Design of a Morphing Wing

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1

Design of a Morphing Wing


by

Jon Reifschneider


Department of Aerospace and Mechanical Engineering

University of Virginia

Charlottesville, VA 22904


Manoranjan Majji


,
Ganesh Mohan


, John Junkins

Ⱐ佴,潮⁒ din楯瑩t


Department of Aerospace Engineering

T
exas A&M University

College Station, Texas 77843








Undergraduate Research Assistant.



Graduate Research Assistant



Distinguished Professor, George Eppright Chair, AIAA Fellow



Associate Professor, AIAA Associate Fellow

Copyright © 2004 by the

American Institute of Aeronautics and Astronautics.


Abstract

This paper details efforts made in the
design
, analysis,

and control of a morphing wing. The wing is being
designed for NASA utilizing cutting
-

edge intelligent
material technology. It consists

of a plastic structure
covered by a flexible elastomer skin with embedded
carbon nanotubes for additional strength. The wing is
twisted at three
points

along the span using a concentric
tube mechanism actuated by a combination of simple
springs and shape
-
memory alloys.
T
he modeling/finite
element program A
BAQUS

CAE
has been used
to model
the wing and analyze the validity of the design. A stress
analysis has been performed on the wing structural
support,
including the alteration of

several parameters to
determine the most feasible design. The skin has been
analyzed under normal operating and extreme conditions
to verify its performance with minimal buckling. A
quantitative method was then developed to compare the
buckling in the skin under different val
ues of internal
pressure and initial pre
-
stress
.

The wing is currently
being build and assembled for design validation and
testing in the wind tunnel. The

wind tunnel tests will
provide sufficient data

to relate the wing geometry
variations to variations
in aerodynamic forces and
moments. The resulting mathematical models will be
used to develop control algorithms for all of the possible
operating conditions.


Introduction

Morphing can be defined as the ability to morph, or to
change the form or character
of, to undergo
transformation
1
. As applied to aircraft design, it
would
refer

to the ability of a plane’s wings to change shape

during flight
,
thereby
providing some aerodynamic
benefit. The concept of a morphable wing

is as old as
the development of the

airplane itself.

All aircraft today
use a small degree of morphing in the form of control
surfaces that are used to control the motion of the plane.
A new definition of a morphing wing is therefore needed
to distinguish a truly “morphing” aircraft from
the
traditional airplane. A morphing wing can thus be
defined as one which has the ability to either alter its
shape in a continuous change along a chord or spar or to
change its shape in a drastic manner.

DARPA has
developed a definition of a morphing

wing as one that
has to ability to perform either a 200% change in aspect
ratio, a 50% change in wing area, a 5 degree change in
wing twist,
or

a 20 degree change in wing sweep
2
.
Morphing
wings of this type
have taken several forms
throughout their histo
ry including variable
-
sweep wings,
telescoping wings, and wings capable of twisting about a
spar.

Motivation

Traditional airplane
s

use

a
set of
rigid
, fixed

wings

to
provide lift and

a combination of flaps and a
iler
ons to
control
roll, pitch, and yaw. Eac
h separate wing
shape
and
configuration has its own set of unique aerodynamic
characteristics, and thus there
usually
exists

an ideal
vehicle configuration to accomplish
each given
task
3
.
During traditional aircraft design, thousands of variables
are redu
ced to a few key design variables, what Raymer
refers to as “the basic six”:
thrust to weight ratio (
T/W
),

2

wing loading (
W/S
), wing thickness
-
to
-
chord (
t/c
), wing
taper ratio (
λ
), wing sweep (
Λ
), and wing aspect ratio
(
b
2
/S
)
4
. Different sized aircraft correspond to different
sets of these values, which result in different
performance capabilities.
For example, large bombers
such as the B
-
52 are well
-
suited for long
-

range crui
sing
missions but must be accompanied by quicker, more
maneuverable fighters for protection against enemy
aircraft.


