Digital Modeling of Electromagnetic Processes in Technological Induction Devices
Keywords:
computer modeling, numerical methods, combined method, electromagnetic field, induction devices, induction heating
Abstract
Development of an electrical calculation method plays the leading role in simulating induction devices. In modeling electrical devices and complexes, it is often necessary to simultaneously solve both chain and field problems, i.e., to deal with both lumped and distributed parameters. The article considers the method of integral equations for induction systems with non-magnetic and ferromagnetic loading, which is based on the theory of long-range action. The method’s key statement is that the field at any point is determined as the sum of the fields produced by all sources, including primary and secondary ones. Another finite element method is based on the theory of short-range action, which describes the electromagnetic wave propagation from point to point, its refraction and reflection at the boundaries of media. The article substantiates the development of a combined method based on using the method of integral equations for calculating the input parameters of inductors (an external problem) and the finite element method for calculating the field distribution in the load (an internal problem). The combined method has well proven itself in modeling induction heating and melting of metals and oxides, heating a tape in a transverse magnetic field, induction plasmatrons, and casting aluminum into an electromagnetic crystallizer.
References
1. Вологдин В.П. Поверхностная индукционная закалка. М.: Оборонгиз, 1947, 291 с.
2. Muehlbauer A. History of Induction Heating and Melting. Essen: Vulkan Verlag, 2008, 212 p.
3. Lucia O., Maussion P., Dede E., Burdio J.M. Induction Heating Technology and Its Applications: Past Developments, Current Technology, and Future Challenges. – IEEE Transactions on Industrial Electronics, 2014, vol. 61.5, pp. 2509–2520.
4. Frolov V.Ya., Ivanov D.V. Calculation of a plasma composition and its thermophysical properties in cases of maintaining or quenching of electric arcs. – Journal of Physics: Conference Series, 2018, 1058(1), 012040.
5. Pigani A., Bobig P., Knights M., Martinis S. Danieli Universal Endless (DUE): The new evolution of Danieli Thin Slab Casting and Rolling plant. – Proceedings of the AISTech International Conference, Pittsburgh Pennsylvania, USA, 2016.
6. Schulze M., Nacke B., Nikanorov A. Design of an one-sided transverse flux induction coil by using a numerical optimization algorithm. – IOP Conference Series: Materials Science and Engineering, 2018, 424, 012065, DOI:10.1088/1757-899X/424/1/012065.
7. Kichigin, V., Nacke, B., Pozniak, I. New process for continuous melting and pouring of oxides with skull melting crucible. – International Journal of Applied Electromagnetics and Mechanics, 2017, vol. 53, pp. 89–94, DOI:10.3233/JAE-162247.
8. Соколов Д., Соловьев С. Цифровые двойники в эпоху Индустрии 4.0. – Connect WIT, 2019, № 5–6.
9. Бессонов Л.А. Теоретические основы электротехники. М.: Высшая школа, 1964, 754 с.
10. Демирчян К.С., Чечурин В.Л. Машинные расчеты электромагнитных полей. М.: Высшая школа, 1986, 240 с.
11. Silvester P.P., Ferrari R.L. Finite elements for electrical Engineers: 3rd ed. – Cambridge: Cambridge University Press, 1996, DOI: https://doi.org/10.1017/CBO9781139170611.
12. Chari M.V.K., Salon S.J. Numerical methods in electromag-netism. London: Academic Press, 2000, 783 p.
13. Тозони О.В. Метод вторичных источников в электротехнике. М.: Энергия, 1975, 296 c.
14. Lupi S., Forzan M., Aliferov A. Analytical and Numerical Methods for Calculation of Induction and Conduction Heating Systems. – Induction and Direct Resistance Heating, 2015, pp. 303–359, DOI: 10.1007/978-3-319-03479-9_5.
15. Немков В.С., Демидович В.Б. Теория и расчет устройств индукционного нагрева. Л.: Энергоатомиздат, 1988, 271 с.
16. Demidovich V.B. Computer simulation and optimal designing of energy-saving technologies of the induction heating of metals. – Thermal Engineering, 2012, vol. 59, No. 14, pp. 1023–1034.
17. Бутырин П.А., Дубицкий С.Д., Коровкин Н.В. Численное моделирование электромагнитных полей: мультифизические задачи, инструментарий и обучение. – Электричество, 2019, № 6, с. 51–58.
18. Demidovich V.B., Chmilenko F.V., Andrushkevich V.V., Rastvorova I.I. 3D-simulation of electromagnetic and temperature fields in the continuous induction heaters. – Coupled Problems 2015 – Proceedings of the 6th International Conference on Coupled Problems in Science and Engineering, 2015, pp. 976–984.
