Tellinen Permanent Magnet - MapleSim Help

Tellinen Permanent Magnet

Permanent magnet based on the Tellinen hysteresis model

 Description The Tellinen Permanent Magnet component is a flux tube element of fixed length and cross-sectional area that models the hard magnetic hysteresis of permanent magnets. The model is similar to Tellinen Hard but has an initial magnetization preset of -100% and an adapted icon for better readability of the diagram.
 Equations $\mathrm{\Phi }={\mathrm{\Phi }}_{p}=-{\mathrm{\Phi }}_{n}=BA$ ${V}_{m}={V}_{{m}_{p}}-{V}_{{m}_{n}}$ $H=\frac{{V}_{m}}{\ell }={H}_{\mathrm{stat}}+{H}_{\mathrm{eddy}}$ ${H}_{\mathrm{eddy}}=\left\{\begin{array}{cc}\frac{\mathrm{\sigma }{d}^{2}}{12}\frac{\mathrm{dB}}{\mathrm{dt}}& \mathrm{Include eddy currents}\\ 0& \mathrm{otherwise}\end{array}$ ${H}_{0}=\frac{1}{2}\mathrm{log}\left(\frac{1+{\mathrm{\mu }}_{0}\frac{{H}_{c}}{{B}_{r}}}{1-{\mathrm{\mu }}_{0}\frac{{H}_{c}}{{B}_{r}}}\right)+M{H}_{c}$ ${\mathrm{hyst}}_{F}={J}_{s}\mathrm{tanh}\left(\frac{{H}_{\mathrm{stat}}M+{H}_{0}}{{H}_{\mathrm{unit}}}\right)+{\mathrm{\mu }}_{0}{H}_{\mathrm{stat}}+\frac{1}{2}\mathrm{eps}$ ${\mathrm{hyst}}_{R}={J}_{s}\mathrm{tanh}\left(\frac{{H}_{\mathrm{stat}}M-{H}_{0}}{{H}_{\mathrm{unit}}}\right)+{\mathrm{\mu }}_{0}{H}_{\mathrm{stat}}-\frac{1}{2}\mathrm{eps}$ $\left\{\begin{array}{cc}\left\{\mathrm{dHyst}=0,k=\frac{1}{100}\right\}& \mathrm{initial}\\ \left\{\mathrm{dHyst}=\frac{d}{\mathrm{dt}}\left(-{H}_{\mathrm{stat}}{\mathrm{\mu }}_{0}+{\mathrm{hyst}}_{R}\right),k=\mathrm{max}\left(\frac{1}{100},\frac{{\mathrm{hyst}}_{F}-B}{\Delta \mathrm{hyst}}\right)\right\}& 0<\frac{{\mathrm{dH}}_{\mathrm{stat}}}{\mathrm{dt}}\\ \left\{\mathrm{dHyst}=\frac{d}{\mathrm{dt}}\left(-{H}_{\mathrm{stat}}{\mathrm{\mu }}_{0}+{\mathrm{hyst}}_{F}\right),k=\mathrm{max}\left(\frac{1}{100},\frac{B-{\mathrm{hyst}}_{R}}{\Delta \mathrm{hyst}}\right)\right\}& \mathrm{otherwise}\end{array}$ $\mathrm{LossPower}={\mathrm{LossPower}}_{\mathrm{stat}}+{\mathrm{LossPower}}_{\mathrm{eddy}}$ ${\mathrm{LossPower}}_{\mathrm{eddy}}={H}_{\mathrm{eddy}}\frac{\mathrm{dB}}{\mathrm{dt}}V$ ${\mathrm{LossPower}}_{\mathrm{stat}}={H}_{\mathrm{stat}}\frac{\mathrm{dB}}{\mathrm{dt}}V$ $\Delta \mathrm{hyst}={\mathrm{hyst}}_{F}-{\mathrm{hyst}}_{R}$ $\frac{\mathrm{dB}}{\mathrm{dt}}=k\mathrm{dHyst}+{\mathrm{\mu }}_{0}\frac{d{H}_{\mathrm{stat}}}{\mathrm{dt}}$ $\frac{\mathrm{dMagRel}}{\mathrm{dt}}=0$ ${T}_{\mathrm{hp}}=\left\{\begin{array}{cc}{T}_{\mathrm{heatPort}}& \mathrm{Use Heat Port}\\ T& \mathrm{otherwise}\end{array}$

Variables

 Name Units Description Modelica ID $B$ $T$ Magnetic flux density B $\mathrm{dHyst}$ $\frac{T}{s}$ Slope of the limiting hysteresis branch dHyst $H$ $\frac{A}{m}$ Magnetic field strength H ${H}_{\mathrm{eddy}}$ $\frac{A}{m}$ Dynamic (eddy currents) portion of the magnetic field strength Heddy ${H}_{\mathrm{stat}}$ $\frac{A}{m}$ Static (ferromagnetic) portion of the magnetic field strength Hstat $\mathrm{LossPower}$ $W$ Loss power leaving component via HeatPort LossPower ${\mathrm{LossPower}}_{\mathrm{eddy}}$ $W$ Eddy current losses (dynamic hysteresis losses) LossPowerEddy ${\mathrm{LossPower}}_{\mathrm{stat}}$ $W$ Ferromagnetic (static) hysteresis losses LossPowerStat $\mathrm{MagRel}$ $1$ Relative magnetization at initialization (-1..1) MagRel $\mathrm{\Phi }$ $\mathrm{Wb}$ Magnetic flux from port_p to port_n Phi ${T}_{\mathrm{heatPort}}$ $K$ Temperature of HeatPort T_heatPort ${V}_{m}$ $A$ Magnetic potential difference between both ports V_m

Connections

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

Parameters

Hystersis

 Name Default Units Description Modelica ID ${B}_{r}$ $1.2$ $T$ Remanence Br ${H}_{c}$ $5·{10}^{5}$ $\frac{A}{m}$ Coercitivity Hc $K$ $1$ $1$ ${\mathrm{\mu }}_{0}$ multiplier K $M$ $10\frac{{H}_{\mathrm{unit}}}{{H}_{c}}$ $1$ Slope of tanh function M

Fixed Geometry

 Name Default Units Description Modelica ID $\ell$ $0.1$ $m$ Length in direction of flux l $A$ $1·{10}^{-4}$ ${m}^{2}$ Area of cross section A

Losses And Heat Parameters

 Name Default Units Description Modelica ID Use Heat Port $\mathrm{false}$ True (checked) enables heat port useHeatPort Include Eddy Currents $\mathrm{false}$ True (checked) enables eddy current losses includeEddyCurrents $\mathrm{\sigma }$ $1·{10}^{7}$ $\frac{S}{m}$ Conductivity of core material sigma $d$ $5·{10}^{-4}$ $m$ Thickness of lamination d

 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.