Inductance and Compression Forces in Double-Layer Coils
Keywords:
single-layer and double-layer solenoids, self-induction coefficient, axial compression forces
Abstract
Expressions for calculating the self-induction coefficients of two-layer and single-layer coils are considered, and related comparisons are carried out. Examples of calculating the induction coefficients for known design versions of coils are given. An expression for calculating axial compression forces in two-layer coils is presented. The axial compression forces in coils as part of three-phase load devices designed for testing generator sets of autonomous power plants have been calculated. The expressions obtained for calculating the inductances and axial compression forces in two-layer coils are quite concise and can be recommended for practical use. These expressions include only the coil design parameters: the number of turns in the layers, layer radii, winding pitches, and layer lengths. The article is illustrated with particular examples of calculating the coil inductance and compression forces.
References
1. Korovkin N.V., Vu Q.S., Yazenin R.A. A Method for Minimization of Unbalanced Mode in Three-Phase Power Systems. – 2016 IEEE NW Russia Young Researchers in Electrical and Electronic Engineering Conference (EIConRusNW), 2016, DOI:10.1109/EIConRusNW.2016.7448257.
2. Korovkin N.V., Chechurin V.L., Hayakawa M. Inverse Problems in Electric Circuits and Electromagnetics. Springer Science, 2007, 331 p,
3. Knight D.W. An Introduction to the art of Solenoid Inductance and Impedance Calculation [Электрон. ресурс], URL: https://www.g3ynh.info/zdocs/magnetics/SolenoidZ.pdf (дата обращения 15.12.2021).
4. Thompson M.T. Inductance Calculations Techniques – Part II: Approximations and Handbook Methods, Power Control and Intelligent Motion, 1999, 11 с.
5. Ramo S., Winnery J.R., Van Duzer T. Fields and Waves in Communication Electronics. Hoboken: Wiley, 1994, 859 p.
6. De Queiroz A.C.M. Mutual Inductance and Inductance Calculations by Maxwell’s Method [Электрон. ресурс], URL: https://www.Researchgate.net/publication/266891743_Mutual-_Inductance_and_ Inductance_Calculations_ by_Maxwell's_Method (дата обращения 15.12.2021).
7. Numerical Methods for Inductance Calculation. Robert Weaver [Электрон. ресурс], URL: http://electronbunker.ca/eb/CalcMethods.html (дата обращения 15.12.2021).
8. Liu X., Hui S.Y. Optimal Design of a Hybrid Winding Structure for Planar Contactless Battery Charging Platform. – IEEE Transactions on Power Electronics, 2008, vol. 23 No. 1, pp. 455–463.
9. Lane J.E., et al. Magnetic Field, Force and Inductance Computations for an Axially Symmetric Solenoid. NASA/TM-2013-217918, 2001.
10. Цицикян Г.Н., Антипов М.Ю. Оценка сжимающих сил, действующих на тонкослойные катушки (соленоиды) с током. – Известия РАН. Энергетика, 2018, № 8, с. 26–31.
11. Wheeler H.A. Inductance Formulas for Circular and Square Coils. – Proc. of the IEEE Letters, 1982, vol.70, No.12, pp. 1449–1451.
12. Цицикян Г.Н., Антипов М.Ю. Расчёт индуктивности однослойного и двухслойного соленоида с учётом особенностей практического применения. – Электричество, 2019, № 10, с. 48–53.
13. Калантаров П.Л., Цейтлин Л.Л. Расчёт индуктивностей. Справочная книга. Л: Энергоатомиздат, 1986, 488 с.
14. Цицикян Г.Н., Бобровников П.В., Антипов М.Ю. Руководство по расчёту индуктивностей и электродинамических сил в токоведущих частях электротехнических комплексов. СПб.: ФГУП «Крыловский государственный научный центр», 2020, 118 с.
#
1. Korovkin N.V., Vu Q.S., Yazenin R.A. A Method for Minimi-zation of Unbalanced Mode in Three-Phase Power Systems. – 2016 IEEE NW Russia Young Researchers in Electrical and Electronic Engineering Conference (EIConRusNW), 2016, DOI:10.1109/EICon RusNW.2016.7448257.
