A VIBRATIONAL ENERGY HARVESTING SYSTEM WITH RESONANT PIEZOELECTRIC DEVICES AND LOW-POWER ELECTRONIC INTERFACE RAN WEI

Transcription

1 A VIBRATIONAL ENERGY HARVESTING SYSTEM WITH RESONANT PIEZOELECTRIC DEVICES AND LOW-POWER ELECTRONIC INTERFACE by RAN WEI Submitted in partial fulfillment of the requirements for the degree of Master of Science Thesis Advisor: Prof. Philip Feng Department of Electrical Engineering and Computer Science CASE WESTERN RESERVE UNIVERSITY May, 2014

2 CASE WESTERN RESERVE UNIVERSITY SCHOOL OF GRADUATE STUDIES We hereby approve the thesis of Ran Wei Candidate for the degree of Master of Science Committee Chair Philip Feng Committee Member Wen H. Ko Committee Member Christian A. Zorman Committee Member Francis Merat Date of Defense March, 20, i-

3 TABLE OF CONTENTS LIST OF FIGURES... v LIST OF TABES... v Chapter INTRODUCTION Motivation an Overview of the Problem Piezoelectric Technology Piezoelectric Materials and Recent works Aluminum Nitride Zinc Oxide Polyvinylidene Fluoride Lead Zirconate Titanate Challenge and Future of Piezoelectric Technology Research Object and Thesis Structure Chapter Piezoelectric Energy Harvesting Theory General Vibration to Electricity Conversion Model Cantilever Structure Frequency Theory Cantilever Structure Surface Stress Theory Piezoelectricity and Piezoelectric Model Piezoelectricity Piezoelectric Model ii-

4 Chapter Cantilever Fabrication and Testing Scheme Device Fabrication Testing Scheme Chapter Characterizing Piezoelectric Cantilevers for Vibration Energy Harvesting Device Energy Conversion Analysis Cantilever Oscillation and Dynamics Resonance Frequency Mechanical Energy Electrical Energy Frequency Response Measurements and Results Conclusions Chapter Energy Harvesting Application Rectifier Circuit Lighting Up LED Pump Energy Harvester Pump Information First Generation Device Four Cantilevers in Series Second Generation Device Small Integrated System Conclusion iii-

5 Chapter Conclusions and Future Work Conclusions Future Work Appendix A: Analysis of Cantilever Resonance Frequency Appendix B: Analysis of Cantilever Surface Stress Appendix C: Printed Circuit Board Fabrication References iv-

6 LIST OF FIGURES Figure 2-1. Schematic diagram of genral vibration converter Figure 2-2. Higher mode 1 st to 6 th of a rectangular shaped cantilever Figure 2-3. Schematice of a two layer composite cantilever structure Figure 2-4. Pictures of a non uniform length cantilever Figure 2-5. Mechanical modeling of the PZT-brass composite cantilevers. (a) part 2 with only brass of the non uniform cantilever. (b) part 1 with PZT and brass of the non uniform cantilever. (c) Illustration for analyzing elastic deflection of a PZT-brass cantilever. The dashed line is the tangent line at the end of PZT layer when the structure is subject to bending, is the deflection angle, d is the deflection at the end of the PZT layer, d is the distance from the initial position at the tip of the brass layer to its expected position based on the elongation of the tangent line, z is the deflection of the brass layer tip beyond the tangent line extrapolation.schematice of a non uniform length cantilever and when it is bend Figure 2-6. Illustration of piezoelectric effects of interest in PZT thin layers. (a) {3-3} mode and {3-1} mode. (b) Simplified equivalent circuit model for the PZT thin-film mechanical-electrical energy converter Figure 3-1. Demenstration of fabrication processing steps. (a) is the actual picture of the PZT disc we use. (b) is the laser cutting machine. (c) is the CAD design of laser cutting area. (d) & (e) are the illustrating of using paper to locate the PZT disc Figure 3-2. Pictures of cut PZT disc Figure 3-3. Experiment setup for mounting proof mass. (a) is the general setup. (b) close up view of the 2 dimensional stage above the heater. (c) clapper that hanging on the 2 dimensional stage s arm with the cantilever facing toward the heater. (d) a photo a cantilever device Figure 3-4. Pictures of fabricated cantilevers with different dimensions and with and without proof mass Figure 3-5. Measurement setup. (a) overview of the three dimensions translational stage. (b) a sharp tip is connected to the Z axis micrometer and is contacted with the free end of the cantilever. (c) a close up view of an initially deflected cantilever. (d) Qualitative illustration of the expected dynamic oscillations of the cantilever tip after a sudden release Figure 4-1. Predicted deflection profiles of cantilever devices #1, #2, #3, respectively, all by finite element modeling using COMSOL. Insets: the deflected device shapes illustrated in COMSOL, color mapped, with red and blue representing maximum and minimum deflection levels Figure 4-2. A system with two cantilevers, each with a proof mass. (a) Two cantilevers assembled together by glue bonding to a common acrylic base (clamping port). (b) Testing setup -v-

7 with the assembled system atop of a circular PZT-brass actuator, which is mounted on top of a circular acrylic ring-shaped sample stage Figure 4-3. Frequency domain measurement of dumbbell structure device. (a) resonance frequency measurement of left cantilever of the device. (b) resonance frequency measurement of right cantilever of the device. (c) resonance frequency measurement of the device when the two cantilevers are connected in series Figure 4-4. Measured data in comparison with theoretical modeling results (from both analytical predictions and equivalent circuit simulations) for cantilever device #1, without proof mass, for open circuit and R load =14.7k. Blue Circles: Experimental data; Red Solid Lines: LTSpice simulations with equivalent circuit; Green Dashed Lines: Analytical modeling based on Eqs. (5) & (6); Black Dashed Lines: Backbone curves in the analytical model Figure 4-5. Measured data from cantilever device #2, without proof mass, at two different loading conditions: open circuit and R load =14.7k Figure 4-6. Measured data from cantilever device #3, without proof mass, at two different loading conditions: open circuit and R load =22.0k Figure 4-7. Measured data from cantilever device #1-M, with proof mass, at two different loading conditions: open circuit and R load =180k Figure 5-1. Schematic of rectification circuit system, including full wave bridge rectifier, smoothing capacitor and resistor load, and the output waveform with ripple voltage Figure 5-2. Experimental demonstration of converting periodic vibrations of PZT devices into AC and DC voltages. (a) Schematic of the testing circuit with device configuration. (b) Measured output voltage waveforms without the 1µF capacitor. Left & Right Panels: output voltage without and with the rectifier circuit, respectively. (c) Measured AC-DC converted output voltage with both the rectifier circuit and capaciator. The R load =432k and the follower (op-amp) are in the circuits for all measurements in (b) & (c) Figure 5-3. Experimental voltage versus current data for blue LED Figure 5-4. Lab fabricated Printed Circuit Board for energy harvesting device and final device with acrylic packaging box. The dark inlet is the snapshot of the striking video to demonstrate it is harvesting energy Figure 5-5. Pump informations and setup pictures Figure 5-6. Time domain and frequency domain measurement of the pump. (a) is the circuit of 3 axis analog accelerometer chip. (b) is the FFT data from the time domain pump measurement. (c) is time domain pump measurement data Figure 5-7. Device & System pictures. (a) is the PZT cantilever that design to has a 120Hz. (b) is the first design system, the four cantilevers can connected both in series and parallel by the wires solder on the board vi-

8 Figure 5-8. Frequency domain measurements. (a) is frequency domain measurement before tuning frequency. (b) is frequency domain measurement after tuning process Figure 5-9. Small integrated system contains one single cantilever with the electrical circuit Figure The results of the measurement ar Time & Frequency domain measurement of the single cantilever small system. (a) is the frequency domain measurement of these three cantilevers before tuning. (b) is the time domain measurement of these three cantilevers before tuning. (c) is the time domain measurement of these three cantilevers after tuning. (d) is the frequency domain measurement of these three cantilevers after tuning Figure Frequency domain measurement of No.1 and No. 2 cantilever before and after tuning. (a) & (b) are No.1cantilever frequency domain measurement before and after tuning. (c) & (d) are No. 2 cantilever frequency domain measurement before and after tuning Figure Time domain measurements of each cantilever assembled with electrical circuit and series and parallel connection measurements. (a) is the measurement of every single assembled cantilever. (b) is the measurement of both series and parallel connections Figure Small integrated system testing. (a) is picutre when turn on the pump, three cantilvers in parallel can light up the blue LED. (b) is picture when turn on the pump, one cantileverl can light up the LED. (c) is the time domain measurement of 3 cantilevers connect in both series and parallel with blue LED as a load. (d) the measuremnt data of No. 2 cantilever with a blue LED vii-

9 LIST OF TABES Table 2-1 Summary of PZT Material Characters Table 2-2 Dimensions of PZT Cantilevers in This Work Table 4-1 COMSOL Simulation Results Table 4-2 Summary of Specifications and Performance of the Cantilever Devices Table 5-1 Dimensions of New PZT Cantilever Table 5-2 Time Domain & Frequency Domain Measurements Table 5-3 Summary of Peer Work of Energy Harvester viii-

10 Abstract A VIBRATIONAL ENERGY HARVESTING SYSTEM WITH RESONANT PIEZOELECTRIC DEVICES AND LOW-POWER ELECTRONIC INTERFACE by Ran Wei All electronic devices need power sources to perform their functions including computing, communication, and sensing. Traditional high-capacity and long-lifetime batteries have a drawback of being bulky and face challenges for implementation and integration into today s increasingly miniaturized devices such as many portable devices and microelectromechanical systems (MEMS). Directly harvesting energy from environments is a very attractive approach to supplying energy for low-power electronics and sensors. In recent years, many materials and techniques for harvesting ambient energy to power electronic devices have been explored. After a comprehensive survey of existing energy harvesting techniques, we choose to focus on investigating the conversion of mechanical vibrations to electricity by using piezoelectric devices. In this active research area, currently there are a number of important open challenges, including how to achieve highest possible energy conversion efficiency, and how to demonstrate novel practical applications. This thesis work first investigates and validates the fundamentals of resonant-mode piezoelectric energy harvesting to gain understandings of design -ix-

11 principles toward achieving high energy conversion efficiency. We then design devices and circuits to demonstrate using spectra-selective energy harvesting to power up optoelectronic devices for solid-state lighting in ambient air. We first describe measurement and modeling of energy harvesters based on oscillating piezoelectric cantilevers, along with careful calibration of energy conversion properties of such devices in their dynamic response. We employ thin-film lead zirconate titanate (PZT)-based cantilevers fabricated by laser micromachining, with efficient proof masses enabled by a heavy alloy with a low melting temperature (65C) for tuning frequency and damping. By measuring devices with different circuit parameters, and analyzing the energy conversion in time-domain oscillations, we show a model that quantitatively reveals the effects of the loading circuit for energy harvesting. We also show the effects of device dimensions on their vibrations and converted voltage output waveforms. In harvesting vibrational energy through cycles of oscillations (in 80Hz-1 khz devices), we obtained a 25%energy conversion efficiency. After carefully studying the principles of the PZT cantilevers, we demonstrate a miniature system on a circuit board for harvest vibrational energy from a small service pump. The miniature system features resonance-matched designs of the cantilevers, and the integration with a full-wave rectifying circuit and a smoothing capacitor in a less than 1cm2 area. The system is calibrated to have a power generation density of 173.6μW/mm3 is demonstrated to be capable of lighting up a blue LED using the harvested vibrational energy. -x-

