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A non-contact linear bearing and actuator via ultrasonic levitation
Sensors and Actuators A 135 (2007) 740–747
A non-contact linear bearing and actuator via ultrasonic levitation Takeshi Ide, James Friend ∗ , Kentaro Nakamura, Sadayuki Ueha Precision and Intelligence Laboratory, Tokyo Institute of Technology, Yokohama 226-8503, Japan Received 27 March 2006; received in revised form 29 June 2006; accepted 10 August 2006 Available online 25 September 2006
Abstract In this study, the design and testing of a linear bearing using near-field acoustic levitation (NFAL) phenomenon was performed. A pair of Langevin transducers placed at either end of a beam with either a right-angle V-shaped or -shaped cross-section was used to excite and absorb ultrasonic flexural vibrations transmitted along the length of the beam from one transducer to the other. The beam was used as a guide rail, supporting a slider formed from a short length of beam with the same cross-section. This arrangement provides a small and inexpensive non-contact bearing with magnetic field immunity and without generating a magnetic field, both useful characteristics for clean room and precision actuators. The slider was levitated by the vibration of the beam up to 100 m, and was moved successfully in either direction by traveling waves transmitted along the guide rail. In a 300-mm long prototype, objects up to 160 g (60.5 kg/m2 ) were levitated and transported. A transportation speed of 138 mm/s was obtained for a slider of 90 g. The stiffness of the levitation was found to be 1.1 N/m/m2 for this prototype. © 2006 Elsevier B.V. All rights reserved. Keywords: Acoustic levitation; Linear actuator; Piezoelectric actuator; Clean room; Non-contact actuator
1. Introduction Linear stages are commonplace in industrial production and research associated with semiconductor, nano-scale, bioengineering, and other technologies where precise positioning is a necessity. Bearings are a fundamental component of and a limiting factor in the performance of linear stages [1]. Linear bearings using contact, including screw actuators [2] and ultrasonic motors [3] have been thoroughly studied. The screw actuator converts rotary motion to linear motion, providing an easy way to generate linear motion from the rotary output of electric motors, but with backlash and wear problems. Improvements in the mechanism, by including balls or riding rollers in threaded grooves for linear contact with the shaft – the Saginaw mechanism [2] – have improved their performance; Awaddy et al. developed precision positioning methods for such actuators [4]. Ball-screw actuators are common in production process automation, steering systems, and aircraft flight actuators. Despite these advancements, their precision is insufficient for many applications [1]. ∗
Corresponding author. Present address: Monash University, Melbourne, Australia. Tel.: +61 3 9905 3551; fax: +61 3 9905 3551. E-mail address: [email protected] (J. Friend). 0924-4247/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.sna.2006.08.005
Linear ultrasonic motors are driven by forces generated between the rotor and the stator, the latter vibrated by piezoelectric elements, generating high linear forces and speeds, with sub-nanometer-order positioning precision [3,5,6]. Such motors have been investigated for several years and are already being used in several practical applications. There are of variety of types and sizes: multilayer piezoelectric actuators [7–10], motors using radial and non-axisymmetric modes [10], a quasi-traveling wave motor [11], a motor using two sandwich-type vibrators [12], self-locking theory [13], two motional function [14], motors using nonresonant piezoelectric effects [15], and a “shaking beam” motor [16], among many others. Motors using surface acoustic waves are an especially powerful version of piezoelectric motors [17,18], but wear and surface treatment failure are especially serious problems for these motors. Unfortunately, wear is a significant drawback not only with all piezoelectric motors using sliding contact, but indeed with all linear actuators that rely on contacting components. Because of wear, friction, and stiction associated with all bearing systems that rely on contact, for applications that require them, air cushion and magnetic levitation systems have remained the only choices for “frictionless” bearings. Air hockey [19,20] is a pedestrian application of the former technology, where objects
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are suspended on a cushion of air pumped through small holes in the surface of the underlying table. Such technology has far more sophisticated applications in spacecraft and multibody dynamics [21]; in particular, Mori and his associates at the Akita Research Institute of Advanced Technology developed a sophisticated linear actuator [22] using air cushioning. In magnetic levitation, either repulsion or attraction between paired magnetic fields, generated on the slider and fixed rail of the actuator, is used. Motion can be generated by manipulating the interaction of the fields [23]. Due to the inherent instability in this interaction (Crenshaw’s theorem), closed-loop control is necessary (with the specific exception of diamagnetic levitation). Just as in bearings with contact, however, dust accumulation and low-frequency vibrations are a problem. Both systems generate low-frequency vibrations (especially with regard to motion along the axis of the rail), reducing positioning accuracy. Moreover, air bearings require a tremendous amount of pure, clean air. In magnetic levitation systems, the levitated object must be magnetic, and the generation of powerful magnetic fields may attract dust and affect surrounding equipment. To address these problems, a non-contact linear bearing based on near-field acoustic levitation (NFAL) is proposed here. NFAL is a phenomenon in which a planar object atop a vibrating surface is levitated in the near-field by the acoustic radiation emanating from the vibrating surface [24–29]. Hashimoto et al. [30] illustrate the phenomenon, using a planar plate levitated about one-tenth of an acoustic wavelength from an ultrasonically vibrating surface. The phenomenon has been studied for non-contact ultrasonic motors and non-contact transportation of ultra-clean glass plates for liquid crystal displays. Yamazaki et al., proposed an ultrasonic motor in which the rotor is levitated and driven to rotate at very high speed by the ultrasonic acoustic field radiated from the stator into the air gap between the rotor and the stator [31–33]. To transport an object, flexural traveling waves transmitted along an extremely long and flat vibrating plate was devised by Hashimoto et al. [34,35], and it was confirmed that levitated objects could be transported without contact along the long axis of the plate. Further, it has been shown [36] that a retaining force acts on the levitated object to hold it in place over the center of acoustic radiation. However, the retaining force is very weak, permitting objects to move perpendicularly to the long axis of the plate. In this study, flexural traveling waves are transmitted along a V-shaped beam to levitate a slider with an identical cross-section, eliminating the degree-of-freedom transverse to the axis of sliding that was a problem in earlier studies. In this way, stable, precise, and virtually frictionless support and actuation can be obtained, requiring neither special materials for the slider nor a levitation control system. In what follows, the bearing actuator’s concept and design are given, followed by the characteristics of levitating a slider using standing waves excited along the beam. Finally, the slider’s linear motion in both directions due to the excitation of traveling waves by the interaction of two transducers placed at either end of the guide rail beam is provided, with details on the strength and fidelity of acoustic levitation as used in this study.
