Modelica.Magnetic.QuasiStatic.FluxTubes.Shapes.FixedShape

Flux tubes with fixed shape during simulation and linear material characteristics

Information

This package provides different reluctance models, based on different geometric data.

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

Package Content

Name	Description
GenericFluxTube	Flux tube with fixed cross-section, fixed length and linear material characteristics
Cuboid	Flux tube with rectangular cross-section of fixed shape and linear material characteristics
HollowCylinderAxialFlux	(Hollow) cylinder with axial flux of fixed shape and linear material characteristics
HollowCylinderRadialFlux	Hollow cylinder with radial flux of fixed shape and linear material characteristics
HollowCylinderCircumferentialFlux	Hollow cylinder with circumferential flux; fixed shape
Toroid	Toroid with circular cross section; fixed shape

Modelica.Magnetic.QuasiStatic.FluxTubes.Shapes.FixedShape.GenericFluxTube

Flux tube with fixed cross-section, fixed length and linear material characteristics

Information

The generic flux tube models the reluctance with constant area of cross section, and length, l the magnetic reluctance by:

,

Extends from BaseClasses.FixedShape (Base class for flux tubes with fixed shape during simulation), Modelica.Magnetic.QuasiStatic.FluxTubes.Icons.Reluctance (Icon for reluctance / permeance components).

Parameters

Name	Description
mu_rConst	Constant relative permeability [1]
Fixed geometry
l	Length in direction of flux [m]
area	Area of cross section [m2]

Connectors

Modelica.Magnetic.QuasiStatic.FluxTubes.Shapes.FixedShape.Cuboid

Flux tube with rectangular cross-section of fixed shape and linear material characteristics

Information

The cuboid models the reluctance with rectangular dimensions a and b, and length, l the magnetic reluctance by:

The area of cross section is determined by:

Extends from BaseClasses.FixedShape (Base class for flux tubes with fixed shape during simulation), Modelica.Magnetic.QuasiStatic.FluxTubes.Icons.Cuboid (Icon for cuboid).

Parameters

Name	Description
mu_rConst	Constant relative permeability [1]
Fixed geometry
l	Length in direction of flux [m]
a	Width of rectangular cross-section [m]
b	Height of rectangular cross-section [m]

Connectors

Modelica.Magnetic.QuasiStatic.FluxTubes.Shapes.FixedShape.HollowCylinderAxialFlux

(Hollow) cylinder with axial flux of fixed shape and linear material characteristics

Information

The axial cylinder models is characterized by the outer diameter, , the inner diameter, , length, . The magnetic reluctance is determined by:

The area of cross section yields:

A hollow cylinder is depicted in the above figure left for . A solid cylindric flux tube an be considered by setting the inner radius, , equal to zero.

A circular sector of the area of cross section with central angle is depicted in the above figure right.

Extends from BaseClasses.FixedShape (Base class for flux tubes with fixed shape during simulation), Modelica.Magnetic.QuasiStatic.FluxTubes.Icons.HollowCylinderAxialFlux (Icon for cylinder with axial flux).

Parameters

Name	Description
mu_rConst	Constant relative permeability [1]
alpha	Central angle [rad]
Fixed geometry
l	Axial length (in direction of flux) [m]
r_i	Inner radius of hollow cylinder (zero for cylinder) [m]
r_o	Outer radius of (hollow) cylinder [m]

Connectors

Modelica.Magnetic.QuasiStatic.FluxTubes.Shapes.FixedShape.HollowCylinderRadialFlux

Hollow cylinder with radial flux of fixed shape and linear material characteristics

Information

The radial cylinder model is characterized by the outer diameter, , the inner diameter, , length, , and the angle . The magnetic reluctance is determined by:

In this model the magnetic flux and the magnetic potential difference, respectively, are radially oriented.

The above figure left shows a radial flux cylinder with . The figure on the right indicates the central angle in case a cylinder section shall be considered.

Extends from BaseClasses.FixedShape (Base class for flux tubes with fixed shape during simulation), Modelica.Magnetic.QuasiStatic.FluxTubes.Icons.HollowCylinderRadialFlux (Icon for cylinder with radial flux).

Parameters

Name	Description
mu_rConst	Constant relative permeability [1]
alpha	Central angle [rad]
Fixed geometry
l	Width (orthogonal to flux direction) [m]
r_i	Inner radius of hollow cylinder [m]
r_o	Outer radius of hollow cylinder [m]

Connectors

Modelica.Magnetic.QuasiStatic.FluxTubes.Shapes.FixedShape.HollowCylinderCircumferentialFlux

Hollow cylinder with circumferential flux; fixed shape

Information

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

For hollow cylindrical flux tubes with a circumferential magnetic flux, the flux density is a function of the radius. For that reason, the characteristic mu_r(B) is evaluated for the flux density at the flux tube's mean radius.

For those flux tube sections of a magnetic device that have a nonlinear material characteristic mu_r(B) and a large aspect ratio of outer to inner radius r_o/r_i, the section can be split up in a series connection of several hollow cylindrical flux tubes with radial flux. This allows for more realistic modelling of the dependence of flux density on the radius compared to modelling with just one flux tube element.

Extends from Modelica.Magnetic.QuasiStatic.FluxTubes.BaseClasses.FixedShape (Base class for flux tubes with fixed shape during simulation), Modelica.Magnetic.QuasiStatic.FluxTubes.Icons.HollowCylinderCircumferentialFlux (Icon for cylinder with circumferential flux).

Parameters

Name	Description
mu_rConst	Constant relative permeability [1]
Fixed geometry
l	Width (orthogonal to flux direction) [m]
r_i	Inner radius of hollow cylinder [m]
r_o	Outer radius of hollow cylinder [m]
alpha	Angle of cylinder section [rad]

Connectors

Modelica.Magnetic.QuasiStatic.FluxTubes.Shapes.FixedShape.Toroid

Toroid with circular cross section; fixed shape

Information

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

For toroidal flux tubes with a circumferential magnetic flux, the flux density is a function of the radius. For that reason, the characteristic mu_r(B) is evaluated for the flux density at the flux tube's mean radius.

For those flux tube sections of a magnetic device that have a nonlinear material characteristic mu_r(B) and a large aspect ratio of outer to inner radius r_o/r_i, the section can be split up in a series connection of several hollow cylindrical flux tubes with radial flux. This allows for more realistic modelling of the dependence of flux density on the radius compared to modelling with just one flux tube element.

Extends from Modelica.Magnetic.QuasiStatic.FluxTubes.BaseClasses.FixedShape (Base class for flux tubes with fixed shape during simulation), Modelica.Magnetic.QuasiStatic.FluxTubes.Icons.Toroid (Icon for toroid).

Parameters

Name	Description
mu_rConst	Constant relative permeability [1]
Fixed geometry
r	Radius of toroid (middle) [m]
d	Diameter of cylindrical core [m]
alpha	Angle of toroid section [rad]

Connectors