Please use this identifier to cite or link to this item: http://ena.lp.edu.ua:8080/handle/ntb/55982
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dc.contributor.authorВасецький, Юрій
dc.contributor.authorМазуренко, Ірина
dc.contributor.authorVasetsky, Yuriy
dc.contributor.authorMazurenko, Iryna
dc.date.accessioned2021-01-22T11:45:43Z-
dc.date.available2021-01-22T11:45:43Z-
dc.date.created2020-02-24
dc.date.issued2020-02-24
dc.identifier.citationVasetsky Y. Parameters for Calculation of Three-Dimensional Electromagnetic Field by Asymptotic Expansion Method / Yuriy Vasetsky, Iryna Mazurenko // Computational Problems of Electrical Engineering. — Lviv : Lviv Politechnic Publishing House, 2020. — Vol 10. — No 1. — P. 37–44.
dc.identifier.urihttp://ena.lp.edu.ua:8080/handle/ntb/55982-
dc.description.abstractПредставлено наближений аналітичний розв’язок тривимірної задачі теорії електромагнітного поля, який оснований на використанні асимптотичного розкладання за умови сильного скін-ефекту для поля, створеного замкнутим струмовим контуром, розташованим поблизу електропровідного півпростору. Зазначено, що кожен член асимптотичного ряду визначається з похибкою, величина якої залежить від значення малого параметра і зростає зі збільшенням номера члена ряду, що обумовлює обмеженість кількості його членів. Встановлено, що при використанні методу асимптотичного розкладання число членів ряду може бути обмежено відносно невеликою кількістю, яка визначається заданими межами припустимої точності розрахунку (відносною похибкою). Визначено оптимальне число членів асимптотичного ряду та вказано оцінку точності розрахунку в залежності від величини малого параметру, а для конкретного електропровідного матеріала в залежності від частоти поля і мінімальної відстані від джерел зовнішнього поля до електропровідного тіла.
dc.description.abstractThe paper deals with an approximate analytical solution of a three-dimensional problem of the theory of electromagnetic field, which is based on the use of asymptotic expansion under the condition of a strong skin-effect for a field produced by a closed current-carrying loop located near a conducting halfspace. It is noted that each member of an asymptotic series is determined with an error, the value of which depends on the value of a small parameter and increases with increasing the index of series member resulting in limited number of its members. It is identified that when using the method of asymptotic expansion, the number of members of a series can be limited by the relatively small number, which is determined by the specified limits of the allowable accuracy of calculation (relative error). The authors determine the optimal number of asymptotic series members, and indicate that calculation accuracy depends on the value of a small parameter, and for a specific conducting material it depends on the field frequency and the minimum distance from external field sources to a conducting body.
dc.format.extent37-44
dc.language.isoen
dc.publisherВидавництво Львівської політехніки
dc.publisherLviv Politechnic Publishing House
dc.relation.ispartofComputational Problems of Electrical Engineering, 1 (10), 2020
dc.subjectanalytical and asymptotic calculation methods
dc.subject3D electromagnetic fields
dc.subjectstrong skin-effect
dc.titleParameters for Calculation of Three-Dimensional Electromagnetic Field by Asymptotic Expansion Method
dc.title.alternativeПараметри для розрахунку тривимірного електромагнітного поля методом асимптотичного розкладання
dc.typeArticle
dc.rights.holder© Національний університет “Львівська політехніка”, 2020
dc.contributor.affiliationInstitute of Electrodynamics, Ukrainian National Academy of Sciences
dc.format.pages8
dc.identifier.citationenVasetsky Y. Parameters for Calculation of Three-Dimensional Electromagnetic Field by Asymptotic Expansion Method / Yuriy Vasetsky, Iryna Mazurenko // Computational Problems of Electrical Engineering. — Lviv : Lviv Politechnic Publishing House, 2020. — Vol 10. — No 1. — P. 37–44.
