Design of Semi-active Variable Impedance
Materials Using Field-Responsive Fluids
by
OF TECHNOLOGY
Douglas Elmer Eastman IV
MAR 0 6 2006
Submitted to the Department of Mechanical Enginee iney LIBRARIE
in partial fulfillment of the requirements for the degree of
Master of Science in Mechanical Engineering
BARKER
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
June 2004
@
Massachusetts Institute of Technology 2004. All rights reserved.
A
Author ............
Department of Mechanical Engineering
May 7, 2004
Certified by.
Neville Hogan
Professor, Mechanical Engineering; Brain & Cognitive Sciences
Thesis Supervisor
67
Accepted by .....
..........
.
. .
.. . . . ........
......
....
Ain A. Sonin
Chairman, Department Committee on Graduate Students
/4
4
1~
9,
4
Design of Semi-active Variable Impedance Materials Using
Field-Responsive Fluids
by
Douglas Elmer Eastman IV
Submitted to the Department of Mechanical Engineering
on May 7, 2004, in partial fulfillment of the
requirements for the degree of
Master of Science in Mechanical Engineering
Abstract
In this thesis, I explored the design of a thin variable impedance material using electrorheological (ER) fluid that is intended to be worn by humans. To determine the
critical design parameters of this material, the shear response of a sandwich of electrodes separated by ER fluid and several different spacer materials was investigated.
After a preliminary test to verify that the shear response is controllable by an applied voltage, a single-axis tensile testing machine was designed and constructed to
carry out more accurate testing. Two different ER fluids, homogeneous and heterogeneous were investigated. A model of the material for each fluid along with a general
model were developed and the parameters of the models were determined through
experiments. The model shows a good fit to the experimental data for the heterogeneous fluid based materials, with prediction errors on the order of 30% for two of the
spacer materials. The homogeneous fluid based materials show a strong deviation
from the model at OV, but fit well when voltage was applied. Polypropylene as a
spacer dramatically reduced or eliminated the ER effect. Some critical design parameters identified include: variation in electrode spacing, spacer material selection, and
breakdown levels.
Thesis Supervisor: Neville Hogan
Title: Professor, Mechanical Engineering; Brain & Cognitive Sciences
3
4
Acknowledgments
First I would like to thank Neville Hogan, for his insightful input in times of doubt
and confusion. I also owe a debt to the entire cast of the Newman lab, who provided
numerous helpful comments during weekly group meetings. This research would not
have been possible without the Institute for Soldier Nanotechnologies, which provided
funding as well as lab space and resources. Thanks is also due to John Rensel at
Bridgestone/Firestone, Inc. and Akio Inoue at Asahi for providing me with samples of
electrorheological fluid. Thanks to Boryana for reading over and editing my drafts and
keeping me sane through the whole writing process. Finally and most importantly,
I'd like to thank my mom and dad for their well-timed words of encouragement and
shipments of tasty treats.
5
6
Contents
19
1 Introduction
2
3
1.1
Material Description
. . . . . . . . . . . . . . . . . . . . . . . . . . .
19
1.2
Military Applications . . . . . . . . . . . . . . . . . . . . . . . . . . .
19
1.3
Other Applications
. . . . . . . . . . . . . . . . . . . . . . . . . . . .
20
1.4
Thesis Scope.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
20
Background
23
2.1
Shear-Thickening Fluid . . . . . . . . . . . . . . . . . . . . . . . . . .
23
2.2
MR Fluid
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
24
2.3
ER Fluid.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
25
2.3.1
Heterogeneous . . . . . . . . . . . . . . . . . . . . . . . . . . .
25
2.3.2
Homogeneous
. . . . . . . . . . . . . . . . . . . . . . . . . . .
28
31
Material Design
3.1
3.2
3.3
. . . . . . . . . . . . . . . . . . . . . . . . . . . .
31
3.1.1
Shear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
31
3.1.2
Valve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
31
3.1.3
Squeeze
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
32
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
32
3.2.1
Channel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
33
3.2.2
Grid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
34
3.2.3
Sandwich
. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
34
. . . . . . . . . . . . . . . . . . . . . . . . . .
35
Force Transmission
Geometry
Design Considerations
7
3.4
3.5
3.3.1
Size
35
3.3.2
Flexible Boundary Conditions . . . . . . . . . . . . . . . . . .
36
3.3.3
Arbitrary Loading
. . . . . . . . . . . . . . . . . . . . . . . .
36
3.3.4
Failure Modes . . . . . . . . . . . . . . . . . . . . . . . . . . .
36
Shear M odel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
36
3.4.1
Heterogeneous ER Fluid . . . . . . . . . . . . . . . . . . . . .
38
3.4.2
Homogeneous ER Fluid
. . . . . . . . . . . . . . . . . . . . .
38
3.4.3
Electrostatics
. . . . . . . . . . . . . . . . . . . . . . . . . . .
38
3.4.4
Dry M aterial
. . . . . . . . . . . . . . . . . . . . . . . . . . .
39
3.4.5
General Model
. . . . . . . . . . . . . . . . . . . . . . . . . .
40
Performance Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . .
41
3.5.1
Parallel Loading.
. . . . . . . . . . . . . . . . . . . . . . . . .
41
3.5.2
Perpendicular Loading . . . . . . . . . . . . . . . . . . . . . .
43
4 Testing
4.1
47
Preliminary Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . .
47
4.1.1
Test Description
. . . . . . . . . . . . . . . . . . . . . . . . .
48
4.1.2
Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
49
4.1.3
Analysis and Results . . . . . . . . . . . . . . . . . . . . . . .
50
Testing System Design . . . . . . . . . . . . . . . . . . . . . . . . . .
52
4.2.1
Goals. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
52
4.2.2
Description
. . . . . . . . . . . . . . . . . . . . . . . . . . . .
52
4.3
Spring Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
55
4.4
Amplifier Characterization . . . . . . . . . . . . . . . . . . . . . . . .
58
4.5
Procedure . . ..
..
. . . . . . . . . . . . . . . .
60
4.5.1
Materials
. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
60
4.5.2
Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
62
4.2
. .. .
...
. ...
5 Heterogeneous Results
63
5.1
Raw Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
63
5.2
Shear Stress Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . .
64
8
5.3
5.4
5.2.1
Calculating Shear Stress . . . . . . . . . . . . . . . . . . . . .
64
5.2.2
Finding Model Parameters . . . . . . . . . . . . . . . . . . . .
65
5.2.3
M odel Performance . . . . . . . . . . . . . . . . . . . . . . . .
69
Energy Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
71
5.3.1
W ork Out . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
71
5.3.2
Energy In . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
74
5.3.3
Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . .
75
Slope/Intercept Difference . . . . . . . . . . . . . . . . . . . . . . . .
78
6 Homogeneous Results
81
6.1
Raw Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
81
6.2
Shear Stress Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . .
81
6.2.1
Calculating Shear Stress . . . . . . . . . . . . . . . . . . . . .
81
6.2.2
Finding Model Parameters . . . . . . . . . . . . . . . . . . . .
82
6.2.3
M odel Performance . . . . . . . . . . . . . . . . . . . . . . . .
87
Energy Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
87
6.3.1
W ork Out . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
87
6.3.2
Energy In . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
90
6.3.3
Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . .
91
. . . . . . . . . . . . . . . . . . . . . . . .
93
6.3
6.4
Slope Intercept Difference
7 Dry Material Results
95
7.1
Coefficient of Friction . . . . . . . . . . . . . . . . . . . . . . . . . . .
96
7.2
Raw Data . . . . . . . . . . . ..
. . . . . . . . . . . . . . . . . . . .
96
7.3
Shear Stress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
97
7.4
M odel Parameters. . . . . . . ..
. . . . . . . . . . . . . . . . . . . .
98
7.5
Energy Analysis.
. . . . . . . . . . . . . . . . . . . . 100
7.6
. . . . . . . ..
7.5.1
W ork Out . . . . . . . ..
7.5.2
Energy In . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
7.5.3
Performance . . . . . . ..
Slope Intercept Difference
..
. ..
. . . . . . . . . . . . . . . 100
. . . . . . . . . . . . . . . . . . . . 103
. . . . . . . . . . . . . . . . . . . . . . . . 104
9
8 Discussion
8.1
8.2
105
Variable Thickness
. . . . .
105
8.1.1
Heterogeneous Fluid
. . . . . . . . . . . . . . . . . . . . . . .
105
8.1.2
Homogeneous Fluid
. . . . . . . . . . . . . . . . . . . . . . .
107
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
107
107
Normal Force
8.2.1
Heterogeneous Fluid
. . . . . . . . . . . . . . . . . . . . . . .
8.2.2
Homogeneous Fluid
. . . . . . . . . . . . . . . . . . . . . . .111
8.3
Spacer Material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .111
8.4
Breakdown Voltage . . . . . . . . . . . . . . . . . . . . . . . . . . . .
113
8.5
Dynamic Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
114
8.6
Conclusions
8.7
Next Steps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
115
8.8
Future Vision . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
116
. . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . 114
A Energy Absorption Simulations
119
B Heterogeneous Fluid Data
123
C Homogeneous Fluid Data
141
D Dry Material Data
159
10
List of Figures
2-1
SEM pictures of heterogeneous and homogeneous ER fluid. . . . . . .
2-2
The characteristic shear stress versus shear rate for heterogeneous and
25
homogeneous ER fluid. . . . . . . . . . . . . . . . . . . . . . . . . . .
29
3-1
The three mechanisms of force transmission for a field-activated fluid.
32
3-2
Illustration of the channel design for an electrorheological fluid based
variable impedance material. The alternating electrodes would create
a pressure difference between two resevoirs of ER fluid. . . . . . . . .
3-3
An illustration of a possible grid type design of an electrorheological
fluid based variable impedance material.
3-4
33
. . . . . . . . . . . . . . . .
34
Three different loading conditions on a sandwich geometry illustrating
the variety of force transmission methods that can be utilized. ....
35
3-5
Illustration of the basic shear stress loading condition . . . . . . . . .
37
3-6
Diagram illustrating the perpendicular loading condition where the
material is pinned on either side and a force acts through the center
causing the layers to slide apart. . . . . . . . . . . . . . . . . . . . . .
4-1
Schematic of the prototype material consisting of a layer of paper saturated in ER fluid and surrounded by two layers of aluminum foil. . .
4-2
43
48
Picture of the prototype on the block used for the shear test. The
electrical connections are made on opposite sides of the sample using
4-3
alligator clips. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
48
A diagram illustrating the prototype test method. . . . . . . . . . . .
49
11
4-4
Data from a preliminary test to determine the static yield stress with
a 60 volt field and a 4.2N normal force. . . . . . . . . . . . . . . . . .
4-5
Yield stress versus voltage for the preliminary testing along with a
linear fit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4-6
50
51
A diagram illustrating the primary components of the testing system
and how they are connected. . . . . . . . . . . . . . . . . . . . . . . .
54
4-7
A picture of the single-axis, horizontal, linear testing system. . . . . .
55
4-8
Plot of the raw data for the 8 mm/s test and the least squares error fit. 56
4-9
Plot of the spring constant measured with the test system versus velocity. 57
4-10 Plot of the residuals of the least squares error fit to an experimental
run at 8mm/s and their frequency content. . . . . . . . . . . . . . . .
4-11 Root mean squared error of the least squares error fit versus velocity.
57
58
4-12 A plot of the voltage and current for five seconds with no movement
of the test stage. The frequency spectrum of the data is also shown. .
59
4-13 A plot of the error between the measured voltage and the commanded
voltage versus the commanded voltage. The error bars represent one
standard deviation. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
60
4-14 Plot of the root mean square of the voltage and current error, which
serves as a measure of the noise in the signal.
5-1
. . . . . . . . . . . . .
61
Raw force data for all three trials of variable impedance material made
with heterogeneous fluid and a kraft paper spacer for two different
testing conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5-2
Plot of the shear stress versus velocity for all voltages and materials
using heterogeneous fluid. . . . . . . . . . . . . . . . . . . . . . . . .
5-3
66
Plot of the slope and intercept of the least squares fit to the shear stress
for materials with heterogeneous fluid.
5-4
64
. . . . . . . . . . . . . . . . .
68
Plot of the mechanical work done by materials with heterogeneous fluid
during the experimental run. . . . . . . . . . . . . . . . . . . . . . . .
12
72
5-5
Plot of the percentage increase in work done in materials with heterogeneous fluid at a particular voltage over the work done at OV. . . . .
5-6
73
Plot of the mean electrical energy input into the material during an
experim ental run. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
74
5-7
Plot of the power density into the material during an experimental run. 75
5-8
Plot of the increase in work over the energy input for heterogeneous
m aterials.
5-9
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
76
Plot of the shear stress versus power density for materials with heterogeneous fluid. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
77
5-10 Plot of the constant force offset during the runs with heterogeneous fluid. 79
6-1
Raw force data for all three trials of variable impedance material made
with homogeneous fluid and a kraft paper spacer for two different testing conditions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6-2
Plot of the shear stress versus velocity for all voltages and materials
using Homogeneous fluid . . . . . . . . . . . . . . . . . . . . . . . . .
6-3
91
Plot of the increase in work over the energy input for homogeneous
m aterials.
6-9
90
Plot of the power density into the homogeneous fluid based materials
during an experimental run. . . . . . . . . . . . . . . . . . . . . . . .
6-8
89
Plot of the mean electrical energy input into the material during an
experim ental run. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6-7
88
Plot of the percentage increase in work done in materials with Homogeneous fluid at a particular voltage over the work done at OV. . . . .
6-6
84
Plot of the mechanical work done by materials with homogeneous fluid
during the experimental run. . . . . . . . . . . . . . . . . . . . . . . .
6-5
83
Plot of the slope and intercept of the least squares fit to the shear stress
for materials with homogeneous fluid. . . . . . . . . . . . . . . . . . .
6-4
82
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
92
Plot of the shear stress versus power density for materials with Homogeneous fluid. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
13
93
6-10 Plot of the constant force offset during the runs with Homogeneous fluid. 94
7-1
Force due to friction versus normal load for dry material. . . . . . . .
7-2
Raw data for the dry material voltage response experiment at OV and
400V .
96
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
97
7-3
Shear stress of the dry material versus velocity for four different voltages. 98
7-4
Friction term, c, in the general model versus the voltage for the dry
m aterial. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
99
7-5
Work done by the dry material. . . . . . . . . . . . . . . . . . . . . .
100
7-6
Percentage increase in the work done by the material over the work
done at OV. ......
................................
101
7-7 Electrical energy input into the dry material. . . . . . . . . . . . . . .
102
7-8
Density of the electrical power going into the dry material. . . . . . .
102
7-9
Increase in output work divided by the input energy for dry material.
103
7-10 Shear stress of the material versus the electrical power density. . . . .
104
7-11 Force offset for the dry material . . . . . . . . . . . . . . . . . . . . . 104
8-1
Plot of the film thickness versus voltage for heterogeneous ERF materials. 106
8-2
Plot of the work versus normal force for heterogeneous ERF materials. 108
8-3
Plot of the shear stress versus normal force for heterogeneous ERF
m aterials.
8-4
109
Plot of the offset force versus the normal force for heterogeneous ERF
m aterials.
8-5
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
110
Effective coefficient of friction for the different materials with heterogeneous ERF. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .111
8-6
Plot of the work versus normal force for homogeneous ERF materials.
8-7
Diagram of a possible method for creating a continuous material using
sandwich geom etry. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
112
117
A-1 Diagram of the simulink model to find the amount of energy absorbed
by the m aterial. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
14
A-2 Final velocity of the mass after interacting with the variable impedance
material versus its initial velocity and the applied voltage.
. . . . . .
120
A-3 Final velocity of the mass with model fit. . . . . . . . . . . . . . . . .
121
A-4 Energy absorbed by the material versus the initial velocity. . . . . . .
122
B-i Raw data for experimental runs using heterogeneous fluid with a kraft
paper spacer at 0 volts. . . . . . . . . . . . . . . . . . . . . . . . . . .
124
B-2 Raw data for experimental runs using heterogeneous fluid with a kraft
paper spacer at 200 volts.
. . . . . . . . . . . . . . . . . . . . . . . . 125
B-3 Raw data for experimental runs using heterogeneous fluid with a kraft
paper spacer at 400 volts.
. . . . . . . . . . . . . . . . . . . . . .I
. 126
B-4 Raw data for experimental runs using heterogeneous fluid with a kraft
paper spacer at 600 volts.
. . .. . . . . . . . . . . . . . . . . . . . . 127
B-5 Raw data for experimental runs using heterogeneous fluid with a tissue
paper spacer at 0 volts. . . . . . . . . . . . . . . . . . . . . . . . . . . 128
B-6 Raw data for experimental runs using heterogeneous fluid with a tissue
paper spacer at 200 volts.
. . . . . . . . . . . . . . . . . . . . . . . . 129
B-7 Raw data for experimental runs using heterogeneous fluid with a tissue
paper spacer at 400 volts.
. . . . . . . . . . . . . . . . . . . . . . . .
130
B-8 Raw data for experimental runs using heterogeneous fluid with a tissue
paper spacer at 600 volts.
. . . . . . . . . . . . . . . . . . . . . . . .
131
B-9 Raw data for experimental runs using heterogeneous fluid with no
spacer at 0 volts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
B-10 Raw data for experimental runs using heterogeneous fluid with no
spacer at 20 volts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
B-11 Raw data for experimental runs using heterogeneous fluid with no
spacer at 40 volts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
B-12 Raw data for experimental runs using heterogeneous fluid with no
spacer at 60 volts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
15
B-13 Raw data for experimental runs using heterogeneous fluid with a PPL
spacer at 0 volts.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
B-14 Raw data for experimental runs using heterogeneous fluid with a PPL
spacer at 200 volts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
B-15 Raw data for experimental runs using heterogeneous fluid with a PPL
spacer at 400 volts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
B-16 Raw data for experimental runs using heterogeneous fluid with a PPL
spacer at 600 volts. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
139
C-1 Raw data for experimental runs using homogeneous fluid with a kraft
paper spacer at 0 volts. . . . . . . . . . . . . . . . . . . . . . . . . . .
142
C-2 Raw data for experimental runs using homogeneous fluid with a kraft
paper spacer at 200 volts.
. . . . . . . . . . . . . . . . . . . . . . . .
143
C-3 Raw data for experimental runs using homogeneous fluid with a kraft
paper spacer at 400 volts.
. . . . . . . . . . . . . . . . . . . . . . . .
144
C-4 Raw data for experimental runs using homogeneous fluid with a kraft
paper spacer at 600 volts.
. . . . . . . . . . . . . . . . . . . . . . . .
145
C-5 Raw data for experimental runs using homogeneous fluid with a tissue
paper spacer at 0 volts. . . . . . . . . . . . . . . . . . . . . . . . . . . 146
C-6 Raw data for experimental runs using homogeneous fluid with a tissue
paper spacer at 200 volts.
. . . . . . . . . . . . . . . . . . . . . . . . 147
C-7 Raw data for experimental runs using homogeneous fluid with a tissue
paper spacer at 400 volts.
. . . . . . . . . . . . . . . . . . . . . . . . 148
C-8 Raw data for experimental runs using homogeneous fluid with a tissue
paper spacer at 600 volts.
. . . . . . . . . . . . . . . . . . . . . . . . 149
C-9 Raw data for experimental runs using homogeneous fluid with no spacer
at 0 volts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
150
C-10 Raw data for experimental runs using homogeneous fluid with no spacer
at 20 volts.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
16
151
C-II Raw data for experimental runs using homogeneous fluid with no spacer
at 40 volts.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
C-12 Raw data for experimental runs using homogeneous fluid with no spacer
at 60 volts.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
153
C-13 Raw data for experimental runs using homogeneous fluid with a PPL
spacer at 0 volts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
154
C-14 Raw data for experimental runs using homogeneous fluid with a PPL
spacer at 200 volts. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
155
C-15 Raw data for experimental runs using homogeneous fluid with a PPL
spacer at 400 volts. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
156
C-16 Raw data for experimental runs using homogeneous fluid with a PPL
spacer at 600 volts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
D-1 Force versus position for the dry material at OV and 4mm/s. . . . . .
160
D-2 Force versus position for the dry material at OV and 8mm/s. . . . . .
160
D-3 Force versus position for the dry material at 200V and 4mm/s. . . . .
161
D-4 Force versus position for the dry material at 200V and 8mm/s. . . . .
161
D-5 Force versus position for the dry material at 400V and 4mm/s. . . . .
162
D-6 Force versus position for the dry material at 400V and 8mm/s. .....
162
D-7 Force versus position for the dry material at 600V and 4mm/s. .....
163
D-8 Force versus position for the dry material at 600V and 8mm/s. . . . . 163
17
18
Chapter 1
Introduction
1.1
Material Description
A variable-impedance material has properties, such as stiffness and damping, that
can be changed in use. Semi-active means that it requires some energy to change the
properties, but no net work is done by the device. The goal is to create a material that
can be worn and interact with the wearer to provide variable mechanical impedance.
Some important qualities for this material include having a fast response time and
low power requirement, being thin and light, and being capable of a significant change
in mechanical properties.
1.2
Military Applications
The larger goal is to create a wearable "armor" that can be selectively activated
depending on the threat level to allow maximum mobility while maintaining adequate
protection. This would ideally be a continuous material that could be integrated into
a soldier's uniform.
The shorter term goals are to engineer specific devices with particular applications
in mind. One possibility is a splint that could be automatically activated when the
wearer fractures a bone or sprains a joint to provide support for the impaired limb and
allow the soldier to continue to function until more advanced care can be administered.
19
Another possibility is incorporating the material into foot and leg wear to provide
variable ankle support. A common injury among paratroopers is ankle damage upon
impact with the ground. To combat this, paratroopers are forced to wear bulky braces
which can get caught in the parachute and require removal once on the ground. Instead, the soldiers could wear a brace made of the variable impedance material which
would be completely unobtrusive and could simply be switched off or automatically
deactivate once the paratrooper is safely on the ground.
The vibration damping properties could potentially be employed to help improve
aim by stabilizing a wearer's arm. Or it could be added to the butt of a rifle to reduce
transmitted movements from wearer caused by things like breathing and heart beat.
1.3
Other Applications
A variable-impedance material has a wealth of non-military applications as well. Devices developed for the military could be readily applied to sports, with applications
such as padding for football or variable ankle support for cross-training. Imagine
having a ski boot that allows you to change the stiffness so you can walk normally
when you are not skiing.
Other possibilities include incorporating the material into haptic devices, providing feedback in a glove, for example, to simulate touching a surface.
1.4
Thesis Scope
This thesis is a preliminary investigation into the design of a variable-impedance
material. Specifically it investigates using electrorheological (ER) fluid, a type of
field-activated fluid, in creating such a material. Possible methods for using the fluid
to create the material are briefly explored, but focus is placed on one particular
design to determine the important factors in the design process. The goal is to begin
to assess the feasibility of creating such a material and compare different methods of
fabrication. We hope to come up with a method for comparing three different types
20
of field activated fluids: electrorheological, magnetorheological, and shear thickening
to determine what applications they are best suited for.
Chapter 2 gives an introduction to field activated fluids and explains their properties. Two types of ER fluids, heterogeneous and homogeneous, are described in
detail.
Chapter 3 describes several possible designs for the material and models the behavior of the design being investigated.
Chapter 4 describes the testing that was carried out on the material including the
design of a unique testing system.
Chapter 5 presents the analysis methods and gives an overview of all the testing
data for the materials that use heterogeneous ER fluid.
Chapter 6 examines the results of the materials that use homogeneous ER fluid.
Chapter 7 explores the properties of the same materials without any fluid in them
for comparison.
Finally, Chapter 8 discusses what can be learned from the test results and proposes
future work in the area.
