Eisenkern: Dynamoblech/Stahl (Dbl/St)

Approximation der Zeitfunktion H(t) (Messkurve)

Messdaten:

datenz = {{0, 103}, {0.12566, 108}, {0.25132, 118}, {0.37699, 
            129}, {0.50265, 162}, {0.62831, 226}, {0.75398, 355}, {0.87964, 
            539}, {1.00531, 754}, {1.13097, 970}, {1.25664, 1120}, {1.38230, 
            1228}, {1.50796, 1239}, {1.63363, 1099}, {1.75929, 
            894}, {1.88495, 657}, {2.01062, 463}, {2.13628, 269}, {2.26194, 
            129}, {2.38761, 
            32}, {2.51327, -22}, {2.63894, -65}, {2.76460, -75}, {2.89026, -86}, {3.01593, -97}, {3.14159, -103}, {3.26726, -108}, {3.39292, -118}, {3.51858, -129}, {3.64424, -162}, {3.76991, -226}, {3.89557, -355}, {4.02124, -539}, {4.146902, -754}, {4.27257, -970}, {4.39823, -1120}, {4.523893, -1228}, {4.64956, -1239}, {4.77522, -1099}, {4.90088, -894}, {5.02655, -657}, {5.15221, -463}, {5.27787, -269}, {5.40354, -129}, {5.52920, -32}, {5.65487, 22}, {5.78053, 65}, {5.90619, 75}, {6.03186, 
            86}, {6.15752, 97}, {6.28318, 103}};

b1 = 
        ListPlot[datenz, 
          PlotStyle -> {Hue[0.7], PointSize[0.015]}];

Approximation

Happrozeit9 = 
      Fit[datenz, {Sin[x], Sin[3 x], Sin[5 x], Sin[7 x], Sin[9 x], 
          Cos[x], Cos[3 x], Cos[5 x], Cos[7 x], Cos[9 x]}, x]

b1z = 
        Plot[Happrozeit9, {x, 0, 2 Pi}, 
          PlotStyle -> {Hue[0.0]}];

Show[b1, b1z];

Hk

x = 0;
Happrozeit9
Clear[x]

H(Subscript[μ, max])

x = Pi/2;
Happrozeit9
Clear[x]

Max[Table[Happrozeit9, {x, 0, Pi, Pi/180}]]

Approximation der Zeitfunktion B(t) (Messkurve) \(B\&^\) =1.1 T

Messdaten:

datenb = {{0, 0}, {0.12566, 0.170}, {0.25132, 0.319}, {0.37699, 
            0.446}, {0.50265, 0.574}, {0.62831, 0.702}, {0.75398, 
            0.830}, {0.87964, 0.926}, {1.00531, 0.979}, {1.13097, 
            1.043}, {1.25664, 1.064}, {1.38230, 1.096}, {1.50796, 
            1.096}, {1.63363, 1.096}, {1.75929, 1.064}, {1.88495, 
            1.032}, {2.01062, 0.989}, {2.13628, 0.936}, {2.26194, 
            0.830}, {2.38761, 0.734}, {2.51327, 0.638}, {2.63894, 
            0.532}, {2.76460, 0.362}, {2.89026, 0.245}, {3.01593, 
            0.096}, {3.14159, 
            0}, {3.26726, -0.170}, {3.39292, -0.319}, {3.51858, -0.446}, {3.64424, -0.574}, {3.76991, -0.702}, {3.89557, -0.830}, {4.02124, -0.926}, {4.146902, -0.979}, {4.27257, -1.043}, {4.39823, -1.064}, {4.523893, -1.096}, {4.64956, -1.096}, {4.77522, -1.096}, {4.90088, -1.064}, {5.02655, -1.032}, {5.15221, -0.989}, {5.27787, -0.936}, {5.40354, -0.830}, {5.52920, -0.734}, {5.65487, -0.638}, {5.78053, -0.532}, {5.90619, -0.362}, {6.03186, -0.245}, {6.15752, -0.096}, {6.28318, 0}};

bb1 = 
        ListPlot[datenb, 
          PlotStyle -> {Hue[0.7], PointSize[0.015]}];

Approximation bis 9. Harmonische

Bapprozeit9 = 
      Fit[datenb, {Sin[x], Sin[3 x], Sin[5 x], Sin[7 x], Sin[9 x], 
          Cos[x], Cos[3 x], Cos[5 x], Cos[7 x], Cos[9 x]}, x]

bb1z = 
        Plot[Bapprozeit9, {x, 0, 2 Pi}, 
          PlotStyle -> {Hue[0.0]}];

Show[bb1, bb1z];

