A NEW SENSOR FOR STATIC AND DYNAMIC FORCE MEASUREMENT
P. Castellini*, R. Montanini°, G.M. Revel*
*Dipartimento di Meccanica, Università degli Studi di Ancona, Via Brecce Bianche 1, I-60131, Ancona, ITALY
°Dipartimento di Ingegneria dei Materiali, Università degli Studi di Messina, Salita Sperone 31, I-98166, Messina, ITALY
ABSTRACT
In this work an innovative sensor for the measurement of
forces is presented. The sensor is a thin film (1 mm
thickness) based on a “sandwich” structure composed of two
sensing elements glued together: one layer is a capacitive
film and the other is a piezoelectric film. Both the layers are
sensitive to compression loads, but they are suitable for
working in different frequency ranges. In fact, while the
capacitive element is capable of measuring from DC up to
about 400 Hz, on the contrary the piezoelectric film works in
the high frequency range. The output of both the sensors are
acquired and then filtered and processed in such a way as to
achieve a unique signal.
This sensor was developed in order to synthesise in a small
and cheap device the capability to measure forces in a wide
range of frequencies. The sensor is very small and can be
used in a variety of problems and applications, also in the
field of modal analysis.
In particular, the very reduced thickness allows to insert such
sensor even in composite materials in order to characterise
loads and excitations, on the surface or between different
components of a more complex system or within the
structure in order to obtain a smart structure.
The paper describes the structure of the sensor and of the
adopted signal processing strategies. The metrological
characterisation procedure is discussed (in particular for
normal forces) and an application is shown.
1
INTRODUCTION
Compact transducers, which allow force measurement in
both static and dynamic ranges, seem to be very attractive
for several engineering applications.
Actually there is a large interest in very small transducers
(film sensors), which have poor intrusivity and low cost. Such
sensors would permit to realise sensible matrix with high
spatial resolution and could extend the applications of
traditional load transducers to study the interaction of
different components in several fields like automotive
(tyre/street contact), mechanical (fluid/structure interface),
robotics (artificial hand), medical (barefoot pressure
distribution, contact pressure in orthopaedic prosthesis).
Several force transducers, which satisfy at least one of the
characteristics mentioned above, are available on the
market. Piezo-resistive sensors use the propriety manifested
by some conductive elastomeric materials (mainly polymers
drugged with carbon) to modify their electrical resistivity
when compressed. Such sensors can measure in dynamic
range but have poor metrological performance due to
hysteresis and creep problems
Magneto-resistive sensors have an high dynamic range,
good linearity and low hysteresis but are sensitive to
electrical noise and magnetic fields.
FSR (Force Sensing Resistor) sensors are particular film
transducers where the electrical resistance decreases when
the applied load increases. This limitation is connected to the
fact that the area and distribution of the load influence their
sensitivity and thus they can be used mostly for qualitative
measurements.
Piezoelectric films (PVDF, [1,2,3,4,5]) are realised in very
thin sheets (9÷1000 µm), have a broad bandwidth, could be
cut in several shapes but cannot measure static forces.
Capacitive sensors [6,7,8,9] have a non-linear behaviour,
could be assembled in a matrix to measure static force
distributions, but have limited dynamic response.
All these transducers can measure forces only in the static
or in the dynamic range. Only electric strain gauges load
cells enable both static and dynamic (up to 1000 Hz) force
measurements (e.g. [10]), but their weight, dimension and
cost, even if drastically reduced in the recent years, are still
considerable.
In order to overcome to such lack, a novel compact
transducer, able to measure forces either static that dynamic
and having an high spatial resolution, is proposed in this
paper.
2
THE PIEZO-CAPACITIVE TRANSDUCER
The desirable metrological characteristics of the novel
transducer are:
•
•
•
•
•
•
•
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2
good spatial resolution (< 1 cm );
measurement range of a single sensor 0÷20 N;
good sensitivity (about 10 mVN-1);
bandwidth from 0 to 8000 Hz at least;
small thickness (< 1 mm);
low hysteresis;
low cost.