21
22
Chapter 2
Background
Field activated fluids have rheological properties (viscosity, yield stress, shear modulus, etc.)
that change upon application of an external field. The primary types
are: shear-thickening (ST) fluid, magnetorheological (MR) fluid, and electrorheological (ER) fluid. An overall comparison of the different fluid properties is presented
in Table 2 (these are values of representative fluids only, the actual fluid parameters
can vary over a wide range).
2.1
Shear-Thickening Fluid
This type of fluid is characterized by a sudden increase in viscosity with increasing
shear rate. At low shear rates, the fluid behaves as a liquid, but once the shear rate
is increases beyond a critical value, the fluid locks up into a solid-like state. When
Property
Density (g/ml)
Viscosity (Pa-s)
Shear Stress (kPa)
Response Time (ms)
Temperature Range (C)
ST
2
MR
2-4
Heterogneous ER
1
Homogeneous ER
0.8
1
>10
<1
-10-150
0.1
30
<10
-40-130
0.1
4
<2
-50-150
10
8
10-80
0-60
Table 2.1: A comparison of typical field-activated fluid properties.
23
the shear stress is removed, the fluid returns to its initial liquid behavior.
This phenomenon occurs in colloidal suspensions, such as corn starch in water,
and is due to the formation of particle clusters, called "hydroclusters," from the
hydrodynamic lubrication forces between particles [6, 1]. The response time of the
transition from liquid to solid has been shown to be on the order of a millisecond or
less [3, 24, 21].
ST fluid has been used in damping and control devices because of its natural ratelimiting feature [22, 13]. Lee, et al. have shown that impregnating ST fluid in Kevlar
can improve the energy absorption of Kevlar fabric which has the potential to make
body armor thinner and more flexible [23].
2.2
MR Fluid
Magnetorheological fluids exhibit controllable rheological behavior upon application
of an external magnetic field. The apparent viscosity increases by more that two
orders of magnitude in a moderate field [2].
MR fluids consist of ferromagnetic dispersed particles with a diameter on the order
of one micron in a carrying fluid, such as silicone oil. Stabilizers are also often added
to prevent settling or agglomeration of the particles. A magnetic field polarizes the
particles and causes chains and structures to form, generating a yield stress in the
fluid. Experimental evidence has shown that the yield stress is generally proportional
to the square of the magnetic field strength [8].
While they were discovered at nearly the same time, MR fluids have not been
researched as extensively as ER fluids. Yet they have recently found more success in
commercial applications. Some examples of applications include an MR fluid brake in
the exercise industry, a controllable MR fluid damper for use in truck seat suspensions
and an MR fluid shock absorber for automobile racing [17].
Some advantages of
MR fluid, especially in automotive applications, include a high shear stress, large
temperature range, and low voltage requirement [2].
24
(b) Homogeneous
(a) Heterogeneous
Figure 2-1: SEM pictures of heterogeneous and homogeneous ER fluid show the
micron sized particles in heterogeneous fluid, whereas the homogeneous fluid is still
continuous at this scale. Both samples were dried for an hour in a vacuum oven before
placed in the SEM. The darker, textured sections of the homogeneous fluid picture
are the conductive tape on the sample holder, not part of the fluid.
2.3
ER Fluid
Electrorheological fluid quickly and reversibly changes its rheological properties in
response to an electric field. There are two primary types of ER fluid: heterogeneous
and homogeneous.
Heterogeneous fluid, shown in Fig. 2-1(a), has solid particles
suspended in a fluid medium, while homogeneous fluid, shown in Fig. 2-1(b), is a
continuous liquid [20]. Both fluids are described in greater detail in the following
sections.
2.3.1
Heterogeneous
Description
Heterogeneous ER fluid is the most common type of ER fluid. It was first discovered
by Winslow in 1949 and consists of micron-sized dielectric particles dispersed in an
insulating fluid medium. Upon application of a field, a yield stress develops in the
fluid as the particles form chains and structures. So the fluid reversibly transforms
from a liquid to a Bingham plastic, or gel, under an electric field.
25
Models
Several different mechanisms for the origin of the ER response have been suggested,
including: degradations of the fibrous structure formed by polarization forces between
particles, distortion and overlap of the electric double layers of colloidal particles resulting in increased energy dissipation, interelectrode circulation of particles, and the
existence of water bridges between particles[19, 4]. The polarization model is generally
accepted as the primary component of the ER effect. Marshall, et al. demonstrated
that the relative suspension viscosity, defined as the apparent viscosity of the electrified suspension divided by that of the continuous phase is a function of only the
Mason number, Mn, defined as:
Mn=
(2.1)
C
2EoEc# 2 E 2
where 1c is the viscosity of the continuous phase, ' is the shear rate of the suspension,
E is the magnitude of the applied electric field, co and c, are the dielectric constants
of free space and the continuous phase, respectively, and 0 = (-EC)
/ (E,+ 2Ec)
where
EP is the dielectric constant of the particle phase. The Mason number is a ratio of the
viscous shear forces to the electric polarization forces acting on the particles in the
system, implying that these forces dominate other forces acting on the particles (van
der Waals, electrostatic, and thermal)[25].
In general, ER fluid can be characterized as a Bingham plastic with a shear stress
defined as:
T = Ty + T7o
(2.2)
where Ty is the dynamic yield stress as shown in Fig. 2-2(a). The ER fluid also has a
static yield stress defined as the minimum shear stress required to cause the ER fluid
to flow. In general, these two yield stresses are not the same[5].
The polarization model predicts that the dynamic yield stress scales as the square
of the applied electric field and a variety of ER suspensions have been shown to have
this behavior[1O].
However, other suspensions have shown a linear dependence on
26
field strength[18, 19]. Choi found that for microencapsulated polyaniline-based ER
fluid, the yield stress is proportional to E2 at low field strengths and approaches E3 /2
at high field strengths[7]. To preserve generality, we describe the relationship between
field strength and yield stress as:
Ty =
where
fp
fpE"
(2.3)
is a measure of the strength of the heterogeneous ER effect.
Performance Factors
Many different parameters affect the performance of heterogeneous ER fluid including
particle size, size distribution, volume fraction, particle composition, and additives.
Particles in ER fluid are generally 0.1 to 100pm. At smaller particle sizes, it is
thought that the Brownian motion will compete with electrical forces to disrupt the
ER effect.
Larger particles would have a slow response and would be more prone
to settling under the influence of gravity [18]. Experimental results show no monotonic relationship between the ER effect and the particle size. A molecular-dynamics
simulation predicts that the shear stress should be proportional to the cube of the
particle diameter [30]. When two different size particles were mixed, the shear stress
was found to decrease both theoretically and experimentally [35, 26].
Based on the polarization model, the yield stress increases with both volume
fraction and the dielectric ratio between the particles and fluid [19].
Using a mi-
crostructural model to relate the yield stress to the electrostatic energy, Bonnecaze
et al. predict a maximum yield stress at a volume fraction of 40% for dielectric ratios
less than 10 [5].
The particle composition ranges from silicates to conductive polymers to carbona-
ceous materials. Before 1985, almost all ER fluids contained a small amount of water
adsorbed on the particle surface. Many of the shortcomings associated with ER fluid
were due to the presence of water, such as limited temperature range, high current
density, and device erosion [12]. Advances in particle design introduced water-free,
27
or anhydrous, ER fluids often with water chemically bonded or crystallized in the
molecule. A good anhydrous ER fluid has a yield stress around 5kPa with a field
strength of 2kV/mm, a current density less than 2OptA/cm 2 , a temperature range
from -30 to 120*C, and a response time less than ims.
There is still room for improvement in the design of ER fluids.
Zhang et al.
recently fabricated a fluid using surface modified complex strontium titanate particles in silicone oil with a volume fraction of 36% and measured a yield stress of
27kPa in a DC field of 3kV/mm. The conductivity at room temperature was only a
few puA/cm 2 [37]. This five to ten time increase in yield stress could open up many
possible applications that were previously infeasable.
2.3.2
Homogeneous
Description
Homogeneous ER fluid, unlike heterogeneous ER fluid, has no solid phase. It can
consist of polar liquids, nonpolar liquids, low molecular weight liquid crystals, or
lyotropic polymeric liquid crystals [14, 15, 28, 11, 36]. Inoue has had particular success
using side-chain type liquid crystal polymers diluted with dimethylsiloxane [16].
In immiscible liquid blends, such as the liquid crystal polymer in solution, the
electric field causes the viscous droplets to elongate and bridge across the electrodes.
With no field, the viscosity is comparable to the low viscosity solution and at high
fields the viscosity is comparable to that of the LCP forming the bridges [29].
Homogeneous fluids don't suffer from the disadvantages in heterogeneous fluid
such as particle settling, agglomeration and abrasion. They also may be more suited
to scaling down to smaller sizes because they are still homogeneous at micron scales
while heterogeneous fluid has solid particles at this scale.
Model
While some fluids such as solutions of poly(-benzoyl-L-glutamate) in dioxane and
dichloroethane exhibit a yield stress varying with field strength just like heterogeneous
28
E
E
CO
Shear Rate [s-1]
Shear Rate [s-1]
(a) Heterogeneous
(b) Homogeneous
Figure 2-2: The characteristic shear stress versus shear rate for both heterogeneous
and homogeneous ER fluid. The heterogeneous ER fluid develops a yield stress with
increasing field strength, while the viscosity remains constant. The homogeneous ER
fluid has an increasing viscosity with field strength.
fluids [16], the majority of homogeneous ER fluids have a viscosity that increases with
field strength and no yield stress as shown in Fig. 2-2(b). There is no well defined
relationship between the viscosity and the field strength, but assuming a power law
relationship,the shear stress can be expressed as:
T
= (ro + fcE n)§
(2.4)
where the initial fluid viscosity is increased with the electric field. The parameter
is measure of the strength of the homogeneous ER effect.
29
f,
30
Chapter 3
Material Design
In this chapter, an initial design of the variable impedance material is presented.
3.1
Force Transmission
To create a material with variable properties, we need a method for translating the
change in fluid properties to mechanical properties such as stiffness and damping.
There are three primary modes of force transmission in field-activated fluids: shear,
valve and squeeze mode, illustrated in Figure 3-1.
3.1.1
Shear
In shear mode, the force is transmitted orthogonal to the field by resisting the motion
of the top and bottom bounding plates. This mode is used in applications such as
clutches and brakes where two concentric cylinders, with fluid in between, are rotated
with respect to each other. The amount of torque transmitted from one cylinder to
the other is determined by the field strength.
3.1.2
Valve
In valve mode, the field strength determines the amount of pressure drop that may
be supported through the electrode gap. This mode is used in piston and cylinder
31
Q
(b) Valve Mode
(a) Shear Mode
4, Q
() T
(c) Squeeze Mode
Figure 3-1: These figures illustrate the three mechanisms of force transmission for a
field-activated fluid.
dampers where the resistance to flow, and hence damping, are controlled by the field
strength.
3.1.3
Squeeze
Finally, in squeeze mode, force is transmitted parallel to the field as the fluid thickness
changes. Compression-type dampers employ this mode of force transmission.
3.2
Geometry
This thesis is an investigation into using field activated fluids to create a thin variable
impedance material. How can we use these force transmission methods in a thin
flexible material? Three different design ideas were considered: channel, grid, and
sandwich. Each of these geometries can be used for all three field-activated fluids,
but specific implementations using ER fluid are presented.
32
I
I '
II
+
Figure 3-2: Illustration of the channel design for an electrorheological fluid based
variable impedance material. The alternating electrodes would create a pressure
difference between two resevoirs of ER fluid.
3.2.1
Channel
A channel geometry exploits the valve mode of force transmission. The general idea
is for macro-scale material deformation to cause the flow of fluid through narrow
channels. The flow through the channels can be regulated by applying a field, thus
regulating the overall material properties.
One possible implementation of the channel geometry using ER fluids is depicted
in Fig. 3-2. Alternating electrodes, with layers above and below as seals, confine
the fluid to narrow pathways. Bending perpendicular to the channel direction would
tend to cause fluid flow, like squeezing toothpaste out of the tube. By applying a
voltage across the electrodes, resistance to flow is increased, and thus increasing the
resistance to bending. Alternating layers could be oriented in different directions, like
in a laminar fiber composite, to control bending in a variety of directions.
Another implementation of this geometry is to fill hollow fibers with the fluid which
could then be woven into a continuous fabric. This would create a material similar
to a traditional textile but with the possibility of some control over its mechanical
properties.
33
Figure 3-3: An illustration of a possible grid type design of an electrorheological fluid
based variable impedance material.
3.2.2
Grid
In a grid geometry, there are two flexible layers with the fluid in between. By dividing
up the sheet into discrete areas where field can be applied, the material can be
selectively controlled. An implementation using ER fluid is shown in Fig. 3-3. There
are electrodes above and below the fluid. The bottom electrode is continuous, but
the top one is broken into squares so that each one can be adjusted independently.
Taylor, et al. created a similar grid, but with a rigid bottom to act as a haptic
display device. By activating different areas, they could create different textures on
the top flexible electrode made of conducting rubber. Running a roller across the
surface, they measured vertical forces up to 150 grams of force when moving from an
inactive cell to an active cell [31, 32].
3.2.3
Sandwich
The third type of geometry involves stacking multiple flexible layers with the fluid in
between them, attaching opposite layers at opposite ends. Figure 3-4 illustrates how
pulling the ends apart involves the shear mode of force transmission as does bending
34
'I
Tension
Bending
Normal Force
Figure 3-4: Three different loading conditions on a sandwich geometry illustrating
the variety of force transmission methods that can be utilized.
the sample. Applying a normal force tends to cause fluid flow and therefore the valve
mode of transmission can be exploited.
For an ER fluid, each layer would be an electrode, with the voltage applied at
opposite ends. Because there are multiple thin layers, the distance between adjacent
electrodes is small, so a low voltage could provide a very high field strength to the
fluid. In order to prevent the adjacent electrodes from contacting, a spacer is added
between each electrode.
3.3
Design Considerations
The material design, whether it involves one or all of these three geometries, will
involve design considerations which are common to all three geometries.
3.3.1
Size
The material must be thin, so it becomes important to understand how these fluids
behave in small spaces. Typical devices have gaps on the order of millimeters; the new
material will have gaps on the order of microns or less. We would like to understand
the scaling laws that determine how the properties of the material behave as the size
is reduced.
35
3.3.2
Flexible Boundary Conditions
The material must also be flexible to allow freedom of movement which creates the
unique situation of unconstrained boundary layers. The distance between the layers
is not rigidly fixed as it is in most applications so the thickness between the electrodes
can vary over time and also over position.
3.3.3
Arbitrary Loading
As it is worn by a human, the material could be subjected to a variety of loading
conditions. For example, the material could be stretched and bent around a joint at
the same time a normal force is applied from an impact.
3.3.4
Failure Modes
It is also important to understand the primary mechanisms for material failure. In
ER fluid based materials, electrical breakdown is a likely candidate. The flexible
electrodes combined with arbitrary loading mean the electrode gap could become
quite small in local areas, resulting in dielectric breakdown. Adding the spacer may
help reduce the risk of failure by preventing the electrodes from coming too close
together. However, there may be an advantage to scaling down the space between
electrodes. Paschens law, which relates the breakdown strength to the product of
the gap spacing and pressure, predicts the breakdown strength of air at atmospheric
pressure reaches a minimum around 4ptm and then increases as the distance becomes
smaller. But recent work indicates the breakdown strength of air actually continues
to decrease below 4pm [33].
3.4
Shear Model
As a preliminary effort to gain insight into some of these design criteria, we intend to
model a simple implementation of the variable impedance material and then compare
the model to experimental results. Since the shear mode of force transmission is
36
Mylar
Aluminum
F
Spacer
L
;'
tf
ER Fluid
te
Figure 3-5: Illustration of the basic shear stress loading condition. The thickness of
the fluid film is tf and the distance between the electrodes is te.
well understood in traditional ER fluid applications, it will be investigated using a
sandwich-type geometry. Without a loss of generality, the geometry can be reduced
to a single layer of fluid with electrodes on the top and bottom and a spacer in the
middle. The force in tension on the sample, which translates to a shear stress on
the fluid, is measured by holding one side fixed while the other is moved as shown in
Fig. 3-5.
To model the behavior of this material the basic fluid models discussed in Chapter 2 will be used. Any discrepancies in the results will help bring out some of the
unique features of this material. The shear force, F, is given by:
F = AT
(3.1)
Where A is the area where the two electrodes overlap. For this configuration, the
area is given by:
A = w(L - x)
(3.2)
where w is the width of the layer, L is the initial length of the overlapping area, and
x is the displacement of the top layer. Combining the previous two equations, we find
that the shear stress is linear with respect to position:
F
= -TWX
37
+ TWL
(3.3)
So we expect the shear force to start out as a maximum and then decrease to zero
when x equals L. Note that this model is assuming the material is loaded in tension
and is therefore only valid when x > 0.
If we assume that the dielectric constant between the electrodes is uniform, the
field strength is simply the applied voltage divided by the distance between the electrodes:
E= -
(3.4)
te
where te is the distance between the electrodes and V is the applied voltage. Furthermore, the shear rate is defined as the velocity of the top layer divided by the fluid
thickness:
(3.5)
tf
where tf is the thickness of the fluid layer and ± is the velocity.
3.4.1
Heterogeneous ER Fluid
We can combine Equations 2.2, 2.3, 3.4, and 3.5 to find the shear stress in the material
with heterogeneous fluid:
- 4 f= V
ten
tf
3.4.2
(3.6)
Homogeneous ER Fluid
Likewise, for the homogeneous fluid, using Equation 2.4 gives:
7o= + fcV%
tf
tntf
3.4.3
(3.7)
Electrostatics
In addition to the standard fluid models, the flexible electrodes will experience electrostatic forces similar to a parallel plate capacitor.The effective capacitance of the
sandwich is given by:
C = rOA
t
38
(3.8)
Assuming the electrodes form an infinite parallel plate capacitor (ignoring edge
effects), the normal force pulling the two electrodes together is given by:
Fn = 2
(3.9)
V2
where K is the dielectric constant of the material between the electrodes, co is the
permittivity of free space (8.854 x 10
12
F/m). While the standard fluid model is not
directly affected by a normal force in the standard configuration, the normal force
may have an indirect effect by changing the thickness.
The force required to slide the electrodes apart based solely on the capacitor model
(ignoring the fluid) is given by:
Fx =
(3.10)
KEOWV2
2te
This equation is derived by differentiating the energy stored in a capacitor:
U = Kf"wV2 (L - x)
2te
(3.11)
with respect to displacement, x. Since this force does not depend on position, it will
add a constant offset to the shear force prediction. The importance of this term is
not readily calculable; it depends on material properties as well as applied voltage,
speed and position. It will be assumed to be negligible in forming the model, but will
be kept in mind as a possible explanation for discrepancies between the model and
experiment.
3.4.4
Dry Material
The voltage dependent normal force found in the previous section implies that the
shear force could be controlled using simple Coulomb friction.
The dry material
behaves as follows:
T
/_tKEOV2
2te
39
2
(3.12)
Where P is the coefficient of kinetic friction between the spacer and the electrode.
It is worth noting that even without an ER fluid the sandwich material still
exhibits a shear stress that is voltage dependent. This reveals an alternate method
for creating this variable-impedance material other than field activated fluids and has
the possibility of saving weight. Because it has the same geometry, it could also be
used in addition to field activated fluid based material. This electrostatic induced
friction is known as the Johnsen-Rahbek effect and was investigated in the mid 50s
at IBM for creating a clutch with fast response time [9].
3.4.5
General Model
The three models presented previously (heterogeneous, homogeneous, and dry material) have similar properties that allow them all to be represented by one general
model to facilitate comparisons between the materials. The homogeneous fluid acts
like a voltage dependent damper, while the dry and heterogeneous fluids act like voltage dependent Coulomb friction. Thus the general model is represented as a voltage
dependent damper and voltage dependent Coulomb friction in series. The shear stress
is given as:
T-
c(V) + b(V)X
(3.13)
Where c and b are the Coulomb friction and damping coefficients, respectively. Using
the fluid models, the shear stress can be expanded to:
T
=
(ao + aVn) + (a 2 + a3 Vn 2 )±
Material
ao
a,
Heterogeneous Fluid
Homogeneous Fluid
0 0
Dry
0
0
O
a2
70
0
(3.14)
0
ni
1-2
0
2
a3
n2
0
0-2
0
Table 3.1: Parameters for general model in terms of material properties.
The relationship between the general model parameters and the material proper40
ties for all three types of material is shown in Table 3.1. Notice that ao is zero for
all models, indicating that none of the models predict a friction force at zero field
strength. This term was added in to provide symmetry and to verify that it actually
is zero rather than assuming it is. Also note that both ni and n 2 are not well understood with relation to the material properties and can only be determined from
empirical data.
3.5
Performance Analysis
With the models for shear stress established, it is useful to come up with a measure for
overall material performance to help compare the different fluids. In general, we would
like to use this material to help abosrb a controllable amount of energy, so looking
at the amount of energy absorbed by this material as it is pulled apart is helpful.
One method for estimating the energy absorption is to compute the work done in
pulling the layers apart at a constant velocity, which approximates the mechanism
for preventing joint motion. Another approach is to look at the amount of energy that
can be absorbed from a mass with some initial kinetic energy, which approximates
the absorption of an impact. Both of these measures are examined in two different
geometrical configurations.
3.5.1
Parallel Loading
In this configuration, the force is applied parallel to the sample, causing the layers
to remain horizontal while being pulled apart. This is the same condition as the one
shown in Fig. 3-5, and the model equations derived previously all apply. In this case
the work done at a constant velocity is given by:
W
=
Fdx
(3.15)
Tw(L--x)dx
(3.16)
L
W
W
j
=
a(c(V) + b(V)±) = or
41
(3.17)
where a = wL 2 /2. So the total work, which is equivalent to the energy absorbed, is
proportional to the shear stress for a given geometry.
The more interesting problem is to determine how much energy would be absorbed
by the material if a given mass, M, with initial energy, EO = 1/2M±2 was attached
to the end of the sample. The force exerted by the sample will slow down the mass
until either the mass comes to a complete stop or the layers separate. The dynamic
equation for the mass is given by:
M ..
c(V)L + b(V)Li - c(V)x - b(V)x,
(± > 0, x
L)
WX
0
(<
L)
0,x
(3.18)
Using Simulink to solve the differential equation, as shown in Appendix A, the
final velocity of the mass can be approximated as:
Xf
{0O
.0
=
-
2 (c(V) + b(V))
(±o
-Oc)
(±O
> 0Oc)
(3.19)
In some cases the final velocity drops to zero, meaning all the initial energy was
absorbed by the material. This occurs when the initial velocity is below a critical
initial velocity, ,Oc,
which is given by:
Xoc
= 2 Mb(V) +
c(V) +
b(V)
(3.20)
Written in terms of the critical initial energy instead of velocity gives:
Eoc = Sb(V)
2-c(V) +±
(2-b(V))
+ 2bV
c(V)
C()+(2
V)
(3.21)
This is the amount of initial energy that can be totally absorbed by the material. Because force is applied only when the layers are in contact, the critical absorbed energy
depends on the mass of the object being stopped, not just the material properties.
42
F
LS
be.Iv.
x
M
D
Figure 3-6: Diagram illustrating the perpendicular loading condition where the material is pinned on either side and a force acts through the center causing the layers
to slide apart.
In general, the overall energy absorbed is given by:
( 0(
[i
ce (c(V) + b(V).,o)
-
9j
1
~ 0~ 9
2M±:'
j
(±0
> i 0 c)
(z >
-
(3.22)
Oc)
Notice that as the energy becomes large, the energy absorbed approaches that predicted by Eq. 3.17, which makes sense because at large energies the velocity hardly
changes, matching the earlier assumption.
