Package 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 Contents

NameDescription
CoaxCylindersEndFacesLeakage flux between the end planes of a inner solid cylinder and a coaxial outer hollow cylinder
EighthOfHollowSphereLeakage flux through one edge and the opposite plane of an eighth of a hollow sphere
EighthOfSphereLeakage flux through one edge and the opposite plane of an eighth of a sphere
HalfCylinderLeakage flux through the edges of a half cylinder
HalfHollowCylinderLeakage flux in circumferential direction through a half hollow cylinder
QuarterCylinderLeakage flux from one edge to the opposite plane through a quarter cylinder
QuarterHollowCylinderLeakage flux in circumferential direction through a quarter hollow cylinder
QuarterHollowSphereLeakage flux through the edges of a quarter hollow sphere
QuarterSphereLeakage flux through the corners of a quarter sphere

Model 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

TypeNameDefaultDescription
Lengthl0.1Axial length orthogonal to flux (=2*pi*r for cylindrical pole and r>>distance between edge and plane)

Connectors

TypeNameDescription
PositiveMagneticPortport_pPositive magnetic port
NegativeMagneticPortport_nNegative magnetic port

Model 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

TypeNameDefaultDescription
Lengthl0.1Axial length orthogonal to flux (=2*pi*r for cylindrical pole and r>>r_i)
Realratio Constant ratio t/r_i

Connectors

TypeNameDescription
PositiveMagneticPortport_pPositive magnetic port
NegativeMagneticPortport_nNegative magnetic port

Model 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

TypeNameDefaultDescription
Lengthl0.1Axial length orthogonal to flux (=2*pi*r for cylindrical pole and r>>distance between edges)

Connectors

TypeNameDescription
PositiveMagneticPortport_pPositive magnetic port
NegativeMagneticPortport_nNegative magnetic port

Model 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

TypeNameDefaultDescription
Lengthl0.1Axial length orthogonal to flux (=2*pi*r for cylindrical pole and r>>r_i)
Realratio Constant ratio t/r_i

Connectors

TypeNameDescription
PositiveMagneticPortport_pPositive magnetic port
NegativeMagneticPortport_nNegative magnetic port

Model 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

TypeNameDefaultDescription
Radiusr0.005Radius of quarter sphere

Connectors

TypeNameDescription
PositiveMagneticPortport_pPositive magnetic port
NegativeMagneticPortport_nNegative magnetic port

Model 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

TypeNameDefaultDescription
Lengtht Thickness of spherical shell

Connectors

TypeNameDescription
PositiveMagneticPortport_pPositive magnetic port
NegativeMagneticPortport_nNegative magnetic port

Model 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

TypeNameDefaultDescription
Radiusr0.01Radius of eighth of sphere

Connectors

TypeNameDescription
PositiveMagneticPortport_pPositive magnetic port
NegativeMagneticPortport_nNegative magnetic port

Model 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

TypeNameDefaultDescription
Lengtht Thickness of spherical shell

Connectors

TypeNameDescription
PositiveMagneticPortport_pPositive magnetic port
NegativeMagneticPortport_nNegative magnetic port

Model 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

TypeNameDefaultDescription
Radiusr_00.01Radius of inner solid cylinder
Radiusr_10.017Inner radius of outer hollow cylinder
Radiusr_20.02Outer radius of outer hollow cylinder
final Distancel_gr_1 - r_0Radial gap length between both cylinders
final Lengthtr_2 - r_1Radial thickness of outer hollow cylinder

Connectors

TypeNameDescription
PositiveMagneticPortport_pPositive magnetic port
NegativeMagneticPortport_nNegative magnetic port

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