The instability of a floating object is the main factor preventing near-field acoustic levitation (NAFL) from being widely used in the manufacture of micro-electro-mechanical systems. Therefore, investigating the restoring force due to the generation mechanisms of NAFL is necessary to ensure the stable levitation of the floating object. This study presents a theoretical analysis to evaluate the restoring force based on the gas-film-lubrication theory. The gas-film pressure between the reflector and the radiator is expressed in the form of the dimensionless Reynolds equation in a cylindrical coordinate system, which is solved by an eight-point discrete grid method due to the discontinuous gas-film distribution. An experimental rig is constructed to measure the restoring force at various eccentricities, which can be used to support the developed numerical model. The theoretical results show that the restoring force increases with an increment in eccentricity, which agrees with experimental results. Furthermore, theoretical prediction results indicate that the restoring force increases when the amplitude of the radiator and weight of the levitator increases, which indicates higher system stability. The results of the radiator vibration mode on the restoring force show that the restoring force is the largest in the first-order mode.

1.
F.
Erzincanli
,
J.
Sharp
, and
S.
Erhal
, “
Design and operational considerations of a non-contact robotic handling system for non-rigid materials
,”
Int. J. Mach. Tool. Manuf.
38
(
4
),
353
361
(
1998
).
2.
O.-S.
Kim
,
S.-H.
Lee
, and
D.-C.
Han
, “
Positioning performance and straightness error compensation of the magnetic levitation stage supported by the linear magnetic bearing
,”
IEEE. Trans. Ind. Electron.
50
(
2
),
374
378
(
2003
).
3.
V.
Vandaele
,
P.
Lambert
, and
A.
Delchambre
, “
Non-contact handling in microassembly: Acoustical levitation
,”
Precis. Eng.
29
(
4
),
491
505
(
2005
).
4.
S.
Ueha
,
Y.
Hashimoto
, and
Y.
Koike
, “
Non-contact transportation using near-field acoustic levitation
,”
Ultrasonics
38
(
1
),
26
32
(
2000
).
5.
T.
Ide
,
J.
Friend
,
K.
Nakamura
, and
S.
Ueha
, “
A non-contact linear bearing and actuator via ultrasonic levitation
,”
Sens. Actuat. A Phys.
135
(
2
),
740
747
(
2007
).
6.
D.
Ha
,
T.
Stolarski
, and
S.
Yoshimoto
, “
An aerodynamic bearing with adjustable geometry and self-lifting capacity. Part 1: Self-lift capacity by squeeze film
,”
Proc. Inst. Mech. Eng. J. Part J
219
(
1
),
33
39
(
2005
).
7.
S.
Zhao
,
S.
Mojrzisch
, and
J.
Wallaschek
, “
An ultrasonic levitation journal bearing able to control spindle center position
,”
Mech. Syst. Signal. Process.
36
(
1
),
168
181
(
2013
).
8.
K.
Feng
,
M.
Shi
,
T.
Gong
,
Y.
Liu
, and
J.
Zhu
, “
A novel squeeze-film air bearing with flexure pivot-tilting pads: Numerical analysis and measurement
,”
Int. J. Mech. Sci.
134
,
41
50
(
2017
).
9.
Y.
Hashimoto
,
Y.
Koike
, and
S.
Ueha
, “
Acoustic levitation of planar objects using a longitudinal vibration mode
,”
J. Acoust. Soc. Jpn. E
16
(
3
),
189
192
(
1995
).
10.
Y.
Wada
,
D.
Koyama
, and
K.
Nakamura
, “
Finite-element analysis of acoustic streaming generated between a bending transducer and a reflector through second-order approximated forces
,”
Acoust. Sci. Technol.
34
(
5
),
322
331
(
2013
).
11.
Y.
Wada
,
T.
Kundu
, and
K.
Nakamura
, “
Mesh-free distributed point source method for modeling viscous fluid motion between disks vibrating at ultrasonic frequency
,”
J. Acoust. Soc. Am.
136
(
2
),
466
474
(
2014
).
12.
Y.
Wada
,
D.
Koyama
, and
K.
Nakamura
, “
Acoustic streaming in an ultrasonic air pump with three-dimensional finite-difference time-domain analysis and comparison to the measurement
,”
Ultrasonics
54
(
8
),
2119
2125
(
2014
).
13.
A.
Minikes
,
I.
Bucher
, and
S.
Haber
, “
Levitation force induced by pressure radiation in gas squeeze films
,”
J. Acoust. Soc. Am.
116
(
1
),
217
226
(
2004
).
14.
A.
Almurshedi
,
M.
Atherton
,
C.
Mares
, and
T.
Stolarski
, “
Modelling influence of Poisson's contraction on squeeze film levitation of planar objects
,”
J. Appl. Phys.
125
,
095303
(
2019
).
15.
Y.
Fan
,
M.
Miyatake
,
S.
Kawada
,
B.
Wei
, and
S.
Yoshimoto
, “
Inertial effect on gas squeeze film for large radius disc excited by standing waves with complex modal shapes
,”
Int. J. Mod. Phys. B
33
(
24
),
1950282
(
2019
).
16.
T.
Stolarski
and
W.
Chai
, “
Inertia effect in squeeze film air contact
,”
Tribol. Int.
41
(
8
),
716
723
(
2008
).
17.
J.
Li
,
W.
Cao
,
P.
Liu
, and
H.
Ding
, “
Influence of gas inertia and edge effect on squeeze film in near field acoustic levitation
,”
Appl. Phys. Lett.
96
(
24
),
243507
(
2010
).
18.
J.
Hu
,
K.
