Access to this full-text is provided by Wiley.
Content available from Journal of Sensors
This content is subject to copyright. Terms and conditions apply.
Review Article
Static Force Measurement Using Piezoelectric Sensors
Kyungrim Kim ,
1
Jinwook Kim ,
2
Xiaoning Jiang,
1
and Taeyang Kim
3
1
Department of Mechanical and Aerospace Engineering, North Carolina State University, Raleigh, NC 27695, USA
2
Joint Department of Biomedical Engineering, The University of North Carolina at Chapel Hill and North Carolina State University,
Chapel Hill, NC 27599, USA
3
Department of Mechanical and System Engineering, Korea Military Academy, Seoul 01805, Republic of Korea
Correspondence should be addressed to Taeyang Kim; tkim8@ncsu.edu
Received 13 November 2020; Revised 8 February 2021; Accepted 3 March 2021; Published 16 March 2021
Academic Editor: Manel Gasulla
Copyright © 2021 Kyungrim Kim et al. This is an open access article distributed under the Creative Commons Attribution License,
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
In force measurement applications, a piezoelectric force sensor is one of the most popular sensors due to its advantages of low cost,
linear response, and high sensitivity. Piezoelectric sensors effectively convert dynamic forces to electrical signals by the direct
piezoelectric effect, but their use has been limited in measuring static forces due to the easily neutralized surface charge. To
overcome this shortcoming, several static (either pure static or quasistatic) force sensing techniques using piezoelectric materials
have been developed utilizing several unique parameters rather than just the surface charge produced by an applied force. The
parameters for static force measurement include the resonance frequency, electrical impedance, decay time constant, and
capacitance. In this review, we discuss the detailed mechanism of these piezoelectric-type, static force sensing methods that use
more than the direct piezoelectric effect. We also highlight the challenges and potentials of each method for static force sensing
applications.
1. Introduction
Force sensation as part of tactile information is an important
feedback mechanism to perceive external stimuli in human
explorations [1–3]. Force sensing is also necessary to obtain
accurate force feedback in robotics and automated medical
device applications [4–7]. For these applications, sensors
have specific requirements such as small size, lightweight,
structural robustness, low cost, and low power consumption
[8–11]. In the last few decades, many electromechanical force
sensing techniques have been developed to satisfy these
requirements, including piezoresistive-, capacitive-, and
piezoelectric-type sensors [12–15]. Among these sensing
methods, piezoelectric (PE) sensing is one of the most popu-
lar methods because it uses a direct piezoelectric effect that
can efficiently measure dynamic forces [16–19]. In addition,
piezoelectric force sensors offer distinct advantages such as
mechanical robustness and noise resistance compared to
other types. However, PE force sensors have a major draw-
back that limits their practical use in static force measure-
ments [20–23]. When a static force is applied to
piezoelectric force sensors, the induced electrostatic charge
begins to exponentially decrease according to the following
equation, q=Qe−t/RC (qis the amount of charge after a cer-
tain time, Qis the original value of generated charge, Ris
the resistance of the feedback resistor, Cis the total capaci-
tance of the sensor system, and tis the measurement time).
The product of Rand Cis known as the discharge time con-
stant (DTC) which implies the time required for the induced
charge to decrease by 37% of its initial value. For the suffi-
ciently long DTC with adequate signal processing, quasistatic
forces can be possibly measured, but there are still limitations
in the time window for measuring static forces due to the cur-
rent leakage [24]. This characteristic makes typical piezoelec-
tric force sensors only suitable for time-varying (dynamic)
force measurements despite their advantages over other types
of force sensors. Numerous designs of piezoelectric sensors
have been suggested for static force sensing using various
measurement parameters including the resonance frequency,
decay time constant, and capacitance [25–30]. Recent studies
also demonstrated that the electrical impedance or admit-
tance amplitude at resonance (or antiresonance) varies by
Hindawi
Journal of Sensors
Volume 2021, Article ID 6664200, 8 pages
https://doi.org/10.1155/2021/6664200
applied force-induced acoustic load variation with feasible
sensitivity and linearity which can be effectively used for
static force sensing [31–33]. Despite increasing attention for
taking full advantage of piezoelectricity in static force sens-
ing, a collective resource that provides a comprehensive
review of each measurement mechanism is hardly available
to date. Several review articles regarding general piezoelectric
force sensors were published, but those articles mainly
focused on the direct piezoelectric sensing of dynamic and
quasistatic force with very limited information of static mea-
surement [34–37]. In this review, we focus on static force
measurement techniques using piezoelectric-type sensors.
Most piezoelectric-type yet static force sensors were reported
later than 2000 since the motivation usually came from their
contrasting performance in static force measurements com-
pared to highly-efficient, well-known piezoelectric sensor
designs for dynamic force measurement. Thus, our review
covers relatively recent literature (mainly from 2000 to
2020) with the keywords of “piezoelectricity”and “static
force sensor”.
