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Sensors and Materials, Vol. 32, No. 7 (2020) 2443–2452
MYU Tokyo
S & M 2273

High-power Characteristics of (Bi,Na)TiO3-BaTiO3 Ceramics
and Application in Miniature Ultrasonic Motor
Susumu Miyake,1* Tomohiro Harada,2 Hiroyuki Shimizu,2Sumiaki Kishimoto,2 and Takeshi Morita1
1

Graduate School of Frontier Sciences, the University of Tokyo,
5-1-5 Kashiwano-ha, Kashiwa, Chiba 277-8563, Japan
2
Taiyo Yuden Co., Ltd., 5607-2 Nakamuroda, Takasaki, Gunma 370-3347, Japan(Received February 17, 2020; accepted July 9, 2020)

Keywords: ultrasonic motor, lead-free piezoelectric material, high-power piezoelectric vibration,
nonlinear vibration

Piezoelectric materials are utilized for high-power ultrasonic devices such as
ultrasonic motors, which are driven under high stress and strain. The nonlinear elastic
vibration of piezoelectric materials is a critical problem because it degrades the output
performance. (Bi,Na)TiO3-BaTiO3 (BNBT) ceramics are one of the lead-free piezoelectricmaterials that show outstanding characteristics under high power driving, such as stablemechanical quality factor and resonance frequency. We evaluated the high-power
characteristics of BNBT ceramics by measuring complex higher-order elastic constants using
a nonlinear piezoelectric vibration model. We found that the absolute value of the higher-orderelastic constant of BNBT was less than 4% of Pb(Zr,Ti)O3 (PZT). Additionally, we developed
a miniature ultrasonic motor using a BNBT multilayered piezoelectric transducer. This
multilayered structure was utilized to enhance the piezoelectric displacement and was equippedwith elastic fins, which convert the longitudinal vibration of the multilayered piezoelectrictransducer into the rotational moment of the rotor. The rotational speed reached 922 rpm at a
preload of 3 N under an input voltage of 58 Vpp and a resonance frequency of 60.0 kHz.

1.

Introduction

Ultrasonic motors utilize the piezoelectric effect to convert electric input into mechanicaloutput, which results in actuating the slider or rotor with frictional force. Recently, numerous
research studies that focus on the novel design and application of ultrasonic motors have been
proposed.(1,2) However, the investigation of piezoelectric materials suitable for ultrasonicmotors is limited. The characteristics of piezoelectric materials are a critical issue of ultrasonicmotors because they directly affect the performance of ultrasonic motors. Pb(Zr,Ti)O3 (PZT)
is an advantageous piezoelectric material that has been applied to ultrasonic motors since its
discovery.(3) This is because of its high piezoelectric constant and outstanding temperature*

Corresponding author: e-mail: smiyake@s.h.k.u-tokyo.ac.jp
https://doi.org/10.18494/SAM.2020.2831
ISSN 0914-4935 © MYU K.K.
https://myukk.org/

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Sensors and Materials, Vol. 32, No. 7 (2020)stability. However, PZT includes lead, which is harmful to human health. Therefore, various
lead-free piezoelectric ceramics, such as alkaline niobate-based and barium titanate-based
composite ceramics are developed as alternative materials for PZT.(4,5) However, it is difficult
to develop lead-free piezoelectric materials with both high piezoelectric properties andoutstanding temperature stability similarly to PZT.(6)However, some lead-free piezoelectric materials show a higher saturated vibration velocity
than PZT under high electrical field, internal stress, and strain.(7,8) In ultrasonic motors,piezoelectric transducers oscillate under high power; therefore, such excellent high-power
characteristics are a promising advantage of lead-free piezoelectric materials. (Bi,Na)TiO3BaTiO3 (BNBT) ceramics are one of the lead-free piezoelectric materials with such greathigh-power characteristics.(9,10) In this research, we evaluated the high-power characteristicsof BNBT ceramics quantitatively by evaluating complex higher-order elastic constants.
(11)
Admittance curves of BNBT and PZT transducers were measured and complex higherorder elastic constants were obtained by curve fitting using a nonlinear piezoelectric vibration
model.(12,13) Then, a miniature ultrasonic motor was developed using a BNBT multilayeredtransducer. This multilayered structure was introduced to enhance the piezoelectric
displacement. The proposed stator was equipped with four elastic fins, which convert thepiezoelectric linear motion into the rotational moment of the rotor.(14)2.

