a rod-shaped vibro touch sensor using pzt thin film · [email protected]). fig. 1....

ieee transactions on ultrasonics, ferroelectrics, and frequency control, vol. 46, no. 4, july 1999 875

A Rod-Shaped Vibro Touch Sensor UsingPZT Thin Film

Takefumi Kanda, Takeshi Morita, Minoru Kuribayashi Kurosawa, Member, IEEE,and Toshiro Higuchi Member, IEEE

Abstract—We have fabricated a probe sensor. This sen-sor is for high precision coordinate measuring machines,surface roughness measuring tools, or scanning probe mi-croscopes (SPM). This sensor consists of a rod vibrating inthe axial direction. The longitudinal vibration was excitedand also detected by PZT thin film. The PZT thin film wasfabricated by a hydrothermal method. The hydrothermalmethod uses the reaction process in hot and high pres-sure aqueous solutions. We made a 27.8-mm long sensor.Its resonance frequency was 116 kHz. The sensitivity andresolution were evaluated by experiments. We succeeded inoscillating the rod and detecting the contact.

I. Introduction

Recently, the demand for probe sensors is increasing.This is because MEMS technology has made progress.

It requires high precision, coordinate measuring machines.A touch sensor that vibrates longitudinally has been pro-posed as a probe of such measuring machines [1]. If theprobe is miniaturized, surface roughness will also be mea-sured; then, it will be applicable to SPM.

In most tactile sensors and SPM probes, bending vi-bration of cantilevers are used [2]. However, the Q valueof cantilevers cannot be so high under a millimeter scalebecause the damping ratio by air viscosity increases. Thesensitivity of vibro probe sensors depends on the mechani-calQ factor. The high damping ratio by air viscosity makesthe Q value lower. However, the longitudinal vibrating rodis not so influenced by the air viscosity damping ratio.Therefore, it is possible to maintain a high Q value. So alongitudinal vibration sensor can obtain higher sensitivityand resolution than cantilevers in micro scale. In addition,because of the small damping ratio, the longitudinal vi-bration sensor is useful in liquid.

Piezo electric materials are used to oscillate probes anddetect the contact. To miniaturize the prove sensor, piezo-electric thin films are useful. By using thin films, the piezomaterial and the rod can be connected without any adhe-sive or bolts.

There are several methods to deposit a piezoelectricthin film. However, it is difficult to obtain enough forcefor oscillators. We deposited a PZT thin film using a hy-drothermal method [3]. With this method, thickness of the

Manuscript received May 11, 1998; accepted November 28, 1998.The authors are with the Department of Precision Machinery

Engineering, Graduate School of Engineering, The University ofTokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan (e-mail:[email protected]).

Fig. 1. Sketch of the measurement of the object shape by the vibrotouch sensor.

film is about 10 µm. Using this method, PZT thin films areformed on three-dimensional complex-shaped bodies, sothat we can miniaturize the oscillator easily. A microultra-sonic motor has been fabricated by using this method [4].

We used PZT thin film by the hydrothermal method foroscillating longitudinal vibration and detecting the con-tact. It may be possible to make much smaller microsen-sors by the hydrothermal method.

II. Structure and Principle

A. Principle

As shown in Fig. 1, the sensor is a rod-shaped vibrator.The sensor vibrator has one-half the wavelength of the lon-gitudinal vibration mode. An exponential horn, which en-larges the vibration amplitude, increases sensitivity. Whenthe tip end of the horn is in physical contact with a work-piece, the resonance frequency of the vibrator is shifted.By detecting the frequency shift, the contact is sensed.

For theoretical consideration, this vibro sensor can bemodeled as shown in Fig. 2 [5]. The sensor is fixed in thenode of the longitudinal vibration. Then, the horn-partand the cylindrical part of the oscillator equally vibrate:both parts are one-quarter wavelength. From the equationof motion, the resonance angular frequency is expressed as:

ω =1m

√(SE

l+Kc

)2

− C2c

2. (1)

0885–3010/99$10.00 c© 1999 IEEE

876 ieee transactions on ultrasonics, ferroelectrics, and frequency control, vol. 46, no. 4, july 1999

Fig. 2. Model of the vibro touch sensor.

