Force sensor utilizing stiffness change of shape-memory polymer based on temperature
Takashima et al. Robomech J
Force sensor utilizing stiffness change of shape-memory polymer based on temperature
Kazuto Takashima 0
Hiroki Kamizono 0
Makoto Takenaka 0 2
Toshiharu Mukai 1
0 Graduate School of Life Science and Systems Engineering, Kyushu Institute of Technology , 2-4 Hibikino, Wakamatsu-ku, Kitakyushu 808-0196 , Japan
1 Department of Information Engineering, Faculty of Science and Technology, Meijo University , 1-501 Shiogamaguchi, Tenpaku-ku, Nagoya 468-8502 , Japan
2 Kagawa Prefectural Industrial Technology Research Center , 587-1 Gotocho, Takamatsu 716-8031 , Japan
In this study, we propose a force sensor using a shape-memory polymer (SMP) whose stiffness varies according to the temperature. An SMP can be deformed above its glass transition temperature (Tg) by applying a small load. A deformed SMP maintains its shape when cooled below Tg and returns to its predefined shape when subsequently heated above Tg. The reversible change in the elastic modulus between the glassy and rubbery states of an SMP can be on the order of several hundred-fold. The relationship between the applied force and the deformation of the SMP changes depending on the temperature. Our sensor consists of strain gauges bonded to an SMP bending beam and senses the applied force by measuring the strain. Therefore, the force measuring range and the sensitivity can be changed according to the temperature. In this study, we evaluate a prototype of the sensor using the SMP sheet with embedded electrical heating wire. Moreover, we improve the sensor by combining the SMP and a stainless steel plate. The enhanced versatility of SMP force sensors is demonstrated through a series of experiments conducted using the prototype.
Shape-memory polymer; Force sensor; Glass transition temperature; Cantilever; Strain gauge
Background
In today’s rapidly aging societies, robotic technology has
been applied to various fields including industrial as well
as nursing and welfare. For example, several power-assist
suits and power assist apparatus have been proposed as
wearable robots for caregivers and rehabilitation systems
[
1
]. In these applications, it is necessary to measure a
wide range of forces to grasp and lift various objects in
the various operating environment accurately [
1
].
Previously, for example, a wide-range and sensitive force
sensor using a quartz crystal resonator was proposed [
2
].
Unlike this research, the characteristic of our proposed
sensor is the utilization of the stiffness change of the
material based on the temperature. To our knowledge,
the stiffness change of the material has not yet been
utilized for wide-range and sensitive force sensors. In the
present study, we exploit the inherent advantageous
properties of shape-memory polymers (SMPs) [
3–18
] for
use in the force sensor.
SMPs are often described as two-phase structures,
comprising a lower-temperature “glassy” hard phase and
a higher-temperature “rubbery” soft phase. The hard and
soft phases represent two elastic moduli: one in the
lowertemperature, higher-stiffness ‘‘glassy’’ plateau and the
other in the higher-temperature, lower-stiffness ‘‘rubbery’’
plateau. For example, in order to explain the
thermomechanical behavior of SMPs, Liu et al. [
3
] developed a
thermomechanical constitutive model of epoxy SMP using
phase transition (frozen phase and active phase) theory.
The reversible change in the elastic modulus between
the glassy and rubbery states of SMPs can be as high as
several hundred-fold. SMPs can be deformed above their
glass transition temperature (Tg) by applying a small load.
Moreover, SMPs maintain their shape after they have
been cooled below Tg and are considered rigid in this
state. When subsequently heated above Tg, they return to
their initial shape and hence exhibit shape recovery. With
these features in mind, SMPs are increasingly being
investigated for use in smart materials such as those found in
textiles, ergonomic utensils, spacecraft solar sails,
morphing skins, intelligent medical devices, and implants for
minimally invasive surgery [
3–18
]. We previously
proposed a position-keeping module [4], soft actuators [
5–8
],
and deployable structures [9] that use SMPs.