Nowadays, all these characteristics cannot be found in a
single force transducer, but complementary properties can
be observed in different sensor typologies. This fact
suggests that it may be possible to realise a new transducer
by “assembling” two sensors based on a different measuring
principle, in order to obtain a transducer that will benefit from
the advantages of each sub-component (Figure 1).
As small thickness and good spatial resolution are desired,
only film sensors could be considered for the realisation of
the new force transducer. Moreover, to obtain a film sensor
able to measure from DC to about 10 kHz, one layer should
be employed for the low frequencies while a second layer for
the higher frequencies.
For these reasons, as sub-component layers for the new
transducer, a capacitive sensor and a piezoelectric film have
been chosen.
2.1 The capacitive layer
The capacitive layer, realised by Novel, consists of two
surfaces, on which a thin metal substrate is deposited,
separated by a polymeric dielectric. When a force is applied
on the sensor surface, the distance between the armature
changes and thus the electric capacity changes too. The
dielectric stiffness is a critical parameter: high value of it
results in a broad frequency response but sensitivity
decreases. A compromise has therefore to be reached. The
input-output characteristic is non-linear, with higher
sensitivity in the low part of the scale. Capacitive sensors
can also be arranged in a matrix, thus permitting to measure
a pressure distribution along a surface with high spatial
resolution.
The capacitive layer is used to measure forces at low
frequencies, from DC to about 400 Hz.
2.2 The PVDF layer
To allow measurement of forces at high frequencies (above
about 400 Hz) a piezoelectric film (PVDF) has been added to
the capacitive layer. A piezoelectric polymer is a plastic
material with groups of molecules linked as orderly
crystallites. The crystallites form in an amorphous matrix of
chemically similar, but differently structured material. The
relative population of crystallites strongly affects the
piezoelectric behaviour of the material. Poly-vinyldene
fluoride is the most popular piezoelectric polymer material for
shock sensors. In order for PVDF to be used as a pressure
gauge, it is important to reproducibly manufacture poled
piezoelectric transducer elements with defined homogeneity
and stability.
PVDF elements have several remarkable features: they are
thin (less than 25µm), unobtrusive, self-powered, adaptable
to complex contours, and available in a variety of
configurations.
the two sensing elements and then layers have been glued
together using an epossidic adhesive.
Both the measuring layers are sensitive to compression
loads, but they are suitable for working in different frequency
ranges. The capability to assess both static and dynamic
forces is a very useful feature. In fact the DC components
allows the monitoring of pre-loading conditions. On the other
hand, the dynamic capability allows the evaluation of
impulsive or high frequency loads.
The sensor is very small, thus an high spatial resolution can
be achieved, and it can be used in a variety of problems and
applications, also in the field of modal analysis. In particular,
the very reduced thickness allows to insert such sensor even
in composite materials or between different components of a
more complex system, thus smart structures could be
realised.
It is worth noting that the two layers are packed using an iron
layer on the top and one on the base. These, although
modify the dynamic behaviour, have a very important
function, which is to distribute whatever applied load in a
pressure distribution uniform on the surface. Otherwise, the
sensor output would be proportional also to the application
area, and not only to the force.
Insulating layer
Capacitive
armature
capacitive element
signal output
Dielectric
PVDF
PVDF element
signal output
Figure 1 – Layout of the new force transducer
The dynamic behaviour of the piezo-capacitive transducer is
influenced by the mass, stiffness and damping properties of
each layer.
2.4 Electronics and signal conditioning
Each sensing layer of the new transducer needs a suitable
electronic circuit in order to power the sensor and to process
the two signals coming out from it.
For what concern the capacitive component of the sensor, in
order to obtain an output signal proportional to the input
force applied on its surface, an amplitude modulation
technique is adopted. A sinusoidal carrier signal of frequency
115 kHz and amplitude 5 Vpp is applied at one armature of
the capacitive element and is modulated in amplitude by the
measuring signal. The signal is then passed through a passband filter, amplified and finally demodulated. See Figure 2.
