Please use this identifier to cite or link to this item: http://ena.lp.edu.ua:8080/handle/ntb/49610
Title: Analytical method of determining the electromagnetic field of the standard current pulses flowing near to a conductive object
Other Titles: Аналітичний метод визначення електромагнітного поля стандартних імпульсів струму, який проходить поблизу електропровідного тіла
Authors: Васецький, Юрій
Vasetskyy, Yuriy
Affiliation: Institute of Electrodynamics, Ukrainian National Academy of Sciences
Bibliographic description (Ukraine): Vasetskyy Y. Analytical method of determining the electromagnetic field of the standard current pulses flowing near to a conductive object / Yuriy Vasetskyy // Computational Problems of Electrical Engineering. — Lviv : Lviv Politechnic Publishing House, 2019. — Vol 9. — No 2. — P. 49–56.
Bibliographic description (International): Vasetskyy Y. Analytical method of determining the electromagnetic field of the standard current pulses flowing near to a conductive object / Yuriy Vasetskyy // Computational Problems of Electrical Engineering. — Lviv : Lviv Politechnic Publishing House, 2019. — Vol 9. — No 2. — P. 49–56.
Is part of: Computational Problems of Electrical Engineering, 2 (9), 2019
Issue: 2
Volume: 9
Issue Date: 20-Mar-2019
Publisher: Lviv Politechnic Publishing House
Place of the edition/event: Львів
Lviv
Keywords: quasi-stationary three-dimensional pulsed electromagnetic field
analytical and asymptotic calculation methods
typical current pulses
Number of pages: 8
Page range: 49-56
Start page: 49
End page: 56
Abstract: Представлено математичну модель, яка основана на розвинутій теорії аналітичного рішення тривимірних квазістаціонарних задач імпульсного струму, який проходить поблизу електропровідного тіла з плоскою поверхнею. Застосовувана математична модель передбачає наближене розв’язання з використанням асимптотичного розкладання для розрахунку напруженостей магнітного і електричного полів у випадку швидкоплинних електромагнітних процесів. Відзначено, що розрахунок наближеним методом обмежений певним проміжком часу від початку імпульсу, однак, зазвичай саме протягом цього проміжку часу поле змінюється найшвидше і досягає максимальних значень. Розглянуто електромагнітне поле при проходженні стандартних імпульсів струму: експоненціально загасаючий імпульс; імпульс, представлений різницею двох згасаючих експонент; коливальний експоненціально згасаючий імпульс. Для них проаналізовано основні особливості застосування наближеного аналітичного методу розрахунку поля. Знайдено інтегральні показники для врахування обмежень по частоті і часу залежно від параметрів імпульсів. Залежності від часу отримано з використанням спеціальних функцій та їхнього представлення у вигляді рядів.
The mathematical model based on the developed theory of the analytical solving the quasistationary tasks of pulse current flowing near to a conductive object with flat surface is introduced. The applied mathematical model includes an approximate solution with the use of asymptotic expansion for computing the intensity of a magnetic and electrical field in the case of transient electro-magnetic processes. It is noted that the calculations by an approximation method are limited to a certain time period from the beginning of a pulse, but, as usual, just within this time period the field changes most rapidly and accesses maximum values. The electrical field is considered at the presence of the standard current pulses such as exponentially decaying pulse, pulse represented by the difference between two decaying exponents, exponentially decaying oscillating pulse. For them the main peculiarities of applying the approximate analytical method of field calculations have been analyzed. Integral indicators for taking into account limitations by frequency and time, depending on the pulse parameters, have been found. Time dependencies have been obtained with the use of special functions and their representation as series.
URI: http://ena.lp.edu.ua:8080/handle/ntb/49610
Copyright owner: © Національний університет “Львівська політехніка”, 2019
References (Ukraine): 1. B. A. Larionov, F. M. Spevakova, A. M. Stolov, and E. A. Azizov, Problems of accumulation and conversion of electromagnetic energy in pulsed power systems with inductive drives. Physics and technology of powerful impulse systems. Moskva: Energoatomizdat, 1987. (Russian)
2. V. O. Brzhezytskyi, I. V. Isakov, and V. V. Rudakov, High voltage engineering and electrophysics. Kharkiv: NTU “KhPI” Tornado, 2005. (Ukrainian)
3. E. P. Velihov, Physics and technology of powerful impulse systems, Moskva: Energoatomizdat, 1987. (Russian)
4. Yu. V. Batygin , N. I. Lavinskyi and L. T. Khimenko, Pulsed magnetic fields for progressive technologies. Kharkiv: Most-Tornado, 2003. (Russian)
5. Yu. M. Vasetskiy, D. I. Vlasov, O. Ya. Konovalov, and V. M. Mikhailov, “Some solutions to the problem of continuation of a plane field in elementary functions”. Materialyi mezhdunarodnoy konferentsii «Modelirovanie-2012». Natsionalnaya akademiya nauk Ukrainyi, Institut problem modelirovaniya v energetike im. G. E. Puhova, pp. 232–236, 2012. (Russian)
6. V. M. Mikhailov, and N. P. Petrenko. “Approximation of Exact Massive Solenoid Profile for Generating Pulsed Magnetic Field”. Tekhnichna Elektrodynamika, no. 1, pp. 13–16, 2018. (Russian)
7. G. V. Stepanov and A. I. Babutskiy, The effect of high-density pulsed electric current on the strength of metallic materials and the stress-strain state of structural elements. Kyiv: Naukova dumka, 2014.
