Dynamic Testing of Polydimethylsiloxane for
Applications in Micro-Contact Roll Printing
by
Emma Claire Benjaminson
Submitted to the Department of Mechanical Engineering
in partial fulfillment of the requirements for the degree of
AOCM
MA-SsACHUSETS NTE
OF TECHNOLOGY
Bachelor of Science in Mechanical Engineering
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
JUL 3
LIBRARIES
June 2014
@ Massachusetts Institute of Technology 2014. All rights reserved.
Author..
redacted.. ................
S ignature
- ------- 1
- ---Department of Mechanical Engineering
May 9, 2014
Signature redacted
Certified by...
David E. Hardt
Ralph E. and Eloise F. Cross Professor of Mechanical Engineering
Thesis Supervisor
Signature redacted
A ccepted by ...........................................................
Annette Hosoi
Associate Professor of Mechanical Engineering, Undergraduate Officer
2
Dynamic Testing of Polydimethylsiloxane for Applications in
Micro-Contact Roll Printing
by
Emma Claire Benjaminson
Submitted to the Department of Mechanical Engineering
on May 9, 2014, in partial fulfillment of the
requirements for the degree of
Bachelor of Science in Mechanical Engineering
Abstract
Micro-contact roll printing is an emerging alternative to photolithography as a means
of cheaply manufacturing MEMS devices. Micro-contact roll printing control systems
can regulate the printing pressure of a polydimethylsiloxane stamp on a polymer sheet,
but the technology cannot adequately control the registration of the stamp on the
sheet because the precise dynamic mechanical behavior of the polydimethylsiloxane
stamp is unknown. The purpose of this thesis is to apply system identification techniques to characterize the dynamic behavior of samples of polydimethylsiloxane by
constructing a test environment that can apply an input force at various frequencies
and measure the output force and position at the test sample. A mechanical structure
which integrates a voice coil actuator with a load cell and linear variable differential
transformer was designed for this purpose. A model and controller were also built
to predict the dynamic behavior of the polydimethylsiloxane. In future work the
mechanical structure and controller will be integrated and used to fully characterize
the behavior of polydimethylsiloxane and other polymers used in micro-fabrication
processes.
Thesis Supervisor: David E. Hardt
Title: Ralph E. and Eloise F. Cross Professor of Mechanical Engineering
3
4
Acknowledgments
It takes a village to raise a child, and the same is true for producing an undergraduate
thesis. I want to thank first Professor David Hardt for agreeing to be my thesis
advisor. He was willing to give me funding for my project (perhaps even a little more
than he initially expected to) and to take the time to meet with me and review my
work at several points in the semester. I am especially grateful that he took me on as
a student this year because I know he already had four graduating masters students
to advise.
Professor Hardt leads an amazing team of graduate students, but most amazing
to me was Maia Bageant. Maia took me under her wing over a year ago and at
that time the quality of my education at MIT increased exponentially thanks to her
mentorship, guidance and good humor. I am forever indebted to Maia for helping
me in every way, from showing me how to use the waterjet ("It is a dangerous game
you play!"), to teaching me everything I know about controls, to guiding me around
the many pitfalls that would have otherwise stymied me and my thesis. I will never
forget how she responded to my frantic e-mails about selecting a capacitance probe
the day before her PhD qualifying exams - that takes a special dedication to peer
mentoring which I am extremely grateful for.
Maia is not alone in her awesomeness, however - I also want to thank Adam Libert
for his persistance in making me think harder and better about my thesis. There were
definitely times when I was afraid to walk into lab because I knew he was going to
ask me another question that would turn my project upside down, but he was always
there to help me turn it back upright again and make it a better project because of
that effort. Adam and Maia have both taught me how to be a better mechanical
engineer.
I also received encouragement and support from Professor Hardt's other graduate
students, including Scott Nill and Larissa Nietner. Thank you for the help, advice
and laughs along the way.
And although he doesn't know it, I owe a huge debt to Professor Martin Culpepper
and his class, Elements of Mechanical Design. I took this class concurrently with my
thesis, and it could not have been better timing. Marty taught me to write functional
requirements, to ask the right questions and to deal with uncertainty. Thank you for
giving me the tools I needed to build a robust machine, Marty.
Finally, I have my home team to thank for supporting me every step of the way. My
friends and housemates have kept me laughing, sane and amply supplied with frozen
yogurt - thank you for listening to my every complaint and giving me the courage
to go back and try again. My family, most of all, has been incredibly supportive
and I am eternally grateful for their love for me. Molly has consistently supplied
me with chocolate and cigars; Grandma, you were always ready to listen to me and
encourage me to keep trying. And Mom, I don't think I have the words to tell you
how much your support and strength has helped me through my entire undergraduate
experience. Thank you for showing me that no obstacle is too great to overcome.
5
6
Contents
1 Introduction
1.1
Motivation. ......
15
.................................
15
1.2 Contribution of Thesis . . . . . . . . . . . . . . . . . . . . . . . . . .
17
1.3
18
Thesis Outline. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2 Background
19
2.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
19
2.2
Context . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
19
2.3
System Identification . . . . . . . . . . . . . . . . . . . . . . . . . . .
23
3 Project Scope
27
3.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
27
3.2
Functional Requirements . . . . . . . . . . . . . . . . . . . . . . . . .
29
3.2.1
Hold a sample of PDMS . . . . . . . . . . . . . . . . . . . . .
30
3.2.2
Apply continuous force to a sample . . . . . . . . . . . . . . .
31
3.2.3
Displace actuator relative to sample . . . . . . . . . . . . . . .
32
3.2.4
Apply force as a sine wave input signal of varying frequencies
32
4 Mechanical Machine Design
4.1
35
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
35
4.2 Overview of Machine Design . . . . . . . . . . . . . . . . . . . . . . .
36
4.2.1
Outer aluminum structure . . . . . . . . . . . . . . . . . . . .
37
4.2.2
Linear voice coil actuator assembly . . . . . . . . . . . . . . .
38
7
4.3
4.2.3
Connection to shaft . . . . . . . . . . . . . . . . . . . . . . . .
39
4.2.4
Top shaft clamp with additional clamp for position sensor . .
40
4.2.5
Sample and sample plate . . . . . . . . . . . . . . . . . . . . .
41
4.2.6
Load cell and adjustable reference plate . . . . . . . . . . . . .
42
Manufacturing Process . . . . . . . . . . . . . . . . . . . . . . . . . .
44
47
5 Electronic Component Design
5.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
47
5.2
Component Selection . . . . . . . . . . . . . . . . . . . . . . . . . . .
48
5.2.1
Data acquisition hardware . . . . . . . . . . . . . . . . . . . .
48
5.2.2
Actuator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
50
5.2.3
Position sensor . . . . . . . . . . . . . . . . . . . . . . . . . .
50
5.2.4
Force sensor . . . . . . . . . . . . . . . . . . . . . . . . . . . .
52
Load Cell Circuit Design . . . . . . . . . . . . . . . . . . . . . . . . .
53
5.3
57
6 Control System
6.1
Introduction . . . . . . . . . . . . . . . .... . . . . . . . . . . . . . .
57
6.2
Plant Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
57
6.3
Controller Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
64
6.3.1
Design iteration 1 . . . . . . . . . . . . . . . . . . . . . . . . .
65
6.3.2
Design iteration 2 . . . . . . . . . . . . . . . . . . . . . . . . .
66
6.3.3
Design iteration 3 . . . . . . . . . . . . . . . . . . . . . . . . .
67
7 Conclusion
71
8 Future Work
73
9 Bibliography
75
A Final Engineering Drawings of Test Environment
77
B Test Environment Design Review
85
B.1 Test Environment Design Review Plan . . . . . . . . . . . . . . . . .
8
85
B.2 Test Environment Design Review Report
87
C Laboratory Experiments
91
C.1 Introduction ...................
91
C.2 Collar Slipping .................
91
C.3 F of Voice Coil Motor .............
93
C.4 Voice Coil Axial Misalignment ..........
96
C.5 Machine Displacements .............
98
C.6 PDMS Material Properties ...........
99
D Preliminary Experimental Procedures
101
D.1 Research Questions ..................
101
D.2 Process for Making PDMS Capacitive Sensor.
102
D.2.1
Equipment/Materials ...........
102
D.2.2 Procedure ...................
102
D.3 Load Cell ...........
103
D.3.2
Procedure . . . . . .
103
D.3.3
Results . . . . . . . .
104
D.4 Capacitance Probe . . . . .
.
104
105
.
.
105
D.4.3 Results . . . . . . . .
105
D.5 Machine Stiffness . . . . . .
106
106
.
.
D.4.2 Procedure . . . . . .
.
Equipment/Materials
.
D.4.1
.
Equipment/Materials
.
103
D.3.1
Equipment/Materials
D.5.2
Procedure . . . . . .
106
D.5.3
Results . . . . . . . .
107
.
.
D.5.1
. . . . . . . . . .
108
.
.
D.6 Voice Coil . . . . . . . . . .
Equipment/Materials
. . . . . . . . . .
108
D.6.2
Procedure . . . . . .
. . . . . . . . . .
109
D.6.3
Results . . . . . . . .
.
.
.
.
D.6.1
.
109
9
D.7 Static Loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
D.7.1 Equipment/Materials . . . . . . . . . . . . . . . . . . . . . . . 110
D.7.2 Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
D.7.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .111
D.8 Roll Contact . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .111
D.8.1 Equipment/Materials . . . . . . . . . . . ... . . . . . . . . . .111
D.8.2 Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
D.8.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
D.9 Dynamic Loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
D.9.1 Equipment/Materials . . . . . . . . . . . . . . . . . . . . . . .
113
D.9.2 Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
D.9.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
10
List of Figures
2-1
Diagram showing micro-contact printing process for casting PDMS
stamps and using them to print patterns in 2 dimensions onto a sheet
of PET polymer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
21
2-2 A diagram showing the overarching concept behind system identification. The engineer is comparing the outputs of a model against the
actual system, and adjusting the model until its output matches (or
closely approximates) the actual system's output. . . . . . . . . . . .
2-3
23
Example of an unknown system that can be investigated using system
identification. An engineer inputs a force signal to the system and
measures the output signal. This measured data can be used to build
or verify a model for the cantilevered beam. . . . . . . . . . . . . . .
24
2-4 A diagram showing the modified system identification workflow for my
thesis. I built a plant model using first principles and estimates for
all of the physical parameters. I then built a controller based on that
plant model. I would then input a force signal via the controller to
the actual PDMS sample and measure the output. I would measure
the error between the PDMS' output signal and the input signal, and
refine the plant model and the controller until the output and input
signals were equal.
. . . . . . . . . . . . . . . . . . . . . . . . . . . .
25
3-1
An isometric view of my final test environment and associated electronics. 28
3-2
Schematic of test environment design. . . . . . . . . . . . . . . . . . .
11
29
3-3
Diagram showing the layout of a typical microfabrication printing pro-
cess. A sheet of PET is being printed, and it is wrapped around a
set of rollers. The rollers are wrapped in a layer of PDMS that has
micron-sized features which act as the stamp for transferring ink to the
PET sheet.
3-4
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
31
Renders comparing the designs of the test environment at different
stages of the project.
. . . . . . . . . . . . . . . . . . . . . . . . . .
34
4-1
Schematic of test environment design. . . . . . . . . . . . . . . . . . .
37
4-2
Diagram showing the geometry used to calculate the equivalent vertical
. .
39
4-3 Renders comparing the original shaft clamp design to the final design.
40
4-4 Renders comparing the designs of the position sensor clamps. . . . . .
41
error in the shaft position given a radial position error of 5.5 pm.
4-5
Sample plate with bolts and washers holding PDMS sample in place;
the helicoil is visible in the center. . . . . . . . . . . . . . . . . . . . .
42
4-6 Using the mill to machine counterbores in the base plate. . . . . . . .
45
4-7 Using the dial indicator to measure the relative flatness of the aluminum side wall as I sanded it down. . . . . . . . . . . . . . . . . . .
46
4-8 Side-by-side comparison of final CAD rendering with fully assembled
test environment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5-1
46
Schematic diagram showing how the controller and the DAQ are connected to the actuator and sensors in my system.
. . . . . . . . . . .
49
. . . . . . . . . . . . . . . .
53
5-2
Final load cell supporting circuit design.
5-3
Photograph of final load cell supporting circuit design.
6-1
Spring mass damper model of my test environment used to develop
. . . . . . . .
56
control model, next to a rendering of my mechanical structure for comparison.
6-2
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
58
Free body diagram of actuator sub-assembly mass, showing forces applied to mass from motor, PDMS and gravity.
12
. . . . . . . . . . . . .
60
6-3
Free body diagram showing forces applied to ground plane. The resultant force is equal to the sum of the damping and spring forces on the
PD M S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
61
6-4 Pole-zero map for the plant. Notice that there is a pair of complex
poles, a pole near the origin, and a zero distantly spaced from the poles. 63
6-5
Bode plots for plant. Notice that the magnitude is always negative,
and there is a 180 degree change in phase. This is not ideal behavior;
a controller is necessary. . . . . . . . . . . . . . . . . . . . . . . . . .
6-6
64
Pole-zero map of entire system, iteration 1. Notice that the system is
unstable because there is a pole on the right side of the plane. This
controller does not meet specifications. . . . . . . . . . . . . . . . . .
66
6-7 Pole-zero plot for second controller design iteration. The system is now
stable. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6-8
67
Bode plot of system. Notice in magnitude plot that the roll-off is
significantly smaller than specified. . . . . . . . . . . . . . . . . . . .
68
System Bode plot for Design Iteration 3. . . . . . . . . . . . . . . . .
69
C-1 View of test setup. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
92
C-2 Close-up of test setup. . . . . . . . . . . . . . . . . . . . . . . . . . .
92
C-3 Setup for determining force of magnetic attraction.
. . . . . . . . . .
94
C-4 Setup for determining spring constant. . . . . . . . . . . . . . . . . .
94
6-9
C-5 Image used to calculate maximum spring extension for shaft collar on
magnet with cardboard spacer.
