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]

Darstellung der Magnetisierungskennlinie

Hμ9zeit = 
      Fit[datenz, {Sin[x], Sin[3 x], Sin[5 x], Sin[7 x], Sin[9 x]}, 
        x]

bildmag9zeit = 
        ParametricPlot[{Hμ9zeit, 1.1  Sin[x]}, {x, 0, 2 π}, 
          PlotStyle -> Hue[0.7]];

Daten: Magnetisierungskennlinie für Eisenkern Dbl/St: \(TraditionalForm\`H\&^\_μ\)(\(TraditionalForm\`B\&^\))

daten1 = {{0.05, 12}, {0.125, 24}, {0.2, 29}, {0.25, 34}, {0.3, 
            40}, {0.4, 54}, {0.5, 75}, {0.55, 95}, {0.6, 115}, {0.65, 
            150}, {0.7, 195}, {0.75, 240}, {0.8, 300}, {0.85, 380}, {0.9, 
            470}, {0.95, 600}, {1. , 750}, {1.05, 965}, {1.1, 
            1250}};

daten1ge = 
        Table[{daten1[[i, 2]], daten1[[i, 1]]}, {i, 
            Length[daten1]}];

bilddge = 
        ListPlot[daten1ge, 
          PlotStyle -> {PointSize[0.01], Hue[0]}];

Show[bildmag9zeit, bilddge];

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}]]

Ummagnetisierungsschleife für Grundwelle der Induktion

bildp1 = 
        ParametricPlot[{Happrozeit9, 1.1  Sin[x]}, {x, 0, 2 π}, 
          PlotStyle -> Hue[0]];

Aummag11g = 
      Integrate[D[(1.1  Sin[x]), x] Happrozeit9, {x, 0,  2  π}] // 
        Chop

Hν9zeit = 
      Fit[datenz, {Cos[x], Cos[3 x], Cos[5 x], Cos[7 x], Cos[9 x]}, 
        x]

bildp2 = 
        ParametricPlot[{Hν9zeit, 1.1  Sin[x]}, {x, 0, 2 π}, 
          PlotStyle -> Hue[0.7]];

Show[bildp1, bildp2];

Show[bildp1, bildp2, bildmag9zeit, bilddge];

Ummagnetisierungsschleife für Grundwelle + 3 Harmonische der Induktion (Annahme)

bildp3 = 
        ParametricPlot[{Happrozeit9, 1.1  Sin[x] +  .1 Sin[3 x]}, {x, 0, 
            2 π}, PlotStyle -> Hue[0.7]];

Aummag11g3h = 
      Integrate[
          D[(1.1  Sin[x] + 0.1 Sin[3 x]), x] Happrozeit9, {x, 0,  
            2  π}] // Chop

Vergleich

Show[bildp1, bildp3];