APPLIED PHYSICS LETTERS 105, 224102 (2014)

Can lubricant enhance the torque of ultrasonic motors? An experimental
investigation
Wei Qiu,a) Yosuke Mizuno, Marie Tabaru, and Kentaro Nakamura
Precision and Intelligence Laboratory, Tokyo Institute of Technology, 4259 Nagatsuta-cho, Midori-ku,
Yokohama 226-8503, Japan(Received 1 October 2014; accepted 20 November 2014; published online 2 December 2014)
Lubrication has been proven to be an effective approach to drastically improve the efficiency ofultrasonic motors without losing the output torque. This phenomenon is attributed to the effective
modulation of the friction force by lubricant, according to the theory described in the Stribeck
curve. Previous findings even show a potential to increase the motor output torque with lubrication.
Here, the torque enhancement of ultrasonic motors using lubricant is extensively studied in hybridtransducer-type ultrasonic motors (HTUSMs) with a size of 25 mm in diameter. The lubricated
HTUSMs could withstand static preload as high as 267 N and maximum torque as large as 1.01 N
m was obtained with lubrication, which were 3.5 times and 2.6 times higher than those in dry
condition, respectively. This result clearly reveals that lubrication can enable ultrasonic motors
to be operated under much higher static preload and hence significantly improve the motor output
C 2014 AIP Publishing LLC.
torque, instead of only reducing the friction force. V[http://dx.doi.org/10.1063/1.4903238]

Ultrasonic motors are typically operated in dry conditionand driven by the friction force between their stator and rotor/
slider.1–4 In the most cases, the friction force is modulated by
the vibration in the preloading direction to produce high driving force in the positive half cycle of the vibration, while thefriction force in the negative half cycle of the vibration should
be suppressed. Ideally efficient modulation is, however,extremely difficult to obtain if the preload is high, because thevibration in the preloading direction is not sufficiently strong
compared with the static preload.5–7 Friction loss induced in
the negative half cycle of the vibration and wear of the friction materials are inevitable, causing low efficiency and shortlife. This feature has been regarded as an inherent problem ofultrasonic motors, which cannot be fully overcome by
the efforts from various aspects, including selection of appropriate friction materials,8,9 optimization of the vibration
systems,10–12 or development of the drive/control techniques.13–15 However, our previous study has shown that functional lubrication can largely reduce the friction loss andimprove the motor efficiency.16 Friction force can be modulated much more efficiently since the coefficient of friction
can be dynamically varied by the characteristics of the lubricant, which is conceptually explained through the well-known
Stribeck curve.17 Somewhat surprisingly, the maximum torque of lubricated ultrasonic motors was not lower, but evenslightly higher than that in dry condition. This phenomenon issignificantly different from our original expectation thatmotors will lose some output force after being lubricated.
Therefore, the potential to improve the torque of ultrasonicmotors using lubricant needs to be further explored.
In this letter, we report on an experimental investigationof the torque enhancement in hybrid transducer-type ultrasonicmotors (HTUSMs) using lubricant. After analyzing the factorsa)Author to whom correspondence should be addressed. Electronic mail:qiu@sonic.pi.titech.ac.jp0003-6951/2014/105(22)/224102/4/$30.00