When there is no contact, Kc = Cc = 0. When the con-tact takes place, these variables change, and the resonancefrequency also shifts. If the workpiece is an elastic body,Kc > Cc, then the resonance frequency of the oscillator in-creases. If the workpiece is plastic or fluid, Kc < Cc, thenthe resonance frequency decreases.

In the model in Fig. 3, the sensor consists of the PZTthin film for driving, the base material (titanium rod),and the PZT thin film for pick up. By considering theinteractions among these parts, the equation of motion iswritten in the form:

md2u

dt2+ Co

du

dt+ SoEo

u

l+ Fo − Fp1 + Fp2 = 0.

(2)

From this equation, the equivalent circuit of this sensor is

Fig. 3. Model of Ti base and PZT thin film. The oscillating rod issupported at the node of the vibration. Then, we can consider thebehavior of the rod by using one-half of the rod.

Fig. 4. Equivalent circuit of the sensor.

obtained as shown in Fig. 4. In this circuit, the pick-upvoltage of the sensor is expressed as:

Vout = −A1A2

ωCd2

Vin

R2 +(ωL− 1

ωC −A2

2ωCd2

)2

×(ωL− 1

ωC− A2

2

ωCd2+ jR

). (3)

At the resonance angular frequency (ω = ωs), the pick-upvoltage is expressed as:

Vout =A1A2

jωRCd2 +A22Vin. (4)

Therefore, by detecting the pick-up voltage, the vibrationcan be detected. Then, the contact can be sensed from thepick-up voltage of the sensor.

Under theoretical consideration, we do not take intoaccount any near field effect. However, it is considered thathydrodynamic friction has some effects [6]. So, to discussthe behavior of the oscillator’s vibration near the surface,we have to consider the hydrodynamic condition.

kanda et al.: a rod-shaped vibro touch sensor 877

Fig. 5. Schematic shape of the sensor.

Fig. 6. Photograph of the sensor.

B. Structure

The structure of the vibro sensor is shown in Figs. 5,6, and 7. Its length and thickness diameter are 27.7 and2.4 mm. The core material of this sensor is titanium. Thetitanium is covered with PZT thin film. The thickness ofthe film is 10 µm. On the surface, there exist four elec-trodes for piezoelectric drive and pick up.

The rod vibrates in the axial direction. One end of therod was formed into an exponential horn. The horn en-larged the vibration amplitude to obtain high sensitivity.The magnification ratio was 4.8.

C. Hydrothermal Method

The PZT thin film formed on this sensor is fabricatedby the hydrothermal method [3]. By using this fabricationmethod, we can obtain the polarized PZT film on titaniumbase. Fig. 8 shows the image of this reaction process. Thisreaction is carried out in a solution that contains Pb2+,Zr4+, and Ti4+. This solution and base material is kept athigh temperature and high pressure.

We used the PZT thin film formed by a single pro-cess hydrothermal method [7]. The reaction conditions areshown in Table I. Fig. 9 shows a scanning electron mi-

Fig. 7. Cross section of the sensor.

Fig. 8. Image of the hydrothermal method.

croscope (SEM) photograph of the surface of the film de-posited by the single process hydrothermal method. Thisreaction was carried out three times so that the thicknessof the film was 10 µm.

The piezoelectric constant d31 was evaluated. This valuecan be calculated from the vibrational amplitude of the bi-morph vibrator and its driving voltage. The displacementof the bimorph vibrator is given by:

δ =3l2

2tYf (1− a2)

Ysa3 + Yf (1− a3)d31E (5)

where l is the length of the vibrator; tf , ts, Yf , and Ys arethe thickness and Young’s moduli of the deposited film andof the titanium substrate; E is the electric field for drivingthe vibrator; and t = ts + 2ts and a = ts/t, respectively[8]. The piezoelectric constant d31 of PZT film deposited bythe single process hydrothermal method was −24 pC/N.This value is a little larger than one-fourth of that of PZTbalk material (Zr:Ti = 52:48; d31 = −93.5 pC/N) [9]. How-ever, this is enough to fabricate oscillators.


