Inductance and Electrodynamic Forces in Circular Turns with Parallel Axes
Keywords:
mutual inductances, turns and coils with parallel axes, electrodynamic forces
Abstract
With a wireless method of transmitting electrical energy to autonomous objects, a need may arise to use connecting devices with inductively coupled structural elements. When choosing such devices, their effectiveness should be evaluated taking into account the technological and design features of the embodiment. Expressions for mutual inductance and electrodynamic forces with parallel displacement of mating turns and disk coils are considered. Simplified expressions for the derivative of the inductance coefficients in the coordinate characterizing the parallel displacement of the loops are obtained. By using the obtained expressions, the effect of parallel displacement of the loops on the electrodynamic interaction forces can be evaluated. The obtained expressions are verified by numerically comparing them with the exact solution. On this basis, the maximum level of convergence of the results has been determined.
References
1. Soma M., Galbraith D.C., White R.L. Radio-Frequency Coils in Implantable Devices: Misalignment Analysis and Design Procedure. – IEEE Transactions on Biomedical Engineering, 1987, vol. 34, No. 4, pp. 276–282, DOI: 10.1109/tbme.1987.326088.
2. Kim K.B. et al. Restoring Foree Between Two Noncoaxial Circular Coils. – IEEE Transactions on Magnetics, 1996, vol. 32, No. 2, pp. 478–484, DOI: 10.1109/20.486535Xplore.
3. Meyer P. et al. Design of contactless Energy – Transfer System for Desktop Peripherals. – IEEE Transactions on Industry Applications, 2011, vol. 47, No. 4, pp. 1643–1651, DOI:10.1109/TIA.2011.2153812.
4. Ren Y. Magnetic Force Calculation between Misaligned Coils for a Superconducting Magnet. — IEEE Transactions on Applied Superconductivity, 2016, vol. 20, No. 6, pp. 2350–2353, DOI:10.1109/TASC.2010.2068297.
5. Raju S. et al. Modeling of Mutual Coupling between Planar Inductors in Wireless Power Applications. – IEEE Transactions on Power Electronics, 2014, vol. 29, No. 1, pp. 481–490, DOI:10.1109/TPEL.2013.2253334.
6. Aebischer H.A. Inductance Formula for Rectangular Planar Spiral Inductors with Rectangular Conductor Cross Section. – Advanced Electromagnetics, 2020, vol. 9, No. 1, pp. 1–18.
7. Derkaoui M. et al. Design and Modeling of Octagonal Planar Inductor and Transformer in Monolithic Technology for RF Systems. – Journal of Electrical Engineering and Technology, 2021, vol. 16(7), pp.1481–1493.
8. Цицикян Г.Н., Кунаев С.Н. Строгие и приближённые выражения для коэффициента взаимной индукции и электродинамических сил соосных витков и плоских (дисковых) катушек с током. – Труды Крыловского государственного научного центра, 2022, т. 2, вып. 400, c. 127–132.
9. Li K.-R. et al. Defects Detection of High-Power DC Feeder with Multiple Parallel Cables Using Inductive Coupling Technigue. – IEEE Transactions on Power Delivery, 2020, vol. 35, No. 2, pp.787–793.
10. Двайт Г.Б. Таблицы интегралов и другие математические формулы: 10-е изд. СПб.: Лань, 2009, 228 с.
11. Цицикян Г.Н. О взаимной индуктивности и электродинамических силах взаимодействия коаксиальных контуров. – Известия РАН. Энергетика, 2018, № 4, c. 40–45.
12. Grover F.W. Inductance Calculation: Working Formulas and Tables. N.Y.: D VanNostrand. 1946, XIV, 286 p.
13. Цицикян Г.Н. К вопросу о коэффициенте взаимной индуктивности соленоида и кругового контура с параллельными осями. – Труды Крыловского государственного научного центра, 2021, т. 2, вып. 396, c. 93–98.
14. Герасимов В.А., Комлев А.В., Филоженко А.Ю. Новая методика расчета силового трансформатора для системы бесконтактного заряда аккумуляторных батарей подводного робота. – Труды Крыловского государственного научного центра, 2022, т. 2, № 400, с. 116–126.