that determine the motor output torque, the dependence of the
maximum torque on static preload is examined. The maximum
torque increases almost linearly with increasing preload andreaches 1.01 N m at the preload of 267 N after being lubricated,
providing a marked contrast to the maximum torque of 0.39 N
m at the preload of 76 N in dry condition. The no-load speed,
the amplitude of torsional vibration velocity, and their ratio
prove that high preload is desirable to the lubricated ultrasonicmotors. The effect of longitudinal vibration on the maximum
torque is also studied experimentally.
The stator of the HTUSM used in the experimentwas 25 mm in diameter and composed of two 4-mm-thick torsional lead zirconate titanate (PZT) disks (polarized incircumferential direction) and six 1-mm-thick longitudinal
PZT disks (polarized in thickness direction), as shown in
Fig. 1(a). The rotor is pressed to the stator by a coil spring toapply the preload. Figure 1(b) illustrates the operating principle of the HTUSM, where a torsional vibrator generates theoutput force and a longitudinal vibrator controls the friction
force. When the torsional vibrator moves rightward, the longitudinal vibrator extends to contact the rotor and the driving
force is transmitted through the friction force between the rotor
and the stator. The displacement of the longitudinal vibrator
should reach its maximum to provide the highest stress when
the torsional vibrator obtains its maximum velocity to theright, hence a 90 phase difference is required to drive thismotor. In contrast, when the torsional vibrator moves leftward,
the longitudinal vibrator shrinks to separate the rotor and thestator. Thus, the rotor can be rotated in one direction due to its
inertia. However, this ideal operating principle can hardly
be realized if high preload is applied to generate sufficient
torque. The rotor and the stator cannot be detached in the negative cycle of the torsional vibration, which induces considerable friction loss and wear of the friction materials. This is the
major reason for the low efficiency of ultrasonic motors, which
has been extensively analyzed in Refs. 6, 7, and 16.

105, 224102-1

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Appl. Phys. Lett. 105, 224102 (2014)

FIG. 1. (a) Dimension of the hybrid transducer-type ultrasonic motor used in this experiment. The polarization directions of torsional and longitudinal PZTdisks are indicated by the arrows. (b) Operating principle of the hybrid transducer-type ultrasonic motor.

Functional lubrication is one of the promising candidates to solve the inherent problems in ultrasonic motors. To
date, lubrication has not been used in commercial ultrasonicmotors since the induced slip might lead to the significant
loss of the output torque. However, considering that the preload and the slip between the two sliding surfaces are instantaneously changed during the motor operation, caused by thevibration in the preloading direction, different lubrication
regimes can possibly be implemented in one vibrating cycle.
According to the theory described in the Stribeck curve, thecoefficient of friction becomes high at the instant of a small
slip between the rotor/slider and the stator, or at a high preload, corresponding to the boundary lubrication regime,
where large output force can be achieved; while it decreases
for the period of a large slip or at a low preload, corresponding to the hydrodynamic lubrication regime, where the friction loss can be reduced. Based on this assumption, weapplied lubricant to HTUSMs and the motor efficiency was
drastically improved under the condition of high static preload.16 Another interesting phenomenon after using lubricant
is that the maximum torque was even slightly higher thanthat in dry condition. However, in our previous experiments,
the applied voltage to the torsional vibrator was fixed andhence the friction force exceeded the torque generated by thetorsional vibrator at high preload, which significantly limited
the maximum output torque in lubricated condition.
In this experiment, sufficiently high voltage was applied
to the torsional vibrator in order to ensure that the torquegenerated by the torsional vibrator was beyond the friction
limit. The voltage to the torsional vibrator was increased
until the maximum torque of the HTUSM stopped increasing
under each preload.5 In addition, the applied voltage to thelongitudinal vibrator should be kept constant under different
static preloads in order to avoid the effect of the longitudinal
vibration on the maximum torque. An HTUSM with independently controllable torsional and longitudinal vibrations
is therefore a desirable platform for this study. The resonance frequency of the longitudinal vibrator was adjusted to
be close to that of the torsional vibrator by changing thelength of the rotor. Since the resonance frequencies vary
under different preloads, the rotors with different lengths
were prepared. Alumina and silicon nitride were selected as
the friction materials on the stator and the rotor sides, respectively. The contact shape on the rotor side followed thedesign in Ref. 16. The grease (Li-complex thickener) with abase oil viscosity grade of 460 and a worked penetration of
290 was selected as the lubricant. The driving signals for the
HTUSM were provided by a function generator with a phaseshifter. In order to drive the motor, power amplifiers andtransformers were employed to obtain sufficient power.
Different weights were applied for the torque measurements,
and the maximum torque of the motor was calculated using
the weight immediately after the motor stopped.
The dependence of the motor maximum torque on static
preload in dry and lubricated conditions is shown in Fig. 2.
The voltage applied to the longitudinal PZTs was fixed at 77
Vrms. The maximum torque increased with increasing
preload until the motor stopped, irrespective of whether the
lubricant was applied or not. Without lubrication, the maximum torque was much higher than that in lubricated condition when the preload was low, since a large slip occurred in
the lubricated HTUSM due to the hydrodynamic lubrication.
However, the motor perfectly stopped at 95 N in dry condition, providing a maximum torque of 0.39 N m. In contrast,
the lubricated motor did not stop until the preload reached
286 N, and the maximum torque of 1.01 N m was obtained.
This torque was 2.6 times higher than that in dry condition
and is the recorded value among the HTUSMs with the same
diameter. This fact that the maximum torque of the