12 Acknowledgements Throughout this research, I have had the opportunity to work with a wide range of people. Not only the technical skill had I learned from them, but also valuable lessons from them. I would like to thank them all, but here I wish to acknowledge some that have been particularly helpful and supportive. I would like to express my great gratitude to my advisor, Dr. Philip Feng, for his inspiriting and encouragement. I appreciate his passion, patience and kindness throughout my graduate study. I would like to extend my thanks to Dr. Wen Ko, who acted as a co-advisor on this project. I am thankful for his inspiration, massive amount of technical wisdom and the direction that he has suggested to the project from the beginning. I would like to thank Dr. Christian Zorman and his group member Andrew Barnes and Jeremy Dunning for training me on the special equipments and allow me to use the facilities in their lab. My colleagues Rui Yang, Tina, Jeasung Lee, Zenghui Wang and Dr. Ko s group member help me tremendous in this work and thank them for their long-term support and the friendship we build. Finally, I would like to thank my dearest wife, my parents in China and my parents in United State Charlie and Alice for their love and believe throughout this project. -xi-

13 Chapter 1 1. INTRODUCTION 1.1 Motivation an Overview of the Problem Batteries add size, weight, and inconvenience to today s mobile computers and other electronic devices. To further decrease the volume of mobile computers or electronic devices, scientists are finding possible ways either to reduce the size of a battery or to make them self-powered. Harvesting or scavenging energy from environment and other traditionally unexploited sources to supply low-power electronic devices has been attractive, and have received explosive attention in recent years. It has been identified as one of the promising means to overcome some important technical challenges such as lifetime limits in various power sources. Compared to batteries, energy harvesting may, in principle, provide a potentially infinite energy source for some applications, e.g., medical implants, wearable devices, wireless devices, and wireless sensor networks [1]. Energy harvesting is also attractive because it does not aim to replace batteries, but instead supplement the traditional sources, as harvested energy can be used to recharge batteries. In an energy harvesting system, energy storage is very important because it is a buffer that can bring constant energy flow from source to load even in variable environment. Miniaturization has led to today s low-power electronic devices and energy-efficient circuits and systems that can operate at microwatt levels. This adds to the attraction of harvesting energy, even in small amounts, from various sources under ambient conditions, such as heat dissipations and vibrations in machineries and buildings in everyday civilian -1-

14 life [1-5]. Among these energy sources, mechanical vibrations in a vast range of systems and environments are highly attractive [1-7]. Vibration energy can be measured in the surface of the building. Unlike solar energy, mechanical vibration energy is independent of the weather and locations. Mechanical vibration sources can be categorized as continuous, impulsive, or intermittent. Continuous means that the amplitude of vibration will keep the same with time. Impulsive vibration refers to a sudden vibration with a certain amplitude and then decay sharply. Intermittent vibration is when the amplitude of the vibration varies with time. From reference [1], the author present several interesting mechanical motion energy source like upper limb motion, walking and finger motion. In reference [2], the author compare the potential energy sources, and the vibration energy, especially piezoelectric conversion, has a very promising power density. Since the vibration energy is obtainable in many environments, so if we can scavenge those energies, we can make wearable device and low power electronic devices practical [8]. It is obvious that study energy harvesting is very necessary in future electronics world. It will also help in the medical implantable device [9-13], so patience can avoid surgery to replace the battery. 1.2 Piezoelectric Technology A number of energy conversion mechanisms and techniques, including electromagnetic, electrostatic, and piezoelectric schemes, have been explored and demonstrated for enabling vibration-driven energy harvesters [2, 3, 14]. Electromagnetic dominate the macro scale electrical generator and electrostatic transducer is more -2-

15 practical in micro scale, like Micro Electro-Mechanical Systems (MEMS) [15-17]. In this thesis, we focus on piezoelectric transducer. Piezoelectric energy harvesters [18] have an attractive attribute of directly converting mechanical strain and motional energy into electrical energy; they don t need voltage supply; and piezoelectric materials can have high energy density [2-4, 7, 19]. In reference [7], the author present the most recent process of piezoelectric technology in kinetic energy harvesting. It reports that the first generator is elongated hexagon shaped polyvinylidene fluoride (PVDF) bimorph. This device converts the bending movement of human football to electrical energy. The author also shows the cantilever structured generator and other types of generator. At the end, the author concludes that the piezoelectric technology has the advantages in simple structure, easy to fabricate and integrate in nowadays technology, and high output voltage. In reference [20], the author states that the most commonly used piezoelectric ceramic is lead-zirconate-titanate (PZT) which we will discuss in detail later. For PZT has very high electromechanical coupling ability. The author believes for any harvesting systems to be attractive, they should be able to miniaturize and integrate into embedded system. The mechanical vibration energy is available widely and at all times. Piezoelectric materials are the right candidate for converting mechanical energy to electrical energy. The nanogenerators we will discuss in following section can even express the ability of being flexible and stretchable [12, 21-24]. In many emerging energy harvesting devices, piezoelectric effects in beam, cantilever, membrane, disk, and plate structures are being exploited, with both static and vibrational modes in operation. In this work, we study the cantilever structure since it is -3-

16 easy to fabricate, easy to analysis. Providing us the insight of energy harvester working principle and can help us to optimize the design [25-27]. In Prof. Amit Lal group, they design the cantilever structure for their piezoelectric micro generator. When the cantilever is bending or oscillating, the surface of the cantilever will have stress, and piezoelectric material will convert the stress into charge. This is a very well studied structure, and our device is design based on this structure. 1.3 Piezoelectric Materials and Recent works Aluminum Nitride Quartz is the main material employed for piezoelectric [18]. Crystalline quartz is naturally piezoelectric and generates electrical charge upon applied force. Convention quartz material is silicone dioxide (SiO2), and most quartz need to synthetic to use in practical. Aluminum nitride (AlN) is piezoelectric material with a wurtzite crystal structure [28]. AlN has excellent mechanical and electrical properties [18], low dielectric constants and electromechanical property can be stable at elevated temperature. The most merit of AlN is it can be sputter-deposited on wafer level and also compatible with Si processing [29]. In references [31, 32], Prof. Al Pisano s group from Berkeley has demonstrate a high output power density AlN circular diaphragm energy harvester. In previous paper [32], they fabricated a 4000-μm diameter AlN harvester on top of silicone carbide (SiC) as substrate. Based on the experiment, they present a 20μW/cm 2 power density under 1.09 psi pressures at 2 KHz resonance frequency. The previous paper was conduct at -4-

17 250. Later paper [31] was conduct at 320, and they add an elastic support around the AlN layer to lower the resonance frequency to 1 KHz. The experiment shows an 87μW/cm 2 power density under 1.48-psi pressure at 1 KHz was achieved. In reference [30], Prof. Schaijk s group designs and fabricates a movable mass attached to AlN beam device in vacuum. The device has a dimension of 1.7mm of beam length 3.0mm of beam width 3.0mm of mass length, AlN is 2.0μm. They achieved a 489μW output power under a sinusoidal excitation which has a maximum input acceleration of 4.5 g. They also put this device on an automotive tire, and obtained a 42μW at 70 km/h Zinc Oxide Zinc oxide (ZnO) is similar with AlN. Like AlN, the polar axis of ZnO cannot be oriented by electric field. Therefore, it need special deposition process to make welloriented ZnO [33]. ZnO can be safely used for in vivo applications and they are biodegradable. In references [34, 35], Prof. Zhong Lin Wang and his teammates from Georgia Institute of Technology presents the work of a two ends bonded piezoelectric ZnO nanowire (NW) as energy harvester. In reference [35], the author demonstrates an output of open circuit voltage and short circuit current can be typically about 50mV and 500pA, respectively. The nanowire had a diameter of nm and a length of μm. In the experiments, the author attached nanowire to the diaphragm of a rat. The inhalation and exhalation generated an expansion and contraction of the diaphragm and thus produced stretching and releasing of the nanowire. In reference [34], the author use the -5-

18 same ZnO nanowire driven by bending finger, the experiment shows a 25mV voltage and a 150pA current can generated by single nanowire. Then two nanowires are connected together and attached to a yellow jacket wore by a hamster. The short circuit current is 0.5nA and open circuit voltage reached to mV. Since the output from ZnO nanowire is ac source based on experiment results, by carefully synchronization of four nanowires, a V output voltage was reported by the author Polyvinylidene Fluoride Polyvinylidene fluoride (PVDF) has piezoelectric effect [36] and it has a low Young s modulus of 6.9Gpa compare with other piezoelectric materials. This gives the PVDF the advantage in low frequency devices. Since PVDF is polymer and has a much better flexibility than inorganic piezoelectric materials, it can achieve a much larger deflection and higher energy density. PVDF has piezoelectric coefficients of -20 to 30pC/N (d 33 ) and about 18pC/N (d 31 ) [37]. Also PVDF has good biocompatibility, therefore allows PVDF to be used in biological system. In reference [37], the authors use PVDF to convert the energy from low-speed air flow to electricity and propose that this can be used for harvesting energy from human respiration. In the experiments, the author builds a 20mm2mm belts, the thickness are from 10 to 26μm. During their lung simulation experiment, they control the flow speed to 2.3ms -1, they found the thinner PVDF belt (17μm thick) can produce more energy. A 12 minutes simulation was conducted and 20μJ of electrical energy was stored. In reference [38], the author claim a 0.25cm 3 PVDF device can generates 16nW energy when tested around a mock artery. The active piezoelectric material has a -6-

19 28mm8mm28μm dimension. This device is curling around the mock artery and when the artery is pumping blood, it will stretch the device and generate electrical power. In reference [39], the author use PVDF as active material in cantilever structure. A 28μm thick PVDF were fabricated, the cantilever has 25mm length, 16mm width and 205μm thickness. A tiny 0.9g NdFeB magnet with a volume of 125mm 3 was attached at the far end of cantilever. The author gets a 16μW output power under 0.92G acceleration and 14Hz vibration. PVDF nanofiber [40, 41] become popular in recent, and more and more scientists devote in this area. Untreated PVDF can have α, β and γ crystalline phases. Only β phase can generate piezoelectricity [42]. Prof. Liwei Lin s group use direct-write by means of near-field electrospinning (NFES) to produce PVDF nanofibers. The diameters of those nanofibers range from 500nm to 6.5μm. The length varies from 100 to 600μm. 5-30mV and 0.5-3nA was generated from those PVDF nanofibers under repeated stretch and release at 2Hz. Later in reference [43], using the same method and same dimension of PVDF nanofiber, the author reports a 18.45pW/cm 2 under repeat stretching and releasing with a strain of 0.05% at 5Hz vibration. Except direct writing method, reference [44] presents randomly oriented electrospun without using poling treatment. In the paper, the author fabricated PVDF nanofibers with a diameter of nm. The energy harvester was a membrane with PVDF thickness of 140μm, the surface area was 2cm 2. They obtained a 0.43V output voltage under 1Hz compressive impact. The interesting observation is when they increase the frequency, they get higher output voltage. -7-