3.5.2
Perpendicular Loading
The perpendicular loading condition is especially suited for a ball-drop test to verify
the energy absorption predictions. In this configuration, the force is exerted orthogonal to the length of the sample with each end of the sample pinned in place as shown
in Fig. 3-6. The layers separate as the center of the sample is pushed down. If we
assume that the displacement causes a triangular deformation, as indicated by the
43
dashed lines in the figures, the overlapping area is given by:
A = w(2Ls - V4x2 + D 2 )
(3.23)
where D is the distance between the supports and L, is the length of each strip. Note
that L, is defined slightly differently than L in the parallel loading case.
Using the model presented in Eq. 3.13 and assuming the tension in the material
is the shear stress times the area of overlap, the force exerted on the object is given
by:
F = 4w c(V) +
b(V)
4 2
-v4x2 + D2
2xL
V4,2+ D2
(3.24)
-x
To make the next step more clear, we first replace D with mL, where m c [1, 2].
Then the work can be calculated as in the previous section by integrating the force
from x = 0 to x
- -V4
-n
2,
which is the point where the layers separate.
2
W = a, (Ac(V) + Bb(V)±)
(3.25)
where
as
wL 8 2
2
(3.26)
A
(2 - M) 2
(3.27)
B
4
2
-rn 2 - 8m arctan
(
-M)
M
+ 2m2 In 2 + v
M
m)
(3.28)
Notice the similarity to equation 3.17. The only difference is that the damping and
friction elements are weighted differently depending on the initial geometry. For
M
=
1, which means that the layers begin completely overlapped (and L, becomes
equivalent to the L in the parallel case), A
=
1 and B ~ 1.18. So in this case, the
effect of the damping element is increased 18% with a corresponding increase in the
overall work done by the material.
Ignoring the effects of gravity, the motion of the mass is described by the following
44
differential equation:
M 2 = 4w c(V) +
4x1
4x
V4x2
+ D2
b(V)
)
(
x
xD
/4X2 + D
2
- x
(3.29)
This equation can be simulated to find the approximate final velocity of the mass, as
in the previous section. Using this final velocity, the total amount of energy absorbed
by the material is given by:
Ea
4
a
Ac(V)JBb v)
a. (Ac(V) + Bb(V)o0 ) [1 _
2
))
G
(
(±o
-4c)
x0
(3.30)
where the critical initial velocity, boc is given by:
X
c=
8 Bb(V) +
2M
- Ac(V ) +
M
(2M
Bb(V)
(3.31)
With these equations, the energy absorption behavior of a material can be predicted after finding the model parameters. As an illustrative example, if the material
was used in an ankle brace, the energy and mass of a falling human body could be
used to find the voltage necessary to absorb enough energy to prevent ankle injury
when the wearer's feet hit the ground.
45
46
Chapter 4
Testing
4.1
Preliminary Testing
To make sure that the sandwich geometry does in fact have a voltage dependent
shear stress, a preliminary test was first carried out. The goal was to examine how
ER fluid behaves in the thin film necessary for incorporation into a uniform and how
the properties of the fluid translate into macroscopic properties.
The first prototype employed a simple sandwich design resembling a parallel plate
capacitor. The ER fluid was contained between two electrode plates along with an
insulator that prevented the electrodes from contacting and shorting.
A schematic of the layers in the prototype is shown in Figure 4-1. The electrodes
were made with aluminum foil, 20 microns thick. The insulator was tissue paper, 30
microns thick. The ER fluid used was manufactured by Bridgestone (F569HT), but is
no longer commercially available. It consisted of carbonaceous particles 1-10 microns
in diameter in silicone oil with a 67% solid volume fraction [271. The electrorheological
properties of the ER fluid were not measured directly, but it was reported to have a
shear yield stress of 4kPa at a field strength of 4kV/mm.
The prototype was constructed by affixing the bottom foil and paper layer to a
plastic block with an adhesive. The paper was then coated with the ER fluid and
another foil layer was placed on top. Finally, a layer of polypropylene was glued to the
top layer of foil for insulation. Electrical connection was made by attaching alligator
47
Paper
Foil
Figure 4-1: Schematic of the prototype
material consisting of a layer of paper saturated in ER fluid and surrounded by two
layers of aluminum foil.
Figure 4-2: Picture of the prototype on the
block used for the shear test. The electrical
connections are made on opposite sides of
the sample using alligator clips.
clips to opposite ends of the two foil layers as shown in Figure 4-2. The spacing
between the two electrodes was estimated to be 0.1 mm by measuring the thickness
of the paper coated with ER fluid. It should be noted that the fluid was absorbed by
the paper layer and was present on both sides of the paper. It was unclear, however,
if the particles in the ER fluid were absorbed into or through the paper.
4.1.1
Test Description
One of the fundamental characteristics of heterogeneous ER fluid is the variation
in shear yield stress with applied electric field. Thus, the shear yield stress of the
prototype material should have an observable dependence on field strength. In this
experiment, the static yield stress, which is the value of stress beyond which the
material undergoes free deformation, was measured.
To determine the static yield stress of the material, a plate was attached to the
top of the prototype and a six-axis force transducer was attached to the plate such
that the X and Y axes were on the same plane as the material as shown in Figure 4-3.
Using a spring as an aid, a force ramp was manually applied to the force transducer
until an observable displacement of about 5mm occurred. During the test, the X, Y,
and Z channels of the force transducer were recorded on a computer at a sampling
rate of 1kHz. The test was repeated three times with each of the following voltages
48
N
F
--
Force
Transducer
Figure 4-3: A diagram illustrating the prototype test method. The spring was compressed manually at an approximately constant rate until movement of the top plate
began. The force measurement was recorded with a three axis force transducer.
across the electrodes: 0, 20, 40, and 60. The top plate and force transducer provided
4.2N of normal force on the prototype during the tests. The series of tests were then
repeated with an additional 200g weight on the top plate resulting in a 6.2N normal
force. The top electrode of the prototype was smaller than the bottom such that a
constant contact area of 41cm2 was maintained throughout the tests.
4.1.2
Model
Since the goal of this experiment was to determine how well the material properties
can be predicted based on the underlying fluid properties, it was useful to derive
a model of the prototype to compare with the experimental results. To make the
model simple, several assumptions were made: the electrodes were perfectly flat, the
distance between the electrodes was a constant 0.1mm, the paper had no effect on
the yield stress, and the fluid was an ideal Bingham plastic. Using these assumptions,
the shear behavior of the material is simply the shear behavior of the fluid.
As discussed in Section 2.3.1, there is no clearly accepted relationship between the
shear yield stress and the electric field strength. However, since experimental evidence
generally supports a linear relationship, that is what was used for the model. Since
49
3
3
Y
2.5
F
y
2.5
22
1 .5
1
2.
0
L-
1.5
X
0
U-
0.5
z
0
0.5
-0 .50
5
10
0
15
(a)
Figure 4-4: These figures
a 4.2N normal force. (a)
the force transducer. (b)
time. The horizontal line
force.
10
5
15
Time [s]
Time [s]
(b)
show the data from a test carried out at 60 volts and with
shows the measured force on the X, Y, and Z channels of
is a plot of the magnitude of the X and Y channels versus
indicates the maximum force which equals the static yield
the thickness was assumed to be constant the model simply reduced to:
CV
Ts
(4.1)
where V is the voltage and C is a constant that indicates the strength of the ER
effect. Ideally, the shear yield stress of the fluid would be determined experimentally
in a controlled environment to determine an estimate for C. But in this case only the
shear yield stress at 4kV/mm was known, which led to a predicted value of 1OPa/V
for C.
4.1.3
Analysis and Results
The force measured on the three transducer axes is graphed as a function of time
in Figure 4-4(a). The initial offset was subtracted from each channel such that the
average force in the first tenth of a second was zero. For all three axes, the force
increased up to maximum at which point the transducer began to move and the force
dropped back to zero.
By taking the magnitude of the X and Y channels, the total force, F, acting on the
50
900800
800-
0 4.2N
0 6.2 N
700-
700 600 -600
600 -
506
L 47 d
..- - -'
.
-
= 4.8V+450
-4'
L5
400
00-:
30000200
GY
100
00
10
20
30
Voltage [V]
10
40
50
60
'0
10
(a)
20
30
Voltage [V]
40
50
60
(b)
Figure 4-5: These figures summarize the data from the preliminary testing. The error
bars represent one standard deviation. (a) plots the yield stress versus voltage for
both values of the normal force. (b) is a plot of the yield stress and error for all the
data, neglecting any normal force effects. The dashed line shows the weighted least
squares error fit to the data and the solid line is the model prediction.
sample was determined as a function of time. The maximum of that plot, shown in
Figure 4-4(b), is the shear yield force, Fy. The force can be converted to shear stress
by dividing by the constant contact area. The yield stress versus the field strength
for all trials is shown in Figure 4-5(a). The two different values of normal force did
not produce noticeably different yield stresses, which supports the model. Combining
the data from both normal forces, an overall mean and standard deviation of the
yield stress versus voltage is plotted in Figure 4-5(b). The yield stress did increase
nearly linearly with the voltage as expected from the model, however there were clear
discrepancies between the experimental result (dashed line) and the model (solid line).
First, the intercept was 450Pa, not zero as expected. Furthermore, the slope, which
corresponds to C in the model, was about half the expected value.
The preliminary test showed that the ER effect can be observed in the sandwich
geometry, which paved the way for more precise studies.
51
4.2
Testing System Design
The design of the testing system was motivated by the desire to run more precise
testing on the shear response. We were interested in measuring the dynamic yield
stress as this represents the maximum force that the material can exert during shear
and is used in the performance equations derived in Section 3.5.
4.2.1
Goals
This section briefly highlights some of the main goals for the testing system. The goals
of the testing system were to preform mechanical testing on the material at velocities
and forces close to human levels. We wanted to be able to shear the material at a
constant velocity as well as apply arbitrary normal forces to determine their effects.
To achieve these goals, we needed a horizontal tensile tester. The available machines
did not meet our requirements for travel, speed, and displacement so we constructed
our own. In designing the machine, some other goals included being able to easily
modify it for other applications, including a bending stiffness tester, or adapting it
to test shear thickening fluid or MR fluid impregnated foam.
4.2.2
Description
The system was designed as a simple horizontal linear tensile tester with a linear
stage providing motion and a force transducer to measure the load on the material.
The primary components of the test system were a linear stage, a motor drive and
controller, a voltage amplifier, a force transducer, a data acquisition (DAQ) board,
and a personal computer (PC).
The linear stage (Parker Daedal 404XR) was driven by a 20mm lead screw and
has 500mm of travel. It has a bidirectional repeatability of ±5pm, but a 1[tm linear
encoder measures the exact displacement of the stage.
The maximum attainable
velocity was 1m/s. The screw was driven by a stepper motor (Parker Compumotor
VS23B) with a stall torque of 267.5oz-in, giving the linear stage a maximum force of
474N assuming 80% effeciency of the transmission system.
52
The motor was controlled and powered by a Parker Gemini GT6K 5 Amp controller/drive, which also read the linear encoder and calculated the stage position.
The GT6K communicated with the PC over an ethernet connection. For the constant
velocity movements that were performed in this experiment, the controller generated
a trapezoidal velocity profile with constant acceleration until the desired velocity was
reached and then constant deceleration until the movement was complete.
The amplifier was a Trek 10/10 with a 1000:1 voltage amplification and a 20kohm
nominal input impedance. It could deliver voltage between ± 10kV with a current
of ± 10mA. It had BNC connections to monitor the actual voltage and current at 1
V/kV and 1V/mA, respectively.
The force transducer (Transducer Techniques MLP-10) was rated to +10 pounds.
It was calibrated in both tension and compression and could easily be replaced with a
larger model if necessary. The output from the force transducer was fed into a signal
conditioner (DPM-3) which adjusted the reading based on the calibration data and
produced a voltage output proportional to the conditioned force.
The DAQ board (UEI PDL-MF) had 16 16-bit analog inputs, 2 12-bit analog
outputs, and 48 digital input/output lines. The analog input could read at 50 kS/s
and the output could update at 100 kS/s. The DAQ board read the force transducer
signal conditioner output, the voltage monitor, and the current monitor from the
amplifier. All three used differential inputs to minimize noise. The analog output
was used to control the voltage amplifier.
A schematic of the test system is shown in Fig. 4-6 illustrating the connections
between components as well as the method for shearing the sample. One side of
the force transducer was mounted to the movable stage and a sample holder, made
of Delrin, was attached to the other side. Another sample holder was fixed to the
opposite end of the positioner, which allowed a sample to be placed between the two
holders and then pulled apart when the stage was moved. There was also a table
between the two holders that the sample rested on, which allowed a normal force to
be applied to the sample by placing weights on top of it.
The entire system was controlled by the PC with a test program written in Lab53
-i--i
- ~------~--
.-
--
-
Ethernet
Drive /UEl
Controller
DJAQ
Board
Signal
Conditioner
Force
Transducer
,Stepper
Motor
Voltage
Amplifier
PCI-*
P
GUI
Sample
Linear Encode-r
Figure 4-6: A diagram illustrating the primary components of the testing system and
how they are connected.
54
Figure 4-7: A picture of the single-axis, horizontal, linear testing system.
View. The program presented the user with a graphical user interface (GUI) that
allowed the voltage, velocity, and displacement for the test to be set. When a test was
run, the computer sent the velocity and displacement to the controller and set the
voltage to the appropriate value. It waited two seconds and then initiated movement.
During the run, the program read the time, position, velocity, force, current, and
voltage every 10ms (100Hz) and stored the values in an array. It also updated the
graph of force versus position shown in the GUI. Once the movement was complete,
the user had the choice to either clear the data or save it to a file. When saved,
the data was stored in ASCII text format with each column representing one data
channel. The file name was automatically generated based on the test parameters.
The software also featured a stop button which sent a kill command to the motor,
and positioning controls that moved the stage a specified distance. The positioning
controls were used to reset the stage to the original position after each run.
4.3
Spring Analysis
After constructing the test system, a simple baseline characterization was performed
to verify that it was working as expected and to identify sources of measurement error,
such as noise. The characterization was chosen to be performed on a spring because of
its well defined behavior. Two springs with different nominal spring constants were
used. They were stretched between two aluminum rods and placed in the sample
holder of the test system. During the tests, the springs were stretched a fixed distance
55
2.8
2.6
2.42.2
2
1.6
1.41.2-
1*
0
5
10
Position [mm]
15
Figure 4-8: Plot of the raw data for the 8 mm/s test and the least squares error fit.
at four different constant velocities: 2, 4, 8, and 16mm/s. The tests were repeated
three times at each velocity.
The raw force data versus displacement for one of the trials is shown in Figure 48. As expected, the force increased linearly with displacement. The least squares
fit to the data is plotted as a solid line in the figure. Using the slope of the line as
a measure of the spring constant and averaging each of the three trials, the spring
constant versus velocity can be plotted as shown in Fig. 4-9.
The actual spring
constants, shown as horizontal lines in the figure, were measured by hanging weights
on the springs and measuring the displacement. The spring constant measured by the
test system clearly falls in the error range of the manually measured values. Also note
that the measurements on the test system did not vary with velocity. The standard
deviation of the spring constants as measured at the four different velocities was only
0.2N/m for both springs.
The typical residual of the least squares fit and the frequency response of the
residual is shown in Figure 4-10. The only prominent frequency component was a
strong 20Hz signal in some of the trials, independent of velocity. The frequency
component existed even without a spring connected, but went away when the force
transducer was removed from the test stand, implying the noise was due to a resonance
56
100:
80 -
60
E
40
20
C0
5
10
20
15
Speed [mm/s]
Figure 4-9: Plot of the spring constant measured with the test system versus velocity.
The error bars represent 95% confidence intervals and the horizontal lines are the
manually measured spring constants.
0.1
0
CO
vy
v
-0.1 F
_0
-0.2' 0
. IS0-
10
5
15
Position [mm]
3
1
0
0.5k
O'
0
10
20
30
40
50
Frequency [Hz]
Figure 4-10: Plot of the residuals of the least squares error fit to an experimental run
at 8mm/s and their frequency content.
57
0.040.035
0.030.025p
0.02-
0.015
0.010.005-
00
5
10
Speed [mm/s]
15
20
Figure 4-11: Root mean squared error of the least squares error fit versus velocity.
somewhere in the test stand.
The root mean squared of the residual, which serves as an average measurement
of noise, is plotted versus velocity in Figure 4-11. It increased with velocity, just as
the magnitude of the 20Hz signal increased. This is likely due to increased excitation
of a natural frequency of the test stand. The overall mean RMS error is 0.024N.
4.4
Amplifier Characterization
Some simple tests were run to understand how the Trek 10/10 amplifier behaves in
conjunction with the UEI Daq board and the test system software. A rod was placed
in each sample holder and the output of the amplifier was connected to each of the
rods, establishing an open circuit driven by the amplifier. Current and voltage data
were taken at 0, 200, 400 and 600 volts for several seconds without moving the stage.
A plot of the data from the 200 volt test and their frequency components is shown
in Figure 4-12. There was a strong 40Hz signal in all of the voltage data. After
increasing the sampling frequency to 130 Hz, it was determined that this noise was
actually at 60Hz, and, therefore, was probably line noise.
The accuracy of the voltage and current measurements was evaluated by comparing them to the expected values. Because the amplifier was driving an open circuit,
58
210
30
oa20
>205
CZ200
,
0*"
0
*
> 19519__
0
2
0
0
4
20
40
20
4Q
X 0-8
0.5
4x10
3
E
2
0
-0.5
0
2
Time [s]
0
0
4
Frequency [Hz]
Figure 4-12: A plot of the voltage and current for five seconds with no movement of
the test stage. The frequency spectrum of the data is also shown.
the current should have been zero. However, the calculated mean current was 71pA
independent of the commanded voltage. It is not clear without further testing what
the nature of this offset is, however for the purposes of this investigation, it was
assumed that this offset was constant and the offset was subtracted off of all the
experimental data.
The difference between the commanded and measured voltage is shown in Figure 413. While the difference did change with voltage, there is no clear relationship between
the voltage error and the commanded voltage. Like the current measurement, the
cause of this error is not clear without further testing and it was ignored for the
purposes of this investigation.
Finally, a measure of the noise of the current and voltage data was computed by
subtracting the mean value from the data and then finding the root mean square of
the residual. A plot of this value versus the commanded voltage for both current and
voltage is shown in Figure 4-14. The mean RMS voltage error was 0.70V and the
59
2.5
5
LU
m1.5- 2
0
1
0.5-
00
100
200
300
400
500
600
Voltage [V]
Figure 4-13: A plot of the error between the measured voltage and the commanded
voltage versus the commanded voltage. The error bars represent one standard deviation.
mean RMS current error was 77pA.
4.5
Procedure
This section explains the actual test methods that were used in the experiment including a description of the materials used and the testing methods.
4.5.1
Materials
The material samples consisted of an electrode, a spacer, and a fluid. The electrodes
were constructed of polyethylene terephthalate (PET) with a coating of aluminum,
several nanometers thick, on one side. The PET was 60 ± 5pm thick. Three different
materials were chosen for the spacer: tissue paper, which is porous to both ER
fluids, and kraft paper and polypropylene (PPL), which are not. The kraft paper and
PPL were chosen because of their extensive use in capacitors and the tissue paper
provides a porous alternative. The thicknesses of each material was measured with a
micrometer: the kraft paper was 4[im thick, the PPL was 8pm thick, and the tissue
paper was 25pm thick. The material was also constructed with no spacer in between
60
0.08
0.8
rF
0.078-
-0.7657
E0
00
ii
U
0.076
-0.72
.
0.074
0
..
o>
LU
0.68")
'0
0.072-
0.07
0
-0.64
100
200
300
400
Voltage [V]
500
600
0.6
Figure 4-14: Plot of the root mean square of the voltage and current error, which
serves as a measure of the noise in the signal.
the electrodes, such that only fluid was between the two aluminum electrodes.
To construct the sample, the bottom electrode and spacer were cut to 40mm wide
and 100mm long and the top electrode was 37mm wide and 100mm long. The extra
width of the bottom layer and the spacer was to minimize breakdown along the edges.
Both electrodes were washed and then cleaned with alcohol. The spacer was taped to
the bottom layer at one end and then both were taped to a copper rod at the same
end using conductive tape. The top electrode was taped to another rod at the end.
The rod with the bottom electrode was placed in the fixed sample holder and
placed on the sample stand such that the aluminum side was facing up. The top
electrode was placed in the movable sample holder such that the aluminum side was
facing down, leaving only the spacer separating the two electrodes. About 785mm 3
of fluid was added above and below the spacer and spread evenly. A plate, the same
width as the sample stand, was placed on top of the sample and a 200 gram weight
was added to help evenly disperse the fluid.
Two different electrorheological fluids were used in the tests. The heterogeneous
fluid, Bridgestone model HP-2, has a zero field viscosity of 0.15Pa-s, a yield stress of
4.2kPa at 4kV/mm, a current density of 14pA/cm 2 at 4kV/mm, and a response time
of 2ms at 25 'C and a shear rate of 1000s 1 according to Bridgestone.
The homogeneous fluid, provided by Asahi Chemical Industry Co., is a solution of
61
liquid crystalline polysiloxane diluted in dimethylsilicone. It has a viscosity of lPa-s
at room temperature and a shear stress of 8kPa at 2kV/mm and a shear rate of
300s- 1 . It can operate between 10 and 60 C.
4.5.2
Methods
Before fluid was added to the material sample, three experimental runs were made
at 0 V and 4 mm/s to find a zero value for the force transducer. The mean value of
force for all three runs was subtracted from all future experiments with that particular
material as discussed in section 5.2.
Once fluid had been added, several preliminary runs were made without taking
data to further spread the fluid. Afterward, the experimental testing began. The
general test procedure was to move the top electrode 60 mm to the left at a constant
velocity, measuring the force as it moved. After each run, the top layer was raised
while the stage was moved back in place. Then the top layer was rolled back down
in an attempt to minimize the amount of trapped air. But it should be noted that
there may still have been some air trapped in the material.
The amplifier was first set to OV and the experiments were run at 2, 4, 8, then
16mm/s with an acceleration of 10mm/s 2 . This was repeated three times before
increasing the voltage. These tests were run at three higher voltages and then again
back at OV. For the materials with spacers, the voltages were 200, 400, and 600. When
the material had no spacer the voltages were reduced to 20, 40, and 60 to prevent
electrical breakdown.
To test the effects of adding a normal force, a plate was placed on one end of
the top electrode such that the plate completely overlapped the bottom electrode
throughout the test. The total area of contact remained constant at 1050mm 2 . The
tests were run at 8mm/s with the same voltages and weights of 50, 100, and 200
grams.
62
Chapter 5
Heterogeneous Results
This chapter presents the data from the heterogeneous material experiments, explains
how the data is analyzed and summarizes the results of the experiments.
5.1
Raw Data
The data from all of the experimental runs is presented in Appendix B. A typical
run at OV and 400V is reproduced in Figure 5-1 for reference. All three trials are
plotted showing the repeatability of the experiment. The shapes of the curves are
very similar for all three trials. There is a slight decrease in the force for consecutive
trials, which is especially evident in the kraft paper data.
The force data is roughly linear as predicted by Eq. 3.3 in the region where the
velocity is constant, denoted by the vertical lines in the graphs. The data taken during
acceleration has interesting behavior that might provide insight into the transient
fluid behavior, but this was not examined in this investigation. There also appears to
be a slight transient after the velocity becomes constant before the data approaches
linearity.
