Modelica_Magnetic.FluxTube.FixedShape

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

Information


Please have a look at Reluctance forces in the Users Guide 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 nonlinear material characteristic my_r(B) must have a fixed shape during simulation of actuator motion. Hence, the dimensions of these flux tubes are defined as parameters in the model components that extend the base class PartialFixedShape.

For initial design of magnetic circuits, the relative permeability of possibly nonlinear flux tube elements can easily be set to a constant value my_rConst (nonLinearPermeability 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 nonLinearPermeability to true and selection of one of the soft magnetic materials of Material.SoftMagnetic.

Package Content

NameDescription
Modelica_Magnetic.FluxTube.FixedShape.PartialFixedShape PartialFixedShape Base class for flux tubes with fixed shape during simulation; linear or nonlinear material characteristics
Modelica_Magnetic.FluxTube.FixedShape.HollowCylinderAxialFlux HollowCylinderAxialFlux (Hollow) cylinder with axial flux; fixed shape; linear or nonlinear material characteristics
Modelica_Magnetic.FluxTube.FixedShape.HollowCylinderRadialFlux HollowCylinderRadialFlux Hollow cylinder with radial flux; fixed shape; linear or nonlinear material characteristics
Modelica_Magnetic.FluxTube.FixedShape.Cuboid Cuboid Flux tube with rectangular cross-section; fixed shape; linear or nonlinear material characteristics


Modelica_Magnetic.FluxTube.FixedShape.PartialFixedShape Modelica_Magnetic.FluxTube.FixedShape.PartialFixedShape

Base class for flux tubes with fixed shape during simulation; linear or nonlinear material characteristics

Modelica_Magnetic.FluxTube.FixedShape.PartialFixedShape

Information


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


Parameters

TypeNameDefaultDescription
Material
BooleannonLinearPermeabilitytrue= true, if non-linear rel. permeability is used, otherwise constant rel. permeability
RelativePermeabilitymy_rConst1Constant relative permeability; used if nonLinearPermeability = false [1]

Connectors

TypeNameDescription
PositiveMagneticPortpPositive magnetic port
NegativeMagneticPortnNegative magnetic port

Modelica definition

partial model PartialFixedShape 
  "Base class for flux tubes with fixed shape during simulation; linear or nonlinear material characteristics" 
  
  extends Modelica_Magnetic.Interfaces.TwoPortComponent;
  
  parameter Boolean nonLinearPermeability = true 
    "= true, if non-linear rel. permeability is used, otherwise constant rel. permeability";
  parameter SI.RelativePermeability my_rConst = 1 
    "Constant relative permeability; used if nonLinearPermeability = false";
  
  replaceable record Material = 
    Modelica_Magnetic.Material.SoftMagnetic.ApproximationData 
    "Ferromagnetic material characteristics; used if nonLinearPermeability = true";
  
  Material mat;
  
  SI.Reluctance R_m "Magnetic reluctance";
  SI.Permeance G_m "Magnetic permeance";
  SI.MagneticFluxDensity B "Magnetic flux density";
  SI.CrossSection A "Cross-sectional area penetrated by magnetic flux";
  
    SI.RelativePermeability my_r "Relative magnetic permeability";
  
equation 
  my_r = if nonLinearPermeability then 
    Modelica_Magnetic.Material.SoftMagnetic.my_rApprox(
          B,
          mat.my_i,
          mat.B_myMax,
          mat.c_a,
          mat.c_b,
          mat.n) else my_rConst;
  R_m = 1/G_m;
  V_mag = Phi * R_m;
  B = Phi/A;
  
end PartialFixedShape;

Modelica_Magnetic.FluxTube.FixedShape.HollowCylinderAxialFlux Modelica_Magnetic.FluxTube.FixedShape.HollowCylinderAxialFlux

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

Modelica_Magnetic.FluxTube.FixedShape.HollowCylinderAxialFlux

Information


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

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


Parameters

TypeNameDefaultDescription
Material
BooleannonLinearPermeabilitytrue= true, if non-linear rel. permeability is used, otherwise constant rel. permeability
RelativePermeabilitymy_rConst1Constant relative permeability; used if nonLinearPermeability = false [1]
replaceable record MaterialApproximationDataFerromagnetic material characteristics; used if nonLinearPermeability = true
Fixed geometry
Lengthl0.01Axial length (in direction of flux) [m]
Radiusr_i0Inner radius of hollow cylinder (zero for cylinder) [m]
Radiusr_o0.01Outer radius of (hollow) cylinder [m]

Connectors

TypeNameDescription
PositiveMagneticPortpPositive magnetic port
NegativeMagneticPortnNegative magnetic port

