Thermal Error Prediction for Gantry Guideway Grinder Spindle Based on CNN-BiLSTM-Attention

Abstract Aiming at the strong nonlinearity, time-series lag, and multi-physics coupling characteristics of spindle thermal error in gantry guideway grinders, as well as the insufficient feature extraction and poor generalization ability of single deep learning models under varying working conditions, a thermal error prediction method based on fuzzy C-means clustering-grey relational analysis (FCM-GRA) for optimizing temperature-sensitive points and a CNN-BiLSTM-Attention hybrid network is proposed. Firstly, temperature and Z-direction thermal error data were acquired via spindle idle tests under multiple rotational speeds. FCM is applied to cluster the seven temperature measuring points, and combined with GRA to screen representative temperature-sensitive points with the strongest correlation with thermal errors, thus eliminating redundant features. Then, a parallel hybrid prediction model consisting of a CNN branch, a BiLSTM branch, and a direct input branch is constructed. In this model, CNN is employed to extract the spatial coupling features of temperature signals, BiLSTM to learn the temporal dynamic laws of thermal errors, and a self-attention mechanism is adopted to adaptively weight and fuse multi-source features, thereby enhancing the model’s fitting ability for complex thermal characteristics. Finally, five-fold leave-one-out cross-validation is adopted to evaluate the model’s performance. The results show that under five rotational speed conditions, the proposed hybrid model achieves an average coefficient of determination R² of 0.954, an average mean absolute error (MAE) of 5.66 µm, and an average root mean square error (RMSE) of 6.15 µm. All these indicators are superior to those of traditional time-series models, including LSTM, BiLSTM, GRU, and BiGRU. This model can effectively realize high-precision prediction of spindle thermal errors under varying working conditions, thus providing a modeling foundation for thermal error compensation of gantry guideway grinders.