Development of a control system for a SMA actuated medical manipulator

Development of a control system for a SMA actuated medical manipulator
Calhoun: The NPS Institutional Archive
Theses and Dissertations
Thesis Collection
1997-12
Development of a control system for a SMA actuated
medical manipulator
Thiel, Richard A
Monterey, California. Naval Postgraduate School
http://hdl.handle.net/10945/8255
NPS ARCHIVE
1997.12
THIEL, R.
NAVAL POSTGRADUATE SCHOOL
MONTEREY, CALIFORNIA
THESIS
DEVELOPMENT OF A CONTROL SYSTEM
FOR A
SMA ACTUATED MEDICAL MANIPULATOR
by
Richard A. Thiel
December, 1997
Thesis
T37225
icsis
Advisor:
Approved
Ranjan Mukherjee
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DUDLEY KNOX LIBRARY
SCHOOL
fAL POSTGRADUATE
93943-5101
NTEREY CA
DUDLEY KNOX LIBRARY
SCHOOL
NAVAL POSTGRADUATE
93943-5101
CA
MONTEREY,
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TITLE
Master's Thesis
AND SUBTITLE
5.
DEVELOPMENT OF A CONTROL SYSTEM
FOR A SMA ACTUATED MEDICAL MANIPULATOR
6.
FUNDING NUMBERS
ARPA Order No.
ARPA Order No.
B-795
8578
Amendment No. 9
AUTHOR(S)
Richard A. Thiel
7.
PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)
8.
PERFORMING ORGANIZATION
REPORT NUMBER
Naval Postgraduate School
Monterey CA 93943-5000
9.
SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)
SPONSORING/MONITORING
10.
AGENCY REPORT NUMBER
Advance Research Projects Agency
11.
SUPPLEMENTARY NOTES
The views expressed
in this thesis are those
of the author and do not
reflect the official policy or position
of the
Department of Defense or the U.S. Government.
12a.
DISTRIBUTION/AVAILABILITY STATEMENT
Approved
13.
for public release; distribution
ABSTRACT
is
12b.
DISTRIBUTION CODE
unlimited.
(maximum 200 words)
This thesis discusses the development of a digital control system for the operation of a conceptual
robotic manipulator for use in minimally invasive surgery. The motion of the manipulator is envisioned
to be accomplished with actuators made of Shape Memory Alloy (SMA).
has the ability to
recover permanent deformation by undergoing a phase transformation. The recovery of the deformation
results in motion of the
material which can be exploited for useful work. SMA was chosen as the
actualtor because it can be miniturized and has a very high power density as compared to conventional
actuators. An Actuator Matrix Driver (AMD) board was designed, as part of the digital control system,
to power and control the
and the use of
The matrix configuration of the
actuators.
Amplitude Modulated Pulsed (AMP) current allows for a reduction in the number of leads for the
powering and control of the actuators. The electrical resistance, a physical property of SMA which
characteristically changes with phase transformation, can be used to determine the state or phase of the
SMA
SMA
AMD
SMA
SMA actuators and can therefore be used
for closed loop control
SUBJECT TERMS
Shape Memory Alloy (SMA), Actuator Matrix Driver (AMD) Board, Amplitude
Modulated Pulsed (AMP) Current
14.
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DEVELOPMENT OF A CONTROL SYSTEM
FOR A
SMA ACTUATED MEDICAL MANIPULATOR
Richard A. Thiel
Lieutenant Commander, United States Navy
B.S., University of Idaho, 1984
Submitted in partial fulfillment
of the requirements for the degree of
MASTER OF SCIENCE IN MECHANICAL ENGINEERING
AND
MECHANICAL ENGINEER
from the
NAVAL POSTGRADUATE SCHOOL
December 1997
DUDLEY KNOX LIBRARY
SCHOOL
NAVAL POSTGRADUATE
93943-5101
MONTEREY CA
ABSTRACT
This thesis discusses the development of a digital control system for the operation
of a conceptual robotic manipulator for use
the manipulator
Alloy (SMA).
is
SMA
has the
ability to
which can be exploited
because
it
made of Shape Memory
the deformation results in motion of the
for useful work.
SMA
was chosen
SMA
as the actuator
can be miniturized and has a very high power density as compared to
conventional actuators.
digital
An
Actuator Matrix Driver
control system, to
configuration of the
AMD
power and
of the actuators.
characteristically
The
(AMD)
control the
board was designed, as part
SMA
electrical
number of leads
resistance,
a
physical
The matrix
actuators.
architecture and the use of Amplitude
current allows for a reduction in the
phase of the
The motion of
recover permanent deformation by undergoing a
The recovery of
material
(AMP)
minimally invasive surgery.
envisioned to be accomplished with actuators
phase transformation.
of the
in
for the
Modulated Pulsed
powering and control
property
of
SMA
which
changes with phase transformation, can be used to determine the state or
SMA actuators and can therefore be used for closed loop control.
VI
TABLE OF CONTENTS
I.
II.
III.
INTRODUCTION
A.
MOTIVATION
B.
BACKGROUND ON SHAPE MEMORY ALLOY
1
3
SMA RESISTANCE TEMPERATURE TESTING
-
7
A.
RESISTANCE - TEMPERATURE TEST
8
B.
TEST PROCEDURE
9
C.
RESISTANCE - TEMPERATURE TEST RESULTS
10
HEAT TRANSFER MODEL
13
A.
MODEL DESCRIPTION
13
B.
HEAT TRANSFER MODEL EVALUATION
15
C.
IV.
1
Monitoring of SMA Wire with Monitoring Current, I m
1
Phase
1
2.
Phase
2:
Heating of
3.
Phase
3:
Cooling of the
:
SMA Wire with Input Current,
I
s
SMA Wire
THERMAL INERTIAL
15
16
18
22
SMA RESPONSE TO AN ELECTRIC HEATING CURRENT
25
A.
RESISTANCE / STRAIN - CURRENT TESTING
25
B.
TEST PROCEDURE
28
C.
RESISTANCE / STRAIN - CURRENT TEST RESULTS
29
1.
Variable
Load Testing
31
vii
2.
V.
Constant Load Testing
37
PROTOTYPE TEST BOARD AND ACTUATOR MATRIX DRIVER
A.
PROTOTYPE TEST BOARD
1.
2.
B.
VI
47
Description
48
Operational Numbering Scheme
50
ACTUATOR MATRIX DRIVER BOARD
51
1.
Description
51
2.
Operation
54
SMA ACTUATOR CONTROL SYSTEM
57
CONTROL SYSTEM HARDWARE
58
A.
1.
2.
Personal Computer (PC) System
58
Data Acquisition Board
58
B COMPUTER SOFTWARE PROGRAM
C.
VII.
47
59
EXPERIMENTAL RESULTS
61
RECOMMENDATIONS AND CONCLUSIONS
63
A.
RECOMMENDATIONS
63
B.
CONCLUSIONS
63
APPENDIX A HEAT TRANSFER MODEL CALCULATIONS
APPENDIX B
Lab VIEW*
PROGRAM
"Wire Control
&
Status.vi"
65
73
LIST OF REFERENCES
77
INITIAL DISTRIBUTION LIST
79
vin
I.
A.
INTRODUCTION
MOTIVATION
Laparoscopic surgery currently involves the use of rigid arms supporting surgical
instruments that are inserted into the torso through a trocar.
Such systems are highly
constrained with respect to the maneuvers available to the surgeon.
overcome through the development of a
In this research,
articulated
composed of
five segments,
Figure
1.1
a conceptual rendition
motion
capability
The
is
controllable flexible surgical manipulator.
is
proposed
in
The design
stipulates
that
a flexible manipulator
motion can be achieved.
where each segment
of each segment
of the
will
This limitation can be
which very complex
the manipulator be
have three degrees of freedom.
will
flexible manipulator.
The
three dimensional
be provided through the use of three actuators.
actuators are to be constructed with shape
memory
alloy
(SMA)
material and a digital
control system will control the motion of the actuators and consequently, of the flexible
manipulator.
The manipulator's design
inch radius.
The
A
will
force of approximately
center space of the manipulator
fibers or cables for the control
to 10
allow
mm or less
of end
is
to perform a 90° to 120° bend within a six
it
two pounds
is
to
be resisted by the manipulator.
to be clear, allowing for the passage of optical
effector.
so that the manipulator can
fit
The diameter of the manipulator
is
limited
through the standard size trocar currently
in use.
The small diameter and hollow center space of the manipulator
actuators and control system be as small as possible.
for using
SMA
material.
more conventional
SMA
actuators.
of the material to be used
for
This
was
requires that the
the primary driving force
has a very high power-to-weight ratio compared to other
Also, the nature of
feedback control.
powering and monitoring/control systems
SMA allows for the electrical
This allows for the integration of the
in to a single
leads required.
1
resistance
system, reducing the
number of
The motion of the
arm will be
given from the keyboard of the control computer. In future, a
man-machine interface will be built so that
the flexible robot arm can be controlled by
voice commands of the surgeon.
controlled by
flexible robot
commands
Control Computer
electrical cables driving the actuators
are connected to the control computer
Tube for blowing air into the
arm for cooling the actuators
standard size trocar
Flexible robot arm with
a
hollow interior
simple mechanical device
to be used by the surgeon
for end- effector control.
End-effector to be connected to the end of the
flexible robot arm. An end-effector like a pair
of scissors, or a gripper will be controlled by
cables that will pass through the hollow space
within the flexible robot arm to a device that
will be controlled by the surgeon.
Figure
1.1:
shown. The
with the
A
conceptual diagram of the flexible manipulator
flexible manipulator's
commands being
sent
motion
will
A
be controlled by a
gripper end effector
digital control
from the keyboard of a personal computer.
is
system
This thesis discusses the concept of thermal inertia to describe the heating and
cooling characteristics of a
SMA
exploited in the development of a
elements using a
The concept of thermal
actuator wire.
leads.
SMA
This control system addresses the
SMA
actuator elements sequentially by selecting a corresponding
Using
this
SMA
method, each
actuator
is
is
control of multiple
new method of actuation and
minimum number of
inertia
sequentially
row and
particular column.
powered by a pulsed
current.
The
magnitude and duration of the pulsed current depends primarily on the environment which
is
cooling the
SMA
actuators and the
maximum number of
elements to be controlled
during a single powering cycle.
Open
resistance feedback, can be used to
compute the magnitude of the pulsed
pulse duration
B.
is
or closed loop control, based on electrical
current once a
determined.
BACKGROUND ON SHAPE MEMORY ALLOY
Shape memory
alloy material has the ability to
amount while the material
is in its
low temperature
transformation temperature causes
material
is
said to
"remember"
it's
state.
deform a
relatively significant
Heating the
SMA to
phase
its
to recover the low temperature deformation and the
it
shape before deformation [Ref
development of the control system, the
SMA chosen to be used as the
1].
For the
initial
was
a wire
actuator
form made of nickel-titanium, NiTi.