63
===ZAN
Voltage:
0.25
Voltage: 400V, Speed: 4mm/s
OV, Speed: 8mm/s
Trial 1
F= -0.15x + 0.16
0.2 -
T
:
2.5 2= -0.0232x + 2.1
2F
4
Trial
--
M.84eran
R :0.992
2
0.5
0.054
.05~-
W.N
Mean Work: 0.00677 NMM
Mean Work:
0
Tral
a Trial 2
0 Trial 3
- Mean
10
20
40
30
Distance [mm]
50
0
60
10
20
0.0711
Nmi
40
30
Distance [mm]
50
60
(b)
(a)
Figure 5-1: Raw force data for all three trials of variable impedance material made
with heterogeneous fluid and a kraft paper spacer. This data is from the experiments
run at 0 V with a velocity of 8 mm/s and 400 V with a velocity of 4 mm/s. The
vertical lines indicate the distances between which the velocity is constant. A least
squares error fit was made to the data where the velocity is constant for each trial
and the mean of the three lines is plotted as a solid line in the figure.
5.2
Shear Stress Analysis
5.2.1
Calculating Shear Stress
To determine the parameters in the models, the average shear stress for each voltage
and velocity first needed to be calculated. First, the force measured before the fluid
was added to the material was subtracted from all the force data. Then a least
squares error fit was made to the force versus position data for all points where the
velocity was constant in each trial. The slope and intercept for all three trials at a
given voltage and velocity were averaged together using a weighted mean based on
the standard error of the parameters. The slope and intercept were then used to
calculate the shear stress using Equation 5.1 and Equation 5.3, with errors given by
equation 5.2 and Equation 5.4. The overlap and width were measured using a ruler
with 1mm increments, so the error in the measurements (6W and 6L) were assumed
to be 0.5mm.
Tm
(5.1)
nF
W
64
6
7b
mF
W
W2
(5.2)
(5.3)
bF
Tb
6
mF
WL
=
WL
±bFbF2 6W +
W L
bF
WL 2
6L
(5.4)
where mF and bF are the slope and intercept of the force data, respectively, and 6
represents the standard error of the measurement.
The shear stress for each of the four spacer materials is plotted in Fig. 5-2. Based
on the model (Eq. 3.3), both the overlap and intercept should give the same value
for the shear stress. This is generally supported by the data with some deviation
at higher voltages, especially in the kraft paper. The significance of this deviation
is discussed in Section 5.4. The shear stress that is calculated from the slope of the
force data is not influenced by a static force offset, so it was used for the remainder
of the analysis.
In Figure 5-2 there are two sets of points that were taken at OV: one was taken at
the start of the experiment, and the second was taken at the end of the experiment.
While the two sets of data are very similar in all the materials, there are some noticable
differences. The second set have consistently higher shear stresses than the first, which
could be due to a loss of fluid over the course of the experiment as will be discussed
in Section 8.1.
For all the spacer materials except polypropylene, the shear stress exhibits Bingham plastic behavior with a yield stress increasing with voltage as expected. The one
exception is the polypropylene spacer, which interestingly, does not appear to have
much dependence on voltage. At every velocity, the shear stress is roughly the same
for each voltage.
5.2.2
Finding Model Parameters
In this section, the shear force data is used to determine the model parameters in
Eq. 3.14 with three different sets of assumptions. First, the damping and friction
terms in Eq. 3.13 can be found. Because the shear stress is expected to be linear
65
2000
O Slope Based
x Intercept Based
600 V
.
1500
1500
400OV
05
000-
6001V
1000-
- - - - -
CO,
U)
(D
V-- -400
500-
500-
0
5
5
1
10
0
15
10
Velocity [mm/s]
5
15
10
Velocity [mm/si
(b) Tissue Paper
(a) Kraft Paper
.
ager
20 1
10,
700
80
600
60V
-
600V
500
60
0
400
300
40 V
'- 'V
.-~4
200
20 V
~ ~-
100
O
40
400V
V ?-"-
5
-------
10
Velocity [mm/s]
0V
20
-j
(2)=
0
15
5
10
Velocity [mm/s]
15
(d) Polypropylene
(c) No Spacer
Figure 5-2: These plots show the shear stress of the material as a function of velocity
for all the voltages in materials using heterogeneous fluid. There are two points for
each measure of shear stress-one calculated from the slope of the force data, the
other from the intercept of the force data. The error bars represent a 95% confidence
interval. A least squares fit through the slope-based measurement is plotted as a
dashed line.
66
with velocity, the weighted least squares error of the shear stress data was calculated.
This line, plotted as a dashed line in Fig. 5-2, appears to be a reasonable fit, although
it is difficult to determine with so few data points. The slope and intercept of the
lines corresponding to b and c, respectively, are plotted versus the applied voltage in
Fig. 5-3.
Heterogeneous Model
Looking at Fig. 5-3, no clear pattern is apparent in the slope (damping) data, while
the intercept (friction) data consistently increases with voltage. The heterogeneous
fluid model predicts that the damping, which is the viscosity divided by the fluid
thickness, should remain constant as the voltage is changed. With this assumption
(a3 =0), the parameter a 2 becomes the weighted mean of the data. The friction,
on the other hand, increases with the voltage according to the fluid model. If the
friction is assumed to be linear in voltage (n, = 1), a weighted least squares fit can
be used to solve for the parameters ao and a,, which are the intercept and slope of
the fit, respectively. The parameters calculated with these assumptions are given in
Table 5.1 along with standard errors. Caution should be taken in interpreting the
parameters because of the small number of data points.
Spacer
Kraft Paper
Tissue Paper
No Spacer
Polypropylene
ao[Pa]
13.9±0.1
38.0±2.0
13.1±0.1
11.0±0.1
ai[Pa/V]
1.45±0.01
1.28±0.01
4.02±0.01
0.007±0.001
a2[Pa-s/mm]
3.22±0.02
9.91±0.07
3.55±0.02
2.90±0.01
Ini
Table 5.1: Parameters for heterogeneous fluid model with ni
1
1
1
1
=
1.
Because the coefficient of the voltage, ni, is fixed at one, the ER strength of the
different materials can be compared by looking at parameter a 1 , which corresponds
to the effect voltage has on the shear stress. The polypropylene clearly has little or
no ER effect, while the material with no spacer appears to have the strongest effect.
It is also worth noting that the parameter ao, which was expected to be zero, is small
but nonzero for all materials. According to the model, parameter ao represents the
67
60
T
E 40[
E 40-
P 20 -
2
20-
0
100
-----------------
200
300
400
Voltage [V]
500
o
600
10
200
100
200
300
400
500
600
300
400
500
600
Voltage [V]
2
CL
1.5-
1.5-
1
1
0.5
-----)
100
200
0.5-
300
400
Voltage [V]
500
600
(a) Kraft Paper
(b) Tissue Paper
60
E
E
6
40
T
20e
M
o2
0
.S
Voltage [V]
10
20
30
Voltage [V]
40
50
60
--------0
2
0.02
1.5-
0.015
1
0.01
0.5-
0.005
0
10
20
30
Voltage [V]
40
50
60
0
(c) No Spacer
-----
-)R------E
100
200
300
400
Voltage [V]
500
600
100
200
300
Voltage
500
600
[V]
400
(d) Polypropelene
Figure 5-3: These plots show the slope (b) and intercept (c) of the least squares fit
to the shear stress data for heterogeneous fluid materials. Based on the model, the
slope is the viscosity of the fluid divided by the thickness of the sample and should
not vary with voltage. The intercept is the shear yield stress of the material and is
expected to increase with voltage. The error bars represent a 95% confidence interval.
A least squares linear fit is plotted as a dashed line through the intercept data and
the weighted mean of the slope data is plotted as a horizontal dashed line.
68
yield stress at OV.
Extended Model
The linear fit to friction, plotted as a dashed line in Fig. 5-3, appears to underestimate
the response for the tissue paper and no spacer materials. Instead of assuming a
linear relationship, an estimate of the coefficient ni was obtained by taking a power
regression of the data. This was accomplished by subtracting the value of c at OV
from the rest of the data, then the least squares fit to the log of c versus the log
of V was found. The slope of that line corresponds to the parameter ni. Table 5.2
summarizes the parameters calculated using this method.
Spacer
Kraft Paper
Tissue Paper
No Spacer
Polypropylene
ao[Pa]
13.9±0.4
38.3+1.0
13.1±0.3
11.8±0.2
a1[Pa/V]
1.7t0.9
0.1±0.1
0.35±0.01
1.63e-6±3e-8
a 2 [Pa-s/mm]
3.22±0.02
9.91±0.07
3.55±0.02
2.90±0.01
ni
0.97±0.02
1.44±0.03
1.78±0.01
2.33±0.01
Table 5.2: Parameters for heterogeneous fluid model with varying nj.
The most interesting parameter in this table is n 1 . The kraft paper is still close to
one, the tissue paper is around 3/2, and the material with no spacer is about 7/4. All
of these are in the expected range of one to two. The one exception is polypropylene,
but this value is questionable because of the small dependence on voltage, shown by
the very small value for a 1 .
General Model
The process described above to determine the parameters ao, a1 and ni can be repeated with the damping data, b, to solve all six parameters in the completely general
model given in Eq. 3.14. The results are presented in Table 5.3.
5.2.3
Model Performance
One application of the model would be as a predictor in a control scheme. In order to
evaluate the effectiveness of this predictor, the mean percentage error for each trial
69
ao [Pa]
a, [Pa/V]
Kraft Paper
13.9±0.4
1.7±0.9
Tissue Paper
38.0±1.0
0.1±0.1
0.35±0.02
13.1±0.3
No Spacer
Polypropylene 11.8±0.2 1.63e-6±3e-8
Spacer
ni
Kraft Paper
0.97±0.02
Tissue Paper
1.44±0.03
No Spacer
1.78±0.01
Polypropylene 2.33±0.01
Spacer
a 2 [Pa-s/mm]
3.22±0.02
9.79±0.07
3.46±0.02
2.55±0.01
a3 [Pa-s/Vm]
0.6±0.7
0.04±0.01
46±3
45.2±0.1
n2
1.46±0.04
2.19±0.01
1.14±0.01
0.418±0.001
Table 5.3: Parameters for general model of materials using heterogeneous fluid.
run was calculated using each of the three sets of parameters calculated above. These
models all rely on the assumption that the force is linear with respect to position, so
the error associated with a least squared fit to the force data was also calculated as a
baseline reference. If the shear stress model were perfect, it would match this linear
error. The results are shown in Table 5.4. Because the parameters and the prediction
error were calculated from the same set of data, the error is likely lower than it would
be in practice.
Spacer
Kraft Paper
Tissue Paper
No Spacer
Polypropylene
Linear
12.1%
4.2%
84.0%
41.1%
Het Model [Ext Model
25.3%
25.7%
28.2%
17.0%
120.0%
102.0%
47.1%
48.4%
[ Gen Model
23.7%
14.4%
102.0%
48.8%
Table 5.4: Average prediction error for the different models of the heterogeneous fluid
based materials.
Table 5.4 is helpful in determining how many parameters should be used to model
the material. For the kraft paper, there is little improvement above the heterogeneous
model, so using three parameters is sufficient. For the tissue paper, there is a substantial improvement by moving to the extended model. In some cases the error actually
gets worse as the number of parameters is increased. This may seem counterintuitive,
but is due to the fact that the prediction error is not what is being minimized to
determine the parameters.
70
It is worth noting that much of this error could be reduced in a real world application using advanced control techniques such as recursive least squares to continuously
update the model parameters.
5.3
Energy Analysis
In the previous section, parameters for shear stress models were determined by looking
at the least squares fit to the force data. In this section, the amount of energy going in
and out of the material is calculated to help analyze the performance of the material.
5.3.1
Work Out
The mechanical work that the material does during the experimental run was calculated by integrating the force over the length of the move for the three trials at
each velocity and voltage. The results are plotted in Fig. 5-4. It is apparent that the
graphs bear a close resemblance to the shear stress plots (Fig. 5-2). This agrees with
Eq. 3.17, in which the work is proportional to the shear stress.
Like the shear stress, the work increases with voltage and velocity. In the actual
material, the amount of work done can be increased by adding more area or more layers. So the change in work with voltage is more important than the actual work done.
For the material to have control authority, there should be a large change in work as
the voltage is increased above OV. To help visualize this measure of performance, the
percentage increase in work over the OV case is plotted in Fig. 5-5.
The amount of control authority really becomes evident in this figure. At the
highest voltage, all the materials, except for polypropylene, have a factor of 20-30
increase in the amount of work done. The figure also demonstrates that although the
amount of work increases with velocity, the percentage increase actually decreases
with velocity.
71
0.251
-.
OV
x 200 V
0.2
o
400 V
600 V
>0 V (2)
0.
A
2-x
200 V
400 V
A- 600 V
0 V (2)
0
T0.15
T 0.15
1z
-.
0
3: 0.1
A
e-
....
0
Z.
0.
$
51
0.05F
0.0
.I 0..
50
5
10
Velocity [mm/s]
15
5
5
0
(a) Kraft Paper
02.
0.2
0
x
02.0
1
10
Velocity [mm/s]
15
(b) Tissue Paper
0.01
0V
20 V
40 V
o
x
60V
OV(2)
0.008
T0.15-~
1z
0V
200 V
o0 V2
S600 V
0>
OV(2)
T 0.006 Iz
0
3:0.1
0.004 -
-
0.05[
00
0.002-
.....
.....
......
...
1.'.+
5
10
15
0
Velocity [mm/s]
(c) No Spacer
5
10
Velocity [mm/s]
15
(d) Polypropylene
Figure 5-4: These plots show the work done by materials with heterogeneous fluid
versus velocity for each of the different voltages with 95% confidence intervals. The
lines simply connect the points at a common voltage and do not indicate a model fit.
72
40
.0
0
0
20
0V
x
0
200 V
400 V
600 V
0V(2)
<2>
T
30
o
bi.
0V
x- 200 V
0 400 V
A 600 V
OV(2)
-0
4030
7
-
20C
C
10-
C.)
C
-10::
10i
0-
00
10
Velocity [mm/si
10
Velocity [mm/sI
1.5
0 V
20 V
0 40 V
A 60 V
'02
OV(2)
0V
200 V
0 400 V
A 600 V
0 V (2)
x
40
.0
30
x
1
0
CD
20
a)
0.5-
,-
C)
Ca
15
(b) Tissue Paper
(a) Kraft Paper
50
5
10
15
4
-0.5
10
0
-1
1
1.
-1
0-
CD
_0
510
-1.
15
Velocity [mm/s]
5
10
Velocity [mm/s]
15
(d) Polypropylene
(c) No Spacer
Figure 5-5: Plot of the percentage increase in work done in materials with heterogeneous fluid at a particular voltage over the work done at OV. The lines simply connect
the points at a common voltage and do not indicate a model fit.
73
2
x- 200V
- 400 V
600 V
0 V(2)
1.5
-
0.5-
)
I
0.5
0
-n
-
-1
I
0,
wi
x, 200V
.
400 V
A 600 V
0V(2)
1.5
1
iJ~
1
0
51
0
10
5
-0.5C
15
'. .
15
Velocity [mm/s
(a) Kraft Paper
(b) Tissue Paper
.-
0.2
0 OV
x
A
0.15-
. 1. -
10
5
Velocity [mm/s]
0.2-
ov
o
-
20 V
40 V
60 V
0 V (2)
0.1
x
4
0.1
i
V (2)
.Ii
0
........
0.05-
>,
0.05
(D
5)
0)j
0-0.05-
0V
200 V
0 400 V
A 600 V
0.15
-0.05
-0.1
-
5
5
10
10
Velocity [mm/s]
-0.1
15
(c) No Spacer
0
5
10
Velocity [mm/s]
15
(d) Polypropylene
Figure 5-6: These plots show the electrical energy input into the material during an
experimental run, computed by integrating the power over the duration of the run
and calculating the mean of the three trials. The lines simply connect the points at
a common voltage and do not indicate a model fit and the error bars represent 95%
confidence intervals.
5.3.2
Energy In
Another concern is the amount of electrical energy being consumed by the material.
The material is intended to be portable, so low power consumption is necessary to
avoid carrying large batteries. The measured current is multiplied by the measured
voltage at each time instant to give a reading for the power at every time step. Integrating this value over the duration of the experimental run gives the total electrical
energy used by the material, which is plotted in Fig. 5-6.
The total energy absorbed decreases with velocity, but the duration of the experimental run does as well. So it is possible that the power remains constant over
74
40
o0
V
x- 200V
-.0 400 V
A 600 V
30
x
o
200 V
400V
A -600 V
30
E
20
a
20
M
10
-
10
0 -
0
-10
+
-
5
10
10
15
5
Velocity [mm/s]
C
(a) Kraft Paper
2,
o
oV
20V
S40 V
A 60 V
1.5
15
(b) Tissue Paper
a)
a)
0.
0
10
Velocity [mm/s
8
6-
0
OV
x
200 V
400 V
A
600 V
4-
0.5
0
CL
CL
I
-
-2-
0
10
-0.
5
10
-
- 41
0
15
Velocity [mm/s]
(c) No Spacer
5
10
Velocity [mm/s]
15
(d) Polypropylene
Figure 5-7: These plots show the electrical power density into the material during an
experimental run. The lines simply connect the points at a common voltage and do
not indicate a model fit.
the range of velocities. To find out, the energy was divided by the time to find the
power and then divided by the average area to find the power density. The power
density for all four materials is plotted in Fig. 5-7. As can be seen from the figure,
the power density is relatively constant with respect to velocity, as suspected. Notice
that, in addition to doing little work, the polypropylene material also absorbs much
less electrical energy.
5.3.3
Performance
An overall measure of the performance of a material would allow the different materials to be compared as well as materials using other field-activated fluids. Two
75
x
x
200V
400 V
A 600V
200V
0 400 V
A 600V
7
0
7
6-
6
5.w
4-
5-
3-
3-
2-
21
00
5
10
Velocity [mm/s]
15
5
(a) Kraft Paper
15
x
0
A
10
Velocity [mm/s]
15
(b) Tissue Paper
20 V
40 V
60 V
x
3
200V
0400V
A- 600V
2
10
S
5 -
0
5
{
1
10
Velocity [mm/s]
-I
-1
-2
-3
15
0
(c) No Spacer
5
10
Velocity [mm/s]
15
(d) Polypropylene
Figure 5-8: These plots show the increase in output work over the amount of electrical
energy input into the system for heterogeneous materials. The lines simply connect
the points at a common voltage and do not indicate a model fit.
important criteria of the material are that it has a significant change in properties
and that it has a low power consumption. Therefore, it is important to minimize the
power input while maximizing the increase in energy absorption. Based on these criteria, one performance measure that can be created is a non-dimensional ratio of the
change in output work to the input energy. This coefficient of performance (COP)
is plotted in Fig. 5-8. For both kraft and tissue paper, the COP decreases as the
voltage increases and also increases with velocity. For the smaller voltages in the
material with no spacer, the relationship is not clear. Based on this measure, the
polypropylene spacer performs poorly as was hinted at in the earlier results, and the
no spacer material performs better than the materials with spacers.
76
1.2-
1. .2 -
0
4-
0.8
,n
-0
0.6
0.6a/)
0"
0.4
0
x
0.2
0
5
10
15
20
2
Power Density [W/m
C/) 0 .4
2 mnm/s
4 mm/s
8 mm/s
S16 mm/s
30
25
S2 mm/s
4 mm/s
3 8 mm/s
A 16 mm/s
0
0
5
10
15
20
Power Density [W/m 2
0r)4
r,
0
0.4
'-
0.035
A
A
A-
0.35
0.3
30
(b) Tissue Paper
(a) Kraft Paper
4A
25
0.03
00
.2
-
0.025
0
0.25
2 0.02
0.2
r
-C
C/)
0
c0.015
0.15
a/)
0.1
0-
x
0
0.05
A
1
0.5
2
Power Density [W/m ]
0.01
2 mm/s
4 mm/s
8 mm/s
16 mm/s
0.005
0
1.5
(c) No Spacer
x
-0
0.5
1
1.5
2
Power Density [W/m 2
02 mm/s
4 mm/s
8 mm/s
A16 mm/s
2.5
3
(d) Polypropylene
Figure 5-9: These plots show the shear stress versus the power density for the material
during an experimental run. The lines simply connect the points at a common voltage
and do not indicate a model fit.
Another figure of merit can be created by plotting the shear stress versus the power
density, rather than the voltage, as shown in Fig. 5-9. Where the voltage is important
for control and breakdown, the power is important for design, as it determines the size
of the batteries. This figure allows one to get an idea of how much power is required
to develop a certain shear stress. Ideally, the material should have a large increase
in shear stress for a small increase in power density, meaning the curve should have
a large slope. From the graphs, it was estimated that the material with no spacer
has the largest slope, followed by the tissue paper, the kraft paper and finally the
polypropylene.
77
5.4
Slope/Intercept Difference
As discussed previously, there was a small difference in the shear stress calculated
using the slope, and the shear stress calculated using the intercept of the force data.
The difference was especially apparent in the kraft paper data shown in Figure 5-2(a).
This difference could be attributed to a constant force offset that could be determined
by calculating the force at the point where the two layers would have separated using
the following equation:
F, = wL(Tb - Tm)
(5.5)
Equation 5.5 assumes that the linear fit calculated for the force data continues, and
extrapolates along the line to find the force at x = L. The plot of this force offset for
each of the four materials is shown in Fig. 5-10.
If the force offset was due to a miscalibration of the force transducer, then it
should be the same for all voltages and speeds, but that does not seem to be the case.
If it was due to the force from separating plates in a capacitor as given in Eq. 3.10,
then it should increase as the square of the voltage. Only the kraft paper seems to
show a pattern of increasing offset with voltage, the rest have smaller offsets with no
clear pattern. In general it is not clear from this data what the nature of this force
offset is.
78
1.5
-e-
oV
-x--
200 V
400 V
L 600 V
-$- 0 V (2)
0.4
0.2
a)
0
a)
0
0
05-
0
L
-0.2
0
10
Velocity [mm/s]
5
-0.
15
n i.
10
Velocity [mm/s]
15
0.02
0.25
0.2
0.15
0.1
5
(b) Tissue Paper
(a) Kraft Paper
LL
0
a)
0
0
LL~
0
-
+
±
0.01
-
0-
L-
0.050-
jt
-.
-----
-[--- -- -
0
aT,----------1Iff --
L
-0.02
-0.05-0.1--
5
10
Velocity [mm/s]
-0.030
15
(c) No Spacer
5
10
Velocity [mm/s]
15
(d) Polypropylene
Figure 5-10: Plot of the constant force offsets along with the mean values for each
voltage plotted as a horizontal line.
79
80
Chapter 6
Homogeneous Results
This chapter presents the data from the homogeneous material experiments, explains
how the data is analyzed and summarizes the results of the experiments.
6.1
Raw Data
The data from all of the experimental runs is presented in Appendix C. Two typical
sets of runs are reproduced in Figure 6-1 for reference. All three trials were plotted
and there is very little variation between them, illustrating the repeatability of the
experiment.
The transients in the homogeneous case were much longer than the
heterogeneous transients especially at low voltages or high velocities. In an attempt
to minimize the effects of the transients, all the force data was analyzed where the
16mm/s run was at a constant velocity. In this window, the force was nearly linear
as expected.
6.2
Shear Stress Analysis
6.2.1
Calculating Shear Stress
The mean shear stress for each experimental run was calculated the same way as
described in Section 5.2. The shear stress calculated from both the slope and intercept
81
Voltage: 400V, Speed: 4mm/s
Voltage: OV, Speed: 8mm/s
4
Trial 1
Trial 2
a
3.
MnF =-0.0482x +4.7
.R-:
Trial 3
Mean
5
3
4
2. 5
0.989
2
0 Trial 3
-- Mean
3
a)
F =-0.0146x + 1.1
R 2: 0.967
C.
Z5
1.
0
-- 2
5
0.
