IEEE TRANSACTIONS ON ULTRASONICS, FERROELECTRICS, AND FREQUENCY CONTROL , vol. 62, no. 12, DECEMBER 2015

2169

Ultrasonic Motors With Polymer-BasedVibrators
Jiang Wu, Yosuke Mizuno, Member, IEEE, Marie Tabaru, and Kentaro Nakamura, Member, IEEE
Abstract—With their characteristics of low density andelastic moduli, polymers are promising materials for making
ultrasonic motors (USMs) with high energy density. Although
it has been believed for a long time that polymers are too lossy
to be applied to high-amplitude vibrators, there are several
new polymers that exhibit excellent vibration characteristics.
First, we measure the damping coefficients of some functional
polymers to explore the applicability of polymers as vibrators
for USMs. Second, to investigate the vibration characteristics,
we fabricate bimorph vibrators using several kinds of polymers
that have low attenuation. Third, a bending mode USM isfabricated with a polymer rod and four piezoelectric platesbonded on the rod as a typical example of a USM. Throughan experimental investigation of the motor performance, it was
found that the polymer-based USMs exhibited higher rotation
velocity than the aluminum-based USM under a light preload,
although the maximum torque of the polymer-based USMs
was smaller than the aluminum-based USM. Among the tested
polymers, polyphenylenesulfide was a prospective material for
USMs under light preloads because of the high amplitude andlightweight of polyphenylenesulfide.

used as the vibrating body of a USM. To reduce weight,
it would be meaningful to examine the possibility of applying polymers as both the vibrator and rotor of a USM.
Polymers usually appear to be very soft and good forabsorbing vibration as a result of high mechanical loss.
However, among new kinds of engineering polymers, someproducts with low mechanical loss exist. To gain a preliminary understanding of the attenuation characteristicsof the polymers, we measured the damping coefficientsof some typical functional polymers: polyetheretherketone(PEEK), polyacetal (POM), acrylonitrile-butadiene-styrene (ABS), polyphenylenesulfide (PPS), and polyphenylenesulfide filled with carbon fiber (PPS/CF). Next, weselected the polymers with low damping coefficients tofabricate bar-type USMs and investigated the vibrationand mechanical characteristics of those USMs.
II. Polymer-Based Bimorphs

I. IntroductionW

ith their characteristics of low speed, high torque,and quick response [1], ultrasonic motors (USM)
have been applied in robots, precision positioning machines, and optical instruments. As an important part of amechanical system, an actuator with high energy density
can decrease the total weight of the system and increase
the operability. Many researchers have focused on developing micro-sized USMs [2]–[10], whose vibrators were madeprimarily of metal or piezoelectric ceramics [11]. MEMS
technology is also used to miniaturize USMs; however, thisis applicable only to micro motors smaller than 1 mm, andavailable materials are limited. On the other hand, reducing the weight of actuators is another important issue. A
variety of new functional polymers have been invented in
the last 30 years with the development of material science,and some of the polymers have good workability and wear
characteristics [12]. In some of the previous reports on
USMs, polymer film was glued to the contacting surface asa friction material to improve the friction and wear characteristics [13]–[16]. However, polymers have never been

Manuscript received April 17, 2015; accepted October 1, 2015. The
authors thank Daicel Corporation for providing some of the polymer
samples tested in the experiments.
The authors are with the Precision and Intelligence Laboratory, Tokyo
Institute of Technology, Yokohama 226-8503, Japan (e-mail: wujiang@
sonic.pi.titech.ac.jp).
DOI http://dx.doi.org/10.1109/TUFFC.2015.007122

A. Introduction of the Tested Polymers
Since the first report about its excellent mechanicalproperties, PEEK has been a promising substitute material for metal. At present, the current version of PEEK
has excellent abrasion resistance and workability [12],[17]. In industrial applications, lightweight gears are often
made of POM because of its high resistance to abrasionand heat [18]. ABS has flowability and high resistance toimpact [19]. PPS is also widely applied in the automotive industry because it has better wear properties than
PEEK [20]. To increase strength, other materials such as
glass, carbon fiber, and aramid fiber are filled in bars orplates of PPS. The composite, using carbon fiber as filler
component with a mass fraction of 30%, is referred to as
PPS/CF. The carbon fibers are filled in parallel in one direction; thus, this composite has obvious anisotropy. The
mechanical characteristics of PEEK, POM, ABS, PPS,and PPS/CF used in the experiments in this paper are
listed in Table I. Note that the elastic modulus of the
PPS/CF shown in Table I is the value in the direction of
the carbon fibers.
B. Preliminary Measurement of the Damping Coefficients
Because the attenuation characteristics for the kilohertz vibration of the polymers used in the experiments
have rarely been reported, we measure the damping coefficients of these functional polymers before conducting our

