Magnetic Materials and 3D Finite Element Modeling explores material characterization and finite element modeling (FEM) applications. This book relates to electromagnetic analysis based on Maxwell’s equations and application of the finite element (FE) method to low frequency devices. A great source for senior undergraduate and graduate students in electromagnetics, it also supports industry professionals working in magnetics, electromagnetics, ferromagnetic materials science and electrical engineering.
The authors present current concepts on ferromagnetic material characterizations and losses. They provide introductory material; highlight basic electromagnetics, present experimental and numerical modeling related to losses and focus on FEM applied to 3D applications. They also explain various formulations, and discuss numerical codes.
• Furnishes algorithms in computational language
• Summarizes concepts related to the FE method
• Uses classical algebra to present the method, making it easily accessible to engineers
Written in an easy-to-understand tutorial format, the text begins with a short presentation of Maxwell’s equations, discusses the generation mechanism of iron losses, and introduces their static and dynamic components. It then demonstrates simplified models for the hysteresis phenomena under alternating magnetic fields. The book also focuses on the Preisach and Jiles–Atherton models, discusses vector hysterisis modeling, introduces the FE technique, and presents nodal and edge elements applied to 3D FE formulation connected to the hysteretic phenomena.
The book discusses the concept of source-field for magnetostatic cases, magnetodynamic fields, eddy currents, and anisotropy. It also explores the need for more sophisticated coding, and presents techniques for solving linear systems generated by the FE cases while considering advantages and drawbacks.
"… an important contribution to the area of numerical design in electromagnetics and in particular in low frequency design, including electric machines and actuators. It is a thorough, balanced presentation of the theory and its application."
—Dr. Nathan Ida, The University of Akron
"Written by specialists in the modeling of electromagnetism …useful for researchers and teachers with experience in the area or for students, wishing to acquire knowledge in the field."
—F. Bouillaultm, Professor at Paris Sud University
"Anyone who wants to learn how to model magnetic cores, especially transformer core materials, in 3D will find this book extremely useful."
—IEEE Electrical Insulation Magazine, January/February 2015
Statics and Quasi-Statics Electromagnetics - Brief Presentation
The Maxwell Equations
The Maxwell Equations: Local Form
The Maxwell Equations: Integral Form
The Maxwell Equations in Low Frequency
Inductance and Mutual Inductance
Fields Defined by Potentials
Ferromagnetic Materials and Iron Losses
Iron Losses under Alternating, Rotating and DC Biased Inductions
Scalar Hysteresis Modeling
The Preisach’s Scalar Model
The Jiles-Atherton Scalar Model
Vector Hysteresis Modeling
Vector Model Obtained with the Superposition of Scalar Models
Vector Generalizations of the Jiles-Atherton Scalar Models
Some Remarks Concerning the Vector Behavior of Hysteresis
Brief Presentation of the Finite Element Method
The Galerkin Method: Basic Concepts using Real Coordinates
Generalization of the FEM: Using Reference Coordinates
Some Finite Elements
Using Edge Elements
Using Nodal Elements with Magnetic Vector Potential
Applying Galerkin Method
Uniqueness of the Solution; the Coulomb’s Gauge
Example and Comparisons
The Source-Field Method for 3D Magnetostatic Fields
The Magnetostatic Case – Scalar Potential
The Magnetostatic Case – Vector Potential
Implementation Aspects and Conventions
Example and Results
The Source-Field Method for 3D Magnetodynamic Fields
Formulation Considering Eddy Currents – Time Stepping
Formulation Considering Eddy Currents – Complex Formulation
The Differential Permeability Method
Example and Results
A Matrix-Free Iterative Solution Procedure for Finite Element Problems
The Classical FEM: T-Scheme
The Proposed Technique: N-Scheme
Implementation of N-Scheme with SOR
Applying Non-Stationary Iterative Solver to the N-Scheme
CG Algorithm Implementation
Examples and Results
Results and Discussion