Nondestructive eddy current testing for the measurement of conductivity and surface buckling of metallic sheets

Abstract

The necessary boundary conditions at the interface between the metallic sheet and air for the system shown in Fig. 1 are II. ELECTROMAGNETIC FIELD DISTRIBUTION Consider a cylindrical coil with inner and outer radii R1, R 2 , height 2h, and number of turns of the winding N. Let the metallic sheet be of thickness L, permeability J.Ln and conductivity (J. Let the distance between the coil center and the sheet be p. Take a cylindrical coordinate system with origin at the midpoint of the coil axis. The coil is fed with a current I having a radial frequency w rad/s. The partial differential equation for the vector potential A for negligible displacement currents in an isotropic medium, which has permeability J.L and conductivity (J, is given by ometrical dimensions of the measuring system can be adapted in order to obtain satisfactory measuring results.This work is concerned with the analytic solution of the electromagnetic field problem. Closed-form expressions for the vector potential as well as for the change of the impedance of the excitation coil are given.The solutions of the electromagnetic fields are expressed at first in the form of infinite integrals. The kernels of these integrals are calculated analytically. In order to simplify the calculations, series expansions are derived. Several results for different geometrical dimensions and different material constants of the metallic sheet are provided. In these cases the calculation of the derivatives of a certain function at the zero point is simplified using parabolic curve fitting based on least-squares approximations. The object of this work is to present expressions which the designer can feed into his own computer.Abstract-A cylindrical excitation coil, fed with ac current, is put in front of a metallic or ferromagnetic sheet. Closed formulae for the vector potential in the space and the change of the impedance of the exciting coil are given. The results are developed to show the effect of the geometrical properties of the measuring system upon the test of the buckling of the sheet, its material purity, and its conductivity. The phase angle rather than the amplitude of the change in the coil impedance is taken as the measured parameter.

Electrical Conductivity Measurement on Metallic Materials With a Cylindrical Resonator

“…Besides, the scattering parameters are measured at the beginning for the cylindrical resonator with homogeneous conductor walls, and the quality factor is calculated. By putting both Q unload and Q load into (12), Q ext can be rewritten as…”

“…As is reported in [1], a TE 011 mode cavity resonator is used for characterizing the electrical conductivities of metallic sheets. According to [9]- [12], electrical conductivities can be characterized by eddy current using Faraday's law of induction. Other methods for measuring the electrical conductivity, permittivity (ε), and permeability (μ) are also published in the literature [13]- [17].…”