2.3 Layers interface
The two sensing elements, capacitive and piezoelectric,
were assembled to form a sandwich, having a thickness less
than 1 mm. An insulating film has been interposed between
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the resolution of the sensor, which is mainly depending by
the AD conversion.
The main metrological characteristics of the piezo-capacitive
transducer determined with the static calibration are reported
in Table I.
Pressure Device
Signal Generator
FREQUENZA
Figure 2 – Capacitive element signal conditioning: 1)
excitation signal; 2) output signal; 3) filtered output signal; 4)
filtered and demodulated output signal.
PC Transducer
The piezoelectric layer is conditioned with a charge amplifier;
connecting cables are glued to the piezo-film using a highly
conductive adhesive.
In
In
layer 1 layer 2
STATIC CALIBRATION
Out
A
B
Figure 3 – Measurement set-up for the static
calibration of the piezo-capacitive transducer
Static calibration of the transducer has been performed
using the pressure device illustrated in Figure 3. It consists
of two steel plates, with a membrane interposed between
them. The upper plate has a hole along which air
compressed is let in. An analogic manometer is used to
measure the pressure level inside the chamber where the
transducer is inserted. When air is introduced in the
chamber, the membrane, which has a very low stiffness, is
deformed elastically and the sensor is uniformly
compressed.
Once known the area of the sensor under calibration, this
device allows to have a very accurate determination of the
input force, as the pressure distribution is highly uniform on
the transducer surface. Clearly, this calibration bench allows
to take into account only normal forces, while the effect of
shear force components has been not yet considered.
The transducer is excited with a 115 kHz carrier sinusoid
having an amplitude of 5 Vpp, produced by a signal generator
and the output signal from the sensor is then sent to the
signal conditioning electronics. Output values are finally read
with a digital voltmeter.
Data have been acquired with both increasing and
decreasing steps, in order to highlight hysteresis effects. An
example of results is shown in Figure 4. It can be observed
that, as expected, the transducer has a non-linear behaviour
due to the presence of a capacitive layer. Sensitivity is
therefore not constant and decreases with the pressure
(force). The maximum sensitivity reduction in the range 0÷60
N is about 20%. It can also be noted that the output signal
for increasing and decreasing pressures is not the same,
thus hysteresis is present. Hysteresis is mainly due to the
viscous-elastic behaviour of the dielectric material used: by
increasing its stiffness, hysteresis effects can be further
reduced but also static sensitivity is affected. A compromise
should therefore be achieved.
The static calibration must be done in the range of interest in
order to minimise the evaluated uncertainty. In addition, the
adequate choice of the calibration range allows to optimise
1000
900
Output voltage [mV]
3
Voltmeter
Signal Conditioning
800
700
600
500
400
0
10
20
30
40
50
60
70
Reference force [N]
Figure 4 – Static calibration of the piezo-capacitive
transducer.
Characteristic
Average sensitivity
Max. sensitivity reduction
Max. hysteresis error
Resolution
Zero offset
Value
see figure 8
21 %
1,2 % f.s.
1/256 f.s. (due to 8 bit
conversion)
435 mV
Table I – Static metrological characteristics of the
new piezo-capacitive transducer
The obtained curve is in practice dominated by the
characteristic of the capacitive layer: thus it can be used to
make linear the capacitive sensor output and make possible
the effect superposition.
The piezoelectric sensor cannot be statically characterised
due to the RC discharge. The proportionality coefficient must
be determined in the dynamic characterisation.
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DYNAMIC CALIBRATION
1
0
0.1 N
1N
10 N
20 N
-4
-6
-8
-1
-1
-2
-3
-4
-5
-6
0
5000
10000
15000
20000
Frequency [Hz]
Figure 6 – Dynamic response of the piezoelectric mounted in
the final sensor
5
SIGNAL CONDITIONING
Due to the non-linearity of the capacitive layer of the sensor,
a compensation algorithm has been implemented in the data
acquisition software. The static calibration curve is used to
calculate the output corresponding to a certain input.
