FEM EquationMagnetodynamic

This equation perform analyses using the Maxwell's equations.

For info about the math of the equation, see the Elmer models manual, section Computation of Magnetic Fields in 3D.

If it is possible to calculate in 2D, simpler math can be used resulting in faster solving times. For 2D, FreeCAD supports therefore Elmer's Magnetodynamic 2D equation.

Usage

 * 1) After adding an Elmer solver as described here, select it in the tree view.
 * 2) Now either use the toolbar button [[Image:FEM_EquationMagnetodynamic.svg|24px]] or the menu.
 * 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  to BiCGStabl , the  to 4 and  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

 * : Refactorizes the system matrix.

Magnetodynamic

 * : The harmonic actuation frequency. It only used if is set to true.
 * : See Elmer Elmer models manual, section Computation of Magnetic Fields in 3D for info.
 * : Ensures divergence-freeness of current density.
 * : If the driving force is harmonically actuated (AC current). If set to true, must have a value > 0.
 * : See Elmer Elmer models manual, section Computation of Magnetic Fields in 3D for info.
 * : Enables second-order approximation of driving current.
 * : See Elmer Elmer models manual, section Computation of Magnetic Fields in 3D for info.
 * : See Elmer Elmer models manual, section Computation of Magnetic Fields in 3D for info.
 * : 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.
 * : See Elmer Elmer models manual, section Computation of Magnetic Fields in 3D for info. Will be ignored if is true.

Results

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

Constraint Information
The magnetodynamic equation takes the following constraints into account if they are set:


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

Results
The available results depend on the solver settings. If none of the 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 $$\rm A/m^2$$
 * Electric field vector values in $$\rm V/m$$
 * Harmonic power loss in $$\rm W$$
 * Magnetic flux density in $$\rm T$$
 * Maxwell stress tensor values in $$\rm As/m^3$$
 * Magnetic field strength in $$ \rm A/m$$
 * Nodal force in $$\rm N$$
 * Joule heating in $$\rm J$$
 * Potential in $$\rm V$$