. . . . . . . . . . . . . . . . . . . . .
96
C-6 Image used to calculate maximum spring extension forl0-32 5/8" screw
on magnet.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
96
C-7 Measuring the displacement of the voice coil actuator with a dial indicator...........................................
97
C-8 Measuring the horizontal displacement of the F4000.
. . . . . . . . .
98
C-9 Measuring the vertical displacement of the F4000. . . . . . . . . . . .
99
13
14
List of Tables
3.1
Functional requirements for the test environment. . . . . . . . . . . .
4.1
Stiffness values for PDMS, load cell and sample plate. PDMS is three
30
orders of magnitude less stiff than the load cell and sample plate, so
we can assume that the sample plate and load cell are relatively rigid.
5.1
43
Bill of materials for main actuator and sensor components in test environm ent. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
47
. . . . . . .
48
5.3 Functional requirements comparison for different voice coil motors. . .
51
5.4 Functional requirements comparison for different position sensors. . .
51
5.5 Specifications for Futek LCM300 load cell. . . . . . . . . . . . . . . .
53
5.2
Functional requirements comparison for DAQ hardware.
5.6 Functional requirements and performance parameters for LM324 op amp. 54
5.7 Functional requirements and performance parameters for AD620 instrumentation amplifier. . . . . . . . . . . . . . . . . . . . . . . . . .
6.1
55
Component stiffnesses for actuator sub-assembly. Since all the stiffnesses are significantly larger than the PDMS stiffness, the entire assembly can be modeled as rigid. . . . . . . . . . . . . . . . . . . . . .
6.2
Estimated values for PDMS stiffness and damping from experiment
and literature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.3
59
59
Stiffness values for load cell, sample plate and outer structure. All stiffnesses are 3 to 4 orders of magnitude larger than the PDMS stiffness,
so they can be modeled as perfectly rigid.
15
. . . . . . . . . . . . . . .
59
6.4 Parameters for plant model. . . . . . . . . . . . . . . . . . . . . . . .
62
6.5 List of poles and zeroes in plant transfer function. . . . . . . . . . . .
63
6.6 Functional requirements for controller. . . . . . . . . . . . . . . . . .
65
16
Chapter 1
Introduction
1.1
Motivation
This thesis describes an extended research project that I have worked on since January
2013, although the work presented here was completed in the spring of 2014 for my
Bachelor of Science thesis requirement. I began this project with two other students in
the Mechanical Engineering Department, Spencer Wilson ('15) and Chandler Douglas
('14). Spencer created the initial mechanical design, and Chandler worked with me to
develop the first iteration of the full system model. I have credited their work within
this thesis at the points where it is relevant.
This project was created by Professor David Hardt, a member of the Laboratory
for Manufacturing and Productivity. This thesis is intended to contribute to the
research conducted by Professor Hardt's group, the Center for Polymer Microfabrication (CPM). I was fortunate to have Maia Bageant, a masters' student with Professor
Hardt, as a direct supervisor. I also received significant guidance from Adam Libert,
as well as Scott Nill, Larissa Nietner and Joe Petrzelka. Polymer- based manufacturing is an emerging industry, and it is the focus of Professor Hardt and the CPM
lab. Polymer-based manufacturing is used to produce microelectromechanical systems (MEMS) devices with micron and submicron-sized features. MEMS devices can
be used for a wide range of disciplines, including chemical, biomedical and photonic
applications. For example, one medical application of MEMS devices is a "lab on
17
a chip" that can be used to screen for diseases like malaria using a small sample of
blood. Polymer-based manufacturing can also be used to produce solar panels and
liquid display screens. The CPM investigates all aspects of the polymer manufacturing process, including material research, equipment and tooling, metrology and
optimizing manufacturing systems [1}.
The technology behind MEMS devices enables us to make revolutionary products
that will impact many industries, but the key to making this impact lies in finding
ways to commercially produce MEMS devices.
The CPM group seeks to under-
stand and optimize all aspects of the manufacturing process and find ways to make
it commercially viable. One common manufacturing method that the CPM group is
currently investigating is contact roll printing, where ink is transferred from a polymer stamp to a polymer sheet and then the sheet is etched to produce micron-sized
features. The roll printing process is similar to the printing press used for printing
newspapers; sheets of polymer (instead of paper) are rolled up and run past a printing
stamp. The printing stamp deposits ink onto the polymer sheet, which is then used
in the etching process to selectively remove material and leave behind microscopic
features. Roll-based processing is an efficient way to mass-produce MEMS devices
because it can be used to print large surface areas at fast rates. Roll-to-roll printing
also uses existing knowledge of how to control roll-based printing methods, so existing
pressure control and spatial recognition techniques can be used to print these devices
[2].
One key problem in printing on polymers is that it is hard for the stamp to apply
uniform pressure across the polymer sheet. Some researchers in the CPM group
(Joe Petrzelka and Hussein Al-Qhatani) developed a flexible polymer capacitance
sensor that can be used to detect the pressure that the stamp is applying to the
polymer sheet. The capacitance sensor is a sandwich, made of alternating layers of a
polymer called polydimethylsiloxane (PDMS) and a conductive layer. By placing a
grid of these capacitive sensors underneath the polymer sheet that is being printed,
a manufacturer could measure in real time the pressure that each part of the sheet
was experiencing. If one region of the sheet experienced less pressure than the rest
18
of the sheet, the manufacturer could take steps to adjust the printing process and
reject that region of printed polymer [3]. However, the control system operating the
printing press would not be able to accurately control the process unless it took into
account the behavior of the capacitive sensors and the polymer sheet (which is usually
made out of PDMS, as well).
1.2
Contribution of Thesis
The purpose of my thesis project is to build a small test environment that is capable
of characterizing the dynamic behavior of PDMS. Once I can accurately describe the
dynamic response of PDMS with a model, the model can be used to build a control
system for a printing press that takes that behavior into account, and therefore can
print microscopic features more accurately than is currently possible.
The scope of my thesis is to design and build the mechanical test environment,
specify and select the right sensors and actuators for the environment, and then
design a control system that would operate the test environment and collect data. I
plan to use system identification techniques to measure the frequency response of the
PDMS test samples; I will use that data to write a transfer function characterizing
the response. The ultimate contribution of this thesis would be an accurate model for
the dynamic behavior of PDMS. Other students in Professor Hardt's research group
can use this model to design control systems for their own projects; other researchers
could also use my test environment and methods to collect data on different kinds of
materials. I have carefully documented the design, construction and operation of the
test environment itself so that Professor Hardt's students could continue to use the
test environment to collect more data after I leave the project.
I partially completed the work that I outlined in the scope of my thesis. I completed a mechanical structure that integrated a set of actuators and sensors that I
selected. I also built a preliminary model for the PDMS, as well as a controller. In
the Future Work section of my thesis I describe the next steps that should be taken to
finish integration of my test environment and I outline the experimental procedures
19
for using the test environment to collect data.
1.3
Thesis Outline
This thesis is organized into six sections. The Background section describes the
industrial context of my research, as well as some work that other students in the
CPM group produced that was relevant to this project. The Background section also
explains the science behind the system identification techniques that I used to collect
and analyze data. The Project Scope section outlines the functional requirements for
my thesis and gives an overview of the design of the entire test environment. The next
three sections document how I designed, built and implemented my test environment.
The Mechanical Machine Design section outlines my mechanical design process and
how I built the hardware; the Electronic Component Design section describes my
selection process for buying the electronics components, and the circuits I used to wire
the components together. In the Control System section I explain how I modeled the
test environment and then used that model to design a full control system. Finally,
the sixth portion contains my Conclusion and Future Work sections, which describes
the final state of the project, as well as the experimental procedures that I recommend
using to collect data. The appendices contain more detailed engineering drawings of
the final hardware design, an overview of the design review process I used to re-design
the first iteration of my mechanical hardware, results from some initial laboratory
testing I conducted, and recommended experimental procedures.
20
Chapter 2
Background
2.1
Introduction
This section describes the context of my thesis; I focus on how industrial manufacturing demands are driving research into micro-fabrication production methods,
and I also survey existing research papers that relate to my own thesis. This section concludes with a brief explanation of system identification, which is the primary
measurement technique I used to answer my research question.
2.2
Context
This thesis project supports current advances in micro-fabrication and lithography.
Lithography is a growing manufacturing sector because it can be used to integrate
electrical, fluidic, optical and mechanical features on a small scale - these kinds of
devices are called microelectromechanical systems (MEMS) devices [4]. My thesis is
concerned with how these devices can be mass produced, so I investigated existing
lithography techniques, the reasons why certain techniques are gaining traction, and
what development still needs to be done to make those emerging methods feasible.
The development of lithography is currently driven by several industries including
biological and medical research, consumer electronics and sensing applications. For
example, in biomedical applications, MEMS devices can be used to filter nanoparticles
21
or even sequence the human genome [5]. Lithography can also be used to make cheap,
flexible displays and large-scale sensor networks [2].
Currently, the dominant lithography technique in commercial manufacturing is
silicon wafer photolithography; it can produce features as small as 25nm with a resolution of 1.6nm, but at a cost of approximately 10 per wafer per layer of features
[2]. Contact lithography was developed as a cheaper alternative to photolithography;
contact lithography uses physical contact to transfer an inked pattern from a master
tool to a substrate layer. There are two main types of contact lithography: nanoimprinting and micro-contact lithography. In nano-imprinting, a 3-dimensional relief
is patterned on to a polymer, and then thermal embossing or UV curing is used to
make the pattern on the substrate polymer. This process is rate-limited by the fluid
flow of the ink and the energy transfer rate of the heat or light energy to the polymer.
There is no physical limitation on the resolution [2].
However, micro-contact lithography is more commonly used because it can achieve
high-rate, high-resolution printing more effectively than nano-imprinting. In microcontact printing a 2-dimensional pattern is transferred from a stamp to a substrate.
Selective etching can be used to achieve 3-dimensional patterns as shown in the diagram below [2]. Micro-contact printing can achieve resolutions of 200nm. Microcontact printing can go down to 100nm-size features, but any features smaller than
this tend to collapse. The production rate is limited by the diffusion of inks, but is
generally faster than nano-imprinting. The precision is limited by the soft elastomer
stamp material - that is, by the dynamic behavior of PDMS, which is the focus of
my thesis [2]. Micro-contact lithography can be used to print both active devices like
sensor networks and passive devices, such as meta-surfaces that need certain local
properties to achieve a bulk property [2].
PDMS is becoming a popular substrate for making MEMS devices because it has
a variety of useful properties. The commercially available Sylgard 184 PDMS (manufactured by the Dow Corning Corporation) is a biocompatible polymer that is also
chemically inert and thermally stable, so it is well-suited to biomedical applications.
PDMS is already in use in medical applications in catheters, as pacemaker insulation
22
Ink (alkenethio)
transferred to gold
layer via PDMS stamp
PDMS stamp cast from master
Master
PET sheet
Mild ferro-cyanic wet
etch removes exposed
gold layer and develops
pattern
Gold layer
Figure 2-1: Diagram showing micro-contact printing process for casting PDMS stamps
and using them to print patterns in 2 dimensions onto a sheet of PET polymer.
and in ear and nose implants. The material is also permeable to gases, simple to
handle and manipulate, conforms to sub-micron features and is low cost - these are
all features that make it a good material for manufacturing consumer products [4].
PDMS is also frequently used to make active system features like micro-valves and
micro-pumps because it takes minimal energy to actuate those features
[61.
Micro-contact lithography techniques have been combined with roll printing to
develop a precise printing method that can operate over large areas to produce cheap
products. The development of this technology has been driven by demand for flexible
displays and sensor networks.
Roll printing, used for centuries to mass produce
newspapers, is a well-understood technology that engineers are leveraging to mass
produce MEMS devices more cheaply than with photolithography [2].
There are three different ways to transfer the ink from the master to the substrate
using rollers: gravure techniques, offset printing and flexographic printing.
I focus
on flexography in this thesis because other students working with Professor Hardt
have adopted this method, so I wanted to stay relevant to their needs. Flexographic
printing uses a patterned roller with a positive relief to transfer ink from the roll to
the substrate [2]. Modern flexography rollers can be 2m in diameter, 3m wide and
operate at top speeds between 5 and 12 m/s with a resolution of 100pm [2].
In roll printing, the manufacturing process needs to control two critical parameters: the stamp contact pressure on the substrate, and registration between the stamp
and the substrate. Automated systems have been developed that can reasonably control the pressure between the stamp and the substrate, but alignment is still difficult
23
to achieve because PDMS is so flexible [2]. In Joe Petrzelka's thesis, he explains
that some preliminary printing testing was done at MIT, but there was "no means of
actively regulating the stamp contact behavior" which demonstrates that there is a
need to better understand and quantify the dynamic mechanical behavior of PDMS
[2]. PDMS can contribute to the error in registration in a variety of ways - for example, the PDMS can swell as fluid concentration varies. PDMS features can also
spontaneously collapse or deform under contact stresses [2]. We need to be able to
characterize the dynamic behavior of PDMS in order to avoid conditions that cause
these mechanical defects.
Other engineers have used a variety of techniques to measure the characteristics
of PDMS. Some of the papers I read during my literature review conducted tensile
testing, gravimetry studies (measuring the polymer's weight) and goniometry studies
(measuring the surface contact characteristics). Other studies used various types of
spectroscopy like Fourier transform infrared spectroscopy (FTIR) and X-ray photoelectron spectroscopy (XPS), as well as a scanning electron microscope, to understand
the molecular structure of PDMS [4].
Most relevant to my thesis were two studies that conducted dynamic mechanical
analyses of PDMS using several tools. One study used a Bose Electroforce 3200, which
can conduct a range of different dynamic mechanical analyses at different frequencies
(ranging from 10-2 Hz to 101 Hz) and temperatures [6]. In essence my thesis is
reproducing the functionality of a Bose Electroforce 3200 on a cheaper scale, with
just enough capabilities to meet the needs of the Laboratory for Manufacturing and
Productivity.
