Design of a Programmable Filter For
Macromolecules
by
Byron Miguel Stancil
8ARr'e
OF TECHNOLOGy
0 f 2 b
L1BRARIES
B.S.E., University of Maryland Baltimore County (1999)
Submitted to the Department of Mechanical Engineering
in partial fulfillment of the requirements for the degree of
Master of Science in Mechanical Engineering
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
June 2002
@ Byron Miguel Stancil, MMII. All rights reserved.
The author hereby grants to MIT permission to reproduce and
distribute publicly paper and electronic copies of this thesis document
in whole or in part.
Author ........
..
Departnzint of Mechanical Engineering
May 24th, 2002
Certified by ...........
Accepted by ................
7
Kamal Youcef-Toumi
Professor of Mechanical Engineering
Thesis Supervisor
......
Ain A. Sonin
Chairman, Department Committee on Graduate Students
j
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Design of a Programmable Filter For Macromolecules
by
Byron Miguel Stancil
Submitted to the Department of Mechanical Engineering
on May 24th, 2002, in partial fulfillment of the
requirements for the degree of
Master of Science in Mechanical Engineering
Abstract
The focus of this thesis is the design of a device that separates biologically-active
macromolecules by particle size. The final apparatus design functions by pumping
molecules in an aqueous solution between two surfaces with flatness on the nanoscale.
The varying gap width between the two surfaces will determine what molecules will
pass through to the solution collector. A controller is used to change the gap width
by utilizing two piezoactuators and readings from two capacitance probes. The goal
of this project is to be able to develop a new method of particle separation utilizing
the best qualities of present methods and eliminating their worst qualities. Particles
should be filtered very quickly without any contaminants on a particle range of 0.5
nanometers to 0.5 microns.
Thesis Supervisor: Kamal Youcef-Toumi
Title: Professor of Mechanical Engineering
2
Acknowledgments
I would like to extend my gratitude to various people for their support. My advisor,
Professor Kamal Youcef-Toumi, has mentored me throughout my stay here. I have
benefited greatly from his guidance, knowledge and persistence in seeing this project
to its completion. Dr. Manzooh Shah, CEO of Alpine Pharmaceutical Co., sponsored
and guided this project from the beginning. Furthermore, Dean Isaac Colbert, Dean
Blanche Staton, Associate Dean Roy Charles, Brima Wurie, Ed Ballo, George Brennan and Heather Fry in the Graduate Student Office provided financial, emotional,
academic and spiritual support in many ways. They've been like family to me here.
Professors George Barbastathis, Jung-Hoon Chun, Dave Pritchard, Peter So, Alex
Slocum, and David Trumper provided invaluable insight and/or assistance from their
labs and through conversations during the course of this project.
I also want to thank Gerry Wentworth, Stephen Haberek and everyone else from
the Central Machine Shop, the Laboratory for Manufacturing and Production and the
Pappalardo Undergraduate Laboratory for allowing me to utilize their machine shops
and for their insight and assistance. I cannot forget Alex Cronin, Patrick Anquetil,
James Tangorra, Bryan Crane, Phoebe Kwan and Andrew Stein, whom have assisted
me in many different ways here. Also my colleagues in the d'Arbeloff's Laboratory
have provided social and academic support. Especially, Bernardo Aumond, Osamah
El Rifai, Vidi Saptiri, Eric Hoarau, Belal Helal, and Eric Wade have assisted me
extensively throughout my stay here.
I want to thank all my family, friends, and colleagues from MIT, UMBC, Maryland
and many other places for their "prayers and wishes". I cannot forget the members
of the Black Graduate Student Association for all their love and support. Plus, I
cannot forget Leslie Regan, Joan Kravit, and Carolyn Skeete for going beyond the
call of duty to assist me in many ways. Of course, I would like to thank Malo Huston,
Reginald Hutchinson, and Mike Johnson for being there for me in many ways. Besides
being the best of colleauges to me, they've been like brothers to me. I cannot go any
further without giving thanks to Treena Boyd, my lovely fiance,, and my parents for
3
all their love, encouragement and emotional and spiritual support. Finally, but first
and foremost, I would like to thank God, because without him, all of this would not
be possible.
4
Contents
1
15
Introduction
1.1
Background . . . . . . . . . . . . . .
15
1.2
Objectives and Technical Issues . . .
16
1.3
Filtration Categories . . . . . . . . .
16
1.4
Conventional Methods of Separation
17
1.5
Approach: Mechanical Programmable Filter (MP F)
19
1.6
1.5.1
Theory of MPF . . . . . . . .
19
1.5.2
Advantages of MPF . . . . . .
20
1.5.3
Challenges of MPF . . . . . .
20
Thesis Outline . . . . . . . . . . . . .
21
25
2 Design Alternatives
2.1
Introduction . . . . . . . . . . . . . . .
25
2.2
Dual Flexure Design
. . . . . . . . . .
25
2.2.1
Material Selection . . . . . . . .
25
2.2.2
Flexure Descriptions . . . . . .
26
2.2.3
Flexure Design Process.....
26
2.3
2.4
Tubular Filtration . . . . . . . . . . . .
28
2.3.1
Material Selection . . . . . . . .
28
2.3.2
Tubular Description
. . . . . .
28
2.3.3
Tube Filtration Process
. . . .
28
Implementation/Sealing of Fused-Silica Quartz Plates
2.4.1
Major Issues . . . . . . . . . . .
5
29
29
2.5
2.6
3
2.4.2
Sealant Test . . . . . . . . . . . . . . . . . . . . . . . . . . . .
29
2.4.3
Fixture Design
. . . . . . . . . . . . . . . . . . . . . . . . . .
30
Fluid Delivery System . . . . . . . . . . . . . . . . . . . . . . . . . .
30
2.5.1
Reynolds Number . . . . . . . . . . . . . . . . . . . . . . . . .
30
2.5.2
Inlet Pressure Calculations . . . . . . . . . . . . . . . . . . . .
31
2.5.3
Outlet Pressure Calculations . . . . . . . . . . . . . . . . . . .
32
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
33
Summary
43
Experimental Setup
3.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
43
3.2
Experimenting with the Probes and Piezoactuators
. . . . . . . . . .
43
3.2.1
Capacitance Probes . . . . . . . . . . . . . . . . . . . . . . . .
43
3.2.2
Piezoactuators
. . . . . . . . . . . . . . . . . . . . . . . . . .
45
3.2.3
System's Resolution, Range, and Noise . . . . . . . . . . . . .
46
. . . . . . . . . . . . . . . . . . . . . . .
47
3.3.1
Characterization of System . . . . . . . . . . . . . . . . . . . .
47
3.3.2
Dynamic Characteristics . . . . . . . . . . . . . . . . . . . . .
48
3.3.3
Designing Controller . . . . . . . . . . . . . . . . . . . . . . .
50
3.3.4
DSPACE Control . . . . . . . . . . . . . . . . . . . . . . . . .
52
3.3
3.4
DSPACE Controller Design
Summary
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
69
4 Experimental Results
5
53
4.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
69
4.2
Flow Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
69
4.3
Actuation and Sensing Test
. . . . . . . . . . . . . . . . . . . . . . .
70
4.4
Filtration Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
71
81
Conclusion and Recommenations
A Company Addresses
89
B Schematics
91
6
107
C Controller Design
C.1 Sensor, Piezoactuator, and Dynamic Signal Analyzer Data . . . . . .
D Material List and Component Characteristics
7
107
129
8
List of Figures
1-1
Electrodialysis process [9]
. . . . . . . . . . . . . . . . . . . . . . . .
22
1-2
Reverse osmosis process [20] . . . . . . . . . . . . . . . . . . . . . . .
22
1-3
High pressure liquid chromatography process [19]
. . . . . . . . . . .
23
1-4
Capillary electrophoresis process [22]
. . . . . . . . . . . . . . . . . .
23
1-5
Plates filtering solution (orange and green are large particles, respectively .) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
24
2-1
Side view of dual flexure design . . . . . . . . . . . .
38
2-2
Top view of dual flexure design . . . . . . . . . . . .
38
2-3
Different types of notch hinges: a) circular, b) elliptic, and c) leaf[23]
39
2-4
Filter tube design . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
39
2-5
Stress versus strain plot of an elastic material [4] . . . . . . . . . . .
40
2-6
Hysteresis plot [3]
. . . . . . . . . . . . . . . . . . . . . . . . . . . .
40
2-7
MPF final filtration design . . . . . . . . . . . . . . . . . . . . . . . .
41
3-1
Digital picture of probe . . . . . . . . . . . . . . . . . . . . . . . . . .
56
3-2
Micrometer stage . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
56
3-3
Voice coil in a speaker [2] . . . . . . . . . . . . . . . . . . . . . . . .
57
3-4
Digital picture of piezo-amplifier . . . . . . . . . . . . . . . . . . . . .
57
3-5
Sensor output versus generator input (stiffness test)
. . . . . . . . .
58
3-6
Simulink model of open loop "unlumped" system
. . . . . . . . .
58
3-7
Simulink model of open loop "lumped" system . . . . . . . . . . . . .
59
3-8
Piezoactuator B and flexure F
/ sensor D
3-9
Piezoactuator B and flexure F
/ sensor
9
.
magnitude bode diagram
D phase bode diagram . . .
59
60
3-10 Piezoactuator A and flexure E
/
sensor D slope in magnitude bode
diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
60
/ sensor D
E / sensor C
3-11 Piezoactuator A and flexure E
slope in phase bode diagram
61
3-12 Piezoactuator A and flexure
magnitude bode diagram
.
61
. . . .
62
3-13 Piezoactuator A and flexure E/ sensor C phase bode diagram
3-14 Piezoactuator A and flexure E
/
sensor C slope in magnitude bode
diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
/
62
sensor C slope in phase bode diagram
63
3-16 Simulink model of a closed loop system . . . . . . . . . . . . . . . . .
63
3-17 Asymptotic curves for basic terms of a transfer function [10] . . . . .
64
3-15 Piezoactuator A and flexure E
3-18 The optimum coefficients based on the ITAE criterion for a step input
[10] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
65
3-19 Root locus of top system . . . . . . . . . . . . . . . . . . . . . . . . .
65
3-20 Root locus of bottom system . . . . . . . . . . . . . . . . . . . . . . .
66
3-21 DSPACE controller model . . . . . . . . . . . . . . . . . . . . . . . .
66
3-22 DSPACE card . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
67
3-23 DSPACE panel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
67
3-24 Sensor output with DSPACE controller . . . . . . . . . . . . . . . . .
68
. . . . . . . . . . . . . . . . . . . . . . . .
4-1
Filtration tube
76
4-2
Sensor output(V) versus piezoelectric output from amplifier
4-3
Magnitude Bode diagram for MPF tube filtration design
77
4-4
Phase Bode diagram for MPF tube filtration design . . . .
77
4-5
Root locus of closed loop system 1 . . . . . . . . . . . . . .
78
4-6
DSPACE controller for filration experiment . . . . . . . . .
78
4-7
Sensor output and square wave input for open loop
. . . .
79
4-8
Sensor output from square wave input for open loop
. . .
79
4-9
Sensor output from square wave input for closed loop . . .
80
(V)
76
B-1 Isometric view of small flexure A (mm) . . . . . . . .
92
B-2 Front view 1 of small flexure A (mm) . . . . . . . . .
92
10
B-3 Front view 2 of small flexure A (mm) . . . . . . . . . . . . . . . . . .
93
B-4 Top view of small flexure A (mm) . . . . . . . . . . . . . . . . . . . .
93
B-5 Side view of small flexure A (mm) . . . . . . . . . . . . . . . . . . . .
94
B-6 Isometric view of large flexure B (mm) . . . . . . . . . . . . . . . . .
94
B-7 Front view of large flexure B (mm)
. . . . . . . . . . . . . . . . . . .
95
B-8 Top view of small flexure B (mm) . . . . . . . . . . . . . . . . . . . .
95
B-9 Side view of small flexure B (mm) . . . . . . . . . . . . . . . . . . . .
96
B-10 Isometric view of piezo-holder M (inches) . . . . . . . . . . . . . . . .
96
B-11 Front view 1 of piezo-holder M (inches) . . . . . . . . . . . . . . . . .
97
B-12 Front view 2 of piezo-holder M (inches) . . . . . . . . . . . . . . . . .
97
B-13 Side view of piezo-holder M (inches) . . . . . . . . . . . . . . . . . . .
98
B-14 Top view of piezo-holder M (inches) . . . . . . . . . . . . . . . . . . .
98
. . . . . . . . . . . . . . .
99
. . . . . . . . . . . . . . . . .
99
. . . . . . . . . . . . . . . . . .
100
B-18 Top view 1 of Sensor-Holder N (inches) . . . . . . . . . . . . . . . . .
100
B-15 Isometric view of sensor-holder N (inches)
B-16 Front view of sensor-holder N (inches)
B-17 Side view of sensor-holder N (inches)
B-19 Top view 2 of Sensor-Holder N (inches) . . . . . . . . . . . . . . . . . 101
. . . . . . . . . . . . . . . . .
101
. . . . . . . . . . . . . . . . . . .
102
B-22 Side view of tube claw 0 (inches) . . . . . . . . . . . . . . . . . . . .
102
B-23 Top view of tube claw 0 (inches) . . . . . . . . . . . . . . . . . . . .
103
B-24 Isometric view of sensor contact P (inches) . . . . . . . . . . . . . . .
103
B-20 Isometric view of tube claw 0 (inches)
B-21 Front view of tube claw 0 (inches)
B-25 Front view 1 of sensor contact P (inches) . . . . . . . . . . . . . . . . 104
B-26 Front view 2 of sensor contact P (inches) . . . . . . . . . . . . . . . . 104
B-27 Side view of sensor contact P (inches) . . . . . . . . . . . . . . . . . . 105
B-28 Schematic of model 2800 series probe [1] . . . . . . . . . . . . . . . . 105
B-29 Piezoactuator Schematic
[7] . . . . . . . . . . . . . . . . . . . . . . .
B-30 Spherical top piece (steel) on moving end
[7]
. . . . . . . . . . . . . .
C-1 Noise plot for sensor output . . . . . . . . . .
11
106
106
109
C-2 Sensor output with bottom piezoactuator at -30 Vdc
. . . . . . . . .
109
C-3 Sensor output with top piezoactuator at -30 Vdc . . . . . . . . . . . . 110
C-4 Sensor output with bottom piezoactuator at 0 Vdc
. . . . . . . . . .
110
C-5 Sensor output with top piezoactuator at 0 Vdc . . . . . . . . . . . . .111
C-6 Sensor output with bottom piezoactuator at 1 Vdc
. . . . . . . . . .111
C-7 Sensor output with top piezoactuator at 1 Vdc . . . . . . . . . . . . .
