T lizes the Rayleigh wave. The Rayleigh wave is one of

Transcription

1 EEE TRANSACTONS ON LrLTRASONCS, FERROELECTRCS, AND FREQUENCY CONTROL, VOL. 46, NO. 4, JULY Sirnula.tion of Surface Acoustic Wave Motor with Spherical Slider Takeshi Morita, Minoru Kuribaj ashi Kurosawa, Member, EEE, and Toshiro Higuchi, Member, EEE Abstract-The operation of a suri'ace acoustic wave (SAW) motor using spherical-shaped sliders was demonstrated by Kurosawa et al. in t was necessary to modify the previous simulation models for usual ultrasonic motors because of this slider shape and the high frequency vibration. A conventional ultrasonic motor has a flat contact surface slider and a hundredth driving frequency; so, the tangential motion caused by the eksticity of the slider and stator with regard to the spherical slider of the SAW motor requires further investigation. 11 this paper, a dynamic simulation model for the SAW motor is proposed. From the simulation result, the mechanism of the SAW motor was clarified (i.e., levitation and contact conditions were repeated during the operation). The transient response of the motor speed was simulated. The relationships between frictional factor and time constant and vibration velocity of the stator and the slider speed were understood. The detailed research regarding the elastic deformation caused by preload would be helpful to construct ;in exact simulation model for the next work., NTRODUCTON HE SAW motor if, a promising linear actuator that uti- T lizes the Rayleigh wave. The Rayleigh wave is one of the SAW that can be generated easily viith DT (interdigital transducer) on piezoelectric material such as LiNbO3 or crystallized quartz. i'ibration amplitude attenuates exponentially into the depth direction, and vibration energy is concentrated near the surface. Therefore, the reverse side that does not vibrate can be held. The purpose of this paper is to prspose a simulation model for a SAW motor [l],[a] to clarify a mechanism of an operation principle. The concentrated vibration energy is useful for conversion to slider motion compared with the general ultrasonic motor. Because of a high operating frequency, the amplitud? of the SAW devive is not larger than a low frequency bending vibration. So, the slider contact surface should be spherical to enlarge contact pressure and to achieve a smooth (contact as reported [l]. Ordinarily, ultrasonic motors have a flat contact surface slider or rotor. Hence, the simulation rnodel did not mention the tangential motion of slider or -otor [3]. The SAW motor had a spherica 1-shaped slider; therefore, a dynamic model is required because the contact condition is varied during the operation. A contact force between the slider Manuscript received July 6, 1998; accepted December 10, The authors are with Department of Precision Machinery Engineering, Graduate School of Engineerin!,, The University of Tokyo, Hongo, Bunkyo-ku, Tokyo 113, Japan ( moritaqintel1ect.pe.u-toe,yo.ac.jp). Soft material \ traveling wave propagation -\ DT for reverse motion DT(400pm pitch, 20 pairs) Fig. 1. LiNb03 and DT for generating SAW. Stator transducer 128 degrees rotated y-cut x-propagation LiNb03 Traveling wave P Fig. 2. Principle of the SAW motor. Vibration velocity and the stator, a frictional force, tangential position of the slider, and normal position of the slider are calculated step by step in our simulation. Hertz contact theorem was used for calculation of the contact force. Namely, the previous model for ultrasonic motors was modified for a SAW motor in this paper. To improve SAW motor performance, the simulation model will be effective. 11. SUMMARY OF THE EXPERMENTAL RESULTS SAW MOTOR OF THE Takahashi et al. [a] used 128 degrees rotated y-cut x- propagation LiNbOy as a stator transducer of a SAW motor. An example of this stator transducer is shown in Fig. l [l],[2]. DT pitch was 400 pm so that the driving frequency was 9.6 MHz. With a RF power source to the DT, the electrical energy is converted to mechanical vibration energy. The elastic traveling wave is propagated through the surface of the LiNbOs. At the end of the stator transducer, the traveling wave is absorbed by the soft material. While the traveling wave is generated, each particle of the stator surface moves elliptically, as shown in Fig. 2. When the traveling wave is transmitted from right to left, the elliptical motion at the surface is counterclockwise. The driving frictional force for the SAW motor is caused by the elliptical motion EEE