The goal of morphing wing research is to develop a wing
that will be able to accomplish contradictory missions
such as these through chan
ges in wing shape.
In general,
w
ing shapes that are long and thick are well
-
suited for
slow, gliding flight while short, thin, swept wings allow
for quick maneuvering.
Chosen wing shapes are a
compromise, allowing for the best performance possible
at each

of the aircraft’
s intended missions.
Changing the
shape of the wing during its missions brings the wing
performance closer to the ideal for each task it is
assigned.

An aircraft with a morph
-
able wing will have
better performance for a far wider variety

of missions.

It
will have the versatility to perform contradictory mission
objectives efficiently and the adaptability to accomplish
unforeseen tasks.


Another aspect of a morph
-
able wing is its ability to
control roll, pitch, and yaw without the need fo
r
ailer
ons
and elevators.
The elimination of these parts
has the
potential to

increase reliability and reduce wing
maintenance.
Another important factor in their
elimination is the removal of seams along the wing. This
results in greater fuel efficiency

by decreasing drag and
lowering the total aircraft weight.
An added

benefit
of a
seamless wing
is the aircraft’
s reduced
susceptibility

to
acquisition by radar

5
.


Birds are a primary source of inspiration for the
development of a morphing wing. The
vers
atility and
control that even the most complex fixed
-

wing planes
can accomplish pales in comparison

to the
performance
that birds can achieve with their wings. Several
researchers are studying these wings in hopes to better
understand how birds can p
erfo
rm such complex
maneuvers.

Figure 1

illustrates
the range of wing
configurations that an eagle can achieve.



Figure 1: Bald Eagle in Various Wing Configurations
3


The flexibility of bird wings allows their shape to be
changed continuously in both planf
orm and profile to
accommodate these various flight conditions. Another
important feature of t
he bird’s wing
s

is that they are
multifunctional. They are used to
provide

lift while at
the same time providing the forces necessary for trim
,
e
liminating the
need for any type

of rudder.


Past Research

As mentioned previously, the morphing wing concept is
as old as the wing itself. The Wright
brothers’
Flyer

la
unched in 1903 was controlled partially through the use
of a morphing concept called wing warping. T
hey used a
series of pulleys and cables that twisted the wing to
change directions.
They too were inspired by nature,
having observed the flight of turkey buzzard over the
Miami, Ohio river
6
.


Several attempts to develop morphing wings have been
made in t
he U.S. throughout the past few decades.
The
B
-
1B bomber
7

developed in the mid
-
1980s had a
blended
-
wing body that was capable of varying its
sweep, providing for wingspans between 78 and 180
feet. The unswept pos
i
tion allowed the B
-
1B to take of
in short
er distances and provided increased range, and
the swept position allowed it to achieve higher speeds.


The Navy’s F
-
14 fighter
8

also uses
variable
-
sweep wings
to achieve different wingspans ranging from 38 to 64 feet
(a range of 20 to 68 degrees), resulti
ng in a range of
aerodynamic characteristics. The variable sweep allows
the F
-
14 to land and takeoff on the short runways of
aircraft carriers while still allowing it to maintain speed
and maneuverability in flight. The large wing pivot

3

mechanism, howeve
r, spans the entire diameter of the
fuselage and greatly increases the weight of the plane.



Figure 2: F
-
111 Mission Adaptive Wing in Flight


The Mission Adaptive Wing
9

was a joint project between
the United States Air Force and the National Aeronautics
and Space Administration to apply morphing technology
to an F
-
111 testbed plane. It was one of the first attempts
at a smooth, variable
-

camber wing. The shape of the
wing’s airfoil cross
-
sections adapted to suit the specific
task of the plane. Hydraul
ic servo
-
systems were used to
change the camber on the leading and trailing edges,
resulting in a possible leading
-
edge rotation of +2 to
-
21
degrees and trailing
-
edge rotation of +4 to
-
22 degrees.
Sliding panels located on the lower edge allowed for
cho
rd changes resulting from the variable camber
, and
the wing wa
s covered with a flexible plexi
-
glass skin.


