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Multifunctional Piezoelectric Energy Harvesting Concepts by Steven R. Anton Dissertation submitted to the Faculty of the Virginia Polytechnic Institute and State University in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Mechanical Engineering Daniel J. Inman, Chair Dong S. Ha Donald J. Leo Shashank Priya Henry A. Sodano April 25, 2011 Blacksburg, Virginia Keywords: energy harvesting, multifunctional, piezoelectric, unmanned aerial vehicle Copyright by Steven R. Anton, 2011 Multifunctional Piezoelectric Energy Harvesting Concepts Steven R. Anton Virginia Polytechnic Institute and State University, 2011 Advisor: Daniel J. Inman, Ph.D. A BSTRACT Energy harvesting technology has the ability to create autonomous, self-powered electronic systems that do not rely on battery power for their operation. The term energy harvesting describes the process of converting ambient energy surrounding a system into useful electrical energy through the use of a specific material or transducer. A widely studied form of energy harvesting involves the conversion of mechanical vibration energy into electrical energy using piezoelectric materials, which exhibit electromechanical coupling between the electrical and mechanical domains. Typical piezoelectric energy harvesting systems are designed as add-on systems to a host structure located in a vibration rich environment. The added mass and volume of conventional vibration energy harvesting designs can hinder to the operation of the host system. The work presented in this dissertation focuses on advancing piezoelectric energy harvesting concepts through the introduction of multifunctionality in order to alleviate some of the challenges associated with conventional piezoelectric harvesting designs. The concept of multifunctional piezoelectric self-charging structures is explored throughout this work. The operational principle behind the concept is first described in which piezoelectric layers are directly bonded to thin-film battery layers resulting in a single device capable of simultaneously harvesting and storing electrical energy when excited mechanically. Additionally, it is proposed that self-charging structures be embedded into host structures such that they support structural load during operation. An electromechanical assumed modes model used to predict the coupled electrical and mechanical response of a cantilever self-charging structure subjected to harmonic base excitation is described. Experimental evaluation of a prototype self-charging structure is then performed in order to validate the electromechanical model and to confirm the ability of the device to operate in a self-charging manner. Detailed strength testing is also performed on the prototype device in order to assess its strength properties. Static three-point bend testing as well as dynamic harmonic base excitation testing is performed such that the static bending strength and dynamic strength under vibration excitation is assessed. Three-point bend testing is also performed on a variety of common piezoelectric materials and results of the testing provide a basis for the design of self-charging structures for various applications. Multifunctional vibration energy harvesting in unmanned aerial vehicles (UAVs) is also investigated as a case study in this dissertation. A flight endurance model recently developed in the literature is applied to model the effects of adding piezoelectric energy harvesting to an electric UAV. A remote control foam glider aircraft is chosen as the test platform for this work and the formulation is used to predict the effects of integrating selfcharging structures into the wing spar of the aircraft. An electromechanical model based on the assumed modes method is then developed to predict the electrical and mechanical behavior of a UAV wing spar with embedded piezoelectric and thin-film battery layers. Experimental testing is performed on a representative aluminum wing spar with embedded self-charging structures in order to validate the electromechanical model. Finally, fabrication of a realistic fiberglass wing spar with integrated piezoelectric and thin-film battery layers is described. Experimental testing is performed in the laboratory to evaluate the energy harvesting ability of the spar and to confirm its self-charging operation. Flight testing is also performed where the fiberglass spar is used in the remote control aircraft test platform and the energy harvesting performance of the device is measured during flight. All images and figures are property of Steven R. Anton and were captured or created between June, 2006 and April, 2011. iii Dedication To my wife Tiffany for her unwaivering love and support, and to my daughter Mia for the joy she brings to my life And to my parents Michael and Vera for giving me such amazing opportunities throughout life iv Acknowledgments There are countless people that have been a part of my life who have all had a special influence in guiding me to this point. From teachers and professors to family and friends, it is impossible to thank every one of these people, but for those of you who have had a part in this great journey, you know who you are and I am forever grateful. First and foremost, I would like to extend my deepest thanks to my advisor, Dr. Daniel J. Inman, for his guidance and support throughout the five years I have spent in graduate school at Virginia Tech. Dr. Inman has been a truly amazing advisor and I could not imagine a better person to work with. His academic guidance and knowledge is invaluable while his humorous nature has provided for many laughs and great memories. Most importantly, Dr. Inman has always treated me with respect and made me feel more like a colleague than a student. He has given me the freedom to explore research topics of my own interest throughout both my Masters and Ph.D. work. This freedom can be a rarity among academic advising, and it has allowed me to develop my own research style and a sense of ownership of my work. Dr. Inman has encouraged me to travel to many research conferences around the US as well as to Scotland, for which I am forever grateful as I have had the opportunity to meet many great people and see many wonderful places. He also allowed me to co-teach a senior capstone design course alongside of him, which was a great learning experience. Throughout graduate school, Dr. Inman has also been extremely understanding about personal and family issues, always allowing me to take time to see my family. I consider Dr. Inman to be a great advisor, a great man, and truly a great friend. Dr. Inman, I look forward to a long and fruitful friendship! I would like to thank Dr. Dong S. Ha, Dr. Donald J. Leo, Dr. Shashank Priya, and Dr. Henry A. Sodano for serving on my committee and helping me with several research topics throughout my Ph.D. work. It has been quite beneficial having the support of such v knowledgeable professors. I would like to make a special thanks to Henry for introducing me to the topics of smart materials and energy harvesting back in our Michigan Tech days. Without your guidance, I would have never found my way to Virginia Tech. Thanks are certainly due to Ms. Beth Howell, the program manager of the Center for Intelligent Material Systems and Structures (CIMSS), for all of her help over the past five years. Anyone working in CIMSS knows that Beth keeps the place running, pun intended! She has been so helpful with academic, financial, and administrative issues, not to mention a great person to talk to. I’ll always remember our nice chats about soccer, teaching, and raising kids. Several of my fellow CIMSS colleagues have been instrumental in my success during graduate school. Thanks to Dr. Benjamin L. Grisso, a fellow Michigan Tech Husky, for introducing my wife Tiffany and I to Blacksburg, for your help around the lab and valuable guidance on graduate school, and for your friendship over the years. Thanks to Dr. Onur Bilgen for your invaluable help around the lab in understanding much of our equipment and for your efforts as a lab co-manager. Also, thanks Onur for showing me the wonders of fiberglasssing and vacuum bagging, which allowed for the fabrication of all of my prototype devices. I would like to thank Justin Farmer, who as a fellow student introduced me to the topic of piezoelectric vibration energy harvesting when I first arrived at CIMSS and who now has returned and graciously relieved me of lab management duties, giving me the chance to finish my Ph.D.! Thanks to Jacob Dodson for your help with anything math related, my electromechanical modeling would not have been possible without your help. Also, thanks Jacob for being such a great friend and office mate. Thanks to Na Kong for your help with the electrical side of piezoelectric energy harvesting. Your help in the development of various energy harvesting circuits was critical in my success and resulted in a fruitful collaboration. I would like to thank Amin Karami for your help on both electromechanical modeling as well as our many nice discussions on searching for jobs. Thanks to Dr. Stephen A. Sarles (Andy) for your help in many lab related issues, you are an encyclopedia of knowledge around the lab! Also, thanks Andy for all the advice you have given me in all academic issues from writing and publishing papers to applying for jobs. Thanks to Geoff Tizard for your help in configuring the Instron load frame, all of the static bending tests would not have been possible without your help. Also, thanks to Robert Briggs and John Coggin for your help in performing the experimental flight testing vi in this work. A special thanks is due to Dr. Pablo A. Tarazaga for introducing me to most of the equipment around the CIMSS lab and for teaching me the intricacies of experimental vibration testing. Also, for teaching me the ways as a lab manager. Additionally, I would like to thank Pablo for coaching and inspiring me in both weightlifting and motorcycling. I have many great memories of early mornings in the gym and beautiful summer evenings carving the Blue Ridge mountains on our bikes. Thanks Pablo for being such a great friend! A very special thanks is in order to Dr. Alper Erturk. Alper and I began graduate school together and we have enjoyed a fruitful collaboration from the beginning. Thanks Alper for your countless hours of help in coursework, modeling efforts, and experimental testing. Surly without the help and guidance of Alper, my Ph.D. work would not have been possible. I feel blessed to have been given the opportunity to collaborate with such a brilliant and kind individual. I have many fond memories of late night experimental vibration testing with temperamental laser vibrometers and wonderful philosophical chats about all walks of life. Alper, it has been amazing working with you and I look forward to a long friendship. I would also like to acknowledge a few special friends that I have made along the way. First, I would like to thank Devon Murphy. Devon and I met during the summer of 2006 as students in the Los Alamos Dynamics Summer School at the Los Alamos National Laboratory in New Mexico. We had tons of great experiences during our nine weeks at the lab including hiking to the top of Wheeler Peak, which is the highest point in New Mexico at 13,161 feet! Throughout our time together in grad school, Devon was an amazing friend, always making people laugh. We had tons of great talks about research related topic as well as life in general. Over the years, Devon has become part of my family. Dev, you will always be my brother! Also, I would like to thank Corey Pitchford. I became quite close with Corey during the summer of 2007. . . that is a summer we will never forget! Although our time together in graduate school was short, I have remained good friends with Corey over the years. We have made many trips between Blacksburg and Kingsport, TN, from which endless good memories have been made. Corey is a video game buddy, a golfing buddy, a motorcycling buddy, and if I could ever convince him, a mountain biking buddy (maybe some day!). Corey has been very supportive throughout graduate school, and a friend I can always vii count on. I would like to thank Daniel J. Inman II for being a great friend over the years. I met Daniel when he was in high school and working in the CIMSS lab over the summers. Our relationship has transformed from me bossing Daniel around the lab and making him do all the cleaning and organizing us graduate students think we are too good to do, to Daniel trying to take over my desk in CIMSS now that I am finished! We have become good friends and have had a lot of fun throughout my time in Blacksburg. Daniel has been a great lifting and running partner and I owe a lot to him for keeping me motivated (I think this is a two way street). Also, thanks for allowing me the privilege of kicking your butt in Halo! OK, I suppose you got me a time or two as well. And thanks for making the CIMSS office an awesome place to work. Thanks to Kahlil Detrich, your friendship over the years has been amazing. From killing me out on the hard climbs at Pandapas Pond on our mountain bikes to enjoying good scotch and cigars on a summer night, to cooking great food with friends, we have made many great memories I will never forget. Also, thanks Kahlil for allowing the use of your house during the final experiments in my Masters work! I would also like to thank all of my past and present CIMianSS for making CIMSS such an amazing place to work. The atmosphere in the office and in the lab is one of a kind. Thanks to Dr. Jamil Renno for your guidance on being a graduate student and for introducing me to LATEX 2ε . Thanks also to Dr. Vishnu Baba Sundaresan for the help with LATEX 2ε . Thanks to Austin Creasy for great discussions on raising children. Thanks to Dr. Armaghan Salehian for your help teaching me graduate vibrations. Thanks to Jason Fox, Josh Stenzler, Jacob Davidson, Brad Butrym, Matt Castellucci, Mana Afshari, and Carlos Carvajal for being great friends and for helping me get into trouble during my time at Tech! A very important thanks is due to my family. To my mother and father for raising me and always putting their children first, giving me the opportunity to attend college, supporting me throughout graduate school, and always being there for me to help with any and all aspects of life. None of this would have been possible without your support and belief in me. You are amazing people, amazing parents, and I love you both with all my heart. And thanks to my brother, Chris, for being an inspiration to me and for all of your advice during graduate school. I am blessed to have an older brother to turn to for advice on all facets of life. viii I would like to thank my beautiful daughter, Mia Jane, for bringing endless joy to my life. The look in your eyes and the smile on your face at the end of a day make any bad moments disappear. You have brought a new meaning to life. I love you so much, you stole my heart with your first breath. Finally, and most importantly, I would like to thank my amazing wife, Tiffany, for her unwavering love and support each and every day of my life. You always challenge me to be the best man I can be. The sacrifices you have made in supporting me throughout graduate school are immense, and I look forward to paying them back throughout the rest of our lives. We have accomplished so much since we have been together, from graduating from college, starting graduate school and your teaching career, to getting married, and to starting a family. I look forward to every day we will spend together. You are beautiful inside and out. You are my best friend. I love US. This work has been supported by the U.S. Air Force Office of Scientific Research MURI under grant number F9550-06-1-0326 titled “Energy Harvesting and Storage Systems for Future Air Force Vehicle” monitored by Dr B. L. “Les” Lee. Furthermore, I would like to thank the Department of Mechanical Engineering at Virginia Tech for their support through the Pratt Fellowship as well as the Virginia Space Grant Consortium for their support through the Graduate VSGC Fellowship. S TEVEN R. A NTON ix Contents Abstract ii Dedication iv Acknowledgments v List of Tables xv List of Figures xvi Nomenclature xxii 1 Introduction 1 1.1 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.1.1 Vibration Energy Harvesting using Piezoelectric Materials . . . . . . 3 1.1.2 Multifunctionality in Energy Harvesting Systems . . . . . . . . . . . 10 1.1.3 Piezoelectric Energy Harvesting in Unmanned Aerial Vehicles . . . . 17 Thesis Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 1.2.1 Research Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 1.2.2 Chapter Summaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 1.2 2 Multifunctional Self-Charging Structure Concept and Electromechanical Modeling 2.1 2.2 24 Overview of Piezoelectric Energy Harvesting . . . . . . . . . . . . . . . . . . 25 2.1.1 Introduction to Piezoelectricity . . . . . . . . . . . . . . . . . . . . . . 25 2.1.2 Introduction to Piezoelectric Energy Harvesting . . . . . . . . . . . . 26 Self-Charging Structure Concept . . . . . . . . . . . . . . . . . . . . . . . . . 28 x 2.3 2.4 3 31 2.3.1 Modeling Assumptions and Device Configuration . . . . . . . . . . . 31 2.3.2 Electromechanical Assumed Modes Model . . . . . . . . . . . . . . . 32 2.3.3 Substitution of the Assumed Solution . . . . . . . . . . . . . . . . . . 37 2.3.4 Lagrange Equations with Electromechanical Coupling . . . . . . . . 39 2.3.5 Equivalent Series/Parallel Representation of the Lagrange Equation 41 2.3.6 Solution of the Equivalent Representation of the Lagrange Equations 42 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 Experimental Testing of Self-Charging Structures 46 3.1 Performance Evaluation of Thin-Film Batteries . . . . . . . . . . . . . . . . . 46 3.1.1 Comparison to Conventional Rechargeable Batteries . . . . . . . . . 47 3.1.2 Battery Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 3.1.3 R Performance Testing of Thinergy Batteries . . . . . . . . . . . . . . 50 Device Fabrication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 3.2.1 Selection of Piezoelectric and Substrate Materials . . . . . . . . . . . 53 3.2.2 Vacuum Bonding and Electrode Attachment . . . . . . . . . . . . . . 55 3.2 3.3 3.4 4 Electromechanical Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . Experimental Validation of Electromechanical Model and Self-Charging Concept . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 3.3.1 Electromechanical Model Validation . . . . . . . . . . . . . . . . . . . 58 3.3.2 Self-Charging Structure Concept Validation . . . . . . . . . . . . . . . 65 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 Strength Analysis of Self-Charging Structures 70 4.1 Static Strength Analysis of Self-Charging Structures . . . . . . . . . . . . . . 70 4.1.1 Strength Calculations for 3-Point Bend Testing . . . . . . . . . . . . . 71 4.1.2 Experimental Testing and Results . . . . . . . . . . . . . . . . . . . . 72 Dynamic Strength Analysis of Self-Charging Structures . . . . . . . . . . . . 76 4.2.1 Strength Calculations for Harmonic Base Excitation Testing . . . . . 76 4.2.2 Experimental Testing and Results . . . . . . . . . . . . . . . . . . . . 78 Static Strength Testing of Various Piezoceramic Materials . . . . . . . . . . . 81 4.3.1 Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 4.3.2 Sample Preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 4.2 4.3 xi 4.4 5 4.3.3 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 4.3.4 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 4.3.5 Statistical Analysis of Bending Strength Results . . . . . . . . . . . . 90 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 Performance Modeling of Unmanned Aerial Vehicles with On Board Energy Harvesting 94 5.1 Piezoelectric Energy Harvesting in Unmanned Aerial Vehicles . . . . . . . . 95 5.2 System Level Flight Endurance Model . . . . . . . . . . . . . . . . . . . . . . 96 5.2.1 5.2.2 6 Flight Endurance of an Electric Powered UAV with On Board Energy Harvesting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 Normalized Change in Flight Endurance . . . . . . . . . . . . . . . . 98 5.3 Theoretical Case Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 5.4 Experimental Case Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 5.4.1 EasyGlider Aircraft Configuration . . . . . . . . . . . . . . . . . . . . 105 5.4.2 Flight Testing Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 5.4.3 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 5.5 Flight Endurance Modeling of Self-Charging Structures in UAVs . . . . . . . 110 5.6 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 Electromechanical Modeling of Multifunctional Energy Harvesting Wing Spar for Unmanned Aerial Vehicles 6.1 6.2 6.3 113 Electromechanical Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 6.1.1 Modeling Assumptions and Device Configuration . . . . . . . . . . . 114 6.1.2 Energy Formulations for the Electromechanical Spar . . . . . . . . . 114 6.1.3 Substitution of the Assumed Solution . . . . . . . . . . . . . . . . . . 118 6.1.4 Lagrange Equations with Electromechanical Coupling . . . . . . . . 119 6.1.5 Solution of the Equivalent Representation of the Lagrange Equations 120 Experimental Validation of the Assumed Modes Formulation . . . . . . . . 121 6.2.1 Representative Energy Harvesting Wing Spar Configuration . . . . . 121 6.2.2 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122 6.2.3 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 xii 7 Energy Harvesting Wing Spar for Electric Unmanned Aerial Vehicle 7.1 Design and Fabrication of Multifunctional Composite Wing Spar . . . . . . 130 7.2 Experimental Evaluation of Energy Harvesting/Energy Storage Performance 132 7.3 7.4 8 129 7.2.1 Frequency Response Measurements . . . . . . . . . . . . . . . . . . . 133 7.2.2 Self-Charging Charge/Discharge Measurements . . . . . . . . . . . . 136 Experimental Flight Testing of Self-Charging Fiberglass Wing Spar . . . . . 138 7.3.1 EasyGlider Aircraft Configuration . . . . . . . . . . . . . . . . . . . . 139 7.3.2 Flight Testing Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142 Conclusions and Recommendations 143 8.1 Research Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144 8.2 Contributions of the Research . . . . . . . . . . . . . . . . . . . . . . . . . . . 146 8.3 Recommendations and Future Work . . . . . . . . . . . . . . . . . . . . . . . 147 Bibliography 150 Appendices 166 A Piezoelectric Constitutive Equations 166 A.1 Constitutive Equations for Bulk Monolithic Piezoelectric Material . . . . . . 166 A.2 Alternative Representations of the Constitutive Equations . . . . . . . . . . 167 A.3 Reduced Form of the Constitutive Equations for a Thin Beam Operating in ‘31’ Mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168 B Bending Stiffness and Mass Density Calculations for Composite Cross-Sections 169 B.1 Bending Stiffness Calculation using the Parallel Axis Theorem . . . . . . . . 169 B.2 Self-Charging Structure Sections . . . . . . . . . . . . . . . . . . . . . . . . . 170 B.3 Self-Charging Wing Spar Sections . . . . . . . . . . . . . . . . . . . . . . . . . 172 C Transformation from Relative to Absolute Frame of Reference for Frequency Response Functions 174 D Charge/Discharge Curves for Dynamic Failure Testing xiii 176 E Load-Deflection Curves for all Piezoelectric Samples Tested xiv 188 List of Tables 2.1 Equivalent electromechanical coupling and capacitance terms for series and parallel electrode connections. . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 3.1 Properties of various secondary batteries. . . . . . . . . . . . . . . . . . . . . 48 3.2 Geometric and material properties of self-charging structure components. . 55 3.3 Load resistance values used in FRF measurements of self-charging structures along with effective load resistances. . . . . . . . . . . . . . . . . . . . . 60 4.1 Failure loads for three-point bending tests. . . . . . . . . . . . . . . . . . . . 75 4.2 Failure strengths for three-point bending tests. . . . . . . . . . . . . . . . . . 75 4.3 Physical dimensions of various piezoceramic materials tested. . . . . . . . . 83 4.4 Various test parameters for the piezoelectric materials investigated. . . . . . 86 4.5 Bending strength parameters for all materials tested with 95% confidence interval given in brackets. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 5.1 Physical properties of the EasyGlider aircraft. . . . . . . . . . . . . . . . . . . 102 5.2 Physical properties of the piezoelectric devices considered. . . . . . . . . . . 103 6.1 Load resistance values used in FRF measurements of aluminum spar along with effective load resistances. . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 xv List of Figures 2.1 Schematic of piezoelectric cantilever harvester configuration subject to harmonic base excitation and its voltage output. . . . . . . . . . . . . . . . . . . 27 2.2 Schematic of self-charging structure. . . . . . . . . . . . . . . . . . . . . . . . 29 2.3 Potential use of self-charging structures: Schematic of small UAV with embedded self-charging structures in wing spar used to provide local power for low-power sensor node. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 30 Piezoelectric self-charging structure configurations showing (a) series and (b) parallel connection of the piezoelectric layers along with the (c) crosssectional views of both composite sections. . . . . . . . . . . . . . . . . . . . 32 3.1 R R Photographs of (a) NanoEnergy and (b) Thinergy thin-film batteries. . . 47 3.2 Experimental setup used to obtain charge/discharge measurements on thinfilm batteries. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 3.3 Transimpedance operational amplifier circuit used for current measurement. 51 3.4 R Characteristic (a) charge and (b) discharge curves of Thinergy batteries. . 52 3.5 R QuickPack QP10n piezoelectric device. . . . . . . . . . . . . . . . . . . . . 54 3.6 Schematic of vacuum bagging procedure for self-charging structures. . . . . 56 3.7 (a) Vacuum bagging setup; (b) Gast 23 Series vacuum pump. . . . . . . . . . 56 3.8 Complete self-charging structure prototype. . . . . . . . . . . . . . . . . . . . 57 3.9 Experimental setup used to obtain frequency response measurements of self-charging structures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 3.10 Experimental and numerical (a) voltage - to - base acceleration FRFs and (b) tip velocity - to - base acceleration FRFs of self-charging structure for series electrode connection case and for various load resistances. . . . . . . . . . . xvi 61 3.11 Experimental and numerical (a) tip velocity - to - base acceleration FRFs and (b) voltage - to - base acceleration FRFs of self-charging structure for parallel electrode connection case and for various load resistances. . . . . . . . . . . 62 3.12 Linear voltage regulator energy harvesting circuit. . . . . . . . . . . . . . . . 63 3.13 Experimental and numerical electrical performance curves of self-charging structure for the peak voltage output in the (a) series and (b) parallel case, current output in the (c) series and (d) parallel case, and power output in the (e) series and (f) parallel case with varying load resistance for the selfcharging structure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 3.14 Experimental setup used to obtain charge/discharge measurements of selfcharging structures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 3.15 Experimental curves for self-charging structures in (a) charging and (b) discharging under ±1.0 g acceleration at 210.0 Hz. . . . . . . . . . . . . . . . . . 67 4.1 Schematic of three-point bending test. . . . . . . . . . . . . . . . . . . . . . . 71 4.2 Experimental setup used for three-point bend testing including Instron/ MTS 4204 test frame and fixture. . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 72 R Various specimens after three-point failure testing including (a) Thinergy R battery, (b) QuickPack QP10n piezoelectric, (c) aluminum substrate, (d) root section of complete self-charging structure, and (e) tip section of complete self-charging structure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4 Load-deflection curves for (a) individual layers and (b) complete self-charging structure sections. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5 80 Optical microscope image of PMN-PZT sample after dicing showing width measurement (5X objective lens). . . . . . . . . . . . . . . . . . . . . . . . . . 4.8 78 Charge/discharge capacities measured for (a) power supply and (b) piezoelectric charging for dynamic failure analysis of self-charging structures. . . 4.7 74 Estimates of the maximum dynamic bending stress in the aluminum, piezoceramic, and battery layers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.6 73 84 Optical microscope images of (a) PMN-PZT and (b) PZT-5H samples showing flaw sizes (20X objective lens). . . . . . . . . . . . . . . . . . . . . . . . . xvii 84 4.9 Diced piezoelectric samples prepared for bending tests including (a) PZT5H, (b) PZT-5A, (c) PZT-8, (d) PZT-4, (e) PMN-PZT, (f) PMN-PT, (g) QP10n, and (h) QP16n. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 4.10 Three-point bend testing experimental setup including (a) Instron 5848 MicroTester frame and (b) fixture. . . . . . . . . . . . . . . . . . . . . . . . . . . 86 4.11 Load-deflection curves for (a) thin samples (PZT-5A, PZT-5H, PMN-PT, PMNPZT, and QP10n) and (b) thick samples (PZT-4 and PZT-8). . . . . . . . . . . 87 4.12 Bending strength values calculated for various piezoelectric materials tested. 88 4.13 Bending strength statistical comparison for all materials tested with error bars representing 95% confidence interval. . . . . . . . . . . . . . . . . . . . 91 5.1 Multiplex USA EasyGlider remote control aircraft test platform. . . . . . . . 101 5.2 Piezoelectric devices including (a) M8507-P1 Macro-Fiber Composite, and (b) Piezoelectric Fiber Composite. . . . . . . . . . . . . . . . . . . . . . . . . . 102 5.3 Simulation results for normalized change in flight time of the EasyGlider aircraft based on the addition of piezoelectric harvesting with varying degrees of multifunctionality. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 5.4 Fiberglass wing spar with (a) surface mounted Macro-Fiber Composite and Piezoelectric Fiber Composite devices (b) inserted in wing. . . . . . . . . . . 106 5.5 XR5-SE-M-50mv voltage data logger shown (a) installed into cockpit of EasyGlider and (b) with fiberglass canopy installed. . . . . . . . . . . . . . . . . . . . . . 106 5.6 UA-004-64 accelerometer data logger shown (a) installed on the underside of the EasyGlider and (b) with fiberglass canopy installed. . . . . . . . . . . 107 5.7 Acceleration measurements recorded during flight in the (a) x-axis, (b) yaxis, and (c) z-axis directions. . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 5.8 Voltage measurements recorded during flight for (a) MFC and (b) PFC piezoelectric devices. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 5.9 Updated simulation results for normalized change in flight time of the EasyGlider aircraft based on the addition of piezoelectric harvesting with varying degrees of multifunctionality. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 5.10 Simulation results for normalized change in flight time of the EasyGlider aircraft based on the addition of self-charging structures. . . . . . . . . . . . 111 xviii 6.1 Multifunctional piezoelectric energy harvesting wing spar configurations showing (a) series and (b) parallel connection of the piezoelectric layers along with the (c) cross-sectional views of both composite sections. . . . . . 115 6.2 Representative aluminum wing spar with embedded self-charging structure. 121 6.3 Experimental setup used to obtain frequency response measurements of the aluminum wing spar. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122 6.4 Experimental and numerical (a) voltage - to - base acceleration FRFs and (b) tip velocity - to - base acceleration FRFs of the aluminum wing spar for series electrode connection case for various load resistances. . . . . . . . . . 124 6.5 Experimental and numerical (a) voltage - to - base acceleration FRFs and (b) tip velocity - to - base acceleration FRFs of the aluminum wing spar for parallel electrode connection case for various load resistances. . . . . . . . . 125 6.6 Experimental and numerical electrical performance curves of aluminum wing spar for the peak voltage output in the (a) series and (b) parallel case, current output in the (c) series and (d) parallel case, and power output in the (e) series and (f) parallel case with varying load resistance. . . . . . . . . . . 127 7.1 Fiberglass wing spar schematic showing foam core with fiberglass layers and embedded self-charging structures. . . . . . . . . . . . . . . . . . . . . . 130 7.2 Schematic of vacuum bagging procedure for fiberglass wing spar fabrication. 132 7.3 Photographs of fiberglass wing spar curing under vacuum. . . . . . . . . . . 132 7.4 Complete self-charging fiberglass wing spar. . . . . . . . . . . . . . . . . . . 133 7.5 Experimental setup used to obtain frequency response measurements of fiberglass wing spar. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 7.6 Frequency response functions of fiberglass wing spar (series electrode connection, 1 MΩ load) showing (a) broad spectrum and (b) detail near the fundamental resonance frequency. . . . . . . . . . . . . . . . . . . . . . . . . 135 7.7 Experimental setup used to obtain charge/discharge measurements of selfcharging fiberglass wing spar. . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 7.8 Experimental curves for fiberglass wing spar in (a) charging and (b) discharging under ±0.5 g acceleration at 43.5 Hz. . . . . . . . . . . . . . . . . . 138 7.9 Self-charging fiberglass wing spar inserted into EasyGlider aircraft wings. . 139 xix 7.10 Photograph of EasyGlider aircraft during flight testing of multifunctional fiberglass wing spar. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 7.11 Flight testing results of fiberglass self-charing spar showing (a) voltage output of piezoelectric device and (b) z-axis acceleration. . . . . . . . . . . . . . 141 B.1 Rigid body with neutral axis x0 . . . . . . . . . . . . . . . . . . . . . . . . . . . 169 B.2 Cross-sectional views of the two composite sections of the self-charging structure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170 B.3 Cross-sectional views of the two composite sections of the self-charging wing spar. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172 D.1 Power supply charge and discharge curves for excitation at (a-b) ±0.2 g and (c-d) ±0.4 g. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176 D.2 Power supply charge and discharge curves for excitation at (a-b) ±0.6 g, (cd) ±0.8 g, and (e-f) ±1.0 g. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177 D.3 Power supply charge and discharge curves for excitation at (a-b) ±1.5 g, (cd) ±2.0 g, and (e-f) ±2.5 g. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178 D.4 Power supply charge and discharge curves for excitation at (a-b) ±3.0 g, (cd) ±3.5 g, and (e-f) ±4.0 g. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179 D.5 Power supply charge and discharge curves for excitation at (a-b) ±4.5 g, (cd) ±5.0 g, and (e-f) ±5.5 g. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180 D.6 Power supply charge and discharge curves for excitation at (a-b) ±6.0 g, (cd) ±6.5 g, and (e-f) ±7.0 g. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181 D.7 Piezoelectric charge and discharge curves for excitation at (a-b) ±0.2 g, (c-d) ±0.4 g, and (e-f) ±0.6 g. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182 D.8 Piezoelectric charge and discharge curves for excitation at (a-b) ±0.8 g, (c-d) ±1.0 g, and (e-f) ±1.5 g. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183 D.9 Piezoelectric charge and discharge curves for excitation at (a-b) ±2.0 g, (c-d) ±2.5 g, and (e-f) ±3.0 g. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184 D.10 Piezoelectric charge and discharge curves for excitation at (a-b) ±3.5 g, (c-d) ±4.0 g, and (e-f) ±4.5 g. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 D.11 Piezoelectric charge and discharge curves for excitation at (a-b) ±5.0 g, (c-d) ±5.5 g, and (e-f) ±6.0 g. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186 xx D.12 Piezoelectric charge and discharge curves for excitation at (a-b) ±6.5 g and (c-d) ±7.0 g. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187 E.1 Load-deflection curves for PZT-5A samples. . . . . . . . . . . . . . . . . . . . 188 E.2 Load-deflection curves for (a) PZT-5H, (b) PZT-4, and (c) PZT-8 samples. . . 189 E.3 Load-deflection curves for (a) PMN-PT, (b) PMN-PZT, and (c) QP10n samples.190 xxi Nomenclature A area ab base acceleration b width C damping matrix C battery capacity CD coefficient of drag CL coefficient of lift Cp capacitance cE 11 elastic modulus at constant electric field D electric displacement, also drag force d31 piezoelectric strain constant E electric field Eb battery energy e31 piezoelectric stress constant eb battery specific energy f forcing function G shear modulus g acceleration of gravity H Heaviside function h thickness I mass moment of inertia i current, also index Jp piezoelectric coupling term xxii j unit imaginary number K stiffness matrix L length, also lift force l index M mass matrix M lumped mass Mf failure bending moment m Weibull modulus N number of modes P power Pf failure load Q electric charge R resistance r index S strain, also wing area s crosshead feed rate sE 11 elastic compliance at constant electric field T stress, also kinetic energy, also thrust t time U potential energy Vabs absolute beam velocity V volume V∞ aircraft velocity v voltage W weight Wie internal electrical energy Wnce work of non-conservative forces wabs absolute displacement wb base displacement wrel relative displacement x spatial coordinate Y elastic modulus xxiii z spatial coordinate α proportional damping constant β proportional damping constant δ Dirac delta function ε strain rate εS33 dielectric permittivity at zero strain η generalized coordinate ηb battery energy extraction efficiency factor ηp motor and propeller efficiency factor θ electromechanical coupling term ν Poisson’s ratio ρ mass density ρ∞ air density σb bending strength σθ Weibull characteristic strength φ admissible function ψ aerodynamic constant ω frequency Subscripts b battery layer cr critical layer e epoxy layer k Kapton layer l lower layer p piezoelectric layer s structure layer u upper layer Superscripts xxiv E property measured at constant electric field eq equivalent representation p parallel electrode connection S property measured at zero mechanical strain s series electrode connection T matrix transpose, also property measured at zero mechanical stress xxv C HAPTER 1 I NTRODUCTION W ITH recent growth in the development of low-power electronic devices such as mi- croelectronics and wireless sensor nodes, as well as the global interest in the con- cept of “green” engineering, the topic of energy harvesting has received much attention in the past decade. The energy requirements of low-power electronics have steadily decreased with advancements in efficient circuitry such that energy harvesting systems can be considered feasible solutions in providing power to self-powered systems. Conventional low-power electronics, such as wireless sensor nodes, rely on batteries to provide power to the device. The use of batteries, however, presents several drawbacks including the cost of battery replacement as well as limitations imposed by the need of convenient access to the device for battery replacement purposes. Wireless sensor nodes, for example, are often used in remote locations or embedded into a structure, therefore, access to the device can be difficult or impossible. By scavenging ambient energy surrounding an electronic device, energy harvesting solutions have the ability to provide permanent power sources that do not require periodic replacement. Such systems can operate in an autonomous, self-powered manner, reducing the costs associated with battery replacement, and can easily be placed in remote locations or embedded into host structures. Energy harvesting is the process of converting available ambient energy into usable electrical energy through the use of a particular material or transduction mechanism. Several classes of material exist with various conversion mechanisms that can be used to harvest energy. Some of the common materials include those with photovoltaic coupling to convert solar energy to electric energy, thermoelectric coupling to convert temperature gradients into electrical energy, and electromechanical coupling to convert mechanical vibration energy into electrical energy. Of the various modes of energy harvesting, vibration energy harvesting is the most versatile technique being developed in the litera- 1 ture. Three main mechanisms of vibration-to-electrical energy conversion exist including electrostatic, electromagnetic, and piezoelectric transduction. Review articles highlighting work performed on all of the transduction mechanisms are given by Beeby et al. [1] and Cook-Chennault et al. [2]. Of the three modes of vibration harvesting, piezoelectric energy harvesting has received the most attention, with three review articles dedicated to recent research on piezoelectric transduction [3–5]. Piezoelectric vibration harvesting is attractive mainly due to the simplicity of piezoelectric transduction and the relative ease of implementation of piezoelectric systems into a wide variety of applications as compared to electrostatic or electromagnetic methods [6, 7]. Unlike electrostatic transduction, which requires the application of an initial voltage to produce usable energy, piezoelectric material inherently generates a direct voltage when strained. Additionally, where electromagnetic harvesting systems become increasingly difficult to fabricate at the micro-scale and electrostatic systems are generally restricted to the micro-scale, piezoelectric materials can easily be fabricated as bulk materials at the macroscale or deposited as thin-films at the micro-scale. Despite these advantages, piezoelectric harvesting does suffer from the large mass density of piezoceramic materials and, like all vibration harvesting techniques, the intrusiveness that an added harvesting system has on a host structure. In an effort to increase the usefulness of various material systems, researchers have begun to investigate the concept of multifunctionality, which has been reviewed by Christodoulou and Venables [8] for several different multifunctional material systems. Piezoelectric energy harvesting can benefit from a multifunctional approach by combining several functions into a single device, such as energy harvesting, energy storage, and structural load bearing ability, that when combined with a host structure can provide a more synergistic and efficient overall system. The introduction of multifunctionality into energy harvesting systems holds promise to increase their utility and practicality, and promote the integration of harvesting systems into many engineering applications. 