Ultrasonics 54 (2014) 455–460

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Ultrasonics
journal homepage: www.elsevier.com/locate/ultras

Plate-shaped non-contact ultrasonic transporter using ﬂexural vibration
Takahiko Ishii a,⇑, Yosuke Mizuno a, Daisuke Koyama a,b,c, Kentaro Nakamura a, Kana Harada d,
Yukiyoshi Uchida daPrecision and Intelligence Laboratory, Tokyo Institute of Technology, 4259 Nagatsuta-cho, Midori-ku, Yokohama 226-8503, Japan
Faculty of Science and Engineering, Doshisha University, 1-3 Tataramiyakodani, Kyotanabe, Kyoto 610-0321, Japanc
Wave Electronics Research Center, Doshisha University, 1-3 Tataramiyakodani, Kyotanabe, Kyoto 610-0321, Japand
Logistics Innovation Division, Toshiba Logistics Corporation, 1-14 Nisshin-cho, Kawasaki-ku, Kawasaki 210-0024, Japanba r t i c l e

i n f oArticle history:
Received 15 April 2013
Received in revised form 14 June 2013
Accepted 3 July 2013
Available online 11 July 2013
Keywords:
Near-ﬁeld acoustic levitation
Non-contact transporter
Flexural vibration
Finite-element analysis

a b s t r a c t
We developed a plate-shaped non-contact transporter based on ultrasonic vibration, exploiting a phenomenon that a plate can be statically levitated at the place where its gravity and the acoustic radiation
force are balanced. In the experiment, four piezoelectric zirconate titanate elements were attached to aluminum plates, on which lattice ﬂexural vibration was excited at 22.3 kHz. The vibrating plates were connected to a loading plate via ﬂexible posts that can minimize the inﬂuence of the ﬂexure induced byheavy loads. The distribution of the vibration displacement on the plate was predicted through ﬁnite-element analysis to ﬁnd the appropriate positions of the posts. The maximum levitation height of this transporter was 256 lm with no load. When two vibrating plates were connected to a loading plate, themaximum transportable load was 4.0 kgf.
Ó 2013 Elsevier B.V. All rights reserved.

1. Introduction
In logistics industry and transport systems in factories, objects
are often manually transported using pallets, where considerable
thrust is needed for heavy load due to the friction force between
the pallets and the ﬂoor. To reduce the friction, non-contact transport systems based on air bearing have been developed [1], butthey required large air compressors and air tubes with sufﬁcientamount of clean air. One of the promising candidates to solve thisproblem is the technique based on near-ﬁeld acoustic levitation(NFAL). With this effect, a planner object can be levitated above avibrating plate via a small air gap due to the acoustic radiation
force generated by the ultrasonic ﬁeld in the gap. There have been
many reports to apply the NFAL to transporting silicone waters onlarge glass plates of liquid crystal display [2–6]. Here, we discuss a
non-contact pallet table, where vibrating plates are levitated on aﬂat ﬂoor with acoustic radiation force.
We have so far reported two types of NFAL-based non-contact
stages: a sliding table with two triangular cross-sectional guiderails [7] and a self-running bidirectional slider with an aluminumrectangular frame [8]. These stages exploit the traveling waves
propagating along the stator guide rails or the slider itself, which
induces acoustic streaming along the air gap, and a thrust force
is generated to the slider through the viscosity force of air [9,10].
Traveling waves can be generated by two vibrating elements with⇑ Corresponding author. Tel.: +81 459245052.
E-mail address: ishii@sonic.pi.titech.ac.jp (T. Ishii).
0041-624X/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved.
http://dx.doi.org/10.1016/j.ultras.2013.07.002

