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Piezoelectric Cantilever Prototype for Energy

Harvesting in Computing Applications

Levent Beker

Micro and NanotechnologyGraduate Program

Middle East Technical University

Ankara, Turkey

levent.beker@mems.metu.edu.tr

Haluk Klah

METU-MEMS CenterMiddle East Technical University

Ankara, Turkey

Ali Muhtarolu

METU NCC REDARMiddle East Technical University

Northern Cyprus Campus

Guzelyurt, Mersin 10 Turkey

Abstract This paper presents a piezoelectric energy harvester

(PEH) to convert vibrations to electrical power. A unimorph

cantilever beam is used to generate voltage on piezoelectric

material bonded close to the anchor of the cantilever beam. A

4.85 x 1 x 0.04 cm structural layer with piezoelectric material

yields peak-to-peak voltage of 64 V at the resonance frequency of

the structure. The empirically confirmed maximum power output

is close to 0.5 mW. The results from validation data on theobserved structure has been correlated to the simulations in finite

element method (FEM) program using piezoelectric analysis

tools.

Keywords: Energy harvesting; piezoelectric conversion; finite

element method; piezoelectric model

I. INTRODUCTION

Advances in integrated circuit (IC) manufacturing, lowpower circuit design and networking techniques have reducedthe power requirements of electronic devices in the order ofmicrowatts. Due to the low energy requirement of electronicdevices, energy harvesting from vibrations emerges as a

possible candidate. Among three possible vibration energyconversion mechanisms, namely electromagnetic, electrostaticand piezoelectric, converting vibrations to electrical powerusing piezoelectric conversion principle received greatestattention within the last decade [1]. Advantages ofpiezoelectric conversion principle are large power densities ofpiezoelectric materials and ease of application .

Piezoelectric energy harvesting is widely studied in theliterature. [2-4]. The problem associated with the modeling ofpiezoelectric energy harvesters is due to the complexity of thepiezoelectric materials. Since these materials involve strainand charge relationship, it is not trivial to model the behavior ofthe systems involving piezoelectric materials. During lastdecade single-degree-of-freedom (lumped parameter)approaches are used to model behavior of the piezoelectricenergy harvesting systems [5], [6]. Since this approximation islimited to single vibration mode, it misses importantinteractions such as dynamic mode shapes and straindistribution [1]. Recently Ertrk et al. reported an analyticalmodel for both unimorph and bimorph uniform configurationswhich are also verified experimentally [7].

Integration of the energy harvesters into the daily lifeapplications is critical due to increased demand on extending

battery life and renewable energy sources. One of the possibleapplications of the energy harvesters is the keyboards due tohigh usage rates and mechanical energy availability. Keyboardscan be used to scavenge energy if input mechanical forceapplied on button can be converted to electrical power.However the frequency of typing is low, around 7.5 Hz evenfor a skilled typist [8]. In order to harvest energy using aresonant cantilever structure with length smaller than 5 cm andnatural frequency around 7.5 Hz, one has to use a tip mass.Usually attached tip mass causes rotational modes at the higherfrequencies. However, both lumped parameter and analyticalmodeling (Euler-Bernoulli model) attempts do not consider therotational effects. Also the tip mass attached to the structurewith such a low natural frequency cannot be modeled as a pointmass, unlike approximate methods.

The aim in the present work is to develop a detailed finiteelement model for piezoelectric energy harvesting applicationsto verify this model against a prototyped system toward lowfrequency (5-10 Hz) piezoelectric energy harvesters for typingapplications. A unimorph PEH has been modeled in a FEA

program and simulated under realistic boundary conditions.Total volume of the PEH is 0.23 cm3 (Fig. 1, Fig. 4). Theresonant frequency of the simulated system is around 124 Hz,and obtained peak-to-peak open circuit voltage in resonance is66 V for 0.1 mm base excitation. A prototype has beenfabricated, and validated under the same conditions as thesimulations to yield resonant frequency around 109 Hz andpeak-to-peak voltage of 65 V. The maximum validated poweroutput was close to 0.5 mW with optimal (matched) loadresistance. The difference between simulation andmeasurement has been explained by fabrication errors.

Section II explains the modeling and design of the PEHprototype. Validation results from fabricated prototype are

discussed in Section III. Finally, conclusions from this work areprovided in the last section.