In this study, utilizing the abovementioned technology
and knowledge of SMP uses, we developed a new force
sensor whose force measuring range and sensitivity can
change according to the temperature. A prototype of this
sensor was made by attaching a strain gauge onto an SMP
sheet with embedded electrical heating wire, and we
evaluated its basic characteristics.
Concept of the force sensor
Most force sensors transform the mechanical deformation
of the detecting area according due to the applied force
into a change in resistance, capacitance, or reflectance
that can be measured using electric signals. For example,
some force sensors consist of strain gauges bonded to a
bending beam. Assuming an elastic cantilever, the strain
on the strain gauge (ε) can be expressed as follows [
19
]:
y
ε =
R
1 = Wx
R EI
W =
bE h2 ε
6x
where y is the distance between the neutral axis and the
strain gauge and R is the radius of curvature. R in turn is
expressed as follows:
where W is the applied load, x is the distance between the
strain gauge and the position where the force is applied,
and E and I are the elastic modulus and area moment of
inertia, respectively, of the beam. When the beam has
uniform stiffness and the cross section of the beam is a
rectangle, from Eqs. (1) and (2), W can be calculated using
the following equation:
where b and h are the width and thickness of the beam,
respectively. Using Eq. (3), we can calculate the applied
force (W) from the strain measured (ε) by a strain gauge
attached to a beam such as a stainless steel plate.
However, once the strain gauge is glued onto the plate, it is
difficult to change the measurement range and
sensitivity. Namely, the deformation range depends on the sensor
material, and it is difficult to change these specifications
after the sensor is produced.
In order to solve these problems, we developed a force
sensor using an SMP sheet as the beam. As described in
(1)
(2)
(3)
"Background” section, E can be changed according to the
temperature. Therefore, the relationship between ε and
W [namely Eq. (3)] can also be changed (Fig. 1). In Fig. 1,
depending on the type of strain gauge and beam, the
measurable strain range is determined (the range shown
on the horizontal axis of Fig. 1). Since the stiffness of the
SMP can be changed according to the temperature, the
measurable force range (the range shown on the vertical
axis of Fig. 1) determined by the above strain range can
also be changed. Moreover, even if the strain resolution
is the same, the force resolution can be changed similarly.
In this way, the measurement range and sensitivity of the
force sensor can be changed according to the
temperature. Note that this concept can be applied to other force
sensors with different structures and measuring elements
(it is not limited to strain gauges bonded to a bending
beam).
Compared with the conventional force sensor, the
new force sensor with SMP properties has the following
advantages:
1. Since the measurement range and sensitivity can be
changed, it is not necessary to replace the force
sensor to match the measurement target.
2. Softening of the surface in the rubbery state could
reduce the impact forces when the sensor moves and
contacts an unexpected object.
First prototype
Prototype
The prototype SMP force sensor (thickness: 1.2 mm)
is shown in Fig. 2. Note that dimensions were not
optimized, but can be scaled depending on the application.
Fig. 1 Relationship between applied force and strain on cantilever
fixed SMP sheet. As the elastic modulus of the SMP can be changed
according to the temperature, the relationship between the strain
and the applied force can also be changed
In the present study, we chose a polyurethane SMP (SMP
Technologies Inc., MP4510, Tg = 45 °C) and prepared
an SMP sheet with an embedded electrical heating wire
in a manner similar to that described in our previous
study [
7
]. The fundamental characteristics of this
material taken from the product catalogue are summarized
in Table 1. The coefficient of linear thermal expansion
of the polyurethane SMP is 11.6 × 10−5 K−1 [
10
] and
larger than that of steel. The two liquid components were
mixed, poured onto a plate, and cured. Then, the thick
and non-uniform SMP sheet was pressed and heated
(held at 190–200 °C for 10 min and cooled at ambient
temperature for at least 30 min), and the SMP sheet
rememorized a thin uniform shape without air bubbles. In
order to heat the SMP sheet, we placed a heating wire
made of Nichrome (outer diameter: 0.26 mm, electrical
resistivity: 108 × 10−6 Ω cm, Young’s modulus: 214 GPa
[
20
], coefficient of thermal expansion: 17.3 × 10−6 K−1
[
20
]) between two pressed SMP sheets, and the sheets
were cohered to each other using a heat press (150 °C,
20 min). The heating wire is shaped like a square wave
so as not to affect the mechanical properties of the SMP
sheet. The total electrical resistivity is 5.7 Ω.
