Aeroelasticity Assignment

advertisement
CRITICAL ANALYSIS OF
LOCKHEED MARTIN X-56A
FROM AEROELASTICITY
PERSPECTIVE
INTRODUCTION
Early aeroelastic design problems
Up until world war I, the aircraft speeds were slow and the structural stiffness were large enough
that the loads due to aeroelastic deformation were inconsequential for almost all airplanes. Back in
1909, six years after the Wright’s first flight, Bleriot flew from France across the English Channel at
the speed of 40 mph. The aeroplane flown over the channel was an externally braced monoplane
with wing wrapping control which became massively popular soon after.
The concept of the wing wrapping design was so that the wing torsional stiffness was relatively low
so that the wing would be twisted by the pilot. However, this design started experiencing failure due
to its low stiffness once the aircraft is mounted by a new engine with a higher power and airspeed.
These failures began to occur for no apparent reason, therefore, at first it was thought that the
structural failure occurs due to insufficient wire bracing strength within the aircraft wing. To
overcome the failure, Bleriot started increasing the stiffness of the wings by strengthening the guy
wires and also increasing the size of the main wing spar but none of these changes addressed the
structural failure.
Due to difficulties on addressing the wing failure, Britain has banned the monoplanes flights in 1912
but years later by the approaching of World War I required rescinding this ban and investigation
started to address the wing failure of the aircraft. The recent finding was indicating that the thin
wing monoplane designed was failing due to the twisting caused by the loads during the
manoeuvring. Due to torsionally flexible wings design, they would allow the load to twist the wing
tips easier at a higher speed overload the load the wing so quickly before the pilot could recover the
aircraft stability.
Most of the designers around the Europe influenced by the new Bleriot’s design which discovered
new aeroelastic effect that later to be associated with the wing divergence effect. However, since
the analysis technology hasn’t been advanced yet, but the basics of the mechanism could be
understood and analysed by designers.
The early aeroelastic wing failures were documented on a fighter aircraft during the World War I
occurred on the German Fokker monoplane. This high-performance aircraft started facing failures
during high-speed pull-out manoeuvres. As it has been obtained from the static strength and
deflection measurements results, it has been obtained that failure were occurred due to wing
torsional deformation caused in increased airloads on the wing same as the Bleriot airplane. To
overcome the failure, it was required to increase the torsional stiffness of the wing by repositioning
a wing structure to eliminate the failure.
During the World War I, British Handley bi-plane bomber started showing vibratory aeroelastic
instability on the horizontal tail of the aircraft which was also known as flutter. Investigation in 1916
revealed that this flutter occurs due to interaction between the fuselage twisting motion and the
anti-symmetrical pitch rotation of the independently actuated right and left elevators. To address
the issue, the designers found out that by connecting the elevators to a common torque tube, they
can eliminate the anti-symmetrical motion. Later on, this design is used for the tail flutter difficulties
by attaching the both elevators to a same torque tube and this became a standard design practice
since.
As time passes by, the engines become lighter and more powerful. As the speed increasing, the
monoplane again start showing failures, but this time, a new type of aeroelasticity instability
occurred called wing-aileron flutter. In this type flutter, the wing warping effected the control and
led to wing divergence and the aileron control led to the dynamic aeroelastic failure.
Wing-aileron flutter occurs when the lift generated by the oscillation of an aileron or tab drives the
wing bending or torsion deformation of the wing. The oscillation frequency is proportional to the air
speed due their characteristic where the aileron acts as a weathervane that its rotational stiffness
increases as the air speed increasing. As the aileron accelerated through the air, as well as air-loads
transmission to the wing will introduce the oscillations of the wing and creates a mutual coupled
vibration throughout the flight.
The aircraft to be analysed in this review is the Lockheed Martin X-56A. It is designed to fly HighAltitude Long Endurance (HALE) and perform high-risk operations. This aircraft’s integrated flight
and aeroelastic controls can manage multiple flutter mode to include; first symmetric body-freedom
flutter (SBFF), first symmetric wing bending-torsion (SWBT) flutter and first anti-symmetric wing
bending-torsion (AWBT) flutter, using a closed loop control system.
