Digital Modeling of Induction Heaters in Metallurgical Production
DOI:
https://doi.org/10.24160/0013-5380-2025-12-18-26Keywords:
induction heating, numerical modeling, digital twin, metamodeling, surrogate modeling, metallurgical productionAbstract
The article discusses matters concerned with computer modeling of induction heaters and technologies in which these devices are applied. Computer modeling is an integral component of the design and operation of complex and energy–intensive installations that use induction heating. Modular or object-oriented approaches are applied in the development of models for induction heating. For constructing the models of induction heaters and for modeling the complexes of metallurgical production lines that contain digital twins of individual units, including induction heaters, a metamodeling method is used. A special feature of the digital twins of induction heaters is their determinism and the possibility to perform numerical simulation of electromagnetic and temperature fields in 2D or 3D areas at the design stage. To perform real-time control of technological heating processes, so called “fast” surrogate models are used. As an example, the development of such model of a modular induction heater with the use of neural networks is given.
References
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#
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2. Muehlbauer A. History of Induction Heating and Melting. Essen: Vulkan-Verlag, 2008, 202 p.
3. Shamov A.N., Bodazhkov V.A. Proektirovanie i ekspluatatsiya vysokochastotnyh ustanovok. Izd. 2-e (Design and Operation of High-Frequency Installations. 2nd Ed.). L.: Mashinostroenie, 1974, 280 p.
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7. Ross N.V. Megawatt Induction Heating for Rolling, Forging, and Extrusion. – World Electrotechnical Congress (WELC), 1977, paper 65.
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11. Demidovich V.B., Chmilenko F.V. Komp’yuternoe modeliro-vanie ustroystv induktsionnogo nagreva (Computer Simulation of Induction Heating Devices). SPb.: Izd-vo SPbGETU «LETI», 2013, 160 p.
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13. Rapoport E., Pleshivtseva Y. Optimal Control of Induction Heating Processes. Boca-Raton: CRC Press, 2006, 349 p.
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15. Demidovich V.B. Tsifrovoe modelirovanie ustroystv induk-tsionnogo nagreva (istoriya i etapy razvitiya v LETI): spravochnoe posobie (Digital Modeling of Induction Heating Devices (History and Stages of Development in LETI): a Reference Guide). SPb.: Izd-vo SPbGETU «LETI», 2025, 106 p.
16. Nemkov V.S., Demidovich V.B. Teoriya i raschet ustroystv induktsionnogo nagreva (Theory and Calculation of Induction Heating Devices). L.: Energoatomizdat, 1988, 280 p.
17. Razumovskiy A.I. 33-ya Mezhd. konf, po komp’yuternoy grafike i mashinnomu zreniyu – in Russ. (33rd Int. Conf, on Computer Graphics and Machine Vision), 2023, pp. 891–895.
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25. Raissi M., Perdikaris P., Karniadakis G.E. Physics-Infor-med Neural Networks: A Deep Learning Framework for Solving Forward and Inverse Problems Involving Nonlinear Partial Differential Equations. – Journal of Computational Physics, 2019, vol. 378, pp. 686–707, DOI: 10.1016/j.jcp.2018.10.045.
26. Rasheed A., San O., Kvamsdal T. Digital Twin: Values, Challenges and Enablers from a Modeling Perspective. – IEEE Access, 2020, vol. 8, pp. 21980–22012, DOI: 10.1109/ACCESS.2020.2970143.
27. Derouiche K. et al. Real-Time Prediction by Data-Driven Models Applied to Induction Heating Process. – International Journal of Material Forming, 2022, vol. 15, DOI: 10.1007/s12289-022-01691-7.
28. Risch M., Walther A., Thus A. Innovative Concept Using IGBT Multiconverter Technology. – Heat Processing, 2006, No. 1, pp. 43–45.
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2. Muehlbauer A. History of Induction Heating and Melting. Essen: Vulkan-Verlag, 2008, 202 p.