0885–3010 © 2015 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.
See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

2170

IEEE TRANSACTIONS ON ULTRASONICS, FERROELECTRICS, AND FREQUENCY CONTROL , vol. 62, no. 12, DECEMBER 2015

TABLE I. Mechanical Characteristics of the Tested
Polymers and Aluminum.
Material

Density(× 103 kg/m3)

Elastic modulus(GPa)

Poisson's
ratio

PEEK
POM
ABS
PPS
PPS/CF
Aluminum

1.28
1.41
1.05
1.35
1.44
2.70

3.5
2.8
2.4
3.45
21.2*
70.3

0.40
0.35
0.36
0.36
—
0.33

*Measured in filling direction.

experiments to make preliminary choice of the polymers
suitable for vibrators. As a comparison, the damping coefficient of aluminum is also measured.
Fig. 1 shows the experimental setup. One end of thebar of 100 mm in length, 10 mm in width, and 1.5 mm
in thickness was fixed to an acrylic base using a bolt. We
hammered the middle of the bar to give it a transientmechanical input, and measured the vibration velocity at
the free end using a laser Doppler velocimeter (NLV1232,
Polytec, Waldbronn, Germany). A damped oscillation of
the velocity v(t) with an exponential envelope, as shownin Fig. 2, is theoretically expected. The vibration velocityv(t) is given by the equationv(t) = V 0 ⋅ e −βω 0t ⋅ sin(ω 0t + θ),(1)

where V0, 2β, ω0, and θ are the initial velocity amplitude,
the damping coefficient, the resonance frequency, and thephase. We calculated the damping coefficients 2β by fitting the measured data with the envelope of (1). The measurements were carried out 20 times for each sample, andthe averaged value was selected as the damping coefficientof the sample.
Fig. 3 shows the results. The damping coefficient of
PPS is 0.003, which is the smallest among the tested polymers. The damping coefficient of PPS/CF increases to0.006 with the carbon fiber filled into the base-material
PPS. The damping coefficients of POM and ABS are eighttimes larger than that of the PPS. The damping coefficient of aluminum is 0.0005, which is 0.17 times that of
PPS. From these results, we decided to use PEEK, PPS,and PPS/CF as the elastomers of bimorphs to test theircapabilities as piezoelectric vibrators.

Fig. 1. The experimental setup of the measurement of the damping coefficient.

Fig. 2. The theoretical output and envelope curve of vibration velocity inthe time domain under a transient input.

C. Structure and Dimensions of the Bimorph
As shown in Fig. 4, two pieces of piezoelectric ceramic
plates with a folded electrode (C213, Fuji Ceramics, Fujinomiya, Japan) of 10 mm in length, 4 mm in width, and
0.5 mm in thickness are glued to the side surfaces of apolymer rectangular cantilever using epoxy. The electricalconnection of the electrodes to the power source is shownin Fig. 4. When an alternating voltage at the resonancefrequency was exerted, a bending mode appeared on thevibrator, although the tested polymers were nonconductive. It should be noted that, for the PPS/CF-based bimorph, the direction of the vibration velocity was approximately vertical to the filling direction of the carbon fibers.
The vibration distribution was measured using a laser
Doppler velocimeter (NLV1232, Polytec). To compare theperformances, bimorphs using PEEK, PPS, and PPS/CF
were made with the same dimensions. Meanwhile, a bimorph made of aluminum with the same structure anddimensions was made as a reference. The admittance characteristics were measured using an impedance analyzer(4294A, Agilent, Santa Clara, CA, USA), and the resultsof the PEEK-, PPS-, PPS/CF-, and aluminum-based bi-

Fig. 3. The measurement results of the damping coefficients.

wu et al.: ultrasonic motors with polymer-based vibrators

2171

morphs are demonstrated in Figs. 5(a)–5(d), respectively.
Electrical responses corresponding to the 1st, 2nd, and3rd bending modes are observed in the admittances. The
3rd bending mode shows the most obvious response because the position of the piezoelectric ceramic is near theantinode of the 3rd mode.
To precisely obtain the mechanical quality factors (Qfactors) of the bimorphs, we measured the frequency response of the vibration velocity at the free end of thevibrator around the resonance frequency of the bending
modes. The Q factors are calculated according to the approximate equation
Q =Fig. 4. Structure and dimensions of the bimorph vibrators.

f0
,
∆f

(2)

where f0 and Δf represent the resonance frequency and the
bandwidth for 1/√2 of the amplitude, respectively.

