Comparison of three formulations for eddy-current problems in a spiral 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), three formulations were applied in a spiral coil electromagnetic acoustic transducer (EMAT) example to solve magnetic vector potential (MVP). The input impedances calculated by Formulation III are in excellent agreement with the experimental measurements. Results show that the errors for Formulations I & II vary with coil diameter, coil spacing, lift-off distance and external excitation frequency, for the existence of eddy-current and skin & proximity effects. And the current distribution across the coil conductor also follows the same trend. It is better to choose Formulation I instead of Formulation III to solve MVP when the coil diameter is less than twice the skin depth for Formulation I is a low cost and high efficiency calculation method.

Keywords

electromagnetic acoustic transducer (EMAT) / eddy current / finite element method (FEM) / skin and proximity effects / spiral coil

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