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Fig. 1. The basic idea of a non-contact linear bearing using fiexural vibration of a pair of right-angle beams (with a “ cross-section”). The beam length is considerably longer than shown in this figure. The slider is levitated acoustically above the rails—there is no direct contact.
2. Principle and configuration of the right-angle acoustic levitation bearing Fig. 1 illustrates the concept of the non-contact linear bearing used in this study. A fiexural traveling wave may be excited along the -cross-sectioned beam with the transducer and horn in the shown configuration, permitting the levitation and propulsion of the slider along the guide rail beam. Due to the right-angle crosssection, the lateral position of the slider is tightly controlled. For this study, two different guide rail configurations were considered for the linear bearing. In both cases, a beam with either a V-shaped or -shaped cross-section was used as both the rail guide and the slider, as shown in the cross-sectional view of the beam and slider for both arrangements in Fig. 2. The experimental setup used to determine the standing-wave levitation characteristics of the system is shown in Fig. 3. A 2-m long right-angle beam was excited using a Langevin transducer with a stepped horn at 18 kHz. The side length and the wall thickness of the beam were 30 mm and 2 mm, respectively. The transducer is mounted diagonally halfway from the corner of the (x = 15 mm), 45 mm from the end of the beam (z = 0). Standing waves are excited as the other end of the right-angle beam is free in this configuration. 2.1. Dispersion charctersistics of the right-angle beam analyzed with FEM Prior to the experiments, the dispersion characteristics of the right-angle beam vibration were analyzed below 30 kHz using the finite element method (FEM). Quadratic quadrilateral shell elements with edge lengths of 7.5 mm were used in the analysis. Matching the experiments, the material was aluminum throughout, with hard PZT complete with anisotropic (∞ mm/6 m) and
Fig. 2. The difference in the configuration of the beam and slider, shown onend, for the (a) and (b) V-shaped configurations, indicating the vibration displacement measurement location.
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Fig. 3. The experimental setup used in this study to determine the levitation characteristics of the system, illustrating the driving transducer mounting method, slider, and vibration displacement measurement using a photonic sensor. The other end of the beam in this arrangement was left free.
piezoelectric coupling to match the characteristics of NEC/Tokin N-61 ceramic material. In addition to the longitudinal mode, the vertically and horizontally-polarized flexural modes, e.g., the modes indicated by the numbers 5 and 6, respectively in Fig. 4(b), can be excited along the beam, as can higher-order modes. Both symmetrical and asymmetrical versions of the fundamental and higher-order modes exist in the structure. The dispersion characteristics of the higher modes from the second to fifth harmonic, and other modes from the sixth to eighth harmonic are shown in Fig. 4. Most – but not all – of the flexural modes have a lower frequency cut off. 2.2. The measured vibration modes The vibration distributions along the x and y directions were measured transverse to the surface of the beam using a laser Doppler vibrometer as shown in Fig. 5. A frequency of 18 kHz was chosen based on the relatively large vibration displacement obtained at this frequency. The measured distribution corresponds to the third mode calculated using FEM and is shown in Fig. 4. In each case, the vibration displacement near the corner of the beam was nearly zero, with the largest displacement almost halfway between the corner and edge of the beam. The measured wavelength along the z direction was 52 mm, almost equal to the analyzed wavelength of 47 mm. Using the Chladni
Fig. 4. Dispersion characteristics of the right-angle beam calculated using FEM, for the (a) first four flexural vibration modes and (b) the higher-order fifth through seventh modes. The mode shape figures illustrate the cross-sectional distortion; in all cases, the distribution of displacement along the axis of the beam was sinusoidal. Note the asymmetric motion occurring in modes identified with numbers 2 and 4, and the symmetric motion identified by numbers 1 and 3.
Fig. 5. Measured vibration distribution along the outer surface of the beam, perpendicular to its surface, vs. the x and y coordinate directions in Fig. 3, cutting through the center of the loop as shown in Fig. 6.
method [37,38], the vibration mode is shown in Fig. 6. The chain-like looping pattern is repeated symmetrically along both faces of the -shaped beam down its entire length. 3. Levitation characteristics using flexural standing waves A 101-mm-long, 29.7-g slider with the same cross-section was levitated above the beam, and the slider’s levitation distance h versus the beam’s vibration displacement amplitude u was measured using a photonic displacement sensor as shown in
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Fig. 8. Slider’s levitation distance vs. its weight per unit area, at a fixed guide rail beam vibration displacement amplitude of 10 m.
Fig. 6. Chladni figure along the structure at 18 kHz.
Fig. 3. The levitation distance was measured as a distance solely in the vertical direction (along eh = −1/2(ex + ey ) in Fig. 3, supposing ei is a unit vector along the ith coordinate direction). The reported vibration displacement amplitude is the maximum vibration amplitude in the entire beam, perpendicular to its surface. Fig. 7 shows the levitation distance h versus the beam’s vibration displacement amplitude u for both the V- and -shaped beams in addition to the theoretical result expected from a flat plate [30]. The levitation distance h versus the weight per unit area w was measured by placing a mass under gravity on the slider and maintaining a constant vibration displacement amplitude u of 10 m. As shown in Fig. 8, for a planar beam and planar slider, the levitation distance is proportional to the displacement amplitude and inversely proportional to the square root of the weight per unit area, independent of the vibration mode used [7]. The experimental results of the right-angle cross-section (“-shaped” in the figure) were slightly different; the levitation distance was proportional to the displacement amplitude raised to the 1.1 power, and to the weight per unit area raised to the −0.9 power. Fig. 8 permits the calculation of the levitation rigidity, defined as the ratio of the change of the slider’s weight per unit area to the slider’s levitation distance. The levitation rigidity was 1.1 N/m/m2 at a levitation distance of 70 m, about l/36th the
Fig. 7. Slider levitation distance vs. the beam’s displacement amplitude for a Vor -shaped beam. The levitation distance is generally higher by about a factor of four for a plate or planar beam [30]. The slider’s mass is 29.7 g.
