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A Project Report on
“STRESS ANALYSIS OF THE LANDING GEAR-
WELL BEAMS AND DAMAGE CALCULATION
DUE TO LANDING CYCLES”
Submitted to
VISVESVARAYA TECHNOLOGICAL UNIVERSITY
BELGAUM -590 018
In Partial Fulfillment Of The Requirements For The Award Of Degree Of
MASTER OF TECHNOLOGY
In
MACHINE DESIGN
By
KARTHIK GOUD R V
USN: 1OX12MMD06
Under the guidance of
Mr. NANDISH R V
Asst. Prof, Mechanical Department
The Oxford College Of Engineering,
DEPARTMENT OF MECHANICAL ENGINEERING
THE OXFORD COLLEGE OF ENGINEERING
BOMMANAHALLI, BANGALORE -560 068
2013-2014
ISSN: 2321-3051
CERTIFICATE OF PUBLICATION
This is to certify that Karthik Goud R V has
published his/her research work entitled
“STRESS ANALYSIS OF THE LANDING GEAR-
WELL BEAMS AND DAMAGE CALCULATION DUE
TO LANDING CYCLES” in International Journal
of Research in Aeronautical and Mechanical
Engineering
Editor-in-chief, IJRAME volume 2 issue 5, May 2014
ii
ABSTRACT
Landing gear is a structure, which supports the aircraft on the ground. Landing
gear structure experiences the load during take-off and landing of the aircraft. These loads
are transferred to the airframe through landing gear beams. Wing box near the root will
have cut-out at the bottom surface to accommodate the retraction of the landing gears.
Landing loads are absorbed by the landing gears and diffused to the larger area of the
wing through connecting members.
In the current project two landing gear beams with a root rib are considered for the
analysis. On either sides of the cut-out region landing gear beams are used to transfer the
landing load from landing gears to the wing and fuselage structure. Landing gear beams
are in the span wise direction of the wing.
Linear static analysis of the beams along with the root rib will be carried out to
identify the fatigue critical location in the structure. Local analysis will be carried to
capture the stress concentration and stress distribution near the high stress location. It is
very rare that these structural members will fail by static over load. Due fluctuating loads
during the service fatigue cracks will get initiated at the high tensile stress location.
Landing gear beams will experience constant amplitude load cycles because of every
landing during service. Fatigue life to crack initiation will be calculated using Miner’s
rule based on the S-N data of the material being used.
iii
ACKNOWLEDGEMENT
Project work is a job of great enormity and it can be accomplished by an
individual all by themselves. Eventually I am grateful to a number of individuals whose
professional guidance, assistance and encouragement have made it a pleasant endeavour
to present this project.
I have a great pleasure in expressing my deep sense of gratitude to the Founder
Chairman SRI. S. NARASA RAJU and to the Executive Director SRI. S.N.V.L.
NARSIMHA RAJU for having provided me with a great infrastructure and well-
furnished labs.
I take this opportunity to express my profound gratitude to the Principal Dr.
NAGARAJ. R for his constant support and encouragement.
I am grateful to the Head of the Department Dr. T NAGESWARA RAO for his
unfailing encouragement and suggestions given to me in the course of the project.
Guidance and deadlines play a very important role in successful project work, I
also convey my gratitude to guide Mr. NANDISH R V, Asst. Professor, Department of
Mechanical engineering.
My sense of gratitude to teaching and non-teaching staff for their encouragement
and help, which was my foundation and I treasure them for my future endeavors.
Finally, I take this opportunity to extend my deep appreciation to my family and
friends; for all that they supported me for the successful completion of my dissertation.
KARTHIK GOUD R V
[USN-1OX12MMD06]
iv
CONTENTS
DECLARATION i
ABSTRACT ii
ACKNOWLEDGEMENT iii
CONTENTS iv
LIST OF FIGURES vi
LIST OF TABLES vii
CHAPTER 1: INTRODUCTION 01
1.1 INTRODUCTION TO AIRCRAFT 01
1.2 PARTS OF AIRCRAFT 01
1.3 COMPONENTS OF WING 07
1.4 STRESSES ON AIRCRAFT 10
1.5 TYPES OF STRUCTURAL STRESS 11
1.6 FATIGUE LIFE 13
1.7 COMPUTATIONAL METHOD 17
CHAPTER 2: LITERATURE SURVEY 19
CHAPTER 3: FINENITE ELEMENT ANALYSIS 28
3.1 FINITE ELEMENT ANALYSIS OF
LANDING GEAR WELL BEAMS 28
3.2 PROCESS FLOW OF FINITE ELEMENT ANALYSI 30
CHAPTER 4: MATERIAL PROPERTIES, LOAD CALCULATION
AND BOUNDARY CONDITION 32
4.1 CHARACTERISTICS OF ALUMINUM 32
v
4.2 LOAD CALCULATION 34
CHAPTER 5: LINEAR STATIC ANALYSIS OF LANDING
GEAR WELL BEAMS 36
5.1 GLOBAL ANALYSIS 37
CHAPTER 6: THEORETICAL VALIDATION 42
6.1 MAXIMUM STRESS IN PLATE WITH HOLE WITH ONE END
FIXED 42
CHAPTER 7: FATIGUE ANALYSIS OF LANDING GEAR WELL BEAMS 46
7.1 CALCULATE MAX STRESS FOR DIFFERENT RANGE 48
7.2 CALCULATION FOR STRESS AND STRESS RATIO 49
CONCLUSION 55
SCOPE FOR FUTURE WORK 56
REFERENCE 57
APPENDIX 59
vi
LIST OF FIGURES
FIGURE NO FIGURE NAME PAGE NO
Fig 1.1 Fuselage and its parts 02
Fig 1.2 Nomenclature of wing 03
Fig 1.3 Parts of tail of aircraft 04
Fig 1.4 Engine of transport aircraft 05
Fig 1.5 Landing gear of typical aircraft 06
Fig 1.6 Components of Wing 07
Fig 1.7 Spar 08
Fig 1.8 Ribs 10
Fig 1.9 The five stresses that may act on-
an aircraft and its parts. 12
Fig 1.10 S N curve 14
Fig 3.1 Process Flow of FEA 31
Fig 4.1 Basic dimension of aircraft 34
Fig 4.2 Meshing and Boundary Condition-
of landing gear well beams. 35
Fig 5.1 Landing Gear beam Catia Model. 38
Fig 5.2 Two Dimensional Model of LG Beams. 38
Fig 5.3 Complete Meshed Model. 39
Fig 5.4 Loaded and Constrained model 39
Fig 5.5 Output of Stress Analysis. 40
Fig 5.6 Location of Maximum Stress in LG beams. 40
Fig 5.7 Elemental values near Maximum Stress Location 41
Fig 6.1 Plate with Hole for Local Analysis 42
Fig 6.2 Mesh and Boundary Condition -
applied to Local Model. 43
Fig 6.3 Local Analysis 44
Fig 6.4 Stress Concentration Factor for Plate with Hole 44
Fig 7.1 Graph for number cycles to failure. 52
vii
LIST OF TABLES
TABLE NO TABLE NAME PAGE NO
Table 4.1 Aluminium Alloy 2024 properties 33
Table 7.1 Variable Load Spectrum for Typical Aircraft 47
Table 7.2 No of cycles and stress ratio 53
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CHAPTER 1
INTRODUCTION
1.1 INTRODUCTION TO AIRCRAFT
When designing an aircraft, it’s all about discovering the right proportion of the
weight of the vehicle and payload. It needs to be robust and rigid enough to withstand the
uncommon circumstances in which it has to operate. Durability is an important factor.
Also, if a part fails, it doesn’t necessarily result in failure of the whole aircraft. The main
sections of an aircraft, the fuselage, tail and wing, gives its external shape. The load
carrying members of the main parts, those subjected to major forces, are called the
airframe. The airframe is what remains if all equipment and systems are disassembled.
In today`s modern aircrafts, the skin plays an vital role in carrying loads. Tension
can only be supported by sheet metals. But if the sheet is folded, it quickly does have the
ability to withstand compressive loads. Stiffeners can be used for that. The combination
of skin and stiffeners is called stringers. An efficient way of using sheet metal skin is in a
thin-walled cylinder, known as monocoque structure. A cylinder with holes, for windows
and doors, is called a semi-monocoque structure. Stiffeners cannot be made from sheet
metal. We can use rolling or drawing process for sheet metal. Usually stiffeners are
attached to the skin. Skin and stiffeners are manufactured from one single solid piece of
material. It is also possible to make some kind of a sandwich structure, in which the skin
has a high rigidity due to its special structure.
1.2 PARTS OF AIRCRAFT
The main parts of an aircraft are
1. Fuselage
2. Wing
3. Tail
4. Engine
5. Landing gear
1.2.1 FUSELAGE
The fuselage should carry the load of passenger and goods, and it is the main
structure to which all other parts are interlinked. It must be able to withstand, torsional
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loads, bending moments and pressurization. The structural robustness and rigidity of the
fuselage must be high enough to withstand the loads. The weight of the aircraft structure
should be as minimum as possible. The shape of passenger aircraft is cylindrical with
tapered nose section. The semi-monocoque construction, which is virtually standard in all
modern aircraft, consists of a stressed skin with added stringers to prevent buckling,
attached to hoop-shaped frames.
The fuselage also has member’s perpendicular to the skin, that supports it and
helps keep its shape. These supports are called frames if they are open or ring-shaped or
bulkheads if they are closed. Doors and window hole in the cylindrical shape fuselage are
called cutouts. They are usually unsuitable to carry many of the loads that are present on
the surrounding structure. Cut-outs are reinforced to withstand the direct loads carrying
on the aircraft. Different aircraft have different doors and window sizes depending on the
necessity. It is therefore necessary for them to transmit some of the loads from the frames
and stringers.
Fig 1.1: Fuselage and its parts.
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1.2.2 WING
The main function of wing is to provide necessary lift for the aircraft. Wing can be
divided into two main parts, First part is internal which consists of spars, ribs and
stringers and second part is skin.
The main aerofoil shape of the wing is given by ribs. Wing consists of control
surfaces, flaps and engines. Presence of ribs provides additional strength, rigidity,
prevents buckling and also separate fuel tanks in the wing. There are many types of ribs,
they are form ribs, plate type ribs, truss ribs, forged ribs, milled ribs and closed ribs.
Stringers run in length wise direction of the wing. Resist bending and axial loads along
with the skin .Divide the skin into small panels and thereby increase its buckling and
failing stresses. Act with the skin in resisting axial loads caused by pressurization.
Spars give the support needed for ribs. These are beams with cross-section usually
of I section. Most of the load is carried by the spars. These are heavily loaded part in the
aircraft structure. More force is acting at the root than at the tip of the wing. Shear force
and bending moment are the major force acting on the spar because it will deflect
upwards due to load acting on wing. Wing undergoes not only bending but also twisting
due to aerodynamic forces acting on it. In order to prevent twisting second spar beam is
introduced. Most of the modern aircraft use torsion box structure which comprises of spar
and strengthened skin. This structure resists both bending and twisting.
Fig 1.2: Nomenclature of wing
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1.2.3 TAIL
The main function of the tail is to provide control and stability of the aircraft. The
ability by which aircraft returns to its original position is called stability. Stability and
control has to be achieved in three directions i.e. longitudinal, lateral and vertical. Aircraft
uses three manoeuvres those are yaw, pitch and roll. Stability for yaw is provided by fin.
Rudder is deflected when aircraft needs to yaw. Stability in pitch is provided by tail
plane. When aircraft needs to climb or descend, rudders are moved. Whenever aircraft
speed is changed, elevator position is changed accordingly.
Fig 1.3: Parts of tail of aircraft
1.2.4 ENGINE
Engines can be of many types like turbo fan, piston engine, turbo prop and ram jet
type. Most transport aircraft use turbo jet engine as they provide high trust. Most engines
are positioned externally, leaving fuselage completely to carry payloads. They can be
wing or rear positioned or both. If the engine is mounted closer to the fuselage more noise
is generated. Transport aircraft which use twin or multi engine must be mounted on the
wing. While for combat aircraft engine can be rear mounted. A turbojet is a type of gas
turbine engine that was originally developed for military fighters during World War II. A
turbojet is the simplest of all aircraft gas turbines. It consists of a compressor to draw air
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in and compress it, a combustion section where fuel is added and ignited, one or more
turbines that extract power from the expanding exhaust gases to drive the compressor, and
an exhaust nozzle that accelerates the exhaust gases out the back of the engine to create
thrust. When turbojets were introduced, the top speed of fighter aircraft equipped with
them was at least 100 miles per hour faster than competing piston-driven aircraft. In the
years after the war, the drawbacks of the turbojet gradually became apparent. Below
about Mach 2, turbojets are very fuel inefficient and create tremendous amounts of noise.
