a piezoelectric parametric frequency increased generator...

JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL. 21, NO. 6, DECEMBER 2012 1311

A Piezoelectric Parametric Frequency IncreasedGenerator for Harvesting Low-Frequency Vibrations

Tzeno Galchev, Member, IEEE, Ethem Erkan Aktakka, and Khalil Najafi, Fellow, IEEE

Abstract—This paper presents the design, fabrication, and test-ing of a piezoelectric parametric frequency increased generatorfor harvesting low-frequency non-periodic vibrations. The gen-erator incorporates a bulk piezoelectric ceramic machined usingultrafast laser ablation. The electromechanical transducer is de-signed as a clamped-clamped spiral beam in order to decreasethe stiffness within a limited footprint. An internal mechanismup-converts the ambient vibration frequency to a higher internaloperation frequency in order to achieve better electromechanicalcoupling and efficiency. To gain maximum power output, the opti-mum width and thickness values of a spiral up-conversion unit arecomputed via multi-physics finite-element analysis simulations.The fabricated device generated a peak power of 100 μW and anaverage power of 3.25 μW from an input acceleration of 9.8 m/s2

at 10 Hz. The device operates over a frequency range of 24 Hz. Theinternal volume of the generator is 1.2 cm3. [2011-0355]

Index Terms—Frequency up-conversion, low-frequency, pa-rametric frequency increased generator (PFIG), piezoelectric,vibration harvesting, vibration scavenging.

I. INTRODUCTION

W IRELESS microsystem technologies have undergonerapid advancement over the past few decades. The

performance and utility of such devices have increased whilethe power consumption has been drastically reduced. Typically,batteries power these devices. However, in many cases, batter-ies cannot last the entire lifetime of the device, and periodic re-placement or recharging is needed. This is preventing wirelessmicrosystems from being truly ubiquitous.

Energy harvesting from ambient sources has gained in-creased interest as an alternative to batteries. While severalambient energy sources have been explored, kinetic energy isone of the most prevalent. However, the vast majority of vibra-tion harvesters are designed to operate at mechanical resonanceand at high frequencies (> 30 Hz) [1], [2]. This is limitingin that these types of harvesters can only operate when thereare high-frequency periodic vibrations such as those created bymachinery and other man made means. Little progress has beenmade in the low-frequency range of ≤ 30 Hz. This frequency

Manuscript received December 4, 2011; revised May 2, 2012; acceptedJune 13, 2012. Date of publication July 27, 2012; date of current versionNovember 27, 2012. This work was supported by the Engineering ResearchCenters Program of the National Science Foundation under Award EEC-9986866 and by Sandia National Laboratories. Subject Editor N. de Rooij.

The authors are with the Center for Wireless Integrated Microsys-tems (WIMS), University of Michigan, Ann Arbor, MI 48109-2122 USA(e-mail: [email protected]; [email protected]; [email protected];[email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/JMEMS.2012.2205901

range is very important for applications such as wearable orimplantable devices, environmental monitoring applications,structural health monitoring, and various security and militaryuses. Additionally, the vibration energy in these applicationshappens over large amplitude and frequency ranges and is likelyto be nonperiodic, all of which make it very challenging forefficient electromechanical conversion.

In order to effectively manage the challenges of harvestinglow-frequency and non-periodic vibrations, a new architecturecalled the parametric frequency increased generator (PFIG) wasintroduced [3], [4]. The PFIG is a non-resonant architecturewhere a low-frequency mechanical structure is used to inducehigh-frequency mechanical oscillations in an electromechanicalharvester. This decoupling of the ambient vibration frequencyfrom the internal operation frequency of the generator allows:1) versatile operation by eliminating the need for tuning; and2) increased velocity of the moving transducer thereby provid-ing better electromechanical coupling. PFIG-type generators, aswell as other harvesters that more generally use frequency up-conversion [5], [6], have shown the highest efficiency to date inthe low-frequency range of interest.

This paper discusses the detailed development and testingof a piezoelectric PFIG previously presented in [7]. In manyways, piezoelectric materials are ideal for energy conversionin a PFIG type of generator, since the internal displacement isfixed and limited. Typically piezoelectric materials are brittleceramics that cannot withstand large deflections (such as thoseproduced by low-frequency vibrations). While several otherpiezoelectric harvesters that are very similar in their opera-tion to the PFIG have been presented [8]–[11], they use animpact-based approach to pass mechanical energy between thelow-frequency and the high-frequency structures. Repeated me-chanical collisions are destructive in the long run and wouldlikely degrade the lifetime of the device. In this paper, a mag-netic latching mechanism is used to transfer energy between themechanical components. This type of force-based actuation ismore heavily dependent on the stiffness of the two structuresand places a much larger design burden on the mechanics ofthe overall system; however, it is likely to be more practical inthe long run. In order to incorporate a brittle bulk piezoelectricceramic (max. 1000 μ strain) while keeping the stiffness lowwithin a confined footprint, a specially designed and machinedspiral structure is utilized. Additional benefits of piezoelectrictransduction include: better electromechanical coupling in themicroscale, reduced volume (halved compared to a previouselectromagnetic implementation [3]), large rectifiable voltage,and the possibility of combining piezoelectric and electro-magnetic transduction mechanisms into a single generator.

1057-7157/$31.00 © 2012 IEEE

1312 JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL. 21, NO. 6, DECEMBER 2012

Section II of this paper will present the overall design of thePFIG. FEM optimization of the spiral transducer design will bediscussed in Section III. The fabrication and assembly of theharvester will be covered in Section IV. Section V will presentthe test results of this study. A discussion of the achieved resultsas well as possible future work will be given in Section VI.Lastly, a conclusion will be offered in Section VII.