measured value for the planar beam. It is believed that the reason for the difference is the complicated vibration distribution present in the right-angle beam, composed of a variety of overlapped modes. The levitation characteristics were measured in a similar way for the V-shaped case. The stepped horn of the transducer was mounted from the opposite side on the right-angle beam as shown in Fig. 9. The transducer is mounted diagonally halfway between the edge and corner of the V (x = 15 mm), and 45 mm from the end of the beam (z = 0). The corresponding results are indicated in Figs. 7 and 8 as “V-shaped”. In Fig. 7, the V-shaped levitation distance for a given amount of weight was 40% larger than the -shaped arrangement. Using Fig. 8, the levitation rigidities for all three configurations could be calculated. The levitation rigidity of the V-shaped beam was 10.7 N/m/m2 when the levitation distance was 70 m, onetenth the rigidity of the -shaped arrangement. By extrapolating the V-shaped structure’s results to a levitation distance of 10 m, the levitation rigidity becomes 11.9 kN/m/m2 , about l/200th the -shaped configuration. As circled in Fig. 2, the edge of the guide rail beam – which happens to be the location of the largest displacement amplitude – is covered by the slider in the Vshaped arrangement, but is not covered in the -shaped arrangement, causing the levitation force of the V-shaped setup to be larger.
Fig. 9. Mounting the transducer for the V-shaped configuration.
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Fig. 11. Beam displacement amplitude vs. the driving position along the x direction using diagonal vibration excitation.
Fig. 10. Transducer mounting for (a) diagonal and (b) vertical vibration excitation.
4. Conditions to excite a traveling wave The excitation of a traveling wave by two transducers driven out of phase with each other while mounted on either end of the beam was considered. The driving position on the beam was optimized using FEM analysis for two mounting methods: (a) diagonal excitation and (b) vertical excitation as illustrated in Fig. 10. Note that in the diagonal arrangement, the transducers are mounted on opposing sides of the beam for true symmetry about the midpoint of the structure. A 300-mm-long right-angle aluminium beam driven at 19 kHz was used for this part of the study. 4.1. Driving position along the beams First, the most efficient position to excite a standing wave was explored using FEM with only one transducer. A harmonic force was applied perpendicularly to the beam surface at one point: the driving position. The displacement amplitude at the corner of the beam (x = 0) and the edge (x = 30 mm) of the beam was calculated while varying the driving position. For diagonal excitation, the most efficient driving position on the x–z plane was explored. The displacement amplitude versus the driving position along the x direction is shown in Fig. 11, where the driving position along the z direction was fixed at 7.5 mm. The displacement amplitude at the corner was generally a tenth of the displacement at the edge. A driving position about halfway from the corner (x = 15 mm) was nearly the best; mounting the transducer on the edge (x = 30 mm) might produce larger displacements according to the result, but mounting the transducer at this location experimentally was difficult. Next, using these results, the driving position was varied along the z direction while the x position was held constant at 15 mm as shown in Fig. 12. The displacement amplitude had a maxima at z = 45 mm. From these results, a driving position of x = 15 mm, z = 45 mm was chosen. The second transducer was attached at a position of x = 15 mm, z = 45 mm in the z–y plane, as measured from the opposite end and shown in Fig. 10(a).
Fig. 12. Beam displacement amplitude vs. the driving position along the z direction using diagonal vibration excitation.
The tip of the stepped horn was fastened perpendicularly to the beam with screws. For vertical excitation, a harmonic force was applied at a driving point on the corner of the beam (x = y = 0), vertically along eh , and the driving point was moved along the z direction, as shown in Fig. 13. The driving positions associated with the maximum displacement at the edge and at the corner of the beam were different. Since the displacement at the beam edge was consistently larger than at the corner, the corner displacement was used to choose an appropriate driving position, at z = 37.5 mm. The second transducer was placed at z = 262.5 mm as shown in Fig. 10(b), in a location symmetric to the first trans-
Fig. 13. Beam displacement amplitude vs. the driving position in z direction using vertical vibration excitation.
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Fig. 14. Standing wave ratio (SWR) vs. the driving phase difference. Note the higher SWR and asymmetry of the diagonal excitation configuration.
ducer. In this case, the horn and the beam were bolted together using a triangular coupler. 4.2. Driven phase difference The vibration distribution of the beam was analyzed using FEM while varying the driven phase difference between the two transducers. The standing wave ratio (SWR) of the vibration in the z direction at the corner of the right-angle cross-section with respect to the driven phase difference is plotted in Fig. 14. For diagonal excitation, the SWR does not change symmetrically about a phase difference of 180◦ because other modes were excited, and the vibration of the x–z and y–z planes differed slightly. Although a traveling wave with a SWR = 5 could be excited, due to the asymmetry of the SWR, the slider speed and thrust might be expected to differ between the forward and reverse directions. In vertical excitation, the vibration distributions of the two planes were the same, and the SWR changes symmetrically with respect to a phase difference of 180◦ . A traveling wave of SWR = 1.7 could be excited in the positive and negative directions with phase differences of 270◦ and 90◦ , respectively. However, the displacement amplitude was one-fifth the diagonal excitation configuration as shown in Fig. 15.
Fig. 15. Beam displacement magnitude vs. the driving phase difference. The vertical and diagonal driving configurations are shown in Fig. 10. The far larger displacement amplitude using diagonal excitation compensates somewhat for the poorer SWR.
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Fig. 16. Slider levitation distance vs. the slider’s weight per unit area for diagonal and vertical excitation.