In order to measure the surface strain of the SMP sheet,
we used two strain gauges (KFG-5-120-C1-16L3M2R,
Kyowa Electronic Instruments Co. Ltd.) and attached one
on each side of the SMP sheet with an embedded
electrical heating wire using a cyanoacrylate adhesive (CC-36,
Kyowa Electronic Instruments Co. Ltd., operating
temperature range: −30 to 100 °C). With the half-bridge
system, the strain gauges were connected to the bridge, one
each to adjacent sides, with a fixed resistor inserted on
the other sides. The half-bridge system was used to
eliminate strain components other than the target strain to
compensate for the thermal expansion of the SMP sheet
[
21
].
Experiments
The experimental apparatus used to evaluate the
proposed sensor is shown in Fig. 3. The applied force was
measured when the SMP sheet was deformed in the
bending direction. The SMP sheet was bent at
temperatures above and below Tg. We evaluated the relationship
between the bending force and the strain when a bending
force was applied to the sensor by an indenter connected
to a load cell (LVS-500GA (T < Tg), LVS-50GA (T > Tg),
Kyowa Electronic Instruments Co. Ltd.). The load cell and
the prototype sensor were attached on a manual and
automatic stage (SGSP26-50, Sigma Koki Co., Ltd.),
respectively. The prototype sensor was automatically displaced
using the automatic stage at a constant speed (20 mm/s).
The distance between the fixed part and the indenter was
50 mm. The applied alternating voltage on the heating
wire was changed by a voltage controller. The experiments
below Tg were performed at room temperature. The
surface temperature was measured using a digital infrared
temperature sensor (FT-H10, Keyence Co.). Since it was
difficult to guarantee a uniform temperature of the SMP
sensor, we raised the temperature to approximately 80 °C
(significantly above the Tg of 45 °C) to ensure that all of
the SMP material in the sensor was well within the
rubbery state. The thermogram of the heated SMP sheet
captured by an infrared thermal camera (NEC Avio Infrared
Technologies Co., Ltd, F30W) is shown in Fig. 4.
Fig. 3 Experimental apparatus used to evaluate the force sensor. A
bending force was applied to the cantilever fixed prototype sensor
by an indenter connected to a load cell. The prototype sensor was
automatically displaced using an automatic stage
From the relationship between the applied force and
the strain obtained using the above experiment, we
calculated the gradient of the linear approximation formula.
We then compared the calculated force using the linear
approximation formula with the applied force measured
by the load cell. We measured these forces when the
sensor tip was displaced randomly.
Results and discussions
The relationship between the applied force and the
measured strain below and above Tg is shown in Fig. 5. In this
figure, the relationship between the applied force and
the strain calculated using Eq. (3) is also shown as
“theoretical” values. As shown in this figure, similarly to Fig. 2,
the change in load for the same strain change can
significantly vary according to the temperature. Namely, the
sensor can measure a minute force above Tg. For
example, as can be seen from the gradient of the linear
approximation formula, 100 με of strain change corresponds to
0.03 N (T < Tg) or 0.01 N (T > Tg) of applied force. For
conventional force sensors, it is necessary to replace the
sensor for different measurement ranges and
sensitivities. However, by changing the temperature, our sensor
can measure a large range of forces without replacing the
sensor. As shown in this figure, the difference between
the measured and theoretical values is large above Tg.
