Analytical modeling of the transient response of a coil encircling a ferromagnetic conducting rod in pulsed eddy current testing

• Analytical solutions for transient response of a coil encircling a rod are obtained.
• Square pulse excitation of a multi-turn coil as used in PEC testing is examined.
• Solutions are for long conducting and ferromagnetic rods with linear permeability.
• Analytical results agree with finite element solutions for the same geometry.
• Model of flux progression elucidates transient phenomena in rod geometries.

Analytical solutions are obtained in the time domain for the electromagnetic response to the leading edge of a square pulse excitation of a multiple turn current coil, encircling a long ferromagnetic rod, in the linear permeability regime. The resulting equations, obtained using a magnetic vector potential formalism, describe the time-dependent progression of flux into and along the rod. Results are in agreement with finite element solutions obtained for the same geometry. The work is motivated by the requirement for rapid analytical solutions and insight into pulsed eddy current response during inspection of multilayer aluminum aircraft structures in the vicinity of ferrous fasteners.