5. The levitation characteristics via flexural traveling waves Fig. 16 shows the measured levitation distance h versus the weight per unit area w of the slider for both diagonal and vertical excitation using an input power of 15 W. A larger maximum displacement amplitude was obtained using diagonal excitation, 28 m0–p compared with only 5 m0–p using vertical excitation, similar to the results obtained earlier using standing waves. Fig. 17 plots the levitation rigidity k versus the levitation distance h as calculated from Fig. 16, and shows that the levitation rigidity k was also higher using diagonal excitation. 6. Measurement of the thrust The movement of the levitated slider by a traveling wave generated by the two transducers driven out of phase with respect to each other was experimentally investigated. Using the diagonal excitation technique, video of the levitation and movement of the slider in Ide2004-slidermotion.mpg, and the value of the thrust acting on the slider was estimated by elevating one end of the beam to counteract the sliding thrust provided by the levitation and transportation mechanism by the weight of the slider along the sliding direction, causing the slider to remain in place. Fig. 18 shows the thrust versus the maximum displacement amplitude using diagonal excitation. Thrust was successfully generated in both directions by changing the driving phase difference, and
Fig. 17. Levitation rigidity vs. the slider’s levitation distance for both diagonal and vertical excitation.
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Fig. 18. Thrust vs. the beam displacement amplitude using the diagonal excitation technique.
there was no difference in thrust or velocity between the two sliding directions, despite the asymmetry in the standing wave ratio seen in the vibration of the beam alone. It is believed that the presence of the slider sufficiently suppressed the vibration to eliminate the difference. A maximum thrust of 1.1 mN was obtained using a displacement amplitude of 28 m0–p , while a maximum speed of 138 mm/s was obtained for this study using the 90-g slider. However, the maximum speed is very dependent on the distance allowed for acceleration; our study did not permit the true maximum speed to be achieved before the slider reached the end of the guide rail beam. For vertical excitation, the displacement amplitude was smaller compared with diagonal excitation, and, as a result, the thrust direction was very difficult to control. The surfaces of the beam and slider were polished, but the quality of the finish and precision of the interface are limited by the use of extruded aluminum as the beam and slider material. Finally, it is important to note the boundary conditions of the beam and the transducers differed from the FEM analysis, adversely affecting a comparison between the measured and computed results. 7. Conclusions A novel linear bearing based on near-field acoustic levitation has been proposed and investigated. A guide rail beam and slider, both with a right-angular cross-section, were used; the slider was levitated using ultrasonic flexural vibration in the rail as expected. Based on the studies of the driving position on the beam and the conditions to excite a traveling wave, the levitated slider was moved successfully in both directions by traveling waves transmitted along the length of the beam. Vertical excitation was found to be inferior to diagonal excitation, but, overall, a maximum thrust of 1.1 mN was obtained. References [1] N. Taniguchi, Nanotechnology: Integrated Procesing Systems for UltraPrecision and Ultra-Fine Products, Oxford University Press, 1996. [2] D. Lange, Ball screws that hang tough, Power Transm. Des. 42 (6) (2000) 29–32. [3] S. Ueha, Y. Tomikawa, Ultrasonic Motors—Theory and Applications, vol. 29 of Monographs in Electrical and Electronic Engineering, Clarendon Press, Oxford, 1993.
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Biographies Takeshi Ide was born in Kumamoto, Japan on September 5th, 1980. He received the B Eng degree from the Tokyo Institute of Technology, Tokyo, Japan, in 2003. He is now pursuing his master’s degree at the Tokyo Institute of Technology, Tokyo, Japan, researching actuators using ultrasonic levitation. Mr. Ide enjoys playing volleyball, baseball, and many other sports, and is a drummer in his friend’s band. In his spare time, he travels with his girlfriend or takes short walks alone. He is a member of the Acoustical Society of Japan and the Institute of Electronics, Information and Communication Engineers. James Friend was born in Lubbock, Texas on September 13, 1970. He received the BS degree in aerospace engineering, and the MS and PhD degrees in mechanical engineering from the University of Missouri-Rolla in 1992, 1994, and 1998,
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respectively. He received the Best Paper award and Jefferson Goblet Student Paper Award from the ASME and AIAA for a paper delivered at the 97th Annual AIAA/ASME/AHS/ASC/ASCE Structural Dynamics and Mechanics Conference in 1996, an award for the encouragement of young scientists at the Symposium for Ultrasonic Electronics and Engineering in 2003 for a presentation on acoustic waveguides, and an award in 2004 for a presentation on the Scream actuator at the Spring Meeting of the Acoustical Society of Japan. From 2001 to 2004, Dr. Friend was an assistant professor at the Precision and Intelligence Laboratory, Tokyo Institute of Technology, and is now a co-director of the MicroNanophysics Research Laboratory, Monash University, Melbourne, Australia, with research interests in micro/nanofluidics and micromechatronics and its applications. He is a member of IEEE, ASME, and Sigma Xi. Kentaro Nakamura was born in Tokyo, Japan, on July 3, 1963. He received the B Eng, the M Eng, and the D Eng degrees from the Tokyo Institute of Technology, Tokyo, Japan, in 1987, 1989, and 1992, respectively. He has been an Associate Professor of the Precision and Intelligence Laboratory, Tokyo Institute of Technology, since 1996. His field of research is the application of ultrasonics and the measurement of vibration and sound using optical methods. He has received the Awaya Kiyoshi Award for encouragement of research from the Acoustical Society of Japan in 1996. Dr. Nakamura is a member of the Acoustical Society of Japan, the Japan Society of Applied Physics, the Institute of Electrical Engineers of Japan, and the Institute of Electronics, Information and Communication Engineers. Sadayuki Ueha was born in Kyoto Prefecture, Japan, on February 28, 1943. He received the B Eng degree in electronic engineering from the Nagoya Institute of Technology in 1965 and the M Eng degree in 1967, and the D Eng degree in 1970, both in electric engineering, from the Tokyo Institute of Technology. He currently conducts research in high power ultrasonics. He has been a Professor of the Precision and Intelligence Laboratory, Tokyo Institute of Technology since 1992. He is a steering committee member of the World Congress on Ultrasonics and serves as the secretariat of WCU97. He received the Best Paper Award from The Japan Society of Applied Physics in 1975 and from the Acoustical Society of Japan in 1980, respectively. Dr. Ueha is a member of the Japan Society of Applied Physics, the Acoustical Society of Japan, the Institute of Electronics, Information and Communication Engineers and the Japan Society of Ultrasonics in Medicine.