The second study used a scanning micro-deformation'microscope to apply deflections on the order of nanometers to a cantilevered PDMS beam, and to oscillate that
beam with a frequency on the order of kilohertz. The microscope then measures the
frequency response of the PDMS beam to characterize its dynamic behavior [6]. This
method is very similar to the one I used in my thesis project, although I was operating on the order of microns and Hertz because I wanted to measure the behavior of
PDMS on the same order of magnitude as the smallest printable features which, as
24
described above for micro-contact lithography and roll printing, are no smaller than
0.1 microns.
From my background research, I decided to focus on studying the dynamic behavior of PDMS in the context of micro-contact roll printing, which can produce features
down to the 0.1 pm range. I also decided to apply system identification techniques
to characterize the PDMS' behavior, similar to the methods used by Le Rouzie et al
to study PDMS with a scanning micro-deformation microscope and a Bose Electroforce 3200. The next section will give a brief overview of the system identification
techniques I used to design my test environment and my experiments.
2.3
System Identification
System identification is a process used to characterize the dynamic behavior of an
unknown system, by building a model and verifying it with experimental data. For
the sake of simplicity, and in order to develop a preliminary understanding of the
behavior of PDMS, I have modeled it as a linear system. Non-linear systems introduce
additional complexity into the process that is unnecessary in initial testing.
Iterate on model
design and parameters
+Error
Figure 2-2: A diagram showing the overarching concept behind system identification.
The engineer is comparing the outputs of a model against the actual system, and
adjusting the model until its output matches (or closely approximates) the actual
system's output.
I will illustrate the basic workflow for system identification with an example: an
engineer is trying to characterize the dynamic mechanical behavior of a cantilevered
beam, as shown in the figure below. The engineer would typically start by collecting
25
experimental data on how the beam responds to force inputs at different frequencies.
Then the engineer would build a theoretical model of the beam and apply the same
inputs to the model as they did to the actual beam, and generate the theoretical
outputs from the model. The engineer would then compare the modeled outputs to
the measured outputs and use the error between the two to adjust the model until it
closely matched the actual cantilevered beam behavior. This is an iterative process
that might require rebuilding the model, or simply changing some of the parameter
values [7].
Input force signal
applied by actuator
Input Signal
Output Signal
Centilevered beam
Force (N)
Force (N)
Time (s)
Time (s)
Output force signal
measured by load cell
Figure 2-3: Example of an unknown system that can be investigated using system
identification. An engineer inputs a force signal to the system and measures the
output signal. This measured data can be used to build or verify a model for the
cantilevered beam.
I modified this workflow because I had to first build a model of my mechanical
structure and my PDMS sample so that I could build a control system for the test
environment. There are two ways to build a model for system identification purposes;
since I have a reasonable understanding of the PDMS and can model it as a springmass-damper system (as described in the controls section of my thesis), I can build
a model using differential equations derived from first principles. This is sometimes
called "gray box modeling." However, if I had no basic knowledge of the PDMS'
behavior, I could use "black box modeling" where I would build a model based on the
data I had collected. For example, given the experimental data in the time domain, I
would plot the amplitude of the response signal against the input signal for a range of
frequencies (in other words, I would create a Bode plot). I could then use the shape
of the Bode plot to write a transfer function for the system. A transfer function is
26
simply a ratio of the output to the input for the system, and it describes how the
system behaves for any frequency and amplitude of the input signal.
Iterate on model
design and parameters
Error
Figure 2-4: A diagram showing the modified system identification workflow for my
thesis. I built a plant model using first principles and estimates for all of the physical
parameters. I then built a controller based on that plant model. I would then input
a force signal via the controller to the actual PDMS sample and measure the output.
I would measure the error between the PDMS' output signal and the input signal,
and refine the plant model and the controller until the output and input signals were
equal.
Once I built my model, I used it to design a controller for the test environment.
Although I was not able to complete this portion of the system identification process
for my thesis, the next step that I would take would be to implement the controller in
LabVIEW and collect experimental data. This data can be in the time or frequency
domain. I should also be careful to collect data at the correct sampling rate and resolution - I described how I wrote and met my data collection functional requirements
in the electronic component selection section of my thesis. Ideally, the data should
also be filtered as necessary to remove outliers and system noise.
Once I collected data, I would compare the output force and position behavior of
the PDMS sample to the input signal. I would adjust the plant model, specifically
the part of the plant model that represents the PDMS, so that its output would more
closely match the data I collected. I would then use my adjusted model to redesign
my controller (because the controller design is based on the predicted plant behavior).
Then I would run another set of experiments and collect a second round of data and
again compare it to the input force signal and adjust my plant model accordingly.
27
I would continue this iterative process until my output data matched my input, at
which point I would have successfully modeled my plant and built a controller that
could accurately control the PDMS sample. I could then use the model of the PDMS
in other control loops in other applications to more precisely print the PDMS with
micron-sized features.
28
Chapter 3
Project Scope
3.1
Introduction
The main purpose of my thesis is to build a test environment that can be used to
collect data on the dynamic behavior of PDMS and other polymers used in printing,
and to generate and refine a model for that behavior. My research question is: how
can the dynamic behavior of a PDMS sample with micron-sized features be accurately
modeled?
The first part of this thesis project was devoted to building the hardware and writing the software necessary to collect data to answer the research question. Professor
Hardt did not have a test environment for this kind of experimentation already set
up in his lab (although other students are working on tangentially related projects).
He also did not want to purchase a device like the Bose Electroforce 3200 because
it did not have the correct force range, nor did it have a sufficiently fine resolution
for my application. Therefore, since I had to build my own test setup, my secondary
research questions was: what is the optimum machine design for testing the behavior
of a PDMS sample? This question drove the first part of my thesis where I iterated on
the design of the mechanical system and selected appropriate actuators and sensors.
My main research question drove the design of my control system.
I developed a machine to test PDMS samples that were made of a single layer of
PDMS and embossed with microscopic features. However, Professor Hardt wanted to
29
have the flexibility to conduct system identification testing on other kinds of PDMS
samples in the future, so I tried to incorporate as much flexibility and versatility in
my design as possible. A photograph of my test environment is shown below.
Figure 3-1: An isometric view of my final test environment and associated electronics.
The machine integrates a force actuator with force and position sensors.
An
outer aluminum structure is built around the actuator assembly. The linear voice coil
actuator at the base of the machine drives a steel shaft upwards to apply a force to
the PDMS sample, which is fixed to an aluminum plate. The steel shaft is kept in
alignment by the air bearing. The load cell is connected to the PDMS sample and
the aluminum plate on one end, and it is connected to the reference ground plane, the
outer structure, on the other end. The position sensor, a linear variable differential
30
transformer (LVDT), moves with the actuator shaft and detects the real-time position
of the actuator shaft, which is affected by the dynamic behavior of the PDMS sample.
Adjustable reference plate
Load cell
PDMS sample
Top shaft clamp
Linear variable
differential transformer
Air bushing
Actuator shaft
Connection to shaft
Outer aluminum
structure
Linear voice coil
actuator
Figure 3-2: Schematic of test environment design.
3.2
Functional Requirements
The functional requirements I wrote for this project are listed in the table below.
They are derived from Joe Petrzelka's research and from the minimum requirements
that Professor Hardt and I agreed on at the start of my project. A more detailed
explanation of each requirement follows.
31
Table 3.1: Functional requirements for the test environment.
Design Parameters
Functional Requirements
Fix 5 degrees of freedom of PDMS; only
Hold a sample of PDMS
allow small displacements in direction
of applied force
F = [5,10N applied directly to sample
Apply continuous force to sample
UF
=O.N
6= [0, 0.005m]
u, > O.JLm
Apply force as a sine wave input signal f 25 Hz
of varying frequencies
u = 0.1 Hz
Displace actuator relative to sample
3.2.1
Hold a sample of PDMS
I based my test environment design on the design of an Instron machine because
Instron machines are also used to measure the material properties of different samples.
Specifically, Instrons can conduct stress-strain tests which are tests where an input
signal is applied to a sample in one direction only, and the corresponding output
signal is measured. My testing method is the same - I will apply an input force signal
in the shape of a sine wave to a sample in a single direction, and then measure the
response.
In an Instron machine, the test sample is fixed in place and then the input force
or strain is applied to that stationary sample. I followed that design concept, which is
why my first functional requirement was to constrain five of the sample's six degrees
of freedom, so that I could isolate my study of its behavior to one direction only.
The behavior of interest in the PDMS' response is how it displaces in the direction
of the external force applied. In an industrial application, sheets of PDMS will be
wrapped around rigid glass rollers, and the force applied to the sheets will be normal
to the surface. The displacement of the PDMS normal to the surface of the roller
is therefore the displacement of interest in this thesis because that displacement will
disrupt the printing control system. If the displacement and force response of the
PDMS in that direction can be characterized, then the disruption could be included
in the control system. Therefore, in the test environment, the force applied to a
32
PDMS sample is also normal to its surface. The sample must therefore be fixed in
every degree of freedom except in the direction normal to the sample's surface, which
in this case is the vertical Z-axis.
on roller
stamp
PDMS
Roller
Ink transferred
to PET surface
PET sheet
Figure 3-3: Diagram showing the layout of a typical microfabrication printing process.
A sheet of PET is being printed, and it is wrapped around a set of rollers. The rollers
are wrapped in a layer of PDMS that has micron-sized features which act as the
stamp for transferring ink to the PET sheet.
3.2.2
Apply continuous force to a sample
The goal of my first planned round of experiments is to measure the step response of
the PDMS sample, and check the measured response against the modeled response.
A step response is easier to generate and model than a sine input, while still providing
useful information about the system and the sample, so it is a logical way to start
testing. I specified that the step response should apply 5 to 1ON of force to the
sample because this is the typical force range for the kinds of printing applications I
am supporting [3]. I should also note that I maintained this force range in my system
identification tests when I used a sine wave input signal as well.
I also specified that I wanted to be able to measure the force output from the
PDMS sample with a resolution of O.1N. I chose this value because I wanted to be
able to measure the force with at least one order of magnitude smaller resolution
than the force that I input to the system. In practice, the load cell that I selected
has a resolution of 0.001N, so I exceeded my functional requirement by two orders of
33
magnitude. This is a good result because I cannot predict how much variation there
will be between the input and output force signals, so having a higher resolution
increases the likelihood that I will be able to detect significant differences between
the two signals.
3.2.3
Displace actuator relative to sample
Although my control system is force-control based, I still needed to specify the overall
travel that my machine would have to allow during testing. This specification helped
me to choose a voice coil actuator with a sufficient stroke length, and a position sensor
with an adequate measurement range. I specified that the actuator must be able to
move up to 5mm relative to the stationary PDMS sample because a typical sample
is between 1 and 5mm thick. Therefore the upper bound on the stroke length occurs
when my test environment completely compresses the thickest PDMS sample that I
expected to see.
For this functional requirement I also specified a much smaller resolution because
PDMS samples are often imprinted with features that can be as small as 1 I m thick.
Therefore, just as in my force resolution specification, I wanted to be able to measure
at least one order of magnitude smaller than the minimum displacement I expected
to see if a PDMS stamped feature collapsed during testing.
3.2.4
Apply force as a sine wave input signal of varying frequencies
As described in the background section, the main purpose of this thesis project is to
conduct system identification testing on a sample of PDMS to determine its dynamic
behavior. Therefore, my test environment has to be apply to input a force in the
form of a sine wave signal to the PDMS sample. Originally I had intended to design
a machine that could generate a signal up to 100 Hz; however, the voice coil actuator
limited the frequency I could reasonably produce, because the maximum input force
required increases with input frequency.
34
Consider the displacement of the actuator characterized as a sine wave:
x = A sin(wt)
(3.1)
Where A is the maximum required displacement, 0.005m, and w is the input
frequency, which at a maximum is 157 rad/s, or 25Hz (the frequency is limited by
the largest motor that I considered).
The acceleration of the actuator is the second derivative of this expression:
i = -A(w 2) sin(wt)
And the acceleration is at a maximum when
=
(3.2)
=0, as shown below:
-A(w') cos(wt)
(3.3)
cos(wt) = 0
(3.4)
Wt =r
(3.5)
tm=
ir
We can therefore calculate the maximum acceleration to be 123
(3.6)
. Therefore,
the force required to move the actuator assembly at that acceleration is given by
Newton's Second Law. For the motor I selected, the force required is 146N; however,
as the size of the motor increases, the force required increases (because the mass of
the actuator coil increases). One can see from this math that increasing the desired
maximum input frequency would increase the maximum acceleration required, which
would require a larger voice coil actuator. I iterated through several options from
different manufacturers until I found a part that reasonably balanced the voice coil
actuator mass with the maximum applied force.
35
Spencer Wilson's design
Intermediate design
Final design
Figure 3-4: Renders comparing the designs of the test environment at different stages
of the project.
36
Chapter 4
Mechanical Machine Design
4.1
Introduction
The purpose of the mechanical structure is to hold all of the actuators and sensors,
and to constrain their motion to a single degree of freedom for testing. I also ensure
that the machine will not contribute noise to the measured position and force signals,
which means that it has to be rigid and that its mode shapes should be far from the
frequency range used in testing.
I inherited the basic design of the mechanical system from Spencer Wilson, and
then went through three design iterations to build the final design presented at the
end of this section. In the figure below the machine design at every iteration is shown
in chronological order, beginning with the design that I received from Spencer.
I began working on the mechanical design in September 2013 when I first took
over the CAD model from Spencer. I conducted an initial design review where I
considered:
1. The design's ability to meet all of the functional requirements.
2. The shape and size of the assembly and the individual parts to make sure there
was adequate clearance for wires, probes and other components.
3. Design for manufacturing.
37
4. Design for assembly.
5. Failure modes.
My design review criteria and report are included in the appendices. This process
helped me to redesign several of the parts, although the overall design remained the
same. I machined the parts in October and November 2013 and finished assembly in
January 2014.
During assembly I found some key design flaws - in particular, the steel shaft I
was using to transfer the force from the actuator to the test sample was experiencing
a very strong force of attraction from the magnet in the linear voice coil motor. The
sample was also fixed to the top plate of the machine and could not be moved around
to line it up with the center of the shaft. I redesigned the machine a second time and
finished machining and building it in March 2014.
