Magnet (unidirectional): spline demagnetization curve
Presentation
This model (Nonlinear magnet described by a spline) defines a magnet with a nonlinear B(H)) characteristic starting from experimental B, H values. The definition of the B(H) behavior law with this model is a little longer than with the analytic models, but the experimental curve is modeled more accurately.
This magnet model is noted as unidirectional because the mathematical model and the direction of magnetization are dissociated (About orientation of magnets). B and H values entered in the dialog box define the demagnetization curve, while the direction of magnetization is defined by the orientation in the region (Orient materials in massive regions: volume (3D) / face (2D)).
Mathematical model
In the direction of magnetization the model is constructed in the following manner:
- entry of experimental B, H values (Limitations for the experimental data)
- linear interpolation between these points with a linear extrapolation beyond the last one
An example of the B(H) dependence in the direction of magnetization is given in the figure below:
In transversal directions, one can write:
where μr⊥ is the transversal relative permeability.
Limitations for the experimental data
The user is advised to use the following steps for the input of the experimental data:
- The first point of the spline curve must have a combination of H < 0 and B = 0 (-HcB in the picture).
- The H values of the spline curve must be purely increasing.
- The user must input at least four values of (H, B).
Direction of magnetization
The various possibilities provided to the user are the same ones as those presented in § Magnet (unidirectional): linear approximation.