A non-contact linear bearing and actuator via ultrasonic levitation Takeshi Ide, James Friend ∗ , Kentaro Nakamura, Sadayuki Ueha Precision and Intelligence Laboratory, Tokyo Institute of Technology, Yokohama 226-8503, Japan Received 27 March 2006; received in revised form 29 June 2006; accepted 10 August 2006 Available online 25 September 2006
Abstract In this study, the design and testing of a linear bearing using near-field acoustic levitation (NFAL) phenomenon was performed. A pair of Langevin transducers placed at either end of a beam with either a right-angle V-shaped or -shaped cross-section was used to excite and absorb ultrasonic flexural vibrations transmitted along the length of the beam from one transducer to the other. The beam was used as a guide rail, supporting a slider formed from a short length of beam with the same cross-section. This arrangement provides a small and inexpensive non-contact bearing with magnetic field immunity and without generating a magnetic field, both useful characteristics for clean room and precision actuators. The slider was levitated by the vibration of the beam up to 100 m, and was moved successfully in either direction by traveling waves transmitted along the guide rail. In a 300-mm long prototype, objects up to 160 g (60.5 kg/m2 ) were levitated and transported. A transportation speed of 138 mm/s was obtained for a slider of 90 g. The stiffness of the levitation was found to be 1.1 N/m/m2 for this prototype. © 2006 Elsevier B.V. All rights reserved. Keywords: Acoustic levitation; Linear actuator; Piezoelectric actuator; Clean room; Non-contact actuator
1. Introduction Linear stages are commonplace in industrial production and research associated with semiconductor, nano-scale, bioengineering, and other technologies where precise positioning is a necessity. Bearings are a fundamental component of and a limiting factor in the performance of linear stages [1]. Linear bearings using contact, including screw actuators [2] and ultrasonic motors [3] have been thoroughly studied. The screw actuator converts rotary motion to linear motion, providing an easy way to generate linear motion from the rotary output of electric motors, but with backlash and wear problems. Improvements in the mechanism, by including balls or riding rollers in threaded grooves for linear contact with the shaft – the Saginaw mechanism [2] – have improved their performance; Awaddy et al. developed precision positioning methods for such actuators [4]. Ball-screw actuators are common in production process automation, steering systems, and aircraft flight actuators. Despite these advancements, their precision is insufficient for many applications [1]. ∗
Corresponding author. Present address: Monash University, Melbourne, Australia. Tel.: +61 3 9905 3551; fax: +61 3 9905 3551. E-mail address: [email protected] (J. Friend). 0924-4247/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.sna.2006.08.005
Linear ultrasonic motors are driven by forces generated between the rotor and the stator, the latter vibrated by piezoelectric elements, generating high linear forces and speeds, with sub-nanometer-order positioning precision [3,5,6]. Such motors have been investigated for several years and are already being used in several practical applications. There are of variety of types and sizes: multilayer piezoelectric actuators [7–10], motors using radial and non-axisymmetric modes [10], a quasi-traveling wave motor [11], a motor using two sandwich-type vibrators [12], self-locking theory [13], two motional function [14], motors using nonresonant piezoelectric effects [15], and a “shaking beam” motor [16], among many others. Motors using surface acoustic waves are an especially powerful version of piezoelectric motors [17,18], but wear and surface treatment failure are especially serious problems for these motors. Unfortunately, wear is a significant drawback not only with all piezoelectric motors using sliding contact, but indeed with all linear actuators that rely on contacting components. Because of wear, friction, and stiction associated with all bearing systems that rely on contact, for applications that require them, air cushion and magnetic levitation systems have remained the only choices for “frictionless” bearings. Air hockey [19,20] is a pedestrian application of the former technology, where objects
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are suspended on a cushion of air pumped through small holes in the surface of the underlying table. Such technology has far more sophisticated applications in spacecraft and multibody dynamics [21]; in particular, Mori and his associates at the Akita Research Institute of Advanced Technology developed a sophisticated linear actuator [22] using air cushioning. In magnetic levitation, either repulsion or attraction between paired magnetic fields, generated on the slider and fixed rail of the actuator, is used. Motion can be generated by manipulating the interaction of the fields [23]. Due to the inherent instability in this interaction (Crenshaw’s theorem), closed-loop control is necessary (with the specific exception of diamagnetic levitation). Just as in bearings with contact, however, dust accumulation and low-frequency vibrations are a problem. Both systems generate low-frequency vibrations (especially with regard to motion along the axis of the rail), reducing positioning accuracy. Moreover, air bearings require a tremendous amount of pure, clean air. In magnetic levitation systems, the levitated object must be magnetic, and the generation of powerful magnetic fields may attract dust and affect surrounding equipment. To address these problems, a non-contact linear bearing based on near-field acoustic levitation (NFAL) is proposed here. NFAL is a phenomenon in which a planar object atop a vibrating surface is levitated in the near-field by the acoustic radiation emanating from the vibrating surface [24–29]. Hashimoto et al. [30] illustrate the phenomenon, using a planar plate levitated about one-tenth of an acoustic wavelength from an ultrasonically vibrating surface. The phenomenon has been studied for non-contact ultrasonic motors and non-contact transportation of ultra-clean glass plates for liquid crystal displays. Yamazaki et al., proposed an ultrasonic motor in which the rotor is levitated and driven to rotate at very high speed by the ultrasonic acoustic field radiated from the stator into the air gap between the rotor and the stator [31–33]. To transport an object, flexural traveling waves transmitted along an extremely long and flat vibrating plate was devised by Hashimoto et al. [34,35], and it was confirmed that levitated objects could be transported without contact along the long axis of the plate. Further, it has been shown [36] that a retaining force acts on the levitated object to hold it in place over the center of acoustic radiation. However, the retaining force is very weak, permitting objects to move perpendicularly to the long axis of the plate. In this study, flexural traveling waves are transmitted along a V-shaped beam to levitate a slider with an identical cross-section, eliminating the degree-of-freedom transverse to the axis of sliding that was a problem in earlier studies. In this way, stable, precise, and virtually frictionless support and actuation can be obtained, requiring neither special materials for the slider nor a levitation control system. In what follows, the bearing actuator’s concept and design are given, followed by the characteristics of levitating a slider using standing waves excited along the beam. Finally, the slider’s linear motion in both directions due to the excitation of traveling waves by the interaction of two transducers placed at either end of the guide rail beam is provided, with details on the strength and fidelity of acoustic levitation as used in this study.
