Characteristics of a Hybrid Transducer-Type Ultrasonic Motor

Transcription

1 I X8 IEEE TRANSACTIONS ON ULTRASONICS. FERROELECTRICS, AKD FREQUENCY CONTROL. VOL. 38. NO. 3. MAY I991 Characteristics of a Hybrid Transducer-Type Ultrasonic Motor Kentaro Nakamura, Minoru Kurosawa, and Sadayuki Ueha Abstract--A hybrid transducer type ultrasonic motor, which the authors proposed previously, employs two ultrasonic transducers to control the Lissajous figure at the contact surface of the stator. This motor is stable even at low speed, and realizes a large output with a high efficiency, due to the high controllability of the Lissajous figure. The experimental investigation of the characteristics of the hybrid transducer type ultrasonic motor is presented. In addition, the maximum torque is roughly estimated by means of a simple model. Then, the dependence of the diameter of the motor (transducer) on the maximum torque is discussed and demonstrated experimentally. I. INTRODUCTION HE ROTOR of the ultrasonic motor is driven through T the frictional force by the high frequency elastic vibration excited on the stator with the piezoelectric effect. Those unique properties such as a large torque at low speed, a quick response and an ability to maintain the position without electric power have begun to arouse wide user interest recently. To realize the ultrasonic motor, two vibration components that are orthogonal spatially and out of phase temporally by 90" are used; one is tangential to the rotor and acts as a driving force. and the other is perpendicular to the rotor and controls the frictional force. Thus, in general, the Lissajous figure of the vibration is elliptic. Several types such as a traveling wave type [ l]-[3] and a vibration conversion type [4]-[7] have been proposed hitherto. In these types, however, the two vibration components are coupled, and the ellipticity of the Lissajous figure of the vibration is peculiar to the mode used, so it is difficult to operate stably at very low speed (i.e., at low vibration amplitude). Because if we reduce the driving component of the vibration to operate the motor at low revolution speed, the component that controls the friction also decreases at the same time and does not work well due to the surface roughness of the rotor. To overcome this difficulty, the authors proposed a hybrid transducer type [8], [9] that generates two vibration components independently. The hybrid transducer that acts as a stator of the motor is composed of a torsional vibrator and a multilayered piezoelectric actuator; the for- Manuscript received June 18, 1990; revised October and November : accepted November 26, The authors are with the Research Laboratory of Precision Machinery and Electronics, Tokyo Institute of Technology, 4259 Nagatsuta. Midorlku, Yokohama 227, Japan. IEEE Log Number mer generates the driving power and the latter controls the frictional force. The key feature of this type is controllability of the Lissajous figure. The authors had already made this motor for trial and confirmed its realizability in [8], where we employed a torsional vibrator 50 mm in diameter and three cubic (5 x 5 X 6 mm3) multilayered actuators. However, some structural problems such as the parasitic bending vibrations excited in the actuators, problems with the choice of the adhesive and the frictional material prevented the further investigation, and the precise characteristics were not clear. In this paper, after our previous work, we fabricate a hybrid transducer type rotary motor 20 mm in diameter with a circular actuator and realize a stable operation. Using this motor, we examine the various characteristics experimentally. In addition, the maximum torque is calculated by means of a simple model. Then, relations between the diameter of the motor (transducer) and the maximum torque is discussed. 