The signals coming out from the capacitive and piezoelectric
layers are then filtered, with a low pass and an high pass
filter, respectively. These operations are performed by the
software, but they could also be realised with hardware
components (active filters) and integrated in the transducer
electronics.
The DAQ software provides the selection of the cut-off
frequency, sampling frequency and trigger levels.
The procedure of signal addition is basically shown in Figure
7.
The signal from the capacitor is linearised and then the high
frequency part is removed. In the same way the signal from
the piezoelectric is high pass filtered. In practice the part of
the spectrum in which each sensor has low sensitivity is
removed.
Problems can arise for the response of each sensor, for the
characteristics of the filters and for the optimisation of the
cut-off frequencies.
-10
-12
Capacitive
sensor
-18
-20
0
500
1000
1500
K
2000
Frequency [Hz]
Figure 5 – Dynamic response of the capacitive mounted in
the final sensor
Piezoelectric
sensor
Filtering
-16
Conversion
to EU
-14
Linearisation
-1
-1
FRF [mVN , 0dB = 10 mVN ]
-2
0.1 N
1N
10 N
20 N
0
-1
In order to perform the dynamic calibration of the sensors it
is necessary to define an accurate procedure, not affected
by problems related to added masses or resonance of
external structures and highly repetitive.
The accuracy can be easily obtained using a precise
reference sensor in the investigated dynamic range, as a
piezoelectric sensor usually applied for modal analysis. In
our case a PCB 280C01 load cell was applied.
More difficult is to guarantee that the reference and the
analysed sensors will be equally and correctly loaded in a
wide frequency range. As example, resonance frequency of
structures that are exciting the sensors can make difficult a
uniform characterisation of the entire bandwidth.
On the other hand, it is well known that the performance of
the load cell itself could be strongly dependent by the mass
of bodies on it.
For such reasons loading systems composed by a shaker
(any kind of it) do not satisfy our requirements and thus we
propose an impact test.
In order to improve the test quality an automatic hammer
was designed and applied. It is able to generate pulses with
a high repeatability both in terms of force modulus, direction
and point of application. The automatic hammer is
composed of an arm, moved by an electro-magnetic
actuator, equipped with a very rigid head (impact point) and
instrumented with the reference load cell.
The frequency response functions achieved at different force
levels are reported in Figures 5 and 6 for the capacitive and
the piezo-electric parts respectively. It is possible to note that
the capacitive response is flat from DC up to about 500 Hz
(low pass filter behaviour due to RC electric equivalent
circuit), while the piezo-electric has a useful range from 1015 Hz up to about 8-10 kHz. In these ranges the input force
level does not seem to be influent, in particular for the piezoelectric part.
FRF [mVN , 0dB=10 mVN ]
4
Piezocapacitive
sensor
K
Figure 7 – Signal conditioning performed by software.
In fact, depending on the cut-off frequency some
discrepancies could appear at frequency of passage
between one sensor to the other, where both sensors are
1023
working in parts of the band in which some attenuation is
present.
In addition the applied filters, even if are of high order,
present a residual transmissivity after the cut-off, and
attention must be paid in the superposition between the
falling part of the low-pass filter and the rising part of the
high-pass filter.
6
DISCUSSION
In Figure 8 is shown the typical dynamic behaviour of the
complete sensor is shown in terms of FRF between the
output voltage and the input force.
The response curve was evaluated on the range 0-20 kHz.
The curve shows a typical effect of a high damping system,
without an evident resonance.
20 N
10 N
1N
0.1 N
0
-1
-1
FRF (mVN , 0 dB = 10 mVN )
1
-1
-2
-3
-4
-5
-6
0
5000
10000
15000
20000
Frequency (Hz)
Figure 8 – Dynamic behaviour of the new piezo-capacitive transducer.
