User Manual

Page 32
∆x 
3/4Vd
31
l
2
t
2
∆x 
3/4(100V) 23x10
12
m/m
V/m
(2x10
2
m)
2
(9x10
6
m)
2
∆x  8.52mm
Figure 30. Lead attachment methods for a
bimorph
Thicker films and multilayers improve the force developed by the bimorph, but sacrifice displacement unless
the unit can be operated at higher fields.
The amount of tip deflection and the force developed are given by:
meters
∆x  3/4d
31
(l
2
/t
2
)V
and
Newtons
F  3/2Ywd
31
(t/l)V
where
∆x = displacement at dc
F = generated force
d
31
= piezoelectric coefficient in the "1" direction
l,t,w = length, thickness, and width of piezo film
V = applied voltage (Volts)
Y = Young's modulus of piezo film (2x10
9
N/m
2
)
By applying an ac voltage, the bimorph can act as a fan, similar to an insect wing. Although the piezo film
bimorph does exhibit a dc response, maximum tip deflections are obtained when the unit is operated at
resonance, determined by the length and thickness of the bimorph beam.
EXAMPLE 4:
100 volts are applied across a 2 cm long cantilever bimorph comprised of two strips of 9
µm
PVDF. The resultant tip displacement is:
∆
x
As shown in the equations, more displacement can be obtained
from a longer bimorph. Larger forces can be obtained from a
wider bimorph. The ratio of displacement at a resonance
frequency and dc is defined by Q which indicates a mechanical
gain. A typical Q value for a piezo film bimorph is 20 to 25.
For example, a 5 mm long 70µm thick bimorph with 120 volts
dc creates a displacement of 57µm. With the same bimorph,
however, displacement can be 1.4 mm at the resonant frequency
of 580 Hz. For applications that require a higher force, such as
cooling fans, multilayer construction can be considered. The
resulting output force is proportionally increased by the number
of layers.
In terms of electrical connections to the bimorph, there are two
basic methods as shown in Figure 30 — parallel and series
connections. In order to generate the same amount of
displacement, the parallel connection requires a lower voltage
than the series connection. Series connections, on the other hand,