Evaluation of High-power Characteristics

To apply piezoelectric materials in ultrasonic motors, high-power characteristics of
piezoelectric materials are a critical problem. Here, piezoelectric high-power characteristicsof BNBT and PZT were evaluated quantitatively by using a nonlinear LCR equivalent circuit
model.(12,13)
2.1

Nonlinear LCR equivalent circuit method

Piezoelectric high-power characteristics can be evaluated by measuring complex higherorder elastic constants.(11) Under huge amplitude piezoelectric vibration with huge internal
stress and strain, higher-order vibration is induced. It originates from the nonlinear relationshipbetween stress and strain, which is represented as
E
E
T1 =
c11
S1 + c11(3)S13 + e31E3 ,

(1)

E
E
where T1, S1, and E3 are the stress, strain, and electric field; c11, c11(3), and e31 are the linear

elastic, cubic elastic, and piezoelectric constants, respectively. Subscripts are based on
the piezoelectric 31 effect because the 31 effect transducer is used to evaluate high-powerE
S13 is mainly considered and othercharacteristics in this section. The higher-order term c11(3)higher-order terms are omitted because the even-ordered term does not affect the signal with

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driving frequency and the effect of greater than 5th-order terms is negligible compared withE
was measured andthat of the 3rd order term.(12) In this research, the cubic elastic constant c11(3)Eutilized for evaluating piezoelectric high-power characteristics. c11(3)was treated as a complex

number as

( )

( )

E
E
E
.
=
c11(3)
Re c11(3)+ jIm c11(3)(2)

To obtain complex higher-order elastic constants, a nonlinear LCR equivalent circuit method
is utilized.(9) A general piezoelectric LCR equivalent circuit is shown in Fig. 1(a). In thiscircuit, the relationship between the voltage V and the current im is given as
L

dim
1
V,
+ Rim + ∫ im dt =
dt
C

(3)

where L, R, and C are the equivalent mass, mechanical loss, and compliance, respectively. Thismodel is based on linear elasticity. The nonlinear LCR equivalent circuit is shown in Fig. 1(b).
In this circuit, the damped capacitance Cd and force factor A are considered constant and theequivalent mechanical loss R and compliance C are functions of the current im. Hence, Eq. (3)is modified as
L

3
dim
1
3
+ R0im + η im3 +
i
dt
+
ξω
i
dt
=
V,
m
m
∫
dt
C0 ∫

(

)

(4)

where ω is the angular frequency, η is the nonlinear mechanical loss coefficient, and ξ is thenonlinear compliance coefficient. The admittance Y = im/V can be calculated using Eq. (4). In
the next section, the admittance curve of BNBT and PZT plate transducers was measured andthe nonlinear coefficients η and ξ were obtained by admittance curve fitting using Eq. (4).
E
were obtained on the basis of their relationship
Complex higher-order elastic constants c11(3)with η and ξ as(a)Fig. 1.

(b)(a) General LCR equivalent circuit. (b) Nonlinear LCR equivalent circuit.

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Sensors and Materials, Vol. 32, No. 7 (2020)

2

E
Re c11(3)( )E
16 c11A2 ,=ξ
9 ρωr L( )E
16 c11A2=
η,
9 ρωr LE
Im c11(3)

(5)

2

(6)

where ρ and ωr are the density and resonance frequency, respectively.
2.2

Admittance curve measurement

Figure 2 shows the setup of the admittance curve measurement. BNBT (Taiyo Yuden
Co., Ltd., 4 × 0.8 × 10 mm3) and PZT (Fuji Ceramics Corporation, C-203, 7 × 2 × 44 mm3)transducers were prepared. The measured admittance curves of the BNBT and PZT transducers
are shown in Figs. 3 and 4, respectively. The admittance curve of the PZT transducer showed
clear admittance jumping and a 1.5% resonance frequency shift; however, the BNBT transducer

Fig. 2.

Fig. 3.

Setup of admittance curve measurement.

(Color online) Admittance curve of BNBT transducer.