a two-phase drive as well [7,8]; one of the vibration elements acts
as a generator of sound waves, and the other as an absorber. We
have also investigated an ultrasonically levitated slider for a selfrunning sliding stage for linear movement [11] as well as a noncontact moving two-dimensional stage [12] without guide rails required in the conventional ultrasonically levitated tables [7,8].
However, these rail-free transporters are applicable only to light
objects.
In this paper, an NFAL-based plate-shaped non-contact transporter for relatively heavy loads is demonstrated. Four piezoelectric zirconate titanate (PZT) elements were attached to analuminum plate, on which lattice ﬂexural vibration was excitedat 22.3 kHz. Two or four vibration plates were bearing an object
with a loading plate, as illustrated in Fig. 1. To minimize the inﬂuence of the deﬂection induced by heavy loads, the vibrating plates
were connected to the loading plate via ﬂexible supporting posts.
With no load, the maximum levitation height of this transporterwas 256 lm. When two vibrating plates were connected to a loading plate, the maximum transportable load of 4.0 kgf was achieved.

2. Conﬁguration of vibrating plate
The conﬁguration of the self-levitation vibrating plate is shownin Fig. 2a–c. The vibrating plate consisted of a square aluminum plate(2  78  78 mm3) and four PZT elements (1  18  18 mm3;
C-203, Fuji Ceramics). The PZT elements, bonded to the aluminum
plate using epoxy, were polarized in the thickness direction. The

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T. Ishii et al. / Ultrasonics 54 (2014) 455–460

Fig. 1. Concept of self-levitating plate.

mass of the vibrating plate was as light as 42.2 g (68.0 N/m2). By
applying an alternating voltage to the PZT elements, lattice-mode
ﬂexural vibration at 22.3 kHz was generated in the aluminum plate,which induced the acoustic radiation force downward to the ﬂat
ﬂoor.
The dimensions of the aluminum plate and the PZT elements,
the locations of the four PZT elements on the aluminum plate,
and the ﬂexural vibrating mode were determined with FEA simulation (ANSYS 11.0) [13] so that the vibration displacement amplitude of the vibrating plate was maximized to obtain large
levitation force. Fig. 3 shows the simulated optimal distributionof the vibration displacement amplitude, where four nodal lines
were observed in both X and Y directions at the resonance frequency of 23.2 kHz. Suitable positions of the PZT elements to maximize the average vibration amplitude over the entire vibratingplate were in every half wavelength of the lattice ﬂexural vibration.
The optimal size of the PZT elements (18 mm) was equal to the half
wavelength of the ﬂexural vibration.

3. Characterization of the ﬂexural vibrations
The displacement amplitude distribution of the lattice-mode
ﬂexural vibration on the prototype was measured using a laser
Doppler vibrometer (LDV), as shown in Fig. 4. The vibration mode
expected through the FEA (Fig. 3) was successfully excited in the
prototype vibrator at 22.3 kHz. All the PZT elements were excitedin phase. The ﬂexible posts for connecting the vibrating plate to
the loading plate should be ﬁxed at the nodal position of the plate because (1) the ﬂexural vibration on the vibrating plate should not be
suppressed and (2) the vibration should not be conveyed to the loading plate. Thus, the positions of the four posts were set, as shown in
Fig. 4, to the four points (indicated as ‘‘P’’) on the nodal lines.
Fig. 5 shows the dependence of the total driving current to thefour PZTs on the normal vibration velocity at the edge of the vibrating plate. The force coefﬁcient, i.e. the slope of the dependence,was 0.59 N/V. Using this value, the vibrating velocity can be estimated simply by measuring the current.

Fig. 2. (a) Conﬁguration, (b) location of the PZTs, and (c) photograph of the vibrating plate.

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T. Ishii et al. / Ultrasonics 54 (2014) 455–460

Fig. 5. Total current vs. vibration velocity.
Fig. 3. Simulated distribution of the vibration displacement amplitude on the plate
at 23.2 kHz. The vibration amplitude is normalized by its maximum value.

Fig. 6. Admittance loop of the vibrating plate with and without the posts.

Fig. 4. Measured distribution of the vibration displacement amplitude at 22.3 kHz.