TABLE IThe Reaction Conditions of the Single Process

Hydrothermal Method.

Pb(NO3)2 1.204 g Melted in 5.5 ml H2OZrOCl28H2O 0.507 g Melted in 2 ml H2OTiCl4 0.71 mol/l 1.78 mlKOH 2.69 g Melted in 11 ml H2OReaction temperature 140 degreesReaction pressure 3.6 atmReaction period 24 h/l process

Fig. 9. SEM photo of the film deposited by the single process hy-drothermal method.

III. Experimental Results

A. Vibrational Amplitude and Pick Up

To estimate the resonance frequency and the longitu-dinal vibration amplitude, we measured the vibrationalvelocity at the horn tip and the pick-up voltage. Fig. 10shows the scheme of the measurement. We used one elec-trode for driving and another one for pick up. These twoelectrodes exist on the opposite sides of the cylinder. Otherelectrodes were connected to the ground. The driving volt-age was kept at 5 Vp-p. The vibration velocity at the horntip was measured by using a laser Doppler vibrometer.The output voltage from the pick-up electrode was alsomeasured by using a lock-in amplifier.

The results are shown in Fig. 11. As shown in the graph,the resonance frequency was 115.24 kHz. The maximumvalue of the amplitude was 7.9 nmo-p at this frequencywhen the driving voltage was maintained at 5 Vp-p. Fromthe value of the piezoelectric constant d31 of the PZT film,the driving voltage appeared to be too large (about twoorders). The pick-up voltage also had its peak at the res-onance. Hence, it is possible to detect the shift of the res-onance frequency by measuring the pick-up voltage. Themechanical Q factor was 610.

Fig. 10. Set up for the measurement of the vibrational amplitude andpick-up voltage.

Fig. 11. Relationship between the amplitude at the horn tip andpick-up voltage.

The resonance frequency calculated in (1) is 126 kHzwhen there is no contact. Then, the measured value wasabout 10% lower than this value because of the thin partof the middle for support. The vibrational amplitude,7.9 nmo-p, is not such a large value compared with oscillat-ing probes, for example, cantilevers. However, in tappingmode of SPM, the amplitude of the vibration is from somenanometer to 100 nm. Then, the amplitude of this probesensor, 7.9 nmo-p, will be of enough value.

The output voltage contained offset as shown in Fig. 12.This offset was considered because of the induced interfer-ence from the driving current to the pick-up wires. At theresonance, the offset was 7.6 mVrms, and the signal fromthe vibration was only 0.3 mVrms. Therefore, the offsetwas not a negligible error. If the offset is diminished or thevibrational signal is improved, the error will decrease.


Fig. 12. Relationship between pick-up voltage and phase.

Fig. 13. Amplitude at the horn tip and the cylindrical tip.

B. Effect of the Exponential Horn

An exponential horn was used for the enlargement ofthe amplitude at the contact point. The sensitivity of thesensor will increase by this sensor. The magnification ratiois determined by the proportion of the cross-section diam-eter in the larger tip to that in smaller tip. By design,the ratio was 4.8. To estimate the effect of the exponen-tial horn, we measured the amplitude at horn tip and thecylindrical tip. The laser Doppler vibrometer was used tomeasure the amplitude.

The results are shown in Fig. 13. Each amplitude wasproportional to the driving voltage. From the comparisonof the inclination of the two straight lines, the actual mag-nification ratio is 5.2. This value is 8% bigger than that indesign because the shape of the horn was not precisely ex-ponential because of the difficulty making the horn. How-ever, the amplitude at the cylindrical tip was enlarged bythe horn in the horn tip, and the magnification ratio is

Fig. 14. Set up for the measurement of the detection of the contact.

almost the same as the ratio by design. Therefore, the ex-ponential horn effectively enlarges the amplitude.

