Finite Element Analysis of Magnetic Saturation and Air Gap Reluctance in a 2D Iron Core

Abstract

This study presents a finite element investigation of an air-gapped soft ferromagnetic core, with numerical results validated against classical magnetic circuit theory. A two-dimensional magnetostatic model of a closed-loop soft ferromagnetic core (70 × 100 mm, 10 mm limb thickness) with a 1 mm air gap on one limb was developed in COMSOL Multiphysics 6.4. Three modeling regimes were compared: a linear model with constant relative permeability (μr = 500), a nonlinear model employing an interpolated B-H saturation curve, and an analytical lumped-parameter magnetic circuit model. A multi-turn coil (N = 100) was excited via a parametric sweep of currents from 1 A to 51 A. Results demonstrate that introducing a 1 mm air gap reduces the linear-regime inductance from 229 mH to 92 mH—a 60% decrease—and renders the linear inductance virtually independent of core permeability, confirming the dominance of the air-gap reluctance (Rgap/Rtotal ≈ 61%). The nonlinear model yields a current-dependent inductance ranging from 120 mH at 1 A down to 37 mH at 51 A, capturing saturation-induced roll-off that the linear model cannot represent. Analytical reluctance-network calculations predict L = 76.7 mH, which is in good agreement with the COMSOL linear result within 16%, with the discrepancy attributed primarily to fringing flux and mean-path-length approximations. These findings underscore that air-gapped magnetic components require simultaneous treatment of saturation and fringing effects for reliable design of inductors, transformers, and reactors.