IEEE TRANSACTIONS ON ULTUSOXICS, FEIIKOELECTRICS, A N D FREQUENCY CONTROL, \'01.. 50: KO. 10. OCTOBER 2003 1377

Electrical Power Generat ion Characteristics of Piezoelectric Generator Under Quasi-Static

and Dynamic Stress Conditions Chok Keawboonclinay. Student Member, IEEE, and Thomas G. Engel, Senzor Member, IEEE

Abstract-The electrical characteristics of a piezoelectric power generator are investigated under quasi-static (dura- tion > 100 ms) and dynamic (stress duration < 10 ms) stress applications. The electromechanical model of piezo- electric generator is presented and used t o explain the ef- fects of the two stress conditions. A computer simulation of the piezoelectric generator is used to compare the the- oretical and experimental results. The simulation predicts that a quasi-static stress will produce a bidirectional gen- erator output voltage, and a dynamic stress will produce a unidirectional output voltage. The simulation also predicts tha t , when equal stresses are applied t o the generator, the dynamic stress will generate a 1OX higher output voltage than the quasi-static stress, contradicting results reported by other investigators. The output voltage is different for the two cases because of the generator's resistive capacitive (RC) t ime constant. The dynamic stress is applied in a t ime tha t is less than the generator's RC t ime constant, and the quasi-static stress is applied in a t ime greater than t h e gen- erator's RC time constant. The piezoelectric capacitance has enough time t o charge in the quasi-static case, result- ing in t h e lower output voltage. The simulation results are experimentally verified for leaded zirconia t i tanate P Z T 5 H and P Z T S A materials. Simulated and experimental results are shown t o he in good agreement.

I. ~NTRODUCTION

IIE clectrical characteristics of a piezoelectric (i.e.> PZ) T . ceramic was previously reported by Xu et al. [ I ] . I11 that investigation, tlie P Z material was subjected to a slowly applied (i.e., quasi-static) stress and a fast impact (i.e., dynamic) stress, both of equal magnitude. The results showed that the quasi-static stress produced a bidirec- tioiial voltage pulsc, the dynamic stress produced a uuidi- rectional voltage pulse, and tlie output voltage magnitudes were practically identical, regardless of stress. No explana- tion was given in [I] as to why the dynamic aud qiiasi-static stress applicatioiis produccd the same output voltage. This irivestigatioii applies quasi-static and dynamic stresses to a PZ material and uses thc electromechanical iriodel to cxplaiii its behavior under the diflerent stress conditions. A computer model of the P Z matcrial also is developed and used to predict its behavior. The P Z materials used in this irivestigatioii are the leaded zirconia titanates PZT 5H and PZT 5A (Morgan-Matroc: hic., New Bedford, MA 02745). The results show that, although the quasi-static

I

Fig. 1. Mechanical configuration of the piezoelectric power generator.

output voltage prodnces a bidirectional output and the dynamic output voltage produces a unidirectional voltage as reported in [l]. this irivestigatioii contradicts the results in [l] finding that the dynamic stress produces an output voltage that is always higher in magnitude than the quasi- static stress.

11. PIEZOELECTRIC POWER GENERATOR MODEL

The piezoelectric power generator model consists of t,wo parts: t,he mechanical model and the clectrical modcl. The model was prcvioiisly investigated in great detail in [2]-[6].

A . Mechanical Model

The mechanical configuration of the piezoelectric power gcrierator is sliowii in Fig. 1 and coiisis& of otic or more PZ elements between two masses; in this investigation made from steel. The force is applied to the generator in parallel with t,he poled directiom of the P Z material.

Although t,he mechanical system can be modeled with bulk elements or with distributed elements, dcuendinl. on

, I Y

the transient nature of tlie applied forces, the bulk element modcl is suitable for this investigation because shock waves are not gerieratcd in the P Z material that would warrant

Manuscript received August fil 2002; accepted May 19; 2003. The authors are at the University of hlisso,lri, Colurr,bia, MO

(email: ck7a5On1iacou.edu axid engelt~rmissonri.edu).

