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<p>In the machining process of intelligent machine tools, thermal error is a significant factor affecting machining accuracy, and precisely estimating it and dynamically compensating it represent a core challenge for improving manufacturing quality. However, existing models generally struggle to balance estimation accuracy with computational efficiency, limiting their application in industrial real-time compensation systems. To address this, this study proposes an intelligent error compensation model that integrates a Back Propagation Neural Network and a Chicken Swarm Optimization algorithm. The model first uses Chicken Swarm Optimization to optimize the key parameters of a Support Vector Machine globally. Subsequently, the optimized Support Vector Machine output is used as a feature and fed into a Back Propagation Neural Network enhanced with steepness and amplification factors, constructing a cascaded thermal error estimation and compensation framework. Experimental results show that the model exhibits excellent performance in thermal error estimation, with an R<sup>2</sup> value of 0.982, a root mean square error consistently below 3.78&#xa0;μm, and a single-sample prediction time of only 0.054–0.078&#xa0;s. Regarding compensation effectiveness, the thermal errors in the X, Y, and Z directions of the spindle were suppressed to within 13.23&#xa0;μm, 6.26&#xa0;μm, and 4.71&#xa0;μm, respectively. The error reduction rates reached 79.30% in rough machining and 83.04% in finish machining, with overall performance significantly outperforming mainstream comparative models. The study demonstrates that the proposed model achieves high accuracy while maintaining good real-time capability and robustness, providing an effective technical solution for thermal error control in intelligent machine tools and offering clear engineering value for advancing the autonomy of high-end CNC equipment and the intelligence of precision manufacturing.</p> Graphical Abstract <p></p>

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Intelligent machine tool machining error estimation and compensation model based on backpropagation artificial neural network and chicken swarm optimization

  • 期刊论文

  • 发表日期：

    2026年3月9日

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  • Xiaomei Hu,
  • Yujing Wang,
  • Chuxiong Xie,
  • Xuan Li

摘要

In the machining process of intelligent machine tools, thermal error is a significant factor affecting machining accuracy, and precisely estimating it and dynamically compensating it represent a core challenge for improving manufacturing quality. However, existing models generally struggle to balance estimation accuracy with computational efficiency, limiting their application in industrial real-time compensation systems. To address this, this study proposes an intelligent error compensation model that integrates a Back Propagation Neural Network and a Chicken Swarm Optimization algorithm. The model first uses Chicken Swarm Optimization to optimize the key parameters of a Support Vector Machine globally. Subsequently, the optimized Support Vector Machine output is used as a feature and fed into a Back Propagation Neural Network enhanced with steepness and amplification factors, constructing a cascaded thermal error estimation and compensation framework. Experimental results show that the model exhibits excellent performance in thermal error estimation, with an R2 value of 0.982, a root mean square error consistently below 3.78 μm, and a single-sample prediction time of only 0.054–0.078 s. Regarding compensation effectiveness, the thermal errors in the X, Y, and Z directions of the spindle were suppressed to within 13.23 μm, 6.26 μm, and 4.71 μm, respectively. The error reduction rates reached 79.30% in rough machining and 83.04% in finish machining, with overall performance significantly outperforming mainstream comparative models. The study demonstrates that the proposed model achieves high accuracy while maintaining good real-time capability and robustness, providing an effective technical solution for thermal error control in intelligent machine tools and offering clear engineering value for advancing the autonomy of high-end CNC equipment and the intelligence of precision manufacturing.

Graphical Abstract