11. CONFIGURATION OF THE MOTOR Fig. 1 shows the configuration of the motor. A hybrid transducer that acts as the stator of the motor consists of a bolt-clamped Langevin type torsional transducer and a multilayered piezoelectric actuator. The construction of the torsional transducer is shown in Fig. 2. Two piezoelectric ceramic (PZT) disks 20 mm in diameter and 4 mm thick, are sandwiched by two duralumin blocks with a bolt. To excite the torsional stress, the PZT disks are polarized in circumferential direction and the electric field is applied in the axial direction. For the purpose of polarization, the disk is once divided into six or eight fanshaped pieces. After polarizing each of them, we arrange them in circular form again. Fig. 3 shows the multilayered piezoelectric actuator. We employed a circular one in order to prevent undesirable vibration and improve the strength of adhesion. The outer diameter, the inner diameter and the height are 18.5 mm, 7.5 mm and 9.0 mm, respectively. The number of layers is The actuator is bonded to the torsional transducer with epoxy adhesive. Since there is no mutual coupling between the torsional vibration and the longitudinal vibration, as is known, we can excite each vibration independently. Experimentally, we found negligible coupling between torsional and longitudinal ports when one was excited and the other's output measured. The torsional resonance fre-

2 symbols NAKAMURA ef ul.: CHARACTERISTICS OF A HYBRID TRANSDUCER-TYPE ULTRASONIC MOTOR l89 1 Stator Torsional Vfbrator &l Fig. I. Configuration of the motor Fig. 4. Principle of the motor B BLOCK Fig. 2. I m~gevln type torsional transducer. The + hymbolh rection of polarizatlon. the dl- Fig. 3. (a) Circular nlultilayered plemelectric actuator. (h) Arrangement of the electrode\ of the multilayered actuator. The + show the drrection of polarization. quency of the hybrid transducer was 24.5 khz, while the longitudinal one was 43.0 khz. The driving frequency for both torsional part and longitudinal part are tuned at the torsional resonance frequency 24.5 khz, because the torsional vibration needs to efficiently generate large power to drive the rotor. On the other hand, though the longitudinal vibration is stimulated out of its resonance, we can obtain sufficient force to control the friction by virtue of the multilayered actuator. A coil spring presses a rotor to the hybrid transducer with a static force F to obtain sufficient vibration. force. frictional 111. PRINCIPLE OF THE MOTOR We drive the torsional transducer and the actuator with a certain phase difference so that the Lissajous figure may be elliptic. In other words, the phase difference between the torsional vibration and the longitudinal one should be 90". Fig. 4 describes the sequence of operation, where one period is divided into four phases (1) - (4). The states at each phase are summarized as follows. l) The torsional vibration velocity is at the maximum, and the actuator extends to clutch the rotor. Then the rotational driving force is transmitted to the rotor. 2) The torsional vibration velocity is equal to zero. The displacement of the actuator is also zero. 3) The direction of torsional vibration velocity is opposite to that of the rotor's revolution. The actuator shrinks not to touch the rotor. 4) Both the torsional vibration velocity and the longitudinal displacement are zero. Only at phase 1) the stator is in contact with the rotor. If we change the phase by 180, we can reverse the revolution direction. We mention here that we should make the phase difference between the applied voltages for the longitudinal and the torsional part 0 or 180", since the torsional vibration is stimulated at its resonance, while the longitudinal one is driven out of resonance. IV. ESTIMATION OF THE MAXIMUM TORQUE In this section, we estimate the maximum output torque being based on some rough approximations. The authors have tried to establish a suitable model of the motor and simulate its operation numerically [ 101. The model employed here is based on the same idea, but much simplified. The rotational force is transmitted to the rotor through the friction determined by the force normal to the contact area. Then we should. in the first place, evaluate the dynamic normal forcefthat is generated by the longitudinal assumptions: some We here, make,