Design Specifications of X-56A;







It has a length of 7.5 ft
wing span of 28 ft
Powered by two 90-pound thrust turbojet engines
Wing aspect ratio of 14
Speed of 222km/hr
Weight of 480 lbs
A set of stiff wings, three sets of flexible wings which forms blended swept back wing
configuration.
Figure 1: Three-view drawing of X-56A aircraft
Generally, designing an aircraft against undesirable aeroelastic phenomena (flutter, divergence,
gust, buckling) comes with a compromise in the performance. Improvement of an aircraft could
translate to introduction of these unwanted phenomena which will make them unrealistic. This
paper presents aeroelastic design for the X-56 in line with its operations. Different optimization and
improvement methods using structural reconfigurations will be reviewed.
METHODOLOGY
Wing flutter
Flutter basically comes down to the number of modes coupling together of motion which facing
oscillations created by aerodynamics forces that enables the energy to be transferred from the
airstream to the structure of the body so that the amplitude of the motion will grows in time.
Flutter has also been discussed on the early aircrafts as a mode of failure and illustrate vibration
modes. Figure below illustrate the importance of acknowledge of the vibration modes on the aircraft
structure during the flutter mode
Figure below indicated the time histories of the three different types of dynamic displacement
behaviour acting against the wing and wing response to the disturbance while the aircraft flying.
Looking at point A, the disturbance at point A caused by the airspeed is decays as the time
increasing, however as the airspeed increase at point B, the harmonic oscillatory motion amplitude
stays fixed regardless of the time length. Operating at point C however can come to disaster since
the amplitude of the oscillation increases as time increase. These three motions are classified as
stable, neutrally stable and unstable.
To explain the forces acting on the wing, there are two characteristics of movements within the
wing. If a sinusoidal force applied to the wing at a dynamic pressure A with a fixed maximum and
minimum values and a specified frequency level, the resonant frequencies will be observed as it is
shown on graph A. the resonant motion however can deform the wing shape either with respect to
the wing cantilever support or it can be appearing as a torsional or twisting form. The wing motion
however is not purely bending nor torsional in nature regardless of the airstream speed, it is purely a
linear combination of both bending and torsional types.
The wing resonant frequencies will get effected as the airspeed and dynamic pressure increase.
According to (Cordier, 2018), once the wing has attaches to the fuselage of the aircraft, it has a
natural structural frequency, however, this frequency can be affected by the external forces such as
relative wind and aerodynamic forces and can create periodic frequency. Once the periodic
frequency of the external force becomes the same as the natural structure frequency on the wing,
the wing will experience a resonance vibration and the amplitude of the vibration can become
critical and results in wing failure if it goes for a certain time.
Burnett (2016), designed and tested for active flutter suppression in the X-56A. He stated that
geometry and mass distribution are very important parameters while considering aeroelastic
behaviour of this aircraft. Modelling for mass distribution were done for both the stiff wings and
flexible wings configurations. By using rigid/flex coupling variables, Rigid Flex Coupling behaviours
were produced from which state-space models were generated. These models were in form of
400*400 state matrices and serve as the mathematical model.
Roots of this matrix were plotted in form of velocity-frequency and velocity-damping plots giving
information about the SBFF, SWBT, AWBT, SW1B, AW1T and SW1T.
Figure 2 : Velocity-frquency and velocity-damping plots of the aircraft (Burnett, 2016)
In a similar development by Wesley (2015) and for purpose of this analysis, design variables were
used iteratively to make geometric and structural changes. The type of design variables is dependent
on shape configuration of the aircraft. Aeroelastic response or feedback serves as a constraint
(inequality, equality and side) for further problem solving.