2 930 EEE TRANSACTOSS or ULTRASOZCS, FERROELECTRCS..AM FREQCES~Y CONTROL. 1-0~. 46, NO. 4> JUL\ Steel bat1 slider Slider ) Fix Fig. 3. Experimental set-up for controlling preload L_1 z a a w & mN ---B -3.7mN OmN Time [msec] Fig. 4. Experimental results of transient response with different preload variables. The normal direction amplitude of the Rayleigh wave was only 20 nmpeak at the driving voltage of 180 Vp&j so, some contrivance for the friction drive was required. Kurosawa et al. [l] used tiny spherical balls as a slider for smooth contact with the stator transducer and higher contact pressure between the stator and the slider. The radius of the slider ball was 1 mm. Preload was controlled by magnetic force, as shown in Fig. 3. The experimental result showed that the transient response of the slider ball was very quick [3], as is shown in Fig. 4. To sum up the major characteristics of the SAW motor, quick response, high speed, and high output force are important. From Fig. 4, the output force with 7 mn preload was calculated to about l mn. Hence, the contact area diameter was about 6 pm; and the output force density was 35 N/mm2 [3]. Therefore, by using a multi-contact slider that has spherical surface balls, the SAW motor generated a larger output force as Chiba et al. [6] reported. Our simulation methods and these results would be effective to consider not only the single but also the multi-contact spherical surface slider operation DFFERENCE BETWEEN SAW MOTOR AND USUAL ULTRASONC MOTOR A high frequency SAW motor and a low frequency traveling wave type ultrasonic motor have similarities in that i/. \ Stator traveling wave Fig. 5. Simulation model for usual ultrasonic motor. they utilize the particle elliptical motion of the traveling wave. High operating frequency such as 10 MHz of SAW causes the smaller amplitude compared with the usual ultrasonic motor at less than 100 khz. The amplitude of a SAW is less than 20 nm, which is much smaller than that of an ultrasonic motor (about 1 pm). Kurosawa et al. [l], [4] and Takahashi et al. [2] proposed that high contact pressure between the slider and the stator was effective for SAW motor operation. This is the main reason why a spherical-shaped slider ball was adopted. High pressure is also effective in the prevention of squeeze film air between slider and stator. n most cases of usual ultrasonic motor simulations, the slider has a flat contact surface, and the traveling wave is generated in the stator transducer. Only the stator contact surface is regarded to be sine in shape. By preload, the pressure distribution between the stator and the slider was generated. This pressure deformation was calculated by using static contact equation. The sine-shaped deformation of the stator transducer largely influences the pressure distribution. During the motor operation, the contact area moves, although the pressure distribution, contact width. and contact force between the slider and the stator is fixed, as is shown in Fig. 5. Therefore, the static consideration is sufficient, and a discussion about a dynamic model is not necessary on condition that the slider (or rotor) speed is lower than the wave propagating velocity of the slider or the stator material [5]. The SAW motor ha5 a spherical slider, and it is expected that the contact condition is changing during the operation. as shown in Fig. 6. Dynamic simulation is required. Of course. when the spherical-shaped rotor was used for an ultrasonic motor, our simulation model would be applied. V. SMULATON MODEL The dimensions and parameters of the stator transducer and the slider are shown in Table. These values are decided by reported papers [l],[a]. The coordinates are defined as shown in Fig. 7. The traveling wave is transmit-