The mechanism
transformation
for the shape
memory
characteristic
is
based on the very complex
of the material between martensite and austenite.
transformation from austenite to martensite
is
The
solid
state
displacive, athermal (time independent), first
order (liberates heat), associated with a hysteresis, and occurs over a temperature span
which both phases
structure,
upon
volume change.
exist.
cooling,
Through Bain
is
strain
and
lattice invariant shear, the austenitic
transformed into a twinned martensitic structure with
Det winning the martensite
in
results in a significant
approximately 4 to 8 percent deformation. This deformation
is
little
shape change of
fully recoverable,
provided
that the applied stress level has not
austenite reformed
austenitic
exhibits
SMA that
the control system will cause the
it.
a
substantial
and martensitic phases.
transformation phases of the
flowing through
when
slip,
the material
heated and
is
[Ref. 1]
The NiTi actuator wire
between the
produced
It is this
SMA
resistance difference
in the
SMA
A command
0.235
3
6.45
lb/in
0.20Btu/lb-R
2282
Melting Point
gm/cm3
6.8 cal/mol.-°C
1250°C
°F
Heat of Transformation
10.4Btu/lb
Thermal Conductivity
10.4BTU/hr-ft-°F
24.19 kJ/kg
1
0.05 cal/sec-cm-°C
Thermal Expansion Coefficient
6
6
Martensite
3.67xl0- /°F
Austenite
6.11xlO- /°F
6.6xlO- /°C
6
6
11.0xlO- /°C
Electrical Resistivity
Martensite
Austenite
42 1 ohms/cir mil
ft
ohms/cir mil
ft
5
1 1
Linear Resistance (approx.)
0.010 inch diameter wire
0.44 ohms/inch
Transformation Temperature
129.2 °F'
0.173 ohms/cm
'
90 °C
Value calculated from figure provided by manufacturer.
Table
1.1:
from
material and leads to the
Metric
English
Heat
between the
actuator to be heated by an electrical current
Property
Density
difference
resistance
the control system will exploit.
Heating causes a phase change
Specific
electrical
Nickel-Titanium alloy physical properties for Flexinol™ Actuator Wire.
recovery of deformation which results
SMA actuator,
resistance of the
the
in
By monitoring
motion
the level of electrical
the control system will be able to determine the phase of
SMA material and therefore,
if
deformation has been recovered.
The NiTi actuator wire was purchased from the Dynalloy
CA. The
SMA
wires are marketed under the trade
The composition of
the nickel and titanium
is
predeformed shape.
Table
1
.
1
lists
almost exactly a
some of
located in Irvine
name of Flexinol™ Actuator Wires.
50%
nickel-titanium ratio slightly changes the temperature at which the
its
Inc.
ratio.
SMA
Varying the
wire remembers
the physical characteristics of the
SMA
wire supplied from Dynalloy.
This thesis investigates the use of
In Chapter
II,
the behavior of
electrical resistance
electrically heated
transfer
of
system and the
and cooled by the environment
actuators
is
is
SMA
wire
is
discussed
in
organized as follows.
transfer
developed
in
model of a
Chapter
III.
SMA wire
The heat
of the concept of thermal
Chapter IV.
The concept
of
inertia.
for the actuation
of the hardware developed for implementation of the
discussed in Chapter V.
elaborated on in Chapter VI.
this thesis research
is
is
specifically the relationship
The heat
will lead to the introduction
circuit description
actuation system
an actuator and
characterized,
is
SMA versus temperature.
model analysis
Actual testing of a
SMA
SMA as
A
control system developed for a set of
Chapter VII
is
SMA
concerned with conclusions for
and with recommendations for further study.
SMA RESISTANCE TEMPERATURE TESTING
-
II.
The data
in
the literature provided by the manufacturer, Dynalloy Inc., resulted
only a sketchy incomplete view of the behavior of
SMA
recommended
no data was provided
that the wire be heated electrically, but
The data
the wires behavior with different current inputs.
material.
that
was
in
The manufacturer
that described
was
furnished
a listing
This was the
for different wire diameters and an associated continuous current value.
continuous current which was recommended not to exceed to avoid material damage.
Only one graph was provided which related the
strain to the
Performance of the wire was only referred to
encouraged to explore the
were
the wire, which
The
listed in the
of the
product
SMA
broad generalities with the user
wire, given the general limitations of
literature.
resistance data listed in the product literature
manufacturer, but
was made
possibilities
in
was reported from
temperature of the wire.
was not determined by
different sources not readily available.
Accounting for changes
in
wire dimensions, as
it
was heated
Table
1.1.
to phase transformation,
data collection experiments were used to gain a clearer understanding of
behavior.
These experiments would determine the magnitude of the resistance
would
change as the temperature was varied and
also,
the resistance changes occurred due to the
SMA phase transformation.
The
temperature.
bath.
in
provide any further illumination on the resistance behavior discrepancy.
Two
SMA
attempt
to verify electrical resistance of the wire, but measured electrical resistance did
not correspond to the data published in the product literature and repeated
failed to
An
1
the
As
measured.
first
experiment involved the
In this experiment, the
the temperature
is
SMA's
SMA wire
is
identify the temperatures at
resistance behavior to changes in
to be placed in a variable temperature
varied, the resistance
of the
The second experiment explores the behavior of
heating electric current.
Both the
which
SMA
a
wire
SMA
test
segment
is
wire to an applied
resistance and strain are monitored as the input current
Per phone conversation with technical support personnel
March, 1993.
7
at
Dynalloy
Inc.
on
is
The
changed.
load placed on the wire
resistance and strain
A.
was
also varied in specific increments as the
was monitored.
RESISTANCE - TEMPERATURE TEST
A test
apparatus was designed to measure the resistance of an
to a constant stress while the temperature
actual test apparatus used.
The
temperature controlled bath.
the wire as the temperature
is
was
SMA wire with
A
digital
varied.
Figure 2.1
SMA wire subjected
is
a constant load applied
multimeter
is
a
diagram of the
is
submerged
d
varied.
a)
/po
Figure
2.
1
:
SMA Wire Resistance
-
a
used to determine the resistance of
HP-3456A Digital Multi-Meter
'
in
Temperature Test Apparatus.
The
SMA
wire used for the experiment was a 0.010 inch diameter wire provided
by Dynalloy. The nominal
The end supports
cm.
test length, L,
to the
SMA
mechanically crimped to the wire.
SMA wire between end
of the
supports
was 10.0
wire are stud ring terminal leads which were
Providing the means to suspend the
SMA
wire
in the
temperature bath and to attach the applied load, the ring stud terminal leads also attached
the multimeter resistance measurement leads to the
wire was used to suspend the
The
resistance of the
SMA
An
wire.
electrically insulated
SMA wire and weight in the bath from a table top
support.
SMA wire was measured with a HP-3456A Digital Voltmeter
manufactured by Hewlett-Packard.
In the four lead resistive
ohm
meter mode, the
digital
voltmeter measures the resistance of the two high end leads and of the two low end leads.
These resistance values are subtracted from the
total resistance
and low leads, leaving only the measured resistance of the
The temperature bath system
is
Rosemount Engineering Company (REC). The
and
fine adjustments, for the setting
Calibration
Bath from the
control panel consists of two dials, course
of temperature of the bath. The
a water and ethylene glycol mixture.
Mfl
SMA wire.
Model 91 3 A
a
measured between the high
Resistance of the bath fluid
fluid in the
was
in
bath
was
excess of 2.0
Temperature of the bath was determined using a Platinum Resistive Thermometer
(PRT).
The PRT, which has
NBS
tracability, is
immersed
Model 920A Commutating Bridge and galvanometer from
resistance of the
PRT. This
resistance
was then
in the
temperature bath.
REC was used to
A
determine the
correlated to a specific temperature using
the PRT's set of calibration tables.
B.
TEST PROCEDURE
For the resistance versus temperature
test
of the
SMA
attached to the bottom end support of the wire test section.
suspended
in the bath.
wire, a static weight
The
A room temperature resistance reading at
taken prior to starting the
test.
The
PRT
entire assembly
was
was then
no load for the wire was
resistance, correlated bath temperature,
and
SMA
wire resistance were recorded
between each
of readings for the
set
performed with a
recorded
is
each selected temperature. Time was allowed
at
gm
weight of 341.2
static
system to
test
For each data
dimensional aspect.
room temperature
incrementally from
is
1.1, is
to approximately a temperature
increased
20 percent greater
The transformation temperature,
90 °C, therefore, the maximum temperature was approximately 108
to
room
°C.
temperature.
RESISTANCE - TEMPERATURE TEST RESULTS
A
series
of resistance
SMA
behavior of the
complete resistance
behavior for the
be seen
that
-
temperature data runs were performed to verify the
resistance as temperature
-
was
varied.
The
temperature data runs.
plot
Figure 2.2
the resistance increases
initially
is
almost
As
flat.
SMA wire
From
temperature
SMA wire begins to undergo a significant
approximately 85 °C, the resistance of the
°C the resistance curve
as the
a plot of three
is
shows extremely
SMA wire resistance as the temperature is changed.
approximately 75 °C, the
By
was
the temperature of the bath
run,
The temperature of the bath was then incrementally reduced down
C.
wire resistance
not corrected due to changes in any
than the stated transformation temperature of the wire.
from Table
SMA
The
and 234.8 gm.
the total resistance for the test wire and
The experiment was
stabilize.
is
consistent
the plot,
it
can
At
increased.
reduction in resistance.
has begun to level off and by 90
the temperature
is
further increased, the
resistance also increases.
As
the temperature
is
resistance decreases as the temperature
resistance begins to increase.
temperature
is
lowered and
The
is
lowered
finally levels
approximately 80 °C when the
of resistance continues as the
off at approximately 57 °C.
is
The
resistance then
lowered.
in resistance as
to the start of formation of austenite.
until at
significant increase
continues to decrease as the temperature
The sudden decrease
The
lowered, the reverse trends of above are noted.
the temperature
This temperature
10
is
is
increased past 75 °C
is
due
referred to as the austenite start
temperature and labeled, T^. At the point where the resistance levels
austenite has
The point
completed.
annotated as T^.
As
the temperature
is
is
the austenite
called
is
T^
is
is
temperature and
is
the symbol used to
By 57
called the martensite start temperature.
formation has completed and the resistance of the wire
transformation. This point
finish
reduced, formation of martensite results in the
increase in resistance which starts at approximately 80 °C.
indicate this point which
the formation of
off,
what
called the martensite finish temperature,
it
°C, martensite
was
prior to the
T^.
SMA WIRE RESISTANCE VS TEMPERATURE
1.9
1.85
1.8
1 1.75
o
i
1.7
1
1
*1.65
1.6
Data Run #1 w/Load=341 .2gm
Run #2 w/Load=341 .2gm
Data Run #3 w/Load=234.8gm
Data
*
1.55
1.5
20
30
40
50
60
70
80
90
100
110
Temperature, degrees Celsius
shows the
SMA
wire's resistance response to varying temperature for the static loads indicated.
