An experimental study of elastic properties of dragonfly like flapping wings for use in biomimetic micro air vehicles (BMAVs) 1 2 4 5 6 7 8 9 10 11 12 13 15 16 17 18 19 20 21 22 23 Chinese Journal of[.]
Trang 19 aDepartment of Mechanical Engineering, University of Malaya, Kuala Lumpur 50603, Malaysia
10 bSchool of Engineering and Physical Sciences, Heriot-Watt University Malaysia, Putrajaya 62200, Malaysia
11 cDepartment of Electrical Engineering, University of Malaya, Kuala Lumpur 50603, Malaysia
12 Received 29 January 2016; revised 4 November 2016; accepted 7 February 2017
13
16
18 Acrylic;
19 Biomimetic micro air vehicle;
20 Flapping mechanism;
22 Wing structure
Abstract This article studies the elastic properties of several biomimetic micro air vehicle (BMAV) wings that are based on a dragonfly wing BMAVs are a new class of unmanned micro-sized air vehicles that mimic the flapping wing motion of flying biological organisms (e.g., insects, birds, and bats) Three structurally identical wings were fabricated using different materials: acrylonitrile butadiene styrene (ABS), polylactic acid (PLA), and acrylic Simplified wing frame structures were fabricated from these materials and then a nanocomposite film was adhered to them which mimics the membrane of an actual dragonfly These wings were then attached to an electromagnetic actu-ator and passively flapped at frequencies of 10–250 Hz A three-dimensional high frame rate imag-ing system was used to capture the flappimag-ing motions of these wimag-ings at a resolution of 320 pixels 240 pixels and 35,000 frames per second The maximum bending angle, maximum wing tip deflection, maximum wing tip twist angle, and wing tip twist speed of each wing were measured and compared to each other and the actual dragonfly wing The results show that the ABS wing has considerable flexibility in the chordwise direction, whereas the PLA and acrylic wings show better conformity to an actual dragonfly wing in the spanwise direction Past studies have shown that the aerodynamic performance of a BMAV flapping wing is enhanced if its chordwise flexibility is increased and its spanwise flexibility is reduced Therefore, the ABS wing (fabricated using a 3D printer) shows the most promising results for future applications
Ó 2017 Chinese Society of Aeronautics and Astronautics Published by Elsevier Ltd All rights reserved 23
24
1 Introduction
25
Micro air vehicles (MAVs) are a relatively new and rapidly
26
growing area of aerospace research They were first defined
27
by the US Defense Advanced Research Projects Agency
* Corresponding author.
E-mail address: T.Ward@hw.ac.uk (T.A Ward).
Peer review under responsibility of Editorial Committee of CJA.
Production and hosting by Elsevier
Chinese Society of Aeronautics and Astronautics
& Beihang University Chinese Journal of Aeronautics
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http://dx.doi.org/10.1016/j.cja.2017.02.011
Trang 228 (DARPA) in 1997 as unmanned aircraft that are less than
29 15 cm in any dimension Later in 2005, the DARPA defined
30 aircraft with all dimensions less than 7.5 cm and lighter than
31 10 g (carrying 2 g payload) as nanoair vehicles (NAVs) MAVs
32 (or NAVs) generally fit into one of the three categories: fixed
33 wing, rotorcraft, or biomimetic Biomimetic MAVs (BMAVs)
34 mimic the flapping wing motion of flying organisms (e.g.,
35 insects, birds, bats, etc.) This allows lift and thrust to be
36 achieved from a relatively small wing surface area This allows
37 BMAVs to be potentially smaller and more lightweight than
38 the other two types These characteristics make BMAVs
ide-39 ally suited for flight missions in confined areas (e.g., around
40 power lines, narrow streets, indoors, etc.) Therefore, BMAV
41 structural components must be ultra-lightweight, compact,
42 and flexible Most past MAV research has focused on fixed
43 wings, which are essentially scaled-down versions of wings
44 on conventional fixed-wing aircraft These wings are
unsuit-45 able for BMAVs due to their lack of flexibility, so a new type
46 of structural wing design is required for BMAVs In this work,
47 a dragonfly wing structure is mimicked to construct a new
48 BMAV wing design A dragonfly (Odonata) was selected for
