Foreword |
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xiii | |
Preface |
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xv | |
Authors |
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xvii | |
1 Introduction |
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1 | (10) |
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1 | (1) |
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1 | (1) |
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2 | (1) |
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1.4 Review of Field Theory |
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2 | (1) |
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3 | (1) |
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4 | (1) |
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4 | (1) |
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1.5.3 Approximation Theorem |
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4 | (1) |
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4 | (1) |
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1.7 Eddy Current Phenomena |
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5 | (1) |
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1.8 Polyphase Induction Machines |
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5 | (2) |
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1.8.1 Laminated Iron Cores |
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6 | (1) |
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1.8.2 Unlaminated Iron Cores |
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6 | (1) |
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1.8.3 Simulation of Armature Winding |
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6 | (1) |
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7 | (1) |
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1.10 Numerical Techniques |
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7 | (1) |
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1.10.1 Finite Element Method |
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7 | (1) |
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1.10.2 Analytical Techniques |
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7 | (1) |
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8 | (3) |
2 Review of Field Equations |
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11 | (20) |
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11 | (1) |
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2.2 Maxwell's Equations in Integral Form |
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11 | (2) |
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2.3 Maxwell's Equations in Point Form |
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13 | (1) |
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2.4 General Equations for One Type of Field |
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14 | (2) |
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2.5 Maxwell's Equations for Fields in Moving Media |
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16 | (1) |
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2.6 Scalar Electric and Magnetic Potentials |
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17 | (1) |
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2.7 Vector Magnetic Potential |
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18 | (3) |
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2.8 Periodic Fields, Field Equations in Phasor Form |
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21 | (2) |
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23 | (2) |
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2.10 Continuity Equation and Relaxation Time |
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25 | (3) |
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28 | (1) |
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29 | (1) |
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29 | (2) |
3 Theorems, Revisited |
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31 | (44) |
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31 | (1) |
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31 | (14) |
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3.2.1 Uniqueness Theorem for Laplace and Poisson Equations |
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31 | (10) |
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3.2.1.1 Example of a Cuboid |
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33 | (4) |
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3.2.1.2 Example of a Rectangular Region |
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37 | (4) |
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3.2.2 Uniqueness Theorem for Vector Magnetic Potentials |
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41 | (2) |
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3.2.3 Uniqueness Theorem for Maxwell's Equations |
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43 | (2) |
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45 | (4) |
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3.4 Generalised Poynting Theorem |
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49 | (8) |
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3.4.1 Components of Power Flow |
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54 | (1) |
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3.4.2 Components of Force |
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55 | (2) |
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3.5 Approximation Theorems |
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57 | (16) |
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3.5.1 Approximation Theorem for Laplacian Field |
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57 | (6) |
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3.5.2 Approximation Theorem for Vector Magnetic Potential |
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63 | (5) |
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3.5.3 Approximation Theorem for Maxwell's Equations |
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68 | (5) |
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73 | (1) |
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73 | (1) |
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74 | (1) |
4 Laplacian Fields |
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75 | (52) |
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75 | (1) |
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4.2 Potential Distribution for Rectangular Double-Slotting |
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76 | (18) |
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4.2.1 Tooth-Opposite-Tooth Orientation |
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76 | (5) |
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4.2.1.1 Evaluation of Arbitrary Constants |
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77 | (4) |
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4.2.2 Tooth-Opposite-Slot Orientation |
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81 | (5) |
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4.2.2.1 Evaluation of Arbitrary Constants |
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82 | (4) |
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4.2.3 Arbitrary Orientation of Tooth and Slot |
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86 | (6) |
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4.2.3.1 Evaluation of Arbitrary Constants |
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88 | (4) |
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92 | (2) |
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4.3 Modelling for Aperiodical Field Distributions |
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94 | (13) |
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4.3.1 Tooth-Opposite-Tooth Orientation |
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94 | (3) |
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4.3.1.1 Evaluation of Unknown Functions |
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95 | (2) |
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4.3.2 Tooth-Opposite-Slot Orientation |
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97 | (2) |
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4.3.2.1 Evaluation of Unknown Functions |