The
Figure
2.2:
SMA
resistance recorded
Wire Resistance versus Temperature.
is the total resistance for the
11
The
plot
nominal wire length of 10
cm (T<T Mf).
Table 2.1 summarizes the results of the resistance
transformation resistance difference, AR,
at
room temperature
resistance
is
a
is
-
temperature
test.
The
the change in resistance measured in the wire
to the resistance at the point of transformation.
This change in
decrease from
at
roughly
11
percent
the
starting
resistance
temperature.
Resistance
-
Temperature Test Results
Temperature
Point
T
75
T
85
Tx Ms
80
T
57
Transformation
Table 2.1:
AR
0.2
Summary of Resistance
12
-
(°C)
ohms
Temperature Test Results.
room
HEAT TRANSFER MODEL
III.
After the
SMA
of
characterization
mathematical model governing the heat transfer
was
to aid in the understanding of
and subsequently cooled during
of the wire response to an
A.
the
wires,
in
next
the wire.
goal
study the
to
The purpose of
what was occurring with the
testing.
was
SMA
wire as
the
model
it is
heated
Thus, the model would allow for the prediction
electrical driving current.
MODEL DESCRIPTION
A
model.
SMA
control
volume was established as shown
Figure 3.1 for the heat transfer
The dimensions of the control volume are the diameter and length of the
wire to be used for the current characteristic testing.
volume dimensions and
SMA
in
is
ambient
the control
air is
The
subjected to an electrical current, the magnitude of which
depends on the particular phase that
in
lists
also contains other terms used in the heat transfer model.
wire control volume
environment
Table 3.1
actual
assumed to
AIR
desired for the
is
SMA.
A
free
convection
exist.
E oui
T^.h
J*
:x
Current, I
:
:
:
*x':
'
:
:
.
^g^hi,
,,,,,;;;;'..
SMA Wire
r\JXr*
Control
i'
Volume
Figure 3.1: Conservation of energy for a control volume of
13
SMA wire shown.
SMA Test Wire Heat Transfer Model Parameters
symbol
Description
d
0.025
cm
length (austenite)
L
7.184
cm
load
W
diameter
a
237.2 grams
%8
% working strain
%
4.7
m
7.522
cm
volume (martensite)
V
0.004
cm 3
surface area (martensite)
A
0.587
cm 2
mass
M
monitoring current
I
heating current
Is
length (martensite)
s
2.479*
m
T amb
ambient temperature
0.1
amp
2.0
amp
25
kg
K
296.2
h
heat transfer coefficient
10" 5
W/m * K
2
Table 3.1: List of test wire parameters for the Heat Transfer Model.
Figure 3
heat
transfer
.
1
shows
model.
all
the possible energy terms that
Appendix
A:
Heat
Transfer
may be
Model
considered for the
Calculations
MATHCAD™ contains the calculations performed for the heat transfer modeling.
14
Using
B.
HEAT TRANSFER MODEL EVALUATION
1.
Phase
In the
before
3.1.
This current
monitoring current results
It is
desired to
The
wire
term,
is
know
first
st
,
is
Due
Is.
in
subjected to only a monitoring current,
I
m as
,
used to determine the resistance value of the wire
to the
SMA
wire's electrical resistance,
the
generation of thermal energy inside the control volume.
in the
law of thermodynamics
shown
is
the wire temperature due to the energy generation.
assumed to be
E
SMA wire
phase, the
heated with current
is
it
Monitoring of SMA Wire with Monitoring Current, Im
initial
Table
listed in
1:
2
in
is
applied to the
SMA wire
a thermodynamic steady state condition,
Figure 3.1
is
equal to
control volume.
The
thus the energy storage
Therefore, the rate of thermal energy
0.
generation equals the rate of energy leaving the control volume:
Eg
where the
rate
=
E out
(3.1)
of thermal energy generation
is
a result of the electrical resistance heating:
Eg =I2 xQ m xL m
and the
rate
(3.2)
of energy out
is
due to the convective heat transfer from the surface of the
Eout
=
hxA
SMA wire:
s
x (Ti
- Tamb )
(3.3)
Substituting Equations 3.2 and 3.3 into 3.1:
I
2
xQ m xL m =hxA
s
x (Ti
- Tamb )
(3.4)
Evaluation of the heat transfer model was performed
utilizing Reference 3.
15
From Equation
Ti
=
substituting in heat transfer
(0.1
_
^
•
X
—
1
-
During
of I
.
s
2:
start,
X
jL/i
— + raw 6
1
.
1
(3.5)
values:
amp) 2 x (0.173
25
-^)
= 304.88
•
g) x (7.522
cm)
•
x
(°- 587
-
2
cw2 )
£
•
Heating of SMA Wire with Input Current,
this phase, the
This current
austenite
,.;
2^
SMA wire can be determined:
|
T,
Phase
Lc
jr-
model Table
(
2.
temperature of the
3.4, the equilibrium
is
SMA wire is subjected to a short
used to heat the martensitic wire to
T^,
and
then
supply
to
the
its
duration step pulse current
transformation temperature of
energy
transformation at the austenite finish temperature, T^,
Is
The
necessary
to
complete
the
short duration of the applied
current allows for the heat transfer out of the control volume,
E out as shown
in
Figure 3.1,
to be neglected.
From
the
first
of control volume.
law, the thermal energy generation will increase the internal energy
The
increase in internal energy will
first
heat the wire to the point of
transformation and then cause the desired phase transformation:
E g = AE
st
=
E h +E
(3.6)
t
16
where the energy required to heat the wire to the point of transformation:
E h = pxVxCp
x (TAs
- T)
(3.7)
t
and the energy required for the phase transformation:
E
t
=Mxh
(3.8)
t
The thermal energy generation
Eg =I 2 x
is
equal to Equation 3.2 over a time period At:
Q m xL m x At
(3.9)
In order to determine the time necessary to heat the wire to the point of transformation,
consider Equations 3.7 and 3.9, solving for the time period, At h
£Xh
px VxC p x(TAs -Tj)
=
t2
1
substituting in heat transfer
(6.505
^h
=
•
£j)
nm
X
l>l
X
•
(310)
T
L,
m
model Table
x (0.004
1.1
cm3) x
values:
(0.2
•
^) x ((343 - 304M)K)
:
(2
Ath
From
:
amp) 1 x (0.173
= 0.152
this point, the
transformation.
•
1
•
sfe) x (7.522
•
cm)
-sec
thermal energy generated
Combining Equations 3.8 and
can be calculated:
17
is
equal to the energy needed for the phase
3.9, the
time for the phase transformation
'
*t= n
(3.11)
>m
substituting in heat transfer
^
^m
model Table
1.1 values:
(2.479. 10- 5 -£g)x (24.19 -g)
At t =
(2
•
amp) 2 x (0.173
•
§) x (7.522
•
cm)
Al = 0.115 -sec
t
SMA wire to complete phase transformation
Therefore, the total time required to heat the
is:
At = At h + At = 0.267
•
t
3.
Phase
The
final
3:
Cooling of the
sec
SMA Wire
phase of the wire characterization
wire while monitoring the resistance as
austenite to martensite.
Of particular
test involves the cooling
concern
will
amp
be discussed
later.
T^. The time
SMA
undergoes the phase transformation from
it
is
the length of time that
temperature of the wire to decay from the austenite
martensite start temperature,
of the
calculated
is
finish
a
is
required for the
temperature,
maximum
limit
TM
,
to the
of concern, as
Therefore, neglecting the relatively low monitoring current of 0.1
will generate a small error to the conservative direction, the true
decay time
will
be
3.1, the rate
of
longer than the calculations will show.
Using the conservation of energy for the control volume of Figure
energy flow out results
in
an equal rate of decrease
-E out = E st
in
energy storage:
(3.12)
18
To
simplify the model, an assumption
made
is
that the temperature in the wire
distributed throughout at any particular time as the wire
basis of the
lumped capacitance method which
equation form
for evaluation.
A
uniformly
This assumption
on the requirement
See Appendix
have minimal temperature gradients.
lumped capacitance method
relies
cooling.
is
is
is
the
that the material
for the justification to use the
Equation 3.12
is
expressed
in its differential
of:
dT
pxVxCp x^
-h x A s x (T- Tamb ) =
(3.13)
dt
An
expression
is
substituted for the temperature difference term to simplify the
integration:
6 =
T— Tamb
and then
—=—
at
substituting Equation 3. 14 a
(3.
14 a
& b)
at
& b into Equation 3.13:
dO
-hxA xQ = px VxCp x^j
(3.15)
s
Rearranging and integrating, see Appendix A, Equation 3.15 results
in the
expression for
the transient temperature response:
Two common
first is
^J^
e
JZz^ =e
«/
(if- lamb)
substitutions can be
made
(3
, 6)
for the term inside the exponential operator.
The
px Vxtp
the resistance to convective heat transfer, R^
19
)xf]
Rt =
7TT
h xA
(317)
s
and the second
is
C
the lumped thermal capacitance,
t
=
C
:
t
pxVxCp
(3.18)
Combining Equations 3.17 and 3.18 and simplifying
time constant, x
yields the expression for the thermal
:
t
Tt
=
R xC
t
(3.19)
t
using the expressions for Equations 3.17 and 3.18:
=
T
'
(
^J)X(pXFxC/,)
substituting in heat transfer
model Table
(6.505
1
which
value.
is
- 13.835
1
values:
£j) x (0.004 cm3) x
•
•
(25-^)
it
.
(320)
x (0.587-
(0.2
•
-^)
cm 2 )
sec
•
the time required for the temperature of the wire to decay to 0.368
Substituting Equation
temperature of the wire results
T=Tamb + Q
l
3.17,
3.18,
its
original
and 3.19 into 3.16 and solving for the
in:
xexp(^)
(3.21)
20
where
f —
i
I
(3.21 a)
1 amb
i
See Figure 3.2 for a plot of Equation 3.20, the transient temperature response of
SMA
wire undergoing free convection cooling. [Ref. 3]
The length of time required
for the
SMA
T^ can be determined by solving Equation 3.21
wire temperature to decay from
for time
,
t,
and substituting
TM
T^ for T
to
and
;
Tms for T:
380
360
\
340
I
\.
^\
i
i
320
i
300
280
10
30
20
40
50
SMA Wire Temperature Response
0.368 Ti
Thermal Time Constant
Figure 3.2:
cooling.
Transient temperature response of
Lumped
response of the
SMA wire
undergoing free convection
capacitance method used to evaluate the transient temperature
SMA wire.
21
t
=
T t x\n(
TMs
Tamb
(3.22)
)
Q
where
= Ta/~ Tamb
6/
substituting in heat transfer
t
model Table
= (13.8835
The time required
for the
(3.22 a)
•
1.1 values:
ln(f§™§) = 2.244
sec) x
•
sec
SMA wire to decay from the austenite finish temperature to the
martensite start temperature
is
2.244 seconds. This
is
8.4 times longer than the total time
required to heat the wire and 19.5 times longer than the time required for transformation.
THERMAL INERTIA
C.