5
0
5Mean
10
Work: 0.1)528 Nm
20
30
40
Distance [mm]
Mean Work:
50
0
60
10
20
0.19 Nmn
30
40
Distance [mm]
50
60
(b)
(a)
Figure 6-1: Raw force data for all three trials of variable impedance material made
with homogeneous fluid and a kraft paper spacer. This data is from the experiments
run at 0 V and a velocity of 8 mm/s and 400 V and a velocity of 4 mm/s. The dashed
vertical lines indicate the distances between which the velocity is constant and the
solid vertical lines are where the data set was truncated for analysis. A least squares
error fit was made to the truncated force data for each trial and the mean of the three
lines is plotted as a solid line in the figure.
of the force data is plotted in Fig. 6-2. Except for kraft paper, the slope and intercept
based data do not agree as well as they did in the heterogeneous fluid case. The
discrepancy is explored further in Section 6.4. As with the heterogeneous fluid, the
slope based stress was used for the remainder of the analysis. In general, the shear
stress matched the homogeneous fluid model, wherein the slope of the shear stress
increases with field strength, but again the polypropylene seems to show no ER effect.
6.2.2
Finding Model Parameters
As with the heterogeneous fluid, the shear stress data was fit to a line with the
slope corresponding to b and the intercept to c using Eq. 3.13. The linear fit, as
plotted in Fig. 6-2, fit well to the kraft and tissue paper data, but not as well to
the polypropylene and no spacer data. The friction and damping calculated from the
linear fit are plotted in Fig. 6-3.
82
C
x
Slope Based
Intercept Based
5
5600 V
_4
4
4-
<i
()
3
600 V
3-
40OV
-
400V
CO
13-2
0
0 V (2)
V
1 j5
15
10
Velocity [mm/s
10
S-
'
00
2
~
15
10
Velocity [mm/s]
5
5
(b) Tissue Paper
(a) Kraft Paper
1
6
5
1.5
0 V (2)
CL 4
C,)
-0-V
40V
93
----cc
400 V
OV.2-)
CO
0
5
10
Velocity [mm/s]
,
0.5F
5- 0
n
200 V
U)
601
2
)
1
---
0'
0
15
5
600V
10
Velocity [mm/s]
15
(d) Polypropelene
(c) No Spacer
Figure 6-2: These plots show the shear stress of the material as a function of velocity
for all the voltages in materials using homogeneous fluid. There are two points for
each measure of shear stress-one calculated from the slope of the force data, the
other from the intercept of the force data. The error bars represent a 95% confidence
interval. A least squares fit through the slope-based measurement is plotted as a
dashed line.
83
400
E300E
200
Ca
00
E 300[
~m
El
2001
10100
200
0..
300
400
Voltage [V]
500
0
600
IMMn
200
300
400
Voltage [V]
500
600
100
200
300
400
Voltage [V]
500
600
0.
05
--0.50
0
100
--0.5100
200
300
400
Voltage [V]
500
0
600
(a) Kraft Paper
(b) Tissue Paper
4UU
100
300El
200
E
_
CL 10
:0
-
0-
---
-50
10
20
30
Voltage [V]
40
50
60
0
100
200
300
400
Voltage [V]
500
600
1
0.5
1.5
06
1
-0.5-1
0
--
0.
1'0
20
3.0
Voltage [V]
40
5..0
0
60
(c) No Spacer
100
200
300
400
Voltage [V]
500
600
(d) Polypropelene
Figure 6-3: These plots show the slope (b) and intercept (c) of the least squares fit
to the shear stress data for homogeneous fluid materials. Based on the model, the
slope is the viscosity of the fluid which should increase with voltage. The intercept is
a static force offset that should be zero. The error bars represent a 95% confidence
interval. A least squares linear fit is plotted as a dashed line through the slope data,
and the weighted mean of the intercept data along with its standard error are plotted
as horizontal dashed lines.
84
Homogeneous Model
The homogeneous model predicts that c should be zero and b should increase with
voltage. To solve for the parameters in this model, c was first assumed to be a constant
(a1=0) and the weighted mean of c, corresponding to ao, was calculated. Next, b was
assumed to be linear (n2=1) the weighted least squares fit was calculated. The slope
of the fitted line corresponded to a3 and the intercept to a 2 . The weighted mean and
least squares fit are plotted as dashed lines in Fig. 6-3. The parameters calculated
using the homogeneous model for each of the materials are given in Table 6.1.
Spacer
Kraft Paper
Tissue Paper
No Spacer
Polypropelene
ao[Pa]
380±50
270±60
140±40
540±60
a 2 [Pa-s/mm] I a 3 [Pa-s/V-mm]
8±150
0.58±0.5
0.15±0.2
100±1600
1.1±14
100±1600
-0.09±0.07
50±870
I n2
Table 6.1: Parameters for Homogeneous fluid model with n 2
1
1
1
1
=
There are a couple things to note about the calculated parameters.
1.
First, the
friction-or yield stress-term, ao, is not zero as expected, but several hundred Pascals. This implies that the homogeneous fluid actually has a yield stress. Yield stress
has been observed in liquid crystal polymers and is thought to increase with the
amount of texture in the fluid. The texture, similar to grain in a metal, is a measure
of the number of domains in the fluid, where a domain is a region of molecules that
point in generally the same direction [34]. Another thing to notice in the parameters
is the strength of the ER effect determined by parameter a 3 . Polypropylene has a
negligible effect, followed by tissue paper, then the kraft paper, and finally the material with no spacer has the strongest effect, although the error for the parameter is
also large, so it is not convincing.
Extended Model
The b data in Fig. 6-3 does not seem particularly suited to a linear fit. Again it is
difficult to draw any convincing conclusions with only four data points, but b seems
to increase rapidly at low voltages and level off at higher voltages. To better capture
85
this behavior, the order of the model was increased by allowing n 2 to vary. The value
of n2 was solved using a power law regression as in the heterogeneous analysis. For
the material with no spacer, the power regression algorithm could not be applied to
the data, so ni was left as one. The parameters for this extended model are given in
Table 6.2.
Spacer
Kraft Paper
Tissue Paper
No Spacer*
Polypropelene
ao [Pa] I a 2 [Pa-s/mm]
380±50
8+1
270±60
95±4
140±40 100±1600
540±60
58±3
a3 [Pa-s/V-mm]
30±5
18±2
1.1±14
-3±30
n2
0.34±0.01
0.24±0.01
1i0
0.5±0.4
Table 6.2: Parameters for homogeneous fluid model with varying n. *Variations in
the no spacer material data prevented the calculation of a power regression, so the
parameters are calculated with n 2 fixed at 1.
General Model
The model was expanded further using the same method as in the heterogeneous fluid
to find all the parameters in the general model given by Eq. 3.14. The results of this
analysis are presented in Table 6.3. Again, for the polypropylene material, both ni
and n 2 were set to one.
Spacer
Kraft Paper
Tissue Paper
No Spacer*
Polypropylene
ao [Pa]
380±50
310±90
150±60
420±90
a1 [Pa/V]
-1±30
-50±800
0.2±4
100±300
Spacer
Kraft Paper
Tissue Paper
No Spacer*
Polypropylene
a 2 [Pa-s/mm]
8±1
95±4
100±1600
58±3
n
0.6±0.9
0.04±0.5
1±0
0.1±0.1
[
a3 [Pa-s/V-mm]
30±5
18±2
1.1±14
-3±30
n2
0.34±0.01
0.24±0.01
1±0
0.5±0.04
Table 6.3: Parameters for general model of materials using homogeneous fluid. *For
the no spacer material ni and n 2 are fixed at 1.
86
6.2.3
Model Performance
The effectiveness of the models were evaluated, as with the heterogeneous fluid, by
calculating the mean percent prediction error using each set of parameters.
The
prediction errors along with the baseline error for a linear fit are shown in Table 6.4.
Spacer
Kraft Paper
Tissue Paper
No Spacer
Polypropelene
Linear I Hom Model
5.8% 20.3%
4.9% 28.2%
6.0% 39.4%
10.3% 33.0%
Ext Model
14.7%
24.4%
39.4%*
32.7%
I Gen
Model
15.9%
25.2%
39.3%*
35.7%
Table 6.4: Average prediction error for the different models of the homogeneous fluid
based materials.
None of the materials show a significant reduction in prediction error by expanding
to the general model. Only kraft paper shows substantial improvement by using the
extended model over the homogeneous model. So in general, the homogeneous model
is sufficient, however the errors are all 3-6 times greater than the baseline linear error
suggesting that there is still room for improvement.
6.3
6.3.1
Energy Analysis
Work Out
The mechanical work done by the material was calculated by integrating the force
over the length of the move just like for the heterogeneous fluid. Figure 6-4 shows
the mean work for all three trials of each experimental condition. As expected, it
is similar to the shear stress plot (Fig. 6-2). At low velocities, the work done has
little dependence on the voltage, but as the velocity increases, the spread of the work
also increases. But again, for polypropylene, there is no discernible dependence on
voltage.
Comparing these results to the heterogeneous ones in Fig. 5-4, it appears that
the homogeneous fluid based material does more work than the heterogeneous once
the velocity is greater than about 5mm/s. However the homogeneous fluid also has a
87
.0x
0.5
0V
oV
200 V
x
0 400 V
600 V
0.5
0 V (2)
0.4
0.4-
z
-0 .30
0.3t
0. 2-
0 .2
0. 1*
0
o
5
10
Velocity [mm/s]
00
15
(a) Kraft Paper
0.
T0
z
4
0 400 V
A 600 V
0 V (2)
5
10
Velocity [mm/s]
15
(b) Tissue Paper
o- 0 V
0. 5-
200 V
A
x 20 V
0 40 V
-- 40 V
0 V(2)
1t6
0.14
0.12
T 0.1
0. 3-
-
0.08 0.06
0. 2-
x-
0.04
0.
1.
. ..
5
~0
5
-
0.02
1
10
A
00
15
Velocity [mm/s]
(c) No Spacer
5
10
Velocity [mm/s]
0 0V
200 V
400 V
600 V
0 V (2)
15
(d) Polypropelene
Figure 6-4: These plots show the work done by materials with homogeneous fluid
versus velocity for each of the different voltages. The lines simply connect the points
at a common voltage and do not indicate a model fit.
88
IU
o oV
x
8.0
x*
200 V
400 V
-
4-
A 600 V
0 V (2)
A
.0
200 V
400 V
600 V
0 V (2)
3
6-
4Ca
0
0
5
10
.4
0
15
5
15
10
Velocity [mm/s
Velocity [mm/s]
(b) Tissue Paper
(a) Kraft Paper
CO
C
5
4
x
0
A
0
1.5
OV
0V
200 V
400 V
600 V
0 V (2)
1.
20 V
40 V
60 V
0 V (2)
x
1
A
1
.0
0
3-
0.5
2
0
CZ
-0.5
0
10
Velocity [mm/s]
15
5
0
(c) No Spacer
10
Velocity [mm/s]
15
(d) Polypropelene
Figure 6-5: Plot of the percentage increase in work done in materials with Homogeneous fluid at a particular voltage over the work done at OV. The lines simply connect
the points at a common voltage and do not indicate a model fit.
larger amount of work done when the voltage is OV, so in applications where a large
change in properties is desired, it may not be as effective.
To penalize a high OV work, the percentage change in work was calculated and
is plotted in Fig. 6-5. For the homogeneous fluid the change in work increases with
increasing velocity, whereas in the heterogeneous fluid (Fig. 5-5) the percent increase
in work decreases at higher velocities. At 2mm/s, the percentage change in work for
the heterogeneous fluid is about an order of magnitude greater than the homogeneous
fluid, however it appears that at higher velocities, the plots may cross so that the
homogeneous fluid materials have a larger percentage increase in work.
89
0V
x 200 V
o 400 V
A 600 V
-0
0.5F
}0
-0.4-
x
0.5 -
V (2)
400 V
A 600 V
4 0 V(2)
0
U,)
0.3
0.3-
0.2-
0 .2-
..............
.
0.1-
0
10
5
V5 10
Velocity [mm/s]
15
0.15
1
00
'
(a) Kraft Paper
.0
x
0.02 5
-
0V
1
-x
20 V
0.25[
40 V
A
o oV
200 V
o 400 V
A 600 V
01 0 V (2)
60 V
4 0 V(2)
0.0 2-
10
Velocity [mm/s]
(b) Tissue Paper
03
-cn
OV
200 V
-0*
0.2
>.0.15
>'0.01 50)
LU0.0
0.1
0.05
0.00 55
0
I
"5
10
Velocity [mm/s]
15
00
(c) No Spacer
0
5 ,
10
Velocity [mm/s]
.
15'
(d) Polypropelene
Figure 6-6: These plots show the electrical energy input into the material during an
experimental run, computed by integrating the power over the duration of the run.
The lines simply connect the points at a common voltage and do not indicate a model
fit.
6.3.2
Energy In
The next property investigated was the amount of electrical energy consumed by the
material. Just as in the heterogeneous fluid, the measured current was multiplied by
the measured voltage at each time instant to give a reading for the power at every
time step. Integrating the power over the duration of the experimental run gave the
total electrical energy used by the material, which is shown in Fig. 6-6.
The energy decreases with velocity as in the heterogeneous fluid implying that
the power may be constant. This is verified by plotting the power density, shown
in Fig. 6-7. The power is generally constant versus the velocity as suspected and
90
E
0V
.0 0 V
x 200 V
0 400V
600 V
0 V(2)
200 V
- 400 V
A 600 V
0 V (2)
X
0
101
5-
a0
5
+
I.
0
5
10
Velocity [mm/s]
5
0
15
(a) Kraft Paper
0.8-
0
x
0
A
0
:
10
Velocity [mm/sI
15
(b) Tissue Paper
0
~I
1i
I'
I'I
0V
20 V
40 V
60 V
0 V (2)
8
-0
x
OV
200 V
400 V
0
8.A
600 V
0 V (2)
0.6
6
C
a,
0
0.4-
a,
a
~1 I
a.
0.2
2L<
-0
4
0
5
.f
10
10
Velocity [mm/s]
0
15
5
10
Velocity [mm/s]
15 N
(d) Polypropelene
(c) No Spacer
Figure 6-7: These plots show the power density into the homogeneous based materials
during an experimental run. The lines simply connect the points at a common voltage
and do not indicate a model fit.
increases with voltage. Comparing with the heterogeneous fluid (Fig. 5-7), the power
density in the homogeneous fluid materials is approximately four times less for all the
spacers except polypropylene where it is about the same for both fluids.
6.3.3
Performance
Next, the two measures of performance that were used in the heterogeneous fluid
analysis are examined. First is the coefficient of performance, defined as the ratio of
the change in work done by the material to the electrical energy put into the material.
The values of the COP for homogeneous fluid materials are shown in Fig. 6-8. Like the
heterogeneous fluid in Fig. 5-8, the COP increases with velocity and decreases with
91
o0
bU
x.. 200 V
400 V
A- 600 V
--
40
.
40
-x 200 V
*.400V
-A 600V
30
30
0 20-
<
10-
20
10
5
VO
10
Velocity [mm/s]
0
15
5
(a) Kraft Paper
300
-x0
250
A
10
Velocity [mm/s]
15
(b) Tissue Paper
50
20 V
40V
60V
40
200
30
150
20
100-
10-
x
0
A.
200 V
400 V
600 V
50
0
5
10
Velocity [mm/s]
15
10
(c) No Spacer
5
10
Velocity [mm/s]
15
(d) Polypropelene
Figure 6-8: These plots show the increase in output work over the amount of electrical
energy input into the system for homogeneous materials. The lines simply connect
the points at a common voltage and do not indicate a model fit.
voltage (except for the point at 60V and 16mm/s in the material with no spacer).
The COP for the homogeneous fluid, however, is about 10 times higher than the
heterogeneous fluid.
The next figure of merit is a plot of the shear stress versus the power density,
shown in Fig. 6-9. The kraft and tissue paper spacers have clear graphs where it appears that the shear stress asymptotically approaches a given value for each velocity.
The material with no spacer has similar behavior except for the last points on the
two highest velocities which have a very high error as shown in the plot of the power
density (Fig. 6-7). The polypropylene has a roughly constant shear stress with power
density. Comparing the plot to the heterogeneous results in Fig. 5-9, the homoge92
3.5
3
3.5
0
x
U
A
2 mm/s
4mm/s
8 mm/s
16 mm/s
U
2
2 .5
E
A
2
U
1.5
1.5
U)
0)
0
.)
2 mm/s
4 mm/s
8 mm/s
16 mm/s
A
2.5
z
O
X
0
3
-
.
0.
0.5
2
4
2
Power Density [W/m ]
10
02
6
4
Power Density [W/m2
6
8
(b) Tissue Paper
(a) Kraft Paper
0..6 -
02
mm/s
X 4 mm/s
0 8 mm/s
A 16 mm/s
1.5
X
-.. .0
0
0..5
40
z
z 0.
(n
U)
U)
1I
S0. 3
4-
0
X"O......
0
x.
El
0
0-
CO
a)
0.5
O'0
0
0.05
C/ 0..2
x
)
0
0.1
-
0.25
0.15
0.2
2
Power Density [W/m ]
0
O2
mm/s
x 4 mm/s
o-0 8mm/s
A 16 mm/s
0. 1
0.3
0.35
-0.5
(c) No Spacer
0
1
0.5
Power Density [W/m2
1.5
(d) Polypropelene
Figure 6-9: These plots show the shear stress versus the power density for the material
during an experimental run. The lines simply connect the points at a common voltage
and do not indicate a model fit.
neous fluid shows a much higher shear stress with much lower power density. But
extrapolating the plots to higher power densities, the heterogeneous fluid will eventually surpass the homogeneous fluid, especially at lower velocities. This illustrates the
fact that if a design requires a high shear stress at a low velocity, the homogeneous
fluid may not be able to provide it, where the heterogeneous could.
6.4
Slope Intercept Difference
Using Equation 5.5, we can plot the force offset as discussed in Section 5.4. The force
offset for all the materials is shown in Fig. 6-10. If the force was due to the capacitor
93
1
0.5
-e- 0 V
-x--
200 V
400 V
V600V
-- 0 V (2) .. ..
0.5
0-
.....
............
. . - - - - - .. I
Ca
0
0
4)
4
-x- 200 V
-- 400 V
A 600 V
-- 0 V (2)
-1.5
5
10
0V
-e-
-1
*
0
-0. L0
----
-0.5
0
0L
4
....
0
15
Velocity [mm/s]
5
(a) Kraft Paper
10
Velocity [mm/s]
15
(b) Tissue Paper
0
(D
C')
0- -21
(D
S-2
0
-
-e- 0V
-x-
-D'
20V
40V
--
0 V (2)
A
-3
0
a)
0
0
LL
1
10
Velocity [mm/s]
-1.50
15
(c) No Spacer
OV
-x-
200 V
- 400 V
-. 600 V
-$- 0 V (2)
60V
5
5
-E-
5
10
Velocity [mm/s]
15
(d) Polypropelene
Figure 6-10: Plot of the constant force offsets along with the mean values for each
voltage plotted as a horizontal line.
equation (Eq. 3.10), then the offset should increase with voltage and be constant with
velocity. There is some indication that that may be the case for the kraft and tissue
paper, but the data is not clear enough to draw any conclusions. It is also interesting
to note that the offset at OV tends to decrease with velocity. It is possible that the
interesting transient behavior seen at OV is playing a role in the offset.
94
Chapter 7
Dry Material Results
In deriving the model for the ER fluid based material, a sandwich geometry with
no fluid was found to also have a voltage dependent shear stress due to Coulomb
friction and electrostatic attraction. In this section we evaluate the performance of
the sandwich geometry with no fluid.
The same experiments as in the ER fluid case were carried out, but without
adding the fluid. However, the paper spacers suffered electrical breakdown problems.
So instead of using the same spacer materials, the dry sandwich material was created
by simply inverting the top electrode of the ER fluid material and removing the fluid
and spacer layer so that the PET on the opposite side of the electrode serves as the
spacer. The thickness of the PET, measured with a micrometer, is approximately
60pm. The reported dielectric constant is 3.2.
The dry material model, given by Eq 3.12, predicts that the shear stress should
increase with the square of the voltage and have no dependence on velocity. The
predicted coefficient of the voltage based on material properties is pco/2t2 All the
variables of this parameter are known expect for the coefficient of friction, P, which
is determined in the next section.
95
0.6
0
L
4 mm/s
8 mm/s
0.5z 0.4W-
y=
0.24x+0.004
0.3.1
C
o
u 0.2-
0.1
0
0.5
1
1.5
Normal Force [N]
2
2.5
3
Figure 7-1: Force due to friction versus normal load for dry material.
7.1
Coefficient of Friction
To determine the coefficient of friction between the PET and the aluminum electrode,
a series of tests were performed with different amounts of normal force applied to the
top electrode using a weight. The tests were run at 4 and 8mm/s with weights of 0,
50, 100, and 200 grams. The mean shear force was calculated for each trial and the
mean of the three trials for one condition are plotted in Fig. 7-1.
The force increases linearly with normal force as expected for Coulomb friction.
The least squares error fit of the data is plotted as a dashed line in the figure. The
slope of the line corresponds to the coefficient of friction, p, which in this case is
0.24t0.1. Using the thickness and dielectric constant of the PET in the electrode,
the predicted model for the shear stress was calculated to be:
T =
7.2
0.001V 2
(7.1)
Raw Data
To determine the voltage response of the dry material, tests were run at 0, 200, 400,
and 600V and at 4 and 8mm/s. Between each run, the sample was rinsed with rubbing
96
0.2
1.2-
a Trial 2
m
0.1
Trial 3
F=-0.0122x+0.8
R: 0.969
R099Mean
Trial 2
Trial 3
Mean
--
0.8
*
-
0.4
0..25
-02
Voltage: 400V, Speed: 8mm/s
1
Trial 1
F =-0.000381x +0.021
R2 0.162
-0.05
,
1.4
Voltage: OV, Speed: 8mm/s
,Trial
-0.15-0
10
20
40
30
Distance [mm]
50
0
60
10
20
40
30
Distance [mm]
50
60
(b)
(a)
Figure 7-2: Raw data for the dry material voltage response experiment at OV and
400V.
alcohol to try to prevent any static charge buildup. All the raw data was plotted in
Appendix D. The raw data for two of the runs is presented in Fig. 7-2 for reference.
The force signal is much noisier than in the materials with fluid. There is still a
clear linear trend however, so the same method for calculating the shear stress in the
ER fluid case can be used for this dry material.
7.3
Shear Stress
The shear stress was calculated using both the slope and intercept as it was for the
ER fluid materials. Figure 7-3 shows the shear stress versus velocity. As expected, the
shear stress is approximately the same at both velocities and increases with voltage.
It is interesting to compare this figure with the heterogeneous fluid material with a
kraft paper spacer shown in Fig. 5-2(a). The two plots are quite similar which lends
support to the claim that the dry material could be as effective as an ER fluid filled
material.
97
100 n
0 Slope Based
Intercept Based
x
800--
----
----------
600 V
0 600U)
CD)
400-
~---------------
-C
400V
200200 V
0
0
3~-------- ----
'
2
4
6
Velocity [mm/s]
V
___
8
10
Figure 7-3: Shear stress of the dry material versus velocity for four different voltages.
The horizontal dashed lines represent the mean of the data at a given voltage.
7.4
Model Parameters
The calculated shear stress can be used to solve for the model parameters. First,
we fit a first-order model of the type in Eq. 7.1. Since the model does not have a
dependence on velocity, the weighted mean of all the data at a given voltage was
calculated and is shown on Fig. 7-3 as the horizontal dashed lines. The plot of the
mean shear stress versus voltage, shown in Fig. 7-4, shows a strong quadratic relation
between the two values.
To determine the model parameters, a weighted least squared fit was performed
on the mean shear stress and the square of the voltage. The slope corresponded to
the voltage parameter, a,, and the intercept, representing a yield stress at zero volts,
corresponded to a0 . The calculated values are shown along with the predicted values
in Table 7.1. The calculated a 1 is twice the predicted value. Some possible explanations for the discrepancy include reduced electrode thickness due to compression
of the PET spacer, or increased coefficient of friction due to wear on the surface or
foreign material entering the system.
