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).

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 qarter 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 |

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

Type | Name | Default | Description |
---|---|---|---|

Length | l | Axial length orthogonal to flux (=2*pi*r for cylindrical pole and r>>distance between edge and plane) [m] | |

Type | Name | Description |
---|---|---|

PositiveMagneticPort | port_p | Positive magnetic port |

NegativeMagneticPort | port_n | Negative magnetic port |

model QuarterCylinder "Leakage flux from one edge to the opposite plane through a quarter cylinder" extends Modelica.Magnetic.FluxTubes.Interfaces.PartialLeakage; parameter SI.Length l( start = 0.1) "Axial length orthogonal to flux (=2*pi*r for cylindrical pole and r>>distance between edge and plane)"; equation G_m = mu_0 * 0.52 * l;end QuarterCylinder;

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

Type | Name | Default | Description |
---|---|---|---|

Length | l | Axial length orthogonal to flux (=2*pi*r for cylindrical pole and r>>r_i) [m] | |

Real | ratio | Constant ratio t/r_i | |

Type | Name | Description |
---|---|---|

PositiveMagneticPort | port_p | Positive magnetic port |

NegativeMagneticPort | port_n | Negative magnetic port |

model QuarterHollowCylinder "Leakage flux in circumferential direction through a quarter hollow cylinder" extends Modelica.Magnetic.FluxTubes.Interfaces.PartialLeakage; parameter SI.Length l( start = 0.1) "Axial length orthogonal to flux (=2*pi*r for cylindrical pole and r>>r_i)"; parameter Real ratio( start = 1) "Constant ratio t/r_i"; equation G_m = 2* mu_0 * l * Modelica.Math.log(1 + ratio) /pi;end QuarterHollowCylinder;

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

Type | Name | Default | Description |
---|---|---|---|

Length | l | Axial length orthogonal to flux (=2*pi*r for cylindrical pole and r>>distance between edges) [m] | |

Type | Name | Description |
---|---|---|

PositiveMagneticPort | port_p | Positive magnetic port |

NegativeMagneticPort | port_n | Negative magnetic port |

model HalfCylinder "Leakage flux through the edges of a half cylinder" extends Modelica.Magnetic.FluxTubes.Interfaces.PartialLeakage; parameter SI.Length l( start = 0.1) "Axial length orthogonal to flux (=2*pi*r for cylindrical pole and r>>distance between edges)"; equation G_m = mu_0 * 0.26 * l;end HalfCylinder;

Type | Name | Default | Description |
---|---|---|---|

Length | l | Axial length orthogonal to flux (=2*pi*r for cylindrical pole and r>>r_i) [m] | |

Real | ratio | Constant ratio t/r_i | |

Type | Name | Description |
---|---|---|

PositiveMagneticPort | port_p | Positive magnetic port |

NegativeMagneticPort | port_n | Negative magnetic port |

model HalfHollowCylinder "Leakage flux in circumferential direction through a half hollow cylinder" extends Modelica.Magnetic.FluxTubes.Interfaces.PartialLeakage; parameter SI.Length l( start = 0.1) "Axial length orthogonal to flux (=2*pi*r for cylindrical pole and r>>r_i)"; parameter Real ratio( start = 1) "Constant ratio t/r_i"; equation G_m = mu_0 * l * Modelica.Math.log(1 + ratio) /pi;end HalfHollowCylinder;

Type | Name | Default | Description |
---|---|---|---|

Radius | r | Radius of quarter sphere [m] | |

Type | Name | Description |
---|---|---|

PositiveMagneticPort | port_p | Positive magnetic port |

NegativeMagneticPort | port_n | Negative magnetic port |

model QuarterSphere "Leakage flux through the corners of a quarter sphere" extends Modelica.Magnetic.FluxTubes.Interfaces.PartialLeakage; parameter SI.Radius r( start = 0.005) "Radius of quarter sphere"; equation G_m = mu_0 * 0.077 * 2*r;end QuarterSphere;

Type | Name | Default | Description |
---|---|---|---|

Length | t | Thickness of sperical shell [m] | |

Type | Name | Description |
---|---|---|

PositiveMagneticPort | port_p | Positive magnetic port |

NegativeMagneticPort | port_n | Negative magnetic port |

model QuarterHollowSphere "Leakage flux through the edges of a qarter hollow sphere" extends Modelica.Magnetic.FluxTubes.Interfaces.PartialLeakage; parameter SI.Length t( start = 0.01) "Thickness of sperical shell"; equation G_m = mu_0 * 0.25 * t;end QuarterHollowSphere;

Type | Name | Default | Description |
---|---|---|---|

Radius | r | Radius of eighth of sphere [m] | |

Type | Name | Description |
---|---|---|

PositiveMagneticPort | port_p | Positive magnetic port |

NegativeMagneticPort | port_n | Negative magnetic port |

model EighthOfSphere "Leakage flux through one edge and the opposite plane of an eighth of a sphere" extends Modelica.Magnetic.FluxTubes.Interfaces.PartialLeakage; parameter SI.Radius r( start = 0.01) "Radius of eighth of sphere"; equation G_m = mu_0 * 0.308 * r;end EighthOfSphere;

Type | Name | Default | Description |
---|---|---|---|

Length | t | Thickness of sperical shell [m] | |

Type | Name | Description |
---|---|---|

PositiveMagneticPort | port_p | Positive magnetic port |

NegativeMagneticPort | port_n | Negative magnetic port |

model EighthOfHollowSphere "Leakage flux through one edge and the opposite plane of an eighth of a hollow sphere" extends Modelica.Magnetic.FluxTubes.Interfaces.PartialLeakage; parameter SI.Length t( start = 0.01) "Thickness of sperical shell"; equation G_m = mu_0 * 0.5 * t;end EighthOfHollowSphere;

Type | Name | Default | Description |
---|---|---|---|

Radius | r_0 | Radius of inner solid cylinder [m] | |

Radius | r_1 | Inner radius of outer hollow cylinder [m] | |

Radius | r_2 | Outer radius of outer hollow cylinder [m] | |

Type | Name | Description |
---|---|---|

PositiveMagneticPort | port_p | Positive magnetic port |

NegativeMagneticPort | port_n | Negative magnetic port |

model CoaxCylindersEndFaces "Leakage flux between the end planes of a inner solid cylinder and a coaxial outer hollow cylinder" extends Modelica.Magnetic.FluxTubes.Interfaces.PartialLeakage; parameter SI.Radius r_0( start = 10e-3) "Radius of inner solid cylinder"; parameter SI.Radius r_1( start = 17e-3) "Inner radius of outer hollow cylinder"; parameter SI.Radius r_2( start = 20e-3) "Outer radius of outer hollow cylinder"; final parameter SI.Distance l_g = r_1 - r_0 "Radial gap length between both cylinders"; final parameter SI.Length t = r_2 - r_1 "Radial thickness of outer hollow cylinder"; equation // [Ro41], p. 139, Eq. (22) G_m = if t <= r_0 then 2 * mu_0 * (r_0 + l_g/2) * Modelica.Math.log(1 + 2*t/l_g) else 2 * mu_0 * (r_0 + l_g/2) * Modelica.Math.log(1 + 2*r_0/l_g);end CoaxCylindersEndFaces;

Automatically generated Fri Nov 12 16:29:52 2010.