From
the above analysis,
it
can be seen that there
between the heating phase and the
temperature
is
down
initial
is
a significant time difference
cooling phase from the austenite finish
to the martensite start temperature.
The time required
to heat the wire
very short compared to the time experienced by the wire for the temperature to decay to
the start of reverse transformation.
maintain this condition, this
is
For the action of causing the wire to contract and
a favorable predicted time difference.
or delay can be referred to as the "thermal inertia" of the system.
exhibit a delay in reverse phase transformation not only
the
SMA
material, but also
analysis has
shown
the cooling time
would show
is
due to the
due to the nature of convective heat
that the heating phase time
is
The time
The
SMA wire
should
hysteresis behavior
transfer.
of
The above
a function of the input current,
a function of the convective heat transfer conditions.
that doubling input currents
difference
I
s
,
while
Similar analysis
would shorten the heating phase time by 50
22
percent while the cooling time would remain constant provided the convective heat
transfer conditions did not change.
Further manipulation of Equation 3.16 yields an expression for the energy loss due
to convective heat transfer for a
EL
= p x Vx
known time
Cp
x 6/ x
[1
period:
- exp(^)]
(3.23)
where
Qi
= (TAf-Tamb )
(3.23 a)
Substituting in the time to the point of reverse transformation calculated using Equation
3.22, the total energy loss to the point of transformation
EL =
-
(6.505
•
-£j) x (0.004
-cm 3 )x
(0.2
•
is:
-^) x (363 - 296.2)
•
K...
m - exp(t 2.244 sec m
X[1
)]
13.835.sec
•
El = 0.203
This energy
to reheat the
loss,
EL
,
-joules
can then be substituted into Equation 3.10 to yield the time needed
SMA wire to the austenite finish temperature:
1
X
z>L
m X
J_j
m
For the heat transfer model investigated,
substituting in heat transfer
values:
23
model Table
1.1
At rh
0.203 -joules
=
(2
•
amp) 2 x (0.173
•
«) x (7.522
•
cm)
At rh =0.041 -sec
Or
if a
cycle time span
reheat the
known, Equation 3.16 can be solved for the current needed to
is
SMA wire to the T^ temperature:
Irh
—xQ
= JtAt
\
77
rh
substituting in heat transfer
cycle time of Dt^
= 0.267
m
xLr-a
model Table
(3
1
.
values, energy loss
1
EL
-
25 )
and assuming a reheat
sec:
0.203 -joules
(0.267
I rh
•
sec) x (0. 173
current
is
•
cm)
•
due to the heat transfer behavior of the
indicates that
wire, considerably less heating time
if
*) x (7.522
= 0.76 amp
The above evaluation
region,
•
is
SMA
required for maintaining the wire in the austenite
the current remains constant.
Alternately, for a given reheat cycle time, the
less than required to heat the wire.
24
IV.
SMA RESPONSE TO AN ELECTRIC HEATING CURRENT
The heat
test elements.
resistance
and
behavior
this
transfer
The next
model provides an expected behavior for the
step
was to
electrically heat the
strain to establish the actual
is
A
test apparatus
wire test element.
wire
is
was designed
Figure 4.1
positioned within the
load to be applied to the
electric current
in
to a
SMA
testing that
test
was
wire under a
wire length and resistance.
passed through the
is
SMA wire
SMA
potential drop across a
The
Test Stand.
resistor
through the resistor and therefore the
the
SMA wire is measured
of the wire.
A
is
is
wire to be measured.
is
determined.
is
The voltage drop across
used to calculate the resistance
A
personal computer with a data acquisition card
test.
Wire Test Stand was designed
for the specific
purpose of testing the
wire's electrical resistance and strain response to an electric current input.
It
the Naval Post Graduate School Mechanical Engineering machine shop.
constructed almost exclusively of aluminum components.
inches,
forms the stand foundation.
The
used to control the output of the dc power supply
used to record and process the data from the
SMA
SMA
probe and
measured and using ohm's law, the current
SMA wire
which provides the current to the wire.
The
A
with the wire.
in series
and together with the current
function generator
test stand allows for a constant
and for the motion of the wire to measured. Current
wire and a resistor
known
A SMA test
a diagram of the actual test apparatus used.
SMA Wire
SMA
measure the resistance and motion of a
to
associated target allow for the contraction of the
is
The
Once
element.
RESISTANCE / STRAIN - CURRENT TESTING
A.
is
SMA wire test
behavior of the
constant and varying load while measuring the change
actuators or
wire and measure the changes in
determined, a control system can be persued.
performed involved applying a heating
SMA
A
12 inch high
25
U
A
frame
one inch thick
is
was
built at
The stand
plate,
is
29 x 8
the upper support for the
SMA
The
test wire.
member
is
U
frame legs are one inch diameter aluminum bars and the cross
a one inch square bar that
center of the cross
bar holds the
member
is
a J
is
6.5 inches long.
hook welded
to a threaded bar.
test
hook assembly made up through
wire
is
The
J
hook
constant load applied on the
The opposite
the beam.
SMA test wire.
The
a three inch square by six inch high column.
wire
threaded
is
12 inches.
A
plain
carbon
fixed
The
hook below the beam
J
The weights provide
end of the cantilever beam
free distance
steel target is
mounted
at
Power Supply
Figure
4.
1
:
SMA Resistance/Strain
26
-
the
a steady
is
set in
the end of the
SMA Wire Resistance and Strain Testing Apparatus
DC
is
J
between the column and
cantilever beam.
HP-6282A
-
connected to a cantilever beam via a double
support for an eye bolt use to hang threaded brass weights.
SMA
a hole drilled in the
SMA test wire in position below the U frame cross member.
The lower end of the
the
Through
Current Test Apparatus.
To determine
electromagnetic displacement transducer,
A
target motion.
full
scale reading
adjusted so that
A
resistor
rated
resistor
is
power of 30
is
known
to measure the
at a target to
J
is
0.500 inches
transducer distance of 0.050 inches
hook allows
at
0.487
The
ohms and
resistor
SMA
with the
in series
By measuring
watts.
flow can be calculated.
Model PA11503, was used
wire,
SMA
for the
wire to be
within the transducers range of operation.
was wired
precisely
Electro-Mike®
The upper threaded
motion
its
an
test
of 10.00 volts occurs when the target
from the transducer. Zero scale occurs
and a 1.000 volt output.
SMA
of the
deflection
the
is
test wire.
The
a variance of less than
resistance of the
percent up to the
1
the voltage drop across the resistor, the current
in series
with the
SMA
wire and, therefore the
same current flows through both elements.
The current
is
supplied by a
The power supply
Hewlett-Packard.
transient recovery time
HP-6282A DC Power Supply manufactured by
is
rated for 0-10 volts at 0-10
amps and has
of less than 50 msec for an output recovery to within 15
a
millivolts
following a current change in the output equal to the current rating of the supply or 5
amperes, whichever
is
Remote programming of the power supply output can be
smaller.
performed using resistance of voltage as the programming device.
can be done
tests
in
Remote programming
both the output modes of constant current and constant voltage.
conducted, the power supply was used
in the
remote programming mode
constant current output using voltage as the programming device.
current output
is
set
For the
In this
by the programming voltage and the voltage output
is
for
mode, the
allowed to vary
to maintain this output current. [Ref. 4]
The programming voltage was provided by a function generator manufactured by
WAVETEK. Model
function generator
145
was used
trigger data acquisition.
signal or
it
is
can operate
in
MHz
The output of the
a
20
to
program the output current of the power supply and
Pulse/Function Generator.
to
The function generator can continuously generate an output
a remote trigger or manual trigger mode.
27
Data acquisition was performed by an
IBM
compatible personal computer (PC)
PC
with an analog and digital I/O data acquisition board installed. The
a
DX2 ISA
80486-66MHz
mother board including an
Intel
integrated enhanced numeric coprocessor, 32-bit local bus, 16
MB
The data
hard disk.
acquisition board
multifunction I/O board which features:
analog inputs, 8
B.
digital
I/O
,
is
80486 processor with an
MB
of
RAM,
ADC, 200 kHz
DACs with voltage
and a 540
AT-MIO-64F-5
a National Instruments®
12-bit
and two 12-bit
system consists of
sampling
rate,
up to 64
outputs.
TEST PROCEDURE
A
of
series
were conducted to determine the behavior of a
tests
As
electric heating current.
the wire
is
SMA
wire to an
heated by, for example, a step function electric
heating current, the resistance and the strain will be calculated, recorded, and plotted.
The
WAVETEK
therefore no signal
front panel.
The
offset.
function generator
was generated
The
signal function
DC
offset
heating current
was
until
it
was operated
was manually
current
was
diameter
maximum
the manufactures
SMA
both with a
heating current
signal function
was approximately
recommended maximum continuous
were performed with the
dials
DC
that the level of pre- and post-
The
wire so that overheating did not occur.
offset selections
step,
This current allowed for the determination of the
wire resistance while minimally heating the wire.
voltage was such that the
triggered using the switch on the
shape chosen was a triangle and a
programming voltage was such
0.1 ampere.
manual trigger mode,
in the
Both the
SMA
programming
amp.
1.0
This
current for the 0.010
signal function
and
"
DC
on the front of the function generator
panel.
The duration of the heating cycle was varied by
on the
front panel
adjusting the frequency/period dial
of the function generator.
The data recorded
for each test
supply, the voltage drop across the
the transducer voltage.
sequence was the voltage output of the
SMA
test wire, voltage
drop across the
DC
power
resistor,
and
Data acquisition was conducted using the computer programming
28
A
software Lab VIEW®.
included in Chapter VI
more
programming software
detailed description of this
SMA ACTUATOR CONTROL SYSTEM.
A Lab VIEW® program titled "SMA wire test SE
Trig.vi" configures the National
-
data acquisition board, specifies the number of scans of data points to
Instruments®
record, the scan rate, channels to access and record, the trigger channel,
and a
pretrigger scans,
file
The program
to write the data to.
A
collected and has the option of not saving the data collected.
panel and the diagram of the program are
The data
was
collected using the
written to a
[Ref. 4]
file
was used
SMA
drop across the
on the
PC
in
system hard
copy of the software front
Appendix B.
"SMA
Lab VIEW® program
The
series resistor data
This
test wire.
disk.
SMA
test
was used to
SMA
wire to determine the
SMA test wire
strain
The
first
wires resistance.
plot
is
SMA
was
electric
is
of
tests involved a fixed heating current with a fixed heating cycle time.
The
of
tests
tests pertained to a
were performed on
SMA
a
wire with a fixed
varied.
is
stated above, the
Lab VIEW® program
to configure the National Instruments®
scans, scan rate
was 150
"SMA
static
is
wire
29
test
weight and a constant
last set
of
tests
was
varied.
test
data acquisition board.
scans/sec, and the
wire
Then, the
conducted with the heating cycle time fixed while the current
2250
MATLAB®
The
of
heating current while the heating cycle time
As
MATLAB®
SMA test wire's
segment.
different series
series
Trig.vi"
and resistance versus time and the second plot
RESISTANCE / STRAIN - CURRENT TEST RESULTS
second
SW
of the three curves of
C.
of
-
the data collected for the voltage
SMA test wire resistance versus time.
first series
test
calculate the current passing
the
Two
wire
The software program
was then used with
then used to generate two sets of plots.
heating current,
shown
number of
also displays the data
to analyze and process the data and calculated the
resistance and strain.
through the
is
-
SW Trig.vi"
was used
The number of scans was
number of pretrigger scans was 75
scans.