49 biomimicry, because they are highly maneuverable flyers,
cap-50 able of hovering, rapid forward flight, and reverse flight
51 Therefore, structurally analyzing their wings could yield results
52 that bioinspire the design of more effective wings for BMAVs
53 This article follows on from research discussed in a previous
54 article (written by the authors) that analyzed the static strength
55 of dragonfly-like wing frames fabricated from common
mate-56 rials used in unmanned aircraft (balsa wood, black graphite
57 carbon fiber, and red pre-impregnated fiberglass).1
58 Several past research studies have been conducted on flying
59 insect wing structures to understand their elastic properties
60 Wootton et al.2conducted numerical investigations on a
teth-61 ered desert locust (Schistocerca gregaria) They concluded that
62 the wings must undergo an appropriate elastic wing
deforma-63 tion (through the course of a wing beat) in order to achieve an
64 efficient aerodynamic flow suitable for lift and thrust
genera-65 tion Several studies showed that flexible wings, capable of
66 changing their camber, generate higher peak lift forces than
67 those of rigid wings.2,3 Wing flexibility also prevents small
68 tears or warping from occurring Young et al.4suggested that
69 dragonfly wings appear to be adapted for reversible failures in
70 response to excess loads, enabling them to avoid permanent
71 structural damages Zhu et al.5conducted a study on the effect
72 of flexibility on flapping wing performance during forward
73 flight A two-dimensional numerical simulation was done by
74 solving the unsteady incompressible Navier-Stokes equations,
75 coupled with the structural dynamic equation for the motion
76 of a wing The results showed that the flexibility of a flapping
77 wing can largely influence its aerodynamic characteristics If
78 the wing has an appropriate flexibility (0.676 x*6 0.91), the
79 flexibility can simultaneously increase both the propulsive
80 and lifting efficiencies of the wing Kei et al.6 conducted a
81 study in which deformation of wings was modeled to examine
82 the effects of bending and torsion on the aerodynamic forces
83 Their numerical simulations demonstrated that flexible torsion
84 reduces flight instability They concluded that living butterflies
85 have structurally flexible wings that improve both the
aerody-86 namic efficiency and flight stability Their experimental
mea-87 surements showed that a uniformly flexible wing generates
88 lower aerodynamic forces than those of rigid wings under
89 steady-state conditions However, the presence of wing veins
90
can substantially enhance aerodynamic performance to match
91
or improve the rigid airfoil These observations agree with
92
those of Zhao et al.7who concluded that flexible insect wings
93
generate greater forces due to an enhanced camber in flight
94
Luo and Fang et al.8,9found that the chordwise
deforma-95
tion of an elastic wing is greater during upstroke than during
96
downstroke In a study conducted by Ha et al.,10the
asymmet-97
ric bending of an Allomyrina dichotoma beetle’s hind wing was
98
investigated Five differently cambered wings were modeled
99
using the ANSYS finite element analysis software These
mod-100
els were subjected to loads and pressures from the dorsal and
101
ventral sides The results revealed that both the stressed
stiffen-102
ing of the membrane and the wing camber affect the bending
103
asymmetry of insect wings In particular, increasing the
chord-104
wise camber increased the rigidity of the wing when a load was
105
applied on the ventral side Alternatively, increasing the
span-106
wise camber increased the rigidity of the wing when a load was
107
applied on the dorsal side These results explained the bending
108
asymmetry behavior of flapping insect wings Yang et al.11
109
conducted research on the effects of chordwise and spanwise
110
flexibility on the aerodynamic performance of micro-sized
flap-111
ping wings Four flapping motions were described: pure rigid
112
flapping (no deformation), pure spanwise flapping, pure
chord-113
wise flapping, and combined chord-spanwise flapping motions
114
Their results showed that a large spanwise deflection reduces
115
the aerodynamic performance (e.g., lift and thrust generation)