1.1 Literature Review The following presents a literature review of the past research performed in the areas of piezoelectric energy harvesting and multifunctionality in energy harvesting systems. Additionally, previous studies involving energy harvesting in unmanned vehicle systems are 2 also reviewed as multifunctional harvesting in an unmanned aerial vehicle is investigated as a case study in this dissertation. 1.1.1 Vibration Energy Harvesting using Piezoelectric Materials Perhaps one of the first suggested applications involving vibration energy harvesting using piezoelectric materials was presented by Wen H. Ko in a 1969 US patent titled “Piezoelectric Energy Converter for Electronic Implants” [9] in which the use of a cantilever piezoelectric beam with a tip mass is proposed for harvesting energy from heartbeats for use in powering implanted medical pacemakers. One of the earliest published works in vibration energy harvesting with piezoelectric materials was presented by Taylor and Burns [10] in 1983 in which they proposed the use of an array of polyvinylidene flouride (PVDF) piezoelectric polymer film to harvest hydrodynamic energy from ocean waves. Although no physical system was proposed or built, it was theorized that a 100 MW power plant utilizing PVDF could deliver power to an onshore grid at a cost of 2.5 cents per kWH. The following year, Hausler et al. [11] performed what appears to be the first experimental study using piezoelectric materials to harvest energy. They proposed the use of a PVDF film as an implantable power source in a biological system. A prototype device was fabricated and implanted in vivo into the ribcage of a dog to harvest energy available from the relative motion of the ribs during breathing. Experimental testing showed that the PVDF harvester could generate a peak voltage of 18 V, corresponding to about 17 µW of power, which was short of the predicted 1 mW goal. Three years later in 1987, Hausler and Stein [12] published a work in which PVDF film was again proposed for use in harvesting energy from ocean waves. A theoretical system was proposed in which one end of a PVDF ‘rope’ is attached to the sea floor and the other end to a float located at the surface of the sea. Relative motion between the float and the sea floor allows the PVDF rope to be stretched, thus generating electrical energy. It was suggested that the system would be well suited to provide power to warning or measurement buoys, with 20 kg of PVDF capable of generating around 100 W of power. Similar to the work of Hausler et al., Schmidt [13], in 1992, also explored the idea of harvesting energy using PVDF film, but in windmill applications. As a means of reducing the danger associated with conventional windmills containing large rotating blades, three independent piezoelectric windmill designs oscillating at high frequency with small 3 amplitude were considered. Experimental testing of each windmill design showed power levels in the microwatt to milliwatt range. The low power output and high costs of such piezoelectric wind generators led to the conclusion that significant improvements to the windmill design and reductions in cost of PVDF film were required in order to produce practical piezoelectric windmills. In the mid 1990’s, several researchers returned to the idea of harvesting energy in biological systems, specifically from human body motion. In 1995, Antaki et al. [14] published the first work on harvesting energy from the human body using piezoelectric material by embedding piezoceramic stacks into the sole of a shoe to scavenge energy during walking and running. The goal of the work was to investigate energy harvesting solutions for providing power to electrically powered artificial organs. The design of the shoe harvester focused on maximum energy transfer to the piezoelectric stacks during the heel-strike and toe-off portions of gait, while retaining the ergonomics of the shoe. A hydraulic oscillator was designed to increase the excitation frequency by exciting the stack harmonically during each step to increase the amount of strain induced in the piezoelectrics. Laboratory simulation experiments on a 1/17 scale harvester yielded peak power outputs ranging from 150 mW to 2.5 W depending upon body mass and gait. Several researchers from the MIT Media Lab also investigated piezoelectric harvesting from human body motion during the same time period. In 1996, Starner [15] published an article outlining the energy expended during various daily activities including walking, breathing, and finger and upper limb motion, as well as the energy available from body heat and blood pressure. It was proposed that the energy scavenged from the body could be used to power wearable computing devices. Several of the sources produced relatively low amounts of available energy (<1.0 W) including breating, finger motion, and blood pressure. Of the higher energy sources including body heat, walking, and upper limb motion, walking was determined to hold the most potential for a practical harvesting system. Two forms of harvesting during walking were discussed including the integration of a conventional rotary electromagnetic generator into a shoe as well as the concept of embedding piezoceramic devices into the sole of a shoe. Following the work of Starner [15], Kymissis [16] further explored the concept of harvesting energy in shoes by fabricating and experimentally testing both piezoelectric and electromagnetic harvester designs. Three designs were investigated, two piezoelectric systems including a PVDF device installed in the toe 4 area of a shoe and a lead zirconate titanate (PZT) ceramic device installed in the heel, as well as an electromagnetic generator attached to the outer heel. Although experimental results show that the electromagnetic generator was capable of harvesting two orders of magnitude more energy than the piezoelectric designs, the obtrusiveness of the generator limits the practical implementation of the design. The piezoelectric prototypes, on the other hand, were easily integrated into the shoe and were capable of harvesting around 1-2 mW of energy. Further details of the work on integrating piezoelectric harvesting into shoes are provided in the Masters Thesis of Shenck [17] of the MIT Media Lab. Also in the mid 1990’s, work was performed by Umeda et al. [18, 19] to explore the fundamentals of impact energy conversion using piezoelectric materials. Umeda et al. [18] first developed an equivalent circuit model to predict the response of a piezoelectric vibrator plate when impacted with a steel ball. Simulation results showed that an optimal load resistance exists for maximum power transfer from the piezoelectric layers, and that much of the potential energy from the steel ball is transfered back to the ball when rebounding off of the vibrator plate, thus decreasing the efficiency of energy conversion. The following year, Umeda et al. [19] performed an experimental study to validate their previously developed model, and also included rectification and storage of the electrical output of the piezoelectric vibrator via a bridge rectifier and storage capacitor. Results of the experimental testing showed the ability of the piezoelectric vibrator to charge the storage capacitor using impact energy, and that for a capacitor pre-charged above 5 V, an efficiency of 35% was achieved. In 1999, Goldfarb and Jones [20] performed research to investigate the efficiency of energy conversion using piezoelectric ceramics. Specifically, a piezoelectric stack consisting of several piezoceramic discs arranged mechanically in series and electrically in parallel was investigated both analytically and experimentally. Results of the study suggest that the major challenge in harvesting mechanical energy using piezoceramic material is that a majority of the mechanical input energy is stored in the piezoelectric and returned back to the excitation source as mechanical energy. Additionally, results showed that maximum conversion efficiency occurs at very low excitation frequencies, several orders of magnitude less than the resonance frequency of the stack. At the start of the 21st century, a surge of research involving piezoelectric energy harvesting occurred. Since the year 2000, hundreds of papers have been published explor5 ing various aspects of vibration energy harvesting using piezoelectric materials including the development of electromechanical models of piezoelectric harvesters, the efficiency of various piezoelectric materials and harvester configurations, energy harvesting circuitry, and various harvesting applications including microelectromechanical systems (MEMS), self-powered sensors, and biological systems. Several articles highlighting the work in piezoelectric energy harvesting in the last 10 years are reviewed in the following. An incessant interest has been placed by the research community on the development of electromechanically coupled models that can predict the behavior of a piezoelectric energy harvesting system with increasing accuracy. Many of the early modeling efforts utilized a simple model of an electromagnetic harvester developed by Williams and Yates [21] in 1996. The model was developed to describe electromagnetic harvesting, therefore, its use is highly inaccurate in modeling piezoelectric transduction. To improve upon the existing models, Roundy and Wright [22] and duToit et al. [23] both presented single-degree-offreedom (SDOF) lumped parameter models of piezoelectric energy harvesters. Although the lumped-parameter solution showed improvement over the Williams and Yates model [21], it is limited to describing a single vibration mode and lacks much of the information necessary to accurately describe the coupled system. In an effort to further refine the piezoelectric harvester models, discrete Rayleigh-Ritz formulations (originally develped by Hagood et al. [24] for piezoelectric actuation) were developed for Euler-Bernoulli cantilever beam harvesters by Sodano et al. [25] and duToit et al. [23, 26] and later improved upon by Elvin and Elvin [27]. The Rayleigh-Ritz formulation provides a discretized approximation (having finite degrees of freedom) of the distributed parameter system and yields more accurate approximations than SDOF models. More recently, Erturk and Inman [28, 29] have presented the exact electromechanical solution of a cantilever piezoelectric energy harvester under harmonic base excitation based on Euler-Bernoulli beam assumptions. The exact analytical solution provides the most accurate model of cantilevered piezoelectric vibration energy harvesting. Additionally, Erturk and Inman [30–32] have also presented improved approximate distributed parameter modeling of piezoelectric energy harvester beams that can be used to model nonuniform beams where an exact solution does not exist. Significant interest has also been placed on improving the efficiency and practicality of piezoelectric harvesting through the investigation of various piezoelectric materials as well 6 as physical configurations of vibration energy harvesters. The most common material used in piezoelectric energy harvesting is lead zirconate titanate (PZT), which is a piezoelectric ceramic. Although widely used in energy harvesting applications, PZT is extremely brittle, causing limitations in the strain that can be applied to the material without causing damage. For this reason, researchers have investigated other, more flexible materials for vibration harvesting. Sodano et al. [33, 34] compared the energy harvesting performance of monolithic piezoceramic to more flexible piezoelectric composite and fiber-based deR vices including Macro Fiber Composites (MFCs) and QuickPack actuators. Lee et al. [35] and Tylor et al. [36] both explored the use of PVDF film for energy harvesting applications. In general, piezoelectric ceramic devices exhibit large electromechanical coupling but are susceptible to brittle failure, where more flexible devices have lower coupling but increased compliance allowing for use in a wider range of potential applications. Research has also been performed to investigate different physical configurations to improve the usefulness of energy harvesters. Ng and Lio [37] presented a study in which they compared the performance of a unimorph cantilever harvester to two bimorph cantilever harvesters, one with the piezoelectric elements connected in series, the other in parallel. They found that each configuration provides optimal performance under a different excitation level, thus all configurations are useful. Mateu and Moll [38] performed a similar study in which they compared a unimorph harvester to two bimorphs, one with a substrate layer, the other without. They also compared a conventional rectangular cantilever configuration to a triangular cantilever and found that the triangular harvester is capable of obtaining higher strains and providing larger power outputs. Kim et al. [39] developed a piezoelectric “cymbal” harvester design which is capable of withstanding large loads while evenly distributing stress in the piezoelectric layers. Platt et al. [40] compared the performance of a piezoceramic stack against a monolithic piezoceramic device of the same geometry, finding that the two devices gave around the same power output, but the matched load resistance is much lower and more manageable for the stack configuration. Studies have also explored the ability to exploit nonlinear phenomenon to create novel energy harvesting configurations. Erturk et al. [41], Barton et al. [42], and Stanton et al. [43] have all investigated the use of a bistable nonlinear magnetoelastic oscillator for energy harvesting purposes where permanent magnets provide attractive and repulsive forces causing nonlinear response in a cantilever beam. The investigations found that nonlinear 7 phenomenon allow for resonance behavior over a broad frequency range, improving upon the limitations of linear systems that suffer from performance loss when excited away from resonance. The development of efficient circuits for energy harvesting applications has captured the interest of numerous researchers in the field of piezoelectric energy harvesting. A key element of any energy harvesting system is an electrical circuit that can condition and store the harvested energy in an efficient manner. Some of the original work on adaptive and efficient energy harvesting circuits for piezoelectric harvesting was performed by Ottman, Hofmann, and Lesiuetre [44–46]. Their work involves improving the efficiency of energy extraction through implementation of a switching DC-DC step-down converter after the conventional bridge rectifier and smoothing capacitor. They found that the optimal duty cycle of the switching converter changes significantly with excitation frequency. Lefeuvre et al. [47] later developed the concept of ‘synchronous electric charge extraction,’ a self-adaptive circuitry in which extraction of the electric charge on a piezoelectric device is synchronized with the system vibration in order to improve the efficiency of energy transfer. The circuit contains a diode bridge rectifier and a flyback switching mode DCDC converter. In similar studies, Badel et al. [48], Guyomar et al. [49], and Lefeuvre et al. [50] developed another synchronous technique called ‘synchronous switch harvesting on inductor’ (SSHI), which contains an electronic switching device that is triggered on the maximum and minimum displacements of the piezoelectric device. The switching device and an inductor in series are placed either in series or in parallel with the piezoelectric before the rectifying diode bridge. More recently, Kong et al. [51] created a nonlinear impedance matching switching circuit that improves upon the circuit developed by Ottman, Hofmann, and Lesiuetre [44–46] by eliminating some bulky components and providing both step-up and step-down ability by using a buck-boost converter operating in discontinuous conduction mode. In addition to circuits being used to transfer energy between a piezoelectric harvester and a load, electronic circuits have also been developed to help optimize energy transfer via frequency tuning. For example, Lallart et al. [52] developed a low-cost self-tuning technique containing both automatic frequency detection and actuation in which a stiffness tuning technique is employed to alter the natural frequency of a cantilever piezoelectric harvester to match the source vibration. With decreases in the energy consumption of electronic devices, researchers are contin8 ually developing novel applications where piezoelectric energy harvesting can be used as a power source, including MEMS, self-powered sensors, biological systems and unmanned vehicles. Early work in piezoelectric harvesting for MEMS devices focused on cantilever designs with similar aspect ratios to conventional macro-scale devices. Lu et al. [53] and Jeon et al. [54] both fabricated and tested cantilever piezoelectric harvesters on the order of 1 - 5 mm long and found resonant frequencies in the kHz range. The disadvantage of these early designs is the impractically high resonance frequency. More recent research in MEMS harvesting has focused on the development of novel geometries in an effort to reduce the natural frequency to a practical level. Karami and Inman [55], for example, have developed a “zig-zag” geometry that is capable of natural frequencies on the order of hundreds of Hz for a device approximately 1 cm x 1 cm in size. An attractive application of piezoelectric energy harvesting is in the development of self-powered sensors that would otherwise depend on batteries as a source of power. Elvin et al. [56, 57] developed self-powered sensor systems consisting of PVDF film used for both strain sensing and damage detection purposes as well as energy harvesting to provide power to the systems. Through experimental testing, it was found that the PVDF generator produced enough energy to allow radio frequency transmission of strain values to a receiver. Roundy and Wright [22] created a small piezoelectric cantilever generator with a volume of around 1 cm3 that was capable of generating around 400 µW and powering a custom radio transmitter. Recently, Zhou et al. [58] developed a self-powered wireless structural health monitoring (SHM) system. The sensor node uses a cantilever piezoelectric device to harvest vibration energy and a microcontroller along with a surface mounted piezoelectric device to perform impedance-based SHM. When experimentally tested, the energy harvesting system was capable of generating around 3 mW of power, sufficient to run the SHM device once every two minutes. Several studies have investigated the use of piezoelectric materials for harvesting energy in biological applications. Platt et al. [40, 59] developed an in vivo piezoelectric harvester and sensor to be used in self-powered total knee replacement units. The piezoelectric stacks installed in the unit are capable of sensing important phenomena in the knee such as joint degradation and misalignment, and also harvesting adequate power for the sensing circuity to operate and transmit data. Sohn et al. [60] investigated the use of PVDF film for harvesting energy from fluctuating pressure sources such as blood 9 flow. Experimental testing of a prototype harvester found that when subjected to pressures similar to human blood pressure, the device was capable of harvesting enough energy to power a chip that could transmit data, such as DNA information, twice a day. Qi et al. [61] performed research on a novel concept of integrating piezoelectric ceramic materials onto stretchable, biocompatible rubber for use in implantable energy harvesting systems. Unlike PVDF film, the piezoelectric rubber composites contain PZT which exhibits high coupling, yet the composite retains flexibility. Although still in the concept phase, it is suggested that this novel technology be used in biological applications as an implantable power source. Over the past decade, a vast amount of research has been performed on the topic of vibration energy harvesting using piezoelectric materials. An overview of some of the pertinent studies has been presented in this section. For a comprehensive review of the previous literature on piezoelectric energy harvesting, the reader is referred to the various review articles published on the topic. Sodano et al. [3] first published a review article in 2004 highlighting the previous literature on piezoelectric vibration harvesting. In 2006, Beeby et al. [1] published a review article highlighting previous works on piezoelectric, electrostatic, and electromagnetic harvesting for micro-scale applications. The next year, two review articles appeared. Priya [5] provided an overview of vibration harvesting using piezoelectrics, and Anton and Sodano [4] published a review of piezoelectric energy harvesting from 2003-2006 as an update to the previous work by Sodano et al. [3]. Finally, in 2008, Cook-Chennault et al. [2] provided an overview of various energy harvesting sources for MEMS applications including solar harvesting, thermal harvesting, and vibration harvesting using electrostatic, electromagnetic, and piezoelectric devices. 1.1.2 Multifunctionality in Energy Harvesting Systems Conventional works on piezoelectric energy harvesting, such as those described in the previous section, consider the harvesting device to simply attach to a host structure with the sole purpose of harvesting energy. Although useful in many applications, this conventional approach for energy harvesting design is not always practical. Host structures that are mass or volume critical, for example, may be intolerant to the addition of a bulky energy harvester not originally included in the design of the structure. In order to address this issue, a multifunctional approach can be considered for vibration energy harvesting 10 systems. The concept of multifunctionality aims to combine several functions into a single material or device as a means of improving usefulness and optimizing the use of space and weight. Multifunctional material systems have been of interest to the research community for the past decade, and several approaches have been explored in the development of multifunctional structures. Christodoulou and Venables [8] give a review of some of the earlier efforts in multifunctional structures in which details are given on the development of structural power material systems, autonomous sensing and actuating material systems, electromagnetic multifunctional material systems, and survivable, damage-tolerant material systems. The goal of these various technologies is to integrate multiple features into material systems to enable novel design concepts otherwise not achievable. A second review has been published by Aglietti [62] in which several multifunctional structures for use in spacecraft and satellite applications have been outlined. Of the four different classes of multifunctional material systems discussed by Christodoulou and Venables [8], structural power systems, which integrate structural function with energy storage ability, are of most interest for energy harvesting applications. Some of the original work on structural power systems involved the development of stiff, lightweight structures with embedded batteries to store energy for use in spacecraft applications. In 1998, Lyman and Feaver [63] of Boundless Corp. introduced the PowerCoreTM device which utilizes nickel-metal hydride (NiMH) rechargeable batteries as the core of a honeycomb composite structure for use in satellites. The battery core of the PowerCoreTM device is fabricated from nickel foam with sintered active electrode materials, and the assembled core is sandwiched between face sheets to form the composite panel. An effective specific energy greater than 80 Wh/kg was reported for fabricated samples, however, challenges involved with the development of large-scale devices were reported. Similar devices have been reported in the literature in more recent years that make use of more efficient lithium battery technology for energy storage in the core of honeycomb structures. In 2002, Marcelli et al. [64] of ITN Energy Systems, Inc. described their LiBaCore device which contains thin-film lithium batteries embedded into the core layers of a conventional aluminum honeycomb composite. Thin-film lithium batteries offer superior performance over the NiMH batteries used by Lyman and Feaver [63], and it was reported that an optimized design could yield specific energy on the order of 350 Wh/kg. Fabrication of the LiBaCore devices, however, showed that deposition of thin-film lithium batteries onto an aluminum 11 core proved difficult. Initial studies on structure power honeycomb materials have focused on the energy storage aspect of the design. More recently, however, Schwingshackl et al. [65, 66] have investigated the structural properties and dynamic response of honeycomb structures with integrated batteries. Schwingshackl et al. [65] first analytically explored ten different honeycomb or corrugated core style composite designs containing embedded batteries in the core structure and an optimal design was selected. Results of the analytical study and finite element simulations showed that the multifunctional design with integrated energy storage provided similar dynamic behavior compared to conventional honeycomb core sandwich panels. In a continuation study, Schwingshackl et al. [66] fabricated and experimentally tested the optimal design found previously [65], and showed that the multifunctional structure again exhibited similar dynamic response compared to a conventional design, but with the added functionality of energy storage. In an effort to introduce multifunctional structures into unmanned vehicle systems, Thomas and Qidwai [67–72] of the Naval Research Laboratory have investigated the concept of the ‘structure-battery.’ In 2002, Thomas and Qidwai [67] first introduced the concept of the multifunctional structure-battery in which polymer-lithium ion battery layers are used to both store energy and support aerodynamic loads in an unmanned aerial vehicle (UAV) system. Formulations for the change in flight endurance of a UAV with an integrated structure-battery considering changes in the battery mass, structure mass, and available energy from the battery were given. Design indices were derived as a metric for ranking different multifunctional composite designs based on both the system-level performance of the device as well as the constituent properties and geometry of the components. The design and fabrication of structural batteries consisting of polymer-lithium ion battery cells, packaging materials, and optional structural additives was outlined. Finally, the Black-Widow flying-wing UAV developed by AeroVironment, Inc. was investigated in this study and it was proposed to replace the original primary (non-rechargeable) battery with multifunctional structural batteries installed in the wings of the aircraft. Preliminary battery testing and fabrication of embedded batteries was performed, however, no flight testing occurred. The design indices introduced in [67] were further developed by Thomas and Qidwai in [68]. In a subsequent study, Thomas and Qidwai [69] investigated the use of structure-batteries in the WASP flying-wing UAV, also developed by AeroVironment, Inc. Several designs were considered using various structural additives 12 and multiple polymer-lithium ion batteries. Additionally, the shear strength of several polymer-lithium ion batteries was obtained experimentally as a means of quantifying the load bearing ability of the batteries. Preliminary analysis and flight testing showed that the multifunctional design with integrated structure-batteries is capable of outperforming the conventional non-multifunctional design. More recently, Thomas and Qidwai [70–72] have investigated the use of structurebatteries in unmanned underwater vehicles (UUVs). Qidwai et al. [70] first described the concept of integrating multifunctionality into UUVs by replacing existing conventional batteries with structure-batteries and relocating them into the skin or hull of the vehicle to reduce mass and make additional space available within the vehicle. The design and fabrication of structure-batteries specifically developed for marine systems, containing lithium-ion batteries embedded within fiber-reinforced polymer layers, was outlined, and three unique multifunctional designs were produced. Continuing the work, Rohatgi et al. [71] presented the experimental evaluation of the three fabricated structure-batteries. The multifunctional composites were tested both mechanically via static three-point bend testing, and electrically through charge/discharge cycling of the battery layers. Experimental results showed successful integration of the polymer-battery layers into the fiberreinforced structural layers. In their latest work, Qidwai et al. [72] investigated the electrical performance of the various structure-battery designs while under load. Both static three-point bend testing and hydrostatic loading were considered. Load-deflection measurements during three-point bend testing show that slight thickness changes are observed and reflected in the load data when charge cycling the composites. Additionally, during hydrostatic testing, the charge/discharge performance of the composites is found to decrease slightly with increasing load. The development of robust, load bearing materials that can be directly used as battery component layers (i.e. packaging, anode, cathode, or electrolyte) to provide structural function integral to the battery itself has also been investigated in the literature. Snyder et al. [73] explored various solid polymer materials for use as the electrolyte layer in a structural battery. A key component of multifunctional electrolytes is the ability of the electrolyte to exhibit both high ion conductivity and good mechanical integrity. Both electrical testing of the ion conductivity of the electrolyte materials via electrochemical impedance spectroscopy, as well as mechanical testing of the stiffness of the electrolytes through com13 pression testing and dynamic mechanical analysis (DMA) were conducted. It was found that generally, increases in mechanical performance are accompanied by decreases in ion conductivity, thus an optimal design exists for each specific application. In a continuation study, Snyder et al. [74] studied the use of copolymer electrolytes, as opposed to the homopolymers investigated previously, with one monomer selected to promote structural behavior and the other monomer selected to promote ion conduction. Results of the study showed that the use of a copolymer design exhibits favorable ion conductivity and mechanical strength over an optimized homopolymer design. Snyder et al. [75] have also examined the usefulness of several commercially available carbon fibers, fabrics, and papers for use as the anode layer in structural batteries. The capacitance as well as the energy storage ability of each material was experimentally investigated, and it was concluded that the use of commercially available materials as anodes in power storage devices is viable. In addition to the work of Snyder et al., Liu et al. [76] have also investigated several different battery components for use in multifunctional structural batteries. Various materials for use as the battery anode, cathode, and electrolyte were considered. A prototype structural battery was fabricated and electrical charge/discharge measurements as well as mechanical three-point bending tests were performed. The prototype was shown to simultaneously support load and store energy, however, both the strength and energy density of the battery showed room for improvement in future designs. Neudecker et al. [77] have considered another approach to creating structural batteries in which thin-film batteries are deposited directly onto thin fiber substrates, such as carbon, glass, silicon carbide, or metals, to form what they call PowerFibers. PowerFibers are made using a rotational shadow mask system that allows sequential vacuum deposition of each thin-film battery component layer. Several combinations of substrate and thin-film battery component layers were investigated, and both single fiber PowerFibers as well as composite PowerFibers composed of multiple individual fibers embedded into an adhesive matrix were fabricated. Experimental charge/discharge testing was performed on the fabricated devices and results showed excellent cycle life and discharge rate capability. The challenge facing the PowerFiber technology is the relatively low storage capacity of individual fibers. Lin and Sodano [78–81] have considered a similar approach to creating multifunctional structure power systems in which a novel piezoelectric structural fiber has been developed. The fiber contains a conventional conductive fiber core which 14 is then coated with piezoelectric material and an outer electrode material. The fiber core acts as both a structural stiffening layer as well as an inner electrode, and the piezoelectric layer allows the active fiber to posses sensing, actuation, and energy harvesting ability. A micromechanics model of the active coated fiber was first developed and validated using a finite element simulation [78]. Next, fabrication of an active fiber containing a silicon carbide core coated with barium titanate piezoelectric material and an outer electrode composed of silver paint was presented [79]. Electromechanical testing of the fiber was performed using a atomic force microscopy to measure the longitudinal free strain of the fiber under the application of an electric field, validating the previously developed model [78]. Lin and Sodano [80] then repeated the electromechanical testing of the active fiber in the presence of an outer polymer lamina layer in order to validate the concept of embedding the fibers in a matrix to create a multifunctional composite material. Results of the testing showed good behavior in the multifunctional fiber, thus proving the ability of the fibers to be embedded into structural composites. Lastly, Lin and Sodano [81] investigated the energy storage ability of the fibers. The dielectric properties of the active barium titanate shell were studied in order to create a structural fiber capacitor. Results of experimental testing showed that the fibers are capable of storing harvested energy. Multifunctional solar energy harvesting systems have also been investigated in the literature and provide a means of combining structure and energy harvesting capabilities in a single device. The use of flexible thin-film solar panels permits the integration of solar harvesting into load bearing structures, and when combined with thin-film battery technology, offers the ability to simultaneously harvest and store energy. In 2000, Clark et al. [82] of ITN Energy Systems, Inc. explored the combination of thin-film photovoltaics along with thin-film lithium batteries to create a flexible, lightweight laminate, called the Flexible Integrated Power Pack (FIPP), that is capable of both harvesting and storing energy. The FIPP was proposed for use as the skin of a satellite, providing structural function in addition to energy harvesting and storage ability. A prototype FIPP was fabricated and tested in the laboratory, and test results showed that energy can be successfully transfered from the thin-film solar panels to the thin-film batteries. Similar research has been presented by Raffaelle et al. [83–85] in which thin-film solar panels are again combined with thin-film lithium batteries to create power systems for satellites. An initial prototype was built utilizing conventional polycrystalline solar panel and lithium coin battery technology, and 15 the prototype was launched on the Starshine 3 satellite in 2001. Several other prototype devices containing thin-film batteries were also fabricated and bench tested and found to successfully harvest and store energy. More recently, Maung et al. [86] introduced the“cocuring” manufacturing process in which thin-film solar panels are directly integrated onto carbon-fiber-reinforced epoxy composites to combine harvesting and structural function in a single device. The process involves simultaneously curing a prepreg epoxy composite and bonding the solar panel to the composite during the curing process. After fabrication, the electrical performance of a multifunctional solar harvesting device was examined under cyclic tensile loading, and it was found that significant degradation in solar panel performance occured above 1.0% strain. Dennler et al. [87] revisited the idea of combining energy harvesting and energy storage and proposed the concept of directly coupling a flexible solar panel with a conventional lithium-polymer battery. Several novel types of flexible solar panels were developed and considered for the device, and a unique flexible interconnection layer was proposed for electrical connection of the solar panel and battery. The interconnection layer consists of embedded microelectronics on a polymer substrate to create a flexible power management circuit layer that can be directly integrated with thin-film solar panels and batteries. A prototype system was built and shown to be capable of providing power to a small temperature sensor. Kim et al. [88] expanded upon the work of Dennler et al. [87] and fabricated and tested a solar power laminate consisting of thin-film solar panels and thin-film flexible lithium-based batteries connected with a flexible interconnect circuit. The work focused on the development of the copper nano-ink piezoelectric inkjet printing method for creating flexible circuits. Once manufactured, the energy harvesting performance of the multifunctional solar battery composite was tested under tensile loading and found to operate up to a strain of 0.45%, at which the battery exhibited failure. The previous research described above has investigated several aspects of multifunctional structure power systems. The next step in the development of these systems is to integrate structural function with energy storage and energy generation in a single multifunctional structure. Preliminary work by Dennler et al. [87] and Kim et al. [88] has examined solar energy harvesting multifunctional structures with integrated energy storage. The goal of the work presented in this dissertation is to design, fabricate, and characterize a multifunctional piezoelectric vibration-based energy harvesting system with integrated 16 energy storage and structural load bearing ability. 