Handbook of Electrical Steel

Description

This book contains all information regarding magnetism and magnetic materials that an electrical engineer needs to know to be able to understand and design magnetic devices.The handbook comprises chapters comprising basic electromagnetism, basic quantum mechanics, ferromagnetism, magnetic materials, magnetic material characterization, modeling of magnetic materials, and magnetic design. A comprehensive description of the physical origin of magnetism of materials is given chapter two and a thorough review of the physics behind ferromagnetism is given in chapter three.All chapters are written in a textbook fashion such that they can easily be assimilated separately. The book gathers in an understandable the multidisciplinary topic of magnetism and magnetic materials in way that it can serve as a comprehensive introduction to engineers that considers use of magnetic materials in their designs.The book covers all major modeling techniques of magnetic materials including the well-known Presiach, Jiles-Atherton and lag models. General magnetic design approaches including major and new design tools also are presented.The book also serves as a guideline regarding the choice of feasible materials in specific applications regarding both soft and hard magnetic materials with an inventory of alternatives to electrical steel. Relevant performance criteria then are given such that appropriate materials can be selected. The final chapter offers a list of current electrical steel and magnetic material suppliers. Contents Preface Concluding Remarks Acknowledgements Chapter 1. A Brief Introduction to Magnetism and Magnetic and Electric Fields 1.1. History of Magnetism 1.2. Some Basic Electromagnetism 1.2.1. The magnetic induction field 1.2.2. The electric field 1.2.3. The electric dipole moment and the displacement field 1.2.4. Magnetic moments 1.2.5. Magnetic moments and the magnetizing field 1.2.6. The magnetization field 1.2.7. The demagnetizing field 1.2.8. The Maxwell’s equations 1.2.9. Magnetic field calculations 1.2.10. Material laws 1.2.11. Electric and magnetic potentials 1.2.12. Electromotive and magnetomotive forces 1.2.13. Dielectric and magnetic media boundaries 1.2.14. The magnetic field outside and inside magnetic materials 1.2.15. Magnetic forces and magnetic energy 1.2.16. Some thermodynamics of magnetic materials References Chapter 2. The Quantum Mechanical Nature of Magnetic Material 2.1. Some Basic Quantum Mechanics 2.2. Electron Spin and Orbitals 2.3. The Free-Electron Model 2.4. Atomic Magnetism 2.4.1. The one-electron atom 2.4.2. Addition of angular momenta of the electrons 2.4.3. Curie law of paramagnetism 2.4.4. Pauli susceptibility 2.4.5. Several electron atoms 2.4.6. Spin–orbit coupling 2.4.7. Theory of electronic magnetism 2.5. Magnetism and Relativity 2.6. Zeeman Interaction 2.7. Paramagnetism 2.8. Molecules 2.8.1. Solid materials 2.9. Covalent solids 2.9.1. Ionic crystals 2.9.2. Hydrogen-bond solids 2.9.3. Molecular solids 2.9.4. Metals 2.10. Magnetism of Electrons in Solids 2.11. Some Basic Solid State Physics 2.11.1. Crystal lattices 2.11.2. Miller indices and crystal directions 2.11.2.1. Some simple closed-packed structures 2.11.3. Reciprocal space 2.11.4. Brillouin zones 2.11.5. Band theory of solids 2.11.5.1. General features of energy band of electrons 2.11.6. Electron motion in periodic structures 2.11.6.1. Energy band gaps and overlap 2.12. Electrical Conductivity References Chapter 3. Ferromagnetism 3.1. Mean Field Theory 3.2. The Landau Theory 