20 1.3.4 Lead Zirconate Titanate Lead zirconate titanate (PZT) is one of the most widely use piezoelectric materials [7, 45-47]. The higher electromechanical coefficient of PZT [48, 49] makes it very attractive in energy harvesting domain. In reference [50], the author fabricates 20 cantilevers on a same bridge, each side of the bridge has 10 cantilevers and they have the same dimension of 1.5mm length, 0.5mm width and 0.25mm thickness. When testing this device under a constant force of 8g at 870Hz, they conclude a 301.3μW/cm 3. In this paper, the author also summaries some of the recent energy harvesting work and he claims that the power density of micro energy harvester can reach to 0.4μW/mm 3 under 78.4m/s 2 and at frequency range of 0.08 to 1kHz [19]. There are also some interesting applications on PZT energy harvester. In reference [51], the author designed and fabricated a mm 3 PZT cantilever to have a resonance frequency of 435Hz. This is because at this frequency, rap music will provide the most vibration components to the cantilever. In the experiment, the author demonstrated that playing rap music can actually vibrate the cantilever and therefore generate electrical energy. PZT ceramic materials are very brittle. When using PZT as the active materials in energy harvesting, the deflection need to be considered. A large deflection may cause the damage or even broken to the PZT materials. In reference [21], the authors developed a suspending sintering technique to fabricate flexible, dense, and rigid PZT nanowires. The diameter of the PZT nanowires is -8-

21 about 370nm and they aligned those nanowires in parallel to make a 20cm 2 area textile. Then they fabricated this PZT textile into a nanogenerator with 1.5cm long, 0.8mm wide and 5μm thick. This nanogenerator is periodically bent and released by a linear motor and a 0.12μW can be generated from this device. Prof. McAlpine s group from Princeton University reports a new way to fabricate flexible and stretchable PZT ribbons for energy harvesting [22, 52]. The printing process consists of three parts [52], first 500nm thick PZT was deposited on a ribbon prepatterned MgO source wafers. Second, etch MgO wafer to release PZT ribbons. Third, transfer printing PZT ribbons to a piece of PDMS. Using this method, they fabricated 500nm thick, 5μm wide PZT ribbons. After the samples were poled at 100kV/cm, they measured a d 31 =79pm/V, which is higher than other materials [7]. This work also opens the gate to implementation of wearable, implantable energy harvesting micro devices. Later, using the same fabrication method, they transferred these PZT ribbons on a prestrained PDMS [22]. The wavy shaped PZT ribbons make the device stretchable, the wavelength and amplitude of those PZT ribbons will determine how much strain can put in the device. 1.4 Challenge and Future of Piezoelectric Technology While tremendous efforts and progresses have been made, many challenges remain. For instances, little work has been done in harvesting energy from random excitations and wide spectra instead of single-frequency vibrations [39]. The primary problem of current energy harvesters is narrow bandwidth, some of the schemes were designed to solve this problem, but most of them have a fundamental drawback of reducing power density significant. Most of the harvesters can only harvest energy in one direction. -9-

22 Cantilever based structure is uniaxial. By making 3 dimensional devices, we can increase the power density. Nowadays, the power density is in the range of 0.8μW/mm 3 [19], which still low for practical use. The other challenges include increasing the electromechanical coupling coefficient, ways to micro fabricate PZT [53, 54] and finding other materials that have strong piezoelectric effect. In many cases, importantly, careful calibration and precise measurement of piezoelectric vibrational energy harvesters are still lacking. In particular, in order to accurately quantify energy-converting attributes and device performance, dynamic responses of such devices and signal transduction details deserve extensive investigations. For wide band energy harvester, researchers in Ref. [55] proposed a single layer piezoelectric element bonded to a bimorph. It was found depending on input power and frequency, the voltage generate by this device can be periodic, quasi-periodic or chaotic. The author also conducted varies frequency, and compare this device with cantilever structure device. The experiment shows a larger and wider power output from this new device. In reference [56], the author designed a main cantilever has a low resonance frequency of 36Hz, the other cantilever is located above this cantilever work as a stopper. When the main cantilever touch the stopper, the effective stiffness of this cantilever will increase and therefore increase the effective resonance to make the device operate in wider bandwidth. Also the top cantilever itself operates in higher resonance frequency. Other ultra wide bandwidth piezoelectric energy harvesting developed in doubly clamped structure [57]. The group of Prof. Inman from University of Michigan developed a linear technology to achieve very low frequency. In his linear technology, he designs a zigzag -10-

23 cantilever structure device [58], he use this design to implement harvesting energy from beating human heart. In reference [59], he indicates that the 39Hz component of heartbeat oscillation has the most amplitude, and by designing 5mm long micro-scale zigzag energy harvester which the piezoelectric material is 3μm thick, he can get a 39nW. However, this is not a real test on heart. Although this zigzag structure can operate in such a low frequency, but the limitation is the output power is very sensitive to heart beat which later in [6], he propose a nonlinear technology [60] to have a broad band energy harvester. The device has a 145mm long, 26mm wide and 0.26mm thick ferromagnetic cantilever with both side covered by piezoelectric material. Two permanent magnets located symmetrically at the near free end. When under harmonic oscillation, this type of device has larger amplitude voltage response at off resonance frequency compared with cantilever without magnet. Except design wide band harvester, new materials with high piezoelectric effect were also received extensive research [61-64]. A novel piezoelectric material, PMN-PT [62, 63], shows a higher piezoelectric constant of ~373pm/V. The strong piezoelectric make this material very attractive, however, a lot of questions about this material are still unanswered [63]. Prof. Espinosa and his group member from Northwestern University report a strong piezoelectricity in three dimensions from GaN nanowire. He designed a hexagonal prism and using the scanning force microscopy to obtain 3D matrix of GaN nanowires [61]. In reference [65], the author first time talks about the scaling rule of nanowires for energy harvester. Within the linear model of a cantilever structured piezoelectric NW, the output voltage scaling with varies radius was calculated for a given NW length at -11-

24 constant force and constant pressure. For energy harvesting, a maximum 4W/cm 3 power density was obtained with smallest integrated NWs (radius=25nm, length=600nm) under constant force. Under constant pressure (0.1Gpa), the power density increased with length and a 3W/cm 3 was recorded for radius 50nm and 10μm length. This work studied extensive experiments with different dimensions of NWs and provides insight in device optimization. 1.5 Research Object and Thesis Structure In this work, we build test systems to perform precise measurements on low frequency oscillating piezoelectric (PZT) cantilevers, and develop a model to explain the energy-converting dynamics quantitatively, shedding light on calibrating and engineering vibration energy harvesters. Later, using the same design with optimization, we achieve a low frequency high power density 173.6μW/mm 3 energy harvester. This device can light up a commercial LED when we mount it onto a working pump. Chapter 1 presents the motivation and an overview of the problem about power electronics devices and implantable devices. Then we proposed an energy harvesting technology to solve this problem. In this thesis, we focus on the conversion of mechanical energy to electrical energy and therefore the piezoelectric material suits this best. Also we review some of the latest works have been done by scientists and propose our idea at the end. Chapter 2 introduces the general vibration model and theoretical modeling of PZT piezoelectric material. The analysis of frequency, surface stress and output charge -12-

25 Chapter 3 investigates the fabrication process. First talk about how to fabricate the PZT cantilever and the equipments we used during this process. Then we present the way to produce the proof mass for low frequency application. The last part is to demonstrate our test setup. Chapter 4 discusses about the experiment of different dimensions of cantilevers. And compare the experiment result to theoretical modeling. The conclusion of this chapter is we can quantitative analyze and predict the waveform of output voltage from PZT cantilever and this shedding light on calibrating and engineering vibration energy harvesters. Chapter 5 presents application of PZT energy harvester. By understanding the voltage current character of a blue LED, we design and fabricate a PZT cantilever harvester together with surface mount rectifier circuit and smoothing capacitor to convert working pump vibration energy to electrical energy to light up this blue LED. A real time frequency tuning process was developed in this work to increase power density of this harvester. Chapter 6 is the summary and future work. -13-

26 Chapter Piezoelectric Energy Harvesting Theory 1.2. General Vibration to Electricity Conversion Model A general model for the conversion of kinetic energy to electrical energy can be represented in this schematic diagram below. This simple model has been proposed by [66]. In this schematic, a seismic mass, m, was attached by a spring k to a box. When the whole system is vibrated, the mass will moves in this box with a different phase, therefore there is a net movement between mass and the box. This net movement will drive transducer which here is represented by d. In this work, the transducer is piezoelectric material (PZT) and will convert the mechanical energy to electrical energy. m k d Figure 2-1. Schematic diagram of genral vibration converter. For analysis, we assume that the movement of the mass inside the box will not affect the movement of the whole generator. If the generator box is vibrated with a -14-

27 displacement of y(t), the net movement of the mass with respect to the housing is z(t). Then the differential equation of motion can be written as: mz( t) dz( t) kz( t) my( t) (2.1) where: m=mass d=damping constant k=spring constant z=spring displacement y=input displacement The term d here includes electrical damping d e and mechanical damping d m [67]. This general model is fairly accurate, but for piezoelectric mechanism, this model needs to be changed. Since this thesis is more focus on experiments, the accurate modeling can be learned from [68-70]. In energy harvesting system, the power of electrical energy is equal to the power converted from mechanical energy by the electrical damping factor d e. From equation 1.1 we can deduce that the electrically induced force is d z() t. zt () is the relative e velocity of the spring, and power is equal to force multiply velocity. So if we integrate d z() t e P 1 2 d z() t (2.2) 2 e -15-

28 Taking the Laplace transform of equation 2.1, we can get the following equation. The detail processing can be learned in [67]. P 2 2 m Y e n n 2 1 n n 3 2 (2.3) where P=magnitude of output power =driving frequency =natural frequency of the mass spring system n =damping ratio; =electrical damping ratio e Y=Laplace transform of input displacement From equation 2.3 we can conclude that when the natural frequency of the system matches the drive frequency, there will be maximum output power. And most of the time, the vibration environment is known beforehand. Therefore design the dimension of the energy harvesting device to match the driving frequency will be the key point to increase output power and power density Cantilever Structure Frequency Theory Generally, the resonance frequency can be calculated by [71]: -16-

29 f r k m, (2.4) where f =resonance frequency r =angular frequency The resonance frequency of a cantilever without a proof mass can be expressed in terms of the flexural rigidity E Y I by [72] f n 2 vn 1 E I Y 2 2 L A, (2.5) where f =nth mode resonance frequency n v = nth mode eigenvalue n L=length of cantilever E =the modulus of elasticity Y I =the area moment of inertia about the neutral axis For a rectangular shaped cantilever, I wt where w is cantilever width and t is the thickness. Substituting this into equation 2.5, we can conclude that the width of the cantilever has no effect on resonance frequency. The thickness is proportional to the resonance frequency and the length is inverse proportional to the resonance frequency. -17-

30 We focus on the first mode scenario which is the lowest resonance frequency. Higher mode is beyond this work s range. However, a picture of rectangular cantilever mode shape is shown below. In this thesis, we are focusing on rectangular shape composite layers of cantilever [73, 74]. The active layer PZT is sit on top of a brass layer shown in Figure below. (a) (b) (c) (d) (e) (f) Figure 2-2. Higher mode 1 st to 6 th of a rectangular shaped cantilever. Figure 2-3. Schematice of a two layer composite cantilever structure. -18-

