PRINCIPLES AND PRACTICE OF ELECTRICAL ENGINEERING
1 Soft magnetic material 1 11 Range and application of commercial bulk magnetic materials 1 12 Industrially important characteristics of soft magnetic materials 3 13 Families of commercial soft magnetic materials 7 14 Electrical steels 14 15 Global impact of energy wastage in electrical steels 21 References 23 2 Basic magnetic concepts 25 21 Magnetic fields, flux density and magnetisation 25 211 Magnetic field (H) 25 212 Magnetic dipole moment (m) 25 213 Magnetic polarisation (J) 28 214 Magnetic flux density (B) 29 215 Permeability (m) 32 216 Relationships between H, B and M 34 217 Demagnetising effects 39 22 Units in magnetism 41 23 Dimensional analysis of magnetic quantities 44 24 Crystal planes and directions 46 References 49 3 Magnetic domains, energy minimisation and magnetostriction 51 31 Magnetic dipole moments and domains 51 32 Weiss theory and molecular field 52 33 Minimisation of free energy 54 34 Domain wall structure and motion 55 35 Domain changes occurring during magnetisation 57 36 Anisotropy energy 59 361 Anisotropy energy in materials with cubic crystal structure (Ek) 59 362 Uniaxial anisotropy energy (Eu) 63 37 Magnetostatic energy (Ems) 63 38 Fundamentals of magnetostriction 64 381 Stress–strain relationship in soft magnetic materials 64 382 Origin of magnetostriction in soft magnetic materials 65 39 Magnetoelastic energy (Eme) 69 310 Domain wall energy (Ew) 72 311 Work and energy in the magnetisation process 73 312 Static domain structure with minimum stored energy 74 313 Domain changes occurring during magnetisation 76 314 Energy (Eh) due to an externally applied field 79 315 Effect of an applied field on a domain wall 80 316 Magnetostriction in soft magnetic materials 81 3161 Saturation magnetostriction along principal crystal axes 81 3162 The special case of (110)[001] oriented silicon–iron 82 3163 Saturation magnetostriction of a polycrystalline material 83 3164 Variation of magnetostriction with flux density 84 317 The Barkhausen effect 88 References 92 4 Methods of observing magnetic domains in electrical steels 95 41 Introduction 95 42 Powder techniques 96 43 Optical methods of surface domain observation 99 431 The magneto-optic effect 99 432 Domain observation using the longitudinal KMO effect 100 433 Observation of rapid domain wall motion using the KMO effect 102 44 Magnetic force microscope 104 45 Domain visualisation from surface field sensors 107 46 Observation of sub-surface domain features 110 461 Electron microscope techniques 110 462 X-ray techniques 112 463 Freeze-in techniques for observing sub-surface structures 112 464 Visualisation of sub-surface domain structures using neutron irradiation 114 47 Use of magnetic bacteria for domain observation 114 48 Magneto-optical indicator films 115 49 Comparison of methods for observations on electrical steels 116 References 118 5 Electromagnetic induction 123 51 Faraday’s law 123 52 Lenz’s law 124 53 Expressions for an induced emf 125 Reference 127 6 Fundamentals of ac signals 129 61 Waveform terminology 129 62 Distortion factor 133 63 Distorted voltages on power systems 134 64 Distorted B or H waveforms due to non-linear magnetisation curves 135 65 Effect of the electric circuit on waveform distortion 136 66 General relationship between harmonics in B and H waveforms 137 67 Calculation of flux density under distorted magnetisation conditions 138 References 140 7 Losses and eddy currents in soft magnetic materials 141 71 Physical and engineering approaches to magnetic losses 141 72 Energy dissipation derived from the area enclosed by a B–H loop 142 73 Derivation of the dependence of loss on B and H using the Poynting vector theorem 145 74 Hysteresis loss 147 75 Eddy current generation in a rod of conducting material 148 76 Eddy currents in a thin sheet 149 761 Skin depth and equivalent depth of uniform magnetisation 153 77 Classical eddy current loss 155 771 Reduction of eddy current loss by use of laminations 156 78 Separation of losses into eddy current and hysteresis components 158 781 Hysteresis loss components 158 782 Separation of total loss into two or three components 158 79 Total loss within a sheet 163 710 Total power loss of a strip expressed in terms of B and H 166 References 168 8 Rotational magnetisation and losses 171 81 Vector representation of a pure rotating magnetic field 173 82 Rotational flux density 175 83 Torque curves and stored magnetocrystalline energy 177 84 Rotational hysteresis loss 182 85 Magnetic domain structures under rotational magnetisation 186 86 Combined alternating, rotational and dc offset magnetisation 193 861 Combined alternating and rotational magnetisation 193 862 Alternating magnetisation combined with dc offset fields 197 87 Rotational loss at power frequency 198 871 Distinction from rotational hysteresis loss 198 872 Total rotational loss in terms of B and H 199 873 Loss separation under rotational magnetisation 202 88 Magnetostriction under rotational magnetisation 208 881 Multidirectional magnetostriction 208 882 Simulation of rotational magnetostriction 210 89 Three-dimensional magnetisation 213 References 216 9 Anisotropy of iron and its alloys 221 91 Magnetisation at an angle to a preferred crystal direction 222 92 Magnetisation at angles to an easy direction under ac magnetisation 228 93 Effect of strip width on magnetisation direction in anisotropic material 230 94 Effect of stacking method on apparent loss of anisotropic strips cut at angles to an easy axis 235 References 239 10 Magnetic circuits 243 101 The basic magnetic circuit 243 102 Magnetic reluctance 248 103 Field and flux density distribution