Modelica.Magnetic.FluxTubes.Shapes.Leakage

Leakage flux tubes with position-independent permeance and hence no force generation; mu_r=1

Information


Please have a look at UsersGuide.ReluctanceForceCalculation for an explanation of the different flux tube categories and resulting sub-packages.

The permeances of all elements of this package are calculated from their geometry. These flux tube elements are intended for modelling of leakage fields through vacuum, air and other media with a relative permeability mu_r=1. Basic.LeakageWithCoefficient accounts for leakage not by the geometry of flux tubes, but by a coupling coefficient c_usefulFlux.

All dimensions are defined as parameters. As a result, the shape of these elements will remain constant during dynamic simulation of actuators and reluctance forces will not be generated in these flux tube elements. A simple leakage flux tube with reluctance force generation is provided with the element Force.LeakageAroundPoles. In cases where the accuracy of that element is not sufficient, the leakage elements of this package can be adapted and extended so that they are able to change their shape with armature motion and to generate reluctance forces. This requires an extension of the partial model Interfaces.PartialForce, a higher variability of the variables representing the flux tube's dimensions, definition of a relationship between armature position and these dimensions and determination of the analytic derivative dG_m/dx of the flux tube's permeance G_m with respect to armature position x.

Extends from Modelica.Icons.VariantsPackage (Icon for package containing variants).

Package Content

NameDescription
Modelica.Magnetic.FluxTubes.Shapes.Leakage.QuarterCylinder QuarterCylinder Leakage flux from one edge to the opposite plane through a quarter cylinder
Modelica.Magnetic.FluxTubes.Shapes.Leakage.QuarterHollowCylinder QuarterHollowCylinder Leakage flux in circumferential direction through a quarter hollow cylinder
Modelica.Magnetic.FluxTubes.Shapes.Leakage.HalfCylinder HalfCylinder Leakage flux through the edges of a half cylinder
Modelica.Magnetic.FluxTubes.Shapes.Leakage.HalfHollowCylinder HalfHollowCylinder Leakage flux in circumferential direction through a half hollow cylinder
Modelica.Magnetic.FluxTubes.Shapes.Leakage.QuarterSphere QuarterSphere Leakage flux through the corners of a quarter sphere
Modelica.Magnetic.FluxTubes.Shapes.Leakage.QuarterHollowSphere QuarterHollowSphere Leakage flux through the edges of a quarter hollow sphere
Modelica.Magnetic.FluxTubes.Shapes.Leakage.EighthOfSphere EighthOfSphere Leakage flux through one edge and the opposite plane of an eighth of a sphere
Modelica.Magnetic.FluxTubes.Shapes.Leakage.EighthOfHollowSphere EighthOfHollowSphere Leakage flux through one edge and the opposite plane of an eighth of a hollow sphere
Modelica.Magnetic.FluxTubes.Shapes.Leakage.CoaxCylindersEndFaces CoaxCylindersEndFaces Leakage flux between the end planes of a inner solid cylinder and a coaxial outer hollow cylinder

Modelica.Magnetic.FluxTubes.Shapes.Leakage.QuarterCylinder Modelica.Magnetic.FluxTubes.Shapes.Leakage.QuarterCylinder

Leakage flux from one edge to the opposite plane through a quarter cylinder

Information


Please refer to the enclosing sub-package Leakage for a description of all elements of this package and to [Ro41] for derivation and/or coefficients of the equation for permeance G_m.

Extends from Modelica.Magnetic.FluxTubes.Interfaces.PartialLeakage (Base class for leakage flux tubes with position-independent permeance and hence no force generation; mu_r=1).

Parameters

NameDescription
lAxial length orthogonal to flux (=2*pi*r for cylindrical pole and r>>distance between edge and plane) [m]
Initialization
PhiMagnetic flux from port_p to port_n [Wb]

Connectors

NameDescription
port_pPositive magnetic port
port_nNegative magnetic port

Modelica.Magnetic.FluxTubes.Shapes.Leakage.QuarterHollowCylinder Modelica.Magnetic.FluxTubes.Shapes.Leakage.QuarterHollowCylinder

Leakage flux in circumferential direction through a quarter hollow cylinder

Information


Please refer to the enclosing sub-package Leakage for a description of all elements of this package and to [Ro41] for derivation and/or coefficients of the equation for permeance G_m.

Extends from Modelica.Magnetic.FluxTubes.Interfaces.PartialLeakage (Base class for leakage flux tubes with position-independent permeance and hence no force generation; mu_r=1).

Parameters

NameDescription
lAxial length orthogonal to flux (=2*pi*r for cylindrical pole and r>>r_i) [m]
ratioConstant ratio t/r_i
Initialization
PhiMagnetic flux from port_p to port_n [Wb]

Connectors

NameDescription
port_pPositive magnetic port
port_nNegative magnetic port

Modelica.Magnetic.FluxTubes.Shapes.Leakage.HalfCylinder Modelica.Magnetic.FluxTubes.Shapes.Leakage.HalfCylinder

Leakage flux through the edges of a half cylinder

Information


Please refer to the enclosing sub-package Leakage for a description of all elements of this package and to [Ro41] for derivation and/or coefficients of the equation for permeance G_m.

Extends from Modelica.Magnetic.FluxTubes.Interfaces.PartialLeakage (Base class for leakage flux tubes with position-independent permeance and hence no force generation; mu_r=1).

