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Study of a new type linear ultrasonic motor with double-driving feetCunyue Lu*, Tian Xie, Tieying Zhou, Yu ChenDepartment of Physics, Tsinghua University, Beijing 100084, ChinaAvailable online 9 June 2006AbstractA new type linear USM with double-driving feet has been developed. The stator consists of eight piezoelectric ceramic plates and onebrass plate. Piezoelectric ceramics plates are polarized along the thickness and are symmetrically bonded to the two surfaces of one rect-angle brass plate. Double-driving feet are assembled on the same side of the brass plate. The working vibration mode is a composite in-plane bimode, which consists of the first longitudinal in-plane vibration mode and the second bending one. The basic size of the linearUSM is determined carefully by FEA. The characteristics of the prototype motor were measured experimentally.? 2006 Elsevier B.V. All rights reserved.Keywords: Linear ultrasonic motor; Laminated plates; Vibration in plan; Piezoelectric ceramic1. IntroductionRecently, linear ultrasonic motors have been of signif-icant research interests. Compared with ordinary electro-magnetic motors, the linear ultrasonic motors have suchadvantages as high torque per volume, operation at theprecision level of nanometers, good control characteristicsat start and stop, good ability to maintain its ownpositionwhenstopped,abilitytoworkinvacuumenvironment, no restriction through induction, simpleconfiguration and flexibility of shape. Not only have thelinear ultrasonic driving mechanisms been applied in pre-cision positioning systems, subminiature driving system,automobile, optics system, national defense and so on,but also have inspired many new conceptual applicationsin fields such as micro electromechanics and nanotech-nology, precision manipulators and micro robots. Linearultrasonic driving techniques have a nice applicationforeground.Many kinds of linear ultrasonic motors have beendescribed in the literature. Concepts of traveling wave,standing wave, surface acoustics wave, and large straintype ultrasonic motors were proposed 16. Some standingwave bimodal linear ultrasonic motors with in-plane vibra-tions has been developed because of their good character-istics, such as higher force (torque) per volume, higherdriving velocity and higher positioning precision, whichshould satisfy the increasing miniaturization demand ofthe motors 79. These motors use single rectangularpiezoelectric ceramic plate as stators and some of themhave one driving foot bonded to one end of the stators.The methods for structure design and control of the motorhave been investigated in the papers. Liu concluded thatthe proper ratio of the length to the width of a thin rectan-gular piezoelectric ceramics plates should be 4.0 10.Zumeris, who is from Nanomotion Ltd., Israel has trans-ferred the technology of ceramic plate linear ultrasonicmotor with bimodal in-plane vibration for commercialapplications 11.A linear ultrasonic motor with double-driving feet at thesame side is designed in this paper. The laminated plate sta-tor of the motor is comprised of a metal plate and eight pie-zoelectric ceramic plates. It is easy for the stator with sucha construction to be clamped. The working mode is a com-posite in-plane bimode. The design concept presented inthis paper is much promising for the applications in high-torch motors with smaller size.0041-624X/$ - see front matter ? 2006 Elsevier B.V. All rights reserved.doi:10.1016/j.ultras.2006.05.191*Corresponding author. Tel./fax: +86 10 62772787.E-mail address: (C. Lu)./locate/ultrasUltrasonics 44 (2006) e585e5892. Working principle2.1. General structureAs a prototype example, a compact ultrasonic motorbased on bimode was fabricated, as illustrated in Fig. 1.It consists of a stator and a pressing mechanism includinga box, a bolt and a plastic cushions. The stator is made of athin brass plate with eight piezoelectric ceramic platesbonded to the upper and down surfaces symmetrically.There are two driving feet at the same side of the brassplate. Piezoelectric ceramic plates were polarized alongthe thickness direction. The polarization direction of thefour piezoelectric ceramic plates bonded to the upper sur-face of the brass plate is against the direction of the otherfour plates bonded to the down surface of the brass plate.A bolt and some plastic cushions were used to fix the statorin the metal shell. The pressure between the stator and theslider can be adjusted, so the motor can work under differ-ent pressure force desired. In order to reduce the influenceof the clamp on the vibration of the stator, the fixed pointshould near the nodal plane of the vibration of the stator.2.2. Working principleThe working bimode of the stator consists of the firstlongitudinal vibration mode and the second bending vibra-tion mode of the stator. Fig. 2(a) shows that