II. PFIG DESIGN AND OPERATION

This paper covers the development of a piezoelectric PFIGharvester. The main goal of the study is to demonstrate thefeasibility of implementing a PFIG device while using piezo-electric transduction. This paper heavily references [3] wherethe electromechanical design of a typical PFIG was discussedin detail. The device in [3] is a sister device to the one discussedin this paper. They share a similar design, application, and a fewof the components (external casing and inertial mass assembly)are reused. The main difference is in the switch to piezoelectrictransduction from electromagnetic. This section will mainlyfocus on the design aspects associated with successfully imple-menting the piezoelectric transduction mechanism. The deviceis geared toward harvesting large amplitude motion such as thatfound on the human body. Studies have shown that humansproduce large non-periodic motion, with peak accelerations inthe 5–9.8 m/s2 range [12], [13]. Of course, human motion is notrapid and is bandlimited to only a few hertz. These requirementsmake the PFIG an ideal choice for harvesting these types oflarge irregular motions.

A. Operation of PFIG Harvester

The parametric generator is a non-resonant architecturewhere a mechanical structure, comprised of a large mass on acompliant suspension, is designed to be sensitive to the particu-lar source vibration, and it is used to initiate high-frequency me-chanical oscillations in an electromechanical transducer. Fig. 1shows an illustration of cross-sectional view along the lengthof a typical PFIG generator and explains its operation. TwoFIGs are oriented to face each other. In this case, each FIG isa piezoelectric electromechanical harvester that has a resonantfrequency > 100× larger than the targeted input vibration.Each FIG is outfitted with a small NdFeB magnet that is usedfor magnetic latching with the inertial mass, which is suspendedin the middle on a compliant spring. The PFIG operation isoutlined in Fig. 1(b). The generator operates such that theinertial mass attaches magnetically to each FIG, alternatingbetween top and bottom. As the mass moves in response toexternal motion, it pulls the FIG spring along. This actiontransfers mechanical energy from the inertial mass and storesit in the FIG spring. As the forces on the FIG spring overwhelmthe holding magnetic force, the inertial mass detaches and ispulled to the opposing FIG. The freed FIG spring now resonatesat its high natural frequency converting the stored mechanicalenergy to electrical. By up-converting the ambient vibrationfrequency to a higher internal operation frequency, the PFIGgenerator is able to achieve better electromechanical couplingand efficiency. This is referred to as frequency up-conversion

Fig. 1. (a) Illustration of the cross section of a typical parametric frequencyincreased generator (PFIG). (b) The PFIG generator depicted at three instancesof time, illustrating its method of operation.

Fig. 2. Rendering showing the design of the piezoelectric PFIG. The spiralPZT bimorph FIGs can be seen in the cutout on the left.

[5]. This entire process is subsequently repeated in the oppositedirection, and the inertial mass moves from FIG to FIG as longas there is sufficient ambient kinetic energy available.

B. PFIG Implementation and Design

Fig. 2 shows a rendering of the physical implementation ofthe parametric generator. The vertical layout of the compo-nents closely mirrors the illustration shown in Fig. 1. A largetungsten-carbide inertial mass is centrally supported by a planercopper spring. Spiral piezoelectric FIGs are machined and sur-round the inertial mass on top and bottom. Four aluminum partsthat comprise the external enclosure hold all of the componentstogether. During bolting together of the harvester, plastic ringsare used to electrically isolate the electrically conductive FIGsand the harvester casing.

The piezoelectric FIG is designed as a clamped-clampedbimorph beam operating in the 31-mode. While piezoelectricmaterials typically offer higher coupling coefficients in the33-mode, where deformation is coaxial to the electric field,the 33-mode operation results in a large stiffness, small

GALCHEV et al.: PIEZOELECTRIC PARAMETRIC FREQUENCY INCREASED GENERATOR FOR LOW-FREQUENCY VIBRATIONS 1313

deflections, and very high resonance frequencies. For this rea-son, the 31-mode is used (where deformation and the electricfield are perpendicular to each other). This mode of operationoffers weaker coupling coefficients: however, larger strains canbe achieved with a weaker force. The piezoelectric materialsare typically used in conjunction with a leveraging mechanism,such as a cantilever beam, which can turn large deflectionsat the tip into high strains along the surface (maximum atthe clamping base). The piezoelectric FIG is designed as aclamped-clamped beam rather than a clamped-free beam, inorder to keep the orientation of the latching magnet rigid in thehorizontal xy-plane. In this way the connection made betweenthe inertial mass and the FIG is reliable. This configuration canbe seen in Fig. 2. Clamping the beam on both ends makes iteven more challenging to generate compliant structures out ofceramic piezoelectric materials, particularly when the volumeand area are limited. Since the spring constant is inverselyproportional to the cube of the length of the structure, length-ening the beam is the preferred way to reduce the stiffness.The challenge of creating a long beam within a confined spaceis addressed by using a spiral geometry. The two arms onthe end of the spiral are designed with a linearly increasingcross section, widening as it moves from the spiral toward theclamped end. This way, the high stress concentration at theclamped end is alleviated, improving reliability, and film stressis more evenly distributed across the spiral arms, utilizing moreof the piezoelectric material for energy conversion [14]. Last, abimorph structure is used for better volume utilization by takingadvantage of the high strain from both top and bottom activelayers while also evenly distributing the stress through the crosssection of the beam.

