Study of Effective Methods of Characterisation of Magnetostriction and Its Fundamental Effect on Transformer Core Noise
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STUDY OF EFFECTIVE METHODS OF CHARACTERISATION OF MAGNETOSTRICTION AND ITS FUNDAMENTAL EFFECT ON TRANSFORMER CORE NOISE PhD thesis Shervin Tabrizi A thesis submitted to the Cardiff University in candidature for the degree of Doctor of Philosophy December 2013 Wolfson Centre for Magnetics Cardiff School of Engineering Cardiff University Wales, United Kingdom i Abstract Magnetostriction of core laminations is one of the main sources of transformer acoustic noise. The magnetostriction of grain oriented silicon steel is extremely sensitive to applied compressive stress. A measurement system using piezoelectric accelerometers has been designed and built. This was optimized for magnetostriction measurements under stress within the range of 10 MPa to -10 MPa on large as-cut sheets. This system was used for characterization of wide range of grain-oriented grades. Laboratories around the world are using many different methods of measurement of the magnetostrictive properties of electrical steel. In response to this level of interest, an international round robin exercise on magnetostriction measurement has been carried out and eight different magnetostriction-measuring systems have been compared. Results show a reasonable correlation between the different methods. In this study the influence of factors such as the domain refinement process, curvature, and geometry on the magnetostriction of 3% grain oriented silicon steel were investigated. The study shows that both laser scribing and mechanical scribing have a similar effect on the sample’s domain structure and would cause an increase in magnetostriction. A proposed domain model was used successfully to estimate the effect of scribing on magnetostriction. Correlation between magnetostriction of 3% grain oriented silicon steel with transformer vibration was investigated. It was shown that increasing the clamping pressure to 4Nm can decrease the out of plane vibration in the joint regions due to the increase of friction and reduction of air gap which reduces the air gap flux and consequently the Maxwell forces. Also it has been shown that the primary source for the differences between the vibration of the cores under the same magnetic excitation and clamping pressure in the measured cores is due to the differences in the magnetostriction characteristics of the grades of electrical steels. Correlations between the magnetostriction harmonics and the vibration of the cores have been determined. ii ACKNOWLEDGMENTS My first and sincere appreciation goes to Dr. Philip Anderson, my senior supervisor for all I have learned from him and for his continuous help and support in all stages of this thesis. I would also like to thank him for being an open person to ideas, and for encouraging and helping me to shape my interest and ideas. I would like to express my deep gratitude and respect to Prof. Anthony Moses whose advices and insight was invaluable to me. For all I learned from him, He always challenged me in alternative views and his insight knowledge improved this work significantly. I am very thankful to Dr. Hugh Stanbury for his guidance and encouragement from the beginning to end of my PhD studies, especially regarding round robin exercise. His supervision and professional expertise improved my work and knowledge significantly. I am also very grateful to Dr. Jeremy Hall and Dr.Yevgen Melikov for their support, guidance and helpful suggestions. And also thanks to my colleague Mr Teeraphon Phophongviwat. I gratefully acknowledge the funding sources that made my Ph.D. work possible. I was funded by ABB AB, AK Steel Crop., Alstom Grid, Brush Transformers Ltd, CG Holdings Belgium N.V., Cogent Power Ltd, Koleltor Etra Energetski transformatorji d.o.o., Kncar Distribution and Special Transformers Inc., Legnano Teknoelectric Company S.p.A., Nuova Eletrofer S.p.A., SGB Starkstorm Gerätebay Gmbh, and ThyssenKrupp Electrical Steel GmbH. I would like to thank my family, especially my mother and father for always believing in me, for their continuous love and their supports in my decisions. Without whom I could not have made it here. And most of all for my loving, supportive, encouraging, and patient wife Khoosheh, whose faithful support during the final stages of this Ph.D., is so appreciated. Thank you. iii List of Symbols Velocity Magnetostriction Misorientation Angle Applied Stress Angular Frequency z Inter laminar Flux µ Permeability A Acceleration B Magnetic induction CGO Conventional Grain Oriented DR Domain Refined E Young’s Modulus E Magnetoelastic Energy EK Magnetocrystalline Anisotropy Energy Em Magnetostatic Energy f Frequency H Magnetic field iv HGO High Permeability Grain Oriented J Magnetic