Half Hollow Cylinder - MapleSim Help

Half Hollow Cylinder

Description

The Half Hollow Cylinder component models the leakage flux through a half-hollow cylinder air-gap, in the circumferential direction.  The equations are

 ${V}_{m}=\mathrm{Φ}\cdot {R}_{m}$ ${V}_{m}\equiv {V}_{{m}_{p}}-{V}_{{m}_{n}}$ ${\mathrm{Φ}}_{p}+{\mathrm{Φ}}_{n}=0$ ${R}_{m}=\frac{1}{{G}_{m}}$ ${G}_{m}=\frac{{\mathrm{μ}}_{0}\cdot l}{\mathrm{π}}\cdot \mathrm{ln}\left(1+\mathrm{ratio}\right)$

Connections

 Name Description Color ${\mathrm{port}}_{p}$ Positive magnetic port Solid orange ${\mathrm{port}}_{n}$ Negative magnetic port Open orange

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

Parameters

 Symbol Default Units Description Modelica ID $l$ $0.1$ $m$ Axial length orthogonal to flux l $\mathrm{ratio}$ 1 - , with ${r}_{o}$ and ${r}_{i}$, the outer and inner radii, respectively. ratio

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