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The inductance of various coil types used in eddy current testing: A theoretical, experimental, and numerical analysis

Year 2025, Volume: 14 Issue: 2, 1 - 1

Abstract

In the transmission of electrical energy, Aluminum Coated Steel (ACS) wires are frequently used. During the manufacturing of these wires, eddy current testing systems, which are one of the non-destructive testing methods, are used to detect deformations that occur on their surfaces. The sensors included in this test system reference inductance changes to detect defects on the material surface. In determining the inductance values in sensors, analytical, numerical, and experimental methods are preferred. In this study, the COMSOL Multiphysics program was used by employing the Harold A. Wheeler method for analytical calculations and the finite element method for numerical calculations. For reference, the inductance values of 26 coils produced with the same parameters were experimentally measured, and the accuracy of the inductance values calculated by the other two methods was compared to determine which method is more reliable for calculating coil inductance. According to the reference LCR meter measurements for the Harold A. Wheeler method, the deviation value ranges from 0.02% to 6.32%, while the deviation value for the developed COMSOL Multiphysics method is calculated to be in the range of 0.18% to 4.83%. It has been shown that this proposed method will be more effective in industrial applications.

Project Number

5220140 nolu 1505 Sanayi Üniversite İşbirliği Projesi

References

  • B. Li, L. Liu, P. Dang, G. Wang, L. Tang, and T. Li, Study on corrosion test of corrosion-proof steel core of high-anticorrosive conductor. In 2020 IEEE International Conference on High Voltage Engineering and Application (ICHVE), pp. 1-4, Beijing, China, 6-10 September 2020.
  • N. A. Jaffrey and S. Hettiwatte, Corrosion detection in steel reinforced aluminium conductor cables. In 2014 Australasian Universities Power Engineering Conference (AUPEC), pp. 1-6, Perth, Australia, 28 September - 1 October 2014.
  • A. S. Arman, S. W. Glass, L. S. Fifield, and M. Ali, Non-conductor-contact surface wave reflectometry for cable insulation damage detection, IEEE Sensors Journal, 22(11), 11065-11074, 2022. https://doi.org /10.1109/JSEN.2022.3167609.
  • K. J. Stevens, K. Lichti, I. A. Minchington, N. Janke-Gilman, T. Mactutis, D. Rook, and P. Bondurant, Conductor damage inspection system for overhead ACSR power cables CDIS on ACSR. In 2013 Seventh International Conference on Sensing Technology (ICST), pp. 901-905, Wellington, New Zealand, 3-5 December 2013.
  • X. Huang, R. Ding, W. Pan, C. Yang, Y. Xu, Y. Miao, Q. Zhuang, J. Zhu, M. Wu, Z. Lei, and Y. Li, Overview of quality control issues related to submarine cables in project cycle of offshore wind power projects in Jiangsu. In 2020 12th IEEE PES Asia-Pacific Power and Energy Engineering Conference (APPEEC), pp. 1-5, Nanjing, China, 20-23 September 2020.
  • T. N. Hung, Methods for fault location in high voltage power transmission lines: A comparative analysis. International Journal of Renewable Energy Development, 11(4), 1134-1141, 2022. https://d oi.org/10.14710/ijred.2022.46501.
  • O. Kara, H. Erdal, ve H. H. Çelik, Tahribatsız test yöntemleri: Karşılaştırmalı bir derleme çalışması. Marmara Fen Bilimleri Dergisi, 29(3), 82-93, 2017. https://doi.org/10.7240/marufbd.326674.
  • K. Tsukada, M. Hayashi, Y. Nakamura, K. Sakai, and T. Kiwa, Small eddy current testing sensor probe using a tunneling magnetoresistance sensor to detect cracks in steel structures. IEEE Transactions on Magnetics, 54(11), 1-5, 2018. https://doi.org/10.1109/T MAG.2018.2845864.
  • G. Peruń, Advances in non-destructive testing methods. Materials, 17(3), 554, 2024. https://doi.org/10.3390/m a17030554.
  • S. K. Dwivedi, M. Vishwakarma, and P. A. Soni, Advances and researches on non destructive testing: A review. Materials Today: Proceedings, 5(2), 3690-3698, 2018. https://doi.org/10.1016/j.matpr.2017 .11.620.
  • C. Wang, M. Fan, B. Cao, B. Ye, and W. Li, Novel noncontact eddy current measurement of electrical conductivity. IEEE Sensors Journal, 18(22), 9352-9359, 2018. https://doi.org/10.1109/JSEN.201 8.2870676.
  • J. García-Martín, J. Gómez-Gil, and E. Vázquez-Sánchez, Non-destructive techniques based on eddy current testing. Sensors, 11(3), 2525-2565, 2011. https://doi.org/10.3390/s110302525.