2. Korovkin N.V., Chechurin V.L., Hayakawa M. Inverse Problems in Electric Circuits and Electromagnetics. Springer Science, 2007, 331 p,
3. Knight D.W. An introduction to the art of Solenoid Inductance and Impedance Calculation [Electron. resource], URL: https://www.g3ynh.info/zdocs/magnetics/SolenoidZ.pdf (Date of appeal 15.12.2021).
4. Thompson M.T. Inductance Calculations Techniques – Part II: Approximations and Handbook Methods, Power Control and Intelligent Motion, 1999, 11 p.
5. Ramo S., Winnery J.R., Van Duzer T. Fields and Waves in Communication Electronics. Hoboken: Wiley, 1994, 859 p.
6. De Queiroz A.C.M. Mutual Inductance and Inductance Calculations by Maxwell’s Method [Electron. resource], URL: https://www.Researchgate.net/publication/266891743_Mutual¬_Inductance_and_ Inductance_Calculations_ by_Maxwell's_Method (Date of appeal 15.12.2021).
7. Numerical Methods for Inductance Calculation. Robert Weaver [Electron. resource] URL: http://electronbunker.ca/eb/CalcMethods.html (Date of appeal 15.12.2021).
8. Liu X., Hui S.Y. Optimal Design of a Hybrid Winding Structure for Planar Contactless Battery Charging Platform. – IEEE Transactions on Power Electronics, 2008, vol. 23 No. 1, pp. 455–463.
9. Lane J.E., et al. Magnetic Field, Force and Inductance Computations for an Axially Symmetric Solenoid. NASA/TM-2013-217918, 2001.
10. Tsitsikyan G.N., Antipov M.Yu. Izvestiya RAN. Energetika – in Russ. (News of the Russian Academy of Sciences. Power Engineering), 2018, No. 8, pp. 26–31.
11. Wheeler H.A. Inductance Formulas for Circular and Square Coils. – Proc. of the IEEE Letters, 1982, vol.70, No.12, pp. 1449–1451.
12. Tsitsikyan G.N., Antipov M.Yu. Elektrichestvo – in Russ. (Electricity), 2019, No. 10, pp. 48–53.
13. Kalantarov P.L., Zeytlin L.L. Raschyot induktivnostey. Spravochnaya kniga (Calculation of Inductances. Reference Book). L: Energoatomizdat, 1986, 488 p.
14. Tsitsikyan G.N., Bobrovnikov P.V., Antipov M.Yu. Ruko-vodstvo 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.
2. Korovkin N.V., Chechurin V.L., Hayakawa M. Inverse Problems in Electric Circuits and Electromagnetics. Springer Science, 2007, 331 p,
3. Knight D.W. An Introduction to the art of Solenoid Inductance and Impedance Calculation [Электрон. ресурс], URL: https://www.g3ynh.info/zdocs/magnetics/SolenoidZ.pdf (дата обращения 15.12.2021).
4. Thompson M.T. Inductance Calculations Techniques – Part II: Approximations and Handbook Methods, Power Control and Intelligent Motion, 1999, 11 с.
5. Ramo S., Winnery J.R., Van Duzer T. Fields and Waves in Communication Electronics. Hoboken: Wiley, 1994, 859 p.
6. De Queiroz A.C.M. Mutual Inductance and Inductance Calculations by Maxwell’s Method [Электрон. ресурс], URL: https://www.Researchgate.net/publication/266891743_Mutual-_Inductance_and_ Inductance_Calculations_ by_Maxwell's_Method (дата обращения 15.12.2021).
7. Numerical Methods for Inductance Calculation. Robert Weaver [Электрон. ресурс], URL: http://electronbunker.ca/eb/CalcMethods.html (дата обращения 15.12.2021).
8. Liu X., Hui S.Y. Optimal Design of a Hybrid Winding Structure for Planar Contactless Battery Charging Platform. – IEEE Transactions on Power Electronics, 2008, vol. 23 No. 1, pp. 455–463.
