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Nonlinear and Hysteretic Magnetomechanical Model for Magnetostrictive Transducers Marcelo Jorge Dapino Iowa State University

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Nonlinear and Hysteretic Magnetomechanical Model for Magnetostrictive Transducers Marcelo Jorge Dapino Iowa State University Iowa State University Capstones, Theses and Retrospective Theses and Dissertations Dissertations 1999 Nonlinear and hysteretic magnetomechanical model for magnetostrictive transducers Marcelo Jorge Dapino Iowa State University Follow this and additional works at: https://lib.dr.iastate.edu/rtd Part of the Electromagnetics and Photonics Commons, Mechanical Engineering Commons, and the Physics Commons Recommended Citation Dapino, Marcelo Jorge, "Nonlinear and hysteretic magnetomechanical model for magnetostrictive transducers " (1999). Retrospective Theses and Dissertations. 12657. https://lib.dr.iastate.edu/rtd/12657 This Dissertation is brought to you for free and open access by the Iowa State University Capstones, Theses and Dissertations at Iowa State University Digital Repository. It has been accepted for inclusion in Retrospective Theses and Dissertations by an authorized administrator of Iowa State University Digital Repository. For more information, please contact [email protected]. INFORMATION TO USERS This manuscript has been reproduced from the microfilm master. UMI films the text directly from the original or copy submitted. Thus, some thesis and dissertation copies are in typewriter face, while others may be from any type of computer printer. The quality of this reproduction is dependent upon the quality of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleedthrough, substandard margins, and improper alignment can adversely affect reproduction. In the unlikely event that the author did not send UMI a complete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyright material had to be removed, a note will indicate the deletion. Oversize materials (e.g., maps, drawings, charts) are reproduced by sectioning the original, beginning at the upper left-harKl comer and continuing from left to right in equal sections with small overlaps. Each original is also photographed in one exposure and is included in reduced form at the back of the book. Photographs included in the original manuscript have been reproduced xerographically in this copy. Higher quality 6" x 9" black and white photographic prints are available for any photographs or illustrations appearing in this copy for an additional charge. Contact UMI directly to order. Bell & Howell Information and Learning 300 North Zeeb Road, Ann Arbor, Ml 48106-1346 USA 800-521-0600 Nonlinear and hysteretic magnetcmechanical model for magnetostrictive transducers by Marcelo Jorge Dapino A dissertation submitted to the graduate faculty in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Major: Engineering Mechanics Major Professor; Alison B. Flatau Iowa State University Ames. Iowa 1999 Copyright © Marcelo Jorge Dapino, 1999. All rights reserved. UMI Niimber: 9940194 UMI Microform 9940194 Copyright 1999, by UMI Company. All rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code. UMI 300 North Zeeb Road Ann Arbor, MI 48103 ii Graduate College Iowa State University This is to certify that the Doctoral dissertation of Marcelo Jorge Dapino has met the dissertation requirements of Iowa State University Signature was redacted for privacy. Committee Member Signature was redacted for privacy. Committee Member Signature was redacted for privacy. Committee Member Signature was redacted for privacy. Committee Member Signature was redacted for privacy. Committee Member Signature was redacted for privacy. Signature was redacted for privacy. Signature was redacted for privacy. For the College iii TABLE OF CONTENTS ACKNOWLEDGMENTS xix ABSTRACT xxi PREFACE xxiii CHAPTER 1. GENERAL INTRODUCTION 1 1.1 Magnetism and Maxwell's Equations 2 1.1.1 The magnetic field 2 1.1.2 Magnetic induction and magnetic flux 8 1.1.3 Magnetization and magnetic moment 9 1.1.4 Relation between 5, H and M 11 1.1.5 Permeability and susceptibility 12 1.1.6 The demagnetizing field 13 1.1.7 Units in magnetism 15 1.1.8 Maxwell's Equations of Electromagnetism 15 1.2 Magnetization in Terms of Domain Processes 19 1.2.1 Magnetic domains 19 1.2.2 Domain processes 21 1.2.3 Magnetic anisotropy 24 1.3 Magnetostriction 27 1.3.1 Definition of magnetostriction 27 1.3.2 Spontaneous magnetostriction 27 1.3.3 Relation between magnetization and magnetostriction 28 1.3.4 Physical origin of magnetostriction 31 iv 1.3.5 Modeling of magnetostriction 33 Bibliography -tl CHAPTER 2. PERFORMANCE CONSIDERATIONS AND EXAMPLES OF MAGNETOSTRICTIVE ACTUATORS 45 2.1 Introduction -45 2.2 Performance Evaluation 47 2.2.1 Quasistatic e - H characteristic curves 48 2.2.2 Transducer electrical impedance 51 2.2.3 Blocked force 53 2.2.4 Output energy and energy densities 55 2.2.5 Projector power