  • W. Cheng, Measurement of magnetic plates at a few hertz with two concentric coils and thickness estimation using mutual inductance. IEEE Transactions on Instrumentation and Measurement, 70, 1-10, 2021. https://doi.org/10.1109/TIM.2021.3087820.
  • S. She, Y. Chen, Y. He, Z. Zhou, and X. Zou, Optimal design of remote field eddy current testing probe for ferromagnetic pipeline inspection. Measurement, 168, 108306,2021. https://doi.org/10.1016/j.measurement. 2020.108306
  • T. P. Theodoulidis and E. E. Kriezis, Impedance evaluation of rectangular coils for eddy current testing of planar media. NDT & E International, 35(6), 407-414, 2002. https://doi.org/10.1016/S0963-8695(02)000 08-7.
  • D. Vyroubal, Impedance of the eddy-current displacement probe: the transformer model. IEEE Transactions on Instrumentation and Measurement, 53(2),384-391,2004. https://doi.org/10.1109/TIM.200 3.822705.
  • S. Hao and B. Li, Calculation inductance of toroidal inductor wound by rectangular cross-sectional wire. IEEE Transactions on Plasma Science, 49(9), 2910-2915, 2021. https://doi.org/10.1109/TPS.202 1.3101570.
  • T. Župan, Š. Ž, and B. Trkulja, Fast and precise method for inductance calculation of coaxial circular coils with rectangular cross section using the one-dimensional integration of elementary functions applicable to superconducting magnets. IEEE Transactions on Applied Superconductivity, 24(2), 81-89, 2014. https://doi.org/10.1109/TASC.2014.2301765.
  • W. Liu, S. Dai, T. Ma, Y. Shi, M. Song, and L. Li, Analytical calculation of mutual inductance of d-shaped coils applied to high-temperature superconducting magnet. IEEE Transactions on Applied Superconductivity, 34(5), 1-5, 2024. https://doi.org/10.1109/TASC.2024.3358765.
  • H. A. Wheeler, Simple inductance formulas for radio coils. Proceedings of the Institute of Radio Engineers, 16(10), 1398-1400, 1928. https://doi.org/10.1 109/JRPROC.1928.221309.
  • J. Kim, K. Kim, B. Kim, and J. Kang, Experimental validation of multi-layer coil inductance estimation method. In 2017 IEEE International Symposium on Antennas and Propagation & USNC/URSI National Radio Science Meeting, pp. 1303-1304, San Diego, California, 2017.
  • S. Kumar and Y. K. Jain, Simulation of circular-shaped PZT-5H sensor for train measurement using COMSOL multiphysics. IEEE Sensors Journal, 15(8), 4380-4387, 2015. https://doi.org/10.1109/JSEN.2015.2419281
  • Z. Xia, A. A. Bhatti, X. Peng, B. Yang, H. Zhou, C. Zhao, and C. Xie, Electric field and temperature distribution of high voltage cables with the addition of particles based on COMSOL simulation. In 2020 IEEE International Conference on High Voltage Engineering and Application (ICHVE), pp. 1-4, Beijing, China, 2020.
  • S. V. Oskin, A. V. Miroshnikov, and D. S. Tsokur, Studying the Aerodynamic Characteristics of Electric Motors in COMSOL Multiphysics. In 2021 International Conference on Industrial Engineering, Applications and Manufacturing (ICIEAM), pp. 350-354, Sochi, Russia, 2021.
  • D. S. Filip and D. Petreus, Simulation of an inductive coupled power transfer system. In IECON 2016 - 42nd Annual Conference of the IEEE Industrial Electronics Society, pp. 6559-6564, Florence, Italy, 2016.
  • S. M. Mousavi and A. Ghayebloo, Design and implementation a new coil and introduction a topology for electric vehicle wireless charger. In 2024 28th International Electrical Power Distribution Conference (EPDC), pp. 1-8, Zanjan, Iran, 2024.
  • F. Gozalpour and M. Yavari, 2-D axisymmetric modeling of circular PCB coils and solenoids in COMSOL multiphysics. In 2023 5th Iranian International Conference on Microelectronics (IICM), pp. 102-106, Tehran, Iran, 2023.
  • K. Slobodnk, Detection and evaluation of subsurface defects using pulse eddy current differential probe. In 2017 18th International Conference on Computational Problems of Electrical Engineering (CPEE), pp. 1-4, Kutna Hora, Czech Republic, 2017.
  • R. Singh and V. Singh, Analysis of eddy current damper for suppression of vibrations using COMSOL software. Engineering Solid Mechanics, 3(4), 215-222, 2015. http://dx.doi.org/10.5267/j.esm.2015.7.004.
  • M. Elbaa, K. Berger, B. Douine, M. Halit, E. H. Ailam, and S. E. Bentridi, Analytical modeling of an inductor in a magnetic circuit for pulsed field magnetization of HTS bulks. IEEE Transactions on Applied Superconductivity, 28(4), 1-6, 2018. https://doi.org/10.1109/TASC.2018.2809438.
  • S. Balaji and P. D. Sundari, COMSOL FEA modeling of square and cirular coil for inductive power transfer in electric vehicle systems. In 2023 Third International Conference on Advances in Electrical, Computing, Communication and Sustainable Technologies (ICAECT), pp. 1-4, Bhilai, India, 2023.