Sensors and Materials, Vol. 32, No. 7 (2020)

Fig. 4.

2447(Color online) Admittance curve of PZT transducer.

showed only a 0.03% resonance frequency shift. Using Eqs. (4)–(6), we applied fitting to these
admittance curves, and complex higher-order elastic constants were obtained as shown in Table 1.
Higher-order elastic constants of BNBT were less than 4% of those of PZT. From Eq. (1),small higher-order elastic constants prevent higher-order vibration. Therefore, BNBT can beconsidered as a promising piezoelectric material that is excited under high power.

3.

Ultrasonic Motor Using BNBT Multilayered Transducer

3.1

Design of ultrasonic motor

We developed a miniature ultrasonic motor using a BNBT multilayered transducer. The
proposed ultrasonic motor and its rotor part are shown in Figs. 5 and 6, respectively. The
dimensions of the BNBT multilayered transducer were 5 × 5 × 8 mm3 and the transducer
consists of 140 layers. On the top surface of the multilayered transducer, four L-shaped elastic
fins and the shaft were bonded. These elastic fins were made of beryllium copper and theangle of the fins was 15°. When the BNBT multilayered transducer was excited by the 1stlongitudinal resonance mode, these elastic fins converted the longitudinal displacement of themultilayered transducer into the rotational movement of the rotor. The preload was given by theupper spring, whose spring constant was 0.118 or 0.765 N/mm.
The driving principle of the elastic fin motor is shown in Fig. 7. From initial state (a) to state(b), the stator (BNBT multilayered transducer) moves upward and the rotor and elastic fin move
together without slippage because of sufficient normal force (= preload force + force from thestator). In state (c), when the stator moves downward, the normal force (= preload − force fromthe stator) decreases and slippage occurs. At the end of state (c), the rotor rotates in the right
direction from state (a). In this manner, the rotor can be driven in one direction by repeating thecycle of state from (a) to (c).

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Sensors and Materials, Vol. 32, No. 7 (2020)

Table 1
Complex higher-order elastic constants of BNBT and PZT.

BNBT
PZT

E
 (N/m 2)
Re  c11 ( 3) −1.4 × 1015
−1.3 × 1017E
 (N/m 2)
Im  c11 ( 3) 
3.2 × 1014
8.5 × 1015

Fig. 5.

Fig. 6.
motor.

3.2(Color online) Proposed ultrasonic motor.

(Color online) Rotor part of ultrasonicFig. 7.
motor.

(Color online) Driving principle of elastic fin

Measurement

To evaluate the performance of the ultrasonic motor, the rotational speed of the rotor wasmeasured using a laser doppler velocimeter (Cannon S-100Z). The experimental setup is shownin Fig. 8. The relationship between the rotational speed and the input voltage at preloads of 2
and 3 N is shown in Fig. 9. The motor was driven by the 1st resonance frequency, which shiftedfrom 60.2 to 60.0 kHz when the preload was changed from 2 to 3 N. However, the resonancefrequency did not change with the driving voltage amplitude. In general, resonant ultrasonicmotors exhibit a resonance frequency shift depending on the driving voltage. This is causedby the nonlinear vibration of piezoelectric materials. As confirmed in Sect. 2, the outstanding
high-power characteristics of BNBT result in the stability of the resonance frequency of the
proposed motor. The rotational speed increased with the input voltage and finally saturated.
The rotation at a preload of 3 N was unstable compared with that at a preload of 2 N and norotation was confirmed at a preload of 4 N. This is because a very large preload inhibits

Sensors and Materials, Vol. 32, No. 7 (2020)

Fig. 8.

Fig. 9.

2449(Color online) Experimental setup to measure rotational speed.

(Color online) Relationship between voltage and rotational speed.