116
and a large chordwise deflection increases the performance
117
They further suggested that the design of a flexible flapping
118
wing should incorporate characteristics that will create a
suit-119
able chordwise deformation angle (25° and above) and limit
120
the spanwise deformation angle (5° and below)
121
Mountcastle and Combes12conducted an experiment using
122
artificially stiffened bumblebee wings (in vivo) by applying a
123
micro-splint to a single flexible vein joint The bees were then
124
subjected to load-lifting tests Bees with stiffened wings showed
125
an 8.6 percent maximum lift reduction This reduction cannot
126
be accounted for by changes in gross wing kinematics, since
127
the stroke amplitude and flapping frequency were unchanged
128
The results revealed that flexible wing design and the resulting
129
passive wing deformations enhance the load-lifting capacity in
130
bumblebees Wu et al.13presented a multidisciplinary
experi-131
ment that correlated a flapping wing’s elasticity and thrust
pro-132
duction, by quantifying and comparing overall thrust,
133
134
hummingbird-shaped membrane wings of different properties
135
were examined The results showed that, for a specific spatial
136
distribution of flexibility, there is an effective frequency range
137
in thrust production The wing deformation at
thrust-138
producing wing beat frequencies indicated the importance of
139
flexibility Both bending and twisting motions interact with
140
aerodynamic loads to enhance wing performance
141
Most past research, that is similar to the objectives of this
142
article, examined the effects of wing flexibility on aerodynamic
143
performance by either using numerical models or
experimenta-144
tion However, very few researchers have attempted to mimic
145
the detailed structure of an actual insect wing In this article,
146
biomimicry of a dragonfly wing (frame structure and
mem-147
brane) is done by fabricating them with different materials:
148
acrylonitrile butadiene styrene (ABS), polylactic acid (PLA),
149
and acrylic The focus of this article is solely on the flexibility
150
of the fabricated wing structures, not the resulting
aerody-151
namic forces that are generated The wings were fixed to a
Trang 3flap-152 ping mechanism and flapped at variable wing beat frequencies.
153 An actual dragonfly has a natural frequency of 120–170 Hz
154 and a wing beat frequency of 30 Hz The mechanism used in
155 this study was able to flap up to a maximum wing beat
fre-156 quency of 250 Hz This allowed us to study the deformation
157 of wing motions at frequencies beyond the ability of an actual
158 dragonfly The resulting wing tip deflection, twisting angles,
159 twisting speed, and bending angles were measured using
ima-160 gery generated by two high frame rate cameras Comparisons
161 were made with a real dragonfly wing in passive flapping
163 2 Materials and methodology
164 2.1 Wing design and fabrication
165 Fig 1shows the comparison between an actual dragonfly wing
166 (Diplacodes Bipunctata) and the simplified wing frame
struc-167 ture used in this study The simplified frame structure was
168 designed based on spatial network analysis, which has been
169 described in a previous article written by the authors.14This
170 analysis utilizes geometric objects within a region specified
171 by vertices or edges Although this method is commonly used
172 in geographical information systems (GIS) to explore
geo-173 graphic spatial patterns, the idea of applying this algorithm
174 to a biological structure was first introduced in this article It
175 was inspired by observing the compactly arranged geometrical
176 patterns inherent to dragonfly wings This method allows this
177 complex biological structure to be mimicked by a simplified
178 frame structure that can be fabricated by machining or 3D
179 printing
180 All of the simplified frame structures were fabricated to be
181 approximately 55 mm in length and 0.05 mm thick As
previ-182 ously mentioned, they were constructed of three different
183 materials: acrylonitrile butadiene styrene (ABS), polylactic
184 acid (PLA), and acrylic (see Fig 2and Table 1) The ABS
185 and PLA wings were fabricated using a Maker Bot Replicator
