Determination of Radial Forces Acting Between Coaxial Coils Located in the Same Plane
DOI:
https://doi.org/10.24160/0013-5380-2022-5-39-42Keywords:
coaxial turns, radial forces, planar coils, tensile forcesAbstract
The electrodynamic forces acting between coaxial turns with current are estimated for the case when the turns belong to different layers in a multilayer coil, which are arranged in the same way. Expressions for the radial components of electrodynamic forces acting on a concentric outer turn are given. The suggested expressions are verified for consistency with the result obtained for the mutual inductance gradient in the radial direction, known from [1]. The expressions for tensile forces in the case of thin-layer disk coils based on their determination in terms of the inductance derivative with respect to the average radius are compared in two versions: with reference to Wheeler's approximating formulas for inductance, one of which is written in [2], and the other in [3]. The article may be useful for specialists dealing with evaluation of inductances and electrodynamic forces in the live parts of electrical systems.
References
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2. Thompson M.T. Inductance Calculations Techniques – Part II: Approximations and Handbook Methods, Power Control and Intelligent Motion, 1999, 11 с.
3. Цицикян Г.Н. Оценка стягивающих и растягивающих сил в тороидальных и линейных накопителях электроэнергии. – Труды Крыловского государственного научного центра, 2021, 4(398), с. 123–128.
4. Цицикян Г.Н. О взаимной индуктивности и электродинамических силах взаимодействия коаксиальных контуров. – Известия Российской академии наук. Энергетика, 2018, № 4, с. 40–45.
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6. Цицикян Г.Н., Бобровников П.В., Антипов М.Ю. Руководство по расчёту индуктивности и электродинамических сил в токоведущих частях электротехнических комплексов. СПб.: ФГУП «Крыловский государственный научный центр», 2020, 118 с.
7. Калантаров П.Л., Цейтлин Л.А. Расчёт индуктивностей. Справочная книга. Л.: Энергоатомиздат, 1986, 488 с.
8. Knight D.W. Solenoid Inductance Calculation, 2003 [Электрон. ресурс], URL: http://g3ynh.info/zdocs/magnetics (дата обращения 15.12.2021).
9. Snow C. Formulas for Computing Capacitance and Inductance. National Bureau of Standards. Circular, 1954.
10. Soma M., Galbraith D., White R. Radio-frequency Coils in Implantable Devices. Misalignment Analysis and Design Procedure. – IEEE Transactions on Biomedical Engineering, 1987, vol. BME-34, No. 4, pp. 276–282, DOI:10. 10.1109/TBME.1987.326088.
11. Johnk C.T.A. Engineering Electromagnetic Field and Waves. New York: Wiley, 1991, 656 p.
12. Paul C.R. Inductance Loop and Partial. N.Y.: John Wiley and Sons, 2010, 379 p., DOI:10.1002/9780470561232.
13. Демирчян К.С. и др. Теоретические основы электротехники: том 3. СПб.: Питер, 2003, 377 с.
#
1. Garrett M.W. Calculation of Fields, Forces and Mutual Induc-tance of Current Systems by Elliptic Integrals. – Journal of Applied Physics, 1963, vol. 34, No. 9, pp. 2567–2573.
2. Thompson M.T. Inductance Calculations Techniques – Part II: Approximations and Handbook Methods, Power Control and Intelligent Motion, 1999, 11 с.
3. Tsitsikyan G.N. Trudy Krylovskogo gosudarstvennogo nauchnogo tsentra – in Russ. (Proceedings of the Krylov State Scientific Center), 2021, 4(398), pp. 123–128.
4. Tsitsikyan G.N. Izvestiya RAN. Energetika – in Russ. (News of the Russian Academy of Sciences. Power Engineering), 2018, No. 4, pp. 40–45.
5. Tsitsikyan G.N. Elektrichestvo – in Russ. (Electricity), 2019, No. 6, pp. 59–65.
6. Tsitsikyan G.N., Bobrovnikov P.V., Antipov M.Yu. Rukovodstvo po raschyotu induktivnostey i elektrodinamicheskih sil v tokovedushchih chastyah elektrotekhnicheskih kompleksov (Manual for the calculation of inductances and electrodynamic forces in current-carrying parts of electrical complexes). SPb.: FGUP«Кrylovskiy gos. nauchnyy tsentr», 2020, 118 p.
7. Kalantarov P.L., Zeytlin L.L. Raschyot induktivnostey. Spravochnaya kniga (Calculation of Inductances. Reference Book). L: Energoatomizdat, 1986, 488 p.
8. Knight D.W. Solenoid Inductance Calculation, 2003 [Electron. resource], URL: http://g3ynh.info/zdocs/magnetics (Date of appeal 15.12.2021).
9. Snow C. Formulas for Computing Capacitance and Inductance. National Bureau of Standards. Circular, 1954.
10. Soma M., Galbraith D., White R. Radio-frequency Coils in Implantable Devices. Misalignment Analysis and Design Procedure. – IEEE Transactions on Biomedical Engineering, 1987, vol. BME-34, No. 4, pp. 276–282, DOI:10. 10.1109/TBME.1987.326088.