15. Ким К.И., Ким К.К., Вешкин В.В. Магнитное поле и силы в гибридной системе левитации высокоскоростного транспорта. – Электричество, 2021, № 6, с. 44–50.
16. Цицикян Г.Н., Антипов М.Ю. Электродинамические силы, действующие на контур с током в поле соленоида при его перемещении вдоль оси. – Электричество, 2020, № 8, c. 58–62.
17. Chen H., Qian Z. Modeling and Characterization of Parasitic Inductive Coupling Effects of differential-Mode EMI Performance of a Boost Converter. – IEEE Transactions of Electromagnetic Compatibility, 2011, vol. 53, No. 4, pp. 1072–1080, DOI:10.1109/TEMC.2010.2102030.
#
1. Soma M., Galbraith D.C., White R.L. Radio-Frequency Coils in Implantable Devices: Misalignment Analysis and Design Procedure. – IEEE Transactions on Biomedical Engineering, 1987, vol. 34, No. 4, pp. 276–282, DOI: 10.1109/tbme.1987.326088.
2. Kim K.B. et al. Restoring Foree Between Two Noncoaxial Circular Coils. – IEEE Transactions on Magnetics, 1996, vol. 32, No. 2, pp. 478–484, DOI: 10.1109/20.486535Xplore.
3. Meyer P. et al. Design of contactless Energy – Transfer System for Desktop Peripherals. – IEEE Transactions on Industry Applications, 2011, vol. 47, No. 4, pp. 1643–1651, DOI:10.1109/TIA.2011.2153812.
4. Ren Y. Magnetic Force Calculation between Misaligned Coils for a Superconducting Magnet. — IEEE Transactions on Applied Superconductivity, 2016, vol. 20, No. 6, pp. 2350–2353, DOI:10.1109/TASC.2010.2068297.
5. Raju S. et al. Modeling of Mutual Coupling between Planar Inductors in Wireless Power Applications. – IEEE Transactions on Power Electronics, 2014, vol. 29, No. 1, pp. 481–490, DOI:10.1109/TPEL.2013.2253334.
6. Aebischer H.A. Inductance Formula for Rectangular Planar Spiral Inductors with Rectangular Conductor Cross Section. – Advanced Electromagnetics, 2020, vol. 9, No. 1, pp. 1–18.
7. Derkaoui M. et al. Design and Modeling of Octagonal Planar Inductor and Transformer in Monolithic Technology for RF Systems. – Journal of Electrical Engineering and Technology, 2021, vol. 16(7), pp.1481–1493.
8. Tsitsikyan G.N., Kunaev S.N. Trudy Krylovskogo gosudarstvennogo nauchnogo tsentra – in Russ. (Transactions of the Krylov State Research Centre), 2022, vol. 2, iss. 400, pp. 127–132.
9. Li K.-R. et al. Defects Detection of High-Power DC Feeder with Multiple Parallel Cables Using Inductive Coupling Technigue. – IEEE Transactions on Power Delivery, 2020, vol. 35, No. 2, pp.787–793.
10. Dvayt G.B. Tablitsy integralov i drugie matematicheskie formuly (Tables of Integrals and Other Mathematical Formulas): 10th ed. SPb.: Lan', 2009, 228 p.
11. Tsitsikyan G.N. Izvestiya RAN. Energetika – in Russ. (News of the Russian Academy of Sciences. Power Engineering), 2018, No. 4, pp. 40–45.
12. Grover F.W. Inductance Calculation: Working Formulas and Tables. N.Y.: D VanNostrand. 1946, XIV, 286 p.
13. Tsitsikyan G.N. Trudy Krylovskogo gosudarstvennogo nauchnogo tsentra – in Russ. (Transactions of the Krylov State Research Centre), 2021, vol. 2, iss. 396, pp. 93–98.
14. Gerasimov V.A., Komlev A.V., Filozhenko A.Yu. Trudy Krylovskogo gosudarstvennogo nauchnogo tsentra – in Russ. (Transactions of the Krylov State Research Centre), 2022, vol. 2, iss. 400, pp. 116–126.