31 The thickness of PZT is defined as t p and the Young s Modulus of PZT is The brass layer has a thickness of t b and Young s Modulus E Yp. E. The dash line is the Yb neutral plane and the position of this neutral plane can be determined by [75]: 0 t p n n E ( ) dz E ( ) dz 0 Yb Yp t, (2.6) 0 b z t z t r r where r =radius of curvature due to the bending t =neutral plane position n By solving equation 2.6, we can get t n 2 2 E t E t Yp p Yb b. Once we know where 2( E t E t ) Yb b Yp p the neutral plane is, we can calculate the bending modulus per unit width (D), according to: 0 t p 2 2 ( ) ( ) Yb n Yp n t, (2.7) 0 D E z t dz E z t dz b Which yield D E t E t 2 E E t t (2t 2t 3 t t ) Yb b Yp p Yb Yp b p b p p b 12( E t E t ) Yb b Yp p, (2.8) Based on equation 2.5, we can write: f n v 1 E I v 1 E I v 1 D 2 2 ( ) n Y n Y n l A l t t w L t t p p b b p p b b, (2.9) -19-

32 where p =density of PZT =density of brass b We substitute equation 2.8 into equation 2.9 and get: f n v 1 E t E t 2 E E t t (2t 2t 3 t t ) n Yb b Yp p Yb Yp b p b p p b 2 2 L 12( E t E t ) ( t t ) Yb b Yp p p p b b, (2.10) If a proof mass is attached to the free end of the cantilever, it can be treated as a loaded mass at the tip, and the frequency can thus be determined by [71] Yb b Yp p Yb Yp b p b p p b p p b b Yb b Yp p 2 v E t E t E E t t t t t t n f n 2 2 L t t m Lw E t E t, (2.11) where m is the proof mass, v v n n 1.4. Cantilever Structure Surface Stress Theory The single layer cantilever structure surface stress is analyzed in appendix B. In this work, we are very interested in the non uniform length cantilever structure shown below: PZT Part 1 PZT and Brass Brass (a) Part 2 Only brass (b) Figure 2-4. Pictures of a non uniform length cantilever. -20-

33 It is clearly that the PZT layer is not cover the whole brass substrate. In reference [76], the author concludes that when the length of the PZT covers 2/3 of the length of the substrate, the output power is maximum. To analyze the surface stress of this structure [77, 78], we can separate the cantilever like Figure 2-4. Part 1 is uniform two layer cantilever structure and part 2 is single layer cantilever structure. The force is act at the only brass end to bend this cantilever. (a) (b) d tan L L b p Clamping Port d d Piezoelectric Layer (PZT) (c) Conductive Layer (Brass) z Figure 2-5. Mechanical modeling of the PZT-brass composite cantilevers. (a) part 2 with only brass of the non uniform cantilever. (b) part 1 with PZT and brass of the non uniform cantilever. (c) Illustration for analyzing elastic deflection of a PZT-brass cantilever. The dashed line is the tangent line at the end of PZT layer when the structure is subject to bending, is the deflection angle, d is the deflection at the end of the PZT layer, d is the distance from the initial position at the tip of the brass layer to its expected position based on the elongation of the tangent line, z is the deflection of the brass layer tip beyond the tangent line extrapolation.schematice of a non uniform length cantilever and when it is bend. From Fig.2-5 (a), the deflection caused by the force is -21-

34 F 3E I Yb ( L L ) b b 3 p z, (2.12) where E =Young s modulus of brass Yb E Yp =Young s modulus of PZT I = moment of inertia of cross section of brass which is b I p wt 12 3 p I p =moment of inertia of cross section of PZT which is I p wt 12 3 p L =length of brass b L p =length of PZT z =deflection at part 1 w =width of the cantilever t =thickness of brass layer b t p =thickness of PZT layer In part 1, the force exert on the free boundary is same with the force in part 2. This is because when the cantilever is bent and reach to its balance, there will be a same amount of the force at the boundary between part 1 and part 2. With the knowledge from appendix B, we can get the stress on PZT surface pzt is: -22-

35 pzt ( x) M ( x) y E Yp E I E I Yp p Yb b, (2.13) where y is the distance from the neutral plane to the top layer surface, based on Eq. 2.6 we can solve E t 2 E t E t y 2 ( E E ) Yp p Yb p Yb b Yp Yb. M( x) is bending moment and it is a function of x: M( x) F ( L x), x is the distance from fixed point to the interest point. p Solving equation 2.13 and integrate the surface stress, we yield pzt F L w E ( E t 2 E t E t ) 2 p Yp Yp p Yb p Yb b 4 ( E I E I ) ( E E ) Yp p Yb b Yp Yb, (2.14) It is also important to know how much deflection at the free end of this cantilever when under certain force. Together with Eq. (2.14) we can deduce the relation between tip deflections and surface stress. This is very useful in later when we introduce piezoelectric materials. The piezoelectric materials will convert those stresses into electrical charge. We can know how much voltage is generated when cantilever is bent with certain distance. When the initial tip deflection is small, in Fig. 2-5 (c) the deflection angle is very small and we have: d z, (2.15) d d L L tan, (2.16) According to Taylor series, when 180<< /2, b p -23-

36 tan The angle θ can be solved by [79], (2.17) d d M, (2.18) ds dx E I Y By solving Eq. (2.18), we have 2 E I FL 2 p E I Yp p Yb b 180, (2.19) 3 E I E I Yp p Yb b 1 3 p F k d d, (2.20) L 3E Yb I b 2 3 F k z z L L b p, (2.21) where k 1 is the stiffness of composite part of the cantilever and k 2 is stiffness of brass only part of the cantilever. Then combine Eqs. ( ) and Eqs. ( ), we can get the relationship between the surface stress and tip deflection Piezoelectricity and Piezoelectric Model Piezoelectricity Piezoelectricity is a coupling between a material s mechanical and electrical behavior. When a thin layer of piezoelectric material (e.g., PZT in this work) undergoes a mechanical stress, polarization and net surface charges are induced and an open circuit voltage can be generated across the material (Fig. 1a). Conversely, a voltage applied -24-

37 upon the piezoelectric layer can induce mechanical deformation. Specifically, as shown in Fig. 2-6 (a), in the {3-3} mode, the electric field and voltage are in the plane of applied stress, while in the {3-1} mode, a transverse electric field or potential can cause in-plane deformation and strain. In a simplified description of such behavior via the constitutive equations, we have the following relations [7]. (a) 3 2 F {3-3} Mode (b) 1 Piezoelectric Material V R s 3 2 F {3-1} Mode I p C p R load F 1 Piezoelectric Material F V Figure 2-6. Illustration of piezoelectric effects of interest in PZT thin layers. (a) {3-3} mode and {3-1} mode. (b) Simplified equivalent circuit model for the PZT thin-film mechanical-electrical energy converter. D d, (2.22) i ij j j j ee, (2.23) ij i i where σ j is the mechanical stress, D i is the electric displacement (charge density), E i is the electric field, d ij and e ij are the piezoelectric coefficients. The indices i=1,2,3 define the normal electric field or displacement orientations; j=1,2,3 denote the normal mechanical stresses or strains and j=4,5,6 are for shear strains or stresses. These simplified equations -25-

38 describe the dependence of electric displacement upon stress (ignoring excess electric displacement due to pure electric field effect), and the dependence of stress upon electric field (ignoring excess stress due to pure mechanical strain). We also note that another important figure of merit in piezoelectric materials is the electromechanical coupling coefficient k ij, k E d, (2.24) 2 Y 2 ij ij where E Y is the elastic (Young s) modulus, ε is the permittivity. The coefficient k ij represents the ratio (percentage) of total mechanical (electrical) energy converted into output electrical (mechanical) energy by the piezoelectric material. For instance, k ij for the {3-1} mode is 0.35, lower than that for the {3-3} mode, The cantilever structure developed the {3-1} mode of piezoelectric coefficient. When the piezoelectric material is stressed, the net charge will generated [78]. Q dt V C C 31 pzt, (2.25) The capacitance of the PZT materials is simply defined as PZT surface area. C A, where A is the t p Table 2-1 Summary of PZT Material Characters d31 (pm/v) d 33 (pm/v) k k (kg/m ) PZT Piezoelectric Model -26-

39 Fig. 2-6 (b) shows the piezoelectric generator model. It can be modeled as a damped oscillator current source I p, with a capacitor C p and a resistor R s. The current source can be modeled as p sin 2 exp I t a f t t, (2.26) 0 mech where a is the initial current amplitude set by the piezoelectric device s initial mechanical stress or deflection, τ mech is the characteristic ring-down time when the amplitude decays to ae -1, and f 0 is the resonance frequency. In Fig. 2-6 (b), C p is the internal capacitance of PZT device, R s is small and may be negligible. The impedance of a PZT device is dominated by the reactance of C p, and depends on frequency. The model is very useful to quantify the character of PZT generator, and with good understanding of PZT physics, you can design specific energy harvester application for different environments. -27-

40 Chapter 3 3. Cantilever Fabrication and Testing Scheme 3.1 Device Fabrication We design and fabricate piezoelectric devices based on singly-clamped cantilevers (Fig. 2-7 (c)). The cantilever structure allows for flexible {3-1} mode operation, such as attaining large deflections and large strains at small input forces, and clear, predictable vibrational modes and their dependency on device dimensions. The {3-1} mode operation of singly-clamped cantilevers directly couples the transverse deflection into inplane strain and thus out-of-plane electric field or voltage drop. Hence, despite the slightly lower kij, the {3-1} mode operation in cantilevers is exploited in this work for energy conversion. From mechanical design and energy conversion viewpoints, it is important to make devices based on composites of piezoelectric-electrode films, and have the piezoelectric film off the neutral plane of the structure. We also note that toward optimized electromechanical designs, the lengths of the piezoelectric and substrate electrode layers can be different. Here we start by having piezoelectric layer just cover 2/3 of the cantilever length (Fig. 2-7 (c)), as suggested in [76]. We make the cantilevers by using commercially available piezoelectric-electrode composites from PUI Audio Company shown in Fig. 3-1 (a), consisting of a 50µm-thick PZT layer on top of a 50µm-thick brass layer. The PZT layer is capped with a very thin silver (Ag) layer as a top electrode (ttop~12µm; this thin layer is not drawn in Fig. 3-1 (c), and its effects on device elastic properties are negligible). We choose to employ PZT materials for their strong {3-1} coupling (e.g., d31~50300pc/n). We first employ laser -28-

41 micromachining [80] (VersaLASER VLS CO2 Laser System) shown in Fig. 3-1 (b) to pattern CAD designs of devices shown in Fig. 2-8 (c). The blue line is the outline of the PZT disc, and the orange color areas are the cutting space. When we cut through the top PZT layer, we first cut the outline of the PZT disc on a piece of paper shown in Fig. 3-1 (d). This is to locate the PZT disc and prepare for next laser cutting step. We put the PZT disc in that area and use the raster parameter to cut the orange areas shown in Fig. 3-1 (e). The last step is to rinse the PZT disc by deionized water (DI water) using an ultra sonic bath from Sonicor. (a) (b) (c) (d) (e) Figure 3-1. Demenstration of fabrication processing steps. (a) is the actual picture of the PZT disc we use. (b) is the laser cutting machine. (c) is the CAD design of laser cutting area. (d) & (e) are the illustrating of using paper to locate the PZT disc. The cut PZT disc is shown in Fig. 3-2 (a) and the next step is to cut the brass part. In the work, the thickness of brass is 50μm, and it is easy to mechanically cut through the -29-

