Magnetodynamics - Frequency-domain

The magneto-dynamic solution in frequency domain describes the distribution of magnetic fields and eddy currents due to time harmonic excitation loads.

We use a quasi stationary approximation. The assumptions are applicable in cases of dimensions << wavelength. Examples are motors, transformers and frequencies from 0 Hz to a few 100 kHz.

Features

2D, 3D or axisymmetric Solution
coupled with Thermal solution possible
Outputs Plot:
- Magnetic Fluxdensity, Magnetic Fieldstrength, Current Density, Eddy Current Losses Density, Hysteresis-, Eddy-, Excess Loss Density - steinmetz, Magnetic Potential (a-Pot).

Outputs Table:
- RotorBand Torque - stresstensor, Magnetic Potential on Conductors - Fluxlinkage, Voltage on Coils, Voltage on Circuits, Electrode Voltage, Electrode Current, Current on Circuits, Power on Circuits, Eddy Current Losses, Hysteresis-, Eddy-, Excess Losses, Ohm Resistance, Coil Inductivity, Phase Shift.

Examples

Transformer Analysis	Circuit Breaker	Lamination Losses	AC Cable

Theory and Basics

Formulations

The basis equations:
(1)        rot h = j
(2)        rot e = -δ_t b
(3)        div b = 0

Constitutive relations:
(4) b = µ h
(5) j = σ e

a-Formulation

The following a-formulation is used for 2D-Magnetodynamics.

Magnetic vectorpotential a:
(6)        b = rot a
(7)        e = -δ_t a

Magnetodynamic  weak  a-formulation:
(8)            ( µ^-1 rot a, rot a’ )_Ω                + (-µ^-1 b_s, rot a’ )_Ω+ (- j, a’ )_ΩC
                + (σ δ_t a, a’ )_Ωc= 0, for all a’ element of Ω

a-v-Formulation

The following a-v-formulation is used for 3D-Magnetodynamics.

Magnetic vectorpotential a, electric scalar potential v:
(9)   b = rot a
(10)   e = -δ_t a – grad v

Magnetodynamic  weak  a-v-formulation:
(11)           (µ^-1 rot a, rot a’ )_Ω
                + (σ δ_t a, a’ )_Ωc
                + (σ grad v, a’ )_Ωc
                + (σ δ_t a, grad v’ )_Ωc   + (σ grad v, v’ )_Ωc= 0

Basic Example: Team Problem 3: The Bath Plate

The problem 3 of the TEAM (Testing Electromagnetic Analysis Methods) is one of the examples for testing eddy current codes. A conductive plate with two holes is placed under a coil. The coil is driven by alternating current of 50 Hz and 1260 ampere turns. The goal is to analyze for the magnetic fluxdensity along a line that goes slightly over the plate.