Electromagnetic Modeling by Finite Element Methods

Note: Supplemental materials are not guaranteed with Rental or Used book purchases.

ISBN: 9780824742690 | 0824742699
Cover: Hardcover
Copyright: 4/1/2003

Rent

(Recommended)

$112.01

Term

Due

Price

Semester

Dec 11

$112.01

Quarter

Nov 28

$106.41

Short Term

Oct 29

$100.82

*This item is part of an exclusive publisher rental program and requires an additional convenience fee. This fee will be reflected in the shopping bag.
Buy New

Usually Ships in 3-5 Business Days

$143.41
eBook

Available Instantly

Online: 180 Days

Downloadable: 180 Days

*To support the delivery of the digital material to you, a digital delivery fee of $3.99 will be charged on each digital item.

$125.40*

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

iii

Mathematical Preliminaries

(26)

Introduction

(1)

The Vector Notation

(1)

Vector Derivation

(2)

The Nabla Operator

(1)

Definition of the Gradient, Divergence, and Rotational

(1)

The Gradient

(3)

Example of Gradient

(2)

The Divergence

(7)

Definition of Flux

(2)

The Divergence Theorem

(2)

The Conservative Flux

(2)

Example of Divergence

(1)

The Rotational

(7)

Circulation of a Vector

(3)

Stokes' Theorem

(3)

Example of Rotational

(1)

Second-Order Operators

(2)

Application of Operators to More than One Function

(1)

Expressions in Cylindrical and Spherical Coordinates

(3)

Maxwell Equations, Electrostatics, Magnetostatics and Magnetodynamic Fields

(96)

Introduction

(1)

The EM Quantities

(7)

The Electric Field Intensity E

(1)

The Magnetic Field Intensity H

(1)

The Magnetic Flux Density B and the Magnetic Permeability μ

(1)

The Electric Flux Density D and Electric Permittivity ε

(1)

The Surface Current Density J

(1)

Volume Charge Density ρ

(1)

The Electric Conductivity σ

(1)

Local Form of the Equations

(5)

The Anisotropy

(2)

The Approximation to Maxwell's Equations

(5)

The Integral Form of Maxwell's Equations

(2)

Electrostatic Fields

(19)

The Electric Charge

(1)

The Electric Field

(1)

Force on an Electric Charge

(1)

The Electric Scalar Potential V

(5)

Nonconservative Fields: Electromotive Force

(3)

Refraction of the Electric Field

(4)

Dielectric Strength

(2)

Laplace's and Poisson's Equations of the Electric Field for Dielectric Media

(3)

Laplace's Equation of the Electric Field for Conductive Media

(1)

Magnetostatic Fields

(5)

Maxwell's Equations in Magnetostatics

(1)

The Equation rotH = J

(3)

The Equation divB = 0

(1)

The Equation rotE = 0

(1)

The Biot-Savart Law

(4)

Magnetic Field Refraction

(3)

Energy in the Magnetic Field

(3)

Magnetic Materials

(24)

Diamagnetic Materials

(1)

Paramagnetic Materials

(1)

Ferromagnetic Materials

(1)

General

(3)

The Influence of Iron on Magnetic Circuits

(2)

Permanent Magnets

(1)

General Properties of Hard Magnetic Materials

(4)

The Energy Associated with a Magnet

(6)

Principal Types of Permanent Magnets

100

(2)

Dynamic Operation of Permanent Magnets

102

(2)

Inductance and Mutual Inductance

104

(1)

Definition of Inductance

104

(1)

Energy in a Linear System

105

(2)

Magnetodynamic Fields

107

(16)

Maxwell's Equations for the Magnetodynamic Field

108

(4)

Penetration of Time-Dependent Fields in Conducting Materials

112

(1)

The Equation for H

113

(1)

The Equation for B

113

(1)

The Equation for E

114

(1)

The Equation for J

114

(1)

Solution of the Equations

115

(8)

Brief Presentation of the Finite Element Method

123

(74)

Introduction

123

(1)

The Galerkin Method -- Basic Concepts

124

(11)

The Establishment of the Physical Equations

124

(1)

The First-Order Triangle

125

(2)

Application of the Weighted Residual Method

127

(4)

