Intelligent Thermal Error Prognostics of Gear Grinding Machine Spindle Based on Model-Data Fusion Approach

Current machine tool thermal error prediction studies struggle to effectively link the underlying mapping relationship between physical mechanisms and machine tool state data, which could lead to challenges such as redundant measurement point layouts, lack of interpretability in prediction modeling, and low accuracy. This study integrates numerical modeling with artificial intelligence by employing a model-data fusion approach to conduct intelligent thermal error predictions on motorized spindles. It effectively imparts physical significance to purely artificial intelligence-driven predictions. The designed methodology mainly includes two parts: the optimization layout of sensitive temperature measurement points and thermal error deformation prediction. The former solves for the steady-state temperature field using finite element numerical models to determine the feasible space of measuring positions. Subsequently, a novel multiobjective optimization algorithm with unsupervised and supervised optimization functions is proposed to precisely solve for the positions of sensor layouts. The latter, grounded in time series modeling methods of transformer architectures, utilizes autoregressive modeling to predict thermal errors. The developed multichannel inverted transformer (iTransformer) algorithm distinctively incorporates temperature signals into multivariate tokens. Utilizing an encoder-decoder architecture, multichannel iTransformer facilitates autoregressive predictive modeling that connects temperature rise signals with thermal error deformation over variable step lengths, effectively overcoming issues such as reduced generalization capability in predictive models caused by lengthy lookback periods and significant computational efficiency demands. Ultimately, the effectiveness and advantages of the proposed model-data fusion approach are validated through real-measured experiments from gear grinding machine tools.