1.1.3 Piezoelectric Energy Harvesting in Unmanned Aerial Vehicles A wide variety of applications can take advantage of the benefits offered by energy harvesting systems. In this dissertation, a small unmanned aerial vehicle platform is investigated as an example application of multifunctional piezoelectric vibration energy harvesting. Energy harvesting in aircraft has been of interest to the research community for several decades. The majority of the early work on energy harvesting for small aircraft focuses on photovoltaic harvesting of solar energy as a means of providing propulsive power for the aircraft. In 1984, Boucher [89] published a review article highlighting all of the previous solar powered flights at the time, dating back to 1974. A total of seven solar powered flights were reviewed, most of which were performed using small manned aircraft. In recent times, a focus has been placed on the development of small unmanned aircraft including both UAVs and smaller micro air vehicles (MAVs). Pines and Bohorquez [90] discuss the drive towards reducing the size of unmanned aircraft while highlighting the challenges facing the development of future MAVs. The topic of solar energy harvesting to provide power for flight remains a focus of many research efforts on the development of future unmanned aircraft. Researchers are continually developing novel photovoltaic materials with increased energy conversion efficiencies and decreased weight that can be used on small, lightweight aircraft. Several other modes of energy harvesting in UAVs have also been investigated in the literature. Thomas et al. [91] discuss the potential of harvesting solar, wind, thermal, and electromagnetic radiation energy on small unmanned vehicles to supplement the vehicle power supply in order to increase flight endurance. The energy available from each potential source is estimated and the current energy conversion devices are discussed. In the past five years, piezoelectric vibration harvesting has gained interest for use in UAVs as a means of harvesting energy from vibrations persistent during the flight of the aircraft in order to create local power sources for low-power electronics. Previous research studies have investigated several aspects of harvesting vibration energy in UAVs using piezoelectric material. De Marqui Jr. et al. [92] explored the use of piezoelectric harvester plates on the wings of UAVs for harvesting vibration energy during flight. An electromechanically coupled finite element model was developed for piezoelectric plates that can 17 be used to predict the energy output of harvester plates in UAVs. Both theoretical and experimental validation was performed on the finite element model against the analytical solution presented by Erturk and Inman [28] and against experimental test results of a cantilever harvester plate also presented by Erturk and Inman [29]. Additionally, a case study was presented in which theoretical optimization was performed on a notional UAV wing spar in which the optimal amount of embedded piezoelectric material is installed into the spar without exceeding a given mass limitation. Results of this work proved the effectiveness of the finite element model in predicting the behavior of cantilever piezoelectric harvester plates as well as the ability to determine an optimal amount and optimal location of piezoelectric material in a UAV wing spar. In a continuation study, De Marqui Jr. et al. [93] coupled their previously developed finite element model with an unsteady aerodynamic model and investigated the effects of airflow excitation on the power output of cantilever piezoelectric energy harvester plates which simulate the wing of a UAV. Various airflow speeds as well as electrode configurations of the piezoelectric (segmented electrodes vs. continuous electrodes) were analyzed. Results showed that energy harvesting performance is optimized for airflow speeds near the flutter speed, although impractical for actual flight situations, and that segmented electrodes can be useful in eliminating voltage cancellation experienced under torsional vibrations. Perhaps one of the more promising uses of piezoelectric energy harvesting in aircraft is in providing power to low power sensor nodes. Several researchers have investigated the possibility of utilizing vibration energy harvesting in aircraft to create self-powered structural health monitoring nodes that are capable of assessing the condition of critical aircraft components during flight. Durou et al. [94] investigated the combination of thermal and vibration harvesting to power SHM sensors on large-scale aircraft. Simulations were performed to predict the power output of both harvesting devices as well as the energy storage performance of a supercapacitor used to store the harvested energy. Results of the simulations suggest that vibration harvesting alone is not suitable to directly power the SHM node, but that it acts as a valuable supplement to the solar harvesting system as the output of the piezoelectric harvester is not environmentally dependent. Moss et al. [95] explored the concept of broadband vibration energy harvesting in aircraft to provide power to SHM sensor nodes. Considering the variability in excitation characteristics during the flight of an aircraft, it was proposed to develop an energy harvesting device with 18 relatively broadband response. A fairly large vibro-impacting device was created and experimentally tested in which a vibrating mass repeatedly impacts and excites a piezoelectric beam. The mass responds to a range of frequencies, thus the overall device is capable of harvesting energy in a broadband sense. Results of experimental testing showed that the harvester responds in the range of 29 - 41 Hz and is capable of harvesting up to 12 mW of power under 0.5 g excitation. Featherston et al. [96] performed research on vibration energy harvesting for SHM sensors on both large scale commercial aircraft as well as small UAVs. A test panel was created using an aluminum plate clamped on all edges in a test frame and included four surface mounted piezoelectric devices for energy harvesting. The panel was excited using a shaker with a stinger connection at the center of the plate for various frequencies corresponding to different air speeds, altitudes, and panel locations along the wing. Results of experimental testing showed that the maximum power harvested by a single device was 23.5 mW. In order to operate a SHM sensor node requiring 50 mW of power, it was concluded that approximately 71 cm2 of piezoelectric material is required under optimal conditions. Many novel UAVs include a multitude of functions requiring a large amount of technology to be placed into a small platform. The concept of multifunctional piezoelectric energy harvesting has been investigated in the literature as a means of creating a noninvasive power source that can be used, for example, to power on board self-powered electronic systems. Apker et al. [97] suggested the use of piezoelectric film on the wings of a small ornithopter flapping-wing MAV to perform aeroelastic energy harvesting during flight. The piezoelectric material would serve as both a load bearing wing surface as well as an energy harvesting system, hence its multifunctional use. Although no modeling efforts were pursued and no physical device was constructed, the work presents a novel concept in multifunctional harvesting for UAVs. Another novel concept for multifunctional piezoelectric vibration harvesting in UAVs involves the integration of piezoelectric material into the landing gear of the aircraft. Magoteaux et al. [98] discussed the concept of using either cantilevered or curved piezoelectric beams as the landing gear for UAVs. Piezoelectric landing gear can be used not only for conventional takeoff and landing purposes, but to harvest energy and recharge the power source during a mission if the aircraft is perched on a vibrating structure. In their work, Magoteaux et al. provided a comparison of the harvesting ability of a traditional piezoelectric cantilever to a curved piezoelectric 19 configuration and found that while having potential to provide larger amounts of power (≈ 5 mW at ≈ 1.0 g), the resonance frequency of the cantilever configuration is impractically low (≈ 3.5 Hz) compared to the curved configuration (≈ 120 Hz), thus the curved device, which provides around 3 mW, is best suited for landing gear applications. In a similar study, Erturk et al. [29] investigated a novel L-shaped configuration for piezoelectric energy harvesting and suggested its use as UAV landing gear. The L-shaped beam mass structure can be tuned to exhibit a two-to-one internal resonance phenomenon where the second resonance frequency is roughly two times the first, and has potential for giving larger power outputs compared to traditional cantilever configurations. Additionally, an L-shaped device is well suited geometrically for use as landing gear. Erturk et al. compared the energy generation capabilities of their proposed L-shaped device to the curved harvester proposed by Magoteaux et al. [98] and found that for devices with similar dimensions and mass, the L-shaped device outperforms the curved device. The integration of vibration energy harvesting systems into unmanned aerial vehicles is relatively novel and has the potential to provide environmentally independent power sources for on board sensors of the next generation of aircraft. A multifunctional approach is paramount as the size of UAVs continues to decrease and the technological demands steadily increase. The work presented in this dissertation aims to integrate a multifunctional piezoelectric vibration-based energy harvester into a UAV platform to simultaneously harvest and store energy in order to provide power for a low-power sensor node and to support structural loads during flight. 1.2 Thesis Overview 1.2.1 Research Objectives It is clear from the previous research highlighted in the Literature Review that piezoelectric vibration-based energy harvesting is an attractive concept for providing power to various low-power electronics. The use of energy harvesting provides the ability for electronic devices to become self-powered and no longer rely on batteries which require replacement. Self-powered devices have the ability to be embedded into a host structure as accessibility is no longer required. Conventional piezoelectric energy harvesting systems, however, suffer from the large mass density of piezoceramic materials as well as the intrusiveness 20 associated with adding a harvesting system to a host structure. The concept of multifunctionality can be utilized in an effort to overcome the drawbacks of classical piezoelectric energy harvesting design, which are prominent in applications sensitive to added mass and volume. The combination of multiple functionalities into a single device can allow piezoelectric vibration harvesting to become useful in many applications where otherwise impractical. Previous research has investigated various aspects of multifunctional material systems including the combination of structural function and energy storage in a single device, and the combination of energy harvesting and energy storage in a single device. The goal of the research presented in this dissertation is to expand upon the current concept of multifunctionality in energy harvesting systems and create a novel multifunctional piezoelectric vibration energy harvesting system. The self-charging structure multifunctional concept created in this dissertation combines piezoelectrics with thin-film batteries to create devices capable of simultaneously harvesting energy, storing the harvested energy, and supporting structural loads. Multifunctional vibration harvesting in unmanned aerial vehicles is investigated as a case study in which self-charging structures are used in a mass and volume critical application. 1.2.2 Chapter Summaries An introduction to the topics of piezoelectric vibration energy harvesting and multifunctionality is given in Chapter 1. Motivation behind the development of piezoelectric energy harvesting systems capable of providing power to low-power electronic devices is given. A literature review is presented in which previous works in the fields of vibration energy harvesting, multifunctionality in energy harvesting systems, and energy harvesting in unmanned aerial vehicles are highlighted. A brief history of piezoelectric energy harvesting is given in which the early works in the literature are reviewed along with some of the more prominent studies conducted in the 21st century. The concept of multifunctionality in energy harvesting systems is also reviewed including works on multifunctional structural power systems as well as photovoltaic harvesting and storage systems. Lastly, a review of the previous work on vibration energy harvesting in unmanned aerial vehicles is given. Chapter 2 presents the concept of multifunctional self-charging structures developed in this dissertation along with an electromechanical model used to predict the behavior of 21 the devices. A brief introduction into piezoelectricity and the concept of piezoelectric energy harvesting is discussed. The design and operational principles behind self-charging structures are given. An experimentally validated electromechanical assumed modes formulation developed by Erturk and Inman [30–32] is employed to model the cantilever piezoelectric harvesters subjected to harmonic base excitation. Details of the model are presented including modeling assumptions, device configuration, and formulations for both the series and parallel electrode connections of the piezoelectric layers of the bimorph harvester. The assumed modes model can be used to predict the coupled vibration and voltage response of the harvester. Experimental validation of the electromechanical model presented in Chapter 2 as well as the self-charging structure concept is given in Chapter 3. Performance evaluation of the thin-film batteries used in self-charging structures is given. Details of the material selection and fabrication of a prototype self-charging structure are presented. Experimental testing is performed on the fabricated device in order to validate the model through electromechanical frequency response function measurements. Additionally, charge/discharge experiments are conducted to prove the ability of the structures to simultaneously generate and store electrical energy in a self-charging manner. Chapter 4 presents an evaluation of the strength properties of prototype self-charging structures. Conventional three-point bend testing is first performed to evaluate the static strength of the fabricated devices and results of the experimental testing are reviewed. Dynamic strength testing is then performed to evaluate the ability of the harvesters to support dynamic loading. Considering the variety of piezoelectric materials available for use in self-charging structures, a separate static strength analysis is then performed on an assortment of commercially available piezoelectric materials and experimental results are summarized. Multifunctional vibration energy harvesting in unmanned aerial vehicles is investigated as a case study in the remaining chapters. Chapter 5 presents the flight endurance modeling of electric UAVs with on board energy harvesting capability. A flight endurance model recently presented by Thomas et al. [91] is used to describe changes in the flight endurance of a UAV based on the power available from added harvesters and the mass of the added harvesters. Details of the derivation of the model are reviewed. The formulation is applied to an EasyGlider remote control foam hobbyist airplane, which is selected as the 22 test platform in this work, and theoretical predictions are made to determine the effects of adding piezoelectric energy harvesting to the aircraft. An experimental case study is then performed in which data recorded during flight of the EasyGlider aircraft with piezoelectric fiber based devices installed in the wing spar is used to update the simulations. Finally, the flight endurance formulation is used to predict the effects of adding self-charging structures to the EasyGlider aircraft. Results of the flight endurance modeling are used to support the concept of multifunctional vibration harvesting in UAVs. Chapter 6 presents the electromechanical modeling of an energy harvesting wing spar with embedded self-charging structures. The model is based on the previously described assumed modes formulation given by Erturk and Inman [30–32] and used in Chapter 2. Details of the derivation of the model are first given in which both the series and parallel connection of the piezoelectric layers are considered. Experimental testing is performed on a representative aluminum wing spar with embedded piezoelectric and thin-film battery layers in order to validate the model. Modeling simulations are compared to experimentally measured frequency response functions for validation purposes. Chapter 7 presents the fabrication and testing of a realistic fiberglass UAV wing spar with embedded self-charging structures for use in the EasyGlider aircraft. Details of the fabrication of the multifunctional energy harvesting wing spar are given. Experimental testing in which the cantilever wing spar is subjected to harmonic resonance excitation is performed to evaluate the energy harvesting performance of the spar and to confirm the ability of the spar to operate in a self-charging fashion. Finally, flight testing is performed in which the fiberglass spar is used in the EasyGlider aircraft and the power output of the multifunctional spar is measured during flight. The final chapter presents a summary of the results of the research performed in this dissertation. The major contributions of this work to the research community are described. Lastly, recommendations for future work are presented in which the advances made by the work in this dissertation can be extended in the future. 23 C HAPTER 2 M ULTIFUNCTIONAL S ELF -C HARGING S TRUCTURE C ONCEPT AND E LECTROMECHANICAL M ODELING T HIS chapter introduces the multifunctional self-charging structure concept that is ex- plored throughout this dissertation. A brief overview of piezoelectricity and piezo- electric energy harvesting is first given. Multifunctionality in vibration energy harvesting is then explored through the development of the self-charging structure concept. The concept involves the combination of energy harvesting, energy storage, and load bearing ability in a single composite harvesting device through the direct integration of piezoelectric material with novel thin-film batteries. The application of an approximate coupled electromechanical model based on the assumed modes method that can be used to predict the vibration and voltage response of self-charging structures under harmonic base excitation is discussed. The model is based on Euler-Bernoulli assumptions for thin beams and is defined for both the series and parallel electrode connections of the bimorph self-charging structures. Energy formulations are first derived for the potential energy, kinetic energy, internal electrical energy, and work of non-conservative forces. The assumed series solution consisting of a finite number of trial functions multiplied by generalized coordinates is then substituted into the energy expressions. The extended Hamilton’s principle is then applied, which leads to the coupled electromechanical Lagrange equations. Solution of the Lagrange equations yields the governing mechanical and electrical equations used to describe the system. Finally, the displacement - to - base acceleration and voltage - to - base acceleration frequency response functions (FRFs) can be defined by assuming harmonic base excitation imposed on the cantilever self-charging structures. 24 2.1 Overview of Piezoelectric Energy Harvesting In this section, a brief introduction to piezoelectricity is first given and the most common form of the piezoelectric constitutive equations is presented. An overview of piezoelectric energy harvesting is then given in which the typical cantilever harvester configuration is reviewed. 2.1.1 Introduction to Piezoelectricity Piezoelectricity was first discovered in 1880 by Pierre and Jacques Curie when they found that certain crystals, most notably quartz and Rochelle salt, produced a surface charge under a compressive load. This generation of electric charge under mechanical loading is known as the direct piezoelectric effect. One year later, the opposite (or converse) piezoelectric effect, where an induced voltage will cause mechanical deformation, was mathematically proven by Gabriel Lippman and later experimentally observed by the Curie brothers. The natural crystals that were initially discovered exhibited weak coupling between the mechanical and electrical domains. More recently however, synthetic piezoelectric materials have been created with increased coupling that enable the use of piezoelectricity in practical applications. The piezoelectric effect exists in several crystalline materials due to the polarity of the unit cells within the material. This polarity leads to the production of electric dipoles in the material which give rise to the piezoelectric properties. The application of mechanical strain causes rotation of the dipoles, leading to an apparent charge flow that can be measured as current by placing electrodes on opposite faces of a piezoelectric material (direct piezoelectric effect). Similarly, the application of a voltage across the material will cause rotation of the dipoles which results in an induced strain in the material (converse piezoelectric effect). Both the direct and converse piezoelectric effects can be described mathematically through the piezoelectric constitutive equations, given in their most common form as (see Appendix A for a formal treatment of the piezoelectric constitutive equations) 0 S sE d T = D d εT E (2.1) where S is the mechanical strain, D is the electric displacement, T is the mechanical stress, E is the electric field, sE is the mechanical compliance (reciprocal of the elastic modulus) 25 measured at constant electric field (denoted by the superscript E), d is the piezoelectric strain constant, and εT is the dielectric permittivity measured at zero mechanical stress (denoted by the superscript T ). The electromechanical coupling of piezoelectric materials allows their ability to act as both sensors when operating in the direct effect, and as actuators when operating in the converse effect, thus piezoelectric material is a versatile solution in many applications. A wide variety of piezoelectric devices are available commercially. The most common piezoelectric material is lead zirconate titanate, a piezoelectric ceramic known as PZT. Piezoelectric ceramics are widely used, however, they are extremely brittle. In an effort to create flexible piezoelectric material, several piezoelectric fiber-based materials have been developed. These materials contain thin extruded strands of piezoceramic fiber embedded in an epoxy matrix with flexible surface electrodes. Piezoelectric fiber-based materials have the advantage of being flexible and can be mounted on curved surfaces, however, their coupling is typically weaker than that of monolithic ceramics. Additionally, piezoelectric polymer material, most notably polyvinylidene fluoride or PVDF, provides the highest degree of compliance but the weakest coupling. The wide range of piezoelectric materials allows for their use in a variety of diverse applications. 2.1.2 Introduction to Piezoelectric Energy Harvesting Energy harvesting is the process of converting ambient energy surrounding a system into electrical energy, which is typically used to power an electronic device. Piezoelectric energy harvesting involves the placement of a piezoelectric device in a vibration rich environment to utilize the electromechanical coupling exhibited by piezoelectric materials in order to create electrical energy. The most common piezoelectric energy harvesting configuration is the cantilever harvester subject to base excitation as shown in Fig. 2.1. Optimal performance of the energy harvesting system is obtained when the frequency of ambient vibration closely matches the resonant frequency of the harvester beam. Under this condition, maximum vibration energy is transfered to the harvester and converted to useful electrical energy. Deviations from resonance typically cause significant decreases in performance, therefore, tuning the system (either passively or actively) is critical. Researchers have begun to investigate alternative configurations for piezoelectric energy harvesting, such as nonlinear configurations using magnetoelastic nonlinearity [41–43], in an effort to 26 Voltage Output Voltage Piezoelectric Cantilever Beam Vibrating Base 0 Time Figure 2.1: Schematic of piezoelectric cantilever harvester configuration subject to harmonic base excitation and its voltage output. create broadband harvester designs as well. In general, the energy delivered by piezoelectric harvesters is in the form of highvoltage, low-current alternating current (AC) signals, as shown in Fig. 2.1, where the majority of small electronics to be powered require low voltage direct current (DC) power supplies (piezoelectric harvesting is most often used in powering small electronics such as sensor nodes). Appropriate electronic circuitry must, therefore, be used to condition the piezoelectric output to a usable form. Basic conditioning circuitry typically contains a full bridge rectifier and smoothing capacitor to perform AC/DC conversion as well as a simple storage medium. Typically, the instantaneous energy produced by a piezoelectric harvester is inadequate for powering electronics, therefore, a storage medium (such as a battery or capacitor) is often used to temporarily store the harvested energy before use. In this case, an operational duty cycle can be defined in which the frequency of operation of the device to be powered is described based on the amount of harvested power and the power required to operate the device. The power output of a piezoelectric harvester depends significantly on the impedance of the circuit or load connected to the piezoelectric device. A matched load exists for each piezoelectric device as well as for each excitation frequency. Several researchers have investigated the design of optimized circuits to improve the efficiency of energy extraction [44, 47, 52]. Recently, the development of impedance matching circuitry in which the circuit and storage medium appear as a pure matched resistive load for maximum power transfer has been investigated as well [51]. The topic of piezoelectric energy harvesting has attracted much attention throughout the research community in the past decade. Several aspects of piezoelectric energy harvesting have been investigated including the development of novel piezoelectric materi27 als, mechanical configurations to optimize power output, electronic control and harvesting circuitry, and mathematical models used to predict the response of piezoelectric systems. Several review articles have been published highlighting the major work in the field [2–5]. 2.2 Self-Charging Structure Concept Conventional piezoelectric energy harvesting systems are designed to be added to a host structure in order to harvest ambient energy, but often cause undesirable mass loading effects and consume valuable space. In order to improve the functionality and reduce the adverse loading effects of traditional piezoelectric harvesting approaches, a multifunctional energy harvesting design is proposed in this dissertation in which a single device can generate and store electrical energy and also carry structural loads. The proposed selfcharging structures, shown in Fig. 2.2, contain both power generation and energy storage capabilities in a multilayered, composite platform consisting of active piezoelectric layers for scavenging energy, thin-film battery layers for storing scavenged energy, and a central metallic substrate layer. It should be noted that the orientation of the piezoelectric and thin-film battery layers is arbitrary and that the layers may be interchanged depending on the application. The operational principle behind the device involves simultaneous generation of electrical energy in the piezoelectric layers when subjected to dynamic loading causing deformations in the structure, as well as energy storage in the thin-film battery layers. Energy is transferred directly from the piezoelectric layers through appropriate conditioning circuitry to the thin-film battery layers, thus a single device is capable of both generating and storing electrical energy. Additionally, self-charging structures are capable of carrying loads as structural members when embedded into a host system due to the stiffness of the composite device. The ability of the device to harvest energy, store energy, and support structural loads provides true multifunctionality. The fruition of the self-charging structure concept is mainly attributed to the development of novel thin-film battery technology which allows for the creation of thin, lightweight, and flexible batteries. As discussed in Subsection 2.1.2 most piezoelectric energy harvesters do not produce adequate energy levels for immediate use, thus the energy must be accumulated for some time prior to use. Conventional energy storage devices, such as capacitors and traditional rechargeable batteries, are large, bulky devices which add signif- 28 Energy Flow Piezoelectric Layer Thin-Film Battery Layer Harvesting Circuitry Substrate Layer Figure 2.2: Schematic of self-charging structure. icantly to the overall mass and volume of the harvesting system. Additionally, traditional storage devices are not suitable for direct integration into the active element of an energy harvesting system as their mass, volume, and rigidness would hinder the ability of the device to harvest energy. Mechanical failure is also a concern with conventional storage elements as they may fail under the loads applied to the harvester. Thin-film lithium-based batteries provide a viable solution for self-charging structures. The batteries are flexible and have a typical thickness on the order of less than a millimeter, mass of around 0.5 grams, and capacity in the milliamp-hour range. The small capacities of these batteries are a good match for the low electrical output levels associated with piezoelectric energy harvesting, and their thin, lightweight platform is ideal for direct integration into piezoelectric harvesters to create compact, multifunctional self-charging structures. A novel aspect of the self-charging structure concept is that the composite harvester can be used as a load bearing member in a host structure. The harvester can be embedded in or used in place of an existing component, thus reducing the total mass added to the host structure. A potential application that can benefit from the energy harvesting, energy storage, and load bearing capabilities of self-charging structures, for example, is in powering remote, low-power sensors in UAVs. Such multifunctional composite harvesting devices can be embedded into the wing spar of a UAV, as shown in Fig. 2.3, with the goal of providing a local power source for remote low-power wireless sensors such as accelerometers, structural health monitoring nodes, or even low-power imaging devices or cameras. Providing a local power source composed of both harvesting and storage elements is beneficial because it eliminates the need to run wires and tap into the propulsive power supply of the aircraft, thus reducing mass and complexity while allowing the sensors to operate 29 Self-charging structures embedded in wing spar (shown with wing removed) Low-power sensor node being powered locally by harvesting system Figure 2.3: Potential use of self-charging structures: Schematic of small UAV with embedded self-charging structures in wing spar used to provide local power for low-power sensor node. wirelessly. Additionally, a multifunctional approach in which the composite harvester is embedded into the wing spar and supports structural loads in the wings is valuable because it can reduce or eliminate the added mass of the harvesting device. The concept of embedding self-charging structures into the wing spar of a UAV will be investigated as a case study later in this dissertation. While the wing spar example described above presents one potential use of self-charging structures, the technology can be used in any low-power application that can benefit from a multifunctional harvesting solution. Embedded electronic systems and remote selfpowered sensor nodes are examples of applications where the added mass and volume of conventional harvesting could present design challenges, and where the multifunctional approach of self-charging structures can be beneficial. Additionally, when coupled with an appropriate piezoelectric device, the mechanical properties of the self-charging structure can be tailored to the meet the needs of various applications. Piezoelectric devices range from stiff, brittle monolithic piezoceramic to flexible piezoelectric fiber-based and polymer-based transducers, allowing a wide range of mechanical properties to be obtained, thus making the self-charging structure a versatile energy harvesting solution. 30 2.3 Electromechanical Modeling The goal of this section is to develop an electromechanical model that can be used to predict the coupled vibration response and voltage response of the self-charging structures at steady state. The experimentally validated assumed modes model presented by Erturk and Inman [30–32] is applied here to the self-charging structures. The assumed modes method is an approximate distributed parameter modeling technique, closely related to the more common Rayleigh-Ritz method (in fact both methods yield identical discretized equations), that uses the extended Hamilton’s principle along with the energy expressions to derive the equations of motion of a system. 2.3.1 Modeling Assumptions and Device Configuration Consider the self-charging structure configurations shown in Fig. 2.4. Details of the design of the self-charging structures are described in Chapter 3 of the dissertation. The energy harvesting beam contains two piezoelectric layers and is symmetric about the xaxis, hence it represents a bimorph configuration. Both series (Fig. 2.4(a)) and parallel (Fig. 2.4(b)) electrode connections of the piezoelectric devices are considered. The structures are excited under translational base acceleration, ab (t), imposed in the transverse direction (z-direction) at the clamped end. The cantilever beam is assumed to be sufficiently thin such that Euler-Bernoulli assumptions hold (shear deformation and rotary inertia effects are negligible). The electrodes covering the piezoelectric surfaces are assumed to have negligible thickness and to be perfectly conductive such that a single elecR tric potential can be defined across them. QuickPack piezoelectric devices manufactured R by Midé Technology, Corp. [99] are used in the harvester. Each QuickPack device con- tains monolithic PZT-5A piezoelectric ceramic bracketed by Kapton, as shown in Fig. 2.4. The piezoelectric layers are attached to the substrate via high shear strength epoxy (3M ScotchWeldTM DP460 [100]). At the free end of the beam, two thin-film batteries are also R included in the harvester. Thinergy MEC 101-7SES thin-film batteries manufactured by R Infinite Power Solutions, Inc. [101] are used. The batteries are attached to the QuickPack surfaces using DP460 epoxy as well. All bonding layers are assumed to be perfect and the thickness of each bonding layer is assumed to be identical. 31 (a) z ab (t ) x0 (b) L1 x Rl vs (t ) x Rl v p (t ) L z ab (t ) x0 L1 L 0 x L1 (c) hp hs hp hk Piezoceramic Layer he h1 Thin-Film Battery Layer Substrate Layer L1 x L Kapton Layer hb Epoxy Layer h2 Electrodes Poling Direction hb Figure 2.4: Piezoelectric self-charging structure configurations showing (a) series and (b) parallel connection of the piezoelectric layers along with the (c) cross-sectional views of both composite sections. 2.3.2 Electromechanical Assumed Modes Model The absolute motion of the harvester is a combination of the base motion and the relative motion of the beam, given by wabs (x, t) = wb (t) + wrel (x, t) (2.2) where wabs is the absolute displacement of the beam, wb is the base displacement and wrel is the displacement of the beam relative to the moving base. 32 The total potential energy, or strain energy, in the beam is given by Z Z 1 U = Sxx Txx dVs + Sxx Txx dVp 2 (2.3) Vp Vs where Sxx is the strain, Txx is the stress, subscript s represents structure materials, subscript p represent piezoelectric materials, and the integrations are performed over the volume of the materials. All non-piezoelectric layers (substrate and battery layers) are considered as structure materials. The only non-zero strain component is given by Sxx (x, z, t) = −z ∂ 2 wrel (x, t) ∂x2 (2.4) All materials are assumed to be linear elastic and obey Hooke’s Law. The stress in the structure layers is given by (2.5) Txx (x, z, t) = Ys Sxx where Ys is the elastic modulus of the structure layer of interest. The strain energy in the structure layers is then 1 Us = 2 Z Ys (x)z 2 ∂ 2 wrel (x, t) ∂x2 2 dVs (2.6) dx (2.7) Vs 1 = 2 ZL Y Is (x) ∂ 2 wrel (x, t) ∂x2 2 0 where I is the area moment of inertia and Y Is (x) is the bending stiffness of the structure materials, which is a function of x as the beam in non-uniform along the length. The bending stiffness of the structure layers is given by Y Is (x) = Y Ic1 H(L1 − x) + Y Ic2 H(x − L1 ) (2.8) where H(x) is the Heaviside step function, and Y Ic1 and Y Ic2 are the bending stiffnesses of the structure materials in the first composite section from 0 < x < L1 and in the second composite section from L1 < x < L, respectively. Calculation of the bending stiffness of a symmetric composite section about the neutral axis through the use of the parallel axis theorem is described in Appendix B. Details of the calculation of the bending stiffness of the self-charging structure composite sections can be found in Appendix B.2. 33 The stress in the piezoelectric layers is (see Appendix A.3) Txx (x, z, t) = T1 = cE 11 S1 − e31 E3 (2.9) where cE 11 is the elastic modulus of the piezoelectric measured at constant electric field, S1 is the strain in the x-direction (i.e. S1 = Sxx ), e31 is the piezoelectric stress constant and E3 is the electric field across the electrodes of the piezoelectric layers (note e31 = d31 /sE 11 , E where d31 is the piezoelectric strain constant and sE 11 = 1/c11 is the elastic compliance of the piezoelectric layer measured at constant electric field). The electric field can be expressed in terms of the voltage output of the piezoelectric layers, however, the expressions will differ between the series and parallel electrode connection cases. From this point on, separate formulations for the series and parallel connections must be given. For the series connection, the voltage across the electrodes of each piezoelectric layer is vs (t)/2, where for the parallel connection case the voltage of each layer is vp (t). Additionally, e31 has differing signs depending on the poling direction of the piezoelectric layer. In the series case, the piezoelectric layers are poled in opposite directions, therefore, e31 has opposite sign. The instantaneous electric fields, however, are in the same direction (i.e. E3 (t) = −vs (t)/2hp , where hp is the thickness of the piezoelectric layer) for both piezoelectric layers. For the parallel connection, the poling direction is the same for both layers so e31 has the same sign, however, the instantaneous electric fields are in opposite directions with E3 (t) = −vp (t)/hp in the top layer and E3 (t) = vp (t)/hp in the bottom layer. The total strain energy in the piezoelectric layers is the sum of the strain energy in the top and bottom layers, giving # 2 2 Z " 2 w (x, t) 1 v (t) ∂ ∂ w (x, t) s rel rel Ups = z 2 cE − ze31 dVpu 11 2 ∂x2 2hp ∂x2 Vpu 1 + 2 # 2 2 Z " 2 w (x, t) ∂ ∂ w (x, t) v (t) s rel rel z 2 cE + ze31 dVpl 11 ∂x2 2hp ∂x2 (2.10) Vpl Upp 1 = 2 Z " z 2 cE 11 ∂ 2 wrel (x, t) ∂x2 2 vp (t) ∂ 2 wrel (x, t) − ze31 hp ∂x2 # dVpu Vpu 1 + 2 # 2 2 Z " vp (t) ∂ 2 wrel (x, t) ∂ wrel (x, t) 2 E + ze31 dVpl z c11 ∂x2 hp ∂x2 (2.11) Vpl where superscript s and p stand for series and parallel connection of the piezoelectric layers and subscript u and l represent the upper and lower piezoelectric layers. Recalling 34 that the upper and lower piezoelectric layers are identical and that the beam is symmetric about the x-axis, the total strain energy in the piezoelectric layers can be simplified and added to the potential energy of the structure to give the following total potential energy expressions 1 Us = 2 2 2 ZL ( ∂ wrel (x, t) Y Is (x) ∂x2 (2.12) 0 + 2 cE 11 Ip 1 U = 2 p ∂ 2 wrel (x, t) ∂x2 2 ∂ 2 wrel (x, t) − Jps vs (t) ∂x2 !) dx 2 2 ZL ( ∂ wrel (x, t) Y Is (x) ∂x2 (2.13) 0 + 2 cE 11 Ip ∂2w rel (x, t) ∂x2 2 − Jpp vp (t) ∂2w rel (x, t) ∂x2 !) dx where cE 11 Ip is the bending stiffness of the piezoelectric layer (again, found using the parallel axis theorem as shown in Appendix B), and the piezoelectric coupling terms are ZZ e31 s Jp = z dy dz (2.14) 2hp p ZZ e31 z dy dz (2.15) Jpp = hp p where the integrals are evaluated over the domain of the piezoelectric layers. The total kinetic energy of the beam is 2 2 Z Z 1 ∂wabs (x, t) ∂wabs (x, t) Tbeam = ρs dVs + ρp dVp 2 ∂(t) ∂(t) (2.16) Vp Vs which can be rewritten as Tbeam 1 = 2 ZL (ρAs (x) + ρAp (x)) (2.17) 0 " × ∂wb (t) ∂t 2 +2 ∂wb (t) ∂wrel (x, t) + ∂t ∂t ∂wrel (x, t) ∂t 2 # dx where ρAs (x) and ρAp (x) are the mass density functions of the structure and piezoelectric layers given by ρAs (x) = ρAc1 H(L1 − x) + ρAc2 H(x − L1 ) (2.18) ρAp (x) = ρAp (2.19) 35 where ρAc1 and ρAc2 are the mass densities of the structure material in the first composite section from 0 < x < L1 and in the second composite section from L1 < x < L, respectively, and ρAp is the mass density of the piezoelectric layers. The mass densities in each section can be found by simply summing the mass density of each material layer in that section. The mass density functions for the self-charging structure composite sections are given in Appendix B.2. The internal electrical energy in the piezoelectric layers is given by Z 1 Wie = E3 D3 dVp 2 (2.20) Vp The electric displacement, D3 , in the piezoelectric layers is (see Appendix A.3) D3 = e31 S1 + εS33 E3 (2.21) where εS33 is the dielectric permittivity measured at zero strain (denoted by the superscript S). The signs of the electric fields, E3 , and the piezoelectric stress constants, e31 , again depend on the poling direction and electrode configuration, and follow the same relationship given when formulating the stress in each piezoelectric layer (Eq. (2.10) and Eq. (2.11)). The total internal electrical energy in the piezoelectric layers is the sum of the electrical energy in the top and bottom layers, which gives Z 2 1 vs (t) ∂ 2 wrel (x, t) s S vs (t) Wie = e31 z + ε33 dVpu 2 2hp ∂x2 4h2p Vpu 1 + 2 Z Vpl Wiep 1 = 2 Z " Vpu 1 + 2 2 vs (t) ∂ 2 wrel (x, t) S vs (t) − e31 z + ε dVpl 33 2hp ∂x2 4h2p v 2 (t) vp (t) ∂ 2 wrel (x, t) S p e31 z + ε 33 hp ∂x2 h2p Z " Vpl (2.22) # vp (t) ∂ 2 wrel (x, t) S vp2 (t) − e31 z ε33 2 hp ∂x2 hp dVpu (2.23) # dVpl Due to the symmetry of the identical piezoelectric layers, the internal electric energy can be simplified to Wies 1 = 2 ZL 2Jps vs (t) ∂ 2 wrel (x, t) 1 dx + Cp vs2 (t) 2 ∂x 4 (2.24) ∂ 2 wrel (x, t) dx + Cp vp2 (t) ∂x2 (2.25) 0 Wiep 1 = 2 ZL 2Jpp vp (t) 0 36 where the internal capacitance of a piezoelectric layer, Cp , is given by Cp = εS33 Ap hp (2.26) where Ap is the electrode area. The effects of base excitation are considered in the kinetic energy term and mechanical damping is to be introduced later in the form of proportional damping, therefore, the only non-conservative work is due to the piezoelectric charge output, giving (2.27) Wnce = Q(t)v(t) where Q(t) is the electric charge output of the piezoelectric layers. 