Sim-to-Real: A multi-stage transfer learning method for thermal error modeling of electric spindles

Thermal error is a major factor limiting the machining accuracy of electric spindle systems. Accurate thermal error modeling (TEM) is therefore essential for precision improvement. However, data-driven neural networks often suffer from performance degradation due to limited real-world training data and increasing model complexity. In practical machining scenarios, acquiring sufficient measured data is challenging because real-time tool tracking is difficult to achieve. To address this issue, this paper proposes a sim-to-real multi-stage transfer learning framework for thermal error prediction under limited-data conditions. First, a thermodynamic model of the electric spindle is constructed to generate large-scale simulation data that are physically consistent with real working conditions. Second, a multi-scale residual network (MSRN) is developed to extract hierarchical thermal features through parallel multi-scale convolutional layers and residual connections. Third, a multi-stage transfer strategy is designed to progressively bridge the gap between simulation and real-world data by sequential pretraining on simulated data, intermediate adaptation using historical measurements with partial layer freezing, and final fine-tuning using limited target-domain samples. The proposed method is evaluated on six transfer tasks. Experimental results demonstrate that it consistently outperforms state-of-the-art baseline methods and achieves superior thermal error prediction performance under data-constrained conditions.