The maximum power that can be generated by a PFIG typeof harvester has been shown to be

Ptotal ∼ mfγ2ω3U2

act (1)

where mf is the mass of the FIG, γ = ωnf/ω (ωnf =natural frequency of the FIG and ω = the ambientvibration frequency), and Uact is the actuation distancethat the inertial mass pulls the FIG before releasing it [3]. Thefrequency ratio γ is related to the up-conversion principle,stating that the higher the FIG frequency, the greater the outputpower (up to a hard-to-reach saturation limit as discussed in[3]). It is intuitive that there is an inherent tradeoff between γ,mf , and Uact. Decreasing the mass or increasing the springconstant can increase ωnf . However, the FIG mass itself hasan explicit effect on output power as seen in (1). What isnot captured by (1) is that the FIG spring constant, kf hasan even greater effect. Fundamentally, Uact, or the distancethe FIG moves before it is released by the inertial mass,is dictated by the strength of the magnetic latching forceversus the restoring force of the FIG spring. In other words,Uact is directly influenced by the spring constant of the FIG.Therefore, optimizing the PFIG means that Uact has to first bemaximized for a given set of design parameters. Second, thefrequency ratio can be increased, if needed, by decreasing theFIG mass, in order to completely convert all energy transferredon to the FIG by the inertial mass per cycle. The relationship

Fig. 3. FIG release distance Uact versus the FIG spring constant. As Uact

increases, the output power increases. The release distance is a function of theFIG spring constant. On the low end, it is bounded by the minimum stiffnessneeded to ensure proper PFIG operation, and on the high end, it is bounded bythe need for a proper PFIG dynamic performance.

between Uact and the FIG spring constant is plotted in Fig. 3.The plot is based on a dynamic simulation of the PFIG andshows the average actuation distance over a number of cycles.As, the spring constant increases, the actuation distance dropsrapidly, and past a certain point the overall PFIG dynamicsbecome affected. The increased stiffness prevents properenergy transfer. Secondary effects such as increased ringingand multiple latching instances can occur. This can alter theoperation by causing missed FIG actuation cycles and overallchanges in the bandwidth and frequency response. On the lowend, kf is bounded by the point at which the FIGs are compliantenough to latch simultaneously to the inertial mass and ceaseup the generator. Further discussion of the PFIG dynamicsare out of the scope of this paper, and interested readers arereferred to [3]. However, the next section presents a discussionon the modeling and optimization of the spiral FIG structure,where kf (and maximizing Uact) plays an important role.

III. PIEZOELECTRIC FIG OPTIMIZATION AND DESIGN

The spiral lead zirconate titanate (PZT) bimorph is a complexstructure to analyze analytically. In order to design the FIGspiral, coupled field FEM is performed using ANSYS. Asdiscussed in the previous section, in order to maximize theenergy transfer in the latching process, the stiffness of thePZT spiral should be as low as possible, but no lower than200–300 N/m to prevent simultaneous latching of the FIGs.

The influence of a number of geometric properties is investi-gated using FEM simulations. Those include the width, w, thearm length, la, the thickness of the PZT layers, tp, the numberof turns, n, the gap between adjacent spiral turns, gs, and theelectrode placement, le. The widening of the arm cross sectionis modeled by Θ, the angle made by the spiral arm with itscenterline. An illustration of the piezoelectric spiral is given inFig. 4, and the various parameters are labeled on the picture.A fixed force in the center of the spiral, mimicking the oneapplied by the inertial mass, is used to simulate FIG actuation.In these simulations, all but one of the variables are held at


Fig. 4. Illustration of the spiral PZT bimorph FIG. The beam is made up of aPZT/brass/PZT bimorph. The relevant parameters are labeled on the image.

TABLE IPIEZOELECTRIC MATERIAL PROPERTIES PZT-5A4E

Fig. 5. Simulated (ANSYS) behavior of the PZT spiral FIG generator as afunction of the gap between the spirals (gs), and arm widening parameter theta(Θ). All other spiral parameters are held constant. The results are shown for afixed force in the center of the spiral. Left axis and dotted red lines are used toshow spring constant variation and the right axis and solid blue lines show thepredicted output power. Results are normalized to the maximum spring constantand power values.

a constant baseline while the influence of the variable understudy is investigated. The baseline configuration is a spiralwith n = 5, w = 600 μm, gs = 200 μm, la = le = 4 mm, andtp = 130 μm. Piezoelectric properties used in the simulationsare listed in Table I. Figs. 5–8 present the results of thesesimulations. The solid blue curves go with the power axison the right-hand side, and the dotted red curves go with thespring constant axis on the left-hand side. Power is computedby using the simulated voltage and the calculated impedanceof the structure (mimicking the peak power value immediately

Fig. 6. Simulated (ANSYS) behavior of the PZT spiral FIG generator as afunction of the spiral beam width (w), and arm widening parameter theta (Θ).Left axis and dotted red lines are used to show spring constant variation andthe right axis and solid blue lines show the predicted output power. All otherspiral parameters are held constant. The results are shown for a fixed force inthe center of the spiral. Left axis and dotted red lines are used to show springconstant variation and the right axis and solid blue lines show the predictedoutput power. Results are normalized to the maximum spring constant andpower values.

