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<p>To address the challenges of directly accessing the internal temperature field of electric spindle, the heavy computational burden and limited of real-time applicability associated with conventional physics based models, and the restricted cross condition robustness of purely data driven framework under small sample sizes and varying operating conditions, this study develops a cross condition temperature prediction framework for electric spindle that transfers knowledge from finite element simulation to real-world measurements, combining proper orthogonal decomposition with Physics-Augmented GRU (PA-GRU) and domain adversarial alignment. First, transient temperature field data under multiple operating conditions are obtained via finite element simulations, and the high dimensional temperature field is decomposed into spatial modes and time coefficients to obtain a low dimensional representation. Second, physical constraints based on thermal equilibrium mechanisms are imported into the GRU to enhance the framework’s physical consistency. Finally, a data acquisition system is developed to gather actual data across various operating conditions. By combining this with domain-specific adversarial learning mechanisms, the discrepancy between simulation derived and measurement derived features is reduced, thereby enhancing transferability across operating regimes. Experimental results show that under low, medium, and high test conditions, the proposed method maintains both MAE and RMSE within 1&#xa0;°C, with an accuracy rate exceeding 90% in all cases, demonstrating excellent predictive performance.</p>

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POD-GRU-PINN for electric spindle thermal modeling

  • 期刊论文

  • 发表日期：

    2026年8月3日

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  • Peng Li,
  • Zhaoyu Shi,
  • Lixiu Zhang,
  • Songhua Li,
  • Ruwei Bao,
  • Shiji Lu

摘要

To address the challenges of directly accessing the internal temperature field of electric spindle, the heavy computational burden and limited of real-time applicability associated with conventional physics based models, and the restricted cross condition robustness of purely data driven framework under small sample sizes and varying operating conditions, this study develops a cross condition temperature prediction framework for electric spindle that transfers knowledge from finite element simulation to real-world measurements, combining proper orthogonal decomposition with Physics-Augmented GRU (PA-GRU) and domain adversarial alignment. First, transient temperature field data under multiple operating conditions are obtained via finite element simulations, and the high dimensional temperature field is decomposed into spatial modes and time coefficients to obtain a low dimensional representation. Second, physical constraints based on thermal equilibrium mechanisms are imported into the GRU to enhance the framework’s physical consistency. Finally, a data acquisition system is developed to gather actual data across various operating conditions. By combining this with domain-specific adversarial learning mechanisms, the discrepancy between simulation derived and measurement derived features is reduced, thereby enhancing transferability across operating regimes. Experimental results show that under low, medium, and high test conditions, the proposed method maintains both MAE and RMSE within 1 °C, with an accuracy rate exceeding 90% in all cases, demonstrating excellent predictive performance.