42 brass. We use a sharp knife to cut this and the cantilever is shown in Fig. 3-2 (b). If the thickness of the brass is more than 100μm, we can also use chemical etching method [7]. Once we cut the PZT disc into a cantilever, we can solder thin wire on both side of the cantilever. (a) Figure 3-2. Pictures of cut PZT disc. 5mm (b) The resonance frequency of this type of cantilever will reach to almost 1 khz. For some circumstance, considering potential applications in energy conversion, and particularly for low-frequency vibrations under ambient conditions, we also make miniature and highly efficient proof masses for some of the devices. We use an alloy with both a high density (=10,200kg/m 3 ) and a very low melting point (65C). We machine a circular aluminum mold with a radius of 2.5mm and depth of 3mm, fill it with melted alloy, and keep the alloy melted on a hot plate. The experiment setup is shown in Fig 3-3 (a). We first design a two dimensional moving stage shown in Fig 3-3 (b). And we assemble the cantilever into a clapper shown in Fig 3-3 (c). This clapper is hanging on the arm of the two dimension stage, letting the extrude cantilever facing to the circular aluminum mold. We control the z axis micrometer to insert the cantilever tip into the melted alloy, followed by cooling the alloy down to solidify the assembled structure. The final device is shown in Fig 3-3 (d). -30-

43 Z axis Y axis Arm (b) (d) Cantilever tip (a) (c) Figure 3-3. Experiment setup for mounting proof mass. (a) is the general setup. (b) close up view of the 2 dimensional stage above the heater. (c) clapper that hanging on the 2 dimensional stage s arm with the cantilever facing toward the heater. (d) a photo a cantilever device. In this work, we fabricate three different dimensions of cantilever and those cantilevers initial dimensions are listed in Table I. The actual device pictures in Fig Table 2-2 Dimensions of PZT Cantilevers in This Work Device ID L p0 (mm) L b0 (mm) w (mm) t p (µm) t b (µm) # # #

44 Deflection (mm) Pulse Actuation for Release of Cantilever Clamping Port Figure 3-4. Pictures of fabricated cantilevers with different dimensions and with and without proof mass. 3.2 Testing Scheme We have built the setup shown in Fig. 3-5 for testing the devices and studying their energy conversion characteristics. We employ a precise X-Y-Z translational stage (Thorlabs) to control a sharp, rigid positioner whose tip pushes the free end of the singlyclamped cantilever to set an initial deflection. For instance, we can precisely set the cantilever tip to bend down 0.5mm initially, by controlling the translational stage (Fig. 3-5 (c)). As the positioner tip is abruptly retracted laterally, the cantilever is released and oscillations are generated, as illustrated in Fig. 3-5 (d). Precise X-Y-Z Translational Stage Clamping Port (c) 0.5 Piezoelectric Cantilever Initial Deflection 0.0 (a) (b) Testing Stage (Optical Breadboard) -0.5 Time (d) Figure 3-5. Measurement setup. (a) overview of the three dimensions translational stage. (b) a sharp tip is connected to the Z axis micrometer and is contacted with the free end of the cantilever. (c) a close up view of an initially deflected cantilever. (d) Qualitative illustration of the expected dynamic oscillations of the cantilever tip after a sudden release. The wires soldered on both side of the cantilever were connected to a circuit which contains a high performance follower (LMC 6482). The input impedance of this operational amplifier is up to 10TΩ. So we can avoid loading effect by using this follower between the PZT and the oscilloscope. The output of the follower was -32-

45 connected with Tektronix TDS 1012C oscilloscope to record the waveform of the output voltage when we release the cantilever. -33-

46 Chapter 4 4. Characterizing Piezoelectric Cantilevers for Vibration Energy Harvesting 4.1 Device Energy Conversion Analysis Cantilever Oscillation and Dynamics Abrupt release of the initially deflected cantilever causes its oscillations (Fig. 3-5 (d)), in which each mechanical oscillating cycle will generate time-dependent charge and potential in the piezoelectric cantilever. Understanding the oscillations is the key to quantifying the energy conversion capability of the device. At initial state (t=0s), the cantilever has an initial deflection 0 =-0.5mm. To make precise measurement, we short the top and bottom electrodes of the PZT cantilever at this initial state. Therefore at t=0s there is no net surface charge or potential drop in the device. Upon release, the cantilever first goes from 0 =-0.5mm to 1 =0mm (the mechanical equilibrium position and the original charge neutral state), then it continues to go beyond this point, and oscillate periodically around the equilibrium position. Considering such dynamical processes, we have a superposition of two effects: (i) From 0 =-0.5mm to 1 =0mm, certain amount of charge is generated and accumulated on the surface of PZT. (ii) The accumulated charge decays with exp t load, where τ load =R load C p, while the damped oscillations shown in Fig. 3-5 (d) induce an oscillating voltage component that is superposed onto the decaying curve. We have developed a model, by decomposing the effects, that the waveform of the output voltage from the PZT cantilever can be described by the following: -34-

47 (i) For 0t1/(4f 0 ) (with f 0 being cantilever fundamental-mode flexural resonance frequency, 1/(4f 0 ) is the first quarter of the oscillation period), sin 2 V t b f t, (4.1) 1 0 where b=az p Z load /(Z p +Z load ), Z p is the impedance of PZT and it is dominated by the capacitance. Z load is the load impedance, for which we only consider resistive load R load in this study. (ii) For 1/(4f 0 ) t< (beyond the first quarter period), 1 1 V t b t b f t t 2 load 0 4 f0 4 f0 exp sin 2 exp mech, (4.2) One thing particularly important in this time-domain dynamic response is what we call the backbone curve, onto which the instantaneous oscillating voltage is superposed. The backbone curve describes the long-term evolution and time dependence of the generated voltage waveform; it is the curve when the mechanical oscillations die out (i.e., in the limit of t >>τ mech ). From Eqs. (4.1) & (4.2) above, we see that the backbone curve is the joint curve defined by Eq. (4.1) and the first term in Eq. (4.2). At t=1/(4f 0 ), the two functions are connected continuously and make a smooth backbone curve. As shown by these Eqs., the backbone curve depends on τ load =R load C p, thus it is strongly affected by the load resistance R load shown in Fig. 2-7 (b). In the measured data we will show and analyze in the following sections, we shall demonstrate that the backbone curve and this model quantitatively explain all the measurements Resonance Frequency -35-

48 In our devices as shown in Fig. 2-7 (c), the PZT layer s length is ~2/3 that of the brass layer. Besides modifying the Eqs. in Chapter 2 cantilever structure frequency theory, we use finite element modeling (COMSOL) to carefully estimate the resonance frequencies of our devices. Table 3-1 shows the results from COMSOL simulations. The lengths (L p, L b ) are shorter than values (L p0, L b0 ) in Table 2-2, because there is 2.6mm length clamped inside the mechanical setup (Fig. 3-5 (b)). The reason we chose 2.6mm is that from Fig. 3-4, we can see that the soldering spot usually occupies about 2mm to 2.6mm distance from the end. The clapped parts of the PZT will have no stress when the whole cantilever is bent. The parts that undergo soldering will also damage some of the piezoelectric coefficient of PZT when it suffer high temperature soldering, so it is better to design the soldering part at the very end of the cantilever and together clapped them into the mechanical setup. Lp (mm) L b (mm) Table 4-1 COMSOL Simulation Results w (mm) t p (µm) t b (µm) Δm (g) Resonance Frequency by COMSOL (Hz) Mechanical Energy Mechanical (strain) energy builds up in the initial state when the cantilever is bent with an initial deflection (Fig. 2-7 (c)). The initially stored mechanical energy is given by [25]. Em k, (4-3) -36-

49 Deflection (mm) Deflection (mm) Deflection (mm) where k is cantilever stiffness and is tip deflection. In our design, the non-uniform length makes the case slightly more complicated. We take the No. 1 cantilever in Table 2-2 as example to calculate the mechanical energy that stored in this cantilever. The composite portion of the cantilever (Fig. 2-7 (c)) has a length of L p =4.6mm and at the edge of the PZT layer, the deflection is d=0.169mm based on Fig. 4-1 (a). The brass-only portion has a length of L b L p =2.5mm and a further deflection of z beyond the extrapolated deflection (Fig. 2-7 (c)). Position (mm) (a) (b) Position (mm) (c) Figure 4-1. Predicted deflection profiles of cantilever devices #1, #2, #3, respectively, all by finite element modeling using COMSOL. Insets: the deflected device shapes illustrated in COMSOL, color mapped, with red and blue representing maximum and minimum deflection levels. As we discussed in Chapter 2 Cantilever Structure Surface Stress Theory, the deflection was controlled to be very small, and based on the deduction from Chapter 2, the mechanical energy stored in the cantilever is E k d k z m 1 2, (4.4)

50 With Eq and Eq. 2.21, we can solve z is equal to 0.171mm. The Young s Modulus of brass is 91Gpa and Young s Modulus of PZT is 66GPa. The calculated mechanical energy for No. 1 cantilever is 7.89μJ Electrical Energy A sudden release of the cantilever excites oscillations. The alternating tensile and compress stresses in the PZT layer generate AC charge and voltage (oscillations). With proper interfacing electrical circuits and loads, the mechanical energy can be converted to electrical energy. The total electrical energy can be estimated by E e t 2 Vout dt. (18) 0 R load When the R load is equal to the impedance of PZT generator Z p, the output electrical energy will be at maximum [81]. The impedance of the PZT cantilever (dominated by the capacitor C p in Fig. 2-8 (b)) is frequency dependent. Here we consider the impedance near the cantilever s resonance frequency. The impedance of cantilever #1 without proof mass is ~16k; with proof mass it is ~203k. Cantilever #2 has ~10k impedance and cantilever #3 has ~26k impedance. Based on the knowledge in Chapter 2, the output voltage from the mechanically deflected or stressed PZT cantilever can be calculated by Eq. V d 31 pzt p, (19) p Lw t pzt -38-

51 where d 31 is piezoelectric coefficient, ε pzt is the permittivity of PZT material and pzt is the integral PZT surface stress, pzt M x E y wdx L p Yp, (20) 0 E I E I Yp p Yb b The electrical energy was calculated by Eqs. (4.1) & (4.2). Those equations depicts the waveform of the output voltage when the initially bend cantilever is abruptly released. And later in the following sections, the experiment data proves the analytical model is correct. The electrical energy from the No. 1 cantilever with a 14.7k is 0.38μJ Frequency Response To study the frequency response of PZT cantilever, two of the No.1 cantilever with proof mass was built. The two cantilevers were sitting on a small acrylic cube base shown in Fig 4-2 (a). The dumbbell structure device has the same dimensions of proof masses. The radius of the device is 2.5mm and height is 3.25mm. A PZT disc is used as actuator shown in Fig 4-2 (b). The materials made of the actuator are the same with the PZT cantilever. Proof Mass Proof Mass (a) Joint Clamping Port 3mm (b) Circular Disk Actuator 3mm -39-