One of the more recent morphing wing projects involved
the addition of an active aeroelastic wing to an F/A
-
18A
Horne
t
10
. Pre
-
production wings for t
he
Hornet

that were
deemed too flexible to be used on the actual plane during
manufacturing were
fitted onto a
Hornet
. The wings
were flexible enough to twist very small amounts at high
speeds, resulting in decreased drag and an increase in
range.


Curren
t Research

The recent develops in the field of smart material have
ignited a buzz of research in the field of morphing wings

in recent years
.
One of the

most prominent

morphing

project
s

is NASA’s own Aircraft Morphing Program, is a
6
-
year program aimed at
developing smart devices for
implementing in airframe application to enable self
-
adapting flight resulting in dramatic improvements in
aircraft efficiency and affordability
11
.

The program
focuses
primarily on the use of a piezo
electric based
actuation sys
tem to create shape alterations in the wing.


A collaboration of DARPA, Air Force Research
Labor
atories, and Northrop Grumman C
orporation called
the Smart Wing program is focused on utilizing other
smart
-

material technologies such as shape
-
memory
alloys a
nd Terfenol
-
D

as actuation mechanisms for wing
shape control
1
2
.


Research is also being conducted at several universities
around the country in the field of morphing wings.
Many student groups are developing morphing wing
designs, such as the Morphing Win
g Design Project at
Virginia Polytechnic and State University which is
developing and testing a telescoping wing design
1
3
.
Several other university groups are developing control
algorithms for the control of actuation systems on
morphing wings.


Project

Goals

The
stated
goal of the project
is

to explore active wing
morphing via actuation by smart materials
.
The wing
design will be for a UAV w
ing with a maximum velocity
of 2
0 m/s.
The completed wing design will undergo
testing in order to construct a ma
thematical model for the
wing aerodynamics in the presence of actuation
.
Different types of smart actuation are to be explored
including, but not limited to, piezoelectric mechanisms
and shape memory alloys. The particular type of
morphing on which this
project focuses is the application
of a wing twist with a smooth distribution along the span.


Actuated Section
at 100% Span
Actuated Section
at 33% Span
Spar Stiff in
Torsion and
Bending
Actuated Section
at 66% Span
Actuated Section
at 100% Span
Actuated Section
at 33% Span
Spar Stiff in
Torsion and
Bending
Actuated Section
at 66% Span
Section
Rotated by
Angle

Section
Rotated by
Angle

Section
Rotated by
Angle

Section
Rotated by
Angle

Section
Rotated by
Angle

Section
Rotated by
Angle


Figure 3: Intended Design for Morphing Wing

As shown in figure 3 above, t
he airfoil sections at 1/3
leng
th, 2/3 length, and
the
wingtip are

to be capable of

rotating about the spar, resulting in wing twist.

Initially
t
he
desired twist angles
range
d

from
-
5 to +
5 degrees of

4

twist

for t
he section at 1/3 length and
-
15 to +15

degrees

relative to the prec
eding section

at 2/3 length and
wingtip
.

The range was lat
e
r modified during testing to

a
maximum
-
5 to +5 degree twist of the root section and a
-
10 to +10 degree twist of the outer two sections
. The
structure and actuation system are to be designed and

the
wing

should undergo
extensive

simulated and
experiment
al analysis.


Wing Design

The design of the wing followed the above stated project
goals. The wing consisted of a NACA0015 airfoil with
variable root chord, wingtip chord, and root
-
to
-
tip span
to be determined in the design process.


Structure

The struc
tural support of the prototype wing was
designed to be made on t
he Rapid Prototyping machine
of

ABS plastic. Rapid prototyping was selected for the
creation of the structure
for several reasons: the
necessary flexibility of the ABS plastic, convenience,
a
nd the short manufacturing time associated with
production on the machine.



Figure 4: Wing Structural Support



In order to maximize flexibility in torsion, the structure
consists of front and rear supports

as shown in Figure

4

connected by cross
-
sectional supports at the three
locations of twist.

Due to size constraints of the Rapid
Prototyping machine the structure was created in three
separate sections. These sections are fastened together
by bolts to maintain the rigidit
y of the structure.