In March, I realized that I had undersized the voice coil motor that I needed,
because I had not yet done the calculations given in the Functional Requirements
section of this thesis. I also still needed to order a position sensor and Adam Libert
encouraged me to consider multiple options beyond the capacitance probe I had settled on in February. I did more research into different options for measuring position
and selected a linear variable differential transformer (LVDT) sensor instead, because
it had greater resolution than my capacitance probe and was also much cheaper. I
then did my third and final redesign to accommodate these new components in my
system. I finished building the final iteration of my machine in April 2014.
4.2
Overview of Machine Design
Below is a detailed rendering of the final CAD design I used for this project. The
labels highlight the key components of the machine. A brief description of each part
of the machine is given below:
38
Adjustable reference plate
Load cell
PDMS sample
Top shaft clamp
Linear variable
differential transformer
Air bushing
Actuator shaft
Connection to shaft
Outer aluminum
structure
Linear voice coil
actuator
Figure 4-1: Schematic of test environment design.
4.2.1
Outer aluminum structure
The framework of the machine is made out of 0.5 inch aluminum 6061 alloy. I chose
to use 0.5 inch aluminum over 0.25 inch aluminum to increase the rigidity of the outer
structure; since I wanted to measure only the displacement and frequency response
of the PDMS samples, I needed to minimize the displacements of the machine itself.
The outer structure is designed in an "0" shape with the driving force applied to
the center of the top plate. This is advantageous because any deflections due to the
driving force will only be in the vertical direction; there will not be lateral components
because the side walls will act symmetrically to prevent deflections in the x-y plane.
I bolted the walls together because that was the simplest, most flexible method to
use for multiple design iterations. And according to my calculations, the net deflection
of the entire structure under the maximum load of 1ON is 3.5 pm. While this is an
39
order of magnitude greater than the resolution I specified for the position sensor, it
is a repeatable error that I can subtract from my data.
4.2.2
Linear voice coil actuator assembly
I selected a linear voice coil motor, an H2W NCC08-34-350-2X without an internal
bearing as my actuator. I considered using other linear actuators such as stepper
stages, rail stages, or even a rotating motor connected to a four-bar linkage that
would convert the rotational motion to linear motion. However, my selection process
was driven by the fact that Spencer had already designed the mechanical system to
use a linear voice coil motor.
I wanted to have more precise control over the axial alignment of the voice coil
motor actuator than an internal bearing would allow; an H2W linear voice coil actuator (NCM-08-35-450-3LB) with an internal bearing with a load rating equivalent to
the actuator I selected has a radial clearance, or error, of 600 pm. It is important to
minimize error in the radial direction of the shaft because I am testing the behavior
of the PDMS samples in one direction only, normal to their surface. I also wanted
to prevent radial motion because that could induce additional vibrations that the
sensors would measure, even though the vibrations would be in the wrong plane.
I chose to buy a motor without an internal bearing (to avoid over-constraining
the system) and controlled the axial alignment with an air bushing instead. The New
Way S302501 air bushing has a maximum radial error of 5.5 pm. In the worst case
scenario, the maximum radial error would exist between the top and bottom of the
air bushing. This would cause the top of the shaft to angle slightly up or down so
that the top part of the shaft (which would contact the PDMS sample first) would be
slightly higher or lower than nominal. I calculated this vertical error using the model
below, where I used simple trigonometry to convert the radial error to an equivalent
vertical error. I found that the maximum radial error contributes a corresponding
vertical error of 7.8 pm. While this error is greater than the specified 0.1 pm position
resolution, it is repeatable so it can be calibrated out of the data.
The motor's stroke length is 0.0203m, which is much larger than the 0.005m spec40
o = 0.003*
L = 0.1143m
Max vertical error
=7.8pm
e=5.5pm
h = 7.8pm
X =5.5
= lym
Max radial error = 5.5Mm
Figure 4-2: Diagram showing the geometry used to calculate the equivalent vertical
error in the shaft position given a radial position error of 5.5 Pm.
ified in the functional requirements. However, this stroke length gives me clearance
space to change out PDMS samples without disassembling the entire machine.
The maximum continuous force that the motor can apply is 156N, which is 1ON
greater than the 146N of required force that I calculated in the functional requirements
section. Note that this continuous force is a conservative estimate for a 10% duty
cycle.
4.2.3
Connection to shaft
The voice coil motor is connected to a precision hardened steel shaft, which acts as
the force actuator on the PDMS sample. The connection between the voice coil motor
and the shaft is made by bolting a plate to the motor and then bolting the plate to
a clamp which holds the shaft.
This part of the design went through several iterations; my first iteration used
a steel shaft collar that was bolted to a disc with slots so that I could adjust the
alignment of the shaft relative to the voice coil motor. However, the steel collar was
magnetically attracted to the voice coil motor's magnet; I estimated the magnitude
of the force to be approximately 24N, which was about double the mass of the entire
41
actuator assembly and would have made it impossible to conduct high frequency
testing with the motor I had selected. The collar was also very heavy, so I redesigned
the connection to use an aluminum clamp which was both lighter and not susceptible
to the magnetic force of attraction from the voice coil motor. The steel bolts were
also attracted to the magnet, so I replaced them with brass screws.
First shaft clamp design
Final shaft clamp design
Figure 4-3: Renders comparing the original shaft clamp design to the final design.
I also increased the thickness of the plate bolted to the voice coil actuator from
0.25 inches to 0.5 inches to increase the distance between the steel shaft and the
motor. The shaft itself was very strongly attracted to the voice coil magnet, but by
doubling the spacing between the bottom of the shaft and the coil, I decreased the
force of attraction by a factor of 4, because F oc 1 where r is the spacing between
the shaft and the coil.
4.2.4
Top shaft clamp with additional clamp for position sensor
This part also went through several design iterations. My initial design for connecting
the LVDT probe, a Macrosensor BBP 315-200, to the top of the shaft was to make
an aluminum plate that clamped around the probe, and was bolted to another steel
shaft collar. I found that the shaft collar was heavy and reduced the amount of force
that the voice coil motor could exert on the PDMS sample, so I chose to integrate
the shaft and probe clamps into a single aluminum clamp.
42
Final position sensor clamp design
First position sensor damp design
Figure 4-4: Renders comparing the designs of the position sensor clamps.
4.2.5
Sample and sample plate
I designed a simple sample plate and cut it from a piece of 0.25 inch thick aluminum.
The plate is large enough to hold a piece of 1 inch by 1 inch PDMS, and 4 bolts with
washers can be used to fix the PDMS in place. (The PDMS is also quite sticky so it
will stay on the plate even when the plate is oriented upside down.) This design is
also versatile because I can bolt samples of different thicknesses to the plate simply
by changing the bolt length.
The plate is made out of 0.25 inch aluminum instead of 0.5 inch aluminum because
I wanted to reduce the damping effect that the mass moment of inertia of the plate
will have on the force response of the PDMS sample. The plate also has a threaded
hole for the load cell to be connected directly to the sample plate.
To learn more about the material properties of PDMS and to intuitively understand its behavior, I made a sample of pure PDMS in the lab and conducted some
static tensile loading tests on the sample. I hung weights from a sample of PDMS
and measured the displacement in order to estimate the PDMS' spring constant. The
values for the PDMS, the plate and the load cell are given in the table below:
Table 4.1: Stiffness values for PDMS, load cell and sample plate. PDMS is three
orders of magnitude less stiff than the load cell and sample plate, so we can assume
that the sample plate and load cell are relatively rigid.
Component
Stiffness (-)
750 + 140
PDMS
2.2 x 106
Load cell
2.3 x 107
Sample plate
I found that PDMS has an average stiffness of 750N/m in tensile loading, which
43
Figure 4-5: Sample plate with bolts and washers holding PDMS sample in place; the
helicoil is visible in the center.
corresponds to a Young's modulus of approximately 8200 Pa. I also tried to apply
a dynamic load to the PDMS sample by tapping the flat sample with a pen, but I
was not able to see any visible response to the input force. The only information
I obtained from that test was that for the typical loads I will apply to the PDMS
during dynamic testing, the response will be smaller than what is visible to the naked
eye, justifying my choice to get a position sensor and load cell with high precision.
The complete list of experiments I conducted, as well as my results, are included in
the appendices.
44
4.2.6
Load cell and adjustable reference plate
I selected a Futek LCM300 25-lb (111N) capacity load cell with threaded connections.
According to my functional requirements I will be applying a maximum of 1ON to the
PDMS sample, so my load cell is somewhat oversized for the application. I selected it
regardless because it was the smallest capacity in-line load cell available, and it had
a high resolution which was desirable.
In my initial design the load cell was located between the voice coil motor and the
shaft actuator. However, I realized during assembly that if the load cell were between
the motor and the shaft, it would read the force applied by the motor to the shaft,
but my point of interest is at the PDMS sample. Therefore, in my second design
iteration I placed the load cell between a slotted reference plate and the sample plate
holding the PDMS sample. The load cell is screwed in to both the reference plate
and the sample plate; I inserted steel helicoils into the tapped holes on the plates.to
prevent the steel load cell threads from locking in the aluminum plate.
The reference plate is connected via slots to the top plate. I added slots to the
top and reference plates so that I could make small modifications to the alignment of
the sample relative to the actuator shaft. With this new design, and assuming that
the sample plate and reference plate are rigid relative to the PDMS sample, the load
cell is now measuring the force response of the PDMS only.
I can assume that the load cell and sample plate are rigid compared to the PDMS
sample because their stiffness values are several orders of magnitude higher than the
stiffness of PDMS that I estimated in my initial experiments. Based on an estimated
stiffness of 750 N/m, the PDMS is 3 to 4 orders of magnitude less stiff than the load
cell and sample plate, so we can approximate them as perfectly rigid. Therefore, the
force measured by the load cell is only the force experienced by the PDMS and is not
affected by the other components in series.
45
4.3
Manufacturing Process
Once I finished my first design review and settled on a preliminary design, I constructed the first iteration of my machine. I used a combination of waterjetting and
machining to make most of the parts - I ordered very few pre-made parts from suppliers. I chose to build my machine structure out of aluminum 6061 alloy because it has
a high strength to weight ratio. Aluminum 6061 is also easy to machine, which made
it ideal for my situation where I prototyped several iterations of the design quickly
because the material was easy to work with.
I used the waterjet to cut the shapes of all the parts I needed, and then added
finishing touches with a mill. Between my first and second iterations I learned how
to make the waterjetting process more efficient for me as a machinist. For example, I
included hole patterns in my waterjet process plans so that I would not have to drill
them out later by hand (which takes longer because I had to zero the part in the
machine and precisely locate each hole manually).
I also learned from experience to add flat sides to the curvature of my clamps so
that I could still easily fixture them in a mill vise. During my second iteration I made
the mistake of trying to clamp circular parts in a straight vise, and had to devise
an imperfect clamping solution to hold the part while I drilled out some holes. By
the third iteration, though, I changed the clamp design to add flat surfaces that were
easier to clamp without compromising the functionality of the clamp.
I have continued to make some mistakes, as well. I am still struggling to find the
optimum way to cut delicate pieces like the clamps. Often I choose a path that cuts
the part away from the stock piece so that it's free to vibrate on the waterjet bed
while I make the final inner cut, and that creates a jagged surface finish. I need to find
a better way to cut thin parts, perhaps by including tabs to hold the parts in place
as they are cut. While I was machining, I mainly added counterbores, countersinks
and slots to parts that I had waterjetted. I also learned to slightly oversize my parts
when I cut them so that I could machine them down to the correct size with a smooth
surface finish so that they would sit flush with coincident parts. For example, I added
46
0.020" to the length of my side walls so that I could mill down the top and bottom
faces so that they would fit smoothly onto the top and base plates.
Figure 4-6: Using the mill to machine counterbores in the base plate.
I was also careful to sand down the important faces on my parts so that they
would be flat to within 0.005". I did this, for example, on the top and bottom faces
of the base plate so that it would sit level on a lab bench, and so that the voice coil
motor would also be level. I selected 0.005" as my tolerance because it is a reasonable
goal to achieve with hand-sanding. I considered using a fly cut to machine down the
surface of my parts, but I learned from Mark Belanger at the Edgerton Student Shop
that fly-cutting a piece of aluminum stock can make it more bent. The aluminum
stock is held flat by the outer layers; they take up much of the stress of keeping the
stock flat. When those layers are removed, the stresses from the inner layers are
released as the entire part bends.
The final design of the machine was completed in April 2014, and the final CAD
rendering and machine photograph is shown below.
47
Figure 4-7: Using the dial indicator to measure the relative flatness of the aluminum
side wall as I sanded it down.
Figure 4-8: Side-by-side comparison of final CAD rendering with fully assembled test
environment.
48
Chapter 5
Electronic Component Design
5.1
Introduction
This section explains the selection process I used to specify the actuators and sensors
for my test environment. I also explain the design process I used to build a circuit
that would provide power to and collect a signal from the load cell, which did not
come with a driver. This section is actually the most critical design step in my thesis,
because the selection of my actuators and sensors drove the design of the rest of the
test environment. I designed a mechanical structure that would integrate the specific
parts I chose, and I built a control system around the capabilities and limitations of
the parts I purchased.
Table 5.1: Bill of materials for main actuator and sensor components in test environnent.
Component
Model
Linear voice coil actuator
H2W NCC08-34-350-2X with LCAM
5/15 driver
Linear voltage differential transformer Macrosensor BBP 315-200 with EAZYCAL LVC-4000
Load cell
Futek LCM300 25-lb (111N)
Data acquisition hardware
NI USB-6211
49
5.2
Component Selection
To meet the functional requirements I set out at the beginning of my project, I needed
an actuator to apply an input force signal to my test sample, and sensors to read the
position of the sample and the forces experienced by the sample. I researched different
sensor and actuator types to choose the best kind of component, and then I researched
different manufacturers and suppliers to find the best part for my system.