This combination resulted
of pre-trigger
data.
The
positively past 0.4 volts.
For both
sets
in
a test duration of 15 seconds of data with 0.5 seconds being
was
trigger
Table
4.
of tests, the
1
DC
set to the
power supply voltage
summarizes the program
SMA test
Therefore, a free convective situation
convective heat transfer coefficient.
wire were
test parameters.
in a relatively
was assumed
increasing
still
air
environment.
to exits but with an aggressive
Reference 3 provided guidance on convective heat
transfer coefficient values.
Program Test Parameters
number of scans
2250 scans
scan rate
1
50 scans/sec
pretrigger scans
75 scans
test duration
15 seconds
pretrigger time
0.5 seconds
DC Power
trigger source
Supply
trigger level
0.4 volts
trigger slope
rising
Table 4.1: Lab View program test parameters for collecting
30
SMA wire test data.
1.
Variable Load Testing
For the
beam
first series
only (no weight),
summarized and
plots,
listed in
of tests, four different loads were used. The loads consisted of
The parameters
130.6 gm, 237.2 gm, and 344.2 gm.
SMA test
Table 4.2 for the variable load tests of the
1) current, resistance,
and
strain versus time
MATLAB®
The
output a programming voltage signal
triangle function.
was
set to
The voltage
signal
Two
and 2) resistance versus time, were
generated for each data run using
function generator
wire.
are
and are shown
in
Figures 4.2 through 4.5.
had a heating cycle lasting for
5
in
the shape of a
seconds and the off
or monitoring cycle lasting for the remaining portion of the test duration, 10 seconds.
Review of Figures 4.2 through 4.5 shows
are practically identical.
the wire increases.
The
For NiTi
martensite to austenite [Ref. 6 and
more
strain is
recovered when the
is
related to the different mechanical properties
alloys,
7],
Young's Modulus of
on the wire.
The
reveal the extent of recovered strain in the
SMA
indicate the phase
from
mechanical behavior,
SMA
wire
is
independent of the
austenite and martensite resistance of the
level.
is
in
of
SMA wire is heated at higher stress levels.
constant and independent of stress
wire
Elasticity increases
Because of this difference
Table 4.2 also shows that the resistance of the
stress or load placed
and monitoring cycles
experienced by the wire increases as the static load on
strain
This behavior
austenite and martensite.
that the heating
of the SMA.
31
SMA
Thus, resistance monitoring will not
wire.
Resistance monitoring will only
Variable
wire length (austenite)
ambient temperature
:
:
Load
8.
1
3
Test
cm
23.0 °C
load
% strain
Q, austenite
Q, martensite
% Q change
beam only
0.71
1.24
1.41
12.06
130.6
gm
2.19
1.25
1.42
11.97
237.2
gm
gm
4.4
1.25
1.41
11.35
5.08
1.25
1.43
12.59
344.2
Table 4.2
testing
:
Variable Weight Test. Test parameters and results for the variable weight
of the
SMA test wire.
32
SMA Wire Response to Current Input
</>
a.
E
w
c
g
o
^
Applied Load =
Beam Only
10
15
Time, sec
Time, sec
Figure 4.2
:
Variable Load Test,
33
Beam
only.
SMA Wire Response to
<0
E
CD
C
S?
i_
rj
o
Current Input
^-^~^^
"\
_c
c
Applied Load = 130.6
gm
c
2S
5
10
15
Time, sec
1.6
E
o
1.5
.c
fli"
1.4
o
c
CO
**
V) 1.3
Applied Load = 130.6
v>
d)
gm
or 1.2
1.1
10
15
Time, sec
Figure 4.3
:
Variable
Load
34
Test, 130.6
gm.
SMA Wire
Response
to Current Input
1.6
tn
E
x:
o
s~\
1.5
1.4
8
r
\\
2 13
Applied Load = 237.2
at
O
gm
*1.2
1.1
15
10
Time, sec
Figure 4.4
:
Variable
Load
35
Test, 237.2
gm.
SMA Wire
1.6
CO
e
sz
o
to Current Input
XA
1.5
1.4
Response
/
\
t
c
CO
1.3
Applied Load = 344.2
«0
<1>
gm
£T 1.2
1.1
10
Time, sec
Figure 4.5
:
Variable Load Test, 344.2 gm.
36
15
Constant Load Testing
2.
For
this series
of
tests,
the load applied to the
The duration and magnitude of the
constant.
the wire's resistance and strain
voltage signal shape
was
electric heating current
current.
was
were recorded.
1.0
amp, the
the step function
was increased while
maximum recommended
was
initial
continuous heating
started at 5 seconds and reduced to the
From
this point, the
amplitude of the
the time of the step duration remained constant.
1) current, resistance,
and
strain versus time
MATLAB®
and 2) resistance
and are shown
in
Figures
4. 13.
the heating cycle time
cause a phase transformation
heating current, the
From
varied while
The function generator programming
versus time, were generated for each data run using
As
was
are summarized and listed in Table 4.3 for the constant load test of the
SMA tests wire. Two plots,
4.6 through
wire was maintained
electrical heating current
point that complete transformation did not occur.
The parameters
test
a step function and of sufficient magnitude such that the
The duration of
current step function
SMA
is
is
reduced, a point
not meet.
energy required
reached when the energy needed to
increasing the magnitude of the electric
again reached and phase transformation occurs.
is
the evaluation of the heat transfer
By
is
model
in
Chapter
III,
for a heating current of 2.0
amps, the heating time required to cause transformation was 8.4 times shorter than the
time required to decay to the phase transformation point.
SMA
amp
electric heating current
was
0.5 seconds while the decay time
and the
was
times longer than the heating cycle time.
test wire's
response
2.5 seconds.
The
with
this constant
is
a plot of the 2.0
The heating
cycle time
The decay time measured
is
5
Chapter
III
It
is
important to note that the
has been sufficiently demonstrated
load testing.
In Figure 4.6
what
in
is
difference can be attributed the inaccuracies
associated in simplification of the heat transfer model.
concept of thermal inertia introduced
Figure 4.12
and
4.7, the resistance
curve indicates that excess heating beyond
needed to cause the phase transformation of the
37
SMA wire
is
taking place.
The
of the
resistance
SMA
reduction in resistance occurs
and then
austenitic start
A
increases as the temperature of the wire increases.
finish
when
sudden
the temperature of the wire passes through the
temperature points. As additional energy
is
supplied to the
wire, the temperature continues to increases, resulting in an increase in the resistance
When
the wire.
the heating on the wire
drop and the resistance also
is
of
stopped, the temperature of the wire starts to
starts to decrease.
At the martensitic
resistance begins to increase as the transformation takes place
The
start
temperature, the
increase in resistance
continues to completion of the martensite transformation and then the resistance begins a
gradual reduction due to cooling of the wire.
Constant Load Testing
constant load
:
237.2
gm
wire length (austenite)
ambient temperature
Heating
heating
current
cycle time
% strain
a,
:
:
8.13
cm
23.0 °C
transformation
austenite
martensite
change
time
1.0
amp
5.0 sec
-4.73
1.18
1.36
13.24
6.0 sec
1.0
amp
2.5 sec
-4.62
1.2
1.38
13.04
3.0 sec
1.0
amp
1.5 sec
-4.53
1.21
1.39
12.95
1.0 sec
1.0
amp
1.0 sec
-3.85
1.25
1.39
10.07
0.5 sec
1.0
amp
0.5 sec
-0.51
1.41
1.36
-3.68
-0 sec
1.5
amp
0.5 sec
-4.43
1.22
1.38
11.59
sec
2.0
amp
0.5 sec
-4.63
1.21
1.39
12.95
2.5 sec
2.5
amp
0.5 sec
-4.57
1.2
1.37
12.41
3.0 sec
Table 4.3
testing
:
Constant Weight Test. Test parameters and results for the constant weight
of the
SMA test wire.
38
SMA Wire
CO
Response
to
Current Input
%2
«J
I
amm
\
J
o
Applied Load = 237.2
o
c-2
gm
^y^
c
*-»
c
2
£
10
15
Time, sec
Time, sec
Figure 4.6
:
Constant Load Test, th
39
=
5.0 sec, Is
=
1.0
amp.
SMA Wire
a
Response
to Current Input
E 2
(0
/
\
lo
o
c-2
^
y/
]£
.-4
c
\
Applied Load = 237.2
gm
V
i
S
W_6
^
10
15
Time, sec
Time, sec
Figure 4.7
:
Constant Load Test, th = 2.5 sec, Is
40
=
1.0
amp.
SMA Wire Response to
<0
Q.
Current Input
E 2
J~
lo
3
o
"V
A
c-2
?
Applied Load = 237.2
\
v
c
gm
~~"
J
#
10
15
Time, sec
1.5
|
1.4
o
<D
Applied Load = 237.2
A
gm
j\
81.3
31.2
1.1
10
15
Time, sec
Figure 4.8
:
Constant Load Test, th = 1.5 sec,
41
Is
=
1.0
amp
SMA Wire Response to
Current Input
£ 2
n
io
-J
"\
o
I
Applied Load = 237.2
gm
c
2
55 .q
*
10
15
Time, sec
Time, sec
Figure 4.9
:
Constant Load Test, th = 1.0 sec,
42
Is
=
1.0
amp.
SMA Wire
CO
Q.
E
Response
to Current Input
2
to
c
n
_j
\
I
O
c
Applied Load = 237.2
gm
c"
S
CO
15
10
Time, sec
1.5
(0
|
1.4
™*
o
Applied Load = 237.2
v*
gm
7
CD
1 1.3
<o
55
5
1.2
1.1
15
10
Time, sec
Figure 4.10
:
Constant Load Test, th = 0.5
43
sec., Is
=
1.0
amp.
SMA Wire
£ 2
w
c
£o
Response
to Current Input
A
o
1
^~~
\
c
^/
Applied Load = 237.2
gm
15
10
Time, sec
1.5
1.4
Applied Load = 237.2
A
gm
*y*~^
'
§1.3
(0
CO
w
5
1.2
V
1.1
15
10
Time, sec
Figure 4.11: Constant Load Test, th = 0.5 sec,
44
Is
=
1.5
amp
SMA Wire
V)
Q.
Response
to Current Input
E
—
*=
•
•
*
V.
3
o
|c -2
#
Applied Load = 237.2
I
gm
4
rf"
1
10
;£
15
Time, sec
1.5
4
Applied Load = 237.2
1.4
gm
^^^A-^^^^V-
81.3
1«
•
1
7
1.1
10
15
Time, sec
Figure 4.12
:
Constant Load Test, th = 0.5
45
sec., Is
=
2.0 amp.
