Modelica.Magnetic.FluxTubes.Examples.Utilities

Utilities to be used in examples

Package Content

NameDescription
Modelica.Magnetic.FluxTubes.Examples.Utilities.TranslatoryArmatureAndStopper TranslatoryArmatureAndStopper Mass with free travel between two stoppers
Modelica.Magnetic.FluxTubes.Examples.Utilities.CoilDesign CoilDesign Calculation of winding parameters (wire diameter, number of turns et al.) and recalculation with optionally chosen parameters; to be adapted to particular design tasks


Modelica.Magnetic.FluxTubes.Examples.Utilities.TranslatoryArmatureAndStopper Modelica.Magnetic.FluxTubes.Examples.Utilities.TranslatoryArmatureAndStopper

Mass with free travel between two stoppers

Modelica.Magnetic.FluxTubes.Examples.Utilities.TranslatoryArmatureAndStopper

Information


In translatory actuators with limited stroke, the armature with its inertia can travel between two stoppers.

Parameters

TypeNameDefaultDescription
LengthL Length of component from left flange to right flange (= flange_b.s - flange_a.s) [m]
Massm Armature mass [kg]
TranslationalSpringConstantc Spring stiffness between impact partners [N/m]
TranslationalDampingConstantd Damping coefficient between impact partners [N.s/m]
Realn2Exponent of spring forces (f_c = c*|s_rel|^n)
Positionx_max Position of stopper at maximum armature position [m]
Positionx_min Position of stopper at minimum armature position [m]

Connectors

TypeNameDescription
Flange_aflange_a 
Flange_bflange_b 

Modelica definition

model TranslatoryArmatureAndStopper 
  "Mass with free travel between two stoppers"

  parameter SI.Length L(start=0) 
    "Length of component from left flange to right flange (= flange_b.s - flange_a.s)";
  parameter SI.Mass m( start=1) "Armature mass";

  parameter Modelica.SIunits.TranslationalSpringConstant c(
      start = 1e11) "Spring stiffness between impact partners";
  parameter Modelica.SIunits.TranslationalDampingConstant d(
      start = 2e7) "Damping coefficient between impact partners";
  parameter Real n(final min=1)=2 
    "Exponent of spring forces (f_c = c*|s_rel|^n)";

  parameter SI.Position x_max(start=10e-3) 
    "Position of stopper at maximum armature position";
  parameter SI.Position x_min(start=0) 
    "Position of stopper at minimum armature position";
  Modelica.SIunits.Position s(start=0) 
    "Absolute position of center of component (= flange_a.s + L/2)";
  Modelica.SIunits.Velocity v(start=0) 
    "Absolute velocity of components (= der(s))";
  Modelica.SIunits.Acceleration a(start=0) 
    "Absolute acceleration of components (= der(v))";
  Modelica.Mechanics.Translational.Components.Mass mass(
                                                    final L=L, final m=m);
  Modelica.Mechanics.Translational.Interfaces.Flange_a flange_a;
  Modelica.Mechanics.Translational.Interfaces.Flange_b flange_b;
  Modelica.Mechanics.Translational.Components.Fixed limit_xMin(
                                                    s0=x_min);
  Modelica.Mechanics.Translational.Components.Fixed limit_xMax(
                                                    s0=x_max);
  Modelica.Mechanics.Translational.Components.ElastoGap stopper_xMax(
    final c=c,
    final d=d,
    final n=n,
    final s_rel0=0);
  Modelica.Mechanics.Translational.Components.ElastoGap stopper_xMin(
    final c=c,
    final d=d,
    final n=n,
    final s_rel0=0);

equation 
  mass.s = s;
  mass.v = v;
  mass.a = a;
  connect(mass.flange_a, stopper_xMin.flange_b);
  connect(limit_xMax.flange,  stopper_xMax. flange_b);
  connect(stopper_xMax.flange_a, mass.flange_b);
  connect(mass.flange_a, flange_a);
  connect(limit_xMin.flange,   stopper_xMin.flange_a);
  connect(flange_b, mass.flange_b);
end TranslatoryArmatureAndStopper;

Modelica.Magnetic.FluxTubes.Examples.Utilities.CoilDesign Modelica.Magnetic.FluxTubes.Examples.Utilities.CoilDesign

Calculation of winding parameters (wire diameter, number of turns et al.) and recalculation with optionally chosen parameters; to be adapted to particular design tasks

Information


This model exemplarily shows dimensioning of a winding (wire diameter, number of turns) based on desired operating conditions (voltage, temperature, current density, conductor filling factor) for a given cross-section area of the winding. It can be modified according to the parameters given and sought after for a particular design project.

The calculated winding resistance and number of turns can be used as input parameters to the electrical subsystem of a device to be modelled. Operating voltage V_op can be minimum, nominal and maximum voltage respectively as specified for a particular design project. In conjunction with the setting of the operating temperature T_op, this enables for analysis of the device under worst-case conditions (e.g. minimum required magnetomotive force, maximum allowed ohmic losses, minimum and maximum force respectively).

