Study of the non-linear eddy-current response in a ferromagnetic plate: Theoretical analysis for the 2D case

Abstract

The non-linear induction problem in an infinite ferromagnetic pate is studied theoretically by means of the truncated region eigenfunction expansion (TREE) for the 2D case. The non-linear formulation is linearised using a fixed-point iterative scheme, and the solution of the resulting linear problem is constructed in the Fourier domain following the TREE formalism. The calculation is carried out for the steady-state response under harmonic excitation and the harmonic distortion is derived from the obtained spectrum. This article is meant to be the theoretical part of a study, which will be complemented by the corresponding experimental work in a future communication.

Identification of the ferromagnetic hysteresis simulation parameters using classic non-destructive testing equipment

“…Different methods have been developed for the simulation of ENDT industrial situations. A space discretization of the Maxwell equations is one solution [15], analytical approaches is another one [16]. In most of the commercial simulation tools dedicated to ENDT, hysteresis is ignored and the relation between the magnetic stimuli and the magnetic state is always taken into account through linear relations.…”

Integral and series solutions for inductance of rectangular coils with parallel end faces

“…Furthermore, with the substitution (19) and perform the integrations ∫ 0 c 1 dδ 1 and ∫ 0 c 2 dδ 2 , we obtain the mutual inductance of rectangular coils with rectangular cross section and parallel end faces:…”

“…For completeness, the coils with all of the possible axial positions will be analysed. Secondly, the alternative solutions based on the truncated region eigenfunction expansion (TREE) method [13][14][15][16][17][18][19][20] will be given for the fast evaluations of the inductance of rectangular coils. These solutions are all 2D series which are by nature more friendly to the numerical computations compared with the integral expressions.…”

Inductance calculations for coaxial iron‐core coils shielded by cylindrical screens of high permeability

“…(i) the eigenvalues p i are changed into the positive roots of J 0 pa = 0 (ii) the function R n (qr) is changed into R n qr = J n qr Y 0 qa − J 0 qa Y n qr (27) (iii) the functions (11) and (13) in source functions should be transformed into (iv) the non-zero elements in matrices S and T (referring to (16) and (17b)) should be transformed into…”

“…These simplified models can be applied in some special situations but they are not accurate enough in most practical cases. In [13][14][15][16], this method was widely used in eddy current probes analysis and termed 'truncated region eigenfunction expansion' (TREE) by Theodoulidis and Bowler. TREE method is a semi-analytical method for solving BVPs.…”