# Modelling eddy currents on a ferromagnetic plate: field in the conductor and magnetic permeability as a function of the frequency

Speaker:
Fava, J.O.; Comision Nacional de Energia Atomica; Argentina

Authors:
Fava, J.O.; Comision Nacional de Energia Atomica; Argentina
Carabedo, F.D.; Comision Nacional de Energia Atomica; Argentina
Ruch, M.C.; Comision Nacional de Energia Atomica; Argentina
Gutierrez, M.; Facultad Regional Haedo, UTN; Argentina

ID: ECNDT-0065-2018
Download: PDF
Session: Modeling and data processing Electromagnetic Techniques 2
Room: J2
Date: 2018-06-12
Time: 10:50 - 11:10

As a contribution to the design and construction of coils and sensors for the eddy current inspection of planar ferromagnetic components, results are presented from the modelling of a pancake coil on different ferromagnetic plates. This contribution is a solution of the well known problem of a cylindrical coil fed with a sinusoidal current of frequency f. The plate on which the coil lies has a thickness d, is infinite in the directions perpendicular to the coil’s axis, and has an electrical conductivity σ and a relative magnetic permeability μr.
Different ferromagnetic materials were selected for the research, which constitutes an approach combining theoretical modelling and experimental measurements. The procedure is as follows: First, for each particular case, the electrical conductivity was measured using van der Pauw’s method. Then, given the geometry of the coils and the thickness and electrical conductivity of the plates, an inverse eddy current technique was applied, in order to determine the magnetic permeability at different ranges of the test frequency. This technique consists on a fitting of the impedance measurements using a least squares algorithm. The fitting function is calculated with the model and the parameter to be adjusted is the relative permeability. Thus effective values of the relative permeability are obtained, which may be interpreted as those which should be considered in an eddy current test. Measurements are made at different frequency ranges, effective μr being obtained for each range.
Finally, with the estimated permeability values the magnetic field within the conductor is calculated, in order to evaluate the influence of the distance to an edge and of the proximity of other coils.