Fig. 5. Admittance characteristics of (a) PEEK-, (b) PPS-, (c) PPS/CF-, and (d) aluminum-based bimorph vibrators.

2172IEEE TRANSACTIONS ON ULTRASONICS, FERROELECTRICS, AND FREQUENCY CONTROL , vol. 62, no. 12, DECEMBER 2015

Fig. 6. Vibration velocity distribution of (a) PEEK-, (b) PPS-, (c) PPS/CF-, and (d) aluminum-based bimorph vibrators for the 1st, 2nd, and 3rd
bending modes at the driving voltage of 60 V.

D. Results
The vibration velocities were measured along the bar at
an interval of 1 mm at a driving voltage of 60 V. Figs. 6(a)–6(d) show the results with Q factors for the PEEK-, PPS-,
PPS/CF-, and aluminum-based bimorphs. The PEEK vibrator had its natural frequencies of the 1st, 2nd, and 3rd
bending modes at 0.54, 4.5, and 11.74 kHz, respectively,
and the maximum vibration velocity reached 363 mm/s
at the free end. The resonance frequencies of the 1st, 2nd,
and 3rd bending modes for the PPS vibrators were 0.54,
4.13, and 11.23 kHz, respectively. The maximum vibration velocity was 550 mm/s at the 3rd bending mode. The
natural frequency of each mode increased for the PPS/CF
vibrator, exhibiting higher values of 0.97, 5.79, and 15.24
kHz; meanwhile, the maximum vibration velocity fell to
250 mm/s at a driving frequency of 5.79 kHz. The Q factors of the PPS- and PPS/CF-based bimorphs were higher
than those of the PEEK-based bimorph. For the aluminum-based vibrator, the natural frequencies of 1st, 2nd,
and 3rd bending modes were 3.62, 12.44, and 31.48 kHz,
respectively. The maximum vibration velocity reached 219
mm/s at a driving frequency of 12.44 kHz. The Q factorsof the aluminum-based vibrators were higher than thoseof the polymer-based vibrators. For comparison, the resonance frequency, the Q factor, and the maximum vibration velocity of the 2nd bending mode are summarizedin Table II. It is clear that the resonance frequency of
the aluminum-based bimorph is three times that of thepolymer-based ones, and the resonance frequencies of the
PEEK- and PPS-based bimorphs exhibit little difference.
The vibration velocities of the polymer-based bimorphs
are larger than that of the aluminum-based bimorph.
Among polymer-based bimorphs, the maximum vibration
velocity of the PPS-based bimorph reaches 543 mm/s,
which is larger than that of the others.

TABLE II. Vibration Performances of Polymer-Based andAluminum-Based Bimorph Vibrators of the 2nd Bending Mode.
Elastomer

Resonance
frequency (kHz)Q factor

Maximum vibration
velocity (mm/s)

PEEK
PPS
PPS/CF
Aluminum

4.50
4.13
5.79
12.44

47
90
75
389

363
543
250
219

wu et al.: ultrasonic motors with polymer-based vibrators

2173

E. Discussion
To discuss the relationship between the performance(resonance frequency and vibration velocity) and the mechanical parameters, an electrical equivalent circuit model
shown in Fig. 7 is introduced [3], [5], [21]. Coefficient A
represents the transformation ratio from voltage V todriving force F, whereas m, k, and μ represent the equivalent mass, bending stiffness, and mechanical resistance ofthe 2nd bending model, respectively. Vibration velocity
v is simulated by the current in the circuit. Resonancefrequency f is determined by the equivalent mass m andbending stiffness k:
1
f =
2π

k
.
m

(3)

Bending stiffness k is closely related to elastic modulus
E, whereas equivalent mass m is proportional to density ρ.
Thus, the resonance frequency is proportional to a squareroot of the elastic modulus and inversely proportional toa square root of the density if the vibration mode is specified. According to [22], the resonance frequency of the 2nd
bending mode of the clamped-free bimorph is given asf =1  4.694 ⋅
2π  l 