112
C-8 Sensor output with bottom piezoactuator at +150 Vdc . . . . . . . .
112
. . . . . . . . . .
113
. . . . . . . . .
113
C-11 Sensor output with top piezoactuator at +1 Vdc . . . . . . . . . . . .
114
C-12 Piezoactuator B and flexure F
114
C-13 Piezoactuator
/ sensor C magnitude bode diagram .
B and flexure F / sensor C phase bode diagram . . . .
B and flexure F / sensor C slope in magnitude bode
115
diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
115
C-15 Piezoactuator B and flexure F/ sensor C slope in phase bode diagram
116
C-16 Piezoactuator A and flexure E/ sensor D magnitude bode diagram . .
116
C-9 Sensor output with top piezoactuator at +150 Vdc
C-10 Sensor output with bottom piezoactuator at +1 Vdc
C-14 Piezoactuator
C-17 Piezoactuator A and flexure E
/
C-18 Piezoactuator A and flexure E
sensor D phase bode diagram . . . .
/
sensor D slope in magnitude bode
diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
C-19 Piezoactuator A and flexure E
/ sensor
12
117
117
D slope in phase bode diagram 118
List of Tables
2.1
Parts list A
2.2
Aluminum comparison
..... ... ... .. .. .. ... .. ..
2.3
Flexure design results A
. . . . . . . . . . . . . . . . . . . . . . . . 35
2.4
Flexure design results B
..... .... .. ... . .. ... .. ..
2.5
Flexure design results C
. . . . . . . . . . . . . . . . . . . . . . . . 35
2.6
Parts list B for filter tube
. . . . . . . . . . . . . . . . . . . . . . . . 36
2.7
Parts list C for MPF . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 6
2.8
Reynolds number results . . . . . . . . . . . . . . . . . . . . . . . . . 3 6
2.9
Pressure results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 6
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
35
35
2.10 Fluid definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 7
. . . . . . . . . . . . . . . . . .
54
.
54
3.1
Sensor outputs
3.2
Amplifier noise outputs versus voltage output
3.3
Sensor outputs and noise due to piezoactuator A versus amplifier volt...
age output.................
3.4
....
. . . .p. . . . . . ..
55
Sensor outputs and noise due to piezoactuator B versus amplifier voltage output . . . . . . . . . . . . . . . . . . . . .
55
4.1
Filtration tube chart . . . . . . . . . . . . . . . . . . . . . . . . . . .
73
4.2
Open loop response due to a square wave input
. . . . . . . . . . . .
74
4.3
Closed loop response due to a square wave input . . . . . . . . . . . .
74
4.4
Filtration test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
75
C. 1 Elasticity test of system
. . . . . . . . . . . . . . . . . . . . . . . . . 108
13
C.2 Dynamic signal analysis of flexure design la . . . . . . . . . . . . . . 119
C.3 Dynamic signal analysis of flexure design lb . . . . . . . . . . . . . .
C.4 Dynamic signal analysis of flexure design 2a
120
. . . . . . . . . . . . . . 121
C.5 Dynamic signal analysis of flexure design 2b . . . . . . . . . . . . . . 122
C.6 Dynamic signal analysis of flexure design 3a
. . . . . . . . . . . . . .
123
C.7 Dynamic signal analysis of flexure design 3b . . . . . . . . . . . . . . 124
. . . . . . . . . . . . . .
125
C.9 Dynamic signal analysis of flexure design 4b . . . . . . . . . . . . . .
126
C.10 Dynamic signal analysis of MPF 1 . . . . . . . . . . . . . . . . . . . .
127
C.11 Dynamic signal analysis of MPF 2 . . . . . . . . . . . . . . . . . . . .
128
P arts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
130
D.2 Probe characteristics [1] . . . . . . . . . . . . . . . . . . . . . . . . .
130
C.8 Dynamic signal analysis of flexure design 4a
D .1
D.3 Piezoactuator characteristics
[7]
. . . . . . . . . . . . . . . . . . . . .
14
131
Chapter 1
Introduction
1.1
Background
In the pharmaceutical industry, a major issue is the separation of biologically active macromolecules.
The present methods take too long, are too costly, or have
contamination issues. So, the industry is racing to find a new method of separation.
Normally, you need a means of detecting, collecting, and purifying samples in three
different stages. Hopefully this coupled-process can be eliminated or the combination
of some of these processes can be accomplished. Usually, the sample, the medium
or both are stained with some type of chemical coloring. This process affects the
purification because the coloring and other contaminants have to be separated from
the sample too. In collecting the sample, an intrusive means is not desired because
contaminants could be added to the sample and/or the sample could be physically
damaged. An attraction method could be used where the sample is collected on a
film. Furthermore present methods are not efficient. Gels are reliable but still interfere
with decontaminating samples. Using radiation and electricity (i.e., ultraviolet rays
or electric charges) possibly has effects on the properties of molecules.
15
1.2
Objectives and Technical Issues
The goal of this project is to design and construct an Autonomous Robotic Purification System (ARPS) using unconventional methods for purification of biologically
active macromolecules. Gels are not desired in this project. Purification will be accomplished by separating particles by diameter size. Particles of diameters of 0.5
nanometers to 0.5 micrometers are desired for separation. Overall, the goal is to find
a method that reduces the number of steps for purification, minimizes process time,
eliminates contaminants and byproducts, records and stores data, and has a remote
control function from a computer through the web (teleoperation).
The maximum dimensions for this device are approximately 11 centimeters x 11
centimeters (4.33 inches x 4.33 inches). The positive aspects of High Performance Liquid Chromatography (HPLC) and Capillary Electrophoresis (CE) are desired. Serious
thought must be put into how samples are held, how the device will interface with
the computer, what type of software to use, what types of experiments to conduct,
building a device from scratch versus coupling devices, and the design and layout.
This project has to have universal application. Plus, FDA approval is also needed for
implementation into the pharmaceutical market.
1.3
Filtration Categories
There are five categories for filtration where the properties of the molecules are used to
exploit the concept. Properties of interest are molecular mass and weight, charge, and
particle size. The major areas are macro, micro and submicron particles [6]. Particles
between 50-100 microns in size are macro particles. Particle filtration is applicable
which includes pre-coat and depth filters and screen. These particles are usually
visible to the naked eye. Examples of these macro particles are sand, hair, pollen,
flour, and mist. An optical microscope is needed to see the next category of particles,
micro particles. These range in size from 0.05 microns to 2 microns. Examples of
these particles are red blood cells, coal dust, yeast cells and latex. Microfiltration is
16
used for filtering these particles. Surface, depth, and pleated filters are used here, as
well.
Submicron particles are broken down into subdivsions of macro molecular, molecular, and ionic particles.
All of these methods involve semipermeable membrane
usage. In the macro molecular and molecular range, particle sizes range from 0.05
microns to 1 micron and 0.002 microns and 0.02 microns, respectively. The macro
molecular range, dimension-wise, is the small resolution end of the micro range. It is
mentioned because on the high end of the micro range, semipermeable membranes are
not always necessary. These particles are viewed using a scanning electron microscope
(SEM). Microfiltration and ultrafiltration is utilized to separate macro molecular and
molecular particles such as tobacco smoke, asbestos, various paint pigments and some
bacteria, and synthetic dyes, viruses, and endotoxins, respectively. Ionic particles are
usually under 0.001 microns in size and viewed with a scanning tunneling microscope
(STM). Hyperfiltration methods, such as reverse osmosis, are used to separate aqueous salts, metal ions, and atomic radius-sized particles. Distillation and deionization
are other means of filtering ionic particles but these methods are not optimal due
to the high amount of chemicals and energy required. When coupled with reverse
osmosis, cost can be minimized using distillation and deionization.
1.4
Conventional Methods of Separation
Many conventional methods of separation are used in the pharmaceutical field. Hydrolysis is the splitting of a compound into fragments by the addition of water; the
hydroxyl group being incorporated in one fragment and the hydrogen atom in the
other [5]. In biological application, water is added to a starch to break the chains to
get glucose. H 2 SO4 is the catalyst and NaOH (salt) is the byproduct. Also, membranes can be implemented into this method to increase the amount of separation.
Even though this method is one of the simplest, the problem with this process is
that too many contaminants are present. First, the water added to the sample must
be checked for purity. Second, the byproduct, salt, must be filtered out, which adds
17
another step to the process. Most importantly, the catalyst, H 2 SO4 is not desired
because it is a very strong solution. Ultrafiltration uses cell membranes to separate
large and small molecules. The only problem with this method is that you have to
clean the sample due to the gel [27].
Electrodialysis is an electric current-induced process where a solution is separated
into its ionic components, cations (negatively charged particles) and anions (positively
charged particles) [9]. Once separated, these particles migrate through a membrane
that allows cations or anions to pass through. The membranes that allow anion or
cations to pass are cation- or anion-exchange membranes, respectively. Usually, two
oppositely charged electrodes are on placed on both ends of the current path. Between
the two electrodes, multiple metal plates, which are the cation and anion exchange
membranes, are placed to gather the ions at different locations in a tank or container.
Depending on the type of membrane, anions and cations will gather on its opposite
sides while some will gather on the electrodes. The accumulation of a salt will be on
one side while cations and anions will be on another. So there will be a removal of salts
and water, leaving a diluted solution in certain set of chambers while a concentrated
solution will be in the ions' chamber. Problems with this method include plate erosion
from the salt byproduct and it only separates by particle charge (particle size and
charge do not always correlate). Figure 1-1 shows the Electrodialysis Process.
Reverse osmosis utilizes the osmotic pressure, which is an applied pressure that
must overcome the chemical driving potential driving force [20]. This action results in
the pure solvent being driven from the solution to the other side of a semipermeable
membrane. This process is "reverse" osmosis because in "regular" osmosis, the solvent
naturally flows through a membrane into solution comprised of a solvent and a solute.
Usually, reverse osmosis is utilized in the desalination of water where fresh water is
driven from a solution (i.e., salt water). For the separation of various particles, you
have to have more than one type of membrane.
So, this method does not have
universal application. Figure 1-2 shows the Reverse Osmosis Process.
Chromatography is the process of separating a biological mixture into its individual components due to their physical (i.e., structure) and chemical (i.e., composition)
18
differences to the solvent in the mobility phase and the column packing in the stationary phase [19]. Physical differences are based on molecular property based methods
that use charge (Ion Exchange) and size (gel permeation and size-exclusion). Usually,
the separation of the solution is based on their mobility or separation speed through
some sort of membrane or porous media. Two types of chromatography are manual and mechanical (i.e., liquid and gas, respectively). Mechanically High Pressure
Liquid Chromatography (HPLC) applies a pressure and separates due to mobility
and charge. If high pressures are involved, the structure must be designed properly
to accommodate for the forces. In addition, various types of mediums are needed
to separate a wide range of molecules. Figure 1-3 shows the High Pressure Liquid
Chromatography Process.
Electrophoresis uses an electric field to move ions and charged macromolecules
through a medium [22]. The mobility of the molecules depends on molecular size,
weight and shape of particles, charge carried, applied current and medium's resistance.
In most setups, molecules move faster if they are smaller and highly-charged. Newer
methods used in electrophoresis are Capillary Gel Electrophoresis and Capillary Isoelectric Focusing Electrophoresis.
CE brings speed, quantitation, reproducibility,
and automation to the conventional method. This method is one of the more optimal
choices but due to the use of membrane, contamination and universal application are
still major factors. Figure 1-4 shows the Capillary Electrophoresis Process.
1.5
Approach: Mechanical Programmable Filter
(MPF)
1.5.1
Theory of MPF
MPF follows a simple methodology. Two parallel plates, with extremely flat contact
surfaces, are adjusted so that various particles can move between them in an aqueous
solution. The plates are moved by some means of actuation to be discussed later in
the thesis. After being calibrated, a sensor is used to check the gap width between
19
the plates. Then the sensor readings will correlate to a certain gap width. Figure
1-5 shows the plates filtering a solution.
1.5.2
Advantages of MPF
As mentioned before, MPF methodology is easy to understand. Secondly, the system
will require more of an understanding of mechanical engineering instead of too many
disciplines (excluding of course the interaction of the particles at the gap). In addition,
a mechanical system will be more robust than an optical or chemical because of less
electronic interference and stability due to environmental changes (i.e., temperature,
lighting, vibrations, etc.). Since it is a physical and tangible system, this methodology hopes to be more intuitive; easier to comprehend and apply. Furthermore, no
mechanical means of separation has been used on the nanoscale.
1.5.3
Challenges of MPF
Even though the methodology is simple, this method has many challenges. First,
the contact surfaces of the plates need a "flatness" less than 0.5 nanometers for this
project to be applicable across the desired range. Secondly, the plates must be aligned
"perfectly" so that only the desired particles pass through the gap. In addition, on
a nano-scale, small temperature gradients may affect the reliability of the plates'
gap (i.e., a temperature change of less than one Fahrenheit may affect the system.).
Another factor to consider is pressure. For such a small orifice, a large pressure may
be required to drive and/or suck the particles through the gap. The system will
have to be designed properly to withstand the pressure distributed through its entire
system. Even excluding everything else, particle behavior under high pressures and at
the interface will be unknown. Since the plates cannot be attached to the actuators,
it will be necessary to design some means of distributng and possibly amplifying the
displacement. The design step for moving the plates is critical for proper resolutions
and stability.
20
1.6
Thesis Outline
In design alternatives, two concepts are investigated for application in this project.
Also, this section involves the structural design and experimental process for filtration.
The experimental setup section covers means of sensing, actuation, and control. Then,
the experimental results sections uses all the information from the previous section to
test the methodology of filtration for this project. Conclusions and recommendations
are given to give a summary of the project and to discuss recommendations for future
research using this concept.
21
8r*~e
________________________
I
S-ot 10 be IQ-iof d
I
A
I
AAnd
C
A
t
A
I,
I
I
A
I,
A
00
-
-
-I
I
I
I
N-Z -6-
I
a
I
I
I
I
I
&an
De-lonied Sot
Figure 1-1: Electrodialysis process [9]
REVERSE
OSMOSiS
OSMOTIC
EQUILIBRIUM
NORMAL
OSMOSIS
P
OSMOTIC
PRESSURE
FRESH
WATER
SALINE
WATER
SEMIPERMEABLE MEMBRANE
Figure 1-2: Reverse osmosis process [20]
22
Iw
-Is
_____
D1frnntlta
migration
--
A
Mobil.
phase (Mn)
C
As
Stationary
phase Cs'
Figure 1-3: High pressure liquid chromatography process [19]
U
S
Electroosmotic flow ueo
0
0
0C
-Sj' 0Sl-+S 0
0
p
0
[22
30808
Figure 1-4: Capillary electrophoresis process [22]
23
Wl''
I
eW
Figure 1-5: Plates filtering solution (orange and green are large particles, respectively.)