19. Frolov V., Ivanov D., Shibaev M. Mathematical modeling of plasma technology for TiO2 fine powder production. – Digest Journal of Nanomaterials and Biostructures, 2014, 9(3), pp. 1233–1240.
20. Демидович В.Б., Григорьев Е.А., Чмиленко Ф.В. и др. Моделирование индукционных нагревателей с учетом особенностей работы тиристорного преобразователя частоты с параллельным инвертором. – Электричество, 2013, № 10, с. 52–59.
21. Сегерлинд Л. Применение метода конечных элементов. М.: Мир, 1979, 392 с.
22. Sablic M.J., Beissner R.E., Choy A. An alternative numerical approach of computing eddy currents: Case of the double-layered plate. – IEEE Transactions on Magnetics, 1984, vol. 20, No. 3, pp. 500–506.
#
1. Vologdin V.P. Poverhnostnaya induktsionnaya zakalka (Surface induction quenching). М.: Oborongiz, 1947, 291 p.
2. Muehlbauer A. History of Induction Heating and Melting. Essen: Vulkan Verlag, 2008, 212 p.
3. Lucia O., Maussion P., Dede E., Burdio J.M. Induction Heating Technology and Its Applications: Past Developments, Current Technology, and Future Challenges. – IEEE Transactions on Industrial Electronics, 2014, vol. 61.5, pp. 2509–2520.
4. Frolov V.Ya., Ivanov D.V. Calculation of a plasma composition and its thermophysical properties in cases of maintaining or quenching of electric arcs. – Journal of Physics: Conference Series, 2018, 1058(1), 012040.
5. Pigani A., Bobig P., Knights M., Martinis S. Danieli Universal Endless (DUE): The new evolution of Danieli Thin Slab Casting and Rolling plant. – Proceedings of the AISTech International Conference, Pittsburgh Pennsylvania, USA, 2016.
6. Schulze M., Nacke B., Nikanorov A. Design of an one-sided transverse flux induction coil by using a numerical optimization algorithm. – IOP Conference Series: Materials Science and Engineering, 2018, 424, 012065, DOI:10.1088/1757-899X/424/1/012065.
7. Kichigin, V., Nacke, B., Pozniak I. New process for continuous melting and pouring of oxides with skull melting crucible. – International Journal of Applied Electromagnetics and Mechanics, 2017, vol. 53, pp. 89–94, DOI:10.3233/JAE-162247.
8. Sokolov D., Solov'ev S. Connect WIT, 2019, No. 5–6.
9. Bessonov L.A. Teoreticheskie osnovy elektrotekhniki (Theoretical foundations of electrical engineering). М.: Vysshaya shkola, 1964, 754 p.
10. Demirchyan K.S., Chechurin V.L. Mashinnye raschety elektromagnitnyh poley (Machine calculations of electromagnetic fields). М.: Vysshaya shkola, 1986, 240 p.
11. Silvester P.P., Ferrari R.L. Finite elements for electrical Engineers: 3rd ed. – Cambridge: Cambridge University Press, 1996, DOI: https://doi.org/10.1017/CBO9781139170611.
12. Chari M.V.K., Salon S.J. Numerical methods in electromagnetism. London: Academic Press, 2000, 783 p.
13. Tozoni О.V. Metod vtorichnyh istochnikov v elektrotekhnike (The method of secondary sources in electrical engineering). М.: Energiya, 1975, 296 p.
14. Lupi S., Forzan M., Aliferov A. Analytical and Numerical Methods for Calculation of Induction and Conduction Heating Systems. – Induction and Direct Resistance Heating, 2015, pp. 303–359, DOI: 10.1007/978-3-319-03479-9_5.
15. Nemkov V.S., Demidovich V.B. Teoriya i raschet ustroystv induktsionnogo nagreva (Theory and calculation of induction heating devices). L.: Energoatomizdat, 1988, 271 p.
16. Demidovich V.B. Computer simulation and optimal designing of energy-saving technologies of the induction heating of metals. – Thermal Engineering, 2012, vol. 59, No. 14, pp. 1023–1034.
17. Butyrin P.A., Dubitskiy S.D., Korovkin N.V. Elektrichestvo – in Russ. (Electricity), 2019, No. 6, pp. 51–58.
18. Demidovich V.B., Chmilenko F.V., Andrushkevich V.V., Rastvorova I.I. 3D-simulation of electromagnetic and temperature fields in the continuous induction heaters. – Coupled Problems 2015 – Proceedings of the 6th International Conference on Coupled Problems in Science and Engineering, 2015, pp. 976–984.
19. Frolov V., Ivanov D., Shibaev M. Mathematical modeling of plasma technology for TiO2 fine powder production. – Digest Journal of Nanomaterials and Biostructures, 2014, 9(3), pp. 1233–1240.