0885-3010/510.00 @ 2003 IEEE

1378 IEEE TRANSACTIONS ON ULTRASOXICS. FERROELECTRICS, AND FREQUENCY CONTROL) \'O1.. 60, NO. 10, OCTOBER 2003

mpiezo

"piem I x = o

n

Fig. 2. Mass-spring model of the piezoelectric power generdtor.

the use of the distributed model. The hulk element model of the P Z material is also conceptually simpler to under- stand than a distributed model. The applied force is as- sumed to be instantly and uniformly distributed through- out the device, which allows the simple mass-spring system of Fig. 2 to he used.

The mechanical system in Fig. 2 is described by the second order equation:

7~piem?picz0 + ~ ~ i ~ & i e , , + kpiczo~pieza = F, (1) where rripiezo is mass, cpielo is darnping constant, k,i,,,, is the spring constant, and xpiezo is the compression distance of P Z material. A detailed analysis of the displacement zpiezo and the computer simulation of the mechanical sys- tem of the piezoelectric power generator have been studied in [SI. For a given displacement, the mechanical compres- sion energy is given by:

Wrnech = FXpiezo . ('4 Relating (2) to Young's modulus, Y , the mechanical

energy expression becomes:

(3)

where h,,,,, is thc,thickness of the P Z material and A is its cross-sectional area.

B. Electncal Model

The electrical model of the piezoelectric power genera- tor is represented as an RC circuit (71 consisting of a stack capacitance. Cat,&, loss resistance, Rio,,, and leakage re- sistance, RI,,~,,,. Fig. 3 illustrates the equivalent circuit of piezoelectric power generator. The open circuit voltage,

cstack L Fig. 3. Equivalent circuit of pieaoelectric power gcnerator.

V', is produced in the P Z material as a result of applied stress.

In modeling the electrical system, the PZ material forms a capacitance, Cstvck, given by:

E n E J c s t a c k = ____,

where 0 is the free space permittivity and E? is the relative permittivity of P Z material. The P Z material has a series resistance, RI,,,, which is the internal dielectric loss of the material expressed as:

hpieeo

where w is the operating angular frequency of the genera- tor and tan6 is the dissipation factor. Measurements have shown that there is little variation in RI,,, under the con- ditions of this investigation and is, therefore, treated as a constant. A parallel resistance, Rl..hgg., represents leaka,:e losses in the material and is on the order of lo6 ohms. The electrical energy stored in the PZ as the result of mechan- ical compression is:

where q = csh,&va is the electrical charge stored in the material. A series connected voltage source, V,, is addcd to the model to account for the energy generated in P Z material as it is compressed. Equating (3) and (6); V' tNe- comes:

Experimentally, the values of RI,,,, Ri,,bg,, and k33 asc measured using a HP 4277A LCZ meter (Agilent Tech- nologies, Palo Alto, CA).

111. CHARACTERISTICS OF PIEZOELECTRIC POWER GENERATOR

The output characteristic of the piezoelectric power generator under dynamic and quasi-static compression

KEAWDOORCHUAY A N D ENGEL' CHARACTERISI'ICS OF PIEZOEI.&CTRIC GI

t

Fig. 4. Open circuit voltage.

* Fig. 5. Electrical model of piezoelectric power generator in Laplace domain.

force is investigated. Typically, the open circuit voltage generated by the compression force can be modeled as a ramp pulse as shown in Fig. 4, where t, is the rise-time, t h is the pulse length, and lf is the fall-time of the ont- put pulse. In the quasi-static case, the applied force pulse length is in the order of 100 ms, and the dynamic case bas duration on the ordcr of 10 ms. Mathematically, the open circuit voltage of Fig. 4 is expresscd as:

K ( t ) = atu( t ) - a(t - t+(t - t l ) - b(t - h ) ~ ( t - t 2 ) + b(t - t a ) ~ ( t - t a ) , (8 )

where a, and bare the slope of the risc-tirne and can be rep- resented as a = Va,max/tr and b = V,,,,,,/t,. The output voltage: Ktackr of the piezoelectric power generator can be solved analytically using Laplace transforms (81. The Laplace domain elcctrical model of the piezoelectric power generator is shown in Fig. 5.

