Continuous Method: A Flexible Solution for Metal Length Expansion Measurement in the Modern Manufacturing Industry

Stephanus Goenawan

doi:10.25170/metris.v26i02.7039

Authors

Stephanus Goenawan School of Bioscience, Technology, and Innovation, Atma Jaya Catholic University of Indonesia

DOI:

https://doi.org/10.25170/metris.v26i02.7039

Keywords:

Thermal expansion, Discrete Method, Continuous Method, Manufacturing industry, Heating

Abstract

Measurement of metal length expansion is crucial in the modern manufacturing industry as it impacts product design, production, and performance. Current conventional method (Discrete Methods/DM) relies on an initial reference length (L0), which limits the flexibility of in-situ and continuous measurements. This study compares the accuracy and flexibility of DM with the Continuous Method (CM), an approach that potentially eliminates the need for L0 after the initial measurement. Using numerical simulations on five metals, this study analyzes calculations for estimating metal length expansion under various heating scenarios. The results show that both methods provide similar differences in metal length thermal expansion values (difference <0.0001 m), confirming their comparative accuracy. However, CM proves significantly more flexible as it allows the calculation of metal length thermal expansion estimates at arbitrary temperatures without the need to refer to L0, unlike DM, which requires L0 for consistency. This flexibility makes CM more practical for both incremental and real-time measurements, supporting the integration of automation into precision manufacturing processes. Implications for the manufacturing industry include increased efficiency of in-situ measurements, reduced reliance on initial data, and the potential for better integration with continuous quality control systems and Digital Twins.

References

Cheng, C.-Y., Pourhejazy, P., Hung, C.-Y., & Yuangyai, C. (2021). Smart Monitoring of Manufacturing Systems for Automated Decision-Making: A Multi-Method Framework. Sensors, 21(20), 6860. https://doi.org/10.3390/s21206860.

Colón Quintana, J. L., Slattery, L., Pinkham, J., Keaton, J., Lopez-Anido, R. A., & Sharp, K. (2022). Effects of Fiber Orientation on the Coefficient of Thermal Expansion of Fiber-Filled Polymer Systems in Large Format Polymer Extrusion-Based Additive Manufacturing. Materials, 15(8), 2764. https://doi.org/10.3390/ma15082764.

Fu, T., Li, P., Shi, C., & Liu, Y. (2024). Digital-Twin-Based Monitoring System for Slab Production Process. Future Internet, 16(2), 59. https://doi.org/10.3390/fi16020059.

Goenawan, S I. (2025). Pengukuran Perubahan Pemuaian Panjang Logam Tidak Langsung Dengan Metode Muai Kontinu Kalkulus (M2K2) Dan Metode Muai Kontinu Pendekatan (M2KP). Paten. Direktorat Jenderal Kekayaan Intelektual (DJKI) Kementerian Hukum dan Hak Asasi Manusia.

He, X., Welo, T., & Ma, J. (2025). In-process monitoring strategies and methods in metal forming: A selective review. Journal of Manufacturing Processes, 138, 100-128. https://doi.org/10.1016/j.jmapro.2025.02.011.

Kim, Y., Kumar, S., Li, X., Kim, S., & Shin, D. (2025). Temperature-dependent mechanical properties and material modifications of carbon fiber composites for optimized structures in high-end industrial applications. Composites Part B: Engineering, 303, 112602. https://doi.org/10.1016/ j.compositesb.2025.112602.

Kul, M., Akgül, B., Karabay, Y. Z., Hitzler, L., Sert, E., & Merkel, M. (2024). Minimum and Stable Coefficient of Thermal Expansion by Three-Step Heat Treatment of Invar 36. Crystals, 14(12), 1097. https://doi.org/10.3390/cryst14121097.

Lenz, J., MacDonald, E., Harik, R., & Wuest, T. (2022). Self-sensing smart products in smart manufacturing systems. Manufacturing Letters, 34, 25-28. https://doi.org/10.1016/j.mfglet.2022.08.014.

Ma, Z., Liu, Y., Liu, J., & Lyu, Y. (2025). Mitigation of thermal effects in bridges: A comprehensive review of control methodologies. Journal of Traffic and Transportation Engineering (English Edition), 12(2), 215-235. https://doi.org/10.1016/j.jtte.2024.12.003.

Marble, E., & Boles, T. (2022). A Review of the Structural Characteristics of Aerospace Composites. Science Insights, 41(7), 749–753. https://doi.org/10.15354/si.22.re102.

Monroe, J., Gehring, D., Karaman, I., Arroyave, R., Brown, D., & Clausen, B. (2015). Tailored thermal expansion alloys. Acta Materialia, 102, 333-341. https://doi.org/10.1016/j.actamat.2015.09.012.