Girdap akım testinde kullanılan farklı tip bobinlerin endüktansının teorik, deneysel ve sayısal incelenmesi

Year 2025, Volume: 14 Issue: 2, 1 - 1

Abstract

Elektrik enerjisinin iletiminde Alüminyum Kaplı Çelik (ACS) teller sıklıkla kullanılmaktadır. Bu tellerin imalatı esnasında yüzeylerinde meydana gelen deformasyonları tespit etmek için tahribatsız muayene yöntemlerinden biri olan girdap akım test sistemleri kullanılmaktadır. Bu test sisteminde yer alan sensörler, malzeme yüzeyindeki kusurların tespitinde indüktans değişimlerini referans almaktadır. Sensörlerdeki indüktans değerlerinin belirlenmesinde analitik, numerik ve deneysel yöntemler tercih edilmektedir. Bu çalışmada analitik hesaplama için Harold A. Wheeler yöntemi ve numerik hesaplama için sonlu elemanlar metodundan faydalanarak COMSOL Multiphysics programı kullanılmıştır. Referans olması için aynı parametrelerle üretilen 26 adet bobinin indüktans değerleri deneysel olarak ölçülmüş ve diğer iki yöntemle hesaplanan indüktans değerlerinin doğruluğu karşılaştırılarak bobin indüktansının hesaplanmasında hangi yöntemin daha güvenilir olduğu belirlenmiştir. Harold A. Wheeler yönteminin referans olarak kullanılan LCR metre ölçümlerine göre sapma değeri %0.02 ile %6.32 aralığında, geliştirilen COMSOL Multiphysics yöntemindeki sapma değeri ise %0.18 ile %4.83 aralığında hesaplanmıştır. Önerilen bu yöntemin endüstriyel uygulamalarda daha etkin olacağı ortaya konulmuştur.

Supporting Institution

TUBİTAK

Project Number

5220140 nolu 1505 Sanayi Üniversite İşbirliği Projesi

Thanks

Bu çalışma TUBİTAK 1505 Üniversite Sanayi iş birliği projesi kapsamında 5220140 kodu ile desteklenmektedir. Ayrıca çalışmamız Hasçelik Kablo San. Tic. A. Ş. Ar-Ge Merkezi bünyesinde gerçekleştirilmiştir. Katkılarından dolayı firmaya ve TÜBİTAK’a teşekkür ederiz.

