Hankel transform application for calculation of ring coils inductance. Part 2





electromagnetic acoustic transducer, inductance, ring coil, Maxwell equations, Hankel transform, ferromagnetic


Changes in the geometric parameters of ring coils, which are an essential element of transducer design used for non-destructive testing of ferromagnetic metals, entail a change in the self-induction coefficient (inductance) of alternating magnetic field source. In the article, on the basis of proposed approach [1], the equations for determining the ring coils inductance are obtained, allowing to take into account real dimensions of inductors. They are equally suitable for situations where coil is located in an empty space, as well as near a conductive ferromagnetic or non-ferromagnetic metal. Calculating the inductance of ring coil located near magnetized, conductive ferromagnetic plate, we found that circuit inductance is the frequency-dependent complex-valued function vs distance between plate and ring coil. The measurements of the inductance of a coil located above a conductive ferromagnetic plate with a change in the non-contact value were carried out. The obtained results testify to physical meaningfulness and reliability of theoretical statements and calculations. These qualitative and quantitative results correspond to generally accepted energy definition of self-induction coefficient.


O. N. Petrischev, M. I. Romanyuk, G. M. Suchkov, “Hankel transform application for calculation of ring coils inductance. Part 1,” Radioelectron. Commun. Syst., vol. 63, no. 5, pp. 235–247, 2020, doi: https://doi.org/10.3103/S0735272720050027.

R. B. Thompson, “Physical principles of measurements with emat transducers,” in Physical Acoustics, vol. 19, Cambridge, MA: Academic Press, 1990, pp. 157–200.

G. M. Suchkov, A. V. Donchenko, A. V. Desyatnichenko, A. A. Kelin, E. L. Nozdracheva, “Increasing the sensitivity of ema devices,” Russ. J. Nondestruct. Test., vol. 44, no. 2, pp. 86–90, 2008, doi: https://doi.org/10.1134/S1061830908020022.

S. Y. Plesnetsov, O. N. Petrishchev, R. P. Migushchenko, G. M. Suchkov, “Modeling of electromagnetic-acoustic conversion when excited torsional waves,” Tekhnichna Elektrodynamika, vol. 2017, no. 3, pp. 79–88, 2017, doi: https://doi.org/10.15407/techned2017.03.079.

A. G. Gorbashova, O. M. Petrischev, M. I. Romanyuk, G. M. Suchkov, S. V. Haschina, “Investigation of the transfer characteristics of ultrasonic tract with electromagnetic excitation and detection of rayleigh waves in ferromagnet. part 1,” Electron. Commun., vol. 0, no. 2, p. 69, 2013, uri: https://elibrary.ru/item.asp?id=21446152.

>[6] R. Ribichini, F. Cegla, P. B. Nagy, P. Cawley, “Study and comparison of different emat configurations for sh wave inspection,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control, vol. 58, no. 12, pp. 2571–2581, 2011, doi: https://doi.org/10.1109/TUFFC.2011.2120.

M. Seher, P. Huthwaite, M. Lowe, P. Nagy, P. Cawley, “Numerical design optimization of an emat for a0 lamb wave generation in steel plates,” in AIP Conference Proceedings, 2014, vol. 1581 33, no. 1, pp. 340–347, doi: https://doi.org/10.1063/1.4864839.

H. M. Seung, C. Il Park, Y. Y. Kim, “An omnidirectional shear-horizontal guided wave emat for a metallic plate,” Ultrasonics, vol. 69, pp. 58–66, 2016, doi: https://doi.org/10.1016/j.ultras.2016.03.011.

D. Rueter, “Induction coil as a non-contacting ultrasound transmitter and detector: modeling of magnetic fields for improving the performance,” Ultrasonics, vol. 65, pp. 200–210, 2016, doi: https://doi.org/10.1016/j.ultras.2015.10.003.

J. Isla, F. Cegla, “Optimization of the bias magnetic field of shear wave emats,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control, vol. 63, no. 8, pp. 1148–1160, 2016, doi: https://doi.org/10.1109/TUFFC.2016.2558467.

J. He, K. Xu, W. Ren, “Designs for improving electromagnetic acoustic transducers’ excitation performance,” Japanese J. Appl. Phys., vol. 57, no. 6, p. 067202, 2018, doi: https://doi.org/10.7567/JJAP.57.067202.

P. L. Kalantarov, L. A. Zeitlin, Calculation of Inductances. Reference Book. Leningrad: Energoatomizdat, 1986.

I. E. Tamm, Fundamentals of Electricity Theory, 11th ed. Moscow: Nauka, 2003.

N. S. Koshlyakov, E. B. Gliner, M. M. Smirnov, Partial Differential Equations of Mathematical Physics. Moscow: Vyssh. Shkola, 1970.

M. Abramowitz, I. A. Stegun, Eds., Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables. Gaithersburg: National Bureau of Standards, 1964.

V. I. Smirnov, Course of Higher Mathematics. St. Petersburg: BKhV-Peterburg, 2008.





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