3.3. The Stoner Criterion 3.4. Exchange Interactions 3.5. Other Ordered Magnetism 3.5.1. Antiferromagnetism 3.5.2. Ferrimagnetism 3.5.3. Miscellaneous ordering 3.5.3.1. Frustration 3.5.3.2. Amorphous magnets 3.5.3.3. Spin glass 3.6. Crystal-field Interaction 3.7. Magnetic Anisotropy 3.7.1. Crystalline magnetic anisotropy 3.7.2. Shape anisotropy 3.7.3. Induced anisotropy 3.8. Magnetostriction 3.8.1. Other magnetoelastic effects 3.9. Ferromagnetic Domains 3.9.1. Introduction 3.9.2. Micromagnetic energies 3.9.2.1. Exchange energy 3.9.2.2. Anisotropy energy 3.9.2.3. Demagnetizing energy 3.9.2.4. Strain energy 3.9.2.5. Magnetostriction energy 3.9.2.6. Minimization of the micromagnetic energy 3.9.3. Domain walls 3.9.3.1. The Bloch wall 3.9.3.2. The N´eel wall 3.10. The Stoner–Wohlfarth Model 3.11. The Nucleation Field 3.12. Domain-Wall Motion 3.13. Examples of Real Hysteresis Loops 3.14. Long-Term Magnetization Features References Chapter 4. Magnetic Materials 4.1. Soft Magnetic Materials 4.1.1. Soft magnetic material characterizing quantities 4.1.1.1. Coercivity 4.1.1.2. Permeability 4.1.1.3. Remanence 4.1.1.4. Linearity and hysteresis 4.1.1.5. Losses 4.2. Available Materials 4.2.1. Soft magnetic material classification 4.2.2. Pure iron 4.2.3. Conventional grain-oriented (CGO) SiFe steel 4.2.4. High permeability grain-oriented electrical steel HiB 4.2.5. Non-oriented electrical steel NO 4.2.6. Special iron-based alloys 4.2.6.1. Rapid solidification 4.2.6.2. The CVD process 4.2.6.3. Alternative texture 4.2.6.4. Alternative to silicon 4.2.7. Nickel and Cobalt-based alloys 4.2.7.1. NiFe alloys 4.2.7.2. Permendur and Perminvar 4.2.8. Amorphous magnetic materials 4.2.9. Nanocrystalline materials 4.2.10. Soft ferrites 4.3. Hard Magnetic Materials 4.3.1. Hard magnetic material characterizing quantities 4.3.1.1. Remanent magnetization 4.3.1.2. Saturation magnetization 4.3.1.3. Coercivity 4.3.1.4. The maximum energy product 4.3.1.5. Squareness coefficient 4.3.1.6. Orientation coefficient 4.3.1.7. Recoil curves and maximum working field 4.3.1.8. The Curie temperature and temperature coefficients 4.4. Available Materials 4.4.1. Hard magnet classification 4.4.2. Alnico magnet alloys 4.4.3. Hard magnetic ferrites 4.4.4. SmCo magnets 4.4.5. NdFeB magnets References Chapter 5. Characterization Methods 5.1. General Overview 5.2. Material Characterization Approaches 5.2.1. Sheet characterization methods 5.2.2. Ring core measurements 5.2.3. Epstein frame 5.2.4. Single sheet and strip testers 5.2.4.1. 1-D measurements 5.2.4.2. 2-D measurements 5.2.4.3. 3-D measurements 5.2.5. Magnetostriction measurement approaches 5.2.5.1. 1-D measurements 5.2.5.2. 2-D measurements 5.2.5.3. 3-D measurements 5.3. Material Data Processing 5.3.1. A measurement method for extraction of the anhysteretic magnetization curve 5.3.2. Extrapolation of the major hysteresis curve References Chapter 6. Modelling of Magnetic Materials 6.1. Models of Magnetic Hysteresis 6.1.1. The Jiles–Atherton model 6.1.2. The Preisach model 6.1.3. The classical Preisach model 6.1.3.1. Identification of model quantities 6.1.4. The generalized scalar Preisach model 6.1.4.1. The moving model 6.1.4.2. The input-dependent model 6.1.4.3. The dynamic model 6.1.4.4. Validity of the Preisach models 6.1.4.5. The model with two inputs 6.1.5. Vector Preisach models 6.1.5.1. Identification of model parameters in the isotropic model 6.1.5.1.1. The 2D model 6.1.5.1.2. The 3D isotropic model 6.1.5.1.3. The 2D anisotropic Preisach model 6.1.5.1.4. The 3D anisotropic Preisach model 6.1.5.2. The