in a circular core 250 104 Iron cored solenoid 251 105 Flux density in a magnetic material measured by an enwrapping search coil 253 106 Field and flux density at the interface between two media 254 107 Forces between magnetised laminations 256 References 257 11 Effect of mechanical stress on loss, permeability and magnetostriction 259 111 Effect of stress on simple magnetic domain structures 260 112 Stress sensitivity derived from domain structures 262 113 Effect of biaxial stress 268 114 Stress sensitivity of GO steel 271 115 Stress sensitivity of NO steel 276 116 Effect of bending stress 280 117 Effect of normal stress 284 118 Effect of stress on components of loss 287 119 Effects of building stresses in electrical machine cores 288 1191 Clamping stress 288 1192 Wound cores 291 1193 Stacked cores 291 1110 Slitting and punching stress in electrical steel 293 11101 Background 293 11102 Practical aspects of the cut edge region 299 11103 Other cutting methods 302 11104 Modelling the effect of the cut edge effect 303 11105 Shrink fitted stator cores 304 References 307 12 Magnetic measurements on electrical steels 315 121 Introduction 315 122 Effect of sample geometry (toroids, single strips, rings and single sheet) 316 1221 Epstein frame 316 1222 Single sheet tester 319 1223 Rings and toroids 323 123 Sensing methods 325 1231 Flux density sensing 325 1232 Magnetic field measurement 328 124 AC magnetic measurements of losses and permeability 330 1241 The wattmeter method 330 1242 Digital interpretation of the wattmeter method 333 1243 Localised measurements 337 1244 Measurements under simulated operational conditions 342 1245 DC biased ac measurements 344 125 2D and rotational magnetic measurements 346 1251 Measurement principles 346 1252 Magnetisation systems 347 1253 Loss measurement 349 126 Magnetostriction measurements 352 1261 Magnetostriction parameters 353 1262 Magnetostriction measurement transducers 353 1263 Rotational magnetostriction 359 127 On-line measurements 361 1271 Practical challenges 361 1272 Non-enwrapping systems 364 128 The dc magnetic measurements 366 1281 Quasi-static measurements 367 1282 Point-by-point measurement 371 1283 Vibrating sample magnetometer 372 1284 Coercimeters 373 1285 Demagnetisation 374 129 Surface insulation testing 377 1210 Barkhausen noise measurement 380 References 381 13 Background to modern electrical steels 389 131 History and development of electrical steels 389 1311 Laminations 390 1312 Increased resistivity 391 1313 Purification 394 1314 Grain size 395 1315 Crystal orientation 397 1316 Coatings 397 132 Metallurgical requirements and control 398 1321 Thickness 398 1322 Chemical composition 399 1323 Grain size 400 1324 Crystal orientation 400 1325 Coatings 401 References 401 14 Production of electrical steels 403 141 Chemical composition 403 142 Hot rolled coil production 404 143 Cold mill processing 405 1431 Grain oriented electrical steel 405 1432 Non-oriented electrical steel 410 144 Final property assessment 412 145 Future development 412 1451 Grain oriented electrical steel 412 1452 Non-oriented electrical steels 414 References 415 15 Amorphous and nano-crystalline soft magnetic materials 417 151 Amorphous materials 417 1511 Production of amorphous magnetic materials 417 1512 Composition 419 1513 Magnetic structure 420 1514 Coatings and surface treatment 423 1515 Stress sensitivity 424 1516 Magnetostriction 426 1517 Consolidated Fe-based amorphous material (POWERCORE) 426 1518 Bulk amorphous material 428 152 Nano-crystalline magnetic materials 430 1521 Production of nano-magnetic material 431 1522 Magnetic properties 433 1523 Coating and surface treatment 434 1524 Stress sensitivity 434 153 General properties of amorphous and nano-materials 435 1531 Families of amorphous materials 435 1532 Commercial materials 435 154 High silicon micro-crystalline ribbon 436 155 Applications of amorphous and nano-crystalline ribbons 439 References 441 16 Nickel–iron, cobalt–iron and aluminium–iron alloys 447 161 Introduction 447 162 Iron, cobalt and nickel 448 1621 Iron 448 1622 Nickel 449 1623 Cobalt 450 163 Nickel–iron alloys 450 164 Perminvar 457 165 Cobalt–iron alloys 458 1651 Stress dependence of magnetic properties of Co–Fe alloys 467 166 Aluminium–iron alloys 470 167 Applications 471 1671 Ni–Fe alloys 471 1672 Co–Fe alloys 472 References 473 17 Consolidated iron powder and ferrite cores 477 171 Background 477 172 Consolidated iron and SiFe powder cores 478 1721 Production 478 1722 SMC compositions for power applications 479 1723 Magnetic properties 479 1724 Loss components in SMCs 482 1725 Applications of iron-based SMCs 484 1726 Opportunities for future developments 485 173 Soft ferrites 486 1731 Basic structure 486 1732 Production 487 1733 Magnetic properties 488 1734 Loss components in ferrite cores 489 1735 Applications 491 References 491 18 Temperature and irradiation dependence of magnetic and mechanical properties of soft magnetic materials 495 181 Effects of temperature on structure insensitive magnetic properties 496 1811 Saturation magnetisation Ms 496 1812 Resistivity 497 1813 Magnetocrystalline anisotropy constants 499 1814 Magnetostriction constants 501 182 Effect of temperature on permeability, coercivity and losses 502 183 The dc and ac properties of silicon steels at elevated temperatures 503 184 Temperature dependencies of magnetic properties of various material 508 185 Modelling high temperature performance 512 186 Magnetic properties at cryogenic temperatures 514 187 Effect of non-uniform temperature gradients in magnetic core laminations 515 188 Effect of irradiation on soft magnetic materials 516 References 517