IntroductionEddy current non-destructive testing is one of the most commonly used methods for detecting flaws in conducting materials.A Dahle-probe which is originally developed for sensing torque [1]and is shown in Fig.1(a),has a unique feature as an ECT probe.Due to its balanced structure,the output does not appear when there is no flaw in a conductive sample.Furthermore,its ability to take the spatial difference in the flux density makes the probe very sensitive to a tiny flaw.Therefore,it is important to establish a quantitative model by which one can predict a response to a given flaw. In this paper,we have developed such a model for a Dahle-probe.Results obtained with the model have been confirmed by experiments.We have successfully applied the model to predict a response to a long flaw.
Method and Experimental ResultsThe probe is made up of a pair of U-shaped cores,one used as an excitation coil and the other as a pickup coil.Because of the symmetrical configuration of the probe,the net induced voltage measured by pickup coils is zero if there is no flaw in the conductor plate,and existence of a flaw causes an unbalance in flux linkage which induces net voltage to the pickup coil.The essential part of the Dahle probe can be expressed by using four ring coils as can be seen in Fig.1(b).The magnetic field and the eddy currents induced in the conductor placed parallel to the ring coil carrying ac excitation current can be expressed by the formula developed by Dodd and Deeds [2].The eddy currents induced by a Dahle probe can be obtained by superposing eddy currents induced by two ring coils carrying currents in opposing directions shown in Fig.1(c).The interaction of a flaw, which is assumed as a small hollow space to the distribution of the eddy current, can be treated by introducing an equivalent current dipole. The magnetic field due to the current dipole can be expressed by a pair of ring currents placed at the location of the flaw in the metal, when its component perpendicular to the surface of the plate is observed [3].To take the scanning process into account, the position of flaw was moved relative to the excitation ring coils. The direction and the magnitude of the equivalent current dipole, hence a pair of imaginary loop currents,are functions of the eddy current at the location of the flaw. The following developed integral expression (1) expresses vector potential out of a conductor plate due to a ring coil placed within the plate.It was calculated numerically and then by integrating it on a circular ring loop (pickup coil) as in formula (2), the induced voltage was obtained.The calculated eddy current field distribution in the first step was utilized for the imaginary loop currents in the latter integral calculation. The configuration of imaginary loop currents is shown in Fig.2 from a top view. The values of the parameters for the numerical calculation can be seen in Table 1.The phase-sensitive-detection process was numerically applied to the calculated magnetic field.A calculated contour plot for...
