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Fabrication and Performance ofPiezoelectric Tubes for CylindricalUltrasonic MicromotorT. Li a , J. Ma a & Y. H. Chen aa School of Materials Engineering, Nanyang Technological University,Nanyang Avenue, 639798, Singapore

Available online: 09 Mar 2011

To cite this article: T. Li, J. Ma & Y. H. Chen (2005): Fabrication and Performance of PiezoelectricTubes for Cylindrical Ultrasonic Micromotor, Ferroelectrics, 315:1, 111-121

To link to this article: http://dx.doi.org/10.1080/00150190590933078

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Ferroelectrics, 315:111–121, 2005Copyright © Taylor & Francis Inc.ISSN: 0015-0193 print / 1563-5112 onlineDOI: 10.1080/00150190590933078

Fabrication and Performance of Piezoelectric Tubesfor Cylindrical Ultrasonic Micromotor

T. LI, J. MA, AND Y. H. CHEN

School of Materials Engineering, Nanyang Technological University,Nanyang Avenue, Singapore 639798

The piezoelectric ceramic tubular transducer is a functional component of the cylin-drical ultrasonic micromotor. In this paper, electrophorectic deposition (EPD) methodwas employed to fabricate the tubular transducer using a modified hard PZT ceramicmaterial 0.95Pb(Zr0.52Ti0.48)O3 · 0.03BiFeO3 · 0.02Ba(Cu0.5 W0.5)O3 + 0.5 wt%MnO2.Characterization of the piezoelectric tube was performed using SEM and X-ray radio-graphy. The piezoelectric constant d31 of the tubular transducer was also determinedto be 5.58 × 10−11 m/v using a ferroelectric tester and a fotonic sensor. The equationsfor static bending displacement with clamped-free and free-free end conditions weretheoretically developed, analyzed and experimentally verified.

Keywords PZT; tubular transducer; displacement; cylindrical ultrasonic micromotor;EPD

1. Introduction

Tubular transducer plays an important role in cylindrical ultrasonic micromotor as it is thedriving component in the device. Such configuration has been proved to be able to producehigher mechanical output torque than disk and ring-type ultrasonic motors [1–8]. The tubulartransducer consists of a PZT piezoelectric tube with silver electrodes applied on the outerand inner surfaces as shown in Fig. 1. The outer electrode is sectioned into quadrants alongthe axial direction. The inner electrode is grounded in operation. By connecting a pair of r.f.sources to the electrodes facing each other, the length-expansion effect of the PZT ceramicswill bend the transducer to a certain degree. The bending displacement can then drive atarget to move. A rotation mode can be excited with two r.f. power sources.

Higuchi et al. [1–8] have reported several works on cylindrical ultrasonic micromotor.This functional tubular transducer was mainly fabricated with hydrothermal method, whichis to deposit film on a titanium tube substrate. The advantage of this method is easy forminiaturization and without poling. However, it has the drawback of limited density (<3g/cm3) of the deposited film [2] and the transducer size is also constrained by the titaniumtube. In this work, another method, known as electrophorectic deposition (EPD), which isan easy and flexible way to deposit miniaturized bulk dense piezoelectric tube [9], was em-ployed. As the motor is a displacement-driven actuator, the key parameter d31 for achievinga large displacement was determined. The static bending displacement of the transducerwith clamped-free and free-free end conditions was also calculated using the equations de-veloped and experimentally confirmed. The effect of several parameters such as dimension,

Received January 2, 2002; in final form July 30, 2002.

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Figure 1. Structure of the tubular transducer.

applied voltage and piezoelectric constant were also discussed. The results obtained in thepresent work can be used to determine the tube dimensions and end conditions for improvedmotor design.