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98 | (1) |
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4.3.3 Arbitrary Orientation of Two Teeth |
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99 | (8) |
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4.3.3.1 Evaluation of Unknown Functions |
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102 | (5) |
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4.4 Fringing Flux for Tooth-Opposite-Tooth Orientation with Small Air Gap |
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107 | (4) |
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4.4.1 Schwarz-Christoffel Transformation |
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108 | (3) |
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4.4.1.1 Transformation from z Plane to w Plane |
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108 | (2) |
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4.4.1.2 Transformation from x Plane to w Plane |
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110 | (1) |
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4.5 Air-Gap Field of a Conductor Deep inside an Open Slot |
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111 | (5) |
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4.5.1 Schwarz—Christoffel Transformation |
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112 | (4) |
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4.5.1.1 Transformation from z-Plane to w-Plane |
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112 | (2) |
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4.5.1.2 Transformation from x-Plane to w-Plane |
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114 | (2) |
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4.6 Magnetic Field near Armature Winding Overhang |
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116 | (8) |
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4.6.1 Surface Current Density |
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117 | (1) |
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4.6.2 Magnetic Field Intensity |
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118 | (3) |
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4.6.2.1 Field in Region 1 |
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118 | (1) |
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4.6.2.2 Field in Region 2 |
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119 | (1) |
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4.6.2.3 Field in Region 3 |
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119 | (1) |
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4.6.2.4 Field in Region 4 |
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120 | (1) |
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4.6.3 Boundary Conditions |
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121 | (6) |
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4.6.3.1 Selection of Field Expressions |
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121 | (1) |
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4.6.3.2 Evaluation of Arbitrary Constants |
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121 | (3) |
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124 | (1) |
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125 | (2) |
5 Eddy Currents in Magnetic Cores |
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127 | (44) |
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127 | (1) |
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5.2 Eddy Current Machines (Solid Rotor Induction Machines) |
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127 | (5) |
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5.2.1 Two-Dimensional Model |
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128 | (4) |
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129 | (1) |
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5.2.1.2 Eddy Current Density |
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130 | (1) |
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5.2.1.3 Eddy Current Loss |
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130 | (1) |
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131 | (1) |
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5.2.1.5 Mechanical Power Developed |
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131 | (1) |
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5.2.1.6 Rotor Power Input |
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131 | (1) |
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5.3 Eddy Currents in Large Plates due to Alternating Excitation Current |
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132 | (5) |
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5.3.1 Single-Phase Excitation |
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133 | (1) |
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5.3.2 Polyphase Excitation |
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134 | (3) |
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5.4 Eddy Currents in Cores with Rectangular Cross-Sections |
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137 | (2) |
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5.5 Eddy Currents in Cores with Triangular Cross-Sections |
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139 | (4) |
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5.6 Eddy Currents in Cores with Regular Polygonal Cross-Sections |
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143 | (14) |
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5.6.1 Cores with Triangular Cross-Sections |
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144 | (5) |
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5.6.2 Cores with Hexagonal Cross-Sections |
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149 | (3) |
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5.6.3 Cores with Octagonal Cross-Sections |
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152 | (5) |
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5.7 Eddy Currents in Circular Cores |
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157 | (2) |
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5.8 Distribution of Current Density in Circular Conductors |
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159 | (2) |
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5.9 Eddy Currents in Laminated Rectangular Cores |
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161 | (7) |
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168 | (1) |
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169 | (2) |
6 Laminated-Rotor Polyphase Induction Machines |
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171 | (28) |
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171 | (1) |
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6.2 Two-Dimensional Fields in Anisotropic Media |
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172 | (3) |
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6.3 Cage or Wound Rotor Induction Machines |
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175 | (9) |
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183 | (1) |
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6.4 Induction Machines with Skewed Rotor Slots |
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184 | (13) |
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186 | (3) |
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6.4.2 Fields in the Anisotropic Rotor Region |
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189 | (5) |
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6.4.3 Determination of Arbitrary Constants |
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194 | (3) |
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197 | (1) |
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197 | (2) |
7 Unlaminated Rotor Polyphase Induction Machines |
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199 | (62) |
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199 | (1) |
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7.2 Tooth-Ripple Harmonics in Solid-Rotor Induction Machines |
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199 | (32) |
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7.2.1 Physical Description |