2.3.3 Substitution of the Assumed Solution The assumed modes method involves the discretization of the energy expressions by substitution of an assumed series solution for the unknown relative beam displacement composed of kinematically admissible functions (or trial functions), φr (x), multiplied by generalized (or modal) coordinates, ηr (t), of the form wrel (x, t) = N X (2.28) φr (x)ηr (t) r=1 The admissible functions must satisfy the geometric boundary conditions. A simple admissible function satisfying the essential boundary conditions of a clamped-free thin beam is [102] φr (x) = 1 − cos (2r − 1)πx 2L (2.29) Substitution of the assumed solution, Eq. (2.28), into the potential energy expressions, Eq. (2.12) and Eq. (2.13), gives ZL ( N N X X 1 00 00 s U = Y Is (x) φr ηr (t) φl ηl (t) 2 r=1 0 + 2 cE 11 Ip N X 00 φr ηr (t) r=1 1 U = 2 p l=1 N X 00 φl ηl (t) − Jps vs (t) (2.30) N X !) 00 φr ηr (t) dx r=1 l=1 ZL ( N N X X 00 00 Y Is (x) φr ηr (t) φl ηl (t) r=1 0 + 2 cE 11 Ip N X r=1 00 φr ηr (t) l=1 N X 00 φl ηl (t) − Jpp vp (t) (2.31) N X r=1 l=1 37 !) 00 φr ηr (t) dx where prime represents ordinary differentiation with respect to the spatial variable, x. The total kinetic energy can be written in a similar manner as 1 T = 2 ZL (ρAs (x) + ρAp (x)) 0 " × (2.32) ∂wb (t) ∂t 2 # N N N X X ∂wb (t) X φr (x)η˙r (t) + φr (x)η˙r (t) +2 φl (x)η̇l (t) dx ∂t r=1 r=1 l=1 where an overdot represents ordinary differentiation with respect to the temporal variable, t. Similarly, the internal electrical energy becomes Wies 1 = 2 ZL 2Jps vs (t) r=1 0 Wiep 1 = 2 N X ZL 2Jpp vp (t) 1 00 φr (x)ηr (t) dx + Cp vs2 (t) 4 N X 00 φr (x)ηr (t) dx + Cp vp2 (t) (2.33) (2.34) r=1 0 The potential, kinetic, and internal electrical energies can be written as N N 1 XX (ηr (t)ηl (t)krl − 2ηr (t)vs (t)θrs ) U = 2 s Up = T = 1 2 r=1 l=1 N X N X 1 2 (ηr (t)ηl (t)krl − 2ηr (t)vp (t)θrp ) (2.35) (2.36) r=1 l=1 N N XX (η˙r (t)η̇l (t)mrl + 2η˙r (t)pr ) r=1 l=1 ZL 1 + 2 (ρAs (x) + ρAp (x)) ∂wb (t) ∂t (2.37) 2 dx 0 Wies N 1X 1 s 2 = 2ηr (t)vs (t)θr + Cp vs (t) 2 2 Wiep = r=1 N X 1 2 2ηr (t)vp (t)θrp + 2Cp vp2 (t) (2.38) (2.39) r=1 where ZL krl = 00 00 Y Is (x) + 2cE 11 Ip φr (x)φl (x) dx (2.40) 0 θrs ZL = 00 Jps φr (x) dx 0 38 (2.41) θrp ZL = 00 Jpp φr (x) dx (2.42) 0 ZL mrl = (ρAs (x) + ρAp (x)) φr (x)φl (x) dx (2.43) ∂wb (t) dx ∂t (2.44) 0 ZL pr = (ρAs (x) + ρAp (x)) φr (x) 0 2.3.4 Lagrange Equations with Electromechanical Coupling The extended Hamilton’s principle for electromechanical systems is [103] Zt2 (δT − δU + δWie + δWnc ) dt = 0 (2.45) t1 where δT , δU and δWie are the first variations of the kinetic energy, potential energy and internal electrical energy, and δWnc is the virtual work of all non-conservative forces. Based on the extended Hamilton’s principle, the electromechanical Lagrange equations are ∂U ∂Wie ∂T d ∂T + − =0 (2.46) − dt ∂ η̇i ∂ηi ∂ηi ∂ηi ∂U ∂Wie d ∂T ∂T + − =Q (2.47) − dt ∂ v̇i ∂vi ∂vi ∂vi where Q is the electric charge output resulting from the non-conservative electrical work, Wnce . The second term in the first of the Lagrange equations is zero, leaving the following non-zero terms N N ∂T 1 XX = ∂ η̇i 2 1 = 2 ∂U s 1 = ∂ηi 2 1 = 2 r=1 l=1 N X N X [(δri η̇l + δli η̇r ) mrl + 2δri pr ] = r=1 l=1 N N XX r=1 l=1 N X N X ∂ η̇r ∂ η̇l ∂ η̇r η̇l + η̇r mrl + 2 pr ∂ η̇i ∂ η̇i ∂ η̇i N X (2.48) (mil η̇l + pi ) l=1 ∂ηr ∂ηl ∂ηr ηl + ηr krl − 2 vs θrs ∂ηi ∂ηi ∂ηi [(δri ηl + δli ηr ) krl − r=1 l=1 2δri vs θrs ] = N X l=1 39 (2.49) (kil ηl − vs θis ) N N ∂U p 1 XX = ∂ηi 2 1 = 2 r=1 l=1 N X N X ∂ηr ∂ηr ∂ηl p ηl + ηr krl − 2 v p θr ∂ηi ∂ηi ∂ηi [(δri ηl + δli ηr ) krl − 2δri vp θrp ] = r=1 l=1 ∂Wies ∂ηi ∂Wiep ∂ηi N X (2.50) (kil ηl − vp θip ) l=1 N 1X ∂ηr s = 2 v s θr = 2 ∂ηi r=1 N 1X ∂ηr = 2 vp θrp = 2 ∂ηi r=1 N 1X 2 1 2 r=1 N X (2δri vs θrs ) = vs θis (2.51) (2δri vp θrp ) = vp θip (2.52) r=1 The temporal derivative of the kinetic energy term gives d dt where ∂pi = ∂t ∂T ∂ η̇i N X ∂pi = mil η̈l (t) + ∂t (2.53) r=1 ZL (ρAs (x) + ρAp (x)) φi (x) ∂ 2 wb (t) dx ∂t2 (2.54) 0 Using these results, the first set of Lagrange equations can be written as N X (mil η̈l + kil ηl − 2θis vs − fi ) = 0 (series connection) (2.55) (mil η̈l + kil ηl − 2θip vp − fi ) = 0 (parallel connection) (2.56) l=1 N X l=1 where fi is the forcing due to base excitation given by ∂pi =− fi = − ∂t ZL (ρAs (x) + ρAp (x)) φi (x) ∂ 2 wb (t) dx ∂t2 (2.57) 0 The non-zero terms in the second of the Lagrange equations are N ∂U s 1X = (−2ηr θrs ) ∂v 2 (2.58) r=1 ∂U p ∂v = N 1X 2 (−2ηr θrp ) (2.59) r=1 N N 1X 1 1X ∂Wies = (2ηr θrs + Cp vs ) = Cp vs + (2ηr θrs ) ∂v 2 2 2 r=1 ∂Wiep ∂v = N 1X 2 (2ηr θrp + 4Cp vp ) = 2Cp vp + r=1 40 1 2 r=1 N X r=1 (2ηr θrp ) (2.60) (2.61) which gives the second set of Lagrange equations as N X 1 Cp v s + Q + (2ηr θrs ) = 0 2 2Cp vp + Q + r=1 N X (2ηr θrp ) = 0 (series connection) (2.62) (parallel connection) (2.63) r=1 Taking the temporal derivative of Eq. (2.62) and Eq. (2.63) gives N X 1 Cp v̇s + Q̇ + (2η̇r θrs ) = 0 2 2Cp v̇p + Q̇ + r=1 N X (2η̇r θrp ) = 0 (series connection) (2.64) (parallel connection) (2.65) r=1 where the time rate of change of the electrical charge output, Q̇, is equal to the electrical current passing through the load resistor, given by Q̇ = v Rl (2.66) Therefore, the second set of Lagrange equations becomes N 1 vs X Cp v̇s + + (2η̇r θrs ) = 0 2 Rl 2Cp v̇p + 2.3.5 vp + Rl r=1 N X (2η̇r θrp ) = 0 (series connection) (2.67) (parallel connection) (2.68) r=1 Equivalent Series/Parallel Representation of the Lagrange Equation At this point it is convenient to introduce an equivalent representation of the electromechanical Lagrange equations for the series and parallel cases, as suggested by Erturk and Inman [32], in which a single formulation with modified electromechanical coupling and capacitance terms is introduced. Observe that the only differences in the coupled Lagrange equations between the series and parallel electrode connection cases involve the electromechanical coupling terms (i.e. θi ) and the capacitance terms. Considering these differences, one can define the following equivalent Lagrange equations N X (mil η̈l + kil ηl − θieq v − fi ) = 0 (2.69) l=1 N Cpeq v̇ + X v (η̇r θreq ) = 0 + Rl r=1 41 (2.70) where the equivalent electromechanical coupling, θeq , and capacitance, Cpeq , are selected from Table 2.1 depending on whether a series or parallel solution is desired. Table 2.1: Equivalent electromechanical coupling and capacitance terms for series and parallel electrode connections (from Erturk and Inman [32]). Series Connection θieq Cpeq RL Parallel Connection 00 Jp φi (x) dx 2 0 RL 00 Jp φi (x) dx 0 1 2 Cp 2Cp where the piezoelectric coupling term, Jp , is given by ZZ e31 Jp = z dy dz hp (2.71) p 2.3.6 Solution of the Equivalent Representation of the Lagrange Equations Rewriting the equivalent Lagrange equations given by Eq. (2.69) and Eq. (2.70) in matrix form and introducing proportional damping in the first equation gives [M] η̈ + [C] η̇ + [K] η − Θeq v = f v + Θeq η̇ = 0 Cpeq v̇ + Rl (2.72) (2.73) where the mass, stiffness and damping matrices ([M], [K], and [C]) are N × N , the generalized coordinates, η, the forcing vector, f , and the electromechanical coupling vector, Θeq , are N × 1, and the damping matrix is given by [C] = α [M] + β [K] (2.74) where α and β are constants of proportionality. Assuming harmonic base excitation of the form wb (t) = wb ejωt , which leads to a base acceleration of ab ejωt (where ab = −ω 2 wb ), the forcing vector becomes f = Fejωt (2.75) The components of the forcing vector are given by ZL Fi = −ab (ρAs (x) + ρAp (x)) φi (x) dx 0 42 (2.76) The assumed harmonic forcing results in a harmonic solution for the generalized coordinates and the voltage of the form η = ηejωt (2.77) v = V ejωt (2.78) Substitution of the assumed solutions into Eq. (2.72) gives − ω 2 [M] ηejωt + jω [C] ηejωt + [K] ηejωt − Θeq V ejωt = Fejωt (2.79) The exponential function is never equal to zero for all positive time, which leads to −ω 2 [M] + jω [C] + [K] η − Θeq V = F (2.80) Similarly, substitution of the assumed solutions, Eq. (2.77) and Eq. (2.78), into Eq. (2.73) gives jωCpeq V ejωt + V ejωt + jωΘeq T ηejωt = 0 Rl where superscript T stands for transpose. Again this can be written as 1 eq jωCp + V + jωΘeq T η = 0 Rl (2.81) (2.82) Equation (2.82) yields V = −jωΘeq T η jωCpeq + R1l (2.83) Substituting Eq. (2.83) into Eq. (2.80) gives jωΘeq Θeq T −ω 2 [M] + jω [C] + [K] + jωCpeq + R1l ! η=F (2.84) Recalling our assumed solution of η = ηejωt , Eq. (2.84) can be rewritten as η(t) = !−1 1 −1 eq eq T eq Θ Θ Fejωt −ω [M] + jω [C] + [K] + jω jωCp + Rl 2 (2.85) Substitution of Eq. (2.85) back into Eq. (2.83) and recalling our assumed solution of v = V ejωt gives v(t) = −jω jωCpeq 1 + Rl −1 Θeq T −ω 2 [M] + jω [C] + [K] !−1 1 −1 eq eq T eq +jω jωCp + Θ Θ Fejωt Rl 43 (2.86) Substitution of Eq. (2.85) into the assumed series solution for the relative displacement given by Eq. (2.28) gives the following expression for the relative displacement wrel (x, t) = ΦT (x) −ω 2 [M] + jω [C] + [K] !−1 1 −1 eq eq T eq Θ Θ Fejωt +jω jωCp + Rl (2.87) Finally, the following electromechanical frequency response functions (FRFs) can be defined for the relative displacement and voltage per base acceleration, as described by Erturk and Inman [30–32] wrel (x, t) = ΦT (x) −ω 2 [M] + jω [C] + [K] ab ejωt !−1 1 −1 eq eq T eq + jω jωCp + Θ Θ F̃ Rl 1 −1 eq T v(t) eq −ω 2 [M] + jω [C] + [K] = −jω jωC + Θ p ab ejωt Rl !−1 −1 1 +jω jωCpeq + Θeq Θeq T F̃ Rl (2.88) (2.89) where the components of the forcing vector are given by ZL F̃i = − (ρAs (x) + ρAp (x)) φi (x) dx (2.90) 0 Equation (2.88) and Eq. (2.89) can be used to predict the coupled vibration and voltage response of the self-charging structures when subjected to harmonic base excitation. 2.4 Chapter Summary An overview of piezoelectric energy harvesting and an introduction to the concept of multifunctional self-charging structures is presented. A brief introduction to both piezoelectricity and piezoelectric energy harvesting is first given. The self-charging structure concept is then discussed. Finally, the application of an approximate coupled electromechanical model used to predict the response of self-charging structures is presented. The multifunctional self-charging structure concept presented in this dissertation involves the realization of several functionalities in a single energy harvesting device. Throu44 gh the combination of piezoceramic devices and novel thin-film batteries, a single composite energy harvester can simultaneously harvest energy in the piezoelectric layers and store the harvested energy in the battery layers. Additionally, if such a composite structure is embedded into a host system, it can be used to help support structural load. Combining energy harvesting, energy storage, and load bearing ability in a single device provides a multifunctional solution to vibration energy harvesting. An approximate electromechanical model based on the assumed modes method is presented to describe the response of the multilayer, nonuniform self-charging structures introduced here. The assumed modes model is based on Euler-Bernoulli beam assumptions and utilizes the extended Hamilton’s principle from which the electromechanical Lagrange equations arise. Both series and parallel electrode connections of the two piezoelectric layers in the symmetric bimorph energy harvesters are considered. Derivation of the electromechanical Lagrange equations for each electrode configuration proves the formulation to be similar for each configuration and leads to an equivalent representation that is used for the remainder of the modeling. Displacement - to - base acceleration and voltage - to base acceleration FRFs are derived by assuming harmonic base excitation. The FRFs can be used to predict the coupled vibration and voltage response of the self-charging structures. 45 C HAPTER 3 E XPERIMENTAL T ESTING OF S ELF -C HARGING S TRUCTURES T HE self-charging structure concept and electromechanical assumed modes model were described in Chapter 2. This chapter presents experimental investigation of self- charging structure prototypes. A detailed investigation of two types of thin-film batteries is first given and the optimal battery type is selected. Fabrication of the prototype selfcharging structures is next discussed including selection of the substrate and piezoelectric layers along with details on vacuum bonding. Finally, experimental testing results are given for both the validation of the electromechanical assumed modes model through frequency response measurements as well as the confirmation of the self-charging ability through charge/discharge measurements. 3.1 Performance Evaluation of Thin-Film Batteries R NanoEnergy thin-film batteries manufactured by Front Edge Technology, Inc. [104] and R Thinergy thin-film batteries produced by Infinite Power Solutions, Inc. [101] are both investigated. Both batteries, shown in Fig. 3.1, are flexible lithium-based secondary (i.e. rechargeable) cells that utilize all solid-state components. Common to both types of thinfilm batteries, the active elements include lithium-metal anodes, lithium cobalt dioxide (LiCoO2 ) cathodes, and lithium phosphorous oxynitride (LiPON) electrolyte layers. The R R most significant difference between NanoEnergy and Thinergy batteries lies in their construction and sealant layers, which will be discussed later in this section. The ability to produce extremely thin (less than 200 microns) and flexible batteries can be attributed to the use of the solid-state LiPON electrolyte as opposed to liquid or gel electrolytes found in 46 (a) (b) R R Figure 3.1: Photographs of (a) NanoEnergy and (b) Thinergy thin-film batteries. conventional rechargeable batteries. LiPON, developed at Oak Ridge National Laboratory [105, 106], exhibits a high lithium ion mobility, lending to its performance as an electrolyte, and a low electron mobility, allowing for low self-discharge rates. 3.1.1 Comparison to Conventional Rechargeable Batteries Compared to traditional rechargeable batteries, thin-film batteries offer a clear advantage in form factor. Table 3.1 presents both physical and electrical properties of various types of R R secondary batteries, in which the mass and volume of both NanoEnergy and Thinergy batteries are shown to be 1-2 orders of magnitude less than conventional batteries. Thinfilm batteries are also flexible, where conventional batteries are rigid. Additionally, thinfilm battery technology offers superior cycle life (on the order of 1,000 - 10,000 cycles) compared to conventional rechargeable designs (typically limited to 100 - 1,000 cycles). The main drawback to thin-film battery technology lies in the low storage capacity of the cells. The limited storage ability in turn causes the energy density and specific energy of the batteries to suffer. Table 3.1 also provides a comparison of both the energy density and specific energy of the various secondary batteries, in which it can be seen that the R R NanoEnergy cells compare reasonably well to the traditional batteries. The Thinergy cells, however, exhibit a much lower energy density and specific energy, which is mainly due to the fact that the packaging material contributes significantly to the mass and volume of the batteries. Although their small capacity restricts their use to low energy applications, the flexibility, slimness, and superior cycle life of thin-film batteries allows them to be used in applications where previously impractical, such as direct integration into composite structures, thus creating countless new possibilities for energy storage systems. Another important difference between conventional batteries and thin-film lithium- 47 Table 3.1: Properties of various secondary batteries. Voltage (V) Capacity (mAh) Mass (g) Volume (cm3 ) Specific Energy (Wh/kg) Energy Density (Wh/l) Energizer NH15-2450 NiMH AA 1.2 2450 30.00 8.34 98.00 352.52 Energizer NH22-175 NiMH 9V 8.4 175 42.00 21.52 35.00 68.31 Varta V15H NiMH button type 1.2 15 1.30 0.32 13.85 60.00 Samsung AB463446FZ Li-ion cell phone 3.7 800 17.90 8.36 165.36 354.07 AA Portable Power Corp. PL-383562-C2 Li-Polymer single cell 3.7 850 18.00 7.26 174.72 152.73 Front Edge Technology, R Inc. NanoEnergy Lithium thin-film 4.2 4 0.45 0.11 76.36 152.73 Infinite Power Solutions, Inc. R Thinergy MEC101-7 Lithium thin-film 4.0 0.7 0.22 0.11 6.22 25.45 Battery based batteries is the internal resistance of the cells. The thin-film batteries under investigation have typical internal resistances on the order of 50 - 200 Ω. This is extremely high compared to the internal resistance of most conventional alkaline, nickel-metal hydride, and lithium-ion secondary batteries, which are on the order of 0.1 - 1 Ω. As current flows through a battery, there is a voltage drop across the internal resistance of the battery equal to vdrop = i × Rint (3.1) where vdrop is the voltage drop, i is the current flowing through the battery, and Rint is the internal resistance of the battery. This voltage drop decreases the terminal voltage as well as the efficiency of charging and discharging. A large internal resistance is detrimental to battery performance because it causes a significant voltage drop under loads drawing a high amount of current. Due to the large internal resistance of thin-film batteries, it is difficult to source high current levels while maintaining rated cell voltage. Additionally, 48 R R the manufacturers of the Thinergy and NanoEnergy batteries suggest that they not be discharged below 2.1 V and 3 V, respectively, to prevent damage to the cells. High currents, therefore, can only be sourced from the thin-film batteries for a short period of time before reaching the cut-off voltage. 3.1.2 Battery Selection R R Both NanoEnergy and Thinergy cells are considered for use in self-charging structures. As stated previously, the primary difference between the cells lies in the packaging material and encapsulation method. R NanoEnergy thin-film batteries are built by encasing the active elements between a R top and bottom mica substrate and sealing the substrate layers with a Surlyn (DuPont) sealant layer around the perimeter of the active elements. Electrical leads are given in the form of 100 µm thick metal foil tabs. Typical battery dimensions are 28.96 mm x 25.40 mm with a thickness of 150 µm and a mass of around 0.220 grams. The nominal voltage of the cells is 4.2 V and their capacities are around 4 mAh. The manufacturer publishes that the batteries have more than 1000 charge/discharge cycles at 100% depth of discharge, can be charged to 70% of rated capacity in just 2 minutes, and can be discharged at rates up to 10C [104]. (Note that battery charge and discharge currents are given in terms of their rated capacity, C. A rate of 10C for a battery with a capacity of 4 mAh, for example, corresponds to a current of 40 mA.) R Thinergy batteries are assembled using a proprietary encapsulation method, how- ever, it can be observed that they utilize a metal foil substrate for the top and bottom outer layers, which act as electrodes, and a sealant layer between the electrode layers to prevent electrical shorting. The nominal operating voltage of the batteries is 4.0 V and the nominal capacity of the cells used here is 0.7 mAh. Typical dimensions are 25.40 mm x 25.40 mm with a thickness of 170 µm and a mass of about 0.450 grams. Infinite Power Solutions R claims that the Thinergy cells can exhibit 10,000 cycles at 100% depth of charge before deteriorating to 80% of the initial capacity at a C/2 discharge rate. They also state that the batteries can be charged to 90% of rated capacity in 10 minutes and can be discharged at rates up to 40C [101]. Differences in the packaging and sealant layers of the thin-film batteries primarily affect the handling and ease of use of the cells. Preliminary testing of both types of thin-film 49 R batteries has revealed that the metal foil substrate of the Thinergy batteries facilitates R convenient electrode application as opposed to the metal foil tabs of the NanoEnergy cells, which are fragile and difficult to use. Additionally, the metal foil substrate also apR pears more robust compared to the mica substrate used on the NanoEnergy cells, which can peel away from the sealant under shear loading. Previous research has reported simiR lar observations in regards to the fragility of the NanoEnergy cells [107, 108]. Although R R the capacity of the NanoEnergy batteries is superior to that of the Thinergy cells (see R Table 3.1), Thinergy batteries are selected for use in self-charging structures due to their increased robustness. 3.1.3 R Performance Testing of Thinergy Batteries R Prior to combining the Thinergy thin-film batteries with piezoelectric devices to create self-charging structures, the performance of the batteries is evaluated experimentally. The experimental setup used for battery charge/discharge measurements is shown in Fig. 3.2. The batteries are placed in a fixture which allows convenient and temporary electrode connections. The batteries are charged using an HP (now Agilent Technologies, Inc. [109]) 6825A power supply/amplifier (not shown), which provides constant-voltage charging, and discharged through standard carbon film resistors. During charging and discharging, the battery voltage as well as the current flowing in/out of the battery are monitored and recorded using a National Instruments Corp. [110] NI 9215 4-channel analog voltage input card with 16-bit precision running a custom LabVIEW code written to perform the data acquisition task. In order to measure the current flowing through the battery, a transimpedance operational amplifier circuit (powered by two HP 6218A power supplies) utilizing an Analog Devices, Inc. [111] OP177 ultra precision op-amp, shown schematically in Fig. 3.3, is used to convert the current into a voltage that is measurable with the NI 9215 card. The circuit utilizes the large impedance of the op-amp to force the input current to flow through the set resistor, Rset , which can then be measured as a voltage at the output terminal of the op-amp. A portion of the input energy is dissipated in the resistor, however, the op-amp compensates for this dissipated energy by supplying an appropriate amount of energy back to the input to hold the non-inverting input terminal at ground. The set resistor, Rset , must be chosen appropriately based on the expected current to yield a voltage output in a range compatible with the data acquisition system. 50 (a) Dual power supplies (b) Transimpedance op-amp circuit (c) Thin-film battery test fixture (d) NI 9215 data acquisition card and computer (a) (b) (c) (d) Figure 3.2: Experimental setup used to obtain charge/discharge measurements on thinfilm batteries. The current measured during charge/discharge testing can be used to quantify the amount of energy flowing through the battery. Batteries capacities are rated in milliamphours (mAh), which describes charge over time. The capacity achieved during charging and discharging can be calculated by performing numerical integration of the current measurement over time as follows [107, 108]: Z C= (3.2) i dt where C is the battery capacity, i is the measured current, and t is time. Typical voltage R and current measurements during charging and discharging of the Thinergy batteries are shown in Fig. 3.4(a) and Fig. 3.4(b), respectively. Charging is performed by supplying 4.1 V of potential to the battery (per manufacturer specification) using the power supply until only about 35 µA of current is sourced by the battery, at which time the battery is considered fully charged. Discharging is performed by applying a resistive load of 2749 Ω across the battery terminals in order to draw roughly 2C (1.4 mA) of current until a Rset I in OP 177 Vout I in Rset + Figure 3.3: Transimpedance operational amplifier circuit used for current measurement. 51 (a) 8 4.1 Voltage 3 Current 4 2 2 Charge Capacity: 0.702 mAh Voltage (V) Current (mA) 6 1 0 0 1000 Time (sec) 0 1500 3 4.1 3.8 Voltage Current (mA) 2 Load Disconnected Current 3 2 1 Voltage (V) (b) 500 Discharge Capacity: 0.704 mAh 1 0 0 500 1000 Time (sec) 1500 2000 0 R Figure 3.4: Characteristic (a) charge and (b) discharge curves of Thinergy batteries. voltage of 3.0 V (the cutoff voltage recommended by the manufacturer) is reached. A rate of 2C is chosen arbitrarily in order to provide a reasonable time to discharge the battery (approximately 30 minutes). The batteries are capable of achieving discharge rates up to 40C, however, such large discharge rates can degrade the performance of the batteries over time. The charge and discharge characteristics displayed in Fig. 3.4 are typical for rechargeable batteries. In charging, the voltage is held constant and an initial current spike is observed, after which the charge current decreases and levels out at a lower value. The discharge curve shows relatively constant voltage and current until the battery is nearly fully discharged, at which point the voltage and current drop rapidly. For this particular 52 battery, an initial voltage drop during discharging of 0.061 V (from 4.096 V to 4.035 V) and a current of 1.467 mA are observed. The corresponding internal resistance of this battery can be calculated using Eq. (3.1) as 41.58 Ω, which is slightly below the manufacturer’s specification of 50 Ω. Carrying out the capacity calculation given in Eq. (3.2), the capacity in charging is calculated as 0.702 mAh, and in discharging as 0.704 mA, which correlate well with the manufacturer’s specification of 0.7 mAh. It is expected that these capacities be reasonably close to one another, which is the case, and in both charging and discharging, R the full 0.7 mAh capacity can be obtained. Overall, the Thinergy battery performs as expected, showing reasonable charge/discharge characteristics and good charge cycling ability. 3.2 Device Fabrication Assembly of the self-charging structures involves several steps including the selection of piezoelectric and substrate materials, bonding the battery, piezoelectric, and substrate layers, and connecting leads to the electrodes of the thin-film batteries and piezoelectric devices. These steps are outlined in the following sections. 3.2.1 Selection of Piezoelectric and Substrate Materials A commercially available piezoelectric material will be used as the active energy harvesting element in self-charging structures. Several companies produce piezoelectric materials that can be considered. Piezoelectric materials to be used in bending can be categorized into three classes including monolithic piezoceramic, piezoceramic fiber-based, and piezoelectric polymer film devices. Piezoelectric polymer films such as polyvinylidene fluoride (PVDF) are extremely compliant with an elastic modulus around 3 GPa, and typically exhibit low electromechanical coupling. The power output of piezoelectric polymer films is typically orders of magnitude less than monolithic and fiber based piezoelectric materials, therefore, they will not be considered for use in self-charging structures. Piezoelectric fiber-based devices such as the Macro Fiber Composite (MFC) (Smart Material Corp. [112]) or the Piezoelectric Fiber Composite (PFC) (Advanced Cerametrics, Inc. [113]) consist of monolithic piezoceramic fibers embedded in a polymer matrix with interdigitated electrodes. The structure of such devices allows flexibility and moderate energy generation 53 capabilities. Monolithic piezoceramic materials exhibit high energy generation abilities compared with fiber and polymer based devices, however, they are brittle in nature and susceptible to failure under loading. As a compromise between high energy generation R and strength under dynamic loading, QuickPack piezoelectric devices manufactured by R Midé Technology Corp. [99] are selected for use in self-charging structures. QuickPack devices contain monolithic piezoceramic (PZT-5A) active elements bracketed by Kapton R (DuPont) layers to protect the active element and provide robustness. QuickPack QP10n piezoelectric devices, shown in Fig. 3.5, are considered in this work. Several substrate materials can be considered for use in self-charging structures. Typical piezoelectric bimorph energy harvesters contain a thin, relatively flexible substrate, such as brass or aluminum, such that the stiffness of the substrate does not dominate the overall structural stiffness in order to allow adequate vibration energy to be induced in the piezoelectric elements. The substrate layer material selected for use in the self-charging structures is 1100-O aluminum alloy. Alternative substrates, however, can be used to alter the characteristics of the self-charging structures to fit the design parameters of a given application. Important physical parameters of the various components used to construct the selfR charging structures are given in Table 3.2. As stated previously, the QuickPack devices consist of a central monolithic piezoceramic (PZT-5A) layer bracketed by 0.0635 mm thick Kapton layers that include embedded electrodes. Dimensions of both the overall device and the active element are given in the table. The piezoelectric material properties are taken from the manufacturer’s datasheet [114] (QP10n utilizes 3195HD piezoelectric material from CTS Corp.), where the battery properties are found from experimental tests and measurements. The mass density of the battery is found by simply measuring its volume and mass, where the elastic modulus is found by fitting a distributed parameter bending R Figure 3.5: QuickPack QP10n piezoelectric device. 54 Table 3.2: Geometric and material properties of self-charging structure components. Aluminum Substrate Property R R Quickpack Quickpack R Thinergy QP10n QP10n MEC Overall Active 101-7SES Device Element Length (mm) 63.500 50.80 45.97 25.40 Width (mm) 25.400 25.40 20.574 25.40 Thickness (mm) 0.152 0.381 0.254 0.178 69 - 67 55 2730 - 7800 4000 - - -190 - - - 14.60 - Elastic Modulus (GPa) (kg/m3 ) Mass Density Piezoelectric Strain Constant, d31 (pC/N) Dielectric Permittivity Constant, S33 (pF/m) beam model to experimental FRF data obtained with a battery mounted in a cantilever configuration and subjected to base excitation. For modeling purposes, the elastic moduli of the Kapton layers and epoxy layers (not listed in the table) are taken as 3.7 GPa and 3 GPa, respectively, and the mass densities are taken as 1233 kg/m3 and 1000 kg/m3 , respectively [115]. 3.2.2 Vacuum Bonding and Electrode Attachment Fabrication of the self-charging structures is performed by separately bonding each layer using a vacuum bagging procedure, shown schematically in Fig. 3.6, to achieve thin, uniform bonding layers. The vacuum bonding setup includes a commercial vacuum pump, vacuum gauge, vacuum bag surrounding both the workpiece and work surface sealed with vacuum bagging tape, and several material layers surrounding the workpiece. Peel ply layers are placed on both the top and bottom surfaces of the workpiece which prevent excess epoxy from bonding to the work surface or other material layers. Additionally, a bleeder/breather layer is placed on top of the workpiece above the peel ply layer to absorb any excess epoxy and to allow even vacuum over the entire workpiece. Photographs of the vacuum bagging setup are shown in Fig. 3.7. When fabricating the self-charging structures, approximately 20 in-Hg of vacuum is achieved using a Gast Manufacturing, Inc. [116] 23 Series 0523-101 vacuum pump, shown in Fig. 3.7(b). 3M [100] ScotchWeld 55 TM Vacuum Gauge 15 20 10 25 5 0 30 in Hg Vacuum Pump Workpiece Work Surface Breather/Bleeder Cloth Peel Ply Vacuum Bag Tape Figure 3.6: Schematic of vacuum bagging procedure for self-charging structures. DP460 two part epoxy is chosen for the bonding layer due to its high shear strength (27.58 MPa when bonded to aluminum) and high volume resistivity (2.4 x 1014 ohm-cm). Bonding is achieved by applying a thin layer of epoxy between two component layers, placing the device in vacuum, and allowing it to cure for 6 hours. After curing, any excess epoxy is removed from the edges of the device and the process is repeated until the self-charging structure is complete. The average epoxy thickness between device layers is measured as 0.0205 mm. The thin-film batteries are selected as the outermost layers to facilitate attachment of electrical leads. They are placed towards the free end of the device to reduce the induced strain in the batteries in order to help prevent electrical or mechanical failure. With all of the self-charging structure layers bonded, the final step in fabrication involves attaching electrical leads to both the piezoceramic and battery layers. The Quick(a) (b) GAST PUMP PIC Hose to vacuum pump Vacuum bag Self-charging structure Figure 3.7: (a) Vacuum bagging setup; (b) Gast 23 Series vacuum pump. 56 R Pack devices contain an electrical connector (Fig. 3.5), however, it is removed to reduce the length and mass of the piezoceramic layer. With the connector removed, a small area of the flat electrodes is exposed by removing the Kapton coating with a razor blade. 28gauge insulated and stranded wire is then soldered to the exposed electrodes to create an R electrical connection. The entire outer faces of the Thinergy batteries serve as electrodes, and there is a slight overlap on one of the edges of the battery such that both positive and negative electrodes are accessible from a single surface. Electrical leads are attached to the batteries by directly soldering 28-gauge wire to the electrode surfaces. A very small amount of solder is used to prevent shorting of the device when attaching the lead to the overlapping electrode, therefore, an additional epoxy coating is placed over the elecR trode connections to provide mechanical strength as well as electrical insulation. Loctite [117] 3381 UV curable epoxy is used to coat the connection points and is cured in about 3 minutes using LED UV light. A photograph of a complete self-charging structure with electrical leads can be seen in Fig. 3.8. 3.3 Experimental Validation of Electromechanical Model and SelfCharging Concept Experiments are performed on the fabricated self-charging structure shown in Fig. 3.8 in order to verify the electromechanical model described in Chapter 2 and to confirm the ability of the device to simultaneously harvest and store electrical energy. The performance of the self-charging structure is evaluated by mounting the device in a cantilever fashion and subjecting it to base excitations while monitoring the mechanical and electrical response, Figure 3.8: Complete self-charging structure prototype. 57 including the energy transfer between the piezoceramic layers and the battery layers. The following sections describe the results of the experimental characterization. 3.3.1 Electromechanical Model Validation In order to validate the electromechanical assumed modes model and to determine the resonant frequency and optimal load resistance of the clamped device, experiments are conducted to obtain the frequency response functions of the self-charging structure for a set of resistive electrical loads (ranging from 100 Ω to 1 M Ω). The experimental setup used for validation of the electromechanical model is shown in Fig. 3.9. The self-charging structure is clamped to a small TMC Solution [118] TJ-2 electromagnetic shaker (powered by an HP [109] 6825A power supply/amplifier operating as a fixed gain amplifier) with an overhang length of 44.2 mm. A DSP Technology, Inc. (now Spectral Dynamics, Inc. [119]) SigLab 20-42 data acquisition system with four input channels and two output channels is used for all FRF measurements. SigLab is used to generate a low amplitude chirp signal that is used to drive the shaker. Five averages are used for each FRF measurement. The input acceleration, which is used as the reference channel for the FRF measurements, is measured using a PCB Piezotronics, Inc. [120] U352C67 accelerometer attached to the base of the clamp with wax. A PCB Piezotronics, Inc. 482A16 charge coupler is used to condition the accelerometer signal prior to measurement with the SigLab acquisition system. The tip velocity is measured using a Polytec, Inc. [121] OFV-303 laser Doppler vibrometer and OFV-3000 controller by placing a small piece of retroreflective tape at the tip of the cantilever structure, and the voltage output of the self-charging structure is measured directly with the SigLab data acquisition system. Two frequency response functions are, therefore, measured; the tip velocity - to - base acceleration FRF and the voltage - to - base acceleration FRF. It is worth noting that the laser vibrometer measures the absolute tip velocity of the beam as opposed to the relative tip displacement that is predicted by Eq. (2.88), however, Eq. (2.88) leads to the following expression for the absolute tip velocity FRF, as shown by Erturk and Inman [29] (see Appendix C for details of the transformation). Vabs (L, t) 1 = + jωΦT (L) −ω 2 [M] + jω [C] + [K] jωt ab e jω !−1 −1 1 + jω jωCpeq + F̃ Θeq Θeq T Rl 58 (3.3) (a) (b) (f) (c) (d) (g) (h) (e) (e) (a) Fixed gain amplifier (b) Accelerometer coupler (c) Laser vibrometer controller (d) Laser vibrometer head (e) Electromagnetic shaker (f) Accelerometer (g) Clamp (h) Self-charging structure (i) SigLab data acquisition system (i) Figure 3.9: Experimental setup used to obtain frequency response measurements of selfcharging structures. Electromechanical frequency response functions are measured for 15 different load resistance values (standard carbon film resistors are used), as listed in Table 3.3. The input channels of the SigLab data acquisition system have an impedance of 1 MΩ which acts in parallel with the load resistors placed across the piezoelectric layers. The effective load that is seen by the self-charging structure is, therefore, affected by the impedance of the measurement system. Table 3.3 also lists the effective load seen by the piezoelectric layers by considering the 1 MΩ input channel impedance. Experimental voltage - to - base acceleration and tip velocity - to - base acceleration FRFs measured for both the series and parallel connection of the electrodes are shown in Fig. 3.10 and Fig. 3.11, respectively (where the base acceleration is given in terms of the acceleration of gravity, g = 9.81 m/s2 ). In order to verify the electromechanical assumed modes formulation for the self-charging structures, the voltage and tip velocity FRFs are 59 Table 3.3: Load resistance values used in FRF measurements of self-charging structures along with effective load resistances. Load Resistor Values (Ω) Effective Resistance Seen by Piezoelectric Layers (Ω) 100 1200 6700 10000 11800 14700 17600 20000 22000 33000 47000 100000 330000 470000 1000000 99.99 1198.56 6655.41 9900.99 11662.38 14487.04 17295.60 19607.84 21526.42 31945.79 44890.16 90909.09 248120.30 319727.89 500000.00 predicted using Eq. (2.89) and Eq. (3.3), respectively, and plotted over the experimental results in Fig. 3.10 and Fig. 3.11. Thirty modes are used in the assumed modes formulation (N = 30) to ensure convergence of the fundamental natural frequency using the admissible functions given by Eq. (2.29). From the results, it is clear that the model accurately predicts the coupled electrical and mechanical response of the structure. As the load resistance increases from 100 Ω (near the short-circuit condition) to 1 MΩ (near the open-circuit condition), the experimentally measured fundamental natural frequency shifts from 203.9 Hz to 211.6 Hz for the series connection case and from 204.2 Hz to 211.7 Hz for the parallel connection case. These frequencies are predicted by the assumed modes model as 204.0 Hz and 211.6 Hz, respectively (the same for both series and parallel connections). The model predictions of the magnitude of the FRFs are also well matched. The experimental voltage FRFs show a maximum peak voltage output (obtained for the largest load resistance) of 31.61 V/g for the series connection and 18.65 V/g for the parallel connection. It should be 60 noted, however, that these measurements are frequency response based linear estimates obtained from low-amplitude chirp excitation and they are not necessarily accurate for large amplitude excitations with nonlinear response characteristics. The maximum voltage output is predicted by the model as 27.30 V/g for the series case and 15.54 V/g for the parallel case. The maximum tip velocity for the short-circuit condition is measured experimentally as 0.408 (m/s)/g and 0.401 (m/s)/g for the series and parallel cases, respectively, and is predicted by the model as 0.458 (m/s)/g and 0.446 (m/s)/g. For the open-circuit condition, maximum tip velocities of 0.392 (m/s)/g and 0.460 (m/s)/g are measured for (a) Experiment Model 2 |Voltage FRF| (V/g) 10 Increasing Rl 0 10 -2 10 180 |Tip Velocity FRF| ((m/s)/g) (b) 190 200 210 220 Frequency (Hz) 230 240 250 0.5 Experiment Model Experiment (circuit connected) 0.4 0.3 0.2 0.1 Increasing Rl 0 190 200 210 220 230 Frequency (Hz) 240 250 Figure 3.10: Experimental and numerical (a) voltage - to - base acceleration FRFs and (b) tip velocity - to - base acceleration FRFs of self-charging structure for series electrode connection case and for various load resistances. 