FIG. 2. Maximum torque as a function of static preload.

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lubricated ultrasonic motor is significantly higher than thatin dry condition has not been expected before. It can be
explained that ultrasonic motors can withstand much higher
static preload after being lubricated, increasing the friction
limit which determines the output torque. At even higher
static preload, the lubricated HTUSM did not completely
stop and the rotation was still observed. However, the motor
stopped automatically after several revolutions, whichshould be attributed to the extremely high preloading force.
The generated friction force was so high that the desirable
modulation by the longitudinal vibration was infeasible evenwith lubrication. Such high static preload should not beapplied for lubricated ultrasonic motors for stable operation.
The no-load speed and the amplitude of torsional vibration velocity with and without lubrication were also investigated, as shown in Figs. 3 and 4, in order to understand why
lubricated ultrasonic motors can withstand much higher
preload. The voltages applied to the torsional and longitudinal PZTs were fixed at 116 Vrms and 77 Vrms, respectively.
The motor rotational speed was measured by a high-speed
digital camera (Integrated Design Tools, Inc., Tallahassee,
FL), and the torsional vibration velocity was measured by a
2D laser Doppler vibrometer (Polytec Gmbh, Waldbronn,
Germany). The no-load speed in dry condition also showed
clear superiority to that in lubricated condition, if low
static preloads were applied. However, the no-load speed
decreased linearly with increasing static preload, if the
HTUSM was not lubricated. The dependence of the no-load
speed on static preload with lubrication showed a different
trend, where it increased first until 114 N was applied andthen decreased. The no-load speed had some fluctuations in
the high-preload region, which might be caused by the undesirable resonant condition. The no-load speed of the lubricated HTUSM still reached 13.89 rad/s at 267 N preload,
which indicates that the motor operation with lubrication
was quite stable even under high static preload. Unlike
the maximum torque and no-load speed, the amplitude of
torsional vibration velocity in dry condition was lower thanthat in lubricated condition even if the preload was low. It
decreased in both conditions with increasing static preload,
but the slope of the velocity decreasing with lubrication was

FIG. 3. No-load speed as a function of static preload.

Appl. Phys. Lett. 105, 224102 (2014)

FIG. 4. Dependence of the amplitude of torsional vibration velocity on static
preload.

much smaller than that without lubrication. With a certain
input voltage to the torsional vibrator, the velocity amplitude
can reach its maximum when the torsional vibrator vibrates
freely (without any load). When a rotor is attached to the torsional vibrator with a certain load, it acts as a block to thetorsional vibrator and the blocking force comes from the friction force between the rotor and the torsional vibrator. Withhigher static preload, the friction force is also increased,
resulting in larger blocking force and the reduction in the torsional velocity amplitude. Under the same static preload, thefriction force in lubricated condition is smaller than thatwithout lubrication, because the average coefficient of friction in one vibration period with lubrication is lower thanthat in dry condition. Therefore, the blocking force to the torsional vibrator is also smaller, and the velocity amplitudewith lubrication is always higher than that in dry condition.
Figure 5 illustrates the speed ratio of the HTUSM as afunction of static preload. The speed ratio was defined as theratio of the no-load speed to the amplitude of the torsional
vibration velocity. This ratio describes the slip between therotor and the stator in the driving period (the amplitude of
torsional vibration velocity is higher than the rotational

FIG. 5. Dependence of the speed ratio on static preload.