3 MORTA et al.: SMULATOV OF SURFACE ACOUS'rC WAVE MOTOR 931 5,-x yslider oslider h Fig. 6. Modified simulation model for SAW motor using the sphericalshaped slider. TABLE PARAMET 3RS USED FOR SMUL 4TON. O X Xslider,Xeip b X Young's modulus of stirel ball 2.15 x 1011 N/m2 Young's modulus of LiNbO x loll N/m2 Poisson ratio of steel kall 0.29 Poisson ratio of LiNb Radius of steel ball 0.5 mm Weight of steel ball 4.0 mg Vibration amplitude 0. SAW (vertical) 19 nm Vibration amplitude os SAW (horizontal) 0.7 x 19 nm nput voltage 180 Vpeak Driving frequency 9.6 MHz Frictional factor 0.47 ted from the right in Fig. 7. The deformation of the stator transducer caused by the traveling wave is expressed as: uellip z= A sin(wt + Jczs1ic er) (1) where A is the vibration amplitude and k is the wave number. This value gellip is the particle position of the stator where the slider exist;;. The slider position is expressed as xslider. The particle motion is elliptical, so the traveling wave has a tangential displacement, which is expressed as: Zellip = Aa cos(wt + kxsl,der) (2) where Q is the ratio of the tangential amplitude to the normal amplitude. n this case, a is 0.7. During operation, two slider situations are considered, as shown in Fig. 6. O'ne situation is a evitation, and the other is a contact sixation. A parameter d is used for judgment whether the slider is contacting or levitating, expressed as: d = Yslider -!/ellip!/slider - A sin(wf + kxslider) where Yslider is the normal position of the slider. f d < 0, the slider contacts the slide, and if d > 0, then the slider is levitating. Between these conditions, thi: motion equations are different. When the slider is levitating, narriely yell;p < uslider, the motion equations are as follows: (3) Fig. 7. Definition of each force and position. where P is the preload to the slider and A4 is the mass of the slider. On the other hand, when the slider is contacting the stator, the slider obtains frictional force in a tangential direction. The direction of the frictional force depends on the tangential velocity of the stator particle and the slider velocity. Tangential velocity means the vibration velocity of the particle to the C direction at the contact point, Cslider. Under the condition wellip > 'Uslider, the frictional force and the slider velocity are in the same direction. Namely, tangential force from the stator to the slider is positive, and the slider is accelerated to the C direction. The motion equation is expressed as: M- d'xslider =F- uslider = pn- Vslider dt2 Vslider 1 (vslider 1 on condition that (5) -Aaw sin(& + kxslider) 1 where p is the frictional factor. To the contrary, when Wellip < uslider, the frictional force is negative for the slider because the frictional force direction is the reverse of the moving direction. So, the slider speed would be decreased. dayslider M-----=NNp-A4g dt2 d2xslider - uslider lvslider M- F- = -pn- dt2 on condition that uslider Vslider The contact force between the slider and the stator was calculated for each position (yslider and yenip) using Herzian contact theorem as:

4 932 EEE TRANSACTONS ON ULTRASONCS, FERROELECTRCS. AD FREQUENCY CONTROL. \-OL. 46, NO. 4. J. L\ 1999 " Time [msec] Fig. 8. Simulation results of transient response with different preload variables Time [ysec] (4 where El and E2 are Young's moduli, and p1 and p2 are Poisson's ratios of steel ball and LiNb03. To calculate the velocities and the position step by step, the Euler method was used as: dx x(tn) = x(tn-l) + -((t,-i)at dt -(in) dx dx d2x + d'x dt = -((tn-l) dt -(tn-l)at. dt2 The acceleration was calculated from the motion equations (6) and (7), which were described previously. Driving frequency of the SAW motor was 9.6 MHz and cycle time was about 100 ns. Calculation was done with 1 ns step time, which is enough to calculate for the simulation. Used hardware specification was Sun Super Sparc2 compatible (Japan Computer Corp.), and the operating system was Sun O.S V. RESULTS Simulation results show that the slider was driven in the reverse direction of the traveling wave propagation. The slider speed was saturated as shown in Fig. 8. As the preload became larger, the time constant and convergent speed decreased, and the output force increased. Output force was calculated from a time constant and steady-state speed in the same way as in the previous paper [l],[2], which reported experimental results. This tendency is similar to the experimental result. However, there seems to be a difference in that the experimental results have an optimum preload for maximum output force. This difference may result from the assumption that the elliptical locus is not influenced by the preload in the simulation model. For further consideration of the proposed simulation model, the conditions of the slider position, the slider speed, and the driving force are shown in Figs. 9 and L Time [pec] b) Time [pee] (c) Fig. 9. (a) Driving force, (b) slider speed, and (c) slider position versus time at the starting point of transient response (preload 7.0 mn). The preload is fixed to 7 mn, which is the optimum preload in the experimental result. The starting time of Fig. 9 is 0 ms, and that of Fig. 10 is 2 ms. Referring to Fig. 8 with 7 mn preload, the slider speed saturated at 2 ms. So, Fig. 9 shows the situation before saturation, and Fig. 10 shows the saturated point. From these graphs, the mechanism of the SAW motor operation was clarified. Before saturation time, the ratio of the driving force is larger compared with that of the reverse force. Here, an average driving force per

