Prediction and Analysis of Transient Eddy-Current Probe Signals

Abstract

In eddy-current nondestructive evaluation, the electromagnetic field is usually excited by a probe carrying a time-harmonic current and flaw information inferred from the amplitude and phase of the probe signal. In principle, transient excitation of eddy-currents would seem to offer great advantages since the probe response contains the equivalent information of a spectrum of frequencies. This paper explores a number of basic transient solutions due to normal air-cored coils and shows how the induced emf in a coil is related to its coupling coefficient. FOURIER LAPLACE TRANSFORMS We can make use of some standard time-harmonic results to calculate transient fields since the frequency and time-domain solutions are related through the Fourier transform. Thus we define F(t) = i, f~oo f(iw)eiwt dw 2 ~; fBr f(s)e•t ds, (1) where F(t) represents the time-domain solution and f(iw) its Fourier transform. Br denotes the Bromwitch contour taking the path of integration with respect to s in the complex plane to the right of any poles. (1) enables us to derive a transient solution from a corresponding time-harmonic solution. Perhaps the most well known time harmonic fields in the theory of eddy-current NDE are those determined by Dodd and Deeds for normal rectangular section coils above multi-layered infinite conducting slabs [1]. To take initially a slightly more general case, suppose we consider a normal axially symmetric coil of arbitrary cross section carrying a current whose density has the form