186 2X 3D printer The acrylic wings were fabricated using micro
187 laser machining Acrylic or polyacrylate is generally known for
188 its resistance to breakage, elasticity, and flexibility.15,16 ABS
189 and PLA are the two most dominant plastics used for 3D
190 printing ABS is chosen due to its strength, flexibility, and
191 machinability,10while PLA is chosen for its biodegradability,
192 lightweight, flexibility, and elasticity.17The densities of ABS,
193 PLA, and acrylic are 1.05, 1.19, and 1.18 g/cm3, respectively
194 A finite element analysis on von Mises stress was conducted
195 to simulate the flexibility of the materials tested
197 frames to serve as a thin (3 mm), ultra-lightweight wing
mem-198 brane This chitosan nanocomposite film was developed by our
199 research team for this specific purpose and has been the subject
200
of another article.18 It has similar properties to those of the
201
chitin membranes of real dragonflies It is formed by
reinforc-202
ing a chitosan suspension with nanometer-scaled
nanocrys-203
talline cellulose (NCC) particles and tannic acid This allows
204
both the mechanical properties and water resistivity of the
chi-205
tosan film to be controlled to achieve suitable design values
206
The use of NCC as a filler material elevates the film’s
mechan-207
ical properties (e.g., rigidity) The addition of tannic acid as a
208
cross-linking agent reduces the swelling behavior, solubility,
209
and rigidity of the nanocomposite film The film was adhered
210
to a wing frame by firstly submerging the frame into the
211
nanocomposite solution This procedure also ensured that
212
the film membrane would have a prescribed, uniform thickness
213
and that both sides of the frame structure were evenly coated
214
The suspension was then transformed into a film by the casting
215
evaporation method Once cured, the film created a shiny,
216
transparent film layer that adhered firmly to the frame
217
structure
218
2.2 Wing flapping mechanism
219
The wing flapping mechanism used in this study was an
elec-220
tromagnetic flapping wing actuator The power supply used
221
in this flapping wing drive was 9 V DC An LM555 crystal
222
clock oscillator integrated circuit (shown inFig 3) was used
223
to generate a stable oscillation The free running frequency
224
and duty cycle were accurately controlled with two resistors
225
and one capacitor The generated oscillation was fed to a
226
Power MOSFET fast switch The output of the Power
MOS-227
FET was used to actuate the miniature PC Board Relay
228
The frequency of the switch (corresponding to the wing beat
229
frequency) can be adjusted by a 22 kX potentiometer Each
230
of the different wings was attached to a flat iron plate (2 mm
231
long and 2.75 mm thick) using super glue This plate (wing
232
platform) was oscillated by an electromagnetic actuator
Fig 1 Dragonfly wing structure comparison
Fig 2 Wing frame materials of PLA, acrylic, and ABS, respectively
Trang 4233 (3 mm 3 mm).Fig 3shows a wing structure attached to the
234 actuator The plate was attached to the hinge of the wing to
235 mimic the joint of an actual dragonfly This flapping
mecha-236 nism is able to create a linear up-down stroke motion at
vari-237 able wing beat frequencies, up to a maximum frequency of
238 250 Hz The flapping degree was set to be 60° which
corre-239 sponds to an actual dragonfly wing flapping angle during
240 hovering flight.15,19
241 2.3 Experimental set-up
243 cameras were used to view a flapping wing from two different
244 directions The cameras’ high frame rate enables a precise
245
sequence of images to be captured of the flapping wing motion
246
within a single wing beat Two cameras were necessary in order
247
to determine the three-dimensional shape and orientation of
248
the wing surface (Fig 4) The cameras were placed
perpendic-249
ular to each other following the procedures established by Gui
250
et al.20Both cameras were equipped with a Nikon F lens A
251
multiple LED lighting system was used to provide sufficient
252
illumination Imagery was recorded at a resolution of 320
253
pixel 240 pixel and a frame rate of 35,000 per second, which
254
allowed the wing beat motion to be precisely captured The
255
motion videos were stored to a computer via two high-speed
256