Fig. 7. Simulated (ANSYS) behavior of the PZT spiral FIG generator as afunction of the PZT layer thickness (tp), and arm widening parameter theta(Θ). Left axis and dotted red lines are used to show spring constant variationand the right axis and solid blue lines show the predicted output power. Allother spiral parameters are held constant. The results are shown for a fixedforce in the center of the spiral. Left axis and dotted red lines are used toshow spring constant variation and the right axis and solid blue lines show thepredicted output power. Results are normalized to the maximum spring constantand power values.

after release). The spring constant and power are normalized tothe maximum value giving a unit-less measure. In this way, theresults from this study are used to present trends observed byvarying the spiral parameters one at a time, and the confusion oftaking the absolute power value as a prediction of output powerduring PFIG operation can be avoided. (The PFIG will generatean output power that is determined by the dynamics inside thedevice as well as the complete transformation of the energystored on the FIG spring as it oscillates and decays during eachlatching event.) Using the observed trends in Figs. 5–8, onecan optimize the FIG performance for a given area and neededstiffness.


Fig. 8. Simulated (ANSYS) stress on the clamped ends of the PZT spiral FIGas a function of the distance from the clamp. Default spiral parameters are used,and a fixed force in the middle of the spiral is applied. A theta (Θ) of 1.5 isincorporated into the final design to reduce stress and to improve reliability.

The influence on power of gs variation is shown in Fig. 5.As the gap increases, the overall spiral length increases, and thespring constant naturally decreases. Power is shown to decreasewith an increase in the gap. The more compliant structureproduces less stress and consequently results in less charge.While the overall deflection of the spiral is increasing, most ofthe additional deflection occurs in the middle area of the spiraland that is why stress is not increasing in the supporting arms.

The width, w, on the other hand, has a more complex effect(Fig. 6). When the width is increased, the spring constant ofthe structure initially increases (kf ∼ w). However, the springconstant plateaus with further increases to the width becausethe overall structure becomes larger and hence the lengthof the beam (kf ∼ 1/L3) tends to become larger. The highcompliance of the structure initially results in very low stressgeneration. Consequently, at first, the stiffness and the powerincrease hand in hand. However, an optimum point exists,because the increasing spring constant ultimately limits thebeam deflection, and hence stress, so power begins to drop.

Widening of the beam cross section (increasing Θ) wasshown to be a negligible contributor to the stiffness of the struc-ture. However, when the gap and/or the width are increased, theoutput power drops with an increase in Θ because of a reductionin the maximum stress in the beam.

The thickness, tp, of the PZT layer is a very importantparameter, and its influence is shown in Fig. 7. One can see thatan optimal thickness exists, once again caused by the interplaybetween the spring constant, the stress, and the deflection.When the structure is very compliant, increasing the thicknesshelps to increase the power output by contributing to higherstress. However, this effect is eventually counteracted by thedecreased deflection. Fig. 8 shows the stress distribution alongthe two arms of the spiral as the cross section is changed. Asexpected, when the arm becomes gradually wider from centerto base, the stress distribution becomes more uniform, makingthe FIG more reliable. The reliability in the arm is important,because the FIG is expected to have large deflections duringoperation (up to 0.5 mm), and alleviating the stress concentra-tion at the base will help with the longevity of the device.

Fig. 9. Simulated (ANSYS) z-axis component of strain as the piezoelectricspiral deflects due to a force applied at the center.

A very important issue that needs to be considered whendealing with a spiral design is the stress/strain distributionwithin the structure. Fig. 9 shows the simulated strain distribu-tion in the z-axis direction along the PZT spiral. It is apparentfrom the figure that the strain changes from positive to negativeat different locations along the structure. This can be explainedby considering how a spiral structure will deflect. As the spiralmoves, the center region will act as a fixed support inducingbending in the arm. Additionally, there will be a torsionalmotion associated with the vertical deflection. The positiveand negative strain values produce both positive and negativepotentials along the surface of the structure. If an electrode wereplaced stretching from the support all the way to the centerof the spiral, charge cancelation will take place reducing thevoltage and hence power. Considering the symmetric distri-bution of the strain, electrodes could be patterned throughoutthe spiral to collect all of the negative charge in one locationand the positive charge in a different location. However, suchan electrode scheme would complicate the fabrication andalignment process. Most of the charge that is generated willoccur at the base and along the long arms on the side. Therefore,electrodes were only placed along the straight arm such thatla = le. Any additional electrode area mainly due to where thewire interconnects are bonded to the spiral should be kept aslow as possible. This is area is not active and will simply add tothe impedance of the spiral, thereby lowering the power output.

Taking into account the modeling results, and making adjust-ments in order to fit into the required area, the final spiral designhas two turns, w = 300 μm and a gap of gs = 250 μm. Dueto the initially unknown characteristics of the laser fabricationmethod, the expected gap was designed to be fairly large. Inorder to keep stress linear, and for structural rigidity reasons,the arm length is set to 5 mm, and a moderate tapper isadded, where Θ = 1.5◦. The number of turns is maximized inthe limited area in order to decrease the stiffness as much aspossible. The final expected spring constant of the device is1914 N/m. This is far from the optimal design range shown inFig. 3; however, the goal was to reuse previously manufacturedhardware from [3] and to achieve a similar form factor. If the


Fig. 10. PZT/Brass/PZT bimorph machined using a femto-second laser.

PZT layer thickness were to be decreased to the optimum valueshown in Fig. 7, then the spring constant (499 N/m) would bewell within the optimum range.