The Laplacc transformation of the open circuit voltage of the piezoelectric power generator is:

ih'EKATOR UNDER DIFFERENT CONDITIONS 1379

Thc solution of the stack voltage is given as:

The loss resistance, RI,,,, is treated as a coustant in (10) because measurements have shown littlc variation in its value in this investigation. The time domain output voltage is found by inverse transforming (10) and is ex- pressed as:

Ktack(t) = -

aC,,,,, - aCst,,ke (RI"=.+"l..i.s.)C.t.=~ ') 4 t ) d - t l )

- (6-'1) ac,t,,k - aCst,,ke (Rlnrr+Rlar*age)Catac~

A . Quasi-Static Force Case

The quasi-static force of this investigation has a rise time, fall time, and pulse length on the order of 100 ms each. The quasi-static stress produces an output voltage having two oppositepolarity peaks: one peak when the force is applied and one peak when the force is removed. This behavior is cxpected and is attributed to the charg- ing and discharging of the PZ capacitance. Initially, the P Z capacitance is in the uncharged state and, with an ap- plication of force, V, will increase and inmediately appear across the load. As time progresses and with the force held constant, V, charges the PZ capacitance. Bccanse the PZ capacitance charges in opposite polarity to V,, the load voltage decreases. Removal of the applied force after the PZ capacitance is completely charged causes V, to decrease to zero. However, the output voltage will reflect the volt- age of the chargcd PZ capacitancc and is negative. Fig. G summarizes the events of the quasi-static force a,pplication described above.

B. Dynamic Force Case

For dynamic force application, the time duration of the applied force is on the order of 10 Ins. The PZ capacitance does not have sufficient time to charge in this case, and the majority of the output voltage is due to V,. In addi- tion; because the P Z capacitance cannot charge, removal of the force does not prodnce a negative peak in the output voltage. Fig. 7 illustrates the simulated results of the dy- namic stress condition. It shows that the dccay of output voltage is very small, a direct result of the short stress- pulse length. Additionally, the peak of the output voltage is higher than the quasi-static case because the PZ capac- itance is not allowed to charge. This finding is in direct

1380 IEEI: TRANSACTIONS ON ULTRASONICS, FERROELECTRICS, AND FREQUENCY cowrnoL, VOL. 50, PO. I O . OCTOBER zoo:: zl~EFEl >m -5000 0 1 2 3 4 5 6 time (s)

(a)

Fig, 6. (a) Open circuit voltage, V, of piezoelectric pulse gencrator, and (b) output voitagc. I/,trch, of piezoelectric power generator under aumi-static stress.

A 0.01 0.02 0.03 0.04 0.05 0.06

-5000

time (s)

I 0 0.01 0.02 0.03 0.04 0.05 0.06

-5001

time (b)

Fig. 7. (EL) Open circuit voltage, V, of piemelectric puis0 genorator, arid (h) outpiit voltage, VHk,,,, of piezoelectric power gencrator under dynamic stress.

conflict with [l], which statcd that the quasi-static and dyiianiic cases produced approximately equal uiagiiitude output voltages.

IV. EXPERIMENTAL AND SIMULATION RESULTS

In this investigation, the piezoelectric power generator is tested nsing both quasi-static and dynamic stress con- ditions to confirm the previous theoretical results.

A . Qtmsi-Static Force Case

In the quasi-static case: the piezoelectric power gener- ator is placed in an arbor press. Fig. 8 illustrates the ex-

i . Fig. 8. Experimental setup for the quasi-static force test.

,,:

, . . . . . . . 2 - . # I :

-2 -

. . 0.00 0.40 0.80 1.20 1.60

Time (s)

Fig. 9. Example of output voltage V,,,,, under the quasi-static cor.- dition.

perimeiital setup. A 3.6 kg steel mass is momentarily hung froni the end of the press handle. With the handle's 1engt.h of 55.5 cm and tlic gear radius of 4 cm, the compression force can he calculated using the moment of force equation as F = (3.6 x 9.8 x 55.5)/4, approximately 490 N.

The experiment is performed on the leadcd zirconia ti- tanate PZT 5H and PZT 5A inatcrials. The PZ material properties and experimental conditions are listed in Ta, ble I.

To create a quasi-static forcc, the steel mass is mo- mentarily hung from the press liaridle. After a short time period, the steel mass is removed froni the press handle. Fig. 9 illustrates the good agreement bctweeii the sim- ulation and experimental resiilts of the quasi-static stre:.s case. The results show that the output voltage of the piezo- electric generator, KtaCk: has a bidirectional peak voltage as theoretically predictcd. The results also show that the magnitude of the negative arid positive peak voltage are almiost identical. The small amount of crror between the experimental and simulated results is small oscillations in the measiired output voltage between the time of force application and force removal. Those oscillations are prtb surnably caused by mechanical bounce of the steel mass and support structure.