20. Demidovich V.B., Grigor'ev E.A., Chmilenko F.V. et all. Elektrichestvo – in Russ. (Electricity), 2013, No. 10, pp. 52–59.
21. Segerlind L. Primenenie metoda konechnyh elementov (Application of the finite element method). М.: Mir, 1979, 392 p.
22. Sablic M.J., Beissner R.E., Choy A. An alternative numerical approach of computing eddy currents: Case of the double-layered plate. – IEEE Transactions on Magnetics, 1984, vol. 20, No. 3, pp. 500–506.
2. Muehlbauer A. History of Induction Heating and Melting. Essen: Vulkan Verlag, 2008, 212 p.
3. Lucia O., Maussion P., Dede E., Burdio J.M. Induction Heating Technology and Its Applications: Past Developments, Current Technology, and Future Challenges. – IEEE Transactions on Industrial Electronics, 2014, vol. 61.5, pp. 2509–2520.
4. Frolov V.Ya., Ivanov D.V. Calculation of a plasma composition and its thermophysical properties in cases of maintaining or quenching of electric arcs. – Journal of Physics: Conference Series, 2018, 1058(1), 012040.
5. Pigani A., Bobig P., Knights M., Martinis S. Danieli Universal Endless (DUE): The new evolution of Danieli Thin Slab Casting and Rolling plant. – Proceedings of the AISTech International Conference, Pittsburgh Pennsylvania, USA, 2016.
6. Schulze M., Nacke B., Nikanorov A. Design of an one-sided transverse flux induction coil by using a numerical optimization algorithm. – IOP Conference Series: Materials Science and Engineering, 2018, 424, 012065, DOI:10.1088/1757-899X/424/1/012065.
7. Kichigin, V., Nacke, B., Pozniak, I. New process for continuous melting and pouring of oxides with skull melting crucible. – International Journal of Applied Electromagnetics and Mechanics, 2017, vol. 53, pp. 89–94, DOI:10.3233/JAE-162247.
8. Соколов Д., Соловьев С. Цифровые двойники в эпоху Индустрии 4.0. – Connect WIT, 2019, № 5–6.
9. Бессонов Л.А. Теоретические основы электротехники. М.: Высшая школа, 1964, 754 с.
10. Демирчян К.С., Чечурин В.Л. Машинные расчеты электромагнитных полей. М.: Высшая школа, 1986, 240 с.
11. Silvester P.P., Ferrari R.L. Finite elements for electrical Engineers: 3rd ed. – Cambridge: Cambridge University Press, 1996, DOI: https://doi.org/10.1017/CBO9781139170611.
12. Chari M.V.K., Salon S.J. Numerical methods in electromag-netism. London: Academic Press, 2000, 783 p.
13. Тозони О.В. Метод вторичных источников в электротехнике. М.: Энергия, 1975, 296 c.
14. Lupi S., Forzan M., Aliferov A. Analytical and Numerical Methods for Calculation of Induction and Conduction Heating Systems. – Induction and Direct Resistance Heating, 2015, pp. 303–359, DOI: 10.1007/978-3-319-03479-9_5.
15. Немков В.С., Демидович В.Б. Теория и расчет устройств индукционного нагрева. Л.: Энергоатомиздат, 1988, 271 с.
16. Demidovich V.B. Computer simulation and optimal designing of energy-saving technologies of the induction heating of metals. – Thermal Engineering, 2012, vol. 59, No. 14, pp. 1023–1034.
17. Бутырин П.А., Дубицкий С.Д., Коровкин Н.В. Численное моделирование электромагнитных полей: мультифизические задачи, инструментарий и обучение. – Электричество, 2019, № 6, с. 51–58.
18. Demidovich V.B., Chmilenko F.V., Andrushkevich V.V., Rastvorova I.I. 3D-simulation of electromagnetic and temperature fields in the continuous induction heaters. – Coupled Problems 2015 – Proceedings of the 6th International Conference on Coupled Problems in Science and Engineering, 2015, pp. 976–984.
19. Frolov V., Ivanov D., Shibaev M. Mathematical modeling of plasma technology for TiO2 fine powder production. – Digest Journal of Nanomaterials and Biostructures, 2014, 9(3), pp. 1233–1240.
20. Демидович В.Б., Григорьев Е.А., Чмиленко Ф.В. и др. Моделирование индукционных нагревателей с учетом особенностей работы тиристорного преобразователя частоты с параллельным инвертором. – Электричество, 2013, № 10, с. 52–59.
21. Сегерлинд Л. Применение метода конечных элементов. М.: Мир, 1979, 392 с.
