model Toroid "Toroid with circular cross section; fixed shape; linear or non-linear material characteristics"
import Modelica.Constants.pi;
extends BaseClasses.FixedShape;
extends Modelica.Magnetic.FluxTubes.Icons.Toroid;
parameter SI.Radius r = 0.1 "Radius of toroid (middle)"
annotation (Dialog(
group = "Fixed geometry",
groupImage = "modelica://Modelica/Resources/Images/Magnetic/FluxTubes/Shapes/Toroid.png"));
parameter SI.Radius d = 0.01 "Diameter of cylindrical core"
annotation (Dialog(group = "Fixed geometry"));
parameter SI.Angle alpha = 0.5 * pi "Angle of toroid section"
annotation (Dialog(group = "Fixed geometry"));
equation
G_m = mu_0 * mu_r * A / (r * alpha);
A = 0.25 * (d ^ 2 * pi) "Area at arithmetic mean radius for calculation of average flux density";
annotation (
defaultComponentName = "cylinder",
Documentation(info = "<html>\n<p>\nPlease refer to the enclosing sub-package <a href=\"modelica://Modelica.Magnetic.FluxTubes.Shapes.FixedShape\">FixedShape</a> for a description of all elements of this package and to <a href=\"modelica://Modelica.Magnetic.FluxTubes.UsersGuide.Literature\">[Ro41]</a> for derivation and/or coefficients of the equation for permeance G_m.\n</p>\n\n<p>\nFor toroidal flux tubes with a circumferential magnetic flux, the flux density is a function of the radius.\nFor that reason, the characteristic <code>mu_r(B)</code> is evaluated for the flux density at the flux tube's mean radius.\n</p>\n\n<p>\nFor those flux tube sections of a magnetic device that have a nonlinear material characteristic <code>mu_r(B)</code> and a large aspect ratio of outer to inner radius <code>r_o/r_i</code>, the section can be split up in a series connection of several hollow cylindrical flux tubes with radial flux. This allows for more realistic modelling of the dependence of flux density on the radius compared to modelling with just one flux tube element.\n</p>\n</html>"));
end Toroid;