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Volume 14
Issue 1
10.3390/machines14010085
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This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

A Temperature-Based Statistical Model for Real-Time Thermal Deformation Prediction in End-Milling of Complex Workpiece

by
Mengmeng Yang
1,
Yize Yang
2,
Fangyuan Zhang
1,
Tong Li
1,
Xiyuan Qu
1,
Wei Wang
1,
Ren Zhang
1,*,
Dezhi Ren
1,
Feng Zhang
3 and
Koji Teramoto
2
1
College of Engineering, Shenyang Agricultural University, No. 120 Dongling Road, Shenhe District, Shenyang 110866, China
2
Division of Engineering, Muroran Institute of Technology, 27-1 Mizumoto, Muroran 050-8585, Hokkaido, Japan
3
College of Water Conservancy, Shenyang Agricultural University, Shenyang 110866, China
*
Author to whom correspondence should be addressed.
Machines 2026, 14(1), 85; https://doi.org/10.3390/machines14010085 (registering DOI)
Submission received: 15 December 2025 / Revised: 30 December 2025 / Accepted: 5 January 2026 / Published: 9 January 2026
(This article belongs to the Section Advanced Manufacturing)
Versions Notes

Abstract

Thermally induced deformation is a major source of dimensional error in end-milling, especially under high-speed or high-load conditions. Direct measurement of workpiece deformation during machining is impractical, while temperature signals can be obtained with good stability using embedded thermocouples. This study proposes an indirect method for predicting milling-induced thermal deformation based on temperature measurements. A three-dimensional thermo-mechanical finite element model is established to simulate the transient temperature field and corresponding deformation of the workpiece during milling. The numerical model is validated using cutting experiments performed under the same boundary conditions and machining parameters. Based on the validated results, the relationship between deformation at critical machining locations and temperature responses at candidate monitoring points is analyzed. To improve applicability to complex workpieces, a statistical prediction model is developed. Temperature monitoring points are optimized, and significant temperature–deformation correlations are identified using multiple linear regression combined with information-criterion-based model selection. The final model is constructed using simulation-derived datasets and provides stable deformation prediction over the entire milling process.
Keywords: thermal deformation; statistical modeling; temperature monitoring; multiple linear regression; end-milling thermal deformation; statistical modeling; temperature monitoring; multiple linear regression; end-milling

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MDPI and ACS Style

Yang, M.; Yang, Y.; Zhang, F.; Li, T.; Qu, X.; Wang, W.; Zhang, R.; Ren, D.; Zhang, F.; Teramoto, K. A Temperature-Based Statistical Model for Real-Time Thermal Deformation Prediction in End-Milling of Complex Workpiece. Machines 2026, 14, 85. https://doi.org/10.3390/machines14010085

AMA Style

Yang M, Yang Y, Zhang F, Li T, Qu X, Wang W, Zhang R, Ren D, Zhang F, Teramoto K. A Temperature-Based Statistical Model for Real-Time Thermal Deformation Prediction in End-Milling of Complex Workpiece. Machines. 2026; 14(1):85. https://doi.org/10.3390/machines14010085

Chicago/Turabian Style

Yang, Mengmeng, Yize Yang, Fangyuan Zhang, Tong Li, Xiyuan Qu, Wei Wang, Ren Zhang, Dezhi Ren, Feng Zhang, and Koji Teramoto. 2026. "A Temperature-Based Statistical Model for Real-Time Thermal Deformation Prediction in End-Milling of Complex Workpiece" Machines 14, no. 1: 85. https://doi.org/10.3390/machines14010085

APA Style

Yang, M., Yang, Y., Zhang, F., Li, T., Qu, X., Wang, W., Zhang, R., Ren, D., Zhang, F., & Teramoto, K. (2026). A Temperature-Based Statistical Model for Real-Time Thermal Deformation Prediction in End-Milling of Complex Workpiece. Machines, 14(1), 85. https://doi.org/10.3390/machines14010085

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