Actuation

A series of four concentric tubes run through the length
of the structure as showing in Figure 4 above. The end
of each section of the structure is fixed onto the tube
passing through. The three innermost tubes are free t
o
rotate independently, resulting in wing twist at the three
supports.

SMAs, or shape memory alloy
s, provide the
actuation for the twisting of the tubes

and thus the torque
required to deform each section
. Shape memory alloys
are wires that change shape
with the application of
voltage. The strain in an SMA is a function of the
voltage applied and temperature

of the SMA
.

SMA
wires are “trained” by applying voltages repeatedly and
allowing the wire to deform. Once the wire is trained the
relationship bet
ween input voltage, temperature, and
strain can be determined.



Figure 5: Schematics of the Actuation Mechanism


Each of the three innermost tubes will have its own
actuation mechanism, allowing it t
o rotate independently.
As shown in figure 5, the SMA wire will run al
ong the
length of the tube prec
eding the one which is to be
actuated. It will pass through an eye hook at the end of
that tube that will route it horizontally and will be
attached to t
he side of the actuated tube. The applied
voltage will cause the length of the SMA wire to
decrease, pulling on the actuated tube and causing it to
rotate.

As shown in the figure, a spring attached to a
wire will run along the length of the other side of

the
tube. This spring will be used in the absence of actuation
to maintain the twist at the
-

θ
max
value. The SMA will
be actuated to twist the section to any angle in the range
-
θ
max

to


max
.



Figure 6: Prototype version of the SMA actuation
mechanism

Spring

SMA wire

Front View

Side View


5


A prototype version of the actuation mechanism, shown
in Figure 6 above, was built and test
ed. The SMA wire
was not previously trained, and thus there was no control
over the amount of torque exerted on the tube. The test
was simply conducted to verify that the concept of using
an SMA wire to exert a torque would work. Voltage was
applied sev
eral times and each time a noticeable twisting
of the tube occurred.

The test also served to bring to
light some of the practical problems associated with the
design such as the need for insulation between the SMA
wire and the tubes and the difficulty of
mounting the
SMA wire to the tubes so that it will not slip under the
loads applied.


Locking Mechanism

Since the SMA wire cannot remain actuated for long
periods of time due to excess heat, a locking mechanism
is employed to hold the sections fixed at the

desired
angle of twist after actuation. The locking mechanism
also provides the ability to rotate only

the outer

one or
two sections while holding the
inner ones closest to the
fuselage

fixed.



Fig
ure 7: Schematics of the locking mechanism


As shown in figure 7 above, the locking mechanism
consists of a gear
with a high diametral pitch
attached to
the tube to be locked. A pinion held in place by a spring
interferes with the rotation of the gear, pr
eventing
twisting. During SMA actuatio
n, a motor attached to the
prec
eding tube is used to pull back the pinion and allow
the tube to rotate freely. When actuation is complete, the
pinion is released and falls back into place in the gear
teeth.





Skin

The structure of the wing is to be covered by a flexible
skin that provides for a continuous twist along the length
of the span. The material chosen for the skin was a
silicone rubber elastomer being developed by Dr.
Andrews of the Mechanical Engineering
Department at
Texas A&M University.



Figure 8: Elastomer Skin


The skin shown in Figure 8 above is formed as a 5 mm
thick sleeve that will be pulled over the assembled
structure and attached onto the fuselage.


The final versio
n of the skin to be used on the wing will
contain a small percentage of carbon nano
-
tubes
embedded in the elastomer for additional strength while
retaining the necessary flexibility. Carbon nano
-
tubes
are carbon atoms arranged in a tubular shape. In test
s
they have demonstrated and extremely high strength
-
to
-
weight ratio, with strengths up to 100 times
that

of steel
and only 1/6 of the weight.