References

  • B. Li, L. Liu, P. Dang, G. Wang, L. Tang, and T. Li, Study on corrosion test of corrosion-proof steel core of high-anticorrosive conductor. In 2020 IEEE International Conference on High Voltage Engineering and Application (ICHVE), pp. 1-4, Beijing, China, 6-10 September 2020.
  • N. A. Jaffrey and S. Hettiwatte, Corrosion detection in steel reinforced aluminium conductor cables. In 2014 Australasian Universities Power Engineering Conference (AUPEC), pp. 1-6, Perth, Australia, 28 September - 1 October 2014.
  • A. S. Arman, S. W. Glass, L. S. Fifield, and M. Ali, Non-conductor-contact surface wave reflectometry for cable insulation damage detection, IEEE Sensors Journal, 22(11), 11065-11074, 2022. https://doi.org /10.1109/JSEN.2022.3167609.
  • K. J. Stevens, K. Lichti, I. A. Minchington, N. Janke-Gilman, T. Mactutis, D. Rook, and P. Bondurant, Conductor damage inspection system for overhead ACSR power cables CDIS on ACSR. In 2013 Seventh International Conference on Sensing Technology (ICST), pp. 901-905, Wellington, New Zealand, 3-5 December 2013.
  • X. Huang, R. Ding, W. Pan, C. Yang, Y. Xu, Y. Miao, Q. Zhuang, J. Zhu, M. Wu, Z. Lei, and Y. Li, Overview of quality control issues related to submarine cables in project cycle of offshore wind power projects in Jiangsu. In 2020 12th IEEE PES Asia-Pacific Power and Energy Engineering Conference (APPEEC), pp. 1-5, Nanjing, China, 20-23 September 2020.
  • T. N. Hung, Methods for fault location in high voltage power transmission lines: A comparative analysis. International Journal of Renewable Energy Development, 11(4), 1134-1141, 2022. https://d oi.org/10.14710/ijred.2022.46501.
  • O. Kara, H. Erdal, ve H. H. Çelik, Tahribatsız test yöntemleri: Karşılaştırmalı bir derleme çalışması. Marmara Fen Bilimleri Dergisi, 29(3), 82-93, 2017. https://doi.org/10.7240/marufbd.326674.
  • K. Tsukada, M. Hayashi, Y. Nakamura, K. Sakai, and T. Kiwa, Small eddy current testing sensor probe using a tunneling magnetoresistance sensor to detect cracks in steel structures. IEEE Transactions on Magnetics, 54(11), 1-5, 2018. https://doi.org/10.1109/T MAG.2018.2845864.
  • G. Peruń, Advances in non-destructive testing methods. Materials, 17(3), 554, 2024. https://doi.org/10.3390/m a17030554.
  • S. K. Dwivedi, M. Vishwakarma, and P. A. Soni, Advances and researches on non destructive testing: A review. Materials Today: Proceedings, 5(2), 3690-3698, 2018. https://doi.org/10.1016/j.matpr.2017 .11.620.
  • C. Wang, M. Fan, B. Cao, B. Ye, and W. Li, Novel noncontact eddy current measurement of electrical conductivity. IEEE Sensors Journal, 18(22), 9352-9359, 2018. https://doi.org/10.1109/JSEN.201 8.2870676.
  • J. García-Martín, J. Gómez-Gil, and E. Vázquez-Sánchez, Non-destructive techniques based on eddy current testing. Sensors, 11(3), 2525-2565, 2011. https://doi.org/10.3390/s110302525.
  • W. Cheng, Measurement of magnetic plates at a few hertz with two concentric coils and thickness estimation using mutual inductance. IEEE Transactions on Instrumentation and Measurement, 70, 1-10, 2021. https://doi.org/10.1109/TIM.2021.3087820.
  • S. She, Y. Chen, Y. He, Z. Zhou, and X. Zou, Optimal design of remote field eddy current testing probe for ferromagnetic pipeline inspection. Measurement, 168, 108306,2021. https://doi.org/10.1016/j.measurement. 2020.108306
  • T. P. Theodoulidis and E. E. Kriezis, Impedance evaluation of rectangular coils for eddy current testing of planar media. NDT & E International, 35(6), 407-414, 2002. https://doi.org/10.1016/S0963-8695(02)000 08-7.
  • D. Vyroubal, Impedance of the eddy-current displacement probe: the transformer model. IEEE Transactions on Instrumentation and Measurement, 53(2),384-391,2004. https://doi.org/10.1109/TIM.200 3.822705.
