model EddyCurrentTorque "Simple model of a rotational eddy current brake"
import Modelica.Electrical.Machines.Thermal.linearTemperatureDependency;
parameter Modelica.SIunits.Torque tau_nominal "Maximum torque (always braking)";
parameter Modelica.SIunits.AngularVelocity w_nominal(min = Modelica.Constants.eps) "Nominal speed (leads to maximum torque) at reference temperature";
parameter Modelica.SIunits.Temperature TRef(start = 293.15) "Reference temperature";
parameter Modelica.Electrical.Machines.Thermal.LinearTemperatureCoefficient20 alpha20(start = 0) "Temperature coefficient of material";
extends Modelica.Mechanics.Rotational.Interfaces.PartialTorque;
extends Modelica.Thermal.HeatTransfer.Interfaces.PartialElementaryConditionalHeatPort;
Modelica.SIunits.Torque tau "Accelerating torque acting at flange (= flange.tau)";
Modelica.SIunits.AngularVelocity w "Angular velocity of flange with respect to support (= der(phi))";
Real w_normalized "Relative speed w/w_nominal";
equation
w = der(phi);
lossPower = tau * w;
tau = 2 * tau_nominal * w_normalized / (1 + w_normalized * w_normalized);
tau = flange.tau;
w_normalized = w / (w_nominal * linearTemperatureDependency(1, TRef, alpha20, TheatPort));
annotation (
Icon(
coordinateSystem(
preserveAspectRatio = true,
extent = {
{-100, -100},
{100, 100}}),
graphics = {
Line(
points = {
{-75, 0},
{75, 0}},
color = {192, 192, 192}),
Line(
points = {
{0, 60},
{0, -50}},
color = {192, 192, 192}),
Line(
points = {
{0, 0},
{4, 25},
{8, 41},
{12, 48},
{16, 50},
{20, 49},
{24, 46},
{28, 42},
{32, 38},
{36, 34},
{46, 25},
{56, 18},
{66, 12},
{76, 8}},
color = {0, 0, 127},
smooth = Smooth.Bezier),
Line(
points = {
{0, 0},
{-4, -25},
{-8, -41},
{-12, -48},
{-16, -50},
{-20, -49},
{-24, -46},
{-28, -42},
{-32, -38},
{-36, -34},
{-46, -25},
{-56, -18},
{-66, -12},
{-76, -8}},
color = {0, 0, 127},
smooth = Smooth.Bezier)}),
Documentation(info = "<html>\n<p>This is a simple model of a rotational <strong>eddy current brake</strong>. The torque versus speed characteristic is defined by Kloss' equation.</p>\n<p><strong>Thermal behaviour:</strong><br>\nThe resistance of the braking disc is influenced by the actual temperature Theatport, which in turn shifts the speed w_nominal at which the (unchanged) maximum torque occurs.<br>\nIf the heatPort is not used (useHeatPort = false), the operational temperature remains at the given temperature T.<br>\nHowever, the speed w_nominal at which the maximum torque occurs is adapted from reference temperature TRef to the operational temperature.</p>\n</html>"));
end EddyCurrentTorque;