XIX Sympozjum Srodowiskowe PTZE - materialy.pdf

XIX Sympozjum PTZE, Worliny 2009
DIRECT PREISACH HYSTERESIS MODELS
FOR FINITE ELEMENT ANALYSIS
OF EDDY CURRENT FIELD
Daniel Marcsa, Miklos Kuczmann
Széchenyi István Egyetem, Laboratory of Electromagnetic Fields
Egyetem tér 1, Győr, H-9026, Hungary
The full paper deals with the numerical analysis of the Problem No. 32 of TEAM Workshops
[1] based on the eddy current field computation taking the ferromagnetic hysteresis account.
The direct (H-based) scalar Preisach hysteresis model [2,4] is integrated on a two-dimensional
time-stepping finite element analysis [2,3,4]. The interface between the Preisach model and
the finite element eddy current field formulation is the Fixed-Point iterative technique [2-5],
which seems to be the most widely used numerical scheme for handling the nonlinearities
introduced by the magnetic hysteresis phenomenon. Here, the problem is a nonlinear eddy
current field problem.
The two-dimensional time-stepping eddy current field potential formulations is the T,Φ – Φ -
potential formulation [3] with direct model of nonlinear constitutive relations. The T,Φ – Φ -
formulation is make it possible the direct model of constitutive relations [2,4], because of the
primary quantity of this formulation is the magnetic field intensity H. In this formulation the
nonlinear constitutive relations between H and B is the following
B µ H + R , (1)
= FP
where µFP is a properly chosen constant, the ideal permeability (Fixed-Point coefficient), and
R is a residual nonlinearity (Fixed-Point residual), which has to be determined iteratively.
The geometry situation of three
limbed ferromagnetic core with two
windings are placed on the external
limbs can be seen in Fig. 1. The
windings has 90 turns and it is
connected to the voltage source
through a 11.74Ω resistance. In Fig. 1,
σ is the conductivity, and permeability
µFP is the Fixed-Point coefficient.
Figure 1. Structure of the core with
windings
111