Biomedical Engineering Reference
In-Depth Information
the applied force on a sensing element,
ψ
1
,
ψ
2
are constants proportional to the electrode
area of the sensing elements, and
d
31
,
d
32
,
d
33
are piezoelectric coefficients in the drawn,
transverse, and thickness directions [14]. Therefore, the output voltage values are given by:
=
P/C
ψ
1
d
31
+
ψ
2
d
32
+
d
33
V
where
C
is the capacitance of the PVDF film. Due to the constrained configuration
of the PVDF (i.e., glued to both silicon and Plexiglas), the exact contribution of each
piezoelectric coefficient in the output voltage is difficult to determine (see Chapter 3 for
detailed information). Thus, the magnitude of the shear force from the output charge,
due to each of the sensing elements, is difficult to determine [14]. However, to compare
the theoretical shear stress values with the experimental values for a given set of tests
(i.e., same applied load), the ratios of the theoretical shear force and output voltage
from each sensing element were plotted against the distance along the sensor. The result
shows that the difference in the theoretical values compared to the experimental values
for each sensing elements was less than 20%. By using the least squares method, an
estimation of the above constant (i.e.,
ψ
1
d
31
+
ψ
2
d
32
+
d
33
) was obtained. The error in
the experiment was also estimated using this method. By multiplying this constant by the
output voltages from each sensing element, the experimental shear force was obtained.
These values were then plotted against the theoretical values for comparison.
The comparison of the theoretical and typical experimental values for each sensing
element is shown in Figure 4.12a - d. It can be seen that the shear force decreases as the
distance from the center of the applied force increases. The stress reduces exponentially
from the sensing element, as shown in Equation 4.1 (see theoretical analysis). The differ-
ence between the experimental and theoretical results was determined to be less than 20%.
Equation 4.3 shows that the slope varies as a function of the location of the applied
force (i.e., parameters 'a' and 'b'). For example, the magnitude of the slope when a force
of 1 N was applied on tooth numbers 1 and 2 (and also for tooth numbers 3 and 4) was
calculated, and the values for the slope were 1.37
×
10
-11
and 1.19
×
10
-13
, respectively.
The magnitude of the slope changes by varying the position of the applied force on the
sensor. The slope at the location of the applied force is used to determine the location of
the load on the sensor.
As previously mentioned, when a force is applied to the tactile sensor unit, bending
stress occurs in the silicon. This stress might have the effect of pulling the PVDF film
in the transverse direction (perpendicular to the applied force), resulting in an additional
output charge, due to the shear stress. However, since the difference between the modulus
of elasticity of the silicon and elastic foundation PVDF/Plexiglas is negligible (i.e., only
two orders of magnitude) and the magnitude of the applied force is relatively small
(2 N max), the bending stress would be small in comparison to the magnitude of the
shear stress. Hence, this effect is ignored in the results.
In the design of the sensor, care has been taken to avoid the pyroelectric effect. Since the
PVDF film was sandwiched between the silicon and Plexiglas, there is sufficient thermal
insulation to reduce this effect and, to reduce it even further during experimental testing,
a thin layer of Mylar film was placed between the probe and silicon. This precaution had
the additional advantage of avoiding any damage to the silicon by a possible impact from
the probe.