15. Ким К.И., Ким К.К., Вешкин В.В. Elektrichestvo – in Russ. (Electricity), 2021, No. 6, pp. 44–50.
16. Tsitsikyan G.N., Antipov M.Yu. Elektrichestvo – in Russ. (Electricity), 2020, No. 8, pp. 58–62.
17. Chen H., Qian Z. Modeling and Characterization of Parasitic Inductive Coupling Effects of differential-Mode EMI Performance of a Boost Converter. – IEEE Transactions of Electromagnetic Compatibility, 2011, vol. 53, No. 4, pp. 1072–1080, DOI:10.1109/TEMC.2010.2102030.
2. Kim K.B. et al. Restoring Foree Between Two Noncoaxial Circular Coils. – IEEE Transactions on Magnetics, 1996, vol. 32, No. 2, pp. 478–484, DOI: 10.1109/20.486535Xplore.
3. Meyer P. et al. Design of contactless Energy – Transfer System for Desktop Peripherals. – IEEE Transactions on Industry Applications, 2011, vol. 47, No. 4, pp. 1643–1651, DOI:10.1109/TIA.2011.2153812.
4. Ren Y. Magnetic Force Calculation between Misaligned Coils for a Superconducting Magnet. — IEEE Transactions on Applied Superconductivity, 2016, vol. 20, No. 6, pp. 2350–2353, DOI:10.1109/TASC.2010.2068297.
5. Raju S. et al. Modeling of Mutual Coupling between Planar Inductors in Wireless Power Applications. – IEEE Transactions on Power Electronics, 2014, vol. 29, No. 1, pp. 481–490, DOI:10.1109/TPEL.2013.2253334.
6. Aebischer H.A. Inductance Formula for Rectangular Planar Spiral Inductors with Rectangular Conductor Cross Section. – Advanced Electromagnetics, 2020, vol. 9, No. 1, pp. 1–18.
7. Derkaoui M. et al. Design and Modeling of Octagonal Planar Inductor and Transformer in Monolithic Technology for RF Systems. – Journal of Electrical Engineering and Technology, 2021, vol. 16(7), pp.1481–1493.
8. Цицикян Г.Н., Кунаев С.Н. Строгие и приближённые выражения для коэффициента взаимной индукции и электродинамических сил соосных витков и плоских (дисковых) катушек с током. – Труды Крыловского государственного научного центра, 2022, т. 2, вып. 400, c. 127–132.
9. Li K.-R. et al. Defects Detection of High-Power DC Feeder with Multiple Parallel Cables Using Inductive Coupling Technigue. – IEEE Transactions on Power Delivery, 2020, vol. 35, No. 2, pp.787–793.
10. Двайт Г.Б. Таблицы интегралов и другие математические формулы: 10-е изд. СПб.: Лань, 2009, 228 с.
11. Цицикян Г.Н. О взаимной индуктивности и электродинамических силах взаимодействия коаксиальных контуров. – Известия РАН. Энергетика, 2018, № 4, c. 40–45.
12. Grover F.W. Inductance Calculation: Working Formulas and Tables. N.Y.: D VanNostrand. 1946, XIV, 286 p.
13. Цицикян Г.Н. К вопросу о коэффициенте взаимной индуктивности соленоида и кругового контура с параллельными осями. – Труды Крыловского государственного научного центра, 2021, т. 2, вып. 396, c. 93–98.
14. Герасимов В.А., Комлев А.В., Филоженко А.Ю. Новая методика расчета силового трансформатора для системы бесконтактного заряда аккумуляторных батарей подводного робота. – Труды Крыловского государственного научного центра, 2022, т. 2, № 400, с. 116–126.
15. Ким К.И., Ким К.К., Вешкин В.В. Магнитное поле и силы в гибридной системе левитации высокоскоростного транспорта. – Электричество, 2021, № 6, с. 44–50.
16. Цицикян Г.Н., Антипов М.Ю. Электродинамические силы, действующие на контур с током в поле соленоида при его перемещении вдоль оси. – Электричество, 2020, № 8, c. 58–62.
17. Chen H., Qian Z. Modeling and Characterization of Parasitic Inductive Coupling Effects of differential-Mode EMI Performance of a Boost Converter. – IEEE Transactions of Electromagnetic Compatibility, 2011, vol. 53, No. 4, pp. 1072–1080, DOI:10.1109/TEMC.2010.2102030.