3 I90 IEEE TRANSACTIONS ON ULTRASONICS. FERROELECTRICS. AND FREQUENCY CONTROL, VOL. 38. NO 3. MAY 1991 Rotor 01 0 v,cos W1 Twin Zener Diode T1:pfr Fig. 5 Sketch ofthe dynamic normal forcefand the longitudinal displacement xi.. '2~5~ is contact duration. Fig. 6. Equivalent circuit for the torsional vibrator and the transmission of the rotational force where T is the instantaneous driving torque, while Q represents the speed of revolution of the rotot, 1) The position of the rotor along the axis does not change, because the mass of the rotor is large enough. 2) The time average of the dynamic forcefis equal to the static force F of the coil spring; f= F, (1) where the bar represents taking the time average. Therefore, the longitudinal displacement at the top of the stator xl and the dynamic forcefare thought to be as illustrated in Fig. 5, where the applied voltage to the multilayered actuator is V, cos wt. We define 2$Ic as a contact duration, and it is a function of F and V,,,. Then, f = 0 (for qbc < wt 27r - qbc), (for 0 < wt < or 27r - wr < 27r) where B is the force which the multilayered actuator generates for a unit voltage, while k is the function of and determined by calculating (1). In the second place, we introduce an equivalent circuit for the rotational motion as shown in Fig. 6, where C, and r,, represent the clamped capacitance and the motional resistance of the torsional vibrator, respectively. The transformation factor, which couples the electric arm and the torsional mechanical arm, is indicated by A. Since the moment of inertia of the rotor is large enough, we assume that the speed of revolution is constant and a current source Q represents the rotor in the equivalent circuit. The instantaneous torque 7 that drives the rotor never exceeds the frictional torque pfr: (2 171 S p"fr (3) where p and rare the frictional coefficient and the contact radius. In the circuit, we describe this by a twin Zener diode, that is composed of two back to back connected Zener diodes and has a bidirectional characteristics as shown in Fig. 7. Then, the Zener voltage V, is equal to pfr. We further define that the output torque of a motor is the time average of the instantaneous torque T: T = 7. (4) The expression of the instantaneous torque T changes depending on the slip between the rotor and the stator, where the slip is defined by the torsional vibration velocity Q(, and the revolution speed of the rotor Q: Then 1) slip = 0, 2) slip > 0, 3) slip < 0, (slip) = Q,) - a. (5) r = AVTcos wt - rmq. (6) r = pfr. (7) r = -pfr. (8) Let us consider the maximum torque T, (revolution Q = 0), for the special case where the contact duration is shorter than a half period: 2& < 7r. (9) If the applied voltage to the torsional vibrator V, is low, (3) is always satisfied (slip = 0). Then, and T = AV, COS wt (10) On the other hand, if V, is so large that 7 is always limited by the frictional force (slip f 0): so T = pfr (12) To = - pfr = pfr. (13) Equations (11) and (13) show that the maximum torque increases in proportion to the applied voltage until it is

4 NAKAMURA et d.: CHARACTERISTICS OF A HYBRID TRANSDUCER-TYPE ULTRASONIC MOTOR 191 saturated at the limitation of the frictional force determined by the static force F and the frictional coefficient. It can also be predicted that the saturation value of T, becomes smaller than p Fr if the contact duration is larger than a half period, since for a certain part of the period 7 is described by (8)..l V. CHARACTERISTICS In this section, we investigate the characteristics of the motor experimentally. First, we show the relations between the speed of revolution and the driving phase difference $. When the frequency of an oscillator was tuned to the torsional resonance frequency 24.5 khz, the speed of revolution became the maximum at $I = 0 and the direction was inverted at $I = 180 as shown in Fig. 8. In the case of driving out of resonance (24 khz and 25 khz), the peak of the speed of revolution shifted because of the change in the phase of the torsional vibration, and at the same time, the maximum value was reduced. These resultshows good agreement with the principle described previously. Then, we measured the speed of revolution as a function of the applied voltage to the actuator VM. The results are shown in Fig. 9, where F denotes the static force pressing the rotor. The speed of revolution increased as the voltage became large. Too