Fig. 6 shows the measured admittance loops of the vibratingplate with and without the posts, from which the resonance characteristics were calculated as described in Table 1. While the resonance frequency and the damped capacitance were almost
unchanged, the quality factor and the motional admittance that affect the vibration performance were moderately reduced by connecting the posts. The reduction is within the range applicable topractical use.
4. Levitation characterization
We investigated the levitation characteristics of the vibratingplate. According to the NFAL theories [14,15], when the vibrating
mode of a sound source is an in-phase piston vibration mode, thelevitation distance of the ﬂat object h is expressed as

h ¼ curﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
1þc
q;
4w

ð1Þ

where c is the sound speed in air, u is the displacement amplitude of
the vibration plate, w is the weight of the levitated object, c is the
speciﬁc heat ratio in air, and q is the density of air. Eq. (1) indicates

Table 1
Resonance characteristics of the vibrating plate.

Resonance frequency f0 (kHz)
Quality factor
Motional admittance Ym0 (mS)
Damped capacitance Cd (nF)

Without posts

With posts

22.28
811.0
16.76
15.29

22.32
578.8
12.39
15.72

that the levitation distance h is proportional to u and w0.5. Fig. 7
shows the levitation distance measured at the edge of the vibratingplate as a function of the maximum displacement amplitude of thevibrating plate. The levitation distance was measured with a digital
microscope (VH-8000 and VH-Z450, Keyence, Co.). In the range of u
from 7 to 12 lm, h was proportional to u0.5, though h should be intheory proportional to u. When the vibration displacement amplitude was 26.0 lm, the maximum levitation distance of 256 lm
was obtained. The experimental values of h were approximately
30% of the theoretical values, probably because the sound ﬁeld leakage between the vibrating plate and the substrate is not taken into
consideration in deriving Eq. (1) and because part of the soundwaves transmitted from the 2-mm-thick vibrating plate was attenuated and converted to heat in the air gap between the plate andthe bottom substrate. In addition, the difference is attributed to458

T. Ishii et al. / Ultrasonics 54 (2014) 455–460

ment amplitude was ﬁxed at 6.0 lm. The theoretical lines basedon Eq. (1) were also provided. As the weight of the loading plate
was increased, the levitation distance h was reduced. When theload was under 1 kgf, h with one unit was larger than that with
two units. In the case of the load over 2 kgf, levitation was not observed with one unit, whereas clear levitation was observed with
two units. The loadable maximum weight of 4.0 kgf was obtainedwith two units. From these results, the large levitation force appears to be achieved by increasing the number of units.

5. Relationship between pull force and displacement amplitudeFig. 7. Measured levitation distance of the vibrating plate as a function of thevibration displacement amplitude.

the assumption in the theoretical model that the vibration mode of
the plate is an in-phase piston mode, not a ﬂexural mode. The
abrupt reduction in h was observed when u was lower than 7 lm,
which might be caused by energy leakage, as theoretically predicted
in Ref. [16].
Next, we connected two vibrating plates to one loading plateusing eight posts, as shown in Fig. 8a, and its levitation distance
was measured as a function of the weight on the loading plate.
Hereafter, the vibrating plate connected with four posts is referred
to as a ‘‘unit’’. Cylindrical rods with the diameter of 10 mm and thelength of 20–30 mm were employed as the posts. The elastic compliance was performed at both sides of the posts to suppress thevibration transmission to the loading plate by attaching an elastic
material, such as a coiled spring (Young’s modulus: 206 GPa), silicone rubber (14.2 MPa), urethane (600 MPa), and silicone gel(0.1 MPa), the photographs of which are show in Fig. 8b. An acrylic
plate (3  80  80 mm3) was used as a loading plate. Since thequality factor of the vibrating plate with the gel was larger thanthat with the other three, the levitation distance h was measured
as a function of load using one and two units with the gel-attachedposts, as shown in Fig. 9. As the levitation distance is reduced by
the load, the radiation impedance of the vibrating plate is raised,
which indicates that the vibration amplitude changes with the load
even if the voltages are the same. In Fig. 9, the voltages applied to
the vibrating plate were adjusted so that the vibration displace-