  • S. Hao and B. Li, Calculation inductance of toroidal inductor wound by rectangular cross-sectional wire. IEEE Transactions on Plasma Science, 49(9), 2910-2915, 2021. https://doi.org/10.1109/TPS.202 1.3101570.
  • T. Župan, Š. Ž, and B. Trkulja, Fast and precise method for inductance calculation of coaxial circular coils with rectangular cross section using the one-dimensional integration of elementary functions applicable to superconducting magnets. IEEE Transactions on Applied Superconductivity, 24(2), 81-89, 2014. https://doi.org/10.1109/TASC.2014.2301765.
  • W. Liu, S. Dai, T. Ma, Y. Shi, M. Song, and L. Li, Analytical calculation of mutual inductance of d-shaped coils applied to high-temperature superconducting magnet. IEEE Transactions on Applied Superconductivity, 34(5), 1-5, 2024. https://doi.org/10.1109/TASC.2024.3358765.
  • H. A. Wheeler, Simple inductance formulas for radio coils. Proceedings of the Institute of Radio Engineers, 16(10), 1398-1400, 1928. https://doi.org/10.1 109/JRPROC.1928.221309.
  • J. Kim, K. Kim, B. Kim, and J. Kang, Experimental validation of multi-layer coil inductance estimation method. In 2017 IEEE International Symposium on Antennas and Propagation & USNC/URSI National Radio Science Meeting, pp. 1303-1304, San Diego, California, 2017.
  • S. Kumar and Y. K. Jain, Simulation of circular-shaped PZT-5H sensor for train measurement using COMSOL multiphysics. IEEE Sensors Journal, 15(8), 4380-4387, 2015. https://doi.org/10.1109/JSEN.2015.2419281
  • Z. Xia, A. A. Bhatti, X. Peng, B. Yang, H. Zhou, C. Zhao, and C. Xie, Electric field and temperature distribution of high voltage cables with the addition of particles based on COMSOL simulation. In 2020 IEEE International Conference on High Voltage Engineering and Application (ICHVE), pp. 1-4, Beijing, China, 2020.
  • S. V. Oskin, A. V. Miroshnikov, and D. S. Tsokur, Studying the Aerodynamic Characteristics of Electric Motors in COMSOL Multiphysics. In 2021 International Conference on Industrial Engineering, Applications and Manufacturing (ICIEAM), pp. 350-354, Sochi, Russia, 2021.
  • D. S. Filip and D. Petreus, Simulation of an inductive coupled power transfer system. In IECON 2016 - 42nd Annual Conference of the IEEE Industrial Electronics Society, pp. 6559-6564, Florence, Italy, 2016.
  • S. M. Mousavi and A. Ghayebloo, Design and implementation a new coil and introduction a topology for electric vehicle wireless charger. In 2024 28th International Electrical Power Distribution Conference (EPDC), pp. 1-8, Zanjan, Iran, 2024.
  • F. Gozalpour and M. Yavari, 2-D axisymmetric modeling of circular PCB coils and solenoids in COMSOL multiphysics. In 2023 5th Iranian International Conference on Microelectronics (IICM), pp. 102-106, Tehran, Iran, 2023.
  • K. Slobodnk, Detection and evaluation of subsurface defects using pulse eddy current differential probe. In 2017 18th International Conference on Computational Problems of Electrical Engineering (CPEE), pp. 1-4, Kutna Hora, Czech Republic, 2017.
  • R. Singh and V. Singh, Analysis of eddy current damper for suppression of vibrations using COMSOL software. Engineering Solid Mechanics, 3(4), 215-222, 2015. http://dx.doi.org/10.5267/j.esm.2015.7.004.
  • M. Elbaa, K. Berger, B. Douine, M. Halit, E. H. Ailam, and S. E. Bentridi, Analytical modeling of an inductor in a magnetic circuit for pulsed field magnetization of HTS bulks. IEEE Transactions on Applied Superconductivity, 28(4), 1-6, 2018. https://doi.org/10.1109/TASC.2018.2809438.
  • S. Balaji and P. D. Sundari, COMSOL FEA modeling of square and cirular coil for inductive power transfer in electric vehicle systems. In 2023 Third International Conference on Advances in Electrical, Computing, Communication and Sustainable Technologies (ICAECT), pp. 1-4, Bhilai, India, 2023.
There are 31 citations in total.

