The Toroid component models a circular toroid with circumferential magnetic flux flow. Because the flux density is a function of radius, the relative permeability, ${\mathrm{\mu }}_r$ is evaluated for the flux density at the tube's mean radius.

If the boolean parameter Nonlinear Permeability is true, the component uses a material parameter to specify the Soft Magnetic Material. A record of that class, with the appropriate name, must exist in the model, either at the same or higher level.

The Use default material boolean parameter, when true, sets the name of the material parameter to SoftMaterial1, which corresponds to the default name assigned to a record of the appropriate class.  To use a different name, uncheck the box and enter the name in the parameter that appears.

$A\=\mathrm{\pi }{\left(\frac{d}{2}\right)}^2$

$B\=\frac{\mathrm{\Phi }}{A}$

$G_m\={\mathrm{\mu }}_0{\mathrm{\mu }}_r\frac{A}{r\mathrm{\alpha }}$

$H\=\frac{B}{{\mathrm{\mu }}_0{\mathrm{\mu }}_r}$

$R_m\=\frac{1}{G_m}$

$\mathrm{\Phi }\={\mathrm{\Phi }}_p\=-{\mathrm{\Phi }}_n$

$V_m\=V_{m_p}-V_{m_n}\=R_m\mathrm{\Phi }$

${\mathrm{\mu }}_r\=\{\begin{array}{cc}{\mathrm{\mu }}_{r_{\mathrm{approx}}}\left(B\,\mathrm{material}\right)& \mathrm{Nonlinear\; Permeability}\\ {\mathrm{\mu }}_{r_{\mathrm{const}}}& \mathrm{otherwise}\end{array}$

The component described in this topic is from the Modelica Standard Library. To view the original documentation, which includes author and copyright information, click here.