Application of the Finite Element Method and Solution

131

(3)

The Boundary Conditions

134

(1)

Dirichlet Boundary Condition -- Imposed Potential

134

(1)

Neumann Condition -- Unknown Nodal Values on the Boundary

135

(1)

A First-Order Finite Element Program

135

(12)

Example for Use of the Finite Element Program

142

(5)

Generalization of the Finite Element Method

147

(19)

High-Order Finite Elements: General

148

(1)

High-Order Finite Elements: Notation

148

(5)

High-Order Finite Elements: Implementation

153

(3)

Continuity of Finite Elements

156

(1)

Polynomial Basis

157

(1)

Transformation of Quantities -- the Jacobian

158

(3)

Evaluation of the Integrals

161

(5)

Numerical Integration

166

(3)

Some 2D Finite Elements

169

(6)

First-Order Triangular Element

171

(1)

Second-Order Triangular Element

172

(1)

Quadrilateral Bi-linear Element

173

(1)

Quadrilateral Quadratic Element

174

(1)

Coupling Different Finite Elements

175

(2)

Coupling Different Types of Finite Elements

175

(2)

Calculation of Some Terms in the Field Equation

177

(5)

The Stiffness Matrix

178

(2)

Evaluation of the Second Term in Eq. (3.72)

180

(1)

Evaluation of the Third Term in Eq. (3.72)

181

(1)

Evaluation of the Source Term

181

(1)

A Simplified 2D Second-Order Finite Element Program

182

(15)

The Problem to Be Solved

182

(2)

The Discretized Domain

184

(1)

The Finite Element Program

185

(12)

The Finite Element Method Applied to 2D Electromagnetic Cases

197

(86)

Introduction

197

(1)

Some Static Cases

197

(16)

Electrostatic Fields: Dielectric Materials

198

(2)

Stationary Currents: Conducting Materials

200

(1)

Magnetic Fields: Scalar Potential

201

(2)

The Magnetic Field: Vector Potential

203

(8)

The Electric Vector Potential

211

(2)

Application to 2D Eddy Current Problems

213

(20)

First-Order Element in Local Coordinates

213

(6)

The Vector Potential Equation Using Time Discretization

219

(7)

The Complex Vector Potential Equation

226

(5)

Structures with Moving Parts

231

(2)

Axi-Symmetric Application

233

(6)

The Axi-Symmetric Formulation for Vector Potential

236

(3)

Advantages and Limitations of 2D Formulations

239

(2)

Non-linear Applications

241

(7)

Method of Successive Approximation

241

(1)

The Newton-Raphson Method

242

(6)

Geometric Repetition of Domains

248

(3)

Periodicity

249

(1)

Anti-Periodicity

250

(1)

Thermal Problems

251

(5)

Thermal Conduction

251

(1)

Convection Transmission

252

(1)

Radiation

252

(1)

FE Implementation

253

(3)

Voltage-Fed Electromagnetic Devices

256

(4)

Static Examples

260

(10)

Calculation of Electrostatic Fields

261

(1)

Calculation of Static Currents

262

(3)

Calculation of the Magnetic Field -- Scalar Potential

265

(2)

Calculation of the Magnetic Field -- Vector Potential

267

(3)

Dynamic Examples

270

(13)

Eddy Currents: Time Discretization

270

(2)

Moving Conducting Piece in Front of an Electromagnet

272

(4)

Time Step Simulation of a Voltage-Fed Device

276

(3)

Thermal Case: Heating by Eddy Currents

279

(4)

Coupling of Field and Electrical Circuit Equations

283

(60)

Introduction

283

(1)

Electromagnetic Equations

283

(8)

Formulation Using the Magnetic Vector Potential

284

(1)

The Formulation in Two Dimensions

285

(1)

Equations for Conductors

285

(1)

Thick Conductors

285

(2)

Thin Conductors

287

(2)

Equations for the Whole Domain

289

(1)

The Finite Element Method

290

(1)

Equations for Different Conductor Configurations

291

(11)

Thick Conductors Connections

292

(1)

Series Connection

292

(2)

Parallel Connection

294

(5)

Thin Conductors Connections

299

(1)

Independent Voltage Sources

300

(1)

