Time-domain analytical solutions to pulsed eddy current model of moving cylindrical conductor

Abstract

The real-time or high-speed eddy current testing for conductor specimens are essential in industrial production and the analytical methods of eddy current field for moving conductor need to be further researched. In this paper, the time-domain analytical model of relative motion between the cylindrical conductor and probe is solved under pulsed current excitation. The basic equations and boundary conditions of moving conductor are presented and the boundary-value problem is established. Then the complex frequency-domain expression of voltage induced in the pick-up coil can be obtained by adopting the Laplace and Fourier transformation. Later, the induced voltage in time-domain is derived through the inverse Laplace transformation via residue theorem. Furthermore, the diffusion process of pulsed eddy current is studied by solving the eddy current density in conductor region and the effects of moving velocity on eddy current field are analyzed quantitatively. These calculations show that the larger the moving velocity, the closer the center area of eddy-current distribution is to the pick-up coil, as well as the larger the amplitude of induced voltage in pick-up coil, which can be equivalent to the decrease of axial distance between the pick-up coil and drive coil. The theoretical values obtained in this paper are in excellent agreement with the experimental results and can be applied to the pulsed eddy current testing for moving conductor or probe.