Early designs also respond very slowly to power changes, a fact that killed many
experienced pilots when they attempted the transition to jets. These drawbacks eventually
led to the downfall of the pure turbojet, and only a handful of types are still in production.
The last airliner that used turbojets was the Concorde, whose Mach 2 airspeed permitted
the engine to be highly efficient.
Fig 1.4: Engine of transport aircraft
1.2.5 LANDING GEAR
Landing gear supports aircraft while it is on ground, while takeoff and landing.
For fast aircraft retractable landing gear is used to reduce drag. Aircraft landing gear
include wheels along with shock absorber. In retractable gear system the space where
wheels are stowed is called wheel wells. The larger the aircraft more wheels are added to
the landing gear. The position of landing gear depends on design, type and load of
aircraft. Some landing gear is mounted on wing and some under fuselage. Most of them
are mounted on wing.
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Multiple redundancies are usually provided to prevent a single failure from failing
the entire landing gear extension process. Whether electrically or hydraulically operated,
the landing gear can usually be powered from multiple sources. In case the power system
fails, an emergency extension system is always available. This may take the form of a
manually operated crank or pump, or a mechanical free-fall mechanism which disengages
the uplocks and allows the landing gear to fall due to gravity. Some high-performance
aircraft may even feature a pressurized-nitrogen back-up system.
Malfunctions or human errors (or a combination of these) related to retractable
landing gear have been the cause of numerous accidents and incidents throughout aviation
history. Distraction and preoccupation during the landing sequence played a prominent
role in the approximately 100 gear-up landing incidents that occurred each year in the
United States between 1998 and 2003. A gear-up landing incident, also known as a belly
landing, is an accident that may result from the pilot simply forgetting, or failing, to lower
the landing gear before landing or a mechanical malfunction that does not allow the
landing gear to be lowered. Although rarely fatal, a gear-up landing is very expensive, as
it causes massive airframe damage. For propeller driven aircraft it almost always requires
a complete rebuild of engines because the propellers strike the ground and suffer a sudden
stoppage if they are running during the impact. Many aircraft between the wars – at the
time when retractable gear was becoming commonplace – were deliberately designed to
allow the bottom of the wheels to protrude below the fuselage even when retracted to
reduce the damage caused if the pilot forgot to extend the landing gear or in case the
plane was shot down and forced to crash-land.
Fig 1.5: Landing gear of typical aircraft
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1.3 COMPONENTS OF WING:
Fig 1.6: Components of Wing
Main structural parts of wing:
1. Spar
2. Stringer
3. Ribs
1.3.1 SPAR: The main structural part of wing is spar. It is positioned along
lengthwise direction of wing and perpendicular to fuselage. Weight of wing and flight
loads is carried by spar. There may be one or more spars which depend on design of
aircraft. While single spar carries majority of load. While aircraft is in flight the load is
acting on skin. The load acting on skin is transferred to ribs and then to spar. Most wing
as two spars one is front and other rear spar. Front spar is located at the leading edge and
rear spar is located at trailing edge. Earlier spars are made of wood , but in modern
aircraft spar is made from metal. Spar is build by joining by many small length beams
attached together to provide structural strength and rigidity.
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Fig 1.7: Spar
1.3.2 STRINGER:
Stringer or longeron or stiffener is thin metal strip fastened to skin. In wings
stringer run span wise and are attached between ribs. The basic function of stringer is to
transfer loads to ribs and then to spars. They resist bending and axial loads. These divide
the skin into small blocks, thus increasing the buckling strength. Stringer is not attached
to any parts other than skin. On larger aircraft stringer is more common in spite of
complex to analyze. In aircraft construction, a longeron, or stringer or stiffener is a thin
strip of material to which the skin of the aircraft is fastened. In the fuselage, stringers are
attached to formers (also called frames) and run in the longitudinal direction of the
aircraft. They are primarily responsible for transferring the aerodynamic loads acting on
the skin onto the frames and formers. In the wings or horizontal stabilizer, longerons run
spanwise and attach between the ribs. The primary function here also is to transfer the
bending loads acting on the wings onto the ribs and spar.
Sometimes the terms "longeron" and "stringer" are used interchangeably.
Historically, though, there is a subtle difference between the two terms. If the longitudinal
members in a fuselage are few in number and run all along the fuselage length (usually 4
to 8), then they are called "longerons". The longeron system also requires that the
fuselage frames be closely spaced (about every 4 to 6 in or 10 to 15 cm). If the
longitudinal members are numerous (usually 50 to 100) and are placed just between two
formers/frames, then they are called "stringers". In the stringer system the longitudinal
members are smaller and the frames are spaced farther apart (about 15 to 20 in or 38 to
51 cm). Generally, longerons are of larger cross-section when compared to stringers. On
large modern aircraft the stringer system is more common because it is more weight-
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efficient, despite being more complex to construct and analyze. Some aircraft use a
combination of both stringers and longerons.
Longerons often carry larger loads than stringers and also help to transfer skin
loads to internal structure. Longerons nearly always attach to frames or ribs. Stringers
often are not attached to anything but the skin, where they carry a portion of the fuselage
bending moment through axial loading. It is not uncommon to have a mixture of
longerons and stringers in the same major structural component.
1.3.3 RIBS:
In an aircraft, ribs are forming elements of the structure of a wing, especially in
traditional construction. By analogy with the anatomical definition of "rib", the ribs attach
to the main spar, and by being repeated at frequent intervals, form a skeletal shape for the
wing. Usually ribs incorporate the airfoil shape of the wing, and the skin adopts this shape
when stretched over the ribs.
There are several types of ribs. Form-ribs, plate-type ribs, truss ribs, closed-ribs,
forged ribs and milled ribs, where form-ribs are used for light to medium loading and
milled ribs are as strong as it can get. Form-ribs are made from a sheet of metal bent into
shape, such as a U-profile. This profile is placed on the skin, just like a stringer, but then
in the other direction. Plate-type ribs consist of sheet-metal, which has upturned edges
and (often has) weight-saving holes cut into it. Truss ribs are built up out of profiles that
are joined together. These joints require great attention during design and manufacture.
The ribs may be light or heavy in design, which make them suitable for a wide range of
loads.
Closed-ribs are constructed from profiles and sheet metal and are suitable for
closing off sections of the wing (e.g.: the fuel tank). Here too, particular care must be
taken with the joints and this type of rib is also suitable for application in a variety of
loading conditions.
Forged ribs are manufactured using heavy press-machinery. The result is fairly rough; for
more refined parts, high-pressure presses are required, which are very expensive. Forged
pieces (usually) have to undergo further treatment (for smoother edges and holes). Forged
ribs are used for sections where very high loads apply - near the undercarriage for
example.
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Milled ribs are solid structures. They are manufactured by milling away excess material
from a solid block of metal (usually using computer-controlled milling machines). The
shape of these ribs is always accurately defined. Such ribs are used under similar
conditions as those for forged ribs. Ribs are made out of wood, metal, plastic, composites,
foam. The wings of kites, hang gliders, paragliders, powered kites, powered hang
gliders, ultralights, windmills are aircraft that have versions that use ribs to form the
wing shape. For full size and flying model aircraft wing structures that are usually made
of wood, ribs can either be in one piece (forming the airfoil at that rib's "station" in the
wing), or be in a three-piece format, with the rib web being the part that the one-piece rib
consisted of, with capstrips for the upper and lower edging of the rib, running from the
leading edge to the trailing edge, being the other two component parts.
Fig 1.8: Ribs
1.4 STRESSES ON AIRCRAFT:
Structural integrity is a major factor in aircraft design and construction. No
production airplane leaves the ground before undergoing extensive analysis of how it will
fly, the stresses it will tolerate and its maximum safe capability. Every airplane is subject
to structural stress. Stress acts on an airplane whether on the ground or in flight. Stress is
defined as a load applied to a unit area of material. Stress produces a deflection or
deformation in the material called strain. Stress is always accompanied by strain. Current
production general aviation aircraft are constructed of various materials, the primary
being aluminium alloys. Rivets, bolts, screws and special bonding adhesives are used to
hold the sheet metal in place. Regard less of the method of attachment of the material,
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every part of the fuselage must carry a load, or resist a stress placed on it. Design of
interior supporting and forming pieces, and the outside metal skin all have a role to play
in assuring an overall safe structure capable of withstanding expected loads and stresses.
The stress a particular part must withstand is carefully calculated by engineers.
Also, the material a part is made from is extremely important and is selected by designers
based on its known properties. Aluminium alloy is the primary material for the exterior
skin on modern aircraft. This material possesses a good strength to weight ratio, is easy to
form, resists corrosion, and is relatively inexpensive.
Wings may be either strut braced or full cantilever, depending on whether (as in
many smaller aircraft) an external brace is employed to help transmit loads from the wing
to the fuselage. Cantilever wings must resist all loads with their own internal structure.
Small, low speed aircraft have straight, nearly rectangular wings. For these wings, the
main load is in bending of the wing as it transmits load to the fuselage, and the bending
load is carried primarily by the spars. In fact, the spars are the main structural pieces in a
wing assembly. Attached to the spars are ribs that give the aerodynamic shape to the
wing. During flight, stresses are transmitted first to the wing skin, then to the ribs, and
finally to the spars. Spars also must carry loads distributed by the fuselage, landing gear
and any nacelles. Stress is a fact of life for airplanes; it is always present in one form or
another. The primary concern for the owner/pilot should be to not put any undue stress on
the aircraft. Treat it gently, by operating it within its design limitations. Normal stress
(and occasional abnormal stress) is not a problem for an aircraft that is properly designed.
But, the airplane must be properly flown and maintained in order to keep it airworthy.
1.5 TYPES OF STRUCTURAL STRESS:
The five basic structural stresses to which aircraft are subject are:
1. Tension
2. Compression
3. Torsion
4. Shear
5. Bending
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Tension is the stress that resists a force that tends to pull something apart. The
engine pulls the aircraft forward, but air resistance tries to hold it back. The result is
tension, which stretches the aircraft. The tensile strength of a material is measured in
pounds per square inch (psi) and is calculated by dividing the load (in pounds)
required to pull the material apart by its cross-sectional area (in square inches).
Compression is the stress that resists a crushing force. The compressive strength
of a material is also measured in psi. Compression is the stress that tends to shorten or
squeeze aircraft parts. Torsion is the stress that produces twisting. While moving the
aircraft forward, the engine also tends to twist it to one side, but other aircraft
components hold it on course. Thus, torsion is created. The torsion strength of a
material is its resistance to twisting or torque.
Shear is the stress that resists the force tending to cause one layer of a material to
slide over an adjacent layer. Two riveted plates in tension subject the rivets to a
shearing force. Usually, the shearing strength of a material is either equal to or less
than its tensile or compressive strength. Aircraft parts, especially screws, bolts, and
rivets, are often subject to a shearing force. Bending stress is a combination of
compression and tension. The rod has been shortened (compressed) on the inside of
the bend and stretched on the outside of the bend.
Fig 1.9: The five stresses that may act on an aircraft and its parts.
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Fittings must be made of carefully selected materials because of their importance
of holding the aircraft together under expected stress and loading. The same holds true for
important fasteners such as bolts and rivets. It is essential that these parts not fail under
stress. It is also essential that these parts not weaken with exposure to stress and weather
elements. Corrosion is also a consideration. A fitting made of one metal cannot be
secured to the structure with a bolt or fastener made of another metal. This situation may
result in "dissimilar metal corrosion" over a period of time and result in a weakening of
the assembly to the extent that the assembly is rendered unsafe.