24
Chapter 2
Design Alternatives
2.1
Introduction
This chapter will look at two approaches for filtrating biological solutions.
One
method transmits displacements through a flexure element while another uses a flexible element. While both have similarities, they have their own advantages and disadvantages. At the end of this chapter, one of the methods will be selected as the
optimal filtration design. In addition, a fluid mechanic analysis will be performed to
see if sufficient flow can be obtained with feasible parameters for the design.
2.2
2.2.1
Dual Flexure Design
Material Selection
A dual flexure design was designed for this project. Ramco Machine Inc. used the
ProE drawings for this project and machined a flexure from Al 7079-T6 (Figure 21 and Figure 2-2).
Aluminum was chosen because it is a relatively inexpensive,
malleable, and flexible metal. It had to be malleable enough to be machined easily
and flexible enough to transmits displacements through the structure. Al 7079-T6
was chosen instead of Al 6061-T6, because the selected material is not as dense and
stiff. With a lower modulus of elasticity, the design is more flexible for the desired
25
application but still stiff enough to resist external disturbances (i.e., small vibrations
and noise).
2.2.2
Flexure Descriptions
In order to change the gap width of the plates, flexure F is used to transmit the
displacement from piezoactuator B. In case of a misalignment of the plates during
assembly, piezoactuator A transmits motion through the flexure E in order to align
the plates together by creating a yaw motion. The fixed plate is curved 2 degrees
because this design eliminates the need for the plates to close "perfectly" face-to-face,
making this a 2-dimensional motion control issue instead of a 3-dimensional case.
2.2.3
Flexure Design Process
The first step in designing was to study different types of flexure elements (i.e., cantilevers, small pivotal designs, etc.). Initially, the maximum force from the piezoactuator, 500 Newtons, was divided by the maximum range of travel, 0.5 microns, to get a
spring constant of 1E+9 N/m. Then, a ProE model was created and this number was
implemented into that system and applied to many possible designs. For completion,
a simulation in ProMechancia was run on the model to see if the range of travel was
accomplished. The tolerances for this system are ± 1E-5 m. It is very important to
get as close to these tolerances as possibly because
1. during machining, accumulating errors will occur as you make each side of a
piece,
2. alignment is a very critical issue here and you want design errors to be minimized
for optimal plate placement,
3. during assembly, accumulating errors will lead to misalignment issues.
After looking at the behavior of various flexure elements, a specific type had to
be chosen. For this project, a notch hinge leaf type flexure was desirable because
of its popularity in the field of flexure elements; more information cited about this
26
flexure element [23]. A circular hinge geometry was selected to make machining easier;
drilling two holes close to each other to form a small pivotal area or flexure element.
Figure 2-3 shows the three different elliptic geomeotry types for notch hinges: a)
circular, b) elliptic, and c) leaf. In designing notch type flexures, the angular stiffness
can be derived from ([23])
(2.1)
Kz = M
Oz
and
2
2*E*b*t/
Mz
M
* E 2**bax5
*(
9*7r
Oz
where Mz is the bending moment,
6
2 .2 )
is the angular deflection about the neutral
z-axis, E is the elastic modulus, b is hinge depth, and a, is half the hinge length.
The true stress at can simply be found with from the stress concentration factor
Kt, the previous information, and the hinge thickness t to be ([23])
=
K
=
6 * Kt * M(
bb ** t2
(1 +
(2.3)
(2.4)
0)9/20
and
t
(2.5)
2 * ax
The angular deflection at the hinge can be derived from the translation necessary
for the desired gap width. From this information, you can calculate the stress on the
flexure element to see if the material will yield. The hinge stress
E *Oz * (1+
ah
9/20)
is
([23])
(2.6)
f * #2
where
f is a dimensionless compliance factor.
Instead of solving for the compliance
factor and the hinge stress, from the ay and Kt equations, t is ([23])
y=9 * a, * (7r * ay *
*(4* E*Kt)2
27
oz)2(27
(2.7)
Substituting the maximum angular deflection
Omax
for 0 and the yield stress ay in
for o-, the maximum stiffness is ([23])
K
Kz,max
The numbers from Tables 2.3,
b * a2 * E4 * Y)5
(19 * ir 4 * Kt * z) 5
(2.8)
2.4, and 2.5 were used to make sure that the
dimensions of the flexures were obtainable for our experiment.
2.3
Tubular Filtration
In this section, we will look at the design that utilizes a flexible element. With this
design, we wanted to eliminate the sealant issues associated with the last design. So
instead of the piezoelectric actuators directly distributing displacement through connected parts to the plates, the displacement is indirectly distributed through neighboring, non-connected, parts. Furthermore, any misalignment issues should be eliminated, hopefully, making this simplier than the 2-DOF criteria in the flexure design.
2.3.1
Material Selection
Silicone and polypropylene tubing was selected for the main housing due to its flexibility, biologically/chemically inert characteristics, waterproof nature, and low cost.
2.3.2
Tubular Description
Here is the assembly design for this project in Figure 2-4. In this method, the cross
sectional area of a tubing will be changed in order to create some filtering points.
2.3.3
Tube Filtration Process
This process simply filters the solution inside of a flexible tubing. An aqueous solution
will enter the tubing and be filtered at a desired, internal location due to the change
in cross sectional area. Since the tubing surface is not flat enough to filter small
particles, some "filtering" pieces will be inside the tubing. A sealant will be used
28
to eliminate all external and internal leaks. As mentioned before, it will have to be
highly flexible for displacemnt transmission form the actuators. The filtering parts
will be sealed inside the tubing in a closed position. When actuation is applied to one
side of the tubing's outer surface, this will cause the plates to move apart. Sensors
will be placed parallel to a metal plate attached to the moving walls of interest, so
that the gap width can be determined.
2.4
Implementation/Sealing of Fused-Silica Quartz
Plates
2.4.1
Major Issues
Both methods mentioned before will require filtering pieces to separate the particles.
Fused silica quarz plates were chosen for the filtering parts. They're chemically and
biologically inert to aqueous solutions and they can be optically-polished to a very
fine flatness of 2-3nm. Due to the flatness limit, the resolution of this project raised
from 0.5 to 10 nanometers. Implementation and sealing of the fused-silica quartz
plates is probably the most critical portion of this project. The two fused silicaquartz plates (5mm x 12.5mm x 5mm) were implemented into the design last. A
fixture for the plates had to hold them with no slippage or the filter resolution would
be unreliable. Moreover, the contact between the fixture and the plates cannot have
high stress concentrations, because the plates are very brittle due to their glass-like
nature. Furthermore, a sealant is needed to come into contact with the fixture, plates,
and surrounding regions to make sure there is no leakage. The applied sealant has to
be elastic enough for the plates to move in any desired direction and return to their
initial positions when there is no displacement applied.
2.4.2
Sealant Test
In order to make sure that the sealant's bond to all moveable parts is really elastic,
a stress versus strain test can be conducted (or load versus displacement). A voltage
29
would be applied to the piezoelectric actuators which would cause them to apply a
displacement or load through the system. Then, the plates would move a certain
distance and the analog outputs of the capacitance probes could be converted into
a displacement. By varying the input voltage to a maximum value then lowering it
back to zero, the output readings are converted into displacements and plotted. If
the sealant is "truly" elastic, the results should look like Figure 2-5. Actually, the
results will probably look like Figure 2-6. This test will be performed in the Results
section.
2.4.3
Fixture Design
Aquarium silicone was selected for the sealant.
It is very elastic, waterproof and
biologically/chemically inert. The solution seals water tanks, comes into contact
with fresh and salt water, and does not bother the bio-environment of the aquarium
(i.e., fish are alive and unaffected). Here is the assembly design for this project in
Figure 2-7.
2.5
2.5.1
Fluid Delivery System
Reynolds Number
When studying fluidic systems, the type of flow has to be known. Before calculations
are made, some assumptions must be stated [12]:
1. Steady flow
2. Incompressible flow
3. Flow along a streamline
4. No friction
5. Uniform velocity in regions before and after filtration
6. No streamline curvature at entrance regions, so pressure is uniform
30
To describe the behavior, one calculates the Reynolds Number, Re [12].
Re=
V*D
p*V*D
(2.9)
V
P
_Q
(2.10)
V = A
4*b*h
D = 4*bh(2.11)
2(b+h)
and
L-_0.06*p*V*D
D
(2.12)
A
where p is the density, V is the flow velocity, D is the equivalent diameter for a
rectangular orifice, b is the average gap width, h contact length of plates, A is the
absolute viscosity, v is the kinematic viscosity,
Q is
the volume flow rate, L is the
entrance length of the tube and A is surface area. If Re is less than 3000, flow is
considered laminar. Turbulent flow occurs when Re is greater than 3000. Then Re,t
is used [12].
4*Q
Re,
(2.13)
Table 2.8 shows the Reynolds Number results. The results show that a laminar
flow is possible with feasible dimensions. NOTE: All calculations are based upon the
minimum flow rate required of Q = 1.67E-11 1 S (equivalent to 1 mL per minute).
2.5.2
Inlet Pressure Calculations
P1 -P 2 is the pressure needed to drive the fluid through the plates. It can be found by
using [12]
Patm- P, = p * g * (hi- h 2 )
(2.14)
where Patm is the atmospheric pressure coming from the top of the tank, P is the
pressure before the plates, p is the pressure of the medium, g is the acceleration due
to gravity, and hi - h2 is the change in elevation from the regions before and after the
31
(assuming it is water), g = 9.81 m, and
plates. With Patm = 101.3 kPa, p = 1000 1
h, - h2= 15 mm (approximately equal to the plate height plus a few millimeters),
P = 101.15 kPa.
2.5.3
Outlet Pressure Calculations
In order to find P2 , a relationship has to be stated between P and P2 . This part
is where the use of fluid mechanics in an orifice becomes useful. Using Bernoulli's
equation [12],
Pi
--
P1
+
V12
2
2
+ g1h1 = constant =
P2
--
+
V22
P2
2
+ g2 h 2
(2.15)
where P is a pressure, p is the density, V is the fluid velocity, h is the elevation
height, and 1 and 2 refers to the inlet and outlet region, respectively, the continuity
equation [12],
V1A 1
V2 A 2
(2.16)
m = p* V * A
(2.17)
=
and the mass flow rate equation [12]
the theoretical mass flow rate is [12]
rnht= A 2 [( 2 * p(Pi - P 2 ))
thA21
=
_ (A9)2
0 5
(2.18)
A1
With this equation, P2 and, evidently, P - P2 , the change in pressure equal to
the pump's induced pressure, was calculated.
Now the theoretical flow rate has to be compared with the actual. The calculated
pressures will be used to do a reverse calculation with a different equation for flow
rate. Using the discharge coefficient C [12],
C = actualmassflowrate/theoreticalmassflowrate
32
(2.19)
the actual mass flow rate is [12]
(2.20)
mhac =CAt[ (2p(Pi
[1-B- P 2]))0.
[1 - B34]
2.0
where At and Dt, the surface area and diameter at the plates, are equal to A 2 and
D 2 when Dt is a very small compared to D 1 . C is obtained from [11] or by using the
discharge coefficient equation for Re greater than 4000 [12]
C = Cinf +
b(2.21)
ReDi * n
where Cinf is the coefficient discharge at an infinite Reynolds number, Rei is the
Reynolds number at D 1 , and b and n are scaling constants. A more general equation
for coefficient discharge is [12]
C = 0.5959 + 0.0312B2. 1 - 0.184B 8 + 91.71B 2 5
(2.22)
(ReD1 )0.75
and
B---
D
(2.23)
This discharge can be used to find and check the flow rates for the system. Listed
in Table 2.9 are the results. NOTE: Before using any of the equations, the Reynolds
number must be calculated because most of these equations are flow-dependent (laminar versus turbulent).
2.6
Summary
From this chapter, the tubular filtration design was chosen over the dual-flexure
design. Spacing and sealant issues were more of a concern with the latter. The tubular
method minimized the amount of sealant needed, provided more sufficient space for
assembly, minimized the alignment issue and displacement distribution issues through
the materials. In addition from the fluid analysis, the actual and theoretical flow
33
rates differed but, feasible parameters are possible within the system. To compensate
for this possible error, two variables pumps would be used in conjunction for this
project. One would assist in pushing the fluid through the plates while the second
would provide additional suction at the orifice.
