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 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