1.6 FATIGUE LIFE:
Because the stress levels of the fatigue critical locations are not known, they are
first approximated with a reference fatigue analysis. The reference fatigue analysis
simulates the original fatigue analysis of the aircraft. The stress values are iterated to such
a value that the fatigue life of the original wing is achieved with the original load spectra.
These reference stresses are transferred to the new fatigue analysis. The modified models
are taken into account when forming the loads. A new fatigue analysis is conducted for
the wing with the survey load spectra and the consumed fatigue life is resolved. Both
analytical fatigue analyses base on the Miner rule. With this process the fatigue life
consumption of the wing is estimated. Also, some representing factors are defined for the
future use. With these factors the operations can be scaled to match the estimated fatigue
life consumption.
The Miner hypothesis, also known as the Miner’s Linear Cumulative Damage
Theory, is widely used in the analytical fatigue analyses. The basic philosophy of this
theory is that the fatigue damage introduced by a given stress level is proportional to the
number of cycles at that stress level divided by the total number of cycles to failure at that
stress level. This ratio is referred as the cycle ratio and it is used to measure damage. The
stress level is here defined as the mean stress and amplitude of the load cycle. All various
cycle ratios are summed together to represent the total damage. The hypothesis states that
the failure occurs when the total damage reaches unity.
Two principal factors govern the amount of time it takes for a crack to start and
grow sufficiently to cause component failure: the component material and stress field.
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Methods for determining fatigue testing of materials go back to August Wöhler who, in
the 19th century, set up and conducted the first systematic fatigue investigation. Standard
laboratory tests apply cyclical loads such as rotating bend, cantilever bend, axial push-
pull, and torsion cycles. Scientists and engineers plot the data resulting from such tests to
show the relationship of each type of stress to the number of cycles of repetition leading
to failure—or S-N curve. Engineers can derive the stress level a material can endure for a
specific number of cycles from the S-N curve.
The curve splits into low and high cycle fatigue. Generally, low cycle fatigue
occurs at fewer than 10,000 cycles. The shape of the curve depends on the type of
material tested. Some materials, such as low-carbon steels, show a flattening off at a
particular stress level—referred to as the endurance or fatigue limit. Materials that contain
no iron show no endurance limit. In principle, components designed so that the applied
stresses do not exceed the known endurance limit shouldn’t fail in service. However,
endurance limit calculations don’t account for localized stress concentrations that may
lead to initiation of cracks, despite the stress level appearing to be below the normal
―safe‖ limit.
Fig 1.10 : S N curve
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Fatigue load history, as determined by testing with rotating bend tests, provides
information about mean and alternating stress. The rate of crack propagation in tests has
been shown to be related to the stress ratio of the load cycle, and the load’s mean stress.
Cracks only propagate under tensile loads. For that reason, if the load cycle induces
compressive stress in the area of the crack, it will not produce more damage. However, if
the mean stress shows that the complete stress cycle is tensile, the whole cycle will cause
damage.
1.6.1 FACTORS THAT AFFECT FATIGUE LIFE:
Cyclic stress state: Depending on the complexity of the geometry and the loading,
one or more properties of the stress state need to be considered, such as stress
amplitude, mean stress, biaxiality, in-phase or out-of-phase shear stress, and load
sequence,
Geometry: Notches and variation in cross section throughout a part lead to stress
concentrations where fatigue cracks initiate.
Surface quality: Surface roughness can cause microscopic stress concentrations that
lower the fatigue strength. Compressive residual stresses can be introduced in the
surface by e.g. shot peening to increase fatigue life. Such techniques for producing
surface stress are often referred to as peening, whatever the mechanism used to
produce the stress. Low plasticity burnishing, laser peening, and ultrasonic impact
treatment can also produce this surface compressive stress and can increase the
fatigue life of the component. This improvement is normally observed only for high-
cycle fatigue.
Material Type: Fatigue life, as well as the behavior during cyclic loading, varies
widely for different materials, e.g. composites and polymers differ markedly from
metals.
Residual stresses: Welding, cutting, casting, grinding, and other manufacturing
processes involving heat or deformation can produce high levels of tensile residual
stress, which decreases the fatigue strength.
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Size and distribution of internal defects: Casting defects such as gas
porosity voids, non-metallic inclusions and shrinkage voids can significantly reduce
fatigue strength.
Air or Vacuum: Certain materials like Metals are more prone to fatigue in air than in
a vacuum. Depending upon the level of humidity and temperature, the lifetime for
metals such as aluminum or iron might be as much as 5 to 10 times greater in a
vacuum. This is mostly due to the effect of the oxygen and water vapour in the air
which will aggressively attack the material and so encourage the propagation of
cracks. Other environments such as oil or seawater may reduce the fatigue life at an
even greater rate.
Direction of loading: For non-isotropic materials, fatigue strength depends on the
direction of the principal stress.
Grain size: For most metals, smaller grains yield longer fatigue lives, however, the
presence of surface defects or scratches will have a greater influence than in a coarse
grained alloy.
Environment: Environmental conditions can cause erosion, corrosion, or gas-phase
embrittlement, which all affect fatigue life. Corrosion fatigue is a problem
encountered in many aggressive environments.
Temperature: Extreme high or low temperatures can decrease fatigue strength.
Fatigue cracks that have begun to propagate can sometimes be stopped
by drilling holes, called drill stops, in the path of the fatigue crack. This is not
recommended as a general practice because the hole represents a stress concentration factor
which depends on the size of the hole and geometry, though the hole is typically less of a
stress concentration than the removed tip of the crack. The possibility remains of a new
crack starting in the side of the hole. It is always far better to replace the cracked part
entirely.
Changes in the materials used in parts can also improve fatigue life. For example,
parts can be made from better fatigue rated metals. Complete replacement and redesign of
parts can also reduce if not eliminate fatigue problems. Thus helicopter rotor blades
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and propellers in metal are being replaced by composite equivalents. They are not only
lighter, but also much more resistant to fatigue. They are more expensive, but the extra
cost is amply repaid by their greater integrity, since loss of a rotor blade usually leads to
total loss of the aircraft. A similar argument has been made for replacement of metal
fuselages, wings and tails of aircraft.
1.7 COMPUTATIONAL METHOD:
In mathematics, the finite element method (FEM) is a numerical technique for
finding approximate solutions to boundary value problems for differential equations. It
uses variational methods (the calculus of variations) to minimize an error function and
produce a stable solution. Analogous to the idea that connecting many tiny straight lines
can approximate a larger circle, FEM encompasses all the methods for connecting many
simple element equations over many small sub-domains, named finite elements, to
approximate a more complex equation over a larger domain.
FE method is an established procedure that enables predictions of deformations
and stresses of products in normal or accelerated loading environments. Although the FE
procedures continue to evolve, there are numerous FE packages that are commercially
available and capable of performing advanced simulations.
Major Input that are needed to perform a FE simulation:
(1) Geometry of the part(s) of interest;
(2) Applied loading and boundary conditions; and
(3) Material behavior of each of the different materials.
The first two of these required inputs are often easy to accurately specify by CAD
software and knowledge about the loading environment. But for the third input,
specification of the material models is typically the most difficult and challenging part of
performing FE simulations.
FEM is best understood from its practical application, known as finite element
analysis (FEA). FEA as applied in engineering is a computational tool for performing
engineering analysis. It includes the use of mesh generation techniques for dividing
a complex problem into small elements, as well as the use of software program coded
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with FEM algorithm. In applying FEA, the complex problem is usually a physical system
with the underlying physics such as the Euler-Bernoulli beam equation, the heat equation,
or the Navier-Stokes equations expressed in either PDE or integral equations, while the
divided small elements of the complex problem represent different areas in the physical
system.
FEA is a good choice for analyzing problems over complicated domains (like cars
and oil pipelines), when the domain changes (as during a solid state reaction with a
moving boundary), when the desired precision varies over the entire domain, or when the
solution lacks smoothness. For instance, in a frontal crash simulation it is possible to
increase hprediction accuracy in "important" areas like the front of the car and reduce it in
its rear (thus reducing cost of the simulation). Another example would be in numerical
weather prediction, where it is more important to have accurate predictions over
developing highly nonlinear.
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CHAPTER 2
LITERATURE SURVEY
Article titled [1] ―Design of an Aircraft Wing Structure for Static Analysis and
Fatigue Life Prediction‖ published by Ramesh Kumar, S. R. Balakrishnan, S. Balaji. In
this paper stress analysis of the wing structure is carried out to compute the stresses at
wing structure and prediction of fatigue life for crack initiation will be carried out at
maximum stress location. The stresses are estimated by using the finite element approach
with the help of ANSYS-12 to find out the safety factor of the structure. It is found out
from the result that maximum stress is identified at wing root which is found out to be
lower than yield strength of the material. It is found that damage accumulated is less than
the critical damage and structure is safe from fatigue. Life of the particular region in wing
structure is predicted to become critical and found out to be 3058 flying hours.
Journal Paper titled [2]―Wing Structure Static Analysis using Superelement‖
published by W Kuntjoro, AMH Abdul Jalil, J Mahmud. In this paper superelement for
the stress and deflection analysis of a typical fighter wing structure were used. Three
methods of analyses were carried out and compared: practical/theoretical analysis; finite
element analysis with the conventional element modelling approach; and finite element
analysis with the superelement modelling. The direct stress and deflection are sought and
to be compared. Result shows a good agreement between the three methods. The
comparison of the stress values between the theoretical approach and the finite element
analysis approaches shows minimal errors. The comparison of the stress values between
the finite element analysis with conventional approach and finite element analysis with
superelement approach shows the same results. The finite element analysis with
conventional approach and superelement approach shows the same results for the
deflection values. This proves that that the superelement approach does not alter the
values obtained from the conventional finite element approach.
Article titled [3] ―Crack Growth Analysis in Aircrft Wing Lug Section and
Fatigue Life Estimation‖ published by K. Mookaiya, S. Balaji, S. R. Balakrishnan. In this
paper a model for estimating the residual fatigue life of attachment lugs is proposed.
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Strength analysis and fatigue life estimation is determined by applying analytical and
numerical methods. This journal work presents a computational model for the crack
growth analysis of the attachment lug with single quarter-elliptical crack as well as with
single through-the-thickness crack. The proposed model examines the stress analysis, the
fatigue life estimation and the crack path simulation. In the stress analysis, both analytical
approaches are employed to determine the stress intensity factor. In the finite element
analyses are conducted using the packages ANSYS and quarter point (Q-P) finite
elements are employed to simulate the stress field around the crack tip.
Journal paper titled [4] ―Fatigue Analysis in Aircraft Landing Gear Axle Shaft To
Develop The Life Cycles‖ published by P. Mohanraj, S. Balaji, S. Senthilkumar. In this
paper the Objective is to analyze main landing gear axle shaft to determine the fatigue
stress behaviour and the displacement of an aircraft landing gear axle during taxing in the
ground. The failure of the left main landing gear of a Boeing 737-400 has been analyzed
in this report the forces and tensions on the landing gear and axle were calculated. The
current material is changed to titanium alloy ASTM Grade 5 which is stronger but also
more expensive. The fatigue cycles are increased to two times greater than the current
axle. The safety factor is also greater than current alloy therefore cost of the new model
compromised by its greater life cycles. So safety is thereby improved.
Article titled [5] ―Fatigue Life Analysis of Aircraft Structural Components‖
published by Stevan Maksimović. This work defines an effective computation procedure
that combines Neuber`s Rule and the finite element method with strain–life criterions in
order to accurately predict fatigue crack initiation life. Miner’s rule was used to calculate
the accumulative damage in the fatigue crack initiation phase. This procedure is then
applied to a plate with a central hole (structural elements with concentrations), and the
results were compared with analytical local strain method and available experimental
data. Fatigue life estimated by the presented procedure closely approximates experimental
results. The defined procedure, for fatigue life prediction of notched aircraft structural
components up to crack initiation, can take into consideration uni-axial and multi-axial
loading with constant and variable amplitude.