61 (a) Experiment Model 2 |Voltage FRF| (V/g) 10 Increasing Rl 0 10 -2 10 180 190 200 210 220 Frequency (Hz) 230 240 250 |Tip Velocity FRF| ((m/s)/g) (b) 0.5 Experiment Model 0.4 0.3 0.2 0.1 Increasing Rl 0 180 190 200 210 220 Frequency (Hz) 230 240 250 Figure 3.11: Experimental and numerical (a) tip velocity - to - base acceleration FRFs and (b) voltage - to - base acceleration FRFs of self-charging structure for parallel electrode connection case and for various load resistances. the series and parallel cases, respectively, and the predicted values are 0.387 (m/s)/g and 0.440 (m/s)/g. After the preliminary analysis for the resistive load case, the piezoceramic and thin-film battery layers are connected to the input and output of a simple linear voltage regulator energy harvesting circuit consisting of a full bridge diode rectifier, smoothing capacitance, and a Texas Instruments, Inc. [122] TPS71501 adjustable output voltage regulator, shown schematically in Fig. 3.12. The electrical boundary conditions of the piezoceramic layers then become more sophisticated. The tip velocity FRF is measured for the series electrode 62 connection case (which will be used in the following section for the charge/discharge measurements), and is plotted in Fig. 3.10(b). It appears from the figure that the case with the largest resistive load (effectively 500 kΩ, which is close to open-circuit conditions) most closely represents the vibration response of the self-charging structure when connected to the circuit. The resonant frequency in this configuration is found to be around 210.0 Hz. Based on the voltage FRFs given in Fig. 3.10(a) and Fig. 3.11(a), several electrical performance curves can be extracted to better describe the electrical behavior of the system. The variation of the peak voltage, current, and electrical power with load resistance can be determined at both the short-circuit and open-circuit resonance frequencies, which are of particular importance for energy harvesting purposes as they provide bounds on the fundamental resonance frequency of the system under examination. For any load resistance, the fundamental natural frequency will lie between the short-circuit and open-circuit resonance frequencies. The variation of the peak voltage with load resistance is presented in Fig. 3.13(a) and Fig. 3.13(b) for the series and parallel electrode connections, respectively. The model predictions are in good agreement with the experimental data. The voltage initially follows a linearly increasing trend with increasing load resistance, but approaches a horizontal asymptote at large load resistance values. The peak voltage output values predicted by the model for the largest load resistance at the short-circuit and open-circuit resonance frequencies are 10.26 V/g and 27.30 V/g, respectively for the series case and 5.21 V/g and 15.54 V/g, respectively for the parallel case. Figure 3.13(c) and Fig. 3.13(d) show the variation of the peak current output with load TPS71501 Voltage Regulator + C1 100 F PZT C 2 0.22 F Bandgap Reference - C 3 0.22 F + Vo - R1 2.24 M R2 950 k Figure 3.12: Linear voltage regulator energy harvesting circuit. 63 (a) 2 (b) 10 1 10 Voltage (V/g) Voltage (V/g) 1 0 10 Experiment (211.6 Hz) Experiment (203.9 Hz) Model (211.6 Hz) Model (204.0 Hz) -1 10 -2 10 2 10 4 10 Load Resistance () 10 0 10 Experiment (211.7 Hz) Experiment (204.2 Hz) Model (211.6 Hz) Model (204.0 Hz) -1 10 -2 10 6 2 10 10 (c) 4 10 Load Resistance () 6 10 (d) 0 0 Current (mA/ g) 10 -1 10 Experiment (211.6 Hz) Experiment (203.9 Hz) Model (211.6 Hz) Model (204.0 Hz) -2 10 2 10 Power (mW/g2) (e) -1 10 10 6 10 (f) 0 10 -1 10 Experiment (211.6 Hz) Experiment (203.9 Hz) Model (211.6 Hz) Model (204.0 Hz) -2 10 -3 2 4 10 Load Resistance () 2 10 1 10 Experiment (211.7 Hz) Experiment (204.2 Hz) Model (211.6 Hz) Model (204.0 Hz) -2 4 10 Load Resistance () 10 10 10 Power (mW/g2) Current (mA/ g) 2 10 4 10 Load Resistance () 1 10 0 10 -1 10 Experiment (211.7 Hz) Experiment (204.2 Hz) Model (211.6 Hz) Model (204.0 Hz) -2 10 -3 10 6 10 6 10 2 10 4 10 Load Resistance () 6 10 Figure 3.13: Experimental and numerical electrical performance curves of self-charging structure for the peak voltage output in the (a) series and (b) parallel case, current output in the (c) series and (d) parallel case, and power output in the (e) series and (f) parallel case with varying load resistance for the self-charging structure. resistance for the series and parallel electrode connection cases, respectively. A converse behavior can be observed in the current output curves compared to the voltage output curves. A horizontal asymptote exists for small load resistance values and the current linearly decreases for larger load resistance values. The peak current output is predicted by the model for the smallest load resistance at the short-circuit and open-circuit resonance frequencies as 0.99 mA/g and 0.32 mA/g, respectively, for the series case and 1.93 mA/g and 0.64 mA/g, respectively, for the parallel case. 64 Lastly, the variation of the power output with load resistance is given in Fig. 3.13(e) and Fig. 3.13(f) for the series and parallel cases, respectively. For both cases, a peak power output exists for each excitation frequency at different optimal load resistance values between short-circuit and open-circuit conditions. Additionally, the peak power output for the short-circuit and open-circuit conditions are roughly equal. Furthermore, the peak powers predicted for the series connection and parallel connection are identical. The peak power output for excitation at the short-circuit resonance frequency is predicted by the model as 2.68 mW/g2 for a load resistance of 10.55 kΩ for the series connection and 2.62 kΩ for the parallel connection. For excitation at the open-circuit resonance frequency, the model predicts a peak power output of 2.70 mW/g2 for a load resistance of 100.1 kΩ for the series connection and 27.77 kΩ for the parallel connection. Again, these peak values are linear estimates based on low-amplitude excitation and are not necessarily accurate for large amplitude excitation. The results presented in Fig. 3.10 and Fig. 3.11 as well as Fig. 3.13 validate the electromechanical assumed modes model through comparison of simulation results to experimental measurements. Both the vibration and voltage response of the self-charging structure over a range of frequencies surrounding the fundamental frequency (which is of most interest in piezoelectric energy harvesting) are successfully predicted by the model. The coupled model can, therefore, be used to accurately predict the behavior of self-charging structures excited via harmonic base excitation. 3.3.2 Self-Charging Structure Concept Validation The ability of the self-charging structures to operate in a self-charging manner in which energy is simultaneously harvested in the piezoelectric layers and stored in the battery layers is explored. Charge/discharge experiments are conducted in which the device is initially excited at resonance with the piezoelectric layers connected through the linear regulator harvesting circuit to charge the battery while the voltage of and current flowing into the thin-film battery layer is monitored. Subsequently, the thin-film battery is discharged while monitoring battery current and voltage. Charge and discharge profiles can then be defined. The resonance frequency of the self-charging structure when connected to the energy harvesting circuit circuit has been obtained in the previous section as 210.0 Hz (Fig. 3.10(b)). 65 The experimental setup for charge/discharge measurements (similar to the setup used for FRF measurements) is shown in Fig. 3.14. The new equipment used here includes a National Instruments Corp. [110] CompactDAQ chassis with a NI 9215 4-channel analog voltage input card with 16-bit precision (used to measure battery voltage and current measurement from transimpedance amplifier), a NI 9233 4-channel 24-bit analog input card with IEPE coupling (used for accelerometer measurement), and a NI 9263 4-channel analog output card with 16-bit precision and ±10 V range (used to excite shaker). A custom LabVIEW program is written to perform the data acquisition and signal generation using the National Instruments hardware. The linear voltage regulator circuit is also pictured in Fig. 3.14. For this experimentation, the two piezoelectric layers of the self-charging (e) (f) (h) (g) (a) (b) (d) (c) (d) (c) (c) (a) (a) NI CompactDAQ data acquisition system and computer; (b) Dual power supplies; (c) Voltage regulator circuit; (d) Electromagnetic shaker; (e) Fixed gain amplifier; (f) Accelerometer; (g) Self-charging structure; (h) Clamp Figure 3.14: Experimental setup used to obtain charge/discharge measurements of selfcharging structures. 66 structure are connected in series for increased voltage output and used to charge a single battery layer. The input base excitation amplitude is set to ±1.0 g. The device is excited at resonance for 1 hour and the battery voltage and current into the battery are measured throughout the test. Once the test is complete, the battery is discharged using a 2749 Ω resistor in order to draw roughly 2C of current (1.4 mA) from the battery. Results from both the charge and discharge tests are shown in Fig. 3.15. From Fig. 3.15(a), it can be seen that the piezoelectric layers are able to supply an average of about 0.08 mA of current into the battery. Using Eq. (3.2), the capacity during charging is found to be 0.0781 mAh. During (a) 0.25 4.1 Current (mA) 0.2 3 0.15 Current 0.1 2 0.05 Voltage (V) Voltage 1 Charge Capacity: 0.0781 mAh 0 0 1000 1500 2000 Time (sec) 2500 3000 0 3 4.1 3.8 Voltage 2 Current (mA) 3500 3 Load Disconnected Current 2 1 Voltage (V) (b) 500 Discharge Capacity: 0.0663 mAh 1 0 0 50 100 150 Time (sec) 200 250 0 Figure 3.15: Experimental curves for self-charging structures in (a) charging and (b) discharging under ±1.0 g acceleration at 210.0 Hz. 67 discharging, the current output is held at 1.4 mA for about 120 seconds before beginning to decay, as shown in Fig. 3.15(b), and a capacity of 0.0663 mAh is calculated. There is a slight difference between the capacities calculated in charging and discharging, which is likely a leakage effect where some of the energy during charging is dissipated, thus there is a small decrease in capacity when discharging. Although a simple linear regulator circuit is used here to evaluate the performance of the self-charging structures (the goal of this analysis is to prove the ability to self-charge), more advanced circuitry can be used to improve the amount of energy extracted from the piezoelectric layers and transferred to the battery layers. Although not shown here, a nonlinear switching circuit with impedance matching ability has been investigated and it has been found that significant increases in efficiency can be obtained for high excitations levels (the power draw of the self-powered switching circuit outweighs any advantages under low level excitation) [51, 123]. The charge/discharge results presented in Fig. 3.15 prove the ability of the self-charging structures to simultaneously generate and store electrical energy in a multifunctional manner, and validate the concept of self-charging. Furthermore, the current of 0.08 mA corresponds to an average power of around 0.306 mW during charging. This is a reasonable value for piezoelectric energy harvesting, where typical harvested powers are in the microwatt to milliwatt range [4]. 3.4 Chapter Summary This chapter presents details of the fabrication and experimental testing of self-charging structures. The evaluation and selection of thin-film batteries is first given. Fabrication of a self-charging structure prototype is then reviewed. Lastly, results of experimental testing are presented including both frequency response function measurements and charge/ discharge measurements to validate the electromechanical model presented in Chapter 2 and the ability of the device to act in a self-charging manner. R R Two types of thin-film batteries are investigated; NanoEnergy and Thinergy cells. R Based on preliminary testing results, Thinergy batteries are selected for use in self-charg- ing structures due to their superior robustness and packaging. Fabrication of the prototype device is achieved through a vacuum bagging procedure using two part epoxy to bond 68 each layer, thus providing thin and uniform bonding layers. Experimental testing is performed to validate both the electromechanical assumed modes model and the self-charging ability of the device. Frequency response measurements are recorded for the self-charging structure mounted in a cantilever configuration and subjected to harmonic base excitation for a range of load resistances. Simulation results predicted by the model are compared to the experimental measurements and the model is found to accurately predict the vibration and voltage response of the harvester for each load resistance tested. Experimental charge/discharge testing is also conducted in which the energy harvesting ability of the self-charging prototype is investigated. With the piezoelectric layers connected in series to charge a single battery, the device is excited at resonance for 1 hour and found to successfully charge the battery. Discharge measurements confirm that the battery was charged during the test. Results of the charge/discharge measurements prove the ability of the device to act in a self-charging fashion. 69 C HAPTER 4 S TRENGTH A NALYSIS OF S ELF -C HARGING S TRUCTURES I T has been proposed that self-charging structures be directly integrated into host struc- tures in a multifunctional manner. Inherent in this proposal is the fact that the self- charging structures must act as load bearing members. Experimental testing is carried out on self-charging structures in order to determine their strength properties. Results of the strength testing can be used as a design tool in the development of embedded selfcharging structure systems. Both static three-point bend testing and dynamic harmonic base excitation testing are considered. Additionally, static testing is performed on a variety of piezoelectric materials as the piezoelectric layer is found to be the critical layer in static failure. The following sections outline the formulations and procedures used to define the failure strength of the self-charging structures and piezoelectric materials, as well as the results of experimental failure testing. 4.1 Static Strength Analysis of Self-Charging Structures Bending tests are typically employed to evaluate the tensile strength of brittle materials (such as the piezoceramic layers in the case of self-charging structures) [124]. Classical three-point bending tests are performed in order to experimentally evaluate the strength of the individual components of the self-charging structures as well as the complete structure under static loading. 70 4.1.1 Strength Calculations for 3-Point Bend Testing Consider the schematic of a three-point bending test setup shown in Fig. 4.1. The rectangular test specimen is loaded in the transverse direction with a load of P . The load is applied at the center of the support span (x = L/2), therefore, the maximum bending moment occurs at this point and is equal to Mmax = P L/4. The load required for failure of the specimen by transition from elastic material behavior to either plastic behavior (for ductile materials) or abrupt failure (for brittle materials) can be defined as the mechanical failure load, Pf , which can be used to define a mechanical failure strength. The maximum bending moment that corresponds to the failure load, Pf , of the complete device is defined as the failure bending moment, Mf . The bending strength of a simple beam placed under three-point bending is defined from Euler-Bernoulli beam theory as σb = 3L Pf 2bh2 (4.1) where σb is the bending strength of the specimen, b is the specimen width and h is the specimen thickness. The maximum bending stress of a given layer of a multilayer composite device, such as the complete self-charging structure, can be defined as σbmax = Yk hkn L Yk hkn Mf = Pf YI 4Y I (4.2) where σbmax is the maximum bending stress of a layer at a given failure load of the device, Yk is the elastic modulus of the layer of interest (layer k), hkn is the distance from the neutral axis to the outer surface of the kth layer, and Y I is the overall bending stiffness of the multilayer beam. The calculation of Y I for a composite beam has been discussed in Chapter 2, and details of the formulation for self-charging structures (both the root section P L Figure 4.1: Schematic of three-point bending test. 71 without battery layers and the tip section with battery layers) are given in Appendix B.2. A beam-like aspect ratio is assumed in the foregoing derivation, where thin-plate parameters can be used for bending of plate-like configurations [30]. Equation (4.1) gives the failure strength of the self-charging structure layers when tested individually, where Eq. (4.2) can be used to estimate the maximum stress of an individual layer for the failure load of the total device. It is worth mentioning that the maximum stress of a layer for the failure load of the entire structure might be lower than its individual failure strength. For example, for the failure load that results in fracture of a piezoceramic layer in a multi-layer assembly, the maximum stress in the substrate layer could be lower than its individual failure strength. Nevertheless, the overall structure is assumed to be failed when any layer starts exhibiting brittle or ductile failure behavior. 4.1.2 Experimental Testing and Results R Experimental testing is performed using an Instron [125] 4204 universal test frame with an MTS Systems Corp. [126] ReNew upgrade package equipped with a 1000 N load cell and a small three-point bend fixture with adjustable supports, shown in Fig. 4.2. Each specimen rests on the two lower support pins, which are spaced 20 mm apart, and the central pin is lowered at a rate of 0.3 mm/min until a prescribed displacement is reached. In each case, the specimens fail before the maximum displacement is achieved. Both the load and the crosshead displacement are recorded throughout each test using MTS TestWorks 4 software. R Three individual samples are tested for the aluminum substrate, QuickPack QP10n Upper loading pin Test specimen Bottom adjustable support pins Figure 4.2: Experimental setup used for three-point bend testing including Instron/MTS 4204 test frame and fixture. 72 R piezoceramic, and Thinergy battery layers. Conventionally, three-point bend testing is performed on beam-shaped samples in order to eliminate Poisson effects. It is desirable, R battery samples in an unmodified state as dicing the bathowever, to test the Thinergy teries could result in damage to the packaging or delamination, therefore, plate-like samples are tested here. The aluminum specimens are cut to 25.4 mm x 25.4 mm, and the R QuickPack samples are cut in half to fit in the test fixture (resulting in two identical sam- ples of about 25.4 mm x 25.4 mm). A single self-charging structure is tested and cut in half such that each section can be tested separately. Photographs of each component after failure testing are shown in Fig. 4.3. Typical load-deflection curves for the individual layers as well as the complete structure are shown in Fig. 4.4. From the results presented R in Fig. 4.4(a), it is clear that the individual QuickPack piezoceramic layers exhibit brittle R failure and the individual aluminum substrate and Thinergy battery layers exhibit duc- tile failure. In the case of the aluminum sample, the failure load is taken where a slight, prolonged drop in the force is observed, as noted in the figure. From Fig. 4.4(b), it can be seen that the root section of the self-charging structure experiences brittle failure, where (a) (b) (c) (d) (e) R Figure 4.3: Various specimens after three-point failure testing including (a) Thinergy R battery, (b) QuickPack QP10n piezoelectric, (c) aluminum substrate, (d) root section of complete self-charging structure, and (e) tip section of complete self-charging structure. 73 (a) 14 QuickPack 12 Brittle Failure Thinergy Load (N) 10 8 Ductile Failure 6 Aluminum 4 Aluminum QuickPack Thinergy Linear Curve Fit 2 0 -2 0 0.5 1 1.5 2 2.5 Displacement (mm) 3 3.5 (b) Simultaneous Ductile/Brittle Failure 180 250 160 Tip Section Root Section Linear Curve Fit 140 Load (N) 200 120 0.1 0.15 0.2 0.25 150 Tip 100 50 0 0 Root 0.5 1 1.5 2 2.5 Displacement (mm) 3 3.5 4 Figure 4.4: Load-deflection curves for (a) individual layers and (b) complete self-charging structure sections. the tip section exhibits simultaneous ductile and brittle failure behavior. This simultaneous failure phenomenon is likely due to failure occurring in the piezoceramic (brittle) and battery (ductile) layers for nearly the same applied load. The failure load results for all of the specimens tested are presented in Table 4.1. With the failure loads obtained, Eq. (4.1) and Eq. (4.2) can be used to obtain the maximum bending stress values for each sample tested. The minimum failure load is used in the calculations for the individual layers to give a conservative estimate. For the complete self-charging structure, the overall bending stiffness, Y I of the root section (containing only the aluminum substrate and piezoceramic layers) is calculated as Y I = 0.0647 Nm2 , 74 Table 4.1: Failure loads for three-point bending tests. Parameter Failure Load (N) Minimum (N) Failure Load (N) Aluminum Substrate QP10n Device R Thinergy Batteries 3.21 7.25 6.58 3.36 8.80 5.47 3.66 8.50 5.89 3.21 7.25 5.47 Complete Self-Charging Structure Root Section Tip Section 39.9 165.3 and of the tip section (containing the aluminum substrate, piezoceramic layers, and battery layers) is calculated as Y I = 0.2380 Nm2 . From the geometry of the device given previously in Section 3.2, the distances from the neutral axis to the outer layers of the aluminum substrate, piezoelectric, and battery layers are calculated as hkn = 0.0762 mm, hkn = 0.4142 mm, and hkn = 0.6760 mm, respectively. The calculated failure strength values for each of the specimens are listed in Table 4.2. It should be noted that the calculation of failure R stress in the QuickPack layers considers the dimensions of only the active element in calculating hkn , ignoring the outer Kapton layer, as the ceramic layer experiences failure. From the results, it can be seen that failure in the root section of the self-charging strucTable 4.2: Failure strengths for three-point bending tests. Parameter Aluminum Substrate QP10n Device R Thinergy Batteries Individual Layers Failure Stress (MPa) 229.27 159.82 199.33 Self-Charging Structure - Root Failure Stress (MPa) 15.84 83.62 - Self-Charging Structure - Tip Failure Stress (MPa) 17.84 94.18 75 126.18 ture is due to failure of the piezoceramic layers. At the point of failure, the maximum stress in the aluminum layer is much less than the failure stress observed in a single aluminum R is about half of the failure stress obtained layer. The maximum stress in the QuickPack for a single layer, however, it is on the same order of magnitude. Although there is a significant difference between the maximum stress of the single layer and composite device, it is typical in brittle failure to observe a wide range of failure loads (thus failure stresses) for a single material. Results for the tip section of the self-charging structure show failure in both the piezoceramic and battery layers with stresses similar to the failure stress of the individual layers in both cases. This result is confirmed by the simultaneous brittle and ductile failure observed in Fig. 4.4(b). Overall, it can be concluded that the piezoceramic and battery layers are the critical layers in three-point bending failure. 4.2 Dynamic Strength Analysis of Self-Charging Structures Piezoelectric energy harvesters must be subjected to dynamic vibration excitation in order to create useful electrical energy. A series of dynamic strength tests are conducted to gain an understanding of the dynamic loading that can be withstood by the self-charging structures without failure. Specifically, harmonic base excitation at increasing acceleration amplitudes is imposed on a cantilever structure which is monitored for signs of mechanical and/or electrical failure. 4.2.1 Strength Calculations for Harmonic Base Excitation Testing Based on the assumed modes model presented in Chapter 2, the maximum dynamic stress of the kth layer of a self-charging structure excited under base excitation can be expressed in terms of a stress - to - base acceleration FRF. Recall from Eq. (2.5) that the stress in a structural layer is given as σ(x, z, t) = Ys Sxx (4.3) ∂ 2 wrel (x, t) ∂x2 Recognizing that the maximum stress in a particular layer of interest will occur at the = −Ys z outermost surface of the layer, the maximum stress in a structural layer can be defined as ∂ 2 wrel (x, t) max σk (xcr , hkn , t) = −Yk hkn (4.4) ∂x2 x=xcr 76 where Yk is the elastic modulus of the kth layer, hkn is the distance from the neutral axis to the outermost surface of the kth layer, and xcr is the position along the length of the beam where the curvature is maximum (e.g. it is the root for the fundamental mode of a uniform cantilever beam). Similarly, for a piezoelectric layer, Eq. (2.9) leads to the following expression for the maximum stress in a piezoelectric layer σkmax (xcr , hkn , t) = −cE 11 hkn ∂ 2 wrel (x, t) v(t) − e31 ∂x2 hkn x=xcr (4.5) Note that the piezoelectric layers include a voltage induced stress contribution that always adds to the stress. The sign of both terms in Eq. (4.5) varies depending on the poling direction of the piezoceramic layer, however, the absolute value of both terms can be used for simplification. The relative beam displacement expression given in Eq. (2.87) leads to ∂ 2 wrel (x, t) 00 = wrel (x, t) = Φ” T (x) −ω 2 [M] + jω [C] + [K] 2 ∂x !−1 −1 1 Fejωt Θeq Θeq T +jω jωCpeq + Rl (4.6) Using Eq. (4.6) and the expression previously given for the voltage output of the selfcharging structures (Eq. (2.86)) along with Eq. (4.4) and Eq. (4.5), the following expression can be defined to describe the maximum stress FRF in any layer of the self-charging structure 00 σkmax (xcr , hkn , t) wrel (xcr , t) vk (t) = Yk hkn + λk e31 ab ejωt ab ejωt hp ab ejωt (4.7) where Yk is the elastic modulus of the kth layer (the elastic modulus measured at constant electric field in the case of a piezoelectric layer) and λk is equal to 1 if layer k is a piezoelectric layer, otherwise it is zero. Using Eq. (4.7), the maximum dynamic stress values of the individual layers can be predicted for a given value of base acceleration. The same self-charging structure prototype described and tested in Chapter 3 (shown in Fig. 3.8) is tested here for dynamic failure. Again an overhang length of 44.2 mm is achieved with the device clamped to the shaker. Both the aluminum and the piezoelectric layers are clamped at the root of the device, therefore, the maximum stress in those layers is expected to occur at the root (i.e. xcr = 0 mm). 77 The battery layers, however, are near the free end of the beam, therefore, the maximum stress occurs at the edge of the battery closest to the root of the cantilever (xcr = 18.8 mm). Estimates of the maximum stress - to - base acceleration FRFs of the aluminum, piezoceramic, and battery layers are given in Fig. 4.5. From the results, the maximum bending stress of the aluminum, piezoelectric, and battery layers are found to be 3.1 MPa/g, 17.7 MPa/g, and 4.6 MPa/g, respectively. These linear estimates of the stress per base acceleration provide insight into the amount of excitation that can be safely imposed on the device. For large amplitude excitations, however, both geometric and material nonlinearities may exist in the cantilever piezoelectric structure, thus the linear estimates must be used with caution. 4.2.2 Experimental Testing and Results Dynamic failure testing is conducted using the same experimental setup used previously in Chapter 3 for charge/discharge measurements (shown in Fig. 3.14) by subjecting the cantilever harvester to resonant base excitations of increasing amplitude until electrical or mechanical failure is observed. Electrical failure is defined as a 10% decrease in either the charge or discharge behavior of the self-charging structure as compared to a baseline charge/discharge profile, signifying failure in the thin-film battery layers. Mechanical failure is defined as fracture or cracking of the aluminum or piezoceramic layers evident from |Maximum Stress FRF| (MPa/g) 20 Aluminum Piezoceramic Battery 15 10 5 0 180 190 200 210 220 Frequency (Hz) 230 240 250 Figure 4.5: Estimates of the maximum dynamic bending stress in the aluminum, piezoceramic, and battery layers. 78 changes in the dynamic behavior of the system and from the ability of the piezoelectric layers to deliver energy to the battery layers. The self-charging structure is clamped to the shaker and remains undisturbed throughout the duration of the dynamic testing. An initial baseline charge/discharge measurement is obtained for the device by following the procedure outlined previously in Subsection 3.1.3 and all future measurements for battery failure are compared to this baseline. Once the baseline is obtained, the device is first excited at resonance at an initial acceleration input level of ±0.2 g for 1 hour. During the test, the piezoceramic layers are connected in series to the linear regulator circuit and used to charge a single thin-film battery layer (which is initially fully discharged to 3.0 V). The battery voltage and current are monitored and recorded in order to evaluate the health of the piezoelectric layers (mechanical failure will cause the output of the piezoelectric layers to vary). After 1 hour, the excitation is ceased and a discharge test is performed on the battery by drawing 2C of current through a 2749 Ω load. The self-charging structure is then allowed to sit for 24 hours before testing is resumed, as chemical failure in the battery (potentially due to delaminations) may require time to take effect. After 24 hours, the thin-film battery is charged using the power supply and subsequently discharged. This charge/discharge data is compared to the baseline charge/discharge profile recorded prior to failure testing and significant changes indicate electrical failure in the battery (caused by the excitation the previous day). Finally, the acceleration amplitude is increased and the process is repeated. It is expected that for larger excitation amplitudes, the piezoelectric layers will provide more power. Deviations in this trend indicate mechanical failure in the piezoelectric layers. Complete results from the dynamic failure testing for the power supply charge/discharge (used to indicate electrical failure) are given in Fig. 4.6(a) for base acceleration values from 0.2 g to 7.0 g. Additionally, the charge/discharge results with the piezoceramic layers charging the battery (used to indicate mechanical failure) are given in Fig. 4.6(b). All of the charge/discharge curves for both the power supply and piezoelectric charging of the battery are given in Appendix D for reference. Based on the maximum stress predictions given in Fig. 4.5, an upper limit of 7.0 g (corresponding to 125 MPa of stress in the piezoceramic layers) is chosen. Recall from Subsection 4.1.2 that the piezoelectric layer exhibited a maximum stress of around 100-125 MPa in static failure. Although linear estimates are used here, they provide a reasonable basis for limiting the dynamic excitation level. 79 From the dynamic failure testing results presented in Fig. 4.6(a), it can be seen that as the excitation amplitude is increased from 0.2 g to 7.0 g, there is no significant change in the power supply charge or discharge behavior. In each case, the charge amplitude is slightly higher than the discharge amplitude, likely due to leakage in the battery. The power supply charge after 5.5 g excitation is abnormally high, thus the battery initially appears damaged, but continuation of testing at higher excitation levels shows that the battery functions properly. This phenomenon may be attributed to experimental variation. Although it was expected that electrical failure would occur in the batteries at the acceler(a) 1 0.9 Charge Discharge Capacity (mAh) 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 Baseline 0.2 0.4 0.6 0.8 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 Acceleration (g) (b) 0.35 Charge Capacity (mAh) 0.3 Discharge 0.25 0.2 0.15 0.1 0.05 0 0.2 0.4 0.6 0.8 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 Acceleration (g) Figure 4.6: Charge/discharge capacities measured for (a) power supply and (b) piezoelectric charging for dynamic failure analysis of self-charging structures. 80 ation levels tested, no electrical failure was observed, hence an electrical failure strength cannot be defined for the device. The piezoelectric charge/discharge results presented in Fig. 4.6(b) show that the piezoelectric layers are able to partially charge the thin-film battery. As the excitation amplitude is increased, the total charge capacity (as well as discharge capacity) monotonically increases. This is expected as higher excitation levels induce more vibration energy into the harvester. The steady increase in charge capacity shows that no mechanical failure is observed in the piezoelectric layers at the acceleration levels tested. The results given in Fig. 4.6(b) also show a difference in the charge and discharge capacities for each test. This variability is likely due to leakage in the battery as the current input from the piezoceramic layers is quite low. Overall, the experimental results show that no electrical battery failure or mechanical piezoelectric failure is observed for any of the excitation levels tested. 4.3 Static Strength Testing of Various Piezoceramic Materials The results presented in Subsection 4.1.2 suggest that the piezoceramic and battery layers are critical in static failure. While the selection of thin-film batteries is limited, a wide variety of piezoelectric ceramics exist for consideration in vibration energy harvesting systems including self-charging structures. In this section, a more rigorous investigation of the static bending strength of several commercially available piezoceramic materials through three-point bend testing is performed to provide a design tool in the development of vibration energy harvesting systems in which the active device is subjected to bending loads. Previous research exists in both the ceramics and smart structures fields in which the bending strength of various types of piezoceramic materials has been investigated [127– 133]. Testing of soft piezoceramics [127–130], hard ceramics [131, 132], and single crystal ceramics [133] has been reported. Researchers have investigated the effects of poling state, surface condition, applied electric field, and temperature on the bending strength of the materials. Although some data exists on the bending strength of piezoceramic materials, the goal of the research presented in this section is to present a more comprehensive study of the bending strength of several commonly used piezoceramic materials as well as more recently developed PMN-PT and PMN-PZT single crystal piezoelectric materials. 81 4.3.1 Materials Several commonly used piezoelectric materials are investigated. Perhaps some of the most commonly used piezoelectric materials in vibration energy harvesting systems, two types of soft PZT ceramic materials are tested. PZT-5A (DOD Type II) and PZT-5H (DOD Type VI) ceramics (PSI-5A4E and PSI-5H4E, respectively) manufactured by Piezo Systems, Inc. [134] are investigated. Both materials utilize vacuum sputtered nickel electrodes and are poled through the thickness. Several researchers have used these PZT ceramics in energy harvesting applications including PZT-5A for self-powered sensor nodes [135] and gunfire shock munitions harvesting [136], and PZT-5H for microgenerators in wireless electronics [22]. Two types of hard PZT ceramic are also tested. PZT-4 (DOD Type I) and PZT-8 (DOD Type III) ceramics (PZT-844 and PZT-881, respectively) manufactured by APC International, Inc. [137] are studied. The materials utilize silver electrodes and are poled through the thickness. While hard PZT is not typically used in energy harvesting applications, PZT-4 has recently been proposed for use in harvesting magnetic energy through the combination of piezoelectric and piezomagnetic material layers in a composite device [138]. In addition to conventional PZT ceramics, two types of single crystal piezoelectric ceramics are also investigated. PMN-PT single crystal ceramics and PMN-PZT single crystals (CPSC 160-95) produced by Ceracomp Co., Ltd. [139] are tested. The materials contain gold electrodes and are poled through the thickness. Several researchers have investigated the use of PMN-PT in energy harvesting applications to utilize its large piezoelectric coupling [140, 141]. Although a relatively new material, some research has also been conducted to investigate the use of PMN-PZT single crystal ceramics for energy harvesting applications [142, 143]. R The final types of piezoelectric material investigated are QuickPack devices. Both QP10n (used in self-charging structures) and QP16n devices are investigated. QP16n are similar to QP10n, with the difference being in the thickness of the devices (0.254 mm thickness for QP16n as opposed to 0.381 mm thickness for QP10n). 82 4.3.2 Sample Preparation All of the materials investigated are supplied as bulk material from the manufacturers, with the exception of the PMN-PT samples which are supplied as beam like specimens that do not require further processing. The physical dimensions as well as the manufacturer part numbers for all of the materials tested in this work are given in Table 4.3. Typical bend test specimens are beam like with large aspect ratios, thus processing of the bulk material is required to obtain appropriate samples for testing. The ASTM C 1161-02c standard, titled “Standard Test Method for Flexural Strength of Advanced Ceramics at Room Temperature” was consulted in preparing the test samples [144]. Samples with dimensions of 4 mm x 3 mm x 45 mm are specified in the standard, however, the thicknesses of the materials acquired dictate a deviation from the standard. In order to maintain beam like samples, the bulk material is cut using a dicing saw to provide samples of approximately 2 mm width. A MicroAutomation 1006 dicing saw is used with 2-6 µm grit, 75 µm wide diamond dicing blades, a spindle speed of 28000 rpm, and a feed rate of 2 mm/sec. The length of the diced samples varies from 20.0 mm to 46.0 mm across the different material types. After completion of the dicing operation, the samples are investigated using a Nikon Instruments, Inc. [145] Eclipse LV100 optical microscope in order to obtain a precise measurement of the width of each sample, and additionally to determine the average flaw size induced in the edges from the dicing process. Figure 4.7 shows an example of an image acquired using the optical microscope in which the width of a PMN-PZT sample Table 4.3: Physical dimensions of various piezoceramic materials tested. Material Manufacturer Part Number Bulk Dimensions (mm) Final Sample Dimensions (mm) PZT-5A T110-A4E-602 72.4 x 72.4 x 0.267 36.18 x 1.959 x 0.267 PZT-5H T110-H4E-602 72.4 x 72.4 x 0.267 36.18 x 1.959 x 0.267 PZT-4 PZT-844 40.0 x 10.0 x 0.5 20.0 x 1.950 x 0.5 PZT-8 PZT-881 25.4 x 25.4 x 1.0 25.4 x 1.914 x 1.0 PMN-29PT 30.0 x 2.012 x 0.28 30.0 x 2.012 x 0.28 PMN-PT PMN-PZT CPSC 160-95 40.0 x 10.0 x 0.28 40.0 x 1.967 x 0.28 R QuickPack QP10n 46.0 x 20.6 x 0.254 46.0 x 1.962 x 0.254 R QuickPack QP16n 46.0 x 20.6 x 0.152 46.0 x 1.960 x 0.152 83 Dicing cut Piezoelectric material Adhesive substrate Figure 4.7: Optical microscope image of PMN-PZT sample after dicing showing width measurement (5X objective lens). has been measured. Characteristic images of the flaws induced during diced are shown in Fig. 4.8, and the average flaw size is found to be about 6 µm, 8 µm, 40 µm, 35 µm, 19 µm, and 19 µm for PZT-5A, PZT-5H, PZT-4, PZT-8, PMN-PT, and PMN-PZT, respectively. The R outer Kapton layers of the QuickPack devices prohibited optical measurement of flaw size in the piezoelectric layers. Figure 4.9 shows the final prepared samples ready for bend testing. The final sample dimensions for each material are also listed in Table 4.3. 4.3.3 Experimental Setup Three-point bend testing is carried out using an Instron [125] 5848 MicroTester frame equipped with a 50 N load cell, along with the same 3-point bend fixture used previously. The experimental setup is shown in Fig. 4.10. Per the ASTM C 1161-02c test standard, the crosshead rate for each test is specified in order to provide a strain rate of 1×10−4 s−1 using (a) (b) Flaw Flaw Figure 4.8: Optical microscope images of (a) PMN-PZT and (b) PZT-5H samples showing flaw sizes (20X objective lens). 84 (a) (b) (d) (e) (c) (f) (g) (h) Figure 4.9: Diced piezoelectric samples prepared for bending tests including (a) PZT-5H, (b) PZT-5A, (c) PZT-8, (d) PZT-4, (e) PMN-PZT, (f) PMN-PT, (g) QP10n, and (h) QP16n. the following relation [144] ε= 6hs L2 (4.8) where ε is the strain rate, h is the thickness of the sample, s is the crosshead rate, and L is the support span. The number of samples, crosshead rate and support span for each type of material tested are listed in Table 4.4. During each test, the load and crosshead displacement are recorded at a sampling rate of 50 Hz using Instron Bluehill 2 software. 85 (a) (b) Instron test frame Test sample 3-point bend fixture Figure 4.10: Three-point bend testing experimental setup including (a) Instron 5848 MicroTester frame and (b) fixture. 