Parameters

NameDescription
lAxial length orthogonal to flux (=2*pi*r for cylindrical pole and r>>distance between edges) [m]
Initialization
PhiMagnetic flux from port_p to port_n [Wb]

Connectors

NameDescription
port_pPositive magnetic port
port_nNegative magnetic port

Modelica.Magnetic.FluxTubes.Shapes.Leakage.HalfHollowCylinder Modelica.Magnetic.FluxTubes.Shapes.Leakage.HalfHollowCylinder

Leakage flux in circumferential direction through a half hollow cylinder

Information


Please refer to the enclosing sub-package Leakage for a description of all elements of this package and to [Ro41] for derivation and/or coefficients of the equation for permeance G_m.

Extends from Modelica.Magnetic.FluxTubes.Interfaces.PartialLeakage (Base class for leakage flux tubes with position-independent permeance and hence no force generation; mu_r=1).

Parameters

NameDescription
lAxial length orthogonal to flux (=2*pi*r for cylindrical pole and r>>r_i) [m]
ratioConstant ratio t/r_i
Initialization
PhiMagnetic flux from port_p to port_n [Wb]

Connectors

NameDescription
port_pPositive magnetic port
port_nNegative magnetic port

Modelica.Magnetic.FluxTubes.Shapes.Leakage.QuarterSphere Modelica.Magnetic.FluxTubes.Shapes.Leakage.QuarterSphere

Leakage flux through the corners of a quarter sphere

Information


Please refer to the enclosing sub-package Leakage for a description of all elements of this package and to [Ro41] for derivation and/or coefficients of the equation for permeance G_m.

Extends from Modelica.Magnetic.FluxTubes.Interfaces.PartialLeakage (Base class for leakage flux tubes with position-independent permeance and hence no force generation; mu_r=1).

Parameters

NameDescription
rRadius of quarter sphere [m]
Initialization
PhiMagnetic flux from port_p to port_n [Wb]

Connectors

NameDescription
port_pPositive magnetic port
port_nNegative magnetic port

Modelica.Magnetic.FluxTubes.Shapes.Leakage.QuarterHollowSphere Modelica.Magnetic.FluxTubes.Shapes.Leakage.QuarterHollowSphere

Leakage flux through the edges of a quarter hollow sphere

Information


Please refer to the enclosing sub-package Leakage for a description of all elements of this package and to [Ro41] for derivation and/or coefficients of the equation for permeance G_m.

Extends from Modelica.Magnetic.FluxTubes.Interfaces.PartialLeakage (Base class for leakage flux tubes with position-independent permeance and hence no force generation; mu_r=1).

Parameters

NameDescription
tThickness of spherical shell [m]
Initialization
PhiMagnetic flux from port_p to port_n [Wb]

Connectors

NameDescription
port_pPositive magnetic port
port_nNegative magnetic port

Modelica.Magnetic.FluxTubes.Shapes.Leakage.EighthOfSphere Modelica.Magnetic.FluxTubes.Shapes.Leakage.EighthOfSphere

Leakage flux through one edge and the opposite plane of an eighth of a sphere

Information


Please refer to the enclosing sub-package Leakage for a description of all elements of this package and to [Ro41] for derivation and/or coefficients of the equation for permeance G_m.

Extends from Modelica.Magnetic.FluxTubes.Interfaces.PartialLeakage (Base class for leakage flux tubes with position-independent permeance and hence no force generation; mu_r=1).

Parameters

NameDescription
rRadius of eighth of sphere [m]
Initialization
PhiMagnetic flux from port_p to port_n [Wb]

Connectors

NameDescription
port_pPositive magnetic port
port_nNegative magnetic port

Modelica.Magnetic.FluxTubes.Shapes.Leakage.EighthOfHollowSphere Modelica.Magnetic.FluxTubes.Shapes.Leakage.EighthOfHollowSphere

Leakage flux through one edge and the opposite plane of an eighth of a hollow sphere

Information


Please refer to the enclosing sub-package Leakage for a description of all elements of this package and to [Ro41] for derivation and/or coefficients of the equation for permeance G_m.

Extends from Modelica.Magnetic.FluxTubes.Interfaces.PartialLeakage (Base class for leakage flux tubes with position-independent permeance and hence no force generation; mu_r=1).

Parameters

NameDescription
tThickness of spherical shell [m]
Initialization
PhiMagnetic flux from port_p to port_n [Wb]

Connectors

NameDescription
port_pPositive magnetic port
port_nNegative magnetic port

Modelica.Magnetic.FluxTubes.Shapes.Leakage.CoaxCylindersEndFaces Modelica.Magnetic.FluxTubes.Shapes.Leakage.CoaxCylindersEndFaces

Leakage flux between the end planes of a inner solid cylinder and a coaxial outer hollow cylinder

Information


Please refer to the enclosing sub-package Leakage for a description of all elements of this package and to [Ro41] for derivation and/or coefficients of the equation for permeance G_m.

Extends from Modelica.Magnetic.FluxTubes.Interfaces.PartialLeakage (Base class for leakage flux tubes with position-independent permeance and hence no force generation; mu_r=1).

Parameters

NameDescription
r_0Radius of inner solid cylinder [m]
r_1Inner radius of outer hollow cylinder [m]
r_2Outer radius of outer hollow cylinder [m]
Initialization
PhiMagnetic flux from port_p to port_n [Wb]

Connectors

NameDescription
port_pPositive magnetic port
port_nNegative magnetic port

Automatically generated Mon Sep 23 17:20:38 2013.