dc.relation.references[1] V. M. Mikhailov, “Continuation of magnetic flux and potential of axisymmetric fields from flat surface”, Elektrichestvo, no 10, pp. 58–64, 2002. (Rus).
dc.relation.references[2] Yu. M. Vasetskiy, D. I. Vlasov, O. Ya. Konovalov, and V. M. Mikhaylov, “Nekotorye resheniya zadachi prodolzheniya ploskogo polya v elementarnykh funktsiyakh”, Zbirnyk prac" konferenciyi SIMULATION, 2012. Kyiv: Instytut problem modelyuvannya v enerhetyci im. H.Ye. Puxova NAN Ukrayiny, pp. 212–216, 2012. (Rus)
dc.relation.references[3] V. M. Mikhaylov, “Green’s functions of axisymmetric electric and magnetic fields above flat boundary surface”, Tekhnichna elektrodynamika, no 4, pp. 5–9, 2018. (Rus)
dc.relation.references[4] V. Rudnev, D. Loveless, R. Cook, and M.Black, Handbook of induction heating. London: Taylor & Francis Ltd. 2017.
dc.relation.references[5] Yu. V. Batyigin, S. F. Golovaschenko, and E. A. Chaplyigin, “Magnetic-Impulse Attraction of Nonmagnetic Metals”. Elektrichestvo, no 2, pp. 40–52, 2014. (Rus)
dc.relation.references[6] G. V. Stepanov and A. I. Babutskiy, Effect of highdensity pulsed electric current on strength of metallic materials and stress-strain state of structural components. Kyiv: Naukova dumka, 2010. (Rus)
dc.relation.references[7] K. M. Polivanov, Theoretical bases of electrical engineering. No. 3. The theory of electromagnetic field. Moskva: Energiya, 1969. (Rus).
dc.relation.references[8] Yu. M. Vasetskyi and K. K. Dziuba, “An analytical calculation method of quasi-stationary threedimensional electromagnetic field created by the arbitrary current contour that located near conducting body”, Technical Electrodynamics, no. 5, pp. pp. 7–17, 2017. (Rus).
dc.relation.references[9] Yu. M. Vasetsky and K. K. Dziuba, “Threedimensional quasi-stationary electromagnetic field generated by arbitrary current contour near conducting body”, Technical Electrodynamics, no 1, pp. 3–12, 2018.
dc.relation.references[10] Yu. M. Vasetskiy, I.L. Mazurenko. “The geometric parameters of electromagnetic systems for highfrequency induction heating of metal tapes”. Technical Electrodynamics, no. 5, pp. 9–15, 2009. (Rus)
dc.relation.references[11] Yu. Vasetskyi, I. Mazurenko “Approximation mathematical models of electromagnetic and thermal processes at induction heating of metal strips”, Computation Problems of Electrical Engineering, no 1, pp. 45–50, 2011.
dc.relation.references[12] Yu. M. Vasetskiy, I. P. Kondratenko, A. P. Rashchepkin, and I. L. Mazurenko, Electromagnetic interactions between current contours and conductive medium. Kyiv: Pro Format, 2019. (Rus)
dc.relation.references[13] A. H. Nayfeh, A Introduction to Perturbation Techniques. New York: A Willey-Interscience Publication, 1981.
dc.relation.references[14] V. I. Smirnov, Higher Mathematics Course, vol. 3, part 2. Moskva: Nauka, 1974. (Rus)
dc.relation.references[15] Yu. Vasetsky, L. Gorodga, and I. Mazurenko, “Approximate model for calculating alternating magnetic field of an arbitrary contour taking into account eddy currents in a conducting half-space”. Tekhnichna elektrodynamika. Tematychnyi vypusk. Modeliuvannia elektronnykh, enerhetychnykh ta tekhnolohichnykh system, no. 1, pp. 88–93, 1999. (Rus)
dc.relation.referencesen[1] V. M. Mikhailov, "Continuation of magnetic flux and potential of axisymmetric fields from flat surface", Elektrichestvo, no 10, pp. 58–64, 2002. (Rus).
