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Electromagnetic Modeling by Finite Element Methods [Kõva köide]

(Universidad Federal de Santa Catarina, Florianopolis, Brazil), (Universidad Federal de Santa Catarina, Florianopolis, Brazil)
  • Formaat: Hardback, 508 pages, kõrgus x laius: 234x156 mm, kaal: 816 g
  • Sari: Electrical and Computer Engineering
  • Ilmumisaeg: 01-Apr-2003
  • Kirjastus: CRC Press Inc
  • ISBN-10: 0824742699
  • ISBN-13: 9780824742690
  • Formaat: Hardback, 508 pages, kõrgus x laius: 234x156 mm, kaal: 816 g
  • Sari: Electrical and Computer Engineering
  • Ilmumisaeg: 01-Apr-2003
  • Kirjastus: CRC Press Inc
  • ISBN-10: 0824742699
  • ISBN-13: 9780824742690
Writing for graduate students, Bastos and Sadowski (both of the U. Federal de Santa Catarina, Brazil) explore the application of the finite element method to electromagnetic classical cases; the coupling of electromagnetic equations with other phenomenon of electromagnetic structures, such as movement and mechanical equations, vibration analysis, eddy currents and nonlinearity; and the analysis of electrical and magnetic losses, including hysteresis, eddy currents, and anomalous losses. Annotation (c) Book News, Inc., Portland, OR (booknews.com)

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
1(26)
Introduction
1(1)
The Vector Notation
1(1)
Vector Derivation
2(2)
The Nabla Operator
2(1)
Definition of the Gradient, Divergence, and Rotational
3(1)
The Gradient
4(3)
Example of Gradient
5(2)
The Divergence
7(7)
Definition of Flux
7(2)
The Divergence Theorem
9(2)
The Conservative Flux
11(2)
Example of Divergence
13(1)
The Rotational
14(7)
Circulation of a Vector
14(3)
Stokes' Theorem
17(3)
Example of Rotational
20(1)
Second-Order Operators
21(2)
Application of Operators to More than One Function
23(1)
Expressions in Cylindrical and Spherical Coordinates
24(3)
Maxwell Equations, Electrostatics, Magnetostatics and Magnetodynamic Fields
27(96)
Introduction
27(1)
The EM Quantities
28(7)
The Electric Field Intensity E
30(1)
The Magnetic Field Intensity H
30(1)
The Magnetic Flux Density B and the Magnetic Permeability μ
31(1)
The Electric Flux Density D and Electric Permittivity ε
32(1)
The Surface Current Density J
33(1)
Volume Charge Density ρ
33(1)
The Electric Conductivity σ
34(1)
Local Form of the Equations
35(5)
The Anisotropy
40(2)
The Approximation to Maxwell's Equations
42(5)
The Integral Form of Maxwell's Equations
47(2)
Electrostatic Fields
49(19)
The Electric Charge
50(1)
The Electric Field
50(1)
Force on an Electric Charge
51(1)
The Electric Scalar Potential V
51(5)
Nonconservative Fields: Electromotive Force
56(3)
Refraction of the Electric Field
59(4)
Dielectric Strength
63(2)
Laplace's and Poisson's Equations of the Electric Field for Dielectric Media
65(3)
Laplace's Equation of the Electric Field for Conductive Media
68(1)
Magnetostatic Fields
68(5)
Maxwell's Equations in Magnetostatics
70(1)
The Equation rotH = J
70(3)
The Equation divB = 0
73(1)
The Equation rotE = 0
73(1)
The Biot-Savart Law
73(4)
Magnetic Field Refraction
77(3)
Energy in the Magnetic Field
80(3)
Magnetic Materials
83(24)
Diamagnetic Materials
84(1)
Paramagnetic Materials
85(1)
Ferromagnetic Materials
85(1)
General
85(3)
The Influence of Iron on Magnetic Circuits
88(2)
Permanent Magnets
90(1)
General Properties of Hard Magnetic Materials
90(4)
The Energy Associated with a Magnet
94(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


João Pedro A. Bastos, Nelson Sadowski