2. Static Force Measurement Using
Piezoelectric Sensors
Several studies have been conducted on static force measure-
ment using piezoelectric sensors. In most cases, piezoelectric
resonant-type sensors based on the inverse piezoelectric
effect have been used for static measurement applications.
The piezoelectric resonant sensor detects the change of the
resonance conditions of a piezoelectric material induced by
external stimuli [38–46]. This sensor also requires the voltage
source to oscillate the resonator at a specific frequency [47–
49]. Since this type of sensor is not affected by leakage cur-
rent, it can be effectively used for both dynamic and static
measurements without the signal drift.
Static force can be measured by using the change in the
resonance frequency of the piezoelectric sensor [25–27, 31–
33]. The resonance frequency is determined by the effective
stiffness (or spring constant) and mass of the sensor struc-
ture. When a force is applied to the sensor, the sensor struc-
ture is deformed and the stiffness changes with respect to the
applied force. As a result, the force can be detected by mea-
suring the resonance frequency shift of piezoelectric mate-
rials. Meanwhile, the piezoelectric property change
including the compliance coefficient and the piezoelectric
constant affects both the resonance frequency and the electri-
cal impedance of the sensor. Since these properties are sensi-
tive to the applied force, a static force can be estimated by
measuring the frequency and impedance shift according to
the piezoelectric property variation. In addition, static forces
can be measured by utilizing the resonance frequency or elec-
trical impedance shift due to a change in boundary condi-
tions such as surface acoustic loading and mechanical
clamping effects. On the other hand, it is known that the
decay time constant of piezoelectric sensors is directly
affected by the applied force [28]. Therefore, it is also possible
to sense the static force through the measurement of the
decay time constant in the piezoelectric sensor system.
Finally, the typical piezoelectric material is a dielectric mate-
rial that can be considered a capacitor [29, 50, 51]. Thus, the
capacitive measurement of the piezoelectric sensors can be
used for static force sensing. In this section, these mecha-
nisms are discussed with a summary of the reported
performances.
2.1. Resonance Frequency Measurement. Gehin et al. have
studied a static force sensing method using the piezoelectric
resonant sensor based on the resonance frequency measure-
ment [25]. The piezoelectric sensor was made of lead titanate
zirconate (PZT), and the structure consisted of a thin circular
steel plate clamped between two aluminum rings as shown in
Figure 1(a). The prototyped sensor was driven by an alternat-
ing voltage, and static forces were applied to the diaphragm
by using an aluminum tube fixed on the circular plate. It
was observed that the resonance frequency (800 Hz) of the
prestressed sensor increased linearly when the applied force
increased ranging from 0 to 17.7 N. The sensitivity was found
to be 6.6 Hz/N with the hysteresis of 1.76% of the span. The
maximum input force was estimated to be 42 N considering
the yield stress of the diaphragm material. The relatively
high-temperature sensitivity (9 Hz/
°
C) was also observed
due to the different coefficients of thermal expansion and
temperature dependence of elastic modulus for the sensor
materials.
Barthod et al. have developed a piezoelectric resonant
sensor with the structure of double-ended tuning forks
(DETF) for force sensing applications [26]. A prototyped
sensor consists of a thin circular plate, two beams, a tube,
and two piezoelectric elements (PZT) as shown in
Figure 1(b). The circular plates and beams were made of
Invar alloy whose thermal expansion coefficient was close
to that of PZT to minimize the temperature effect. The beams
were directly machined into the circular plate by using a
chemical machining technique to avoid unequal loading
effects. The piezoelectric elements were attached to the top
surface of the beams using the conductive paste. An alternat-
ing voltage was applied to one of the piezoelectric elements to
obtain the second vibrational mode of sensor structures.
When the force was applied to the circular plate through
the tube, the beams were also stressed, and thus, the reso-
nance frequency increased. The experimental results of the
prototyped sensor showed that the resonance frequency
increased linearly over the tested force range (10.8 N to
30 N). The sensitivity and hysteresis were found to be
10.5 Hz/N and 1.8%, respectively. It is noteworthy that a
much less temperature sensitivity of 0.3 Hz/
°
C was observed
compared to the typical diaphragm design sensor (9 Hz/
°
C).
Recently, Safour and Bernard have investigated a piezo-
electric resonant sensor for high static force (~1500 N) sens-
ing applications [27]. A ring-shaped piezoelectric specimen
made of PZT was prepared for the experiments, and a com-
pression machine (Zwick/Roell Z030) was used to compress
the specimen as shown in Figure 1(c). The preliminary exper-
imental results showed that the resonance frequency
increased nonlinearly with respect to the applied force. Low-
ered spectrum quality for higher force values (>500 N) was
observed due to the parasitic vibration modes on the main
spectrum which limited the force measuring range
2 Journal of Sensors
significantly. The unwanted vibration modes were mainly
caused by the constrained condition at the contact interfaces.