5.2.1
Data acquisition hardware
I will begin this section with an explanation of how I chose my data acquisition
hardware, and how that affected the rest of my component selection.
The functional requirements I used to select my DAQ are summarized in the
table below. First, I was looking for a DAQ that had sufficient bits to accurately
sample the dynamic range of my position sensor. I considered dividing the signal
into approximately 1000 discrete levels as sufficient to draw a smooth sine wave, so I
looked for DAQ devices that had greater than 10 bits (because 210 = 1024 levels). I
also needed a DAQ that could collect approximately 1000 samples per period of the
sine wave, which meant that the DAQ would need a sampling rate of at least 1000
samples per period x 50Hz = 50,000 S/s.
Table 5.2: Functional requirements comparison for DAQ hardware.
NI-USB 6210 NI-USB 6211 NI-USB 6212
Functional Requirements
Number of bits > 10
16
16
16
Number of AI channels = 2
16
16
16
Number of AO channels = 1
0
2
2
Sampling rate > 500 Hz
250000 S/s
250000 S/s
400000 S/s
Input voltage range (analog)
10V (max)
10V (max)
10V (max)
200mV (min)
200mV (min)
200mV (min)
Input voltage resolution (analog) 2.69mV (max)
2.69mV (max)
2.71mV (max)
0.088mV (min) 0.088mV (min) 0.089mV (min)
Output voltage range (analog)
10V
10V
Output current range (analog)
2mA
2mA
Cost
$584.10
$792.00
$1008.00
Ultimately I selected the USB-6211 because it had 16 bits, 2 analog output chan50
nels (I needed 1 channel to send a signal to the voice coil actuator driver) and 16
analog input channels (I needed 2 to collect data from the load cell and position sensors). I did not choose the USB-6212 because, although it had a higher sampling rate,
as I explain below, the 250,000 S/s sampling rate was sufficient for this application,
and the USB-6211 was also a cheaper option than the USB-6212.
My electronic control system consists of my computer which is running a LabVIEW program, the data acquisition card, and then a set of sensors and actuators
and their corresponding drivers. This is shown in the diagram below.
Actuator
Controller
Sensors
Figure 5-1: Schematic diagram showing how the controller and the DAQ are connected
to the actuator and sensors in my system.
The slowest component in this system is my computer and the LabVIEW software.
From other students' experience, I am limited to a relatively low operating frequency
(i.e. how quickly I can send signals to my voice coil actuator) when running a real-time
loop in LabVIEW. However, my operating frequency can actually be faster because
the DAQ hardware I selected can buffer the signal so that it will store many data
points and be able to deliver them at a faster rate. In future work I could also use a
real-time controller to send and receive data much more rapidly than the DAQ that
I currently use can.
51
5.2.2
Actuator
I was set on buying a voice coil motor from the start of my project because that was
the type of actuator that Spencer Wilson ('15) used in his design. Ultimately, the
voice coil motor best suited my key functional requirements which were input signal
versatility (i.e. having the ability to apply a constant load to the PDMS sample, as
well as a sinusoidal force) and to travel in one direction only. I did some research
to find different voice coil manufacturers and the products they offered. I checked
each motor against my force calculations as described in the functional requirements
section, to make sure that the motor actuator coil mass, as well as the continuous
force applied, would both be adequate to meet my overall functional requirements.
(That is why the functional requirement for the force given here is between 60N and
600N; because that is the range of forces the motors must be able to supply to operate
at 100Hz.) I considered the overall stroke length just to be sure the motor could move
the shaft far enough up and down to fit comfortably in the hardware I built. I also
checked the electric time constant of the motor to get a better sense of how quickly
it responded to changes in the input signal.
Although the Moticont motor seemed to be a better motor for the cost, I selected
an H2W motor because from my experience they proved to be a more reliable and
responsive manufacturer. The Moticont specification sheet for choosing a driver was
very difficult to understand and even after I finished working through it, I still was not
confident that I had selected the right driver for the motor I had selected. Instead,
H2W offered a driver that their engineers confirmed would work with the motor I
wanted.
5.2.3
Position sensor
I researched a variety of position sensing options before finally selecting a particular
sensor; I looked at capacitance probes, linear variable differential transformers and
optical encoders. I have summarized my research in the table below.
My two critical functional requirements came from the overall project goals, which
52
Table 5.3: Functional requirements comparison for different voice coil motors.
Functional Requirements
Moticont
H2W
BEI
Kimco
(070-089-02)
(NCC08Magnetics
34-350-2X)
(LA38-48OOOA)
60N < F < 600N
150.7N
156N
185N
0.5in < stroke < 1.5in
1 in
0.8 in
0.3 in
Cost
$495(motor) + $795(motor) + $985(motor)
Electric time constant
$644(driver) =
$790(driver) =
$1139
0.65 msec
$1585
0.8 msec
1.12 msec
Table 5.4: Functional requirements comparison for different position sensors.
Functional
Capacitance Probe LVDT (BBP Optical
Encoder
Requirements (Lion
Precision 315-200)
(Ti0200)
C18)
1mm < range < 5mm
i5mm
unlimited
5mm
0.075pim
0.15pm
0.1pm (tape is to 1nm)
Cost
Cap probe + driver =
$5035
$459(LVDT) +
$521(driver) =
$446(readhead)
$529(interpolator)
$980
$40(scale) = $1015
66667
4MHz clocked output for
Dynamic range
66667
+
<0.1p1m
+
Resolution
max speed of 0.33 m/s
Linearity error
Repeatibility error
0.2%FS = 25pm
n/a
500pm (max)
Listed as being
the same as reso-
0.0375pmfor3mmlength
lution = 0.15 pm
were a range of 1 to 5mm, and a resolution of 0.1 jLm or better. The cost was also
an important factor because this was not the only electronic component I needed to
purchase.
I calculated the dynamic range for each device as well; I defined dynamic range
as:
Rangedyn. , =
Range
Resolution
(5.1)
The dynamic range is the number of discrete steps the probe's signal could take,
53
if you were to digitize the analog signal. The dynamic range would drive the selection
of my data acquisition (DAQ) hardware, because a higher dynamic range required a
DAQ system with more bits. I also checked the linearity error and the repeatability
error because if they were significantly larger than the device's resolution, I would
have to consider the device as being less precise than advertised. Finally, my ease to
integrate criteria considered how much additional design and rework it would take to
change my mechanical design to accommodate the probe.
Ultimately I selected an LVDT probe, a Macrosensor BBP 315-200 precision sensor
and corresponding driver, the EAZY-CAL LVC-4000. I did not choose the optical
encoder system because it required a higher-speed data acquisition card than I could
afford to purchase and I was concerned that I would not be able to easily integrate
that sub-system into the rest of my machine. I did not choose the eddy probe because
it did not have the full range that I needed. Although the capacitance probe had a
better resolution and less linearity error, it was very expensive and so I selected the
LVDT because it offered the most comparable performance for one-fifth of the cost
of the capacitance probe.
Note that while the LVDT maximum linearity error is 500 pm, which is much
higher than the resolution I want to have, the nominal linearity error that I expect
to see is on the order of 0.1 pm. I calculated this based on the assumption that I
will actually see displacements between 10 and 100 pm (because the stamp features
themselves are 1 to 100 pm high), which corresponds to a linearity error of 0.05 pm
to 0.5 pm. This range of error is on the same order of magnitude as the resolution I
specified, so it is acceptable for this application.
5.2.4
Force sensor
The load cell was one of the first devices I purchased for this project. The load cell
I purchased, a Futek LCM300 25-lb (111N), fit my functional requirements. The
critical specifications for the load cell are listed below.
54
Table 5.5: Specifications for Futek LCM300 load cell.
Parameter
Value
Rated output
2mV/V
Excitation voltage
15V max
Linearity error
i0.5%ofRO
Hysteresis error
t0.5%ofRO
Non-repeatibility error
t0.1%ofRO
5.3
Load Cell Circuit Design
When I bought the Futek load cell, there was no driver available for it so I designed
and built a small circuit that could power the load cell and collect its output signal.
My thesis graduate student supervisor, Maia Bageant, helped me to design the circuit
and guided me to selecting the right components as well. The design went through
several iterations based on what electronic components were available in the lab, but
the overall concept remained the same. The final circuit design is shown below.
LM324
AD620
4700
LM324
Legend:
5.k
LM324
---
Power
Signal
5V
2.7 kO
Figure 5-2: Final load cell supporting circuit design.
The purpose of this circuit is to provide power to the load cell, and to collect
the output signal and send it to the DAQ hardware. The circuit begins with the
55
power supply, which supplies 15V. The load cell draws 15V, but the op amps require
a smaller voltage, so I also pass the input power through a voltage divider to step
it down to 5V, which is the nominal power supply required by the op amps in my
circuit. The values for the resistors in my voltage divider are shown above.
After the voltage divider, I put a Texas Instruments LM324 op amp on both
the 15V and the 5V lines to act as a buffer. The op amps are wired in a "unity
gain" configuration which means that the gain from the input to the output is 1.
Furthermore, the op amps separate the input side of the circuit from the output side
of the circuit so that no matter how the output side's voltage draw changes, the op
amp will always output the voltage that the input side is designed to deliver. This is
useful in my project because the load cell's voltage draw may change with the amount
of load it sees, but the op amp will ensure that the voltage divider circuit's voltage
does not change.
I selected an LM324 op amp primarily because it was readily available in our lab.
It also meets all of the functional requirements for this circuit, as shown in the table
below:
Table 5.6: Functional requirements and performance parameters for LM324 op amp.
LM324 Value
Functional Requirement
Voltage output to load cell = [1, 15V]
Voltage output = [0, 28V]
Voltage output to AD620 = [i2.3, +18V]
Voltage output to LM324 = [3, 32V]
Current output to load cell = [0, 20mAJ
Current output to AD620 = [0, 1.3mAJ
Current output to LM324 =
[0,
Output current = [-20, -60mAJ
0.8mAJ
I was concerned with the output voltage and current ranges for the LM324 because
I used it as a power conditioner for all the other components in the circuit. Therefore,
I set functional requirements on the voltage and current outputs for each component
that the LM324 would be supplying with power (including itself).
The other op amp I selected was an Analog Devices AD620 instrumentation amplifier. I used one of these in the circuit to boost the output signal from the load cell
which is, at most, 30mV. According to the AD620 specifications sheet, I can set the
56
gain using the following equation:
Gain
49.4kQ
R +1
(5.2)
Where R is the value of the resistor I connect externally to the instrumentation
amplifier. I chose to use a 470Q resistor at first because that set the gain to approximately 1.1, which is close to 1. The DAQ specifications state that it can read an
analog input with a voltage range of 200mV and a precision of 0.088mV, so nominally
the DAQ should be able to read the load cell's signal. However, I still included the
instrumentation amplifier in the circuit in case I needed the flexibility to boost the
gain on the load cell signal during my actual testing. I would boost the gain by
changing the value of the resistor connected to the AD620.
I chose to use an AD620 again because it was easily available in the lab; I also
confirmed that its performance characteristics met the functional requirements of my
system, as shown in the table below.
Table 5.7: Functional requirements and performance parameters for AD620 instrumentation amplifier.
Functional Requirement
Gain = [1, 100
Voltage input = 30mV
AD620 Value
Can be set by user
Voltage input = [t2.3, t5V]; either
range will accommodate input voltage
Voltage output = [0, 1.5VI
Voltage output = [-3.9V, 3.8V
I was primarily concerned with checking that the AD620 could take in the signal
from the load cell and deliver an output signal at the right current and voltage for
the final LM324 op amp and DAQ to read it. After the load cell signal is boosted by
the AD620, it passes through another LM324 so that the impedance of the load cell
signal matches the impedance of the DAQ.
The USB-621 1 has an impedance of greater than lOG Q at the analog inputs where
the load cell signal is received. It is important to match the impedance of the DAQ
receiving the signal with the impedance of the LM324 delivering the signal because
that ensures maximum power transfer of the signal to the DAQ. Otherwise, if the
57
DAQ has a much higher resistance than the op amp, the DAQ cannot read the signal
because the signal is not powerful enough to be read across such a high resistance.
Conversely, if the DAQ and the LM324 have a similar resistance, the signal power
should be sufficient for the DAQ to read it. A photograph of the final circuit (reflecting
the circuit diagram above) is shown here.
Figure 5-3: Photograph of final load cell supporting circuit design.
58
Chapter 6
Control System
6.1
Introduction
The final step towards integrating the entire design was to build a control system for
the test environment. I started designing a control system in January 2013 because
that was my first task on this project; however, the design and my modeling methods
changed considerably in a year, and my final control system model came out of what
I learned in 2.14: Analysis and Design of Feedback Controls. To design the control
system, I needed to characterize the plant (which included the mechanical structure
and the PDMS sample), the closed loop controller, and the feedback for the controller,
as shown in the diagram below. This section describes the model I developed for the
plant, the loop shaping techniques I used to design the controller and the feedback
system for running the test environment.
6.2
Plant Model
I began my design process by modeling the plant itself. I chose to consider only
the mechanical structure, the actuator and the sample itself; I ignored the dynamic
behavior of the sensors and their drivers, as well as the voice coil actuator's driver,
because I assumed that they would be much more responsive than the rest of the
system.
59
I modeled the plant as a mass-spring-damper system coupled to a classic model of
a motor. A diagram of my model is shown below. I considered the motor's inductance
(L), internal resistance (R), back emf (e) and force constants. The motor acts as a
transformer, converting electrical power to mechanical power.
FR
K
B
-
FA
-
L
R
e
V
Figure 6-1: Spring mass damper model of my test environment used to develop control
model, next to a rendering of my mechanical structure for comparison.
On the mechanical side, I lumped together the actuator assembly (including the
voice coil, the shaft, and the shaft clamps) as a single mass that is rigid.
I can
justify this because the shaft, shaft connection plate and screws are all 5 orders of
magnitude stiffer than the PDMS that they are interacting with. The stiffness values
for the actuator assembly components are given in the table below. For comparison,
I calculated the approximate stiffness of the PDMS to be 750 t 140N/m.
