MES: Równanie magnetodynamiczne

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Równanie magnetodynamiczne

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Rozwiąż→ Równania elektromagnetyczne → Równanie magnetodynamiczne
Środowisko pracy
FEM
Domyślny skrót
brak
Wprowadzono w wersji
0.21
Zobacz także
Równanie magnetodynamiczne 2D

To równanie przeprowadza analizę z użyciem równań Maxwella.

Informacje o teorii stojącej za tym równaniem można znaleźć w dokumencie Elmer models manual, w sekcji Computation of Magnetic Fields in 3D (obliczenia pól magnetycznych w 3D).

Jeśli możliwe jest przeprowadzenie analizy 2D, prostsze sformułowanie może być uzyte skutkując krótszymi obliczeniami. Do 2D, FreeCAD wspiera równanie magnetodynamiczne 2D solvera Elmer.

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 → Magnetodynamic equation.
  3. Change the equation's solver settings or the general solver settings if necessary.
  4. It is recommend to set in the Linear System solver settings the DANELinear Iterative Method to BiCGStabl , the DANEBiCGstabl Degree to 4 and DANELinear Preconditioning to None. This assures the equation can be solved in most cases. If so, these parameters can be changed if necessary.

Solver Settings

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

The magnetodynamic equation provides these special settings:

Linear System

  • DANELinear System Refactorize: Refactorizes the system matrix.

Magnetodynamic

  • DANEAngular Frequency: The harmonic actuation frequency. It only used if DANEIs Harmonic is set to true.
  • DANEAutomated Source Projection BCs: See Elmer Elmer models manual, section Computation of Magnetic Fields in 3D for info.
  • DANEFixInput Current Density: Ensures divergence-freeness of current density.
  • DANEIs Harmonic: If the driving force is harmonically actuated (AC current). If set to true, DANEAngular Frequency must have a value > 0.
  • DANELagrange Gauge Penalization Coefficient: See Elmer Elmer models manual, section Computation of Magnetic Fields in 3D for info.
  • DANEQuadratic Approximation: Enables second-order approximation of driving current.
    Note: The default order of Gmsh meshes in FreeCAD is 2nd order. When using 2nd order meshes, it is mandatory to set this option to true. Otherwise you will get this error: ERROR:: GetEdgeBasis: Can't handle but linear elements, sorry.
    However, for most applications, a 1st order mesh is sufficient. An exception is the case when an Isocontour filter should be applied to visualize the results. In this case using a 2nd order mesh and thus setting DANEQuadratic Approximation to true is recommended.
  • DANEStatic Conductivity: See Elmer Elmer models manual, section Computation of Magnetic Fields in 3D for info.
  • DANEUse Lagrange Gauge: See Elmer Elmer models manual, section Computation of Magnetic Fields in 3D for info.
  • DANEUse Piola Transform: Must be true if basis functions for edge element interpolation are selected to be members of optimal edge element family or if second-order approximation is used.
  • DANEUse Tree Gauge: See Elmer Elmer models manual, section Computation of Magnetic Fields in 3D for info. Will be ignored if DANEUse Piola Transform is true.

Results

  • DANECalculate Current Density: Calculates the current density.
  • DANECalculate Electric Field: Calculates the Electric vector field.
  • DANECalculate 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.
  • DANECalculate Harmonic Loss: Calculates the linear and quadratic harmonic power loss. See the Elmer models manual, section Loss Estimation Using the Fourier Series for details
  • DANECalculate Joule Heating: Calculates the Joule heating.
  • DANECalculate Magnetic Strength: Calculates the Magnetic field strength.
  • DANECalculate Maxwell Stress: Calculates the Maxwell stress tensor field.
  • DANECalculate Nodal Fields: Calculates the fields for every mesh node. The default is true. If no other DANECalculate * is set to true, it only calculates the magnetic flux density.
  • DANECalculate Nodal Forces: Calculates the forces for every mesh node. The results can be used for further mechanical analysis.
  • DANECalculate Nodal Heating: Calculates the Joule heating scalar field for every mesh node.

Analysis Feature Information

The magnetodynamic 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 DANECalculate * settings was set to true, only the electric electric (called av in the results) potential 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