Magnetodynamic-Frequencydomain

Outputs of the solution are:

  • Plot: Magnetic Fluxdensity, Magnetic Fieldstrength, Current Density, Eddy Current Losses Density, Vectorpotential, Nodal Force - virtual, Nodal Moment - virtual, Lorentz Force, Displacement, Error Estimation.
  • Table: Total Force - virtual, Total Moment - virtual, Total Lorentz Force, RotorBand Torque - stresstensor, RotorBand Force - stresstensor, Vectorpotential on Conductors - Fluxlinkage, Voltage on Coils, Voltage on Circuits, Electrode Voltage, Electrode Current, Current on Circuits, Power on Circuits, Eddy Current Losses, Ohm Resistance, Coil Inductivity, Phase Shift.
  • NVH Coupling: Forces in time and frequency domain on teeth.
  • 4D Fields:  Force - virtual NodeID Table, Forcedensity - virtual XYZ Table, Lorentz Force NodeID Table.
  • Coupled Thermal: Temperature.

Theory

Magnetodynamic

The magnetodynamic solutions describe the distribution of magnetic fields and eddy currents due to moving magnets and time variable currents.

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.

The basis equations:
(1)        rot h = j
(2)        rot e = -δt 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 = -δt a

Magnetodynamic  weak  a-formulation:
(8)            ( µ-1 rot a, rot a’ )Ω
                + (-µ-1 bs, rot a’ ) Ω
                        
+ (- ja’ ) ΩC
                + (σ δt aa’ ) 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 = -δt – grad v

Magnetodynamic  weak  a-v-formulation:
(11)           (µ-1 rot a, rot a’ )Ω
                + (σ δt aa’ ) Ωc
                + (σ grad v, a’ ) Ωc 
                + (σ δt a, grad v’ ) Ωc
                + (σ grad v, v’ ) Ωc
                      
= 0

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.

Point and Cylinder Example

Mesh

Point and Cylinder Example

Results

Fluxdensity and  Induced Current

Fluxdensity as contourplot
Fluxdensity of TEAM20

Fluxdensity as vectorplot
Fluxdensity of TEAM20

Induced currentdensity as contourpolot
Induced currentdensity as contourplot

Induced currentdensity as vectorplot
Induced currentdensity as vectorplot