𝑓(𝑋) = 𝑡𝑜𝑡𝑎𝑙 𝑠𝑡𝑟𝑢𝑐𝑡𝑢𝑟𝑎𝑙 𝑤𝑒𝑖𝑔ℎ𝑡 𝑜𝑟 𝑓𝑙𝑢𝑡𝑡𝑒𝑟 𝑠𝑝𝑒𝑒𝑑𝑠
Where;
Inequality constraints, 𝑔𝑗 (𝑋) ≤ 0, 𝑗 = 1, 𝑀
Equality constraints, ℎ𝑘 (𝑋) = 0, 𝑘 = 1, 𝐿
Side constraints, 𝑥𝑖𝐿 ≤ 𝑥𝑖 ≤ 𝑥𝑖𝑈 , 𝑖 = 1, 𝑁
𝑥𝑖𝐿 𝑎𝑛𝑑 𝑥𝑖𝑈 are the lower and upper bounds on each design variables
Using data made available by Armstrong flight research centre, aeroelastic design of the aircraft
against flutter was reviewed. Aeroelastic optimization and structural analysis was done by a MSC
Nastran code and a CFD solver in an MDAO tool. A matrix describing pressure changes due to
unsteady aerodynamics were generated using the double lattice method in the MSC Nastran. The
flutter analyses using MSC Nastran PK solution method merges structural and aerodynamics grids by
spline interpolation and derives a general aeroelastic matrix using structural modal matrix.
Figure 3: Flowchart of flutter analysis for Aeroelastic mass balancing and tailoring in MDAO tool
AEROELASTICITY ANALYSIS OF LOCKHEED MARTIN X-56A
Aeroelastic Tailoring
Aeroelastic tailoring can be defined as “the embodiment of directional stiffness into an aircraft
structural design to control aeroelastic deformation, static or dynamic, in such a fashion as to
affect the aerodynamic and structural performance of that aircraft in a beneficial way,” [1].
Conventionally, tailoring has been carried out with composite shell structures using bendtwist coupling inflicting either wash-in affect (causing tip leading edge up) or similarly washout affect (causing tip leading edge down). Conventional aeroelastic tailoring of X-56A targets
on stiffness-primarily based techniques by designing a basic wing structure to avoid flutter
action exceeding the given flight envelope with minimum structural weight and still meet the
design parameters. Certain limitation factors were placed such composite failure index(CFI),
flutter speed, buckling load factors (BLF) and flutter frequency.
After the flutter constraints was set to values between 0.002- 0.003 with an additional
tolerance parameter, with the initial wing structure designed to be operated with safety
factor 1.5 manoeuvre loads condition and able with stand G-force acting between a range of
2.5g and -1.0g, to guarantee flutter free within the given flight envelope the lowest flutter
speed value ought to be greater than the normalized speed of 1.62.
Once different design variables were set to optimize with minimization of weight of aircraft
wing by tailoring, two cases were investigated, case 1 being 12 design variables that consists
of ply thickness only and case 2 being 24 design variables which considers both ply thickness
and ply orientation. Initially hybrid optimisation approach was executed by means of 2 steps,
first using genetic algorithm (GA) and discrete design variable (DDV) which produces several
thousands of feasible solutions which a tedious and time-consuming process, hence to resolve
the accurate optimum design a continuous design variable (CDV) with design optimization
tools (DOT) was implemented.
Table 1 – Aeroelastic Tailoring Cases
As for structural and normalized flutter responses cases 1 and 2 both have similar flutter
mechanisms, but due to the application of different initial ply angles there is small difference
in the flutter frequency and flutter speed.
Once the results of both case 1 and case 2 were compared, was able to determine that case
2 which included both ply thickness and ply orientation had produced a much better design
which additionally provides 10% of weight reduction on the overall wing design than the case
1. The only drawback in this that it is not very practical to manufacture these composite ply,
as the airframe manufacture industry is able to produce only predefined composite ply
thickness, therefore it must be round up or down to try and meet the design variables,
although by this approach the critical flutter speed and frequency were satisfied with a
minute weight reduction of the aircraft.
In conclusion the concept of aeroelastic tailoring allows us to investigate the strength of
composite materials and how vastly the orientation of these ply affects it, also using
aeroelastic tailoring with hybrid optimization has improved the final design with flutter speed
constraints under the flight envelope, while simultaneously maintain the least possible
structural weight.