4.3.4 Experimental Results Typical load-displacement curves recorded during the bending tests for each material investigated are shown in Fig. 4.11. Separate graphs are presented for the ‘thin’ samples (PZT-5A, PZT-5H, PMN-PT, PMN-PZT, and QP10n) and for the ‘thick’ samples (PZT-4 and PZT-8) for clarity. It should be noted that the QP16n samples did not exhibit any internal cracking or failure throughout the entire displacement range of the test. Although both R QuickPack devices contain identical PZT-5A active material, the piezoceramic layer con- tained in the QP16n samples is considerably thinner than that of the QP10n devices, thus Table 4.4: Various test parameters for the piezoelectric materials investigated. Material Number of Samples Crosshead Rate (mm/min) Support Span (mm) PZT-5A 50 2.341 25 PZT-5H 50 2.341 25 PZT-4 30 0.450 15 PZT-8 30 0.400 20 PMN-PT 30 2.232 25 PMN-PZT 10 3.214 30 QP10n 30 4.823 35 QP16n 30 8.059 35 86 (a) 0.6 0.5 Load (N) 0.4 0.3 PZT-5A PZT-5H PMN-PT PMN-PZT QP10n 0.2 0.1 0 0 1 2 3 4 5 Crosshead Displacement (mm) 6 7 (b) 8 Load (N) 6 4 2 PZT-4 PZT-8 0 0 0.05 0.1 0.15 Crosshead Displacement (mm) 0.2 Figure 4.11: Load-deflection curves for (a) thin samples (PZT-5A, PZT-5H, PMN-PT, PMNPZT, and QP10n) and (b) thick samples (PZT-4 and PZT-8). the maximum curvature obtained during testing is not large enough to induce the strains required for failure of the piezoceramic layer in the QP16n samples. No failure data is obtained for the QP16n samples and the material will not be discussed further. The failure loads observed during testing are used in Eq. (4.1) to determine the bending strength of each sample. The failure load, Pf , is taken as the maximum load observed during the test for the materials exhibiting classic brittle failure (PZT-5A, PZT-5H, PZT-4, PZT-8, PMN-PT, and PMN-PZT), and as the first peak in the load, which occurs immediately before the initial cracking, in the QP10n material. Bending strengths calculated using the failure loads obtained from the experiments are presented in Fig. 4.12 for all materials tested. Load87 displacement plots for all samples of each material tested are given in Appendix E for reference. A summary of the experimental results for each material investigated is given below. PZT-5A and PZT-5H Both PZT-5A and PZT-5H materials exhibit similar brittle behavior during 3-point bending tests, which can be observed from the results shown in Fig. 4.11(a). Both materials (whose samples are of identical dimensions) follow a similar load-displacement trend with an abrupt failure typical of brittle materials, however, PZT-5H fails at a slightly lower load than PZT-5A. From the bending strength results shown in Fig. 4.12, it can be seen that the PZT-5H samples, on average, have lower strength values than PZT-5A over the entire sample set. Strength testing of ceramic materials often exhibits significant variability between samples [146]. The variability observed in the PZT-5A and PZT-5H strength data is quite reasonable, and the results are considered to be favorable. PZT-4 and PZT-8 From Fig. 4.11(b) it can be seen that both PZT-4 and PZT-8 samples exhibit linear loaddisplacement trends and classic brittle failure. The sample sizes for both materials differ, therefore, direct comparison of the load-deflection curves cannot be made. Based on the 300 PZT-5A PZT-5H PZT-4 PZT-8 PMN-PT PMN-PZT QP10n Failure Strength b (MPa) 250 200 150 100 50 0 Sample Figure 4.12: Bending strength values calculated for various piezoelectric materials tested. 88 calculated failure strength values presented in Fig. 4.12, however, it can be shown that the two material exhibit very similar average bending strengths, which lie between the bending strengths of PZT-5A and PZT-5H. PMN-PT and PMN-PZT Single Crystals As with the other monolithic ceramics tested, both PMN-PT and PMN-PZT materials fail in a brittle fashion, as shown in Fig. 4.11(a). Again, the sample sizes differ between materials, so comparison of the load-deflection diagrams will not be made. The bending strength values given in Fig. 4.12 show that the bending strengths of the single crystal materials are significantly lower than those of the other materials tested. This difference in strength can be explained due to the unique crystal structure of the PMN-PT and PMN-PZT samples which allows for rapid propagation of cracks originating at flaw sites. The single crystal samples are expected to give lower bending strengths as compared to the other ceramic materials investigated (the appeal of single crystal piezoelectric material for energy harvesting purposes is the significant increase in piezoelectric coefficients over conventional piezoceramic materials). Variability in the bending strength results for single crystal samples is also rather low and compares well to the results observed for the monolithic samples. Additionally, the bending strength of PMN-PT samples is slightly higher than the bending strength of PMN-PZT samples. R QuickPack QP10n Load-displacement data for the QP10n samples exhibits unique behavior. Figure 4.11(a) shows a typical load-displacement curve in which the load is observed to drop sharply after an initial fracture, however, the samples recover and continue to exhibit several brittle failures while maintaining a fairly constant average load. This unique behavior occurs because of the outer Kapton layers surrounding the inner PZT-5A layer. The brittle failures observed during the test are a result of the inner piezoceramic layer cracking, however, unlike the traditional monolithic and single crystal ceramic samples, the QP10n sample does not completely fail upon cracking of the PZT-5A layer. The outer Kapton is able to maintain the integrity of the sample after cracking, and in fact, the samples never exhibit complete fracture as the Kapton is able to resist complete failure throughout the entire displacement range of the test. The maximum load observed immediately before the initial 89 R cracking is taken as the failure load of the QuickPack samples. Based on the failure strength data presented in Fig. 4.12, it can be observed that the average bending strength for the QP10n samples is notably higher than that of the conventional ceramic materials. R This can possibly be attributed to the composite construction of the QuickPack devices which includes high shear strength epoxy on the piezoceramic surfaces. Additionally, the variability between samples is significantly higher compared to that of the other materials tested. The increased variability is likely due to the non-uniformity of the test samples R as the electrode layers of the QuickPack devices do not cover the entire surface of the device, hence some diced samples contained outer electrode layers while others lacked such layers. It was observed that samples with outer electrode layers exhibited higher strength values than samples absent of electrode layers. 4.3.5 Statistical Analysis of Bending Strength Results As a means of quantifying the average bending strength and sample variability of each material investigated, the bending strength data presented in Fig. 4.12 is fit to a Weibull distribution, which is common practice for tensile and bending failure strengths of ceramic materials [146]. The Weibull distribution is described by the following cumulative distribution function − F =1−e σb σθ m (4.9) where F is the probability of failure, σb is the failure strength, σθ is the Weibull characteristic strength, and m is the Weibull modulus. The Weibull distribution is left-skewed which better represents the flaw dependent failure mode of ceramic materials as opposed to the standard normal distribution. The Weibull characteristic strength, σθ , provides an estimate of the strength observed over the entire sample set, and the Weibull modulus, m, gives a measure of the variability in the strength data, with a larger value of m corresponding to a small amount of variation in the data. As suggested in the ASTM C 1161-02c test standard, materials with sample sizes of 30 or more (PZT-5A, PZT-5H, PZT-4, PZT-8, PMN-PT, and QP10n) are fit to the Weibull distribution, where materials with sample sizes less than 30 (PMN-PZT) are fit to the Normal distribution with simple mean and standard deviation calculations made [144]. Results of the statistical analysis for all materials tested are given in Fig. 4.13 as well as Table 4.5 where both the Weibull characteristic strength and Weibull 90 250 Weibull Distribution Bending Strength b (MPa) Normal Distribution 200 150 100 50 0 PZT-5A PZT-5H PZT-4 PZT-8 PMN-PT PMN-PZT QP10n Material Figure 4.13: Bending strength statistical comparison for all materials tested with error bars representing 95% confidence interval. modulus (mean strength and standard deviation for PMN-PZT samples) are given along with a 95% confidence interval on all terms. The results confirm the strength and variability trends described previously and provide numerical measures of those properties. The Weibull characteristic strength of PZT-5A is slightly higher than the strength of PZT5H with values of 140.4 MPa and 114.8 MPa, respectively. PZT-4 and PZT-8 have nearly identical strengths at 123.2 MPa and 127.5 MPa, respectively, which lie between PZT-5A and PZT-5H. The strengths of the PMN-PT and PMN-PZT single crystal samples are considerably lower than the other materials tested, with values of 60.6 MPa and 44.9 MPa, R respectively. Lastly, the QuickPack QP10n samples exhibit the highest strength with a value of 206.4 MPa. 4.4 Chapter Summary Analysis of the static and dynamic strength of self-charging structures is presented. Classic three-point bend testing is first performed on the individual self-charging structure material layers as well as the complete structure. Expressions are derived to predict the maximum stress in each layer for a given failure load in three-point bending. Dynamic testing is then performed in which a cantilever self-charging structure is excited at resonance with increasing base excitation amplitude while monitoring for signs of dynamic mechanical or 91 electrical failure. An expression to predict the maximum dynamic stress FRF per base acceleration input is also given. Lastly, a comprehensive study of the static bending strength of several commercially available piezoelectric materials is given as a design tool to aid in the creation of self-charging structures. Results of the static three-point bend testing show that the complete self-charging structure has a bending strength of around 100 - 125 MPa. Additionally, it is shown that the piezoceramic and battery layers are the critical layers in bending failure, with both layers failing at roughly the same load in the tip section of the self-charging structure. These results provide insight into which material layers must be chosen carefully in order to avoid failure in a specific application. Dynamic testing results show that neither mechanical failure in the aluminum or piezoelectric layers or electrical failure of the battery layer is experienced for up to 7.0 g of harmonic excitation. The strength testing results presented in this chapter provide a basis of the static and dynamic loads that can be safely imposed on self-charging structures. Overall, self-charging structures exhibit reasonable static strength and prove to be robust under dynamic resonant excitation. A comprehensive experimental study of the static bending strength of various commercially available piezoceramic materials including hard, soft, single crystal, and composite piezoelectric material/devices is presented. All samples are prepared and tested using the Table 4.5: Bending strength parameters for all materials tested with 95% confidence interval given in brackets. Material Weibull Characteristic Strength (MPa) σb Weibull Modulus m PZT-5A 140.4 [137.6;143.2] 14.6 [11.7;18.2] PZT-5H 114.8 [112.8;116.9] 16.6 [13.5;20.3] PZT-4 123.2 [121.0;125.5] 20.6 [15.6;27.1] PZT-8 127.5 [124.6;130.5] 16.3 [12.6;21.1] 60.6 [58.7;62.5] 12.1 [9.3;15.6] 206.4 [195.2;218.2] Mean Strength (MPa) 6.8 [5.2;8.9] PMN-PT QP10n PMN-PZT 44.9 [42.1;47.7] 92 Standard Deviation 3.9 [2.7;7.1] same equipment. Bending strength results show a relatively small amount of variability for the monolithic piezoceramic samples tested. The strength of the soft (PZT-5A and PZT-5H) and hard (PZT-4 and PZT-8) ceramics are relatively similar, with the strengths of the single crystal materials (PMN-PT and PMN-PZT) considerably lower than the other monolithic materials tested. This result is expected considering the susceptibility to crack propagation R found in single crystal materials. The strength values of the QuickPack QP10n samples exhibit a considerable amount of variation, which is due to the non-uniformity in electrode layers between samples. On average, the strength values of the QP10n samples are much greater than the monolithic materials, likely due to the composite structure of the device. Overall, the results provide a foundation for the selection of active material in piezoelectric energy harvesters in which load bearing capability is required, such as self-charging structures. 93 C HAPTER 5 P ERFORMANCE M ODELING OF U NMANNED A ERIAL V EHICLES WITH O N B OARD E NERGY H ARVESTING U NMANNED aerial vehicles present a potential application in which the benefits of a multifunctional energy harvesting solution could enable the use of vibration energy harvesting. As suggested in Chapter 2, self-charging structures can be incorporated into UAVs with the goal of creating local autonomous power sources for low-power sensors. In the following chapters, the use of self-charging structures for vibration energy harvesting in UAVs is explored as a case study. This chapter presents theoretical performance modeling of unmanned aircraft with on board energy harvesting systems. A system level model is first described in which changes to the flight endurance of a UAV with the addition of an energy harvesting system can be predicted. The model is then applied to a small Multiplex USA [147] EasyGlider remote control (RC) aircraft which is chosen as the test platform for the case study. Theoretical predictions are first made to describe flight endurance changes with the addition of a piezoelectric harvesting system. Experimental flight testing is then performed in which the EasyGlider aircraft is flown with on board vibration harvesting and the power output of the piezoelectric harvesters is measured during flight. The results are used to update the initial predictions. Lastly, the flight endurance formulation is used to predict the effects of adding self-charging structures to the EasyGlider aircraft. 94 5.1 Piezoelectric Energy Harvesting in Unmanned Aerial Vehicles Previous energy harvesting approaches for small aircraft mainly focus on harvesting solar energy through the use of photovoltaic panels in order to provide propulsive power for aircraft flight. More recently, however, researchers have begun to investigate alternate sources of energy that can be harvested in UAVs. Thomas et al. [91] explore the energy available from solar, wind, thermal, and electromagnetic radiation sources during flight. Vibration energy harvesting has also been investigated by several researchers [29, 94, 95, 97, 98]. Piezoelectric vibration harvesting is attractive because, where other sources may be dependent on environmental conditions, piezoelectric harvesting is effective any time the aircraft is in flight. Additionally, piezoelectric harvesters are typically small and can be easily integrated into an aircraft structure. The power available from piezoelectric energy harvesters, however, is inadequate for providing propulsive power to an aircraft. Instead, the focus of piezoelectric harvesting in UAVs is to provide a local power source for lowpower sensors, enabling the concept of self-powered sensors that do not draw from the main power source of the aircraft. A critical aspect of the integration of any energy harvesting system into a UAV is the potential effect that the added system can have on the performance of the aircraft. While the additional energy available from harvesting provides a clear benefit, the added mass and volume of a harvesting system can have a detrimental effect on the flight performance of the host aircraft. Both mass and drag are significant parameters in determining the power required for flight, and increases in these quantities present obvious challenges. It proves beneficial to have a means of predicting the impact of an energy harvesting system on a host aircraft in order to help develop harvesting solutions that provide optimal power output without negative effects on the flight performance. A system level approach is investigated here for analyzing the effects of adding piezoelectric energy harvesting systems to UAVs on the flight performance of the aircraft. 95 5.2 System Level Flight Endurance Model A mathematical model used to predict the change in flight endurance of an electric unmanned aerial vehicle with on board harvesting as a result of changes to subsystem masses, amount of battery power, and amount of harvested power has recently been presented in the literature by Thomas et al. [91]. The formulation utilizes a basic aerodynamic model of aircraft flight in order to relate the power required for flight to the power available from battery and harvester sources, allowing for calculation of the flight endurance of an aircraft that contains energy harvesting systems. Details of the derivation of the flight endurance formulation derived by Thomas et al. [91] are given in this section. Formulations for both the flight endurance and the normalized change in flight endurance based on changes to subsystem masses and harvester parameters are presented. 5.2.1 Flight Endurance of an Electric Powered UAV with On Board Energy Harvesting The flight endurance of an electric powered UAV with on board energy harvesting is given by Thomas et al. [91] as tE = 3/2 WT EB ηB − PHarv 3 ρ∞ SCL 2 2CD 1/2 ηP ρ∞ SCL3 2 2CD 1/2 ηP (5.1) where tE is the flight endurance, EB is the energy available in the battery, ηB is the energy extraction efficiency factor of the battery, WT is the total weight of the aircraft, PHarv is the power supplied by the harvester, ρ∞ is the air density, S is the wing area, CL is the coefficient of lift, CD is the coefficient of drag, and ηP is the motor and propeller efficiency. This formulation can be derived by considering a basic aerodynamic model to describe the flight of an aircraft as a balance between the energy required for steady, level flight and the energy available from all power sources. The basic relationships can be found in most introductory aerodynamics texts, such as Anderson [148]. In steady level flight, thrust is equal to drag and lift is equal to weight as follows T =D (5.2) L=W (5.3) 96 where T is thrust, W is the aircraft weight, L is lift, and D is drag. The thrust required for flight can be expressed as D D W W = W = W L L/D TR = D = (5.4) The thrust required for flight is, therefore, dependent on the weight of the aircraft as well as the lift-to-drag ratio. Lift-to-drag is a direct measure of the aerodynamic efficiency of an aircraft, hence it is a very important parameter affecting aircraft performance. The liftto-drag ratio can be shown to be equal to the ratio of coefficient of lift, CL , to coefficient of drag, CD , by considering lift and drag in terms of air density, aircraft speed, and the respective coefficients in the following 1 2 SC ρ∞ V∞ L CL L = 12 = 2 D CD 2 ρ∞ V∞ SCD (5.5) where V∞ is the aircraft velocity. Next, the power required for steady level flight is given by (5.6) PR = TR V∞ Substituting Eq. (5.4) and Eq. (5.5) into Eq. (5.6), the power required for flight can be rewritten as PR = W V∞ CL /CD (5.7) 2 SC , the aircraft velocity can be written as Recalling that L = W = 21 ρ∞ V∞ L s 2W V∞ = ρ∞ SCL (5.8) Substituting Eq. (5.8) into Eq. (5.7) gives an expression for the power required for steady level flight W PR = CL /CD s 2W = ρ∞ SCL s 2 2W 3 CD ρ∞ SCL3 (5.9) If the efficiency of the aircraft propeller and motor in converting electrical energy to thrust, which can be expressed as ηP , is considered, Eq. (5.9) can be rewritten as s 2 2W 3 CD PR = /ηP ρ∞ SCL3 (5.10) In order to determine the flight endurance of an aircraft, one can first consider the definition of power to yield the following relationship between power, energy, and time Power = Energy Energy ⇒ Time = Time Power 97 (5.11) The energy available in an electric aircraft with a battery as well as a harvesting system that supplements the propulsive power supply can be written as (5.12) Eavail = EB ηB + PHarv tE A balance between the energy available in the aircraft for flight with the power required for flight leads to EB ηB + PHarv tE Eavail EB ηB + PHarv tE tE = = r = 2 3 PR W 3/2 2W CD /η P 3 ρ SC ∞ ρ∞ SCL3 2 2CD 1/2 ηP (5.13) L Solving for tE yields Eq. (5.1), as given by Thomas et al. [91] tE = 3/2 WT EB ηB − PHarv 3 ρ∞ SCL 2 2CD 1/2 ηP ρ∞ SCL3 2 2CD 1/2 ηP (5.14) where W has been replaced with WT . 5.2.2 Normalized Change in Flight Endurance The flight endurance of an electric UAV with energy harvesting is given in Eq. (5.14). It is of interest to determine the effects of an added energy harvesting system on the flight endurance of an aircraft, therefore, a formulation for the change in flight time (which can be normalized for comparison purposes) is desired. Following the work of Thomas et al. [91], a linear Taylor series expansion of the flight time, tE , about the point PHarv = 0 can be used to formulate the normalized change in flight endurance. By taking the aerodynamic terms in Eq. (5.14) as constant ψ= ρ∞ SCL3 2 2CD 1/2 ηP (5.15) the flight time can be rewritten as tE = EB ηB 3/2 WT − PHarv ψ −1 3/2 ψ ψ = EB ηB WT − PHarv ψ (5.16) Recalling the linear multivariable Taylor expansion, given by ∂f ∂f ∂f f (x, y, z) ≈ f (x0 , y0 , z0 )+ (x−x0 )+ (y −y0 )+ (z −z0 ) (5.17) ∂x x0 ,y0 ,z0 ∂y x0 ,y0 ,z0 ∂z x0 ,y0 ,z0 98 and defining x − x0 = ∆x, the flight endurance can be estimated with the linear Taylor series as ∂tE ∂tE ∆tE = tE − ≈ ∆EB ηB + ∆WT ∂EB ηB PHarv =0 ∂WT PHarv =0 ∂tE + ∆PHarv ∂PHarv toE (5.18) PHarv =0 Evaluating the partial derivative terms, Eq. (5.18) can be rewritten as ∆tE ≈ ψ ∆EB ηB − 3/2 WT 3 EB ηB ψ EB ηB ψ 2 ∆PSC ∆W + T 2 W 5/2 WT3 (5.19) T The change in flight time can be normalized by the flight time for an electric aircraft without added energy harvesting (non-harvesting design), which can be expressed by setting PHarv = 0 in Eq. (5.14) giving tE = EB ηB ψ 3/2 WT (5.20) Normalizing Eq. (5.19) by Eq. (5.20) gives ∆EB ηB 3 ∆WT ψ ∆tE ≈ + + 3/2 ∆PSC tE EB ηB 2 WT WT (5.21) From the non-harvesting design given by Eq. (5.20), the following relationship can be defined ψ 3/2 WT = tE EB ηB (5.22) Using Eq. (5.22) in Eq. (5.21) the normalized change in flight time can be written as ∆tE ∆EB ηB 3 ∆WT ∆PHarv ≈ + + tE EB ηB 2 WT EB ηB /tE (5.23) The total weight of the aircraft, WT , can be expanded to include several subsystem weights as WT = WB + WST + WHarv (5.24) where WB is the weight of the battery, WST is the structural weight including the motor, electronics, and control surface actuators, and WHarv is the weight of the harvesting system. Using Eq. (5.24) in Eq. (5.23), the normalized change in flight endurance becomes ∆tE ∆EB ηB 3 ∆WB + ∆WST + ∆WHarv ∆PHarv ≈ + + tE EB ηB 2 WB + WST + WHarv EB ηB /tE 99 (5.25) Equation (5.25) can be written in terms of changes in mass by using the following relations EB = eB mB W = mg PHarv = pHarv mHarv EB ηB /tE = pave mB (5.26) (5.27) (5.28) (5.29) where eB is the specific energy of the battery (i.e. J/kg), mB is the mass of the battery, g is the acceleration of gravity, pHarv is the specific power of the harvester (i.e. W/kg), mHarv is the mass of the harvesting system, and pave is the average specific power supplied by the battery in the non-harvesting design, i.e. pave = EB ηB /tE mB . Using these relations, the normalized change in flight endurance can be written in terms of changes in mass, as given in Thomas et al. [91] as follows ∆tE ∆mB 3 ∆mB + ∆mST + ∆mHarv pHarv ∆mHarv ≈ − + tE mB 2 mT pave mB (5.30) where mT is the total mass of the aircraft. Equation (5.30) is valid for an electric aircraft in steady, level flight containing any energy harvesting system (vibration, solar, thermal, etc.) with the assumption of a constant power output from the harvester. The simple aerodynamic model used in the derivation naturally adds several assumptions about the flight of the aircraft and the ambient environmental conditions, namely imposing constant conditions. The formulation, however, can be used to provide insight into the effects of adding energy harvesting systems to electric powered UAVs. 5.3 Theoretical Case Study In this section, a theoretical case study is performed in which the normalized change in flight time of the EasyGlider aircraft test platform, shown in Fig. 5.1, with the addition of piezoelectric vibration energy harvesting is investigated using the formulation presented in the previous sections. It is proposed that flexible fiber-based piezoelectric devices be installed onto the wing spar of the EasyGlider aircraft to harvest vibration energy in the wings caused by aerodynamic loading during flight. Multifunctional energy harvesting approaches will be considered in which structural mass is removed from the aircraft structure to compensate for the addition of a harvesting system. Changes to flight endurance 100 are calculated for varying degrees of multifunctionality and with increasing size of the harvesting system. Although the focus of piezoelectric harvesting in UAVs is to provide power to low-power sensors as significant increases in flight time are not expected due to the low power output of piezoelectric harvesting, the power output of the piezoelectric system is modeled as contributing to the propulsive power supply of the aircraft for analysis purposes. The goal of this case study is to identify harvester designs in which the flight endurance does not significantly suffer with the addition of piezoelectric harvesting. The EasyGlider aircraft has a wing span of 1.8 m, length of 1.1 m, and is powered by an 11.1 V, 2100 mAh lithium polymer rechargeable battery. Several parameters can be defined for the standard, non-harvesting EasyGlider aircraft, as given in Table 5.1, where the total mass of the aircraft is simply the sum of the battery mass and the structure mass, the battery efficiency factor is estimated as 0.8, the original flight endurance for steady, level flight is given as 10 minutes based on previous flight testing estimates [149], and the wing spar area is used to limit the number of piezoelectric devices that can be installed in the aircraft. Using these parameters, the average specific power supplied by the battery in the non-harvesting design, pave , can be calculated as pave = EB ηB = 388.5 W/kg mB tE (5.31) Two flexible fiber-based piezoelectric devices are considered for use in the EasyGlider wing spar, namely the M8507-P1 Macro-Fiber Composite (MFC) manufactured by Smart Figure 5.1: Multiplex USA EasyGlider remote control aircraft test platform. 101 Table 5.1: Physical properties of the EasyGlider aircraft. Property Symbol Value Battery mass mB 144 g Structure mass mST 945.2 g Total aircraft mass mT 1089.2 g Battery energy EB 83916 J Battery efficiency factor ηB 0.80 Original flight endurance tE 600 s Wing area SW 0.416 m2 Wing spar area SW S 0.0252 m2 Material, Corp. [112] and the Piezoelectric Fiber Composite (PFC) manufactured by Advanced Cerametrics, Inc., [113] both shown in Fig. 5.2. Relevant physical properties of the devices are given in Table 5.2 The specific power output of a piezoelectric harvester will vary considerably based on the physical configuration of the device and the vibration environment in which it is placed. Theoretical specific power values are, therefore, generally not given by device manufacturers. In order to perform the piezoelectric simulation, a single specific power value can be assigned for a representative piezoelectric fiber-based device. Sodano et al. R [34] performed a study in which a QuickPack QP10ni fiber-based device of dimensions 50.8 mm x 25.4 mm x 0.381 mm and mass of about 3.0 g was surface mounted near the root of a 83.8 cm long aluminum cantilever beam and excited harmonically. The specific power of this device can be used as a generic reference value in this simulation. At the beam’s third resonance frequency of 64 Hz, the device was found to perform optimally and harvest (a) (b) Figure 5.2: Piezoelectric devices including (a) M8507-P1 Macro-Fiber Composite, and (b) Piezoelectric Fiber Composite. 102 Table 5.2: Physical properties of the piezoelectric devices considered. Symbol Macro-Fiber Composite Piezoelectric Fiber Composite Device length lP 102 mm 145 mm Device width wP 16 mm 15 mm Device thickness tP 0.3 mm 0.3 mm Device mass mP 3.0 g 2.0 g Property a maximum power of 29.5 µW, corresponding to a specific power of pHarv = 0.0098 W/kg. The specific power of the piezoelectric device is several orders of magnitude lower than that average specific power supplied by the battery, hence the goal of vibration energy harvesting is to create local power sources for low-power electronics and not to provide propulsive power for the aircraft. In the simulation, the mass of the battery is assumed to stay fixed, ∆mB = 0, and only changes to the piezoelectric harvester mass and structure mass are allowed. The number of piezoelectric devices (correspondingly, harvester mass) added to the aircraft is varied, with an upper bound based on half of the total available surface area of the wing spar, SW S /2. Voltage generation of a piezoelectric material is based on induced strain and the strain in the wing spar of an aircraft is largest at the fuselage and decreases towards the wing tip. It is, therefore, proposed to install piezoelectric devices only near the root of each wing as harvesters located near the wing tip would not produce significant amounts of energy. For each discrete number of piezoelectric devices added, the change in structure mass (to compensate for the addition of the harvesters) is allowed to vary from ∆mST = 0, which corresponds to the completely non-multifunctional design in which no structure mass is removed, to ∆mST = −∆mHarv , which is the fully multifunctional design in which all of the added piezoelectric mass is removed from structure mass, thus the total mass of the aircraft remains unchanged with the addition of the harvesting system. Using Eq. (5.30), simulation results for the normalized change in flight time based on the parameters described above are given in Fig. 5.3 for various discrete numbers of piezoelectric devices used in the harvesting system. Upon investigating the results, it appears as if there is only a single line, however, the magnified view shows that indeed there are multiple lines, each corresponding to a different number of piezoelectric devices. Values along the y-axis 103 0.005 -0.0138 0 -0.0138 tE/tE -0.01 -0.0138 9.996 9.9985 10.001 -0.02 Increasing Number of Piezo Devices -0.03 -0.04 0 5 10 15 20 Total Added Mass (g) 25 30 Figure 5.3: Simulation results for normalized change in flight time of the EasyGlider aircraft based on the addition of piezoelectric harvesting with varying degrees of multifunctionality. (total added mass = 0) indicate fully multifunctional solutions, where progressing along the x-axis indicates decreasing degrees of multifunctionality. It should be noted that in this simulation, only the mass of the piezoelectric material contributes to mHarv and the mass of any requisite harvesting components, such as circuitry or mounting hardware, are ignored as these quantities would depend on specific applications and may also perform additional functions on the aircraft. The results of the simulation show that a net loss in flight time occurs for all but the fully multifunctional case where the overall aircraft mass remains unchanged. While the focus of a piezoelectric system is not on achieving an increase in flight time, the goal is to choose a design in which the flight endurance does not suffer. These results clearly show that a fully multifunctional design is necessary for the integration of piezoelectric vibration harvesting into the EasyGlider aircraft. The loss in flight time observed in the simulation results from the mass loading and low specific power of piezoelectric energy harvesting. 5.4 Experimental Case Study In this section, data collected from experimental flight testing is used to update the simulation results with an accurate measure of the power output of the harvesting devices during flight to provide more realistic estimates of the change in flight endurance with the 104 addition of energy harvesting systems to the EasyGlider aircraft. 5.4.1 EasyGlider Aircraft Configuration The EasyGlider aircraft is modified to include both MFC and PFC piezoelectric devices on a custom made fiberglass wing spar. The original round carbon fiber reinforced plastic wing spar rod is replaced by a rectangular fiberglass spar with a foam core. Replacing the original round spar with a rectangular spar helps facilitate mounting of the MFC and PFC devices. The stiffness of the wing spar is an important factor in the design and performance of the aircraft, therefore, the stiffness of the fiberglass spar is designed to closely match the stiffness of the original carbon fiber spar. Fabrication of the custom spar is accomplished by first modifying the round channels in the aircraft wings to accept a rectangular spar, then shaping a foam core with a hot wire cutter to fit in the modified channel, and finally using a vacuum bagging procedure to apply fiberglass layers over the foam core with West System [150] 105/205 two part epoxy and allowing the spar to cure under vacuum. Once cured, the MFC M8507-P1 piezoelectric device and PFC device are bonded to the surface of the spar using the same epoxy and vacuum bagging procedure. The original foam covers used to secure the carbon fiber spar are replaced with two fiberglass covers molded to the underside surface of the wings and attached with cyanoacrylate adhesive. Photographs of the MFC and PFC patches attached to the fiberglass spar as well as the spar inserted into the wing are shown in Fig. 5.4. The EasyGlider aircraft is also modified to house two data loggers used to record measurements during flight. An XR5-SE-M-50mv eight channel, 0-5 V data logger from Pace Scientific, Inc. [151] is used to measure the voltage output of the piezoelectric harvesters and a UA-004-64 Pendant G 3-axis accelerometer data logger with a range of ±3 g from Onset Computer Corp. [152] is used to measure the aircraft accelerations. Each data logger is battery powered and stores data on internal memory. The XR5-SE-M-50mv logger has dimensions of 12.4 cm x 5.6 cm x 3.3 cm and weighs 120 g, where the UA-004-64 logger has dimensions of 3.7 cm x 2.5 cm x 0.7 cm and weighs 8 g. The XR5-SE-M-50mv unit is installed in the cockpit of the aircraft and a custom fiberglass canopy is created to allow its installation. The data logger and canopy are shown installed in the aircraft in Fig. 5.5. In order to compensate for the added mass of the logger, an additional steel mass is added at the tail of the aircraft inside the fuselage to maintain the proper center of gravity. The 105 UA-004-64 accelerometer logger is installed on the underside of the aircraft at the center of gravity and an aerodynamic fiberglass canopy is created to cover and protect the logger. The accelerometer data logger and protective canopy are shown in Fig. 5.6. 5.4.2 Flight Testing Results Flight testing is performed where the voltage output of both piezoelectric devices as well as the accelerations experienced by the aircraft are recorded during flight. The piezoelectric (a) (b) Figure 5.4: Fiberglass wing spar with (a) surface mounted Macro-Fiber Composite and Piezoelectric Fiber Composite devices (b) inserted in wing. (a) (b) Figure 5.5: XR5-SE-M-50mv voltage data logger shown (a) installed into cockpit of EasyGlider and (b) with fiberglass canopy installed. 106 (a) (b) Figure 5.6: UA-004-64 accelerometer data logger shown (a) installed on the underside of the EasyGlider and (b) with fiberglass canopy installed. devices are each connected through a full bridge diode rectifier to an optimal resistive load (found as 330 kΩ for both devices). The voltage across the load is measured at a sampling rate of 200 Hz. The accelerometer data logger is configured to record accelerations in all three axes at a sampling frequency of 50 Hz. During the flight test, the aircraft is flown for about 6 minutes on a sunny day with winds approximately 10-15 km/h. The aircraft is hand launched and a simple wide circle pattern is flown. An airspeed of approximately 45 km/h at an altitude of around 30 m is achieved. Results of the flight testing are shown in Fig. 5.7 and Fig. 5.8 for the acceleration and voltage, respectively. It should be noted that both data loggers begin recording data approximately 60 seconds prior to the launch of the aircraft. From the acceleration measurements presented in Fig. 5.7, it can be estimated that the average acceleration in the x- and y- axis, which correspond to the horizontal directions from propeller to tail and from wing tip to wing tip, respectively, is about ±1.5 g, and the average acceleration in the z-axis is about ±1 g. The z-axis acceleration is centered around -1 g due to the acceleration of gravity and the orientation of the logger when attached to the underside of the fuselage. The measurements give insight into the typical acceleration levels experienced in a small unmanned aircraft. The voltage measurements given in Fig. 5.8 show that both piezoelectric devices exceed the 5 V limit of the data logger several times during flight. The data can still be used, however, to give a rough estimate of the power harvested during flight. The average power 107 X-Axis Acceleration (g) (a) 2 0 -2 0 50 100 150 200 Time (sec) 250 300 350 50 100 150 200 Time (sec) 250 300 350 50 100 150 200 Time (sec) 250 300 350 Y-Axis Acceleration (g) (b) 2 0 -2 0 Z-Axis Acceleration (g) (c) 2 0 -2 0 Figure 5.7: Acceleration measurements recorded during flight in the (a) x-axis, (b) y-axis, and (c) z-axis directions. output of the piezoelectric devices is calculated from the flight measurements using the following relation Pave = 2 vRM S R (5.32) where Pave is the average power, vRM S is the root mean square (RMS) voltage, and R is the load resistance. The average power output of the MFC and PFC devices is found to be 11.3 µW, and 10.1 µW, respectively. The exact power output values are expected to be larger than these averages because of the voltage clipping effects of the data logger. 5.4.3 Simulation Results The power density value used in Section 5.3 is based on high frequency sinusoidal excitation, which is not likely attainable during flight, and is expected to give an overestimate 108 (a) MFC Piezoelectric Voltage (V) 5 4 3 2 1 0 0 (b) 50 100 150 200 Time (sec) 250 300 350 50 100 150 200 Time (sec) 250 300 350 AFC Piezoelectric Voltage (V) 5 4 3 2 1 0 0 Figure 5.8: Voltage measurements recorded during flight for (a) MFC and (b) PFC piezoelectric devices. of the normalized change in flight time. Results of the experimental flight testing are used here to update the simulation results with a more accurate measure of the power harvested during flight. Based on the average power values calculated during flight, the following specific power values can be defined for each piezoelectric device pM F C = 0.00377 W/kg (5.33) pP F C = 0.00505 W/kg (5.34) where pM F C is the specific power of the MFC and pP F C is the specific power of the PFC. Using these updated specific power values, the normalized change in flight time is recalcu109 lated, giving the results presented in Fig. 5.9, where the effect of adding each piezoelectric device is considered individually. Although the results are similar to the those presented in Fig. 5.3 for the theoretical case study, a slight decrease in the normalized change in flight time is observed. The results clearly confirm that a fully multifunctional solution is required to avoid a loss in flight time when adding piezoelectric harvesting to UAVs. 5.5 Flight Endurance Modeling of Self-Charging Structures in UAVs The results presented in the previous sections have shown that a multifunctional design is needed in order to incorporate piezoelectric vibration harvesting into a UAV without adversely affecting the flight time. The integration of multifunctional self-charging structures into UAVs is investigated in this section. From the experimental testing performed on the self-charging structure prototype in Chapter 3, a power output of 0.306 mW is obtained for a cantilever self-charging structure excited at resonance (210 Hz) under ±1.0 g of harmonic base excitation. The excitation frequency experienced by the device when installed in the wing spar of the EasyGlider will likely not match this optimal condition, and the excitation amplitude will be considerably lower, therefore, a power output of 10 times less (30.6 µW) -3 1 x 10 0 -3 MFC Patch PFC Patch -1.377 x 10 -1.3771 tE/tE -1 -1.3771 1 -2 1 1 -3 -4 -5 0 0.5 1 1.5 2 2.5 Total Added Mass (g) 3 3.5 Figure 5.9: Updated simulation results for normalized change in flight time of the EasyGlider aircraft based on the addition of piezoelectric harvesting with varying degrees of multifunctionality. 110 is assumed for the self-charging structure when integrated into the wing spar of a UAV. With a power output of 30.6 µW, the specific power of the self-charging structure (which has a mass of 6.2 g) is calculated as pSCS = 0.00494 W/kg. As discussed in Chapter 2, self-charging structures can be integrated into the wing spar of a UAV in a multifunctional manner by supporting aerodynamic loading on the wing such that structure mass can be removed to compensate for the added mass of the harvester. The flight endurance formulation is used here to predict the effects of integrating self-charging structures into the EasyGlider aircraft. Consistent with the previous simulations, the battery mass is assumed to remain constant, ∆mB = 0, and only changes to the harvester and structure masses are allowed. Discrete numbers of self-charging structures are considered with a limit based on half of the wing spar area. Varying degrees of multifunctionality are considered by changing the amount of structure mass removed from the aircraft to compensate for the addition of the piezoelectric harvesting system. Results of the simulation are presented in Fig. 5.10. As in the theoretical case study presented in Section 5.3, it again appears as if there is only a single line, however, multiple lines corresponding to different numbers of devices are present although each gives almost identical results. As expected, the simulation results agree with those previously presented for piezoelectric harvesting and suggest that a fully multifunctional design is required in order to avoid potential losses in flight endurance. Incorporating a fully multi0.01 -0.0207 0 -0.0207 -0.01 tE/tE -0.02 -0.0207 14.9987 15.0001 15.0016 -0.03 -0.04 Increasing Number of Self Charging Structures -0.05 -0.06 -0.07 0 10 20 30 Total Added Mass (g) 40 50 Figure 5.10: Simulation results for normalized change in flight time of the EasyGlider aircraft based on the addition of self-charging structures. 111 functional self-charging structure harvesting system into the aircraft, however, can enable self-powered sensors in the aircraft wings while the flight endurance remains unchanged. 