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Journal paper titled [6] ―Initial Fatigue Life Predictions of a Notched Structural
Components Under Variable Amplitude Loading‖ published by Slobodanka Boljanovic
and Stevan Maksimovic. This paper presents numerical procedure for initial fatigue life
of structural components under load spectra. Fatigue crack initiation at the notch root is
considered to be due to localized low-cycle fatigue. The cycle behaviour of the steel was
investigated in terms of stress and strain relations. This work presents an effective
procedure to predict fatigue life up to crack initiation. Miner`s rule was used to calculate
the accumulative damage in the fatigue crack initiation phase. Comparative results
demonstrate that the fatigue life estimated by the presented procedure closely
approximates experimental results. It is very important to stress that presented procedure
for prediction of fatigue life up to crack initiation provides good correlation with
experimental data even with low and high fatigue domains. The defined procedure, for
fatigue life prediction up to crack initiation, can take in consideration uni-axial and multi-
axial loading with constant and variable amplitude.
Journal paper titled [7] ―Fatigue Crack Growth Analysis of Damaged Structural
Components Under Mode-I and Mixed Modes‖ Published by Katarina Maksimović, MSc
(Eng). The work presents a life prediction methodology of damaged structural
components under the interspersed mode-I and the mixed-mode (I and II). This work
considers the numerical computation methods and procedures for predicting the fatigue
crack growth life for cracks at notched structural components. The strain energy density
and MTS criteria are used to determine the crack trajectory or the angle of crack growth
in thin walled structures with cracks emanating from holes. Attention in this work is
focused on the crack growth analyses of damaged structural components under fracture
mechanics for mode I and the mixed modes. The aim of this work is to investigate the
strength behaviour of the notched structural elements such as the cracked lugs. In the
fatigue crack growth and the fracture analysis of lugs, an accurate calculation of SIFs is
essential. An analytic expression for the stress intensity factor of the cracked lug is
derived using the correction function. The contact finite element analysis for the true
distribution of the pin contact pressure is used for the determination of stress
concentration factors that is used in the correction function. Good agreement between the
derived analytic SIFs of the cracked lug with finite elements is obtained.
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Journal paper titled [8] ―Stress Analysis for Wing Attachment Bracket of a six
seater Transport Airframe Structure‖ published by Harish E.R.M, Mahesha. K, Sartaj
Patel. In this paper study the stress analysis of wing-fuselage attachment bracket is
considered. Stress analysis will be carried00 out for the given geometry of the wing-
fuselage attachment bracket of a six seater transport airframe structure. Finite element
method is used for the stress analysis. Stress analysis helps in prediction of fatigue life of
structural component of airframe structure. Stress analysis of the wing fuselage lug
attachment bracket is carried out and maximum tensile stress is identified at one of the
rivet hole of I-spar plate.FEM approach is followed for the stress analysis of the wing
fuselage lug attachment bracket.)A validation for FEM approach is carried out by
considering a plate with a circular hole. Maximum tensile stress of 1373N/mm2 (i.e., 140
kg/mm2) is observed in the I-spar plate. Several iterations are carried out to obtain a mesh
independent value for the maximum stress. A fatigue crack normally initiates from the
location maximum tensile stress in the structure, further fatigue life estimation can be
carried out to predict the life of the airframe component.
Article titled [9] ―Fatigue Life Estimation Of Notched Structural Components:
Computation and Experimental Investigations‖ published by S. Maksimović, Z. Burzić,
K. Maksimović. This work considers the analytical/numerical methods and procedures for
obtaining the stress intensity factors and for predicting the fatigue crack growth life for
cracks at notched structural components. A variety of methods have been used to estimate
the SIF values, such as approximate analytical methods, finite element (FE), finite
element alternating, weight function, photo elasticity and fatigue tests. Single through
crack in the attachment lug analysis is considered. For this purpose analytic expressions
are evaluated for SIF of cracked lug structures. For validation of the analytic stress
intensity factors of cracked lugs, FEM with singular finite elements is used. The aim of
this work is to investigate the strength behaviour of the notched structural elements such
as the cracked lugs. In the fatigue crack growth and fracture analysis of lugs, accurate
calculation of SIF is essential. Analytic expression for stress intensity factor of cracked
lug is derived using correction function. The contact finite element analysis for the true
distribution of pin contact pressure is used for determination of stress concentration
factors that is used in correction function. Good agreement between derived analytic SIF
of cracked lug with finite elements is obtained. In this paper the predicted crack trajectory
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using quarter-point singular finite elements together to the strain energy density criteria
were nearly identical to the trajectories predicted with X-FEM.
Journal titled [10] ―Stress Intensity Factors for Elliptical Surface Cracks in Round
Bars and Residual Life Estimation‖ published by Marija Blažić, Mirko Maksimović,
Ivana Vasović, Yasmina Assoul. This work investigates the behaviour of structural
components with surface cracks1,2 . The attention is focused on a circular bar with an
elliptical surface crack under tension load. Stress intensity factors (SIF) are considered
using the finite element method. For that purpose a straight round bar under tension is
investigated. Stress intensity factors of elliptical surface cracks in tensile round bars are
calculated by using three-dimensional finite element analysis (FEA) models with singular
20-node elements arranged around the crack tip. The stress intensity factors are
determined by singular finite elements for various crack depths. Using these discrete
values of the stress intensity factors, a general analytic expression of stress intensity
factors is derived. An empirical expression for the SIFs as a function of crack geometry is
obtained by fitting the numerical results. These analytic expressions are used in the crack
growth analysis of a cracked structural component. Therefore, the empirical expression
can be used conveniently in the life prediction of notched bars with various notch
geometries and stress concentration coefficients at least within the range of parameters
studied in this work.
Journal paper titled [11] ―An Approach to the Fatigue Analysis of Vertical Axis
Wind Turbine Blades‖ published by pauls. Veers sandia natlonal laboratories
albuquerque, new mexico 87185 and livermore, california 94550. Examination of the real
time stress signal from VAWT blades during operation demonstrate that a single
vibratory stress level at each wind speed does not characterize the state of stress of an
operating turbine’s blades. Combining the Rayleigh distribution with the S-N data using
Miner’s Rule results in an expression for the number of operating cycles to failure at each
wind speed. Implementing the cumulative damage rule again to account for the wind
speed distribution provides a method of predicting the total wind turbine life for a given
wind site and given cut-in and cut-out wind speeds.
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Article titled [12] ―Fatigue Life Estimation Considering Damaging and
Strengthening of Low amplitude Loads under Different Load Sequences Using Fuzzy
Sets Approach‖ published by SHUN-PENG ZHU, HONG-ZHONG HUANG* AND
ZHONG-LAI WANG. Based on the Miner rule, this study refers not only to the
damaging and strengthening effect of low amplitude loads below the fatigue limit, but
also the effects of load sequence and load interaction. Compared with the traditional
Miner rule, results of those fatigue tests clearly indicate that the proposed Miner rule
gives more accurate and reliable predictions on fatigue lives. The strengthening and
damaging of low amplitude loads below the fatigue limit are investigated within the
Miner rule.
Article titled1 [13] ―Literature Review on Aircraft Structural Risk and Reliability
Analysis‖ published by Yu Chee Tong Airframes and Engines Division Aeronautical and
Maritime Research Laboratory. Probabilistic Damage Tolerant approach or Structural
Risk and Reliability Analysis have been identified as the potential tool for satisfying these
requirements. It has also been proven that probabilistic method can be extended to
provide very useful information to help managers in making decisions regarding the
operation and inspection time of the fleet in order to maintain airworthiness. It is capable
of identifying the sources of variables affecting the fatigue life and fatigue strength of the
structure in terms of risk.
Practice paper titled [14] ―Structural Stress Analysis” from Goddard Space Flight
Center (GSFC), NASA. This paper describes the general methodology for performing
stress analysis for structures used in space applications. Reliability of spacecraft structural
components is greatly increased, and their cost and weight reduced by the systematic and
rigorous application of sound stress analysis principles as an integral part of the design
process. Structural loads are specified at the maximum expected level and referred to as
the design or limit loads. . A major difference could be absence of ribs and multiple spars
(more than 2) in the vertical tail construction. Vertical tails have symmetrical airfoil cross
sections. Therefore in the absence of rudder deflection there is no aerodynamic load
acting on the fuselage. However significant side loads develop due to rudder deflection
and this is the major design load for the vertical tail
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Article titled [15] ―Design of Constructions with Respects to Fatigue and Fracture
Mechanics” published by Dr Stevan Maksimović, Marija Blažić, Mirko Maksimović. In
this investigation analytic method for determination of the stress intensity factors to
surface cracks at the 3-D solid structural elements is established. Primary attention of this
paper is to establish analytic expressions of SIF’s for surface crack which can be effective
used in crack growth propagations and residual life estimations. Good agreement analytic
with finite element results is obtained in domains static fracture mechanics and crack
growth analyses. The complete computation procedure for crack growth analysis is
illustrated to aircraft nose landing gears. Procedure is based on using finite element
method to determine critical locations with respects to fatigue and fracture mechanics
with one side and to use analytic expressions for determination of SIF’s and residual life
of structural components with other side.
Journal titled [16] ―A Statistical Analysis of the Aircraft Landing Process‖
published by Babak Ghalebsaz-Jeddi, George L. Donohue, John F. Shortle. We obtained
the wake vortex weight class for 98.6% of aircraft landing in peak periods. This paper
extended our initial report where some statistics of the aircraft approach on all runways
collectively were presented, Jeddi et al. (2006). Samples were additionally conditioned on
weight class of follow-lead aircraft and aggregated for the ones with a minimum
separation standard of 3 nm and 4 nm, whereas the initial report was only about 3 nm
pairs under ILS.
Journal paper titled [17] ―Analytical Fuselage and Wing Weight Estimation of
Transport Aircraft‖ published by Mark D. Ardema, Mark C. Chambers, Anthony P.
Patron, Andrew S. Hahn, Hirokazu Miura, and Mark D. Moore. A method of estimating
the load-bearing fuselage weight and wing weight of transport aircraft based on
fundamental structural principles has been developed. This method of weight estimation
represents a compromise between the rapid assessment of component weight using
empirical methods based on actual weights of existing aircraft, and detailed, but time-
consuming, analysis using the finite element method Using statistical analysis techniques,
relations between the load-bearing fuselage and wing weights calculated by PDCYL and
corresponding actual weights were determined.
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Paper titled [18] ―AIRCRAFT LOADS‖ published by Dr. M. Neubauer, G.
Günther. In this paper Structural loads, leading to fatigue as well as corrosion, depending
on the usage environment, are the major reason for degradation of structures. The many
different classes of loads, the generation of loading conditions during the design phase, as
defined in the weapons systems specification, consideration of static and fatigue loads for
structural lay-out and validation concepts are presented. The procedure of converting
overall aircraft loads (―external loads‖) into individual component loads is shown in
principal.
Article titled [19] ―Design and Analysis of A Spar Beam For The Vertical Tail of
A Transport Aircraft‖ published by Vinod S. Muchchandi, S. C. Pilli. IN THIS PAPER
Vertical tail and the rudder are important structural components of an aircraft. Movement
of the rudder controls the yawing of an aircraft. Structurally speaking vertical tail is a
typical mini-wing construction. A major difference could be absence of ribs and multiple
spars (more than 2) in the vertical tail construction. Vertical tails have symmetrical airfoil
cross sections. Therefore in the absence of rudder deflection there is no aerodynamic load
acting on the fuselage. However significant side loads develop due to rudder deflection
and this is the major design load for the vertical tail. For transport aircraft side gust load is
also important from a design point of view. In this project a typical spar of a vertical tail
of a transport aircraft will be analysed. Loads representative of a small transport aircraft
will be considered in this study. An efficient tapered spar beam will be designed for this
load. SOM approach will be used for preliminary sizing of the spar. This will be followed
by FEA for a more accurate stress analysis that will be used to improve the design. The
objective of the present study is to investigate the stresses acting in the spar beam of the
vertical tail with and without cut outs. The analysis shows that increase in the air drag
load increases the maximum stress. The differential air drag load is applied between the
ranges 62 to 620 Kg which varies non-linearly. In this study, the effects of stresses in
aircraft spar beam structure with and without cut outs are determined. A typical spar
beam with and without cut outs of standard configurations is loaded and analysed.
