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

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

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

Parameters

Name	Description
l	Axial length orthogonal to flux (=2*pi*r for cylindrical pole and r>>distance between edge and plane) [m]
Initialization
Phi	Magnetic flux from port_p to port_n [Wb]

Connectors

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

Parameters

Name	Description
l	Axial length orthogonal to flux (=2*pi*r for cylindrical pole and r>>r_i) [m]
ratio	Constant ratio t/r_i
Initialization
Phi	Magnetic flux from port_p to port_n [Wb]

Connectors

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

Parameters

Name	Description
l	Axial length orthogonal to flux (=2*pi*r for cylindrical pole and r>>distance between edges) [m]
Initialization
Phi	Magnetic flux from port_p to port_n [Wb]

Connectors

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

Parameters

Name	Description
l	Axial length orthogonal to flux (=2*pi*r for cylindrical pole and r>>r_i) [m]
ratio	Constant ratio t/r_i
Initialization
Phi	Magnetic flux from port_p to port_n [Wb]

Connectors

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

Parameters

Name	Description
r	Radius of quarter sphere [m]
Initialization
Phi	Magnetic flux from port_p to port_n [Wb]

Connectors

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

Parameters

Name	Description
t	Thickness of spherical shell [m]
Initialization
Phi	Magnetic flux from port_p to port_n [Wb]

Connectors

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

Parameters

Name	Description
r	Radius of eighth of sphere [m]
Initialization
Phi	Magnetic flux from port_p to port_n [Wb]

Connectors

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

Parameters

Name	Description
t	Thickness of spherical shell [m]
Initialization
Phi	Magnetic flux from port_p to port_n [Wb]

Connectors

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

Parameters

Name	Description
r_0	Radius of inner solid cylinder [m]
r_1	Inner radius of outer hollow cylinder [m]
r_2	Outer radius of outer hollow cylinder [m]
Initialization
Phi	Magnetic flux from port_p to port_n [Wb]

Connectors