Bobbin coil signal variation due to an axisymmetric circumferential groove in a tube

Abstract

<p>We have developed a general method for finding new solutions in eddy current nondestructive evaluation by introducing truncation boundaries in configurations that are otherwise unbounded. Here we consider an application of the method to the case of a tube containing a co‐axial bobbin coil near a circumferential groove of rectangular cross section. The groove can be on the internal or external wall of the tube. The problem is axially symmetric and easily solved using numerical methods however, we seek an accurate semi‐analytical solution. Take the axis of the system to be perpendicular to two truncation planes with the groove bisected by a mid plane halfway between them. Boundary conditions are applied on the truncation planes where we suppose that the tangential electric field is zero. In order to ensure that the predicted field is close to that expected in the corresponding unbounded domain problem, the truncation planes are far apart, well away from the coil and the groove. The solution is expressed as series expansions for different regions that are matched across cylindrical boundaries using the continuity properties of the electromagnetic field. This process gives the expansion coefficients in the series in terms of the expansion coefficients that represent the field of the source coil. From the solutions, the coil signal due to the groove can be deduced. The accuracy of the calculation is easily controlled by adjusting the distance between the truncation planes and∕or the number of terms in the series expansions.</p>