34
Table 2.1: Parts list A
Name
A
B
C
D
E
F
Variable
Top Piezoactuators
Bottom Piezoactuators
Master Sensor
Slave Sensor
Top Flexure
Bottom Flexure
Figure Location
2-1
2-1
2-2
2-2
2-1
2-1
Table 2.2: Aluminum comparison
Al Types
Al 6061-T6
Al 7079-T6
Density(kg/m 3 )
2700
2740
Elastic Modulus(Pa)
7.31E+10
7.142E+10
Poisson Ratio
0.33
0.33
Table 2.3: Flexure design results A
Variable
M,
Oz
Kz
Units
radians
N
GPa
Value
1335.056
1.5281
873.6577
b
E
m
71.42
m
5.02158E-2
Table 2.4: Flexure design results B
Variable
Units
Values
t
ax
Kt
m
2.032E-3
m
2.921E-3
O-t
GPa
1
M
1.1438
44.19
3.4783E-1
Table 2.5: Flexure design results C
Variable
Units
Values
ixh
f
Og
ty
Kz,max
GPa
N/A
N/A
N/A
GPa
71.143
m
34.47E16
N*m
ras
35
2.2045E+3
Table 2.6: Parts list B for filter tube
Name
G
H
I
J
K
Variable
Tube Housing
Sealant Region
Silica Plates
Tube Claw
Sensor Contact
Table 2.7: Parts list C for MPF
Name
L
M
N
0
P
Variable
Tube Housing
Piezo-Holder
Sensor-Holder
Tube Claw
Sensor Contact
Table 2.8: Reynolds number results
P(f )
1000
D (n)
D(m)
5.1E-7
A(m 2 )
2.04E-13
V( )
6.55E-3
b(m)
h(m)
255E-9
12E-3
N*s
V(2
Q( )
p
)
vf)
1E-3
1E-6
Re
Re,t
3.34E-3
N/A
n
1.67E-11
L(m)
1.02E-10
Table 2.9: Pressure results
9.81
rth~f
1.67E-11
B
2.68E-5
h-h 2 (m)
15E-3
Patm(Pa)
101.3E+3
A,1(M2)
2.85E-4
C
0.5959
P2 (Pa)
101.15E+3
rmac(m)
7.12E-21
36
P,(Pa)
101.15E+3
D1 (m)
0.01905
N/A
N/A
Table 2.10: Fluid definitions
Units
N/A
p
V
Definition
Reynolds number
Fluid density
Fluid velocity
Q
Volume flow rate
A
D
p
v
b
h
L
Re,t
hrh2
Surface area
Orifice diameter
Absolute viscosity
Kinematic viscosity
Average gap width
Plate contact length
Entrance length
Turbulent Reynolds number
Atmospheric pressure
Pre-plate pressure
Post-plate pressure
acceleration due to gravity
Change in elevation height above and below plates
Th
Mass flow rate
nht
D_
A1
Di
Theoretical mass flow rate
Actual mass flow rate
Surface area at Plates
Diameter at Plates
Surface area at Plates
Diameter at Plates
C
C
Cinf
n
ReDi
Variable
Re
Patm
P1
P2
g
mac
At
M
Values
3.34E-3
1000
6.55E-3
:
1.67E-11
m2
m
2.04E-13
5.1E-7
1E-3
1E-6
2.55E-7
1.2E-3
1.02E-10
N/A
101.3
101.15
101.15
9.81
15E-3
y
N/A
m
S
m
m
m
N/A
kPa
kPa
kPa
1.67E-11
m2
m
m2
7.12E-21
N/A
N/A
m
2.85E-4
1.905E-2
Discharge coefficient
N/A
05959
Discharge coefficient
Discharge coefficient at Large Re
N/A
N/A
05959
N/A
Scaling constant
Reynolds number at D 1
N/A
N/A
N/A
N/A
37
Figure 2-1: Side view of dual flexure design
Figure 2-2: Top view of dual flexure design
38
a)
b)
(half
c)
widt)
(Lpth)
r
14
0
Y,
61 '
14
Z~
Figure 2-3: Different types of notch hinges: a) circular, b) elliptic, and c) leaf[23]
F u.
2 using
Silica
0
Pla
s I
or
t
Tubae Claw ,J
Figure 2-4: Filter tube design
39
Sa
an*
Sion
B
(77
--
--
M
6
Figure 2-5: Stress versus strain plot of an elastic material [4]
r P
A
/
r
F,
/)0
Figure 2-6: Hysteresis plot [3]
40
Sensor-Holder
N
D(
Trub
C
Plezo-Holder M
Figure 2-7: MPF final filtration design
41
42
Chapter 3
Experimental Setup
3.1
Introduction
Now that the design and calculations are done for the filtration process, the controller
must be implemented in order for the system to be programmable. This step will
involve implementing a sensing and actuation element to make the system a closedloop system. Due to the interest of time and the ongoing design process on the Tube
Filtration method, the dual-flexure was used to check the functionality of the sensors
and actuators and for familiarization in designing a controller. All Tube Filtration
information pertaining to the sensors and probes will be mentioned in the Results and
Conclusion section. Therefore this entire chapter is geared towards implementation
of the dual-flexure for analysis and observation purposes.
3.2
Experimenting with the Probes and Piezoactuators
3.2.1
Capacitance Probes
To obtain the gap width, capacitance sensors were implemented. Capacitance sensors
depend on the equations for "the ratio of charge to potential difference" and "potential
difference between two plates" [26]. These equations are listed below, respectively
43
[26].
C= -
(3.1)
V =Q*d
(3.2)
V
and
eo * A
So
eo * A * V2
C
(33)
where C is the capacitance, Q is charge magnitude, V is voltage between the
plates, d is the gap width, A is plate surface area, and e, is a universal constant.
The 3800 Model OEM Gaging system was ordered for this project. Its maximum
bandwidth is five kHz but this setting was lowered to 100Hz so high frequency noise
would not interfere with the system. The 2805-1 probes were ordered for measurements. Their range was
+/-
50 microns (or 100 microns). After proper calibration,
the range of the probes corresponds to +/- 10 Vdc from the analog output. Figure 3-1
shows the Digital Picture of Probe.
If calibrated correctly, -10 V (or +10 V) is the near standoff distance, zero V is
the nominal standoff distance, and +10 V (or -10 V) is the far standoff distance. So,
as the gap width goes from 0.5 microns to 0.5 nanometers, the analog output should
become more negative. If the calibration is correct, then the calibration factor is
±50pm
±l0Vdc
_
100pum
20Vdc
_
5pum
Vdc
(34)
Therefore, 0.5 nanometers should be achieved at 0.1 mVdc.
This system has two capacitance probes which are used differently for the two
different designs. Using the dual flexure design shown in Figure 2-1, if the sensors'
analog outputs are not equal, then the two edges of the flexure and plates are not
parallel. So, the sensors are used to check if the plates are parallel. Then, the yaw
for alignment can be controlled by looking at the analog outputs. Secondly, the gap
width can be determined by using the calibration factor. From the analog output, the
44
gap width can be determined and varied. With the Tube Filtration method, the two
plates will be moved from a closed position. So the absolute change in output from
both probes will give a value that correlates to the gap width using the calibration
factor.
In calibrating the probes, a micrometer incorporated in a stage was used to move
the sensors. Figure 3-2 shows the Stage, Micrometer, Mounting Piece and Intermediate Piece.
3.2.2
Piezoactuators
In choosing a means of actuation, the two choices were between a voice coil and a
piezoactuator. A voice coil was not selected because they have too much vibration
and electrical noise. Figure 3-3 shows the voice coil in speaker.
Due to vibrations, a voice coil would have to be slightly modified for this application. Usually, the permanent magnet is fixed to the housing while the voice coil's
core is allowed to move in the vertical direction. In this application, the core would
need to be fixed and the magnet would be free to move vertically. The magnet's
heavy weight would aid in vibration reduction. Since a piezoactuator would require
no modifications, this means of actuation is more desirable.
A PZT 150/4/20 VS09 and 150/5/20 VS1O stack piezoactuators were chosen for
this application. They both had a 20-micron stroke, a maximum input voltage of
+150 Vdc and a mechanical compressive load of 50ON-1000N, depending on which
actuator is used. See Table D.3 for all primary specifications. The actuators were
powered by a triple channel amplifier with an input and output voltage range of -1 to
+5
Vdc and -30 to +150 Vdc, respectively. From the maximum distance and voltage
input, the resolution is
2O"'
+150V
or
= 1.33E-lm
V
nanometers, is obtained at 3.75 mVdc.
45
133.33nm
+lvdc
So the desired resolution, 0.5
3.2.3
System's Resolution, Range, and Noise
After calibration, the linearity of the probes was checked by varying the frequency of
a frequency generator and reading the outputs from the probes. The input signal was
fed into the piezoactuator B from Figure 2-1. Table 3.1 shows the sensor outputs
at various frequencies, but Figure 3-5 shows the data on a plot. From this plot, the
information looks "linear" and reliable over a small voltage range, 15 Vdc.
Now that the piezoactuators' and capacitance probes' functions have been checked
and both are ready to be implemented in either design, now one must check to see
if the desired resolution and range of the system are obtainable. In addition, noise
in the system must be checked to see if it is negligible. In order for the noise to be
negligible, the peak-to-peak voltage reading from analog outputs of the probes must
be less than 0.1 mVdc. The manufacturers use a voltmeter and measure the output
voltage Vac for noise. From the purchased merchandise, when the two electronics are
coupled, a t 1 mVac, equivalent to a 10 nanometer error. Then, the peak-to-peak
Vdc was plotted from an oscilloscope. ± 2 mVac was the input noise from the power
source in the breadboard. Figure C-1 shows the noise plot for sensor output.
In the following analysis, the data is differentiated from outputs produced by
piezoactuators A and B from Figure 2-1, which corresponds to the top and bottom,
respectively, and outputs from the master and slave probes, C and D, respectively,
shown in Figure
2-2. The master probe is connected to the power source, while
the slave gets its power from the master. In addition, the slave's electronics had to
synchronized to the master's.
As shown in Figure
C-1, a peak-to-peak noise of 2 mVdc, equivalent to a 10
nanometer error, came from both probes. The master probe was closer to the parellel
plate at -0.892 Vdc, while the slave was at 0.852 Vdc. These voltage readings were
the initial location of the probes. There was no motion involved in this test. Since,
a peak-to-peak noise of 2 mVdc is equivalent to
+/-1
Vdc, the voltmeter and the
oscilloscope gave the same error. The noise found in the system is probably from the
power source but that needs to be tested.
46
To test the sensor output at full range it was time to incorporate the piezoactuators. First, the output noise of the amplifier was tested with a power supply at a
13.618 Vdc setting. The peak-to-peak noise from the supply was 60 mV (0.15 pm
error). Then, the peak-to-peak amplifier noise was taken up to the maximum input
for the oscilloscope, 100 Vdc. Table 3.2 shows the results of this test for amplifier
noise versus its output. The behavior of the noise is a "stepping-average" where, as
the output increases, its noise is relatively-constant over a certain range of values
until it reaches a maximum. So the noise does not change linearly.
The next series of tests involved inputting a variety of voltages and checking the
probes' analog outputs and the corresponding noise. Each tables' data is from a
different piezoactuator, but both sensors are used in each. Table 3.3 and Table 3.4
shows the sensor outputs and noise versus amplifier voltage output.
As expected, the noise increased with the output voltage. This observation proves
that the amplifier affects the amount of noise in the sensors. Even though the noise
will affect the resolution, the sensors are working fine. To find the resolution and
filter the noise, a test will have to be done in Matlab with the controller to fine tune
the voltage output. Some noise-filtering methods will be needed in eliminating the
noise (i.e., better low-pas filter, shorter cables, minimizing external noise, etc.). The
amplifier's output is too large to output a small enough voltage to get even close to
10 nanometers. Figures C-2 through C-11 show the sensor output with different
inputs to the piezoactuators A and B.
3.3
3.3.1
DSPACE Controller Design
Characterization of System
A dynamic analyzer was used to characterize entire open loop system, which included
the flexures, the piezoactuators, the capacitance probes and the sensor electronics.
Characterization is a very useful method, because an "unlumped" system can be
viewed as a "lumped" system; meaning the overall components of a system are viewed
47
as one system. Figures 3-6 and 3-7 show samples of a simulink model of an open
loop "unlumped" and "lumped" system.
The dynamic analyzer inputs a sinusoidal signal into the system through the
piezoactuators and the data from the capacitance probes' analog outputs will be
converted into a bode diagram.
Using control knowledge from [10], the transfer
function for the lumped system can be calculated.
3.3.2
Dynamic Characteristics
Two controllers will be needed to control the translation motion for closing the plates,
and to control the yaw motion for aligning the plates. The dynamic analyzer will
input a sinusoidal wave into piezoactuators A and B shown in Figure 2-1, separately
and independently. In addition, data will be collected from sensors C and D shown in
Figure 2-2, separately and independently. This process is shown in Figure 3-6. From
all these components, four sets of bode plots can be found to ultimately create two
controllers, one for opening and closing the plates and the other for turning the plates.
Listed below are the combinations of parts that will be used in this experiment:
1. Piezoactuator B, flexure F, and sensor C (Figures 2-1 and 2-2),
2. Piezoactuator B, flexure F, and snesor D (Figures 2-1 and 2-2),
3. Piezoactuator A, flexure E, and sensor C (Figures 2-1 and 2-2) and
4. Piezoactuator A, flexure E, and sensor D (Figures 2-1 and 2-2).
Using the data collected from the dynamic analyzer and Excel, the bode diagrams
were found by plotting the magnitudes and phase from the digital analyzer versus
the frequency. Each bode diagram has a corresponding slope plot which was part of
the process of approximating of Bode plots. Figures C-12, C-13, C-14, C-15, 3-8,
3-9, 3-10, 3-11, 3-12, 3-13, 3-14, 3-15,
C-16, C-17, C-18, and C-19 show the
Bode plots and their corresponding slope plots.
The slope equations were used to calculate how much the data dropped in decibels
per decade. Using the equations and conversion tools from Figure 3-17, the transfer
48
functions were found. A transfer function of Parts A, E and C from Figure 2-1 was
chosen over a lumped system of Parts A, E and D, because a clearer was signal was
obtained from the former results. Since both were the same system with opposite
readings for the sensors, there was no need to make two transfer functions. With
Part B, there should be no difference in readings from Parts C or D, because they
are next to each other. Figure 2-2 shows how when Part B is closing the gap, both
sensors should be reading the same displacement. When Part A is turning the plates,
one sensor will read the flexure getting closer while the other is reading an increasing
displacement.
Figure 3-17 showed how to calculate a transfer function from the bode diagrams
using straigh line approximation. With these figures, the cutoff frequencies, w1, was
estimated to be 500 rad. This value was found by making a trendline in Excel for the
latter values. Then by setting the independent variable (magnitude) equal to zero in
the trendline, the dependent variable (frequency) is found. Using the trendline, data,
interpolation and Figure 3-17, the magnitudes were approximated to be dropping
-40 decibels (dB) over every a decade (dC). This observation meant that two poles
existed for every
-IdB.
So the general transfer function, G(s), was a multiplication
of the "gain times the multiple pole functions" or [10]
G(s)
K * -N
D
k
(3.5)
K = 10 T
(3.6)
N = 1
(3.7)
and
D = (1 +
49
W1
Y(3.8)
)s
where k is the value on the bode plot when the slope of the magnitude is zero,
K is the DC gain, p is the number of poles, and s is the LaPlace Transform complex
variable. The transfer functions correspond to a sinusoidal input from the analyzer
and an analog output from the sensors. During application, the input will be a DC
voltage input to the piezoactuators. Including the higher order responses, the transfer
functions were
G
~7.08E - 1(39
topS) = 1.6E - u1s 4 + 3.2E - 8s 3 + 2.4E - 5S2+
8E - Is +
and
Gbottom (S) =+8
3.2E - 14s
3.3.3
5
8.91E
.1
JS
-
2
+8E- 11s 4 +8E - 8s 3 + 4E - 5s 2 +1E - 2s + 1
(3.10)
Designing Controller
The next step involved designing the controller, Gc(s), for the top and bottom figure
and making a closed-loop system (Figure 3-16).
