<p>Thermal deformation of machine tool spindles is a major source of machining errors. Effective thermal error compensation remains challenging due to difficulties in selecting representative temperature measurement points and developing prediction models capable of handling temperature fluctuations and thermal hysteresis. This study proposes an integrated thermal error prediction method for CNC machine tool spindles based on virtual temperature sensors and a multi-feature gated recurrent unit (GRU)-based model. The thermal behavior of the spindle system is analyzed using finite element simulation, and the surface mesh nodes of the spindle housing are regarded as virtual temperature sensors. Based on the simulated temperature data, k-means clustering combined with grey relational analysis is applied to determine the optimal number and locations of temperature-sensitive points, where physical temperature sensors are then installed on an actual machine tool. To improve prediction robustness under different speed conditions, multiple temperature features are extracted to describe short-term temperature variation, local thermal stability, and spatial thermal coupling. These features are incorporated into the GRU-based prediction model to capture the thermal hysteresis behavior of spindle deformation. Experimental validation is conducted under both constant-speed and variable-speed operating conditions. Comparisons with a conventional GRU model and a convolutional neural network (CNN)–GRU hybrid model show that the proposed method achieves higher prediction accuracy and better generalization ability, with coefficients of determination (R<sup>2</sup>) reaching 0.995, 0.985, and 0.981 under different operating conditions. The proposed method offers a practical and effective solution for thermal error prediction and compensation in CNC machine tool spindles.</p>

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A method for predicting thermal error in machine tool spindles based on multi-feature GRU network

  • Jianfeng Mao,
  • Yongjian Li,
  • Qinghui Xue,
  • Zhousheng Zheng,
  • Bin Sun,
  • Peng Sun,
  • Zhongyu Piao

摘要

Thermal deformation of machine tool spindles is a major source of machining errors. Effective thermal error compensation remains challenging due to difficulties in selecting representative temperature measurement points and developing prediction models capable of handling temperature fluctuations and thermal hysteresis. This study proposes an integrated thermal error prediction method for CNC machine tool spindles based on virtual temperature sensors and a multi-feature gated recurrent unit (GRU)-based model. The thermal behavior of the spindle system is analyzed using finite element simulation, and the surface mesh nodes of the spindle housing are regarded as virtual temperature sensors. Based on the simulated temperature data, k-means clustering combined with grey relational analysis is applied to determine the optimal number and locations of temperature-sensitive points, where physical temperature sensors are then installed on an actual machine tool. To improve prediction robustness under different speed conditions, multiple temperature features are extracted to describe short-term temperature variation, local thermal stability, and spatial thermal coupling. These features are incorporated into the GRU-based prediction model to capture the thermal hysteresis behavior of spindle deformation. Experimental validation is conducted under both constant-speed and variable-speed operating conditions. Comparisons with a conventional GRU model and a convolutional neural network (CNN)–GRU hybrid model show that the proposed method achieves higher prediction accuracy and better generalization ability, with coefficients of determination (R2) reaching 0.995, 0.985, and 0.981 under different operating conditions. The proposed method offers a practical and effective solution for thermal error prediction and compensation in CNC machine tool spindles.