Smart Materials and Structures
Smart Mater. Struct. 28 (2019) 125017 (11pp)

https://doi.org/10.1088/1361-665X/ab4d5d

A traveling-wave ultrasonic motor utilizing aring-shaped alumina/PZT vibrator
Jiang Wu1,2,3,4 , Yosuke Mizuno3

and Kentaro Nakamura3,4

1

State Key Laboratory for Reliability and Intelligence of Electrical Equipment, Hebei University ofTechnology, Tianjin 300130, People’s Republic of China
2
Hebei Key Laboratory of Robot Perception and Human-robot Interaction, Hebei University ofTechnology, Tianjin 300130, People’s Republic of China
3
Laboratory for Future Interdisciplinary Research of Science and Technology, Tokyo Institute ofTechnology, Yokohama 226-8503, Japan
E-mail: wujiang@sonic.pi.titech.ac.jp and knakamur@sonic.pi.titech.ac.jp
Received 29 May 2019, revised 25 August 2019
Accepted for publication 14 October 2019
Published 8 November 2019
Abstract

Considering that high Young’s moduli and low ultrasonic attenuation of ﬁne ceramics may
enhance driving force and reduce energy dissipation, in this study, we exploit the usage of ﬁne
ceramics as vibrating bodies of ultrasonic motors. Several alumina vibrating bodies were
fabricated and bonded to annular lead-zirconate-titanate (PZT) disks to form ring-shaped
vibrators, where traveling waves with the 3rd bending modes were excited to frictionally drive
the rotor. First, we explored the fundamental vibration properties. As predicted, the alumina/
PZT vibrators provided relatively high force factors, high electromechanical coupling factors,
and low damping compared to the stainless-steel/PZT one with similar structure. Subsequently,
through experimental assessment on load characteristics, we found that the rotation speed of thealumina/PZT motor at 20 V was larger than that of the stainless-steel/PZT motor at 250 V, andmeanwhile, it exhibited superior maximal-torque-to-voltage and maximal-output-power-tovoltage ratios; these results imply that satisfactory performance is achievable with our motor.
Besides, alumina’s chemical resistance and electrical resistance make our motor potentiallyapplicable to the acid/alkaline atmosphere and the intensively alternating-current magnetic ﬁeld.
Keywords: ultrasonic motors, alumina, high young’s modulus, low ultrasonic attenuation(Some ﬁgures may appear in colour only in the online journal)
1. Introduction

Young’s moduli and low ultrasonic attenuation, which contributed to enhancing the driving force and suppressing
energy dissipation [1, 4, 8, 12], were desirable for vibrating
bodies [10–12].
In previous studies [1, 8, 13–18], ﬁne-ceramic layers
were generally coated onto metal-based vibrators’ and/or
rotors’ surfaces to improve USMs’ frictional and abrasional
characteristics, but they were too thin to affect vibration
properties [1, 8]. To date, there has been almost no reportabout ﬁne-ceramic-based USMs except Aoyagi et al’s motor[19]: a thin PZT ﬁlm was printed onto a ﬁne ceramic plate tosuppress thermally-induced stress in the poling process, but
its vibration properties were roughly studied and the load
characteristics were completely not explored [19]. Besides,
this motor is seemingly incapable of working even when a

Since ultrasonic motors (USMs) offer the capability to provide quick response, simple structure, and absence ofelectromagnetic radiation [1–5], they have achieved practicalapplication to several ﬁelds [6–9], e.g. auto-focusing system
in digital cameras [1]. Vibrators and rotors are the main
components of USMs [1, 8] and vibrators basically consist ofvibrating bodies (commonly made of metals) and piezoelectric materials [typically, lead zirconate titanate (PZT)][1, 5, 7, 8]. After preliminarily investigating how vibrating
bodies’ material constants affected USMs’ vibration properties in former studies [4, 10–12], we predicted that high4

Authors to whom any correspondence should be addressed.

0964-1726/19/125017+11$33.00

1© 2019 IOP Publishing Ltd Printed in the UKSmart Mater. Struct. 28 (2019) 125017

J Wu et al

Figure 1. (a) Conﬁguration of the tested alumina/PZT motor; (b) the ring-shaped vibrator, consisting of an alumina vibrating body and (c) anannular PZT disk; and (d) the rotor.

small preload is applied because its PZT ﬁlm is too thin to
generate sufﬁcient vibration amplitude [19]. Thus, it would bemeaningful to design new ﬁne-ceramic/PZT motors to
examine the actuating capability.
In this study, we fabricated a ring-shaped alumina/PZT
vibrator to form a traveling-wave USM and systematicallyinvestigated its vibration properties and load characteristics.
Here, alumina is employed owing to its relatively low ultrasonic attenuation among commonly-used ﬁne ceramics [12].
Additionally, the ring shape, which has been widely studied
in the development of USMs [4, 10, 20–25], is selected as its
small proﬁle and hollow structure are attractive advantages
for practical usage [1, 8].

