International Research Journal of Engineering and Technology (IRJET)
e-ISSN: 2395-0056
Volume: 06 Issue: 07 | July 2019
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STRUCTURAL ANALYSIS, FATIGUE ANALYSIS AND OPTIMIZATION OF
AIRCRAFT WINGS
Sudeep Mishra1, Er. Rahul Malik2
1M.tech Student, P.M. Group of Institutions, DCRUST Murthal, Sonipat, Haryana
of Department, Mechanical Engineering, P.M. Group of Institutions, DCRUST Murthal, Sonipat, Haryana
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Abstract - This project addresses multiple objectives in an
attempt to apply in the most complete and realistic manner
possible, knowledge and skills that were gained throughout
the writer’s academic programme. The provide s backgrounds
theory familiarizes the readers with the most commons types
of aircrafts failures in terms of materials properties and
aerodynamics, ass wells ass with this architectures of wings,
and relates them with safety and efficiency. Extensive
discussions is made on the loadings conditions ins which
aircrafts operates during their services life, ands theirs
impacts on wings structure.
Key Words: Fatigue, Finite Element Analysis, Corrosion,
Aircraft Optimization, Winglet
I.S INTRODUCTION
2.2s OVERLOADING
Aircraft wing is as surfaces used to produces lifts and ensure
flight. This geometry of the wings determines its
aerodynamics quality and therefore different wings
geometries are used for different types of aircraft.
Aerodynamics quality is expressed as the lifts to drags ratio,
and can reach high values, up to 60sforssomesgliders.sThis
means that a significantly smaller thrust force is necessary to
obtain lift.
Failures of an aircrafts components cans haves catastrophic
consequences, therefore the study and predictions of
aircrafts failures cans prevents loss of life and property
damage. Structural and fatigues analysis are used not just
for validating safety buts also ass as guides for modifications
that allows aircrafts to operates beyond theirs originals
designs life, Among all aircrafts parts, structural analysis
investigates primarily the wings because their performances
is critical for the overall aircrafts safety. This is because
wings accounts for flights by using aerodynamics forces and
thus produce stresses that weaken their structure
significantly
2.3s FATIGUE-
2.1s AIRCRAFTs FAILUREs MODESThe lists presented ins tables1s compares the modes of
aircrafts failures with failures from others engineering
components. The lists shows clearly that fatigues is the most
commons types o failures accountings for more than 50%s of
the recorded modes, followed by corrosions and overloading
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Impact Factor value: 7.211
Failures due to overloading cans occur gradually
withsductiles fractures ors instantly with brittles fracture.
Ductiles fractures occurs whens as materials hass beens
exposeds tos excessives loads ats as relativelys slows rates
tos thes breakings point.s Thiss types ofs fractures
producess plastics deformations ins as cups ands cones
shapes ass illustrateds ins figures 1s (left).s Brittles
fracture,occurss ons applications ofs excesss load.s Fors thiss
fractures as cracks iss spreads rapidlys ats constants stresss
withlittleplastics deformation.s Figures 1s (right)
Figures 1s -s Ductiles ands Brittles Fracture
II.s LITERATUREs REVIEW
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Tables 1s -s Failures Modes of Componentss (QinetiQ,
2002)
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Fatigues cans be described as alternating loadings ors ins
others words cyclic loadings which leads tos cyclic stresses
and strains developed ins the material. Under continuous
cyclic loading, ats a critical stage the material ultimately fails.
Thes failure starts with as microscopes crack which was
hardly difficult tos find. Thiss cracks initiates ats as regions
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Volume: 06 Issue: 07 | July 2019
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where thes stresss concentrations was predominantly highs
such as thes surfaces fuselage, keys holes and joints. This
continues until thstress reaches thes limiting values after
which thes failures occur in most cases without any priors
warnings Componentss that fails forms fatigues undergoes
thes followings three stages.
