Modeling of thermal errors in electric spindle based on a hybrid approach of thermal deformation theory and data drive

The structure of spindles is often complex owing to the demands of the working conditions, making temperature and deformation the most complex part of the machine tool. Analyzing and establishing a model for the thermal error of spindles is extremely challenging. Previous studies on thermal error models for spindles have mainly focused on the identification of temperature distributions, resulting in the weak generalization ability of these models. To address this, numerical simulation was conducted to establish a hybrid model integrating physical and data-driven approaches to forecast the spindle’s thermal error by analyzing the thermal deformation law within spindle assembly. Moreover, a multi-link thermal error model was developed by structural analysis and decomposed using the Taylor formula, where the linear part is calculated by the equivalent area method, and the nonlinear part is predicted by a multi-module long short term memory (LSTM) network. In multi-case experiments on a self-built experimental rig, the effectiveness of the method was confirmed, which showed that the method had a better predictive result than the equivalent area method, with a 45% reduction in residuals. The results show that the method had better robustness and reliability in small sample scenarios with different operating conditions and thus has good potential for modeling thermal errors in complex operating conditions of spindles.