For future development there are interchanges between curvilinear and straight structurers
to design wings using curvilinear ribs, spars and panel stiffeners, also it might be beneficial to
allow tow steering or material grading to vary within the small sections of wing to have high
impact and excellent buckling operation when compared to non-steered panels.
Flutter Mass Balancing for X-56A
A Wing design adjustment technique was adopted to ensure flutter speeds were within the flight
envelope. Using an object-oriented, MDAO (multidisciplinary design, analysis, and optimization) tool
as an alternative to trial and error, various wing configuration analysis were carried out
simultaneously. Flutter speeds of the aircraft non-validated design with EFEW (Empty Fuel Empty
Water) configuration were within design requirement. A subsequent validated design after
necessary ground vibration test (GVT) leaves the second and third predicted flutter outside the flight
envelope. The validated design was taken as a baseline design for the flutter mass balancing
simulation. At the speed of 222km/hr, normalized SWBT and AWBT flutter speeds are 1.48 and 1.68
respectively which are relatively high. The mass balancing technique was employed to checkmate
these flutter speeds and put them back into flight envelope while total ballast weight meets with the
requirement. This method is carried out without the need to alter wing ply thickness and orientation
angles (aeroelastic tailoring).
To enable change of total weight of the aircraft while flying, multi-points design was adopted. Two
weight configurations, EFEW (Empty Fuel Empty Water) and FFFW (Full Fuel Empty Water) were
accounted for. Design requirements for flutter speed and frequency constraints serve as the
standard for the optimization. First flutter, SBFF (symmetric body freedom flutter) is 0.79 to 0.98,
second flutter, SWBT (Symmetric wing bending torsion) is 0.98 to 1.18, the third flutter AWBT (Antisymmetric wing bending torsion) is 0.98 to 1.30. Initial predictions were made for baseline
configuration. The velocity-damping and velocity-frequency graphs show EFEW baseline
configuration. The graphs show that the symmetric wing first bending (SW1B) and the symmetric
wing first torsion (SW1T) mode coupling created a SWBT normalized flutter speeds of 1.48 and
AWBT of 1.68.
Figure 4: The speed-damping and speed-frequency graphs for empty fuel and empty water ballast
configuration: (a) initial design; (b) final design with 20-lb nose and 4-lb trailing wing tip
These speeds need to be moved into the flight envelope. Mass balancing optimization using design
optimization tool with continuous design variable helped to investigate ballast location of three wing
configurations. For proper mass distribution and structural integrity, ballast masses were distributed
from left to right sides of the wing. For configuration 1, six mass ballasts of around 5 lb were
positioned at the leading edge. For configuration 2, thirteen mass ballasts were used. Ten of those of
around 5 lb were shared between wing leading and trailing edges, one mass ballasts of 20 lb at the
nose of the centre body. For configuration 3, mass distribution was improved by increasing the
trailing wing tip up to 25-in in length having five mass ballast. Segments were formed at a 5-in length
by each mass ballast. Configuration 3 is an improvement on configuration 1 and 2. A total of eleven
mass ballasts were used to include a centre body nose ballast, and the five corresponding ballasts at
the trailing edges.