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Fig. 1. The basic idea of a non-contact linear bearing using fiexural vibration of a pair of right-angle beams (with a “ cross-section”). The beam length is considerably longer than shown in this figure. The slider is levitated acoustically above the rails—there is no direct contact.
2. Principle and configuration of the right-angle acoustic levitation bearing Fig. 1 illustrates the concept of the non-contact linear bearing used in this study. A fiexural traveling wave may be excited along the -cross-sectioned beam with the transducer and horn in the shown configuration, permitting the levitation and propulsion of the slider along the guide rail beam. Due to the right-angle crosssection, the lateral position of the slider is tightly controlled. For this study, two different guide rail configurations were considered for the linear bearing. In both cases, a beam with either a V-shaped or -shaped cross-section was used as both the rail guide and the slider, as shown in the cross-sectional view of the beam and slider for both arrangements in Fig. 2. The experimental setup used to determine the standing-wave levitation characteristics of the system is shown in Fig. 3. A 2-m long right-angle beam was excited using a Langevin transducer with a stepped horn at 18 kHz. The side length and the wall thickness of the beam were 30 mm and 2 mm, respectively. The transducer is mounted diagonally halfway from the corner of the (x = 15 mm), 45 mm from the end of the beam (z = 0). Standing waves are excited as the other end of the right-angle beam is free in this configuration. 2.1. Dispersion charctersistics of the right-angle beam analyzed with FEM Prior to the experiments, the dispersion characteristics of the right-angle beam vibration were analyzed below 30 kHz using the finite element method (FEM). Quadratic quadrilateral shell elements with edge lengths of 7.5 mm were used in the analysis. Matching the experiments, the material was aluminum throughout, with hard PZT complete with anisotropic (∞ mm/6 m) and
Fig. 2. The difference in the configuration of the beam and slider, shown onend, for the (a) and (b) V-shaped configurations, indicating the vibration displacement measurement location.
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Fig. 3. The experimental setup used in this study to determine the levitation characteristics of the system, illustrating the driving transducer mounting method, slider, and vibration displacement measurement using a photonic sensor. The other end of the beam in this arrangement was left free.
piezoelectric coupling to match the characteristics of NEC/Tokin N-61 ceramic material. In addition to the longitudinal mode, the vertically and horizontally-polarized flexural modes, e.g., the modes indicated by the numbers 5 and 6, respectively in Fig. 4(b), can be excited along the beam, as can higher-order modes. Both symmetrical and asymmetrical versions of the fundamental and higher-order modes exist in the structure. The dispersion characteristics of the higher modes from the second to fifth harmonic, and other modes from the sixth to eighth harmonic are shown in Fig. 4. Most – but not all – of the flexural modes have a lower frequency cut off. 2.2. The measured vibration modes The vibration distributions along the x and y directions were measured transverse to the surface of the beam using a laser Doppler vibrometer as shown in Fig. 5. A frequency of 18 kHz was chosen based on the relatively large vibration displacement obtained at this frequency. The measured distribution corresponds to the third mode calculated using FEM and is shown in Fig. 4. In each case, the vibration displacement near the corner of the beam was nearly zero, with the largest displacement almost halfway between the corner and edge of the beam. The measured wavelength along the z direction was 52 mm, almost equal to the analyzed wavelength of 47 mm. Using the Chladni
Fig. 4. Dispersion characteristics of the right-angle beam calculated using FEM, for the (a) first four flexural vibration modes and (b) the higher-order fifth through seventh modes. The mode shape figures illustrate the cross-sectional distortion; in all cases, the distribution of displacement along the axis of the beam was sinusoidal. Note the asymmetric motion occurring in modes identified with numbers 2 and 4, and the symmetric motion identified by numbers 1 and 3.
Fig. 5. Measured vibration distribution along the outer surface of the beam, perpendicular to its surface, vs. the x and y coordinate directions in Fig. 3, cutting through the center of the loop as shown in Fig. 6.
method [37,38], the vibration mode is shown in Fig. 6. The chain-like looping pattern is repeated symmetrically along both faces of the -shaped beam down its entire length. 3. Levitation characteristics using flexural standing waves A 101-mm-long, 29.7-g slider with the same cross-section was levitated above the beam, and the slider’s levitation distance h versus the beam’s vibration displacement amplitude u was measured using a photonic displacement sensor as shown in
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Fig. 8. Slider’s levitation distance vs. its weight per unit area, at a fixed guide rail beam vibration displacement amplitude of 10 m.
Fig. 6. Chladni figure along the structure at 18 kHz.
Fig. 3. The levitation distance was measured as a distance solely in the vertical direction (along eh = −1/2(ex + ey ) in Fig. 3, supposing ei is a unit vector along the ith coordinate direction). The reported vibration displacement amplitude is the maximum vibration amplitude in the entire beam, perpendicular to its surface. Fig. 7 shows the levitation distance h versus the beam’s vibration displacement amplitude u for both the V- and -shaped beams in addition to the theoretical result expected from a flat plate [30]. The levitation distance h versus the weight per unit area w was measured by placing a mass under gravity on the slider and maintaining a constant vibration displacement amplitude u of 10 m. As shown in Fig. 8, for a planar beam and planar slider, the levitation distance is proportional to the displacement amplitude and inversely proportional to the square root of the weight per unit area, independent of the vibration mode used [7]. The experimental results of the right-angle cross-section (“-shaped” in the figure) were slightly different; the levitation distance was proportional to the displacement amplitude raised to the 1.1 power, and to the weight per unit area raised to the −0.9 power. Fig. 8 permits the calculation of the levitation rigidity, defined as the ratio of the change of the slider’s weight per unit area to the slider’s levitation distance. The levitation rigidity was 1.1 N/m/m2 at a levitation distance of 70 m, about l/36th the
Fig. 7. Slider levitation distance vs. the beam’s displacement amplitude for a Vor -shaped beam. The levitation distance is generally higher by about a factor of four for a plate or planar beam [30]. The slider’s mass is 29.7 g.