Figure 1. Piezoelectric energy harvester

Piezoelectric Material

y(t)Voc(t)

Structural Layer

MER, TUBITAK (sponsors)

978-1-4673-0465-8/11/$26.00 2011 IEEE

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II. PIEZOELECTRIC ENERGY HARVESTER (PEH)DESIGN

Piezoelectric materials have ability to produce an electrical

charge when deformed mechanically, or conversely, deform

mechanically when exposed to an electrical field. The relation

between deformation mechanism and the electrical charge

produced on piezoelectric materials is defined by the

piezoelectric constitutive equations (Eqn.s1 and 2) [9]:

kkijkl

E

ijklij EdTsS (1)

k

T

ikklikli ETdD (2)

In above equations Sij represents strain components, Tklrepresents stress components,Ekrepresents electric field and Direpresents electric displacement. Also dikl term includespiezoelectric coupling term, sijkl is the compliance datameasured under constant electric field, and ik is thepermittivity data under zero stress field.

Vibration energy harvesting systems can be modeled assingle degree of freedom systems (SDOF) as depicted in Fig. 2.In the figure, x(t) is the displacement of the relevant point of

the structure (i.e. tip of the cantilever beam) where y(t)represents the base vibrations. The equivalent stiffness of thestructure is represented by keq and the equivalent damping isrepresented by ceq. In order to find the relative displacement ofthe vibrating structure,z(t)can be calculated as in equation (3)and (4) [11].

)()()( tytxtz (3)

jwt

o

eqeqeq

eqeY

jwcmwk

mwtz

2

2

)( (4)

SDOF representation gives information about the behavior

of the system. However, this approach misses important

factors about the dynamics of the structure, such as strain

distributions and their effects on the electrical response [1].

Although modeling of a uniform cantilever beam is a well-

studied topic, modeling attempts for a beam with varying cross

section and large tip mass only leads to approximate solutions.

Finite element modeling provides fast and reasonable solution

for the investigation of composite beams with non-uniform

cross sections. The model developed in this paper serves as the

foundation for the development of very low frequency

piezeoelectric energy harvesters. ANSYS finite element

program has capability to analyze piezoelectric materials,since SOLID226 element can relate the structural field with

the electrostatic field [11]. Modal analysis has been conducted

to observe the natural frequency of the modeled structure.

Electrical response of the structure has been simulated by

conducting a coupled harmonic analysis. Parameters used

during the simulations are summarized in Table 1. Natural

frequency of the simulated PEH is obtained as 124 Hz. A

harmonic analysis is conducted by sweeping the frequency

between 40 Hz and 130 Hz in order to obtain the voltage

frequency response functions (FRFs) produced by the

piezoelectric material to 0.1 mm base excitation. A close up

view of the voltage produced on the upper electrode over the

piezoelectric material after harmonic analysis is depicted in

Fig. 3.

Figure 2. Commonly used lumped-parameter model of vibration energy

harvesters

Table 1. Simulation parameters

PZT5A Brass Unit

Density 7800 8410 [kg/m3]

ElasticModulus

3: 5.2e10 9.2e10 [Pa]

1: 6.6e10 - [Pa]

Poisson's ratio - 0.35 -

Element type SOLID226 SOLID186 -

Mesh Free -

Piezoelectric

coefficients

d33: 390e-12 - [m/V]

d31: -190e-12 - [m/V]

Dielectric

constants

K3: 1800 - -

K1: 1730 - -

Relative

dielectric

constants

11/0: 916 - -

33/0: 830 - -

Constant

damping ratio0.01 -

Figure 3. Results after harmonic analysis and close up view of voltage

produced on the piezoelectric material

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III. PROTOTYPE DEVELOPMENT AND VALIDATION

A prototype of the designed PEH has been fabricated asdepicted in Fig. 4. The dimensions are provided in Table 2.Brass is used as a structural layer. Piezoelectric material usedin the experiment is the commercially available PSI-5A4E(Piezo Systems Inc.) and the polarization direction is throughthe thickness of the material as shown in Fig. 1. Upper andlower surfaces of the piezoelectric material are coated with

nickel, and are thus conductive. Piezoelectric material isbonded to the structural layer, in order to transfer the stressproduced on the structural layer to piezoelectric material.