1381

1 PZT 5H 0.13 1.27 3400 111 8.5 5.0 3.00 15.00 2 PZT 5A 0.051 0.95 1700 106 8.0 5.0 2.09 10.45

TABLE I1 SUMMARY OF EXPERIMENTAL A N D Slh4UI.KI'loS RESULTS OF QUASI-STATIC CONDITIOX

Peak vacack (v) power density (pW/cm') Exp.' Positive Negative Positive Ncgiltive

Exp. Sim.' Exp. Sim. Exp. Sirn. Exp. Sim.

I 4.20 4.59 -4.50 -6.35 10.71 m 8 0 12.30 24.49 2 3.50 :3.38 -2.44 -2.31 33.88 31.60 16.46 14.76

'Exp. is the abbreviation for experiment. 2Sim. is the abhreviation for siniulation.

Table I1 surnrmarizes the experiniciital results of the quasi-static force case. The rcsults show good agreement between the experimental and simulated results. In the first experiment using PZT 5H material, the positive arid negative peaks measured at 4.2 V and -4.5 V, re- spectively. The output power density is calculated to be 10.71 pW/cm3 and 12.30 /1W/cm3, respectively. In the second experiment using PZT 5A material, the peak volt- ages are 3.50 V and -2.44 V with an output power density of 33.88 pW/cm3 and 16.46 pW/cm3, respectively.

B. Dynamic Force Case

To produce a dynamic force, the piczoclcctric power generator is placed in a PVC tube. A 0.25 kg mass is dropped from 10 cm. A computer model that simulates the dropping mass has been constructed. The output volt- age is experimentally measured and used in the model to calculate the impact force. The data show that brief peak impact forces of approximately 500 N are produced when tlic mass is dropped. The output voltage of the generator is measured with oscilloscope leads connected to the steel masses that sandwich the PZ material. Fig. 10 illustratcs the experimental setup of the dynamic force test.

The PZT 5A and PZT 5H are also used in this exper- imental series. Experimental test conditions are listed in Table I. The simulated and experimental results of the dy- namic st,ress condition are illustrated in Fig. 11 and show that the output voltage has only one positive peak that slowlv decavs.

I

Fig. 10. Experimental setup of the dynamic force test.

TABLE I11 EXPERIMENTAL RESULT OF DYNAMIC CONDITION.

The results of the dynamic stress test are contained Peak V,,,,k (V) Power density (mW/cm3) in Table 111. In the fist experiment using PZT 5H, the Exp.' Exp. Sini' Exp. Sim. peak output voltage is 58.40 V with a power density of 1 58.40 64.90 2.07 2.55 - 2.07 mW/cm3. Thc experimental results are in good agree- 2 70.00 68.35 13.55 12.92 ment with the simulated results. In the second experiment using PZT 5A, the peak output voltage is 70.00 V with a power density of 13.55 mW/cm3.

i ~ ~ ~ , is the abbreviatiorr for experiment, 'Sim. is the abbreviation for simulation.

1382 LEEE TRAXSACTIONS ON ULTRASONICS. FERROELECTRICS, AND FKEQUENCY CONTROL, VOL. 50, NO. 10, OCTOBER 2003

I REFERENCES 80 1

0 - --.. ... ---...-...- . _ _

Comparing the quasi-static and dynamic stress tests shows a significant difference bctwcen the relative mag- nitudes of the output voltage. The dynamic stress test produces approximately 10 times higher output voltagc than tlic quasi-static test. The impact time of the dynamic stress test (i.c.; i 10 ms) is faster than the'RC time con- stant (i.e.: approximately 15 ms) of the piezoelectric ma- terial. The PZ capacitance does not have time to charge. resulting in a higher output voltage.

