Electromagnetic Modeling by Finite Element Methods

PREFACE MATHEMATICAL PRELIMINARIES Introduction The Vector Notation Vector Derivation The Gradient The Divergence The Rotational Second-Order Operators Application of Operators to More than One Function Expressions in Cylindrical and Spherical Coordinates MAXWELL EQUATIONS, ELECTROSTATICS, MAGNETOSTATICS, AND MAGNETODYNAMIC FIELDS Introduction The EM Quantities Local Form of the Equations The Anisotropy The Approximation of Maxwell's Equations The Integral Form of Maxwell's Equations Electrostatic Fields Magnetostatic Fields Magnetodynamic Fields BRIEF PRESENTATION OF THE FINITE ELEMENT METHOD Introduction The Galerkin Method - Basic Concepts A First-Order Finite Element Program Generalization of the Finite Element Method Numerical Integration Some 2D Finite Elements Coupling Different Finite Elements Calculation of Some Terms in the Field Equation A Simplified 2D Second-Order Finite Element Program THE FINITE ELEMENT METHOD APPLIED TO 2D ELECTROMAGNETIC CASES Introduction Some Static Cases Application to 2D Eddy Current Problems Axi-Symmetric Application Advantages and Limitation of 2D Formulations Non-Linear Applications Geometric Repetition of Domains Thermal Problems Voltage-Fed Electromagnetic Devices Static Examples Dynamic Examples COUPLING OF FIELD AND ELECTRICAL CIRCUIT EQUATIONS Introduction Electromagnetic Equations Equations for Different Conductor Configurations Connections Between Electromagnetic Devices and External Feeding Circuits Examples MOVEMENT MODELING FOR ELECTRICAL MACHINES Introduction The Macro-Element The Moving Band The Skew Effect in Electrical Machines Using 2D Simulation Examples INTERACTION BETWEEN ELECTROMAGNETIC AND MECHANICAL FORCES Introduction Methods Based on Direct Formulations Methods Based on the Force Density Electrical Machine Vibrations Originated by Magnetic Forces Example of Coupling Between the Field and Circuit Equations, Including Mechanical Transients IRON LOSSES Introduction Eddy Current Losses Hysteresis Anomalous or Excess Losses Total Iron Losses The Jiles-Atherton Model The Inverse Jiles-Atherton Model Including Iron Losses in Finite Element Calculations BIBLIOGRAPHY INDEX