2

EI
,
ρS

(4)

where l, I, and S represent the length, the area momentof inertia, and the cross-sectional area of the cantilever,respectively. Although the resonance frequency is determined by the ratio of the elastic modulus to the density, the lower resonance frequency of the polymer-based
bimorph compared with the aluminum-based bimorph ismainly attributed to the lower elastic modulus. This is because the ratio of aluminum to PPS in the elastic modulus
is much larger than that of the density. The PEEK- andPPS-based vibrators show little difference in their resonance frequencies because their elastic moduli and densities are almost the same. According to (4), the effective
elastic modulus of PPS/CF in the bending mode is lower
than 21.2 GPa.
Next, we carry out an analysis of the relationship between the vibration velocity and the mechanical parameters. Based on the circuit shown in Fig. 7, under the
resonant state, the vibration velocity is
v =

VA
.
µ

(5)

In a mechanical resonance system, the mechanical resistance μ can be expressed with the mechanical quality factor Q, the equivalent mass m, and the bending stiffness kof the vibrator [21]:
µ=

k ⋅m
.
Q

Substituting (6) into (5), we obtain(6)

Fig. 7. Electrical equivalent circuit representing the vibration characteristics of the 2nd bending mode. (a) The bimorph vibrator in the 2nd
bending mode, (b) electrical equivalent circuit.

v = VA ⋅

Q
.
k ⋅m

(7)

Because the bending stiffness is related to the elastic modulus, and the equivalent mass is determined by the density, vibration velocity v is proportional to the Q factor, andinversely proportional to the square root of the productof elastic modulus E and density ρ. First, let us compare
the vibration velocity of the polymer-based vibrator withthat of the aluminum-based vibrator. The polymer-based
vibrators exhibit higher vibration velocities than the aluminum vibrator as summarized in Table II. This is attributed mainly to the extremely low elastic modulus of thepolymers compared with that of the aluminum. Second,the difference in the vibration velocities of the PEEK- andthe PPS-based vibrators mainly originates in the difference in the Q factors because the elastic moduli and densities are almost the same.
To summarize, we draw the following conclusions forthe bimorph vibrators made of different materials undercertain dimensions:
1) Resonance frequency of the polymer-based bimorph
is lower than the aluminum-based one with the same
dimensions because of a lower elastic modulus.
2) Vibration velocity of the polymer-based bimorph ishigher than that of the aluminum-based one becauseof a lower elastic modulus.
3) PPS-based bimorph has a higher vibration velocity
than other polymer-based ones because of its high Q
factor.

III. Standing Wave USM With Two Orthogonal
Bending Modes
A. Experimental System
The structure of the polymer-based USM for our experiments is depicted in Fig. 8(a). Four pieces of piezoelectric ceramic plates (10 mm × 6 mm × 0.5 mm) arebonded on the four surfaces of a rectangular bar made ofpolymer. The length and width of the bar are 44 mm and6.2 mm, respectively. The end has a disk shape of 8 mm in

2174

IEEE TRANSACTIONS ON ULTRASONICS, FERROELECTRICS, AND FREQUENCY CONTROL , vol. 62, no. 12, DECEMBER 2015

Fig. 9. Experimental setup to evaluate the mechanical characteristics.

Fig. 8. Dimensions and principle of the polymer-based ultrasonic motorwith rectangular bar shape. (a) Structure and dimensions of the vibrator, (b) formation of the elliptical motion with the phase drive of two
orthogonal vibrations.

diameter and 4 mm in thickness for contact with a rotor.
The piezoelectric elements are grouped into two parallelpairs. Two orthogonal bending vibrations are excited witha 90-degree phase difference, with phased voltages applied
to the two pairs of the piezoelectric ceramics. The free
end of the bar shows an elliptical motion at the driving
frequency. A rotor pressed on the free end is driven by theelliptical orbit, as illustrated in Fig. 8(b). The weights of
the PEEK-, PPS-, and PPS/CF-based vibrators are 2.649,
2.709, and 2.844 g, respectively. The rotor is composed ofan acrylic sleeve and is supported with an aluminum bar
via a ball bearing. The total weight of the rotor and thebar is 3.525 g. The experimental system depicted in Fig.
9 is used to measure the mechanical characteristics of the
motor. A high-speed camera (M5, Integrated Design Tools
Inc., Tallahassee, FL, USA) is used to record the angular
position of a marker pasted on the rotor. The angularvelocity of the rotor is calculated from the pictures takenwith the camera by counting the number of turns of therotor and the time interval. A force gauge [ZP(Z2)-50N,
Imada Co. Ltd., Toyohashi, Japan] is used to simultaneously measure the preload exerted between the vibratorside and the rotor. Output torque is measured by pullingup a weight.
B. Results
First, we measured the angular velocities of the rotor
without load under different preloads. The driving frequency was adjusted to obtain the maximum velocity as
the preload was varied. The experimental results for the
angular velocity and driving frequency are shown in Fig.
10.
The angular velocities of the PPS- and PPS/CFbased USMs were over 30 rad/s, and fell sharply after
the preload exceeded 800 mN. The cutoff preload of the
PPS-based USM was around 1800 mN, which was lower
than that of the PPS/CF-based USM (2400 mN). The
maximum angular velocity of the PEEK-based USM wasaround 20 rad/s and decreased to 0 with a preload of
500 mN. The variations in the optimal driving frequency