the particleson the friction face of the driving feet vibrate transverselyin the first longitudinal vibration mode of the stator.Fig. 2(b) shows that the particles on the friction face ofthe driving feet vibrate vertically when the stator vibratesin the second bending vibration mode. If there is a certainphase difference between the two modes, the track of parti-cles on the friction face of the driving feet should be anellipse when the stator vibrates in the bimode, as illustratedin Fig. 2(c). The metal shell was fixed on the operating plat-form. Two feet of the stator drive the slider to make a lin-ear motion. The friction pair is ceramic to ceramic. If thephase difference of the vibrations changes, the shape ofthe ellipse track of the particles changes too. Thus the movespeed of the slider changes. Commonly, the desired phasedifference of the two vibrations is 90? so that the slidercan be driven efficiently.2.3. Exciting mechanismThe vibration exciting method of the stator is shown inFig. 3. Eight piezoelectric ceramic plates are classified intofour pairs. Each pair includes two ceramic plates symmet-rically bonded to the both sides of the brass plate. Thediagonal two pairs of piezoelectric ceramic plates areexcited by a sine signal of Asin(xt), and the other diagonalsets are excited by a signal of Asin(xt + u). The metal plateis the ground. Actually, the frequency of longitudinal modeand the bending one of the stator can not agree wellbecause of the influence of such facts as an error of manu-facture and variety of temperature. So, for the sake of thebimode vibrations on the stator being effectively excited, anexciting frequency fdbetween the longitudinal mode fre-quency fland bending one fbwas chosen, as shown inFig. 3.There is a phase difference u between the two excitingsignals, which should cause a phase difference betweenthe vibrations. Fig. 4 shows that if the exciting frequencyfdchanges, the phase of resonance vibration changes too.The more the exciting frequency be close to the modal fre-quency of the stator, the greater the phase of the resonancevibration changes. The driving frequency changes, thephase difference of the resonance vibrations changes too.Fig. 1. The stator of the motor with metal shell.Fig. 2. The vibration modes of the stator: (a) the first longitudinal mode,(b) the second bending mode and (c) the composite in-plane bimode.Fig. 3. The exciting method.e586C. Lu et al. / Ultrasonics 44 (2006) e585e589The traveling direction of the drive can be changed byswitching the one pair crossing connected electrodes toanother pair. This changes the bending mode phase by pand results in reversing the direction of surface ellipticalmotion. The velocity of the slider can be changed by adjust-ing the exciting voltage or phase difference of the two excit-ing signals.When the frequency fland fbare the same, the phase dif-ference of the two vibrations changes very little as thefrequency fdvaries. So, it is very important to make thefrequency of the two vibrations be as consistent as possible.3. Structure design of the motorAn electromechanical coupling dynamic model of thestator is built using a FEM software ANSYS for the struc-ture design. Only when the natural frequency of the firstlongitudinal mode is close to the second bending one ofthe stator, the needed bimode could be effectively excitedon the stator. Therefore the frequency consistency of thetwo modes should be considered when the stator beingdesigned and manufactured.Fig. 5 shows the predicted frequencies of the vibrationmodes as functions of the length of the brass plate. It canbe found from Fig. 5 that both the frequencies of the lon-gitudinal and bending vibration modes decreases with thelength of brass plate, but the frequency of the bendingmode decreases faster. This modeling revealed that aneffective method of frequency consistence adjustmentwould be changing the length dimension of the brass plate.The calculated length of the brass plate is 40.5 mm. Thenatural frequency of the bending mode is 39980 Hz, andthe frequency of the longitudinal mode is 40010 Hz. Thefrequencies are approximately equal to each other.In consideration of the errors from calculation and man-ufacturing, the brass plate was made at first with 41 mm inlength, which was 0.5 mm longer than the calculated value.By reducing the length of the brass plate gradually, theconsistency of the mode frequencies of the stator can beachieved in virtue of frequency measuring instruments.Double-driving feet strategy was adopted. The two feetdrive by turns. The two driving feet should be arrangedsymmetrically because of the requirement of the reversedriving.The shape of the driving feet is rectangle. For keepingthe friction pair contacting well in order that the slidercan be driven steadily, the flexural amplitude of the con-tacting face on each foot should be consistent in the direc-tion of bending