Biomedical Engineering Reference
In-Depth Information
2
, where
a
is the acceleration of the
system, the previous equation can be rewritten as
P
d
5
1
Using the expression
a
5
Y
0
ω
m
a
2
ω
1
2ζ
t
(2.5)
2
where the last term is also known as the
Q
factor (
Q
5
z/Y
0
5
1/(2
ζ
))
leading to
m
a
2
ω
P
d
5
1
2
Q
(2.6)
Yeatman (2008) described four limiting parameters for energy gen-
eration: the proof mass
m
, the input displacement amplitude
Y
0
, the
proof mass displacement
z
, and the vibration frequency
. For exam-
ple, from
Eq. (2.5)
, high-frequency vibrations would produce a higher
power output, but high-frequency acceleration is commonly related to
small displacements and relatively low accelerations. In considering the
inherent relationship between acceleration
a
, frequency
ω
ω
, and dis-
2
placement
Y
as
a
5
ω
Y
, the limiting parameters are further restricted.
Because the acceleration, frequency, and displacement are given by the
external vibrating source, rather than being of free selection, the energy
generation parameters are reduced to three. Then, the relevant factors
are the acceleration-squared-to-frequency (which is an input source
constraint), the proof mass
m
(a sizing factor), and the
Q
factor (a gen-
erator design constraint).
The acceleration-squared-to-frequency term will be referenced as
ASTF
or
σ
ω
, which will also be considered as a figure of merit for the
energetic content of the source (m
2
/s
3
units) and equal to
a
2
ω
σ
ω
5
(2.7)
The
Q
factor is a dimensionless parameter that relates the total
energy stored to the energy lost in a single cycle. The
Q
factor is then
a measure of the quality of an energy harvester. Conversely, the
ASTF
or the
σ
ω
term represents the energy level from the source. Therefore,
energy harvesters are ultimately limited by the level of energy from the
source (
σ
ω
) and by the energy generation process (
Q
factor). Thus,
Eq. (2.6)
can be written as
P
available
5
1
2
mσ
ω
Q
(2.8)