IV. FABRICATION

The PFIG components are separately manufactured using anumber of techniques and assembled together by hand. Thepiezoelectric FIGs pose the greatest fabrication challenge. Acommercial (Piezo Systems, Inc, Woburn, MA) PZT bimorphis used consisting of a brass shim sandwiched between twosheets of PZT-5A4E (material properties in Table I), withPZT/Brass/PZT thickness of 130/130/130 μm. Each side ofthe bimorph is covered with a thin nickel electrode. In orderto create the spiral pattern, the piezoelectric bimorph is ma-chined using a Ti-Sapphire femto-second laser. The laser hasa wavelength of 780 nm, with a 150 fs pulse duration and a1 kHz repetition rate. In order to enable complex shape pat-terning and automated machining of several samples in a serialprocess, the pieces are placed on a computer controlled XYZ-Φ motion stage, on which the laser beam is focused through ashutter. Compared to other bulk PZT substrate patterning tech-nologies, femto-second laser machining provides a smaller fea-ture size with a high aspect ratio, minimum undercut, and lessdamage to the material. Results presented previously suggestthat repolarization of the material and any morphologic changesinduced by the laser machining process are only confined to asmall area around the machined edge [15], and they have littleeffect on the structure as a whole. An SEM image of one of theFIGs is shown in Fig. 10 as well as a close-up of the spiralregion in Fig. 11. A gap of 50 μm was achieved using thisfabrication method.

Electrical connections to the FIGs are made by adhering thinwires to each side. Small electrical pads are formed at the endof each spiral arm by trimming the nickel surface using thediagnostic laser on a Suss MicroTec probe station. Once thepad is isolated, wires are bonded using conductive silver epoxy.The diagnostic laser is also used to define the length of theelectrodes, le, on each arm of the spiral. NdFeB magnets areadhered to the spiral center using cyanoacrylate. The finishedFIG is shown in Fig. 12(a).

Fig. 11. Close-up of the micro-machined spiral. A gap of 50 μm was achievedusing this fabrication technology.

Fig. 12. (a) Assembled piezoelectric FIG with insulating rings and electricalinterconnects. (b) Inertial mass and spring suspension. (c) Partially assembledgenerator showing the FIG and partial casing ring. (d) Entire PFIG in front of aUS quarter.

Tungsten carbide (density of 14.9–17.7 g/cm3) is used for theinertial mass. It is machined using electric discharge machiningand ground down for planarization. It consists of two 10 mmdiameter pieces each of which is 3.9 mm thick. They are bondedon either side of a planar copper spring on top of a 1 mmthick spacer. The spring suspension is made from a 127 μmthick copper foil. The copper sheets are mounted on carriersilicon wafers using photoresist, lithographically patterned, andimmersion etched in FeCl3 at 45 ◦C. The inertial mass assemblycan be seen in Fig. 12(b).

The PFIG external enclosure consists of four aluminumpieces, which clamp the active components in place whenbolted together. The external casing is manufactured using acomputer-controlled mill. During the assembly process, thinstyrene rings are added on either side of the FIGs to electricallyisolate the transducer from the casing body [Fig. 12(c)]. Theyare designed with a smaller inner diameter than the inertialmass. The styrene spacer has a secondary role in that it actsas a shock stop to the inertial mass and prevents it fromunexpectedly colliding with the FIG. The final harvester canbe seen in Fig. 12(d).


TABLE IIPIEZOELECTRIC PFIG SUMMARY

Fig. 13. Optimal impedance measurement of the FIGs. Power delivered to theload is monitored while actuating the FIG at resonance and varying the loadimpedance.

V. TEST RESULTS

Initial test results are carried out to determine the perfor-mance and characteristics of each FIG. A summary of deviceconfiguration parameters is shown in Table II. The devices aremounted on an Unholtz-Dickie 5PM electrodynamic shakerand actuated using a small 1 m/s2 acceleration in order tofind their resonance frequency. The FIGs were then actuatedat resonance while the load was varied in order to find theiroptimal impedance. The point of optimal loading is foundwhere power delivered to the load is maximized. Fig. 13 shows

the resultant plot for one of the FIG arms. While performingthis measurement, it is important to take into account anyincident impedance such as the 1 MΩ input impedance ofthe oscilloscope used in this study. Impulse response tests arecarried out to determine the damping characteristics of theFIG. This procedure has previously been outlined in [4] andinvolves using the centrally attached magnet to provide animpulse to the FIG and to estimate the quality factor based onthe decay. The quality factor while optimally loaded, QT, is64, while the open circuit quality factor, Qm, is 77 (a higher Qsignifying a lower degree of damping). From these two values,the electric quality factor can be calculated as Qe = 379. Ascan be seen, the device is limited by its mechanical damping.Further, the value is very close to the published quality factorof the material [16], meaning that the performance is limited bythe quality of the PZT ceramic. Fig. 11 shows how granular thematerial is and so the main contribution to mechanical dampingis likely to be internal friction and loss. In the case of PFIGgenerators, the parasitic damping should be as low as possible[3]. PFIG harvesters are not limited by the criteria that Qe =Qm. The PFIG harvester has (on the first order) a fixed appliedforce by the magnetic latching mechanism and therefore a“fixed” Uact actuation distance. Since Uact, is set irrespectiveof the parasitic damping in the system, the mechanical parasiticdamping should be minimized (highest possible Qm). On theother hand, the electrical damping should be increased as muchas possible (lowest possible Qe). Provided that the electricaldamping force remains an order of magnitude less than themagnetic latching force, it will have minimal effect on Uact. Ifthe electrical damping becomes a dominant force affecting thesystem dynamics, numerical optimizations of the entire PFIGsystem will become necessary to set this parameter. One way todecrease Qe of the FIG is to extend the electrodes not only ontop of the arms but also on the spiral structure in the middle.The thickness of the PZT layer can also be manipulated tooptimize the structure. Table II shows a summary of designedand measured PFIG parameters.