dynamic vector Preisach model 6.1.5.2.1. In two dimensions 6.1.5.2.2. In three dimensions 6.1.5.3. Generalized vector Preisach models 6.1.5.3.1. The isotropic 2D generalized Preisach model 6.1.5.3.2. The isotropic 3D generalized Preisach model 6.1.5.3.3. The isotropic 2D generalized dynamic Preisach model 6.1.5.3.4. The anisotropic 2D generalized Preisach model 6.1.5.4. The isotropic 2D Preisach model with generalized input projection 6.1.6. A differential Preisach-like model 6.1.6.1. The differential Preisach model approach 6.1.6.2. The gate model 6.1.7. The Bergqvist model 6.1.7.1. The direct computational approach 6.1.7.2. The variational approach 6.1.7.3. Some remarks regarding the distributed friction model 6.2. Models of Magnetic Losses 6.2.1. Loss separation 6.2.2. Hysteresis losses 6.2.3. Eddy current losses 6.2.3.1. Linear magnetization law 6.2.3.2. Step magnetization law 6.2.4. Excess losses 6.2.4.1. The single domain-wall movement 6.2.4.2. Periodic domain-wall movements 6.2.4.3. Random domain-wall movements 6.2.5. Correlation regions 6.2.5.1. Loss dependence on magnetization and frequency 6.3. The Complex Permeability Model 6.4. Magnetostrictive Models 6.4.1. Magnetostriction model for alternating polarization 6.4.2. Magnetostriction model for rotating polarization References Chapter 7. Magnetic Design 7.1. General 7.1.1. Attain a certain flux density within a given volume 7.1.1.1. Constant flux density 7.1.1.2. Time-varying flux density 7.1.2. Attain a certain force caused by the magnetic flux 7.1.3. Attain a certain induced voltage and/or current 7.1.4. Attain a certain amount of magnetic energy 7.2. Design Tools 7.2.1. The design process 7.2.2. Lumped element methods 7.2.2.1. Cauer circuits 7.2.3. The finite element method 7.2.3.1. Use of the finite element method in magnetic design 7.2.4. Reluctance network methods 7.3. Design Approaches 7.3.1. Equivalent circuits 7.3.1.1. Electric circuit modeling approaches 7.3.2. The TTM approach 7.3.2.1. A simulation example 7.4. Condensed Electrical Steel Selection Guide 7.4.1. Electrical steel suppliers 7.4.2. Electrical steel supplier contact info References Appendix A A.1. Some Vector Algebra and Analysis A.1.1. Definition of vectors in two and three dimensions A.1.2. The scalar or dot product of two vectors A.1.3. The cross or vector product of two vectors A.1.4. Various formulas involving dot and cross vector products A.1.5. Formulas involving derivatives A.1.6. The nabla or del operator A.1.7. The gradient, divergence, curl and Laplacian operators in spherical and cylindrical coordinate systems A.1.8. Various formulas involving the nabla operator A.1.9. Special relations involving the nabla operator A.1.10. Integral vector relations Appendix B B.1. Demagnetization Factors of Rotational Symmetric Ellipsoids Appendix C C.1. Reduced Spontaneous Magnetization Versus the Reduced Temperature Appendix D D.1. One Method to Extract the Jiles–Atherton Hysteresis Model Parameters Reference Appendix E E.1. Some Functions and Polynomials E.1.1. The Brillouin function E.1.2. The Langevin function E.1.3. Spherical harmonics and Legendre functions E.1.4. Legendre functions E.1.5. Chebyshev polynomials E.1.6. Miscellaneous functions E.1.6.1. The gamma function References Appendix F F.1. Some Particle Statistics F.1.1. Fermi–Dirac statistics F.1.2. Maxwell–Boltzmann statistics F.1.3. Bose-Einstein statistics Used Symbols Roman Symbols Greek Symbols Units, Unit Conversion and Conversion Factors Physical Constants Tables of Typical Soft and Hard Magnet Data Index