2-D Analytical Model of Sinusoidal Eddy Current Field Based on Permeability Distortion

In pipeline inspection, defects cause a nonuniform magnetic field distribution, resulting in permeability distortion along the surface of the ferromagnetic material. This article studies a 2-D axisymmetric problem of the sinusoidal eddy field for the ferromagnetic material with longitudinally partitioned regions of different magnetic permeability, which has not been reported before. Applying the truncated region eigenfunction expansion (TREE) method, a 2-D analytical model of the sinusoidal eddy field based on permeability distortion is derived, and the analytical expressions of the vector magnetic potential and the coil impedance are obtained. The coil impedance variation is analyzed and validated by the finite element method (FEM) and the experiment. In Model 1, the maximum errors of the changes in the resistance and the reactance are 0.52% and 0.29%, respectively. In Model 2, the maximum errors of the changes in the resistance and the reactance are 0.88% and 2.05%, respectively. The effect of the number of subregions is examined, and the results show that increasing the number of subregions can improve the accuracy.