For manufacturing of a winding, the obtained wire diameter d_wireCalculated must be rounded to that of an available wire. In order to analyse the influence of this rounding, one can enter the chosen wire diameter d_wireChosen and number of turns N_chosen as optional input. Calculation of the resulting winding parameters enables for comparison with the ones obtained otherwise.

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

Parameters

TypeNameDefaultDescription
Resistivityrho_200.0178e-6Resistivity of conductor material at 20�C (default: Copper) [Ohm.m]
LinearTemperatureCoefficientalpha_200.0039Temperature coefficient of conductor material's resistivity at 20degC (default: Copper) [1/K]
TemperatureT_op293.15Operating temperature of winding [K]
Lengthh_w Height of winding cross-section [m]
Lengthb_w Width of winding cross-section [m]
Lengthl_avg Average length of one turn [m]
VoltageV_op Operating voltage (nominal/ minimum/ maximum voltage depending on design objective) [V]
CurrentDensityJ_desired4e6DESIRED current density at operating temperature and voltage resp. [A/m2]
Realc_condFillChosen0.6CHOSEN conductor filling factor = total conductor area without insulation/ total winding area
Chosen feasible parameters (optional)
Diameterd_wireChosend_wireCalculatedCHOSEN available wire diameter (without insulation) [m]
RealN_chosenN_calculatedCHOSEN number of turns

Modelica definition

record CoilDesign 
  "Calculation of winding parameters (wire diameter, number of turns et al.) and recalculation with optionally chosen parameters; to be adapted to particular design tasks"
  extends Modelica.Icons.Record;

  parameter SI.Resistivity rho_20 = 0.0178e-6 
    "Resistivity of conductor material at 20�C (default: Copper)";
  parameter Modelica.SIunits.LinearTemperatureCoefficient alpha_20=
                                                                0.0039 
    "Temperature coefficient of conductor material's resistivity at 20degC (default: Copper)";
  parameter SI.Temperature T_op = 293.15 "Operating temperature of winding";

  final parameter SI.Resistivity rho = rho_20 * (1 + alpha_20 *(T_op - 20+273.15)) 
    "Resistivity at operating temperature";

  parameter SI.Length h_w "Height of winding cross-section";
  parameter SI.Length b_w "Width of winding cross-section";

  final parameter SI.Area A_w = h_w * b_w "Cross-section area of winding";

  parameter SI.Length l_avg "Average length of one turn";

  parameter SI.Voltage V_op 
    "Operating voltage (nominal/ minimum/ maximum voltage depending on design objective)";

  parameter SI.CurrentDensity J_desired = 4e6 
    "DESIRED current density at operating temperature and voltage resp.";

  parameter Real c_condFillChosen = 0.6 
    "CHOSEN conductor filling factor = total conductor area without insulation/ total winding area";

  final parameter Real N_calculated = V_op/ (rho * l_avg * J_desired) 
    "CALCULATED number of turns";

  final parameter SI.Diameter d_wireCalculated = sqrt(4 * A_w * c_condFillChosen /(pi * N_calculated)) 
    "CALCULATED wire diameter (without insulation)";

  final parameter SI.Area A_wireCalculated = pi * d_wireCalculated^2 / 4 
    "Calculated wire cross-section area";

  final parameter SI.Resistance R_calculated = rho * N_calculated * l_avg / A_wireCalculated 
    "Winding resistance at operating temperature and voltage resp. with CALCULATED number of turns and wire diameter";

  final parameter SI.Power P_calculated = V_op^2 / R_calculated 
    "Winding's ohmic losses at operating temperature and voltage resp. with CALCULATED number of turns and wire diameter";

  parameter SI.Diameter d_wireChosen = d_wireCalculated 
    "CHOSEN available wire diameter (without insulation)";

  parameter Real N_chosen = N_calculated "CHOSEN number of turns";

  final parameter SI.Area A_wireChosen = pi * d_wireChosen^2 / 4 
    "Wire cross-section area resulting from CHOSEN wire diameter";

  final parameter SI.Resistance R_actual = rho * N_chosen * l_avg / A_wireChosen 
    "Winding resistance at operating temperature and voltage resp. resulting from CHOSEN number of turns and wire diameter";

  final parameter SI.Power P_actual = V_op^2 / R_actual 
    "Winding's ohmic losses at operating temperature and voltage resp. resulting from CHOSEN number of turns and wire diameter";

  final parameter SI.CurrentDensity J_actual = V_op * 4/(R_actual * pi * d_wireChosen^2) 
    "Current density at operating temperature and voltage resp. resulting from CHOSEN number of turns and wire diameter";

  final parameter Real c_condFillActual = N_chosen * pi * d_wireChosen^2 /(4 * A_w) 
    "Conductor filling factor resulting from CHOSEN number of turns and wire diameter";


end CoilDesign;

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