I modeled the PDMS itself as a spring-damper system rigidly fixed to ground.
I chose to model the PDMS with both a spring and a damper to produce the most
general model possible. I neglected the PDMS' mass because it was stationary relative
60
Table 6.1: Component stiffnesses for actuator sub-assembly. Since all the stiffnesses
are significantly larger than the PDMS stiffness, the entire assembly can be modeled
as rigid.
Component
Stiffness (N/m)
Shaft
6.7 x 108
Shaft connection plate
7.2 x 108
Brass screw
1.5 x 108
to the outer structure since it was fixed to the sample plate. I used the data I collected
in lab testing to estimate the spring constant and mass of the PDMS sample. I used
a damping estimate from another paper that attempted to measure the viscoelastic
properties of PDMS [8]. The values are listed in the table below.
Table 6.2: Estimated values for PDMS stiffness and damping from experiment and
literature.
PDMS Parameter
Value
Stiffness
750 140N/m
Damping
0.015N8
I entered these values as part of my plant model, although during my testing I
tried changing the values of these parameters and measuring the effect that had on
my control loop and its performance.
As with the actuator assembly, I modeled the sample plate, load cell and outer
structure as perfectly rigid compared to the PDMS itself. The values for the structural
components' stiffnesses are given below.
Table 6.3: Stiffness values for load cell, sample plate and outer structure. All stiffnesses are 3 to 4 orders of magnitude larger than the PDMS stiffness, so they can be
modeled as perfectly rigid.
Component
Stiffness (N/m)
Load cell
2.2 x 101
Sample plate
2.3 x 101
Outer structure
2.8 x 10
Now that I had established a logical model for the system, I wrote out the defining
system equations in terms of the state space variables. The first equation defined the
behavior of the motor:
61
di
Vs =iR+ L-+
dt
dx
Kb--
dt
(6.1)
Where Vs is the source voltage to the motor, i is the current through the motor, R
is the motor resistance, L is the motor inductance, ! is the change in motor current
over time, Kb is the back emf constant, and 4 is the velocity of the voice coil actuator.
I wrote a second equation defining the behavior of the mechanical system, taking
into account all the forces that the actuator mass would experience. A free body
diagram shows those 4 forces below - the mass would see a force from the motor, FM,
forces from the PDMS' damper (FB) and spring (FK), and the mass' own weight, Fg.
FB
FK
Fm
Fg
Figure 6-2: Free body diagram of actuator sub-assembly mass, showing forces applied
to mass from motor, PDMS and gravity.
Together these produce a system equation:
d2 X
m-=
F. - F - FB- FK
(6.2)
Which can be rewritten in state space variables as:
m
d2x
2
dt
dx
=Kmi-mg-B--- Kx
dt
(6.3)
Where Km is the motor force constant, B is the PDMS' damping coefficient, and
K is the PDMS stiffness. We can rewrite both of these equations in terms of the state
space variables, x, 4, and i:
di
dt
_
1
R.
s - L
L
L
62
KBdx
dtL dt
(6.4)
B dx K
dx-- = Km.
-- - g - M--- t -xM(65)
M
dt2
6.
The two equations were connected by the motion of the actuator assembly (as
expressed by x and Q). In state space matrix representation, the equations can be
written as follows:
0
X
[
=.-L
S0
X
1
0
-.
-iL]
+
-R
K&
i
0
0
0
-]
1
0
(6.6)
[9
I also wrote a matrix representation of my output variable, FR, the resultant force
on the PDMS sample. From the free body diagram shown below, I calculated that
the resultant force is simply the sum of the damping and spring forces on the PDMS
sample.
FR
FR
FK
Figure 6-3: Free body diagram showing forces applied to ground plane. The resultant
force is equal to the sum of the damping and spring forces on the PDMS.
From that force balance, I wrote the output equation in matrix form:
[FR]
= [-K -B
0]
[t
+ [0 0]
Vs
(6.7)
At first I tried using a number of mathematical programs like MATLAB and Mathematica to try to calculate a symbolic representation of the transfer function from
these steps. However, neither program was able to produce an algebraic expression
for the transfer function, so I went back and calculated all the numerical values for the
variables I used. The complete list of values is given in the table below. Then I ran
a numerical program in MATLAB to generate the numerical version of the transfer
63
function.
Table 6.4: Parameters for plant model.
Value
Sub-Assembly Parameter
Resistance
6.250
5 x 10-3 H
Inductance
64.2N/A
Voice coil motor Force constant
Back emf constant
64.2V/m/s
Voltage source
87.5V
PDMS
Actuator mass
0.96kg
Damping coefficient
Stiffness
0.015s
750N/m
The complete transfer function for the plant was:
=
-200.6s - 1.003 x 107
53 + 1250S2 + 8.595s + 9.766 x 105
Given the transfer function, I ran several different analyses on it. First, I plotted
all the poles and zeroes of the transfer function. I noticed that there was a pair of
complex poles and a pole near the origin, all grouped together on one side of the
plane, and then a zero far away on the negative side of the real axis. All of the poles
and zeros are on the left side of the real axis, so the plant is stable.
I also generated a list of all the poles and zeroes as listed below.
Table 6.5: List of poles and zeroes in plant transfer function.
Type
Value
684i
-624
Poles
-1
Zeroes
-50000
I also generated the Bode plots for my frequency range of interest (0 to 100Hz).
The Bode magnitude plot shows that the plant's gain is always negative, which is
undesirable in a control loop. The magnitude also varies within our frequency range
of interest; we will need to implement a controller to make the response constant
across this frequency range. The phase also changes a full 180 degrees, from +90
degrees to -90 degrees, which suggests that there is a zero at the origin, and at least
two poles in the system.
64
Plant Pole-Zero Plot
X
0 -------------------------------------------------------------------------.
E
X
I
I
I
Real Axis
Figure 6-4: Pole-zero map for the plant. Notice that there is a pair of complex poles,
a pole near the origin, and a zero distantly spaced from the poles.
In conclusion, the plant is stable, but it does not demonstrate ideal behavior
because the gain decreases significantly over the frequency range of interest. The
gain is also negative. In the next section I will describe how I designed a controller
to modify the plant behavior.
6.3
Controller Design
Now that I had a model for my plant and a basic understanding of how it worked, I
set out a list of functional requirements for how I wanted the final control system to
look. I then used this list of functional requirements and my plant model to design a
controller to achieve the final design.
I chose to control my system based on the forces it was experiencing because this
is the most critical variable in my project. I need to accurately input a force signal to
65
Plant Bode Plot
0
-801
901
01
90
I
11a
I
102
Frequency (Hz)
Figure 6-5: Bode plots for plant. Notice that the magnitude is always negative, and
there is a 180 degree change in phase. This is not ideal behavior; a controller is
necessary.
the PDMS sample and measure the output in order to gain a better understanding of
the behavior of PDMS under dynamic loading. I specified a flat, constant gain over
my frequency range of interest (up to 500Hz, which is about five times greater than
the maximum frequency I will be operating at - this is a safety margin built into the
control system). I specified a flat gain because I want the system output to closely
follow the setpoint (i.e. input) I give to my system.
I specified a settling time and rise time because I designed my controller to be able
to implement step inputs to conduct stress-strain tests as well as system identification
tests. In this kind of experiment, it is important that the system can reach the desired
stress value as quickly as possible to start producing accurate data.
Finally, I specified that the system should attenuate all signals above 500Hz (again,
500Hz gives me a safe margin of error above my frequency range of interest which is
66
Table 6.6: Functional requirements for controller.
Functional
Re- Design Parameter
quirement
Type of control sys-
Force
tem
Flat gain over [0,
10OHz]
Stable system
Fast settling/rise time
High frequency signal
attenuation
Gain is constant to within 1 dB over [0,
500Hzj
Completely stable system
Settling/rise time < 0.005s
Cutoff at 500Hz, magnitude decreases
by a factor of 2 by 1000Hz
actually 0 to 100Hz). In case there are some higher order harmonics in my system
that I did not account for in my control model, I want to ensure that those harmonics
are damped out so that they do not cause resonance or noise in my data collection.
6.3.1
Design iteration 1
Once I set those functional requirements, I began to apply loop shaping techniques
to build my controller. In the first iteration of my controller design, I implemented
a gain of 100 and a zero near the origin to cancel out the action of the pole at -1. I
also included a feedback loop with a gain of I =
to decrease the feedback signal
amplitude back down to the same order of magnitude as the input signal (or setpoint).
The complete system, however, was unstable, as shown by the pole-zero map below.
The controller combined with the plant produced some additional poles on the right
side of the real axis, which created an unstable system. This controller did not meet
specifications.
6.3.2
Design iteration 2
In my next controller design, I attempted to cancel out the behavior of the pole on
the right hand side of the real axis by adding a zero at the same location. This design
was partially successful, because it eliminated the unstable pole. However, the Bode
plot showed that the system's frequency response only rolled off about 0.0004 dB
from 100 to 500Hz, which did not meet specifications.
67
System Pole-Zero Plot
400
200
-
E -2w
-400-
400
-5
-3
-4
-2
1
-10
Real Axis
4
x 10
Figure 6-6: Pole-zero map of entire system, iteration 1. Notice that the system is
unstable because there is a pole on the right side of the plane. This controller does
not meet specifications.
I should also note that it is generally not good practice to try to cancel out the
effect of poles with zeroes at the same position, because it can be very difficult in
practice to build a controller that has zeroes in exactly the right positions. In the
next iteration of my design, I would re-examine my controller design methodology to
use a more robust strategy for building an effective controller.
6.3.3
Design iteration 3
In my third design iteration, I used the same controller as in Design Iteration 2, but
I added two poles on the real axis at -628 in an attempt to negate the effect of the
two complex poles at -624
684i. This design iteration was also stable and had a
better roll-off performance, but the roll off began at approximately 50Hz instead of
100Hz, so the system did not completely meet specifications. The magnitude of the
system's frequency response also started to decrease by 3 to 5 decibels around 20Hz,
which was outside the specified range in the system functional requirements.
68
System Pole-Zero Plot
400
200
0
E
.----
-200
-400
-aM
-M
-8
i
-5
e
4
i
-3
Real Axis
i
-2
-1
i
0
1
x 10'
Figure 6-7: Pole-zero plot for second controller design iteration. The system is now
stable.
Although this design did not completely meet specifications, it was the best of
the three designs I developed. In future iterations of the controller design process, I
would refine Design Iteration 3 further to build a more robust controller that does
not rely on overlapping poles and zeroes to adequately control the system.
69
System Bode Plot
400002
0
S
*0
S
40
39.9998
39,9M
394
3-3
-
15
-
-U
10
5
0
-5
i02
10
Frequency (Hz)
Figure 6-8: Bode plot of system. Notice in magnitude plot that the roll-off is significantly smaller than specified.
System Bode Plot
20
10
0
-10
-20
FL
-301
180
90
0
-90
101
10
Frequency (Hz)
Figure 6-9: System Bode plot for Design Iteration 3.
70
Chapter 7
Conclusion
The ultimate goal of my thesis was to build a test environment that could be used to
input a force at varying frequencies to a polymer sample, and then measure the force
and position responses of that sample. I would then use the data to refine a model
for the dynamic mechanical behavior of PDMS.
I successfully designed and built the mechanical structure for the test environment.
I built the first iteration of my test environment somewhat hastily. I set out clear
functional requirements for my system after the first design iteration and used those
requirements to guide the next designs. I went through several design iterations
because at each iteration I learned more about how to properly design and machine
parts. At each iteration I also refined the selection of my electronic components based
on the functional requirements, and this also created a need for further iterations.
I also built a small circuit that I used to power my load cell and collect a signal
from it. I used a combination of op-amps and instrumentation amps to build the
circuit and match the load cell's impedance to the DAQ's impedance.
I conducted some initial laboratory tests to make rough estimates of the material
properties of PDMS, and used this data to help me build the initial model for the
PDMS and the mechanical structure of the test environment. I used the model to
build the plant transfer function, which then drove my design of my controller. I
iterated through three initial controller designs, although I recommend continuing to
iterate on the design before implementing it, because I did not use the most robust
71
controller design methods possible. Once the controller design is finalized, it will need
to be implemented in LabVIEW. Finally, I wrote initial test procedures for the tests I
had intended to conduct with the completed test environment. These test procedures
need to be refined and carried out to begin the system identification process for
developing an accurate model for the dynamic mechanical behavior of PDMS.
72
Chapter 8
Future Work
As described in the conclusion, there are several points in my thesis that need further
refinement. The current controller design is not robust and should be redone to fit
the functional requirements I set out. Once the controller design is finished it should
be implemented in LabVIEW.
The electronics need to be integrated into the system as well. They all fit with the
test environment hardware, but the drivers need to be connected to power amplifiers
and all of the supporting electronics should be stored safely in a cabinet. The DAQ
needs to be connected to both the drivers and a computer running the LabVIEW
script.
Once the system is finished, it should be used to run a series of system identification experiments. I have written out a preliminary series of experiments that focus
mainly on calibrating the test environment. My experiment procedures for the actual
data collection process need to be more detailed and more extensive, allowing for
iterations in which the plant model is modified based on error between theoretical
and experimental data. The procedures also do not explain how the data should be
analyzed - that information should be included as well. Once the experimental procedures are fully defined, the system should be used to collect data on the dynamic
mechanical behavior of PDMS, and to refine a first-principles model of the PDMS.
In the long term, this machine could be used to characterize the dynamic mechanical behavior of other polymers as well. I would like to see the machine used to define
73
the behavior of all the different materials that the LMP staff use in their projects.
The other students in the LMP have also developed various types of PDMS stamps
with different features and properties (such as fluorescence); this test environment
could be used to characterize their behaviors as well. Ultimately, this project should
be used to build and validate useful models of the dynamic behaviors of different
polymers used in micro-fabrication processes.
74
Chapter 9
Bibliography
[11 Center for Polymer Microfabrication, n.d., http://web.mit.edu/cpmweb/index.
html.