Fig. 10. Variation of angular velocities and optimal frequency of bimorphs as the preload increases.

wu et al.: ultrasonic motors with polymer-based vibrators

2175

CF-, and aluminum-based USMs all doubled under a 310mN preload, as shown in Fig. 12, whereas the maximum
angular velocities of the PPS- and PPS/CF-based USMs
decreased to 34.1 and 30.3 rad/s, respectively. Mild drops
in the velocity-torque characteristics were observed in the
PPS- and PPS/CF-based USMs. Meanwhile, the PEEKbased USM was stopped under this preload.
When heavy preloads of over 2300 mN were applied,the PPS- and PPS/CF-based USMs stopped, whereas thealuminum-based USM continued to rotate although the
speed was low, as shown in Fig. 13. The maximum torquemeasured for the aluminum-based USM was over 1800
μNm and a higher torque could also be loaded.
Fig. 11. Mechanical characteristics under a preload of less than 310 mN.

C. Discussion

for the polymer-based USMs were smaller than 0.1 kHz
before the USMs stopped. For the aluminum-based USM,
angular velocity decreased from 11 to 5 rad/s when the
preload was exerted to 2500 mN. Even though the driving
frequency varied by more than 0.6 kHz, the rotor continued to rotate when the preload exceeded 2800 mN.
Next, we measured the mechanical characteristics ofeach USM under three different preload conditions. The
experimental results are shown in Figs. 11, 12, and 13.
The maximum angular velocity of the PPS-based USM
was 36.9 rad/s for a preload of less than 310 mN. The rotor stopped rotating when the torque reached 210 μNm,
as shown in Fig. 11. For the PPS/CF-based USM, themaximum angular velocity was approximately 30.5 rad/s,
and the maximum torque reached 248 μNm. The angularvelocities dropped suddenly at a certain torque in boththe PPS- and the PPS/CF-based USMs. This implies thatthe friction force was insufficient because of the light preload. The aluminum-based USM also showed this feature;
however, the maximum angular velocity was 12.5 rad/s,
which was much lower than those of the PPS- and PPS/
CF-based USMs. Maximum torque was approximately 500
μNm.
When the preload was increased to a medium range ataround 770 mN, the maximum torques of the PPS-, PPS/

To summarize our experimental results, there are thefeatures of the polymer-based USMs: (1) polymer-based
USMs have large angular velocities under light preload,(2) the maximum torque of a polymer-based USM is much
lower than that of an aluminum-based USM because alarge preload cannot be exerted on the polymer-based vibrator, and (3) among the tested materials, PPS is considered to be the suitable for vibrators of USMs under light
preloads.
As discussed in previous studies [23], the rotation velocity of a USM is mainly determined by the vibration velocity of the stator. In the previous section, we explained thereason for high-vibration velocities in polymer vibrators.
However, the rotation velocity of a polymer-based USM
decreases rapidly as the preload increases. To consider thisphenomenon, we measured the vibration velocities in the
preloading direction (y-axis) and the tangential direction(z-axis) while the preload was increasing. Figs. 14 and 15
show the velocity variations in the PPS and the aluminum-based vibrators.
As the preload increases to 1600 mN, the vibration velocity along the z-axis decreases from 1000 to 200 mm/s,
whereas the vibration velocity along the y-axis decreases
from approximately 600 mm/s to 0. The variation in theresonance frequency is 0.05 kHz. By contrast, the vibration velocities of the aluminum-based vibrator in both di-

Fig. 12. Mechanical characteristics under a preload of around 770 mN.