Ethernet cables They were played-back and analyzed using
257
the Vision Research Phantom Camera Control Software
(Ver-258
sion 2.6.749.0)
Table 1 Mechanical properties of frame structure materials.15,17
Material Density (kg/m 3 ) Modulus of elasticity (N/m 2 ) Poisson ratio Shear modulus of elasticity (N/m 2 ) Thickness (m)
0.35 1.03 10 9
2 10 4
Fig 3 Flapping mechanism used in this study
Fig 4 Experimental set-up: two high-speed cameras perpendicular to each other along with multi LED lighting
Trang 5259 Measurements were taken of each of the three wings while
260 flapping at varying frequencies: 10–250 Hz.Fig 5 shows the
261 front and side views of the wing motions that were measured
262 and recorded from captured imagery.Fig 5(a) illustrates the
263 bending angle (h) and the displaced distance or deflection
264 (d) Fig 5(b) defines the wing tip angle (a) and the wing tip
265 rotational twist speed (x)
266 3 Results and discussion
267 3.1 Stress simulation results (without a membrane)
268 A stress simulation analysis was done on the wing frame
mate-269 rials (without and with a membrane) tested in this experiment
270 using Autodesk Simulation Multiphysics 2015 These results
271 directly relate to the flexibilities of the materials tested in this
272 experiment The results are shown inFigs 6 and 7
273 Fig 6shows the von Mises stress results of all the three
dif-274 ferent frame structures The highest stresses in the forewing
275 recorded for PLA, acrylic, and ABS are 13, 17, and 23 N/
276 mm2, respectively This shows that ABS is the least flexible
277 material among all three materials tested without a membrane
278 3.2 Stress simulation results (with a membrane)
279 Fig 7shows the forewing models of all three materials used in
280 this experiment Based on Fig 6, the maximum von Mises
281 stress occurs at approximately the same location for all three
282 materials The highest stresses occur in regions where the
283 surface-to-area ratio is minimum The maximum stresses
284
recorded are 14.77, 17.29, and 24.23 N/mm2for PLA, acrylic,
285
and ABS, respectively BothFigs 6 and 7show that ABS
exhi-286
bits the maximum stress among all three materials
287
3.3 Dragonfly wing flapping motion
288
The experiment was conducted on each of the three types of
289
wings (both with and without the chitosan membrane) This
290
was done to study the flexibility of each wing frame material
291
and to determine the best material for use in a BMAV An
292
actual dragonfly wing (Diplacodes Bipunctata) was also tested
293
to study its motion during passive flapping at different
fre-294
quencies and compare it with the fabricated wings The
295
nomenclature for wing rotation about different axes is shown
296
inFig 8.Figs 9 and 10show a sequence of images, illustrating
297
the wing motion of an actual flapping dragonfly wing during
298
one complete flapping cycle The wing beat frequency for these
299
images was 30 Hz, which is the nominal wing beat frequency of
300
this species of dragonfly
301
Dragonfly wings greatly deform during flight This was
302
observed in our experiment as well as by others.22Despite
hav-303
ing a certain degree of rigidity, dragonfly wings undergo a
con-304
siderable amount of bending, twisting, and rotational motions
305
Figs 9 and 10show the motion of a flapping wing in one
com-306
plete cycle at 30 Hz (side and front views) It was shown that in
307
both directions (chord and spanwise), an asymmetric
twist-308
bend motion was observed Figs.9(d), (f), and 10(d) clearly
309
show these asymmetric motions mentioned At the end of an
310
upstroke (observed inFig 8(e)), the wing momentarily
exhib-311
ited a symmetrical twisting motion A large feathering rotation
Fig 5 Front and side views of wing motion captured (and measurement axes)
Fig 6 Stress simulation results for ABS, PLA and acrylic (without a membrane)
Trang 6312 range of 154°–179° of the entire wing was observed at the
313 beginning of the downstroke and the end of the upstroke
314 (for all frequencies) (Fig 10(a) and (e)) Even during the steady
315 phase (passive moment occurring when the flapping angle was
316 zero), the wing was observed to undergo internal torsion This
318 et al.2,23
319 Besides the nominal 30 Hz wing beat frequency, the