To eliminate this phenomenon, soft material-based layers
such as a rubber or Polytetrafluoroethylene (PTFE) were
applied to the surface of the piezoelectric material. The
experiment results showed the improved sensor performance
with the increased linearity and eliminated parasitic mode.
The maximum force range and the sensitivity were found
to be 1500 N and 1.9 Hz/N, respectively. However, there
was also a decrease in the quality factor due to the high
mechanical loss of the layer, which means that it is necessary
to design an appropriate soft layer according to the required
sensing applications.
2.2. Electrical Impedance Measurement. Lin et al. have dem-
onstrated a static force sensing technique through electrical
impedance (admittance) measurement of a piezoelectric reso-
nant sensor [31]. A unimorph cantilever beam (UCB) with a
PZT layer and an aluminum layer was used for the prototyped
sensor to take advantages of simple structures compared to the
Piezoelectric materials
Steel diaphragm
Aluminum rings Aluminum tube
Force
(a)
Base plate
Tube
Double ended tuning for
k
Piezoelectric materials
Force
(b)
Bottom plate
Top plate
Piezoelectric material
Force
(c)
Figure 1: Schematics of piezoelectric sensors for static force measurements using the resonant frequency measurement method: (a) typical
diaphragm design, (b) double-ended tuning fork design, and (c) ring-shape design.
Fixtures
Aluminum layer
Piezoelectric material Force
(a)
PDMS sensing layer
Piezoelectric material
Substrate
Electrodes
Force
(b)
So silicone rubber
Piezoelectric material
Force
(c)
Figure 2: Schematics of piezoelectric force sensors for static force measurements using the electrical impedance measurement method: (a)
unimorph cantilever beam design, (b) hyperelastic sensing layer on the resonator design, and (c) embedded resonator design for the smart
skin application.
3Journal of Sensors
double-ended tuning fork-type sensors as shown in Figure 2(a).
The static force was applied to the top of the beam, and com-
pression forces were measured by a load cell. The minimum
and maximum force ranges for the experiment were deter-
mined to be 0.5 N and 5 N considering the linear response
and the yield stress of the cantilever, respectively. Then, the elec-
trical admittance shift at the fixed frequency (3903 Hz) of the
resonant sensor was measured, and the applied static force
was computed with obtained data. From the experimental
results, the full-scale output (FSO) was found to be 10:1×10
−5S for 0.5 to 5 N force range, which was corresponding to
the electrical impedance of 9900 ohms and the force sensitivity
of 2200 ohms/N. In addition, the nonlinearity was found to be
25.4% FSO and the hysteresis error was 9.2% FSO.
Recently, Kim et al. have studied a static force measure-
ment technique using a specially designed piezoelectric reso-
nator and sensing layers [32]. In this study, a face-shear
mode lead magnesium niobate-lead titanate (PMN-PT)
single-crystal resonator was adopted for the sensing element
to take an advantage of its high sensitivity to the acoustic load
[52]. Also, the concept of a hyperelastic sensing layer was first
introduced and applied for converting the applied static force
into the acoustic load impedance. When the force is applied
to the sensing layer, the elasticity of the layer changes due
to the characteristic of the cross-linking system of hyperelas-
tic materials [53, 54]. As a result, the acoustic impedance of
the sensing layer also increases since the acoustic impedance
is determined by the values of its elasticity and density [55,
56]. The change in acoustic load impedance due to the
change in elasticity can be measured with high sensitivity
using the acoustic load sensing technique with face-shear
mode piezoelectric resonators [52, 57]. The acoustic load
impedance is directly related to the electrical impedance of
the sensor, and thus, the static force can be simply sensed
by measurement of the resonator’s electrical impedance.
The schematic of the prototyped sensor is shown in
Figure 2(b). For the force sensing test, normal forces ranging
from 0.1 to 2.0 N were applied to the prototyped sensor and
the electrical impedance shift of the sensor was measured
through the top and bottom electrodes. It was observed that
the electrical impedance increased linearly as applied normal
forces increased. The sensitivity and accuracy of the sensor
were found to be 51 ohms/N and 50 mN (±2.5%) in the range
of 0.1-2 N from an ideal transfer function, respectively.
Liu et al. have developed a static force sensing technique
using an electromechanical impedance measurement with
the piezoelectric resonator for smart skin applications [33].
A prototyped sensor was made of a PZT plate with a reso-
nance frequency of 900 kHz and embedded in the skin-like
soft silicon rubber material as shown in Figure 2(c). Calibra-
tion weights (0.5 N–2.5 N) were used for applying static
forces, and the impedance signal was recorded using an
impedance analyzer with frequency ranges of 100 kHz to
3 MHz. The tactile index (TI) was used as a diagnostic
method that compared the average impedance values to
reduce the noise effects. As a result of the experiment, it
was observed that the TI value consistently increased as the
static force increased, and the sensitivity was found to be
about 1.8%/N with the resolution of 0.5 N. In this study, a
detailed numerical simulation was also successfully per-
formed to model the electromechanical impedance response
of piezoelectric sensors.