A Proportional-Integral-Derivative (PID) controller was selected for this application where [10],
Gc(s)
K, + K + Kds
s
(3.11)
or
G,(s)
= KdS2
+ K~s + K
(3.12)
where Kp, Ki, and Kd are the proportional, integral, and derivative gain coefficients. Then, using general control theory knowledge [10]
Gc(s) * G(s)
1 + Gc(s) * G(s)
and values for the system and control transfer functions, the top and bottom
closed loop transfer functions were found to be
50
T"(s)
[At * (Kps 2 + Kis + Kd)]
(B * S5 + Ct * S4 + Dt * S3 + (Et + Ft * Kd)s 2 + (1 + Gt * Kp)s + Ht * Kj)
(3.14)
where At= 7.08E-1, Bt = 1.6E-11, Ct = 3.2E-8, Dt = 2.4E-5, Et = 8E-1, Ft
=
7.08E-1, G = 7.08E-1, and Ht = 7.08E-1 and
Tbottom (S)
=-
(B
* S6
+ C1 * S5 + Dt *
[At * (Kps 2 + Kis + Kd)]
S4 + Et * S3 + (Ft + Gt)s 2 + (1 + Ht * Kd)s + It * Ki)
(3.15)
where At = 8.91E-2, Bt = 3.2E-14, Ct = 8E-11, Dt = 8E-8, Et = 4E-5, Ft = 1E-2,
Gt = 8.91E-2, Ht = 8.91E-2, and It = 8.91E-2.
Even though the transfer function for the entire feedback system is found, the gain
coefficients, Kp, Ki, and Kd, are still unknown. The optimal gain coefficients can be
found using the characteristic equations based on the "integral of time multiplied
by absolute error"(ITAE) criterion for a step input found in Figure 3-18.
ITAE
minimizes large initial errors and steady-state errors. Matching the characteristic
equations in Figure 3-18 with the closed loop transfer functions of the same order,
values for the coefficients were found.
When it was possible to get two values for a coefficient, the average of the two
were used. Kp,top, Ki,top, Kd,top, Kp,bottom, Ki,bottom, and Kd,bottom were found to be
10.77, 2260.88, 1.94E-1, 137.32, 23947.2, and 3.28E-1, respectively. So, by using the
ITAE criterion for characteristic equations and averaging multiple values from ITAE,
the optimal PID controller was calculated to be
2
Gecs)
G,(s) == 1.94E - Is + 10.77s + 2260.88
(3.16)
3.6
and
3.28E - is 2 + 137.32s + 23947.2
Gc(s) = M
(3.17)
Using a Matlab tool rltool, the root locus was found for the top and bottom closed
51
loop system. Using this tool, you can find the ideal gain for the system for the best
stability. For the top and bottom, the ideal gain was found to be 9.64E-4 and 1.24E3, respectively. Figures 3-19 and 3-20 shows the Root Locus of Top and Bottom
System.
3.3.4
DSPACE Control
DSPACE is a Matlab tool that allows the user to create a digital controller from
a frequency domain or z domain transfer function. With the controllers found in
previous section, the following DSPACE controller was constructed.
Figure
3-21
shows the DSPACE Controller Model.
The capacitance probes send signals to the Analog-to-Digital converters (ADC)
from their analog outputs. Signals go into the DSPACE card, shown in Figure 3-22,
and into the digital controller in the DSPACE software. A virtual control panel can
be created for operating your signal (Figure 3-23). The digital control consists of
the "gain block", which contains the gain value obtained from rlTool, and the PID
controller. Since the derivative component of the PID controller was much smaller
than the other gain values, the controller was simplied into a PI. Due to the derivative
coefficient being very small relative to the other coefficients, this deletion was not
considered to have a major effect. After the controller processes the information, the
signals leave the DSPACE card through the Digital-to-Analog converters (DAC) into
the piezoactuators.
The controller did not seem to increase the stability of the signals. The noise was
6.13 mV and 4.5 mV for the sensors C and D, respectively. These results were not
too different from the previous results from experimenting with the sensors. Further
tests need to be done for adjusting the constants and gains and seeing the response
of the system. Figure 3-24 shows the sensor output with DSPACE Controller .
52
3.4
Summary
The capacitance probes, amplifier and actuators are functioning properly. A signicant
amount of noise seems to be affecting the system (10 nanometer error from oscilloscope
and sensors and 0.15 micrometer error from the amplifier). A means of minimizing
the noise will need to be proposed or the desired resolution of the project will have
to be modified even further. For the final design, an attempt will be made to use
a new micrometer-integrated stage to check the sensors' calibrations.
The entire
range will be used in case of problems with the system beyond 0.5 micrometers.
In addition, a new analyzer test needs to be done to characterize the new system.
So far, the controller does not perform adequately in adjusting the gap width or
reducing the noise, but results were affected by the DSPACE card's location (not on
an air table). In addition, an error may have been made in calculating the transfer
functions from the bode diagram, but this step was more for familiarization with the
bode calculations. An over-approximation may have occured using the straight line
approximation method from Figure 3-17 over too large a frequency range. Since low
frequency behavior is of primary interest, high frequency responses will be neglected
in the next chapter. Plus, the DSPACE card and its computer could not be moved
at the specific time. For testing the methodology, all components will be moved to
the air table for better results.
53
Table 3.1: Sensor outputs
Freq Input(V)
1.04
2.14
3.32
4.42
7.06
8.11
8.93
10.8
12.2
14.5
Sen Output(mV)
121
272
463
663
1142
1146
1450
1684
1850
1965
Sen Output(p m)
0.0605
0.136
0.2315
0.3315
0.571
0.573
0.725
0.842
0.925
0.9825
Table 3.2: Amplifier noise outputs versus voltage output
Input
13.618
13.618
13.618
13.618
13.618
13.618
13.618
13.618
13.618
13.618
13.618
13.618
13.618
13.618
13.618
13.618
13.618
13.618
13.618
13.618
13.618
13.618
13.618
13.618
Input Noise
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
60
Amp setting
0
1
5
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
105
Offset Output(V)
232
1.1294
2.0081
5.313
10.371
15.375
20.692
25.874
30.588
35.231
40.522
45.777
50.630
55.483
60.329
65.523
70.410
75.201
80.833
85.223
90.451
95.371
100.71
105.17
54
Output Noise (mV)
13
13
15
60
130
130
190
250
250
250
500
500
500
500
500
500
500
500
500
500
500
500
500
500
Table 3.3: Sensor outputs and noise due to piezoactuator A versus amplifier voltage
output
Amp Out (Vdc)
-30
0
1
+150
Parts A and C/Noise(V)
1.1448+/-0.0058
-0.06147+/-0.00595
-1.3367+/-0.00625
-8.2671+/-0.0065
Parts A and D/Noise(V)
N/A
0.68739+/-0.00543
0.84282+/-0.0078
2.9305+/-0.0083
Table 3.4: Sensor outputs and noise due to piezoactuator B versus amplifier voltage
output
Amp Out (Vdc)
-30
0
1
+150
Parts B and C/Noise(V)
1.0761+/-0.005
-0.04756+/-0.0058
-1.2095+/-0.00565
-8.2337+/-0.00705
55
Parts B and D/Noise(V)
N/A
0.682+/-0.0166
0.87335+/-0.0078
2.8826+/-0.00815
4:
Figure 3-1: Digital picture of probe
Figure 3-2: Micrometer stage
56
Figure 3-3: Voice coil in a speaker [2]
Figure 3-4: Digital picture of piezo-amplifier
57
1.2
y = 0.0737x + 0.003
0
0
0
2
6
8
10
Generator Input (V)
12
16
14
Figure 3-5: Sensor output versus generator input (stiffness test)
24~s+
~.s+B~
Jj]
,
L
E3. 3+~s+&s+H3
EA+F2s24 2.r12
Analog: Outputl
Sine Wive Input
Moom or Top Piezoaduator Laigevo Small R~enei Ma~er or Slave Prob and Ele0ronis
Figure 3-6: Simulink model of open loop "unlumped" system
58
As 3+8~s 4Cs~D
Anaiog "OuPIut
Sinre Wave
em
FLu-mped
p
p
Figure 3-7: Simulink model of open loop "lumped" system
0
-10
A M
-20
-30
-40
-M
-50
-60 +-
-70
-80 -
I
------
--
-
-----
I---LIJ
Figure 3-8: Piezoactuator B and flexure F
59
--El
I
Frequency(rad/s)
/
nOO rad/a
sensor D magnitude bode diagram
0
PUU
I
-60
-100
-160
ill
-200
0-250
-300
-350
-400
-
Frequency(radls)
Figure 3-9: Piezoactuator B and flexure F
/
sensor D phase bode diagram
LA
-10
f
-20
i
-30
0)
-40
I.:+
-60
-70
-80
firH
H --V-------Frequency(rad/s)
Figure 3-10: Piezoactuator A and flexure E
diagram
60
/
y
=O:Ndft'd179
sensor D slope in magnitude bode
0
r
suu
-50
-100
-15n
-200
U2
I
0-250
-300
-350
-400
y
Frequency(rad/s)
Figure 3-11: Piezoactuator A and flexure E
/
=
-'045'
5.96
sensor D slope in phase bode diagram
0
FfU0
-L
-10
-r
-20
wL
-
K A~
IT
-30
-40
-50
-.......................
T I...
..... ..........
.......
..................
.....
I.....
.....
r....
.......
-60
-70
Frequency (rad/s)
Figure 3-12: Piezoactuator A and flexure E
61
/
500 rad/s
sensor C magnitude bode diagram
0
inn
41-
-50
-100
150
-200
-
%k
-250
-300
[-LJ
-35
Frequency (radls)
Figure 3-13: Piezoactuator A and flexure E/ sensor C phase bode diagram
0
I
LL
I
I
I 1
1
100
-10
-20
-30
If
-40
A
I
-50
-60
-70
F r111111y
I
sI
Freq uency(radls)
Figure 3-14: Piezoactuator A and flexure E
diagram
62
/
.y....
Y -0.01
13.412
sensor C slope in magnitude bode
0
6;w
-50
-100
-150
4)
0..-250-
-300
-350
-400
I I I
.1
I yLI
isI
Frequency(radls)
Figure 3-15: Piezoactuator A and flexure E
/
y
....
......
sensor C slope in phase bode diagram
Sine WaveI
C s+G
Controller
s+1
Gain
XY Graph
System
Figure 3-16: Simulink model of a closed loop system
63
1. Gain,
G(jw)
Phase, 4(w)
Magnitude 20 log GI
Term
K
40
904
201
45&
0
0'
dB
-0
2. Zero,
40
90
201
45
0
dB
4x
---
-20 1
4
40
90
3.Pole
-
49T
------
4
G(Aj )
-01
(I + job)
4---
--
.(..
- w4
2-01
0(.1w,
4.Pole at the origin
1/jo
G(jw)
-
00
0
dB
-
l0o,
1
-
010
0)
0w
1
10
100
10
100
90,
4
4.
d)
0
dB
0.01
-
0"
940 - ---
0A
100
10
001
.
....
0.1
18
40
80
5. Two complex poles
0.1 < < 1. G(jw)=
(1 + i24u -u2)
20
dB
0
&(W)
00
20
90,*
40
0.01
18_
0.1
1
10
U
100
0.01
-
0.1
1
U
Figure 3-17: Asymptotic curves for basic terms of a transfer function [10]
64
S+(
s3.5~ 2 +215os+(
s4& +27is+ W4
s4±2.1gs +W
S6
4
s28~ S
J~)S3+5s+34S + O
5+ A6WS+86Oos + AS., +3.95(ons +(On
325L)s
Figure 3-18: The optimum coefficients based on the ITAE criterion for a step input
[10]
400 -
200-
<
0
/
-
- - - - - --..........
-............... - + - - -----
---------- --- -- - -- - ------
-200 -
-400-
-600-
-8001
-1500
-1000
-500
Real Axis
Figure 3-19: Root locus of top system
65
0
2000
1000 -
07
-1000-
-2000-
-3000
-3000
-2500
-2000
-1500
-1000
-500
Real Axis
0
500
1000
1500
2000
Figure 3-20: Root locus of bottom system
Ba d Unk
L -
-
SII
-
DS1103MUX.A.CCON1
Top3
C
Top Confol
DS113AC C
Top Constant
137.3s+230000
DS1103MUX.ADC-CON2
Bottom Gain
Bottomn
DS1103DACC2
Controi
Bottom Constant
Figure 3-21: DSPACE controller model
66
Figure 3-22: DSPACE card
Figure 3-23: DSPACE panel
67
Figure 3-24: Sensor output with DSPACE controller
68
Chapter 4
Experimental Results
4.1
Introduction
This chapter is partitioned into three sections. The first section will involve testing the
flow rate of water through the partially closed plates. The mock plates are "partiallyclosed", because they do not have a good resolution of flatness. In the second section,
the system will be tested to see if the proper displacement are being distributed and
detected through the system. Plus, the elasticity of the sealant can be viewed from
the results. In the last section, the filtration test will see what range of particles can
be separated.
4.2
Flow Test
This test involved seeing if water could flow properly throughout the system. Peristaltic pumps were used for this process because of their unique pumping feature.
The pump contracts and expands the tubing that runs through it. This contraction
and expansion creates a suction by increasing and decreasing the inner cross sectional
area. By the fluid staying in the tube and not contacting any portion of the pump,
this method is contaminant-free.
A VWRbrand medium-flow, peristaltic pump was used to draw the solution from
its container to the filter. This pump's bidirectional flow rate ranged from 4 to 85
69
. Using some tube reducers and tubing, the filtration chamber was built (Figure
??). The components are described in Table 4.1. To reduce the risk of bottlenecking
mn
and clogging at the filter, another pump with a much larger flow rate was placed after
the filter. A Barnant E-Seires peristaltic pump was used to suck the solution through
the filter and into a container. Its flow rate was 375 1.
min
For the flow test, the actual filter plates were not used. Plexiglass plates were
being tested instead of the fused silica quartz. The results of this test was sufficient
flow throughout the system. A 0.6" buildup in water occurred after about 45 seconds
but it quickly diminished. As expected, the large flow pump eliminated the potential
clogging of the system and its flow rate dominated the process.
One observation
was that the plates were in a closed position, but fluid was still flowing between the
"mock" plates. This was not a surprise because the plates were not "perfectly" flat
at the edges. The test did show the sufficient flow through a small gap width was
possible. Instead of the minium of 1 -,
4.3
the results were approximately 50 -!.
Actuation and Sensing Test
The micrometer-stage setup seen in Figure
3-2 was not accurate enough for our
application, because the probes kept slipping in the fixture to the stage. Due to other
more pertinent issues, this test was not completed so the manufacturer's calibration
factor was used.