drag-320 onfly wing was also flapped at frequencies ranging from 10
321 to 250 Hz The pattern of deformations was similar for all of
322 the frequencies observed The measured bending angle, wing
323 tip deflection, wing tip twist angle, and speed for the different
324 wing frames (without and with a membrane) were plotted in
325 comparison to the results obtained from an actual dragonfly
326 wing inFigs 11–14
327 3.4 Bending angle versus flapping frequency
328 The bending angle is directly proportional to the flexibility of a
329 wing Both inertial and aerodynamic loads influence it
Woot-330 ton23 found that most insect wings have relatively stiff
sup-331
porting zones near the wing base and leading edge Adding
332
to this in a later article, Wootton24wrote that the wing veins
333
taper in diameter from base to tip The resulting reduction in
334
stiffness reduces the inertial load at the wing tip, reducing
335
the energy expenditure and stress at the wing base Ennos
336
and Wootton25showed that wings having a tapered stiffness
337
distribution from base (high) to tip (low) are well suited to with
338
stand torques This article also showed that spanwise bending
339
moments due to the inertia of flapping wings are
approxi-340
mately two times larger than those due to aerodynamic forces
341
A structural finite element analysis by Jongerius and Lentink26
342
of a dragonfly wing model also showed that the inertial forces
343
along the wingspan are 1.5–3 times higher than the
aerody-344
namic forces Similarly, Combes and Daniel27modeled
drag-345
onfly and hawkmoth wings, and found that the flexural
346
stiffness declined exponentially from wing base to tip
347
Although inertial loading dominates, Young et al.4 showed
348
that aerodynamic forces (e.g., lift and thrust) generated by a
349
flapping wing also has an influence on wing flexibility
350
This study focuses only on the chordwise flexibility of a
pas-351
sive flapping wing Bending angles were measured along the
352
chordwise direction Kang and Shyy22also investigated
chord-353
wise flexibility, but for simple, non-anisotropic wing
struc-354
tures They presented a detailed assessment of the effects of
355
structural flexibility on the aerodynamic performance of
flap-356
ping wings The Reynolds number (Re = 100) considered in
357
this study is relevant to small insect flyers, such as fruit flies
358
However, this study only includes the roles of chordwise
flex-359
ibility and passive pitch in two-dimensional plunging motions
360
Our study involves a much more complex wing design than
361
those in many past studies However, tapering the thickness
362
(declination from base to tip) of the veins in our physical
mod-363
els (similar to actual insect wings) was not possible due to
fab-364
rication limitations Our wings have tapered flexibility
365
(declining from base to tip and from leading to trailing edge)
366
solely due to a reduction in the frame planform width sizes
367
(mimicking veins) in these directions.Fig 11shows the
bend-368
ing angles as the wing beat frequency is varied for the three
369
fabricated wing frames (without and with a membrane) in
370
comparison to that of an actual dragonfly wing.Fig 11shows
Fig 7 Stress simulation results for ABS, PLA, and acrylic (with a membrane)
Fig 8 Degrees of freedom for wings of a flying insect.21
Trang 7371 that the maximum bending angle (hmax) for all the wings
372 occurs during the upstroke This was observed for both frames
373 without and with a membrane This agrees with the results of
374 previous research done by Jongerius and Lentink,26in which
375 this asymmetry (difference in the bending angle between the
376 upstroke and downstroke) was attributed to the directional
377 bending stiffness in a wing structure (e.g., one-way hinge or
378 a pre-existing camber in the wing surface)
380 was recorded to be about 6° The wings were observed to have
381 a maximum bending angle of 10.7° at 120 Hz (natural
fre-382 quency of an actual dragonfly) This is an increase of 78.3%
383 from 30 Hz ABS shows a high level of flexibility compared
384 to the other two materials used.Fig 11shows that the bending
385 angle curves of the fabricated ABS wings are more similar to
386 that of the actual dragonfly wing than those of the other two
