Modelica.Magnetic.FluxTubes.Shapes.Force

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.

Package Content

Name	Description
HollowCylinderAxialFlux	(Hollow) cylinder with axial flux; constant permeability
HollowCylinderRadialFlux	Hollow cylinder with radial flux; constant permeability
CuboidParallelFlux	Cuboid with flux in direction of motion, e.g., air gap with rectangular cross-section; constant permeability
CuboidOrthogonalFlux	Cuboid with flux orthogonal to direction of motion; constant permeability
LeakageAroundPoles	Leakage flux tube around cylindrical or prismatic poles

Modelica.Magnetic.FluxTubes.Shapes.Force.HollowCylinderAxialFlux

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.

Parameters

Name	Description
useSupport	= true, if support flange enabled, otherwise implicitly grounded
mu_r	Relative magnetic permeability [1]
dlBydx	Derivative of flux tube's varying dimension with respect to armature position; set to +1 or -1
r_i	Inner radius of (hollow) cylinder [m]
r_o	Outer radius of (hollow) cylinder [m]
Initialization
Phi	Magnetic flux from port_p to port_n [Wb]
Variable geometry
l	Axial length (in direction of flux) [m]

Connectors

Name	Description
port_p	Positive magnetic port
port_n	Negative magnetic port
flange	Generated reluctance force at armature position
support	Support/housing of component

Modelica.Magnetic.FluxTubes.Shapes.Force.HollowCylinderRadialFlux

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.

Parameters

Name	Description
useSupport	= true, if support flange enabled, otherwise implicitly grounded
mu_r	Relative magnetic permeability [1]
dlBydx	Derivative of flux tube's varying dimension with respect to armature position; set to +1 or -1
r_i	Inner radius of hollow cylinder [m]
r_o	Outer radius of hollow cylinder [m]
Initialization
Phi	Magnetic flux from port_p to port_n [Wb]
Variable geometry
l	Axial length (orthogonal to direction of flux) [m]

Connectors

Name	Description
port_p	Positive magnetic port
port_n	Negative magnetic port
flange	Generated reluctance force at armature position
support	Support/housing of component

Modelica.Magnetic.FluxTubes.Shapes.Force.CuboidParallelFlux

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.

Parameters

Name	Description
useSupport	= true, if support flange enabled, otherwise implicitly grounded
mu_r	Relative magnetic permeability [1]
dlBydx	Derivative of flux tube's varying dimension with respect to armature position; set to +1 or -1
a	Width of rectangular cross-section [m]
b	Height of rectangular cross-section [m]
Initialization
Phi	Magnetic flux from port_p to port_n [Wb]
Variable geometry
l	Axial length (in direction of flux) [m]

Connectors

Name	Description
port_p	Positive magnetic port
port_n	Negative magnetic port
flange	Generated reluctance force at armature position
support	Support/housing of component

Modelica.Magnetic.FluxTubes.Shapes.Force.CuboidOrthogonalFlux

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.

Parameters

Name	Description
useSupport	= true, if support flange enabled, otherwise implicitly grounded
mu_r	Relative magnetic permeability [1]
dlBydx	Derivative of flux tube's varying dimension with respect to armature position; set to +1 or -1
a	Width of rectangular cross-section [m]
b	Height of rectangular cross-section (in flux direction) [m]
Initialization
Phi	Magnetic flux from port_p to port_n [Wb]
Variable geometry
l	Length in direction of motion (orthogonal to flux) [m]

Connectors

Name	Description
port_p	Positive magnetic port
port_n	Negative magnetic port
flange	Generated reluctance force at armature position
support	Support/housing of component

Modelica.Magnetic.FluxTubes.Shapes.Force.LeakageAroundPoles

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.

Parameters

Name	Description
useSupport	= true, if support flange enabled, otherwise implicitly grounded
mu_r	Relative magnetic permeability [1]
dlBydx	Derivative of flux tube's varying dimension with respect to armature position; set to +1 or -1
w	Width orthogonal to flux; mean circumference of flux tube in case of cylindrical poles [m]
r	Radius of leakage field [m]
Initialization
Phi	Magnetic flux from port_p to port_n [Wb]
Variable geometry
l	Axial length (in direction of flux) [m]

Connectors

Name	Description
port_p	Positive magnetic port
port_n	Negative magnetic port
flange	Generated reluctance force at armature position
support	Support/housing of component