Dynamic modeling for spindle thermal error in machine tools under time-varying rotational speeds and cooling states

To accurately predict and compensate for spindle thermal error under time-varying rotational speeds and cooling states, this paper proposes a novel dynamic thermal error modeling method characterized by a dual-attention-enhanced parallel branch architecture. Theoretical analysis and experimentation reveal a complex nonlinear relationship between temperature and thermal error, exhibiting multi-layered hysteresis loops. To effectively construct this intricate mapping, the proposed architecture adopts two-layer stacked LSTMs with improved activation functions to extract temperature features. Two distinct parallel 1D convolutional layers are applied to transform features from different dimensions. Crucially, temporal pattern attention and self-attention are employed to form parallel dual attention mechanisms, focusing on key temperature variation patterns and long-term dependencies, respectively. These extracted features are then adaptively fused and nonlinearly activated to create a comprehensive understanding of thermal dynamics. By operating in parallel, the two branches collectively distill discriminative temperature information from complementary perspectives. Experimental results demonstrate that the developed dynamic thermal error model achieves excellent prediction performance, with average MAE and RMSE values of 2.49 μm and 2.90 μm, respectively. After compensation, the average absolute thermal error is reduced to only 1.9 μm and 4.7 μm, with compensation rates of 93% and 86%. The effectiveness and superiority of the proposed dynamic modeling method are well validated, offering a novel approach for thermal error modeling and compensation in complex operating conditions.