2. Conﬁguration
Figure 1(a) schematically illustrates the developed motor,
dominantly composed by a vibrator and a rotor. As depicted
in ﬁgure 1(b), the vibrator incorporates an alumina vibrating
body (A995, NTK Ceratec, Sendai, Japan) and an annular
PZT disk (C213, Fuji Ceramics, Fujinomiya, Japan). The
alumina product has the Young’s modulus, bulk density,
Poisson’s ratio, and purity of 380 GPa, 3.9×103 kg m−3,0.24, and 99.5% [26], respectively. It consists of a back disk
0.5 mm in thickness and a cylindrical part 30 and 20 mm inouter and inner diameters, respectively. Average roughness ofthe driving surface is 0.12 μm [27], far lower than thevibration amplitude [∼7 μm (see the following section)].
Some 1 mm deep 0.5 mm wide slots were created on thecylindrical part with 10° intervals. Here, several vibratorswith varying un-slotted part’s thickness h were prepared to

Figure 2. Photos of the alumina/PZT vibrator prototype taken fromthe (a) top and (b) bottom views and those of the stainless-steel/PZT
vibrator prototype taken from the (c) top and (d) bottom views. Note
that, though the central holes on bottom disks have different
diameters, they should exhibit little effect on the vibration properties
as the ﬁxed parts (in yellow) have the same diameters.

explore how the h affects vibration properties. A central hole
was introduced on the back disk to ﬁx the vibrator. A polar
coordinate system (z, θ, and r axes) is established on the upper2

Smart Mater. Struct. 28 (2019) 125017

J Wu et al

Figure 3. (a) Resonance frequency and (b) force factor of the alumina/PZT vibrators with varying unslotted-part thickness. The solid lines

and circles are simulated and experimental results of the alumina/PZT vibrators, respectively. The dashed lines and triangles are the values ofthe stainless-steel/PZT vibrator.

surface. As shown in ﬁgure 1(c), the PZT disk has an outer
diameter of 30 mm, an inner diameter of 20 mm, and a
thickness of 0.5 mm. One side of the silver electrode was
evenly divided into 12 parts with identical polarization
directions. The undivided side was bonded to the back surfaceof the alumina vibrating body with epoxy resin. Whenalternating voltages with phases, i.e. U0cos(ωt), −U0cos(ωt),
U0sin(ωt), and −U0sin(ωt), where U0, ω, and t are
respectively voltage, angular working frequency, and time,
are applied; the 3rd bending mode is excited on the vibrator.
Since the sum of these four voltages is zero, electricalpotential of the undivided part should be equal to zero[1, 4, 12] and as a consequence, it is not required to connect
this side to the ground [1]. The aluminum rotor shown inﬁgure 1(d) has two parts with different diameters. A bearing
is inserted into the part with a 33 mm outer diameter, while
the bottom surface of the other part is in contact with the outeredge of the vibrator. A spring is used to apply preloads to therotor to generate frictional force.
Figures 2(a) and (b) illustrate the photos of an alumina/
PZT vibrator taken from the top and bottom views, respectively. Instead of feeding lines, a ﬂexible electrode (purchasedfrom Nihon Membrane, Tokyo, Japan) was bonded to the
PZT disk’s divided side with the non-conductive epoxy-resin
adhesive. Here, the applied pressure during thermal solidiﬁcation and the adhesive’s volume were adjusted to achieveboth sufﬁcient bonding strength and electrical connection. As
shown in ﬁgures 2(c) and (d), a stainless-steel (SUS304)/PZT
motor was fabricated for performance comparison. Its structure is almost the same as the alumina/PZT ones (seeﬁgure 1(b)) except the 4 mm thick unslotted part; the reason
for choosing this thickness is explained in the following
section.

