FEM EquationMagnetodynamic2D: Difference between revisions

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{{Docnav
{{Docnav
|[[FEM_EquationElectricforce|Electricforce equation]]
|[[FEM_EquationMagnetodynamic|Magnetodynamic equation]]
|[[FEM_EquationFlow|Flow equation]]
|[[FEM_EquationFlow|Flow equation]]
|[[FEM_Workbench|FEM]]
|[[FEM_Workbench|FEM]]
|IconL=FEM_EquationElectricforce.svg
|IconL=FEM_EquationMagnetodynamic.svg
|IconR=FEM_EquationFlow.svg
|IconR=FEM_EquationFlow.svg
|IconC=Workbench_FEM.svg
|IconC=Workbench_FEM.svg
}}
}}


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{{GuiCommand
{{GuiCommand
|Name=FEM EquationMagnetodynamic2D
|Name=FEM EquationMagnetodynamic2D
|MenuLocation=Solve → Electromagnetic Equations → Magentodynamic2D equation
|MenuLocation=Solve → Electromagnetic Equations → Magnetodynamic2D equation
|Workbenches=[[FEM_Workbench|FEM]]
|Workbenches=[[FEM_Workbench|FEM]]
|Version=1.0.
|Version=0.21
|SeeAlso=[[FEM_EquationElectrostatic|FEM Electrostatic equation]]
|SeeAlso=[[FEM_EquationMagnetodynamic|Magnetodynamic equation]]
}}
}}


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This equation perform electrostatic analyses using a 2D version of the [https://en.wikipedia.org/wiki/Maxwell%27s_equations Maxwell equations] when the unknown is the z-component (or φ-component).
This equation performs analyses using a 2D version of the [https://en.wikipedia.org/wiki/Maxwell%27s_equations Maxwell's equations] when the unknown is the z-component (or φ-component).


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For info about the math of the equation, see the [http://www.elmerfem.org/blog/documentation/ Elmer models manual], section ''Computation of Magnetic Fields in 2D''.
For info about the math of the equation, see the [http://www.elmerfem.org/blog/documentation/ Elmer models manual], section ''Computation of Magnetic Fields in 2D''.


==Usage== <!--T:11-->
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For more general analyses in 3D using the Maxwell's equations FreeCAD supports Elmer's [[FEM_EquationMagnetodynamic|Magnetodynamic equation]]. Nevertheless, if it is possible to perform the analysis in 2D, this is recommended since the math behind this is then more simple and the calculation time is therefore faster.


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==Usage== <!--T:6-->

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# After adding an Elmer solver as described [[FEM_SolverElmer#Equations|here]], select it in the [[Tree_view|tree view]].
# After adding an Elmer solver as described [[FEM_SolverElmer#Equations|here]], select it in the [[Tree_view|tree view]].
# Now either use the toolbar button [[Image:FEM_EquationMagnetodynamic2D.svg|24px]] or the menu {{MenuCommand|Solve → Electromagnetic Equations → Magentodynamic2D equation}}.
# Now either use the toolbar button [[Image:FEM_EquationMagnetodynamic2D.svg|24px]] or the menu {{MenuCommand|Solve → Electromagnetic Equations → Magnetodynamic2D equation}}.
# Change the [[#Solver_Settings|equation's solver settings]] or the [[FEM_SolverElmer_SolverSettings|general solver settings]] if necessary.
# Change the [[#Solver_Settings|equation's solver settings]] or the [[FEM_SolverElmer_SolverSettings|general solver settings]] if necessary.


==Solver Settings== <!--T:13-->
==Solver Settings== <!--T:8-->


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For the general solver settings, see the [[FEM_SolverElmer_SolverSettings|Elmer solver settings]].
For the general solver settings, see the [[FEM_SolverElmer_SolverSettings|Elmer solver settings]].