[21 Petrzelka, Joseph E., 2012, "Contact Region Fidelity, Sensitivity, and Control
in Roll-Based Soft Lithography," PhD thesis, Department of Mechanical Engineering,
Massachusetts Institute of Technology.
[31 Petrzelka, Joseph E., Al-Qhatani, Hussain, 2012, "Experimental Characterization
of a Flexible Capacitive Pressure Transducer," ASPE Annual Meeting, San Diego.
[41 Mata, Alvaro, Fleischman, Aaron J., Roy, Shuvo, 2005, "Characterization of Polydimethylsiloxane (PDMS) Properties for Biomedical Micro/Nanosystems," Biomedical Microdevices, 7(4), pp. 281-293.
[5] Shilpiekandula, Vijay, Burns, Daniel J., El Rifai, Khalid et al, 2006, "Metrology
of Microfluidic Devices: A Review," ICOMM No. 49, from http://web.mit.edu/
cpmweb/library/300000_Metrology-ofMicrofluidicDevicesAReview_2006_Shilpieka.
pdf
[6] Le Rouzie, J., Delobelle, P., Vairac, P., Cretin, B., 2009, "Comparison of Three Different Scales Techniques for the Dynamic Mechanical Characterization of Two Polymers (PDMS and SU8)," The European Physical Journal Applied Physics, 48(11201),
pp. 1-14.
[71 Ljung, Lennart, 2012, "Introduction to System Identification," from http: //www.
mathworks. com/videos/introduction-to-system-identification-81796.html?
form-seq=confl302&confirmation-page&wfsid=5575930
[81 Friedenberg, Matthew C., Mate, C. Mathew, 1996, "Dynamic Viscoelastic Properties of Liquid Polymer Films Studied by Atomic Force Microscopy," Langmuir, 12,
pp. 6138-6142.
75
76
Appendix A
Final Engineering Drawings of Test
Environment
This appendix contains a selection of the critical drawings used to construct the test
environment.
77
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Appendix B
Test Environment Design Review
B.1
Test Environment Design Review Plan
Purpose: To go over the design of the test environment to ensure it is
robust, easy to build and will perform to specification.
Functionality
1. Does it do everything we want?
2. Apply a force to a sample at high frequency
3. Hold a sample in place
4. Record displacement'data
5. Is there anything in the model that doesn't make sense? Is there anything
fastened together that shouldn't be?
6. Can it be easily modified to test different samples or apply different kinds of
tests?
7. How does it hold the sample in place during testing?
85
Basic Part Sizing and Arrangement
1. Are there any missing parts?
2. Are there any unnecessary parts?
3. Is there anything in the model that doesn't make sense?
4. Will everything fit inside the rig (static)?
5. Will everything fit inside the rig when it is in operation - is there enough
clearance for all moving parts?
6. Is there room for electrical components/wiring?
7. Is there enough clearance for wiring and electrical components to move during
operation?
Design for Manufacturability
1. Is it designed to be easily machined?
2. Is it designed with clearances and large tolerances in mind to be forgiving if
some of the machining is off?
3. Are all the connections standardized?
4. Are all of the commercial parts modeled to specification (from the manufacturer)?
5. Are the raw materials selected appropriate for machining? (And for the application in general?)
Design for Assembly
1. Can all the connection points be easily accessed by someone's hand with a
screwdriver?
86
2. Are there any parts that are unnecessarily small or awkwardly shaped?
3. Can all of the components be easily removed and replaced as needed?
4. Is it easy to reach all the points where electrical components will be connected
by wiring?
Failure Modes
1. Are all of the components secured well enough that they won't slip during high
frequency vibration operation?
2. Can it be fixed to a lab bench? Should it be isolated from the bench with a
spring-dashpot system?
3. Is everything fastened together securely?
4. Are there any obvious weak points that will fail under high frequency vibration
operation?
5. Where will it fail first? Can these places be reinforced?
B.2
Test Environment Design Review Report
Purpose: To present the design questions that I had after reviewing the
CAD model. (This document is presented in the same order as the original
design review document.)
Functionality
1. There are some questions that arose:
(a) The model currently has no means of holding a test sample in place - see
4. Also, I'm not clear about what the sample should be fixed to? Should
it be independent of both the voice coil motor and the load cell above?
87
Or should it be fixed to both the motor and the load cell? Or just one of
those two?
(b) The MTI capacitive displacement sensor we've been looking at has an
operational range of 0.010" - is this sufficient?
(c) I can't tell from the Futek load cell data sheet what its resolution is - will
it register small changes in load from the test sample?
(d) Also, the load cell is rated to have a maximum of 50 lbs (223N) - would
it be better to scale back to 25 lb (111N)?
2. There is a problem: the capacitance probe has to be within 0.5" (or maybe
its 0.01" - the spec sheet doesn't make complete sense to me) of the thing its
reading, but the stroke of the voice coil motor is 1.25". So when we're actually
testing we'll have to keep the vibrations from the motor small, but we might
want to stroke longer than 0.01". We need to either:
(a) Choose a new capacitance probe that has a wider range OR
(b) Find a way to adjust the distance between the probe and the plate so that
it is always close enough to get accurate readings.
3. If we want to keep the model versatile, I would say to oversize the frame pieces
so that we could swap out larger components if we wanted to put in a larger
voice coil motor or load cell. Should I go ahead and do that, or do we expect
that we will operate in the same general load range if we do other kinds of tests?
4. My ideas on how to hold the sample included:
(a) Use adhesive (i.e. super glue) - Prof. Hardt suggested this
(b) Screw the sample down to the voice coil motor
(c) Use prongs (like on a microscope slide)
(d) Ziptie
(e) Leave a depression in the voice coil motor plate that the sample could sit
in
88
Basic Part Sizing and Arrangement
1. Should we add something to absorb the impact of the shaft plates against the
top plate in case that ever happens? Like little fabric nibs or something that
we can just stick on post-machining?
2. N/a
3. Yes.
4. Yes, there's enough clearance for the full stroke operation of the voice coil motor.
However, need to look into making sure the capacitance probe is close enough
to a plate to get accurate readings.
5. Yes.
6. Yes.
Design for Manufacturability
1. Are there tricks to making a box with all the sides flush (where each side is
machined separately and then screwed together)? Maybe this is something to
ask a shop guy. I also considered redesigning the top plate to be two separate
slats that connect the side walls together to make the box more forgiving to
manufacture and assemble - is that design actually a good idea, or would it
be under-constrained? Also, should we increase the side wall thickness to 0.75"
because the holes are 0.25" - it seems like a thicker wall will be easier to machine
and the holes will be more secure.
2. I'm not sure if the bracket plates are going to be easy to machine or if it's
easier to buy them? If we machine them can we tighten them the way we want?
Maybe I should check dimensions against a commercial grade version before
manufacturing?
3. The connections are not standardized. Aside from holes that are dictated by
external parts, can we stick with . -20 screws? Is this a good standard size to
89
use? Also, is it necessary to secure plates together by putting nuts on the other
end, or are threads enough?
4. No they're not - I'll correct the discrepancies I found in my updated model.
5. I have selected aluminum 6061 - is this the best for machining?
Design for Assembly
1. I considered a way to make it easier to access the tightening points on the
clamping plates - take a look at the drawing - is this a worthwhile change or
is it unnecessary and weakens the assembly?
2. No.
3. Yes.
4. Yes - I considered adding slots in the side walls for the wires to go through and
move up and down during operation - are they worthwhile or also unnecessary?
Failure Modes
1. The only component I'm worried about slipping out is the capacitance probe,
but 2/3 of it will be clamped in a plate so I don't think it is too likely to fall
out. We could zip-tie it to the plate if necessary.
2. Will vibrations be enough to warrant isolation? I personally doubt it, I think
we could widen the base of the design enough to allow a clamp to hold it in
place if we really needed it.
3. Yes.
4. No.
5. I think it will fail first at the clamping plates (so we should manufacture a couple
extra) and at the corners, but I don't want to reinforce the corners because I
don't think it's likely.
90
Appendix C
Laboratory Experiments
C.1
Introduction
The purpose of these experiments was to collect some rough data and better understand the physical characteristics of the system I am designing. This data can be
used to justify design decisions and inform later epxeriments.
C.2
Collar Slipping
Objective:
To determine if the shaft collars are likely to slip during testing.
Method:
1. Fix shaft with collar attached in vise.
2. Clamp dial indicator to shaft so that it is touching collar.
3. Apply maximum force to collar and measure displacement on dial indicator.
91
Figure C-1: View of test setup.
Results:
There was no displacement of the collar when I applied as much force
as I could. The entire lab bench started rolling and there was still no noticeable
displacement of the collar on the shaft.
92
C.3
F of Voice Coil Motor
Objective:
To determine the force applied by the voice coil motor magnet to the
components near it (denoted Eb).
Method:
1. Determine the spring constant of the spring by setting it up as shown in Figure
3 and loading with weights while measuring the spring extension. Record the
different masses and corresponding spring extensions.
2. Setup ruler, voice coil motor magnet and cardboard spacer as shown in Figure
4. Attach component of interest (shaft collar) to hook and attach spring to
hook. Use the cardboard spacer to separate the collar from the magnet because
otherwise the force required to lift the collar off the magnet will exceed Hook's
Limit for the spring in use. (The cardboard was not used for the screw, which
experienced a smaller force of attraction.)
3. Use camera to film as force is slowly applied to spring and shaft collar is lifted
off the magnet.
4. Collect maximum spring extension from-video frames and calculate force of
magnetic attraction between voice coil and shaft collar using spring constant
determined in Step 1.
5. Repeat steps 2 - 4 for a 10-32 5/8" screw (that is the type of screw used to bolt
an aluminum plate to the voice coil actuator).
93
Figure C-3: Setup for determining force of magnetic attraction.
li
'f
Figure C-4: Setup for determining spring constant.
94
Results:
We calculated the spring constant for the spring to be approximately
380N/m. For the shaft collar, F = 24N and for the screw, F = 30N (the film
stills used to calculate the maximum spring extension for the shaft collar and screw
are shown in Figures 4 and 5 below). The F for the screw was larger than for the
shaft collar because there was a cardboard spacer between the collar and the magnet.
The conclusion we can draw is that the forces of attraction are on the same order as
the force that the voice coil motor can exert, so we will need to redesign the shaft
connection to use aluminum and brass parts.
95
Figure C-5: Image used to calculate maximum spring extension for shaft collar on
magnet with cardboard spacer.
Figure C-6: Image used to calculate maximum spring extension forlO-32 5/8" screw
on magnet.
C.4
Voice Coil Axial Misalignment
Objective:
To determine the approximate axial misalignment the voice coil motor
can experience at different points in the stroke.
96
Method:
1. Setup the dial indicator against the circumference of the black voice coil motor
actuator while the actuator is fully seated in the magnet.
2. Push the actuator towards the dial indicator until it stops against the magnet,
and record displacement.
3. Repeat steps 1-2 while the actuator is extended upwards to different heights
(2cm, 3cm, 4cm), recording the displacements each time.
Figure C-7: Measuring the displacement of the voice coil actuator with a dial indicator.
Results:
The displacements for different actuator heights were:
y(cm)
x(in)
0
0.032
2
0.058
3
0.150
4
0.140
This data shows that there is a significant displacement of the voice coil motor that
we will need to correct for or control in our design.
97
C.5
Machine Displacements
Objective:
To determine how far the entire machine will displace under maximum
loading conditions.
Method:
1. Setup the fully built F4000 and bolt to the desktop. Setup a dial indicator
against one of the walls to measure its displacement.
2. Apply the maximum force possible by hand to the opposite side of the F4000
from where the dial indicator is located, and record displacement shown on
indicator.
3. Repeat steps 1 and 2 while pushing on different locations of the F4000, measuring displacements in both horizontal directions, and also in the vertical direction.
Figure C-8: Measuring the horizontal displacement of the F4000.
98
Figure C-9: Measuring the vertical displacement of the F4000.
No matter which direction I loaded the F4000, it never displaced more
Results:
than 0.005", at loadings much greater than 25N. I will need to compare these estimates with calculated values I derive from my mass-spring-damper model of the
F4000, and then determine if they can be neglected.
C.6
PDMS Material Properties
Objective:
To determine the spring constant of pure PDMS.
Method:
1. Cut a rectangular strip of PDMS and attach one end to a hook that is fixed
above the bench surface.
2. Attach a second hook at the bottom end of the PDMS strip.
3. Use a ruler to measure the length of the PDMS strip, and record it.
4. Add approximately 100g of weight to the hook at the bottom of the strip and
record the extension of the strip.
5. Repeat step 4, gradually adding 100g at a time until the PDMS has seen 500g
of weight.
99
Results: I found that the PDMS had a spring constant of 750 N/m, with an uncertainty of
140 N/m.
100
Appendix D
Preliminary Experimental Procedures
D.1
Research Questions
We will use the force and position data that we collect to answer several key questions, including:
" What is the dynamic behavior of PDMS/sensor?
" Is our analytical model for the dynamic behavior of PDMS/sensor accurate?
" How does the PDMS/sensor's hysteresis curve change with varying frequency,
force and displacement?
* How does the PDMS/sensor's recovery time change with varying frequency,
force and displacement?
" How does changing the number of layers in the sensor affect its dynamic behavior?
" How does the dynamic behavior of pure PDMS differ from the behavior of
stamped PDMS?
" How does the dynamic behavior of stamped samples of PDMS vary with the
type of backing on the sample?
101
D.2
Process for Making PDMS Capacitive Sensor
D.2.1
Equipment/Materials
" 100mm silicon wafer
" SU-8 2005 Microchem permanent epoxy negative photoresist (datasheet is http:
//microchem. com/pdf/SU-82000DataSheet2000_5thru2Oi5Ver4.pdf)
" Hexamethyldisilazane
" PDMS from Dow Corning (Sylgard 184) (datasheet is http: //wwW1. dowcorning.
com/DataFiles/090007b281eb2ba9.pdf)
" PE-DOT:PSS conductive polymer (Heraeus Clevios S V3 HV) (datasheet is
http://www.heraeus-clevios.com/media/webmedia-local/media/datenblaetter/
81076863_CleviosS-V3_HV_20101222.pdf)
D.2.2
Procedure
1. Pattern a 100mm silicon wafer with SU-8 2005 to make a hexagonal pattern of
5pm features.
