Modelica.Magnetic.FluxTubes.Shapes.FixedShape

Flux tubes with fixed shape during simulation and linear or non-linear material characteristics

Information

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

Due to the restrictions on reluctance force calculation outlined there, flux tube elements with a possibly non-linear material characteristic mu_r(B) must have a fixed shape during simulation of converter motion. Hence, the dimensions of these flux tubes are defined as parameters in the model components that extend the base class BaseClasses.FixedShape.

For initial design of magnetic circuits, the relative permeability of possibly non-linear flux tube elements can easily be set to a constant value mu_rConst (non-linearPermeability set to false). In some cases, this can simplify the rough geometric design of a device's magnetic circuit. Once an initial geometry is found, the magnetic subsystem can be simulated and fine-tuned with more realistic non-linear characteristics of ferromagnetic materials. Doing so requires setting of the parameter non-linearPermeability to true and selection of one of the soft magnetic materials of Material.SoftMagnetic.

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

Package Content

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

Modelica.Magnetic.FluxTubes.Shapes.FixedShape.GenericFluxTube

Flux tube with fixed cross-section and length; linear or non-linear material characteristics

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.

Extends from BaseClasses.FixedShape (Base class for flux tubes with fixed shape during simulation; linear or non-linear material characteristics), Modelica.Magnetic.FluxTubes.Icons.Reluctance (Icon for reluctance / permeance components).

Parameters

Name	Description
Initialization
Phi	Magnetic flux from port_p to port_n [Wb]
Material
nonLinearPermeability	= true, if non-linear rel. permeability is used, otherwise constant rel. permeability
mu_rConst	Constant relative permeability; used if nonLinearPermeability = false [1]
material	Ferromagnetic material characteristics; used if nonLinearPermeability = true
Fixed geometry
l	Length in direction of flux [m]
area	Area of cross section [m2]

Connectors

Modelica.Magnetic.FluxTubes.Shapes.FixedShape.Cuboid

Flux tube with rectangular cross-section; fixed shape; linear or non-linear material characteristics

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.

Extends from BaseClasses.FixedShape (Base class for flux tubes with fixed shape during simulation; linear or non-linear material characteristics), Modelica.Magnetic.FluxTubes.Icons.Cuboid (Icon for cuboid).

Parameters

Name	Description
Initialization
Phi	Magnetic flux from port_p to port_n [Wb]
Material
nonLinearPermeability	= true, if non-linear rel. permeability is used, otherwise constant rel. permeability
mu_rConst	Constant relative permeability; used if nonLinearPermeability = false [1]
material	Ferromagnetic material characteristics; used if nonLinearPermeability = true
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.FluxTubes.Shapes.FixedShape.HollowCylinderAxialFlux

(Hollow) cylinder with axial flux; fixed shape; linear or non-linear material characteristics

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.

Set the inner radius r_i=0 for modelling of a solid cylindric flux tube.

Extends from BaseClasses.FixedShape (Base class for flux tubes with fixed shape during simulation; linear or non-linear material characteristics), Modelica.Magnetic.FluxTubes.Icons.HollowCylinderAxialFlux (Icon for cylinder with axial flux).

Parameters

Name	Description
Initialization
Phi	Magnetic flux from port_p to port_n [Wb]
Material
nonLinearPermeability	= true, if non-linear rel. permeability is used, otherwise constant rel. permeability
mu_rConst	Constant relative permeability; used if nonLinearPermeability = false [1]
material	Ferromagnetic material characteristics; used if nonLinearPermeability = true
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.FluxTubes.Shapes.FixedShape.HollowCylinderRadialFlux

Hollow cylinder with radial flux; fixed shape; linear or non-linear material characteristics

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 cylindric flux tubes with a radial 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 cylindric 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 BaseClasses.FixedShape (Base class for flux tubes with fixed shape during simulation; linear or non-linear material characteristics), Modelica.Magnetic.FluxTubes.Icons.HollowCylinderRadialFlux (Icon for cylinder with radial flux).

Parameters

Name	Description
Initialization
Phi	Magnetic flux from port_p to port_n [Wb]
Material
nonLinearPermeability	= true, if non-linear rel. permeability is used, otherwise constant rel. permeability
mu_rConst	Constant relative permeability; used if nonLinearPermeability = false [1]
material	Ferromagnetic material characteristics; used if nonLinearPermeability = true
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.FluxTubes.Shapes.FixedShape.HollowCylinderCircumferentialFlux

Hollow cylinder with circumferential flux; fixed shape; linear or non-linear material characteristics

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 BaseClasses.FixedShape (Base class for flux tubes with fixed shape during simulation; linear or non-linear material characteristics), Modelica.Magnetic.FluxTubes.Icons.HollowCylinderCircumferentialFlux (Icon for cylinder with circumferential flux).

Parameters

Name	Description
Initialization
Phi	Magnetic flux from port_p to port_n [Wb]
Material
nonLinearPermeability	= true, if non-linear rel. permeability is used, otherwise constant rel. permeability
mu_rConst	Constant relative permeability; used if nonLinearPermeability = false [1]
material	Ferromagnetic material characteristics; used if nonLinearPermeability = true
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.FluxTubes.Shapes.FixedShape.Toroid

Toroid with circular cross section; fixed shape; linear or non-linear material characteristics

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 BaseClasses.FixedShape (Base class for flux tubes with fixed shape during simulation; linear or non-linear material characteristics), Modelica.Magnetic.FluxTubes.Icons.Toroid (Icon for toroid).

Parameters

Name	Description
Initialization
Phi	Magnetic flux from port_p to port_n [Wb]
Material
nonLinearPermeability	= true, if non-linear rel. permeability is used, otherwise constant rel. permeability
mu_rConst	Constant relative permeability; used if nonLinearPermeability = false [1]
material	Ferromagnetic material characteristics; used if nonLinearPermeability = true
Fixed geometry
r	Radius of toroid (middle) [m]
d	Diameter of cylindrical core [m]
alpha	Angle of toroid section [rad]

Connectors