In the extended model, the exponent of the voltage, ni, was allowed to vary.
The exponent was determined as in the previous sections, by performing a power
98
0.80.70.60.5C.)
0.4-
0.30.2F
0.1
0
200
100
300
Voltage [V]
400
500
600
Figure 7-4: Friction term, c, in the general model versus the voltage for the dry
material.
Predicted
Dry Model
Extended Model
ao
1000a 1
ni
Prediction Error
0
3.8±0.2
4.7±0.4
1
2±0
0.81±0.01
2
2
2.15
Linear: 208%
Dry: 264%
Extended: 293%
Table 7.1: Predicted and fitted parameters for the dry material along with prediction
errors for the parameters.
99
r)8)A
.
o ov
x.- 200 V
0 400V
0.06 -A 600 V
0.040.020-0.02)
0
2
4
6
8
10
Velocity [mm/s]
Figure 7-5: Work done by the dry material.
regression to the data. The parameters for this model are also shown in Table 7.1.
Prediction errors were calculated for each of the models and also for the baseline
linear assumption. The errors were all larger than those found in the fluid based
materials, confirming the original observation that the dry force data was not as
smooth as the fluid based materials. The variations in the force data might be due
to a stick-slip phenomenon or surface irregularities. This highlights an advantage of
using fluid in the material, as it acts as a lubricant to smooth the response. Notice
that the dry model does a reasonable job of modeling the behavior as the error is not
substantially higher than the baseline linear error. Furthermore, increasing the order
to the extended model makes the prediction error even worse.
7.5
Energy Analysis
7.5.1
Work Out
The amount of work done by the material was calculated, as in the ER fluid materials,
by integrating the force data with respect to the distance. The work, shown in Fig. 75, shows close resemblance to the shear stress graph as expected.
The percentage increase in work is plotted in Fig. 7-6. In this figure, the small
100
I
500
I
.0. 0 V
x.
200 V
400 V
400 -
A 600 V
3000
8 200
100-
0'
0
6
2
10
Velocity [mm/s]
Figure 7-6: Percentage increase in the work done by the material over the work done
at OV.
and likely negligible variations in work with velocity are amplified. The errors in this
measure are large, making it difficult to draw any conclusions from the data, but it
is exciting to see that at 600V, the work could be as much as 200 times greater than
the OV work, which is almost an order of magnitude larger than the heterogeneous
fluid data.
7.5.2
Energy In
The electrical energy input into the material is plotted in Fig. 7-7. The energy is
small, making the error in the measurement quite large. In general it is comparable
to the polypropylene based ER fluid materials. Except for the 600V, 8mm/s test, the
energy increases with voltage as expected.
The power density was calculated by dividing the energy by the time of the run
and the average area of the sample. Plotted in Fig. 7-8, the power density is very low,
which is another advantage of the dry material over the fluid based material. Again,
the error in the measurement is very large, but even the high end of the confidence
interval (5 W/m 2 ) it is comparable to the homogeneous ER fluid and an improvement
over the heterogeneous fluid.
101
0.1 r5I
x- 200 V
400 V
0
0.1
A 600 V
0.05F
.......
..
..
..
0)
0
U)
-0.05F
-0.1'-
0
2
4
6
Velocity [mm/s]
8
10
Figure 7-7: Electrical energy input into the dry material.
4
E
o
0V
x
200V
. 400V
-A. 600V
3
2
C
0
CL
..-.-.-.--.-.
0
-1'-
0
2
4
6
Velocity [mm/s]
8
10
Figure 7-8: Density of the electrical power going into the dry material.
102
5
4-
x- 200 V
U 400 V
A 600 V
0
2-
0
2
4
6
Velocity [mm/s]
8
10
Figure 7-9: Increase in output work divided by the input energy for dry material.
7.5.3
Performance
As with the fluid-based materials, we can combine the energy input and work output
to develop measures of performance of the material. First, the ratio of change in
work to energy input, or COP, was computed. The results are plotted in Fig. 7-9.
Unfortunately the errors in the data combine to make the error in this measurement
particularly large.
The plot with the results is enlarged to show the distinction
between the majority of the runs, but one point is not shown and the error bars
are truncated. For reference, the 600V, 8mm/s data point is near 100. With this
performance measure, the dry material does not particularly stand out and is similar
to the heterogeneous fluid measures.
The figure of merit, shear stress versus power density, is shown in Fig. 7-10. While
the error bars are not shown on this plot it should be noted that the error in the power
density is rather large as was illustrated in Fig. 7-8. The last point in the 8mm/s data
is likely not characteristic of the behavior. This figure bears a striking resemblance
to the heterogeneous material with no spacer in Fig. 5-9(c).
103
0.45
0
0.4
0.35
E 0.3
z
cn 0.25
0.2
-
0.15
0.1
0.05
0
x
0.5
4 mm/s
8 mm/s
1
1.5
Power Density [W/mn23
2
Figure 7-10: Shear stress of the material versus the electrical power density.
7.6
Slope Intercept Difference
The force offset can be calculated as explained in Section 5.4. The offset for the
dry material is shown in Fig. 7-11. There is a clear dependence on voltage, which
would normally indicate that the offset is related to the force required to separate the
plates of a capacitor(Eq. 3.10), however the offset is negative, rather than positive as
that equation would predict. Clearly there is some behavior here that has yet to be
explained.
0l
-0.1
-e - 0 V
-x- 200V
--a- 400V
A 600V
.
..... _...
----
- - - -
-0.2
U)
0
0
LL
-0.3
-0.4
-0
.-0
2
4
Velocity
6
(mm/s]
8
10
Figure 7-11: Force offset for the dry material.
104
Chapter 8
Discussion
After analyzing all the data, some of the issues that were first introduced in section 3.3
are reexamined.
Then the conclusions of the report are summarized followed by
recommendations for future work and visions for the future.
8.1
Variable Thickness
In this material, the electrodes are not fixed a certain distance apart as they are in
traditional ER fluid applications. This allows the electrode spacing to vary over time,
changing the field strength and possibly affecting the overall ER strength. Furthermore, the electrodes are flexible which allows the thickness to vary in space. One
region might be far apart and another practically touching. While direct measurements of the thickness were not taken, some of the collected data could be used to
make an estimate of the thickness.
8.1.1
Heterogeneous Fluid
In the heterogeneous fluid, the viscosity is thought to remain constant with voltage;
only the yield stress changes. Assuming the viscosity remains constant at the reported
value of 0.15Pa-s, the film thickness can be determined at each voltage using the
slope of the shear stress versus velocity. From Table 3.1, the film thickness, tf, is the
105
16,
Initial
(<-
0<- Initial
14-
40Final
4+-
12 -
30
10
<- Final
8
20
6-
21
10
40
200
400
Voltage [V]
600
80C
0
200
(a) Kraft Paper
600
80 0
600
800
(b) Tissue Paper
140
60
120-
58
100-
56
)+-
80-
T
Initial
5452-
604
400
Voltage [V]
-
Initial
50
4-Final
<- Final
20-
UO
48
20
40
Voltage [V]
60
440
0
80
(c) No Spacer
200
400
Voltage [V]
(d) Polypropelene
Figure 8-1: These plots show the film thickness of the sample assuming a constant
viscosity.
viscosity divided by the slope. The evaluated film thickness is plotted in Figure 8-1.
The thickness generally decreases with voltage, as would be expected from the
compression due to the electrostatic normal force. Furthermore, the final thickness is
always less than the initial thickness which would be expected from fluid loss during
the course of the experimental runs. Finally, note that the kraft paper, polypropylene,
and no spacer materials all have film thicknesses around 50pm, whereas the tissue
paper thickness is significantly less. The tissue paper is also the only spacer material
that is porous to the ER fluid. With ER fluid absorbed into the tissue paper, it makes
sense that the layer of pure fluid on top of the paper might be smaller than in the
other materials.
106
tj
Spacer
Kraft Paper
Tissue Paper
No Spacer
Polypropylene
[pml
130±20
10.5±0.5
9.1±0.4
17±1
Table 8.1: Homogeneous film thickness.
8.1.2
Homogeneous Fluid
For the homogeneous ER fluid, the viscosity changes with voltage so a similar analysis
of film thickness as a function of voltage cannot be carried out. However, the film
thickness can be estimated at OV assuming the viscosity is lPa-s. A table of these
values are shown in Table 8.1. The order of magnitude of the thicknesses is reasonable,
but it is surprising that the no spacer and polypropylene materials have thicknesses
less than the heterogeneous case. The homogeneous fluid has a higher viscosity than
the heterogeneous fluid, so it seems likely that the homogeneous fluid might have a
greater thickness.
8.2
Normal Force
Another important consideration in the design is how external forces will affect the
behavior of the material. This section explores the effects of adding a normal force to
the sample. The tests were run at 8 mm/s at four different voltages and with three
different normal forces which were applied by placing a weight on a plate resting on
the top of the sample. The plate was on one end of the top layer and had a contact
area of 1050mm 2 . As the top layer and plate were pulled across the bottom layer, the
area covered by the plate always overlapped the bottom layer, so the area of contact
remained constant.
8.2.1
Heterogeneous Fluid
First, the materials with heterogeneous ER fluid are evaluated.
The normal force
does not have a large effect on the shape of the raw force curve-it is still generally
107
0. 4
0.21?5
x
0
0
OV
5x200 V
0 400 V
0. 5- 3-A 600 V
200V
400 V
600 V
0.3
0 .2
z
A
.
0.2
0.1 &
A
5-
A_
A
0
0
2
0
0
0.1
0.1 5
.
0.0
.
0
0.5
1
1.5
Normal Force [N]
0.' 1
x
0
2
x
0
0
0.0
0-0
2. 5
0.5
(a) Kraft Paper
1
1.5
Normal Force [N]
-
2
2.5
2
2.5
(b) Tissue Paper
0.1 4
U.02
A
20V
40 V
A2A 60 V
2 x
0.1 2-0
0 .1
XX
x
x200V
0400V
).015 .05A
600V
-
0.c 8-
0.01
1 0.0 6-
0
0
0.0
0.5
1
. .
5.
-x
0.0
2x.
o
'O0.5
0.
1
1.5
Normal Force [N]
2
2.5
Normal Force [N]
(c) No Spacer
(d) Polypropelene
Figure 8-2: These plots show the amount of work done in an experimental run versus
the normal force applied to the sample.
linear-so the analysis techniques used in the previous chapters can be used to find
the shear stress. The normal force does, however, add some low frequency (0.5-2 Hz)
oscillations to the force data that increase in amplitude at lower voltages and higher
normal forces.
To get a general idea of how the normal force affects the behavior of the material, the work done during the experimental run is plotted versus the normal force
(Figure 8-2). The work tends to increase with normal force.
If the normal force is increasing the effectiveness of the ER effect, the shear stress
should increase as the normal force increases. But, as shown in Figure 8-3, the shear
stress as calculated by the slope of the force curve tends to remain constant over the
range of normal forces. The shear stress calculated by the intercept of the force curve
108
1500
"
0 Slope Based
x
Intercept Based
O Slope Based
x
Intercept Based
600 V
2000
1~OOQI
1500
400 V
(D
U
000
200V
1
20 V
500-
$
V~
500
A
0.5
1.5
1
Normal Force [N]
2
'jo
2.5
0.5
120
Slope Based
x
2.5
(b) Tissue Paper
(a) Kraft Paper
10( 'C.
2
1.5
1
Normal Force [N]
Intercept Based
Slope Based
x Intercept Based
100
8( 10
80
60 V
6C
V
60
a
a2
Cl 40,
4
Co
040 V
20 0
00.V~~~
-0
0.5
V0
T0
20
.
1.5
1
Normal Force [N]
0V
-~0
2
"0
2.5
0.5
_0 0.5
1.5
1
1.5
1
Normal Force [N]
2
2.5
(d) Polypropelene
(c) No Spacer
Figure 8-3: These plots show the shear stress versus the normal force applied to the
sample.
tends to increase, hinting that there may be something else going on.
To further explore this trend, the force at the point where the layers would separate
was calculated. This offset force should be zero according to the model, but a nonzero
value accounts for a constant force effect such as friction. Figure 8-4 shows that this
offset force generally increases with normal force, which strongly resembles a friction
effect. A weighted least squares fit was also calculated and plotted for each set of
data. The slope of this line is essentially a coefficient of friction for the material.
Interestingly, this coefficient seems to increase with voltage.
The coefficient of friction is plotted versus voltage for each of the four materials in
Fig. 8-5. Except for the 600V case in the tissue paper material and the polypropylene
material, the coefficient increases with voltage. This is an interesting effect that needs
109
- x- 200 V
-0- 400 V
600 V
1.5A
0.5
-x
-0
A
0.4
200V
400 V
600V
0.3
0
U-
0
1~
0
IL
0.
.....
,
0.1
--
-0.1
0
0.5
1
1.5
Normal Force [N]
2
-0.2
2. 5
0
0.5
(a) Kraft Paper
-e0.6
1
1.5
Normal Force [N]
2
2. 5
(b) Tissue Paper
0.15
v
-x- 20V
*0*40 V
A60 V
S-e- o v
200V
-x-
400 V
60V
0.1
0.4
0
0
IL
0.2
-- -
0.05-
0
LL
n
-0.2L
0.5
1
1.5
Normal Force [N]
2
2.5
n
"O0.5
(c) No Spacer
1
1.5
Normal Force [N]
2.5
(d) Polypropelene
Figure 8-4: These plots show the offset force versus the normal force applied to the
sample.
110
0.
n Y Kraft Pa or
0.6 -
8 0.5 -A
-
- ---
Tissue Paper
0 No Spacer
PPL
0.4-
U-
0.4-
0.2
0.1
0
0
100
200
300
400
500
600
Voltage [V]
Figure 8-5: Effective coefficient of friction for the different materials with heterogeneous ERF.
to be investigated further to be understood.
8.2.2
Homogeneous Fluid
For homogeneous ER fluid based materials, the work absorbed for different values of
normal force is shown in Fig 8-6. In the homogeneous case, there is not as clear a
trend for the work with respect to normal force. The work generally increases for the
polypropylene and the no spacer materials, but increases at OV and decreases at all
other voltages for the other two materials. The shear stress and force offset for the
homogeneous fluid materials do not provide any significant insight into the effect of
the normal force, so they will not be presented.
In general, it is clear that the normal force has some effect on the behavior of the
material. While it may not drastically alter its performance, it may play a role in
designing the material for particular applications.
8.3
Spacer Material
In order to prevent the electrodes from touching under a variety of loading conditions,
a spacer between the electrodes is necessary. This prevents a sharp impact from pene111
0.4
0.35
0.
0.4
x
0.2a
0.2
x
0
A
0.15
0.1
*
T 0.15
x
0V
x
AX
0
0-
-
0 ..........
V
o0
200 V
400 V
600 V
00
0
....
0
x
o
0.05-
A
200 V
400 V
600 V
0.05
0.5
1
1.5
Normal Force [N]
2
0
2.5
0.5
(a) Kraft Paper
1
1.5
Normal Force [N]
2
2.5
(b) Tissue Paper
0. 25,
.x
0.2
A
A
0.1
0.15
Iz
0
z
0.1
0V
x
E
0.05
0
_0
A
0.S
0.5
1.5
1
1
1.5
Normal Force [N]
2
0V
x 200 V
o 400 V
A 600oV
0
0.05F
20 V
40 V
60 V
0
2.5
(c) No Spacer
0.5
1
1.5
Normal Force [N]
2
2.5
(d) Polypropelene
Figure 8-6: These plots show the amount of work done in an experimental run versus
the normal force applied to the sample for homogeneous ERF materials.
112
trating the fluid layer and causing an electrical breakdown. In this experiment, three
different spacer materials were chosen and they were compared with a material constructed with no spacer. Each of the different materials behaved differently, meaning
the choice of spacer material is an important design consideration.
One influence the spacer has is the separation between the electrodes. A thick
spacer may have a high dielectric breakdown strength, but would separate the electrodes reducing the field strength for a given voltage.
The spacer material may affect friction in the system.
Both the kraft paper
material and the material with no spacer showed evidence of friction. The results
seem to indicate that adding a spacer to the material might actually reduce the
amount of friction.
Finally the strength of the ER effect may be affected by the spacer material.
Clearly the results show that using polypropylene as a spacer dramatically reduces or
eliminates the ER effect. Possible explanations include a variation in the field strength
across the thickness of the material such that the field strength in the fluid is reduced
in the presence of the polypropylene spacer, or low conductivity of the polypropylene
reducing the current flowing through the fluid and consequently reducing the ER
effect.
8.4
Breakdown Voltage
Electrical breakdown was the primary means of material failure in the experiment.
The heterogeneous fluid material with no spacer had electrical breakdown at 200V
and the dry material began to breakdown along the edges at 600V. The rest of the
materials had breakdown strengths above 1kV. Using the aluminized PET is one
method to prevent catastrophic failure in the event of a breakdown. The heat from
the electrical arc vaporizes enough of the metal to prevent further breakdown.
However, a greater understanding of this mechanism is important to the design
of the material.
Creating a material with a high breakdown strength allows the
field strength and, therefore, the response of the fluids to be high. A comprehensive
113
investigation into the breakdown strength of various materials and how they are
affected by decreasing gap distance or sharp impacts would be helpful.
8.5
Dynamic Effects
The raw data for both the ER fluids indicated that there are some transient effects
occurring in the fluid. While the heterogeneous fluid showed merely a slight settling
time, the homogeneous fluid, especially at OV, had very slow transients that essentially
dominated the response.
While these effects were not specifically investigated, the data obtained could
be analyzed further to try to gain more insight into the source of these interesting
behaviors.
8.6
Conclusions
In this investigation, a model based on the ER fluid properties was developed and
shown to demonstrate a reasonable match to the shear response of a variable-impedance
material, even though the boundaries of the material are unconstrained. The parameters of the model were determined for several different spacer materials and two types
of ER fluid.
Furthermore, several important design considerations were introduced and shown
to have an effect on the material including: the choice of the spacer material, the loading conditions, the breakdown mechanism, and transient effects. Of special importance was the realization that using certain materials as spacers, such as polypropylene, effectively eliminates the ER effect in the fluid.
The idea of creating the material using electrostatic induced friction, known as the
Johnsen-Rahbeck effect, as an alternative to field activated fluids was also introduced.
The dry material was briefly investigated and shown to have similar properties to the
ER fluids without the added weight and leakage problems of a fluid-based material.
114
8.7
Next Steps
There are many different investigations that could be carried out to gain further
insight into the behavior of this material and how to best design it.
One approach is to carry out more elaborate measurements of the field-activated
fluid properties and use these to predict the model parameters. These parameters
could be compared to the parameters experimentally determined in this investigation.
Agreement between the parameters would further validate the model, and
discrepancies might lead to insight in improving the model and understanding the
material.
Another branch of future research could be in analyzing more properties of the
sandwich material developed in this thesis. Of special interest are the bending stiffness, the thickness, and the transient response. The bending stiffness could be measured by slightly modifying the single-axis tester designed for this project. The stiffness of a single layer of the material may be difficult to measure, but using a large
stack may produce a measurable response.
The transient response could be explored using some of the data recorded in this
work. Another interesting experiment would be measuring the energy absorption in
a ball-drop test and comparing the results to the predicted values based on Eq. 3.30
and the material parameters determined in this investigation. A large discrepancy
would be a good indication that the transient effects are important in impact-type
applications.
As one of the fundamental differences with this material over other ER fluid
applications is the unconstrained boundary, precise measurements of the thickness
both over time and over space would be very helpful in improving the understanding
of the material as well as comparing the results to computer simulations.
Scaling is also an important factor to look at. The performance of the material
may change dramatically as the size is scaled down. The next step in understanding
how properties scale could be performing a similar analysis to what was done in this
paper using spacers of the same material but with varying thicknesses.
115
Finally, as mentioned above, it is important to understand the failure modes of
the material, especially electrical breakdown.
Experiments should be carried out
specifically to determine what the breakdown strength of different materials are, how
it scales, and how it is affected by movement and loading.
8.8
Future Vision
This thesis has focused mainly on the behavior of a simple sandwich geometry with
the intent of gaining insight into the design of a more general variable impedance
material. However, the sandwich material developed here could have the potential for
direct applications. By adding a mechanism to allow repeatable movement, such as an
internal elastic band that pulls the material back together after being stretched apart,
the material would be useful in providing controllable impedance in one direction in
applications requiring very low profile mechanisms. For example, one could use such
a sandwich in a haptic glove device where individual strips are connected to each
finger, providing a resistance to bending and hence, touch feedback, that is controlled
by voltage.
But the long term goal is to create a continuous material with versatile properties.
One possible method for creating this material using the sandwich geometry studied
here is to create a network of small nodes that are linked to their neighbors with
interwoven layers. The nodes could be attached to a continuous material such as a
fabric above and below to contain the fluid and maintain a nominal spacing as shown
in Fig. 8-7. By making each node individually addressable, just like in an LCD display,
the properties of the material as a whole could be adjusted. For example, imagine
creating a material that is stiff in the vertical direction while remaining compliant
horizontally by simply turning on alternating columns of nodes. Or imagine activating
a small area where an impact is expected and adjusting its properties over the course
of the impact to maximize energy absorption and minimize injury to the wearer. With
advances in ER fluid properties and a greater understanding of their behavior, the
prospect of creating such a material looks promising.
116
+E 7
H
T-T
.
I
1
i
ER Fluid
Fabric
Flexible Electrodes
Figure 8-7: Diagram of a possible method for creating a continuous material using
sandwich geometry.
117
118
Appendix A
Energy Absorption Simulations
This appendix discusses the simulation of the differential equation describing the
motion of a mass acted upon by the material in the parallel loading condition. The
equation of motion for the mass is given by:
M
WX where c= ao + aiV" and b
(L - x)(c+b)
0
a2 + a 3 V2.
(> 0,x < L)
(i < 0, x > L)
Assuming the mass has an initial velocity,
vo, the differential equation can be represented in Simulink as shown in Fig. A-1.
Appropriate values are chosen for the parameters a and n, which characterize the
properties of the variable impedance material. Then, using a variable step ode45
solver, the simulation is run with a variety of different initial velocities and voltages.
The simulation is run until the velocity remains constant, which occurs when x > L,
or the velocity drops to zero. The simulated final velocity versus the initial velocity
is plotted in Fig. A-2.
Note that this figure is generally linear, so it is straightforward to come up with
a model of this behavior. After adjusting all the parameters and rerunning the simulation to determine the weight each parameter has on the final velocity the following
119
a(1)+a(27V~n(1)
4
x
overlap
apa)+a(47VAn(2)
-
veLIFinal
>O'M
O5'M'v0^2
ini
2Enrgy
AEcyrbed
--
0
4
-waii'M
7Enrgy
energyAbsorbed
Inifial Energy
Figure A-1: Diagram of the simulink model to find the amount of energy absorbed
by the material.
0
5-
0
A
OV
200 V
400 V
S600 V0
4
(b
E5
0
0
3
0
0
1
0
A
[IA
'InV
T
Initial Velocity [mis]
6
Figure A-2: Final velocity of the mass after interacting with the variable impedance
material versus its initial velocity and the applied voltage.
120
I
El
0V
o 200 V
A 400 V
0 600 V
... Model
6
4
I
I
I
.1
4-l
EE
3
00
1A
6
Initial Velocity [mis]
>o
-
.0,
V)
zo>zc
Figure A-3: Final velocity of the mass with model fit.
model of the final velocity was determined:
(y =
0
)(A.2)
Where the critical initial velocity, xoc, below which the final velocity is always zero,
is defined as:
XOc
2 Mb(V)
+
c(V) +
(A.3)
This model applied to the previous set of data is shown in Fig. A-3. The average error
of the model for the data shown is 0.007m/s. So there is a small discrepancy between
the model and the simulated data, but it is a close match between the two. The
model of the final velocity can be used to calculate the final energy of the mass and,
subtracting that from the initial energy, the energy absorbed by the material. A plot
of the simulated energy absorption along with the model fit are shown in Fig. A-4.