52 Figure 4-2. A system with two cantilevers, each with a proof mass. (a) Two cantilevers assembled together by glue bonding to a common acrylic base (clamping port). (b) Testing setup with the assembled system atop of a circular PZT-brass actuator, which is mounted on top of a circular acrylic ring-shaped sample stage. Fig 4-3 shows the measured resonance frequency of each single cantilever and two cantilevers connect in series by HP 3577a network analyzer. For the series connection, the surface of cantilever 1 is connected with the bottom of cantilever 2 and the surface of cantilever 1 and bottom of cantilever 2 will be the positive and negative output connection. The actuator PZT disc is driven by this network analyzer and the frequency is swept from 50Hz to 100Hz. The positive and negative connection of the device is connected to the input of network analyzer. Fig 9 (a) is the result of the left cantilever which in Fig 8 (a) has a blue mark on the acrylic. Fig 9 (b) is the data for right cantilever and (c) is the plot of both cantilevers connected in series. The graphs clearly show that the left cantilever has a resonance of 78.5Hz and the right cantilever has a resonance of Hz. At 77Hz, this device has a highest output voltage. The output voltage from the two cantilevers in series supposes to be the sum of each one s output voltage. But in Fig 4-3 (c), we can clearly see that the output voltage is smaller than the sum of individual output voltage. This suggests that only when the two cantilevers have the exactly same frequency, the output voltage will add up. The output voltage from each cantilever is AC voltage. Any different phase in these two cantilevers will cancel some of the voltage instead of adding them together. -40-

53 Voltage (uv) Voltage (uv) Voltage (uv) mV 200mV 300mV 400mV 500mV 600mV 700mV 800mV 900mV 1000mV 1100mV 1200mV mV 200mV 300mV 400mV 500mV 600mV 700mV 800mV 900mV 1000mV 1100mV 1200mV mV 200mV 300mV 400mV 500mV 600mV 700mV 800mV 900mV 1000mV 1100mV 1200mV Frequency (Hz) Frequency (Hz) (a) (b) (c) Frequency (Hz) Figure 4-3. Frequency domain measurement of dumbbell structure device. (a) resonance frequency measurement of left cantilever of the device. (b) resonance frequency measurement of right cantilever of the device. (c) resonance frequency measurement of the device when the two cantilevers are connected in series. 4.2 Measurements and Results We first carefully measure the conversion from the ring-down oscillations of abruptly released cantilevers to voltage oscillations. Initially deflected devices as shown in the setup in Fig. 3-5 (b) are wired up to various load resistors, then fed to an op-amp follower amplifier (with a Gain1), with data recorded by a high-speed oscilloscope (Tektronix). Figure 4-4 demonstrates measured data, in comparison to analytical predictions and circuit simulations for cantilever #1 without proof mass. For the circuit simulations, we use LTSpice to build the model. We draw the PZT source current like Fig. 2-8 (b) with a 14.7k load resistance. We set the current source with a damped oscillation with Eq. (2-26). For the analytical predictions, we use the Mathmatica to plot the graphs. Experimental data have been taken for two representative cases: (i) Open load no R load connected, and the nominal input resistance of the op-amp is R in 10T, which we take as open ; and (ii) R load =14.7k. -41-

54 Voltage (V) Voltage (V) 6 4 R load : Open Experimental Data LTSpice Simulation Analytical Model Backbone Curve τ load ~ R load =14.7k τ load =0.144ms 3mm Time (ms) Figure 4-4. Measured data in comparison with theoretical modeling results (from both analytical predictions and equivalent circuit simulations) for cantilever device #1, without proof mass, for open circuit and R load =14.7k. Blue Circles: Experimental data; Red Solid Lines: LTSpice simulations with equivalent circuit; Green Dashed Lines: Analytical modeling based on Eqs. (5) & (6); Black Dashed Lines: Backbone curves in the analytical model. The measured data in Fig. 4-4 clearly demonstrate the effects of load resistance R load on measuring the converted voltage, as predicted in Eqs. (4.1) & (4.2), and numerically verified here by the results, especially the backbone curves. With an open load, load~, i.e., the accumulated charge and potential due to initial static deflection decays extremely slowly, thus causing a quasi-dc voltage offset, upon which the vibrationconverted oscillating voltage is superposed. With R load =14.7k, we have load =0.144ms (smaller than the vibrational period, and load << mech ), thus the initial deflection induced charge and potential quickly decays and the measured voltage is dominated by the oscillating voltage directly converted from the mechanical oscillations. Such measurements also clearly help determine the mechanical ring-down time mech and the quality (Q) factor of the device (Q=f 0 mech ). These results are collected and listed in -42-

55 Voltage (V) Voltage (V) Table III. We also note that the discrepancy between data and analytical/simulation results at oscillations beyond tens of cycles is related to the single-tone (f 0 ) assumptions in the modeling τ load ~ R load : Open τ load =0.226ms R load =14.7k Experimental Data Backbone Curve -4 3mm Time (ms) Figure 4-5. Measured data from cantilever device #2, without proof mass, at two different loading conditions: open circuit and R load =14.7k. 4 τ load ~ R load : Open 2 0 τ load =0.451ms R load =22.0k -2 Experimental Data Backbone Curve 3mm Time (ms) Figure 4-6. Measured data from cantilever device #3, without proof mass, at two different loading conditions: open circuit and R load =22.0k. -43-

56 Voltage (V) Figures 4-5 & 4-6 demonstrate measured data from cantilevers #2 & #3, respectively. In each case, again the effects of load resistance are unambiguously verified and clearly shown by the backbone curves, with corresponding load values. In all cases, our analytical model predictions are in quantitative and excellent agreement with the measured data, and clearly reveal the contributions from different effects in the device dynamics, along with their time-dependent evolutions. 6 τ load ~ R load : Open Experimental Data Backbone Curve τ load =3.69ms R load =180k -2 3mm Time (ms) Figure 4-7. Measured data from cantilever device #1-M, with proof mass, at two different loading conditions: open circuit and R load =180k. Figure 4-7 presents experimental results from cantilever #1-M, with a proof mass of m=0.4g. Table 4-1 demonstrates the performance of 4 measured devices. We note that, from the experimental results in the cases with open load (Figs. 4-4~4-7), given the same initial deflection (0.5mm), the measured peak voltage depends more on device length than on width. As shown in Tables 2-2 & 4-1, the shorter cantilevers (#1, #2, #1-M), despite their different width, yield higher peak voltage with similar values, while the longer cantilever (#3) leads to a lower peak voltage value. Based on the calculation from -44-

57 output electrical energy, when L p (length) is fixed, increasing w (width) can help generate more energy. For harvesting energy over all vibration cycles, increasing Q will also help. Device ID Table 4-2 Summary of Specifications and Performance of the Cantilever Devices m (g) a (ma) C p (nf) f (Hz) Z p (kω) R load (kω) load (ms) mech (ms) Q E m (μj) E e (μj) Conversion Efficiency Backbone Peak Voltage, Measured & Calculated (R load: Open) # % 3.5V 3.36V # % 3.8V 4.10V # % 1.9V 2.08V #1-M % 3.1V 3.05V 4.3 Conclusions We have demonstrated vibration energy converters based upon PZT thin-film piezoelectric cantilevers that operate in ring-down oscillation mode, for converting oscillation mechanical energy into electrical energy. We have developed an analytical model to quantitatively reproduce and predict the precisely measured waveform of output oscillating voltage which is converted from vibrations. These measurements and analysis clearly reveal and quantify the effects of the load impedance in the down-stream circuits that are necessary for interfacing with the piezoelectric harvesters to fulfill the conversion and storage of the harvested vibration energy. The study shows energy conversion efficiency can be as high as ~25%. Upon abrupt excitation with a certain initial deflection or displacement, high-frequency and high-q cantilevers may be expected to demonstrate high energy generation abilities. -45-

58 Chapter 5 5. Energy Harvesting Application 5.1 Rectifier Circuit Before we enter into the application of energy harvesting, it is very important to introduce rectifier circuit. When the PZT cantilever is bending, the surface of the PZT will have alternative tensile stress and compress stress. This alternative force will generate positive and negative charges. So the output voltage across a resistive load from the PZT cantilever while it is oscillation is AC voltage. To power any electronics, a DC voltage is required, so we need to develop a circuit to convert AC to DC. The common way to achieve this is to use rectifier circuit [82]. Diode has an advantage of conduct current in one direction and blocks the current in reverse direction. This character made diode a very wide use in rectification. However, the physics of the diode is beyond this work. In this work we developed full wave bridge rectifier shown in Fig 5-1. This configuration flips every cycle of the negative AC into positive AC, by adding a smoothing capacitor following the rectifier circuit, the output waveform will become qusi-dc in Fig 5-1. The ripple voltage in Fig. 5-1 is determined by V ripple I f load, where C I load is the current going through the resistor load in Fig. 5-1, f is the frequency of the ripple and C is the capacitance of the smoothing capacitor. -46-

59 Voltage (V) Voltage (V) Figure 5-1. Schematic of rectification circuit system, including full wave bridge rectifier, smoothing capacitor and resistor load, and the output waveform with ripple voltage. Piezoelectric Layer (PZT) Tektronix TDS 1012C Agilent 33250A Conductive Layer (Brass) Proof Mass Acrylic Cube Substrate V+ Coax + (a) 1µF 432k - V (b) (c) Time (ms) Time (ms) Time (ms) Figure 5-2. Experimental demonstration of converting periodic vibrations of PZT devices into AC and DC voltages. (a) Schematic of the testing circuit with device configuration. (b) Measured output voltage waveforms without the 1µF capacitor. Left & Right Panels: output voltage without and with the rectifier circuit, respectively. (c) Measured AC-DC converted output -47-

60 voltage with both the rectifier circuit and capaciator. The R load =432k and the follower (op-amp) are in the circuits for all measurements in (b) & (c). The experiment setup is shown in Fig We use the dumbbell structure device in this experiment. From Fig. 4-3 (c), the resonance of this dumbbell device is 77Hz. The base actuator is connected to Agilent 33250A function generator. The function generator generates a 77Hz 10V peak to peak sine wave. The positive and negative output of this device was connected with a rectifier circuit build of schottky diodes and a 1μF capacitor as smoothing ripple voltage when the load is pure 432kΩ resistor as shown in Fig 10 (a). The output was connected with a high performance follower (LMC 6482) to avoid loading effect and then connected to Tektronix TDS 1012C oscilloscope. Fig 5-2 (b) is the data extracted from the dumbbell structure device with 432k load before it goes through the rectifier circuit. It has a peak voltage of ±0.86V. The actuator PZT was fed with 10V, 76Hz sine wave. Fig 5-2 (c) is the data after rectifier circuit but before the capacitor with the 432k load, the max voltage is 0.6V. Fig 5-2 (d) is the data after the capacitor with 432k load. From the results, it is clear that the rectifier circuit has a 0.26V voltage drop and also increases the frequency to two times higher. The output voltage from this system is 0.32V with ripple voltage of 40mV. 5.2 Lighting Up LED With a good understanding of PZT energy converting dynamics and the circuits, we can build small self generated system [83]. Light-emitting diode (LED) becomes so popular these days. It is small volume, cheap to buy and some are low power consumption. Lighting up a LED is very attractive and it becomes the main task for this -48-