limitations 57 2.2.6 Figures of merit (POM) 58 2.3 Devices for Magnetostrictive Actuation 61 2.3.1 Low-Frequency Sonar Applications 62 2.3.2 Actuators for generation of motion and force 70 2.3.3 Other Actuator Applications 81 Bibliography 81 PART I TERFENOL-D MATERIAL AND TRANSDUCER PROPERTY CHARACTERIZATION 89 CHAPTER 3. MEASURED TERFENOL-D MATERIAL PROPERTIES UNDER VARIED APPLIED MAGNETIC FIELD LEVELS 90 3.1 Background 91 3.2 Description of Experiment 92 3.2.1 Experimental factors 92 3.2.2 Instrumentation 97 3.2.3 Randomization 99 3.2.4 Test-to-test repeatability 100 V 3.3 Modeling Material Properties 100 3.4 Results 103 3.4.1 Data analysis 103 3.4.2 Material property data 104 3.5 Conclusions 113 Acknowledgments 113 Bibliography 113 CHAPTER 4. STATISTICAL ANALYSIS OF TERFENOL-D MATERIAL PROPERTIES 115 4.1 Introduction 115 4.2 Methods 118 4.2.1 Terfenol-D material 118 4.2.2 Transducers and testing environment 118 4.2.3 Material properties calculation 119 4.2.4 Test modalities 119 4.2.5 Statistical analysis 120 4.3 Results and Discussion 122 4.3.1 Baseline study 122 4.3.2 Repeatability study 129 4.3.3 Mass load sensitivity study 132 4.4 Concluding Remarks 135 Acknowledgments 135 Bibliography 136 vi PART II MAGNETOMECHANICAL MODEL FOR MAGNETOSTRIC- TIVE TRANSDUCERS 138 CHAPTER 5. ON IDENTIFICATION AND ANALYSIS OF FUNDAMEN­ TAL ISSUES IN TERFENOL-D TRANSDUCER MODELING 139 5.1 Introduction 139 5.2 Discussion 141 5.2.1 Magnetization 143 5.2.2 Stress 146 5.2.3 Coupling between magnetization and stress 148 5.2.4 Additional operating effects 150 5.3 Concluding remarks 160 Acknowledgments 161 Bibliography 161 CHAPTER 6. A STRUCTURAL-MAGNETIC STRAIN MODEL FOR MAG- NETOSTRICTIVE TRANSDUCERS 166 6.1 Introduction 166 6.2 Transducer Model 169 6.2.1 Magnetization of magnetostrictive core 171 6.2.2 Active component of strain 175 6.2.3 Passive component and total strain output 178 6.3 Model Summary 182 6.4 Approximation Method 186 6.5 Model VaJidation 188 6.5.1 Terfenol-D transducer 188 6.5.2 Experimental analysis 189 6.5.3 Parameter estimation 190 6.5.4 Magnetization and strain results 191 6.6 Concluding Remarks 193 vii Bibliography 197 CHAPTER 7. A COUPLED STRUCTURAL-MAGNETIC STRAIN AND STRESS MODEL FOR MAGNETOSTRICTIVE TRANSDUCERS . 202 7.1 Abstract 202 7.2 Introduction 202 7.3 Magnetization of Magnetostrictive Element 206 7.3.1 Field-induced magnetization: differential susceptibility 206 7.3.2 Stress-induced magnetization changes: magnetomechanical effect .... 210 7.4 Active Component of Strain 215 7.5 Passive Component and Total Strain 217 7.6 Transducer Model Summary 218 7.7 Model Validation 221 7.7.1 Example 1 223 7.7.2 Example 2 224 7.8 Concluding Remarks 229 Acknowledgments 231 Bibliography 231 CHAPTER 8. DISSERTATION CONCLUSIONS 235 8.1 Discussion 236 8.1.1 Summary review of transducer models 236 8.1.2 Model critique 238 8.1.3 Future work 240 APPENDIX A. VECTOR NOTATION 241 APPENDIX B. MAGNETOSTRICTION OF ANISOTROPIC MATERIALS 242 viii LIST OF TABLES Table 1.1 Demagnetizing factors for various geometries, from [5] 1-1 Table 1.2 Principal magnetic units 15 Table 1.3 Nominal maximum quasistatic strain of common magnetostrictive ma­ terials 28 Table 2.1 Maximum magnetomechanical coupling coefficient along the longitudi­ nal axis and magnetostriction along easy axes. After [2] 59 Table 3.1 Transducer coil rating and DC magnetization due to Alnico V perma­ nent magnet 93 Table 3.2 Rows 1-2: Rod number and corresponding serial number. Row 3: Hq (rod), DC magnetic field bias needed to obtain symmetric ±500 mi- crostrain. Row 4-7: DC current (in ampere) needed to supplement transducer's permanent magnet field to obtain DC magnetic bias of row 3. Nominal transducer coil ratings: 300 Oe/A 96 Table 3.3 Sets of ten tests were run for two Terfenol-D samples at four drive levels. Transducers were assigned randomly. Prestress was set at 1.0 ksi, temperature range was 20-30 °C 100 Table 4.1 Classification of tested material 118 Table 4.2 Baseline study: mean square of error (MSE), coefficient of determina­ tion (i2^), and degrees of freedom of error (df) in the regression models. Asterisks indicate weighted least squares fits 130 ix Table 4.3 Repeatability study: type-D material. Summary statistics for Young's modulus at constant applied field, by rod and by drive level. Each set of repetitions was performed in transducer 'Tr' 130 Table 4.4 Repeatability study: average coefScients of variation (%) by rod type and by property. Asterisks indicate data affected by a faulty accelerom- eter 133 Table 6.1 Structural-magnetic model characterizing the magnetization magnetostriction X{t,x), and total strain £(t,x) 185 Table 6.2 Parameters used to obtain the model simulations shown in Figure 5.10. 195 Table 7.1 Coupled structural-magnetic model quantifying the magnetization, strain. and stress 222 X LIST OF FIGURES Figure 1.1 Magnetic field lines; (a) Straight conductor, (b) single circular loop.
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