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199 | (4) |
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7.2.1.1 Slip/Torque Characteristics |
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200 | (1) |
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7.2.1.2 Idealised Configuration |
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200 | (3) |
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7.2.2 Field Distribution in Stator Slots |
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203 | (3) |
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7.2.2.1 Vector Magnetic Potential |
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203 | (1) |
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7.2.2.2 Magnetic Field Intensity |
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204 | (2) |
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7.2.3 Field Distribution in the Air Gap |
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206 | (11) |
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7.2.4 Field Distribution in the Solid Rotor |
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217 | (10) |
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7.2.5 Machine Performances |
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227 | (4) |
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7.2.5.1 Eddy Current Loss |
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228 | (1) |
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229 | (1) |
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7.2.5.3 Mechanical Power Developed |
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229 | (1) |
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7.2.5.4 Rotor Input Power |
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230 | (1) |
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231 | (1) |
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7.3 Three-Dimensional Fields in Solid-Rotor Induction Machines |
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231 | (28) |
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231 | (2) |
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7.3.2 Field Distributions |
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233 | (15) |
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7.3.3 Effects of Finite Machine Length |
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248 | (1) |
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7.3.4 Effect of Different Rotor and Stator Lengths |
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248 | (1) |
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7.3.5 Performance Parameters |
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248 | (13) |
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7.3.5.1 Eddy Current Loss |
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252 | (5) |
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257 | (1) |
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7.3.5.3 Mechanical Power Developed |
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258 | (1) |
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7.3.5.4 Rotor Input Power |
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259 | (1) |
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7.3.5.5 Slip-Power Relation |
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259 | (1) |
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259 | (1) |
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259 | (2) |
8 Case Studies |
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261 | (52) |
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261 | (1) |
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8.2 Slot Leakage Inductance for Conductors in Open Slots |
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261 | (4) |
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8.2.1 Physical Configuration |
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261 | (1) |
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8.2.2 Current Density Distribution |
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261 | (2) |
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8.2.3 Vector Magnetic Potential |
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263 | (1) |
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263 | (1) |
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264 | (1) |
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8.3 Leakage Inductance of Transformers |
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265 | (8) |
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8.3.1 Physical Configuration |
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266 | (1) |
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8.3.2 Current Density Distribution |
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266 | (1) |
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8.3.3 Vector Magnetic Potential |
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267 | (2) |
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8.3.4 Magnetic Flux Density |
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269 | (1) |
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8.3.5 Arbitrary Constants |
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270 | (1) |
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271 | (2) |
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8.4 Field Theory of Hysteresis Machines |
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273 | (13) |
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8.4.1 Simplifying Assumptions |
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274 | (1) |
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8.4.2 Field Distributions |
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274 | (4) |
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8.4.3 Induction Machine Action |
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278 | (3) |
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8.4.3.1 Eddy Current Density |
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278 | (1) |
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8.4.3.2 Eddy Current Loss |
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278 | (1) |
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279 | (1) |
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280 | (1) |
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8.4.3.5 Slip-Power Relation |
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280 | (1) |
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8.4.4 Hysteresis Machine Action |
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281 | (2) |
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282 | (1) |
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8.4.4.2 Slip-Power Relation |
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283 | (1) |
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8.4.5 Impact of Different Parameters |
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283 | (3) |
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8.5 Single-Phase Induction Motors with Composite Poles |
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286 | (12) |
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8.5.1 Simplifying Assumptions |
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287 | (1) |
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8.5.2 Idealised Machine Structure |
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287 | (1) |
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288 | (10) |
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8.6 Transient Fields in Plates due to Type 2 Impact Excitations |
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298 | (12) |
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8.6.1 Current Impact Excitation |
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300 | (5) |
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8.6.2 Voltage Impact Excitation |
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305 | (5) |
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310 | (1) |
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310 | (3) |
9 Numerical Computation |
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313 | (52) |
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313 | (1) |
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313 | (1) |