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The magentodynamic 2D equation provides these special settings:
The magnetodynamic 2D equation provides these special settings:
* {{PropertyData|Angular Frequency}}: The harmonic actuation frequency. It only used if {{PropertyData|Is Harmonic}} is set to ''true''.
* {{PropertyData|Angular Frequency}}: The harmonic actuation frequency. It is only used if {{PropertyData|Is Harmonic}} is set to ''true''.
* {{PropertyData|Calculate Current Density}}: Calculates the current density.
* {{PropertyData|Calculate Current Density}}: Calculates the [https://en.wikipedia.org/wiki/Current_density current density].
* {{PropertyData|Calculate Electric Field}}: Calculates the electric field strength.
* {{PropertyData|Calculate Electric Field}}: Calculates the [https://en.wikipedia.org/wiki/Electric_field Electric vector field].
* {{PropertyData|Calculate Elemental Fields}}: Calculates the electromagnetic fields for every mesh element. This is useful to see discontinuities in meshes.</br> '''Note''': at the moment FreeCAD cannot display these results properly. Therefore it is at the moment of no practical usage.
* {{PropertyData|Calculate Elemental Fields}}: Calculates the electromagnetic fields for every mesh element. This is useful to see discontinuities in meshes.</br>'''Note''': at the moment FreeCAD cannot display these results properly. Therefore it is at the moment of no practical use.
* {{PropertyData|Calculate Harmonic Loss}}: Calculates the linear and quadratic harmonic power loss. See the [https://www.elmerfem.org/blog/documentation/ Elmer models manual], section ''Loss Estimation Using the Fourier Series'' for details
* {{PropertyData|Calculate Joule Heating}}: Calculates the [https://en.wikipedia.org/wiki/Joule_heating Joule heating].
* {{PropertyData|Calculate Magnetic Strength}}: Calculates the [https://en.wikipedia.org/wiki/Magnetic_field Magnetic field strength].
* {{PropertyData|Calculate Maxwell Stress}}: Calculates the [https://en.wikipedia.org/wiki/Maxwell_stress_tensor Maxwell stress tensor] field.
* {{PropertyData|Calculate Nodal Fields}}: Calculates the fields for every mesh node. The default is ''true''. If no other {{PropertyData|Calculate *}} is set to ''true'', it only calculates the magnetic flux density.
* {{PropertyData|Calculate Nodal Forces}}: Calculates the forces for every mesh node. The results can be used for further mechanical analysis.
* {{PropertyData|Calculate Nodal Heating}}: Calculates the Joule heating scalar field for every mesh node.
* {{PropertyData|Is Harmonic}}: If the driving force is harmonically actuated (AC current). If set to ''true'', {{PropertyData|Angular Frequency}} must have a value > 0.
* {{PropertyData|Is Harmonic}}: If the driving force is harmonically actuated (AC current). If set to ''true'', {{PropertyData|Angular Frequency}} must have a value > 0.


==Constraint Information== <!--T:16-->
==Analysis Feature Information== <!--T:11-->


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The magentodynamic 2D equation takes the following constraints into account if they are set:
The magnetodynamic 2D equation takes the following analysis features into account if they are set:


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* [[Image:FEM_ConstraintElectrostaticPotential.svg|24px]] [[FEM_ConstraintElectrostaticPotential|Electrostatic potential constraint]]
* [[Image:FEM_ConstraintElectrostaticPotential.svg|24px]] [[FEM_ConstraintElectrostaticPotential|Electrostatic potential boundary condition]]
* [[Image:FEM_ConstraintCurrentDensity.svg|24px]] [[FEM_ConstraintCurrentDensity|Current density constraint]]
* [[Image:FEM_ConstraintCurrentDensity.svg|24px]] [[FEM_ConstraintCurrentDensity|Current density boundary condition]]
* [[Image:FEM_ConstraintMagnetization.svg|24px]] [[FEM_ConstraintMagnetization|Magnetization boundary condition]]
* [[Image:FEM_ConstantVacuumPermittivity.svg|24px]] [[FEM_ConstantVacuumPermittivity|Constant vacuum permittivity]]
* [[Image:FEM_ConstantVacuumPermittivity.svg|24px]] [[FEM_ConstantVacuumPermittivity|Constant vacuum permittivity]]


==Results== <!--T:21-->
==Results== <!--T:14-->


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The available results depend on the [[#Solver_Settings|solver settings]]. If none of the {{PropertyData|Calculate *}} settings was set to ''true'', only the electric force density and the electric potential are calculated. Otherwise also the corresponding results will be available.
The available results depend on the [[#Solver_Settings|solver settings]]. If none of the {{PropertyData|Calculate *}} settings was set to ''true'', only the electric potential (called '''av''' in the results) is calculated. Otherwise also the corresponding results will be available.


