Toroid - MapleSim Help
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Toroid

Toroid with circular cross section; fixed shape; linear or non-linear material characteristics

 Description 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.
 Equations $A=\mathrm{\pi }{\left(\frac{d}{2}\right)}^{2}$ $B=\frac{\mathrm{\Phi }}{A}$ ${G}_{m}={\mathrm{\mu }}_{0}{\mathrm{\mu }}_{r}\frac{A}{r\mathrm{\alpha }}$ $H=\frac{B}{{\mathrm{\mu }}_{0}{\mathrm{\mu }}_{r}}$ ${R}_{m}=\frac{1}{{G}_{m}}$ $\mathrm{\Phi }={\mathrm{\Phi }}_{p}=-{\mathrm{\Phi }}_{n}$ ${V}_{m}={V}_{{m}_{p}}-{V}_{{m}_{n}}={R}_{m}\mathrm{\Phi }$ ${\mathrm{\mu }}_{r}=\left\{\begin{array}{cc}{\mathrm{\mu }}_{{r}_{\mathrm{approx}}}\left(B,\mathrm{material}\right)& \mathrm{Nonlinear Permeability}\\ {\mathrm{\mu }}_{{r}_{\mathrm{const}}}& \mathrm{otherwise}\end{array}$

Variables

 Name Units Description Modelica ID ${V}_{m}$ $A$ Magnetic potential difference between both ports V_m $\mathrm{\Phi }$ $\mathrm{Wb}$ Magnetic flux from port_p to port_n Phi ${R}_{m}$ ${H}^{-1}$ Magnetic reluctance R_m ${G}_{m}$ $H$ Magnetic permeance G_m $B$ $T$ Magnetic flux density B $A$ ${m}^{2}$ Cross-sectional area penetrated by magnetic flux A $H$ $\frac{A}{m}$ Magnetic field strength H ${\mathrm{\mu }}_{r}$ $1$ Relative magnetic permeability mu_r

Connections

 Name Description Modelica ID ${\mathrm{port}}_{p}$ Positive magnetic port port_p ${\mathrm{port}}_{n}$ Negative magnetic port port_n

Parameters

 Name Default Units Description Modelica ID $r$ $0.1$ $m$ Radius of toroid (middle) r $d$ $0.01$ $m$ Diameter of cylindrical core d $\alpha$ $\frac{\mathrm{\pi }}{2}$ $\mathrm{rad}$ Angle of toroid section alpha Nonlinear Permeability $\mathrm{true}$ True (checked) means ${\mathrm{\mu }}_{r}$ is non-linear, otherwise it is constant nonLinearPermeability Use default material $\mathrm{true}$ True (checked) uses softMaterial1 as the name for the material parameter useDefaultMaterial ${\mathrm{\mu }}_{r,\mathrm{const}}$ $1$ $1$ Constant relative permeability; used if Nonlinear Permeability is false mu_rConst $\mathrm{material}$ Soft Magnetic Material; used if Nonlinear Permeability is true material

 Modelica Standard Library 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.