2.3. Decay Time Measurement. Ozeri and Shmilovitz have
developed a static force sensing technique based on the decay
time constant measurement of the piezoelectric sensor [28].
A disk-shaped PZT element with a resonance frequency of
70 kHz was prepared, and natural rubbers were attached to
the top and bottom of the element as described in
Figure 3(a). For experiments, the static forces (from 14.1 N
to 141.3 N) are applied to the sensor and excited with a sinu-
soidal voltage signal (exciting phase). At the end of the exci-
tation phase, the series RLC current begins to exponentially
decrease (free oscillating phase). Then, the change in current
during a specific time is measured, and the decay time con-
stant is calculated with measured values. Since the decay time
constant directly reflects the amount of change in the force
applied to the sensor, it can be effectively used for static force
measurement. From the experiments, it was revealed that the
decay time decreased as the applied static force increased
nonlinearly. In this method, the circuit system constituting
the sensor can be simplified because it uses the amount of
change in the current for a certain period for the measure-
ment rather than the current that occurred at a certain
moment.
2.4. Capacitance Measurement. Sekalski et al. have investi-
gated static force sensing using capacitance measurement
with a stacked piezoelectric resonator [29, 50]. A commercial
PZT piezostack (Physik Instrument) was used for force sens-
ing experiments, and the normal forces ranging from 730 N
to 4 kN were applied to the PZT stack as shown in
Natural rubber
Piezoelectric material
Electrodes
Force
(a)
Piezo-stac
k
Fixtures
Force
(b)
Figure 3: Schematics of static force sensing technique: (a) current decay time measurement using a disk-shaped PZT element and (b)
capacitance measurement using a commercial PZT piezostack.
4 Journal of Sensors
Figure 3(b). It was observed that the capacitance increased as
a function of the loaded force with the sensitivity of 25 nF/kN
and the repeatability of ±5%. When a relatively large force
(>500 N) was applied, the capacitance increased linearly,
whereas, in the case of a small force loading (<100 N), it
showed nonlinear behavior. This is believed to be due to
the large elastic modulus of the piezostack, which makes it
difficult to change the capacitance with small force loading.
The capacitance measurement method using the piezostack
showed potential for the large static force sensing applica-
tions due to its linearity and wide measuring range.
3. Conclusion and Future Work
The piezoelectric force sensor is widely used for measuring
dynamic and quasistatic forces due to its distinct advantages
over other types of sensors. For static force sensing, various
types of piezoelectric sensing technique have been researched
including resonance frequency, electrical impedance, current
decay time, and dielectric capacitance measurements. The
main features of these types of sensors are summarized in
Table 1. The frequency measurement method which is most
widely researched shows excellent linearity compared to
other methods. On the other hand, the electrical impedance
measurement method is one of the most promising tech-
niques and is suitable especially for small force measure-
ments because it presents a high sensitivity to small forces.
However, both the frequency measurement and electrical
impedance measurement methods suffer from a large tem-
perature effect since resonance frequency and electrical
impedance are strongly affected by the environmental tem-
peratures. This influence on the temperature can be mini-
mized by using proper piezoelectric material that is
relatively insensitive to temperature changes [58–62]. In
addition, the temperature effect can be reduced when the
sensor structure is designed in consideration of the coeffi-
cient of temperature for all sensor components [63, 64].
Meanwhile, it was revealed that the sensitivity of the electrical
impedance measurement varies depending on the vibration
mode of piezoelectric material [52, 57]. Thus, for piezoelec-
tric force sensors utilizing the electrical impedance method,
it is necessary to determine the optimized vibration mode
of piezoelectric sensing materials. The decay time measure-
ment method has the advantage of broad operating fre-
quency and simple and low-cost circuit, but further
research will be needed for practical applications. In the case
of the capacitance measurement method, it is suitable for
large force measurement, but it can be inappropriate for
small force measurement due to the high stiffness of piezo-
electric materials. To obtain a high sensitivity to the small
force, piezoelectric polymers with low stiffness such as poly-
vinylidene fluoride (PVDF) can be considered sensing mate-
rials [65–67]. Alternatively, a dielectric polymer layer or a
cavity structure can be added to the sensing layer to increase
the total capacitance change [68, 69]. Finally, a dual-mode
piezoelectric sensor design can be potentially used by com-
bining multiple operation modes. By analyzing the variations
of more than two different parameters by force variations, the
higher sensitivity and higher repeatability are possibly
expected for force sensing applications. We expect that the
summary in this review can be a foundation for designing
highly sensitive, low-cost, piezoelectric static force sensors.
Conflicts of Interest
The authors declare that there is no conflict of interest
regarding the publication of this paper.
Acknowledgments
This research was partly funded by the 2020 research fund of
Korea Military Academy (Hwarangdae Research Institute)
Table 1: Comparisons of different types of piezoelectric static force sensing methods.
