Biomedical Engineering Reference
In-Depth Information
the fact that
d
31
and
d
32
>
0 while
d
33
<
0. The results of the simulation for
μ>
1
show that the variation in the output voltage is negligible. It is important to note that
maximum gain can be obtained at low friction for uniaxial PVDF film in the sandwiched
configuration. Figure 3.14 also reveals the dependency of maximum output voltage on
the friction coefficient, particularly for
μ<
0.1. This explains why accurate measurement
of
d
33
, using the direct method, is so difficult. On the other hand, this behavior could
be beneficial for the accurate measurement of low friction forces and coefficients.
Figure 3.14 illustrates the results for a state in which no friction exists (
μ
=0)and
conforms to classical theory. Since the metalized piezoelectric PVDF film can be modeled
as a capacitor, the relationship between the generated charge and the potential across its
electrodes can be written as:
Q=CV
in which
C
is the capacitance of the PVDF specimen.
Conversely, the capacitance of a PVDF film with area
A
and thickness
t
can be calculated
from the known relationship:
C=
ε
0
ε
r
A/t
,inwhich
ε
0
= 8.854
×
10
-12
Fm
-1
is the
permittivity of free space and
ε
r
, the relative permittivity of PVDF, is 12. Substitution of
the above relations into Equation 3.27 reads:
d
33
t
ε
0
ε
r
P
V
=
(3.28)
in which
P=F
n
/
A
is the applied pressure on the PVDF film. The numerical value of
voltage in Equation 2.28 for the data given for the present case is 1.864, which agrees
with the result in Figure 3.14 obtained for
μ
=0.
In order to elaborate upon the results obtained in our previous analysis, a second
simulation was performed in which the top surface of the PVDF film was covered with
10 electrodes of equal width that were evenly positioned on the surface. The bottom
surface of the PVDF film was considered as the common ground for all the electrodes.
The results of this model under a constant load are depicted in Figure 3.15, which shows
2.0
1.8
m
= 0
m
= 0.05
m = 0.1
m
1.6
= 0.3
m
= 1
1.4
1.2
1.0
0.8
0.6
0
0.2
0.4
PVDF length
0.6
0.8
1.0
Figure 3.15
The relationship between the output voltage of each segment and different friction
coefficients