Details

Primary Language Turkish
Subjects Mechanical Engineering (Other)
Journal Section Articles
Authors

Memduh Suveren 0000-0003-4545-5378

Emir Esim 0000-0003-0801-9155

Tuğba Baktır 0009-0006-6135-0866

Serhat Karaca 0009-0001-2584-5590

Furkan Korkmaz 0000-0003-0497-1632

Omer Enes Yildiz 0009-0004-8297-784X

Project Number 5220140 nolu 1505 Sanayi Üniversite İşbirliği Projesi
Early Pub Date March 3, 2025
Publication Date
Submission Date October 30, 2024
Acceptance Date January 11, 2025
Published in Issue Year 2025 Volume: 14 Issue: 2

Cite

APA Suveren, M., Esim, E., Baktır, T., Karaca, S., et al. (2025). Girdap akım testinde kullanılan farklı tip bobinlerin endüktansının teorik, deneysel ve sayısal incelenmesi. Niğde Ömer Halisdemir Üniversitesi Mühendislik Bilimleri Dergisi, 14(2), 1-1. https://doi.org/10.28948/ngumuh.1574899
AMA Suveren M, Esim E, Baktır T, Karaca S, Korkmaz F, Yildiz OE. Girdap akım testinde kullanılan farklı tip bobinlerin endüktansının teorik, deneysel ve sayısal incelenmesi. NOHU J. Eng. Sci. March 2025;14(2):1-1. doi:10.28948/ngumuh.1574899
Chicago Suveren, Memduh, Emir Esim, Tuğba Baktır, Serhat Karaca, Furkan Korkmaz, and Omer Enes Yildiz. “Girdap akım Testinde kullanılan Farklı Tip Bobinlerin endüktansının Teorik, Deneysel Ve sayısal Incelenmesi”. Niğde Ömer Halisdemir Üniversitesi Mühendislik Bilimleri Dergisi 14, no. 2 (March 2025): 1-1. https://doi.org/10.28948/ngumuh.1574899.
EndNote Suveren M, Esim E, Baktır T, Karaca S, Korkmaz F, Yildiz OE (March 1, 2025) Girdap akım testinde kullanılan farklı tip bobinlerin endüktansının teorik, deneysel ve sayısal incelenmesi. Niğde Ömer Halisdemir Üniversitesi Mühendislik Bilimleri Dergisi 14 2 1–1.
IEEE M. Suveren, E. Esim, T. Baktır, S. Karaca, F. Korkmaz, and O. E. Yildiz, “Girdap akım testinde kullanılan farklı tip bobinlerin endüktansının teorik, deneysel ve sayısal incelenmesi”, NOHU J. Eng. Sci., vol. 14, no. 2, pp. 1–1, 2025, doi: 10.28948/ngumuh.1574899.
ISNAD Suveren, Memduh et al. “Girdap akım Testinde kullanılan Farklı Tip Bobinlerin endüktansının Teorik, Deneysel Ve sayısal Incelenmesi”. Niğde Ömer Halisdemir Üniversitesi Mühendislik Bilimleri Dergisi 14/2 (March 2025), 1-1. https://doi.org/10.28948/ngumuh.1574899.
JAMA Suveren M, Esim E, Baktır T, Karaca S, Korkmaz F, Yildiz OE. Girdap akım testinde kullanılan farklı tip bobinlerin endüktansının teorik, deneysel ve sayısal incelenmesi. NOHU J. Eng. Sci. 2025;14:1–1.
MLA Suveren, Memduh et al. “Girdap akım Testinde kullanılan Farklı Tip Bobinlerin endüktansının Teorik, Deneysel Ve sayısal Incelenmesi”. Niğde Ömer Halisdemir Üniversitesi Mühendislik Bilimleri Dergisi, vol. 14, no. 2, 2025, pp. 1-1, doi:10.28948/ngumuh.1574899.
Vancouver Suveren M, Esim E, Baktır T, Karaca S, Korkmaz F, Yildiz OE. Girdap akım testinde kullanılan farklı tip bobinlerin endüktansının teorik, deneysel ve sayısal incelenmesi. NOHU J. Eng. Sci. 2025;14(2):1-.

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