Figure 5: Flutter mass balancing optimization design configurations
Flutter
Mode
Normalized Speed
Normalized Frequency
Lower
EFEW FFFW Upper
Lower
EFEW FFFW
bound
bound
bound
requirement
requirement requirement
SBFF
0.79
1.13
1.16 0.98
0.53
0.68
0.53
SWBT
0.98
1.48
1.48 1.18
1.17
2.34
2.25
AWBT
0.98
1.68
1.68 1.30
1.50
1.52
2.43
Table 2: Mass balancing baseline flutter predictions and requirements at Mach 0.16
Configuration
1
Number
of ballast
mass
6
Objective
Min. total ballast
mass and target
flutter speed
Upper bound
requirement
1.76
2.35
3.52
Design requirements
Nose ballast (lb)
Wing ballast (lb)
Lower limit Upper limit
Lower limit Upper limit
N/A
N/A
0.0
5.0
2
13
Min. total ballast
0.0
20.0
mass and target
flutter speed
3
11
Min. the first
0.0
20.0
flutter speed
Table 3: Flutter mass balancing design configurations descriptions
Configuration 1
Final value
Lower limit
Wing leading edge ballast (lb)
1
0.0
0.0
0.0
2
0.0
0.0
0.0
3
0.0
0.0
0.0
4
0.0
0.0
0.0
5
0.0
0.0
0.0
Wing trailing edge ballast (lb)
6
0.0
5.0
0.0
Table 4: Flutter mass balancing configuration 1 design variables
Variable Ballast
Initial value
0.0
5.0
0.0
5.0
Upper limit
5.0
5.0
5.0
5.0
5.0
5.0
Configuration 2
Variable Ballast
Initial value
Final Value
Lower limit
Nose ballast (lb)
1
0.0
20.0
0.0
Wing leading edge ballast (lb)
2
0.0
0.0
0.0
3
0.0
0.0
0.0
4
0.0
0.0
0.0
5
0.0
0.0
0.0
6
0.0
0.0
0.0
7
0.0
0.0
0.0
Wing trailing edge ballast (lb)
8
0.0
0.0
0.0
9
0.0
0.0
0.0
10
0.0
0.0
0.0
11
0.0
0.0
0.0
12
0.0
0.0
0.0
13
0.0
5.0
0.0
Table 5: Flutter mass balancing configuration 2 design variables
Variable
Ballast
Case I
Initial
value
Final
value
Case II
Initial
value
Configuration 3
Case III
Final
Initial
value
value
Upper limit
20.0
5.0
5.0
5.0
5.0
5.0
5.0
5.0
5.0
5.0
5.0
5.0
5.0
Final
value
Design requirement
Lower
Upper
limit
limit
Nose ballast (lb)
1
20.0
20.0
20.0
20.0
20.0
Wing tip boom ballast (lb)
2
0.0
0.0
0.0
0.0
1.0
3
0.0
0.0
4.8
0.0
1.0
4
0.0
0.0
0.0
0.0
1.0
5
0.0
0.0
0.0
0.3
1.0
6
0.0
5.0
0.0
4.7
1.0
Wing tip ballast x location (inch)
7
216
216
216
216
216
8
221
221
221
221
221
9
226
226
226
226
226
10
231
231
231
231
231
11
236
236
236
236
236
Table 6: Flutter mass balancing configuration 3 design variables
Flutter mode
1
SBFF
SWBT
AWBT
EFEW
1.16
1.49
1.59
2
FFFW
1.18
1.67
1.57
Flutter mode
1
EFEW
FFFW
SBFF
0.66
0.52
SWBT
1.28
1.25
AWBT
2.09
2.02
*Flutter occurs before SBFF
20.0
0.0
20.0
0.0
0.04
0.04
2.4
5.0
0.0
0.0
0.0
0.0
0.0
5.0
5.0
5.0
5.0
5.0
216
221
226
231
236
211
216
221
226
231
216
221
226
231
236
Normalized flutter speeds
Configuration
3-case I
3-case II
EFEW
1.12
1.49
1.56
FFFW
EFEW
FFFW EFEW
1.12
1.13
1.14
1.13
1.67
1.11*
1.18
1.12*
1.55
1.29
1.26
1.29
Normalized flutter frequency
Configuration
2
3-case I
3-case II
EFEW
FFFW
EFEW
FFFW EFEW
0.71
0.58
0.72
0.58
0.72
1.28
1.25
1.07
1.03
1.07
2.07
2.01
1.57
1.55
1.57
3-case III
FFFW
1.14
1.18
1.26
EFEW
1.14
1.06*
1.30
FFFW
0.58
1.03
1.54
3-case III
EFEW FFFW
0.71
0.57
0.99
0.95
1.44
1.42
Table 7: Flutter mass balancing flutter results
For configuration 1, the change in ballast 6 from 0.0 to 5.0 shows that a 5-lb ballast was added to the
wing tip causing third flutter speed decrease from 1.68 to 1.59 (EFEW) and 1.67 (FFFW). Comparing
results of configurations 1 and 2, the additional mass of 5 lb of ballast to the wing tip shows similar
increase in mass effectiveness of the load. Configuration 2, also shows that addition of 20-lb mass at
nose of the centre body reduces the normalized SBFF speed from values of 1.16 to 1.12 (EFEW) and
1.18 to 1.12 (FFFW). Based on this understanding, optimization of configuration 3 was performed
where trailing wing tip design was adopted, since the objective is to get second and third flutter speed
into flight envelope and to further reduce first flutter speed. The constraints were; 0.98 < V2 < 1.18,
0.98 < V3 < 1.3 which represents the second and third flutter speed. The three optimization cases in
table 6 produced similar outcomes by adding 5-lb ballast of the trailing wing tip boom. Final design of
Case I is the most implementable, having lighter weight than case III.
