Thermal Image Input-based ResNet Method for Thermal Error Modeling of Machine Tool Spindles

doi:10.3969/j.issn.1004-132X.2025.09.018

China Mechanical Engineering ›› 2025, Vol. 36 ›› Issue (9): 2057-2067.DOI: 10.3969/j.issn.1004-132X.2025.09.018

Thermal Image Input-based ResNet Method for Thermal Error Modeling of Machine Tool Spindles

Mingfan LI¹^,²(), Long YANG³^,⁴, Sheng LI⁵, Huan GUO⁶, Guoqiang FU³^,⁴()

^1.College of Mechanical Engineering，Zhejiang University of Water Resources and Electric Power，Hangzhou，310018
^2.Key Laboratory of Key Technologies for Mechanical Industry Hydroelectric Power Generation Pump Turbine，Zhejiang University of Water Resources and Electric Power，Hangzhou，310018
^3.School of Mechanical Engineering，Southwest Jiaotong University，Chengdu，610031
^4.Intelligent Manufacturing Dragon City Laboratory，Changzhou，Jiangsu，213000
^5.Linker Technology Research Co. ，Ltd. ，Hangzhou，310000
^6.Henan Yuguan Safety Development Co. ，Ltd. ，Zhengzhou，450000

Received:2024-08-13 Online:2025-09-25 Published:2025-10-15
Contact: Guoqiang FU

以热图像为输入的基于ResNet的机床主轴热误差建模方法

李明范¹^,²(), 杨龙³^,⁴, 李晟⁵, 郭欢⁶, 付国强³^,⁴()

^1.浙江水利水电学院机械工程学院, 杭州, 310018
^2.浙江水利水电学院机械工业水力发电水泵水轮机技术重点实验室, 杭州, 310018
^3.西南交通大学机械工程学院, 成都, 610031
^4.智能制造龙城实验室, 常州, 213000
^5.宏龙科技(杭州)有限公司, 杭州, 310000
^6.河南省豫冠安全发展有限公司, 郑州, 450000

通讯作者: 付国强
作者简介:李明范，男，1976 年生，博士、高级工程师。研究方向为机电一体化产品开发、传感与检测技术。E-mail：Leesapper@163.com
付国强*（通信作者），男，1988 年生，副教授、博士研究生导师。主要研究方向为复杂高端装备精度提升理论与技术，复杂高端装备热、力、几何等多误差源误差测量装置及方法。E-mail：fuguoqiang@swjtu.edu.cn。
基金资助:
国家自然科学基金(52175486);智能制造龙城实验室开放课题(LK202404);浙江省自然科学基金公益项目(LGG21F010004);机械传动国家重点实验室开放基金(SKLMT-MSKFKT-202201);中央高校基本科研业务费(2682024ZTPY028)

Abstract

Abstract:

To achieve a high-precision and highly generalizable thermal error model of machine tools， a thermal image input-based ResNet method was proposed for thermal error modeling of CNC machine tool spindles. A thermal image dataset labelled was constructed with thermal error rounding， and a ResNet-based classification model was trained for thermal error prediction using thermal images as inputs. Considering the regression characteristics of the machine tool thermal error time series， a regression output layer was constructed by integrating the probabilities of different classification labels from the classification output layer in a weighted manner， enabling thermal error regression prediction without retraining. The deep features of thermal images and the classification performance of the ResNet model were visualized， confirming the effectiveness of ResNet in feature extraction and strong classification ability. Finally， the ResNet model was compared with GoogLeNet and VGGNet models under different operating conditions， demonstrating the high accuracy and generalization of the ResNet-based thermal error classification and regression models.

Key words: thermal image, spindle thermal error, ResNet classification model, regression prediction, feature visualization

摘要：

为了获得高精度高泛化的机床热误差模型，提出了以热图像为输入的基于ResNet的数控机床主轴热误差建模方法。构建以热误差取整为标签的热图像数据集，训练以热图像为输入的热误差ResNet分类预测模型。在此基础上，针对机床热误差时序序列的回归特性，将分类输出层的不同标签值对应的概率通过加权集成方式构建回归输出层，实现热误差回归预测，无需重新训练。对热图像深度特征和ResNet分类模型的分类效果进行可视化分析，验证ResNet模型对热图像特征提取的有效性以及良好的分类能力。最后，将ResNet模型与GoogLeNet和VGGNet模型在不同工况下进行比较，分别验证ResNet热误差分类模型和回归模型的高精度和高泛化性。

关键词: 热图像, 主轴热误差, ResNet分类模型, 回归预测, 特征可视化

CLC Number:

TG659

Mingfan LI, Long YANG, Sheng LI, Huan GUO, Guoqiang FU. Thermal Image Input-based ResNet Method for Thermal Error Modeling of Machine Tool Spindles[J]. China Mechanical Engineering, 2025, 36(9): 2057-2067.