Modelica definition

model HollowCylinderAxialFlux 
  "(Hollow) cylinder with axial flux; fixed shape; linear or nonlinear material characteristics" 
  
  extends Modelica_Magnetic.FluxTube.FixedShape.PartialFixedShape;
  
  parameter SI.Length l = 0.01 "Axial length (in direction of flux)";
  parameter SI.Radius r_i = 0 
    "Inner radius of hollow cylinder (zero for cylinder)";
  parameter SI.Radius r_o = 0.01 "Outer radius of (hollow) cylinder";
  
equation 
  A = pi*(r_o^2 - r_i^2);
  G_m = (my_0 * my_r * A)/ l;
  
end HollowCylinderAxialFlux;

Modelica_Magnetic.FluxTube.FixedShape.HollowCylinderRadialFlux Modelica_Magnetic.FluxTube.FixedShape.HollowCylinderRadialFlux

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

Modelica_Magnetic.FluxTube.FixedShape.HollowCylinderRadialFlux

Information


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

For hollow cylindric flux tubes with a radial magnetic flux, the flux density is a function of the radius. For that reason, the characteristic my_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 my_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.


Parameters

TypeNameDefaultDescription
Material
BooleannonLinearPermeabilitytrue= true, if non-linear rel. permeability is used, otherwise constant rel. permeability
RelativePermeabilitymy_rConst1Constant relative permeability; used if nonLinearPermeability = false [1]
replaceable record MaterialApproximationDataFerromagnetic material characteristics; used if nonLinearPermeability = true
Fixed geometry
Breadthb0.01Breadth (orthogonal to flux direction) [m]
Radiusr_i0.01Inner radius of hollow cylinder [m]
Radiusr_o0.02Outer radius of hollow cylinder [m]

Connectors

TypeNameDescription
PositiveMagneticPortpPositive magnetic port
NegativeMagneticPortnNegative magnetic port

Modelica definition

model HollowCylinderRadialFlux 
  "Hollow cylinder with radial flux; fixed shape; linear or nonlinear material characteristics" 
  
  extends Modelica_Magnetic.FluxTube.FixedShape.PartialFixedShape;
  
  parameter SI.Breadth b = 0.01 "Breadth (orthogonal to flux direction)";
  parameter SI.Radius r_i = 0.01 "Inner radius of hollow cylinder";
  parameter SI.Radius r_o = 0.02 "Outer radius of hollow cylinder";
  
equation 
  A = b * pi*(r_o + r_i); //Area at arithmetic mean radius for calculation of average flux density
  G_m = 2* pi* my_0* my_r* b/ Modelica.Math.log(r_o/r_i);
  
end HollowCylinderRadialFlux;

Modelica_Magnetic.FluxTube.FixedShape.Cuboid Modelica_Magnetic.FluxTube.FixedShape.Cuboid

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

Modelica_Magnetic.FluxTube.FixedShape.Cuboid

Information


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


Parameters

TypeNameDefaultDescription
Material
BooleannonLinearPermeabilitytrue= true, if non-linear rel. permeability is used, otherwise constant rel. permeability
RelativePermeabilitymy_rConst1Constant relative permeability; used if nonLinearPermeability = false [1]
replaceable record MaterialApproximationDataFerromagnetic material characteristics; used if nonLinearPermeability = true
Fixed geometry
Lengthl0.01Length in direction of flux [m]
Breadtha0.01Breadth of rectangular cross-section [m]
Heightb0.01Height of rectangular cross-section [m]

Connectors

TypeNameDescription
PositiveMagneticPortpPositive magnetic port
NegativeMagneticPortnNegative magnetic port

Modelica definition

model Cuboid 
  "Flux tube with rectangular cross-section; fixed shape; linear or nonlinear material characteristics" 
  
  extends Modelica_Magnetic.FluxTube.FixedShape.PartialFixedShape;
  
  parameter SI.Length l = 0.01 "Length in direction of flux";
  parameter SI.Breadth a = 0.01 "Breadth of rectangular cross-section";
  parameter SI.Height b = 0.01 "Height of rectangular cross-section";
  
equation 
  A = a * b;
  G_m = (my_0 * my_r * A)/ l;
  
end Cuboid;

Modelica_Magnetic.FluxTube.FixedShape.PartialFixedShape.Material Modelica_Magnetic.FluxTube.FixedShape.PartialFixedShape.Material

Ferromagnetic material characteristics; used if nonLinearPermeability = true

Parameters

TypeNameDefaultDescription
RelativePermeabilitymy_i1Initial relative permeability at B=0 [1]
MagneticFluxDensityB_myMax1Flux density at maximum relative permeability [T]
Realc_a1Coefficient of approximation function
Realc_b1Coefficient of approximation function
Realn1Exponent of approximation function

Modelica definition

replaceable record Material = 
  Modelica_Magnetic.Material.SoftMagnetic.ApproximationData 
  "Ferromagnetic material characteristics; used if nonLinearPermeability = true";

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