 componentLibrary/magnetic/shapes/hysteresis/TellinenTable - MapleSim Help

Tellinen Table

Generic flux tube with ferromagnetic hysteresis based on the Tellinen model and table data  Description The Tellinen Table component is a flux tube element of fixed length and cross-sectional area that models ferromagnetic and dynamic hysteresis (eddy currents). The ferromagnetic hysteresis behavior is defined by the Tellinen hysteresis model. The rising and falling branch of the limiting ferromagnetic hysteresis loop are specified by table data. Almost any hysteresis shape is possible. The Hysteresis Material parameter specifies a record containing a table, it should be the instance name of a magnetic material from the palette Magnetic > Material > Hysteresis > Table Based. See Magnetic Material with Table-based Hysteresis. The Use default material boolean parameter, when true, sets the name of the Hysteresis Material parameter to hysteresisTableMaterial1, 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 for the parameter that appears. Equations $\mathrm{\Phi }={\mathrm{\Phi }}_{p}=-{\mathrm{\Phi }}_{n}=BA$ ${V}_{m}={V}_{{m}_{p}}-{V}_{{m}_{n}}$ $H=\frac{{V}_{m}}{\ell }={H}_{\mathrm{stat}}+{H}_{\mathrm{eddy}}$ ${H}_{\mathrm{eddy}}=\left\{\begin{array}{cc}\frac{\mathrm{\sigma }{d}^{2}}{12}\frac{\mathrm{dB}}{\mathrm{dt}}& \mathrm{Include eddy currents}\\ 0& \mathrm{otherwise}\end{array}$ ${H}_{0}=\frac{1}{2}\mathrm{log}\left(\frac{1+\frac{{B}_{r}}{{J}_{s}}}{1-\frac{{B}_{r}}{{J}_{s}}}\right)$ ${\mathrm{hyst}}_{F}={H}_{\mathrm{stat}}{\mathrm{\mu }}_{0}+{T}_{\mathrm{unit}}{\mathrm{tabfal.y}}_{1}+\mathrm{eps}$ ${\mathrm{hyst}}_{R}={H}_{\mathrm{stat}}{\mathrm{\mu }}_{0}+{T}_{\mathrm{unit}}{\mathrm{tabris.y}}_{1}+\mathrm{eps}$ ${\mathrm{tabfal.u}}_{1}={\mathrm{tabris.u}}_{1}={H}_{\mathrm{stat}}$ $\left\{\begin{array}{cc}\left\{\mathrm{dHyst}=0,k=\frac{1}{100}\right\}& \mathrm{initial}\\ \left\{\mathrm{dHyst}=\frac{d}{\mathrm{dt}}\left(-{H}_{\mathrm{stat}}{\mathrm{\mu }}_{0}+{\mathrm{hyst}}_{R}\right),k=\mathrm{max}\left(\frac{1}{100},\frac{{\mathrm{hyst}}_{F}-B}{\Delta \mathrm{hyst}}\right)\right\}& 0<\frac{{\mathrm{dH}}_{\mathrm{stat}}}{\mathrm{dt}}\\ \left\{\mathrm{dHyst}=\frac{d}{\mathrm{dt}}\left(-{H}_{\mathrm{stat}}{\mathrm{\mu }}_{0}+{\mathrm{hyst}}_{F}\right),k=\mathrm{max}\left(\frac{1}{100},\frac{B-{\mathrm{hyst}}_{R}}{\Delta \mathrm{hyst}}\right)\right\}& \mathrm{otherwise}\end{array}$ $\mathrm{LossPower}={\mathrm{LossPower}}_{\mathrm{stat}}+{\mathrm{LossPower}}_{\mathrm{eddy}}$ ${\mathrm{LossPower}}_{\mathrm{eddy}}={H}_{\mathrm{eddy}}\frac{\mathrm{dB}}{\mathrm{dt}}V$ ${\mathrm{LossPower}}_{\mathrm{stat}}={H}_{\mathrm{stat}}\frac{\mathrm{dB}}{\mathrm{dt}}V$ $\Delta \mathrm{hyst}={\mathrm{hyst}}_{F}-{\mathrm{hyst}}_{R}$ $\frac{\mathrm{dB}}{\mathrm{dt}}=k\mathrm{dHyst}+{\mathrm{\mu }}_{0}\frac{d{H}_{\mathrm{stat}}}{\mathrm{dt}}$ $\frac{\mathrm{dMagRel}}{\mathrm{dt}}=0$ ${T}_{\mathrm{hp}}=\left\{\begin{array}{cc}{T}_{\mathrm{heatPort}}& \mathrm{Use Heat Port}\\ T& \mathrm{otherwise}\end{array}$ Variables

 Name Units Description Modelica ID $B$ $T$ Magnetic flux density B $H$ $\frac{A}{m}$ Magnetic field strength H $\mathrm{Heddy}$ $\frac{A}{m}$ Dynamic (eddy currents) portion of the magnetic field strength Heddy $\mathrm{Hstat}$ $\frac{A}{m}$ 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 Material

 Name Default Units Description Modelica ID Hysteresis Material  Table-based hysteresis material mat Use default material $\mathrm{true}$ True (checked) uses hystersisTableMaterial1 as the name for the Hystersis Material parameter useDefaultMaterial

 hystersisTableMaterial1 Hysteresis

 Name Default Units Description Modelica ID $K$ $1$ Slope of hysteresis in the saturation region (Kmu_0) K 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

 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.