The PFIG is assembled and tested on the shaker table. Its re-sponse to a range of accelerations and frequencies is evaluated.Due to shaker table limitations, the lowest frequency at whichmeasurements can be made is 10 Hz. Additionally, the PFIGis tested in the horizontal direction, in other words, under anapplied acceleration orthogonal to gravity. The reason for thisis that the present PFIG design does not account for gravity.The static gravitational bias is effectively eliminated by theinertial mass spring which is only designed to be flexible in onedirection. During testing, each FIG is loaded with its optimalimpedance, and the voltage across this impedance is monitored.Fig. 14 shows one such waveform where the voltage from eachFIG is recorded in response to an acceleration of 9.8 m/s2 at afrequency of 10 Hz. The voltage waveform is indicative of thePFIG method of operation. One can see the points in time whenthe inertial mass latched to each FIG and subsequently releasedit. It should be noted that each FIG has four active sections (thetwo arms on top and on the bottom of the bimorph), and Fig. 14only plots one from each FIG.

The minimum operating threshold for the PFIG was found tobe 6.86 m/s2. This value is mainly a function of the inertial mass


Fig. 14. Oscilloscope recording of the parametric generator operating undera sinusoidal acceleration of 9.8 m/s2 at 10 Hz. Out of four electrode pairs, twoare plotted (one from each FIG). The inertial mass can be seen moving fromFIG to FIG. Due to the high FIG stiffness, a secondary latching event can beseen.

weight and the magnetic latching force magnitude. Dampingcan also play a role if it were to provide a force on the sameorder as the magnetic and inertial forces. However, to thefirst degree, making the inertial mass bigger and the magneticforce lower can be used to reduce the minimum accelerationthreshold and vice versa.

The dynamics of the PFIG are not as straightforward asprevious implementations [3], [4]. The waveform is not as cleanas one would expect mainly because the FIG stiffness, despitethe spiral design, is higher than desirable. There is an uncharac-teristically large peak each time the inertial mass makes contactwith the FIG. Because of the high FIG stiffness (kf is evenhigher than the designed value due to a manufacturing problemand this issue is further elaborated in the discussion section), theimpact of the inertial mass is more pronounced, and the spiraldoes not move immediately. Instead, the inertial mass ricochetsand causes the ringing seen in the plot, then it comes back downand attaches again, essentially resulting in two latching events.Second, the inertial mass does not actuate the devices well (Uact

is small), as seen by the big discrepancy in the voltage betweenthe initial spike and that where the inertial mass unlatches fromthe FIG. On the first order, the main element influencing thisis the larger than needed FIG stiffness versus the magneticlatching force. This effect is also primarily responsible for whyone of the FIGs has a smaller response than the other.

The performance of the PFIG as a function of frequencyis evaluated at 9.8 and 19.6 m/s2 (1 g and 2 g) (Fig. 15).The fabricated device generated a peak power of 100 μW andan average power of 3.25 μW when actuated at 1 g with afrequency of 10 Hz. At that acceleration level, the device isable to operate over a frequency range of 20 Hz. While thedynamics of PFIG type generators have been shown to span anumber of different operating ranges [3], in the present device,only one of these conditions is seen. The PFIG operates in a“velocity limited” regime, and its bandwidth performance isdominated by the resonant system formed by the inertial massand its spring suspension. Therefore, the frequency at which thegenerated power begins to decrease is predominantly influencedby the natural frequency of the inertial mass/spring system.

Fig. 15. Frequency response of the PFIG generator at different accelerations.The average power is computed over multiple cycles.

With an increase in acceleration, there is more velocity, andthe inertial mass can surmount the distance to the FIG even athigher frequencies, so when tested at 2 g, the cutoff bandwidthis higher. However, secondary effects which have been shownto increase the bandwidth [3], including taking advantage of theincreased FIG inertia at higher frequencies, are not evident inthis implementation mainly because of the large stiffness of thespiral, and a higher than necessary gap between the FIG and theinertial mass. These parameters can be optimized in the futureif an even higher bandwidth is desired for a certain application.

VI. DISCUSSION

The performance of the piezoelectric PFIG is comparedto previously reported self-contained harvesters in the low-frequency range of interest in Table III. The volume figure ofmerit (FoMv) and bandwidth figure of merit (FoMBW) arecomputed as defined in [2], with the exception that in this work,the 3 dB bandwidth is used for FoMBW (instead of 1 dB asoriginally defined) and the center frequency is taken to meanthe lowest frequency of interest. The internal volume of theharvester is used in the computation. The efficiency of the PFIGcompares favorably to harvesters reported by others; however, itdoes not exceed the performance of a previous electromagneticPFIG implementation. This was to be expected, as the devicewas not able to perform as predicted during simulation.

The main issue hampering performance was the very con-servative design, which in turn led to a very high kf , andconsequently, it modified the dynamic operation of the PFIG.While the designed spring constant was already higher thanneeded for optimal performance, a manufacturing complicationresulted in an even higher stiffness. A spiral width of 300 μmand a gap of 250 μm was designed. The main reason for thelarge gap was because it was not known what can be achievedwith the laser ablation process. During the machining, the laserwas programed to cut along a spiral centerline. However, itturned out that the resulting gap was only 50–60 μm; A muchsmaller value than the designed tolerance of 250 μm. Thisautomatically added the extra area to the spiral, and the widthbecame 500 μm. The increased width directly influenced the