0-100 % strain
-20
0
20
40
60
80
100
120
0
20
40
60
80
100
120
Strain(%)
Stress (psi)
Plain 0.1% without PVP
0.3 % without PVP
0.1 % with PVP

Figure 9: Stress
-
Strain Curve of Silicone Rubber with
various percentages of carbon nano
-
tubes


The graph ab
ove shows the stress
-
strain curve for
silicone rubber. The critical point of plain silicone
-
rubber elastomer lies at roughly 83 psi. The critical point
rises with the addition of nano
-
tubes, up to 109 psi for a
0.3% nano
-
tube elastomer. Because of the c
urrent
difficulties of both manufacturing nano
-
tubes and
creating the elastomer with a uniform distribution of

6

nano
-
tubes, all analyses done on the skin have used the
properties of the plain silicone
-
rubber elastomer.



Figure 10: The skin mold and die


The skin is to be created using the casting process. The
liquid elastomer will be poured into the mold
shown
above
and the die will inserted so that the liquid spreads
itself out into the gap between t
hem. Once the liquid has
cured the die will be removed and the skin will be
assembled on the structure. As will be mentioned later, a
degree of pre
-
stress is needed in the skin as it is
assembled on the wing. The mold has been designed in
accordance wit
h this pre
-
stress strain value, thus the skin
produced by the mold will be stretched during assembly
on the structure, producing the desired value of strain.


Analysis

Extensive analysis was done to refine and validate the
wing design. A CFD analysis of t
he wing was
conducted, with the results used to develop a finite
element model of the wing’s functions. The FEA
highlighted two specific issues with the wing design,
which were further analyzed until remedied.


CFD
Analysis

Initial CFD calculations were p
erformed using the fluids
program GAMBIT.


Figure 11: Coefficient of lift versus angle of twist



Figure 12: Coefficient of pitching m
oment versus angle
of twist



A wing section was analyzed for diff
erent angles of
attack at a twist of 0 to 15 degrees, with the results
shown in the Figures 11 and 12 above. The effects of the
wing twist on both lift and pitching moment can easily
be seen. At low levels of attack the relationships are
fairly linear, t
ending slightly toward non
-
linearity at
higher angles of attack. From the simulation a graph of
the pressure distribution along the wing cross
-
section
for
a speed of 2
0 m/s
was also produced.


Finite Element Analysis

A finite element analysis of the wing

was conducted
using the finite element/modeling program ABAQUS
CAE. Initially only one of the three wing sections was
modeled. The boundary conditions applied were those of
a cantilevered beam, with the structure held fixed on one
end at the fuselage.
The nodes at the other end were
given displacements corresponding to a specified angle
of twist at the cross
-
section. Aerodynamic loads
calculated from the CFD analysis were placed on the
wing
. The analysis showed a small degree of
deformation of the ski
n due to the twisting and
aerodynamic loads.


Another analysis was later conducted involving two wing
sections. For simplicity of modeling, the chord length of
the sections was chosen to remain constant rather than
tapered as in the actual configuration.

A cross
-
sectional
support was introduced between
the sections.
D
isplacement boundary conditions were given at both
the cross
-
sectional support and the section end as shown
in the figure below.



"Coefficient of Pitching Moment Vs Angle of Twist" @ different angles of attack
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0
2
4
6
8
10
12
14
16
Angle of Twist (in deg)
Coefficient of Pitching Moment
0 deg
3 deg
6 deg
9 deg
12 deg
15 deg

"Coefficient of Lift Vs Angle of Twist" @ different angles of attack
0
0.2
0.4
0.6
0.8
1
1.2
0
2
4
6
8
10
12
14
16
Angle of Twist (in deg)
Coefficient of Lift
0 deg
3 deg
6 deg
9 deg
12 deg
15 deg

7


Figure 13: Boundary conditions
of the two
-
section finite
element model


Simulations were run for several different combinations
of twist angles.
Initial simulations were run without the
aerodynamic loads to determine the effects of twisting
alone on the wing. A small amount of skin buc
kling was
noticeable from observation of the deformed plots.
Simulations were then run with the addition of
aerodynamic loads. Several cases were run, including
t
he extreme case of a
-
10 degree middle twist and a +
10
degree end twist (absolute)
.