3. Vibration properties
First, we calculated resonance frequencies and force factorsof the alumina/and stainless-steel/PZT motors through ﬁnite
element analysis (FEA) [software: ANSYS (ver. 16.0,
ANSYS Inc. Canonsburg, USA)]. Here, the force factor A isdeﬁned as the ratio of the current (measured with a current
probe: P6021, Tektronix, Beaverton, USA) to the θ-axis
vibration velocity (measured with an in-plane vibrometer:
IPV100, Polytec, Waldbronn, Germany) [1, 4, 11, 12].
Figure 3(a) shows that the resonance frequencies monotonically increase as the vibrators become thicker. Owing tohigh stiffness [11], the alumina/PZT vibrator exhibits relatively high resonance frequencies compared to the stainlesssteel/PZT one. Figure 3(b) demonstrates that the force factors
reach peak values when the alumina/and stainless-steel/PZT
vibrators have 3 and 4 mm thick unslotted parts, respectively.
Moreover, the maximal force factor is 2.4 times higher for thealumina/PZT than for the stainless-steel/PZT vibrator dominantly owing to alumina’s high Young’s modulus [12]. Our
previous studies [11, 28] have proved that, among the stainless-steel/PZT motors in disk shape (as shown in ﬁgures 2(c)and (d)), the one with a large force factor tends to exhibit highperformance. On the basis of this knowledge, only the one
with a 4 mm thick unslotted part was prepared in this study.
Whereas alumina/PZT motors with varying thickness were
fabricated to test whether they had the same tendency.
Subsequently, we investigated the vibration properties
based on the equivalent circuit model [1]. The motional
admittance Ym0, resonance frequency fr, anti-resonance frequency fa, and bandwidth corresponding to 0.707 times of thepeak amplitude Δf, were initially measured with an impedance analyzer (4294A, Agilent, Santa Clara, CA, USA).
3

Smart Mater. Struct. 28 (2019) 125017

J Wu et al

Table 1. Equivalent circuit parameters of alumina/PZT and stainless-steel/PZT vibrators.

Alumina/PZT
Unslotted part thickness (h)/mm
Resonance frequency ( fr)/kHz
Anti-resonance frequency ( fa)/kHzElectromechanical coupling factor (k)Force factor (A)/N V−1
Q factorEquivalent damper (γm)/N s m−1
Equivalent stiffness (sm)/106 N m−1
Equivalent mass (mm)/10−3 kg

1

3

5

Stainless-steel/PZT
449.56749.658
6.1%
0.012
880
0.624
171
1.76

71.22572.073
15.3%
0.033
769
0.516
177
0.90

98.12698.889
10.7%
0.019
775
0.645
308
0.81

26.12426.155
4.9%
0.014
379
2.089
130
4.82

[12]. In the meantime, the alumina/PZT vibrators exhibit
higher Q factors, resulting in lower equivalent damping[1, 4, 8]. Besides, they possess relatively high equivalent
stiffnesses and low equivalent masses, which are assumed tooriginate from the relatively high Young’s modulus andmoderate density of alumina, respectively [1, 4, 11, 12].
Finally, we explored how the vibration velocity and the
Q factor depended on the voltage applied to the h3 vibrator.
As ﬁgure 4 showed, the vibration velocity linearly increased
from 0 to 512 mm s−1. In the meantime, the Q factor
exhibited almost no variation as the voltage increased from 0
to 10 V, but a reduction in the voltage range from 10 to 20 V
as a consequence of PZT’s nonlinearity. Besides, no hysteresis was observed in the vibration-velocity and Q-factor
dependences on voltage.
Figure 4. Variation of the θ-axis vibration velocity as functions ofapplied voltage (0–20 V).

4. Motor performance
4.1. Experimental setup

Then, the electromechanical coupling factor k, mechanicalquality factor Q, equivalent damping γm, equivalent stiffnesssm, and equivalent mass mm are calculated with the following
equations [1, 18]:
⎛ f ⎞2
1-⎜ r⎟ ,⎝ fa ⎠

(1 )

Q=

fr
,
Df

(2 )

gm =

A2
,
Ym0

(3 )

2pfr · Q · A2
,
Ym0

(4 )

k=

sm =

In this section, we measured load characteristics of the alumina/PZT motors and made comparison with the stainlesssteel/PZT one. Figure 5(a) depicts the experimental setup.
First, two signals with a 90° phase shift were ampliﬁed withbipolar power ampliﬁers (HSA4051, NF Corp., Yokohama,Japan). Then, inverted signals were created with center-tapped transformers. Two high-frequency power meters (3335,
Hioki E. E. Corp., Nagano, Japan) were arranged between theampliﬁers and the transformers to measure the electrical input
power. Figure 5(b) schematically illustrates the system forevaluating the load characteristics. The torque was measured
by pulling up a weight while the rotation speed was estimatedwith a self-made rotation meter. The mechanical output power
equals the product of the torque and the rotation speed.