2. Fabrication of Transducer

The ceramic used to fabricate the transducer is a hard material with a composition of0.95Pb(Zr0.52Ti0.48)O3 · 0.03BiFeO3 · 0.02Ba(Cu0.5W0.5)O3 + 0.5wt%MnO2 [10]. It hasa low sintering temperature and suitable to be used as the functional material for mi-cro actuator. The raw oxide powders of PbO(>99.9%), ZrO2(>99.9%), TiO2(>99.9%),Bi2O3(>99.99%), Fe2O3(>99%), BaO(>99%), CuO(>99.99%), WO2(>99%) andMnO2(>99.99%) were first mixed with the designed stoichiometrical composition andthen balled-milled for 24 hours. Considering the volatility of PbO during sintering, addi-tional 5% of PbO was added into the raw powders. The mixed powders were then calcinedat 750◦C for 2 hours. Finally, the calcined powders were ground by a planetary ball-millingmachine at a speed of 150 rpm in ethanol for 8 hours. The ground powders were measuredto have a mean particle size of 1.4 µm using an acoustic particle sizer (DT-1200, DispersionTechnology, USA).

Suspensions were prepared by adding prepared powders in ethanol and then subjectedto ultrasonic agitation for 6 minutes. The powder concentration in the suspension was 50 g/1and the suspension pH was controlled to be 4 at room temperature. The suspension wasstirred for 3 to 6 hours to make sure the complete dissolution and dispersion of the powdersin the medium. The electricphorectic deposition system is schematically shown in Fig. 2.The electrophoretic cell includes a cathodic graphite rod substrate placing in the center ofa stainless-steel counter-electrode. The deposition was performed at a constant voltage of100 v for 3 to 8 minutes depending on the desired thickness of the tube. The deposits weredried for 12 hours and then sintered in a programmable furnace at 1100◦C for 1 hour.

The sintered tube was then cut into the designed length and brush-painted with silverpaste as electrode before firing at 850◦C for 20 minutes. Poling was next carried out in

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Piezoelectric Tubes for Cylindrical Ultrasonic Micromotor 113

Figure 2. Schematic drawing of electrophoretic apparatus.

silicone oil at 100◦C by applying a DC field of 2 kv/mm along the radial thickness directionfor 2 hours.

3. Microstructure of Piezoelectric Tube

In this section, the cross section microstructure of the prepared PZT tube was observed usingSEM. X-ray Radiography was also applied to examine the uniformity of the fabricated tube.

Figure 3 shows the cross section SEM micrograph of the sintered PZT tube. The samplewas polished and then thermal etched at 1025◦C for 15 minutes. It can be seen that the grainsize was grown from around 1.4 µm to about 5 µm. Small residual pores were observed

Figure 3. Cross section of the sintered piezoelectric tube.

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Figure 4. X-ray radiography photo for different size tubes.

over the cross section. This is in agreement with other result reported in the literature [10].The density of the tube was measured to be 7.54 g/cm3 using an electronic densimeter(MD-200s), which is approximately 95% of the theoretical value. The density achieved hasshown great improvement compared to that obtained using hydrothermal method [2].

Figure 4 shows the X-ray radiography (Smart Andrex 285) photograph of the varioussizes PZT tubes. It can be seen that the structure is reasonably uniform in diameter and wallthickness.

4. Piezoelectric Properties of Transducer

In this section, the piezoelectric constant d31 of the tubular transducer was determined usingthe standard equations

S1 = d31 E3 (1)

where the S1 is the strain in the length direction of the tube and

S1 = �L

L(2)

where �L and L are transducer displacement and length respectively. E3 is the averageelectric field and [11]

E3 = 2V

(ro + ri ) ln rori

(3)

where V is voltage added to the wall thickness direction; ro and ri are outer and inner radiusrespectively.

The setup for displacement measurement consists of a RT6000HVS ferroelectric testsystem (Radiant Technologies, Inc.), a Vrbroplane (RS Kinetic Systems, Inc.), a MTI-2000fotonic sensor (probe: MTI2032RX. MTI Instruments) and the tube assembled together asshown in Fig. 5. The tubular transducer used for the measurement has a dimension shown inTable 1. The whole area of both the inner and outer surfaces was painted with silver paste asconducting electrode. One end of the tube was fixed to the vibraplane with epoxy in orderto avoid any vibration-induced errors. The other end was attached with a reflection mark.The fotonic sensor probe was targeted at the center of the mark and placed parallel to thelongitudinal direction. During measurement, a bipolar step voltage was applied in the wallthickness direction of the tube. The step voltage was increased from zero to maximum setvoltage V , then decreased to negative maximum set voltage −V , and finally return to zero.