61 Current (ma) work. We test different colors of LED and from the experiment, blue LED has the lowest power budget as shown in Fig The data was recorded by Keithley semiconductor parameter analyzer Voltage (V) Figure 5-3. Experimental voltage versus current data for blue LED. From the data, the LED can be light up at around 2.5V at dim condition. The power for dim condition is about 200μW, the resistance of this blue LED at dim condition is around 25k. From Fig. 5-3, we can see that as the voltage increase, the resistance of the LED will decrease and therefore, the LED needs more energy. A good energy source should have zero impedance or at least less than the load. From Fig. 2-7 (b) we can see that the impedance of the cantilever is dominated by the capacitance, science R s is small enough to be negligible. And the impedance of a capacitor depends on frequency. So in order to decrease the PZT energy source impedance, we either increase the capacitance of the cantilever or increase the frequency of the cantilever. From Eqs. (2.10) and Eqs. (2.11), the length plays important role in design the cantilever. For example, decrease the length by a factor of 2 can decrease the frequency by a factor of 4 and therefore the -49-

62 overall impedance of the PZT cantilever will get smaller. For our first generation prototype, we use the existing No. 1 cantilever with proof mass in Table 2-2. Then we estimate the power that one PZT cantilever can generate from Fig. 4-7 when the load is 180k. From the plot, this single PZT cantilever can generate maximum power from the first peak of a 0.02mW, so approximately we need 10 PZT cantilevers to light up the LED. Also, notice that the voltage generated in Fig. 4-7 is defined by the cantilever when it is mechanically bend down 0.5mm. We believe when we test this device, the cantilever can bend down more than that and therefore will generate more power than we estimate. So even the LED has a small resistance when it gets lighter and this may cause the loading effect, the overall power transferred from cantilever to LED still large enough to light up the LED. Fig. 5-4 shows the printed circuit board of this energy harvester and the final device. Appendix C will introduce the fabrication of printed circuit board made in our lab. Those cantilevers were sitting along the edge of the circuit board, those cantilevers were connected in parallel, and so if the cantilevers are identical, the output voltage of the 10 cantilevers should equal to the output voltage from any single one cantilever, but the impedance will decrease 10 times, because they are connected in parallel. We use conductive epoxy to adhere the bottom of cantilever to the cantilever location. Then we use wire bonding technique to connect together the surface of cantilevers. We bond the surface of cantilever to the next brass line adjacent. In the middle of the circuit board are the rectifier circuit and the smoothing capacitor, we soldered these component on the backside of the circuit board. Finally we package the whole system with acrylic box to -50-

63 protect the device. And we use black color epoxy from Hysol to protect the wire bonding. This epoxy can also used as clamping. Rectifier circuits Clamping Area for Cantilever Blue LED Cap 10mm Acrylic Stand Figure 5-4. Lab fabricated Printed Circuit Board for energy harvesting device and final device with acrylic packaging box. The dark inlet is the snapshot of the striking video to demonstrate it is harvesting energy. After assemble the device and packaging, we make three test experiments. We bond this device to the door and close the door suddenly; we also drop the device to the palm; and we did striking the device to the hand. The recording videos show that most of the time the device will light up the LED, and the intensity of the light is brighter than what we expect. 5.3 Pump Energy Harvester -51-

64 Finding a constant vibration source is always attractive for energy harvesting. By the inspiration of [84], we want to harvest energy from a working pump. Instead of store energy, we use the same design in the previous section to light up the blue LED Pump Information We find a pump from Becker Pumps Corp. in our lab that can provides a relatively constant frequency output. The pump and the setup were shown in Fig The model of this pump is D Wuppertal, the speed of this pump is 1700 RPM and the motor number of this pump is from Becker Company. -52-

65 Voltage (V) db Figure 5-5. Pump informations and setup pictures. The most important parameter for energy harvesting is frequency. We need to design our PZT cantilever to match the frequency of the pump in order to generate the most energy. We use a 3 axis analog output accelerometer DXL325 to measure the frequency domain data of this pump. The accelerometer and the measured data are shown in Fig Power supply Z axis node Power supply (a) Frequency (Hz) (b) (c) Time (ms) Figure 5-6. Time domain and frequency domain measurement of the pump. (a) is the circuit of 3 axis analog accelerometer chip. (b) is the FFT data from the time domain pump measurement. (c) is time domain pump measurement data. In Fig. 5-6 (a), we only employ the z axis measurement, and according to the data sheet, we assembled a 0.01μF filter capacitor as illustrated in Fig. 5-6 (a) 2. A bigger filter capacitor 1 was assembled between the power supply and ground to filter noise. -53-

66 The output from this device is analog and this time domain measurement was recorded first, then we use FFT math function to generate a frequency domain measurement shown in Fig 5-6 (b) First Generation Device Four Cantilevers in Series When the cantilever s frequency is fixed, the better way to decrease the PZT cantilever impedance is to increase the capacitance. The thinnest PZT we have is 50μm, so we can only adjust the width of the cantilever. Because we need to mount proof mass on the free end to lower the resonance frequency, the width is limited by the width of the proof mass and also limited by the technology of mounting proof mass. In all, we chose a dimension of cantilever shown in Table 5-1 in this specific situation. We chose the resonance frequency to be higher than 120Hz. This is because of the limitation of our frequency tuning process which will introduce later in this section. The technique of tuning frequency is limited to only lower down the frequency. Four identical cantilevers shown in Fig. 5-7 (a) are fabricated. The whole system is shown in Fig. 5-7 (b), we use surface mount schottky diode, capacitor and green LED. We wire out the positive and negative output of the PZT so we can control we want the four cantilevers to be connected in series or parallel. a 5 mm b 4 3 Green LED

67 Figure 5-7. Device & System pictures. (a) is the PZT cantilever that design to has a 120Hz. (b) is the first design system, the four cantilevers can connected both in series and parallel by the wires solder on the board. L p (mm) Table 5-1 Dimensions of New PZT Cantilever L b (mm) w (mm) t p (mm) t b (mm) m (g) As we discuss the importance of the frequency, it is unrealistic that the four cantilevers in Fig. 5-7 (b) will have the exactly same resonance frequency. This is due to the any minor difference between length, width, thickness and weight of proof mass, or the difference in clamping distance. So how to tune those frequency to a same value is critical significant in this work. We develop a way to tune frequency by using transparency fast cure epoxy. We first apply a very thin layer of epoxy on top of the proof mass. However, the epoxy is so light for large value frequency tuning. In some case we need to put more weight to tune the frequency, so we use the same proof mass material to adhere on the thin epoxy layer. During the experiment, we use hp3577a network analyzer to measure the frequency domain data, and we are adding the proof mass while observe the frequency shift from the network analyzer until all the four cantilevers resonance frequency become about 120Hz. In Fig. 5-8, it shows the frequency domain measurement data of this device. -55-

68 Voltage (uv) Voltage (uv) No. 1 No. 2 No. 3 No No. 1 No. 2 No. 3 No (a) Frequency (Hz) (b) Frequency (Hz) Figure 5-8. Frequency domain measurements. (a) is frequency domain measurement before tuning frequency. (b) is frequency domain measurement after tuning process. From the figure above, we can see that this tuning process can be very precise. However, the time domain measurement was not included here is because when we measure the output voltage from each cantilever, the voltage is not becoming higher than we expect and when we connect them in series, the output voltage is actually becoming less than the output from one cantilever. Later in the following section, we will explain the reason based on experimental data Second Generation Device Small Integrated System The failure in first generation device illustrate us that even the resonance frequency of the cantilevers are the same, it is still hard to generate more energy when you connect them in series. The hypothesis is that the four cantilevers are not sitting in the exactly same position of the pump, and the surface of the pump is not ideally flat, there may have initial phase different, so the AC output voltage waveform will cancel each other when -56-

69 we connect them in series. So the idea of making each cantilever a small system which including its own rectifier circuit and smoothing capacitor may tackle this problem. Since adding AC voltage is hard, making the output of each cantilever a DC voltage is promising. Fig. 5-9 show the new design and the cantilever s dimensions are the same with Table GND 37nF Proof mass PZT cantilever 5mm Figure 5-9. Small integrated system contains one single cantilever with the electrical circuit. We first test the frequency domain measurement of the three cantilevers. Using hp 3577A network analyzer, we find resonance frequency of each cantilever shown in Fig (a), and then we measured the time domain output voltage when we put each cantilever onto that working pump. The data was shown in Fig (b). These measurements are only output of the PZT cantilever without any electrical circuit. Then we tune the frequency and this time we tune the frequency in real time. This means that we put the device on the pump and turn the pump on. While the cantilever is vibration, we add the proof mass. When we were adding the proof mass, we connect the output of the PZT cantilever to the oscilloscope, when it reached the highest output voltage, we will stop adding proof mass. Fig (c) is the time domain measurement after the tuning process and Fig (d) is the frequency domain measurement. -57-

70 Voltage (V) Voltage (uv) Voltage (uv) Voltage (V) (a) No. 1 No. 2 No Frequency (Hz) Time (ms) No. 1 No. 2 No. 3 No. 1 No. 2 No. 3 (b) (c) Time (ms) No. 1 No. 2 No Frequency (Hz) (d) Figure The results of the measurement ar Time & Frequency domain measurement of the single cantilever small system. (a) is the frequency domain measurement of these three cantilevers before tuning. (b) is the time domain measurement of these three cantilevers before tuning. (c) is the time domain measurement of these three cantilevers after tuning. (d) is the frequency domain measurement of these three cantilevers after tuning. All the data are listed in Table 5-2. In the Table, the subscript b stands for before tuning, a stands for after tuning. p-p is peak to peak voltage. The No. 3 cantilever in Table 5-2 is set to a control experiment, the frequency of this cantilever after tuning is higher than the other two. In theory, the output voltage should be smaller than the other two and from the data we find it is true. Other observation is that after tuning, No.1 and No.2 cantilever s resonance frequency is not 120Hz as suggested in Fig. 5-6 (b). The explanation is first there is no calibration between the accelerometer and the network analyzer and second we find out when we increase the driving force (amplitude) in -58-

71 Voltage (uv) Voltage (uv) Voltage (uv) Voltage (uv) network analyzer, the resonance frequency shift a little bit to lower frequency as shown in Fig And compare to the driving ability of this network analyzer, the pump has much higher driving amplitude. Table 5-2 Time Domain & Frequency Domain Measurements Device ID f b f a V p-p (b) V p-p (a) V min (a) V max (a) (V) (Hz) (Hz) (V) (V) (V) # # # (a) (c) 200mV 400mV 600mV 800mV 1000mV Frequency (Hz) 400mV 600mV 800mV 1000mV 1200mV Frequency (Hz) (b) (d) 400mV 600mV 800mV 1000mV 1200mV Frequency (Hz) 400mV 600mV 800mV 1000mV 1200mV Frequency (Hz) Figure Frequency domain measurement of No.1 and No. 2 cantilever before and after tuning. (a) & (b) are No.1cantilever frequency domain measurement before and after tuning. (c) & (d) are No. 2 cantilever frequency domain measurement before and after tuning. -59-