C. Detection of the Contact

The shift of the resonance frequency caused by the con-tact of the horn-tip with an object was measured from thepick-up signal. We used the measurement set up as shownin Fig. 14 to detect the contact with this sensor and todetermine its resolution. We used a linear stage driven bya stepping motor for large-scale displacement and a multi-layer type PZT element for small-scale displacement. Thedisplacement corresponding to one step of the motor was1 µm of the linear stage. The displacement by the PZT el-ement was 66 nm/1 V D.C. The displacement of the PZTelement was measured by using a capacitance displace-ment meter. Onto the layer-type PZT element, we fixedan aluminum sheet as a workpiece. Then, the test to de-tect the contact was carried out by bringing the workpiececlose to the horn end of the sensor. To determine contact,we also measured the electric resistance between the work-piece and the sensor.

The results are shown in Fig. 15. The graph indicatesthe relationship between the resonance frequency and thedisplacement of the workpiece. The resonance frequencywas sensed from the pick-up voltage, which gave the max-imum value. A contact or non-contact condition was alsodetected by the resistance between the horn tip and theworkpiece. The shift of the resistance and that of reso-nance frequency begins at the same displacement. There-fore, the contact can be detected by monitoring the pick-upvoltage. In this measurement, the workpiece moved every66 nm. Therefore, the resolution of the contact detectionwas higher than 66 nm.

The contact will be detected not only by the shift ofthe resonance frequency, but also by monitoring the de-crease of the oscillator amplitude. We measured the vibra-tion amplitude when the contact took place. In addition


Fig. 15. Resonance frequency shift by the contact.

Fig. 16. Vibration amplitude decrease by the contact.

to the measurement set-up in Fig. 14, the vibration am-plitude at the cylindrical end was measured with the laserDoppler vibrometer. The driving frequency was kept atthe resonance frequency at noncontact.

Fig. 16 indicates the relationship between the shift ofthe vibration amplitude and the displacement. The de-crease in the amplitude appeared at the displacementwhere the resistance changed to null. So, when the con-tact takes place, the vibration amplitude decreased. Asthe vibration amplitude decreases, the pick-up voltage de-creases. When the frequency of the driving voltage is fixed,the contact can be detected by monitoring the pick-upvoltage.

D. Oscillation in Liquid

In liquid, the bending vibrating oscillators, for example,cantilevers, are much influenced by the liquid viscosity.Then, its mechanical Q factor decreases. However, we uselongitudinal vibration. So, the oscillator is not so muchinfluenced by the liquid as by the bending vibration. The

Fig. 17. Relationship between the frequency and the vibrational am-plitude in air and in water. d is the depth of the horn tip from thesurface of water.

TABLE IIOscillation in Liquid (Water).

Resonance Amplitude atDepth frequency resonance Mechanical Q[mm] [kHz] [nmo-p] factor

(In air) 115.03 2.59 6054 114.95 2.31 4118 114.95 2.18 371

Q value becomes higher; then, we can make the resolutionmuch higher.

To estimate mechanical Q factor of this sensor’s vibra-tion in liquid, we measured the vibration amplitude of theoscillator. We measured the amplitude at the cylindricalend. So, the amplitude was not enlarged by the exponen-tial horn. We used pure water as liquid. The tip of theexponential horn was under the surface of water, and itsdepth was 4 and 8 mm.

The decrease of the amplitude is shown in Fig. 17. Theresonance frequency and estimated mechanical Q factorare shown in Table II. The amplitude decreased 16% atbest. The resonance frequency also decreased. This factcan be explained by (1). In this case, the workpiece iswater; so, the coefficient of viscosity is much more effectivethan the module of elasticity.