Parametric studies were done to examine the effects of different cut outs. Based on the
results of finite element predictions and by the calculations of the stress analysis
approach, it is apparent that the air drag load has more effect on the top and bottom
flange. From the load cases the maximum stress is compared with yield stress and
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ultimate stress of 2024 T351 aluminium alloy.This study refers not only to the damaging
and strengthening effect of low amplitude loads below the fatigue limit, but also the
effects of load sequence and load interaction. Compared with the traditional Miner rule,
results of those fatigue tests clearly indicate that the proposed Miner rule gives more
accurate and reliable predictions on fatigue lives. The strengthening and damaging of low
amplitude loads below the fatigue limit are investigated within the Miner rule.
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CHAPTER 3
FINITE ELEMENT ANALYSIS
3.1 FINITE ELEMENT ANALYSIS OF LANDING GEAR
WELL BEAMS
Finite Element Analysis is a numerical analysis technique used to obtain solutions
to the differential equations that describe or approximately describe a wide variety of
physical (and non-physical) problems physical problems range in diversity from solid,
fluid and soil mechanics to electromagnetism or dynamics.
FEA uses a complex system of points called nodes which make a grid called
a mesh. This mesh is programmed to contain the material and structural properties which
define how the structure will react to certain loading conditions. Nodes are assigned at a
certain density throughout the material depending on the anticipated stress levels of a
particular area. Regions which will receive large amounts of stress usually have a higher
node density than those which experience little or no stress. Points of interest may consist
of: fracture point of previously tested material, fillets, corners, complex detail, and high
stress areas. The mesh acts like a spider web in that from each node, there extends a mesh
element to each of the adjacent nodes. This web of vectors is what carries the material
properties to the object, creating many elements.
The underlying premise of the method states complicated domain can be sub-
divided into a series of smaller regions in which the differential equations are
approximately solved by assembling the set of equations for each region the behaviour
over the entire problem domain is determined each region is referred to as an element and
the process of subdividing a domain into a finite number of elements is referred to as
discretization elements are connected at specific points called nodes and the assembly
process requires that the solution be continuous along common boundaries of adjacent
elements.
FEA has become a solution to the task of predicting failure due to unknown
stresses by showing problem areas in a material and allowing designers to see all of the
theoretical stresses within. This method of product design and testing is far superior to the
manufacturing costs which would accrue if each sample was actually built and tested.
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FE models can be created using one-dimensional (1D beam), two-dimensional
(2D shell) or three-dimensional (3D solid) elements. By using beams and shells instead of
solid elements, a representative model can be created using fewer nodes without
compromising accuracy. Each modeling scheme requires a different range of properties to
be defined, such as:
Section areas
Moments of inertia
Torsional constant
Plate thickness
Bending stiffness
Transverse shear
To simulate the effects of real-world working environments in FEA, various load
types can be applied to the FE model, including:
Nodal: forces, moments, displacements, velocities, accelerations, temperature and heat
flux
Elemental: distributed loading, pressure, temperature and heat flux
Acceleration body loads (gravity)
Types of analysis include:
Linear statics: linear analysis with applied loads and constraints that are static
Nonlinear statics and dynamics: effects due to contact (where one part of the model
comes into contact with another), nonlinear material definitions (plasticity, elasticity, etc.)
and large displacement (strains that exceed small displacement theory that limits a linear
analysis approach)
Normal modes: natural frequencies of vibration
Dynamic response: loads or motions that vary with time and frequency
Buckling: critical loads at which a structure becomes unstable
Heat transfer: conduction, radiation and phase change
Typical results calculated by the solver include:
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Nodal displacements, velocities and accelerations
Elemental forces, strains and stresses
Benefits of FEA:
FEA can be used in new product design, or to refine an existing product, to ensure
that the design will be able to perform to specifications prior to manufacturing. With FEA
you can:
Predict and improve product performance and reliability
Reduce physical prototyping and testing
Evaluate different designs and materials
Optimize designs and reduce material usage
3.2 PROCESS FLOW OF FINITE ELEMENT ANALYSIS
In practice, a finite element analysis usually consists of three principal steps:
1. Pre-processing: The user constructs a model of the part to be analyzed in which the
geometry is divided into a number of discrete sub regions, or ―elements," connected at
discrete points called ―nodes." Certain of these nodes will have fixed displacements, and
others will have prescribed loads. These models can be extremely time consuming to
prepare, and commercial codes vie with one another to have the most user-friendly
graphical pre-processor to assist in this rather tedious chore. Some of these preprocessors
can overlay a mesh on a pre-existing CAD file, so that finite element analysis can be done
conveniently as part of the computerized drafting-and-design process. Computation of the
mathematical model. The solver runs after you have defined your material, fixtures, and
loads. The solver constructs a system of equations from the elements based on these
parameters and solves for them either directly or iteratively.
2. Analysis: The dataset prepared by the preprocessor is used as input to the finite
element
code itself, which constructs and solves a system of linear or nonlinear algebraic
equations
Kijuj = fi,
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where u and f are the displacements and externally applied forces at the nodal
points. The formation of the K matrix is dependent on the type of problem being attacked,
and this module will outline the approach for truss and linear elastic stress analyses.
Commercial codes may have very large element libraries, with elements appropriate to a
wide range of problem types. One of FEA's principal advantages is that many problem
types can be addressed with the same code, merely by specifying the appropriate element
types from the library.
3. Postprocessing: In the earlier days of finite element analysis, the user would pore
through reams of numbers generated by the code, listing displacements and stresses at
discrete positions within the model. It is easy to miss important trends and hot spots this
way, and modern codes use graphical displays to assist in visualizing the results. Typical
postprocessor display overlays colored contours representing stress levels on the model,
Showing a full-field picture similar to that of photo elastic or moire experimental results.
The general steps followed in a finite element analysis with a commercial FEM package
is as shown in figure 3.1
Fig 3.1 Process Flow of FEA
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CHAPTER 4
MATERIAL PROPERTIES, LOAD CALCULATION
AND BOUNDARY CONDITION
The material taken for the landing gear wells beams is assumed to be made of
aluminium alloy AA 2024 T351. Aluminium alloy 2024 is an aluminium alloy,
with copper as the primary alloying element. This is the most common of the the high-
strength aluminum alloys. It is aircraft quality. 2024-T3 aluminum sheet is thought of as
the aircraft alloy because of its strength. It has excellent fatigue resistance. Welding is
generally not recommended. Typical uses for 2024-T3 Alclad aluminum sheet are aircraft
skins, cowls, aircraft structures, and also for repair and restoration because of its shiny
finish (2024-T3 Alclad). Ultimate strength is 62000 PSI with a shearing strength of 40000
PSI. It is used in applications requiring high strength to weight ratio, as well as
good fatigue resistance. It is weldable only through friction welding, and has
average machinability. Due to poor corrosion resistance, it is often clad
with aluminium or Al-1Zn for protection, although this may reduce the fatigue strength.
Aluminum alloy 2024 has a density of 2.78 g/cm³ (0.1 lb/in³), electrical
conductivity of 30% IACS, Young's Modulus of 73 GPa (10.6 Msi) across all tempers,
and begins to melt at 500 °C (932 °F).
2024 aluminum alloy's composition roughly includes 4.3-4.5% copper, 0.5-
0.6% manganese, 1.3-1.5% magnesium and less than a half a percent of silicon, zinc,
nickel, chromium, lead and bismuth. T3 temper 2024 sheet has an ultimate tensile
strength of 58-62 ksi (400-427 MPa) and yield strength of at least 39-40 ksi (269-276
MPa). It has an elongation of 10-15%.
4.1 CHARACTERISTICS OF ALUMINUM:
At high temperatures (200-250°C) aluminum alloys tend to lose some of their
strength. However, at subzero temperatures strength increases while retaining their
ductility, making aluminum an extremely useful low-temperature alloy, high flying
commercial aircraft commonly fly at -50°C so they profit from this property.
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It also has good electrical (ground for aircraft antenna) and thermal
conductivities and is highly reflective to heat and light. Copper is the more widely
used conductor (copper bus bars and wiring among other things), having a
conductivity of approximately 160% that of aluminum. Aluminum connectors have a
tendency to become loose after repeated usage and this can lead to arcing and fire,
which requires extra precaution and special design when using aluminum wiring in
buildings.
Corrosion resistance: Aluminum alloys also have a good strong resistance to
corrosion which is a result of an oxide skin that forms as a result of reactions with the
atmosphere. These reactions occur very quickly, usually within minutes. This
corrosive skin protects aluminum from most chemicals, weathering conditions. It is a
very versatile metal and can be cast in any form. It can be rolled, stamped, drawn,
spun, roll-formed, hammered and forged. The metal can be extruded into a variety of
shapes and can be turned, milled, and bored in the machining process. Aluminum can
riveted, welded, brazed, or resin bonded (aluminum/composite aircraft are a good
example). For most applications, aluminum needs no protective coating as it can be
finished to look good, however it is often anodized to improve color and strength.
Young`s modulus
73 GPa
Poisson`s ratio
0.33
Yield strength
324 MPa
Ultimate tensile strength
427 MPa
Load factor
1.5
Density
2.78g/cm3
Elongation
10-15 %
Electrical conductivity
30% IACS
Table 4.1: Aluminium Alloy 2024 properties
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4.2 Load calculation:
Type of aircraft used for analysis: 13 seater aircraft
Total weight of aircraft: W= 6.1 ton = 6100 kg
Fig 4.1: Basic dimension of aircraft
Base length of aircraft = B = 6.465 m
Fm=
Hcg =1.88 m
Fmdy=
aT = vertical sink rate.
Hcg = Height from ground to center of gravity.
Fmdy = 2660.79 kg
Total load on main landing gear during normal touch down:
F = 2660.79 + 6100 = 8760.79 kg
Force per landing gear: F = 8760.79/2 = 4380.4 kg
Force acting on pin diameter:
=46.4775 kg/mm.
Force acting on each side of pin:
= 23.23 kg/mm.
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Fig 4.2: Meshing and Boundary Condition of landing gear well beams.
The load is calculated for a 13 seater aircraft. Total weight of aircraft is 6100 kg
or 6.1 ton. The base dimension of aircraft is 6.465 m. The distance between ground and
centre of gravity is 1.88 m. The load calculated by using above equation is total load on
main landing gear during normal touchdown is combination of total weight and dynamic
forces acting on it during flight level which is 8760.9 kg. As there are two landing gears
per aircraft one is main landing gear and other is nose landing. As main landing gear
takes maximum load during landing, hence main landing gear is analyzed. The main
landing gear contains two landing gear hence load is divided equally between the two
landing gear. Total load per landing gear is 4380.4 kg.
The load is acting on pin of diameter is 46.4775 kg/mm. There are two sides in a pin and
hence load acting on each pin hole is 23.23 kg/mm. In the structure the flange of rib is
fixed and load is applied to pin hole.
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CHAPTER 5
LINEAR STATIC ANALYSIS OF LANDING GEAR
WELL BEAMS
Linear analysis is used to solve static problems, such as determining if a structure
will fail under a prescribed load, and can also be used to solve transient problems where
loads change over time. Linear analysis has been used for decades to evaluate structural
performance for applications in a variety of industries, such as understanding how an
airframe reacts to flight loads, determining the amount of pressure a new keypad can
handle on an electronic device, or how much weight beams can hold in a civil structure
before buckling.
A series of assumptions are made with respect to a linear static analysis:
1. Deflections should be small relative to structure.
2. Rotations should be less than 10 degrees to 15 degrees.
3. Material should be linear elastic.
4. Boundary conditions should be constant
Linear static FEA process begins with taking the geometry and discretizing it into
a series of smaller elements. Currently only basic shapes have analytical solutions. CAD
geometry is often complex and must be broken down, or discretized, into a series of
continuous elements which can be solved for displacements and subsequently stresses and
strains.
There are many different types of elements that FEA programs use to handle
different classes of problems. SolidWorks has three main types of elements, 3-D solid
tetrahedral, 2-D triangular shell, and 2-D beam elements. The model of the LG beams
geometry is built up with solid 3D brick elements. The element is defined by eight nodes
having three degrees of freedom at each node. The landing gear beams is modeled using
Catia V5, meshed using Patran and analyzed using the Nastran software.
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5.1 GLOBAL ANALYSIS:
In global analysis the meshed model along with boundary condition applied is
analyzed. The main objective in this analysis is to find maximum stress location, because
cracks are initiated at maximum stress location. Magnitude of maximum stress and stress
distribution is also obtained from global analysis.