Nakamura
, and
S.
Ueha
, “
Stability analysis of an acoustically levitated disk
,”
IEEE Trans. Ultrason. Ferr.
50
(
2
),
117
127
(
2003
).
19.
J.
Saito
,
J.
Friend
,
K.
Nakamura
, and
S.
Ueha
, “
Resonant mode design for noncontact ultrasonic motor with levitated rotor
,”
Jpn. J. Appl. Phys.
44
(
6B
),
4666
4668
(
2005
).
20.
D.
Koyama
,
K.
Nakamura
, and
S.
Ueha
, “
A stator for a self-running, ultrasonically-levitated sliding stage
,”
IEEE Trans. Ultrason. Ferr.
54
(
11
),
2337
2343
(
2007
).
21.
J.
Hu
,
G.
Li
,
H.
Chan
, and
C.
Choy
, “
A standing wave-type noncontact linear ultrasonic motor
,”
IEEE Trans. Ultrason. Ferr.
48
(
3
),
699
708
(
2001
).
22.
Y.
Koike
,
S.
Ueha
,
A.
Okonogi
,
T.
Amano
, and
K.
Nakamura
, “
Suspension mechanism in near field acoustic levitation phenomenon
,” in
Proceedings of the 2000 Ultrasonics Symposium
,
San Juan, Puerto Rico
(
October 22–25
,
2000
), pp.
671
674
.
23.
E.
Matsuo
,
Y.
Koike
,
K.
Nakamura
,
S.
Ueha
, and
Y.
Hashimoto
, “
Holding characteristics of planar objects suspended by near-field acoustic levitation
,”
Ultrasonics
38
(
1–8
),
60
63
(
2000
).
24.
J.
Li
,
P.
Liu
,
H.
Ding
, and
W.
Cao
, “
Nonlinear restoring forces and geometry influence on stability in near-field acoustic levitation
,”
J. Appl. Phys.
109
(
8
),
084518
(
2011
).
25.
W.
Li
,
Y.
Liu
, and
K.
Feng
, “
Modelling and experimental study on the influence of surface grooves on near-field acoustic levitation
,”
Tribol. Int.
116
,
138
146
(
2017
).
26.
A.
Minikes
and
I.
Bucher
, “
Noncontacting lateral transportation using gas squeeze film generated by flexural traveling waves—Numerical analysis
,”
J. Acoust. Soc. Am.
113
(
5
),
2464
2473
(
2003
).
27.
A.
Minikes
and
I.
Bucher
, “
Coupled dynamics of a squeeze-film levitated mass and a vibrating piezoelectric disc: Numerical analysis and experimental study
,”
J. Sound. Vib.
263
(
2
),
241
268
(
2003
).
28.
T.
Stolarski
and
W.
Chai
, “
Self-levitating sliding air contact
,”
Int. J. Mech. Sci.
48
(
6
),
601
620
(
2006
).
29.
S.
Mohite
,
V.
Sonti
, and
R.
Pratap
, “
A compact squeeze-film model including inertia, compressibility, and rarefaction effects for perforated 3-D MEMS structures
,”
J. Microelectromech. Syst.
17
(
3
),
709
723
(
2008
).
30.
B. J.
Hamrock
,
S. R.
Schmid
, and
B. O.
Jacobson
,
Fundamentals of Fluid Film Lubrication
, 2nd ed. (
CRC Press
,
Boca Raton, FL
,
2004
), Chap. 6, pp.
165
167
.
31.
S.-K.
Chen
,
H.-C.
Chou
, and
Y.
Kang
, “
Stability analysis of hydrodynamic bearing with herringbone grooved sleeve
,”
Tribol. Int.
55
(
2
),
15
28
(
2012
).
32.
H.
Heshmat
,
J.
Walowit
, and
O.
Pinkus
, “
Analysis of gas-lubricated foil journal bearings
,”
J. Lubr. Technol.
105
(
4
),
647
655
(
1983
).
33.
K.
Feng
,
Y.
Liu
, and
M.
Cheng
, “
Numerical analysis of the transportation characteristics of a self-running sliding stage based on near-field acoustic levitation
,”
J. Acoust. Soc. Am.
138
(
6
),
3723
3732
(
2015
).
34.
R. W.
Fox
,
A. T.
McDonald
, and
P. J.
Pritchard
,
Fox and McDonald's Introduction to Fluid Mechanics
, 8th ed. (
John Wiley & Sons
,
New York
,
2011
), Chap. 9, pp.
445
448
.
35.
F. A.
Morrison
,
An Introduction to fluid Mechanics
(
Cambridge University Press
,
New York
,
2013
), Chap. 5, pp.
369
379
.
36.
K.
Uchiage
,
Y.
Ishino
,
M.
Takasaki
, and
T.
Mizuno
, “
Enlargement of floater size in ultrasonic suspension by arranging the shape of vibrating surface
,” in
Proceedings of the 2014 IEEE International Ultrasonics Symposium
,
Chicago, IL
(
September 3–6
,
2014
), pp.
2510
2513
.
37.
M.
Takasaki
,
S.
Chino
,
Y.
Kato
,
Y.
Ishino
, and
T.
Mizuno
, “
Actuation force measurement mechanism for non-contact ultrasonic suspension
,”
Key Eng. Mater.
523–524
,
727
732
(
2012
).
38.
P.
Liu
,
J.
Li
,
H.
Ding
, and
W.
Cao
, “
Modeling and experimental study on near-field acoustic levitation by flexural mode
,”
IEEE Trans. Ultrason. Ferr.
56
(
12
),
2679
2685
(
2009
).
You do not currently have access to this content.