Biomedical Engineering Reference
In-Depth Information
TABLE 2-4
Piezoelectric Characteristics of PVDF and PZT
Material Property
PVDF
PZT
Density
ρ
(g/cm
3
)
1.78
7.6
Relative permittivity
ε
12
1700
Young's modulus
E
(N/m
2
)
×
10
9
83
×
10
9
d
31
=
20
×
10
−
12
d
31
=
180
×
10
−
12
Piezoelectric constant (C/N)
10
−
12
10
−
12
d
33
=
30
×
d
33
=
360
×
Coupling constant (CV/Nm)
0.11
k
31
=
0
.
35
k
33
=
0
.
69
Piezoelectric or rotary generators that convert some of the heel-strike energy into
electrical power for storage and later use are the commonest energy scavenging devices.
Consider a device that can capture the energy over a distance
x
=
30 mm during heel-strike
of a typical 70 kg person. The work per stride per leg is
W
=
mgx
=
70
×
9
.
8
×
30
×
10
−
3
=
6J
At two strides per second, the total power available is 41 W.
Rotary generators need to spin rapidly to achieve good efficiencies, so pure mechan-
ical coupling involves high gear ratios and a fairly complex mechanism that is prone to
failure. Alternatives include miniature hydraulic pump/turbine combinations or pneumatic
systems that store power in compressed air.
Piezoelectric materials produce an electrical charge when mechanically stressed. It is
interesting to note that human skin and bone both exhibit this property, albeit with very
low coupling efficiencies. Common alternatives are polyvinylidene fluoride (PVDF) and
lead zirconate titanate (PZT), whose characteristics are shown in Table 2-4.
The coupling constant is the efficiency with which the material converts mechanical
energy to electrical, with the subscripts indicating the direction of the interaction in the
three axes. For example, d
31
is the strain caused to axis-1 by an electrical charge gradient
along axis-3.
It is not feasible to extract power by compressing the piezoelectric material as the
Young's modulus is too high. However, it is possible to bend the material to take advantage
of the 31 mode. In the case of a PZT cantilever beam, the maximum allowed deflection,
x
(m), at the tip is determined by the yield stress,
S
20
.
=
50 MPa (Fett, Munz et al., 1999)
using the following relationship
2
l
2
3
Et
S
x
=
(2.2)
where
l
(m) is the length of the beam,
t
(m) is the thickness of the material, and
E
(N/m
2
)
is the Young's modulus for PZT.
Consider mounting a 150 mm cantilever beam made of a 0.5 mm thick slab of PZT
within the sole of a shoe. The maximum deflection before the material fractures will be
2
l
2
S
3
Et
x
=
2
×
250
×
10
−
3
2
×
50
×
10
6
=
10
9
10
−
3
3
×
83
×
×
0
.
5
×
=
50 mm