TABLE IIISELF-CONTAINED HARVESTERS OPERATING AT ≤ 10 Hz

Fig. 16. Simulation of the displacement of the two FIGs during PFIG opera-tion resulting from a 10 Hz sinusoidal actuation at 1 g. The FIGs are simulatedusing a stiffness of 4600 N/m to compare the behavior of the PFIG to thatrecorded during testing. A hard collision and ringing is seen in the simulationssimilar to the recorded voltage waveforms of Fig. 14. The lost energy results ina lower actuation distance for the FIG after inertial mass detachment.

spring constant, and it more than doubled from the designedvalue of 1914 N/m to (4637 N/m measured/4298 N/m simulatedin Ansys). The higher spring constant has a direct influencein the dynamic operation of the PFIG. The latching/actuationof the FIG is highly impacted because of the lost energy inthe collision and ringing between the inertial mass and FIG.The collision and ringing can plainly be seen in the voltagewaveform of Fig. 14. This behavior can be reproduced in sim-ulations of the dynamic behavior of the PFIG when a very stiff(4600 N/m) FIG spring constant is employed. Fig. 16 showsthe displacement of the two FIGs during PFIG operation (1 g,10 Hz). The hard collision of the inertial mass and the FIG canbe seen in the simulated behavior. Subsequently, the actuationdistance Uact is substantially reduced as a consequence of thelost energy during the ringing. The reduction of the actuationdistance means that less energy is stored in the FIG when theinertial mass detaches as a result of ambient acceleration, andthe average power produced by the device is mainly dependenton the initial spike rather than continued conversion over time.The behavior of the PFIG when the FIG spring constant ismuch more compliant can be seen in [3]. Future designs can bemore accurately modeled based on a better understanding of thelaser machining process, and it is expected that the transducerdimensions can be controlled much more accurately.

Enhancing the power generating capability of the FIG be-yond simple geometric optimizations becomes progressivelymore challenging. One of the simplest methods to achieve ahigher power output is to reduce the thickness of the piezoelec-tric layer. This was discussed in Section III; however, it was

not implemented. As previously shown in Fig. 7, an optimalpoint exists with respect to the piezoelectric layer thickness.Further gains in energy can be attained by fully utilizing thespiral structure. Currently, electrodes were only patterned onthe arms, which means the remainder of the spiral only hasmechanical functionality. Electrodes can be placed on the wholespiral in such a manner so that the areas with positive chargecollect on one electrode and those with a negative charge onanother. This technique has been demonstrated for meanderingstructures [17]. A similar idea is proposed in [15], although in-stead of selective electrode placement, the piezoelectric layer isselectively repolarized in certain areas in order to prevent theirbeing positive and negative charge areas on the same surface.

VII. CONCLUSION

This paper discussed the design and development of alow-frequency non-periodic piezoelectric PFIG generator. Thepiezoelectric implementation of the PFIG offers a number ofbenefits including a reduced volume, a large rectifiable voltage,and the possibility of combining piezoelectric and electromag-netic transduction mechanisms into a single generator. Thescalability of the PFIG architecture was also demonstrated bymanufacturing the smallest (1.2 cm3) parametric generator todate. The PFIG architecture is excellent for the microscalewhere displacements are limited because all of the motioninside the PFIG is predetermined and designed into the sys-tem. The harvester produced 3.25 μW of average power whenexcited with a sinusoidal acceleration of 9.8 m/s2 at 10 Hz. Theharvester was tested up to accelerations of 19.6 m/s2 and hada usable bandwidth of 20 Hz. The volume figure of merit ofthe piezoelectric PFIG was calculated to be 0.035%, which is avery competitive number in the frequency range of interest.

REFERENCES

[1] S. P. Beeby, M. J. Tudor, and N. M. White, “Energy harvesting vibrationsources for microsystems applications,” J. Meas. Sci. Technol., vol. 17,no. 12, pp. 175–195, Dec. 2006.

[2] P. D. Mitcheson, E. M. Yeatman, G. K. Rao, A. S. Holmes, and T. C.Green, “Energy harvesting from human and machine motion for wirelesselectronic devices,” Proc. IEEE, vol. 96, no. 9, pp. 1457–1486, Sep. 2008.

[3] T. Galchev, H. Kim, and K. Najafi, “Micro power generator for harvestinglow-frequency and non-periodic vibrations,” J. Microelectromech. Syst.,vol. 20, no. 4, pp. 852–866, Aug. 2011.

[4] T. Galchev, H. Kim, and K. Najafi, “Non-resonant Bi-stable frequencyincreased power generator for low-frequency ambient vibration,” in Proc.15th Int. Conf. TRANSDUCERS, Denver, CO, 2009, pp. 632–635.

[5] H. Kulah and K. Najafi, “Energy scavenging from low-frequency vibra-tions by using frequency up-conversion for wireless sensor applications,”IEEE Sensors J., vol. 8, no. 3, pp. 261–268, Mar. 2008.

[6] O. Zorlu, E. T. Topal, and H. Kulah, “A vibration-based electromagneticenergy harvester using mechanical frequency up-conversion method,”IEEE Sensors J., vol. 11, no. 2, pp. 481–488, Feb. 2011.


[7] T. Galchev, E. E. Aktakka, H. Kim, and K. Najafi, “A piezoelectricfrequency-increased power generator for scavenging low-frequency ambi-ent vibration,” in Proc. IEEE MEMS, Hong Kong, 2010, pp. 1203–1206.

[8] G. Lei, “Low-frequency piezoelectric energy harvesting prototype suit-able for the MEMS implementation,” Microelectron. J., vol. 42, no. 2,pp. 277–282, Feb. 2011.

