Biomedical Engineering Reference
In-Depth Information
between two plates that also act as electrodes. These plates transmit the normal force to
the surface of the PVDF such that they transform the applied point load to a distributed
load over the piezoelectric surface. Traditionally, to avoid the complexity of considering
friction forces, the sensor package is treated as being a black box in which the relationship
between the input and output is considered. Therefore, for a given set of piezoelectric
elements and surfaces, the output of the sensor is empirically calibrated in terms of the
input load.
However, in this case, the output charge of the PVDF is a combination of the thickness
mode charge and another component, caused by the friction force. Therefore, the response
of such piezoelectric sensor is highly sensitive to the surface condition and varies with
any changes in the manufacturing process that may affect the surface.
As can be seen in this section, the results of this study are helpful in modification
and optimization of commercial piezoelectric force sensors. Although this research is
performed on piezoelectric PVDF film, the results could equally be applied to any other
piezoelectric force sensor in which the friction force cannot be neglected. This study
also has another fundamental application in the measurement of
d
33
, namely the piezo-
electric coefficient in the thickness mode. This coefficient is difficult to measure because
it is extremely difficult to apply a normal force to the film, yet, at the same time, not
constrain the lateral movement of the film, which would otherwise induce other stresses
that can cause faulty output readings. In order to avoid difficulties associated with the
direct measurement of
d
33
, most researchers use two indirect ways of calculating this
value [14, 16, 18, 22]. In one method,
d
33
is determined by using the converse piezo-
electric effect in which a known electric field is applied and the change in thickness of
a small sample is measured. The problem with this approach is in mounting the sample
in such a way that its lateral motion is not restricted, which, otherwise, could affect the
accuracy of the measurement [18]. In the second method,
d
33
is measured indirectly by
measuring the hydrostatic piezoelectric coefficient
d
3
h
. Using this value, and knowing
the values of
d
31
and
d
32
, the value of
d
33
can be calculated. For a hydrostatic pressure
P
, the amount of charge is related to all three coefficients (Kepler and Anderson [18]):
Q
/
A
=
−
−
(
d
31
+
d
32
+
d
33
)=
d
3
h
.
This section introduces a new approach to this problem. The effect of friction on the
PVDF output can be characterized by finding the trend of variations for some known fric-
tion coefficients; it is then possible to calculate
d
33
in those cases where friction is almost
0. Therefore, a finite element (FE) contact analysis was performed in which piezoelectric
PVDF was considered as being an orthotropic material in which the coefficient of fric-
tion was varied between 0 and 1 and the output recorded. The results were validated by
performing an experiment on a similar geometry using pre-characterized surfaces. It was
found that the inverse procedure can also be used in determining the friction coefficient
of surfaces. This method confers many advantages over traditional friction measurement
methods, such as
in situ
friction measurement, being non-invasive, low weight, and cost.
When a PVDF film is compressed between two rigid flat surfaces, assuming no friction
between the surfaces and the PVDF films, the film is free to expand laterally, that is, in
the 1 and 2 directions. The output charge can thus be calculated from Equation 3.19 as:
Q
=
d
33
F
n
(3.27)
where
F
n
is the normal applied load. This assumption, however, is difficult to use in
practice. Frictional force always exists and causes unwanted components in the output
charge. Therefore, in the presence of such a friction-inducing component, the total output
(
d
31
+
d
32
+
d
33
)
P
,inwhich
