Comparison of three formulations for eddy-current and skin and proximity problems in a meander coil electromagnetic acoustic transducer

Abstract

Three differential equations based on different definitions of current density are compared. Formulation I is based on an incomplete equation for total current density (TCD). Formulations II and III are based on incomplete and complete equations for source current density (SCD), respectively. Using the weak form of Finite Element Method (FEM), the three formulations were applied in a meander coil Electromagnetic Acoustic Transducer (EMAT) example to solve magnetic vector potential (MVP). The FEM results from frequency domain and time domain models are in excellent agreement with previously published works. Results show that the errors for Formulations I and II vary with coil dimensions, coil spacing, lift-off distance and external excitation frequency, for the existence of eddy-current and skin and proximity effects. And the current distribution across the coil conductors also follows the same trend. It is better to choose Formulation I instead of Formulation III to solve MVP when the coil height or width are less than twice the skin depth, due to the low cost and high efficiency of Formulation I.