22. Sablic M.J., Beissner R.E., Choy A. An alternative numerical approach of computing eddy currents: Case of the double-layered plate. – IEEE Transactions on Magnetics, 1984, vol. 20, No. 3, pp. 500–506.
#
1. Vologdin V.P. Poverhnostnaya induktsionnaya zakalka (Surface induction quenching). М.: Oborongiz, 1947, 291 p.
2. Muehlbauer A. History of Induction Heating and Melting. Essen: Vulkan Verlag, 2008, 212 p.
3. Lucia O., Maussion P., Dede E., Burdio J.M. Induction Heating Technology and Its Applications: Past Developments, Current Technology, and Future Challenges. – IEEE Transactions on Industrial Electronics, 2014, vol. 61.5, pp. 2509–2520.
4. Frolov V.Ya., Ivanov D.V. Calculation of a plasma composition and its thermophysical properties in cases of maintaining or quenching of electric arcs. – Journal of Physics: Conference Series, 2018, 1058(1), 012040.
5. Pigani A., Bobig P., Knights M., Martinis S. Danieli Universal Endless (DUE): The new evolution of Danieli Thin Slab Casting and Rolling plant. – Proceedings of the AISTech International Conference, Pittsburgh Pennsylvania, USA, 2016.
6. Schulze M., Nacke B., Nikanorov A. Design of an one-sided transverse flux induction coil by using a numerical optimization algorithm. – IOP Conference Series: Materials Science and Engineering, 2018, 424, 012065, DOI:10.1088/1757-899X/424/1/012065.
7. Kichigin, V., Nacke, B., Pozniak I. New process for continuous melting and pouring of oxides with skull melting crucible. – International Journal of Applied Electromagnetics and Mechanics, 2017, vol. 53, pp. 89–94, DOI:10.3233/JAE-162247.
8. Sokolov D., Solov'ev S. Connect WIT, 2019, No. 5–6.
9. Bessonov L.A. Teoreticheskie osnovy elektrotekhniki (Theoretical foundations of electrical engineering). М.: Vysshaya shkola, 1964, 754 p.
10. Demirchyan K.S., Chechurin V.L. Mashinnye raschety elektromagnitnyh poley (Machine calculations of electromagnetic fields). М.: Vysshaya shkola, 1986, 240 p.
11. Silvester P.P., Ferrari R.L. Finite elements for electrical Engineers: 3rd ed. – Cambridge: Cambridge University Press, 1996, DOI: https://doi.org/10.1017/CBO9781139170611.
12. Chari M.V.K., Salon S.J. Numerical methods in electromagnetism. London: Academic Press, 2000, 783 p.
13. Tozoni О.V. Metod vtorichnyh istochnikov v elektrotekhnike (The method of secondary sources in electrical engineering). М.: Energiya, 1975, 296 p.
14. Lupi S., Forzan M., Aliferov A. Analytical and Numerical Methods for Calculation of Induction and Conduction Heating Systems. – Induction and Direct Resistance Heating, 2015, pp. 303–359, DOI: 10.1007/978-3-319-03479-9_5.
15. Nemkov V.S., Demidovich V.B. Teoriya i raschet ustroystv induktsionnogo nagreva (Theory and calculation of induction heating devices). L.: Energoatomizdat, 1988, 271 p.
16. Demidovich V.B. Computer simulation and optimal designing of energy-saving technologies of the induction heating of metals. – Thermal Engineering, 2012, vol. 59, No. 14, pp. 1023–1034.
17. Butyrin P.A., Dubitskiy S.D., Korovkin N.V. Elektrichestvo – in Russ. (Electricity), 2019, No. 6, pp. 51–58.
18. Demidovich V.B., Chmilenko F.V., Andrushkevich V.V., Rastvorova I.I. 3D-simulation of electromagnetic and temperature fields in the continuous induction heaters. – Coupled Problems 2015 – Proceedings of the 6th International Conference on Coupled Problems in Science and Engineering, 2015, pp. 976–984.
19. Frolov V., Ivanov D., Shibaev M. Mathematical modeling of plasma technology for TiO2 fine powder production. – Digest Journal of Nanomaterials and Biostructures, 2014, 9(3), pp. 1233–1240.
20. Demidovich V.B., Grigor'ev E.A., Chmilenko F.V. et all. Elektrichestvo – in Russ. (Electricity), 2013, No. 10, pp. 52–59.
21. Segerlind L. Primenenie metoda konechnyh elementov (Application of the finite element method). М.: Mir, 1979, 392 p.
22. Sablic M.J., Beissner R.E., Choy A. An alternative numerical approach of computing eddy currents: Case of the double-layered plate. – IEEE Transactions on Magnetics, 1984, vol. 20, No. 3, pp. 500–506.