3. Шамов А.Н., Бодажков В.А. Проектирование и эксплуатация высокочастотных установок. Изд. 2-е. Л.: Машиностроение, 1974, 280 с.
4. The International Energy Agency (IEA) [Электрон. ресурс], URL: https://www.iea.org/ (дата обращения 14.09.2025).
5. Бааке Э., Йорн У., Мюльбауэр А. Энергопотребление и эмиссия СО2 при промышленном технологическом нагреве. Essen: Vulkan, 1997, 173 c.
6. Ross N.V. A System for Induction Heating of Large Steel Slabs. – IEEE Transactions on Industry and General Applications, 1970, vol. 6, No. 5, pp. 449–454, DOI: 10.1109/TIGA.1970.4181214.
7. Ross N.V. Megawatt Induction Heating for Rolling, Forging, and Extrusion. – World Electrotechnical Congress (WELC), 1977, paper 65.
8. Организация Объединенных Наций. Парижское соглашение [Электрон. ресурс], URL: https://www.un.org/ru/climatechange/paris-agreement (дата обращения 14.09.2025).
9. Baake E. Energy Efficient Use of Electricity in Metallurgical Processes. – XVI International UIE Congress on Electricity Applications in Modern World (EAMW´08), 2008.
10. Baake E. et al. The Scope for Electricity & Carbon Saving in the EU Through the Use of EPM Technologies XVII International UIE Congress “The International Union for Electricity Applications”, 2012, pp. 215–222.
11. Демидович В.Б., Чмиленко Ф.В. Компьютерное моделирование устройств индукционного нагрева. СПб.: Изд-во СПбГЭТУ «ЛЭТИ», 2013, 160 с.
12. Рапопорт Э.Я., Плешивцева Ю.Э. Оптимальное управление температурными режимами индукционного нагрева. М.: Наука, 2012, 309 с.
13. Rapoport E., Pleshivtseva Y. Optimal Control of Induction Heating Processes. Boca-Raton: CRC Press, 2006, 349 p.
14. Rhein S., Utz T., Graichen K. Optimal Control of Induction Heating Processes Using FEM Software. – European Control Conference (ECC), 2015, рр. 515–520, DOI: 10.1109/ECC.2015.7330595.
15. Демидович В.Б. Цифровое моделирование устройств индукционного нагрева (история и этапы развития в ЛЭТИ): справочное пособие. СПб.: Изд-во СПбГЭТУ «ЛЭТИ», 2025, 106 с.
16. Немков В.С., Демидович В.Б. Теория и расчет устройств индукционного нагрева. Л.: Энергоатомиздат, 1988, 280 с.
17. Разумовский А.И. Метамоделирование цифровых двойников. – 33-я Межд. конф, по компьютерной графике и машинному зрению, 2023, с. 891–895.
18. Modelica [Электрон. ресурс], URL: https://modelica.org/ (дата обращения 14.09.2025).
19. Боровков А.И. и др. Цифровые двойники: вопросы терминологии. СПб.: Политех-Пресс, 2021, 28 с.
20. Передовые производственные технологии: возможности для России. Экспертно-аналитический доклад / под ред. А.И. Боровкова. СПб.: Политех-Пресс, 2020, 436 с.
21. Демидович В.Б. Цифровые двойники процессов индукционного нагрева в металлургической промышленности. – Электричество, 2023, № 4, с. 55–60.
22. Самарский А.А. Вычислительный эксперимент в задачах технологии. – Вестник АН СССР, 1984, № 3, с. 77–88.
23. Negri E., Fumagalli L., Macchi M. A Review of the Roles of DT in CPS-Based Production Systems. – Procedia Manufacturing, 2017, vol. 11, pp. 939–948, DOI: 10.1016/j.promfg.2017.07.198.
24. Kotlan V., Dolezel I. New Trends in the Modeling of Coupled Technical Problems. – 10th International Scientific Colloquium Modelling for Electromagnetic Processing, 2025, pp. 60–61.