Fig. 13. Mechanical characteristics under a preload of 2440 mN.

2176

IEEE TRANSACTIONS ON ULTRASONICS, FERROELECTRICS, AND FREQUENCY CONTROL , vol. 62, no. 12, DECEMBER 2015preload direction and in the friction direction is the maincause of the decrease in the angular velocity of the rotor.
IV. Conclusions
To explore the feasibility of polymers in USMs, in thispaper, PEEK, PPS, and PPS/CF were tested as vibrators of USMs. The polymer-based USMs worked successfully in the same way as conventional metal-based USMs,
and their performances were compared with that of thealuminum-based USM. From our experiments, we reached
the following conclusions:Fig. 14. Variation in the vibration velocities on the y-axis and z-axis
and the resonance frequency of the PPS-based vibrator as the preload
increases.

rections show little variation even with a large preload;
however, the resonance frequencies of the vibrations in
z-axis and y-axis are separating each other. The resonancefrequencies along both z-axis and y-axis are the same
without a preload, as summarized in Fig. 15. However,when the vibration velocity on the z-axis reaches its maximum value of 194 mm/s under a preload of 1.1 N, thevelocity on the y-axis is only 10 mm/s. This implies thatthe orbit degenerates from an ellipse into a line, and motor operation becomes impossible. Although the driving
frequency is set at 12.43 kHz, where the elliptical orbit canbe maintained, the vibration velocity along the z-axis is
insufficient to drive the rotor at this frequency. The shift
in resonance frequency becomes larger and the angularvelocity decreases further under a higher preload of 2.1 N.
In summary, for the polymer-based USM, the sharp
decrease in the vibration velocity of the vibrator owing toincreased preload leads to a decrease in the angular velocity of the rotor. For the aluminum-based USM, separation
between the resonance frequencies of the vibrations in the1) Resonance frequencies of the polymer-based bimorphs are lower than that of the aluminum-based
bimorph because of lower elastic modulus.
2) Vibration velocity of the polymer-based bimorph ishigher than that of the aluminum-based bimorph because of lower elastic modulus.
3) The PPS-based bimorph has a higher vibration velocity than the other polymer-based bimorphs because it has a higher Q factor than the other polymers.
4) Polymer-based USMs have large angular velocities
under light preloads, and the maximum torque ofthe polymer-based USM is lower than that of thealuminum-based USM because a large preload cannot be exerted on the polymer-based vibrator.
5) PPS is a suitable polymer for vibrators under light
preloads, considering its vibration amplitude andlight weight.
6) The sharp decrease in vibration velocity in the caseof a polymer-based vibrator with a heavy preload
leads to a decrease in angular velocity. Separationin the resonance frequencies of the vibrations in the
preload direction and the friction direction in theFig. 15. Vibration velocity variations of the aluminum-based vibrator under increasing preloads and motor operation.