measured value for the planar beam. It is believed that the reason for the difference is the complicated vibration distribution present in the right-angle beam, composed of a variety of overlapped modes. The levitation characteristics were measured in a similar way for the V-shaped case. The stepped horn of the transducer was mounted from the opposite side on the right-angle beam as shown in Fig. 9. The transducer is mounted diagonally halfway between the edge and corner of the V (x = 15 mm), and 45 mm from the end of the beam (z = 0). The corresponding results are indicated in Figs. 7 and 8 as “V-shaped”. In Fig. 7, the V-shaped levitation distance for a given amount of weight was 40% larger than the -shaped arrangement. Using Fig. 8, the levitation rigidities for all three configurations could be calculated. The levitation rigidity of the V-shaped beam was 10.7 N/m/m2 when the levitation distance was 70 m, onetenth the rigidity of the -shaped arrangement. By extrapolating the V-shaped structure’s results to a levitation distance of 10 m, the levitation rigidity becomes 11.9 kN/m/m2 , about l/200th the -shaped configuration. As circled in Fig. 2, the edge of the guide rail beam – which happens to be the location of the largest displacement amplitude – is covered by the slider in the Vshaped arrangement, but is not covered in the -shaped arrangement, causing the levitation force of the V-shaped setup to be larger.
Fig. 9. Mounting the transducer for the V-shaped configuration.
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Fig. 11. Beam displacement amplitude vs. the driving position along the x direction using diagonal vibration excitation.
Fig. 10. Transducer mounting for (a) diagonal and (b) vertical vibration excitation.
4. Conditions to excite a traveling wave The excitation of a traveling wave by two transducers driven out of phase with each other while mounted on either end of the beam was considered. The driving position on the beam was optimized using FEM analysis for two mounting methods: (a) diagonal excitation and (b) vertical excitation as illustrated in Fig. 10. Note that in the diagonal arrangement, the transducers are mounted on opposing sides of the beam for true symmetry about the midpoint of the structure. A 300-mm-long right-angle aluminium beam driven at 19 kHz was used for this part of the study. 4.1. Driving position along the beams First, the most efficient position to excite a standing wave was explored using FEM with only one transducer. A harmonic force was applied perpendicularly to the beam surface at one point: the driving position. The displacement amplitude at the corner of the beam (x = 0) and the edge (x = 30 mm) of the beam was calculated while varying the driving position. For diagonal excitation, the most efficient driving position on the x–z plane was explored. The displacement amplitude versus the driving position along the x direction is shown in Fig. 11, where the driving position along the z direction was fixed at 7.5 mm. The displacement amplitude at the corner was generally a tenth of the displacement at the edge. A driving position about halfway from the corner (x = 15 mm) was nearly the best; mounting the transducer on the edge (x = 30 mm) might produce larger displacements according to the result, but mounting the transducer at this location experimentally was difficult. Next, using these results, the driving position was varied along the z direction while the x position was held constant at 15 mm as shown in Fig. 12. The displacement amplitude had a maxima at z = 45 mm. From these results, a driving position of x = 15 mm, z = 45 mm was chosen. The second transducer was attached at a position of x = 15 mm, z = 45 mm in the z–y plane, as measured from the opposite end and shown in Fig. 10(a).
Fig. 12. Beam displacement amplitude vs. the driving position along the z direction using diagonal vibration excitation.
The tip of the stepped horn was fastened perpendicularly to the beam with screws. For vertical excitation, a harmonic force was applied at a driving point on the corner of the beam (x = y = 0), vertically along eh , and the driving point was moved along the z direction, as shown in Fig. 13. The driving positions associated with the maximum displacement at the edge and at the corner of the beam were different. Since the displacement at the beam edge was consistently larger than at the corner, the corner displacement was used to choose an appropriate driving position, at z = 37.5 mm. The second transducer was placed at z = 262.5 mm as shown in Fig. 10(b), in a location symmetric to the first trans-
Fig. 13. Beam displacement amplitude vs. the driving position in z direction using vertical vibration excitation.
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Fig. 14. Standing wave ratio (SWR) vs. the driving phase difference. Note the higher SWR and asymmetry of the diagonal excitation configuration.
ducer. In this case, the horn and the beam were bolted together using a triangular coupler. 4.2. Driven phase difference The vibration distribution of the beam was analyzed using FEM while varying the driven phase difference between the two transducers. The standing wave ratio (SWR) of the vibration in the z direction at the corner of the right-angle cross-section with respect to the driven phase difference is plotted in Fig. 14. For diagonal excitation, the SWR does not change symmetrically about a phase difference of 180◦ because other modes were excited, and the vibration of the x–z and y–z planes differed slightly. Although a traveling wave with a SWR = 5 could be excited, due to the asymmetry of the SWR, the slider speed and thrust might be expected to differ between the forward and reverse directions. In vertical excitation, the vibration distributions of the two planes were the same, and the SWR changes symmetrically with respect to a phase difference of 180◦ . A traveling wave of SWR = 1.7 could be excited in the positive and negative directions with phase differences of 270◦ and 90◦ , respectively. However, the displacement amplitude was one-fifth the diagonal excitation configuration as shown in Fig. 15.
Fig. 15. Beam displacement magnitude vs. the driving phase difference. The vertical and diagonal driving configurations are shown in Fig. 10. The far larger displacement amplitude using diagonal excitation compensates somewhat for the poorer SWR.
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Fig. 16. Slider levitation distance vs. the slider’s weight per unit area for diagonal and vertical excitation.
