It is essential to precisely model the spindle thermal error due to its dramatic influence on the machining accuracy. In this paper, the deep learning convolutional neural network (CNN) is used to model the axial and radial thermal errors of horizontal and vertical spindles. Unlike the traditional CNN model that relies entirely on thermal images, this model combines the thermal image with the thermocouple data to fully reflect the temperature field of the spindle. After pre-processing and data enhancement of the thermal images, a multi-classification model based on CNN is built and verified for accuracy and robustness. The experimental results show that the model prediction accuracy is approximately 90 %–93 %, which is higher than the BP model. When the spindle rotation speed changes, the model also shows good robustness. Real cutting tests show that the deep learning model has good applicability to the spindle thermal error prediction and compensation.

由于主轴热误差会严重影响加工精度，因此必须精确建模主轴热误差。本文使用深度学习卷积神经网络（CNN）对水平和垂直主轴的轴向和径向热误差进行建模。与完全依赖于热图像的传统CNN模型不同，该模型将热图像与热电偶数据结合在一起，以完全反映主轴的温度场。在对热图像进行预处理和数据增强之后，建立了基于CNN的多分类模型，并对其准确性和鲁棒性进行了验证。实验结果表明，该模型的预测精度约为90％–93％，高于BP模型。当主轴转速变化时，该模型也显示出良好的鲁棒性。