large a V, reduced the speed of revolution, since too strong a longitudinal vibration made the contact unstable. To realize the same speed of revolution with a large pressing force F, we have to increase the voltage to the actuator VM. It is thought that these two values determine the contact duration. Next, Fig. 10 summarizes the relation between the speed of revolution and the applied voltage to the torsional vibrator V,. Here, the ratio of V, to F was kept constant to maintain the contact duration same. The revolution became large as V, increased. Although the linearity of the curve is not excellent, the low speed operation is possible, since the gradient of the curve is not very sharp. In Fig. 11, the maximum torque was plotted against the applied voltage to the torsional vibrator V,. The maximum torque increased in proportion to V, until it was saturated at a certain voltage. The rigid lines show the rneasured torque, while the dotted ones represent the calculated value according to Section IV. They agreed well each other, except that the saturation levels for the measured data were lower than p Fr. This implies that the real contact duration is longer than designed, and, the surface roughness is thought to have a large influence on this. To predict the exact contact duration, we need to improve the model used in Section IV. The load characteristics were measured as shown in Fig. 12. These curves showed decreasing characteristics; the speed of revolution was reduced linearly with the load torque. In Fig. 12(a), the decreasing set of curves showed good linearity, since F was large and the frictional limitation was high enough. But, in Fig. 12(b) where F is Fig. 8. Speed of revolution againsthe phase difference between the applied voltages. Fig. 9. Speed of revolution as a function of the applied voltage to the multilayered actuator (MPA), where F is the pressing force by a coil spring. P I I I Appl~ed Voltage to TBLT I Vrms I Fig. 10. Speed of revolution as a function of the applied voltage to the torsional transducer (TBLT), where F and V, denote the pressing force by a coil spring and the applied voltage to the actuator, respectively. col / Appffed Voltage to TRLT V, lvrmzl Fig. 11. Maximum torque as a function of the applied voltage to the torsional transducer (TBLT). Rigid lines show the measured torque, and dotted lines the calculated torque.

5 I92 IEEE TRANSACTIONS ON ULTRASONICS, FERROELECTRICS, AND FREQUENCY CONTROL, VOL. 38. NO. 3, MAY 1991 Torque(kgf.cm) (a) Fig. 14. Torsional PZT disk E 1. Torque(kgf.cm) (b) Fig. 12. Load characteristics. (a) F = 40 kgf. V,u = 7 V,,,,, (b) F = IO kgf. V, = 7 V,,,,,. Fig. 15. Relation between the maximum torque and the diameter of the motor (transducer) Fig. 13. Input electric power P,, to the torsional transducer and efficiency 7. where F = 40 kgf, V, = 7 V,,,,,, and V, = 250 V,,",. can generate determines the maximum torque as a motor. As is illustrated in Fig. 14, the output torque of the torsional PZT TPZT for an unit voltage can be calculated as follows [ 1 l]. A small element, ds in area, t in thickness and located at the distance r from the central axis, generates the torque for a unit voltage: dtpzt = eisr ds/t. (14) Then, integrating dtpz, over the area: small, you can observe the effect of the frictional limitation in the curve for V, = 200 Vms. Fig. 13 presents the input electric power Pi, to the torsional vibrator and the efficiency that is the ratio of the mechanical output power to P,,, and the speed of revolution for V, = 250 Vms. The input power decreased as the speed of revolution was reduced by the load torque, because the impedance of the torsional transducer became high according to the load torque. The maximum torque was about 3 kgf. cm, and the maximum efficiency was nearly 40%. The power consumption of the multilayered actuator was about 2 W, and then the overall efficiency of the motor was about 21 %. VI. SIZE AND THE MAXIMUM TORQUE As is described in Section IV. the maximum torque is proportional to the applied voltage to the torsional vibrator unless it goes up to the limitation of the frictional force. In other words, the torque the torsional PZT disk where do, d,, t, and e15 