Measurement
type Material Sensor structure Sensitivity Sensing
range
Output
central value
Linearity
error Hysteresis Thermal
drift Repeatability Ref.
Resonant
frequency
measurement
PZT
(CeramTec) Diaphragm 6.6 Hz/N 0-17.7 N 890 Hz 3.5% 1.76% 9 Hz/C 0.7% [25]
PZT Double-ended
tuning forks 10.5 Hz/N 10.8-
30 N 2500 Hz 3.6% 1.80% 0.3 Hz/C 2% [26]
PZT (Noliac) Ring shape 1.9 Hz/N 50-
1500 N 172 kHz 6.7% —— —[27]
Electrical
impedance
measurement
PZT Unimorph
cantilever beam
2200
ohms/N 0.5-5 N 3900 ohms 25.4% 9.20% —15.1% [31]
PMN-PT Embedded in the
polymer
51
ohms/N 0.1-2 N 318.5 ohms 4.3% —— —[32]
PZT (APC
ceramics)
Embedded in the
polymer 1.8%/N 0.5-2.5 N 2700 ohms 11.2% —— —[33]
Current
decay time
measurement
PZT Disk shape 1 μsec/N 14.1-
141.3 N 186.5 μsec 11.9% —— —[28]
Dielectric
capacitance
measurement
PZT
(PICMA) Piezostack 25 nF/kN 0.7-4 kN 3170 nF 3.6% 10% ——[29]
5Journal of Sensors
and the National Research Foundation of Korea Grant
funded by the Korean Government (2019R1G1A109954512).
References
[1] T. Kotoku, K. Komoriya, and K. Tanie, “A force display system
for virtual environments and its evaluation,”in IEEE Interna-
tional Workshop on Robot and Human Communication,
pp. 246–251, Tokyo, Japan, 1992.
[2] T. Hachisu and M. Fukumoto, “VacuumTouch: attractive
force feedback interface for haptic interactive surface using
air suction,”in SIGCHI Conference on Human Factors in Com-
puting Systems, pp. 411–420, Toronto, Canada, 2014.
[3] Y. Kazashi, H. Matsuda, and T. Nakata, “Effective contact
method without lateral inhibition in virtual force perception
device,”in 2018 International Workshop on Advanced Image
Technology (IWAIT), pp. 1–4, Chiang Mai, Thailand, 2018.
[4] A. Edsinger-Gonzales and J. Weber, “Domo: a force sensing
humanoid robot for manipulation research,”in 4th IEEE/RAS
International Conference on Humanoid Robots, 2004, pp. 273–
291, Santa Monica, CA, USA, 2004.
[5] E. Bayo and J. Stubbe, “Six-axis force sensor evaluation and a
new type of optimal frame truss design for robotic applica-
tions,”Journal of Robotic Systems, vol. 6, no. 2, pp. 191–208,
1989.
[6] G. De Maria, C. Natale, and S. Pirozzi, “Force/tactile sensor for
robotic applications,”Sensors and Actuators A: Physical,
vol. 175, pp. 60–72, 2012.
[7] N. Kumar, O. Piccin, L. Meylheuc, L. Barbé, and B. Bayle,
“Design, development and preliminary assessment of a force
sensor for robotized medical applications,”in 2014
IEEE/ASME International Conference on Advanced Intelligent
Mechatronics, pp. 1368–1374, Besacon, France, 2014.
[8] C. Lebosse, P. Renaud, B. Bayle, and M. de Mathelin, “Model-
ing and evaluation of low-cost force sensors,”IEEE Transac-
tions on Robotics, vol. 27, no. 4, pp. 815–822, 2011.
[9] L. Paredes-Madrid, P. Torruella, P. Solaeche, I. Galiana, and
P. G. de Santos, “Accurate modeling of low-cost piezoresistive
force sensors for haptic interfaces,”in 2010 IEEE International
Conference on Robotics and Automation, pp. 1828–1833,
Anchorage, AK, USA, 2010.
[10] S. H. Jeong, H. J. Lee, K.-R. Kim, and K.-S. Kim, “Design of a
miniature force sensor based on photointerrupter for robotic
hand,”Sensors and Actuators A: Physical, vol. 269, pp. 444–
453, 2018.
[11] F. Cuellar, T. Yamamoto, and H. Ishiguro, “Design and devel-
opment of a low power tactile multi-sensor network for
robotic systems,”in 2014 IEEE International Conference on
Mechatronics and Automation, pp. 331–336, Tianjin, China,
2014.
[12] E. Peiner, A. Tibrewala, R. Bandorf, S. Biehl, H. Lüthje, and
L. Doering, “Micro force sensor with piezoresistive amorphous
carbon strain gauge,”Sensors and Actuators A: Physical,
vol. 130, pp. 75–82, 2006.
[13] B. Komati, J. Agnus, C. Clévy, and P. Lutz, “Prototyping of a
highly performant and integrated piezoresistive force sensor
for microscale applications,”Journal of Micromechanics and
Microengineering, vol. 24, no. 3, article 035018, 2014.