andQ · A2mm =,2pfr · Ym04.2. Load characteristics(5 )Figure 6 illustrates the variation in the no-load rotation speedof the h3 motor against the phase at the voltage, frequency,
and preload of respectively 10 V, 71.2 kHz, and 3.3 N. Whenthe phases were −90° and 100°, the motor provides maximal
rotation speeds in clockwise and counterclockwise directions,
respectively. Figures 7(a)–(c) respectively plot how therespectively. As table 1 shows, the alumina/PZT vibrator
with a 3 mm thick unslotted part (h3 vibrator) exhibits arelatively high electromechanical coupling factor compared tothe h1 and h5 vibrators as well as the stainless-steel/PZT one
4

Smart Mater. Struct. 28 (2019) 125017

J Wu et al

Figure 5. Schematics of (a) the electrical system for applying voltage and (b) the mechanical system for measuring the load characteristics.

became higher as the voltage increased from 5 to 10 V, andapproached the saturated value at 10 V [2, 11]. At 6.3 N, themaximal torque (25.9 mN m) was limited by the voltage
rather than the preload [2]. The no-load rotation speed
increased as the voltage became higher. The maximal output
power reached 141 mW. When the voltage and preload wererespectively 20 V and 3.3 N, the h3 motor exhibited the
maximal efﬁciency (∼8%).
Figures 9(a)–(d) plot the maximal torque, maximal noload speed, maximal output power, and maximal efﬁciency of
the alumina/PZT motors against their unslotted part thickness, respectively. To avoid their failure (see appendix A), thevoltage was set to 20 V. Similar to stainless-steel/PZT ones,
the h3 motor exhibits the maximal torque owing to the relatively high force factor [1, 2, 4, 12]. No-load speed is dominantly affected by the θ-axis vibration velocity [2, 11]. The
maximal output power achievable with the h3 motor is higher
as a consequence of its larger electromechanical coupling
factor [4, 18]. The maximal efﬁciency does not show obvious
difference among the alumina/PZT motors as their friction
materials are identical [1, 14].

Figure 6. Variation in no-load rotation speed of alumina/PZT motor
against phase.

rotation speed, output power, and efﬁciency change withvarying torque. The voltage, working frequency, and phasewere set to 10 V, 71.2 kHz, and 100°, respectively. At 3.3 N,
the maximal torque, output power, and efﬁciency reached12.8 mN m, 58.2 mW, and 6.8%, respectively. When the
preload increased to 6.3 N, there existed a reduction inmechanical output as a consequence of lowered efﬁciency.
Figures 8(a)–(d) respectively demonstrate how the maximal torque, no-load rotation speed, maximal output power,
and maximal efﬁciency of the h3 motor depend on the voltage
under different preloads. Every time the voltage and/or preload were varied, the working frequency was adjusted toenable the vibrator to provide maximal vibration velocity.
There initially existed a dead region at <2 V [2]. Then, thetorques corresponding to the preloads of 2.4 and 3.3 N

4.3. Performance comparison

Table 2 compared the performance between the h3 motor andthe stainless-steel/PZT one. The h3 motor operates in thehigh vibration region even when the voltage is as low as 20 V.
Whereas, at the same voltage, the stainless-steel/PZT motor
works in the low vibration region and provides inferior performance. At 250 V, larger preload can be applied to thestainless-steel/PZT vibrator as it stores higher vibrationenergy [4]. Meanwhile, the frictional coefﬁcient between
stainless steel and aluminum (∼0.35) is higher than thatbetween alumina and aluminum (∼0.25) [29]. Both of themcause relatively high torque of the stainless-steel/PZT motor
at 250 V. However, the maximal-torque-to-voltage (T-to-U)
ratio of the alumina/PZT motor is 6.9 times the value of the5Smart Mater. Struct. 28 (2019) 125017

J Wu et al

Figure 7. Load characteristics of the h3 motor at 10 V. (a) Rotation speed, (b) output power, and (c) efﬁciency as functions of torque.

Figure 8. Variations in (a) maximal torque, (b) no-load speed, (c) maximal power, and (d) maximal efﬁciency of the h3 motor against applied

voltage.