SMA Wire Response to
(0
Q.
Current Input
c
OS
2
_-
c
*
o
•
•
a>
i_
i—
*
°
^^~~
2
\
I-
—
U-
Applied Load = 237.2
"
gm
1
w -6
10
2*
15
Time, sec
1.5
Applied Load = 237.2
1
gm
*B
1.4
o
-
""V- "'^^-^--'^JKm*
:
"
:
g1.3
CO
+->
.52
a:
1Z
f^_
^>
1.1
15
10
Time, sec
Figure
4. 13
:
Constant Load Test, th = 0.5 sec,
46
Is
=
2.5 amp.
V.
PROTOTYPE TEST BOARD AND ACTUATOR MATRIX
DRIVER
In Chapter
demonstrated
heating the
in
III,
the notion of thermal inertia
Chapter IV.
Now
was introduced and was subsequently
a control and powering system for discontinuously
SMA elements of a manipulator is considered.
This system
will heat the
SMA
elements sequentially using a cycle of short current pulses and relatively long periods of no
Due
current.
to thermal inertia, a
SMA
element can be alternately heated to phase
transformation with a short current pulse and then no current applied while other elements
Before the
are heated with a short current pulse.
phase transformation,
it is
Actuator Matrix Driver
SMA
element can cool to the point of
heated again by a short current pulse.
(AMD)
and
is
designed to use a
This system
is
called the
minimum number of
required
leads by fully integrating the powering system with the control system.
The configuration of the
SMA actuators was based
motion requirements of the manipulator.
SMA
test
physical dimensions and
board was designed to
test the
actuator control and powering system and simulates the manipulator's intended
design for
A.
A prototype
on the
SMA actuator location.
PROTOTYPE TEST BOARD
The
size restrictions
of the manipulator necessitated that the motion requirements
be met with the minimum number of elements.
Accordingly,
through the use of three actuators per segment.
For the
3D
motion was realized
initial
manipulator would be developed using a total of five (5) segments.
actuator configuration results in a total of fifteen (15)
designed and constructed to simulate this arrangement.
47
SMA
actuators.
investigation,
the
The manipulator's
A
test
board was
1.
Description
The
SMA
actuator prototype test board, designed and constructed to simulate the
operation of the manipulator,
show
is
in
Figure
The prototype's base board
5.1.
is
constructed of 0.5 inch Plexiglas with overall dimensions of approximately 12 inches wide
by 25.5 inches long.
on the bottom
Stiffening
is
provided by four
1
inch square ribs running lengthwise
of the board.
side
Arranged on the base board are
SMA test
fifteen (15)
This pattern simulates the envisioned arrangement of
manipulator design. The
indicate
actuator.
when
a
Each
SMA test
command
test
elements mimic an
elements
SMA
in
a 3 x 5 pattern.
actuators intended for the
SMA actuator and its purpose is to
has been successfully directed to and received by a
element consists of two brass bolts anchored
in
the Plexiglas
approximately eight (8) inches apart, a spring providing a bias return force, and a
wire.
Indication
5.3 for detailed
is
provided by an infra-red switch and a
drawings of an individual
SMA
LED
light.
SMA
SMA
See Figures 5.2 and
Successful receipt of a
test element.
Digital
16
I1.nl
(2.n)
-C=DO\
Ct
=tK
E
[3.n]
-t=^i
iEEgl
-<=Hj»l
-cr=>oi
3 ^
crr>o|6-
l=
^=>^l
Addiess
oi Leads
£gg
W
s
-crziK)!
^9 E
L§
<="?\
32
64
128
Matrix
Location
oi
|m.1J
|m,2)
(m.3)
|m.4]
(m.5)
Test
Figure
5.1:
SMA actuator prototype test board.
Show
are the matrix location of the
SMA test elements and the digital number assignment of the lead used for control and
power of the
test elements.
48
Inferred Switch
I
LED
Indicator Light
SMA Wire
Bias Force Spring
Brass Bolts
Figure
5.2:
SMA test
element, top view.
bolts anchored into the test board,
spring,
To
and
LED
Each
test
element
is
composed of two brass
indicator light, infra-red switch, bias force
SMA wire.
AMD
Bias Force S P rin 9
SMA Wire
To
AMD
Inferred Switcr
i
Brass Bolts
Figure
SMA test element, side view. The connector between the bias force spring
SMA wire blocks the infra-red beam of the switch. This causes the LED
5.3:
and the
indicator to light, indicating that the wire has contracted.
49
command
beam of the
infra-red switch to
beam sends
the
of the
signal results in the contraction
SMA
This causes the infra-red
wire.
be block by the wire to spring connection. Interruption of
current to the indicator light which turns
command
has been properly sent,
connected
in a
matrix pattern as
Figure
in
The
and executed.
received,
shown
on to mark
5.1.
One end of each
connected together within each column and the opposite end of the
is
The
connected together within each row.
Figure
numbering scheme
SMA test
SMA
element
actuators are
of eight leads as show
result is a total
is
The
(3,5).
element from the
Each lead
16, 32, 64,
is
in
elements such that the columns
test
left test
element (2,3)
is
Figure 4.1
is
located in the second column and
is
The
SMA test element (2,4)
SMA test element (3,1),
leads
,
1
leads
significantly
and 128 must be selected.
is
of 16
SMA
reduced from what would normally be expected.
total
leads.
reduced to only eight
By
(8),
test
numbered 8 and 64 must be
SMA
test
1
If a
elements would
number of leads would be
system could reduce the number of leads to
for a total
required leads
SMA
matrix type arrangement, the number of leads needed to access the
have a minimum of two leads per element and the
common ground
the third
Refer to Figure 5.1 for the numbering sequence of the leads.
i.e.
system will be used to access the leads which control the
this
is
test
4, 8,
conventional means of actuation and control were used, each
ground lead
and the lower right
(1,1)
1, 2,
For access to
elements
is
in
assigned a digital address number in the base 2 system,
elements. Therefore, to access
From
element
row numbered one through
left.
and 128.
digital address
selected.
SMA test
assigned to the
elements are number one through three and each
Therefore, the upper
element
test
SMA test
Operational Numbering Scheme
A
five.
elements are
5.1.
2.
of
test
that the wire
30.
5 active leads and
A
one
using this matrix connection, the number of
a reduction of almost
50
50%. As the number of
segments
is
increased, the conventional
method with
common ground
a
three lead wires per segment and requires (3«+l) lead wires for
of actuation adds
n segments.
The matrix
connection adds a single lead wire for every additional segment and requires (w+3) lead
wire for n segments.
B.
ACTUATOR MATRIX DRIVER BOARD
that
is
The use of only
eight leads for access to the
SMA test
able to directly
power
elements and use the same leads for
measuring the
electrical condition
these desired actions and
Driver
(AMD)
is
of
to the matrix
test
A
of each element.
elements requires a system
system was developed to
called the Actuator Matrix Driver.
sends power to the intended
SMA
test
facilitate
The Actuator Matrix
element while simultaneously
providing for the monitoring of the electrical condition of that test element.
1.
Description
AMD
The
consists of three external interface units and a control board
which
determines the magnitude of power sent to the test elements and which elements receive
power. The three external interface units allow for control from a computer system to be
received by the
AMD,
for the connection
for the monitoring
of the
test
of the
elements by the computer system, and
element leads and power source to the
external interface units used to transfer data
pin connectors.
test
between the
24 port wire connector.
component
and the computer are 50
These two 50 pin connectors make up to a 100 pin cable compatible with
a personal computer installed data acquisition board.
connections.
AMD
AMD. The two
Figure 5.4
The
final external interface unit is a
It
has the capability of providing twelve simple point to point
is
a diagram showing the
location.
51
AMD's
overall physical layout and
The
column
AMD
control board
driver transistors, five
transistor.
resistors
A LM7805C
NPN
row
list.
AMD
74LS240
inverting buffer, three
and miscellaneous driver
Figure 5.5
is
SMA test
and the wiring scheme of the
diagram of the
a
driver transistors, and one
5 volt regulator
complete the component
interface units
composed of
is
control board showing the
NPN
power
transistors,
amplifier
diodes and
a schematic diagram of the
elements.
Figure 5.6
is
PNP
AMD's
a schematic
components and pin connections of the
board. Refer to Figures 5.5 and 5.6 for component and pin location.
The actuator matrix
have a
common
driver
is
composed of three
input control voltage.
Each
identical current amplifiers
current amplifier
is
in series
which
with a solid-state
To Computer System
Computer Analog Input
Test Etemert Mooftortog
Computer Anolog/Digital Output
(P4)
0,5 ohm Resistor Vattage
(P3)
f\rrAmp Contraf
DC
Power
Supply
NPN Row
Figure 5.4:
Diagram of the Actuator Matrix Driver (AMD).
overall physical layout
and component location of the
52
AMD.
Driver Transistors
Diagram shows the
switch.
These switches, Rl, R2 and R3, form the 'column' drivers of the matrix.
additional solid-state switches,
R4
through R8, form the 'row' drivers of the matrix.
through 4 of the computer
Bits
pins 7 through
I
digital
output are connected via connector P2
to the driver networks for the row-drive solid-state switches.
outputs are on PI pins
I
through
Five
5.
The row
Bits 5 through 7 of the computer digital output are
connected via connector P2 pins 4 through 6 to the driver networks for the column-drive
solid-state switches.
A regulated
The column outputs
on connector PI pins 6 through
are
12 V, 250 Watt, switching DC. power supply
feeds the current-amplifier power transistors.
MJ0030 power
transistors, a
0.09437
Q precision resistor,
various resistors, diodes and capacitors.
VCC
provided by
and an additional
through the precision 0.09437
Q
5
V
resistor
the absolute value of the current.
Each current
VDD
bias
is
for the
power
The
individual
The computer
SMA
the voltage across each
matrix.
single-ended
MC3358
dual amplifier, and
operational amplifiers
The output
current
is
(VSS)
dialital-to-analog converter output
PIC
pin
Three
8.
Each
is
identical
is
high-speed
individually connected in
element,
across these elements. In order to measure
the computer's analog-to-digital
PI A and P1B are connected via
The DT-709Y
amplifies them,
MC3358
composed of two
measured from the value of the current pulsed through the
is
SMA elements and the voltage drop
at
is
VEE)
source) to one of the three column' solid-state switches.
resistance
channel inputs
an
supply.
precision current amplifiers are used for redundancy.
VSS
amplifier
source and
sampled by the amplifier and used to control
connected to the current-amplifier inputs via
series (as the
(VCC
8.
differentially
JI
through a modified
multiplexed
DT-709Y
samples the voltages across the
SMA
to the
elements,
provides an offset proportional to the current pulse and delivers a
voltage
to
the
analog-to-digital
converter's
multiplexed
inputs.
The
amplification and offset are required to provide a higher degree of resolution for the
voltage measurement.
Three
to
TB2
sets
of five of the
pins 2 through 16.
