Flaw Characterization Using a Double-D Pickup Coil in an Axis Symmetric Excitation

摘要

We developed a method to evaluate the induced voltage in a double-D pickup coil caused by flaw-eddy current interaction by the axis symmetric excitation, Eddy current distribution in the aluminum plate is numerically calculated and a flaw within the plate is replaced by equivalent pair of imaginary circular currents. The current amplitude for the imaginary circular currents is obtained from the numerical result of eddy current distribution calculation. The secondary magnetic field caused by the pair of circular currents was obtained analytically. Utilizing the analytical result, we evaluated the induced voltage in a double-D pickup coil which was placed co-axially and coplanar to the exciting ring coil. Eddy current distribution in a flawless plate due to axis symmetric excitation was numerically calculated. Fig.1 shows the result for the amplitude of eddy current distribution 1.5 mm under the surface of aluminum plate, with 5 mm thickness, and conductivity s - 3.5 X 10~7 S/m. In this calculation we considered an exciting ring coil with 6.5 mm radius and 2 mm lift-off. Sinusoidal current with frequency of 2 kHz and amplitude of 1 ampere was considered. A further explanation about the calculation can be found in [1], Eddy current path changes when facing a flaw. Hence we can replace the flaw with a pair of imaginary circular currents and calculate the vector potential field produced by these two circular currents which we call it secondary field. We obtained the analytical expression for vector potential of the secondary magnetic field out of the plate: a (r,z) = integral_0~x B_1(a)e~(-az)J_1(ar)da. We calculated the voltage induced in a double-D pickup coil caused by pair of circular currents, the one of which can be seen in Fig.2. Four different overlapping of circular currents is considered. The resulted graph for induced voltage in the pickup coil can be seen in Fig.3. This figure shows how the overlap between imaginary circular currents affects on the induced voltage. By increasing the overlap between the pair of loops, the induced voltage decreases.