6Smart Mater. Struct. 28 (2019) 125017

J Wu et al

Figure 9. (a) Maximal torque, (b) maximal no-load speed, (c) maximal output power, and (d) maximal efﬁciency as functions of unslottedpart thickness. The solid lines in (a)–(c) are estimated via FEA. The method to calculate electromechanical coupling factors is given inappendix B.

Table 2. Performance comparison between alumina/PZT and stainless-steel/PZT motors.

Alumina/PZT with h3
vibrator
PerformanceHigh vibration region

Stainless-steel/PZT
Low vibration
region

20
40
71.2
0.033
0.516
6.3
511
15.3%
25.9
27.7
141.0
7.8%
1.3
7.1

20
40
26.1
0.014
2.089
0.8
58
4.9%
3.2
4.2
3.8
1.4%
0.2
0.2

Applied voltage/VElectric ﬁeld intensity in PZT/V mm−1
Driving frequency/kHz
Force factor/N V−1
Equivalent damper/N s m−1
Applicable preload/N
θ-axis vibration velocity/mm s−1
Electromechanical coupling factor
Maximal torque/mN m
Maximal rotation speed/rad s−1
Maximal output power/mW
Maximal efﬁciency
Ratio of maximal torque to applied voltage/mN m V−1
Ratio of maximal output power to applied voltage/mW V−1stainless-steel/PZT one. On the other hand, the high Young’s
modulus leads to a relatively high electromechanical coupling
factor of the alumina/PZT motor. In the meantime, it has

High vibration
region
250
500
25.4

13.8
366
46.8
20.8
351.6
5.6%
0.2
1.4

slightly higher efﬁciency; these reasons enable the alumina/
PZT motor to exhibit a higher maximal-output-power-tovoltage (P-to-U) ratio [1, 8].
7

Smart Mater. Struct. 28 (2019) 125017

J Wu et al

4.4. Potential application areas

Recently, robotics and/or precision machines have become
increasingly required in the chemical industry [30, 31]. For
conventional metal/PZT USMs, shields are required to isolate
their metal parts from the acid or alkaline atmosphere to avoid
corrosion [30]. It is known that alumina has high chemical
resistance [32] (for instance, the weight losses of alumina
products with >99.5% purity are respectively <0.07 and<0.05 g cm-2 per 24 h in HNO3 and NaOH [30]). As a consequence, our motor can be applied directly to the acid/alkaline environment if its rotor and accessory parts are madeof alumina (currently, alumina bearings are commerciallyavailable [33] and the rotor can be specially ordered [27]).
Another potential application ﬁeld goes to the intensively
alternating-current magnetic ﬁeld as alumina’s high conductive
resistance (>1014 Ω m) [34] may suppress the eddy current andconsequently the temperature rise in the vibrator [35]. Here, itwould be worthwhile to mention the alumina/PZT motor’s
expense, averagely 240 dollars for these prototypes. Though
it is higher than that of the stainless-steel/PZT one (nearly
40 dollars), in mass production, the expense may be lowered as
the mold and/or the machining tool for fabricating alumina
vibrating bodies are reusable [36]. To sum up, our motor would
be applicable for some special environments owing to alumina’s unique property.

Figure A1. Variation of the θ-axis vibration velocity as functions ofapplied voltage (0–23 V).

Table A1. Critical voltage and corresponding stress of alumina/PZT

vibrators.

5. Conclusions
In this study, we fabricated an alumina/PZT ring-shaped
vibrator and employed it to form a traveling-wave USM.
Owing to the high Young’s modulus and low ultrasonicattenuation, this motor was capable of providing high force
factors, high electromechanical coupling factors, and low
damping; this partially veriﬁed the validity of our proposal. At
20 V, the alumina/PZT motor (h3) yielded the maximal torque, no-load speed, and maximal output power of 25.9 mN m,
27.7 rad s−1, and 141 mW, respectively. Compared to thestainless-steel/PZT motor with similar structure, the alumina/
PZT one provided relatively high T-to-U and P-to-U ratios.
Besides, the highly chemical resistance and highly conductive
resistance may make our motor applicable to several special
environments. Through this investigation, we have gained anunderstanding on alumina/PZT motors and anticipate thatthese results would provide adequate information for structural
optimization in the future.