Figure 14: Top and bottom views of wing in a
-
5, +10
degree configuration



In all cases that were run
there was noticeable buckling
of the skin under the loads

as shown in Figure 14 above
.
The buckling

is found primarily on the lower surface of
the skin. Two methods were developed to
compensate
for the buckling. Pre
-
stressing the skin in both the axial
and cross
-
sectional directions during assembly would
serve to reduce the buckling. The second metho
d
developed was to introduce a small pinhole at a location
on the wing to be determined
which

would equate the
pressure inside the section to the stagnation pressure at
the location where the hole meets the exterior free
-
stream conditions. The internal pr
essure resulting could
be set to any value from 0 to the maximum pressure
exerted on the outer surface of the wing. Simulations
were run
for a
-
5, +10 degree configuration
for various
combinations of internal pressure and initial pre
-
stress.
From the sim
ulations it was apparent that the
combination of pre
-
stress and internal pressure served to
greatly reduce the amount of skin buckling. Both the
cross
-
sectional pre
-
stress and t
he internal pressure had a
noticeable

effect on the buckling, while the effect

of the
axial pre
-
stress was not as apparent.

Increases in pre
-
stress resulted in small changes in the degree of
buckling. Changes in the internal pressure had a larger
effect on the amount of skin deformation. Larger values
of internal pressure cause
d the structure to balloon out,
negating the effect of the aerodynamic forces. Above a
certain value,

however, the skin ballooned

too much,
causing bumps along the top of the wing.


Skin Deformation Analysis

From looking at the deformed plots, it was no
t obvious
which combination of internal pressure and pre
-
stress
resulted in the minimum degree of buckling.

Thus a
method was needed to better compare the amounts of
buckling for each case. An ideal configuration for the
wing (no buckling) was generated
in Matlab by
constraining each cross
-
section to retain its airfoil shape
during rotation.

The outputs from the ABAQUS
analyses were read into Matlab and the deformed plots of
the ABAQUS output and the Matlab ideal shape output
were compared.





Figure 15: Plots comparing the ABAQUS and Matlab
wing configurations for the no
-
load, no
-
prestress, no
internal pressure case


The comparison plot
s

for the no
-
load, no
-
prestress, no
internal pressure c
ase ar
e

shown in Figure 15 above.
The
Matlab generated ideal deformed coordinates are plotted
as the rainbow
-
colored surface. Because the plotting of
the ideal configuration of the outside of the skin would

8

have made it impossible to see the areas of buckling,

the
ideal configuration of the inner surface of the skin was
plotted instead. The ABAQUS deformed profiles are
plotted in blue for the wing’s top surface and red for the
bottom. The regions where the rainbow
-
colored surface
is visible represent areas
wh
ere the skin deforms so much
that the outside surface is actually inside of where ideally
the inner surface should be.






Figure 16: Plots comparing the ABAQUS and Matlab
configurations for the c
ase of aerodynamic loads applied,
200 Pa internal pressure, and
10% prestress


This method was used for several cases of different
values of internal pre
-
stress and internal pressure. From
Figures 15 and 16 the decrease in buckling with the
application o
f the pre
-
stress and internal pressure is
obvious. Buckling is almost eliminated along the top
surface and greatly decreased in the bottom.


While this method provided a better comparison between
different cases, it also had its flaws. The ideal
configur
ation generated by Matlab would not the same as
the real ideal configuration because the Matlab profile
assumed uniform linear twisting of the structure while in
reality this will not be true.
Also, although ideally the
skin would retain the airfoil cross
-
section at each point
along the span during twisting, physically this would not
happen. A small amount of
buckling is

necessary for the
skin to achieve the configurations that the angles of twist
dictate.