5. The levitation characteristics via flexural traveling waves Fig. 16 shows the measured levitation distance h versus the weight per unit area w of the slider for both diagonal and vertical excitation using an input power of 15 W. A larger maximum displacement amplitude was obtained using diagonal excitation, 28 m0–p compared with only 5 m0–p using vertical excitation, similar to the results obtained earlier using standing waves. Fig. 17 plots the levitation rigidity k versus the levitation distance h as calculated from Fig. 16, and shows that the levitation rigidity k was also higher using diagonal excitation. 6. Measurement of the thrust The movement of the levitated slider by a traveling wave generated by the two transducers driven out of phase with respect to each other was experimentally investigated. Using the diagonal excitation technique, video of the levitation and movement of the slider in Ide2004-slidermotion.mpg, and the value of the thrust acting on the slider was estimated by elevating one end of the beam to counteract the sliding thrust provided by the levitation and transportation mechanism by the weight of the slider along the sliding direction, causing the slider to remain in place. Fig. 18 shows the thrust versus the maximum displacement amplitude using diagonal excitation. Thrust was successfully generated in both directions by changing the driving phase difference, and
Fig. 17. Levitation rigidity vs. the slider’s levitation distance for both diagonal and vertical excitation.
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Fig. 18. Thrust vs. the beam displacement amplitude using the diagonal excitation technique.
there was no difference in thrust or velocity between the two sliding directions, despite the asymmetry in the standing wave ratio seen in the vibration of the beam alone. It is believed that the presence of the slider sufficiently suppressed the vibration to eliminate the difference. A maximum thrust of 1.1 mN was obtained using a displacement amplitude of 28 m0–p , while a maximum speed of 138 mm/s was obtained for this study using the 90-g slider. However, the maximum speed is very dependent on the distance allowed for acceleration; our study did not permit the true maximum speed to be achieved before the slider reached the end of the guide rail beam. For vertical excitation, the displacement amplitude was smaller compared with diagonal excitation, and, as a result, the thrust direction was very difficult to control. The surfaces of the beam and slider were polished, but the quality of the finish and precision of the interface are limited by the use of extruded aluminum as the beam and slider material. Finally, it is important to note the boundary conditions of the beam and the transducers differed from the FEM analysis, adversely affecting a comparison between the measured and computed results. 7. Conclusions A novel linear bearing based on near-field acoustic levitation has been proposed and investigated. A guide rail beam and slider, both with a right-angular cross-section, were used; the slider was levitated using ultrasonic flexural vibration in the rail as expected. Based on the studies of the driving position on the beam and the conditions to excite a traveling wave, the levitated slider was moved successfully in both directions by traveling waves transmitted along the length of the beam. Vertical excitation was found to be inferior to diagonal excitation, but, overall, a maximum thrust of 1.1 mN was obtained. References [1] N. Taniguchi, Nanotechnology: Integrated Procesing Systems for UltraPrecision and Ultra-Fine Products, Oxford University Press, 1996. [2] D. Lange, Ball screws that hang tough, Power Transm. Des. 42 (6) (2000) 29–32. [3] S. Ueha, Y. Tomikawa, Ultrasonic Motors—Theory and Applications, vol. 29 of Monographs in Electrical and Electronic Engineering, Clarendon Press, Oxford, 1993.
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Biographies Takeshi Ide was born in Kumamoto, Japan on September 5th, 1980. He received the B Eng degree from the Tokyo Institute of Technology, Tokyo, Japan, in 2003. He is now pursuing his master’s degree at the Tokyo Institute of Technology, Tokyo, Japan, researching actuators using ultrasonic levitation. Mr. Ide enjoys playing volleyball, baseball, and many other sports, and is a drummer in his friend’s band. In his spare time, he travels with his girlfriend or takes short walks alone. He is a member of the Acoustical Society of Japan and the Institute of Electronics, Information and Communication Engineers. James Friend was born in Lubbock, Texas on September 13, 1970. He received the BS degree in aerospace engineering, and the MS and PhD degrees in mechanical engineering from the University of Missouri-Rolla in 1992, 1994, and 1998,
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respectively. He received the Best Paper award and Jefferson Goblet Student Paper Award from the ASME and AIAA for a paper delivered at the 97th Annual AIAA/ASME/AHS/ASC/ASCE Structural Dynamics and Mechanics Conference in 1996, an award for the encouragement of young scientists at the Symposium for Ultrasonic Electronics and Engineering in 2003 for a presentation on acoustic waveguides, and an award in 2004 for a presentation on the Scream actuator at the Spring Meeting of the Acoustical Society of Japan. From 2001 to 2004, Dr. Friend was an assistant professor at the Precision and Intelligence Laboratory, Tokyo Institute of Technology, and is now a co-director of the MicroNanophysics Research Laboratory, Monash University, Melbourne, Australia, with research interests in micro/nanofluidics and micromechatronics and its applications. He is a member of IEEE, ASME, and Sigma Xi. Kentaro Nakamura was born in Tokyo, Japan, on July 3, 1963. He received the B Eng, the M Eng, and the D Eng degrees from the Tokyo Institute of Technology, Tokyo, Japan, in 1987, 1989, and 1992, respectively. He has been an Associate Professor of the Precision and Intelligence Laboratory, Tokyo Institute of Technology, since 1996. His field of research is the application of ultrasonics and the measurement of vibration and sound using optical methods. He has received the Awaya Kiyoshi Award for encouragement of research from the Acoustical Society of Japan in 1996. Dr. Nakamura is a member of the Acoustical Society of Japan, the Japan Society of Applied Physics, the Institute of Electrical Engineers of Japan, and the Institute of Electronics, Information and Communication Engineers. Sadayuki Ueha was born in Kyoto Prefecture, Japan, on February 28, 1943. He received the B Eng degree in electronic engineering from the Nagoya Institute of Technology in 1965 and the M Eng degree in 1967, and the D Eng degree in 1970, both in electric engineering, from the Tokyo Institute of Technology. He currently conducts research in high power ultrasonics. He has been a Professor of the Precision and Intelligence Laboratory, Tokyo Institute of Technology since 1992. He is a steering committee member of the World Congress on Ultrasonics and serves as the secretariat of WCU97. He received the Best Paper Award from The Japan Society of Applied Physics in 1975 and from the Acoustical Society of Japan in 1980, respectively. Dr. Ueha is a member of the Japan Society of Applied Physics, the Acoustical Society of Japan, the Institute of Electronics, Information and Communication Engineers and the Japan Society of Ultrasonics in Medicine.