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Piezoelectric Tubes for Cylindrical Ultrasonic Micromotor 115

Figure 5. Setup for displacement measurement.

The fotonic sensor then measured the displacement �L of the tube in response to the givenvoltage. 100 points were measured in one voltage cycle.

The measured displacement �L as a function of the set voltage V is shown in Fig. 6.

y = 5.58 × 10−11x (4)

The slope of 5.58 × 10−11 provides the d31 value of the material. This value is found to becomparable to that reported in the literature [10], which indicates that the EPD techniquecan produce equally good piezoelectric ceramic as that by the conventional pressing andsintering method. Nevertheless, EPD technique has several other advantages over the tra-ditional method such as the flexibility in component shape and ability to produce smallercomponent (<1 mm).

5. Bending Displacement of Piezoelectric Tube

In this section, the equations for bending displacement of the piezoelectric tube withclamped-free and free-free end conditions were derived and experimentally verified forthe general static case. Figure 7 shows the schematic illustration of the measurement set-up.The origin O of the system lies at one end of the transducer. The neutral plane, X-Y plane,passes through the origin O. The transverse displacement takes place along the Z direction.As shown in Fig. 7(b), the electroded driving parts 2 and 4, and the unelectroded drivenparts 1 and 3, are aligned mirror-symmetrically according to the Z-axis. Angle β, whichdetermines the driving parts area, varies from 0 to 90◦.

Table 1Structure and properties of the fabricated tubular transducer

Outer radius Inner radius Length Angle β d31

ro (mm) ri (mm) L (mm) (degree) (10−11 m/v)

1.45 1.19 9.98 45 −5.58

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Figure 6. Determination for piezoelectric constant d31.

The tensile or compressive stress and strain along the longitudinal direction are denotedas T1 and S1 for the driving parts and T ′

1 and S′1 for the driven parts, respectively. According

to the piezoelectric relationship, the stresses along the X-axis are expressed to be:

T1 = 1

s E11

S1 − d31

s E11

E3 (5)

T ′1 = 1

s E11

S′1 (6)

where s E11 is the elastic compliance constants. The electric field in thickness direction E3 is

expressed as [11]

E3 = V

r ln rori

(7)

Figure 7. Coordinate system of tubular transducer.

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Piezoelectric Tubes for Cylindrical Ultrasonic Micromotor 117

where r is radius between outer radius ro and inner radius ri . Assuming that the cross sectionkeeps plane under deflection, S1 can be written as

S1 = −z1

ρ= −z

dz2

dx2 (8)

where ρ is the radius of curvature. Finally, the bending moment of the a cross section atposition x can be expressed as

M =∫

s1+s3zT ′

1ds +∫

s2+s4zT1ds (9)

Putting Equations 5 to 8 into 9, we obtain

M = − π

4ρs E11

(r4

o − r4i

) − 2d31V

s E11 ln ro

ri

(r2

o − r2i

)cos β (10)

Since in the static equilibrium condition the total bending moment over a cross section iszero [12, 13], i.e., M = 0, we get

1

ρ= − 8d31V cos β

π(r2

o + r2i

)ln ro

ri

(11)

As the radius of curvature keeps constant in the static situation, and since

1

ρ= dz2

dx2(12)

it can be easily derived from Equation 4 that

dz

dx= 1

ρx + C (13)

z = 1

2

1

ρx2 + Cx + D (14)

where C and D are constants.The constant C and D can be determined by considering the following boundary

conditions.