STEPS IN LINEAR STATIC STRESS ANALYSIS:
STEP 1: Requirements and loads determination
Loads
-Static (or equivalent static)
-Strength, displacement, cyclic life
STEP 2: Material Characterization
-Structural goals vs. material parameters
STEP 3: Structural modelling
-Discretized numerical model (e.g., finite element model)
-Analytical (closed form) solution of idealized geometry and loading
STEP 4: Determination of structural response
-Linear/non-linear
-Deformations, internal forces and stresses
STEP 5: Failure modes check
-Margin of safety for ultimate failure, yielding, instability etc.
-Safe life for fracture if applicable
STEP 6: Optimization and redesign if necessary
STEP 7: Documentation
Generally the following method is used for doing global analysis, They are:
Importing Solid model designed using modeling software( CATIA V5).
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Fig 5.1: Landing Gear beam Catia Model.
Converting 3D into 2D model.
Fig 5.2: Two Dimensional Model of LG Beams.
Meshing: The 2D model is meshed using Quad 4 and Tria element type.
Meshing is done in patran software.(pre-processor)
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Fig 5.3: Complete Meshed Model.
Cross-section of beams must be assigned.
Material properties must be assigned. Such as young's modulus (7000) and
possion`s ratio (0.33).
Boundary condition and loads are applied to structure.
Fig 5.4: Loaded and Constrained model
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Output.
Fig 5.5: Output of Stress Analysis.
The above figure gives the stress distribution in landing gear beam for given load.
The magnitude of maximum stress is 94.8 N/mm2. The location of maximum stress is at
the lower end of fixed beam. The maximum stress is found to be located at the rivet
location in the beam
.
Fig 5.6: Location of Maximum Stress in LG beams.
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Fig 5.7: Elemental values near Maximum Stress Location
The above fig shows the value of stress of element near maximum stress location.
In the model the rivet is not simulated as a hole instead it is taken as one dimensional
beam element, Hence the load acting as point load. Which results is high stress value at
point load, but in real the stress at the rivet is much lower than the value obtained. To get
the stress value near rivet average stress value in between two adjacent rivets is taken as
shown in box in fig 6.7. The average of four stresses is whose value is 22.725 kg/mm2 is
taken for local analysis or theoretical formulation.
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CHAPTER 6
THEORETICAL VALIDATION
It is very important that the theoretical results should matches with the
experimental or analysis results. Where the convergence of results plays a major role in
the software analysis. Convergence can achieved with the element size and shape which
is called as H-type convergence, in P-type convergence the polynomial order of the
differential equation can be considered to achieve the required result.
6.1 MAXIMUM STRESS IN PLATE WITH HOLE WITH
ONE END FIXED.
In local analysis, the location where maximum stress is found is considered for
analysis. Here maximum stress is obtained at rivet location. A plate with hole is taken to
stimulate the rivet location. The main objective in this analysis is to find the maximum
stress at the cut out rivet region. The model for local analysis is a plate with hole with
length 50mm, width 25mm, thickness 5mm and hole with diameter 5mm
.
Fig 6.1: Plate with Hole for Local Analysis
For local model analysis, a plate with hole is taken of length = 50mm, width = 25mm and
thickness = 8mm.
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Nominal stress acting on global model is 14.9+14.5+29.3+32.2 = 22.725kg/mm2
Load acting on the local model:
Stress average = Load / Area
Load = Stress avg*Area
= 22.725*25*5
= 2840.625 kg
One side of plate with hole is fixed and other end load applied is 2840.6/25= 113.625
kg/mm.
Fig 6.2: Mesh and Boundary Condition applied to Local Model.
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Fig 6.3: Local Analysis
The magnitude of maximum stress in local model is 54 N/mm2. The ultimate
tensile stress for aluminum is 45 N/mm2.
Fig 6.4: Stress Concentration Factor for Plate with Hole
To find Kt value we need to know the ratio d/w, which is 5/25 = 0.2.From stress
concentration graph Kt is found to be 2.5.
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We know that, stress concentration factor is ratio of maximum stress to nominal stress.
Kt =
Maximum stress = Kt * nominal stress
= 2.5*22.725
= 56.8 N/mm2
From the above result we can say that the analysis value almost equal to the
theoretical value obtained from Kt equation. Hence the analysis is considered as valid
process. The present model thickness is not sufficient to withstand the stress generated.
Hence the thickness needs to be increased to 8 mm for the landing gear beams to be safe.
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CHAPTER 7
FATIGUE ANALYSIS OF LANDING GEAR WELL
BEAMS
The definition of fatigue, in fact, is: failure under a repeated or otherwise varying
load, which never reaches a level sufficient to cause failure in a single application Fatigue
life evaluation of mechanical components under complex loading conditions is of great
importance to optimize structural design, and improve inspection and maintenance
procedures. Under variable amplitude loading, every same stress – strain cycle make the
same damage, and is independent of the place in the load spectrum. The mechanism of
fatigue can be broken down into three interrelated processes:
1. Crack initiation
2. Crack propagation
3. Fracture
4. Fits together
FEA stress analysis can predict crack initiation. A number of other technologies,
including dynamic nonlinear finite element analysis, can study the strain issues involved
in propagation. Because design engineers principally want to prevent fatigue cracks from
ever starting,
Fatigue damages under variable amplitude were estimated by Palmgren-Miner rule.
The Miner law is adopted, the damage D is expressed as follows:
D=Σ
Nfi is the cycle count at the time of failure under of axial (multiaxial) loading, the value ni
is the actual cycle count at the adequate stress level. Then the block load spectrum T
when the structure is failure can be expressed as follows:
T =
The above equation represents a statement of the linear damage rules used by the
local strain fatigue life predictions.
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SN curve is based on stress levels only, and uses the Wöhler method only.
Although unsuitable for components with areas of plasticity, and providing poor accuracy
for low cycle fatigue, it is the easiest to implement, has ample supporting data, and offers
a good representation of high cycle fatigue. Most components undergo a varying load
history in real life conditions, in terms of both amplitude and mean stress. Therefore, a far
more general and realistic approach considers variable amplitude loading, in which the
stresses, although repetitive over time, have varying amplitude, making it possible to split
them into load ―blocks.‖
Normally aircraft landing gear beams experiences variable spectrum loading
during takeoff and landing. A typical transport aircraft is considered for flight load
spectrum is for the fatigue analysis of the landing gear well beams structure. Calculation
of fatigue life estimation is carried out by using Miner`s Rule. Damage calculation is
carried out for the full service life of the aircraft. The load factor ―g‖ is defined as the
ratio of the lift of an aircraft to its weight. This gives a measure of the load which aircraft
experiences. As we know the maximum stress value obtained from the analysis is
corresponding to 1.5 g condition.
Therefore the stress value corresponding to 1.5 g condition is obtained as 53.7 N/mm2.
LOAD SPECTRUM FOR FATIGUE LIFE ESTIMATION:
Sl no
G range
Cycles
1
0.5g to 0.75g
57000
2
0.75g to 1g
28000
3
1g to 1.25g
24000
4
1.25g to 1.5g
18000
5
0 to 1.5 g
50
6
-0.5 g to 1.5g
100
Table 7.1: Variable Load Spectrum for Typical Aircraft
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The above table 7.1 gives load spectrum of a typical 13 seater aircraft. This data is
provided by the designer and other various design teams. This is collected from the
existing aircraft during the flight. The table gives various cycles of loading at different
range.
Correction factors for fatigue life calculations of landing gear well beams structure are
• Surface Correction Factor = 1
• Loading Type = 1
• Design Reliability = 0.897
Surface Roughness = 0.8
7.1 CALCULATE MAX STRESS FOR DIFFERENT RANGE:
Case 1: 0.5 g
Local model considering 1.5 g Load = 114 kg/mm
Local model considering 0.5 g Load = 38 kg/mm
After applying 38 kg/mm load to Local model i.e. plate with hole, we get maximum stress
of magnitude 11.3 kg /mm2.
Case 2: 0.75 g
Local model considering 1.5 g Load = 114 kg/mm
Local model considering 0.75 g Load = 57 kg/mm
After applying 57 kg/mm load to Local model i.e. plate with hole, we get maximum stress
of magnitude 16.9 kg /mm2.
Case 3: 1 g
Local model considering 1.5 g Load = 114 kg/mm
Local model considering 1 g Load = 76 kg/mm
After applying 76 kg/mm load to Local model i.e. plate with hole, we get maximum stress
of magnitude 22.6 kg /mm2.
Case 4: 1.25 g
Local model considering 1.5 g Load = 114 kg/mm
Local model considering 1.25 g Load = 95 kg/mm
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After applying 95 kg/mm load to Local model i.e. plate with hole, we get maximum stress
of magnitude 28.2 kg /mm2.
Case 5: 1.5 g
Local model considering 1.5 g Load = 114 kg/mm
After applying 114 kg/mm load to Local model i.e. plate with hole, we get maximum
stress of magnitude 33.8 kg /mm2.
Case 6: 1.75 g
Local model considering 1.5 g Load = 114 kg/mm
Local model considering 1.75 g Load = 133 kg/mm
After applying 133 kg/mm load to Local model i.e. plate with hole, we get maximum
stress of magnitude 37.5 kg /mm2.
For different g condition maximum stress is different, hence it is calculated for
each range. Initially for 1.5 g and load 114 kg/mm, maximum stress obtained is 54
kg/mm2. By using relation with 1.5 g range other range stress can be calculated as shown
above.
7.2 CALCULATION FOR STRESS AND STRESS RATIO:
1. Range 0.5 g to 0.75 g:
σmax = 16.9 kg/mm2
σmin = 11.3 kg/mm2
σ
=
= 22.26 kg/mm2
σ
=
= 14.88 kg/mm2
σamp =
= 3.69 kg/mm2
In ksi
σmax =
= 31.8 ksi
σmin =
= 21.25 ksi
σamp =
= 5.27 ksi
Stress ratio = R=
= 0.6682
2. Range 0.75 g to 1g:
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σmax = 22.9 kg/mm2
σmin = 16.9 kg/mm2
σ
=
= 29.77 kg/mm2
σ
=
= 22.26 kg/mm2
σamp =
= 3.755 kg/mm2
In ksi
σmax =
= 42.5 ksi
σmin =
= 31.8 ksi
σamp =
= 5.36 ksi
Stress ratio = R=
= 0.7482
3. Range 1 g to 1.25 g:
σmax = 28.2 kg/mm2
σmin = 22.6 kg/mm2
σ
=
= 37.15 kg/mm2
σ
=
= 29.77 kg/mm2
σamp =
= 3.69 kg/mm2
In ksi
σmax =
= 53.07 ksi
σmin =
= 42.52 ksi
σamp =
= 5.27 ksi
Stress ratio = R=
= 0.8
4. Range 1.25 g to 1.5 g:
σmax = 33.8 kg/mm2
σmin = 28.2 kg/mm2
σ
=
= 44.53 kg/mm2
σ
=
= 37.15 kg/mm2
σamp =
= 3.69 kg/mm2
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In ksi
σmax =
= 63.61 ksi
σmin =
= 53.07 ksi
σamp =
= 5.27 ksi
Stress ratio = R=
= 0.83
5. Range 0 g to 1.5 g:
σmax = 33.8 kg/mm2
σmin = 0 kg/mm2
σ
=
= 44.53 kg/mm2
σ
=
= 0 kg/mm2
σamp =
= 22.26 kg/mm2
In ksi
σmax =
= 63.61 ksi
σmin =
= 0 ksi
σamp =
= 31.80 ksi
Stress ratio = R=
= 0
6. Range -0.5 g to 1.5 g:
σmax = -11.3 kg/mm2
σmin = 33.8 kg/mm2
σ
=
= 44.53 kg/mm2
σ
=
= -14.88 kg/mm2
σamp =
= 29.705 kg/mm2
In ksi
σmax =
= 63.61 ksi
σmin =
= -21.25 ksi
σamp =
= 42.43 ksi
Stress ratio = R=
= -0.33
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Fig 7.1: Graph for number cycles to failure.
Above fig 7.1 is for design purposes is called master diagram which accumulates
fatigue data under different mean stresses and presents each line as the fatigue life under
the net of maximum and minimum stresses in addition to mean stress and alternating
stress as the reference axises. It is used to check the maximum and minimum stress
directly. Define R is the ratio of minimum stress to the maximum stress. Alternatively,
define A is the ratio of alternating stress to mean stress.