DT-709Y
Five sets of the
input channel's
DT-709Y
53
'Hi'
inputs are wired in parallel
input channel's *Lo' inputs are wired
TB
in parallel to
pins 2 through 16.
I
on PI pins
drive lines
I
DT-709Y
is
connected to the eight wire
through 8 and allows the voltage on each wire to be individually
The computer
sampled.
This arrangement
command
digital-to-analog
offset control line at
W17/18
(not
shown
voltage
in the
routed to the
also
is
diagram).
This allows the
measured; voltage to be amplified by a factor of 10 for increased resolution.
to the
DT-709Y
2.
and
is
SMA
elements are individually heated by using the pulsed short current
transistor
is
closed.
regulated by the
This allows power from the unregulated
AMD
by an analog voltage
row
the
control board
signal
SMA
combination.
power
A tightly controlled
each
SMA
is
power supply
sent to the
The power
circuit is
amplifier
controlled
completed by closing a
selected
AMD. The
is
now
SMA
applied
column and row
transistor
SMA element
through a
is
voltage drop across the selected
is
programmed
The amplitude of
the current pulse
is
number of
maximum of
1
elements,
any given time.
54
SMA
adjusted to ensure the
heated to the required level needed for phase transformation.
manipulator considered, a
its
to generate duty cycle pulse for
element, the duration of the duty cycle being dependent on
is
is
sampled and used with the value of the pulsed current to determine
Ohm's Law. The computer
elements
to be sent
SMA test elements is
and highly accurate current pulse
Monitoring of the power applied to the selected
Elements to be actuated.
SMA
The
DC
from a computer. This connects a row of
element which results from the
element
resistance via
amplifier.
from the computer.
separate parallel connection point on the
SMA
The power
test elements.
transistor via digital output
elements to ground.
element matrix composed of three columns
from a computer determines which positive column driver
column of SMA
to the selected
to
SMA
sequentially routed through the
five rows. Digital output
selected
20 from PI A.
fed via Jl pins 19 and
Operation
The 15
which
is
DC. power
For the
two per segment, may be actuated
at
P3 part of MIO subconnectcr pins
nil
iIe
Hi jpijp
ate
We
p p
j=
1
wll
thru
50
s
I
2
-2
2
PI Driver Board I/O Connector
Figure 5.5
the
:
Schematic diagram of the
AMD's
SMA test elements.
55
interface units
and the wiring scheme of
CN
ai
(
I
Figure 5.6
:
pppmp
8,
in^ in= an? ^ns ^ns
a?
8
8
e
8J
s
8
S
8
=
«-
p __
8
r
g(Qj
mmmmmmmn
Schematic diagram of the
AMD control board showing the components
and pin connections of the board.
56
SMA ACTUATOR CONTROL SYSTEM
VI.
A scheme for powering the SMA test elements was developed
behavior that was observed
AMD
directs
power
in
monitoring of these actuators.
DOS
To
SMA
6.1
an
is
HP-6282A DC Power
control the
AMD,
i
6.
1
:
a computer software program
based Personal Computer (PC) which
commands and
diagram
of
the
SMA
utilizes
was
a Data
the collection of data.
actuator
control
system.
Supply
<
Figure
overall
The
actuators and allows for the simultaneous
Acquisition board to facilitate the performance of
Figure
SMA's
the resistance and strain response to current testing.
to the matrix of
developed for use on a
based on the
ho|
i
6
Qlo-
cizD-o|b
—
r=ra|6
i=z3-ol(i
-<=H>\
'-—^t
SMA Actuator Control
comprise the system prototype for
h0|6
System.
testing.
57
All
—
i
f-o
-<=^\
major components are shown which
The 15
SMA
elements are individually controlled and monitored using the matrix
The computer
connection composed of three columns and five rows.
row and column and
AMD,
generates tightly controlled and highly accurate current pulse.
via an analog-to-digital converter with a multiplexed channel input,
SMA element.
sample the voltage drop across each
and the sampled voltage, the resistance of the
Ohm's
digitally selects a
The computer
law.
duty cycle for each
SMA
is
programmed
used to
Using the values of the current pulse
SMA
elements can be calculated using
to generate a
The pulse amplitude
element.
is
The
pulsed current with a specified
is
adjusted to allow the wire to
IBM
compatible personal computer
heat to the proper level.
A.
CONTROL SYSTEM HARDWARE
1.
Personal Computer (PC) System
Control of the manipulator
(PC) with an analog and
consists of a
digital
is
performed by an
I/O data acquisition board installed.
80486-66MHz DX2 ISA mother board
including an Intel
with an integrated enhanced numeric coprocessor, 32-bit local bus, 16
540
The PC system
80486 processor
MB
of RAM, and a
MB hard disk.
2.
Data Acquisition Board
The
data
acquisition
board
multifunction I/O board which features:
analog inputs, 8
digital I/O
,
a
is
12-bit
and two 12-bit
National
ADC, 200 kHz
DACs
58
Instruments®
AT-MIO-64F-5
sampling
with voltage outputs.
rate,
up to 64
B.
COMPUTER SOFTWARE PROGRAM
The computer program was developed using
LabVIEW®
package.
is
graphical
a
the
icon based
Lab VIEW®
software programming system for
Programs are written using LabVIEW® by
instrumentation.
application software
assembling
graphically
software modules or virtual instruments (Vis), represented by program icons, into an
executable program.
&
The Lab VIEW® program "Wire Control
Status, vi" is enclosed in
Appendix C.
The program has two
panel
parts, the
The
Front Panel and the Block Diagram.
front
where the operator controls which elements of the manipulator are to be
is
The operator can
energized.
also control the duty cycle
by slowing down the loop
sequence of the program and can also control the amplitude of the pulsed current sent to
each group of wires.
There
The block diagram
the actual program.
flow as
is
also status graphs to see
is
It
the functional type icons to be used in the
the elements are operating.
provides a visual representation of the data
would actually occur. Programming
it
how
is
accomplished
LabVIEW® by
in
program and wiring them up
into a
selecting
working
block diagram that direct the flow of data.
For control of the manipulator, the front panel
Control Boards
A mouse
is
is
element
is
The lower
energized.
set
the resistance of each
front panel
A double
set
is
the
set
of three Wire
command
group.
corresponds to the actuator element
of boards returns a lighted
signal
when
current sent to each group
below the control boards. Three
SMA wire test element within each group.
real time
the actuator
is
controlled
graphs monitor
These graphs are located
below the controls mentioned above.
The block diagram
listed in the
group of actuators, but the loops are
is
light that
The amplitude of the pulsed
individually with the slide gages
on the
used.
used to control the manipulator. The upper
used to highlight the numbered
to be energized.
is
Appendix B displays only the loop
identical for
all
three groups.
The outer
for the first
large block
a while loop and continues to operate the program inside as long as there are no errors
59
and the stop button
is
The icons
not engaged.
to the
left
of the while loop are concerned
with configuring the computer system and data acquisition board.
that each icon
routines or
the icon.
Each
which
a subprogram
is
may be
Double
level in turn
its
clicking
should be mentioned
These icon subprograms may be simple
own.
very complex program
in their
own
depending on the purpose of
right,
on a icon brings up to the screen of the particular subprogram.
has a series of icons which contain a set of programming
contain more icons,
in turn
all
It
etc.
Only the top
level will
all
there
own
be discussed.
Contained within the while loop are the logical stop controls, the loop delay for
minor time control, and a sequence frame.
The sequence frame controls the
sequential
progression of the program from one group or column of actuators to the next and then
starts
over again. Inside the sequence frame
of times
is
a for loop which executes the
Within the for loop
that there are actuators in each group.
controls which get their
commands from
The program then
number
specified
on the
The voltage drop across a
drop across a precisely calibrated
SMA wire.
This data
When
an error
and the block to the
is
is
resistor
SMA
on the
is
in
digital
going to the monitoring section
wire
AMD
is
measured, then the voltage
board
is
used to determine the
Using Ohm's Law, the resistance
sent to the front panel for display
received or the stop button
right
generated for use
front panel.
Simultaneously, the same address information
actual current through the wire.
is
Based on
sequentially steps through the routine, determining if a
SMA actuator gets power at the level
within the for loop.
located the Boolean
the front panel wire control boards.
the light combinations on the front panel, a
addressing.
is
same number
of the loop takes over.
to a safe condition so than no miscellaneous
Its
power
60
is
is
is
calculated for the
and monitoring.
engaged,
purpose
is
all
operations are halted
to return
all
port openings
circulating through the system.
C.
EXPERIMENTAL RESULTS
SMA
Experiments were conducted with the
The
SMA elements were controlled
to use the
AMD
resistance of the
open-loop mode because the primary objective was
The computer program
SMA elements,
via
AMD
has provisions for measuring the
therefore closed-loop control of the
SMA elements using
by simply modifying the software for the control
was discussed
earlier that
among
elements would be actuated simultaneously
operated any combination of up to 10
maximum number of
duty cycle.
SMA
The experimental
Figure 6.2 shows the variation
a current pulse of 1.6 A, 6
resistance of 2.1
Q
ms
and the
the 15
at
SMA
any given time.
SMA elements,
maximum of
elements, a
maximum of two
per segment.
For
elements actuated, the current pulse operated on a
10%
results for a single
in the resistance
in
SMA
of the
duration and a
10%
element are shown in Figure
10%
duty cycle.
total resistance in the lead
less than the martensitic resistance.
that the pulse current
is
able to maintain the wire in
results in Figure 6.2 indicates that the
multiple
AMD
SMA elements using fewer lead wires.
61
6.2.
SMA wire as the wire is actuated by
The wire had an
its
initial
wires was approximately 0.6 Q.
Q
to around 2.5
Previous experiments have shown that the austenitic resistance of an
approximately
10
Therefore, the program
Figure 6.2 shows that the resistance drops almost immediately from 2.7
Q.
the
SMA elements.
It
the
elements could be actuated using
The performance of the open-loop control was judged from
resistance feedback can be incorporated
of the
SMA
to demonstrate that multiple
fewer lead wires.
resistance plots.
in
Actuator System described above.
SMA
is
Therefore, Figure 6.2 indicates
austenite state at
all
times.
The
can be used effectively for the control of
10
15
time (seconds)
Figure 6.2
:
Variation in the resistance of a
the current pulse duration
SMA wire with time
was 6 ms and the duty
62
cycle
was 10%.
for the case
where
VII.
A.
RECOMMENDATIONS AND CONCLUSIONS
RECOMMENDATIONS
SMA material
return to
it
austenitic shape
when heated
temperature.
Upon
undergoes
dependent on the stress applied. Therefore,
a motion
is
upon
cooling,
it
forms martensite.
contraction, the return to
its
material with a
that
does not rely on an external force for
Lab VIEW® can be a very
phase transformation
The amount of elongation the material
if
the material
A
its
versatile
internal
PC
clock which
is
B.
reliable
It is
of the
motion
motion.
programming
tool.