[14] Y. Sun, B. J. Nelson, D. P. Potasek, and E. Enikov, “A bulk
microfabricated multi-axis capacitive cellular force sensor
using transverse comb drives,”Journal of Micromechanics
and Microengineering, vol. 12, no. 6, pp. 832–840, 2002.
[15] C.-H. Chuang, D.-H. Lee, W.-J. Chang, W.-C. Weng, M. O.
Shaikh, and C.-L. Huang, “Real-time monitoring via patch-
type piezoelectric force sensors for Internet of things based logis-
tics,”IEEE Sensors Journal,vol.17,no.8,pp.2498–2506, 2017.
[16] E. J. Curry, K. Ke, M. T. Chorsi et al., “Biodegradable piezo-
electric force sensor,”Proceedings of the National Academy of
Sciences, vol. 115, no. 5, pp. 909–914, 2018.
[17] B. Gil, B. Li, A. Gao, and G.-Z. Yang, “Miniaturized piezo force
sensor for a medical catheter and implantable device,”ACS
Applied Electronic Materials, vol. 2, no. 8, pp. 2669–2677, 2020.
[18] Y. Wang, J. Zheng, G. Ren, P. Zhang, and C. Xu, “Aflexible
piezoelectric force sensor based on PVDF fabrics,”Smart
Materials and Structures, vol. 20, no. 4, article 045009, 2011.
[19] P. Yu, W. Liu, C. Gu, X. Cheng, and X. Fu, “Flexible piezoelec-
tric tactile sensor array for dynamic three-axis force measure-
ment,”Sensors,vol. 16, no. 6, p. 819, 2016.
[20] H. Hu, Y. Han, A. Song, S. Chen, C. Wang, and Z. Wang, “A
finger-shaped tactile sensor for fabric surfaces evaluation by
2-dimensional active sliding touch,”Sensors, vol. 14, no. 3,
pp. 4899–4913, 2014.
[21] P. Saccomandi, E. Schena, C. M. Oddo, L. Zollo, S. Silvestri,
and E. Guglielmelli, “Microfabricated tactile sensors for bio-
medical applications: a review,”Biosensors, vol. 4, no. 4,
pp. 422–448, 2014.
[22] M. I. Tiwana, S. J. Redmond, and N. H. Lovell, “A review of
tactile sensing technologies with applications in biomedical
engineering,”Sensors and Actuators A: Physical, vol. 179,
pp. 17–31, 2012.
[23] S. Zhang, E. F. Alberta, R. E. Eitel, C. A. Randall, and T. R.
Shrout, “Elastic, piezoelectric, and dielectric characterization
of modified BiScO/sub 3/-PbTiO/sub 3/ceramics,”IEEE
Transactions on Ultrasonics, Ferroelectrics, and Frequency
Control, vol. 52, no. 11, pp. 2131–2139, 2005.
[24] Y. Wei and Q. Xu, “An overview of micro-force sensing tech-
niques,”Sensors and Actuators A: Physical, vol. 234, pp. 359–
374, 2015.
[25] C. Gehin, C. Barthod, and Y. Teisseyre, “Design and character-
isation of a new force resonant sensor,”Sensors and Actuators
A: Physical, vol. 84, no. 1-2, pp. 65–69, 2000.
[26] C. Barthod, Y. Teisseyre, C. Géhin, and G. Gautier, “Resonant
force sensor using a PLL electronic,”Sensors and Actuators A:
Physical, vol. 104, no. 2, pp. 143–150, 2003.
[27] S. Safour and Y. Bernard, “Static force transducer based on res-
onant piezoelectric structure: root cause investigation,”Smart
Materials and Structures, vol. 26, no. 5, article 055012, 2017.
[28] S. Ozeri and D. Shmilovitz, “Static force measurement by pie-
zoelectric sensors,”in 2006 IEEE international symposium on
circuits and systems, p. 4, Kos, Greece, 2006.
[29] P. Sekalski, A. Napieralski, M. Fouaidy, A. Bosotti, and
R. Paparella, “Measurement of static force at liquid helium
temperature,”Measurement Science and Technology, vol. 18,
no. 8, pp. 2356–2364, 2007.
[30] T. Kim, A. Saini, J. Kim et al., “Piezoelectric floating element
shear stress sensor for the wind tunnel flow measurement,”
IEEE Transactions on Industrial Electronics, vol. 64, no. 9,
pp. 7304–7312, 2017.
[31] C.-H. Lin, M.-C. Tsai, and S.-W. Hsiao, “Static force measure-
ment for automation assembly systems,”Sensors and Actua-
tors A: Physical, vol. 187, pp. 147–153, 2012.
6 Journal of Sensors
[32] K. Kim, T. Kim, J. Kim, and X. Jiang, “A face-shear mode pie-
zoelectric array sensor for elasticity and force measurement,”
Sensors, vol. 20, no. 3, p. 604, 2020.
