1st Edition

Electromagnetic Modeling by Finite Element Methods

    508 Pages
    by CRC Press

    Unlike any other source in the field, this valuable reference clearly examines key aspects of the finite element method (FEM) for electromagnetic analysis of low-frequency electrical devices. The authors examine phenomena such as nonlinearity, mechanical force, electrical circuit coupling, vibration, heat, and movement for applications in the electrical, mechanical, nuclear, aeronautics, and transportation industries.

    Electromagnetic Modeling by Finite Element Methods offers a wide range of examples, including torque, vibration, and iron loss calculation; coupling of the FEM with mechanical equations, circuits, converters, and thermal effects; material modeling; and proven methods for hysteresis implementation into FEM codes.

    Providing experimental results and comparisons from the authors' personal research, Electromagnetic Modeling by Finite Element Methods supplies techniques to implement FEM for solving Maxwell's equations, analyze electrical and magnetic losses, determine the behavior of electrical machines, evaluate force distribution on a magnetic medium, simulate movement in electrical machines and electromagnetic devices fed by external circuits or static converters, and analyze the vibrational behavior of electrical machines.

    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

    Biography

    João Pedro A. Bastos, Nelson Sadowski