The Q factor decreases as the depth of the tip increases.When the depth was 8 mm, the mechanical Q factor was61% of that in air. As compared with cantilevers [10], thisdecline of Q factor was very small.

IV. Discussions

The constants of the equivalent circuit elements inFig. 4 were calculated using the horn-tip amplitude, equiv-


TABLE IIIConstants of the Equivalent Circuit.

Resonance frequency [kHz] 115.24Mechanical Q factor 610

L Equivalent mass [H] 1.0× 10−4

C Equivalent capacitance [F] 1.9× 10−8

R Equivalent resistance [Ω] 1.2× 10−1

Cd1 Capacitance [F] 1.3× 10−8

A1 Force factor [N/V] 5.3× 10−5

Fig. 18. Flat-type oscillator.

alent mass, and the mechanical Q value. The constants areshown in Table III.

From Fig. 12, the phase was around 60 degrees. How-ever, by comparing the real part and imaginary part of (4)using values in Table III, the phase of pick-up voltage isderived to be 90 degrees at the resonance. The main causeof this difference is the induced interference of the drivingcurrent. This influence emerged as an offset in Fig. 12. Thisoffset is defined as the value that remains when the reso-nance peak is eliminated from the pick-up voltage. Fromthe measurement, the offset was approximately 23 timesas high as the resonance peak. By this offset, the reso-nance peak would be cancelled, and the sensitivity wouldbe diminished. The offset is thought to be due to the inter-ference of driving current between supply wires. However,from the measurement of capacitance between electrodes,the leakage is derived to be not so serious.

To obtain higher signal to noise ratio, the proportion ofPZT to Ti base has to be increased. If the proportion in-creases, the generating force of the PZT element per unitvolume decreases. Then, the driving voltage for the vibra-tion will be reduced, and the pick-up voltage will increase.Therefore, the resonance peak of the pick-up voltage willbe clearly visible. So, the sensitivity of the sensor can beimproved. As a result, the actual signal of the vibrationwill increase against the leakage signal.

As the oscillator is miniaturized, the proportion of PZTto Ti base increases because the volume of PZT dependson the surface area of Ti base. In addition, if the oscillatorhas a flat configuration as shown in Fig. 18, the proportionincreases.

V. Conclusions

We succeeded in oscillating the rod-shaped sensor anddetecting the contact by using PZT thin film fabricatedby the hydrothermal method. The resolution for detectingthe contact was higher than 66 nm. The horn-end ampli-tude at the resonance was 7.9 nmo-p. So, the resolutionof the sensor would be up to 10 nm. The pick-up volt-age included offset. Then, it influenced the sensitivity andresolution. By improving the structure of the sensor, theinfluence of the offset will decrease. It will be possible toachieve higher sensitivity and resolution by miniaturizingthe sensor and making the resonance frequency higher. Itwill also be effective in liquid.

References

[1] S. M. Harb and M.Vidic, “Resonator-based touch-sensitiveprobe,” Sens. Actuators A, vol. 50, pp. 23–29, 1995.

[2] G. Binnig and C. F. Quate, “Atomic force microscope,” Phys.Rev. Lett., vol. 56, no. 9, pp. 930–933, Mar. 1986.

[3] K. Shimomura, T. Tsurumi, Y. Ohba, and M. Daimom, “Prepa-ration of lead zirconate titanate thin film by hydrothermalmethod,” Jpn. J. Appl. Phys., vol. 30, no. 9B, pp. 2174–2177,Sep. 1991.

[4] T. Morita, M. Kurosawa, and T. Higuchi, “A micro ultrasonicmotor using bending cylindrical transducer based on PZT thinfilm,” Sens. Actuators A, vol. 50, pp. 75–80, 1996.

[5] M. Nishimura, K. Hidaka, M. Teraguti,in Proc. Annu. SpringMeeting JSPE, Tokyo, 1994, pp. 765–766 (in Japanese).