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9.2.1 Computational Errors |
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314 | (1) |
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9.2.2 Numerical Stability |
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314 | (1) |
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9.3 Domain of Numerical Analysis |
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314 | (9) |
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9.3.1 Values of Functions |
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314 | (1) |
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9.3.2 Equations and Systems of Equations |
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315 | (1) |
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9.3.2.1 Linear Algebraic Equations |
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315 | (1) |
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9.3.3 Eigen-Value or Singular Value Problems |
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316 | (1) |
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9.3.4 Optimisation Problem |
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316 | (1) |
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9.3.5 Differential Equations |
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317 | (1) |
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9.3.5.1 Finite Difference Method |
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317 | (1) |
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9.3.5.2 Finite Element Method |
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317 | (1) |
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9.3.6 Numerical Integration |
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318 | (4) |
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9.3.6.1 Integration over Bounded Intervals |
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318 | (1) |
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9.3.6.2 Integration over Unbounded Intervals |
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319 | (3) |
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322 | (1) |
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323 | (40) |
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9.4.1 Relations without Summation or Integration |
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324 | (5) |
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324 | (1) |
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9.4.1.2 Air-Gap Field of a Conductor Deep inside an Open Slot |
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324 | (1) |
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9.4.1.3 Analysis of Eddy Current Induction Machines |
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325 | (1) |
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9.4.1.4 Eddy Currents in a Conducting Plate |
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325 | (1) |
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9.4.1.5 Eddy Currents within a Circular Core |
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326 | (1) |
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9.4.1.6 Distribution of Current Density in a Circular Conductor |
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326 | (1) |
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9.4.1.7 Two-Dimensional Fields in Anisotropic Media |
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326 | (1) |
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9.4.1.8 Field in the Cage or Wound Rotor Machine |
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327 | (1) |
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9.4.1.9 Induction Machine with Skewed Rotor Slots |
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327 | (1) |
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9.4.1.10 Field Theory of Hysteresis Machines |
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328 | (1) |
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9.4.2 Relations Involving Simple Summations |
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329 | (2) |
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9.4.2.1 Eddy Currents in Rectangular and Square Cores |
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329 | (1) |
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9.4.2.2 Eddy Currents in Triangular Core |
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329 | (1) |
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9.4.2.3 Slot Leakage Inductance |
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330 | (1) |
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9.4.2.4 Leakage Inductance of Transformers |
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330 | (1) |
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9.4.2.5 Transient Fields in Plates |
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330 | (1) |
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9.4.3 Summations Leading to Simultaneous Linear Algebraic Equations |
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331 | (16) |
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9.4.3.1 Potential Distributions in Tooth-Opposite-Tooth Orientation Case |
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331 | (3) |
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9.4.3.2 Potential Distributions in Tooth-Opposite-Slot Orientation |
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334 | (2) |
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9.4.3.3 Potential Distributions in Arbitrary Tooth Orientation |
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336 | (2) |
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9.4.3.4 Air-Gap Permeance |
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338 | (1) |
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9.4.3.5 Magnetic Field near Armature Winding Overhang |
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338 | (1) |
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9.4.3.6 Eddy Currents in Regular Polygonal Cross-Section Cores |
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339 | (2) |
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9.4.3.7 Eddy Currents in Laminated Rectangular Cores |
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341 | (1) |
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9.4.3.8 Tooth-Ripple Harmonics in Solid Rotor Induction Machines |
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341 | (3) |
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9.4.3.9 Three-Dimensional Fields in Solid Rotor Induction Machines |
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344 | (2) |
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9.4.3.10 Single-Phase Induction Motors with Composite Poles Being Considered |
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346 | (1) |
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9.4.4 Integrations Leading to Simultaneous Algebraic Equations |
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347 | (16) |
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9.4.4.1 Tooth-Opposite-Tooth Orientation Case |
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348 | (4) |
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9.4.4.2 Tooth-Opposite-Slot Orientation |
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352 | (6) |
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9.4.4.3 Arbitrary Orientation of Teeth |
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358 | (5) |
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363 | (2) |
Appendix 1: Hilbert Transform |
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365 | (2) |
Appendix 2: Evaluation of Integrals Involved in Section 4.3.1 |
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367 | (8) |
Appendix 3: Evaluation of Integrals Involved in Section 4.3.2 |
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375 | (6) |
Appendix 4: Evaluation of Integrals Involved in Section 4.3.3 |
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381 | (14) |
Appendix 5: Evaluation of Arbitrary Constants Involved in Section 5.9 |
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395 | (4) |
Appendix 6: Current Sheet Simulation of Stator Winding |
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399 | (10) |
Index |
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409 | |