The next step was to verify if the sensors could detect any displacements applied
on the outer tubing by the piezoactuators. In addition, output readings will be taken
at random input voltages to test for repeatability of the system. This is the sealant
test mentioned in Chapter 2. If repeatability is good, that means that the elastic
nature of the silicone sealant, vinyl tubing, and rubber cement for the displacement
distributor is working properly. Then the data plot should resemble either Figure 2-5
(if optimal) or Figure 2-6 (more realistic). The master sensor (Part C) in Figure 2-2
was tested first. If the master test is successful, the results would also be considered
for the slave (Part D). Figure 4-2 shows the result of this test. An input of 13.54 V
70
with a peak-to-peak noise of 90 mV was driven into the amplifier by a 15 V power
source. The amplifier's output depends on its settings. The peak-to-peak noise from
the sensors ranged from 23 to 30 mV. Then the setup was reinvestigated and it was
discovered that the filter piece was slipping. That is why consistent readings were
not given. The piezo- and sensor-holders' tube claw were not sufficient for support,
so a stand with a two 3-prong clamps was used to hold the filter. Then the test was
performed again with much better results. Table C.1 shows the data. The input
voltage was increased to its maximum value then decreased back to its initial value
(0 V). Figure 4-2 shows that it resembles a hysteresis plot but its loop is not large
(top curve: increasing and bottom curve: decreasing). In addition, it returns to its
initial value. The change in voltage from the minimum to the maximum value was
0.77 V. Going by the calibration factor mention in Chapter 2, this is equivalent to
3.85 micrometers.
4.4
Filtration Test
Using a dynamic signal analyzer, the MPF Tube Filtration design was characterized
into a transfer function. Table C.10 and Table C.11 shows the data for this analysis.
From this information, bode diagrams were plotted in Figure 4-3 and Figure 4-4.
The magnitude plot started at a gain of -29 dB and dropped 40 dB over 2 dC. This
observation is equivalent to a first order equation. Since higher frequency responses
are not interest of this analysis, this assumption will be taken. Referring to Figure
3-17 and using equations from the previous chapter, the system's lumped transfer
function was
Gf(s) = Kf * (1 +
-29
(4.1)
-)
WC
where Kf equals 109 dB (gain) and w, (cutoff frequency) equals 314.16
a
r.
Using the same assumptions and general equations for the control equation, the
overall transfer was
71
Tf (s)
=
s
Kf * (Kpf * s + Kif)
(Z*Lpf +-w,) *s+Z*Kf(4.2)
Before solving the characteristic equation, the natural frequency needs to be found.
For a second-order equation, a settling time criterion of ± 2 percent is desired. Since
IT
= -
(4.3)
wc
(= 0.7
(4.4)
and for the ± 2 percent criterion
4 *T =
4(4.5)
( * Wn
the natural frequency w,, equals 314.16 Id. With this value and matching the coefficients for a second-order characteristic equations from Figure 3-18 with the coefficients in the denominator of the overall transfer function, Kpf and Kif are 3541.6844
and 2781632.45824, respectively. Now using "rltool" in Matlab, the root locus is
shown in Figure 4-5. The figure seems very stable so the controller appears to be
appropriate for this application.
The next stage involves testing the open and closed loop system to see if it the will
work in an actual experiment. A step input will be applied using a DC power supply
to apply a voltage. Looking at the settling time, steady state error, and steady state
value, the controller will be evaluated. First, a DSPACE model of the controller was
constructed in Simulink (Figure 4-6), but the open-loop case was investigated prior
to the closed-loop. Then a square wave input was applied to the open loop system
and Figures 4-7 and 4-8 show the results. Table 4.2 shows the performance of
the open loop system. The closed loop system performed much better(Figure 4-9
and Table 4.3). Since the signal settled so quickly, most of the performance values
could not be obtained and the oscilloscope could not record all the data (nanosecond
reaction).
72
After running all the mechanical and electrical test, the final step is to test the
methodology of the MPF. The test particles to be separated are of diamater sizes of
are 0.079, 0.304, 0.482, 0.093, and 1.03 microns. They came in 10 ml vials. First,
water would run through the system at 0 V to test to see if the tests are properly
closed. If this preliminary test suceeded, then the test would continue by trying to
separate a solution of 1.03 micron particles from water. Once filtrated, the voltage
reading would be recorded and the next smallest size would be tested. This process
would continue until all particle solutions are filtrated or no more could be possibly
filtrated. Table 4.4 was to show the results of the filtration test, but unfortunately,
results were not obtainable. At 0 V, water passed through the filter region when the
plates were supposed to be closed. In addition, a major leak sprang from one side of
the filter where the tubing connected with the contact plates. So this test had to be
concluded prematurely.
73
Table 4.1: Filtration tube chart
Q
Part Name
0.75" ID filter chamber
R
0.75" to 0.375" tubing reducer
S
0.375" to 0.25" tubing reducer
T
pump connector
Part Label
Table 4.2: Open loop response due to a square wave input
Initial Input(V)
2.81mV
Initial Time (s)
Steady State Value (V)
Steady State Time(V)
Max-Min(V)
0.1 percent (V)
0.1 percent (s)
0.9 percent (V)
0.9 percent(s)
Rise Time (s)
Settling Time (s)
Peak Value (V)
Peak-to-Peak Value (V)
Percent Overshoot
Os
-9.69mV
20ms
-12.5mV
1.56mV
0.005ms
-8.44mV
4.5ms
4.445ms
5.025ms
-10.25mV
23mV
5.779 per.
74
Table 4.3: Closed loop response due to a square wave input
Initial Input(V)
Initial Time (s)
Steady State Value (V)
Steady State Time(V)
Max-Min(V)
0.1 percent (V)
0.1 percent (s)
0.9 percent (V)
0.9 percent(s)
Rise Time (s)
Settling Time (s)
Peak Value (V)
Peak-to-Peak Value (V)
Percent Overshoot
5.63mV
109.2ns
5mV
142ns
-0.63mV
N/A
N/A
N/A
N/A
N/A
30ns
5mV
8mV
0 per.
Table 4.4: Filtration test
Particle Size(microns)
0.079
0.304
0.482
0.093
01.03
Input Voltage (V)
N/A
N/A
N/A
N/A
N/A
75
Master Sensor (V)
N/A
N/A
N/A
N/A
N/A
Slave Sensor (V)
N/A
N/A
N/A
N/A
N/A
S
T
Figure 4-1: Filtration tube
11.7
11.6
-
11.5
11.4
11.3
.
11.2
Increasing
Volts
w Decreasing Volts
J11.1
11
10.9
10.8
10.7
0
20
40
60
80
Ampimffer
100
120
140
160
Input(V)
Figure 4-2: Sensor output(V) versus piezoelectric output from amplifier (V)
76
LOU
U
*.0
- Vak~s (Y) AXIS Maor GrdkI
0
a'~
Frequency (Hz)
so Hz
Figure 4-3: Magnitude Bode diagram for MPF tube filtration design
i
i i
!I .
rob
a
0~
wu
FU
-1
4-
p i i
i
I1
Frequency (Hz)
Figure 4-4: Phase Bode diagram for MPF tube filtration design
77
Figure 4-5: Root locus of closed loop system 1
---
3.5416844e+003s+2.78163246824e4006
Bad nk>
-+
S
DS03ADCC17
Gain
7
Bad Link
DS1103DACCl
Controller
Sine Wave
Figure 4-6: DSPACE controller for filration experiment
78
3.00E+00
2..0
00
1.OGE
00
-
a,
+
0)
0
-6.0 QE-02
-4.OOE-02
2.OOE-02
0.001 -+00
-2.00E-02
4.OOE-02
6.00 E-02
Square Input 1
m Sensor Output
2
1.AGE an
Time(seconds)
Figure 4-7: Sensor output and square wave input for open loop
4:SOE-62-
0.
S~
-6.01
dE-02
-4.OOE-02
-2.OOE-02
0.00
4
2.OOE-02
4.OOE-02
6.00f E-02
0
C-
0
1.96E 82
co
1.50E 82
time(seconds)
Figure 4-8: Sensor output from square wave input for open loop
79
-------------
Figure 4-9: Sensor output from square wave input for closed loop
80
Chapter 5
Conclusion and Recommenations
Even though the Tube Filtration method was not actually tested, all the preliminary
steps were investigated and this method seems very possible with some modifications. First, due to the 2-3 nanometer flatness of the plates, the 0.5 nanometer gap
width had to be increased to 10 nanometers. Also, there was a 5 nanometer error
from the sensors. The sensors are supposed to be able to achieve a 0.5 nanometer
resolution. After further test on the equipment and seeing how the error increased
to 150 nanometers when the setup was completely assembled, it was concluded that
the error was due to electronic noise from the equipment. A better low-pass filter
needs to be designed for this system. All wiring needs to be secured and minimized
in length. An air-table (or any vibration-reducing table) is vital because the sensors
are very sensitive. Furthermore, external noise may play some small role in the error as well. For optimal results, this experiment should be conducted in a noise-free
environment. The controller was very effective in minimizing noise in the actual test
with the filter tube. Due to the mock test being performed on a counter (DSPACE
computer could not be moved at that time), the results were flawed. The air table
assisted tremendously the filter tube controller test. Reducing the noise from 23 mV
to 8 mV means that a ± 0.5 nanometer error exists. So the controller will enable
resolutions below 10 nanometers to be obtained.
The dual-flexure design had potiental for achieving the resolutions, but problems
evolved when trying to implement the filtering part. Initially, the silica plates were
81
to be attached to Part E (top flexure) and have a chamber built around them. This
idea failed when too many leakage issues arose and there was now a major spacing
contraint (flexure was already built). Instead of investing the time into designing
another flexure, another method was implemented to simplify this application.
The tube filtration method was ideal. The plates were already inside the tubing.
With more forethought about design around the filter, the leakage and spacing issues
were eliminated. With the fluid analysis through a tubing, it seemed very feasible to
achieve the minimum flow rate. When the actual flow test was conducted, a flow of 50
ML was obtained and that far exceeded the 1 4 minimum. A problem
still persists
min
min
in sealing the plates inside the tube. In the mock test, the plates were sealed while
they were inside the sensor contacts. While the sealant cured, the sensor contacts
were mounted to a metal mounting bar that supported the tube housing and plates.
In the methodology test, the sensor contacts had to be modified at the last minute
and they no longer fit the mounting bar for sealing. In this case, the tubing was
supported by a chemistry stand and the sensor contacts were attached to the tube
housing. While sealing, the plates probably shifted because the tubing was too elastic
and did not provide a firm support.
In the sensing and actuation test, there was a hysteresis effect observed. This effect
was probably due to the rubber cement wearing after multipe usage. The tube claw
started to slip out after about a week. At a maximum input voltage of 150 V for the
piezoactuaters, going by the calibration factor, only 3.85 micrometers were obtained
for motion. This value was more than what was needed (limit of 0.5 micrometers).
So the motion factor from the amplifier is 25.67 "'. Since the piezoactuators have a
maximum stroke of 20 micrometers, this shows a loss in performance. Probably the
elasticity of the tubing and sealant absorbed some of the motion. Still this filtration
method seems possible.
For further work on the Tube Filtration method, a few guidelines and suggestions
need to be followed. It is crucial to cut the openings "perfectly-parallel" so that both
sensors on each side can get proper reading. Second, make sure that the tube claws are
perfectly aligned with the tube's center and each, or the motion will not be straight.
82
In addition, some method in DSPACE or electronically needs to be designed to be able
to get voltage outputs from the amplifier lower than 1 V. The amplifier's resolution
was too high to obtain submicron motion.
A lever to decrease the displacement
output of the piezoactuators may mechanically enable the resolutions to be obtained.
83
84
Bibliography
[1] http://www.adetech.com/2800.shtml
[2] http://www.aa.washington.edu/controls/classes/448w96/lab5bc.jpg
[3] http://fibec.flight.wpafb.af.mil/fibec/hysteresis.html
[4]
http://www.mse.cornell.edu/courses/engri111/modulus.htm
[5] http://www.ndif.org/Terms/hydrolysis.html.
[6] http://www.osmonics.com/products/Page710.htr.
[7] http://www.piezomechanik.com
[8] M. C. Bekker, J.P. Meyer, L. Pretorius, and D.F. Van Der Merwe "Separation of
solid-liquid suspensions with ultrasonic acoustic energy", Water Resources, Vol.
31, No. 10, (March 1997).
[9] G. Belfort (ed.), "Synthetic Membrane Processes: Fundamental and Water Applications", Academic Press, Orlando(1984).
[10] R.C. Dorf and R.H. Bishop, "Modern Control Systems", Addison-Wesley,
Menlo(1998).
[11] J.A. Fay, "Introduction to Fluid Mechanics", MIT Press, Cambridge(1998).
[12] R.W. Fox and A.T. McDonald, "Introduction to Fluid Mechanics, 4 th Ed.", John
Wiley & Sons, Inc., New York(1992).
85
[13] T. Hanai (ed.), "Liquid Chromatography in Biomedical Analysis", Elsevier, Amsterdam(1991).
[14] W.S. Hancock (ed.), "High Performance Liquid Chromatography in Biotechnology", John Wiley & Sons, New York(1990).
[15]
J.J. Hawkes and W.T. Coakley "A continuous flow ultrasonic cell-filering
method", Enzyme and Microbial Technology, Vol. 19, No. 1, (July 1996).
[16] J.J. Hawkes, J.J. Cefai, D.A. Barrow, W.T. Coakley, and L.G. Briarty "Ultrasonic manipulation of particles in microgravity", Journal of Applied Physics, Vol.
31, No. 14, (July 1998).
[17] A. Henschen, K.P. Hupe, F. Lottspeich, and W. Voelter (ed.), "High Performance
Liquid Chromatography in Biochemistry", VCH, Weinheim(1985).
[18] I.L. Holwill, G.B. Davies, N.J. Titchenerhooker, and M. Hoare "Particle Manipulation by ultrasonic standing-wave fields to complement dynamic light-scattering
experiments", Particle & ParticleSystems Characterization,Vol. 12, No. 3, (June
1995).
[19] I.S. Krull, R.L. Stevenson, K. Mistry, and M.E. Swartz, "Capillary Electrochromatography and Pressurized Flow Capillary Electrochromatography: An Introduction", HNB Publishing, New York(2000).
[20] Parekh(ed.), "Reverse Osmosis Technology: Applications for High-Purity-Water
Production", Marcel Dekker Inc., New York(1988).
[21] M. Saito, T. Daian, K. Hayashi, and S. Izumida "Fabrication of a polymer composite with periodic structure by the use of ultrasonic waves",
[22] H. Shintani and J. Polonsky, "Handbook of Capillary Electrophoresis Applications", Blackie Academic & Professional, London(1997).