Polarization LDV Laser Doppler Vibrometer Lva A-weighted Magnetostriction Velocity M Magnetisation ND Demagnetising Factor Ps Specific Power Loss RD Rolling Direction x Susceptibility X Displacement α, Direction cosines v ABSTRACT ....................................................................................................................... II ACKNOWLEDGMENTS ............................................................................................... III LIST OF SYMBOLS ....................................................................................................... IV 1. CHAPTER 1: INTRODUCTION AND OBJECTIVES ......................................12 1.1. INTRODUCTION: ............................................................................................................. 12 1.2. PARAMETERS AFFECTING NOISE: ................................................................................ 12 1.2.1. Transmission: .................................................................................................................... 12 1.2.2. Sound barrier: ............................................................................................................... 12 1.2.3. Sound source: ................................................................................................................ 13 1.3. OBJECTIVES: ................................................................................................................... 16 REFERENCES FOR CHAPTER 1 ..................................................................................................... 18 CHAPTER 2: ELECTROMAGNETISM ......................................................................20 2.1. BASIC TERMS IN MAGNETISM ....................................................................................... 20 2.2. FERROMAGNETISM ........................................................................................................ 21 2.3. ENERGIES OF A FERROMAGNETIC ............................................................................... 21 2.3.1. Magnetocrystalline anisotropy energy ............................................................. 21 2.3.2. Magnetostatic Energy ............................................................................................... 22 2.3.3. Domain Wall Energy ................................................................................................. 24 2.3.4. Magnetoelastic Energy and Spontaneous Magnetostriction .................. 25 2.4. FERROMAGNETIC DOMAIN STRUCTURE .................................................................... 27 2.5. THE EFFECT OF APPLIED FIELD .................................................................................. 31 2.6. MAGNETOSTRICTION UNDER APPLIED FIELD........................................................... 34 REFERENCES FOR CHAPTER 2 ..................................................................................................... 37 CHAPTER 3: DOMAIN STRUCTURE UNDER APPLIED STRESS .....................38 3.1. DOMAIN STRUCTURE UNDER IN PLANE APPLIED STRESS ........................................ 38 vi 3.1.1. Tensile Stress in the Rolling Direction ............................................................... 38 3.1.2. Longitudinal Compressive Stress ......................................................................... 39 3.1.3. Applied stress in the transverse direction........................................................ 41 3.2. THE EFFECT OF A MAGNETIC FIELD ON DOMAIN STRUCTURE UNDER APPLIES STRESS………………………………………………………………………………………………………………….42 3.2.1. Domain structure under longitudinal Tensile Stress ................................. 43 3.2.2. Domain structure under longitudinal compressive Stress ....................... 44 3.3. EFFECT OF STRESS ON MAGNETOSTRICTION OF GRAIN ORIENTED SILICON STEEL……………………………………………………………………………………………………………………45 3.3.1. Domain structure under longitudinal tensile stress ................................... 46 3.3.2. Domain structure under longitudinal compressive Stress ....................... 46 3.4. EFFECT OF STRESS ON LOSS OF GRAIN ORIENTED SILICON STEEL ......................... 50 REFERENCES FOR CHAPTER 3 ..................................................................................................... 52 CHAPTER 4: METHODS OF MAGNETOSTRICTION MEASUREMENT ..........53 4.1. VIBRATION MEASUREMENT METHODS: ..................................................................... 54 4.1.1. Resistance strain gauge ........................................................................................... 54 4.1.2. Linear variable differential transformers ....................................................... 56 4.1.3. Capacitive displacement sensors ......................................................................... 57 4.1.4. Piezoelectric displacement