V. CONCLUSIONS

In this investigation, the output voltage .of a piezoelec- tric power generator is theoretically and experimentally characterized under quasi-static and dynamic stress con- ditions. The electro-mechanical model of the piezoelectric power generator is prcscntcd arid used to predict and un- derstand the behavior of the generator under these two stress comditioms. Under quasi-static stress, the piezoelec- tric power generator produces a bidirectional (i.e., posi- tive and ncgative peak) output voltage. The bidircctional output voltage is produced because the P Z capacitance charges and reduces the magnitude of the P Z output volt- age. The reduction in output voltage is especially evident when the rise time of thc force is larger than or equal to the RC time constant. In contrast to the quasi-static stress condition, the dynamic stress conditio11 produces a unidirectional output voltage and, in this investigation, is 10 times larger than the quai-static c a e . The dynamic case produces a higher output^ voltage because the PZ ca- pacitance does riot have time t,o charge and subsequcntly reduce the PZ voltage. The results of this investigation are in disagreement with results reported by other inves- tigators 111. The results also show that to produce high

I21

I31

I41

151

I61

171

I81

C. Xu, M. Akiyanm, K. Nonaka, and T. Watanabe, "Elsctri- cal power generation chirrircteristics of P Z T piezoelectric ceram- ics," IEEE Trans. Ultmsm., Fenaelect. , Freg. Contr., vol. 45, no. 4, pp. 1065-1070, July 1998. T. G. Engel, W. C. Nonnnlly, and N. B. VanKirk, "Compact kinetic-teelectrical energy conversion," in Proc. 11th IEEE Int. Pulsed Power Conf., 1997, pp. 1503-1607. T. G. Engel, W. C. Nunnally, and J. E. Becker. "Research progress on the devciopment of miniature high power radar sources," in Pmc. SPIE, Detection and Remediation Technolo- gies for Mines and Mhelilie Targets IV, vol. 3710, pp. 124-130, 1999. T. G. Engel, C. Keawboonchnay, and W. C. Nunnally, "En- CIF" conversion and hieh nower oulse oroduction mine minia- _" 1 . I ture piezoelectric comprcssors," IEEE Trans. Plasma Sci., vol. 28, pp. 1338-1341, Oct. 2001. C. Keawboonchuay, "Exploration of high power piemelectric ki- netic to electrical energy converter,'' Master's thesis, University of Missouri-Columbia, May 2000. C. Keawboonchuay and T. G. Engel, "Design, modeling, and implementation of a 30 k W Diemelectric ~ u l s e Kenerator." IEEB &ns. Plasma Sci.. vol. 30: DD. 679-686. Aor.2002. . . S . W. Angrist, Direct Energ?/ Conversion. Boston, MA: Allyn arid Bacon, 1,982, pp. 415-420. R. J. hkyhan, Discrete-Time and Continuous-Time Linear Sys- tem. Reading, MA: Addisorr-Wesley, 1983, pp. 491-554.

Chok Keawboonchuay (S'96) was born on October 12, 1975, in Bangkok, Thailand. He studied in The Royal Thai Arnred Forces Academy Preparatory School, Bangkok, Thai- land,,for 2 years. He then fufthered his study at the Royal Thai Naval Academy, Samut Prakam, Thailand. In 1994, he received the scholarship from the Royal Thai Navy to study in the United States. He received B.S. and M.S. degrees in electrical engineering from the University, of Missouri-Columbia, His M.S. thesis is Exdoration of Hieh Power -

Piezoelectric Kinetic to Electrical Energy Converter. Currently, he is pursuing a P1k.D. degree at the University of Missouri-Columbia.

T. G . Engel (S'87-M'89-S'89-M'S&SM'OZ) received the Ph.D. degree in electrical engi- neering from Teras Tech University, Lubbock, TXI in 1990. He joined the R&D firm Enfitek, Inc. located in Lubbock, TX, later becoming Vice-president of Research and Development. In 1993, hc became a Research Assistant Pro- fessor at the Texas Tech Universitv Pulsed

I ~

1

1 Power Laboratory.

Dr. Engel moved to Columbia, MO, in 1995 to become an assistant professor and, in 2001, an associate professor. At the University

of Missouri, he has taught both graduate and undergraduate courses: including circuits, systems; clectrical machines, energy conversion, pulsed power engineering, high voltage engineering, and engineering mathematics.

Dr. Engel has consulted for academia, industry, and federal agen- cies. His oublication record includes more than 50 iournal. confer- . . -

piezoelectric gcncrator voltages, the RC time constant of the generator circuit be greater than the du- ration of the applied force.

ence, and book publications in mrious fields of specialization. His current research interests include pulsed power, direct energy con- version, and electromechanical systems. Dr. Engel is a member 0 1 Tau Beta Pi, Eta Kappa Nu, and Sigma Xi.