Star Connection with Neutral

300

(1)

Polygon Connection

301

(1)

Star Connection without Neutral Wire

301

(1)

Connections Between Electromagnetic Devices and External Feeding Circuits

302

(32)

Reduced Equations of Electromagnetic Devices

303

(1)

Feeding Circuit Equations and Connection to Field Equations

303

(1)

Calculation of Matrices G1 to G6

304

(1)

Circuit Topology Concepts

305

(10)

Determination of Matrices G1 to G6

315

(9)

Example

324

(5)

Taking Into Account Electronic Switches in the Feeding Circuit

329

(1)

Discretization of the Time Derivative

330

(4)

Examples

334

(9)

Simulations with Known Voltage Waveforms

334

(1)

A Didactical Example

334

(3)

Three-Phase Induction Motor

337

(1)

Massive Conductors in Series Connection

337

(2)

Modeling of a Static Converter-Fed Magnetic Device

339

(4)

Movement Modeling for Electrical Machines

343

(24)

Introduction

343

(1)

Methods with Non-Discretized Airgaps

343

(1)

Methods with Discretized Airgaps

344

(1)

The Macro-Element

344

(5)

The Moving Band

349

(4)

The Skew Effect in Electrical Machines Using 2D Simulation

353

(9)

Examples

362

(5)

Three-Phase Induction Motor

362

(2)

Permanent Magnet Motor

364

(3)

Interaction Between Electromagnetic and Mechanical Forces

367

(52)

Introduction

367

(1)

Methods Based on Direct Formulations

368

(21)

Method of the Magnetic Co-Energy Variation

368

(2)

The Maxwell Stress Tensor Method

370

(13)

The Method Proposed by Arkkio

383

(1)

The Method of Local Jacobian Matrix Derivation

384

(2)

Examples of Torque Calculation

386

(3)

Methods Based on the Force Density

389

(12)

Preliminary Considerations

389

(2)

Equivalent Sources Formulations

391

(1)

Equivalent Currents

392

(1)

Equivalent Magnetic Charges

393

(1)

Other Equivalent Source Distributions

394

(1)

Formulation Based on the Energy Derivation

395

(3)

Comparison Among the Different Methods

398

(3)

Electrical Machine Vibrations Originated by Magnetic Forces

401

(12)

Magnetic Force Calculation

402

(1)

Mechanical Calculation

402

(1)

Calculation of the Natural Response

403

(1)

Calculation of the Forced Response Directly in Harmonic Regime

404

(1)

Calculation of the Forced Response Using the Modal Superposition Method

405

(2)

Example of Vibration Calculation

407

(6)

Example of Coupling Between the Field and Circuit Equations, Including Mechanical Transients

413

(6)

Iron Losses

419

(52)

Introduction

419

(1)

Eddy Current Losses

420

(3)

Hysteresis

423

(7)

Anomalous or Excess Losses

430

(3)

Total Iron Losses

433

(5)

Example

435

(3)

The Jiles-Atherton Model

438

(14)

The JA Equations

438

(3)

Procedure for the Numerical Implementation of the JA Method

441

(2)

Examples of Hysteresis Loops Obtained with the JA Method

443

(4)

Determination of the Parameters from Experimental Hysteresis Loops

447

(5)

Numerical Algorithm

452

(1)

The Inverse Jiles-Atherton Model

452

(3)

The Inverse JA Method

452

(2)

Procedure for the Numerical Implementation of the Inverse JA Method

454

(1)

Including Iron Losses in Finite Element Calculations

455

(16)

Hysteresis Modeling by Means of the Magnetization M Term

457

(2)

Hysteresis Modeling by Means of a Differential Reluctivity

459

(4)

Inclusion of Eddy Current Losses in the FE Modeling

463

(2)

Inclusion of Anomalous Losses in the FE Modeling

465

(1)

Examples of Iron Losses Applied to FE Calculations

466

(5)

Bibliography

471

(12)

Index

483

FREE SHIPPING

Rent More, Save More! Use code: BBRENTAL

5% off 1 book, 7% off 2 books, 10% off 3+ books

Electromagnetic Modeling by Finite Element Methods

Summary

Author Biography

Table of Contents

Supplemental Materials