Modelica_Magnetic.Material.SoftMagnetic

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

Information


The magnetisation characteristics my_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 my_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 my_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.

Package Content

NameDescription
Modelica_Magnetic.Material.SoftMagnetic.Steel Steel Various ferromagnetic steels
Modelica_Magnetic.Material.SoftMagnetic.ElectricSheet ElectricSheet Various electric sheets
Modelica_Magnetic.Material.SoftMagnetic.PureIron PureIron Pure iron
Modelica_Magnetic.Material.SoftMagnetic.CobaltIron CobaltIron Cobalt iron
Modelica_Magnetic.Material.SoftMagnetic.NickelIron NickelIron Nickel iron
Modelica_Magnetic.Material.SoftMagnetic.my_rApprox my_rApprox Approximation of relative permeability my_r as a function of flux density B for soft magnetic materials
Modelica_Magnetic.Material.SoftMagnetic.ApproximationData ApproximationData Coefficients for approximation of soft magnetic materials


Modelica_Magnetic.Material.SoftMagnetic.my_rApprox Modelica_Magnetic.Material.SoftMagnetic.my_rApprox

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

Information


The relative permeability my_r as a function of flux density B for all soft magnetic materials currently included in this library is approximated with the following function [4]:

Equation for approximation my_r(B)


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

Inputs

TypeNameDefaultDescription
RealB Flux density in ferromagnetic flux tube element
Realmy_i Initial relative permeability at B=0
RealB_myMax Flux density at maximum relative permeability
Realc_a Coefficient of approximation function
Realc_b Coefficient of approximation function
Realn Exponent of approximation function

Outputs

TypeNameDescription
Realmy_rRelative magnetic permeability of ferromagnetic flux tube element

Modelica definition

function my_rApprox 
  "Approximation of relative permeability my_r as a function of flux density B for soft magnetic materials" 
  
  extends Modelica.Icons.Function;
  
  input Real B "Flux density in ferromagnetic flux tube element";
//Material specific parameter set: 
  input Real my_i "Initial relative permeability at B=0";
  input Real 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 Real my_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);
  my_r := 1 + (my_i-1 + c_a*B_N)/(1 + c_b*B_N + B_N^n);
  
end my_rApprox;

Modelica_Magnetic.Material.SoftMagnetic.ApproximationData Modelica_Magnetic.Material.SoftMagnetic.ApproximationData

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.


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

record ApproximationData 
  "Coefficients for approximation of soft magnetic materials" 
  
  extends Modelica.Icons.Record;
  
  parameter SI.RelativePermeability my_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 ApproximationData;

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