72 From Fig (c), we can also see that the phase of each cantilever is not the same, especially for No. 1 and No. 2. The resonance frequency and phase measured from the network analyzer is exactly the same, but this time domain measurement shows nearly 90 degree difference. And since No. 1 and No. 2 cantilever is sitting in a different position as shown in Fig. 5-5, so this result can prove our assumption that because the surface of the pump is not flat, there will be an initial phase different. After these measurements, we assembled the circuit on the board and then take time domain measurement. For the measurement, we did a series connection and parallel connection measurements. From Chapter 2 piezoelectric model, we can see the impedance is dominated by the capacitance. Under this 120Hz, this power source has a roughly of 88kΩ. When connected in series, the output voltage should be the sum of each individual one and when connected in parallel, the output voltage should be equal the average output voltage of the three devices, but the impedance will drop to one third. In Fig (a), it shows the measurement of the three assembled cantilevers with electrical circuit. No.1 has a 7V output voltage, and this is 1.2V smaller than the V max. This is because there are two forward voltage drops in the rectifier circuit when the voltage goes through. No.2 has a 9.2V. The difference here may caused by the different location where the cantilever sitting on the pump, some place may have relative higher amplitude and thus may cause higher output voltage. No.3 has a 6.2V output. In Fig (b), it shows the measurement of both series connection and parallel connection. In series connection, the output voltage is 20V, less than the sum of three cantilevers. This can be explained by when you connected these three cantilevers in series, the impedance -60-

73 Voltage (V) Voltage (V) Voltage (V) Voltage (V) is increasing, and your load remains the same (1MΩ for oscilloscope). Thus your source now will consume more than before. In parallel connection, the output voltage is 7.8V (a) No. 1 No. 2 No Time (ms) (b) Series Parallel Time (ms) Figure Time domain measurements of each cantilever assembled with electrical circuit and series and parallel connection measurements. (a) is the measurement of every single assembled cantilever. (b) is the measurement of both series and parallel connections. Using a piece of bread board, we assembled the three cantilevers with a blue LED in both series and parallel connections. Then we turn on the pump, and the blue LED will light up immediately as shown in Fig (a). We then just using single one cantilever, here we chose the No. 2 cantilever since it has the highest output voltage. It also lights up the blue LED as shown in Fig (c) and with the same intensity. The output data from these two experiments are shown in Fig (b) & (d). (a) (b) (c) Series Parallel Time (ms) (d) Time (ms) -61-

74 Figure Small integrated system testing. (a) is picutre when turn on the pump, three cantilvers in parallel can light up the blue LED. (b) is picture when turn on the pump, one cantileverl can light up the LED. (c) is the time domain measurement of 3 cantilevers connect in both series and parallel with blue LED as a load. (d) the measuremnt data of No. 2 cantilever with a blue LED. From the Fig (c), the data show no obvious different between series and parallel connection, the output voltage is about 2.6V. This is because when we adding more cantilevers, based on the I-V curve of blue LED, the current going through the LED is increasing, but the voltage is increase just a little and may be negligible. when we only apply one cantilever, the output voltage is about the same, based on the Fig. 5-3, the power transformed to the blue LED is around 0.24mW. And from the VI cure of the blue LED, we can also explain why three cantilevers not generate higher voltage. This is because the best cantilever can generate 0.24mW. Three cantilevers then can generate about 0.7mW, and based on the curve, that response to around 2.65V. This means that 2 more cantilevers can only provide less than 0.1V to the LED. We also test other LED, including surface mount type of LED and through hole type of LED. Besides blue color, we also try green and red. Three cantilevers can light up green surface mount LED and the blue LED, but cannot light up the red one. In the future, we can just add more these small systems to provide more power for any other applications. 5.4 Conclusion Table 5-3 Summary of Peer Work of Energy Harvester Reference Active Material Active Area (mm 2 ) Active Volume (mm 3 ) Acceleratio n (g) Frequency (Hz) Power (μw) Power Density -62-

75 Pisano 2012 Schaijk 2011 AlN AlN μw/cm 2 48 mw/mm 3 Wang 2009 ZnO μw/mm 3 Brooks 2008 Maenaka 2010 PVDF PVDF nw/mm μw/mm 3 Lin 2010 PVDF pw/cm 2 Morimoto 2010 Duron 2010 PZT, d PZT μw/mm μw/mm 3 Xu 2011 PZT Lei 2011 PZT μw/mm μw/mm 3 Fang 2006 Aktakka 2011 CWRU 2013 PZT, d PZT, d PZT, d μw/mm μw/mm μw/mm 3 This chapter presents the applications we developed based on PZT cantilever. First, we discuss the electronic circuit that can convert the AC voltage to DC voltage, so we can use our harvested energy to electrical devices. Then we study the VI curve of the -63-

76 blue LED and our goal is to design an energy harvesting system that can light up the LED. At last, with careful analyze of the pump performance and careful design the cantilever based on this pump, we achieved a high power density energy harvesting system that can light up this blue LED when we turn on the pump. Table 5-3 list the power density from recent work and previous work compare to our work. The blue column is our work, and in low frequency and PZT material, we have the highest power density. -64-

77 Chapter 6 6. Conclusions and Future Work 6.1 Conclusions PZT cantilever structure generator works in d 31 mode was optimized and designed based on commercial available PZT disc, targeting at 120Hz and test under 1.78g acceleration mechanical environment. The final design of this generator has an active PZT dimension of 7.1 length, 4mm width and 0.05mm thickness. A 0.45g proof mass of high density, low melting temperature alloy was attached at the cantilever tip. Assembled with full wave rectifier bridge and smoothing capacitor, this harvester can generates 250μW with a load of blue LED. We also developed an analytical model to quantitatively reproduce and predict the precisely measured waveform of output oscillating voltage. This model reveals the effect of load impedance in the downstream circuits that are necessary for interfacing with the piezoelectric harvesters. From this study, we also achieve a high conversion efficient of about 25% from mechanical energy to electrical energy. Details of the fabrication process were introduced through this thesis. A real time frequency tuning process was developed in this work and it shows strong evidence that this step is the key for optimization harvesting design. 6.2 Future Work Energy harvesting used in biomedical is very promising. A pacemaker usually has a life time of 6 to 9 years. That means after 6 to 9 years later, patient need to have a big -65-

78 surgery to replace the battery. Energy harvesting, provide an alternative way to provide power for pacemaker. By putting a cantilever structure harvester on the heart [85], the harvester can converts heart beating mechanical energy to electrical energy. With the proper design, which is match the device frequency to the heart beat frequency at which it will has the highest amplitude, we can make pacemaker self sustaining. The other issue related to the implantable device is the material. PZT has a very strong piezoelectric coefficient, but it contains lead which will not tolerant by human body. PVDF is bio-compatible and has good electrical mechanical coupling, so it is very promising in this work. The way to bond this device to heart also shows big interesting and challenge. We have an idea that make a flexible strip and around the heart and attach the device on the strip. The strip was made of thin PDMS, we use laser to cut pattern on PDMS to make the strip stretchable. -66-

79 Appendix A: Analysis of Cantilever Resonance Frequency Consider the transverse vibrations of a prismatic beam in the x-y plane shown below: y v x x dx l 2 v ( A) dx t 2 M V V V dx x M M dx x When the beam is vibrating transversely, the dynamic equilibrium condition for forces in the y direction is: dx 2 V v V V dx ( A) dx 0 2 x t, (3) And the moment equilibrium condition gives: M Vdx dx 0 x Substitution of V from equation (4) into equation (3) gets:, (4) 2 2 M v dx ( A) dx 2 2 x t, (5) We know that the curvature of bending beam is: -67-

80 k 2 v 2 x M E I, (6) So we can get: This equation can also be written as: v v E I dx ( A) dx x t, (7) v v x a t, (8) where 2 E I a. A When a beam vibrates transversely in one of its natural modes, the deflection at any location varies harmonically with time, as follows: v X ( Acost Bsin t), (9) Substitute equation (9) into equation (8) results in: d X dx, (10) a 4 2 X As an aid to solve this differential equation, we introduce the notation 2 k 2 a 4. So: 4 d X k X dx, (11) We let X e nx and obtain: -68-

81 nx 4 4 e ( n k ) 0, (12) Thus, the values of n are found to be n 1 wherei 1. So: k, n2 k, n3 ik, n4 ik, X C sin kx C cos kx C sinh kx C cosh kx, (13) The constantsc, C, C and C must be determined in each particular case from the boundary conditions at the ends of the beam. For beam with one end fixed, other end free, we have the boundary conditions that at the fixed end, the deflection is 0 and the slope is also 0. At the free end of the cantilever, the bending moment is 0 and the shear force is also 0. dx ( X ) 0 x ( ) 0 0 x 0 dx 2 d X ( ) 0 2 x l dx 3 dx ( ) 0 3 x l dx, (14) Based on the first two conditions, we can conclude that C C So: X C (cos kx cosh kx) C (sin kx sinh kx), (15) 2 4 From the other two conditions we can get: C ( cos kl cosh kl) C ( sin kl sinh kl) C (sin kl sinh kl) C ( cos kl cosh kl) 0 2 4, (16) A solution for the constants C and C can be obtained only when the determinant 2 4 of the coefficients in equation (16) vanishes. In this manner we determine the following frequency equation: -69-

82 2 ( cos kl cosh kl) ( sin kl sinh kl)(sin kl sinh kl) cos kl cosh kl 2cos kl cosh kl sinh kl sin kl cosh kl sinh kl 2cos kl cosh kl cos kl sin kl 0 cos kl cosh kl 1, (17) The consecutive roots of this conclusion are as follows: kl kl kl kl kl kl Approximate values of these roots may be calculated with the formula: 1 k l ( i ) n, (18) 2 Now, we know that 2 4 k 2 and f r a 2, we can get the frequency of the vibration of any mode is: f n a k 2 2 n, (19) which gives us the equation of f n 2 vn l E I A, (20) -70-

83 Appendix B: Analysis of Cantilever Surface Stress When a cantilever is bent, the surface of the cantilever will have a stress. First, let us assume that there is a constant force F that applied at the end of a cantilever shown below: t l w Based on Hook s Law, we can find out the maximum deflection happen at the end of the cantilever: d 3 Fl 3 E I, (1) Which I is moment of inertia: I wt 12 3, (2) So the relation between the force and the deflection at tip of the cantilever is F E wt 3 4l 3 d, (3) The stress is equal to x E, (5) x -71-

84 where E is young s modulus, is strain x x, (6) l where is elongation. From the picture below, we can see that the elongation will be t ( r ) d r d 2 t r d 2 r, (7) where, r is radius of curvature. It is known that the radius curvature is equal to EI M. So we can know that the stress will be x t M t F ( l x) 6 F ( l x) I 2 wt wt 12, (8) -72-

85 Appendix C: Printed Circuit Board Fabrication (a) (b) (c) (e) (f) (d) Thermometer and heater To fabricate the printed circuit board, a mask is important. In the figure (a), we show the PCB layout of the circuit board for energy harvesting system including full -73-

86 wave bridge rectifier circuit, smoothing capacitor, LED and the clapping area of the cantilever shown in big red area. The small areas are for soldering spot and wire bonding spot. We then printed out the 1 to 1 ratio layout into a transparency film (3M PP2500) shown in figure (b). This transparency together with of a single sided presensitized copper clad board were put into Kinsten KVB-30d Exposure Unit shown in figure (c). An exposure time of 90s was set and after exposure, the copper board was put into the sodium persulphate etching tank shown in figure (e). The heater is to heat the chemical etchant to 55, which will increase the etching rate and save time. (i) (g) (h) 5mm After developing the copper board, the circuit is shown in figure (g). We solder all the components on the board and using conductive epoxy (CW2400) to glue the bottom brass of the cantilever to the clapping area which is connected to the negative input of rectifier circuit. After the conductive epoxy was cured, the surface PZT was wire bonded to the adjacent copper area to connect into the positive input of rectifier circuit. We use -74-