8. Yu. M. Vasetskyi, I. P. Kondratenko, O. M. Pashchyn, and K. K. Dziuba, “Machining welded joints with a pulsed electromagnetic field with a strong skin effect”. Pratsi Instytutu elektrodynamiky NANU, Kyiv: IED NANU, 2018, vyp. 49, pp. 68–76, 2018. (Ukrainian)
9. Yu. M. Vasetskiy and I. L. Mazurenko. “The geometric parameters of electromagnetic systems for highfrequency induction heating of metal tapes”. Технічна електродинаміка, no. 5, pp. 9–15, 2009. (Russian)
10. 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.
11. 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. (Russian)
12. 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”. Технічна електродинамік”а, no. 5, pp. 7–17, 2017. (Russian)
13. Yu. M. Vasetskyi and K. K. Dziuba. “ThreeDimensional Quasi-Stationary Electromagnetic Field Generated by Arbitrary Current Contour Near Conducting Body”. Технічна електродинаміка, no. 1, pp. 3–12, 2018.
14. A. H. Nayfeh, A Introduction to Perturbation Techniques. New York: A Willey-Interscience Publication, 1981.
15. V. I. Smirnov, Higher Mathematics Course, vol. 3, part 2. Moskva: Nauka, 1974. (Russian)
16. K. Dziuba, I. Mazurenko, and Yu. Vasetsky , “An Assessment of Accuracy of Approximate Mathematical Model of Pulse Electromagnetic Field of Current Flowing near Conductive Body”. 16th Intern. Conference on Computational Problems of Electrical Engineering (CPEE-2015). Lviv: Vydavnytstvo Lvivskoi politekhniky, pp. 36–38, 2015. IEEE Xplore. DOI: 10.1109/CPEE.2015.7333331.
17. Yu. M. Vasetsky, Three-dimensional quasi-stationary electromagnetic field of the current near conducting body. Pro Format, 2019. (Russian)
18. K. M. Polivanov, Theoretical bases of electrical engineering. No. 3. The theory of electromagnetic field. Moskva: Energiya, 1969. (Russian)
References (International): 1. B. A. Larionov, F. M. Spevakova, A. M. Stolov, and E. A. Azizov, Problems of accumulation and conversion of electromagnetic energy in pulsed power systems with inductive drives. Physics and technology of powerful impulse systems. Moskva: Energoatomizdat, 1987. (Russian)
2. V. O. Brzhezytskyi, I. V. Isakov, and V. V. Rudakov, High voltage engineering and electrophysics. Kharkiv: NTU "KhPI" Tornado, 2005. (Ukrainian)
3. E. P. Velihov, Physics and technology of powerful impulse systems, Moskva: Energoatomizdat, 1987. (Russian)
4. Yu. V. Batygin , N. I. Lavinskyi and L. T. Khimenko, Pulsed magnetic fields for progressive technologies. Kharkiv: Most-Tornado, 2003. (Russian)
5. Yu. M. Vasetskiy, D. I. Vlasov, O. Ya. Konovalov, and V. M. Mikhailov, "Some solutions to the problem of continuation of a plane field in elementary functions". Materialyi mezhdunarodnoy konferentsii "Modelirovanie-2012". Natsionalnaya akademiya nauk Ukrainyi, Institut problem modelirovaniya v energetike im. G. E. Puhova, pp. 232–236, 2012. (Russian)
6. V. M. Mikhailov, and N. P. Petrenko. "Approximation of Exact Massive Solenoid Profile for Generating Pulsed Magnetic Field". Tekhnichna Elektrodynamika, no. 1, pp. 13–16, 2018. (Russian)
7. G. V. Stepanov and A. I. Babutskiy, The effect of high-density pulsed electric current on the strength of metallic materials and the stress-strain state of structural elements. Kyiv: Naukova dumka, 2014.
8. Yu. M. Vasetskyi, I. P. Kondratenko, O. M. Pashchyn, and K. K. Dziuba, "Machining welded joints with a pulsed electromagnetic field with a strong skin effect". Pratsi Instytutu elektrodynamiky NANU, Kyiv: IED NANU, 2018, vyp. 49, pp. 68–76, 2018. (Ukrainian)
9. Yu. M. Vasetskiy and I. L. Mazurenko. "The geometric parameters of electromagnetic systems for highfrequency induction heating of metal tapes". Tekhnichna elektrodynamika, no. 5, pp. 9–15, 2009. (Russian)
10. 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.
11. 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. (Russian)
12. 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". Tekhnichna elektrodynamik"a, no. 5, pp. 7–17, 2017. (Russian)
13. Yu. M. Vasetskyi and K. K. Dziuba. "ThreeDimensional Quasi-Stationary Electromagnetic Field Generated by Arbitrary Current Contour Near Conducting Body". Tekhnichna elektrodynamika, no. 1, pp. 3–12, 2018.
14. A. H. Nayfeh, A Introduction to Perturbation Techniques. New York: A Willey-Interscience Publication, 1981.
15. V. I. Smirnov, Higher Mathematics Course, vol. 3, part 2. Moskva: Nauka, 1974. (Russian)
16. K. Dziuba, I. Mazurenko, and Yu. Vasetsky , "An Assessment of Accuracy of Approximate Mathematical Model of Pulse Electromagnetic Field of Current Flowing near Conductive Body". 16th Intern. Conference on Computational Problems of Electrical Engineering (CPEE-2015). Lviv: Vydavnytstvo Lvivskoi politekhniky, pp. 36–38, 2015. IEEE Xplore. DOI: 10.1109/CPEE.2015.7333331.
17. Yu. M. Vasetsky, Three-dimensional quasi-stationary electromagnetic field of the current near conducting body. Pro Format, 2019. (Russian)
18. K. M. Polivanov, Theoretical bases of electrical engineering. No. 3. The theory of electromagnetic field. Moskva: Energiya, 1969. (Russian)
Content type: Article
Appears in Collections:Computational Problems Of Electrical Engineering. – 2019 – Vol. 9, No. 2



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