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The possible results are:
The possible results are:
* Electric energy density in <math>\rm J/m^3</math>
* Current density in <math>\rm A/m^2</math>
* Electric field in <math>\rm V/m</math>
* Electric field vector values in <math>\rm V/m</math>
* Electric flux in <math>\rm A\cdot s/m^2</math>
* Harmonic power loss in <math>\rm W</math>
* Electric force density in <math>\rm N/m^2</math>
* Magnetic flux density in <math>\rm T</math>
* Maxwell stress tensor values in <math>\rm As/m^3</math>
* Magnetic field strength in <math> \rm A/m</math>
* Nodal force in <math>\rm N</math>
* Joule heating in <math>\rm J</math>
* Potential in <math>\rm V</math>
* Potential in <math>\rm V</math>
* Potential loads in <math>\rm C</math>




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{{Docnav
{{Docnav
|[[FEM_EquationElectricforce|Electricforce equation]]
|[[FEM_EquationMagnetodynamic|Magnetodynamic equation]]
|[[FEM_EquationFlow|Flow equation]]
|[[FEM_EquationFlow|Flow equation]]
|[[FEM_Workbench|FEM]]
|[[FEM_Workbench|FEM]]
|IconL=FEM_EquationElectricforce.svg
|IconL=FEM_EquationMagnetodynamic.svg
|IconR=FEM_EquationFlow.svg
|IconR=FEM_EquationFlow.svg
|IconC=Workbench_FEM.svg
|IconC=Workbench_FEM.svg

Latest revision as of 13:02, 22 November 2023

Other languages:

FEM EquationMagnetodynamic2D

Menu location
Solve → Electromagnetic Equations → Magnetodynamic2D equation
Workbenches
FEM
Default shortcut
None
Introduced in version
0.21
See also
Magnetodynamic equation

This equation performs analyses using a 2D version of the Maxwell's equations when the unknown is the z-component (or φ-component).

For info about the math of the equation, see the Elmer models manual, section Computation of Magnetic Fields in 2D.

For more general analyses in 3D using the Maxwell's equations FreeCAD supports Elmer's Magnetodynamic equation. Nevertheless, if it is possible to perform the analysis in 2D, this is recommended since the math behind this is then more simple and the calculation time is therefore faster.

Usage

  1. After adding an Elmer solver as described here, select it in the tree view.
  2. Now either use the toolbar button or the menu Solve → Electromagnetic Equations → Magnetodynamic2D equation.
  3. Change the equation's solver settings or the general solver settings if necessary.

Solver Settings

For the general solver settings, see the Elmer solver settings.

The magnetodynamic 2D equation provides these special settings:

  • DataAngular Frequency: The harmonic actuation frequency. It is only used if DataIs Harmonic is set to true.
  • DataCalculate Current Density: Calculates the current density.
  • DataCalculate Electric Field: Calculates the Electric vector field.
  • DataCalculate Elemental Fields: Calculates the electromagnetic fields for every mesh element. This is useful to see discontinuities in meshes.
    Note: at the moment FreeCAD cannot display these results properly. Therefore it is at the moment of no practical use.
  • DataCalculate Harmonic Loss: Calculates the linear and quadratic harmonic power loss. See the Elmer models manual, section Loss Estimation Using the Fourier Series for details
  • DataCalculate Joule Heating: Calculates the Joule heating.
  • DataCalculate Magnetic Strength: Calculates the Magnetic field strength.
  • DataCalculate Maxwell Stress: Calculates the Maxwell stress tensor field.
  • DataCalculate Nodal Fields: Calculates the fields for every mesh node. The default is true. If no other DataCalculate * is set to true, it only calculates the magnetic flux density.
  • DataCalculate Nodal Forces: Calculates the forces for every mesh node. The results can be used for further mechanical analysis.
  • DataCalculate Nodal Heating: Calculates the Joule heating scalar field for every mesh node.
  • DataIs Harmonic: If the driving force is harmonically actuated (AC current). If set to true, DataAngular Frequency must have a value > 0.

Analysis Feature Information

The magnetodynamic 2D equation takes the following analysis features into account if they are set:

Results

The available results depend on the solver settings. If none of the DataCalculate * settings was set to true, only the electric potential (called av in the results) is calculated. Otherwise also the corresponding results will be available.

The possible results are:

  • Current density in
  • Electric field vector values in
  • Harmonic power loss in
  • Magnetic flux density in
  • Maxwell stress tensor values in
  • Magnetic field strength in
  • Nodal force in
  • Joule heating in
  • Potential in