A digital twin-assisted deep transfer learning method towards intelligent thermal error modeling of electric spindles

Thermal error modeling (TEM) is essential for preserving machining accuracy and enhancing the reliability of electric spindle systems. However, the major challenges in TEM lie in the limited or unavailable labeled thermal error samples due to the difficulties in data acquisition, as well as the problem of large distribution discrepancy between training and testing data under variable working conditions. Recently, digital twin (DT) has emerged as a promising tool in intelligent manufacturing. The DT model of the electric spindle can simulate system thermal behavior data that closely resembles real working conditions, providing a remarkable opportunity for TEM. Additionally, deep transfer learning (DTL) leverages existing knowledge to minimize data distribution discrepancies, bridging the gap between virtual and real data, and ultimately enhancing the generalization and adaptation ability of the model. Thus, this paper proposes a DT-assisted DTL method for TEM of electric spindles. Firstly, the DT model for the electric spindle is built by establishing a high-fidelity simulation model based on the physical system's thermal behavior mechanism. Furthermore, temperature field information for all interested working conditions can be simulated from the constructed DT model. Subsequently, the distance-guided domain adversarial network (DGDAN) is developed, with data generated by the DT model constructed as the training data in the source domain, while partially collected data from the physical system is used as the target domain for training. To validate the effectiveness of the proposed method, a case study is conducted using datasets from both the DT model and the physical system. The experimental results demonstrate that the proposed method successfully achieves TEM in scenarios where the thermal error data is limited or unavailable from the physical system, and the goodness of fit is higher than the state-of-the-art methods by 11.73%.