Ummagnetisierungsschleife für Approxination der Induktion

a = Table[i, {i, -1250, 1250, 50}];

b = Table[i, {i, -1.2, 1.2, 0.1}] // Chop;

bildbp1 = 
        ParametricPlot[{Happrozeit9, Bapprozeit9}, {x, 0, 2 π}, 
          PlotStyle -> Hue[0], GridLines -> {a, b}];

Aummag11g9h = 
      Integrate[D[Bapprozeit9, x] Happrozeit9, {x, 0,  2  π}] // 
        Chop

Darstellung der Grundwelle von B über (Subscript[H, ν])

bildbp2 = 
        ParametricPlot[{182.3969 Cos[x] - 132.0550 Cos[3 x] + 
              62.8357 Cos[5 x] - 10.1929 Cos[7 x] + 0.5389 Cos[9 x], 
            1.1 Sin[x]}, {x, 0, 2 π}, PlotStyle -> Hue[0], 
          GridLines -> Automatic];

Darstellung der approximierten Zeitfunktion bis zur 9. Harmonischen von B über (Subscript[H, ν])

bildbp2a = 
        ParametricPlot[{182.3969 Cos[x] - 132.0550 Cos[3 x] + 
              62.8357 Cos[5 x] - 10.1929 Cos[7 x] + 0.5389 Cos[9 x], 
            Bapprozeit9}, {x, 0, 2 π}, PlotStyle -> Hue[0.7], 
          GridLines -> Automatic];

Show[bildbp2, bildbp2a];

Approximation bis 3. Harmonische

Bapprozeit3 = 
      Fit[datenb, {Sin[x], Sin[3 x], Cos[x], Cos[3 x]}, x]

bb1z3 = 
        Plot[Bapprozeit3, {x, 0, 2 Pi}, 
          PlotStyle -> {Hue[0.0]}];

Show[bb1, bb1z3];

Aummag11g3h = 
      Integrate[D[Bapprozeit3, x] Happrozeit9, {x, 0,  2  π}] // 
        Chop

Darstellung der Grundwelle von B über (Subscript[H, ν]), (Subscript[H, μ]) und H (bis 9. Harmonische)

bildbp3 = 
        ParametricPlot[{{182.3969 Cos[x] - 132.0550 Cos[3 x] + 
                62.8357 Cos[5 x] - 10.1929 Cos[7 x] + 0.5389 Cos[9 x], 
              1.1 Sin[x]}, {739.4927 Sin[x] - 350.0197 Sin[3 x] + 
                75.0494 Sin[5 x] - 3.4031 Sin[7 x] + 5.8242 Sin[9 x], 
              1.1 Sin[x]}, {182.3969 Cos[x] - 132.0550 Cos[3 x] + 
                62.8357 Cos[5 x] - 10.1929 Cos[7 x] + 0.5389 Cos[9 x] + 
                739.4927 Sin[x] - 350.01970 Sin[3 x] + 
                75.0494 Sin[5 x] - 3.4031 Sin[7 x] + 5.8242 Sin[9 x], 
              1.1 Sin[x]}}, {x, 0, 2 π}, 
          PlotStyle -> {Hue[0], Hue[0.7], Hue[0.4]}, 
          GridLines -> Automatic];

Fläche bei Grundwelle

Aummag2g = 
      Integrate[
          D[1.1 Sin[x], 
              x] (182.3969 Cos[x] - 132.0550 Cos[3 x] + 
                62.8357 Cos[5 x] - 10.1929 Cos[7 x] + 
                0.5389 Cos[9 x]), {x, 0,  2  π}] // Chop

bildbp4 = 
        ParametricPlot[{182.3970 Cos[x] - 132.0550 Cos[3 x] + 
              62.8357 Cos[5 x] - 10.1929 Cos[7 x] + 0.5389 Cos[9 x] + 
              739.4927 Sin[x] - 350.0197 Sin[3 x] + 75.0494 Sin[5 x] - 
              3.4031 Sin[7 x] + 5.8242 Sin[9 x], 1.1 Sin[x]}, {x, 0, 
            2 π}, PlotStyle -> {Dashing[{0.05, 0.015}], Hue[0.7]}, 
          GridLines -> Automatic];

Show[bildbp1, bildbp4];

bildbp5 = 
        ListPlot[
          Transpose[{Table[
                datenz[[i, 2]], {i, 
                  Length[datenz]}], 
Table[
                datenb[[i, 2]], {i, Length[datenb]}]}], 
          PlotStyle -> {Hue[0.3], PointSize[0.012]}];

Show[bildbp1, bildbp4, bildbp5];