Package 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.​MaterialPropertiesPackage (Icon for package containing property classes).

Package Contents

NameDescription
BaseDataCoefficients for approximation of soft magnetic materials
CobaltIronCobalt iron
ElectricSheetVarious electric sheets
mu_rApproxApproximation of relative permeability mu_r as a function of flux density B for soft magnetic materials
NickelIronNickel iron
PureIronPure iron
SteelVarious ferromagnetic steels

Record 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 records).

Fields

TypeNameDescription
parameter RelativePermeabilitymu_iInitial relative permeability at B=0
parameter MagneticFluxDensityB_myMaxFlux density at maximum relative permeability
parameter Realc_aCoefficient of approximation function
parameter Realc_bCoefficient of approximation function
parameter RealnExponent of approximation function

Function 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 functions).

Inputs

TypeNameDescription
MagneticFluxDensityBFlux density in ferromagnetic flux tube element
RelativePermeabilitymu_iInitial relative permeability at B=0
MagneticFluxDensityB_myMaxFlux density at maximum relative permeability
Realc_aCoefficient of approximation function
Realc_bCoefficient of approximation function
RealnExponent of approximation function

Outputs

TypeNameDescription
RelativePermeabilitymu_rRelative magnetic permeability of ferromagnetic flux tube element

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