Package Modelica.​Magnetic.​FluxTubes.​Shapes.​Force
Flux tubes with reluctance force generation; constant permeability

Information

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

Flux tube elements with generation of a reluctance force are intended for modelling of position-dependent air gap sections and permanent magnet sections respectively of translatory actuators. By default, the position co-ordinate of the mechanical connector flange.s is identical with the dimension l of the package's flux tube elements. l is the dimension changes with armature motion. If needed, the identity l=flange.s can be replaced by an actuator-specific equation, for example, when a flux tube length increases with decreasing armature position. The position co-ordinate of an element's translatory connector flange.s in turn will be identical with the armature position x in most cases, as the examples illustrate.

The derivative of each element's permeance with respect to armature position dGmBydx is calculated from the derivative of the flux tube's permeance with respect to its varying dimension dGmBydl and the derivative of this dimension with respect to armature position dlBydx:

    dG_m   dG_m   dl
    ---- = ---- * --
     dx     dl    dx

The parameter dlBydx must be set in each flux tube element to +1 or -1 according to the definition of the armature co-ordinate and the position of the element in a device's magnetic circuit. Proper match between armature motion and resulting variation of the flux tube length assures that the element's reluctance force acts in the right direction.

The shapes of the flux tubes defined in this package are rather simple. Only one dimension varies with armature motion. Flux tubes with more complex variations of dimensions with armature motion can be defined by extending the base class Interfaces.PartialForce, if needed. Determination of the analytic derivative dGmBydl could become more complex for those flux tubes.

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

Package Contents

Model Modelica.​Magnetic.​FluxTubes.​Shapes.​Force.​HollowCylinderAxialFlux
(Hollow) cylinder with axial flux; constant permeability

Information

Please refer to the enclosing sub-package Force 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.​PartialForce (Base class for flux tubes with reluctance force generation; constant permeability).

Parameters

Components

Connectors

Model Modelica.​Magnetic.​FluxTubes.​Shapes.​Force.​HollowCylinderRadialFlux
Hollow cylinder with radial flux; constant permeability

Information

Please refer to the enclosing sub-package Force 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.​PartialForce (Base class for flux tubes with reluctance force generation; constant permeability).

Parameters

Components

Connectors

Model Modelica.​Magnetic.​FluxTubes.​Shapes.​Force.​CuboidParallelFlux
Cuboid with flux in direction of motion, e.g., air gap with rectangular cross-section; constant permeability

Information

Please refer to the enclosing sub-package Force 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.​PartialForce (Base class for flux tubes with reluctance force generation; constant permeability).

Parameters

Components

Connectors

Model Modelica.​Magnetic.​FluxTubes.​Shapes.​Force.​CuboidOrthogonalFlux
Cuboid with flux orthogonal to direction of motion; constant permeability

Information

Please refer to the enclosing sub-package Force 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.​PartialForce (Base class for flux tubes with reluctance force generation; constant permeability).

Parameters

Components

Connectors

Model Modelica.​Magnetic.​FluxTubes.​Shapes.​Force.​LeakageAroundPoles
Leakage flux tube around cylindrical or prismatic poles

Information

Please refer to the description of the enclosing sub-package Force for a description of all elements of this package.

Leakage flux around a prismatic or cylindric air gap between to poles can be described with this model. Due to its constant radius of the leakage field r, the model is rather simple. Whereas in reality the leakage radius is approximately constant for air gap lengths l greater than this radius, it decreases with air gap lengths less than the leakage radius. This decrease for small air gaps is neglected here, since the influence of the leakage flux tube compared to that of the enclosed main air gap (connected in parallel) decreases for decreasing air gap length l.

Note that in [Ka08] the equation for G_m is accidentally swapped with that of a similar element.

Extends from Modelica.​Magnetic.​FluxTubes.​Interfaces.​PartialForce (Base class for flux tubes with reluctance force generation; constant permeability).

Parameters

Components

Connectors