#
1. Soma M., Galbraith D.C., White R.L. Radio-Frequency Coils in Implantable Devices: Misalignment Analysis and Design Procedure. – IEEE Transactions on Biomedical Engineering, 1987, vol. 34, No. 4, pp. 276–282, DOI: 10.1109/tbme.1987.326088.
2. Kim K.B. et al. Restoring Foree Between Two Noncoaxial Circular Coils. – IEEE Transactions on Magnetics, 1996, vol. 32, No. 2, pp. 478–484, DOI: 10.1109/20.486535Xplore.
3. Meyer P. et al. Design of contactless Energy – Transfer System for Desktop Peripherals. – IEEE Transactions on Industry Applications, 2011, vol. 47, No. 4, pp. 1643–1651, DOI:10.1109/TIA.2011.2153812.
4. Ren Y. Magnetic Force Calculation between Misaligned Coils for a Superconducting Magnet. — IEEE Transactions on Applied Superconductivity, 2016, vol. 20, No. 6, pp. 2350–2353, DOI:10.1109/TASC.2010.2068297.
5. Raju S. et al. Modeling of Mutual Coupling between Planar Inductors in Wireless Power Applications. – IEEE Transactions on Power Electronics, 2014, vol. 29, No. 1, pp. 481–490, DOI:10.1109/TPEL.2013.2253334.
6. Aebischer H.A. Inductance Formula for Rectangular Planar Spiral Inductors with Rectangular Conductor Cross Section. – Advanced Electromagnetics, 2020, vol. 9, No. 1, pp. 1–18.
7. Derkaoui M. et al. Design and Modeling of Octagonal Planar Inductor and Transformer in Monolithic Technology for RF Systems. – Journal of Electrical Engineering and Technology, 2021, vol. 16(7), pp.1481–1493.
8. Tsitsikyan G.N., Kunaev S.N. Trudy Krylovskogo gosudarstvennogo nauchnogo tsentra – in Russ. (Transactions of the Krylov State Research Centre), 2022, vol. 2, iss. 400, pp. 127–132.
9. Li K.-R. et al. Defects Detection of High-Power DC Feeder with Multiple Parallel Cables Using Inductive Coupling Technigue. – IEEE Transactions on Power Delivery, 2020, vol. 35, No. 2, pp.787–793.
10. Dvayt G.B. Tablitsy integralov i drugie matematicheskie formuly (Tables of Integrals and Other Mathematical Formulas): 10th ed. SPb.: Lan', 2009, 228 p.
11. Tsitsikyan G.N. Izvestiya RAN. Energetika – in Russ. (News of the Russian Academy of Sciences. Power Engineering), 2018, No. 4, pp. 40–45.
12. Grover F.W. Inductance Calculation: Working Formulas and Tables. N.Y.: D VanNostrand. 1946, XIV, 286 p.
13. Tsitsikyan G.N. Trudy Krylovskogo gosudarstvennogo nauchnogo tsentra – in Russ. (Transactions of the Krylov State Research Centre), 2021, vol. 2, iss. 396, pp. 93–98.
14. Gerasimov V.A., Komlev A.V., Filozhenko A.Yu. Trudy Krylovskogo gosudarstvennogo nauchnogo tsentra – in Russ. (Transactions of the Krylov State Research Centre), 2022, vol. 2, iss. 400, pp. 116–126.
15. Ким К.И., Ким К.К., Вешкин В.В. Elektrichestvo – in Russ. (Electricity), 2021, No. 6, pp. 44–50.
16. Tsitsikyan G.N., Antipov M.Yu. Elektrichestvo – in Russ. (Electricity), 2020, No. 8, pp. 58–62.
17. Chen H., Qian Z. Modeling and Characterization of Parasitic Inductive Coupling Effects of differential-Mode EMI Performance of a Boost Converter. – IEEE Transactions of Electromagnetic Compatibility, 2011, vol. 53, No. 4, pp. 1072–1080, DOI:10.1109/TEMC.2010.2102030.
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2022-11-17
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