李明范, 杨龙, 李晟, 郭欢, 付国强. 以热图像为输入的基于ResNet的机床主轴热误差建模方法[J]. 中国机械工程, 2025, 36(9): 2057-2067.

Figures/Tables 37

Fig.1 Experimental Setup

Tab.1 Experimental conditions setting

实验序号	固定转速/ （r·min^-1）	实验时长/h	热图像采样频率/ min^-1
2000-a	2000	4	0.5
2000-b
2000-c
3000-a	3000
3000-b
3000-c
4000-a	4000
4000-b
4000-c

Fig.2 Environmental temperature for three sets of experiments at 2000 r/min

Fig.3 Thermal error for three sets of experiments at 2000 r/min

Fig.4 Acquisition of absolute heat gain map

Fig.5 Crop thermal images

Fig.6 Augmented thermal images

Fig.7 Thermal error corresponding to thermal images at 2000 r/min

Fig.8 ResNet-based classification model

Fig.9 Residual block of two-layer structure

Fig.10 Structure of residual learning

Fig.11 Improving the ResNet classification model to construct a regression model

Fig.12 Loss function values and accuracy for the validation set

Tab.3 Regression model metrics for different epoches

训练轮数N	最大残差	MAE
50	8.7982	1.0625
100	4.6753	0.6158
150	1.8097	0.4184

Fig.13 Arrangement of temperature sensors in the spindle area

Tab.4 Correlation coefficients between temperature variables and thermal deformation

温度传感器	T1	T2	T3	T4	T6
相关系数R	0.9269	0.8692	0.8571	0.9310	0.8767

Fig.14 Visualization of Grad-CAM features across different layers of the ResNet model

Fig.15 Feature extraction results of thermal images for other categories

Fig.16 T-SNE visualization results for ResNet model at 2000 r/min

Fig.17 Classification prediction results of different models at 2000 r/min

Tab.5 Errors of different models at 2000 r/min

模型	最大残差	RMSE	MAE
ResNet	5	1.65	0.84
GoogLeNet	7	2.35	1.42
VGGNet	6	2.39	1.76

Fig.18 T-SNE visualization results for GoogLeNet model at 2000 r/min

Fig.19 T-SNE visualization results for VGGNet model at 2000 r/min

Fig.20 Classification prediction results of different models at 3000 r/min

Fig.21 Classification prediction results of different models at 4000 r/min

Tab.6 Errors of different models at 3000 r/min and 4000 r/min

转速/ （r·min^-1）	模型	最大残差/μm	RMSE/μm	MAE/μm
3000	ResNet	6	1.72	0.98
	GoogLeNet	7	2.31	1.53
	VGGNet	7	2.41	1.58
4000	ResNet	6	1.66	0.93
	GoogLeNet	7	2.43	1.85
	VGGNet	6	2.52	1.77

Fig.22 T-SNE visualization results for ResNet model at 3000 r/min

Fig.23 T-SNE visualization results for GoogLeNet model at 3000 r/min

Fig.24 T-SNE visualization results for the VGGNet model at 3000 r/min

Fig.25 Regression prediction results for different models at 2000 r/min

Tab.7 Regression model results at 2000 r/min

模型	最大残差	RMSE	MAE
ResNet	4.64	1.59	1.05
GoogLeNet	6.17	2.38	1.68
VGGNet	6.31	2.41	1.85

Fig.26 Regression prediction results for different models at 3000 r/min

Fig.27 Results for different models at 4000 r/min

Tab.8 Regression model results at 3000 r/min

模型	最大残差	RMSE	MAE
ResNet	5.75	1.68	1.07
GoogLeNet	6.93	2.44	1.65
VGGNet	7.38	2.51	1.65

Tab.9 Regression model results at 4000 r/min

模型	最大残差	RMSE	MAE
ResNet	5.95	1.73	1.25
GoogLeNet	6.37	2.40	1.83
VGGNet	6.16	2.52	1.95

Fig.28 Classification prediction results of different models in Y-direction at 2000 r/min

Tab.10 Errors of different regression models in Y-direction at 2000 r/min

模型	最大残差	RMSE	MAE
ResNet	5	1.69	1.24
GoogLeNet	8	2.59	2.04
VGGNet	7	2.64	2.04

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Thermal Image Input-based ResNet Method for Thermal Error Modeling of Machine Tool Spindles

以热图像为输入的基于ResNet的机床主轴热误差建模方法

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