25. Raissi M., Perdikaris P., Karniadakis G.E. Physics-Informed Neural Networks: A Deep Learning Framework for Solving Forward and Inverse Problems Involving Nonlinear Partial Differential Equations. – Journal of Computational Physics, 2019, vol. 378, pp. 686–707, DOI: 10.1016/j.jcp.2018.10.045.
26. Rasheed A., San O., Kvamsdal T. Digital Twin: Values, Challenges and Enablers from a Modeling Perspective. – IEEE Access, 2020, vol. 8, pp. 21980–22012, DOI: 10.1109/ACCESS.2020.2970143.
27. Derouiche K. et al. Real-Time Prediction by Data-Driven Models Applied to Induction Heating Process. – International Journal of Material Forming, 2022, vol. 15, DOI: 10.1007/s12289-022-01691-7.
28. Risch M., Walther A., Thus A. Innovative Concept Using IGBT Multiconverter Technology. – Heat Processing, 2006, No. 1, pp. 43–45.
29. Демидович В.Б., Никитин Б.М., Титов А.В. Модульные индукционные установки нагрева прутков повышенной надежности. – Индустрия, 2007, № 1, с. 19.
30. Brown D. Modular Induction System Offers Billet-Heating Advantages. – Forge, 2008, pp. 13–16.
31. Голембиовский Ю.М., Костерев А.А. Модульность как средство повышения эффективности систем индукционного нагрева. – Вестник Саратовского государственного технического университета, 2011, т. 4, № 4 (62), с. 145–149.
32. Демидович В.Б. и др. Модульные индукционные установки для непрерывного нагрева заготовок перед обработкой давлением. – Известия СПбГЭТУ «ЛЭТИ», 2016, № 9, с. 34–37.
#
1. Bogdanov V.N., Ryskin S.E., Shamov A.N. Induktsionnyy na-grev v kuznechnom proizvodstve (Induction Heating in Blacksmithing). M.-L.: Mashgiz, 1956, 196 p.
2. Muehlbauer A. History of Induction Heating and Melting. Essen: Vulkan-Verlag, 2008, 202 p.
3. Shamov A.N., Bodazhkov V.A. Proektirovanie i ekspluatatsiya vysokochastotnyh ustanovok. Izd. 2-e (Design and Operation of High-Frequency Installations. 2nd Ed.). L.: Mashinostroenie, 1974, 280 p.
4. The International Energy Agency (IEA) [Electron. resource], URL: https://www.iea.org/ (Accessed on 14.09.2025).
5. Baake E., Yorn U., Myul’bauer A. Energopotreblenie i emissiya SO2 pri promyshlennom tekhnologicheskom nagreve (Energy Consumption and CO2 Emissions from Industrial Process Heating). Essen: Vulkan, 1997, 173 p.
6. Ross N.V. A System for Induction Heating of Large Steel Slabs. – IEEE Transactions on Industry and General Applications, 1970, vol. 6, No. 5, pp. 449–454, DOI: 10.1109/TIGA.1970.4181214.
7. Ross N.V. Megawatt Induction Heating for Rolling, Forging, and Extrusion. – World Electrotechnical Congress (WELC), 1977, paper 65.
8. Organizatsiya Ob’edinennyh Natsiy. Parizhskoe soglashenie (The United Nations. The Paris Agreement) [Electron. resource], URL: https://www.un.org/ru/climatechange/paris-agreement (Accessed on 14.09.2025).
9. Baake E. Energy Efficient Use of Electricity in Metallurgical Processes. – XVI International UIE Congress on Electricity Applications in Modern World (EAMW´08), 2008.
10. Baake E. et al. The Scope for Electricity & Carbon Saving in the EU Through the Use of EPM Technologies XVII International UIE Congress “The International Union for Electricity Applications”, 2012, pp. 215–222.