The average error in the energy absorption prediction is 0.003J.
Using Simulink, an approximate model of a particuar solution to a complex differential equation was determined with a close correspondence between the simulated
and predicted energy absorption.
121
18
16
14-
!;'12-
11
0V
0 200 V
A 400 V
600 V
Model
g
-
5
6
" 10
w
64
2
1
2
3
4
Initial Velocity [m/s]
Figure A-4: Energy absorbed by the material versus the initial velocity.
122
Appendix B
Heterogeneous Fluid Data
123
Voltage:
OV, Speed: 2mm/s
Voltage: OV, Speed: 4mm/s
0.10
Trial 1
"
"
F=-0.000764x+0.1
R: 0.672
0.15
Trial2
0.14
Trial3
Mean
-
0.12*
F =-0.(XYY966x + 0. 12
.m
2:0.7 89'+
-. ,
.-.
Me-n Wr 000-1 N-Mean
0
Trial 2
M
Trial 3
Til
0.1*
a) 0.1
0
LiL
0.04
0.05
0.02
10
20
30
Distance [mm]
40
'0
6D
50
10
=
R:
0.24
Nmn
-0.001 5x
0.784
+
20
40
30
Distance [mm]
60
50
Voltage: OV, Speed: 16mm/s
Voltage: OV, Speed: 8mm/s
F
0.00531
20037
Nm
Mean Work:
0
0
-
Mean Work:
0.16
Trial 1
Trial 2
Trial 3
*
0
-
F = -0 .Y239x
2
R : 0.397
0.3
+
m Trial 1
" Trial 2
" Trial 3
0.24
Mean
Mean
-
0.25
-- 0.15
0
LL
j
a
0-
0.1
0.2
0.15
0.1
0.05
fi
'0
Mean Work: 0.00677 Nm
10
20
30
40
Distance [mm]
Mean Work:
0.05
50
60
10
10
20
0.8)909 Nm-
40
30
Distance [mm]
.4
50
60
Figure B-1: Raw data for experimental runs using heterogeneous fluid with a kraft
paper spacer at 0 volts.
124
-~
u
--
F = -0.01
Trial 1
8 Trial 2
Trial 3
16y + .
R2:0.989
-~
Voltage: 200V, Speed: 4mm/s
Voltage: 200V, Speed: 2mm/s
1.5
-
F=-0.0121x+
R : 0.994
1.2
Men W-
-Mean
Trial 1
1.1
U
Trial 3
Mean
1
K 0.6
0
L
.
0.4
0.2
Mean Work: 0.0388 Nm
S
10
20
30
Distance [mm]
Voltage: 200V, Speed: 8mm/s
1
F = -0.0126x + 1.2
R2: 0.988
1.2
0
F
0
6(
50
40
Mean Work:
10
0.0395 Nmi
20
40
30
Distance [mm]
6
50
0
Voltage: 200V, Speed: 16mm/s
1.
*
Trial 21
Trial
-
TriaI3
4
oTrial+ 1W
F =-0.014x
2:0,960
n2
.'
''
s...-
1
a Trial 2
0 Trial 3
Mean
0
0 0.6f
U-
5
0.4
0.2
0
.
Mean Work: 0.0448 Nm
'
10
'
20
Mean Work;
-
40
30
Distance [mm]
-
50
- -
0
60
10
20
0.05(Y) Nin
40
30
Distance [mm]
50
60
Figure B-2: Raw data for experimental runs using heterogeneous fluid with a kraft
paper spacer at 200 volts.
125
Voltage: 400V, Speed: 4mm/s
Voltage: 400V, Speed: 2mm/s
2.5
F = -0.0212x + 2
2
R : 0.993
Trial 1
Trlal2
U
F = -0.0232x + 2.1
2
R : 0.992
2
2
a
Trial 1
"
Trial 2
Trial 3
U
Mean
1.5
0
U-i
a.
0.51
Mean Work: 0.07 Nm
CI
0
20
10
Mean Work:
612
50
40
30
Distance [mm]
10
Voltage: 400V, Speed: 8mm/s
2.0
V = -n0024A
.
R2-
20
.
x + 22I
0.996
2
-
Trial 1
a
Trial
M
Trial 3
-- Mea
Nmi
30
40
Distance [mm]
50
6(
Voltage: 400V, Speed: 16mm/s
r
2
STrial 1
a' Trial 2
E Trial 3
-- Mean
F = -0.025x + 2.3
R2; 0.983
.
n -
20
0.0711
2
1.5
1.
LL
0.5
0.5f
Mean Work: 0.0806 Nm
0
10
20
30
40
Distance [mm]
Mean Work:
50
'0
60
10
20
0.0844 Nmn
30
Distance [mm]
40
50
60
Figure B-3: Raw data for experimental runs using heterogeneous fluid with a kraft
paper spacer at 400 volts.
126
Voltage: 600V, Speed: 4mm/s
Voltage: 600V, Speed: 2mm/s
3..
I
F = -0.0317x + 3.1
R: 0.982
3
F
J.to
-Trial 1
Trial 2
2
0 Trial 36
--
F=2 -0.0343x
n Trial 1
+ 3.4
Trial 2
a Trial 3
Mean
R : 0.982
3
a
Mean
2.5
2.5
2-
1.5
1.5
1
1
0.51
0.51
Mean Work:
10
10
0.122
Mean Work: 0.135 Nm
Nin
3.0
410
.20
Distance [mm]
5..0
20
10
60
F =-0.0365x
R2: 0.982
+ 3.6
a
N
3
Trial 1
Trial 2
Trial 3
-Mean
3
0
61
4
.
inTrial 1
F = -0.035x + 4
R2: 0.984
w Trial 2
a Trial 3
Mean
32 .5
2.5
0
50
Voltage: 600V, Speed: 16mm/s
Voltage: 600V, Speed: 8mm/s
3.5
40
30
Distance [mm]
2, 2
0
2
LL
LI-
1.5[
0.5
0.5i
0
1
Mean Work: 0.151 Nm
10
20
40
30
Distance [mm]
50
Mean Work:
10
60
20 D0
0.163 Nmn
30
Distance [mm]
40
50
60
Figure B-4: Raw data for experimental runs using heterogeneous fluid with a kraft
paper spacer at 600 volts.
127
Voltage: OV, Speed: 2mm/s
0.4
0.35
F2= -0.00202x +0.19
R : 0.933
0.3
z
S
LL
0 .3
*
F =-4).00327x + 0.27
R :0.956a
MaTrial 1
Tra2
Trl2
riaTrial 3
-Mean
0 25
0.25
0.2
0.2
S00. 15
0.15
0
0.1
0.05
Mean Work:
0.45
0.00792
10
10
.
0.4-
20
0.
40
30
Distance (mm]
.
.
.
A.F =-0.00429x + 0.34
*
1 1 Mean Work: 0.011 Nm
Nm
Voltage: OV, Speed: 8mm/s
.
0.35
0.31
R2: 0.949
.
..
.
0)
0
50
20
10
50
40
30
Distance [mm]
60
Voltage: OV, Speed: 16mm/s
0.7
l1
-2 Trial
a Trial 2
Trial 1
F = -0.00659x + 0.49
2
R : 0.879
0.6
0 Trial 3
Mea n
U
U
-
Trial 2
Trial 3
Mean
0.5
0.25
0
IL
Voltage: OV, Speed: 4mm/s
0. 3G
Trial 1
n Trial 2
U Trial 3
Mean
-
Z
0.2
*
0.4
W
80.3
0.15t
0.2
0.11
0.05
'I
'0
Mean Work:
'
10
0.11
0.0138 Nrn
20
40
30
Distance [mm]
50
60
10
F
Mean Work:
10
20
0.0179 Nm
40
30
Distance [mm]
50
60
Figure B-5: Raw data for experimental runs using heterogeneous fluid with a tissue
paper spacer at 0 volts.
128
Voltage: 200V, Speed: 4mm/s
Voltage: 200V, Speed: 2mm/s
1.' 4
.
F 2=-0.0107x + 0.89
R :0.984
2
F 0. 8
4
Trial 1
UTrial 2
U Trial 3
Mean
F =-0.0132x +
-
0 Trial 3
Mean
8
.0
M
1.1Tra1
.R: 0.985
2
L 0. 6
0. 6
0. 4
0. 4
0.
2
0. 2
1
Mean Work: 0.0355 Ni
20
10
40
30
Distance [mm]
Voltage: 200V, Speed:
1 4A
8mm/s
F = -0.015 Ix + 1.2
R 2: 0.988
1.2
50
00
6C
Mean Work: 0.0434 Nm
10
30
Distance [mm]
1
Trial 1
in Trial 2
E Trial 3
Mean
60
50
40
Voltage: 200V, Speed: 16mm/s
-r
'
20
F = -0.0174x + 1.4
n2.
n,.
K
Trial 1
" Trial2
" Trial 3
Mean
-
1
1
L 0.8
L.
0.5
0.4
0.2
Mean Work:
0
10
0.0487
20
Nni
30
40
50
00
60
Distance [mm]
110
Mean Work: 0.0547 Nm
20
40
30
Distance [mm]
J
50
60
Figure B-6: Raw data for experimental runs using heterogeneous fluid with a tissue
paper spacer at 200 volts.
129
-q
Voltage: 400V, Speed: 4mm/s
Voltage: 400V, Speed: 2mm/s
F =-0.0306x + 2.7Tra1
F= -0.0269x + 2.3
Ma 0.994 0
2.5
R2:0.95
2.5
Trial 3
-- Mean
Trial 3
-
Mean
2
2
(, 1.5
1.5
0
0
LL
U-
0.5
0.51
Mean Work:
U0
0.0916 Nm
20
10
Voltage: 400V, Speed:
.
50
40
30
Distance [mm]
0.118 N m
1
20
o
60
8mm/s
*11 R-:
0.998
50
30
40
Distance [mm]
60
Voltage: 400V, Speed: 16mm/s
3 .5
a
3
Mean Work:
E
.
Trial 2
3
Trial 3
-Mean
F = -0.0423x + 3.5
R2: 0.993
-
2 .5
2.5r
;
m
Trial 1
Trial 2
8
Trial 3
-Mean
*
2,
0
LL
0.51
0 .5 t
'
-
Memn Work:
'
10
0.126 Nm
20
Mean Work:
i
30
Distance [mm]
40
50
60
10
10
20
0. 124 Nm
40
30
Distance [mm]
50
60
Figure B-7: Raw data for experimental runs using heterogeneous fluid with a tissue
paper spacer at 400 volts.
130
Voltage: 600V, Speed: 4mm/s
Voltage: 600V, Speed: 2mm/s
F = -0.046
R2: o.989
b
Trial 1
1x + 4.2
F = -- ).0515x + 4.8
R2: 0.993
Trial 2
Trial 3
M W:Mean
R
4
4
MaTrial 1
a
Trial 2
0
Trial 3
Mean
--
3
32
0
LL 2
0
1
Mean Work:
Mean Work: 0.2 Nmn
0. 168 Nin
20
10
5-
6,
a
0
ra
Trial 3
0
--
Mean
r
F2= -0.065x + 5.6
R : 0.99o1
5
Trial 3
"
Mean
4
4'
LL
2
21
Mean Work:
0
6(
50
40
30
Distance [mm]
Voltage: 600V, Speed: 16mm/s
Voltage: 600V, Speed: 8mm/s
F = -0.0567x + 5.3
R2: 0990
20
00
6C
50
40
30
Distance [mm]
10
2A
0.217 Nm
20
Mean Work: 0.216 Nm
30
Distance [mm]
40
50
'0
60
10
20
40
30
Distance [mm]
50
60
Figure B-8: Raw data for experimental runs using heterogeneous fluid with a tissue
paper spacer at 600 volts.
131
Voltage: 0V, Speed: 2mm/s
0.15
F 2= -0.000726x
R : 0.698
+
0.057
Voltage:
0.1 2
Trial 1
" Trial 2
" Trial 3
Mean
OV, Speed: 4mm/s
m Trial 1
Trial2
-10.00t04x+0.084
1
0.
0 17.
Trial 3
Mean
0.0 8M-
0.1
a)
6-
0
LL
0.0 4-
0.0
2Men WorL-.0.6024 rbjrn
102*
0
20 Dt10 30
Mean Work:
4
50
40
60
0.0033
Nni
20 Dt
10
50
40
60
Voltage: OV, Speed: 16mm/s
Voltage: OV, Speed: 8mm/s
0.2
F=-0.00151x +0.13
R2: 0.776
0.3r-
Trial 1
Trial 2
Trial 3
Mean
X
N
-
0.15
30
Distance [mm]
Distance [mm])
[
F = -0.00227x + 0.19
0.25F
R2:
(
0.397
X
N
Trial 1
Trial 2
Trial 3
-- Mean
0.2
0.1
L)
0
0.15
L-
0.1
Me.
W.
0
0.05!
0.05
Mean Work:
O
10
0.00495 Nm
20
40
30
Distance [mm]
-
--
50
Mean Work: 0.00655 Nmi
n
60
~0
10
20
30
40
Distance [mm]
-
50
I
60
Figure B-9: Raw data for experimental runs using heterogeneous fluid with no spacer
at 0 volts.
132
Voltage: 20V, Speed: 4mm/s
Voltage: 20V, Speed: 2mm/s
0.
45
0.35
F = -0.00339x + 0.28
-R':
0.964
t3 ---
0.
-
Trial 1
a Trial 2
2 Trial 3
Mean
T
0.3.
0.25!
0.2 5
S0. 2
Trial 1
F = -0.00396x + 0.33
2: 0.975
e
0.35
M
o
3 0.21
0
LL
0.1
0.15
0.
0.1
0.0 5
n
0
0.75
Mean Work: 0.0 12 Nin
20
10
Mean Work:
40
30
Distance [mm]
50
0
60
Voltage: 20V, Speed: 8mm/s
0.45
0.4
F = -0.00489x + 0.39
R: 0.975
0.35
.-
"
a
E
10
50
40
30
60
Distance [mm]
"
0.6[
F = -0.00538x
2
R : 0.797
-Mean
0.5
0.3
0.25
20
Voltage: 20V, Speed: 16mm/s
0 7r
.
Trial 1
Trial 2
Trial 3
0.0 14 Nmn
+
Trial 1
Trial 2
" Trial 3
0.5
-
Mean
LL 0.3~
0.15
0.2
0.11.
0.05[
0
0.1
Mean Work:
10
Mean Work:
0.0 16 Nm
20
40
30
Distance [mm]
50
U
_0
60
10
20
0.0197
Nm
40
30
Distance [mm]
50
60
Figure B-10: Raw data for experimental runs using heterogeneous fluid with no spacer
at 20 volts.
133
Voltage: 40V, Speed: 4mm/s
Voltage: 40V, Speed: 2mm/s
1.4
1.2
F
= -0.03x
R-.
+
Trial 1
" Trial 2
* Trial 3
1.2
0.93
0.992
en
-
1
1
20.8
20.8
LL0.6
U-0.6
0.41
Mean
F=-0.0107x + 0.91
R: 0.995
Mean
O.4
0.2
0.2
Mean Work:
0
0.0388 Nin
10
20
30
40
Distance [mm]
50
60
10
F2=-0.0114x
30
40
Distance [mm]
1.
4.
Trial 1
Trial 2
a
+ 0.97
R : 0.990
20
50
6(
Voltage: 40V, Speed: 16mm/s
Voltage: 40V, Speed: 8mm/s
1 4A1.2-
Mean Work: 0.0337 Nm
1 .2F
F = -0.011Ix
R2: 0.923
Mral
-
+
0.98
Trial 1
" Trial 2
" Trial 3
Mean
1 P
08
0.81 'I
LL
0.6
LL00.6
0.4
0.4
*00
0.2
0.2
Mean Work: 0.0366 Nmi
Mean Work: 0.0381 Nm
10
10
20
40
30
Distance [mm]
50
0
60
10
20
40
30
Distance [mm]
50
60
Figure B-11: Raw data for experimental runs using heterogeneous fluid with no spacer
at 40 volts.
134
Voltage: 60V, Speed: 4mm/s
Voltage: 60V, Speed: 2mm/s
2: 0.994
F = -0.0177x
STrial 1
Trial 2
F = 4).0179x + 1.7
'
enW
+ 1.7
Trial 1
R : 0.987
E Trial 3
Mean
1 . 5.
1.5
1
0
LL
0
LL
0.5
0. 5
Mean Work:
0.067 t Nai
20
10
2r
2
Mean Work:
50
40
30
Distance [mm]
0
60
F = -4).0222x + 1.9
RM : 0.996
8MeanN
20
30
40
Distance [mm]
60
50
Voltage: 60V, Speed: 16mm/s
Voltage: 60V, Speed: 8mm/s
-
0.0703 Nmn
10
*
Trial 1
Trial 2
Trial 3
Trial 1
ra
F = -0.0214x + 1.89
R2: 0.979
--
a
o
.n
1
(0
-M ria
NMean
.5
0
U-
LL
0
0
0.j
10
Mean Work:
10
0.0681
20
Mean Work: 0.0669 Nm
Nni
40
30
Distance [mm]
50
'b
60
10
20
40
30
Distance [mm]
50
60
Figure B-12: Raw data for experimental runs using heterogeneous fluid with no spacer
at 60 volts.
135
N
Voltage: OV, Speed: 4mm/s
Voltage: OV, Speed: 2mm/s
0.
F = -0.000764x +0.1
5R2: 0.672
0.1
5
Trial 1
Trial 2
Trial 3
Mean
£
0.08
-Mean
.~
F = -0.(X)0808x
2
R:
+
N
0.062
0.851
-
0.06
5
2
0
U-
0.1
M kTrial 1
a Trial 2
0 Trial 3
0
LL
0.
0.04
0.02
Mean Work: 0.00437 Nm
(A-
0
10
20
Mean Work: 0.00214 Nm
30
40
Distance [mm]
Voltage: DV, Speed: 8mm/s
0.4G
6(
50
10
F = -0.0012x + 0.096
R: 0.805
0.2r
-
50
60
OV, Speed: 16mm/s
F = -O.00196x +0.16
R: 0.377
Trial 2
Trial 3
Mean
N
30
40
Distance [mm]
Voltage:
-r-
Trial 1
x
20
Trial I
N
0
Trial 2
Trial 3
Mean
0.15
0.1
a
0
0
U-
U-
-%
()1I
0.05
0.05
Mean Work: 0.00335 Nm*
10
10
20
40
30
Distance [mm]
Mean Work:
50
60
~0
10
20
0.00507 Nmn
30
40
Distance [mm]
50
60
Figure B-13: Raw data for experimental runs using heterogeneous fluid with a PPL
spacer at 0 volts.
136
.
.
.
. Trial
0.07,
*
0.06
F =-0.000633x
R 2:
0.05
-
1
Trial 2
Trial 3
z
-
.
0
U-
-a.
0.02
0.01
Mean Work:
20
40
30
Distance [mm]
F = -0.00128x + 0.1
0.1
R':
0.811
M Wok
m
Trial 2
Trial 3
Mean
'.
0.03
0.02
0.01
-
Mean Work: 0.00227 Nm
0
60
50
Voltage: 200V, Speed: 8mm/s
*--
U
:
0.05-
0.00139 Nm*
10
P Trial 1
0.939
-
0.04'
.
.
6
.R':
0.06
Mean
+ 0.043
0.08
F = -0.000872x + 0.065
0.07
0.916
0.04
0.03
Voltage: 200V, Speed: 4mm/s
Voltage: 200V, Speed: 2mm/s
0.08
10
20
30
Distance [mm]
50
40
Voltage: 200V, Speed: 16mm/s
n
Trial 1
Til1
a Trial 2
- Trial 3
Mean
60
a Trial 2
0.2 5
n Trial 3
F = -0.00205x + 0.17
R2: 0.354
-
Mean
0.2
0.08
2 0.1 5
0.06
,.
0
LL
0
0
0.04
0.0
0.02f
Mean Work:
0
10
0.00366
20
Nin
40
30
Distance [mm]
Mean Work: 0.00574 Nmi
'
50
_0
60
10
20
30
40
Distance [mm]
50
60
Figure B-14: Raw data for experimental runs using heterogeneous fluid with a PPL
spacer at 200 volts.
137
Voltage: 400V, Speed: 4mm/s
Voltage: 400V, Speed: 2mm/s
STrial 1
STrial 1
Trial 2
Trial 3
*
*
0.08
0.08
Mean
-
F= -0.000717x + 0.045
2
R 0.936
-0.06
Trial 2
U
F = -0.00103x + 0.07
R 2: 0.955
-Ma
-0.06
0
U- 0.04
-L0.041
0.02,
0.021
Mean Work: 0.00234 Nin
Mean Work: 0.00137 Nm
0
20
10
30
40
Distance [mm]
50
U6
60
10
F =-0.0014x
,
a
2:
+0.11
0.889
40
6C
50
s
Trial 1
N Trial 2
Trial 3
Trial 1
N Trial 2
0.25{
F = -0.00231x + 0.18
-Mean
0.1
30
Distance [mm]
Voltage: 400V, Speed: 16mm/s
Voltage: 400V, Speed: 8mm/s
0.12-
20
a Trial 3
Mean
R2: 0.391
-
0.2
~0.15
0
U-
0.1
0.04
0.05
0.02
n
"0
Mean Work: 0.01575
Mea n Work: 0.0 0376 Nm
10
20
30
40
Distance [mm]
50
10
60
10
20
Nm
40
30
Distance [mm]
50
60
Figure B-15: Raw data for experimental runs using heterogeneous fluid with a PPL
spacer at 400 volts.
138
Voltage: 600V, Speed: 4mm/s
Voltage: 600V, Speed: 2mm/s
0.1 2
0.1
-
0.0
F -0.000855x + 0.05
R: 0.933
MaTrial 1
STrial 2
Trial 1
N Trial 2
3 Trial 3
Mean
F = -0.00108x + 0.073
R.2: 0.950
0.08
Trial 3
0
Mean
-
3
,0.06
C) 0.0 6
0
u.
L-
0.04
MenWr:0029-
0.0 4
0.02
0.0 2
Meani Work: 000139 Nm
20
10
50
30
40
Distance [mm]
60
'O
Voltage: 600V, Speed: 8mm/s
0.1 4
F-
F = -0.00155x + 0.12
R2: 0.870
0.12
10
40
30
Distance [mm]
a
0.25[
F = -0.00241x
R : 0.413
0.1
50
E0
Voltage: 600V, Speed: 16mm/s
0.3
Trial 1
Trial 2
N Trial 3
-- Mean
20
+ 0.18
Trial 1
w Trial 2
m Trial 3
Mean
0 .2
.0.08
a
(D 0: 15-
4.*
0
LL
LL 0.06*
0
0.04
05
0.02
_i
0
Mean Work:
10
Mean Work: 0.0056 Nm
0.00395 Nm
20
40
30
Distance [mm]
50
10
60
10
20
40
30
Distance [mm]
50
60
Figure B-16: Raw data for experimental runs using heterogeneous fluid with a PPL
spacer at 600 volts.