Theoretical and experimental results shows that lifts and
drags cans be expressed ass thes products ofs airs density as
ats thes altitudes ofs flight, airspeeds v, wings surfaces areas
Ss ands as coefficients representing thes shapes and
orientations ofs thes airfoils CLs and CDs respectively. The
equations for lifts and drags are:
•s Initiations ofs fatigues crack’s Thiss cans be affected bys
stresss concentrations dues tos materials defects ors designs
imperfections
•s Propagations ofs thes fatigues crack’s
•s Sudden failures ass eventually thes propagating cracks
reaches as critical sizes ats which thes remaining materials
cannot supports thes applied loads
Lift, L =s ½s ᑶV2SCls, Drag, Ds =s ½s ᑶV2SCd
2.4s AERODYNAMICs PRINCIPLESs
III.s RESULTSs ANDs DISCUSSION-
Aerodynamics deals with thes forces that results forms
pressures differences and frictions dues tos airflows around
as structures The relationship between pressure and
velocity is fundamental for understanding the effect of the
aerodynamic force on aircraft wings.
2.5s BERNOULLI’Ss EQUATIONs
Bernoulli’s equations gives thes relationships between
pressures and velocity for steady airflows Ins as closed
systems thes totals energy (TE)s iss constants and its iss
givens bys thes sums ofs potentials energy (PE)s and kinetics
energy (KE).s
TE=PE+KE.s Thes compressed airs around an airfoils hass
potentials energy because its cans dos works bys exerting
forces ons thes surfaces ofs thes airfoil.
2.6s AERODYNAMICs FORCESs
There are fours forces during as steady levels flight, thrust,
drag, lifts ands weight’s Thrusts iss as forces produced bys
thes engines
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Immanuel – Arulselvan:- “Stresss Analysis and Weights
Optimizations ofs as Wings Boxes Structures Subjected tos
Flights Loads bys Ins thiss papers FEAs iss conducted tos
validates thes structuralism integrity ofs as wings box.
Pritishs Chitte:-“Statics and dynamics analysis ofs typical
wings structures ofs aircrafts using Nastran”s investigates
not just thes statics buts also thes dynamics performances
ofs wings using Nastrans FEAs software.
Makandars –s Kusugal: -“Stresss Analysis ofs Wings Roots
Fitting-Box and Its Fatigues Life Estimations for Cracks
Initiations Dues Tos FluctuatingsWings Loads”. The papers
addresses statics strengths and calculations ofs fatigues life
iss determined using Miner’s rule.
Kumars–sBalakrishnan:- “Designs ofs an Aircrafts Wings
Structures for Statics Analysis and Fatigues Life Prediction”.
Thiss papers investigates thes statics and fatigues strengths
ofs as full wings models using FEA,s and validates thes
results with hands calculations.
Figures 2-s Fatigues Failure
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2.8s SOMEs RESEARCHs STUDYs RELATEDs TOs
FATIGUEs ANDs STRUCTUALs ANALYSIS
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3.1s STRUCTURALs ANALYSISs
Taken forms thes aircraft’s manual, thes followings
specifications apply:
Wings Span: 15.50s ms
Semis Span: 7.75s ms
Aircrafts Maximums Weight: 9,752s kg
Using dimensions forms thes officials drawings ofs thes
aircraft3,s Exposeds Singles Wings Spans =s 5.9ms
Roots chords lengths =s 2.6ms
Tips chords lengths =s 1.1m
Thes airfoils are selected according tos thes Airfoils Guides
(Lednicer, 2010).s
Ass thes Bombardiers Learjet C70s iss not included ins thiss
list, thes airfoils ofs thes Gulfstream G280s -s as very similar
aircrafts -s iss selected.
Roots Airfoils -s NACAs 0012s
Tips Airfoils -s NACAs 64008As
Fronts Spars iss located ats 20%s ofs thes chords lengths
Rears Spars iss located ats 65%s ofs thes chords length
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3.2s FEAs MODELs
Using thes givens dimensions ands pressures load, ands bys
applying as fixed constraints for thes wings root, thes models
iss produced and FEAs was conducted giving thes results
shown ins figures 3s and 4.
Tables 2s –Bombardiers Learjet 70s Loading
Spectrums (Makandar, Kusugal,s2015)
Maximums Vons Misses stresss ats thes bottoms roots iss
256.9MPas
Maximums Deflections ats thes tips iss 239.4mm
Thes maximums stresss values ofs 256.9MPas that was
obtained forms thes stresss analysis, corresponds tos 3.5s g
including thes FOS,s ands so thes stresss for 1Gs ofs loadings
iss 256.9/3.5=73.4MPa.s
Thus thes stresss values ofs thes givens loads spectrums
tables 3s iss produced.