[33] C. Liu, Y. Zhuang, A. Nasrollahi, L. Lu, M. F. Haider, and F.-
K. Chang, “Static tactile sensing for a robotic electronic skin
via an electromechanical impedance-based approach,”Sen-
sors, vol. 20, no. 10, article 2830, 2020.
[34] A. R. R. Morales and M. E. Zaghloul, “Highly sensitive wear-
able piezoelectric force sensor with quasi-static load testing,”
IEEE Sensors Journal, vol. 18, no. 24, pp. 9910–9918, 2018.
[35] J. Lee, W. Choi, Y. K. Yoo et al., “A micro-fabricated force sen-
sor using an all thin film piezoelectric active sensor,”Sensors,
vol. 14, no. 12, pp. 22199–22207, 2014.
[36] D. Van den Ende, W. Groen, and S. Van der Zwaag, “Develop-
ment of temperature stable charge based piezoelectric compos-
ite quasi-static pressure sensors,”Sensors and Actuators A:
Physical, vol. 163, no. 1, pp. 25–31, 2010.
[37] X. Jiang, J. Kim, and K. Kim, “Relaxor-PT single crystal piezo-
electric sensors,”Crystals, vol. 4, no. 3, pp. 351–376, 2014.
[38] E. Benes, M. Gröschl, W. Burger, and M. Schmid, “Sensors
based on piezoelectric resonators,”Sensors and Actuators A:
Physical, vol. 48, no. 1, pp. 1–21, 1995.
[39] M. Maezawa, T. Imahashi, Y. Kuroda, H. Adachi, and
K. Yanagisawa, “Tactile sensor using piezoelectric resonator,”
in International Solid State Sensors and Actuators Conference,
pp. 117–120, Chicago, IL, USA, 1997.
[40] W. Pang, L. Yan, H. Zhang, H. Yu, E. S. Kim, and W. C. Tang,
“Femtogram mass sensing platform based on lateral exten-
sional mode piezoelectric resonator,”Applied Physics Letters,
vol. 88, no. 24, article 243503, 2006.
[41] R. Thalhammer, S. Braun, B. Devcic-Kuhar et al., “Viscosity
sensor utilizing a piezoelectric thickness shear sandwich reso-
nator,”IEEE Transactions on Ultrasonics, Ferroelectrics, and
Frequency Control, vol. 45, no. 5, pp. 1331–1340, 1998.
[42] J. Wang, M. D. Ward, R. C. Ebersole, and R. P. Foss, “Piezo-
electric pH sensors: AT-cut quartz resonators with amphoteric
polymer films,”Analytical Chemistry, vol. 65, no. 19, pp. 2553–
2562, 1993.
[43] G. M. Krishna and K. Rajanna, “Tactile sensor based on piezo-
electric resonance,”IEEE Sensors Journal, vol. 4, no. 5,
pp. 691–697, 2004.
[44] W. Pang, H. Zhao, E. S. Kim, H. Zhang, H. Yu, and X. Hu,
“Piezoelectric microelectromechanical resonant sensors for
chemical and biological detection,”Lab on a Chip, vol. 12,
no. 1, pp. 29–44, 2012.
[45] B. Morten, G. De Cicco, and M. Prudenziati, “Resonant pres-
sure sensor based on piezoelectric properties of ferroelectric
thick films,”Sensors and Actuators A: Physical, vol. 31, no. 1-
3, pp. 153–158, 1992.
[46] H. Han and J. Kim, “Active muscle stiffness sensor based on
piezoelectric resonance for muscle contraction estimation,”
Sensors and Actuators A: Physical, vol. 194, pp. 212–219, 2013.
[47] J. Soderkvist and K. Hjort, “The piezoelectric effect of GaAs
used for resonators and resonant sensors,”Journal of Micro-
mechanics and Microengineering, vol. 4, no. 1, pp. 28–34, 1994.
[48] T. Manzaneque, V. Ruiz-Díez, J. Hernando-García et al., “Pie-
zoelectric MEMS resonator-based oscillator for density and
viscosity sensing,”Sensors and Actuators A: Physical,
vol. 220, pp. 305–315, 2014.
[49] H. Shintaku, T. Nakagawa, D. Kitagawa, H. Tanujaya,
S. Kawano, and J. Ito, “Development of piezoelectric acoustic
sensor with frequency selectivity for artificial cochlea,”Sensors
and Actuators A: Physical, vol. 158, no. 2, pp. 183–192, 2010.
[50] S. Sekalski and A. Napieralski, “Static absolute force measure-
ment for preloaded piezoelements used for active Lorentz
force detuning system,”in Proceedings of LINAC 2004,
p. 486, Lübeck, Germany, 2004.
[51] M. Fouaidy, N. Hammoudi, and I. Orsay, “Characterization of
piezoelectric actuators used for SRF cavities active tuning at
low temperature,”11th Superconducting Radio Frequency
workshop,2003, Lübeck, Germany, 2003, 2003.