2. Treat the wafer with hexamethyldisilazane to prevent adhesion.
3. Apply PDMS to wafer, degas in a vacuum degasser and spin coat to thin.
4. Cure the PDMS overnight.
5. Apply the conductive polymer PE-DOT by spin coating, then anneal.
6. Use injection molding to cast a thick layer of PDMS against the wafer.
Once the PDMS sensor has been made, it needs to be mounted on a PCB board.
The board should have one channel etched to separate the sides of the board. A
conducting drop of PE-DOT liquid should be used to establish contact between the
sensor and the PCB on the positive side of the PCB board.
102
The purpose of this section is to test and verify the Fantabulous 4000's components
and then determine the properties of the whole system without a test sample. This
set of experiments will prove that the machine is accurate, and these experiments will
also get us the data we need to adjust the control system for the properties of the
test system.
Load Cell
D.3
Objective: verify the load cell is accurate to manufacturer's specifications.
D.3.1
Equipment/Materials
" Futek load cell
" Five (5) 100g weights
" Three (3) 1kg weights
" National Instruments DAQ (and associated instrumentation)
* Computer
Note:
we test with a maximum of 3kg (approx. 30N) because that is the maximum
force that the voice coil motor in our system can apply.
D.3.2
Procedure
1. Set up load cell and DAQ system to collect force readings from load cell. The
load cell should rest on the surface of a lab bench. The test excitation voltage,
according to the manufacturer, is 1OVDC.
2. Place a 100g weight on the top part of the load cell. Record the force reading
from the DAQ.
103
3. Repeat step 2 increasing the weight in 100g increments until the load cell has
been tested with 500g of mass.
4. Remove the mass from the load cell, and replace it with a 1kg mass. Record
the force reading from the DAQ.
5. Repeat step 4 increasing the weight in 5OOg increments until the load cell has
been tested with a maximum of 3kg.
6. Repeat steps 2-5 three times to improve accuracy of results.
D.3.3
Results
The data points collected should be plotted on a graph of input force vs. output
reading. Analyze the slope of the best-fit line to determine how accurate the load cell
is and if its accuracy correlates to the manufacturer specifications.
The manufacturer specifies that the calibration test excitation voltage is 1OVDC,
therefore the following paramters will apply to our test data:
* Rated output = 2mV/V = 2mV/V * 10V = [OV, 0.02V]
* Nonlinearity = t0.5% * 0.02V = 0.1mV
" Hysteresis = O.lmV
* Non-repeatability = i0.1% * 0.02V = 0.02mV
D.4
Capacitance Probe
Objective: verify the capacitance probe is accurate to the manufacturer's
specifications.
104
D.4.1
Equipment/Materials
" Lion Precision capacitance probe
" Lion Precision driver
" Fantabulous 4000
" Aluminum gage blocks
" National Instruments DAQ (and associated instrumentation)
" Computer
D.4.2
Procedure
1. Set up the Fantabulous 4000, insert the capacitance probe into its fixture, and
set up the DAQ system to collect data from the probe. The voice coil motor
should also be connected to the DAQ so that it can be driven by the computer.
2. Move the voice coil up until the capacitance probe is touching the reference
plate, and zero the capacitance probe.
3. Move the voice coil down and slide in an aluminum gage block. Adjust the voice
coil until the aluminum gage block is being held in place by the shaft; there
should be no load on the block, it should be barely held in place by the shaft.
4. Record the displacement given by the capacitance probe on the DAQ.
5. Repeat steps 2-4 for increasing thickness gage blocks.
6. Repeat steps 2-5 three times to improve accuracy of results.
D.4.3
Results
The data points should be plotted on a graph of gage block thickness vs. output
reading. Analyze the slope of the best-fit line to determine how accurate the load cell
is and if its accuracy correlates to the manufacturer specifications.
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The following parameters apply to our capacitance probe that has a range of
5000ptm and a voltage range of
l0V:
" Range = 5000pm
" Gain = 20000mV/50OOpm = 4mV/pm
" Resolution (at 100Hz) = 0.0005% * 5000pm
D.5
0.025pm
Machine Stiffness
Objective: Calculate the combined stiffness of the Fantabulous 4000.
D.5.1
Equipment/Materials
" Fantabulous 4000 (including all DAQ equipment)
" Three (3) aluminum beams of known dimensions
" Computer
D.5.2
Procedure
1. Set up the Fantabulous 4000 so that the DAQ is transmitting a signal to the
voice coil and recording data from both the load cell and the capacitance probe.
2. Fix the ends of the aluminum beam to the reference plate of the F4000.
3. Command the voice coil to apply a force of 10ON to the aluminum beam; collect
force and displacement data.
4. Repeat steps 2-3 three times to improve accuracy of results, replacing the aluminum beam each time.
106
D.5.3
Results
Given the dimensions of the beam and the Young's modulus of aluminum, we should
be able to calculate the expected deformation of the beam. We will compare this expected value to the measured deformation from the capacitance probe. The difference
between the measured and the expected values will be the amount of deformation of
the machine itself. We can use this displacement difference and the measured force
applied to the system to calculate the stiffness of the machine using F = kx. We can
use this stiffness value to adjust our control model for the system.
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D.6
Voice Coil
Objective: develop a calibration curve for the voice coil motor.
D.6.1
Equipment/Materials
* Fantabulous 4000 (including all DAQ equipment)
" Computer
Note:
the Moticont voice coil motor has the following parameters:
" Maximum continuous force = 29.4N
" Force constant = 9.6N/A
" Coil resistance = 3.91
* Maximum continuous power = 36W
We will use a safety factor of 2 so that we never exceed a maximum power of 18W
on the voice coil motor. We will use a safety factor in testing to prevent the voice
coils from burning; even with a safety factor we will still be able to draw a smooth
calibration curve for our motor.
We will drive the voice coil with current because the current determines the Lorentz
force applied to the coil in the motor. Therefore, we can calculate the corresponding
voltage that we should use from the maximum continuous power of the motor (after
adjusting for the safety factor). For example, if we start by exciting the motor with
0.5A, we will need a voltage of:
P
_18W
V - - =
=36V
i
0.5A
108
(D.1)
With the given force constant, 0.5A will produce an output force of:
F
D.6.2
=
c * i = 9.6N/A * 0.5A
=
4.8N
(D.2)
Procedure
1. Set up the Fantabulous 4000 so that the DAQ is transmitting a signal to the
voice coil and recording data from both the load cell and the capacitance probe.
2. Adjust the height of the reference plate above the shaft so that the shaft is just
touching the reference plate when the voice coil motor is off.
3. While the current going to the voice coil is 0, record the force reading from the
load cell.
4. Send 0.5A of current to the voice coil and record the resulting force reading
from the load cell. (The corresponding voltage of the signal should be enough
to produce a signal power of 18W, as explained in the note above.)
5. Repeat step 4, stepping up the current by 0.5A each time, up to 3A of current.
D.6.3
Results
Use the data points to draw a calibration curve for the voice coil motor. We will
use this data to run the voice coil motor in future experiments.
The purpose of this section is to outline the experiments we will conduct to collect
data about the bulk material properties of PDMS and of the PDMS capacitance sensor
in static and dynamic loading. We will collect this data so that we can compare it to
previous findings to verify that our experimental setup is accurate and agrees with
existing literature. These experiments replicate the work done by Joe Petrzelka in
his ASPE paper and PhD thesis.
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The experiments we will conduct are:
1. Static Loading
(a) Pure PDMS sample
(b) PDMS sensor
2. Roll Contact
(a) Pure PDMS sample
(b) PDMS sensor
3. Dynamic Loading
(a) Pure PDMS sample
(b) PDMS sensor
Note:
During these experiments, we will connect the PDMS sensor to the DAQ sys-
tem so that we can determine the sensor's performance characteristics. The PDMS
sensor can be connected to the DAQ system using a resistor-capacitor low pass circuit connected to the DAQ via an RMS-DC converter. The sensor's data should be
sampled at 40kHz.
D.7
Static Loading
Objective: to repeat Joe Petrzelka's tensile tests for PDMS using the
F4000.
D.7.1
Equipment/Materials
" Fantabulous 4000 (including all DAQ equipment)
" Computer
110
*
3 pure PDMS samples prepared for tensile testing in I-beam shape with w =
4mm and I = 20mm
* 3 PDMS sensor samples prepared for tensile testing in I-beam shape with w =
4mm and 1 = 20mm
D.7.2
Procedure
1. Secure first sample in F4000 by clamping it to the reference plate and the voice
coil/shaft.
2. Begin the tensile test by straining the sample at a constant strain rate of 0.01/s.
Collect both force and displacement data on the sample.
3. Stop testing when the stress reaches 50kPa.
4. Repeat steps 1-3 with each sample of PDMS and PDMS sensor.
D.7.3
Results
Use the force and displacement data to draw force-displacement curves. Then analyze the data to draw stress-strain curves. Determine each sample's Young's Modulus
value, including confidence intervals. Compare these values to the data that Joe
obtained to verify the F4000 is accurate.
D.8
Roll Contact
Objective: to repeat Joe Petrzelka's roll contact tests for PDMS with the
F4000.
D.8.1
Equipment/Materials
" Fantabulous 4000 (including all DAQ equipment)
" Computer
111
*
3 pure PDMS samples with dimensions 20mm x 20mm
* 3 PDMS sensor samples with dimensions 20mm x 20mm
D.8.2
Procedure
1. Secure the first sample in the F4000 by flooding a slide with water and positioning the PDMS sample on the slide.
2. Use a load proffle that runs from ON to 40N at a rate of 2N/s. Once the loading
reaches 40N, hold the load for 5s and then release at the same rate. Collect
both force and displacement data during the process.
3. Repeat steps 1-2 for each sample of PDMS and PDMS sensor.
4. Adjust the experimental setup so that the F4000 can be used to do tensile
testing.
5. Secure the first sample in the F4000 and do a tensile test by loading up to
50kPa at a strain rate of 0.01/s.
6. Repeat tensile test for each sample and collect force and displacement data.
D.8.3
Results
Draw force-displacement curves for each sample. Compare to Joe's plots to verify
the F4000 is accurate. Use the tensile test data to calculate the Young's modulus of
each sample and compare data to previous experiments.
D.9
Dynamic Loading
Objective: to repeat Joe Petrzelka and Hussein Al-Qhatani's work in measuring the hysteresis of PDMS under dynamic loading.
112
D.9.1
Equipment/Materials
* Fantabulous 4000 (including all DAQ equipment)
* Computer
* 21 pure PDMS samples with dimensions 20mm x 20mm
* 21 PDMS sensor samples with dimensions 20mm x 20mm
D.9.2
Procedure
This section is divided into two main parts. The first part tests the samples with
small displacements; the strain rates will vary, but the amplitude of force applied will
remain constant. The second part tests the samples with large displacements; the
amplitudes will vary, but the strain rate will remain constant.
Small Displacements
1. Secure the first sample in the F4000 by flooding a slide with water and positioning the PDMS sample on the slide.
2. Using a strain rate of 0.5pim/s, load the sample up to 5kPa.
3. Instantaneously release the load on the sample and measure the material recovery using the load cell and the capacitive probe.
4. Repeat steps 1-3 for a total of 3 pure PDMS samples and 3 PDMS sensor
samples.
5. Repeat steps 1-4 with a strain rate of 2.0pm/s, 10.0pm/s and 20.Opm/s. Repeat
each test 3 times for each kind of PDMS sample. (At the end of this step,
12 samples of pure PDMS and 12 samples of PDMS sensor should have been
tested.)
6. Adjust the experimental setup so that the F4000 can be used to do tensile
testing.
113
7. Secure the first sample in the F4000 and do a tensile test by loading up to
50kPa at a strain rate of 0.01/s.
8. Repeat tensile test for each sample and collect force and displacement data.
Large Displacements
1. Secure the first sample in the F4000 by flooding a slide with water and positioning the PDMS sample on the slide.
2. Using a strain rate of 0.5pm/s, load the sample up to 5kPa.
3. Instantaneously release the load on the sample and measure the material recovery using the load cell and the capacitive probe.
4. Repeat steps 1-3 for a total of 3 pure PDMS samples and 3 PDMS sensor
samples.
5. Repeat steps 1-4 with a maximum load of 12.5kPa and 25kPa. Repeat each
test 3 times for each kind of PDMS sample. (At the end of this step, 9 samples
of pure PDMS and 9 samples of PDMS sensor should have been tested.)
6. Adjust the experimental setup so that the F4000 can be used to do tensile
testing.
7. Secure the first sample in the F4000 and do a tensile test by loading up to
50kPa at a strain rate of 0.01/s.
8. Repeat tensile test for each sample and collect force and displacement data.
D.9.3
Results
For both sets of experiments, we can plot the load against the displacement of
the sample, and, in the case of the PDMS sensors, against the sensor's capacitance
readings. Compare these plots to the data from Joe and Hussein's ASPE paper to
determine the accuracy of the F4000. We can also use the tensile test data to calculate
the Young's modulus for each sample.
114
The purpose of this section is to outline the experiments we will use to characterize
pure PDMS and the PDMS sensor under dynamic loading. This is a new area of
research, so we will not necessarily be able to compare our results to literature values.
The goal is to derive a transfer function that characterizes the behavior of PDMS
under dynamic loading, which we will do by measuring the frequency response of
PDMS. There are several variables that we can modify in dynamic loading conditions:
" Frequency of oscillations (from 10Hz to 100Hz)
" Force applied (from 1N to 25N)
" Displacement range (from Om to 0.030 m)
Note:
During these experiments, we will connect the PDMS sensor to the DAQ sys-
tem so that we can determine the sensor's performance characteristics. The PDMS
sensor can be connected to the DAQ system using a resistor-capacitor low pass circuit connected to the DAQ via an RMS-DC converter. The sensor's data should be
sampled at 40kHz.
115