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.
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).
|BaseData||Coefficients for approximation of soft magnetic materials|
|Steel||Various ferromagnetic steels|
|ElectricSheet||Various electric sheets|
|mu_rApprox||Approximation of relative permeability mu_r as a function of flux density B for soft magnetic materials|
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).
|RelativePermeability||mu_i||1||Initial relative permeability at B=0 |
|MagneticFluxDensity||B_myMax||1||Flux density at maximum relative permeability [T]|
|Real||c_a||1||Coefficient of approximation function|
|Real||c_b||1||Coefficient of approximation function|
|Real||n||1||Exponent of approximation function|
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";
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]:
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).
|MagneticFluxDensity||B||Flux density in ferromagnetic flux tube element [T]|
|RelativePermeability||mu_i||Initial relative permeability at B=0 |
|MagneticFluxDensity||B_myMax||Flux density at maximum relative permeability [T]|
|Real||c_a||Coefficient of approximation function|
|Real||c_b||Coefficient of approximation function|
|Real||n||Exponent of approximation function|
|RelativePermeability||mu_r||Relative magnetic permeability of ferromagnetic flux tube element |
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);