Figure 17:
Error ra
tio plot for case of 200 Pa internal
pressure, 10% chord
-
wise and 10% axial prestress


Figure 18: Error ratio plot for the case of 250 Pa internal
pressure, 10% chordwise and 10% axial prestress


The skin deformations for variou
s cases were also
compared to the deformation values for the no
-
loads, no
internal pressure and no pre
-
stress case, where any
buckling would result solely from twisting. Figures
17
and 18 above are plots of the ratio of the difference in
skin deformation
between specific cases and the no
-
loads
case to the total deformation of the no
-
loads case at
points along the span. The error ratio plots for each case
provided a quantitative comparison of the deformation
values for the different cases. The higher rati
o values
seen in Figure 18 reflect the ballooning out of the top
surface due to the internal pressure.


The difference in skin deformation between the loaded
cases and the no
-
loads case were also plotted along the
chord
and span, providing visual display o
f both the
location and the magnitude of the buckling for each case.
The results for one case are shown in Figure 19 below.



9




Figure 19: Plots of the difference in skin deformation
between the 200
Pa internal pressure, 10% chord
-
wise
and span
-
wise prestress and the no
-
loads case on the top
(upper figure) and bottom (lower figure) of the wing.


The combination of these methods of deformation
analysis provided an accurate picture of the effect of pre
-
stress and internal pressure on the amount of buckling in
the wing. The conclusion of the analysis was that an
internal pressure of 200 Pa and a chord
-
wise and span
-
wise pre
-
stress of 10% would be sufficient to reduce the
buckling in the skin. Although h
igher values of pre
-
stress would yield decreased buckling, their effects were
small enough to be discounted due to the increased
difficulty

of assembling
a skin with a greater pre
-
stress
onto the structure.


Structural Analysis

The finite element analysis
was also run on ABAQUS
with the skin removed to determine the stresses in the
structural support. The structure was subjected to a
-
5
degree middle twist and a +10 degree end twist. The
original design called for solid supports in the front and
rear of t
he wing. The analysis showed that local stress
levels in the structure reached as high as 144 MPa, far
exceeding the failure point of the ABS plastic, roughly
45 MPa. As seen in Figure
20 below, stress levels were
particularly high near the joints connec
ting the rear
support to the cross
-
sectional support.



Figure 20: Stress levels in solid structure subjected to
-
5,
+10 degree twist


Several variations of the original design were attempted
with
little success in reducing the
local stresses. The
front and rear supports were eventually remodeled to be
hollow and open to the inner section of the wing.
Several different cases were run varying the geometric
parameters of the supports until the configuration
resulting in the lowes
t stress levels was determined.



Figure 21: Stress levels in hollow structure subjected to

-
5, +10 degree twist


The maximum stress level reached for the configuration
shown in Figure 21 above was 44 MPa, just under the
critic
al point of 45 MPa. In addition to lowering the
stresses, the hollow supports offer several other
important benefits. They require less torque to deform to
a given angular displacement, resulting in lower forces
needed from the SMA. They also provide mo
re interior
room in the wing and decrease the total weight,
important factors in the final design.


Experimental Validation

After the structural and skin deformation analyses were
completed, the
wing structure was built and the tubes
were assembled onto
it as shown below.



10


Figure 22: Assembled wing structure


Experimental validation was necessary to determine the
torques required to achieve different angles of twist and
to verify the skin deformations from the ABAQUS
analysis.



Torque Requirements

An initial analysis of the torques required for actuation
was done using the information garnered from the finite
element analysis. The torques for various angular
configurations were computed using the reaction forces
determined b
y ABAQUS at the sections of twist.
The
torque value for
a

maximum angular displacement of 15
degrees was computed to be approximately 0.9 N
-
m.
The values of the reaction forces, however, were very
eratic and so the need arose to check the torque
requirem
ents experimentally.

The decision was made to
validate the torques required to achieve angular
displacements of up to 5 degrees for the root section and
10 degrees for the two outer sections rather than the 15
degrees that had been simulated.


An experime
nt was set up to determine the relationship
between the applied torque and the angular displacement
for the wing sections. Because of the very low torque
values, the available torsion testers were not able to
measure the required torques. A simple method

shown
in Figure 23 below was set up using weights applied at a
known distance from the center of the tube.