dc.relation.referencesen[2] Yu. M. Vasetskiy, D. I. Vlasov, O. Ya. Konovalov, and V. M. Mikhaylov, "Nekotorye resheniya zadachi prodolzheniya ploskogo polya v elementarnykh funktsiyakh", Zbirnyk prac" konferenciyi SIMULATION, 2012. Kyiv: Instytut problem modelyuvannya v enerhetyci im. H.Ye. Puxova NAN Ukrayiny, pp. 212–216, 2012. (Rus)
dc.relation.referencesen[3] V. M. Mikhaylov, "Green’s functions of axisymmetric electric and magnetic fields above flat boundary surface", Tekhnichna elektrodynamika, no 4, pp. 5–9, 2018. (Rus)
dc.relation.referencesen[4] V. Rudnev, D. Loveless, R. Cook, and M.Black, Handbook of induction heating. London: Taylor & Francis Ltd. 2017.
dc.relation.referencesen[5] Yu. V. Batyigin, S. F. Golovaschenko, and E. A. Chaplyigin, "Magnetic-Impulse Attraction of Nonmagnetic Metals". Elektrichestvo, no 2, pp. 40–52, 2014. (Rus)
dc.relation.referencesen[6] G. V. Stepanov and A. I. Babutskiy, Effect of highdensity pulsed electric current on strength of metallic materials and stress-strain state of structural components. Kyiv: Naukova dumka, 2010. (Rus)
dc.relation.referencesen[7] K. M. Polivanov, Theoretical bases of electrical engineering. No. 3. The theory of electromagnetic field. Moskva: Energiya, 1969. (Rus).
dc.relation.referencesen[8] Yu. M. Vasetskyi and K. K. Dziuba, "An analytical calculation method of quasi-stationary threedimensional electromagnetic field created by the arbitrary current contour that located near conducting body", Technical Electrodynamics, no. 5, pp. pp. 7–17, 2017. (Rus).
dc.relation.referencesen[9] Yu. M. Vasetsky and K. K. Dziuba, "Threedimensional quasi-stationary electromagnetic field generated by arbitrary current contour near conducting body", Technical Electrodynamics, no 1, pp. 3–12, 2018.
dc.relation.referencesen[10] Yu. M. Vasetskiy, I.L. Mazurenko. "The geometric parameters of electromagnetic systems for highfrequency induction heating of metal tapes". Technical Electrodynamics, no. 5, pp. 9–15, 2009. (Rus)
dc.relation.referencesen[11] Yu. Vasetskyi, I. Mazurenko "Approximation mathematical models of electromagnetic and thermal processes at induction heating of metal strips", Computation Problems of Electrical Engineering, no 1, pp. 45–50, 2011.
dc.relation.referencesen[12] Yu. M. Vasetskiy, I. P. Kondratenko, A. P. Rashchepkin, and I. L. Mazurenko, Electromagnetic interactions between current contours and conductive medium. Kyiv: Pro Format, 2019. (Rus)
dc.relation.referencesen[13] A. H. Nayfeh, A Introduction to Perturbation Techniques. New York: A Willey-Interscience Publication, 1981.
dc.relation.referencesen[14] V. I. Smirnov, Higher Mathematics Course, vol. 3, part 2. Moskva: Nauka, 1974. (Rus)
dc.relation.referencesen[15] Yu. Vasetsky, L. Gorodga, and I. Mazurenko, "Approximate model for calculating alternating magnetic field of an arbitrary contour taking into account eddy currents in a conducting half-space". Tekhnichna elektrodynamika. Tematychnyi vypusk. Modeliuvannia elektronnykh, enerhetychnykh ta tekhnolohichnykh system, no. 1, pp. 88–93, 1999. (Rus)
dc.citation.issue1
dc.citation.spage37
dc.citation.epage44
dc.coverage.placenameЛьвів
dc.coverage.placenameLviv
Appears in Collections:Computational Problems Of Electrical Engineering. – 2020 – Vol. 10, No. 1



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