Modelica.Magnetic.FluxTubes.Material.SoftMagnetic

Characteristics mu_r(B) of common soft magnetic materials; hysteresis neglected

Information


The magnetisation characteristics mu_r(B) of all soft magnetic materials currently included in this library are approximated with a function. Each material is characterised by the five parameters of this function. The approximated characteristics mu_r(B) for most of the ferromagnetic materials currently included are shown in the plots below (solid lines) together with the original data points compiled from measurements and literature.

Approximated magnetization characteristics of selected steels

Approximated magnetization characteristics of miscellaneous soft magnetic materials

Approximated magnetization characteristics of included electric sheets

For the nonlinear curve fit, data points for high flux densities (approximately B>1T) have been weighted higher than the ones for low flux densities. This is due to the large impact of saturated ferromagnetic sections in a magnetic circuit compared to that of non-saturated sections with relative permeabilities mu_r>>1.

Note that the magnetisation characteristics largely depend on possible previous machining and on measurement conditions. A virgin material normally has a considerably higher permeability than the same material after machining (and packet assembling in case of electric sheets). This is indicated in the above plots by different magnetisation curves for similar materials. In most cases, the original data points represent commutating curves obtained with measurements at 50Hz.

Additional user-specific materials can be defined as needed. This requires determination of the approximation parameters from the original data points, preferably with a nonlinear curve fit.

Extends from Modelica.Icons.Library (Icon for library).

Package Content

NameDescription
Modelica.Magnetic.FluxTubes.Material.SoftMagnetic.BaseData BaseData Coefficients for approximation of soft magnetic materials
Modelica.Magnetic.FluxTubes.Material.SoftMagnetic.Steel Steel Various ferromagnetic steels
Modelica.Magnetic.FluxTubes.Material.SoftMagnetic.ElectricSheet ElectricSheet Various electric sheets
Modelica.Magnetic.FluxTubes.Material.SoftMagnetic.PureIron PureIron Pure iron
Modelica.Magnetic.FluxTubes.Material.SoftMagnetic.CobaltIron CobaltIron Cobalt iron
Modelica.Magnetic.FluxTubes.Material.SoftMagnetic.NickelIron NickelIron Nickel iron
Modelica.Magnetic.FluxTubes.Material.SoftMagnetic.mu_rApprox mu_rApprox Approximation of relative permeability mu_r as a function of flux density B for soft magnetic materials


Modelica.Magnetic.FluxTubes.Material.SoftMagnetic.BaseData Modelica.Magnetic.FluxTubes.Material.SoftMagnetic.BaseData

Coefficients for approximation of soft magnetic materials

Information


The parameters needed for approximation of the magnetisation characteristics of included soft magnetic materials are declared in this record.

Extends from Modelica.Icons.Record (Icon for a record).

Parameters

TypeNameDefaultDescription
RelativePermeabilitymu_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

record BaseData 
  "Coefficients for approximation of soft magnetic materials"

  extends Modelica.Icons.Record;

  parameter SI.RelativePermeability mu_i = 1 
    "Initial relative permeability at B=0";
  parameter SI.MagneticFluxDensity B_myMax = 1 
    "Flux density at maximum relative permeability";
  parameter Real c_a = 1 "Coefficient of approximation function";
  parameter Real c_b = 1 "Coefficient of approximation function";
  parameter Real n = 1 "Exponent of approximation function";

end BaseData;

Modelica.Magnetic.FluxTubes.Material.SoftMagnetic.mu_rApprox Modelica.Magnetic.FluxTubes.Material.SoftMagnetic.mu_rApprox

Approximation of relative permeability mu_r as a function of flux density B for soft magnetic materials

Information


The relative permeability mu_r as a function of flux density B for all soft magnetic materials currently included in this library is approximated with the following function [Ro00]:

Equation for approximation mu_r(B)


Two of the five parameters of this equation have a physical meaning, namely the initial relative permeability mu_i at B=0 and the magnetic flux density at maximum permeability B_myMax. B_N is the flux density normalized to latter parameter.

Extends from Modelica.Icons.Function (Icon for a function).

Inputs

TypeNameDefaultDescription
MagneticFluxDensityB Flux density in ferromagnetic flux tube element [T]
RelativePermeabilitymu_i Initial relative permeability at B=0 [1]
MagneticFluxDensityB_myMax Flux density at maximum relative permeability [T]
Realc_a Coefficient of approximation function
Realc_b Coefficient of approximation function
Realn Exponent of approximation function

Outputs

TypeNameDescription
RelativePermeabilitymu_rRelative magnetic permeability of ferromagnetic flux tube element [1]

Modelica definition

function mu_rApprox 
  "Approximation of relative permeability mu_r as a function of flux density B for soft magnetic materials"

  extends Modelica.Icons.Function;

  input Modelica.SIunits.MagneticFluxDensity B 
    "Flux density in ferromagnetic flux tube element";
  //Material specific parameter set:
  input Modelica.SIunits.RelativePermeability mu_i 
    "Initial relative permeability at B=0";
  input Modelica.SIunits.MagneticFluxDensity B_myMax 
    "Flux density at maximum relative permeability";
  input Real c_a "Coefficient of approximation function";
  input Real c_b "Coefficient of approximation function";
  input Real n "Exponent of approximation function";

  output Modelica.SIunits.RelativePermeability mu_r 
    "Relative magnetic permeability of ferromagnetic flux tube element";

protected 
  Real B_N 
    "Flux density B normalized to flux density at maximum relative permeability B_myMax";

algorithm 
  B_N := abs(B/B_myMax);
  mu_r := 1 + (mu_i-1 + c_a*B_N)/(1 + c_b*B_N + B_N^n);

end mu_rApprox;

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