Miner's rule assumes the fatigue life is consumed by the linear combination of
different portion of stress state, both cycles and magnitude. This approximation, which is
simple and straight forward, does not take the sequences of loading history into account.
For example, a serial of high stress loading, which weaken the material, followed by a
serial low stress loading may cause more damage than a serial of low stress loading
followed by a serial of high stress loading. But Miner's rule cannot catch this effect.
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Sl no
Range
Stress ratio(R)
Stress amp(ksi)
Cycles
1
0.5g to 0.75g
0.6682
5.27
infinite
2
0.75g to 1g
0.75
5.36
Infinite
3
1g to 1.25g
0.8
5.27
Infinite
4
1.25g to 1.5 g
0.83
5.27
infinite
5
0 to 1.5 g
0
31.80
2.5*104
6
-0.5g to 1.5g
-0.33
42.43
13750
Table 7.2: No of cycles and stress ratio
Table 7.2 gives number of cycles to failure for different g range. It is obtained by
fig 7.1 by using stress ratio, mean stress and alternating stress. Stress ratio, mean stress
and alternating stress is calculated in above section.
Range 1: 0 to 1.5g
1=
= 0.002
Range 2: -0.5 g to 1.5 g
2=
= 0.007
Total damage accumulated is =
1 +
2
= 0.002+0.007
= 0.009
Total damage accumulated is 0.009, which is less than 1. Therefore a crack will
not get initiated from the location of maximum stress in the landing gear well beams
structure for given load spectrum. Hence total damage is 0.009 for 1 block of loading or
for 100 flights. One flight is considered 10 flying hours which eventually means 100
flights as 1000 flying hours.
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For damage to become critical (D= 1), the number of blocks required is 111.11
blocks or 111110 hours. Hence it is advised to meet the wing structure components
maintenance at least by this required time.
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CONCLUSION
Stress analysis of the Landing gear well beams is carried out and maximum stress
is identified near rivet location at fixed end which is found out to be lower than
yield strength of the material.
Normally the fatigue crack initiates in a structure where there is maximum tensile
stress is located. The fatigue calculation is carried out for the prediction of the
structural life of landing gear well beams. Since the damage accumulated is less
than the critical damage in the well beams structure is safe from fatigue
considerations.
Life of the particular region in landing gear well beams structure is predicted to
become critical and found out to be 111110 flying hours or 111.11 blocks, hence
advised to conduct the maintenance without fail during this period. Fatigue crack
growth analysis can be carried out in the other parts of the landing gear well
beams structure.
In the future work damage tolerance evaluation and structural testing of the
landing gear well beams structure can be carried out for the complete validation of
all theoretical calculations. As well as beam structure optimization can also be
carried out to meet the appropriate factor of safety of landing gear beam section.
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SCOPE FOR FUTURE WORK
The same work can be extended with the modifications of the material in use with
the stress and fatigue properties are more of the materialist in nature.
One can vary cross-section the beams and can perform stress analysis.
Similarly different loading condition can be considered for further analysis. These
are future scope of work which can give the strong knowledge of the failure
analysis like failure prediction and critical usage of materials or part.
Similar analysis can be carried out by using composite material and result may be
compared with conventional materials.
Analysis can for carried for different loads and boundary condition.
STRESS ANALYSIS OF THE LANDING GEAR- WELL BEAMS AND DAMAGE
CALCULATION DUE TO LANDING CYCLES
Dept of Mechanical Engineering, TOCE Page 57
REFERENCE
[1]. A. Ramesh Kumar, S. R. Balakrishnan and S. Balaji ― Design Of An Aircraft
Wing Structure For Static Analysis And Fatigue Life Prediction‖ International
Journal of Engineering Research & Technology Vol. 2 Issue 5, May – 2013 ISSN:
2278-0181
[2]. W Kuntjoro, AMH Abdul Jalil and J Mahmud(2012) ―Wing Structure Static
Analysis using Superelement‖ International Symposium on Robotics and
Intelligent Sensors 2012 (IRIS 2012)
[3]. K. Mookaiya, S. Balaji and S. R. Balakrishnan ―Crack Growth Analysis In
Aircrft Wing Lug Section And Fatigue Life Estimation‖ International Journal of
Engineering Research & Technology (IJERT) ISSN: 2278-0181 Vol. 2 Issue 6,
June - 2013
[4]. P.Mohanraj1, S. Balaji2, S. Senthilkumar3 ―Fatigue Analysis In Aircraft Landing
Gear Axle Shaft To Develop The Life Cycles‖ International Journal of
Engineering Research & Technology (IJERT) ISSN: 2278-0181 Vol. 2 Issue 6,
June - 2013
[5]. Stevan Maksimović ―Fatigue Life Analysis of Aircraft Structural Components‖,
Scientific-Technical Review,Vol.LV,No.1,2005
[6]. Slobodanka Boljanovic and Stevan Maksimovic ― Initial Fatigue Life Predictions
of a Notched Structural Components Under Variable Amplitude Loading‖ 15-
17,2004 BOOK OF PAPERS Printing Faculty of Mathematics, University of
Belgrade 1 - 15
[7]. Katarina Maksimović ―Fatigue Crack Growth Analysis of Damaged Structural
Components Under Mode-I and Mixed Modes‖ Scientific Technical
Review,Vol.LIX,No.1,2009
[8]. Harish E.R.M, Mahesha.K, and Sartaj Patel ― Stress Analysis for Wing
Attachment Bracket of a six seater Transport Airframe Structure‖ International
Journal of Innovative Research in Science, Engineering and Technology Vol. 2,
Issue 7, July 2013
STRESS ANALYSIS OF THE LANDING GEAR- WELL BEAMS AND DAMAGE
CALCULATION DUE TO LANDING CYCLES
Dept of Mechanical Engineering, TOCE Page 58
[9]. S. Maksimović, Z. Burzić, K. Maksimović ‖FATIGUE LIFE ESTIMATION OF
NOTCHED STRUCTURAL COMPONENTS: Computation and Experimental
Investigations‖.
[10]. Marija Blažić, Mirko Maksimović Ivana Vasović and Yasmina Assoul ―Stress
Intensity Factors for Elliptical Surface Cracks in Round Bars and Residual Life
Estimation‖ Scientific Technical Review, 2011,Vol.61,No.1
[11]. Pauls. Veers sandia ―An Approach to the Fatigue Analysis of Vertical Axis
Wind Turbine Blades‖ published by natlonal laboratories albuquerque, new
mexico 87185 and livermore, california 94550.
[12]. SHUN-PENG ZHU, HONG-ZHONG HUANG* AND ZHONG-LAI WANG
published ―Fatigue Life Estimation Considering Damaging and Strengthening of
Low amplitude Loads under Different Load Sequences Using Fuzzy Sets
Approach‖ School of Mechatronics Engineering, University of Electronic Science
and Technology of China, Chengdu, Sichuan, 611731, China.
[13]. ―Literature Review on Aircraft Structural Risk and Reliability Analysis‖
published by Yu Chee Tong Airframes and Engines Division Aeronautical and
Maritime Research Laboratory.
[14]. ―Structural Stress Analysis” from Goddard Space Flight Center (GSFC), NASA.
[15]. Dr Stevan Maksimović * Marija Blažić and Mirko Maksimović”DESIGN OF
CONSTRUCTIONS WITH RESPECTS TO FATIGUE AND FRACTURE
MECHANICS” Paper number: 8(2010)3,184, 181-188
[16]. A Statistical Analysis of the Aircraft Landing Process‖ published by Babak
Ghalebsaz-Jeddi, George L. Donohue, John F. Shortle.
[17]. ―Analytical Fuselage and Wing Weight Estimation of Transport Aircraft‖
published by Mark D. Ardema, Mark C. Chambers, Anthony P. Patron, Andrew S.
Hahn, Hirokazu Miura, and Mark D. Moore.
[18]. Dr. M. Neubauer, G. Günther AIRCRAFT LOADS DaimlerChrysler Aerospace
GmbH Military Aircraft, MT22, Postfach 80 11 60 81663 Munich, Germany
Paper presented at the RTO AVT Lecture Series on 13-16 November 2000, and
published in RTO EN-015.
[19]. Vinod S. Muchchandi1, S. C. Pilli2 Design and Analysis of A Spar Beam For
The Vertical Tail of A Transport Aircraft International Journal of Innovative
Research in Science, Engineering and Technology Vol. 2, Issue 7, July 2013
STRESS ANALYSIS OF THE LANDING GEAR- WELL BEAMS AND DAMAGE
CALCULATION DUE TO LANDING CYCLES
Dept of Mechanical Engineering, TOCE Page 59
APPENDIX
MSC SOFTWARE
STRUCTURAL ANALYSIS:
It has been nearly 50 years since we created the world's first structural analysis
program, Nastran. Today MSC Software continues its long history by continuously
developing best-in-class structural analysis tools for all types of engineering applications.
MSC Software provides a family of high performance solutions for FEA that meet
the needs of experienced experts and designers, new engineers, and everyone in between.
These solutions help companies meet their business challenges by helping engineers gain
deeper insight in their products through virtual testing. Engineers using MSC's structural
analysis programs are able to evaluate many different types of designs, giving high
confidence that the final design will successfully meet prescribed requirements before the
physical product is built.
From single components to large complex systems, from linear static to highly
non-linear dynamic problems, MSC's structural analysis capabilities are built to grow
with your business, optimize your cost of ownership, and support you in achieving your
goals.
DESCRIPTION ABOUT SOFTWARE USED
MSC NASTRAN:
MSC Nastran is a multidisciplinary structural analysis application used by
engineers to perform static, dynamic, and thermal analysis across the linear and nonlinear
domains, complemented with automated structural optimization and award winning
embedded fatigue analysis technologies, all enabled by high performance computing.
Engineers use MSC Nastran to ensure structural systems have the necessary
strength, stiffness, and life to preclude failure (excess stresses, resonance, buckling, or
detrimental deformations) that may compromise structural function and safety. MSC
Nastran is also used to improve the economy and passenger comfort of structural designs.
STRESS ANALYSIS OF THE LANDING GEAR- WELL BEAMS AND DAMAGE
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Dept of Mechanical Engineering, TOCE Page 60
Manufacturers leverage MSC Nastran’s unique multidisciplinary approach to
structural analysis at various points in the product development process. MSC Nastran
may be used to:
Virtually prototype early in the design process, saving costs traditionally associated with
physical prototyping.
Remedy structural issues that may occur during a product’s service, reducing downtime
and costs.
Optimize the performance of existing designs or develop unique product differentiators,
leading to industry advantages over competitors.
MSC Nastran is based on sophisticated numerical methods, the most prominent
being the Finite Element Method. Nonlinear FE problems may be solved either with built-
in implicit or explicit numerical techniques. A number of optimization algorithms are
available, including MSCADS and IPOPT. The fatigue capability in MSC Nastran has
been developed jointly by nCode International Ltd. and MSC Software.
MSC Nastran Advantages:
Multidisciplinary Structural Analysis.
Structural Assembly Modeling.
Automated Structural Optimization.
Event Simulation.
High Performance Computing.
FIG 1: Example of MSC Nastran Software.
STRESS ANALYSIS OF THE LANDING GEAR- WELL BEAMS AND DAMAGE
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Dept of Mechanical Engineering, TOCE Page 61
MSC PATRAN:
MSC Patran is the world's most widely used pre/post-processing software for
Finite Element Analysis (FEA), providing solid modeling, meshing, analysis setup and
post-processing for multiple solvers including MSC Nastran, Marc, Abaqus, LS-DYNA,
ANSYS, and Pam-Crash.
Patran provides a rich set of tools that streamline the creation of analysis ready
models for linear, nonlinear, explicit dynamics, thermal, and other finite element
solutions. From geometry cleanup tools that make it easy for engineers to deal with gaps
and slivers in CAD, to solid modeling tools that enable creation of models from scratch,
Patran makes it easy for anyone to create FE models. Meshes are easily created on
surfaces and solids alike using fully automated meshing routines, manual methods that
provide more control, or combinations of both. Finally, loads, boundary conditions, and
analysis setup for most popular FE solvers is built in, minimizing the need to edit input
decks.