Unslotted part thickness (h)/mm

1

3

5

Critical voltage/V
Maximal stress corresponding to critical voltage/MPa

22
29

22
23

28
22

Appendix A. Failure condition
As mentioned in section 3, the vibration velocity of the h3
vibrator is hysteresis-freely dependent on the voltage in therange of 0–20 V (see ﬁgure 4). However, when the voltage
was increased to 23 V, the vibration velocity sharply
decreased from 528 to 15 mm s−1 and did not recover its priorstate (see ﬁgure A1). The permanent failure also existed on
h1 and h5 vibrators (see table A1), while it did not appear on
the stainless-steel/PZT vibrator, where the applied voltage
reached 250 V.
The reason for the permanent failure was analyzed throughFEA. Figure A2(a) illustrates the model and ﬁgure A2(b)shows the stress distribution of the h3 vibrator at its criticalvoltage (22 V). Here, a 50 μm thick epoxy-resin bonding layer,
whose Young’s modulus, density, and Poisson’s ratio arerespectively 5.0 GPa, 1.2×103 kg m−3, and 0.38 [37, 38], issandwiched between the alumina vibrating body and the PZT
disk. As ﬁgure A2(c) illustrates, stress concentration exists on
the part of the alumina vibrating body that is in contact with thebonding layer. Besides, the maximal stress reaches 23 MPa,
approaching epoxy-resin’s shear strength (∼25 MPa) [39, 40].
Whereas the maximal stress of the stainless-steel/PZT vibratoris ∼12 MPa (see ﬁgure A2(d)) despite the applied voltage of
250 V. Previous studies [41, 42] also demonstrate that, for

Acknowledgments
The authors thank the staff members of the Precision and
Manufacturing Center, Technical Department, Tokyo Instituteof Technology, for machining the motor components. They
also thank Mr Yidi Zhou and Dr Jixiao Liu, who are with
Hebei University of Technology, for the help in using the
microscope. This work was supported by JSPS KAKENHI(Grant Number 17J05057) and National Key Research andDevelopment Plan (Number 2016YFE0128700).
8Smart Mater. Struct. 28 (2019) 125017

J Wu et al

Figure A2. Analysis of stress concentration in vibrators. (a) and (b) are the FEA model and stress distribution of the entire vibrator. (c) and (d)show the stress distributions of the alumina/and stainless-steel/PZT vibrators at 22 and 250 V, respectively.

(3) Calculate the electrical energy as [44, 45]

multilayer composites, stress concentration tends to intensively
exist when sandwiched and sandwiching layers have great
difference in Young’s moduli. Recently, metallic foils havebeen reported to be utilized as the bonding layers of piezoelectric vibrators [43]; this approach possibly mitigates theabove problem as metals generally have higher Young’s
moduli than epoxy resin [11, 12].

Ue =

(A2)

where Cd and u represent the electrical capacitance andthe applied voltage, respectively; and ε33, S, and tp
denote the permittivity, the electrode’s area, and the
PZT disk’s thickness, respectively.
(4) Estimate the electromechanical coupling factor with thefollowing equation [45]:Appendix B. Method of calculating
electromechanical coupling factor
The electromechanical coupling factor; which is, in this study,
deﬁned as the ratio of mechanical energy to the sum of
mechanical and electrical energies stored in the vibrator [44];is calculated with the following procedures [44]:

k=

Um
.
Um + Ue(A3)

Using this method, we calculated the electromechanicalcoupling factors of the vibrators whose unslotted parts havevarying thickness. As shown in ﬁgure 9(c), the alumina/PZT
vibrators with thickness of 3–4 mm exhibit higher electromechanical coupling factors probably because of their better
acoustic impendence matching than the others [11].

(1) Calculate the vibration velocity distribution through FEA.
(2) Estimate the vibration energy stored in the vibrator fromthe above results as [44]

å i= 1(vz2- i + vq2- i + vr2- i ) ,
1
m·
2
n

1
1 e S
Cd u2 = · 33 · u2 ,
2
2
tp

n

Um =

(A1)

Appendix C. Microscope photos of motors’ surfaces

where m represents the vibrator’s mass; vz-i, vθ-i, and vr-i
denote vibration velocities of the ith node along thevertical (z), circumferential (θ), and radial (r) directions,
respectively; and n is the total number of the model’s
nodes.