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FIG. 6. Maximum torque as a function of the input voltage applied to thelongitudinal vibrator at 267 N static preload.

speed of the motor). It is ideal that the speed ratio is highbecause a low speed ratio means that the slip between therotor and the stator is large in the driving period. If the same
velocity is obtained, i.e., the stick between the rotor and thestator, the friction loss and wear in the driving period can besuppressed.13,14 In dry condition, the speed ratio was high at
low static preloads, and in principle, the no-load speed
should equal the amplitude of torsional vibration velocity if
the rotor only contacts the stator when the torsional vibration
velocity reaches its maximum. However, with increasing
static preload, the speed ratio drastically dropped, indicatingthat a large slip occurred at high static preload and hence
induced considerable friction loss and wear. In contrast, thelubricated HTUSM possessed a low speed ratio at low static
preloads, since large slip occurred due to the presence ofhydrodynamic lubrication, as we have analyzed before. With
increasing static preload, boundary lubrication was achieved
and the coefficient of friction became high in the driving period, resulting in the improvement of the speed ratio. Though
the speed ratio also decreased if too high static preload wasapplied, it was still kept at 70% at high-preload region,
which again indicates that the lubricated motor performed
well at high preload.
The effect of longitudinal vibration on the motor maximum torque in lubricated condition was also examined, as
shown in Fig. 6. The static preload was kept at 267 N, where
the highest maximum torque was obtained. The motor did
not rotate when the applied voltage to the longitudinal PZTs
was lower than 33 Vrms. With increasing static preload, themaximum torque increased until reaching its maximum
when 80 Vrms was applied to the longitudinal vibrator. The
saturation of the maximum torque is due to the limit of thefriction force. The output torque of ultrasonic motors is theintegral of the instantaneous torque, which is calculated as
the production of the coefficient of friction, the dynamic
preload, and the contact radius. The time-averaged dynamic
preload should equal the static preload, and hence the limitof the output torque is equal to or less than (depends on thecontact duration) the production of the coefficient of friction,

Appl. Phys. Lett. 105, 224102 (2014)

the static preload, and the contact radius. The output torquedoes not increase with increasing the input power to thelongitudinal vibrator, if it has already reached its limit. The
maximum torque slightly decreased when the input voltage
to the longitudinal vibrator was higher than 80 Vrms. It might
be caused by the undesirable coupling system to the rotor,
which induced some irregularities in longitudinal vibration
when too high power was applied. This operating condition
should be avoided because it may destroy the PZTs and significantly increase the power consumption for longitudinal
vibration as well as the wear of the friction materials.
In conclusion, we investigated the torque of ultrasonicmotors in lubricated condition, and significant improvement inmotor output torque was observed. The maximum torque ashigh as 1.01 N m was obtained in a 25-mm-diameter HTUSM,
which was 2.6 times higher than that in dry condition. The torque enhancement was attributed to the fact that the motor withlubrication can withstand much higher static preload than thatwithout lubrication. The results of the no-load speed, theamplitude of torsional vibration velocity, and the speed ratio
illustrate that high static preload is desirable for lubricatedultrasonic motors. The finding in this work will explore thehigh-torque applications of ultrasonic motors to a great extent.
The work of W. Qiu was supported by a Grant-in-Aid
for the research fellow of Japan Society for the Promotion of
Science (JSPS) (Grant No. 26011842). The authors areindebted to Professor K. Adachi at Tohoku University,
Japan, for his insightful discussion and Idemitsu Kosan Co.,
Ltd. for providing the lubricant. They also appreciate thestaff members of the Precision and Manufacturing Center,
Technical Department, Tokyo Institute of Technology,
Japan, for machining the metal components of the motor
used in the experiment.
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