(1) Clamped-Free Boundary Condition

Under this condition,

dz

dx= 0

z = 0(15)

it is obtained that C = D = 0. Thus, the maximum displacement at the free tip end isobtained to be

ζ = L2

2ρ= − 4d31V cos βL2

π(r2

o + r2i

)ln ro

ri

0 < β <π

2(16)

The relation between the displacement ζ and piezoelectric constant d31, angle β, voltageV and length L can then be obtained from Equation 16. Figure 8 shows an illustration of

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Figure 8. Displacement in response to changes of radius ro and ri.

the displacement with respect to changes of radius ro and ri . The parameters used ared31 = −4.5 × 10−11 m/v, L = 10 mm, β = 45◦ and V = 30 v. The outer radius ro variesfrom 0.5 to 2.5 mm. The inner radius ri varies from near zero to 0.95 of the outer radius. Itcan be concluded from the present analysis that for the same outer radius, with increasingthe inner radius, the displacement increases; and the larger the outer radius, the smaller thedisplacement for the same inner radius.

(2) Free-Free Boundary Conditions

In this case, the transducer was supported at the two nodal points a and L − a as shown inFig. 9. The nodal point is the position where the displacement is zero at resonance frequency.Thus, following the same procedure as in clamped-free condition and using the boundary

Figure 9. The free-free end condition coordinate system.

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Piezoelectric Tubes for Cylindrical Ultrasonic Micromotor 119

conditions

dz

dx

∣∣∣∣x<0.5L

= − dz

dx

∣∣∣∣L−x

z = 0|x=a,L−a

(17)

the shape equation can be derived to be

z = 1

2ρ

[(x − L

2

)2

−(

a − L

2

)2](18)

Thus, the displacement can be calculated as

ζ1 = 1

2ρa(L − a)

ζ2 = − 12ρ

(a − L

2

)2

ζ3 = L2

8ρ

(19)

It can be seen that the functional displacement ζ1 was reduced. The total deflectionζ3 is equal to one quarter of the tip displacement in clamped-free condition. As a result,the clamped-free end condition is a better design to be used for the motor in terms ofdisplacement. This has also offered method for miniaturization of the functional transducersince a clamped-free transducer provides larger displacement for the same size. In addition,the clamped-free end condition tube has lower resonant frequency compared with free-freeconfiguration tube.

Figure 10. Bending displacement in response to step voltage.

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Figure 11. Comparison of calculated and measured end displacement of the transducer.

In order to verify the above-derived equations, the end displacement of the clamped-free transducer was measured. The transducer set up and the measurement procedure is thesame as that used for d31 measurement as shown in Fig. 7. However, the outer electrode isdivided into 4 parts, and the angle β is equal to 45◦.

Figure 10 shows one cycle of the displacement in response to the step voltage undera given set value 300 v. A good linear property with small hysteresis is clearly shownfor a typical hard material. Figure 11 shows the comparison of the measured results andthe calculated results using Equation 16 for the displacement under 300 v. The appliedparameters are tabulated in Table 1. It can be seen that the calculated value is in goodagreement with the measured results.

Conclusions

Electropheretic deposition is shown to be a good method to fabricate small, dense bulkpiezoelectric tube with desired perovskite phase and fine microstructure to be used astubular transducer. The piezoelectric constant d31 of the tubular transducer was determinedby the measurement of displacement along the longitudinal direction. The derived equationsto calculate the static bending displacement with clamped-free and free-free end conditionshave indicated that (1) the bending displacement is proportional to the piezoelectric constantd31, the voltage V added in the thickness direction, the square of transducer length L andcos β (0 < β < π/2); (2) at a given outer radius, the displacement increases with increaseof the inner radius; the larger the outer radius, the smaller the displacement for the sameinner radius; (3) the transverse displacement will decrease when the boundary conditionschanges from clamped-free to free-free.

References

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Piezoelectric Tubes for Cylindrical Ultrasonic Micromotor 121

3. T. Morita, M. K. Kurosawa, and T. Higuchi, IEEE Transactions on Ultrasonics, Ferroelectrics,and Frequency Control 45, 1178 (1998).

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