11. Demidovich V.B., Chmilenko F.V. Komp’yuternoe modeliro-vanie ustroystv induktsionnogo nagreva (Computer Simulation of Induction Heating Devices). SPb.: Izd-vo SPbGETU «LETI», 2013, 160 p.
12. Rapoport E.Ya., Pleshivtseva Yu.E. Optimal’noe upravlenie temperaturnymi rezhimami induktsionnogo nagreva (Optimal Control of Induction Heating Temperature Conditions). M.: Nauka, 2012, 309 p.
13. Rapoport E., Pleshivtseva Y. Optimal Control of Induction Heating Processes. Boca-Raton: CRC Press, 2006, 349 p.
14. Rhein S., Utz T., Graichen K. European Control Conference (ECC), 2015, rr. 515–520, DOI: 10.1109/ECC.2015.7330595.
15. Demidovich V.B. Tsifrovoe modelirovanie ustroystv induk-tsionnogo nagreva (istoriya i etapy razvitiya v LETI): spravochnoe posobie (Digital Modeling of Induction Heating Devices (History and Stages of Development in LETI): a Reference Guide). SPb.: Izd-vo SPbGETU «LETI», 2025, 106 p.
16. Nemkov V.S., Demidovich V.B. Teoriya i raschet ustroystv induktsionnogo nagreva (Theory and Calculation of Induction Heating Devices). L.: Energoatomizdat, 1988, 280 p.
17. Razumovskiy A.I. 33-ya Mezhd. konf, po komp’yuternoy grafike i mashinnomu zreniyu – in Russ. (33rd Int. Conf, on Computer Graphics and Machine Vision), 2023, pp. 891–895.
18. Modelica [Electron. resource], URL: https://modelica.org/ (Accessed on 14.09.2025).
19. Borovkov A.I. et al. Tsifrovye dvoyniki: voprosy terminologii (Digital Twins: Terminology Issues). SPb.: Politekh-Press, 2021, 28 p.
20. Peredovye proizvodstvennye tekhnologii: vozmozhnosti dlya Rossii. Ekspertno-analiticheskiy doklad (Advanced Manufacturing Technologies: Opportunities for Russia. Expert and Analytical Report) / Ed. by A.I. Borovkov. SPb.: Politekh-Press, 2020, 436 p.
21. Demidovich V.B. Elektrichestvo – in Russ. (Electricity), 2023, No. 4, pp. 55–60.
22. Samarskiy A.A. Vestnik AN SSSR – in Russ. (Bulletin of the USSR Academy of Sciences), 1984, No. 3, pp. 77–88.
23. Negri E., Fumagalli L., Macchi M. A Review of the Roles of DT in CPS-Based Production Systems. – Procedia Manufacturing, 2017, vol. 11, pp. 939–948, DOI: 10.1016/j.promfg.2017.07.198.
24. Kotlan V., Dolezel I. New Trends in the Modeling of Coupled Technical Problems. – 10th International Scientific Colloquium Modelling for Electromagnetic Processing, 2025, pp. 60–61.
25. Raissi M., Perdikaris P., Karniadakis G.E. Physics-Infor-med Neural Networks: A Deep Learning Framework for Solving Forward and Inverse Problems Involving Nonlinear Partial Differential Equations. – Journal of Computational Physics, 2019, vol. 378, pp. 686–707, DOI: 10.1016/j.jcp.2018.10.045.
26. Rasheed A., San O., Kvamsdal T. Digital Twin: Values, Challenges and Enablers from a Modeling Perspective. – IEEE Access, 2020, vol. 8, pp. 21980–22012, DOI: 10.1109/ACCESS.2020.2970143.
27. Derouiche K. et al. Real-Time Prediction by Data-Driven Models Applied to Induction Heating Process. – International Journal of Material Forming, 2022, vol. 15, DOI: 10.1007/s12289-022-01691-7.
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2025-10-30
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