5.6 Chapter Summary A system level approach for examining the effects of adding energy harvesting systems to unmanned aerial vehicles is investigated. A formulation recently presented by Thomas et al. [91] is applied to an EasyGlider remote control aircraft in order to predict the effects of adding energy harvesting systems on the aircraft flight endurance. Details of the derivation of the flight endurance formulation are first given. A theoretical case study is then performed where simulations are carried out to predict the change in flight endurance based on the addition of flexible piezoelectric energy harvesting devices to the aircraft. An experimental case study is then given in which flight test data is used to update the specific power values used in the theoretical simulation. Lastly, the addition of multifunctional self-charging structures to the EasyGlider aircraft is investigated through the use of the flight endurance formulation. Results of both the theoretical and experimental simulations show that a fully multifunctional design, where all harvester mass added to the aircraft is removed in structure mass, is required for piezoelectric harvesting systems in order to avoid a loss in flight endurance. With a fully multifunctional design, however, self-charging structures can be used to create self-powered sensor systems on board UAVs. The results presented in this chapter enforce the need for multifunctional piezoelectric harvesting designs for use in unmanned aerial vehicle applications. 112 C HAPTER 6 E LECTROMECHANICAL M ODELING OF M ULTIFUNCTIONAL E NERGY H ARVESTING W ING S PAR FOR U NMANNED A ERIAL V EHICLES T HIS chapter presents the electromechanical modeling of a multifunctional energy har- vesting wing spar for unmanned aerial vehicles utilizing embedded self-charging structures. The model described here is an adaptation of the experimentally validated assumed modes model given by Erturk and Inman [30–32] and described previously in Chapter 2. Details of the derivation are first given for both the series and parallel electrode connection of the piezoelectric layers. Following the procedure outlined in Chapter 2, energy formulations are derived for the structure, an assumed solution composed of trial functions multiplied by generalized coordinates is substituted into the energy expressions, and Hamilton’s principle is applied yielding the coupled electromechanical Lagrange equations. The Lagrange equations are solved, giving the mechanical and electrical governing equations, and finally the displacement - to - base acceleration and voltage - to - base acceleration frequency response functions are defined. Experimental testing of a representative wing spar with an embedded self-charging structure is also performed in order to validate the model. A cantilever wing spar is subjected to harmonic base excitation in order to obtain experimentally measured frequency response functions which are then compared to those predicted by the model for validation purposes. 113 6.1 Electromechanical Modeling The electromechanical assumed modes model presented in this section for a multifunctional energy harvesting wing spar is based on the previously described assumed modes model presented by Erturk and Inman [30–32]. Differences between the formulation given here and the model presented in Chapter 2 are highlighted. 6.1.1 Modeling Assumptions and Device Configuration Consider the piezoelectric energy harvesting wing spar configurations shown in Fig. 6.1 for a 1/2 spar model with the moving base representing the aircraft fuselage. The spar contains an embedded self-charging structure, hence it represents a bimorph configuration. Both series (Fig. 6.1(a)) and parallel (Fig. 6.1(b)) connections of the piezoelectric devices are considered. Translational base acceleration, ab (t), is imposed in the transverse direction at the clamped end. The structures are assumed sufficiently thin such that Euler-Bernoulli assumptions hold. The perfectly conductive electrodes covering the surfaces of the piezoelectric layers allow a single electric potential to be defined across them. Once again, the R piezoelectric layers used in the spar are QuickPack QP10n devices and the thin-film batR teries used are Thinergy MEC 101-7SES devices. 3M [100] ScotchWeldTM DP460 two part epoxy is used to bond all layers, and each bonding layer is assumed to be perfect with identical thickness. In order to prevent electrical shorting of the batteries (recall, whose outer substrate serve as the electrodes), a Kapton film layer is placed between the substrate and the batteries. Lastly, a sensor node is modeled as a lumped mass at an arbitrary location near the free end of the spar. 6.1.2 Energy Formulations for the Electromechanical Spar As with the assumed modes model presented for the self-charging structures in Chapter 2, the motion of the spar is a combination of the base motion and the relative motion of the beam, given by Eq. (2.2) as wabs (x, t) = wb (t) + wrel (x, t) (6.1) where wabs is the absolute displacement of the beam, wb is the base displacement and wrel is the displacement of the beam relative to the moving base. 114 (a) z ab (t ) x0 (b) L1 L2 L3 L4 x Rl vs (t ) x Rl v p (t ) L z ab (t ) x0 L1 L2 L3 L4 L L1 L L2 (c) hp hk hs1 he hp Piezoceramic Layer h Thin-Film Battery Layer Substrate Layer b Kapton Layer L2 L L3 hb hki hs 2 Epoxy Layer Electrodes h Poling Direction hb b Figure 6.1: Multifunctional piezoelectric energy harvesting wing spar configurations showing (a) series and (b) parallel connection of the piezoelectric layers along with the (c) cross-sectional views of both composite sections. The strain energy in the structure layers is given by Eq. (2.7) as Us = 1 2 Z Ys (x)z 2 ∂ 2 wrel (x, t) ∂x2 2 dVs (6.2) dx (6.3) Vs 1 = 2 ZL Y Is (x) ∂ 2 wrel (x, t) ∂x2 2 0 where Ys is the elastic modulus of the structure layers, I is the area moment of inertia, and Y Is (x) is the bending stiffness of the structure materials, which varies along the xdirection. The bending stiffness of the structure layers for the wing spar differs from the 115 self-charging structure and is given by Y Is (x) = Y Is [H(L1 − x) + H(x − L3 )] + Y Ic1 H(x − L1 )H(L2 − x) (6.4) + Y Ic2 H(x − L2 )H(L3 − x) where H(x) is the Heaviside step function and Y Is , Y Ic1 , and Y Ic2 are the bending stiffnesses of the substrate material in the uniform sections from 0 ≤ x ≤ L1 and L3 ≤ x ≤ L, in the first composite section from L1 < x < L2 , and in the second composite section from L2 < x < L3 , respectively. Again, the symmetry of the spar about the x-axis allows the use of the parallel axis theorem in calculating the bending stiffness of the composite sections. Calculation of the bending stiffnesses of the multifunctional spar are given in Appendix B.3. The total strain energy in the piezoelectric layers is given by Eq. (2.10) and Eq. (2.11), and when combined with the strain energy in the structure layers given by Eq. (6.3), yields the following total strain energy in the structure ZL 1 U = 2 s ∂ 2 wrel (x, t) ∂x2 2 ∂ 2 wrel (x, t) ∂x2 2 ∂ 2 wrel (x, t) ∂x2 2 ∂ 2 wrel (x, t) ∂x2 2 Y Is (x) 0 ZL2 dx (6.5) cE 11 Ip + ∂ 2 wrel (x, t) − Jps vs (t) ∂x2 ! dx L1 ZL 1 U = 2 p Y Is (x) dx 0 ZL2 + (6.6) cE 11 Ip ∂ 2 wrel (x, t) − Jpp vp (t) ∂x2 ! dx L1 where cE 11 is the elastic modulus of the piezoelectric measured at constant electric field, p s cE 11 Ip is the bending stiffness of the piezoelectric layer (see Appendix B.3), Jp and Jp are the piezoelectric coupling terms given by Eq. (2.14) and Eq. (2.15), v(t) is the voltage output of the piezoelectric layers, and superscript s and p stand for series and parallel connection of the piezoelectric layers. The total kinetic energy of the beam is given by Eq. (2.16) as Tbeam 1 = 2 ZL (ρAs (x) + ρAp (x)) (6.7) 0 " × ∂wb (t) ∂t 2 +2 ∂wb (t) ∂wrel (x, t) + ∂t ∂t 116 ∂wrel (x, t) ∂t 2 # dx where ρAs (x) and ρAp (x) are the mass density functions of the structure and piezoelectric layers, which again differ from the self-charging structure derivation, and are given by ρAs (x) = ρAs [H(L1 − x) + H(x − L3 )] + ρAc1 H(x − L1 )H(L2 − x) (6.8) + ρAc2 H(x − L2 )H(L3 − x) ρAp (x) = ρAp H(x − L1 )H(L2 − x) (6.9) where ρAs , ρAc1 , and ρAc2 are the mass densities of the substrate material in the uniform sections from 0 ≤ x ≤ L1 and L3 ≤ x ≤ L, in the first composite section from L1 < x < L2 , and in the second composite section from L2 < x < L3 , respectively, and ρAp is the mass density of the piezoelectric layers in the first composite section from L1 < x < L2 . Calculation of the mass densities is given in Appendix B.3. The kinetic energy of the lumped mass must be taken into consideration (again differing from the self-charging structure derivation), and is given by " # 1 ∂wb (t) ∂wrel (L4 , t) ∂wrel (L4 , t) 2 ∂wb (t) 2 Tmass = M +2 + 2 ∂t ∂t ∂t ∂t (6.10) where M is the mass of the lumped mass. The total kinetic energy of the system can be expressed as a sum of the kinetic energy of the beam and the kinetic energy of the lumped mass, given by 1 T = 2 ZL (ρAs (x) + ρAp (x)) 0 # ∂wb (t) 2 ∂wb (t) ∂wrel (x, t) ∂wrel (x, t) 2 × +2 + dx ∂t ∂t ∂t ∂t " # 1 ∂wb (t) 2 ∂wb (t) ∂wrel (L4 , t) ∂wrel (L4 , t) 2 + M +2 + 2 ∂t ∂t ∂t ∂t " (6.11) The internal electrical energy is given by Eq. (2.22) and Eq. (2.23), and can be simplified for the wing spar as Wies 1 = 2 ZL2 2Jps vs (t) ∂ 2 wrel (x, t) 1 dx + Cp vs2 (t) 2 ∂x 4 (6.12) ∂ 2 wrel (x, t) dx + Cp vp2 (t) ∂x2 (6.13) L1 Wiep 1 = 2 ZL2 2Jpp vp (t) L1 117 where the internal capacitance of a piezoelectric layer, Cp , is given by Eq. (2.26). Lastly, the work of non-conservative forces is given by Eq. (2.27) as (6.14) Wnce = Q(t)v(t) where Q(t) is the electric charge output of the piezoelectric layers. 6.1.3 Substitution of the Assumed Solution Substitution of the assumed solution given by Eq. (2.28) as wrel (x, t) = N X (6.15) φr (x)ηr (t) r=1 which consists of a series of trail functions (φr (x)) multiplied by generalized coordinates (ηr (t)), leads to the following expressions for the potential, kinetic, and internal electrical energy terms N Us = Up = N T = N 1 XX (ηr (t)ηl (t)krl − 2ηr (t)vs (t)θrs ) 2 (6.16) 1 2 (6.17) r=1 l=1 N X N X (ηr (t)ηl (t)krl − 2ηr (t)vp (t)θrp ) r=1 l=1 N 1 XX (η˙r (t)η̇l (t)mrl + 2η˙r (t)pr ) 2 r=1 l=1 ZL 1 + 2 (ρAs (x) + ρAp (x)) ∂wb (t) ∂t 2 1 dx + M 2 ∂wb (t) ∂t 2 (6.18) 0 Wies N 1X 1 s 2 = 2ηr (t)vs (t)θr + Cp vs (t) 2 2 Wiep = r=1 N X 1 2 2ηr (t)vp (t)θrp + 2Cp vp2 (t) (6.19) (6.20) r=1 where ZL krl = 00 ZL2 00 Y Is (x)φr (x)φl (x) dx + 2 0 00 00 cE 11 Ip φr (x)φl (x) dx (6.21) L1 θrs = ZL2 00 Jps φr (x) dx (6.22) L1 θrp ZL2 = 00 Jpp φr (x) dx L1 118 (6.23) ZL mrl = (ρAs (x) + ρAp (x)) φr (x)φl (x) dx + M φr (L4 )φl (L4 ) (6.24) ∂wb (t) ∂wb (t) dx + M φr (L4 ) ∂t ∂t (6.25) 0 L Z pr = (ρAs (x) + ρAp (x)) φr (x) 0 where prime represents ordinary differentiation with respect to the spatial variable, x, and an overdot represents ordinary differentiation with respect to the temporal variable, t. 6.1.4 Lagrange Equations with Electromechanical Coupling The electromechanical Lagrange equations for the energy harvesting wing spar follow from the extended Hamilton’s principle. The first set of Lagrange equations are given by Eq. (2.55) and Eq. (2.56) as N X l=1 N X (mil η̈l + kil ηl − 2θis vs − fi ) = 0 (6.26) (mil η̈l + kil ηl − 2θip vp − fi ) = 0 (6.27) l=1 where the forcing due to base excitation for the spar configuration (which also differs from the self-charging structure derivation), fi , is ∂pi =− fi = − ∂t ZL (ρAs (x) + ρAp (x)) φi (x) ∂ 2 wb (t) ∂ 2 wb (t) dx + M φ (L ) i 4 ∂t2 ∂t2 (6.28) 0 The second set of Lagrange equations are given by Eq. (2.67) and Eq. (2.68) as N 1 vs X Cp v̇s + + (2η̇r θrs ) = 0 2 Rl 2Cp v̇p + vp + Rl r=1 N X (2η̇r θrp ) = 0 (6.29) (6.30) r=1 As described in Subsection 2.3.5, the equivalent series/parallel representation of the Lagrange equations (as suggested by Erturk and Inman [32]) is given by Eq. (2.69) and Eq. (2.70) as N X (mil η̈l + kil ηl − θieq v − fi ) = 0 (6.31) l=1 N Cpeq v̇ + X v (η̇r θreq ) = 0 + Rl r=1 119 (6.32) where the equivalent electromechanical coupling, θeq , and capacitance, Cpeq , terms are selected from Table 2.1 based on the series or parallel electrode connection. 6.1.5 Solution of the Equivalent Representation of the Lagrange Equations Following the solution procedure outlined in Subsection 2.3.6, the equivalent form of the Lagrange equations can be rewritten in matrix form with proportional damping introduced in the first equation, given in Eq. (2.72) and Eq. (2.73) as [M] η̈ + [C] η̇ + [K] η − Θeq v = f v Cpeq v̇ + + Θeq η̇ = 0 Rl (6.33) (6.34) where [M], [K], and [C] are the N × N mass, stiffness, and damping matrices, η, f , and Θeq are the N × 1 vectors of generalized coordinates, forcing functions, and electromechanical coupling terms. The damping matrix is given by [C] = α [M] + β [K] (6.35) where α and β are constants of proportionality. Solution of the matrix equations leads to the frequency response functions given by Eq. (2.88) and Eq. (2.89), as follows wrel (x, t) = ΦT (x) −ω 2 [M] + jω [C] + [K] ab ejωt !−1 1 −1 eq eq T eq + jω jωCp + Θ Θ F̃ Rl 1 −1 eq T v(t) eq Θ −ω 2 [M] + jω [C] + [K] = −jω jωCp + ab ejωt Rl !−1 1 −1 eq eq T eq +jω jωCp + Θ Θ F̃ Rl (6.36) (6.37) where the components of the forcing vector for the harvester spar include the effects of the lumped mass, and are given by L Z F̃i = − (ρAs (x) + ρAp (x)) φi (x) dx + M φi (L4 ) 0 120 (6.38) 6.2 Experimental Validation of the Assumed Modes Formulation In order to validate the electromechanical assumed modes formulation developed in the previous section for a piezoelectric energy harvesting wing spar, a representative wing spar with embedded piezoelectric and thin-film battery layers is experimentally tested and the results are compared to the model predictions. 6.2.1 Representative Energy Harvesting Wing Spar Configuration A 3003-H14 aluminum alloy beam is selected as the substrate layer of the representative wing spar. The overall dimensions of the aluminum substrate, which has a modulus of 69 GPa and a mass density of 2730 kg/m3 , are 304.80 mm x 26.62 mm x 3.237 mm. Two opposite faces of the beam are precisely machined to allow bonding of the piezoelectric and thin-film battery layers on the symmetric structure, such that the thickness along the R length of the beam is constant. QuickPack QP10n piezoelectric devices are bonded near R the root of the beam and Thinergy MEC 101-7SES thin-film batteries are bonded just after the piezoelectric layers. Each layer is bonded using a vacuum bagging procedure, as described previously in Subsection 3.2.2, with ScotchWeldTM DP460 two part epoxy used as the bonding layer. The fabricated representative wing spar is shown in Fig. 6.2 where two magnets placed near the end of the beam create a lumped mass representative of a sensor node. The geometric and material properties of the piezoelectric and battery layers have been given previously in Table 3.2, and the material properties of the Kapton and epoxy layers are discussed in Subsection 3.2.1. Figure 6.2: Representative aluminum wing spar with embedded self-charging structure. 121 6.2.2 Experimental Setup The device is clamped to an APS Dynamics, Inc. [153] 113 long-stroke shaker, which is powered by an APS Dynamics, Inc. 125 power amplifier, with an overhang length of 25.40 cm, as shown in Fig. 6.3. In the clamped configuration, the device becomes a 5-segment beam with an initial 25.40 mm segment containing only the aluminum substrate, followed by a 9.53 transition section containing only the reduced thickness substrate to allow for the electrode connection of the QP10n device, a 50.80 mm composite section containing the substrate layer and symmetric piezoelectric layers bonded with epoxy to the substrate, a 25.40 mm composite section containing the substrate and symmetric thin-film battery layers insulated with Kapton and bonded with epoxy, and finally a 142.88 mm segment which again contains only the aluminum substrate. A 15.6 g lumped mass in the form of two rectangular magnets of dimension 25.4 mm x 6.35 mm x 6.35 mm placed on opposite faces of the beam is fixed at a distance of 203.2 mm from the root of the beam. A DSP Technology, Inc. [119] SigLab 20-42 data acquisition system is used for all FRF measurements. Low amplitude chirp signals are used to excite the shaker, and 5 averages are taken for each measurement. The input acceleration is measured using a PCB Piezotronics, Inc. (a) (b) (h) (f) (g) (c) (c) (d) (d) (a) SigLab data acquisition system (b) Laser vibrometer (c) Clamp (d) Electromagnetic shaker (e) Amplifier (f) Load resistances (g) Energy harvester wing spar (h) Accelerometer (e) Figure 6.3: Experimental setup used to obtain frequency response measurements of the aluminum wing spar. 122 [120] U352C67 accelerometer attached to the base of the clamp, the tip velocity is measured at the tip of the beam using a Polytec, Inc. [121] PDV-100 laser Doppler vibrometer, and the voltage output of the self-charging structure is measured directly with the SigLab data acquisition system using an Agilent Technologies, Inc. [109] N2862A 10:1 probe. The overall test setup is shown in Fig. 6.3. As with the FRF measurements made on the self-charging structure in Subsection 3.3.1, the laser vibrometer measures the absolute tip velocity of the beam, thus Eq. (3.3) can be used to predict the absolute tip velocity - to - base acceleration FRFs. 6.2.3 Experimental Results Both the voltage - to - base acceleration and tip velocity - to - base acceleration FRFs are measured for the series and parallel electrode connections for a set of resistive loads ranging from 100 Ω to 1 MΩ. The Agilent 10:1 probe used to measure the piezoelectric voltage output introduces a 10 MΩ resistance in parallel with the load resistances used, therefore, it must be considered in calculating the total effective load seen by the piezoelectric layTable 6.1: Load resistance values used in FRF measurements of aluminum spar along with effective load resistances. Load Resistor Values (Ω) Effective Resistance Seen by Piezoelectric Layers (Ω) 100 470 1200 6800 10000 22000 47000 100000 330000 470000 680000 1000000 99.99 469.98 1199.86 6795.38 9990.01 21951.71 46780.13 99009.90 319457.89 448901.62 636704.12 909090.91 123 ers. Table 6.1 lists the load resistor values used as well as the effective loads seen by the piezoelectric layers. The voltage and tip velocity FRFs for the series and parallel electrode cases are shown in Fig. 6.4 and Fig. 6.5, respectively, where the model predicted FRFs are plotted over the experimental results in order to validate the model. Forty modes are used in the assumed modes formulation (N = 40) to ensure convergence of the fundamental natural frequency. The admissible functions given by Eq. (2.29) are used in the model. The FRF results show good correlation between the model predictions and the experimental measurements and confirm the ability of the model to accurately predict the vibration and (a) 4 Experiment Model |Voltage FRF| (V/g) 10 Increasing R l 2 10 0 10 -2 10 24 26 28 30 Frequency (Hz) 32 34 |Tip Velocity FRF| ((m/s)/g) (b) Experiment Model 1 10 Increasing R l 0 10 27 27.5 28 28.5 29 Frequency (Hz) 29.5 30 Figure 6.4: Experimental and numerical (a) voltage - to - base acceleration FRFs and (b) tip velocity - to - base acceleration FRFs of the aluminum wing spar for series electrode connection case for various load resistances. 124 (a) 4 Experiment Model |Voltage FRF| (V/g) 10 Increasing Rl 2 10 0 10 -2 10 24 26 28 30 Frequency (Hz) 32 34 |Tip Velocity FRF| ((m/s)/g) (b) Experiment Model 1 10 Increasing R l 0 10 27 27.5 28 28.5 29 Frequency (Hz) 29.5 30 Figure 6.5: Experimental and numerical (a) voltage - to - base acceleration FRFs and (b) tip velocity - to - base acceleration FRFs of the aluminum wing spar for parallel electrode connection case for various load resistances. voltage response of the multifunctional energy harvester spar. As the load resistance increases from near the short-circuit condition at 100 Ω to near the open-circuit condition at 1 MΩ, the experimentally measured fundamental natural frequency shifts from 28.13 Hz to 28.38 Hz for both series and parallel connection cases. These frequencies are predicted by the assumed modes formulation as 28.10 Hz and 28.40 Hz, respectively. The amplitude predictions of the model also fit the experimental measurements well. The experimental voltage FRFs show a maximum peak voltage output of 968.1 V/g for the series connection and 674.1 V/g for the parallel connection at the largest load resistance. As 125 discussed in Subsection 3.3.1, these FRF measurements are linear estimates obtained from low-amplitude excitation and are not necessarily accurate for large amplitude excitations. The model predicts these peak voltage outputs as 875.0 V/g and 593.9 V/g for the series and parallel case, respectively. The maximum tip velocity is measured as 10.57 (m/s)/g and 10.30 (m/s)/g for the series and parallel cases, respectively, when excited at shortcircuit conditions. The model predicts these peak velocities as 10.64 (m/s)/g and 10.59 (m/s)/g. For excitation at the open-circuit condition, the experimentally measured peak tip velocities are 6.83 (m/s)/g and 9.15 (m/s)/g for the series and parallel cases, respectively, and are predicted by the model as 6.67 (m/s)/g and 9.21 (m/s)/g. Using the voltage FRF data given in Fig. 6.4(a) and Fig. 6.5(a), electrical performance curves for the peak voltage, current, and power output with varying load resistance can be created. Excitation at both the short-circuit and open-circuit resonance frequencies is considered. It should be noted again that the performance curves are based on linear FRF measurements and may be inaccurate for predicting the response under large amplitude excitations. The variation of the peak voltage with load resistance is given in Fig. 6.6(a) and Fig. 6.6(b) for the series and parallel cases, respectively. The model agrees well with the experimental data. The peak voltage output values predicted by the model at the short-circuit and open-circuit frequencies for the largest load resistance are 439.5 V/g and 875.0 V/g, respectively for the series case and 230.4 V/g and 593.9 V/g, respectively for the parallel case. The variation of the peak current output with load resistance is presented in Fig. 6.4(c) and Fig. 6.4(d) for the series and parallel electrode connections, respectively. The peak current output occurs for both the short-circut and open-circuit resonance frequencies at the smallest load resistance. The peak currents are predicted by the model for excitation at the short-circuit and open-circuit resonance as 7.32 mA/g and 2.71 mA/g, respectively, for the series case and 14.58 mA/g and 5.42 mA/g, respectively, for the parallel case. Figure 6.4(e) and Fig. 6.4(f) present the variation of the peak power output with load resistance for the series and parallel cases, respectively. For both electrode connection cases, peak power outputs (which are roughly equal) exist for separate load resistance values for excitation at the short-circuit and open-circuit resonance frequencies. The peak power outputs predicted for the series and parallel cases are identical. The model predictions for the peak power output for excitation at the short-circuit resonance are 884.9 mW/g2 for a load 126 4 10 (b) Experiment (28.38 Hz) Experiment (28.13 Hz) Model (28.40 Hz) Model (28.10 Hz) 2 Voltage (V/g) Voltage (V/g) (a) 10 0 4 10 Experiment (28.38 Hz) Experiment (28.13 Hz) Model (28.40 Hz) Model (28.10 Hz) 2 10 0 10 10 2 10 4 10 Load Resistance () 10 6 (c) 2 10 (d) 4 10 Load Resistance () 10 6 2 10 1 Current (mA/ g) 0 10 Experiment (28.38 Hz) Experiment (28.13 Hz) Model (28.40 Hz) Model (28.10 Hz) -1 10 2 10 Power (mW/g2) (e) 1 10 0 10 10 10 6 4 2 10 Experiment (28.38 Hz) Experiment (28.13 Hz) Model (28.40 Hz) Model (28.10 Hz) 0 10 2 4 10 Load Resistance () 10 2 10 4 10 Load Resistance () 6 10 2 10 Experiment (28.38 Hz) Experiment (28.13 Hz) Model (28.40 Hz) Model (28.10 Hz) 0 10 6 10 4 (f) 10 10 Experiment (28.38 Hz) Experiment (28.13 Hz) Model (28.40 Hz) Model (28.10 Hz) -1 4 10 Load Resistance () Power (mW/g2) Current (mA/ g) 10 10 2 4 10 Load Resistance () 10 6 Figure 6.6: Experimental and numerical electrical performance curves of aluminum wing spar for the peak voltage output in the (a) series and (b) parallel case, current output in the (c) series and (d) parallel case, and power output in the (e) series and (f) parallel case with varying load resistance. resistance of 64.04 kΩ for the series connection and 16.09 kΩ for the parallel connection. For excitation at the open-circuit condition, the model predicts the peak power outputs as 913.9 mW/g2 for a load resistance of 503.3 kΩ for the series connection and 126.1 kΩ for the parallel connection. 127 6.3 Chapter Summary Electromechanical modeling is presented for a multifunctional energy harvesting wing spar with embedded self-charging structures. The assumed modes model presented in Chapter 2 is modified to include the effects of the mass and stiffness distribution of the wing spar, including the effects of a lumped mass, in order to predict the coupled vibration and voltage response of the cantilever wing spar model. The energy harvesting spar configuration is first described in which both series and parallel electrode connections of the bimorph structure are considered. Details of the assumed modes formulation are then reviewed. Experimental testing is performed on a representative aluminum wing spar with embedded piezoelectric and thin-film battery layers in order to validate the model. Experimentally measured voltage and tip velocity frequency response functions are compared to those predicted by the assumed modes model. Lastly, several electrical performance curves are created, again comparing experimental data with model predicted results. The assumed modes model developed in this chapter is based on the model previously described in Chapter 2 and developed by Erturk and Inman. Differences in the models result from the presence of a lumped mass placed at an arbitrary position in the x-direction as well as the unique bending stiffness and mass density functions of the wing spar configuration. Comparison of the experimentally measured voltage and tip velocity FRFs to those predicted by the model show good correlation and confirm the ability of the model to predict the vibration and voltage response of the representative wing spar. 128 C HAPTER 7 E NERGY H ARVESTING W ING S PAR FOR E LECTRIC U NMANNED A ERIAL V EHICLE P IEZOELECTRIC vibration energy harvesting in unmanned aerial vehicles has been in- troduced as a case study in this dissertation. Chapter 5 presents the performance modeling of electric UAVs with on board energy harvesting systems while Chapter 6 describes the electromechanical modeling of a UAV wing spar with embedded self-charging structures along with experimental validation of the model in which a representative aluminum spar is tested. In this chapter, the development and testing of a realistic composite multifunctional energy harvesting wing spar with embedded self-charging structures for use in the EasyGlider RC aircraft test platform is given. A stiff, lightweight fiberglass wing spar is developed here with piezoelectric and thin-film battery layers embedded in the layup of the spar. Details of the design and fabrication of the wing spar are first given. Experimental bench testing is then performed on the spar in which frequency response measurements are made to gain information about the fundamental natural frequency of the spar, and charge/discharge testing is performed in which the spar is excited harmonically at resonance while the piezoelectric layers are connected to directly charge the thin-film battery layers. Lastly, experimental flight testing is performed in which the fiberglass spar is used in the EasyGlider aircraft and the energy harvesting performance during flight is investigated. 129 7.1 Design and Fabrication of Multifunctional Composite Wing Spar A fiberglass wing spar with embedded self-charging structures is designed for use in the EasyGlider aircraft. The physical configuration of the wing spar is shown in Fig. 7.1. The main construction of the spar consists of a polystyrene foam core (which provides shape and is extremely lightweight) wrapped in several layers of fiberglass. The wing spar is shaped to fit in the tapered wing cavity of the EasyGlider aircraft (recall, a fiberglass spar with surface mounted piezoelectric devices has been previously tested in the EasyGlider aircraft, as described in Section 5.4, hence the wings have been previously modified to accept a rectangular spar). The foam core has a length of 99.0 cm, a width of 2.87 cm, and a maximum thickness of 1.4 cm at the center of the spar and 0.8 cm at the ends of R the spar. Two piezoelectric layers (QuickPack QP10n devices) and two thin-film battery R layers (Thinergy MEC-1017SES batteries) are used on both the top and bottom surfaces of the spar, effectively creating two self-charging structures with the foam core becoming the substrate layer. The self-charging structures are embedded between layers of fiberglass, thus they are integral to the wing spar. Each self-charging structure is placed 3.8 cm from the center of the wing spar, which corresponds to the root of the wing against the fuselage when the spar is inserted into the wings and the aircraft is fully assembled. This location will experience the largest strain during flight, hence the placement of the piezoelectric devices at the root of the wings. Additionally, extra fiberglass layers are included in the region between the piezoelectric devices to help increase the stiffness of the spar section that passes through the fuselage and for maximum strain to be induced in the piezoelectric devices. Based on preliminary testing of various foam cores and fiberglass layers, extruded Fiberglass Layers Thin-Film Battery Layers Piezoelectric Layers Foam Core 7.6 cm 1.4 cm 99 cm Figure 7.1: Fiberglass wing spar schematic showing foam core with fiberglass layers and embedded self-charging structures. 130 polystyrene insulating foam from The Dow Chemical Company [154] is selected as the foam core material and 1080-50 E-Glass fiberglass cloth (which has a density of 1.45 oz/sq. yd.) from Aircraft Spruce and Specialty Co. [155] is selected as the fiberglass layer. Additionally West System [150] 105/205 two part epoxy is chosen as the epoxy layer in the fiberglass layup. Three layers of 1080-50 cloth are chosen in order to best match the stiffness of the original round carbon fiber reinforced plastic wing spar rod. The self-charging structures are placed between the second and third layer of fiberglass. An additional layer of fiberglass is added to the center section of the spar between the piezoelectric devices. Electrodes are attached to each piezoelectric device and battery prior to fabrication of the wing spar. Fabrication of the spar involves first cutting a foam core using a hot wire cutter to the dimensions shown in Fig. 7.1. A single piece of fiberglass cloth large enough to wrap the entire foam core three times is then cut. The fiberglass is saturated in epoxy and wrapped R around the foam core. Between the second and third fiberglass layer, the QuickPack and R Thinergy devices are placed on the upper and lower surfaces of the spar. Small slits are cut in the fiberglass cloth such that the device electrodes can be passed through the fiberglass. With three layers of fiberglass covering the spar, an additional layer is added to the center of the spar. The wing spar is cured using a vacuum bagging procedure similar to that described in Subsection 3.2.2. A schematic of the vacuum bagging setup used for the wing spar fabrication is shown in Fig. 7.2. The spar is surrounded on all sides by a peel ply layer, a perforated ply layer (which controls the amount of epoxy absorbed away from the spar), and a bleeder/breather layer because of the large amount of epoxy which must be removed from the saturated fiberglass cloth to yield a lightweight spar. Once placed in the vacuum bag, the spar is allowed to cure under approximately 20 in-Hg of vacuum for 6 hours. Photographs of the wing spar placed in the vacuum bag for curing are shown in Fig. 7.3. The fabricated fiberglass wing spar is shown in Fig. 7.4. The original carbon fiber reinforced plastic spar weighs 53 g, and the fiberglass spar weighs 50 g, comparing favorably. Additionally, the stiffness of the fiberglass spar is found to be similar to the original spar. 131 Vacuum Gauge 15 20 10 25 5 0 30 in Hg Vacuum Pump Wing Spar Work Surface Breather/Bleeder Cloth Peel Ply Perforated Ply Vacuum Bag Tape Figure 7.2: Schematic of vacuum bagging procedure for fiberglass wing spar fabrication. 7.2 Experimental Evaluation of Energy Harvesting/Energy Storage Performance Experiments are performed on the fiberglass wing spar in order to evaluate its ability to simultaneously harvest and store energy in a self-charging manner. Harmonic base excitation at the fundamental natural frequency of the spar will be used, therefore, the resonance frequency must first be obtained. Frequency response function measurements are made on the spar mounted in a double cantilever configuration (clamped at the center of the spar) for this purpose. Once the fundamental natural frequency of the spar is found, charge/discharge measurements are made in which the spar is excited at resonance while the piezoelectric layers are used to charge the battery layers. Figure 7.3: Photographs of fiberglass wing spar curing under vacuum. 132 Figure 7.4: Complete self-charging fiberglass wing spar. 7.2.1 Frequency Response Measurements The frequency response of the fiberglass wing spar is first obtained experimentally. The experimental setup used for the tests, shown in Fig. 7.5, is similar to the setup used for testing the aluminum wing spar (see Fig. 6.3). The spar is mounted to an an APS Dynamics, Inc. [153] 113 long-stroke shaker, powered by an APS Dynamics, Inc. 125 power amplifier. A double cantilever configuration is used in which the spar is clamped at the center, effectively creating a cantilever beam on either side of the clamp, as shown in Fig. 7.5. This configuration is used to simulate the operating condition of the spar when inserted into the EasyGlider aircraft (where the fuselage effectively becomes a rigid base used to excite each side of the spar). In the clamped configuration, each cantilever has an overhang length of 47.0 cm. A DSP Technology, Inc. [119] SigLab 20-42 data acquisition system is used for the FRF measurements, which are obtained using low amplitude chirp excitation. Five averages are taken for each measurement. The input acceleration is measured using a PCB Piezotronics, Inc. [120] U352C67 accelerometer attached to the base of the clamp, the tip velocity is measured at the tip of the spar using a Polytec, Inc. [121] PDV-100 laser Doppler vibrometer, and the voltage output of the self-charging structure is measured directly with the SigLab data acquisition system using an Agilent Technologies, Inc. [109] N2862A 10:1 probe. The frequency response functions of the spar with two piezoelectric layers of a self- 133 (b) (a) (a) SigLab data acquisition system (b) Laser vibrometer (c) Fiberglass wing spar (d) Electromagnetic shaker (e) Amplifier (f) Accelerometer (g) Clamp (c) (d) (c) (e) (f) (g) (d) Figure 7.5: Experimental setup used to obtain frequency response measurements of fiberglass wing spar. charging structure connected in series to a 1 MΩ load resistance (creating an effective load resistance of 909090.91 Ω when taking the 10 MΩ Agilent probe into consideration) are recorded and are given in Fig. 7.6, where Fig. 7.6(a) shows the entire spectrum and Fig. 7.6(b) shows the results near the fundamental resonance frequency. Recalling the results presented in Fig. 3.10(b), where the response of the self-charging structure connected to the linear regulator energy harvesting circuit was found to closely match the case with the largest resistive load, a load of 1 MΩ is chosen here as the same linear regulator circuit will be used for charge/discharge measurements. The frequency response measurements given in Fig. 7.6 show that the fundamental resonance frequency of the spar is around 43 Hz. It can be seen that the measurements contain several peaks, and while atypical for a uniform cantilever beam, this behavior is expected for the non-uniform composite fiberglass spar. In addition to various bending modes, such a structure may experience 134 (a) 2 Voltage FRF (V/g) Tip Velocity FRF ((m/s)/g) FRF Magnitude 10 0 10 -2 10 -4 10 0 100 200 300 Frequency (Hz) 400 500 (b) Voltage FRF (V/g) Tip Velocity FRF ((m/s)/g) 2 FRF Magnitude 10 0 10 10 20 30 40 50 Frequency (Hz) 60 70 80 Figure 7.6: Frequency response functions of fiberglass wing spar (series electrode connection, 1 MΩ load) showing (a) broad spectrum and (b) detail near the fundamental resonance frequency. torsional vibration modes due to non-uniformity. Additionally, the clamp condition is not perfect as a large clamping force would cause mechanical failure of the wing spar. Thin pieces of foam are also inserted between the spar and clamp interface to help protect the spar. The non-ideal clamping condition likely introduces several of the peaks observed in the measurement. It can be observed from Fig. 7.6(b) that two peaks exist at the fundamental frequency, making the exact resonance frequency difficult to assess. These FRF measurements, however, give a basis for the fundamental natural frequency of the fiberglass spar. Precise tuning can be performed during the charge/discharge measurements. 135 7.2.2 Self-Charging Charge/Discharge Measurements With a general measure of the fundamental natural frequency obtained, the energy harvesting performance of the self-charging fiberglass wing spar is investigated. The spar is excited at resonance with two piezoelectric layers connected through the linear regulator energy harvesting circuit, shown previously in Fig. 3.12, to charge a single thin-film battery layer. A base excitation level of ±0.5 g is chosen for the testing based on the flight acceleration measurements found previously in Chapter 5 (shown in Fig. 5.7(c)), which show an average acceleration of around ±1.0 g in the z-direction. Considering that the excitation frequency experienced on the aircraft does not match the resonance of the harvester, an acceleration level of half of the measured acceleration is chosen, however, the resonance tests performed here will likely still overestimate the harvesting ability of the spar during flight. After some preliminary tests, the two piezoelectric layers of a single self-charging structure will be connected in parallel to the energy harvesting circuit for increased current output as the voltage level under ±0.5 g excitation is sufficient for charging the battery layer. The experimental setup used for the charge/discharge measurements is shown in Fig. 7.7. The setup is similar to that used in Subsection 3.3.2, however, a Keithley Instruments Inc. [156] 2611A SourceMeter is used for the current measurement in charging and for both current and voltage measurements in discharging. The SourceMeter is capable of simultaneously sourcing or sinking either current or voltage while measuring both quantities. In discharging, the SourceMeter is used to draw a constant current out of the battery throughout the entire discharge test (which is not possible by using a simple resistive load to discharge the battery, as done previously, because the voltage of the battery drops slightly throughout the test). In charging, a National Instruments Corp. [110] CompactDAQ chassis utilizing a NI 9215 4-channel analog voltage input card is used measure the battery voltage. Additionally, a NI 9233 4-channel analog input card with IEPE coupling is used to measure the accelerometer signal to ensure ±0.5 g excitation is achieved, and a NI 9263 4-channel analog output card is used to excite the shaker. Both the Keithley SourceMeter and National Instruments CompactDAQ chassis are controlled by custom written LabVIEW programs running on separate computers. Prior to running the charge/discharge test, the exact resonance frequency of the fiberglass spar when connected to the energy harvesting circuit is found by fine tuning the 136 (a) Keithley SourceMeter (b) NI CompactDAQ data acquisition system (c) Fiberglass spar (d) Clamp (e) Accelerometer (f) Electromagnetic shaker (a) (b) (e) (c) (d) (a) (f) Figure 7.7: Experimental setup used to obtain charge/discharge measurements of selfcharging fiberglass wing spar. excitation frequency around 43 Hz while monitoring for the largest power output from the piezoelectric layers, resulting in a resonance frequency of 43.5 Hz. The fiberglass spar is excited for 3 hours while the piezoelectric layers are used to charge the battery layer. Both the Keithley SourceMeter and the NI CompactDAQ data acquisition system are configured to record the current and voltage data at 10 Hz sampling rates. Results of the test are presented in Fig. 7.8. The results of the charge test are given in Fig. 7.8(a), where it can be seen that an average of about 110 µA of current flows into the battery at a voltage of 3.9 V, corresponding to an average power of 0.430 mW. Both the current and the voltage remain fairly constant throughout the duration of the test. The charge capacity is calculated using Eq. (3.2) as 0.323 mAh. From the discharge test results presented in Fig. 7.8(b), it can be seen that a constant current of 2C (1.4 mA) is drawn from the battery throughout the test. The voltage remains constant at the beginning of the test and tapers off quickly near the end. In discharging, a capacity of 0.324 mAh is calculated. The discharge capacity is slightly higher than the charge capacity, likely because some small residual charge existed in the battery prior to the test. The results of the charge/discharge testing show the ability of the fiberglass spar to operating in a self-charging manner, and give an estimate of the power that can be harvested by the spar. 137 (a) 0.25 4.1 Current (mA) 0.2 3 0.15 Current 0.1 2 Charge Capacity: 0.323 mAh 0.05 Voltage (V) Voltage 1 0 0 8000 10000 0 5 4 Current (mA) 4000 6000 Time (sec) 4.1 3.8 Voltage 3 3 Load Disconnected 2 Current 2 Voltage (V) (b) 2000 1 Discharge Capacity: 0.324 mAh 0 0 200 400 Time (sec) 600 1 800 0 Figure 7.8: Experimental curves for fiberglass wing spar in (a) charging and (b) discharging under ±0.5 g acceleration at 43.5 Hz. 7.3 Experimental Flight Testing of Self-Charging Fiberglass Wing Spar Flight testing is performed in which the self-charging fiberglass wing spar is used in the EasyGlider aircraft test platform. Vibration energy harvesting is performed during flight and several measurements are made using data loggers. Details of the EasyGlider aircraft configuration as well as the flight testing measurement results are reviewed. 