Figure 23: Experimental setup to validate torque
requirements


An electronic level was attached to a flat surface on

the
fixture fastening the tubes to the cross
-
sectional supports.
The angular displacements were recorded as different
combinations of weights were applied. In the first test,
the first section was rotated to a maximum displacement
of 5 degrees and the t
wo outer sections were rotated to
10 degrees. The tube connected to the root chord was
held fixed and all other tubes were free to rotate,
meaning that in this test all rotations were distributed
along the span. The results from this test are shown in
th
e graph below.


Deflected Angle vs. Torque
0
2
4
6
8
10
12
0
0.5
1
1.5
2
2.5
3
Torque (N-m)
Deflected Angle (degrees)
Section 1
Sections 1
& 2
All Sections

Figure 24: Graph of deflected angle versus applied
torque for the three sections


As can be seen from the graph, the highest torque
required for achieving the goal angular displacements is
roughly 2.1 N
-
m to give the first section the max
imum 5
degree twist. This corresponds to an 83 N force required
from the SMA, well within the acheivable force range of
SMA wires.


Skin Deflection

Experimental validation of the skin deflection results
from the ABAQUS simulation will be done using a nove
l
structured light sensing system being developed at Texas
A&M University.




Figure 25: Structured light setup for measuring skin
displacements



As shown in Figure 25 above, stripes are marked along
the along the span of the wing and a laser is reflecte
d off
of the stripes to a camera. Initial calibration of the
system is conducted before twisting and then the process
is repeated after twisting to determine the displacements

11

along the marked stripe. This test will be used to
calibrate the deformation r
esults from the ABAQUS
simulations.


Future Research

After the validation testing is completed the actuation
and locking mechanisms will be assembled onto the
structure. The skin mold will be created and the skin
will be
put on the wing. The completed wi
ng will be
mounted in the wind tunnel for testing. Different twist
configurations will be tested to gather data so that a
mathematical model can be created to relate the
variations in wing geometry to variations in aerodynamic
forces and moments. Control

algorithms will then be
created to actuate the wing to different configurations
depending on the desired aerodynamic characteristics.


Conclusions

The morphing wing project is still in the early stages of
development. The basic design for the wing has be
en
developed and simulated. Validation testing has begun
to ensure the results o
f the simulations are accurate.
From the design analysis that has been completed thus
far the design has proven to be feasible and capable of
performing as stated in the proj
ect goals, barring any
unforeseen issues.


Conclusions
-

Skin Deformation


The skin deformation analysis has led to the conclusion
that a small degree of buckling is necessary to achieve
the desired wing configurations and is to be expected.
The extensive

analysis on the various possible
combinations of pre
-
stress and internal pressure has led
to the selection of an internal pressure of 200 Pa and a
chord
-
wise and span
-
wise pre
-
stress of 10%. The
analysis has also highlighted the necessity of a nano
-
tube
reinforced
skin for additional strength to

further decrease
buckling, as even the best possible combination of pre
-
stress and internal pressure could not eliminate all excess
buckling.


Conclusions
-

Structural Analysis

The structural analysis has shown tha
t the original design
calling for solid front and rear supports was unfeasible.
It led to a redesign of the structure with hollow supports
open to the interior which decreased the stresses to safe
levels. The analysis has shown that for a maximum
rotatio
n of 15 degrees per section the structure should not
fail.


Conclusions
-

Torque Validation

From the torque validation testing relationships could be
determined between the applied torque and angular
displacement for each of the sections. From these
relati
onships the maximum force needed fro
m the SMA
to achieve all of the desired angular configurations was
determined to be approximately 84 N, well below the
maximum force of 94 N that the particular diameter
SMA being used is capable of. The torque testing
also
proved that the stresses in the structure remained in the
safe region for all of the desired angular configurations.


Acknowledgements

This work was sponsored by the Texas Institute for
Intelligent Bio
-
Nano Materials and Structures for
Aerospace Vehic
les

(TiiMs)
, funded by NASA
Cooperative Agreement No.

NCC
-
1
-
02038
.


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