Peng, J., Harsha Gunda, N., Bridges, C. A., Lee, S., Allen Haynes, J., & Shin, D. (2022). A machine learning approach to predict thermal expansion of complex oxides. Computational Materials Science, 210, 111034. https://doi.org/10.1016/j.commatsci.2021.111034.

Qin, X., Cao, G., Geng, M., Liu, S., & Liu, Y. (2023). A high-resolution dilatometer using optical fiber interferometer. arXiv preprint, arXiv:2311.16641. https://doi.org/10.48550/arXiv.2311.16641.

Ren, Z., Wang, Q., Fang, R., Huang, Z., & Shi, X. (2025). Development of a predictive model for the thermal expansion coefficient of elastic disordered microporous metal rubber based on virtual manufacturing technology. Chinese Journal of Mechanical Engineering, 38(61), 1-14 . https://doi.org/10.1186/s10033-024-01165-8.

Stuart Robertson, Andrew McClintock, Kenny Jolley, Han Zhou, Sam Davis, Houzheng Wu, Changqing Liu, Scott Doak, Zhaoxia Zhou (2024). Measuring coefficient of thermalexpansion of materials of micrometre size using SEM FIB microscope with in situ MEMS heating stage. Journal of Microscopy. https://doi.org/10.1111/jmi.13290.

Schödel, R. (2008). Ultra-high accuracy thermal expansion measurements with PTB's precision interferometer. Measurement Science and Technology. 19(8) https://dx.doi.org/10.1088/0957-0233/19/8/084003.

Schukraft, J., Roßdeutscher, J., Siegmund, F., & Weidenmann, K. A. (2022). Thermal expansion behavior and elevated temperature elastic properties of an interpenetrating metal/ceramic composite. Thermochimica Acta, 715, 179298. https://doi.org/10.1016/j.tca.2022.179298.

Shang, S.-L., Gong, R., Gao, M. C., Pagan, D. C., & Liu, Z.-K. (2024). Revisiting first principles thermodynamics by quasiharmonic approach: Application to study thermal expansion of additively-manufactured Inconel 625. Materials Science. https://doi.org/10.48550/arXiv.2405.09445.

Sprengel, W., & Würschum, R. (2024). High-Precision Dilatometry for the Study of Precipitation Processes and Microalloying Effects in Lightweight Alloys - A Specific Review. Advanced Engineering Materials, 26(19), 2400426. https://doi.org/10.1002/adem.202400426.

Subedi, A., Kim, H., Lee, M.-S., & Lee, S.-J. (2025). Thermal Behavior of Concrete: Understanding the Influence of Coefficient of Thermal Expansion of Concrete on Rigid Pavements. Applied Sciences, 15(6), 3213. https://doi.org/10.3390/app15063213.

Takamoto, S., Izumi, S., Nakata, T., Sakai, S., Oinuma, S., & Nakatani, Y. (2014). Analytical method for estimating the thermal expansion coefficient of metals at high temperature. Modelling and Simulation in Materials Science and Engineering, 23(1). DOI: 10.1088/0965-0393/23/1/015010.

Tesfaye, F., Lindberg, D., Sukhomlinov, D., Taskinen, P., & Hupa, L. (2022). Thermal Analysis and Optimization of the Phase Diagram of the Cu-Ag Sulfide System. Energies, 15(2), 593. https://doi.org/10.3390/en15020593.

Thomaz, F., Teixeira Malaquias, A. C., & Coelho Baêta, J. G. (2021). Thermal management of an internal combustion engine focused on vehicle performance maximization: A numerical assessment. Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering, 235(8) https://doi.org/10.1177/0954407020982825.

Wankhede, S., & Gawande, S. (2023). Design and analysis aspect of metal expansion bellows: A review. Forces in Mechanics, 13, 100244. https://doi.org/10.1016/j.finmec.2023.100244.

Yakout, M., Elbestawi, M., & Veldhuis, S. C. (2020). A study of the relationship between thermal expansion and residual stresses in selective laser melting of Ti-6Al-4V. Journal of Manufacturing Processes, 52, 181-192. https://doi.org/10.1016/j.jmapro.2020.01.039.

Zheng, F., Tan, Y., Lin, J., Ding, Y., & Zhang, S. (2015). Study of non-contact measurement of the thermal expansion coefficients of materials based on laser feedback interferometry. Rev. Sci. Instrum, 86(4). https://doi.org/10.1063/1.4917554.

Zhu, X., & Lanza, F. (2016). Thermal Stress Measurement in Continuous Welded Rails Using the Hole-Drilling Method. Experimental Mechanics, 57, 165-178. https://doi.org/10.1007/s11340-016-0204-8.