11. Johnk C.T.A. Engineering Electromagnetic Field and Waves. New York: Wiley, 1991, 656 p.
12. Paul C.R. Inductance Loop and Partial. N.Y.: John Wiley and Sons, 2010, 379 p., DOI:10.1002/9780470561232.
13. Demirchyan К.S., et al. Teoreticheskie osnovy elektrotekhniki (Theoretical Foundations of Electrical Engineering): vol. 3. SPb.: Piter, 2003, 377 p.
2. Thompson M.T. Inductance Calculations Techniques – Part II: Approximations and Handbook Methods, Power Control and Intelligent Motion, 1999, 11 с.
3. Цицикян Г.Н. Оценка стягивающих и растягивающих сил в тороидальных и линейных накопителях электроэнергии. – Труды Крыловского государственного научного центра, 2021, 4(398), с. 123–128.
4. Цицикян Г.Н. О взаимной индуктивности и электродинамических силах взаимодействия коаксиальных контуров. – Известия Российской академии наук. Энергетика, 2018, № 4, с. 40–45.
5. Цицикян Г.Н. О коэффициентах взаимной индукции и силах взаимодействия круговых коаксиальных контуров. – Электричество, 2019, № 6, с. 59–65.
6. Цицикян Г.Н., Бобровников П.В., Антипов М.Ю. Руководство по расчёту индуктивности и электродинамических сил в токоведущих частях электротехнических комплексов. СПб.: ФГУП «Крыловский государственный научный центр», 2020, 118 с.
7. Калантаров П.Л., Цейтлин Л.А. Расчёт индуктивностей. Справочная книга. Л.: Энергоатомиздат, 1986, 488 с.
8. Knight D.W. Solenoid Inductance Calculation, 2003 [Электрон. ресурс], URL: http://g3ynh.info/zdocs/magnetics (дата обращения 15.12.2021).
9. Snow C. Formulas for Computing Capacitance and Inductance. National Bureau of Standards. Circular, 1954.
10. Soma M., Galbraith D., White R. Radio-frequency Coils in Implantable Devices. Misalignment Analysis and Design Procedure. – IEEE Transactions on Biomedical Engineering, 1987, vol. BME-34, No. 4, pp. 276–282, DOI:10. 10.1109/TBME.1987.326088.
11. Johnk C.T.A. Engineering Electromagnetic Field and Waves. New York: Wiley, 1991, 656 p.
12. Paul C.R. Inductance Loop and Partial. N.Y.: John Wiley and Sons, 2010, 379 p., DOI:10.1002/9780470561232.
13. Демирчян К.С. и др. Теоретические основы электротехники: том 3. СПб.: Питер, 2003, 377 с.
#
1. Garrett M.W. Calculation of Fields, Forces and Mutual Induc-tance of Current Systems by Elliptic Integrals. – Journal of Applied Physics, 1963, vol. 34, No. 9, pp. 2567–2573.
2. Thompson M.T. Inductance Calculations Techniques – Part II: Approximations and Handbook Methods, Power Control and Intelligent Motion, 1999, 11 с.
3. Tsitsikyan G.N. Trudy Krylovskogo gosudarstvennogo nauchnogo tsentra – in Russ. (Proceedings of the Krylov State Scientific Center), 2021, 4(398), pp. 123–128.
4. Tsitsikyan G.N. Izvestiya RAN. Energetika – in Russ. (News of the Russian Academy of Sciences. Power Engineering), 2018, No. 4, pp. 40–45.
5. Tsitsikyan G.N. Elektrichestvo – in Russ. (Electricity), 2019, No. 6, pp. 59–65.
6. Tsitsikyan G.N., Bobrovnikov P.V., Antipov M.Yu. Rukovodstvo po raschyotu induktivnostey i elektrodinamicheskih sil v tokovedushchih chastyah elektrotekhnicheskih kompleksov (Manual for the calculation of inductances and electrodynamic forces in current-carrying parts of electrical complexes). SPb.: FGUP«Кrylovskiy gos. nauchnyy tsentr», 2020, 118 p.
7. Kalantarov P.L., Zeytlin L.L. Raschyot induktivnostey. Spravochnaya kniga (Calculation of Inductances. Reference Book). L: Energoatomizdat, 1986, 488 p.
8. Knight D.W. Solenoid Inductance Calculation, 2003 [Electron. resource], URL: http://g3ynh.info/zdocs/magnetics (Date of appeal 15.12.2021).
9. Snow C. Formulas for Computing Capacitance and Inductance. National Bureau of Standards. Circular, 1954.
10. Soma M., Galbraith D., White R. Radio-frequency Coils in Implantable Devices. Misalignment Analysis and Design Procedure. – IEEE Transactions on Biomedical Engineering, 1987, vol. BME-34, No. 4, pp. 276–282, DOI:10. 10.1109/TBME.1987.326088.
11. Johnk C.T.A. Engineering Electromagnetic Field and Waves. New York: Wiley, 1991, 656 p.
12. Paul C.R. Inductance Loop and Partial. N.Y.: John Wiley and Sons, 2010, 379 p., DOI:10.1002/9780470561232.
13. Demirchyan К.S., et al. Teoreticheskie osnovy elektrotekhniki (Theoretical Foundations of Electrical Engineering): vol. 3. SPb.: Piter, 2003, 377 p.
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2022-02-04
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