9. Lane J.E., et al. Magnetic Field, Force and Inductance Computations for an Axially Symmetric Solenoid. NASA/TM-2013-217918, 2001.
10. Цицикян Г.Н., Антипов М.Ю. Оценка сжимающих сил, действующих на тонкослойные катушки (соленоиды) с током. – Известия РАН. Энергетика, 2018, № 8, с. 26–31.
11. Wheeler H.A. Inductance Formulas for Circular and Square Coils. – Proc. of the IEEE Letters, 1982, vol.70, No.12, pp. 1449–1451.
12. Цицикян Г.Н., Антипов М.Ю. Расчёт индуктивности однослойного и двухслойного соленоида с учётом особенностей практического применения. – Электричество, 2019, № 10, с. 48–53.
13. Калантаров П.Л., Цейтлин Л.Л. Расчёт индуктивностей. Справочная книга. Л: Энергоатомиздат, 1986, 488 с.
14. Цицикян Г.Н., Бобровников П.В., Антипов М.Ю. Руководство по расчёту индуктивностей и электродинамических сил в токоведущих частях электротехнических комплексов. СПб.: ФГУП «Крыловский государственный научный центр», 2020, 118 с.
#
1. Korovkin N.V., Vu Q.S., Yazenin R.A. A Method for Minimi-zation of Unbalanced Mode in Three-Phase Power Systems. – 2016 IEEE NW Russia Young Researchers in Electrical and Electronic Engineering Conference (EIConRusNW), 2016, DOI:10.1109/EICon RusNW.2016.7448257.
2. Korovkin N.V., Chechurin V.L., Hayakawa M. Inverse Problems in Electric Circuits and Electromagnetics. Springer Science, 2007, 331 p,
3. Knight D.W. An introduction to the art of Solenoid Inductance and Impedance Calculation [Electron. resource], URL: https://www.g3ynh.info/zdocs/magnetics/SolenoidZ.pdf (Date of appeal 15.12.2021).
4. Thompson M.T. Inductance Calculations Techniques – Part II: Approximations and Handbook Methods, Power Control and Intelligent Motion, 1999, 11 p.
5. Ramo S., Winnery J.R., Van Duzer T. Fields and Waves in Communication Electronics. Hoboken: Wiley, 1994, 859 p.
6. De Queiroz A.C.M. Mutual Inductance and Inductance Calculations by Maxwell’s Method [Electron. resource], URL: https://www.Researchgate.net/publication/266891743_Mutual¬_Inductance_and_ Inductance_Calculations_ by_Maxwell's_Method (Date of appeal 15.12.2021).
7. Numerical Methods for Inductance Calculation. Robert Weaver [Electron. resource] URL: http://electronbunker.ca/eb/CalcMethods.html (Date of appeal 15.12.2021).
8. Liu X., Hui S.Y. Optimal Design of a Hybrid Winding Structure for Planar Contactless Battery Charging Platform. – IEEE Transactions on Power Electronics, 2008, vol. 23 No. 1, pp. 455–463.
9. Lane J.E., et al. Magnetic Field, Force and Inductance Computations for an Axially Symmetric Solenoid. NASA/TM-2013-217918, 2001.
10. Tsitsikyan G.N., Antipov M.Yu. Izvestiya RAN. Energetika – in Russ. (News of the Russian Academy of Sciences. Power Engineering), 2018, No. 8, pp. 26–31.
11. Wheeler H.A. Inductance Formulas for Circular and Square Coils. – Proc. of the IEEE Letters, 1982, vol.70, No.12, pp. 1449–1451.
12. Tsitsikyan G.N., Antipov M.Yu. Elektrichestvo – in Russ. (Electricity), 2019, No. 10, pp. 48–53.
13. Kalantarov P.L., Zeytlin L.L. Raschyot induktivnostey. Spravochnaya kniga (Calculation of Inductances. Reference Book). L: Energoatomizdat, 1986, 488 p.
14. Tsitsikyan G.N., Bobrovnikov P.V., Antipov M.Yu. Ruko-vodstvo 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.
Published
2021-12-15
Issue
Section
Article