wu et al.: ultrasonic motors with polymer-based vibrators

aluminum-based USM is the main cause of a decrease in the angular velocity of the rotor.
From these conclusions, we have a rough understandingof the feature of the polymer-based vibrators and USMs.
However, all of the experiments were carried out at frequencies lower than the ultrasonic range. In the future, wewill adjust the working frequency of the polymer-based
motor to the ultrasonic range by decreasing its dimensions. The wear conditions on the contacting surface andthe appropriate materials for the rotor are also worth investigating in future studies.
References[1] K. Uchino, “Piezoelectric ultrasonic motors: Overview,” Smart Mater. Struct., vol. 7, no. 3, pp. 273–285, 1998.
[2] B. Watson, J. Friend, and L. Yeo, “Piezoelectric ultrasonic resonant
motor with stator diameter less than 250 μm: The Proteus motor,”J. Micromech. Microeng., vol. 19, no. 2, art. no. 022001, 2009.
[3] T. Morita, M. K. Kurosawa, and T. Higuchi, “A cylindrical micro
ultrasonic motor using PZT thin film deposited by single processhydrothermal method (Φ 2.4 mm, L = 10 mm stator transducer),”IEEE Trans. Ultrason. Ferroelectr. Freq. Control, vol. 45, no. 5, pp.
1178–1187, 1998.
[4] T. Morita, M. K. Kurosawa, and T. Higuchi, “A cylindrical shaped
micro ultrasonic motor utilizing PZT thin film (1.4 mm in diameterand 5.0 mm long stator transducer),” Sens. Actuators, vol. 83, no.
1–3, pp. 225–230, 2000.
[5] T. Kanda, A. Makino, T. Ono, K. Suzumori, and M. K. Kurosawa,“A micro ultrasonic motor using a micro-machined bulk PZT transducer,” Sens. Actuators, vol. 127, no. 1, pp. 131–138, 2006.
[6] H. Zhang, S. Dong, S. Zhang, T. Wang, Z. Zhang, and L. Fan,
“Ultrasonic micro-motor using miniature piezoelectric tube with diameter of 1.0 mm,” Ultrasonics, vol. 44, no. 22, pp. e603–e606, 2006.
[7] Y. Chen, K. Lu, T. Zhou, T. Liu, and C. Lu, “Study of a mini-ultrasonic motor with square metal bar and piezoelectric plate hybrid,”
Jpn. J. Appl. Phys., vol. 45, no. 1, pp. 4780–4781, 2006.
[8] S. Manuspiya, P. Laoratanakul, and K. Uchino, “Integration of apiezoelectric transformer and an ultrasonic motor,” Ultrasonics, vol.
41, no. 2, pp. 83–87, 2003.
[9] S. Dong, S.-P. Lim, K.-H. Lee, J. Zhang, L.-C. Lim, and K. Uchino,“Piezoelectric ultrasonic micromotor with 1.5 mm diameter,” IEEE
Trans. Ultrason. Ferroelectr. Freq. Control, vol. 50, no. 4, pp. 361–
367, 2003.
[10] D. Yamagichi, T. Kanda, K. Suzumori, K. Fujisawa, K. Takegoshi,
and T. Mizuno, “Ultrasonic motor using two sector-shaped piezoelectric transducers for sample spinning in high magnetic field,” J.
Robot. Mechatron., vol. 25, no. 2, pp. 384–391, 2013.
[11] M. Takano, M. Takimoto, and K. Nakamura, “Electrode design ofmultilayer piezoelectric transducer for longitudinal-bending ultrasonic actuators,” Acoust. Sci. Technol., vol. 32, no. 3, pp. 100–108,
2011.
[12] D. P. Jones, D. C. Leach, and D. R. Moore, “Mechanical propertiesof poly(ether-ether-ketone) for engineering applications,” Polymer(Guildf.), vol. 26, no. 9, pp. 1385–1393, 1985.
[13] T. Ishii, S. Ueha, K. Nakamura, and K. Ohnishi, “Wear properties
and life prediction of friction materials for ultrasonic motors,” Jpn.
J. Appl. Phys., vol. 34, no. 1, pp. 2765–2770, 1995.
[14] J. Qu and T. Zhou, “An electric contact method to measure contact
state between stator and rotor in a traveling wave ultrasonic motor,”
Ultrasonics, vol. 41, no. 7, pp. 561–567, 2003.
[15] P. Rehbein and J. Wallaschek, “Friction and wear behavior of polymer/steel and aluminum/alumina under high-frequency fretting
conditions,” Wear, vol. 216, no. 2, pp. 97–105, 1998.
[16] S. K. Sinha, S.-L. Thia, and L.-C. Lim, “A new tribometer for friction drives,” Wear, vol. 262, no. 1–2, pp. 55–63, 2007.
[17] P. J. Rae, E. N. Brown, and E. B. Orler, “The mechanical properties of ploy(ether-ether-ketone) (PEEK) with emphasis on the large
compressive strain response,” Polymer (Guildf.), vol. 48, no. 2, pp.
598–615, 2007.

2177[18] K. Nakamae, T. Nishino, Y. Shimizu, and K. Hata, “Temperaturedependence of the elastic modulus of crystalline regions of polyoxymethylene,” Polymer (Guildf.), vol. 31, no. 10, pp. 1909–1918, 1990.
[19] S. R. Owen and J. F. Harper, “Mechanical, microscopical and fire
retardant studies of ABS polymers,” Polym. Degrad. Stabil., vol. 64,
no. 3, pp. 449–455, 1999.
[20] H. W. Hill and D. G. Brady, “Properties, environmental stability,
and molding characteristics of polyphenylene sulfide,” Polym. Eng.
Sci., vol. 16, no. 12, pp. 831–835, 1976.
[21] B. F. Ley, S. G. Lutz, and C. F. Rehberg, Linear Circuit Analysis.
New York, NY, USA: McGraw-Hill Inc., 1959, pp. 278–279.
[22] K. F. Graff, Wave Motion in Elastic Solids. New York, NY, USA:
Dover, 1991, pp. 155–158.
[23] K. Nakamura, M. Kurosawa, and S. Ueha, “Characteristics of a
hybrid transducer-type ultrasonic motor,” IEEE Trans. Ultrason.
Ferroelectr. Freq. Control, vol. 38, no. 3, pp. 188–193, 1991.