387 types.Fig 11(a) shows that the bending angle of an ABS wing
388 (without a membrane) at 30 Hz is 8.5° and 5.9° at 120 Hz At
389 30 Hz, the percentage difference between an ABS wing
391 42% The PLA and acrylic wings recorded reduced percentage
392
differences of 30% and 70%, respectively InFig 11(b), ABS
393
exhibited much larger bending angles at 30 Hz when the
mem-394
brane was added The value of the ABS wing (with a
mem-395
brane) is 20.1° at 30 Hz and 34.9° at 120 Hz This angle is
396
much larger than that of the actual dragonfly wing The
per-397
centage increase between the ABS and the actual dragonfly
398
wing is 233% The other two materials (PLA and acrylic)
399
exhibited much smaller bending angles than that of the actual
400
dragonfly wing The percentage reductions in PLA and acrylic
401
(in comparison to the actual dragonfly wing) are 83% and
402
75%, respectively
403
These observations confirm that the overall flexibility of a
404
wing decreases after a membrane is attached, except for ABS
405
wings At a frequency of 120–170 Hz, the dragonfly wing
406
bends at a very large angle Previous research showed that
407
dragonflies do not flap at their natural frequency (120–
408
170 Hz).28 Therefore, this result is likely due to a resonance
409
effect caused by the wing beat frequency being proximate to
410
the natural frequency of the wing This result confirms that
411
dragonflies have a maximum wing beat frequency limitation
412
in this range The ABS wing frame shows a similar trend at
Fig 9 Side view of dragonfly flapping wing (gray scale) captured by high speed camera during one flapping cycle at 30 Hz
Trang 8413 120 Hz The bending angle is reduced at frequencies greater
414 than120 Hz for both the actual dragonfly wing and the three
415 fabricated wings
416 3.5 Wing tip deflection versus flapping frequency
417 Fig 12shows the wing tip deflection for varying wing beat
fre-418 quencies of the three fabricated wing frames (without and with
419 a membrane) in comparison to that of an actual dragonfly
420 wing Similar to the bending angle, deflection is another
mea-421 surement that can be used to assess a flapping wing’s flexibility
422
As mentioned earlier, past studies have shown that wing
flex-423
ibility has a significant effect on the wing’s ability to generate
424
a suitable time-averaged lift or thrust.7 Similar to hmax in
425
Fig 10, Fig 12 shows that the maximum deflection (dmax)
426
occurs during the upstroke This again was observed for both
427
frames without and with a membrane This agrees with the
428
results of previous research done by Luo et al.8
429
Fig 12(a) shows that all of the fabricated wing frames
430
(without a membrane) deflect at magnitudes that are similar
431
(only slightly reduced) to that of the actual dragonfly wing
432
at 30 Hz which is about 7.1 mm At 30 Hz, ABS has a
percent-433
age increase of 24% PLA and acrylic both have percentage
Fig 10 Front view of dragonfly flapping wing captured by high speed camera (gray scale) during one flapping cycle at 30 Hz
Trang 9434 reductions of 48% and 62%, respectively However,Fig 12(b)
435 shows that the fabricated wing frames (with a membrane) have
436 very different deflections from that of the actual dragonfly
437 wing Only the ABS wing showed a comparable level of
deflec-438
tion, however the dragonfly wing is 41% higher than the ABS
439
wing The PLA and acrylic wings have percentage reductions
440
of 94% and 66%, respectively, compared to the dragonfly
441
wing The actual dragonfly wing is able to undergo a large
Fig 11 Bending angles of different wing frames
Fig 12 Wing tip deflection of different wing frames
Fig 13 Wing twist angle of different frames versus flapping frequency
Trang 10442 deflection at the tip region This supports the findings of
previ-443 ous studies, which explain that the difference between the
444 deflections at the tip and the surface is created by the difference
445 in the rigidity (due to the vein and corrugations) along the
446 wing surface.29
447 The difference in deflection between the wing frames
with-448 out and with a membrane shows that the attachment of a
449 membrane causes an increase in rigidity This increase in
rigid-450 ity was observed to be the highest in the PLA wing Only the