5 MORTA et al.: SMULATON OF SURFACE ACOU;TC WAVE MOTOR /a / Time [2msec+us] (4 - / Time [msec] Time[2msec+ps] (b) 1 Time[2msec+psl (c) Fig. 10. (a) Driving force, (b) slider speed,.md (c) slider position versus time at the convergence point of tranc.ient response (preload 7.0 mn). cycle (Fave) is defineld as: where T is a period of driving frequency. At the starting situation, F, is positive as is showii in Fig 9; so, the slider is driven in the +x direction. The convergent speed is fixed E, to be 0. As described before, simulation remlts agree qualitatively with the experimental results. And, it clarifies the principle of the SAW motor, which has a spherical-shaped steel ball, Our simulation model has a variable parameter, Frictional Factor (p) (b) Fig. 11. (a) Simulation results of transient response with frictional coefficient; (b) the relationship between frictional coefficient and time constant. namely the frictional coefficient p. This parameter p determines the time constant, as shown in Fig. ll. t should be noted that the convergent speed was not under the influence of the change of p. This parameter p is adopted as 0.47, which is experimentally measured. To fit the time constant of simulation and experimental result, a parameter p should be equal to Similarly, the vibration amplitude det,ermines the convergent speed. The quantitative difference between the simulation and the experimental results may come from the disregard for a change in p and amplitude because of the preload. Now, we are trying to estimate these factors. V. CONCLUSON Our dynamic simulation model, which utilized the Hertz contact theorem, was effective for SAW motor operation analysis. The levitation and contact condition was con-

6 934 EEE TRANSACTONS ON ULTRASONCS, FERROELECTRCS. AND FREQUEWY CONTROL. 1-OL. 46, NO. 4, JULY 1999 firmed, and the velocity saturation mechanism was clarified. This investigation is the first trial to construct a model for the SAW motor; so, exact quantitative agreement was not realized. Detailed measurement of frictional factor and analysis of wave deformation because of preload is required for a precise model. REFERENCES M. Kurosawa, M. Takahashi, and T. Higuchi, An ultrasonic X- Y stage using 10 MHz surface acoustic wave, in Proc. EEE Ultrason. Symp., Cannes, France, 1994, pp M. Takahashi, M. Kurosawa, and T. Higuchi, Direct frictional driven surface acoustic wave motor, in Proc. nt. Conf. Solidstate Sens. Actuators, Transducers 95, Stockholm, Sweden, 1995, pp M. Kurosawa, M. Takahashi, and T. Higuchi, Elastic contact conditions to optimize friction drive of surface acoustic wave motor, EEE Pans. Ultrason., Ferroelect., Freq. Contr., vol. 45, no. 5, Sep M. Kurosawa, M. Chiba, and T. Higuchi, Evaluation of a surface acoustic wave motor with a multi-contact-point slider, Smart Materials and Structures, vol. 7, no. 2, Jun H. Hirata and S. Ueha, Revolution speed characteristics of an ultrasonic motor estimated from the pressure distribution of the rotor, Jpn. J. Appl. Phys., M. Chiba. M. Takahashi. M. vol. 31; suppl. 31-1, pp :, Kurosawa, and T. Higuchi, Evaluation of a surface acoustic wave motor, in Proc. EEE Workshop on Micro Electro Mechanical Systems, Nagoya, Japan, 1996, pp Minoru Kurosawa (formerly Kuribayashi) (M 95) was born in He received the B. Eng. degree in electrical and electronic engineering and the M. Eng. and Dr. Eng. degrees from Tokyo nstitute of Technology, Tokyo in 1982, 1984, and 1990, respectively. He was a Research Associate at the Precision and ntelligence Laboratory, Tokyo nstitute of Technology, Yokohama, Japan from Since 1992, he has been an Associate Professor at Graduate School of Engineering, University of Tokyo, Tokyo, Japan. His current research interests include ultrasonic motor, micro actuator, PZT thin film, SAW sensor and actuator, and 1-bit digital control system. Toshiro Higuchi (M 87) was born in He received the B.S., M.S., and Dr. Eng. degrees in precision engineering from University of Tokyo, Japan in 1972, 1974, and 1977, respectively. He was a lecturer at the nstitute of ndustrial Science, University of Tokyo from 1977 to 1978 and an Associate Professor from 1978 to Since 1991, he has been a Professor in the Department of Precision Engineering, University of Tokyo. His research interests include mechatronics., maa- netic bearing, electrostatic actuator, stepping motors robotics, and manufacturing. Takeshi Morita was born in He received the B. Eng. and the M. Eng. degrees in precision machinery engineering from the University of Tokyo, Japan in 1994 and He is currently a doctor course student of the Graduate School of Engineering. His research interests are micro ultrasonic motor and PZT thin film.