[9] M. Renaud, P. Fiorini, R. van Schaijk, and C. van Hoof, “Harvestingenergy from the motion of human limbs: The design and analysis of animpact-based piezoelectric generator,” Smart Mater. Struct., vol. 18, no. 3,p. 035001, Mar. 2009.

[10] S. Moss, I. Powlesland, M. Konak, A. Barry, S. Galea, and G. Carman,“Broad-band vibro-impacting energy harvester,” in Proc. 7th PRICM,Cairns, Australia, 2010, pp. 2799–2802.

[11] S. Moss, I. Powlesland, S. Galea, and G. Carman, “Vibro-impacting powerharvester,” in Proc. Active Passive Smart Struct. Integr. Syst., San Diego,CA, 2010, p. 76431A.

[12] T. von Buren and G. Troster, “Design and optimization of a linearvibration-driven electromagnetic micro-power generator,” Sens. ActuatorsA, Phys., vol. 135, no. 2, pp. 765–775, 2007.

[13] C. R. Saha, T. O’Donnell, N. Wang, and P. McCloskey, “Electromagneticgenerator for harvesting energy from human motion,” Sens. Actuators A,Phys., vol. 147, pp. 248–253, 2008.

[14] N. M. White, P. Glynne-Jones, and S. P. Beeby, “A novel thick-film piezo-electric micro-generator,” Smart Mater. Struct., vol. 10, no. 4, pp. 850–852, Aug. 2001.

[15] E. E. Aktakka, H. Kim, and K. Najafi, “Energy scavenging from insectflight,” J. Micromech. Microeng., vol. 21, no. 9, p. 095016, Sep. 2011.

[16] Piezo Systems Inc., Jun. 2011. [Online]. Available: http://www.piezo.com/catalog.html

[17] D. Berdy, P. Srisungsitthisunti, X. Xu, J. Rhoads, B. Jung, and D. Peroulis,“Compact low frequency meandered piezoelectric energy harvester,” inProc. PowerMEMS, Washington, DC, 2009, pp. 71–74.

[18] B. Cavallier, P. Berthelot, H. Nouira, E. Foltete, L. Hirsinger, andS. Ballandras, “Energy harvesting using vibrating structures excited byshock,” in Proc. IEEE Ultrason. Symp., Rotterdam, Netherlands, 2005,pp. 943–945.

Tzeno Galchev (M’11) received B.S. degrees in bothelectrical and computer engineering, and the M.S.and Ph.D. degrees in electrical engineering from theUniversity of Michigan, Ann Arbor, MI, in 2004,2006, and 2010, respectively.

Currently, he is a Research Fellow in the Depart-ment of Electrical and Computer Engineering andthe Center for Wireless Integrated Microsystems atthe University of Michigan. His research interestslie in the development of autonomous microsystemsincluding the development of energy harvesting de-

vices, sensors, actuators, analog and digital integrated circuits, and microfabri-cation and packaging technologies.

Dr. Galchev was the sole recipient of the University of Michigan Excellencein Engineering Fellowship in 2006, support for which was provided by SandiaNational Laboratories. In 2008, he was nominated for the John Atanasoff Awardand was one of two finalists awarded by the President of Bulgaria for theircontributions to the information society. The John Atanasoff Award is givento young scientists under the age of 36 for significant contributions in thedevelopment of information technologies.

Ethem Erkan Aktakka received the B.S. degree inelectrical engineering from the Middle East Techni-cal University, Ankara, Turkey, in 2006, and the M.S.and Ph.D. degrees in electrical engineering from theUniversity of Michigan, Ann Arbor, in 2008 and2012, respectively.

Currently, he is a Research Fellow in the Depart-ment of Electrical and Computer Engineering at theUniversity of Michigan. His research interests in-clude microfabrication technologies, smart materialsand transducers, energy harvesting/storage, analog

and digital integrated circuits, micropackaging, and acoustic/ultrasonic sensingand actuation.

Dr. Aktakka received first place in Turkey’s nationwide university entranceexam in 2002, TUBITAK Graduate Research Fellowship Award in 2006, JCITen Outstanding Young Persons of Turkey Award in 2010, DTE Clean EnergyPrize in 2010, and Distinguished Achievement Award from the Universityof Michigan in 2011. He cofounded and served as the first President of theNanotechnology and Integrated Microsystems Student Association in 2010,which aims to create an academic career development network among itsmore than 300 members across the University of Michigan.

Khalil Najafi (F’00) received the B.S., M.S., andthe Ph.D. degree in electrical engineering from theUniversity of Michigan, Ann Arbor, in 1980, 1981,and 1986, respectively.

He has been the Schlumberger Professor ofEngineering, and Chair of Electrical and ComputerEngineering at the University of Michigan sinceSeptember 2008. He served as the Director of theSolid-State Electronics Laboratory from 1998 to2005, has been the Director of NSF’s National Nan-otechnology Infrastructure Network since 2004, and

the Deputy Director of the NSF ERC on Wireless Integrated Microsystemsat the University of Michigan. His research interests include micromachiningtechnologies, micromachined sensors, actuators, MEMS, analog integrated cir-cuits, implantable biomedical microsystems, micropackaging, and low-powerwireless sensing/actuating systems.

Dr. Najafi has been active in the field of solid-state sensors and actuators for30 years. He has been involved in several conferences and workshops dealingwith micro sensors, actuators, and microsystems, including the InternationalConference on Solid-State Sensors and Actuators, the Hilton-Head Solid-StateSensors and Actuators Workshop, and the IEEE/ASME MEMS Conference. Hehas served as Associate Editor or Editor of several journals. He is a Fellow ofthe American Institute for Medical and Biological Engineering.

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