451 ABS wing shows a curvature trend similar to that of the actual
452 dragonfly wing around 120 Hz At 120 Hz, a reduction in
per-453 centage of 45% (without a membrane) or 70% (with a
mem-454 brane) is seen in the ABS wing frame Compared to the PLA
455 wing, there is a percentage reduction of 83% (without a
mem-456 brane) or 95% (with a membrane) The acrylic wing has a
458 membrane attached The trend of the graph again shows that
459 there is a decrease in flexibility after the membrane has been
460 attached Two high peaks were observed for the actual
dragon-461 fly wing (30 and 120 Hz) As already stated, the natural
fre-462 quency of dragonfly wings has been reported to be between
463 120 to 170 Hz.28 The extreme fluctuation observed in this
464 range confirms the reporting
465 3.6 Wing twist angle versus flapping frequency
466 Fig 13shows the maximum wing tip twist angle of the three
467 fabricated wing frames in comparison to that of an actual
468 dragonfly wing The maximum twist angle was recorded
dur-469 ing the stroke reversal (transition from upstroke to
down-470 stroke) The twist angle for the actual dragonfly wing at
471 30 Hz is 154.58° Untwisted wings have large, drag producing
472 wing surfaces that are exposed to flow, and hence the
impor-473 tance of twisting in wings is justified Wing tip twist also plays
474 an important role in enhancement of flight performance The
475 mid-stroke timing of wing deformation in a butterfly,
exam-476 ined by Zheng et al.,29 suggests that the deformation is not
477 due to wing inertia, because the acceleration of the wing is
478 small at this point in the stroke They suggested that this is
479 instead due to elastic effects, since the aerodynamic forces
480 are very large at mid-stroke
481
Fig 13(a) and (b) shows that both the PLA and acrylic
482
wing frames (both without and with a membrane) closely
483
match the performance of an actual dragonfly wing At
484
30 Hz, the ABS wing (without and with a membrane) has
per-485
centage reductions of 20% and 1% respectively in comparison
486
to that of the actual dragonfly wing The PLA wing (without
487
and with a membrane) has percentage increases of 5% and
488
10%, respectively The acrylic wing (without and with a
mem-489
brane) has percentage increases of 7% and 12%, respectively
490
At 120 Hz, the ABS and acrylic wings (without a membrane)
491
have percentage reductions of 10% and 3%, respectively,
com-492
pared to that of the dragonfly wing, while the PLA wing
(with-493
out a membrane) has a percentage increase of 3% The ABS
494
wing (with a membrane) has a percentage reduction of 36%
495
compared to that of the dragonfly wing, while the PLA and
496
acrylic wings have percentage increases of 5% and 3%,
respec-497
tively Based on these results, the PLA and acrylic wings are
498
more similar to the actual dragonfly wing than the ABS wing
499
The large fluctuation of the ABS wing across varying flapping
500
frequencies (10–250 Hz) makes it a more complicated BMAV
501
option
502
Another trend observed from Fig 13is that the wing tip
503
twist angle of the dragonfly wing does not vary significantly
504
as the flapping frequency is varied This matches the finding
505
of a previous study by Zhao et al.8(mentioned earlier) which
506
showed that the flexibility of insect wings increases more
507
chordwise than spanwise, due to the rigid leading edge vein
508
This is true for both categories of wing frames (with and
with-509
out a membrane)
510
3.7 Wing tip twist speed versus flapping frequency
511
Fig 14 shows the wing tip twist speed for the three wing
512
frames (without and with a membrane) in comparison to that
513
of an actual dragonfly wing The wing tip twist speed was
mea-514
sured using the Vision Research Phantom Camera Control
515
Software associated with our high frame rate cameras Vogel30
516
stated that the wing tip twist speed varies according to size and
517
must exceed a ratio to flight speed (wing tip twist speed: flight
518
speed) by 3.7 or more to enable forward flight.Fig 14shows
519
that the PLA and acrylic wing frames (both without and with
520
a membrane) show a curvature trend similar to that of the
Fig 14 Wing tip twist speed of different frames versus flapping frequency