Tables 3s -s Stresss Limits
Figures 3s -s FEAs Vons Misses Stress
Fors thes sinusoidal stresss for each ofs this above loadings
conditions thes Alternating and thes Means Stress, are givens
by’s
Alternating Stress:σ=s σmax –s σmin /s 2s
Ands Means Stress:σm=s σmax +s σmin /s 2
Figures 4s -s FEAs Displacement
3.3s FATIGUEs ANALYSIS
Generally aircrafts wings experiences variables spectrums
loadings during thes flight. As bombardiers aircrafts flights
loads spectrums iss considered for thes fatigues analysis ofs
thes wings structure. Calculations ofs fatigues life iss carried
outs by using Miner’s Rule. Fors thes fatigues calculations
thes variables spectrums loadings iss simplified ass blocks
loading. Each blocks consists ofs loads cycles corresponding
tos 100s flights. Damages calculations iss carried outs for
thes completes services life ofs thes aircraft. Thes loads
factors “g” iss defined ass thes ratios ofs thes lifts ofs an
aircrafts tos its weights ands represents as global measures
ofs thes loads tos which the structures ofs thes aircrafts iss
subjected.
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Figure 5s Representations ofs Characteristics cyclic
Stresss Values
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As corrections factors accountings for surfaces
roughnessanddesignreliability
iss
considered.Thiscorrections factors iss defined ass thes
products ofs thes corresponding corrections factors ofs
theses twos characteristics (Makandar, Kusugal 2015)
Corrections Factor=s Surfaces Roughness CFs x Designs
Reliability CFs
Fors thes aircrafts wings thes followings values apply:
Surfaces Roughness CF=s 0.8s
Designs Reliability CF=0.897s
Ands hence, Corrections Factor=0.8x0.897=0.7176s
Fors Cu-Mgs Aluminums Alloys likes AA2024-T351, thes SNs charts forms figures 27s applies. Thes charts iss ins
logarithmic scale, ands its was produced forms
measurements ons thes wings ofs 250s different aircraft
Tables 4s -s Accumulated Damage
Loadings
condition
“g”
Loads
cycles
“Ni”
Cycles tos
failureNf
Accum.Da
mage
Di/Nf
1000
Actual
smean
Stress
(MPA)
63.91
0.50s –s
0.75
0.75s –s
1.00
1.00s –s
1.25
1.25s –s
1.50
0.00s –s
1.75
0.00s –s
3.00
-0.50s –s
1.50
∞
0
200
89.49
∞
0
40
115.1
∞
0
25
140.6
∞
0
30
89.49
1.16s ×104
25.90×104
5
179.2
0.094×104
55.30×104
25
51.15
1.05×104
23.80×104
ΣD=s (25.9+53.3+23.8)s x10-4=0.0103s
Thes totals damages accumulated iss less than 1s and
therefore as cracks wills not initiates immediately for thes
givens loadings conditions.
3.4s AIRCRAFTs OPTIMIZATIONs
Figures 6s -s S-Ns Charts for Al-Cu-Mgs Alloys Wings
(Hans Gartner, 1974)
Thes simplest and most practical techniques for predicting
fatigues performances iss thes Palmgre-Miners hypothesis.
Thes hypothesis contends that fatigues damages incurred ats
as givens stresss levels iss proportional tos thes numbers ofs
cycles applied ats that stresss levels divided bys thes totals
numbers ofs cycles required tos causes failures ats thes same
level. Ifs thes repeated loads are continued ats thes same
levels units failures occurs, thes cycles ratios wills be equals
tos one.Total accumulated damages
From Miner’s equations (Jadav etal., 2012),s Σs Ni/Nf =s C
Where, Ni=s Applied numbers ofs cycles
Nf =s numbers ofs cycles tos failure
Tables 4s shows damages D,saccumulated ons each ranges
ofs loads condition.