In order to evaluate the non-linearity effects, the test was
repeated with different level of force peak. As shown in
Figure 8, the variation of the behaviour of the complete
sensor is of about the 3% of the actual value when the force
peak is varying in a range from 0.1 to 20 N.
The system is represented by a series of springs, dampers
and masses highly not uniform.
In particular the capacitive layer has the lowest stiffness, and
therefore from the dynamic point of view it works as a lowpass filter of forces through the sensor, conditioning also the
behaviour of the piezoelectric film.
In addition also the impedance of the complete sensor is
basically dependent only on the capacitive.
The capacitive is the weak point of the sensor: it is the direct
responsible of the static performances, such as hysteresis,
non-linearity and sensitivity, and limits indirectly the dynamic
behaviour. Unfortunately it is not possible to increase the
dielectric stiffness without a dramatic loss of SNR and static
sensitivity, related to the thickness change of the layer under
the analysed load. Therefore, the choice of the capacitive
characteristics must be done in accordance with the desired
performances of the complete sensor.
On the other hand, the piezoelectric layer represents a
relatively stiff support for the capacitive one, demonstrating a
general good compatibility with other sensors, coupled with
it.
Finally, the small layer of iron added in order to pack
sensor and to distribute the applied load uniformly over
sensor surface determines an additional mass load on
sensitive elements. This must be taken into account for
design of the sensor.
7
the
the
the
the
A SIMPLE APPLICATION
In order to demonstrate the capabilities of the new sensor a
simple test was performed: some water is gently poured
from a bottle in a glass and the weight variation is measured
with the new film sensor positioned between the glass and
the table.
This test highlights the ability of the proposed device to
measure the applied load both in static and in dynamic
range. In addition the test should show the sensitivity of the
sensor, which is working in the range 0-20 N.
As a reference a high sensitivity piezoelectric load cell was
used; the static load is simply evaluated at initial and final
conditions.
The results (Figure 9) demonstrate the good agreement
between the two sensors in the dynamic range: as shown in
points B and C of Figure 9 both sensors are capable of
measuring the impulsive effect of the water drops falling into
the glass.
In addition the proposed sensor presents the possibility of
assessing the static component of the load with satisfactory
1024
accuracy (not possible with the traditional piezoelectric load
cell).
The load at initial time is due to the glass weight, while the
final load is due to the added quantity of water (about 100 g).
This feature is very useful in several applications, where also
the pre-load must be determined.
Some limits can be noted in terms of useful frequency
bandwidth: the force peaks with a short duration are
underestimated, as it is evident at point A of the graph.
As previously discussed, this is due to the low stiffness of
the capacitive layer, which limits the dynamic response of
the sensor.
Fortunately several different polymers are available on the
market for the assembling of capacitive sensor, and
therefore a better compromise could be found between DC
and AC performances, also depending on the specific
application.
450
400
A
350
New piezo-capacitive
film sensor
Load [g]
300
250
C
B
200
Traditional piezoelectric load cell
150
100
B'
C'
50
0
-50
0
0.02
0.04
0.06
Time [s]
0.08
0.1
0.12
Figure 9 – Measurement of weight force variations of a glass while small water quantities are poured.
8
CONCLUSIONS
[3]
In the present work a new double-layer film sensor has been
presented for the measurement of static and dynamic forces.
The sensor has many potential applications (also in the field
of modal analysis), in particular for its reduced dimension
and for its capability of measuring from DC up to 8 kHz with
a flat response. The sensor is composed by a layer of
capacitive film (capable of measuring from DC to about 400
Hz) coupled with a piezo-electric film (measuring in the high
frequency range). Its design can be optimised for the
application of interest, in particular changing the
characteristics of the capacitive layer (mainly thickness and
stiffness). The static and dynamic characterisations of the
sensor loaded by normal forces are described along the
paper, as well as a simple application. The effect of shear
forces on the sensors will be considered in future
developments.
[4]
[5]
[6]
[7]
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