The friction surfaces after intermittent operation of ∼2 h wereobserved with a microscope (SMZ-745T, Nikon, Tokyo,
Japan). Figures A3(a) and (b) illustrate that aluminum powder, scratched from the rotor, exists on the alumina/PZT
vibrators’ friction surfaces. Figures A3(c) and (d) illustratethat the severe wear regime on the rotor’s surface is

9Smart Mater. Struct. 28 (2019) 125017

J Wu et al

Figure A3. Microscope photos of (a) the alumina/and (b) stainless-steel/PZT vibrators. Those in (c) and (d) are the rotors of the alumina/and

stainless-steel/PZT motors.
[3] Pan S, Wu Y, Zhang J, Zhou S and Zhu H 2018 Modeling andcontrol of a 2-degree-of-freedom gyro-stabilized platform
driven by ultrasonic motors J. Intell. Mater. Syst. Struct. 29
2324–32[4] Wu J, Mizuno Y and Nakamura K 2018 Polymer-based
ultrasonic motor utilizing high-order vibration modes IEEE/
ASME Trans. Mechatronics 23 788–99[5] Zhu Z, To S, Ehmann K F and Zhu X 2017 Design, analysis,
and realization of a novel piezoelectrically rotary spatial
vibration system for micro/nanomachining IEEE/ASME
Trans. Mechatronics 22 1227–37[6] Ozeki S, Kurita K, Uehara C, Nakane N, Sato T and
Takeuchi S 2018 Analysis of coiled stator ultrasound motor:
Fundamental study on analysis of wave propagation on
acoustic waveguide for coiled stator Japan. J. Appl. Phys. 57
07LB12[7] Zhang Q, Chen W, Liu Y, Liu J and Jiang Q 2017 A frog-shaped
linear piezoelectric actuator using ﬁrst-order longitudinal
vibration mode IEEE Trans. Ind. Electron. 64 2188–95[8] Zhao C 2011 Ultrasonic Motors: Technologies andApplications (Beijing: Science Press) pp 448–68[9] Shi S, Huang Z, Yang J, Liu Y, Chen W and Uchino K 2018
Development of a compact ring type MDOF piezoelectric
ultrasonic motor for humanoid eyeball orientation system
Sensors Actuators A 272 1–10
[10] Wu J, Mizuno Y, Tabaru M and Nakamura K 2015 Ultrasonicmotors with polymer-based vibrators IEEE Trans. Ultrason.
Ferroelectr. Freq. Control 62 2169–77

seemingly smaller for the alumina/than for the stainlesssteel/PZT motor. Though these results may indicate thealumina/PZT motor’s high durability [27], we still need to
fully prove it by conducting a long-term performance test.
Such a long-term life test is left for further studies.

ORCID iDs
Jiang Wu https://orcid.org/0000-0002-6899-5601
Yosuke Mizuno https://orcid.org/0000-0002-3362-4720
Kentaro Nakamura https://orcid.org/0000-00032899-4484

References[1] Ueha S and Tomikawa Y 1993 Ultrasonic Motors—Theory
and Applications (New York: Oxford University Press)
pp 4–13[2] Nakamura K, Kurosawa M and Ueha S 1991 Characteristics ofhybrid transducer-type ultrasonic motor IEEE Trans.
Ultrason. Ferroelectr. Freq. Control 38 188–93
10Smart Mater. Struct. 28 (2019) 125017