Jiang Wu was born in Liaoning, China, on January 29, 1988. He received the B.E. degree in mechanical engineering from Dalian University ofTechnology (DUT), China, in 2010. From 2010 to2012, he studied in the State Key Laboratory of
Robotics and Systems, Harbin Institute of Technology (HIT), China, and received the M.E. degree in mechatronic engineering from HIT in 2012.
He is currently a doctoral candidate in the Precision and Intelligence Laboratory, Tokyo Instituteof Technology (TITECH), Japan. His research interests include piezoresistive and piezoelectric materials, permanentmagnet-based sensing technology, ultrasonic transducers and actuators,
and ferroelectric film.

Yosuke Mizuno was born in Hyogo, Japan, on
October 13, 1982. He received the B.E., M.E., andDr.Eng. degrees in electronic engineering from the
University of Tokyo, Japan, in 2005, 2007, and2010, respectively.
From 2007 to 2010, he was engaged in Brillouin optical correlation-domain reflectometry
for his Dr.Eng. degree at the University of Tokyo. From 2007 to 2010, he was a Research Fellow(DC1) of the Japan Society for the Promotion of
Science (JSPS). From 2010 to 2012, as a Research
Fellow (PD) of JSPS, he worked on polymer optics at Tokyo Instituteof Technology, Japan. In 2011, he stayed at BAM Federal Institute forMaterials Research and Testing, Germany, as a Visiting Research Associate. Since 2012, he has been an Assistant Professor at the Precision
and Intelligence Laboratory, Tokyo Institute of Technology, where he isactive in fiber-optic sensing, polymer optics, and ultrasonics.
Dr. Mizuno is the winner of the Funai Research Award 2010, theAndo Incentive Prize for the Study of Electronics 2011, the NF Foundation R&D Encouragement Award 2012, and the Challenging ResearchAward 2013. He is a member of the IEEE, the Japanese Society of Applied Physics (JSAP), and the Institute of Electronics, Information, andCommunication Engineers (IEICE) of Japan.

Marie Tabaru was born in Tokyo, Japan. She
received her B.Eng. degree in electrical and electronic engineering from the Tokyo Institute ofTechnology in 2002 and her M.E. degree in humansystem science in 2005. She studied image signal
processing of medical ultrasound at the Universityof Washington, Seattle, from 2002 to 2003. She
received the Best Student Paper Award in Engineering Acoustics from the Acoustical Society ofAmerica in 2006. She received her D.E. degreefrom the Tokyo Institute of Technology in 2007.
She has been an associate professor of the Precision and Intelligence
Laboratory, Tokyo Institute of Technology, since 2013. She is a memberof the Acoustical Society of Japan, the Japan Society of Ultrasonics in
Medicine, and the Institute of Electronics, Information and Communication Engineers.

2178

IEEE TRANSACTIONS ON ULTRASONICS, FERROELECTRICS, AND FREQUENCY CONTROL , vol. 62, no. 12, DECEMBER 2015

Kentaro Nakamura was born in Tokyo, Japan,
on July 3, 1963. He received the B.E., M.E., andDr.Eng. degrees from the Tokyo Institute of Technology, Japan, in 1987, 1989, and 1992, respectively.
Since 2010, he has been a Professor at thePrecision and Intelligence Laboratory, Tokyo
Institute of Technology. His research field is theapplications of ultrasonic waves, measurement ofvibration and sound using optical methods, andfiber-optic sensing.

Prof. Nakamura is the winner of the Awaya Kiyoshi Award for encouragement of research from the Acoustical Society of Japan (ASJ)
in 1996, and the Best Paper Awards from the Institute of Electronics,
Information and Communication Engineers (IEICE) in 1998 and fromthe Symposium on Ultrasonic Electronics (USE) in 2007 and 2011. Healso received the Japanese Journal of Applied Physics (JJAP) Editorial
Contribution Award from the Japan Society of Applied Physics (JSAP)in 2007. He is a member of the IEEE, the ASJ, the JSAP, the IEICE,
and the Institute of Electrical Engineers of Japan (IEEJ).