1st Edition

Magnetic Materials and 3D Finite Element Modeling

    400 Pages 263 B/W Illustrations
    by CRC Press

    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.

    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
    The Electrostatics
    Magnetostatic Fields
    Magnetic Materials
    Inductance and Mutual Inductance
    Magnetodynamic Fields
    Fields Defined by Potentials
    Final Considerations

    Ferromagnetic Materials and Iron Losses
    Basic Concepts
    Losses Components
    Iron Losses under Alternating, Rotating and DC Biased Inductions
    Final Considerations

    Scalar Hysteresis Modeling
    The Preisach’s Scalar Model
    The Jiles-Atherton Scalar Model
    Final Considerations

    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
    Final Considerations

    Brief Presentation of the Finite Element Method
    The Galerkin Method: Basic Concepts using Real Coordinates
    Generalization of the FEM: Using Reference Coordinates
    Numerical Integration
    Some Finite Elements
    Using Edge Elements

    Using Nodal Elements with Magnetic Vector Potential
    Main Equations
    Applying Galerkin Method
    Uniqueness of the Solution; the Coulomb’s Gauge
    Example and Comparisons
    Final Considerations

    The Source-Field Method for 3D Magnetostatic Fields
    The Magnetostatic Case – Scalar Potential
    The Magnetostatic Case – Vector Potential
    Implementation Aspects and Conventions
    Computational Implementation
    Example and Results

    The Source-Field Method for 3D Magnetodynamic Fields
    Formulation Considering Eddy Currents – Time Stepping
    Formulation Considering Eddy Currents – Complex Formulation
    Field-Circuit Coupling
    Computational Implementation
    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


    João Pedro A. Bastos completed his doctoral thesis (Docteur d’Etat) at Université Pierre et Marie Curie, Paris VI, in 1984. He then returned to Brazil at the Universidade Federal de Santa Catarina (UFSC) and became a full professor in 1992. He founded GRUCAD in 1985—a group that plays an important role in the development of the area of electromagnetic field analysis in Brazil. Dr. Bastos worked as a visiting professor at the University of Akron, Ohio, in 1992 and 2001. He is also the author of four books and has published several papers in periodic journals and conferences.

    Nelson Sadowski received his engineering and master of science degrees from Universidade Federal de Santa Catarina (UFSC) in 1982 and 1985, respectively. In 1993, he received his PhD from the Institut National Polytechnique de Toulouse (INPT). He then returned to Brazil and continued his research and teaching activities at GRUCAD-UFSC and became a full professor in 1996. In 2000, he received his HDR (Habilitation) diploma, also from the INPT. Dr. Sadowski has been active on international agreements with universities in France, Germany, and Belgium. He is also the author of several conference and journal papers. He is also very active on industrial consulting.

    "… 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