J Wu et al[27] Qiu W, Mizuno Y and Nakamura K 2016 Tribological
performance of ceramics in lubricated ultrasonic motors
Wear 352/353 188–95[28] Hirata H and Ueha S 1992 Force factor design of disk vibrators
used for ultrasonic motors J. Acoust. Soc. Japan E 13 77–84[29] Santos A, Cordoba E, Ramirez Z, Sierra C and Ortega Y 2017
Determination of the coefﬁcient of dynamic friction between
coating of alumina and metallic materials IOP J. Phys.:Conf. Ser. 935 012042[30] Zheng L, Liu S and Wang S Current situation and future ofChinese industrial robot development Int. J. Mech. Eng.
Robot. Res. 5 295–300[31] Nishioka H and Takeuchi A 2018 The development of hightechnology industry in Japan The Development of HighTechnology Industries—An International Survey (NewYork: : Routledge, Taylor and Francis Group) pp 265–8[32] Richerson D W 2006 Modern Ceramic Engineering—
Properties, Processing, and Use in Design (New York:
USA: Taylor and Francis Group) pp 573–9[33] Davis J R 2000 Corrosion: Understanding the Basics(Materials Park: ASM International) pp 295–7[34] Kyocera ﬁne ceramics (https://kyocera.co.jp/prdct/fc/
product/pdf/material.pdf) [Accessed: 22 Oct 2019][35] Mason W P 1956 Physical acoustics and the properties ofsolids J. Acoust. Soc. Am. 28 1197–206[36] Bengisu M 2001 Engineering Ceramics (New York: Springer)
pp 85–102[37] Jin F-L, Li X and Park S-J 2015 Synthesis and application of
epoxy resins: a review J. Ind. Eng. Chem. 29 1–11
[38] Wu C and Xu W 2006 Atomistic molecular modelling ofcrosslinked epoxy resin Polymer 47 6004–9[39] Epoxy adhesive application guide (http://epotek.com/site/ﬁles/brochures/pdfs/adhesive_application_guide.pdf)[Accessed: 22 Oct. 2019][40] Technical data sheet of Henkel’s epoxy-resin adhesive (http://
loctiteproducts.com/tds/EPXY_QSET_S_tds.pdf)[Accessed: 22 Oct. 2019][41] Mousa S and Kim G-Y 2015 Experimental study on warm rollbonding of metal/polymer/metal multilayer composites
J. Mater. Process. Technol. 222 84–90[42] Jafari M and Ardalani E 2016 Stress concentration in ﬁnite
metallic plates with regular holes Int. J. Mech. Sci. 106
220–30[43] Nicolay P, Bardong J, Chambon H and Duﬁlie P 2018
Glue-less and robust assembly method for SAW strain
sensors Proc. 2018 IEEE Int. Ultrasonics Symp.
[44] Wu J, Mizuno Y and Nakamura K 2019 Piezoelectric motor
utilizing an alumina/PZT transducer IEEE Trans. Ind.
Electron. (https://doi.org/10.1109/TIE.2019.2937047)[45] Morita T 2017 Piezoelectric Phenomena (Tokyo: Morikita
Publication) pp 36–9 (In Japanese)[11] Wu J, Mizuno Y and Nakamura K 2017 Structural parameter
study on polymer-based ultrasonic motor Smart Mater.
Struct. 26 115022[12] Wu J, Mizuno Y and Nakamura K 2018 Ultrasonic motors with
poly phenylene sulﬁde/alumina/PZT triple-layered
vibrators Sensors Actuators A 284 158–64[13] Wachtman J B, Cannon W R and Matthewson M J 2009
Mechanical Properties of Ceramics 2nd edn (New York:
Wiley) pp 89–115[14] Rehbein P and Wallaschek J 1998 Friction and wear
behavior of polymer/steel and alumina/alumina
under high-frequency fretting conditions Wear 216
97–105[15] Song J, Liu X, Zhao G, Ding Q and Qiu J 2019 Effect of
surface roughness and reciprocating time on the tribologicalproperties of the polyimide composites Polym. Eng. Sci. 59
483–9[16] Wang L, Hofmann V, Bai F, Jin J and Twiefel J 2018
Modeling of coupled longitudinal and bending vibrations ina sandwich type piezoelectric transducer utilizing thetransfer matrix method Mech. Syst. Signal Process. 108
216–37[17] Zhao G, Wu C, Zhang L, Song J and Ding Q 2018 Friction andwear behavior of PI and PTFE composites for ultrasonicmotors Polym. Adv. Technol. 29 1487–96[18] Liu Y, Yan J, Wang L and Chen W 2019 A two-DOF
ultrasonic motor using a longitudinal-bending hybrid
sandwich transducer IEEE Trans. Ind. Electron. 66
3041–50[19] Aoyagi M, Beeby S P and White N M 2002 A novel
multi-degree-of-freedom thick-ﬁlm ultrasonic motor
IEEE Trans. Ultrason. Ferroelect. Freq. Control 49
151–8[20] Wang L, Shu C, Jin J and Zhang J 2017 A novel travelingwave piezoelectric actuated tracked mobile robot utilizing
friction effect Smart Mater. Struct. 26 035003[21] Li X and Zhou S 2016 A novel piezoelectric actuator with ascrew-coupled stator and rotor for driving an aperture Smart
Mater. Struct. 25 035027[22] Liu Y, Shi S, Li C, Chen W, Wang L and Liu J 2018
Development of a bi-directional standing wave linear
piezoelectric actuator with four driving feet Ultrasonics 84
81–6[23] Li X and Yao Z 2016 Analytical modeling and experimental
validation of a V-shape piezoelectric ultrasonic transducer
Smart Mater. Struct. 25 075026[25] Kurosawa M and Ueha S 1988 Efﬁciency of ultrasonic motorusing traveling wave J. Acoust. Soc. Japan. 44 40–6
(In Japanese)[26] Alumina ceramic products (http://ceratech.co.jp/product/
material/alumina) [Accessed: 22 Oct. 2019]11