One reason is that the embedded heating wire is stiffer
than the SMP sheet in the rubbery state, and the change
of the elastic modulus between two states became small
similarly to as observed in our previous study [
7
].
Substituting the strain measured by the prototype sensor
into the linear approximation formula in Fig. 5, we
calculated the applied force and compared it with that obtained
by the load cell when a random force was applied.
Comparisons of the two forces below and above Tg are shown
in Figs. 6 and 7, respectively. As shown in these figures,
the two forces are almost identical in both experiments.
Namely, our sensor can accurately measure the applied
force. In Figs. 6 and 7, the absolute average differences
between the two forces are 0.0081 and 0.021 N,
respectively. The differences correspond to 1.7 and 21% of each
maximum measured force, respectively. As shown in
Fig. 7, the difference between the two forces gradually
increased above Tg. One reason is the creep deformation
of the SMP sheet. Another reason is that the SMP sheet
could not recover to the initial shape quickly because
of the viscosity of the SMP sheet, and the load could not
accurately measure the force. Creep and stress relaxation
are large in the SMP. Therefore, we will consider the effects
of the viscous term and modify Eq. (3) in future studies.
Second prototype
Problems with prototype sensor
As shown in “First prototype” section, the strain measured
by the prototype sensor is smaller than the theoretical values
above Tg. One reason other than the stiffness of the
embedded heating wire described in “First prototype” section is
that the difference in stiffness between the strain gauge and
the SMP in the rubbery state is too large to transmit the
deformation from the SMP to the strain gauge. Moreover,
the adhesive would affect the mechanical properties of the
attached surface of the SMP sheet. On the other hand, the
changes in measurement range and sensitivity depend on
the Young’s modulus of the SMP (a change of 100- to
1000fold) and are not adjustable. However, the change may be
too large for some application areas. Therefore, in this
section, we improved the proposed sensor by bonding the SMP
and steel sheet and attaching the strain gauge onto the steel.
Theory
We assumed that the embedded wire is negligible. When
the composite beam using SMP and steel sheets (Fig. 8) is
bent, R is expressed as follows [
19
]:
1 =
R
Wx
EMI M′ + ETI T′
where EM and ET a′re the e′lastic moduli of SMP and steel,
respectively, and IM and IT are the area moments of
inertia of the SMP and steel abou′t the ne′utral axis of the
composite beam, respectively. IM and IT are expressed as
follows:
where hM and hT are the thicknesses of the SMP and steel
plates, respectively. hN is the distance between the
neutral axis and the SMP surface and expressed as follows:
hN =
EMh2M + ET(2hMhT + h2 )
T
2(EMhM + EThT)
(hM + hT − hN)x
From Eqs. (1) and (4), using the strain on the surface of
the steel plate (ε), W is expressed as follows:
W = (EMI M′ + ETIT)ε (8)
′
ε below and above Tg is expressed as εg and εr,
respectively. We calculated the relationship between hT/hM and
εr/εg substituting the dimension of the prototype (see
the next subsection for more details) and material
properties (Table 1) into Eq. (8) (Fig. 9). We assumed that
ET = 193 GPa. As shown in this figure, by changing the
thickness of the steel plate, the change in strain based
on temperature can be modified. Therefore, the change
in the measurement range based on temperature can be
modified. On the other hand, when the strain gauge is
attached on the SMP side, using the strain on the surface
of the SMP sheet ( ε′), W is expressed as follows:
W = −
(EMI M′ + ETI T′)ε′
hNx
.
(9)
We also calculated the relationship between hT/hM
and εr′/εg′ (dotted curve in Fig. 9). Although the change
in strain based on temperature can also be modified by
changing the thickness of the steel plate, the large
difference in stiffness between the strain gauge and the SMP
would affect the measurement accuracy. Therefore, in
this study, we attached the strain gauge on the steel plate.
In future studies, we will consider another kind of design
method to improve the force sensor, in which two
stainless plates are bonded to the two sides of the SMP sheet
and the half-bridge system with two strain gauges are
used. Moreover, the evaluation of the effect of different
thickness SMP sheet is beyond the scope of this paper.