indicate outer diameter, inner diameter, thickness and piezoelectric stress constant, respectively. You can see that TPzT is approximately proportional to the cube of the diameter. Therefore, it can be predicted that the maximum torque of a motor is also proportional to the cube of the diameter of the motor (transducer). In addition to the motor 20 mm in diameter, we fabricated motors 11 mm and 30 mm in diameter. The result, as plotted in Fig. 15, agreed well with the previous discussion. VII. CONCLUSION The characteristics of a hybrid transducer type ultrasonic motor have been studied experimentally. The maximum torque 3 kgf. cm was marked with a motor 20 mm in diameter. About 40%, at the maximum, of the input

6 NAKAMURA c/ al.: CHARACTERISTICS OF MOTOR A HYBRID TRANSDUCER-TYPE ULTRASONIC 1Y3 electrical power to the torsional transducer was transformed to the mechanical output power, and overall efficiency of the motor was 2 1 o/c. The maximum torque of the motor was discussed by means of a simple model. It is proportional to the applied voltage to the torsional vibrator. but it never exceeds the frictional torque determined by the static pressing force of the spring and the frictional coefficient. This limit of the maximum torque of the experimental motor turned out smaller than predicted. To design the limit exactly, an improved model is needed to describe the dynamic normal force at the contact surface. The maximum torque is nearly proportional to the cube of the diameter of the motor (transducer). REFERENCES [l] T. Saahida, Japanese Pat. No , Feb. 25, M. Kurosawa and S. Ueha. High speed ultrasonic linear motor with high transmission cfficxncj. U/tro.wu., v no. 1. pp Jan [3] M. Kurosawa, K. Nakamura, T. Okarnoto. and S. Ueha, An ultrasonic motor using bending vibrations of a short cylinder, leee TruuT. Ulrruson. Ferroelec. Freq. Confr.. vol. 36. pp Sept. ly T. Sashida, Trial construction and operation of an ultrasonic vibrdtion driven motor, OwBur.turi, vol. 51, no. 6. pp (in Japanese). 15) A. Kurnada, A piezoelectric ultrasonic motor. Jupuncse J. Appl. Phv.\., vol. 24. SUPPI pp [6] J. S. Schoenwald, P. M. Beckman, R. A. Rattner, B. Vanderlip. and B. E. Shi, Exploiting solid state ultrasonic motors for robotics, Proc. IEEE 1988 Ulrrasotz. Symp., vol. I. pp M. Fleischer, D. Stein, and H. Meixner, Ultrasonic motor with longitudinally oscillating. amplitude-transforming resonator, leee Trurzs. Ulrruson. Ferrorlec. Frey. Conrr.. vol. 36. no. 6. pp Nov M. Kurosawa and S. Ueha, Hybrid transducer type ultrasonic motor, IEEE Truns. L ltrmon. Ferroelec. Frey. Conrr.. vol. 38. pp , Mar. I M. Kurosawa, H. Yamada. and S. Ueha. Hybrid transducer type ultrasonic linear motor. Juptrrwse J. 4ppl. Phm.. vol. 28. suppl pp [ I O ] M. Kurosawa and S. Ueha. Numerical study ot hybrid transducer type ultrasonic motor. in Pwc. l3rh Irrr. Con,yrc,.\s.4(,i)it.$I.. v01 3. no. 9.4, pp [ I I I S. Nemoto and E. Mon. Bolt-clamped electrostrictlve torsic~nal v- brator. J. ilcoust. Soc. Jupcm, vol. 28, no. 3. pp Mar. 1972, (in Japanese). Kentaro Nakamura wah born in Tokyo. Japan. on July He received the B.Eng. degree and the M.Eng. degree from the Tokyo Imtltute oftechnology. Tokyo, Japan, in 1987 and respectively. He is currently studying for the D.Eng. degree at Tokyo Institute of Technology. Hia research interest has been in the application of ultraaonics. Mr. Nakamura is a member of the Institute of Electronics, Information and Communication Engineers and The Acoustical Society of Japan. Minoru Kurosawa (formerly Kuribayashi) wah burn in Nagano, Japan. on April 24, Hc received the B.Eng. degree in electrical and electronic engineering. the M.Eng. and D.Eng. degree from Tokyo Institute of Technology. Tokyo. in 1982, and 1Y90, respectively. Since 1984 he has been an associate of Research Laboratop of Precision Machinery and Elcctronics. Tokyo Institute of Technology. His research interests include ultrasonic motor and high-power ultrasonics. Dr. Kurosawa is a member of the In\titute of Electronics. Information and Communication Engineers and The Acoustical Socicty of Japan. He has received the Awaya Kiyoshi Award for encouragement of research from The Acoustical Society of Japan.