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<p>The thermal stability of the spindle in spiral bevel gear grinding machines plays a critical role in determining machining accuracy. To address the limitations of traditional modeling approaches in capturing long-term dependencies and nonlinear thermal behavior, this study proposes a hybrid GRU–transformer model for thermal error prediction under varying spindle speeds. Experiments conducted at 1000, 1500, and 2000&#xa0;rpm integrated real-time sensor measurements with finite element simulations, identifying axial deformation as the dominant thermal error component. To mitigate feature redundancy, K-means clustering and grey relational analysis were employed to reduce the number of temperature sensors from 10 to 3. Comparative experiments demonstrated that the proposed model consistently outperformed conventional GRU, RNN, and transformer networks in both accuracy and robustness. With the aid of transfer learning, the hybrid model achieved a prediction performance of <i>R</i><sup>2</sup> = 0.9932 and RMSE = 0.0010&#xa0;mm, demonstrating high precision and strong generalization ability. Furthermore, a thermal error compensation experiment on a gear grinding machine confirmed that the proposed model effectively reduced tooth surface profile deviations, thereby validating its practical applicability.</p>

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Thermal error modeling and compensation of CNC spiral bevel gear spindles using a GRU–transformer network

  • 期刊论文

  • 发表日期：

    2025年10月22日

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  • Rui Xue,
  • Jiang Han,
  • Lian Xia,
  • Xiaoqing Tian,
  • Jie Xiao,
  • Kan Xing,
  • Zhiyong Wang

摘要

The thermal stability of the spindle in spiral bevel gear grinding machines plays a critical role in determining machining accuracy. To address the limitations of traditional modeling approaches in capturing long-term dependencies and nonlinear thermal behavior, this study proposes a hybrid GRU–transformer model for thermal error prediction under varying spindle speeds. Experiments conducted at 1000, 1500, and 2000 rpm integrated real-time sensor measurements with finite element simulations, identifying axial deformation as the dominant thermal error component. To mitigate feature redundancy, K-means clustering and grey relational analysis were employed to reduce the number of temperature sensors from 10 to 3. Comparative experiments demonstrated that the proposed model consistently outperformed conventional GRU, RNN, and transformer networks in both accuracy and robustness. With the aid of transfer learning, the hybrid model achieved a prediction performance of R2 = 0.9932 and RMSE = 0.0010 mm, demonstrating high precision and strong generalization ability. Furthermore, a thermal error compensation experiment on a gear grinding machine confirmed that the proposed model effectively reduced tooth surface profile deviations, thereby validating its practical applicability.