vibration. The position of the driving feeton the stator influences the consistence of the vibrationvelocity of the feet.There are five equidistant nodes on each meshed feet ofthe FEM model, as shown in Fig. 6. The relation of theflexural amplitude of the nodes on each foot versus the cen-tre distance between the two feet was calculated, as shownin Fig. 7. While the centre distance equals to 13.7 mm, theflexural amplitudes of the five nodes were nearly the same.The velocity consistency of the two driving feet isanother important factor affecting the driving capabilityof the stator. Different mounting location of the drivingfeet brings on different vibration amplitude, as well as dif-ferent driving force provided by the two feet.The vibration behaviors of the stator were calculated byusing the electromechanical coupling dynamic model. Theapplied voltage on the electrodes of the PZT plates is40 V. The driving frequency is 40080 Hz. A constant3939.54040.5413.9544.054.14.15x 104Length, mmFrequeny, kHzFrequency of the first longitudinal modeFrequency of the second bending modeFig. 5. The relation between the modal frequency and the length of thebrass plate.Fig. 6. Five equidistant nodes on each meshed feet.Fig. 4. The frequency and the phase of the vibration modes.C. Lu et al. / Ultrasonics 44 (2006) e585e589e587damping ratio of 0.003 is set for use in the harmonicresponse. The vibration amplitudes of a ridge on the stator,where the driving feet mounted, were calculated and plot-ted in Fig. 8. UXis the displacement in the direction ofthe longitudinal vibration. UYis the displacement in thedirection of the bending vibration. UZis the displacementin the direction of thickness vibration. USUM is the com-posite displacement. It is shown that the displacement UZisas tiny as to be ignored. The displacement UYis symmetri-cally distributed. The flexural amplitude reaches its maxi-mum at the situation that the distance between thecenters of two feet equals to 13.7 mm, and the amplitudeis basically symmetrical. UXis not symmetrically distrib-uted. The UXamplitude of the right foot is a little greaterthan that of the left foot. Thus, the composite displacementUSUM of the right foot is a little greater than that of theleft foot too.Since only when the distance between the centers of twofeet is 13.7 mm, the flexural amplitude UYreaches its max-imum and the vibration speed of the nodes on the divingfeet keeps consistent in the direction of bending vibration,the size of the stator is determined as shown in Fig. 9.The size of the rectangular brass plate is 40.5 mm inlength, 11 mm in width and 2 mm in thickness. The piezo-electric ceramic plates are 17 mm in length, 4 mm in widthand 0.8 mm in thickness.4. Experimental investigationsThe frequency response characteristic of the stator mea-sured with impedance analyzer is shown in Fig. 10. The res-onant frequency of the first longitudinal vibration mode is38.8 kHz, while the resonant frequency of the second bend-ing vibration mode is 40.8 kHz. The bending vibration fre-quency is about 2 kHz higher than the longitudinal one.121314151.82x 10-6Distance, mmAmplitude, m121314151.8x 10-6Distance, mmAmplitude, mnode1node2node3node4node5node1node2node3node4node5Fig. 7. Vibration of the feet.Fig. 8. The calculated vibration amplitudes of a ridge on the stator, wherethe driving feet mounted.Fig. 9. The size of the stator.Fig. 10. The measured resonant frequency of the stator.36373839404142020406080100Frequency, kHzDriving speed, mm/sLeft footRight footVoltage=50VrmsFig. 11. The relation between the driving speed and the frequency.e588C. Lu et al. / Ultrasonics 44 (2006) e585e589Fig. 11 shows the relation between the driving speed andthe driving frequency. The driving electric voltage is about50 V in rms. At a resonant frequency of 38.6 kHz, themotor has a maximum speed of 94.5 mm/s. In the fre-quency range from 38.6 to 40.8 kHz, the speed varies above42 mm/s.The driving speed of the motor varies proportionallywith an applied voltage. This result is in agreement witha no-load working condition of the slider, as shown inFig. 12. The exciting frequency is about 39.6 kHz.5. ConclusionsA new type linear USM with double-driving feet hasbeen developed. The stator consists of eight piezoelectricceramic plates and one brass plate. The basic size of themotor is determined carefully and the position of the driv-ing feet on the stator is determined by FEA. Simulationshows that the frequency of the first in-plane longitudinalvibration mode and the second in-plane bending vibrationmode can be easily regulated to the same by adjusting thelength of the brass plate. The characteristics of the proto-type motor were measured experimentally. The motor hasa maximum speed of 94.5 mm/s when the driving electricvoltage is about 50 V in rms and the frequency is 38.6 kHz.AcknowledgementsThe authors thanks for the financial supports fromtheNat