time. Particularly, Spearman's rank correlation coefficient method is first adopted for temperature-sensitive point selection to capture the nonlinear relationship between temperature and thermal error variables. Furthermore, a variable-forgetting factor-based recursive least square (VFF-RLS) algorithm is proposed to improve the prediction performance, in which the proposed variable forgetting factor is adaptively updated according to real-time thermal error data collected by online measurement. The experimental results showed that the proposed VFF-RLS method can maintain a high prediction accuracy of 1.75 μm and robustness of 0.16 μm on both constant and dynamic working conditions. The effectiveness of the VFF-RLS method is validated by verification experiments.