Table 2Comparison with other miniature ultrasonic motors.
DesignTransducer size (mm) Piezoelectric materialØ11.5 × Ø7.5 × 0.45
PZT
Zhao et al.(15)(50 µm × 9 layers)(16)
Doshida et al.
12 × 3 × 1(Sr,Ca)2NaNbO15
Proposed motor
5×5×8
BNBT

d33 (pC/N) Rotational speed (rpm)
593

2100

260
77

190
922

slippage in the state in Fig. 3(c). The maximum rotational speed was determined to be 898 rpm
at a preload of 2 N and 922 rpm at a preload of 3 N. Table 2 shows the performance comparisonof our proposed ultrasonic motor with existing miniature ultrasonic motors that use the PZTmultilayer transducer(15) and crystal-oriented (Sr,Ca)2NaNbO15 transducer.(16) (Sr,Ca)2NaNbO15
is a lead-free piezoelectric material with great high-power characteristics reported by
Doshida et al.(9,10) Our proposed ultrasonic motor showed the smallest piezoelectric constant(d33 = 77 pC/N) and a higher rotational speed than the lead-free ultrasonic motor. We have toconsider that Doshida et al. used 31 mode piezoelectric vibration of stator transducer, but our
proposed motor realized high rotational speed owing to the multilayered structure and BNBT’s
high-power characteristics.

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Sensors and Materials, Vol. 32, No. 7 (2020)

Conclusions

In this research, complex higher-order elastic constants of BNBT ceramics were evaluatedusing a nonlinear LCR equivalent circuit model. The measured complex higher-order elastic
constants of BNBT were less than 4% of PZT. This indicates that BNBT is a promisingpiezoelectric material under high power. A miniature elastic fin-type ultrasonic motor wasdeveloped utilizing a BNBT multilayered transducer. It provided stability of resonancefrequency, and the maximum rotational speed reached 922 rpm at a preload of 3 N under
an input voltage of 58 Vpp. The performance difference between BNBT and lead-based
piezoelectric materials will be examined in terms of their usage for the stator of the ultrasonicmotor.

Acknowledgments
This work was supported by JSPS KAKENHI Grant number JP18J22170.

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About the Authors
Susumu Miyake received his B.S. Eng. and M.S. degrees from the Universityof Tokyo in 2016 and 2018, respectively. He is currently pursuing his
doctorate degree at the University of Tokyo. His current research interests arein the high-power characteristics of piezoelectric and lead-free piezoelectricmaterials. (smiyake@s.h.k.u-tokyo.ac.jp)

Tomohiro Harada received his M.S. degree in engineering science from
Tokyo University of Science in 2009. He has been working on piezoelectricmaterial design and processing at Taiyo Yuden Co., Ltd., since 2009. In 2018,
he received an award for an outstanding paper published in the JCS-Japan in
the field of crystal orientation of piezoelectric ceramics. His current researchinterests are in lead-free piezoelectric materials and high-power applications.
(tharada@jty.yuden.co.jp)

Hiroyuki Shimizu received his Ph.D. degree in materials science fromNara Institute of Science and Technology in 2006. He has been working on
piezoelectric material design and actuator development in Taiyo Yuden Co.,
Ltd. since 2006. He received the 66th JCS-Japan award for advancement inindustrial ceramic technology in 2012 in the field of textured ceramic design.
From 2012 to 2014, he researched on antiferroelectric and piezoelectricmaterials as a visiting scientist in Pennsylvania State University. His current
research and development focuses on lead-free piezoelectric materials andapplications. (h-shimizu@jty.yuden.co.jp)

Sumiaki Kishimoto received his M.S. degree in electrical engineeringfrom Tokyo University of Science in 2002. He has been working on process
technology for MLCC and piezoelectric materials in Taiyo Yuden Co., Ltd.,
since 2002. Currently, he is the manager in charge of piezoelectric material
development. His current research interests are in piezoelectric materials andapplications in sensors and actuators. (s-kishimoto@jty.yuden.co.jp)

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Sensors and Materials, Vol. 32, No. 7 (2020)

Takeshi Morita received his B.S. Eng., M.S. Eng., and Ph.D. Eng. degrees inprecision machinery engineering from The University of Tokyo in 1994, 1996,
and 1999, respectively. After working as a postdoctoral researcher at RIKEN(the Institute of Physical and Chemical Research) and EPFL (Swiss Federal
Institute of Technology), he became a research associate at Tohoku University
in 2002. He obtained a position at The University of Tokyo as an associate
professor in 2005 and has been a full professor since 2018. His researchinterests include piezoelectric actuators and sensors, and their fabrication
processes and control systems. (morita@edu.k.u-tokyo.ac.jp)