Convolutional neural network-attention-gate recurrent unit-attention hybrid framework for spindle thermal error modeling with joint feature analysis under complex variable speed conditions

Deep learning-based spindle thermal error modeling and compensation methods can effectively enhance manufacturing precision. The complex variable working conditions and thermal hysteresis effects in machine tool machining bring significant challenges for high-precision thermal error modeling. To address this issue, a hybrid structure network based on the feature extraction capability of Convolutional Neural Network (CNN) and the thermal hysteresis effect resolution capability of deep Gate Recurrent Unit (GRU) is established. A dual-layer attention mechanism is introduced to enhance spatial features and temporal features for improving the model's robustness and accuracy. First, complex variable working conditions result in complexity and nonlinearity of data. CNN is employed to extract spatial features due to its powerful feature extraction capability. A self-attention mechanism is introduced after CNN block to further filter important features. Due to the influence of thermal hysteresis effects, a deep GRU block is established to extract temporal features. A channel attention mechanism is introduced as the final layer of the network to achieve feature selection across different temperature channels. Second, features extracted by two attention mechanism layers are visualized and analyzed using t-distributed stochastic neighbor embedding (t-SNE) algorithm to explain the effectiveness of the dual-layer attention mechanism structure. The probability density distribution of the predicted results is calculated by kernel density estimation. Model performance is analyzed from the perspective of data distribution. Finally, the proposed model is compared with advanced methods under complex working conditions on two machine tools. The effectiveness of the proposed model is further validated through actual cutting compensation.