138 7.3.1 EasyGlider Aircraft Configuration The EasyGlider aircraft configuration used for flight testing with the self-charging fiberglass spar is similar to the aircraft configuration described previously in Subsection 5.4.1. No further modification is required to the aircraft wings to allow insertion of the selfcharging fiberglass spar, which is shown in Fig. 7.9. The two fiberglass canopies developed previously are used again to facilitate the installation of the Pace Scientific, Inc. [151] XR5-SE-M-50mv eight channel, 0-5 V data logger (Fig. 5.5) and the UA-004-64 Pendant G 3-axis accelerometer data logger from Onset Computer Corp. [152] (Fig. 5.6). 7.3.2 Flight Testing Results Flight testing is performed in which the energy harvesting performance of the self-charging fiberglass spar is evaluated in flight. Although it is desirable to measure the operation of the wing spar in a self-charging manner during flight (in which the piezoelectric layers are used to charge a battery layer), several challenges exist making this test condition impractical with the current configuration. The energy harvesting circuitry required to allow the transfer of energy from the piezoelectric layers to the battery layers would require miniaturization, perhaps incorporating the entire circuit on a single chip, in order to physically fit in the aircraft. The linear regulator circuit has been constructed on a breadboard for de- Figure 7.9: Self-charging fiberglass wing spar inserted into EasyGlider aircraft wings. 139 velopment purposes, shown previously in Fig. 3.14(c), and is too large to fit in the cockpit of the aircraft. Additionally, the available data loggers lack current measuring capability for monitoring the current transfered from the piezoelectric layers to the battery layer. Furthermore, in the short flight time of the aircraft (on the order of 5-10 minutes), it is expected that the amount of energy harvested by the piezoelectrics may not show appreciable increase in the battery capacity beyond any recovered capacity the battery naturally achieves after being discharged. Therefore, during the flight test, the output of a single R QuickPack piezoelectric device across a matched load of 130 kΩ is measured with the XR5-SE-M-50mv data logger at a sampling frequency of 100 Hz. The aircraft acceleration in the z-axis (vertical axis) is also measured during flight with the UA-004-64 accelerometer data logger at a sampling rate of 100 Hz. During the flight test, the aircraft was hand launched and flew on a sunny day with light and variable winds experiencing gusts up to 10 km/h for about 10 minutes, of which about 7 minutes of data was recorded with the data loggers. Figure 7.10 shows a photograph of the EasyGlider aircraft in flight during testing. The aircraft followed a wide circle flight pattern with several climb, cruise, descend cycles. In cruise conditions, a maximum altitude of around 75 m and a cruise speed of around 30 km/h was achieved, with maximum speeds reaching around 40 km/h. Results of the flight testing are presented in Fig. 7.11. It should be noted that the air- Figure 7.10: Photograph of EasyGlider aircraft during flight testing of multifunctional fiberglass wing spar. 140 craft is launched after about 60 seconds of data logging (evident from the acceleration measurement). From the voltage results presented in Fig. 7.11(a), it can be seen that the R device exceeds the 5 V limit of the data logger at various points output of the QuickPack throughout the flight. The results, however, can still be used to provide a rough estimate of the power harvested during flight. Using Eq. (5.32), the average power output of the piezoelectric device is calculated as 3.22 µW. Due to the voltage clipping experienced by the data logger, it is expected that the results underestimate the actual power harvested during flight. (a) Piezoelectric Voltage (V) 5 4 3 2 1 0 0 (b) 100 200 300 Time (sec) 400 500 100 200 300 Time (sec) 400 500 4 Z-Axis Acceleration (g) 3 2 1 0 -1 0 Figure 7.11: Flight testing results of fiberglass self-charing spar showing (a) voltage output of piezoelectric device and (b) z-axis acceleration. 141 The acceleration measured in the z-axis during flight is given in Fig. 7.11(b). The results show an an average acceleration of around ±0.75 g (note the acceleration during flight is centered around 1.0 g due to the acceleration of gravity acting on the accelerometer). Peak acceleration values reach up to ±2.0 g at times during the flight test. These results provide a baseline for the excitation levels experienced during flight. 7.4 Chapter Summary Details of the design, fabrication, and experimental testing of a multifunctional energy harvesting/energy storage fiberglass UAV wing spar are presented. The fiberglass spar, which contains two self-charging structures, is designed for use in the EasyGlider test platform. Piezoelectric and battery elements are embedded near the center of the spar at the root of the wings for maximum induced strain in the piezoelectrics during flight. Experimental testing is performed on the fabricated spar to evaluate its energy harvesting ability. Frequency response measurements are first obtained to determine the fundamental resonance frequency of the spar. Charge/discharge measurements are then performed by subjecting the spar to resonant base excitation while the piezoelectric layers are used to charge the battery layers. Lastly, flight testing is performed in which the spar is used in the EasyGlider aircraft and the output of a piezoelectric layer is monitored during flight. Experimental evaluation of the charge/discharge performance of the multifunctional spar under harmonic base excitation at the fundamental natural frequency confirms the ability of the spar to simultaneously harvest energy in the piezoelectric layers and store energy in the battery layers. At an excitation level of ±0.5 g, an average power of 0.430 mW transfered from the piezoelectric layers to the battery layers through a simple linear regulator harvesting circuit is found. Through the use of more efficient energy harvesting circuity, the amount of harvested/transfered power is expected to increase. Flight testing of the wing spar installed in the EasyGlider aircraft provides a realistic example of the use of self-charging structures in an application where multifunctional solutions are necessary. Results of the flight testing show that an average of about 3.22 µW of energy can be harvested from each piezoelectric device. Although the harvested energy is small, recall the focus of piezoelectric harvesting in UAVs is to provide autonomous power sources for low-power sensors, which is likely possible with this level of harvested energy. 142 C HAPTER 8 C ONCLUSIONS AND R ECOMMENDATIONS E NERGY harvesting is a critical technology for the development of autonomous, self- powered electronic devices. As the energy requirements of low-power electronics decrease, the use of energy harvesting systems in providing them power is becoming more promising. Energy harvesting technology has the potential to revolutionize the way in which power is provided to small electronics; transitioning from a reliance on battery power to self-powered, autonomous systems. In this dissertation, multifunctional piezoelectric vibration energy harvesting concepts have been investigated. Perhaps one of the most promising applications of piezoelectric vibration energy harvesting is in providing power to autonomous sensor nodes. Piezoelectric vibration energy harvesting utilizes the electromechanical coupling exhibited in piezoelectric materials to convert ambient vibration energy surrounding a system into useful electrical energy. The harvested energy is typically stored in a battery or capacitor for use in powering a small electronic device. The multifunctional concepts explored in this dissertation aim to add functionality to classical piezoelectric energy harvesting systems such that a single harvester can not only generate useful electrical energy, but store the harvested energy and support structural load as an integrated component in a host structure. Multifunctional energy harvesting solutions work to enable the use of energy harvesting in systems where added mass and volume are critical and a fully integrated solution is desirable. This final chapter provides a summary of the research presented in this dissertation. Significant contributions made to the field of piezoelectric energy harvesting are reviewed. Finally, recommendations are made to extend the reach of this research in the future. 143 8.1 Research Summary Several aspects of the development of multifunctional piezoelectric self-charging structures are investigated in this dissertation. Introduction of the self-charging structure concept as well as the application of an electromechanical model used to predict the electrical and mechanical response of self-charging structures is given in Chapter 2. Self-charging structures consist of piezoelectric layers directly bonded to thin-film battery layers in a bimorph configuration with a passive substrate layer such that excitation of the device allows for simultaneous energy generation in the piezoelectric layers and energy storage in the battery layers. Self-charging structures can also be embedded into a host structure and used to support structural load, thus providing energy harvesting, energy storage, and load bearing ability. An approximate distributed parameter electromechanical assumed modes model developed by Erturk and Inman is applied to cantilever self-charging structures subjected to harmonic base excitation. Electromechanical displacement - to - base acceleration and voltage - to - base acceleration frequency response function expressions are derived to describe the mechanical and electrical response of the structures. Experimental evaluation of a self-charging structure prototype is presented in Chapter 3 in order to validate the electromechanical model presented in Chapter 2 and to confirm the ability of the device to simultaneously harvest and store electrical energy. Simulation results using the assumed modes model are found to closely match the experimentally measured electromechanical frequency response functions over a range of load resistances from 100 Ω to 1 MΩ for both the series and parallel connection of the piezoelectric layers. Both the voltage FRF and the tip velocity FRF show good correlation between model and experiment, thus validating the electromechanical model. Results of charge/discharge testing in which the self-charging structure prototype is excited harmonically while the piezoelectric layers are used to charge the battery layers through a linear regulator energy harvesting circuit show simultaneous energy generation and energy storage ability. Under ±1.0 g of base excitation at the fundamental resonance frequency of the device, approximately 0.3 mW of power is harvested and stored in a thin-film battery layer. It is proposed that self-charging structures be integrated into host structures in a multifunctional manner to support structural load. Chapter 4 presents analysis of the strength of self-charging structures including both static strength testing and dynamic strength test- 144 ing. Static three-point bend testing is performed on a prototype device. Results of the testing show that the bending strength of a complete self-charging structure is around 100 - 125 MPa. Dynamic testing is performed in which a cantilever self-charging structure is subjected to harmonic base excitation of increasing amplitude while monitoring for mechanical or electrical failure of the device. Self-charging structures are found to be quite robust under dynamic excitation, experiencing no failure at excitation levels up to ±7.0 g of base acceleration. Static three-point bend testing is also performed on a variety of piezoceramic materials including monolithic, single crystal, and composite piezoelectrics. Results of the comprehensive testing can be used as a design tool to aid in the development of self-charging structures, allowing the most appropriate piezoelectric material to be selected for various applications. Vibration energy harvesting in unmanned aerial vehicles is explored as a case study in this dissertation in which multifunctional self-charging structures are used in a mass and volume critical application. The goal of piezoelectric vibration harvesting in UAVs is to provide local power sources for autonomous sensors. Modeling of the flight performance of electric UAVs with on board energy harvesting systems is presented in Chapter 5. A flight endurance formulation recently published by Thomas et al. is applied to the EasyGlider remote control aircraft, which is chosen as the test platform explored in this dissertation. Simulation results of the normalized change in flight time with the addition of piezoelectric vibration energy harvesting indicate that a fully multifunctional design in which all mass added to the aircraft by the harvesting system be removed from the structural mass of the aircraft in a multifunctional manner is required to prevent loss in flight time. This result is mainly attributed to the large density and low specific power output of piezoelectric materials. Simulations performed to predict the effects of adding self-charging structures to the EasyGlider aircraft confirm the need for a multifunctional solution to prevent significant loss in flight endurance. Electromechanical modeling of a multifunctional UAV wing spar with embedded selfcharging structures is described in Chapter 6. An electromechanical assumed modes formulation for a cantilever 1/2 spar model (where the moving base represents the aircraft fuselage) based on the model presented by Erturk and Inman is developed to predict the response of a UAV wing spar with integrated piezoelectric and thin-film battery layers. Experimental testing of a representative aluminum wing spar with embedded self-charging 145 structures is performed in order to validate the model. Comparison of experimental voltage and tip velocity FRFs to those predicted by the model show good correlation for both the series and parallel electrode connection of the piezoelectric layers over a range of load resistances, thus validating the model. Fabrication and experimental testing of a realistic fiberglass wing spar with embedded self-charging structures for use in the EasyGlider test platform is presented in Chapter 7. A lightweight wing spar composed of several layers of fiberglass surrounding a foam core is fabricated with piezoelectric and thin-film battery layers integrated between layers of fiberglass. Experimental charge/discharge testing is performed where the spar is clamped at the center and excited harmonically at resonance. Results show that the spar is able to operate in a self-charging manner, with two piezoelectric layers delivering an average of 0.43 mW of power to a thin-film battery layer at ±0.5 g of excitation. Experimental flight testing is also performed in which the fiberglass spar is used in the EasyGlider aircraft and the energy harvesting performance of the spar is evaluated during flight. Although it was not feasible to connect the piezoelectric layers to charge a thin-film battery layer during the flight testing, the output of a single piezoelectric layer was measured across a matched load resistance and an average power of about 3 µW was recorded during flight. These results present the use of self-charging structures in a realistic application that can benefit from a multifunctional approach. 8.2 Contributions of the Research The self-charging structure concept presented in this dissertation is the first multifunctional vibration energy harvesting system to combine energy harvesting, energy storage, and load bearing ability in a single device. A summary of the main contributions of this work and reference to the corresponding publications is given below. • A multifunctional energy harvesting concept that directly combines piezoelectric elements for energy generation and thin-film battery elements for energy storage has been investigated. The proposed self-charging structures work to mitigate the drawbacks of conventional vibration energy harvesting approaches, in which the harvesting system is retrofit to an existing host structure, potentially hindering the performance of the original system, to enable more synergistic solutions to piezoelectric 146 energy harvesting [157]. • Comprehensive design, modeling, and experimental evaluation of the self-charging structure concept has been performed. An electromechanical assumed modes model has been presented to predict the coupled mechanical and electrical response of cantilever self-charging structures subject to harmonic base excitation. Experimental testing of a prototype device validates the electromechanical model and also confirms the ability of the device to simultaneously harvest and store electrical energy in a self-charging manner [115, 123, 157–159]. • Strength properties of prototype self-charging structures have been determined through both static three-point bend testing and dynamic resonance excitation testing. Test results can be used in the design of embedded self-charging structure applications [123, 157]. • Experimental analysis of the bending strength of a variety of commercially available piezoceramic materials including hard, soft, single crystal, and composite piezoelectrics is performed. Previously lacking in the literature, the results can not only be used in the design of optimal self-charging structures, but in any piezoelectric system in which the active material is subject to bending loads [160]. • Multifunctional vibration harvesting in unmanned aerial vehicles using embedded self-charging structures is explored as a case study. The electromechanical modeling, design, fabrication, and experimental testing of a multifunctional energy harvesting/energy storage UAV wing spar provides one of the first works of piezoelectric energy harvesting in UAVs in which extensive modeling and experimental studies are carried out [161, 162]. 8.3 Recommendations and Future Work The multifunctional energy harvesting concepts explored in this dissertation provide an initial investigation into the potential use and benefits of a multifunctional approach to vibration energy harvesting. The results presented here show successful application of simultaneous energy harvesting and energy storage, however, further investigation is required before such a multifunctional solution is seen as a practical replacement for bat147 teries. A more comprehensive understanding of the energy harvesting/energy storage ability of self-charging structures when subjected to realistic excitation profiles is required. Future investigation should consider a variety of ambient excitation sources consistent with potential applications of self-charging structures. The design of self-charging structures, including selection of piezoelectric material, substrate material, and geometry, can also be tailored to best suit specific applications. Another key issue that must be addressed involves the development of more efficient energy harvesting and management circuitry for the transfer of harvested energy from the piezoelectric layers to the battery layers for storage as well as management of the energy consumed by the sensor node. In addition to improving the efficiency of harvesting circuitry, future work should investigate the development of electronics that can be directly embedded in the energy harvesting device. In this work, the harvesting circuit is external to the multifunctional self-charging structures, however, the system can be improved with the integration of all required components into a single device. Novel flexible electronic circuitry can be investigated for this purpose. Lastly, a critical element to be addressed in the future involves the investigation of the longevity of a multifunctional piezoelectric energy harvesting system. Investigation of the ability of the harvesting system to operate autonomously for the lifetime of a sensor node, including robustness against varying ambient vibration conditions, temperature, and other environmental factors, is paramount. While the electromechanical modeling presented in this dissertation can be used to accurately predict the response of cantilever self-charging structures subjected to harmonic base excitation, new models can be developed to describe the behavior of the devices in a variety of configurations and applications. Accurate models that can predict the response of surface mounted devices and devices subject to stochastic ambient vibration excitation, for example, should be explored. Although the strength of self-charging structures themselves has been thoroughly investigated, the effects of embedding self-charging structures on the strength of host structures should also be considered. 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R. and Inman, D. J., 2011, “Performance modeling of unmanned aerial vehicles with on-board energy harvesting,” in Proceedings of the 18th SPIE Annual International Symposium on Smart Structures and Materials & Nondestructive Evaluation and Health Monitoring. [162] Anton, S. R. and Inman, D. J., 2011, “Electromechanical modeling of a multifunctional energy harvesting wing spar,” in Proceedings of the 52nd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference. [163] IEEE Standard 176, 1987, “IEEE Standard on Piezoelectricity,” IEEE. 165 A PPENDIX A P IEZOELECTRIC C ONSTITUTIVE E QUATIONS A.1 Constitutive Equations for Bulk Monolithic Piezoelectric Material The constitutive equations for linear piezoelectric material are well documented in the IEEE Standard on Piezoelectricity [163]. Both the direct and converse piezoelectric effects can be expressed mathematically as a relationship between four field variables including stress, S, strain, T , electric field, E, and electric displacement, D. Four forms of the constitutive equations can be written by considering any two field variables as independent variables. The most common representation of the constitutive relations can be expressed in tensor (or indicial) notation as [163] Sij = sE ijkl Tkl + dkij Ek (A.1) Di = dikl Tkl + εTik Ek (A.2) where Sij is the mechanical strain, Tkl is the mechanical stress, Ek is the electric field, Di is the electric displacement, sE ijkl is the mechanical compliance (reciprocal of the elastic modulus) measured at constant electric field, dikl is the piezoelectric strain coefficient, and εTik is the dielectric permittivity measured at zero mechanical stress. Based on the symmetry of tensors, the constitutive equations can be written in compact matrix form as where a superscript S 0 sE d T = D d εT E 0 (A.3) denotes transpose. Here the following notation (known as Voigt 166 notation) is adopted S1 = S11 T1 = T11 (A.4) S2 = S22 T2 = T22 (A.5) S3 = S33 T3 = T33 (A.6) S4 = S23 + S32 T4 = T23 + T32 (A.7) S5 = S13 + S31 T5 = T13 + T31 (A.8) S6 = S12 + S21 T6 = T12 + T21 (A.9) The fully populated constitutive matrices can be further reduced for orthotropic materials (most piezoelectric materials are orthotropic) as follows S1 S2 S3 1 Y1E ν12 − Y E 1 ν − 31E = Y3 0 S4 S 0 5 S6 0 D 1 − Yν12E 0 0 0 1 − Yν13E 1 Y1E − Yν23E 1 0 0 0 − Yν32E 1 Y3E 0 0 0 0 0 1 GE 23 0 0 0 0 0 1 GE 13 0 0 0 0 0 1 GE 12 3 1 0 0 0 0 d15 D2 = 0 0 0 d24 0 D d13 d23 d33 0 0 3 T 0 0 d 1 13 T2 0 0 d 23 E1 T3 0 0 d 33 + E 2 0 d24 0 T4 E 3 T5 d15 0 0 T6 0 0 0 T1 T 2 T E1 0 ε 0 0 T3 11 + 0 εT22 0 E2 0 T4 E T 0 0 0 ε 3 33 T5 T6 (A.10) where Y is the elastic modulus, ν is Poisson’s ratio, G is the shear modulus, and the components of the elastic compliance matrix, sE ijkl , have been expressed in terms of these quantities. A.2 Alternative Representations of the Constitutive Equations As noted above, four unique forms of the constitutive equations can be written based on the choice of independent variables. In addition to Eq. (A.3), the three alternative forms 167 are given as T cE −e S = 0 D e εS E D S s g T = 0 T E D −g β T cD −h S = 0 S E −h β D e = cE d 0 εS = εT − d cE d (A.11) g = dβ T 0 sD = sE − dβ T d (A.12) h = cD g 0 β S = β T + g cD g (A.13) The transformations listed in Eq. (A.11), Eq. (A.12), and Eq. (A.13) can be used to help move between each form of the constitutive equations. A.3 Reduced Form of the Constitutive Equations for a Thin Beam Operating in ‘31’ Mode A common operating mode of a piezoelectric material is the ‘31’ mode, in which the electric field is applied/produced in the 3-direction (it is common practice to align the 3-direction axis of the material with the poling direction, which is assumed here) and the voltage is applied/generated in the 1-direction. For a thin beam allowing Euler-Bernoulli beam assumptions operating in ‘31’ mode, the only non-zero stress component is in the 1-direction, giving T2 = T3 = T4 = T5 = T6 = 0 (A.14) Focusing on the electric field in the 3-direction, this leads to the following reduced form of the constitutive equations (applying the first alternative representation given in Eq. (A.11)) T1 = cE 11 S1 − e31 E3 D3 = e31 S1 + εS33 E3 168 (A.15) A PPENDIX B B ENDING S TIFFNESS AND M ASS D ENSITY C ALCULATIONS FOR C OMPOSITE C ROSS -S ECTIONS B.1 Bending Stiffness Calculation using the Parallel Axis Theorem For a symmetric composite structure, the neutral axis of the cross-section lies in plane with the x-axis at the center of the structure. The bending stiffness of a symmetric composite section can, therefore, be found using the parallel axis theorem to calculate the area moment of inertia of each material section about the neutral axis. The parallel axis theorem allows the moment of inertial of a rigid body to be found about any axis. Consider the rigid body shown in Fig. B.1. The parallel axis theorem states Ix = Ix0 + Az 2 (B.1) where Ix is the area moment of inertia of the rigid body about the arbitrary axis, x, Ix0 is the area moment of inertia of the body about its neutral axis, x0 , A is the area of the body, and z is the distance of the neutral axis to the arbitrary axis. x' z x Figure B.1: Rigid body with neutral axis x0 . 169 B.2 Self-Charging Structure Sections Consider the self-charging structure configuration shown in Fig. 2.4(c) and repeated again in Fig. B.2. The neutral axis lies in the geometric center of the substrate layer in both sections. 0 x L1 hp hs hp hk Piezoceramic Layer he h1 Thin-Film Battery Layer Substrate Layer L1 x L Kapton Layer hb Epoxy Layer Electrodes h2 Poling Direction hb Figure B.2: Cross-sectional views of the two composite sections of the self-charging structure. For the first composite section from 0 < x < L1 , the bending stiffness of each material section is given using Eq. (B.1) as follows Outer Kapton Layer Y Iko = Yk Piezoelectric Layer Y Ip = Yp Inner Kapton Layer Y Iki = Yk Epoxy Layer Y Ie = Ye Substrate Layer Y Is = Ys ! hs 3hk 2 + he + hp + 2 2 ! bh3p hp 2 hs + bhp + he + hk + 12 2 2 ! bh3k hs hk 2 + bhk + he + 12 2 2 ! bh3e hs he 2 + bhe + 12 2 2 bh3k + bhk 12 bh3s 12 (B.2) (B.3) (B.4) (B.5) (B.6) where Yk , Yp , Ye , and Ys are the elastic moduli of the Kapton, piezoelectric, epoxy, and structure materals, respectively. The total bending stiffness is the sum of the bending stiffness of each material section. For the structural materials, the bending stiffness is given by Y Ic1 = Y Is + 2Y Ie + 2Y Iki + 2Y Iko 170 (B.7) For the piezoelectric materials, the bending stiffness is simply cE 11 Ip = 2Y Ip (B.8) The mass density of the first composite section is simply (B.9) ρAc1 = ρs bhs + 2ρe bhe + 4ρk bhk + 2ρp bhp For the second composite section from L1 < x < L, the individual bending stiffness of each material section is Battery Layer Y Ib = Yb Outer Epoxy Layer Y Ieo = Ye Outer Kapton Layer Y Iko = Yk Piezoelectric Layer Y I p = Yp Inner Kapton Layer Y Iki = Yk Inner Epoxy Layer Y Iei = Ye Substrate Layer Y Is = Ys bh3b + bhb 12 hs hb + 2he + 2hk + hp + 2 2 ! 3he 2 hs bh3e + bhe + 2hk + hp + 12 2 2 ! bh3k hs 3hk 2 + bhk + he + hp + 12 2 2 ! bh3p hp 2 hs + bhp + he + hk + 12 2 2 ! bh3k hs hk 2 + bhk + he + 12 2 2 ! bh3e hs he 2 + bhe + 12 2 2 bh3s 12 2 ! (B.10) (B.11) (B.12) (B.13) (B.14) (B.15) (B.16) where Yb is the elastic modulus of the battery layer. The total bending stiffness of the structure materials is then Y Ic2 = Y Is + 2Y Iei + 2Y Iki + 2Y Iko + 2Y Ieo + 2Y Ib (B.17) The bending stiffness of the piezoelectric layers is once again cE 11 Ip = 2Y Ip (B.18) The mass density of the second composite section is ρAc2 = ρs bhs + 4ρe bhe + 4ρk bhk + 2ρp bhp + 2ρb bhb 171 (B.19) B.3 Self-Charging Wing Spar Sections Consider the self-charging structure wing spar configuration shown in Fig. 6.1(c) and repeated again in Fig. B.3. The neutral axis lies in the geometric center of the substrate layer in both sections. L1 L L2 hp hk hs1 he hp Piezoceramic Layer h Thin-Film Battery Layer b Substrate Layer Kapton Layer L2 L L3 hb hki hs 2 Epoxy Layer Electrodes h Poling Direction hb b Figure B.3: Cross-sectional views of the two composite sections of the self-charging wing spar. The bending stiffness and mass density of the uniform structure sections from 0 < x < L1 and L3 < x < L are simply Y Is = Ys bh3 12 (B.20) (B.21) ρAs = ρs bh The bending stiffness of the materials in the first composite section from 0 < x < L1 , are given using Eq. (B.1) as Outer Kapton Layer Y Iko = Yk Piezoelectric Layer Y Ip = Yp Inner Kapton Layer Y Iki = Yk Epoxy Layer Substrate Layer Y Ie = Ye Y Is1 = Ys ! hs1 3hk 2 + he + hp + 2 2 ! bh3p hp 2 hs1 + bhp + he + hk + 12 2 2 ! bh3k hs1 hk 2 + bhk + he + 12 2 2 ! bh3e hs1 he 2 + bhe + 12 2 2 bh3k + bhk 12 bh3s1 12 172 (B.22) (B.23) (B.24) (B.25) (B.26) The total bending stiffness is the sum of the bending stiffness of each material section. For the structure materials in the first composite section, this gives (B.27) Y Ic1 = Y Is1 + 2Y Ie + 2Y Iki + 2Y Iko The bending stiffness of the piezoelectric layers is simply cE 11 Ip = 2Y Ip (B.28) The mass density of the first composite section is (B.29) ρAc1 = ρs bhs1 + 2ρe bhe + 4ρk bhk + 2ρp bhp For the second composite section from L1 < x < L, the individual bending stiffness of each material section is bh3b + bhb 12 Battery Layer Y Ib = Yb Epoxy Layer Y Ie = Ye Substrate Layer Y Is = Ys hs2 hb + he + 2 2 ! bh3e hs2 he 2 + bhe + 12 2 2 bh3s2 12 2 ! (B.30) (B.31) (B.32) The total bending stiffness is then Y Ic2 = Y Is2 + 2Y Ie + 2Y Ib (B.33) The mass density of the second composite section is ρAc2 = ρs bhs2 + 2ρe bhe + 2ρb bhb 173 (B.34) A PPENDIX C T RANSFORMATION FROM R ELATIVE TO A BSOLUTE F RAME OF R EFERENCE FOR F REQUENCY R ESPONSE F UNCTIONS The relative displacement frequency response function given in Eq. (2.88) is valid for the displacement of the beam relative to the moving base. It is common practice in laboratory experiments to measure the absolute displacement or velocity of the beam (where the measurement system is stationary while the beam vibrates). Recalling Eq. (2.2), the absolute displacement of the beam is the sum of the base displacement and the relative displacement given by wabs (x, t) = wb (t) + wrel (x, t) (C.1) which leads to wabs (x, t) = wb ejωt + ΦT (x) −ω 2 [M] + jω [C] + [K] !−1 1 −1 eq eq T eq +jω jωCp + Θ Θ Fejωt Rl (C.2) Considering this relationship, the relative displacement FRF given in Eq. (2.88) can be modified to give the following expression for the absolute displacement FRF wabs (x, t) 1 = − 2 + ΦT (x) −ω 2 [M] + jω [C] + [K] ab ejωt ω !−1 1 −1 eq eq T eq + jω jωCp + Θ Θ F̃ Rl (C.3) The absolute velocity can be found by simply taking the temporal derivative of the 174 absolute displacement as follows Vabs (x, t) = d (wb (t) + wrel (t)) dt (C.4) which gives Vabs (x, t) = jωwb ejωt + jωΦT (x) −ω 2 [M] + jω [C] + [K] !−1 −1 1 Θeq Θeq T +jω jωCpeq + Fejωt Rl (C.5) The absolute velocity FRF can then be written as Vabs (L, t) 1 = + jωΦT (L) −ω 2 [M] + jω [C] + [K] jωt ab e jω !−1 −1 1 + jω jωCpeq + Θeq Θeq T F̃ Rl 175 (C.6) A PPENDIX D C HARGE /D ISCHARGE C URVES FOR D YNAMIC FAILURE T ESTING The following figures provide the charge/discharge curves measured for both power supply and piezoelectric charging of the battery layers in dynamic failure testing. Voltage Current (mA) 2 2 Voltage (V) Current (mA) 3 Current 4.1 3.9 Voltage 6 4 3 4.1 2 3 Current 2 1 1 1 0 0 0 (c) 500 1000 Time (sec) 1500 2000 0 0 (d) 8 2 2 Current (mA) 4 Voltage (V) 3 1000 Time (sec) 1500 0 2000 4.1 3.9 Voltage 6 Current 500 3 4.1 Voltage Current (mA) Voltage (V) (b) 8 2 3 Current 2 1 1 Voltage (V) (a) 1 0 0 0 500 1000 1500 Time (sec) 2000 0 0 500 1000 Time (sec) 1500 0 2000 Figure D.1: Power supply charge and discharge curves for excitation at (a-b) ±0.2 g and (c-d) ±0.4 g. 176 Voltage 2 2 Current (mA) 4 Voltage (V) 3 Current 4.1 3.9 Voltage 6 2 3 Current 2 1 1 1 0 0 0 (c) 500 1000 Time (sec) 1500 0 0 (d) 8 2 2 Current (mA) 4 Voltage (V) Current (mA) 3 1500 2 3 Current 2 1 1 1 0 0 0 (e) 500 1000 Time (sec) 1500 0 0 (f) 8 Voltage 2 2 Current (mA) 4 1000 Time (sec) 1500 0 2000 4.1 3.9 Voltage Voltage (V) 3 Current 500 3 4.1 6 Current (mA) 0 2000 4.1 3.9 Voltage 6 Current 1000 Time (sec) 3 4.1 Voltage 500 Voltage (V) Current (mA) 3 4.1 Voltage (V) (b) 8 2 3 Current 2 1 1 Voltage (V) (a) 1 0 0 0 500 1000 Time (sec) 1500 0 0 500 1000 Time (sec) 1500 0 2000 Figure D.2: Power supply charge and discharge curves for excitation at (a-b) ±0.6 g, (c-d) ±0.8 g, and (e-f) ±1.0 g. 177 Voltage Current (mA) 2 2 Voltage (V) 2 3 Current 2 1 1 1 0 0 0 (c) 500 1000 Time (sec) 1500 0 0 (d) 8 2 2 Current (mA) 4 Voltage (V) Current (mA) 3 1500 2 3 Current 2 1 1 1 0 0 0 (e) 500 1000 Time (sec) 1500 0 0 (f) 8 Voltage 2 2 Current (mA) 4 1000 Time (sec) 1500 0 2000 4.1 3.9 Voltage Voltage (V) 3 Current 500 3 4.1 6 Current (mA) 0 2000 4.1 3.9 Voltage 6 Current 1000 Time (sec) 3 4.1 Voltage 500 Voltage (V) Current (mA) 3 Current 4.1 3.9 Voltage 6 4 3 4.1 Voltage (V) (b) 8 2 3 Current 2 1 1 Voltage (V) (a) 1 0 0 0 500 1000 Time (sec) 1500 0 2000 0 500 1000 Time (sec) 1500 0 2000 Figure D.3: Power supply charge and discharge curves for excitation at (a-b) ±1.5 g, (c-d) ±2.0 g, and (e-f) ±2.5 g. 178 Voltage Current (mA) 2 2 Voltage (V) 2 3 Current 2 1 1 1 0 0 0 (c) 500 1000 Time (sec) 1500 0 0 (d) 8 2 2 Current (mA) 4 Voltage (V) Current (mA) 3 1500 2 3 Current 2 1 1 1 0 0 0 (e) 500 1000 Time (sec) 1500 0 0 (f) 8 Voltage 2 2 Current (mA) 4 1000 Time (sec) 1500 0 2000 4.1 3.9 Voltage Voltage (V) 3 Current 500 3 4.1 6 Current (mA) 0 2000 4.1 3.9 Voltage 6 Current 1000 Time (sec) 3 4.1 Voltage 500 Voltage (V) Current (mA) 3 Current 4.1 3.9 Voltage 6 4 3 4.1 Voltage (V) (b) 8 2 3 Current 2 1 1 Voltage (V) (a) 1 0 0 0 500 1000 Time (sec) 1500 0 0 500 1000 Time (sec) 1500 0 2000 Figure D.4: Power supply charge and discharge curves for excitation at (a-b) ±3.0 g, (c-d) ±3.5 g, and (e-f) ±4.0 g. 179 Voltage Current (mA) 2 2 Voltage (V) 2 3 Current 2 1 1 1 0 0 0 (c) 500 1000 Time (sec) 0 1500 0 (d) 8 2 2 Current (mA) 4 Voltage (V) Current (mA) 3 1500 2 3 Current 2 1 1 1 0 0 0 (e) 500 1000 Time (sec) 0 1500 0 (f) 8 Voltage 2 2 Current (mA) 4 1000 Time (sec) 1500 0 2000 4.1 3.9 Voltage Voltage (V) 3 Current 500 3 4.1 6 Current (mA) 0 2000 4.1 3.9 Voltage 6 Current 1000 Time (sec) 3 4.1 Voltage 500 Voltage (V) Current (mA) 3 Current 4.1 3.9 Voltage 6 4 3 4.1 Voltage (V) (b) 8 2 3 Current 2 1 1 Voltage (V) (a) 1 0 0 0 500 1000 Time (sec) 1500 2000 0 0 500 1000 Time (sec) 1500 0 2000 Figure D.5: Power supply charge and discharge curves for excitation at (a-b) ±4.5 g, (c-d) ±5.0 g, and (e-f) ±5.5 g. 180 Voltage Current (mA) 2 2 Voltage (V) 2 3 Current 2 1 1 1 0 0 0 (c) 500 1000 Time (sec) 1500 0 2000 0 (d) 8 2 2 Current (mA) 4 Voltage (V) Current (mA) 3 1500 2 3 Current 2 1 1 1 0 0 0 1000 Time (sec) 1500 0 0 (f) 8 4 2 2 1000 Time (sec) 1500 0 2000 4.1 3.9 Voltage Current (mA) 3 Current 500 3 4.1 Voltage 6 Current (mA) 500 Voltage (V) (e) 0 2000 4.1 3.9 Voltage 6 Current 1000 Time (sec) 3 4.1 Voltage 500 Voltage (V) Current (mA) 3 Current 4.1 3.9 Voltage 6 4 3 4.1 Voltage (V) (b) 8 2 3 Current 2 1 1 Voltage (V) (a) 1 0 0 0 500 1000 Time (sec) 1500 0 0 500 1000 Time (sec) 1500 0 2000 Figure D.6: Power supply charge and discharge curves for excitation at (a-b) ±6.0 g, (c-d) ±6.5 g, and (e-f) ±7.0 g. 181 3 4.1 3.9 4.1 Voltage 3 0.1 2 0.05 (c) 1000 2000 Time (sec) 3000 2 1 1 0 0 0 3 Current 1 Current 2 0 0 (d) 0.25 50 100 Time (sec) 150 3 4.1 3.9 4.1 Voltage 0.15 3 0.1 2 Current 0.05 Current (mA) Voltage Voltage (V) Current (mA) 0.2 (e) 1000 2000 Time (sec) 3000 3 2 1 1 0 0 0 2 Current 1 0 0 (f) 0.25 50 100 Time (sec) 150 200 4.1 3.9 3 0.1 2 Current 0.05 2000 Time (sec) 3000 3 2 1 1 0 0 1000 2 Current 1 0 Current (mA) Voltage Voltage (V) Current (mA) Voltage 0.15 0 3 4.1 0.2 0 Voltage (V) 0.15 Current (mA) Voltage Voltage (V) Current (mA) 0.2 Voltage (V) (b) 0.25 Voltage (V) (a) 0 0 50 100 Time (sec) 150 0 Figure D.7: Piezoelectric charge and discharge curves for excitation at (a-b) ±0.2 g, (c-d) ±0.4 g, and (e-f) ±0.6 g. 182 3 4.1 3.9 4.1 Voltage Current 0.1 2 0.05 (c) 2000 Time (sec) 3000 2 1 1 0 0 1000 3 Current 1 0 2 0 0 (d) 0.25 50 100 150 Time (sec) 200 3 4.1 3.9 4.1 Voltage 3 0.15 Current 0.1 2 0.05 Current (mA) Voltage Voltage (V) Current (mA) 0.2 (e) 2000 Time (sec) 3000 3 Current 2 1 0 0 1000 2 1 1 0 0 0 (f) 0.25 50 100 150 Time (sec) 200 250 4.1 3.9 3 Current 0.1 2 0.05 2000 Time (sec) 3000 3 Current 2 1 0 0 1000 2 1 1 0 Current (mA) Voltage Voltage (V) Current (mA) Voltage 0.15 0 3 4.1 0.2 0 Voltage (V) 3 0.15 Current (mA) Voltage Voltage (V) Current (mA) 0.2 Voltage (V) (b) 0.25 Voltage (V) (a) 0 0 50 100 150 Time (sec) 200 250 0 Figure D.8: Piezoelectric charge and discharge curves for excitation at (a-b) ±0.8 g, (c-d) ±1.0 g, and (e-f) ±1.5 g. 183 3 4.1 3.9 4.1 Voltage Current 0.1 2 0.05 (c) 2000 Time (sec) 3000 2 1 0 0 1000 3 Current 1 1 0 2 0 0 (d) 0.25 50 100 150 200 Time (sec) 250 300 3 4.1 3.9 4.1 Voltage 0.15 3 Current 0.1 2 0.05 Current (mA) Voltage Voltage (V) Current (mA) 0.2 (e) 2000 Time (sec) 3000 3 Current 2 1 0 0 1000 2 1 1 0 0 0 (f) 0.25 50 100 150 200 Time (sec) 0 250 3 4.1 3.9 0.15 Current Voltage 3 0.1 2 0.05 2000 Time (sec) 3000 3 Current 2 1 0 0 1000 2 1 1 0 Current (mA) Voltage Voltage (V) Current (mA) 4.1 0.2 0 Voltage (V) 3 0.15 Current (mA) Voltage Voltage (V) Current (mA) 0.2 Voltage (V) (b) 0.25 Voltage (V) (a) 0 0 50 100 150 200 Time (sec) 250 300 0 Figure D.9: Piezoelectric charge and discharge curves for excitation at (a-b) ±2.0 g, (c-d) ±2.5 g, and (e-f) ±3.0 g. 184 3 4.1 3.9 3 0.2 Current 2 0.1 0 (c) 1000 2000 Time (sec) 3000 3 Current 2 1 1 1 0 2 0 0 0 (d) 0.4 100 200 Time (sec) 300 3 4.1 3.9 Voltage 3 0.2 Current 2 0.1 0 1000 2000 Time (sec) 3000 2 3 Current 2 1 1 1 0 (e) Current (mA) Voltage Voltage (V) Current (mA) 4.1 0.3 0 0 0 (f) 0.4 100 200 Time (sec) 300 4.1 3.9 0.2 2 0.1 0 1000 2000 Time (sec) 3000 2 3 Current 2 1 1 1 0 Current (mA) 3 Voltage (V) Current (mA) Voltage Voltage Current 0 3 4.1 0.3 0 400 Voltage (V) 0.3 Voltage Current (mA) Voltage Voltage (V) Current (mA) 4.1 Voltage (V) (b) 0.4 Voltage (V) (a) 0 0 0 100 200 300 Time (sec) 400 0 500 Figure D.10: Piezoelectric charge and discharge curves for excitation at (a-b) ±3.5 g, (c-d) ±4.0 g, and (e-f) ±4.5 g. 185 3 4.1 3.9 3 0.2 Current 2 0.1 0 (c) 1000 2000 Time (sec) 3000 3 Current 2 1 1 1 0 2 0 0 0 (d) 0.4 100 200 300 Time (sec) 400 500 3 4.1 3.9 Voltage 3 0.2 Current 2 0.1 0 1000 2000 Time (sec) 3000 2 3 Current 2 1 1 1 0 (e) Current (mA) Voltage Voltage (V) Current (mA) 4.1 0.3 0 0 0 (f) 0.4 100 200 300 400 Time (sec) 500 4.1 3.9 Current 0.2 2 0.1 0 1000 2000 Time (sec) 3000 2 3 Current 2 1 1 1 0 Current (mA) Voltage Voltage (V) Current (mA) Voltage 3 0 600 3 4.1 0.3 0 Voltage (V) 0.3 Voltage Current (mA) Voltage Voltage (V) Current (mA) 4.1 Voltage (V) (b) 0.4 Voltage (V) (a) 0 0 0 100 200 300 400 Time (sec) 500 600 0 Figure D.11: Piezoelectric charge and discharge curves for excitation at (a-b) ±5.0 g, (c-d) ±5.5 g, and (e-f) ±6.0 g. 186 Current 0.2 2 0.1 Voltage (V) 3 Current (mA) 0.3 1000 2000 Time (sec) 3000 Voltage 3 Current 2 1 0 0 0 (d) 0.4 2 1 1 0 100 200 300 400 Time (sec) 500 3 Current 0.2 2 0.1 0 1000 2000 Time (sec) 3000 2 3 Current 2 1 1 1 0 0 4.1 3.9 Voltage 0.3 600 3 4.1 Current (mA) Current (mA) 4.1 3.9 Voltage 0 (c) 3 4.1 Voltage (V) Voltage Voltage (V) (b) 0.4 Voltage (V) Current (mA) (a) 0 0 0 200 400 Time (sec) 600 0 Figure D.12: Piezoelectric charge and discharge curves for excitation at (a-b) ±6.5 g and (c-d) ±7.0 g. 187 A PPENDIX E L OAD -D EFLECTION C URVES FOR ALL P IEZOELECTRIC S AMPLES T ESTED The following figures provide the load-deflection curves measured for all piezoelectric samples tested. The point at which the sample is considered to be failed is marked by a red circle for each trace. 0.6 PZT-5A 0.5 Load (N) 0.4 0.3 0.2 0.1 0 -0.1 0 0.2 0.4 0.6 0.8 1 1.2 Crosshead Displacement (mm) 1.4 1.6 Figure E.1: Load-deflection curves for PZT-5A samples. 188 (a) 0.6 PZT-5H 0.5 Load (N) 0.4 0.3 0.2 0.1 0 -0.1 0 (b) 0.2 0.4 0.6 0.8 1 Crosshead Displacement (mm) 1.2 1.4 3 PZT-4 2.5 Load (N) 2 1.5 1 0.5 0 0 (c) 0.05 0.1 0.15 Crosshead Displacement (mm) 0.2 10 PZT-8 Load (N) 8 6 4 2 0 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 Crosshead Displacement (mm) 0.16 0.18 Figure E.2: Load-deflection curves for (a) PZT-5H, (b) PZT-4, and (c) PZT-8 samples. 189 (a) 0.35 PMN-PT 0.3 Load (N) 0.25 0.2 0.15 0.1 0.05 0 0 (b) 0.2 0.4 0.6 0.8 1 1.2 1.4 Crosshead Displacement (mm) 1.6 1.8 0.2 PMN-PZT Load (N) 0.15 0.1 0.05 0 0 0.5 1 1.5 Crosshead Displacement (mm) 2 (c) 0.8 QP10n Load (N) 0.6 0.4 0.2 0 0 1 2 3 4 5 6 Crosshead Displacement (mm) 7 8 Figure E.3: Load-deflection curves for (a) PMN-PT, (b) PMN-PZT, and (c) QP10n samples. 190