43 capacity of 1000 cc vibrates at around 30 Hz and when accelerated at 1.23 ms
2
was calculated to produce 33.5
m of vibration amplitude.
Figure 3-1: Typical low level ambient vibration sources. Microwave Casing
Stationary Car with Engine Switched On
Blender
Casing
Bus Travelling at Moderate Speed
Kitchen ventilation Fan at Lower Speed
Kitchen ventilation Fan at Higher Speed
0.1 0.2
0.3 0.4
0.5 0.6
0.7 0.8
50 100
150 200
250 300
Frequency Hz
A c
c e
le ra
ti o
n m
s 2
0.2 0.4
0.6 0.8
1 1.2
50 100
150 200
250 300
Frequency Hz
A c
c e
le ra
ti o
n m
s 2
0.05 0.1
0.15 0.2
0.25
50 100
150 200
250 300
Frequency Hz
A c
c e
le ra
ti o
n m
s 2
0.2 0.4
0.6 0.8
1 1.2
1.4
50 100
150 200
250 300
Frequency Hz
A c
c e
le ra
ti o
n m
s 2
5 10
15 20
25
50 100
150 200
250 300
Frequency Hz
A c
c e
le ra
ti o
n m
s 2
0.2 0.4
0.6 0.8
1 1.2
50 100
150 200
250 300
Frequency Hz
A c
c e
le ra
ti o
n m
s 2
44 Table 3-1 shows the summary of all measured vibration sources in terms of fundamental
resonant frequencies, acceleration magnitude and calculated excited amplitudes. Generally, the results show that, the vibrations available around us are at low level with
frequencies lower than 500 Hz and at an acceleration of around 1 ms
2
0.1 g.
Table 3-1: Summaries of Measured Vibration Sources. Vibration Sources
Acceleration ms
2
Frequency Hz
Amplitude m
Blender Casing 21.8
275 7.32
Microwave Casing 0.68
100 1.72
Refrigerator coil x-direction 0.09
100 0.21
Kitchen ventilation fan Speed I
0.2 200
0.13 Speed II
1.1 38
19 Kitchen door when closed
0.42 433
0.06 Desktop PC
Normal operation 0.21
543 0.018
Running CD ROM 0.26
154 0.28
Laptop Normal operation
0.26 90.2
0.081 Running CD ROM
0.66 43.2
0.896 Knock on wooden table
0.3 – 0.4
400 - 800 0.016
– 0.063 Lift
0.078 7.3
37.1 Vending machine
0.12 100
0.29 Bus
Stationary 0.37
111 0.75
Travelling at moderate speed
1.04 10.8
226
Car 1000 cc
Engine 1.23
30.5 33.5
Near to radiator 0.16
29.5 4.66
Near to headlight 0.23
29.5 6.64
Bonnet 0.18
29.5 5.18
Dashboard 0.04
30 1.07
Roof 0.26
29.5 7.54
Notes: Lift just about to stop at higher level.
The vibration was measured on the upper floor of a double decker bus. Stationary measurement.
45
3.3 The Design Considerations
The design features and dimensions of a thick-film free-standing structure have to be based on the constraints imposed by thick-film technology. The minimum feature which
can be printed is about 100 µm in length and depends on the mesh density of a screen- printing mask and also the properties of the thick-film pastes. The minimum thickness
of the cantilever structure that can be produced is governed by the particle size of the pastes being used e.g PZT, which is typically 0.8
– 2 m. There is no definite upper
limit of thickness for the PZT film that can be produced, but films with thickness greater than 200
m would be inferior compared to bulk piezoelectric ceramics for the same thickness.
The free-standing cantilever structure is designed to be operated in an ambient vibration environment, where the first natural frequency mode of the cantilever has to be matched
with the frequency of ambient vibration sources, which are generally lower than 500 Hz. In order to achieve low resonant frequency level, the dimensions of the cantilever
can be adjusted and a proof mass can be added to fine-tune the natural frequency of the structure to suit the desired application. However, at low vibration frequency, the
excited amplitude of the cantilever is inversely proportional to the resonant frequency squared. This will translate into a relatively big deflection and stress on the cantilever. A
thick-film ceramic structure is relatively brittle and fragile; therefore the cantilever structure has to be designed to operate within the limit of stress that the structure can
withstand.
The smaller the feature size of the energy harvester the better it is for miniature system integration. However, there is another issue that must be considered which is that the
output electrical energy reduces as the size of the generator decreases. Therefore an optimum design is needed to trade-off between the electrical energy output and the
compactness of the device.
After considering all the physical limitations of a ceramic free-standing structure, the next step is to optimise the performance of the energy harvester in order to produce
useful electrical energy for powering microsystem. An open circuit output voltage is an important indicator to determine the practical usage of the device. For most of the
46 electronic applications, usually the AC voltages generated by a micro-generator are
converted to usable DC voltage. In this conversion, diodes are normally used for simple full wave direct rectification, which need a minimum forward voltage of 300 mV for
each diode to operate. The minimum voltage was able to be reduced to 150 mV by replacing the diodes with active switches in a four stages voltage multiplier circuit as
studied by Saha
et al
[89]. A few tens of micro-watts of electrical power are needed for powering ultra low-power electronics, MEMS sensors and RF communications system.
As reported by Torah
et al
[65], 58 W of power is needed to power an accelerometer
based micro-system.
3.4 Theoretical Analysis of Multilayer Structures
Generally, the base excited harmonic motion is modelled as a spring-mass-damper system with the equation of motion [90],
3-1
where
y
denotes the displacement of the base and
x
the displacement of the mass from its static equilibrium position. The vibration body is assumed to have a harmonic
motion, 3-2
By defining the relative displacement
z
=
x
–
y
. The magnitude of the displacement and acceleration can be derived as,
3-3
3-4
and the phase difference is, 3-5
y x
y x
b x
M
t Y
t y
sin
Y
r r
r Z
2 2
2 2
2 1
Y
r r
Z
2 2
2
2 1
1
2
1
1 2
tan
r r