[52] K. Kim, S. Zhang, and X. Jiang, “Surface load induced electrical
impedance shift in relaxor-PbTiO3crystal piezoelectric reso-
nators,”Applied Physics Letters, vol. 100, no. 25, article
253501, 2012.
[53] T. Inoue and S. Hirai, “Elastic model of deformable fingertip
for soft-fingered manipulation,”Robotics, IEEE Transactions
on, vol. 22, no. 6, pp. 1273–1279, 2006.
[54] Y. Ren, Y. Zhang, W. Sun et al., “Methyl matters: an autonomic
rapid self-healing supramolecular poly(N-methacryloyl glyci-
namide) hydrogel,”Polymer, vol. 126, pp. 1–8, 2017.
[55] M. Marc, Volume A: Theory and User Information, MSC Soft-
ware Corporation, 2001.
[56] W. Huang, J. Kim, K. Kim et al., “A novel ultrasound tech-
nique for non-invasive assessment of cell differentiation,”
IEEE Sensors Journal, vol. 16, no. 1, pp. 61–68, 2016.
[57] K. Kim, S. Zhang, and X. Jiang, “Surface acoustic load sensing
using a face-shear PIN-PMN-PT single-crystal resonator,”
IEEE Transactions on Ultrasonics, Ferroelectrics, and Fre-
quency Control, vol. 59, no. 11, pp. 2548–2554, 2012.
[58] X. Jiang, K. Kim, S. Zhang, J. Johnson, and G. Salazar, “High-
temperature piezoelectric sensing,”Sensors, vol. 14, no. 1,
pp. 144–169, 2014.
[59] S. Zhang, F. Li, X. Jiang, J. Kim, J. Luo, and X. Geng, “Advan-
tages and challenges of relaxor-PbTiO
3
ferroelectric crystals
for electroacoustic transducers - a review,”Progress in Mate-
rials Science, vol. 68, pp. 1–66, 2015.
[60] S. Zhang and F. Yu, “Piezoelectric materials for high tempera-
ture sensors,”Journal of the American Ceramic Society, vol. 94,
no. 10, pp. 3153–3170, 2011.
[61] S. Zhang, Y. Fei, E. Frantz, D. W. Snyder, B. H. Chai, and T. R.
Shrout, “High-temperature piezoelectric single crystal
ReCa4O(BO3)3 for sensor applications,”IEEE Transactions
on Ultrasonics, Ferroelectrics, and Frequency Control, vol. 55,
no. 12, pp. 2703–2708, 2008.
[62] S. Zhang, R. E. Eitel, C. A. Randall, T. R. Shrout, and E. F.
Alberta, “Manganese-modified BiScO3–PbTiO3 piezoelectric
ceramic for high-temperature shear mode sensor,”Applied
Physics Letters, vol. 86, no. 26, article 262904, 2005.
[63] K. Kim, S. Zhang, G. Salazar, and X. Jiang, “Design, fabrication
and characterization of high temperature piezoelectric vibra-
tion sensor using YCOB crystals,”Sensors and Actuators A:
Physical, vol. 178, pp. 40–48, 2012.
[64] K. Kim, S. Zhang, W. Huang, F. Yu, and X. Jiang, “YCa4O
(BO3) 3 (YCOB) high temperature vibration sensor,”Journal
of Applied Physics, vol. 109, no. 12, p. 126103, 2011.
[65] M. F. Barsky, D. Lindner, and R. Claus, “Robot gripper control
system using PVDF piezoelectric sensors,”IEEE Transactions
on Ultrasonics, Ferroelectrics, and Frequency Control, vol. 36,
no. 1, pp. 129–134, 1989.
[66] Y. Shen, N. Xi, W. J. Li, and J. Tan, “A high sensitivity force
sensor for microassembly: design and experiments,”in
7Journal of Sensors
Proceedings 2003 IEEE/ASME International Conference on
Advanced Intelligent Mechatronics (AIM 2003), pp. 703–708,
Kobe, Japan, 2003.
[67] C. K. Fung, I. Elhajj, W. J. Li, and N. Xi, “A 2-D PVDF force
sensing system for micro-manipulation and micro-assembly,”
in 2002 IEEE International Conference on Robotics and Auto-
mation, pp. 1489–1494, Washington, DC, USA, 2002.
[68] J.-i. Yuji and C. Sonoda, “A PVDF tactile sensor for static con-
tact force and contact temperature,”in SENSORS, 2006 IEEE,
pp. 738–741, Daegu, Korea (South), 2006.
[69] A. Koschan, J. Dargahi, M. Kahrizi, N. P. Rao, and
S. Sokhanvar, “Design and microfabrication of a hybrid
piezoelectric-capacitive tactile sensor,”Sensor Review, vol. 26,
no. 3, pp. 186–192, 2006.
8 Journal of Sensors
Available via license: CC BY 4.0
Content may be subject to copyright.