FFFW
1.14
1.10*
1.26
Figure 8: X-56A ballast configuration flight envelope
Conclusion and Recommendation
From this analysis it has been proven that the second and third flutter speed can be lowered to meet
flutter speed requirement by using trailing wing tip blast system. It is seen that for EFEW
configuration, the normalized SBFF speed is 1.13 and the normalized SWBT flutter speed is 1.11. A
significant reduction occurred in the SWBT flutter speed when ballast of 5-lb was applied. The
object-oriented MDAO tool also proved to be an effective analytical wing configuration tool.
However, further improvements can be carried out either by adjusting ballast mass at various
locations, further adjustment of the trailing wing tip boom design or design of complementary
trailing wing tip at strategic locations.
References
[1] Shirk, M., Hertz, T., Weisshaar, T., “Aeroelastic Tailoring – Theory, Practice,
Promise,” Journal of Aircraft, Vol. 23, No. 1, pp. 6-18, 1986. 22, 03, 2018
Burnett, E., Beranek, J., Holm-Hansen, B., Atkinson, C. and Flick, P. (2016). Design
and flight test of active flutter suppression on the X-56A multi-utility technology
test-bed aircraft. The Aeronautical Journal, 120(1228), pp.893-909.
Cordier, E. (2018). Flutter is an unstable oscillation which can lead to
destruction.. [online] Aviation.cours-de-math.eu. Available at:
http://aviation.cours-de-math.eu/ATPL-081-POF/flutter.php [Accessed 25 Apr.
2018].
Jutte, C., Stanford, B., Wieseman, C. and Moore, J. (2013). Aeroelastic Tailoring of
the NASA Common Research Model via Novel Material and Structural
Configurations. SciTech AIAA Paper, [online] pp.1-3 and 16-18. Available at:
https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20140007306.pdf
[Accessed 12 Apr. 2018].
Li, W. and Pak, C. (2015). Mass Balancing Optimization Study to Reduce Flutter
Speeds of the X-56A Aircraft. Journal of Aircraft, 52(4), pp.1359-1365.
Luciano, A., Roberto, A., Breno, C., Marto, A. and Alonso, A. (2005). A planar
doublet-lattice code for teaching and research in aeroelasticity. Congress of
Mechanical Engineering.
Weisshaar, T., “Aircraft Aeroelastic Design and Analysis,” 1995 (second edition –
2009)
https://engineering.purdue.edu/AAE/Academics/Courses/aae556/2010/Class%20n
otes%20Chapter%201., [Accessed 28 March. 2018].
Weisshaar, T. A., “Aeroelastic Tailoring of Forward Swept Composite Wings,”
AIAA Journal of Aircraft, Vol. 18, No. 8, 1981, [Accessed 10 Apr. 2018].
W. W. Li and C.-G. Pak, “Aeroelastic optimization study based on the X-56A
model,” in Proceedings of the AIAA Atmospheric Flight Mechanics Conference
(AIAA AVIATION '14), AIAA, Atlanta, Ga, USA, June 2014. , [Accessed 10
March. 2018].
Download
Random flashcards
State Flags

50 Cards Education

Countries of Europe

44 Cards Education

Art History

20 Cards StudyJedi

Sign language alphabet

26 Cards StudyJedi

Create flashcards