[23] S.T. Smith, "Flexures: Elements fo Elastic Mechanisms", Gordon and Breach
Science Publishers, Australia(2000).
86
[24] S. Sourirajan and T. Matsuura(ed.), "Reverse Osmosis and Ultrafiltration",
American Chemical Society, Washington, D.C., 1985.
[25] K.S. Spiegler and A.D.K. Laird(ed.), "Principles of Desalination: Part A.,
2n
Ed.", Academic Press, New York(1980).
[26] R. Wolfson and J.M. Pasachoff, "Physics: with Modern Physics for Scientists
and Engineers, 2 nd Ed.", Harper Collins College Publishers, New York(1995).
[27] L.J. Zeman and A.L. Zydney, "Microfiltration and Ultrafiltration: Principles and
Applications", Marcel Dekker Inc., New York(1996).
87
88
Appendix A
Company Addresses
1. Active Electronics, 73 First St., Cambridge, Massachusetts 02141, Tel: (617)8643588, Fax: (617)864-055
2. ADE Technologies, 77 Rowe St., Newton, Massachusetts 02466, Tel: (617)8318000, Fax: (617)243-4400, www.adetech.com
3. Coghlin Electric/Electronics, A Div. Of Wesco Distribution Inc., 35 Otis St./PO
Box 5100, Westboro, Massachusetts 01581-5100, Tel: (508)870-5000, Fax: (508)8705157
4. The Home Depot, 75 Mystic Ave, Somerville, MA 02145, Tel: (617)623-0001
5. Manostat: Division of Barnant Co., 28W092 Commercial Ave, Barrington, IL
60010-2392, Tel: (800)637-3739, Fax: (847)381-7053
6. McMaster-Carr Supply Company, 473 Ridge Rd, Dayton, NJ 08810-0317, Tel:
(732)329-3200
7. Power-One, Inc., 740 Calle Plano, Camarillo, California 93012, Tel: (805)9878741, Fax: (805)388-0476
8. RadioShack.com, 3131 West Bolt St., Fort Worth, TX 76110-5813, Tel: (800)4645365, http://www.radioshack.com
89
9. Ramco Machine, Inc., 416 Calbot St., Beverly, Massachusetts 01915, Tel: (978)9214600, Fax: (978)921-8448
10. Ted Pella, Inc., 4595 Mountain Lakes Blvd, Redding, CA 96003-1448, Tel:
(530)243-2200
11. Thorlabs, Inc., 435 Route 206, Newton, NJ 07860, Tel: (973)579-7227, Fax:
(973)383-8406
12. US EuroTek, Inc., 25315 Costeau St., Laguna Hills, California 92653, Tel:
(949)458-6794, Fax: (949)916-9121, useurotek~juno.com
13. Valley Design Corp., East Coast Division: 63 Power Rd., Westboro, Massachusetts 01866, Tel: (978)692-1971, Fax: (978)692-9549, eastcvalleydesign.com;
West Coast Division: 151-D Harvey West Blvd., Santa Cruz, California 95060,
Tel: (831)430-0595, Fax: (831)430-0592, west@valleydesign.com
14. VWR Scientific Products, 200 Center Square Rd., Bridgeport, New Jersey
08014, Tel: (800)932-5000, www.vwrsp.com
90
Appendix B
Schematics
91
.........
Figure B-i: Isometric view of small flexure A (mm)
i
-
22
-W--__---2
-
-
06
35
50
-
-- i 2....---
Figure B-2: Front view 1 of small flexure A (mm)
92
-03
10
-
- -
--(7~
_
_
_4
_
3.5
R2 . 5
10
...
F..
12
2
]
20
]0
I
Figure B-4: Top view of small flexure A (mm)
93
(
.
Lf
Figure B-5: Side view of small flexure A (mm)
-..........
....
ZMy
....
Figure B-6: Isometric view of large flexure B (mm)
I
~IZIf~-66
I
Ii
1 70
...
........
....
.
8
-0
f2
7
148
40
Figure B-7: Front view of large flexure B (mm)
'L
01
15 10 [
o-
L
5 3.0
7
I
'5
Figure B-8: Top view of large flexure B (mm)
95
*
-I
I
~
................................................................................................................................................................
ML---
-
4.5
f>;9-s...
......................................
..... II-OFT-T......
.....
.....
.....................
...........
........
..............
...
......
.......
z
3; 3
........
........
I -......
.....
Figure B-9: Side view of large flexure B (mm)
Figure B-10: Isometric view of piezo-holder M (inches)
96
__1.00000000000
0 46968503937
1.
1.000
Figure B-11: Front view 1 of piezo-holder M (inches)
25
0000000-r0-
1.00
.5
----
1.2348425196
----
IL.
-
Figure B-12: Front view 2 of piezo-holder M (inches)
97
.24
1.125
4
45O-
.50
1.23484244*9- 1
00
0----,----
--t-
120
Figure B-13: Side view of piezo-holder M (inches)
.325
010
2.00d
1.23484251969
.. I 675
1.49
-
1
-
2.0 00___.
00
Figure B-14: Top view of piezo-holder M (inches)
98
Figure B-15: Isometric view of sensor-holder N (inches)
1401
_____
8
1.80'
-
.30
.00 .30 -
Figure B-16: Front view of sensor-holder N (inches)
99
.50 .50
25590551 8
5UM1O*~
r-
I
L
fA1 IT
n
74 -
Figure B-17: Side view of sensor-holder N (inches)
i
0
I.....
111Il . ......
t
1......._......
325
197456692913
1it:
2 0000110 0000
Fe.
.675
2.000
-.32
I
0-
Figure B-18: Top view 1 of Sensor-Holder N (inches)
100
2.
10
©J12 _
©
3)
.~ ...
-01159
25590551 18
.8074
Figure B-19: Top view 2 of Sensor-Holder N (inches)
.~..........
Figure
B-20:
Isometric
view
101
of
tube
claw
0
(inches)
W-. 150 ;;
T
*-
.....
F
50
1.00
Figure B-21: Front view of tube claw 0 (inches)
~~1
Figure B-22: Side view of tube claw 0 (inches)
102
125
525000
-01.0000
.50
.28
Figure B-23: Top view of tube claw 0 (inches)
Figure B-24: Isometric view of sensor contact P (inches)
103
I.
1
.0
67
4
OO
00
50000000o
3i
Figure B-25: Front view 1 of sensor contact P (inches)
13657480315
-T
-54
18
1 10k
-362
-
-
-
05
4
1 89
Figure B-26: Front view 2 of sensor contact P (inches)
104
1.00000
.....
.875
2-
1.704 0000-
56 75
.1
L
-45000-
Figure B-27: Side view of sensor contact P (inches)
GRO
GO3CO
T AREA.
R j.0
4 15 M
Al i.mm Imp
'I
TT.IH~
ACVEEAIA,
5 mM (0.2')
Figure B-28: Schematic of model 2800 series probe [1]
105
I~
4 mm
A~.
~
if"''
~4aaO.S
I
t
i
I
6.1f
P -t
IT
a
a
*s
4
mm
mu
e-vm
s
Figure B-29: Piezoactuator Schematic [7]
30
IIT
f
*1 1 1 I I
I1
I
11
4r
Figure B-30: Spherical top piece (steel) on moving end [7]
106
Appendix C
Controller Design
C.1
Sensor, Piezoactuator, and Dynamic Signal
Analyzer Data
NOTE: In dynamic signal analysis, -360 was added to phase once it was positive to
plot.
107
Table C.1: Elasticity test of system
Increasing
Input(V)
0
7
10
17
26
32
43
52
59
63
72
75
80
89
95
108
113
120
125
140
145
N/A
N/A
N/A
N/A
N/A
N/A
N/A
Output(V)
11.57
11.55
11.54
11.5
11.44
11.4
11.33
11.28
11.24
11.21
11.15
11.13
11.11
11.04
11.01
10.94
10.93
10.89
10.87
10.81
10.8
N/A
N/A
N/A
N/A
N/A
N/A
Decreasing
Input(V)
140
135
129
125
116
109
104
94
87
83
80
75
67
61
55
54
50
44
36
30
24
26
18
13
5
1
0
108
N/A
Output(V)
10.81
10.82
10.84
10.85
10.88
10.91
10.93
10.97
11.01
11.03
11.04
11.07
11.11
11.14
11.15
11.18
11.21
11.24
11.29
11.34
11.38
11.43
11.46
11.48
11.53
11.56
11.57
Figure C-1: Noise plot for sensor output
-I-I
-I-I--I-IA
.. ..
....
t~'Y
AL
0,
-
-
- .4
Figure C-2: Sensor output with bottom piezoactuator at -30 Vdc
109
II
At~
*14I.
I,1'
'1
["
&
i~i..i4 14.Ln
k P
I
17,
.
[.1
L I,
1''
4......
,Ag
Ij
p
I
r
Figure C-3: Sensor output with top piezoactuator at -30 Vdc
AtV~
I
NW...
*
4$-ti'
IIl
t
WA
Figure C-4: Sensor output with bottom piezoactuator at 0 Vdc
110
I
.........
........
...
t
~
W
arr
I
Figure C-5: Sensor output with top piezoactuator at 0 Vdc
Figure C-6: Sensor output with bottom piezoactuator at 1 Vdc
111
-
Figure C-7: Sensor output with top piezoactuator at 1 Vdc
Figure C-8: Sensor output with bottom piezoactuator at +150 Vdc
112
I
ffiI~
I
.......
4
4
4"'
4'
*
I
..............
A
Figure C-9: Sensor output with top piezoactuator at +150 Vdc
'I-i-I-I-.-.-.-.-.
~f
I0%72
17-L
11
I-Ij111
4
4
4
*T
-4.
*'
IL
r
*
...
.A..
-.-.....
70
T~
T* V44
.
~
ur~
0
-~-'~-
i1ji"~
June
Figure C-10: Sensor output with bottom piezoactuator at +1 Vdc
113
___j
Figure C-11: Sensor output with top piezoactuator at +1 Vdc
0
LPUU
-10
-20
-30
ca
-40
-50
-60
-70
-80
Frequency(radls)
Figure C-12: Piezoactuator B and flexure F
114
/
sensor C magnitude bode diagram
0
bo
i
I
I
DOG
000
-50
-100
I
-:-150
-200
C
-250
-300
-350
-400 -L
L.
Frequency(rad/s)
Figure C-13: Piezoactuator B and flexure F
/
sensor C phase bode diagram
0
PUU
-10
-20
-30
~40
I
I
)
-
-50
-60
-70
-80
Frequency(radls)
Figure C-14: Piezoactuator B and flexure F
diagram
115
/
y = -0.01 38x - 32.771
sensor C slope in magnitude bode
0
-F0
4-
-100
-150
-200
c
0.L
-250
-I
-300
I
-350
II.......
_
--. 1..L. 1 ..
Frequency(rad/s)
400
Ly
--
1.82
O.O428~t-
Figure C-15: Piezoactuator B and flexure F/ sensor C slope in phase bode diagram
I I rI I .ILE
KJU
0
-~~~~~~~~~
ThrIIzzi±±~h
±
±Hzz
-10
I
I IZLIUZL
I I rtUU
H iHi
I
I
I
-20
-30
at
-40
fl$
-50
i -60
-70
.
i i i i iii i i
!
i i ! i H ii
i i i i i i !i
i [ !iHH!
i
i
i
i
i
i
I I I
Hi
1 1 1 11
I I 1111
1
Frequency(radls)
.1.U
Figure C-16: Piezoactuator A and flexure E/ sensor D magnitude bode diagram
116
-
200-
..............
I......... ......
T1111
T1
1
I
150
100
50
-
]-
0
Po
I
11 PI00
-50
100
150
-2
00
4-
_1I
..... A - I
j
I
I
1 1 . -
1-
-
, -1- A
L IA
.
L- ..-...
---
--- ----
--' -
A
---
Frequency(radis)
Figure C-17: Piezoactuator A and flexure E
/
sensor D phase bode diagram
0
00
-10
-20
-30
C,
-40
-50
-- 166x - 13.418
-60
-70 -
I
I I I[II:
I
- I
L 1- ]I l
Frequency(radls)
Figure C-18: Piezoactuator A and flexure E
diagram
117
/
sensor D slope in magnitude bode
0
[Nil
-20
-40
-60
-60
-100
iL
-120
-140
-160
-180 -
-
-
II
I
.
.
