149 coupling coefficient can be improved with adjusting the optimum resistive load in this
region, with the assumption that the mechanical damping can be modified.
Figure 6-22: Coupling coefficient as a function of optimum resistive load for different damping ratio for sample D5, with resonant frequency at 505.5 Hz and capacitance of 6.82 nF.
Figure 6-23 shows the relationships between the efficiency of energy conversion for a piezoelectric cantilever with the coupling factor and
Q
-factor. The efficiency can be improved by increasing the coupling factor and the
Q
-factor of the cantilever structure.
Figure 6-23: Efficiency of energy conversion as a function of coupling coefficient and
Q
-factor.
= 0.25 = 0.1
= 0.01 = 0.001
150 In an experiment with sample D as shown in Figure 6-24, the efficiency decreases with
increasing cantilever length. The shortest cantilever sample appears to have an initial level of efficiency at about 35 and the longest sample has an efficiency of about 25
.
Figure 6-24: The energy conversion efficiency equation
6-10
as a function of cantilever length with 5 error.
The
Q
-factor of sample D5 was reduced but the coupling factor,
k
increased when proof mass is attached. This shows that more energy is stored in the structure at resonance
[111], and hence more electrical energy can be extracted with improved energy conversion efficiency as demonstrated in equation 6.10, which is in good agreement
with experimental results shown in Figure 6-25. Sample D5 has as efficiency of 25 initially, which increases to around 35 with the addition of a 2.2 g proof mass.
Figure 6-25: The energy conversion efficiency as a function of mass for sample D5.
151
6.7 Conclusion
The mechanical properties of the cantilever samples were measured. Shorter cantilevers were found to suffer energy loss at the support of the cantilever while the surface loss is
dominant for longer cantilevers, which can be explained by the measured
Q
-factor and the damping ratio of the structures. The
Q
-factor for the samples with length between 4.5 mm to 18 mm is in the range of 100
– 220, which results in a calculated damping ratio of 0.002 to 0.0045.
The resonant frequency is inversely proportional to the length of a cantilever while the electrical output power increases gradually with the cantilever length. The
improvement, however is not as effective as adding additional proof masses. In order to operate at a low level ambient condition while keeping the overall device size as small
as possible, additional proof masses is therefore the preferred method for improving the output power. The present of proof mass also increases the energy conversion efficiency
of the device from 25 to about 35 when a 2.2 g proof mass was attached.
The electrical output power, however, do not increases infinitely with proof mass. A maximum output power of about 40 nW was measured when a proof mass of 2.2 g with
dimension 9 mm × 5mm × 1 mm was attached to the tip of a cantilever having a length of 13.5 mm. The power can be further increased by increasing the acceleration level. In
a separate measurement, the output power of a cantilever having a length of 18 mm, increases from 10 nW to 280 nW when accelerated to 0.1 g and 1.0 g respectively.
Another factor which is important in increasing the output power is the distance from the centroid of the active piezoelectric layer to the neutral axis of the composite
cantilever. The experiment results show that the greater the distance from the neutral axis the great output power it produced which is in good agreement with the theoretical
calculation in Chapter 3. The neutral axis factor will be discussed in detail in next chapter.
152
Chapter 7 Multimorph
Cantilevers
7.1 Introduction
A multimorph is a multilayer composite structure consists of more than two active piezoelectric layers separated by electrodes in between them. The main advantage in
producing a multimorph structure consisting of alternating layers of PZT and AgPd electrodes, is that it generates larger electrical output than would be possible with a
single layer unimorph structure having the same total thickness. This is because the individual PZT layer is arranged away from the neutral axis of the whole structure and
the resultant stress would be increased when the cantilever structure bends, therefore increasing the electrical output from the piezoelectric materials.
Another advantage of multimorph structures compared to traditional piezoelectric cantilevers fabricated on a substrate is the flexibility offered in the configuration of
electrode terminals to operate as either current sources or voltages sources.
A model of a multimorph structure will be discussed in the following section and a series of multimorph structures were fabricated to verify the model. The multimorph
structures were fabricated using a co-firing temperature profile with a peak temperature of 950 °C. For simplification the structures were fabricated with three similar laminar
sections of PZT having thicknesses of about 40 µm and physically separated by thin layers of AgPd electrodes of equal thickness of 12 µm as shown in Figure 7-1.