Prototype and experiments
The prototype of the SMP force sensor with a steel plate
is shown in Fig. 10. The SMP sheet with the embedded
heating wire was prepared similarly to that described
in “First prototype” section. The total electrical
resistivity is 5.3 Ω. We bonded the SMP sheet (thickness (hM):
1.2 mm) and steel plate (SUS304H, thickness (hT): 0.05,
0.1, 0.2, 0.3, 0.5 mm) using double-sided tape. As the
strains on the two surfaces are different, we cannot use
the half-bridge system with two strain gauges. Therefore,
we attached one strain gauge (KFG-5-120-C1-16L3M2R,
Kyowa Electronic Instruments Co. Ltd.) onto the steel
plate and measured the strain on the surface of the
steel plate. We evaluated this prototype similarly to that
described in the previous section.
Results and discussions
Some results of the relationship between the measured
strain and the applied force is shown in Fig. 11. In this
figure, “theoretical” values calculated using Eq. (8) and the
linear approximation formula are also shown. As shown
in this figure, the measured force range can be changed
according to the thickness of the steel plate. On the other
hand, the proposed sensor can measure a minute force
above Tg, and the measured force range below Tg is larger
than that above Tg, similarly to Figs. 1 and 5. Moreover,
we could also construct a force sensor using both SMP
and steel plates whose measurement can change
according to the temperature without the replacing the sensor.
In Fig. 11a and b, the changes in gradients became larger
than that shown in Fig. 5 because the difference in
stiffness between the strain gauge and the steel plate is small,
and the strain gauge became easy to deform.
Furthermore, the difference between the experimental and
theoretical values became small above Tg (Fig. 11).
The relationship between hT and εr/εg is shown in
Fig. 12. In this figure, the theoretical values calculated by
Eq. (8) are also shown. The measured values are almost
the same as those calculated using Eq. (8). However,
when hT is small, the difference is large. One reason is the
effect of the embedded wire being relatively large when
the steel plate is thin. Moreover, note that in practical
applications it is more necessary for this type of sensor
to maintain a constant temperature and eliminate the
thermal expansion of the SMP than that shown in the
previous section because there is only one strain gauge.
Furthermore, we should consider the difference of the
thermal expansions between the SMP and the embedded
Nichrome wire in future studies.
We compared the calculated force using the
linear approximation formula in Fig. 11 with the applied
force measured by the load cell. As an example, when
hT = 0.05 mm, the transitions of the force below and
above Tg are shown in Figs. 13 and 14, respectively. The
sensor tip was displaced randomly using a stage. As
shown in Figs. 13 and 14, similarly to Figs. 6 and 7, the
two measured forces are almost identical. In Figs. 13 and
14, the absolute average differences between the two
forces are 0.19 and 0.042 N, respectively. The differences
correspond to 5.2 and 14% of each maximum measured
force, respectively. Moreover, although we applied a
similar displacement below and above Tg, the measured force
range is significantly different.
Conclusion
We have developed a force sensor using an SMP sheet
with an embedded electrical heating wire. In this study,
we evaluated two types of prototype sensors. Through
experiments on the prototypes, which utilize the stiffness
change of the SMP based on the temperature, we showed
that with the proposed sensor the measurement range
and sensitivity can be changed without replacing the
actual sensor. The first prototype consists of strain gauges
bonded to the bending SMP beam. Moreover, by adding
a steel plate, we fabricated a second prototype. The
second proposed sensor can be improved and can alter the
change ratio of the strain according to the thickness of
the steel plate.
Authors’ contributions
KT conceived and led the study, and wrote this paper as corresponding
author. HK developed the sensor, carried out all experiments, and analyzed
data. MT and TM participated in the research design. All authors read and
approved the final manuscript.
Acknowledgements
Not applicable.
Competing interests
The authors declare that they have no competing interests.
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