139
140
Appendix C
Homogeneous Fluid Data
141
Voltage: OV, Speed: 4mm/s
Voltage: OV, Speed: 2mm/s
4
Trial 1
a Trial 2
3 Trial 3
Mean
2.5
0
33
F = -0.0169x + 1.3
R : 0.887
2
F =-0.0144x + 1.1
R2:0.973
2
0
0
L-
LL
Mean Work:
00
10
20
Mean Work: 0.046l Nm
0.0453Nm
40
30
Distance [mm]
50
0
60
10
2.5
L)
30
40
Distance [mm]
50
6C
-Trial 1
Trial 1
. Trial 2
N Trial 3
Mean
3
20
Voltage: OV, Speed: 16mm/s
Voltage: OV, Speed: 8mm/s
4
Trial 1
Trial 2
Trial 3
Mean
5
*
*
3.5
3
3-
Trial 2
Trial 3
Mean
-
2.5
2
F = -0.0229x +
R2: 0.913
S2
F =-0.0146x + 1.1
R2: 0.967
1.6
1.5
1
1.5
.5Mean
10
Work:
20
0.5f
0.0528 Nmi
40
s0 30
Distance [mm]
50
60
'0
Mean Work:
10
20
0.0597 Nmn
30
Distance [mm]
40
50
60
Figure C-1: Raw data for experimental runs using homogeneous fluid with a kraft
paper spacer at 0 volts.
142
Voltage: 200V, Speed: 4mm/s
Voltage: 200V, Speed: 2mm/s
3
F -0.0276x +2.5
R2: 0.974
2. 5
F =-0.0417x
3.5
Trial 3
Mean
R :
+ 3.9
0988
Trial 3
-- Mean
3
2.5
2
a
0 1020
i50 6
3T40
LL
5j
0.
5f
06
Mean Work:
20
1'0
0.51
0.102 Nm
Mean Work: 0.155 Nm
50
3'0
40
Distance [mm]
0
60
Voltage: 200V, Speed: 8mm/s
7.
: Trial 1
a Trial 2
" T ria l 3
-
20
50
40
30
Distance [mm]
60
Voltage: 200V, Speed: 16mm/s
12
F -0.0722x + 6.6
R~: 0.9994
6
10
Trial 1
U Trial 2
10
F= -0.126x+11
R2: 0.999
Mean
5
-
Trial 3
Mean
8
2)
6
0
U-
IL3
4
2
2
1
Mean Work: 0.241 Nm
0
10
20
40
30
Distance [mm]
Mean Work:
50
1O
60
10
20
0.341
Nm
40
30
Distance [mm]
50
60
Figure C-2: Raw data for experimental runs using homogeneous fluid with a kraft
paper spacer at 200 volts.
143
-4
Voltage: 400V, Speed: 4mm/s
Voltage: 400V, Speed: 2mm/s
3
ETil3
F =-O.0308x +2.9
'*
F = -0.0482x + 4.7
R 2: 0.988
4
Trial 1
a
0
Trial 2
Trial 3
-Mean
2. 5
-3
0
1. 5
0.
01
0
Mean Work:
10
20
Mean Work:
0.119 Nm
50
40
30
Distance [mm]
60
0(
10
F = -0.085
2
R : 0.993
1x + 8.1
7
0.19 Nin
30
40
Distance [mm]
50
60
Voltage: 400V, Speed: 16mm/s
Voltage: 400V, Speed: 8mm/s
14
9.-
8
20
Trial 1
Trial 2
Trial 3
Mean
*
0
-
12
--
6
F = -0. 154x + 14
R2: 0.998
Trial 1
a Trial 2
a Trial 3
-- Mean
10-
-5
6
0
LL
3
2
2
Mean Work: 0.313 Nrn
"0
10
20
40
30
Distance [mm]
50
60
Mean Work:
10
0.459 Nni
40
n30
Distance [mm]
20 D
50
60
Figure C-3: Raw data for experimental runs using homogeneous fluid with a kraft
paper spacer at 400 volts.
144
Voltage: 600V, Speed: 4mm/s
Voltage: 600V, Speed: 2mm/s
F = -0.0325x + 3.1
"
Trial 1
Trial 2
Trial 3
R-: 0.966
-
Mean
"
3.5
3
a
F =-0.0556x + 5.2
R2: 0.992
5
m
-
Trial 1
Trial 2
Trial 3
Mean
4
-2.5
LL1.51
2
1
0.51
Mean Work:
10
10
0.
.
20
Mean Work: 0.2(Y) Nm
0.127 Nm
60
50
40
30
Distance [mm]
- 10
U
I
76-
*
*
Trial 1
Trial 2
Trial 3
I
8
64
173x + 15
0.998
14
Mean
-
=-0.
R2:
14F
STrial 1
Trial 2
0 Trial 3
a
Mean
1210
I
F5
60
50
40
.__________
F = -0.0969x + 9
2
R : 0.997
8
30
Distance [mm]
Voltage: 600V, Speed: 16mm/s
Voltage: 600V, Speed: 8mm/s
._____.___
20
8
-
6
3
4
1
2f
0
Mean Work:
Mean Work: 0.346 Nm
jf
10
20
40
30
Distance [mm]
50
)0
60
10
20
0.527 Nm
30
40
Distance [mm]
50
60
Figure C-4: Raw data for experimental runs using homogeneous fluid with a kraft
paper spacer at 600 volts.
145
Voltage: OV, Speed: 4mm/s
Voltage: OV, Speed: 2mm/s
F = -0.0174x + 1.4
R2: 0.977
1.5
m
Trial 1
Trial 2
U
Trial 3
Trial 1
0 Trial 2
0 Trial 3
-- Mean
.5
F =-0.0299x
R: 0.973
2
1.9
.5 0
U-
0
L
0.5
Mean Work: 0.0588 Nm
00
220
1
40
3'0
Distance [mm]
- Mean
50
Mean Work: 0.0675 Nm
00
60
10
.5
2
U
3.5-
-0.0656x + 3.8
R': 0.976
F=
3
F = -0.0382x +2.2
R 2: 0.969
.5
50
6(
0
Trial 1
Trial 1
STrial 2
Trial 3
Mean
3- 1
40
30
Distance [mm]
Voltage: OV, Speed: 16mm/s
Voltage: OV, Speed: 8mm/s
3
20
E
-
Trial 2
Trial 3
Mean
2.5
0
0
1 .5
2
1.5
1.
0.5j
0.5
Mean Work:
0
10
20
Mean Work: 0.119 Nm
0.08 Nm
30
40
Distance [mm]
50
0
60
10
20
30
40
Distance [mm]
50
60
Figure C-5: Raw data for experimental runs using homogeneous fluid with a tissue
paper spacer at 0 volts.
146
Voltage: 200V, Speed: 4mm/s
Voltage: 200V, Speed: 2mm/s
2
.5
2
F=-0.0212x + 1.8
R2: 0.979
.5,
.5
Trial 1
8 Trial 2
0 Trial 3
Mean
2 .5
STrial 1
F = -0.0323x + 2.8
a
R2: 0.990
m Trial 3
Trial 2
-Mean
2
1
2
0
L-
0
U-
.5.
0.5
Mean Work: 0.1 Nm
Mean Work: 0.0642 Nin
0
1
20
50
40
30
Distance [mm]
0
60
Voltage: 200V, Speed: 16mm/s
Voltage: 200V, Speed: 8mm/s
5
F =-0.0577x + 4.9
R: 0.998
4
0
Distance [mm]
9w
Trial 1
Trial 2
X Trial 3
7-
Mean
-
F = -0.104x + 8.5
2
R : 0.999
8.
.
Trial 1
a
Trial 2
0
Trial 3
Mean
63-
K5
aL
4-
21
3
2
1
Mean Work: 0.273 Nm
Mean Work: 0.167 Nm
n
0
10
20
40
30
Distance [mm]
50
00
60
10
20
40
30
Distance [mm]
50
60
Figure C-6: Raw data for experimental runs using homogeneous fluid with a tissue
paper spacer at 200 volts.
147
Voltage: 400V, Speed: 4mm/s
Voltage: 400V, Speed: 2mm/s
*
a
F = -0.0219x + 1.8
2
R2:
Trial 1
Trial 2
Trial 3
F =-0.0342x + 2.9
R0994
2.5
.90-Mean
Trial 1
N Trial 2
a Trial 3
-- Mean
2
I.5
z
0
L-
0
1. 5 [
Mean Work: 0.0666 Nm
%
10
20
Mean Work: 0.113 Nmi
30
40
Distance [mm]
50
0
60
0
LL
Voltage: 400V, Speed: 8mm/s
F = -0.0614x + 5.2
5-
R2:
0.998
-
10
20
30
40
Distance [mm]
50
Voltage: 400V, Speed: 16mm/s
10
Trial 1
a Trial2
U Trial 3
Mean
60
F=-O.l I x +9.5
R2: 0.998
8
ma
STrial I
--
Til
Trial 2
Mean
4-
63.
LL
4
2
2
Mean Work: 0.191 Nm
10
10
20
30
Mean Work:
40
50
60
10
Distance [mm]
0.31 2 Nm
20 Dt 30
40
Distance [mm]
-
50
60
Figure C-7: Raw data for experimental runs using homogeneous fluid with a tissue
paper spacer at 400 volts.
148
Voltage: 600V, Speed: 4mm/s
Voltage: 600V, Speed: 2mm/s
2.5
.
0
L
0
8
= -0.0224x
DF+ 1.9
R2: 0.979
2
1M
Trial 1
Trial 26
Trial 3
Mean
-
3
Trial 1
Trial 2
Trial 3
Mean
0
0
--
2.5
1.5
W
0.51
0.5a
Mean Work:
'0
F = -0.0358x + 3.1
R2: 0.993
10
20
0.0717 Nrn
Mean Work:
40
30
Distance [mm]
50
0
6C(
Nmn
60
50
40
30
Distance [mm]
10
Trial 1
Trial 2
0 Trial 3
-- Mean
5-
0. 12
Voltage: 600V, Speed: 16mm/s
Voltage: 600V, Speed: 8mm/s
F = -0.6637x + 5.4
R2: 0.999
20
10
F =-0. 114x + 9.9
R2: 0.999
8
Trial 1
a
m
Trial 2
Trial 3
-
Mean
46-2,
0
LL
S3
u
4
2
2
1
Mean Work: 0.204 Nm
0
10
20
30
Distance [mm]
Mean Work:
40
50
60
"0
10
20
0.336 Nrn
40
30
Distance [mm]
50
60
Figure C-8: Raw data for experimental runs using homogeneous fluid with a tissue
paper spacer at 600 volts.
149
Voltage:
OV, Speed: 2mm/s
2e
F =-0.0128x + 1.2
R: 0.969
1
.5
.5-
Voltage: OV, Speed: 4mm/s
Trial 1
a Trial 2
0 Trial 3
Mean
m
2 .5
F= -0.0263x + 1.8
R.: 0.991
N
-
Trial 1
Trial 2
Trial 3
Mean
2
.5
0
LL
0
LL
.5t
Mean
0
0
60
50
40
30
Distance [mm]
20
10
Mean Work: 0.0697 Nm
Work: 0.0549 Nm
10
3
F = -0.0353x + 2.3
R
0.981
40
30
Distance [mm]
Voltage:
Voltage: DV, Speed: 8mm/s
3.5
20
-
F2= -0.0681x
3 .5
Mean
+3.8
R2:0.956
3\
2.51
60
OV, Speed: 16mm/s
4
Trial 1
a Trial 2
a Trial 3
50
Trial 1
n Trial 2
* Trial 3
-- Mean
2.51
2
z
a
U-
1 .5
0.5e
0.5M
Mean Work: 0.0855 Nun
0
2,
0
.5
0O1
10
20
30
40
Distance [mm]
:
Mean Work:
50
0
60
10
20
0.123 Nmn
30
40
Distance [mm]
50
60
Figure C-9: Raw data for experimental runs using homogeneous fluid with no spacer
at 0 volts.
150
Voltage: 20V, Speed: 4mm/s
Voltage: 20V, Speed: 2mm/s
2. 5
.
.
Trial 1
Trial 2
Trial 3
Mean
N
0
2
F2= -0.0182x + 1.7
R :0.984
3.5
-
3
-0.0339x + 2.8
F =2=0039+.
R: 0.996
2.5
5
Trial 3
Mean
2
0
LL
LL0
0. 5
1.5
0.5
Mean Work: 0.0686 Nm
0
Trial 1
Trial 2
a
9
-
10
20
Mean Work: 0.0987 Nin
50
40
30
Distance [mm]
60
S
10
F = -0.074x + 4.5
R-: 0.991
50
40
30
Distance [mm]
6C
Voltage: 20V, Speed: 16mm/s
Voltage: 20V, Speed: 8mm/s
5
4
20
Trial 1
n Trial 2
-
Trial 3
Mean
a
F =-0.x+5.6
2
R : 0.952
5
Trial 1
I
Trial2
U
-
Trial 3
Mean
4
3
S3
0
LL
LL21
2
Mean Work:
O
2
10
20
0. 125 Nmr
40
30
Distance [mm]
Mean Work: 0.146 Nm
50
60
~0
10
20
30
40
Distance [mm]
50
60
Figure C-10: Raw data for experimental runs using homogeneous fluid with no spacer
at 20 volts.
151
Voltage: 40V, Speed: 4mm/s
Voltage: 40V, Speed: 2mm/s
3.5-
STrial 1
F = -0.01 79x + 1.6
R: 0.983
1 .5
n Trial 2
-- Mean
F = -0.0331x +2.9
R2: 0.996
3
2.5
Trial 1
Trial 2
Trial 3
N
U
Mean
-
2
U-
0)
1.5
LL
0.
0.51
Mean Work: 0.0645 Nm
10
20
Mean Work: 0.104 Nm
50
40
30
Distance [mm]
0
0
61
10
. .,
30
40
Distance [mm]
60
50
Voltage: 40V, Speed: 16mm/s
Voltage: 40V, Speed: 8mm/s
r
20
,
F = -0.0548x + 4.8
STrial 1
RI: 0.998
4
8R2:
UTrial 2
0.994
Trial 3
Mean
*
-
7
Mean
-
Trial 1
F=-.141x +8.7
6
23
5
0
U..
2
3
2
1
Mean Work: 0.234 Nm
Mean Work: 0.174 Nm
08
10
20
40
30
Distance [mm]
50
60
10
10
20
30
40
Distance [mm]
50
60
Figure C-11: Raw data for experimental runs using homogeneous fluid with no spacer
at 40 volts.
152
Voltage: 60V, Speed: 4mm/s
Voltage: 60V, Speed: 2mm/s
F= -0.0191x
+
Trial 1
1.6
a Trial 2
R: 0.987
-
.
3.5
N Trial 3
Mean
Trial 1
m Trial 2
N Trial 3
-- Mean
F2= -0.034x + 2.8
R :0.994
3
2.5
2
0
L
0
U-
1.5
1~
.
05
0.5
Mean Work: 0.0642 Nm
0
10
20
Mean Work: 0.111 Nm
40
30
Distance [mm]
6
50
0
10
20
30
Distance [mm]
40
4-
60
Voltage: 60V, Speed: 16mm/s
Voltage: 60V, Speed: 8mm/s
G .
F = -0.0572x + 4.9
R2: 0.998
50
*
Trial 1
Trial 2
Trial 3
8 -R2:
-
Mean
7-
*
Trial 1
" Trial 2
" Trial 3
- Mean
F = -0. 104x + 8.6
0.999
63
0
LL
5
2
3
2
1
Mean Work: 0.182 Nm
00
10
20
40
30
Distance [mm]
Mean Work:
50
00
60
10
20
0.283 Nm
30
40
50
60
Distance [mm]
Figure C-12: Raw data for experimental runs using homogeneous fluid with no spacer
at 60 volts.
153
Voltage: OV, Speed: 4mm/s
Voltage: OV, Speed: 2mm/s
*
2.5
U
-
F = -0.0169x
2
0
Trial 1
Trial 2
Trial 3
Mean
Trial 1
" Trial 2
" Trial 3
Mean
3
2.5
+ 1.3
R2: 0.887
2s
F = -0.0236x + 1.7
2
R : 0.961
.5
1.5
0..5
0.5
Mean Work: 0.0602 Nm
Mean Work: 0.0453 Nm
10
20
30
40
Distance [mm]
Voltage:
6(
0
10
0V, Speed: 8mm/s
2. 5
F=-0.031x +2.1
R-: 0.967
2
50
0
20
30
40
Distance [mm]
50
60
Voltage: OV, Speed: 16mm/s
3.
Trial 1
* Trial 2
a Trial 3
Mean
F-4x.Trial
F = -0.0489x + 3.3
2
R : 0.968
3
1
Trial 2
U
-
Trial 3
Mean
2. 5
2
m
81. 5
0
L- 1 . 5
Z5
U-
1
0. 51
0.
Mean Work:
Mean Work: 0.0733 Nni
O
10
20
30
40
Distance [mm]
50
0
60
10
20
0.103
Nm
30
40
Distance [mm)
50
60
Figure C-13: Raw data for experimental runs using homogeneous fluid with a PPL
spacer at 0 volts.
154
Voltage: 200V, Speed: 4mm/s
Voltage: 200V, Speed: 2mm/s
Trial 1
a Trial 2
N Trial 3
2. 5
F = -0.0294x + 2.2
2
R : (.988
Mean
-
3'
2
8
0
Trial 1
" Trial 2
* Trial 3
Mean
3.5
2.5
F =-0.0234x + 1.8
R: 0.993
2) 2
1.
0
U-
1.5
51
0. 5M
Mean Work:
0
10
20
0.5[
0.0806 Nm
40
30
Distance [mm]
50
60
Mean Work: 0.0682 Nm
10
10
4
Trial 1
Trial 2
Trial 3
-- Mean
3.5
3
F = -0.0258x + 2.1
R: 0(.989
F = -0.0485x +3.2
R2: 0.955
.
-
Mean
2 .5
2
0
LL
60
. Trial 1
a Trial 2
N Trial 3
4
3
3.5k
50
40
30
Distance [mm]
Voltage: 200V, Speed: 16mm/s
Voltage: 200V, Speed: 8mm/s
4
20
0
1.5
2
1.5
1)
0..5
0.5
Mean Work: 0.0852 Nm
0
10
20
40
30
Distance [mm]
50
0
60
Mean Work: 0.103 Nm
10
20
30
40
50
60
Distance [mm]
Figure C-14: Raw data for experimental runs using homogeneous fluid with a PPL
spacer at 200 volts.
155
iurr~-
~.~->-----
- -
Voltage: 400V, Speed: 4mm/s
Voltage: 400V, Speed: 2mm/s
3. 5
4.57-
Trial 1
* Trial 2
a Trial 3
Mean
3
3
2
0
F =-0.0233x + 1.7
R2: 0.992
2.5:
62
1 .5
L
-
3.51
F = -0.0309x + 2.3
2
R : 0.988
2.
IL15
0. 51
0.5 t.
Mean Work: 0.0652 Nm
Mean Work: 0.0758 Nm
0
10
20
40
30
Distance [mm]
50
6C
S
10
Trial 1
N Trial 2
* Trial 3
Mean
3.
3
2
60
50
40
Trial 1
Trial 2
Trial 3
Mean
*
*
-
F =-0.0433x + 2.8
R: 0.941
-3
F = -0.0207x +
30
Distance [mm]
4
2. 5
2
20
Voltage: 400V, Speed: 16mm/s
Voltage: 400V, Speed: 8mm/s
1.7
R : 0.984
0
"- 2
0L
1. 5
0. 5M
Mean Work: 0.0998 Nm
Mean Work: 0.0747 Nin
0
Trial 1
Trial 2
Trial 3
Mean
"
"
4
10
20
30
40
50
10
60
Distance [mm]
10
20
40
30
Distance [mm]
50
60
Figure C-15: Raw data for experimental runs using homogeneous fluid with a PPL
spacer at 400 volts.
156
Voltage: 600V, Speed: 4mm/s
Voltage: 600V, Speed: 2mm/s
5T
35
STrial 1
U Trial 2
3
F =-0.0314x + 2.2
R-: 0.989
2. 5
Trial 1
35
a Trial 3
Mean
U
Trial 2
*
Trial 3
Mean
-
3
2.5
F2=-0.021tx + 1.6
2
R
: 0.989
2'
0 1. 5
LL
0.51
0.
Mean Work: 0.0726 Nm
0
10
20
50
40
30
Distance [mm]
0
Mean Work: 0.063 Nm-
10
61
20
Voltage: 600V, Speed: 16mm/s
Voltage: 600V, Speed: 8mm/s
Trial 1
Trial 1
" Trial 2
3.5
31
*
Trial 3
-
Mean
" Trial 2
4
" Trial 3
-
3.5
F = -0.0205x
R2: 0.970
S2
+
1.7
Mean
F= -0.0451x + 2.8
2
R : 0.921
3,
2.5
60
50
40
30
Distance [mm]
2.5
LL 2
1.5
0.5j
0.5$
Mean Work:
'0
10
20
Mean Work: 0.0968 Na
0.0713 Nm
40
30
Distance [mm]
50
6
60
10
40
30
20
Distance [mm]
50
60
Figure C-16: Raw data for experimental runs using homogeneous fluid with a PPL
spacer at 600 volts.
157
158
Appendix D
Dry Material Data
159
Voltage: OV, Speed: 4mm/s
0.15
F = -0.00012x + 0.0074
R2: 0.031
I
Trial 1
Trial 2
3
U
0.1
Trial 3
Mean
-
0.05
*0
-0.1
0
20
10
30
60
50
40
Distance [mm]
Figure D-1: Force versus position for the dry material at OV and 4mm/s.
Voltage: OV, Speed: 8mm/s
0.2
Trial 1
F = -0.000381x + 0.021
0.15
i
U
R 2 :0.162
-
-0.05
Trial 2
Trial 3
Mean
-
--
-015
-0.2
0
10
20
30
40
50
60
Distance [mm]
Figure D-2: Force versus position for the dry material at OV and 8mm/s.
160
-
0.6
-
Voltage: 200V, Speed: 4mm/s
F = -0.00243x + 0.16
R2: 0.744
0.5-
*
*
Trial 1
Trial 2
Trial 3
-
Mean
0.4
000.3
0
U-
P
0.2
A
0.1!
* ''
0
20
10
*4
50
40
30
Distance [mm]
60
Figure D-3: Force versus position for the dry material at 200V and 4mm/s.
0.7
0.6
Voltage: 200V, Speed: 8mm/s
F=
-0.0033
R2: 0.770
1x + 0.22
*
*
Trial 1
Trial 2
Trial 3
-
Mean
0.5
F-
z0.4
00.3
0.2
1=
0.1
U0-
10
20
30
40
50
60
Distance [mm]
Figure D-4: Force versus position for the dry material at 200V and 8mm/s.
161
Voltage: 400V, Speed: 4mm/s
1
Trial 1
a Trial 2
m Trial 3
Mean
-
0.8
-0.6
0
0.2
F
-0.01 17x + 0.75
R2
0.927
10
2
60
50
40
20 Dn 30[
Distance [mm]
Figure D-5: Force versus position for the dry material at 400V and 4mm/s.
Voltage: 400V, Speed: 8mm/s
1.4
1.2
F = -0.0122x + 0.8
R2: 0.969
*
m
-
Trial 1
Trial 2
Trial 3
Mean
K 0.8
UO
0.60.4-
0.2i
00
10
20
40
30
Distance [mm]
50
60
Figure D-6: Force versus position for the dry material at 400V and 8mm/s.
162
Voltage: 600V, Speed: 4mm/s
Trial 1
i
F = -0.0275x + 1.7
R 2 0.977
2
Trial 2
-
Trial q
Mean
-
I
1
G)
0
LL
0.5
0
10
20
30
Distance [mm]
40
60
50
Figure D-7: Force versus position for the dry material at 600V and 4mm/s.
!. .
.
Voltage: 600V, Speed: 8mm/s
1
Trial 1
Trial 2
N Trial 3 m
F = -0.0264x + 1.7
R 2:0.986
2.5
-
Mean
2
zi
0
U-
1.5
105
0.5f
0
10
20
40
30
Distance [mm]
50
60
Figure D-8: Force versus position for the dry material at 600V and 8mm/s.
163
164
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