Leakage Around Poles - MapleSim Help

Leakage Around Poles

Description

The Leakage around Poles component models the leakage magnetic flux around a prismatic air-gap between two poles.  It models the radius of the leakage field, $r$, as a constant parameter, independent of the length of the air-gap, $l$.

The equations are

 ${V}_{m}=\mathrm{Φ}\cdot {R}_{m}$ ${\mathrm{Φ}}_{p}+{\mathrm{Φ}}_{n}=0$ ${R}_{m}=\frac{1}{{G}_{m}}$ ${G}_{m}=\frac{{\mathrm{μ}}_{0}\cdot w}{\mathrm{π}}\cdot \mathrm{ln}\left(1+\frac{\mathrm{π}\cdot r}{l}\right)$ $f=-{F}_{m}$ ${F}_{m}=\frac{1}{2}\cdot {V}_{m}^{2}\cdot \frac{ⅆ{G}_{m}}{ⅆx}$ $\frac{ⅆ{G}_{m}}{ⅆx}=-\frac{{\mathrm{μ}}_{0}\cdot w\cdot r}{{l}^{2}\cdot \left(1+\frac{\mathrm{π}\cdot r}{l}\right)}\cdot \frac{ⅆl}{\mathrm{dx}}$ $s=l$ $s={\mathrm{flange}}_{s}-{\mathrm{support}}_{s}$

Connections

 Name Description Color ${\mathrm{port}}_{p}$ Positive magnetic port Solid orange ${\mathrm{port}}_{n}$ Negative magnetic port Open orange $\mathrm{flange}$ Armature connection Open green $\mathrm{support}$ Solid green

Variables

 Symbol Units Description Modelica ID ${V}_{m}$ $A$ Magnetic potential across component V_m ${V}_{{m}_{x}}$ $A$ Magnetic potential at port_x.V_m ${\mathrm{Φ}}_{x}$ $\mathrm{Wb}$ Magnetic flux into ${\mathrm{port}}_{x}$, port_x.Phi $\mathrm{Φ}$ $\mathrm{Wb}$ Magnetic flux through component Phi ${R}_{m}$ ${H}^{-1}$ Magnetic reluctance Rm ${G}_{m}$ $H$ Magnetic permeance Gm $f$ $N$ force on $\mathrm{flange}$ flange.f ${F}_{m}$ $N$ Reluctance force F_m $l$ $m$ Axial length (separation of air-gap) l $s$ $m$ Position of $\mathrm{flange}$ s

Parameters

 Symbol Default Units Description Modelica ID $w$ 0.1 $m$ Width orthogonal to flux w $r$ 0.01 $m$ Radius of leakage field r $\frac{\mathrm{dl}}{\mathrm{dx}}$ $+1$ integer Derivative of flux tube's varying dimension with respect to the armature position. Set to +1 or -1. dlBydx $\mathrm{useSupport}$ $\mathrm{false}$ boolean Enables conditional support flange support

Initial Conditions

 Symbol Units Description Modelica ID ${V}_{\mathrm{m0}}$ $A$ Magnetic potential across component V_m ${\mathrm{Φ}}_{0}$ $\mathrm{Wb}$ Magnetic flux through component Phi ${R}_{\mathrm{m0}}$ ${H}^{-1}$ Magnetic reluctance Rm ${G}_{\mathrm{m0}}$ $H$ Magnetic permeance Gm $\genfrac{}{}{0}{}{\frac{{\mathrm{dG}}_{m}}{\mathrm{dx}}}{\phantom{y}}|\genfrac{}{}{0}{}{\phantom{x}}{0}$ $\frac{H}{m}$ Initial change of permeance with length dGmBydx ${F}_{\mathrm{m0}}$ N Initial reluctance force F_m ${l}_{0}$ m Initial length of air gap l ${s}_{0}$ m Initial position of flange s