Even when the levitating transporter is not completely noncontact, the reduction in the pull force due to the suppression of
the friction is practically useful in transporting objects. The pullforce in the horizontal direction was measured with a digital force
gauge as a function of the mass on the loading plate with one andtwo units. The relationship between the vibration amplitude andthe pull force is summarized in Fig. 10, where the posts with thefour materials (described in the previous section) attached wereused. The weight of the mass was ﬁxed at 2.0 kgf. Under all theconditions, the pull force was decreased with the increase in thedisplacement amplitude: for example, the pull force was 1.1 N
when the vibration amplitude was 8.0 lm with two units andthe posts with the gel. This result implies that the pull force was
reduced to 75% when compared to that without vibration excitation. With one unit, the pull force was reduced to 45%.
The static deﬂection at the center of the loading plate caused by
the weight of the transported object affects the levitation characteristics. Fig. 11 shows the changes in the pull force when the distances between the two units d were 40 and 80 mm. When aweight of 3 kgf was put on the loading plate, the static deﬂections
were 0.9 and 3.5 mm for d = 40 and 80 mm, respectively. While thepull force was reduced by increasing the vibration amplitude, onlya slight difference was observed between the results for d = 40 and
80 mm. The larger static deﬂection of the loading plate induces theacoustic streaming from the center to the edges of the vibratingplate, because the sound pressure amplitude at the center part ofthe vibrating plate is higher than that at the edges. This indicatesthat part of the acoustic energy in the air layer between the plate
and the substrate are transformed to the acoustic streaming anddissipated. In addition, the larger static deﬂection also means a larger gap between the vibrating plate and the ﬂoor, where the soundﬁeld is weakened. Therefore, the small static deﬂection improves
the levitation force, leading to the reduction in the pull force.

Fig. 8. Photographs of (a) self-levitating plate involving two vibrating plates (i.e., two units), and (b) four kinds of posts used in the experiments.

T. Ishii et al. / Ultrasonics 54 (2014) 455–460

Fig. 9. Levitation distance of the vibrating plate vs. load when gel-attached posts
were employed.

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Fig. 12. Measured pull forces as functions of load when the unit number was 1, 2,
and 4.

in Fig. 12. The number of the units was changed from one to four.
With one and two units, the maximum transportable weights were
1 and 4 kgf, respectively. The pull forces were drastically increased
to the values without excitation, if the weights over these maximum values were applied. The weight of 9 kgf was transportedwith four units and the pull force was 2.5 N, which is 1.25 times
larger than that with no loading. From comparison between the results with the four units and without excitation, the pull force wasdecreased to 1/10 by the ultrasound levitation, since the frictional
resistance between the vibrating plate and the bottom substrate
was reduced. When the vibration amplitude was increased to
5.2 lm, the maximum transportable weight was increased to
12 kgf, while the pull force was not changed under 9 kgf. The electrical power consumption per unit was approximately 13 W.
7. Conclusions
Fig. 10. Relationship between the pull force and the vibration displacement
amplitude when the number of unit was 1 and 2.

A plate-shaped non-contact transporter exploiting NFAL wasdeveloped. The transporter consisted of ﬂexural vibrating plates
and a loading plate connected via supporting posts. The acoustic
radiation force from the vibrating plates produced the levitation
force of the transporter. The conﬁguration of the vibrating plate
was determined by use of FEA. The loadable maximum weight of
4 kgf was achieved. The levitation force was increased with thenumber of units, which decreased the pull force in the horizontal
direction. From the results obtained in this study, a 320-kgf load
is expected to be carried using about 140 units, with the total input
electrical power of 1.8 kW. We believe that the non-contact selflevitating plate presented in this paper will be of great use in transporting heavy objects in logistics with its various advantages
including structure simplicity, cost efﬁciency, and applicability to
non-electric/magnetic materials.
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Fig. 11. Relationship between the pull force and the vibration displacement
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6. Levitation characteristic with four units
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