.I
Frequency(radls)
Figure C-19: Piezoactuator A and flexure E
118
/
y
=0-
3 8k;;47 078
sensor D slope in phase bode diagram
Table C.2: Dynamic signal analysis of flexure design la
Lt Probe/Tp Piezo
INPUT
(HZ)
5
14.9
24.8
34.7
44.6
54.5
64.4
74.3
84.2
91.625
92.863
94.1
104
115.138
125.038
134.938
144.838
154.738
164.638
175.775
185.675
195.575
205.475
N/A
INPUT
(RAD/S)
31.41592654
93.61946108
155.8229956
218.0265302
280.2300647
342.4335992
404.6371338
466.8406683
529.0442029
575.6968538
583.4754372
591.2477374
653.4512719
723.4333899
785.6369244
847.840459
910.0439935
972.2475281
1034.451063
1104.426897
1166.630432
1228.833966
1291.037501
119
N/A
MAG
(dB)
-3.132
-4.15096
-5.19313
-6.30853
-7.48723
-8.75977
-10.1266
-11.5976
-13.1809
-14.4426
-14.6544
-14.8663
-16.6287
-18.6683
-20.4838
-22.3058
-24.0914
-25.8415
-27.524
-29.4045
-30.9247
-32.5452
-33.9815
N/A
PHASE
(Deg)
-21.4564
-43.8148
-64.5002
-83.9115
-102.405
-120.121
-137.121
-153.41
-168.72
-179.527
-178.726
176.979
163.85
150.529
139.891
130.305
121.695
114
107.137
100.389
93.9279
89.5737
84.7065
Table C.3: Dynamic signal analysis of flexure design lb
Lt Probe/Tp Piezo
INPUT
(HZ)
215.375
225.275
235.175
245.075
254.975
264.875
274.775
284.675
295.813
305.713
315.613
325.513
335.413
345.313
355.213
365.113
375.013
384.913
396.05
405.95
415.85
425.75
435.65
445.55
455.45
465.35
475.25
N/A
INPUT
(RAD/S)
1353.241036
1415.44457
1477.648105
1539.851639
1602.055174
1664.258708
1726.462243
1788.665777
1858.647895
1920.85143
1983.054964
2045.258499
2107.462033
2169.665568
2231.869103
2294.072637
2356.276172
2418.479706
2488.455541
2550.659075
2612.86261
2675.066145
2737.269679
2799.473214
2861.676748
2923.880283
2986.083817
120
N/A
MAG
(dB)
-35.4416
-36.7826
-38.1748
-39.4201
-40.6861
-41.8613
-43.0625
-44.117
-45.4548
-46.5135
-47.518
-48
-49.3806
-50.6682
-51.4048
-52.2944
-53.1495
-54.1121
-54.8516
-55.8666
-56.6994
-57.2524
-58.234
-58.6173
-59.5667
-60.0306
-60.7755
N/A
PHASE
(Deg)
80.0955
75.9424
72.1972
68.906
65.6772
62.6932
59.9237
56.8906
53.7013
51.2112
50.3351
47.0217
43.4869
44.1102
41.8138
39.7233
38.8971
36.4525
32.8334
33.1369
31.3441
29.7661
27.6247
26.7657
27.2549
27.6169
26.6101
Table C.4: Dynamic signal analysis of flexure design 2a
Lt Probe/Bt Piezo
INPUT
(HZ)
5
14.9
24.8
35.938
45.838
55.738
65.638
75.538
85.438
95.338
96.575
105.238
115.138
125.038
134.938
1146.075
155.975
165.875
175.775
185.675
195.575
205.475
N/A
INPUT
(RAD/S)
31.41592654
93.61946108
155.8229956
225.8051136
288.0086481
350.2121827
412.4157172
474.6192517
536.8227863
599.0263208
606.798621
661.2298554
723.4333899
785.6369244
847.840459
917.8162937
980.0198283
1042.223363
1104.426897
1166.630432
1228.833966
1291.037501
121
N/A
MAG
(dB)
-21.2377
-22.2101
-23.1015
-24.1525
-25.163
-26.2143
-27.4276
-28.7924
-30.2249
-31.8147
-32.0152
-33.441
-35.1449
-36.7652
-38.3836
-40.52
-42.4958
-44.0519
-45.5873
-46.5025
-48.3214
-49.4819
N/A
PHASE
(Deg)
-20.33
-40.7702
-60.1497
-81.0327
-98.9319
-116.437
-133.152
-149.492
-164.757
-179.313
178.995
167.628
155.487
144.42
134.509
119.805
116.428
110.33
105.894
99.7541
92.5037
89.3792
Table C.5: Dynamic signal analysis of flexure design 2b
Lt Probe/Bt Piezo
INPUT
(HZ)
215.375
225.275
235.175
245.075
254.975
264.875
274.775
285.913
295.813
305.713
315.613
325.513
335.413
345.313
355.213
365.113
375.013
386.15
396.05
405.95
415.85
425.75
435.65
445.55
455.45
465.35
475.25
485.15
N/A
INPUT
(RAD/S)
1353.241036
1415.44457
1477.648105
1539.851639
1602.055174
1664.258708
1726.462243
1796.444361
1858.647895
1920.85143
1983.054964
2045.258499
2107.462033
2169.665568
2231.869103
2294.072637
2356.276172
2426.252006
2488.455541
2550.659075
2612.86261
2675.066145
2737.269679
2799.473214
2861.676748
2923.880283
2986.083817
3048.287352
122
N/A
MAG
(dB)
-50.9592
-52.1374
-53.3294
-54.3999
-55.6418
-56.5107
-57.1387
-58.6616
-59.985
-60.9484
-62.0578
-62.1311
-64.4222
-64.7992
-65.2131
-66.5474
-67.1869
-68.191
-68.6242
-69.4766
-68.3737
-69.281
-69.7738
-71.0817
-69.4183
-71.933
-71.1978
-70.3661
N/A
PHASE
(Deg)
83.6187
78.311
76.0191
72.4009
65.5622
66.447
61.0581
51.593
52.3132
51.1797
47.1574
39.1374
31.359
42.3933
39.6273
38.8048
38.8289
36.7647
31.0064
34.1842
29.4043
22.2619
19.7137
32.1998
21.2463
19.2854
18.0418
25.7117
Table C.6: Dynamic signal analysis of flexure design 3a
Rt Probe/Tp Piezo
INPUT
(HZ)
5
14.9
24.8
35.938
45.838
55.738
65.638
75.538
85.438
95.338
96.575
105.238
115.138
125.038
134.938
146.075
155.975
165.875
175.775
185.675
195.575
205.475
215.375
N/A
INPUT
(RAD/S)
31.41592654
93.61946108
155.8229956
225.8051136
288.0086481
350.2121827
412.4157172
474.6192517
536.8227863
599.0263208
606.798621
661.2298554
723.4333899
785.6369244
847.840459
917.8162937
980.0198283
1042.223363
1104.426897
1166.630432
1228.833966
1291.037501
1353.241036
123
N/A
MAG
(dB)
-3.38552
-4.39704
-5.42789
-6.66989
-7.84981
-9.11407
-10.486
-11.961
-13.5578
-15.2447
n/a
-17.0045
-18.8038
-20.6211
-22.4333
-24.4471
-26.1873
-27.842
-29.4869
-31.1203
-32.6378
-34.1135
-35.5623
N/A
PHASE
(Deg)
158.696
136.485
115.961
94.3273
76.0366
58.4834
41.5271
25.4256
10.2463
-3.87665
n/a
-16.8387
-28.6408
-39.3137
-48.9045
-58.5677
-66.248
-72.922
-78.995
-85.5244
-90.6466
-94.6227
-98.9881
Table C.7: Dynamic signal analysis of flexure design 3b
Rt Probe/Tp Piezo
INPUT
(HZ)
225.275
235.175
245.075
254.975
264.875
274.775
285.913
295.813
305.713
315.613
325.513
335.413
345.313
355.213
365.113
375.013
384.913
396.05
405.95
415.85
425.75
435.65
445.55
455.45
465.35
475.25
485.15
N/A
INPUT
(RAD/S)
1415.44457
1477.648105
1539.851639
1602.055174
1664.258708
1726.462243
1796.444361
1858.647895
1920.85143
1983.054964
2045.258499
2107.462033
2169.665568
2231.869103
2294.072637
2356.276172
2418.479706
2488.455541
2550.659075
2612.86261
2675.066145
2737.269679
2799.473214
2861.676748
2923.880283
2986.083817
3048.287352
124
N/A
MAG
(dB)
-36.8816
-38.2135
-39.515b
-40.7845
-41.9256
-43.1502
-44.3218
-45.6116
-46.5869
-47.5013
-48.6186
-49.6428
-50.4986
-51.3656
-52.3872
-53.3435
-54.1544
-54.9458
-55.9383
-56.7783
-57.1897
-58.1033
-58.869
-59.6022
-60.8774
-60.703
-62.1952
N/A
PHASE
(Deg)
-103.226
-106.673
-110.508
-113.588
-116.57
-120.046
-122.492
-124.632
-126.46
-128.205
-131.881
-134.772
-135.447
-138.524
-140.362
-141.62
-143.598
-144.689
-147.078
-148.695
-148.284
-150.75
-150.735
-152.236
-156.178
-158.144
-156.388
Table C.8: Dynamic signal analysis of flexure design 4a
Rt Probe/Bt Piezo
INPUT
(HZ)
5
14.9
24.8
35.938
45.838
55.738
65.638
75.538
85.438
95.338
96.575
105.238
115.138
125.038
134.938
144.838
155.975
165.875
175.775
185.675
195.575
205.475
215.375
N/A
INPUT
(RAD/S)
31.41592654
93.61946108
155.8229956
225.8051136
288.0086481
350.2121827
412.4157172
474.6192517
536.8227863
599.0263208
606.798621
661.2298554
723.4333899
785.6369244
847.840459
910.0439935
980.0198283
1042.223363
1104.426897
1166.630432
1228.833966
1291.037501
1353.241036
125
N/A
MAG
(dB)
-21.3065
-22.2421
-23.1262
-24.1829
-25.2013
-26.257
-27.5069
-28.8663
-30.3509
-31.9162
-32.1167
-33.5418
-35.2745
-36.9033
-38.5241
-40.291
-42.6603
-43.8698
-45.8687
-46.8446
-48.7036
-50.1258
-51.0322
N/A
PHASE
(Deg)
-20.2289
-40.7964
-60.2623
-81.2439
-99.2608
-116.667
-133.382
-149.893
-165.316
-179.63
178.69
167.226
155.252
144.363
134.169
122.119
116.8
109.124
101.564
99.2181
96.0367
88.3451
83.104
Table C.9: Dynamic signal analysis of flexure design 4b
Rt Probe/Bt Piezo
INPUT
(HZ)
225.275
235.175
245.075
254.975
264.875
274.775
285.913
295.813
305.713
315.613
325.513
335.413
345.313
355.213
365.113
375.013
384.913
396.05
405.95
415.85
425.75
435.65
445.55
455.45
465.35
475.25
485.15
N/A
INPUT
(RAD/S)
1415.44457
1477.648105
1539.851639
1602.055174
1664.258708
1726.462243
1796.444361
1858.647895
1920.85143
1983.054964
2045.258499
2107.462033
2169.665568
2231.869103
2294.072637
2356.276172
2418.479706
2488.455541
2550.659075
2612.86261
2675.066145
2737.269679
2799.473214
2861.676748
2923.880283
2986.083817
3048.287352
126
N/A
MAG
(dB)
-52.4258
-53.5037
-54.806
-55.3729
-57.0411
-57.3818
-58.8365
-60.0914
-60.5119
-61.8403
-61.9458
-62.9584
-65.2482
-65.7363
-66.7573
-67.3654
-67.9877
-68.7795
-67.6922
-69.9703
-69.3106
-70.3536
-69.5599
-70.6195
-72.3766
-69.9427
-70.5405
N/A
PHASE
(Deg)
78.1209
75.5326
69.9195
68.5061
65.4402
63.369
50.686
56.049
54.8751
52.8149
43.5044
31.8963
31.5821
32.5532
34.1446
33.9895
37.6903
33.5132
31.2689
24.671
17.1439
21.7782
18.8388
11.8233
24.4627
23.4534
12.8642
Table C.10: Dynamic signal analysis of MPF 1
Hz
0.1
0.1998
0.2994
0.4034
0.5045
0.6046
0.7093
0.8059
0.9061
1.008
1.097
1.372
1.929
2.337
3.115
3.855
4.977
5.715
6.923
7.7
8.938
9.837
10.94
11.42
15.38
21.17
24.57
Mag(Log db)
0.034822
0.0322643
0.031687
0.0308083
0.0294867
0.0293718
0.0291263
0.0290577
0.0289469
0.028719
0.0286832
0.0279589
0.0274643
0.0274348
0.0269128
0.0261942
0.0260554
0.0254092
0.0252998
0.0253432
0.0249462
0.024466
0.0238369
0.0234754
0.0229894
0.021087
0.0207078
Phae(Deg)
169.996
172.111
173.941
172.236
170.76
172.174
170.854
171.624
171.628
171.891
171.696
171.325
170.58
169.704
167.71
167.528
165.527
164.225
162.943
162.787
159.832
158.292
155.999
156.053
147.838
140.572
133.398
127
K(dB)
21.66965493
21.54241042
21.5137935
21.47030904
21.40507213
21.3994098
21.38731646
21.38393845
21.37848354
21.36726792
21.36550664
21.32990375
21.30562583
21.30417867
21.27858751
21.24340827
21.23661998
21.20504487
21.19970393
21.20182257
21.18245028
21.15904176
21.12841388
21.11083424
21.08722324
20.99505398
20.97673036
Table C.11: Dynamic signal analysis of MPF 2
32.07
35.67
39.26
46.06
53.46
61.39
64.75
73.57
77.6
88.17
107.9
112.6
117.5
122.6
129.4
133.5
148.6
189.8
217.9
242.4
293.6
337.2
371.1
430.8
469.1
500
0.0172708
0.0162759
0.0185403
0.0143372
0.0146369
0.0103712
0.00807178
0.0029962
0.00724308
0.0343488
0.0128517
0.00533539
0.0036433
0.0058238
0.00671831
0.00824914
0.0212462
0.00814071
0.00305248
0.00232058
0.00145735
0.00103618
0.000838793
0.000830028
0.000492234
0.000304348
126.725
126.854
124.429
110.705
103.392
87.7254
84.7341
145.187
177.805
127.416
129.2952
114.812
93.3213
80.5108
103.906
114.362
58.2951
-21.683
-42.724
-23.035
-42.918
-37.8
-47.391
-62.1
-87.954
-84.628
128
20.811376
20.76375499
20.87229939
20.67127172
20.68554157
20.48335989
20.37519509
20.13845717
20.33635318
21.6460569
20.60068662
20.24721925
20.16848589
20.27000219
20.31179504
20.38351774
21.00275158
20.37842924
20.14106707
20.10715268
20.06722618
20.04777482
20.03866517
20.03826075
20.02268106
20.01402066
Appendix D
Material List and Component
Characteristics
129
Table D.1: Parts
Part Name
Piezactuator A
Piezoactuator B
Sensor C
Sensor D
Flexure E
Flexure F
Tube Housing(0.75" ID, 1" OD) G
Sealant Region H
Plates(average size: 5 x 12 x 5mm) I
Tube Claw J (s)
Sensor Contact K
Tube Housing(0.75" ID, 1" OD) L
Piezo-Holder M
Sensor-Holder N
Tube Claw 0
Sensor Contact P
0.75" ID Filter Chamber Q
0.75" to 0.375" Tubing Reducer R
0.375" to 0.25" Tubing Reducer S
Pump Connector T
Material Type
PZT
PZT
Stainless Steel
Stainless Steel
Aluminum
Aluminum
Vinyl
Silicone
Fused Silica Quartz
Aluminum
Aluminum
Vinyl
Aluminum
Aluminum
Aluminum
Aluminum
Vinyl
Nylon
Nylon
Nylon
Table D.2: Probe characteristics [1]
Range +p m (in)
Standoff pi m (in)
Resolution nm (p in)
Sensor Diameter (mm)
Overall Diameter (mm)
Minimum Recommended Target Size (mm)
Capacitance transducers
Non-contact
No probe wear
130
50(0.002)
100(0.004)
0.5(0.02)
5
8
10
Coaxial passive probes
Non-destructive
Easily fixtured
Table D.3: Piezoactuator characteristics [7]
Type
Max Voltage Input (V)
PZT 150/5/20 VS1O
+150
PZT 150/4/20 VS09
Max Stroke (p m)
20
20
Prestress Force (N)
Mechanical Compressive Load (N)
Length (mm)
Capacitance (nF)
Stiffness (L)
Resonance Frequency (Hz)
150
1000
28
800
25
30
100
500
28
340
12
30
131
+150