Analytical expressions of induced coil voltages generated by pulsed eddy currents for metal pipe testing

This paper solved the eddy current field induced by pulse current in saddle-shaped coil outside the metal pipe with linear conductivity and permeability. By using the second order vector potential, the magnetic field in the air could be described by a single scalar function, and the calculation process could thus be simplified. We presented the boundary value problems of this electromagnetic model and obtained the linear equations for unknown coefficients. Then, we reduced the condition number of the coefficient matrix through substitution of variables and solved the linear equations by using block matrix. Based on the Fourier Transform, we obtained the analytical solution of the coil voltage induced by arbitrary waveform current in the multi-turn saddle-shaped drive coil. The analytical expressions were verified through a comparison of the theoretical curves with the experimental curves of the austenite stainless steel pipes. Results in this paper provide theoretical basis for simulation calculation and experimental study of the pulsed eddy current testing for pipes.