[6] M. Giousouf, M. Weinmann, W. Scheerer, F. Assmus, andW. V. Munch, “Dynamic behaviour of a quartz extensional-mode non-tactile profile sensor,” Sens. Actuators A, vol. 61, pp.287–292, 1997.

[7] T. Morita, T. Kanda, M. Kurosawa, and T.Higuchi, “Single pro-cess to deposit lead zirconate titanate (PZT) thin film by a hy-drothermal method,” Jpn. J. Appl. Phys., vol. 36, no. 5B, pp.2998–2999, May 1997.

[8] Y. Ohba, M. Miyauchi, T. Tsurumi, and M. Daimon, “Analy-sis of bending displacement of lead zirconate titanate thin filmsynthesized by hydrothermal method,” Jpn. J. Appl. Phys., vol.32, no. 9B, pp. 4095–4098, Sep. 1993.

[9] B. Jaffe, W. William, R. Cook, and H. Jaff, Piezoelectric Ce-ramics. New York, NY: Academic Press, 1971.

[10] T. Itoh, J. Chu, I. Misumi, K. Kataoka, and T. Suga, “New dy-namic scanning force microscopes using piezoelectric PZT mi-crocantilevers,” in Proc. IEEE Int. Conf. Solid-State Sens. andActuators, Chicago, IL, 1997, pp. 459–462.

Takefumi Kanda was born in Fukuoka,Japan on June 18, 1972. He received theB. Eng. degree in precision machinery engi-neering from The University of Tokyo, Japanin 1997. He is currently a master course stu-dent of the Graduate School of Engineering.His research interests are microsensor andPZT thin film.

He is a member of the Japan Society forPrecision Engineering.


Takeshi Morita was born in Tokyo, Japanon August 4, 1970. He received the B. Eng.and the M. Eng. degree in precision machin-ery engineering from The University of Tokyo,Japan in 1994 and 1996, respectively. He iscurrently a doctor course student of the Grad-uate School of Engineering. His research inter-ests are microultrasonic motor and PZT thinfilm.

He is a member of the Institute of Electri-cal Engineers of Japan, the Ceramic Societyof Japan, and the Japan Society for PrecisionEngineering.

Minoru Kuribayashi Kurosawa (formerlyKuribayashi) (M’95) was born in Nagano,Japan on April 24, 1959. He received theB. Eng. degree in electrical and electronicengineering and the M. Eng. and Dr. Eng.degrees from Tokyo Institute of Technology,Tokyo in 1982, 1984, and 1990, respectively.

He was a Research Associate at the Pre-cision and Intelligence Laboratory, Tokyo In-stitute of Technology, Yokohama, Japan from1984. Since 1992, he has been an AssociateProfessor at the Graduate School of Engineer-

ing, The University of Tokyo, Tokyo, Japan. His current research in-terests include ultrasonic motor, microactuator, PZT thin film, SAWsensor and actuator, and single-bit digital signal processing and itsapplication to control systems.

Dr. Kurosawa is a member of the Institute of Electronics Informa-tion and Communication Engineers, the Acoustical Society of Japan,IEEE, the Institute of Electrical Engineers of Japan, and the JapanSociety for Precision Engineering.

Toshiro Higuchi (M’87) was born in Ehime,Japan on February 26, 1950. He received theB. E., M. S., and Ph.D. degrees in precisionengineering from The University of Tokyo,Japan in 1972, 1974, and 1977, respectively.He was a Lecturer at the Institute of Indus-trial Science, The University of Tokyo in 1977and an Associate Professor in the same insti-tute from 1978. Since 1991, he has been a Pro-fessor at the Graduate School of Engineering,The University of Tokyo. His present interestsinclude mechatronics, magnetic bearing, step-

ping motors, electrostatic actuator, robotics, and manufacturing.Dr. Higuchi is a member of the Japan Society for Precision Engi-

neering, the Japan Society of Mechanical Engineers, and the Societyof Instrument and Control Engineers.

a rod-shaped vibro touch sensor using pzt thin film · [email protected]). fig. 1....

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