It
provides not only data
This visual aid
Screen updates significantly slow
LabVIEW®
recommended
down
in
the
operating system clock uses the
not very dependable and subject to
software and hardware interrupts.
more
Also,
status
superelasticity material also with defined
a cost in speed.
system's ability to process data.
to effect
two way shape memory
control and processing but a visual aid for control and processing.
computer programming has
was used
normal position would be dependent on the
would be unknown.
more defined motion or a
its
With only resistance to determine
internal bias force plus the external load.
actuation elements, the exact position
to
management problems with
that a faster system
be used with a
time system.
CONCLUSIONS
This thesis presents a digital control system used for the control of a manipulator
composed of
SMA
changes and
behavior as the temperature
transformation.
of the
SMA
SMA
SMA
actuators or elements.
The behavior of
element.
SMA was
is
exhibits very defined physical property
varied and the material undergoes phase
estimated by evaluating a heat transfer model
This heat transfer analysis provided an expected behavior for the
element and lead to the introduction of the concept of thermal
63
inertia.
Thermal
inertia allows for
SMA
tightly controlled
and highly accurate short pulsed current followed by a significant off
time.
elements arranged
During the off time, other
monitoring
is
SMA
a matrix form to be individually heated by a
elements are sequentially heated.
acceptable for determining the phase of the material.
adequate for determining the amount of
determination
in
with
only
resistance
strain
recovered or given up.
information
is
inappropriate.
discontinuous heating with sequential powering, control,
Resistance
Resistance
The
principle
elements.
The actuator matrix
matrix of
SMA
the open-loop
elements.
elements.
mode
The
results
of monitoring a single
modifying the computer software program.
64
SMA
developed to control and monitor the
SMA
element indicates that
actuation system effectively controlled the matrix of 15
Closed-loop control of the matrix of
of
and monitoring allows the
leads to be reduced by 50 percent, just eight leads for a system with 15
(AMD) was
not
Therefore, position
number of
driver
is
SMA
SMA
element can be accomplished by
APPENDIX A. HEAT TRANSFER MODEL CALCULATIONS
65
Appendix
A
SMA Wire
:
Heat Transfer Model Calculations
Characteristics*
—
lb
Density
p
:
:=
0.235-
p
=
6.505
gm
-s_
3
cm 3
in
Specific Heat
C
:
_
P
BTU
lb R
0.20
:=
„
Cn =
"P
BTU
Heat
of Transformation
:
h
,
h
10.4
=
+
1
+
=
cal
0.2
gm-K
kJ
24.19
l
kg
lb
BTU
Thermal Conductivity
k
:
watt
,
k =
10 4
=
If
m-K
hrft-R
Linear Resistance
:
ohm
—
_
nominal:
=0.44
ft
ohm
_
fl
=
0.173
cm
in
Electrical Resistivity
Martinsite
:
ohm
R_
m
:
„
R
Austinite:
421
=
cirmil
-
ohm
511
cirmil
* -
SMA wire
ft
ft
characteristics provide by manufacturer of Flexinol™ Actuator Wires,
Dynallooy, Inc.
Makers
Irvine,
of
Dynamic
Alloys
CA 92715
Transformation Temperatures
(as determined from Resistence
-
Temperature measurements)
T As
T Ms
:=
T pj
343-
353K
66
T Mf
=
=
363-
331K
Appendix
A
:
Heat Transfer Model Calculations (continued)
Test Wire Characteristics
load
:
Dimensions
@ stated load
W
:
d
diameter
austenite
martensite
Lm
:
La =
2.8285 in
=
=
La
%e
=
d =0.025 -cm
= 0.01 in
La
:
% strain:
gm
237.2-
:=
:
%8
+
LaLm
7.184
=
7
-cm
522*
cm
100
nominal length
volume
:
:
Lm
La +
L
=
V
:=
—
71
L
L =
7.353
V =
0.004
*cm
•
cm
4
surface area
mass
Test Conditions
:
A„
M
:
=
= p-
— Lm
tt
1
monitor current
I
step current:
I
ambient temperature
^s
d-L
71-
:
=
T
1
2
=
M
u
=
*
:=
296.2
K
watt
2
m K
Test Sequence
:
1)
Initial
monitoring with
l
m
current
2) Heating with step current, s
l
3) Cooling, post heat monitoring with
67
l
m
cm
2.479-10
amp
=25
h
:
° 587
amp
free convection
heat transfer coefficient
=
current
-kg
4.7
Appendix A
:
Heat Transfer Model Calculations (continued)
Test Sequence
1)
- Initial
rate of
monitoring with
energy generation
rate of energy loss
due
is
l
m
current
equal to
therfore,
to convetion:
ER s ^ =
ER =ER out
g
2
fi
I
m L = hA s5
solving for the equilibrium
temperature
I
T
:
(T:
\
T oo
-
1
m QmL
=
h
assume
-
Heating
:
T amb
=
304.884
As
T
Test Sequence 2)
+
"
,
i
j
«K
E ou + = 0.
neglect convective heat trasfer out of CV,
the energy input to
CV is
equal to the amount of energy required to
heat wire to the transformation temperature plus the enegy required to cause
phase transformation
:
E =E
g
energy required
+
h
Et
to
heat to transformation
E
:
E
energy generation
increase
in
d
/
results
^
h
=
=
p
•
2
\
Lm Cp(^As~ ^
71
0.791 -joule
in
energy storage(heating)
:
E =I
Q m Lm
s
time to heat to
transformation temperature
At
:
^
I
At
68
h
=
s-
E
^
Q
m-
0.152 -sec
At
Lm
^=
E
^
i
Appendix
A
Heat Transfer Model Calculations (continued)
:
energy of transformation
E t-M
:
h
t
during athermal phase transformation,
energy generated = energy of transformation
2
I
s
therefore, the time required to
M
At
if
-
=
At
t
Mh
cause transformation
^
t
:
h
t
t
=0.115 »sec
At
=
At u + At
At
=
0.267 -sec
At
:=
t
Total time to transformation
Test Sequence 3)
D m Lm
E =E
:
:
Cooling, post heat monitoring with
l
m
*
current
assume no heat generation
E = 0.
(worst case situation)
loss of internal energy storage
due
is
-
to convective heat transfer
use lumped capacitance method
ER out - ER st
:
d\\.
d
h.(*d-L)-(T-T )]-r>^-Lj.C -=-T
p
(8
let:
0=T-T amb
am u
then:
4_0 = 4_t
dt
dt
/
energy balance equation becomes
:
(h
(71
d
L) 0)=p
\
69
d
2
tt
4
\
L
-C _
/
—
F dt
Appendix
A
:
Heat Transfer Model Calculations (continued)
simplifying
—
«p V C
h-A„0
S
:
e
n
P dt
'
e
V c
p
integrating
de=
:
h-A s
~
ldx
6-Tj-
where:
i
A
h
e
In
pVC p
0^
-
e
transient tmperatu re
:
response
5
p-V-C
Resistance to
Convective Heat Transfer
R
:
h
and
hA
- = exp
9:
let
T amb
e
Lumped Thernal Capacitance
thermal time constant
C*
:
x
:-
t
n
substituting results in
assume
finish
=
t
/
= exp
A
p-V-C D
R C
t
Rt
=
watt
joule
C*
0.02
K
=
T
K
681.708
13.835
t
t
sec
n
wire at austenite
temperature, then
i
since
0=T
-
~ 668 *K
T Af~ T amb
:
i
T amb
substituting
temperature of wire
in
free convection cooling
Tn
T amb
+
i
ex P!
R C
t
70
t
Appendix
A
:
Heat Transfer Model Calculations (continued)
380
360
340
-
320
-
300
-
280
SMA Wire Temperature Response
0.368 Ti
Thermal Time Constant
Transient temperature response of
SMA wire
undergoing free convection cooling. Lumped
capacitance method used to evaluate the transient temperature response of the
solving for the time required for
SMA wire
T
temperature to decay to the martensite
start
temperature
SMA wire.
(R t C t Vln
:
Ms
T amb
-
9;
t
the associated energy loss
EL
:
=
2.244* sec
=(pV)C
Gj
(1 -
expf-T
t
EL -
reheat time
@ step current,
Is
At
At
rh
rh
71
0.203 -joule
h
am
=0.041 -sec
La
Appendix
A
Heat Transfer Model Calculations (continued)
:
Validity of
Lumped Capacitance Method
characteristic length
or
more
:
conservatively
:
:
V
L
_
=
L
_
=
—d
L
since Biot
sum
number:
number
is
Bi
less than 0.1
capacitance method
iis
,
Bi
:=
=
L=
hL c
Boit
_
=
0.006
•
cm
0.013* cm
1.764-10
4
the error associated with using the lumped
small
72
APPENDIX B. LabVIEW® PROGRAM "Wire
73
Control
& Status.vi"
0%
o
1
o
j
„®
s
*;#
O
a
3
UJ
#
$
o
o
CD
o
t
O
f ;
r
a)
o
74
n
75
76
LIST OF REFERENCES
[ 1 ]
Product Literature, Technical Characteristics of FLEXINOL™ Actuator
Wires, pgi (1993).
[2]
Wayman,
C M.
W
and Duerig, T.
;
An
Introduction to Martensite and
Shape Memory (Engineering Aspects of Shape Memory Alloys),
(T.
,
Duerig, K. N. Melton, D. Stockel,
C M.
Butterworth-Heinemann Ltd, Great
[3]
pg 3-20 (1990).
.
&
Sons, pg 9, 14-17, 226-232 (1990).
Hewlett-Packard Operating Manual for the
Table 1-1: Specifications
[5]
Britain,
editors),
Incropera, F. P. and DeWitt, D. P.; Introduction to Heat Transfer John
Wiley
[4]
Wayman
W.
What
is
ME
(NPS
HP-6282A DC Power
Supply,
Shop copy).
MATLAB? MATLAB® Reference Guide,
.
The Math Works,
Inc.
Natick, Mass. (August 1992).
[6]
Waram,T.; Design Principles For Ni-Ti Actuators (Engineering Aspects of
,
Shape Memory Alloys),
Wayman
editors),
(T.
W.
Duerig, K. N. Melton, D. Stockel, C.
Butterworth-Heinemann Ltd, Great
Britain,
M.
pg 234-244,
(1990).
[7]
Melton, K. N.; Ni-Ti Based Shape
Memory
Alloys, (Engineering Aspects
of Shape
Memory
Alloys), (T.
Wayman
editors),
Butterworth-Heinemann Ltd, Great
W.
(1990).
77
Duerig, K. N. Melton, D. Stockel, C.
Britain,
pg 21-35
M.
78
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Naval Postgraduate School
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R. Mukherjee
Associate Professor
Department of Mechanical Engineering
Michigan State University
East Lansing,
5.
Prof. T.
R
MI 48824-1226
McNelley, Code
ME/Mc
...,
Chairman
Department of Mechanical Engineering
Naval Postgraduate School
700 Dyer Rd.
Monterey,
6.
CA 93943-5100
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A. Thiel,
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..
Diving and Salvage Officer
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