Determination of Radial Forces Acting Between Coaxial Coils Located in the Same Plane
Keywords:
coaxial turns, radial forces, planar coils, tensile forces
Abstract
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
1. Garrett M.W. Calculation of Fields, Forces and Mutual Inductance 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. 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.
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.
Published
2022-02-04
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