Figure 4. Fabricated piezoelectric energy harvester

Table 2. Structure dimensions

Property Dimension (in cm)

Cantileverbeam

Structural

layer

length 4.85

width 1

thickness 0.04

PZT

length 0.7

width 1

thickness 0.05

Conductive epoxy is used as a bonding layer to make

contact with lower surface of piezoelectric material. After

coating the lower surface of the piezoelectric material with

conductive epoxy, structure is put into oven for 20 minutes at

110 C for the curing of the bonding layer. A fixture is

designed to hold the structure and connect to the upper and

lower surfaces of the piezoelectric material (Fig. 4). The

structure has been mounted on a shaker, and 0.1 mm base

excitations are given to the structure while sweeping the

frequency of the vibrations. Experimental setup used for

measurements is shown in Fig. 5.

The natural frequency of the structure is validated as 109Hz, 12% less than the simulated value. This difference isexpected, because the bonding layer in simulations is uniformthroughout the bottom surface of the piezoelectric material,while the bonding layer of the structure used in experiments isnot. Uniform bonding layer increases the stiffness of thestructure, and explains the higher natural frequency of thesimulated PEH. Another possible reason for higher naturalfrequency in the simulation environment is the mismatch in thematerial properties used with the actual properties.

The fabricated PEH was excited with 0.1 mm base

displacements while sweeping the frequency. Comparison of

Figure 5. Experimental setup

the voltage FRFs between experiment and simulations can be

found in Fig. 6. The peak-to-peak voltage at the resonance

frequency of the simulated structure is 65 V, which is almost

equal to experimentally obtained value. Due to ideal bonding

layer in the simulation environment, stiffness of the simulated

model is more than the fabricated structure. While bonding the

piezoelectric material to the host structure, conductive epoxy

is cured under 110 C. After the curing operation, small voids

between the piezoelectric material and structural layer have

been observed. These voids led to a decrease in the resonance

frequency of the fabricated structure. A load resistance sweep

has been used to identify the maximum power output of the

system as 484 W when the load resistance is to 400 k and

rms voltage is 14 V, as shown in Fig. 7.

Figure 6. Comparison of experimental and simulation peak-to-peak voltageFRFs

Piezoelectric

material

Brass

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Figure 7. Power output of piezoelectric energy harvester with various load

resistances

A volume figure of merit [12], calculated as in Eqn. 5, can

be used to calculate the size-normalized performance of

piezoelectric energy harvesters, where Yo is the excitation

amplitude, Au is the density of gold, Vo is the volume of thedevice, and wis the excitation frequency. Table 3 reports thismetric for the previous models and the present study. The data

indicates that the performance of the harvester prototypereported in this work is comparable to previous results or

better, while being model-correlated and designed to fit the

requirements of the targeted application.

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16

1

..

wVY

OutputPowerUsefulFoM

oAuo

V

(5)

Table 3. Comparison of piezoelectric energy harvesters

Author Reference V [cm3] Y [um] w [Hz] Power [uW] FoM

Roundy 13 1 4 120 80 0,39

Roundy 13 1 7,9 85 90 0,62Roundy 13 1 16 60 180 1,74

Wright 13,14 4,8 36 40 700 1,25

Tanaka 2 9 10 50 180 0,26

Fang 3 0,0006 4,4 609 2,16 1,44

Ng 4 0,2 180 100 16,3 0,026

Mide 15 40,5 99 50 8000 0,16

Mide 15 40,5 11 150 1800 0,012

0,23 100 109 484 0,89This Work

IV.

CONCLUSION

FEA method has been used to model a unimorph PEH for

better accuracy of low frequency structures compared to

previous lumped parameter and analytical models. A 0.23 cm3

PEH prototype of 4.85 cm2 was then fabricated and validated

against the model in order to lay ground for further

development toward energy harvesting in computing (typing).

The measurements correlated with the simulation results

within 12% for resonant frequency of the structure, and 2% for

the output voltage, both attributed to fabrication imperfections.

The maximum validated power output under optimal loading

conditions was close to 0.5 mW. The harvester lays the

groundwork for further development toward computing

application.

ACKNOWLEDGMENT

This work is in part supported by MER, a partnership betweenIntel Corporation and King Abdul-Aziz City for Science andTechnology, to conduct and promote research in the MiddleEast. This work is in part supported by TUBITAK, Turkey.

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[1]

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[2]

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Mide.PEH20W Datasheet, [Online] Available: http://www.mide.com/products/volture/peh20w.ph

0

5

10

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20

25

0

100

200

300

400

500

600

0 200 400 600 800 1000 1200

Vrms

[V]

Power[W]

Load Resistance [k]

Power Vrms