Leakage Around Poles - MapleSim Help

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Leakage Around Poles

Leakage flux tube around cylindrical or prismatic poles

Modelica Standard Library

	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 as a constant parameter, independent of the length of the air-gap.

	Equations
	$F_{m} = \frac{1}{2} V_{m}^{2} \frac{{dG}_{m}}{dx}$ $G_{m} = μ_{0} \frac{w}{π} \log (1 + π \frac{r}{ℓ})$ $R_{m} = \frac{1}{G_{m}}$ $Φ = Φ_{p} = - Φ_{n}$ $V_{m} = V_{m_{p}} - V_{m_{n}} = R_{m} Φ$ $\frac{{dG}_{m}}{dx} = \frac{- μ_{0} w r}{ℓ^{2} (1 + π \frac{r}{ℓ})} \frac{d ℓ}{dx}$ $f_{flange} = - F_{m}$

Variables

Name	Units	Description	Modelica ID
$V_{m}$	$A$	Magnetic potential difference between both ports	V_m
$Φ$	$Wb$	Magnetic flux from port_p to port_n	Phi
$F_{m}$	$N$	Reluctance force	F_m
$s$	$m$	Distance between flange and support	s
$R_{m}$	$H^{−1}$	Magnetic reluctance	R_m
$G_{m}$	$H$	Magnetic permeance	G_m
$\frac{{dG}_{m}}{dx}$	$\frac{H}{m}$	Derivative of permeance with respect to armature position	dGmBydx
$ℓ$	$m$	Axial length (in direction of flux)	l

Connections

Name	Description	Modelica ID
${port}_{p}$	Positive magnetic port	port_p
${port}_{n}$	Negative magnetic port	port_n
$flange$	Generated reluctance force at armature position	flange
$support$	Conditional Support Flange	support

Parameters

Name	Default	Units	Description	Modelica ID
$μ_{r}$	$1$	$1$	Relative magnetic permeability	mu_r
$\frac{d ℓ}{dx}$	$1$	$1$	Derivative of flux tube's varying dimension with respect to armature position; set to +1 or -1	dl/dx
$ω$	$0.1$	$m$	Width orthogonal to flux; mean circumference of flux tube in case of cylindrical poles	w
$r$	$0.01$	$m$	Radius of leakage field	r
Use Support	$false$		True (checked) enables the support flange	useSupport

	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.

See Also

Magnetic Library

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