A Space Discretized Ferromagnetic Model for Non-Destructive Eddy Current Evaluation

B Gupta,B Ducharne,T Uchimoto,G Sebald

doi:10.1109/tmag.2017.2773517

Abstract

Accurate magnetic material laws are necessary to understand and interpret electrical signals generated by eddy current testing non-destructive control technique. Taking into account simultaneously, both microscopic and macroscopic eddy currents, a numerical resolution is obtained which leads to the global magnetic behavior that can be compared to measured quantities. The 2-D or 3-D (depending on the dimension of the test sample) finite differences space discretization is used for the resolution of the diffusion equation and dynamic hysteresis model is locally simultaneously solved for the microscopic eddy currents (domain wall movements) consideration. Local cracks defects are considered in this model as a variation in the local electrical conductivity and magnetic permeability. The numerical issues such as the proposed solutions for the implementation are described in this paper.

Highlights

T HE development of new electromagnetic designs, such as the improvement of already existing ones, requires precise simulation tools
Similar tools can be used for the understanding and interpretation of non-destructive eddy current testing (ECT) and Barkhausen noise measurements’ electrical signatures
Recent scientific investigations around ferromagnetic model mainly focus on coupling space discretization techniques (SDT), finite-elements method, finite differences method (DFM) extended with accurate scalar or vectorial, dynamic or static, and considering hysteresis material law

Summary

INTRODUCTION

T HE development of new electromagnetic designs, such as the improvement of already existing ones, requires precise simulation tools. Recent scientific investigations around ferromagnetic model mainly focus on coupling space discretization techniques (SDT), finite-elements method, finite differences method (DFM) extended with accurate scalar or vectorial, dynamic or static, and considering hysteresis material law. For this magnetic material law, it seems that the best results come from the extension of the quasi-static hysteresis model (Preisach’s model [2]–[5]) to dynamic behavior as a result of the separation losses techniques as proposed by Bertotti [6]. To correctly simulate ECT technique, the electromagnetic model must be able to provide the local and time evolution of both magnetic induction B and excitation field H. To overcome numerical issues due to fixed point or Newton Raphson’s algorithm, solving the diffusion equation (linked to the macroscopic eddy currents) and the dynamic hysteresis model (microscopic eddy currents) simultaneously is proposed

Diffusion Equation—Macroscopic Eddy Current Contribution

Material Law—Microscopic Eddy Current Contribution

Simultaneous Resolution

CONCLUSION