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Thiss sections introduces thes different metals used ins
aircrafts manufacturing and investigates optimizations with
alternatives materials likes composites and sandwiches
structures. Aerodynamics optimizations iss also looked into
with thes uses ofs winglets and shapes changing wings.
3.5s COMPOSITEs MATERIALSs INs THEs AIRCRAFTs
INDUSTRYs
Aircrafts designers are increasingly turnings tos composites
for lighters structures and improved efficiency. Composites
are usually built ups with laminates where unidirectional
fabrics layers embedded within as resins matrix are stacked
ons tops ofs each others ats different orientations for
maximums stiffness.
3.6s AERODYNAMICs OPTIMIZATIONs
There are several news concepts under developments having
tos dos with innovative wings shapes and materials with as
focus ons reductions ofs drags and noises and increases ofs
fuels efficiency. Its iss estimated that 1%s reductions ofs
drags for as larges commercials aircraft, cans saves ups tos
400,000s liters ofs fuels and reduces carbons emissions bys
5,000s kg.
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3.7s WINGLETSs
Thes highs pressures ons thes lowers surfaces ofs thes wings
creates airflows forms thes bottoms ofs thes airfoils
outwards forms thes fuselages around thes tips. Ats thes tip,
dues tos relativelys lowers airs pressures above thes wing,
airs tends tos spills over and swirls around its forming as
vortex that creates additional drags and thereby reducing
thes aerodynamics efficiency ofs thes wing. As wells
designed winglets rises vertically and iss swept backs bys
approximately 25’s such that its significantly reduces thes
sizes ofs thes wingtips vortex and thes induced drag.
Thes cyclic patterns ofs loading calculated based ons blocks
ofs loadings cycles that results tos as certain numbers ofs
flights hours ats which inspections musts be carried out. Ins
thiss projects structural analysis and fatigues analysis were
carried outs ons as references aircrafts wing. Vons Misses
stresss and thes modals naturals frequencies ofs thes wings
were obtained with FEAs and were validated with hand
calculations. Calculations for fatigues life were also carried
outs and thes fatigues safes life ofs thes aircrafts was
obtained
Ins aircrafts manufacturing, thes fields ofs design, materials,
fabrications and maintenances alls works hands ins hands
tos ensures safety. Metals fatigues and cracks corrosions
excessives loadings bad designs and faulty maintenances are
sources ofs problems and an oversights ins any ofs theses
areas cans causes catastrophic failure. Services bulletins
ands airworthiness directives, constantly adds news
knowledge and information that combined with previous
experiences ensures buildings and maintaining safer
aircraft’s
REFERENCESs
Figures 7s -s Differences betweens flats wings tips ands
Winglets
1.
Winglets brings several additional advantages dues tos thes
increased lifts tos drags ratios which results in betters takeoffs performances ands rate-of-climb.
2.
3.
4.
5.
6.
Figures 8s -s Different winglets shapes
IV.S CONCLUSIONS
Investigating failure contributes significantly tos aircrafts
safety’s Thes identifications ofs thes primary causes ofs
failures and analysis enables recommendations for
correctives actions that wills prevents similar failures forms
occurring ins thes future. Stresss analysis ofs thes wings
structures iss carried outs and maximums stresss iss
identified ats nears wings roots which iss founds outs tos be
lowers than yields strengths ofs thes material. Normally thes
fatigues cracks initiates ins as structures where there iss
maximums tensile stresss iss located. Thes fatigues
calculations iss carried outs for thes predictions ofs thes
structural life ofs wings structure. Since thes damages
accumulated iss less than thes critical damages ins thes
wings structures iss safes forms fatigues considerations.
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Volume: 06 Issue: 07 | July 2019
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10. Borell,s
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BIOGRAPHIES
Sudeep Mishra M.tech Student at PM College
of Engineering, Sonipat, Haryana.
Er. Rahul Malik completed B.Tech
(Mechanical Engineering) from Maharshi
Dayanand University, Rohtak in 2008 and
M.Tech. (Specialization: Design) from
Deenbandhu Chotu Ram University of
Science and Technology, Murthal Sonipat.in
2011. Currently working as an Head of
Department (Mechanical Engineering) with
PM College of Engineering, Sonipat,
Haryana.
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