Patran's comprehensive and industry tested capabilities ensure that your virtual
prototyping efforts provide results fast so that you can evaluate product performance
against requirements and optimize your designs.
Capabilities:
Direct Access of CAD Geometry.
Advanced Geometry Creation, Editing and Feature Recognition.
Support for Multiple FEA Solvers.
Post-processing and Reporting Tools for Easy Results Evaluation.
Patran Command Language.
Fig 2: Example of MSC Patran Software.
INTERNATIONAL JOURNAL OF RESEARCH IN AERONAUTICAL AND MECHANICAL ENGINEERING
Vol.2 Issue.5,
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Pgs: 61-69
Karthik Goud R V , Trupti P Wani
61
ISSN (ONLINE): 2321-3051
INTERNATIONAL JOURNAL OF RESEARCH IN
AERONAUTICAL AND MECHANICAL ENGINEERING
STRESS ANALYSIS OF THE LANDING GEAR-WELL BEAMS AND
DAMAGE CALCULATION DUE TO LANDING CYCLES
Karthik Goud R V
1
, Trupti P Wani
2
1
PG student, M .Tech (Machine Design), The Oxford College of
engineering,Bangalore,karthikrv09@gmail.com
2
Asst. prof, Mechanical department, The Oxford College of engineering, Bangalore, wani.trupti@gmail.com
Author Correspondence: PN 57, Bhuvanagiri colony, sirguppa road, Bellary.
8867224289,karthikrv09@gmail.com
Abstract
Landing gear is a structure, which supports the aircraft on the ground. Landing gear structure
experiences the load during take-off and landing of the aircraft. These loads are transferred to the airframe
through landing gear beams. Wing box near the root will have cutout at the bottom surface to accommodate
the retraction of the landing gears. Landing loads are absorbed by the landing gears and diffused to the larger
area of the wing through connecting members. In the current project two landing gear beams with a root rib
are considered for the analysis. On either sides of the cutout region landing gear beams are used to transfer
the landing load from landing gears to the wing and fuselage structure. Landing gear beams are in the span
wise direction of the wing. Linear static analysis of the beams along with the root rib will be carried out to
identify the fatigue critical location in the structure. Local analysis will be carried to capture the stress
concentration and stress distribution near the high stress location. It is very rare that these structural members
will fail by static over load. Due fluctuating loads during the service fatigue cracks will get initiated at the
high tensile stress location. Landing gear beams will experience constant amplitude load cycles because of
every landing during service. Fatigue life to crack initiation will be calculated using Miner’s rule based on the
S-N data of the material being used.
Keywords
: Stress analysis, Finite element method, Fatigue, Fatigue life estimation, Crack initiation.
1. Introduction
An aircraft fly using lift generated by the wing as it is pushed by the thrust developed by the jet engine. Earlier
major focus of structural design in the early development of aircraft was on strength. But at present days
structural designers also deal with fatigue life, corrosion resistance, maintenance, producability and structural
integrity. The rigidity of wing is provided by the spar beams and ribs which gives support to the aircraft
structure. Now a day’s aircraft structures are designed using a semi-monocoque structure concept. It consists of
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load carrying frames, longerons and skin which are in turn supported by spars and ribs members. An aircraft is
to be designed in such a way that it should be light in weight and strong enough to withstand loads acting on it.
An aircraft is subjected to various kinds of loads and forces during takeoff, landing and in flight. These loads
cause high stress in the aircraft structure. The main aim of design is to reduce or completely eliminate stress
concentration, detect critical crack region, arrest crack, and avoid failure of the component under service life of
an aircraft.
Stress analysis is used to locate the critical region in the structure where there is a possibility for the
crack to occur. Stress analysis gives the maximum magnitude of stress in the structure. Crack initiate at the
region of maximum stress.
Fatigue is experienced by the material when it is subjected to repeated loading both cyclic and non
cyclic. Fatigue is progressive and localized structural damage that happens when a material is subjected to
cyclic loading. Fatigue cracks are caused generally by tensile stress but sometimes can occur by compressive
stress also. Fatigue life is influenced by various factors such as surface roughness, temperature, residual stress,
microstructure of material used. Fatigue is a cumulative process, it cannot be reversed. Fatigue failure can be
avoided by various method like fail safe approach, damage tolerant design, choosing correct material etc.
1.1 SOFTWARE DISCRIPTION
Software used in this work is MSC Patran and MSC Nastran.
MSC Patran: It is graphical software pre and post processor used for finite element analysis. It is widely used
in aeronautical industry. It easy to use and gives efficient result. Here three dimensional models can be
converted into two dimensional models. The solid model can be meshed using various elements like tria, quad,
hex etc. material properties and boundary condition can be assigned to the finite element model.
MSC Nastran: It is developed by NASA and later acquired by MSC. It is a finite element solver. It does not
have the meshing capability. MSC Nastran is commonly utilized for performing structural analysis. It is widely
used in aerospace and automobile industries. We can perform various analyses such as dynamic, rotor
dynamic, non linear thermal, impact and fatigue analysis using these software.
1.2 MODEL, MATERIAL PROPERTIES, LOAD CALCULATION AND BOUNDARY
CONDITION:
Fig -1: Model Landing Gear Well Beams
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The material taken for the landing gear wells beams is assumed to be made of Aluminium Alloy AA 2024
T351 and material properties of the Aluminium Alloy AA 2024 T351 are taken as
Young's Modulus 7000 MPa
Poisson's Ratio 0.3
Yield Strength 324. MPa
Ultimate Tensile Strength 427. MPa
Load Factor 1.5 G
Load calculation:
Type of aircraft: 13 seater aircraft
Total weight of aircraft: W= 6.1 ton = 6100 kg
Fig 2: Typical Position Of Landing Gear In Aircraft.
Base =B= 6.465 m
F
m
=
H
cg
=1.88 m
F
mdy
=
aT = vertical sink rate.
Hcg = Height from ground to center of gravity.
F
mdy
= 2660.79 kg
Total load on main landing gear during normal touch down:
F = 2660.79 + 6100 = 8760.79 kg
Force per landing gear : F = 8760.79/2 = 4380.4 kg
Force acting on pin diameter: =46.4775
Force acting on each side of pin: = 23.23
The flange region of rib is constrained with six degree of freedom.
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1.3 FINITE ELEMENT ANALYSIS
The Finite Element Method (FEM) is a numerical technique for finding approximate solutions to boundary
value problems for differential equations. Finite element method uses variational methods (the calculus of
variations) to minimize an error function and produce a stable solution. The main idea that connecting many
tiny straight lines can approximate a larger circle, in the same way FEM encompasses all the methods for
connecting many simple element equations over many small sub domains, named finite elements, to
approximate a more complex equation over a larger domain.
The elements used for meshing of landing gear well beam are QUAD 4 and TRIA. But most of the elements
are QUAD 4 type and only few are TRIA elements. Using more QUAD elements will more accurate result.
Fig 3: Finite Element Model Of LG Well Beams.
2. STRESS ANALYSIS:
After applying the load and boundary condition and running the analysis stress in the model is found.
Maximum stress is found at the region near the rivet location at the beam and rib part neat the fixed end. The
maximum value of stress is found to be 94.2 kg/mm
2
near the rivet location. Since the rivet is not simulated,
the stress value is taken little away from the rivet to get average value of stress which is found to be 22.725
kg/mm
2
.
Fig 5: Meshed Model
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Fig4: Maximum Stress In The Model.
Fig 5: Two Dimentional Model and Analysis Model
From global stress analysis we find the maximum stress location. Mostly crack initiates at the region
of maximum stress location, since tensile stress is high at that region. In this model maximum stress is found
to be at the rivet location. We need to know the stress around the rivet location. For that we need to know
the stress at elements around the maximum stress location. We use marker option for knowing the stress of
individual element and take average stress, since stress is distributed unevenly in the model.
2.2: THEORETICAL VERIFICATION:
For local model analysis, a plate with hole is taken of length = 50mm, width = 25mm and thickness = 8mm.
Nominal stress acting on global model is 14.9+14.5+29.3+32.2 = 22.725kg/mm
2
Load acting on the local model:
Stress average = Load / Area
Load = Stress avg*Area
= 22.725*25*5
= 2840.625 kg
One side of plate with hole is fixed and other end load applied is 2840.6/25= 113.625 kg/mm2
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Fig 7: Mesh and boundary condition applied to local model
.
Fig 8: Local Analysis
The magnitude of maximum stress in local model is 54 N/mm
2
. now we have to compare the stress result with
theoretical value for validation of analysis result.
Fig 9: No Of Cycles To Failure.
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The fig 9 gives the stress concentration for plate with hole. Here y axis represents stress concentration and x
axis represents d/w ratio. Where d is diameter of hole and w is width of the plate. Ratio is calculated and is
checked in the graph and stress concentration is found out.
From the S-N curve of plate with a hole of d/w ratio 0.2.
d/w = 5/25 = 0.2.
Kt = 2.5
Kt= max stress/nominal stress
Max stress = Kt* nominal stress
= 22.725*2.5
Max stress = 56.8 kg/mm2.
3. FATIGUE LIFE ESTIMATION
Normally aircraft landing gear beams experiences variable spectrum loading during takeoff and landing. A
typical transport aircraft is considered for flight load spectrum is for the fatigue analysis of the landing gear
well beams structure. Calculation of fatigue life estimation is carried out by using Miner`s Rule. Damage
calculation is carried out for the full service life of the aircraft. The load factor “g” is defined as the ratio of the
lift of an aircraft to its weight. This gives a measure of the load which aircraft experiences. As we know the
maximum stress value obtained from the analysis is corresponding to 1.5 g condition.
Therefore the stress value corresponding to 1.5 g condition is obtained as 53.7 N/mm
2
. Correction factors
for fatigue life calculations of landing gear well beams structure are
• Surface Correction Factor = 1
• Loading Type = 1
• Design Reliability = 0.897
• Surface Roughness = 0.8
Load spectrum for fatigue life estimation:
Table 1: Variable Load Spectrum for typical aircraft
Sl no
G range
Cycles
1
0.5g to 0.75g
57000
2
0.75g to 1g
28000
3
1g to 1.25g
24000
4
1.25g to 1.5g
18000
5
0 to 1.5 g
50
6
-0.5 g to 1.5g
100
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Fig 10: Graph for No of Cycles To Failure
Table 2: Range \, stress ratio and cycles
Sl no
Range
Stress
ratio(R)
Stress
amp(ksi)
Cycles
1
0.5g to
0.75g
0.6682
5.27
infinite
2
0.75g to
1g
0.75
5.36
Infinite
3
1g to
1.25g
0.8
5.27
Infinite
4
1.25g to
1.5 g
0.83
5.27
infinite
5
0 to 1.5 g
0
31.80
2.5*10
4
6
-0.5g to
1.5g
-0.33
42.43
13750
Range: 0 to 1.5g
Ni/Nf = 50/25000 = 0.002
Range: -0.5g to 1.5 g
Ni/Nf = 100/13750 = 0.007
Total damage accumulated is 0.002+0.007 = 0.009
Total damage accumulated is 0.009 which is less than 1. Hence the structure is safe i.e. structure does not fail
due to fatigue with in service life.
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4. CONCLUSIONS
Stress analysis of the Landing gear well beams is carried out and maximum stress is identified near rivet
location at fixed end which is found out to be lower than yield strength of the material. Normally the fatigue
crack initiates in a structure where there is maximum tensile stress is located. The fatigue calculation is carried
out for the prediction of the structural life of landing gear well beams. Since the damage accumulated is less
than the critical damage in the well beams structure is safe from fatigue considerations. Life of the particular
region in landing gear well beams structure is predicted to become critical and found out to be 111110 flying
hours or 111.11 blocks, hence advised to conduct the maintenance without fail during this period. Fatigue
crack growth analysis can be carried out in the other parts of the landing gear well beams structure. In the
future work damage tolerance evaluation and structural testing of the landing gear well beams structure can be
carried out for the complete validation of all theoretical calculations. As well as beam structure optimization
can also be carried out to meet the appropriate factor of safety of landing gear beam section
References
1) Adarsh Adeppa, Patil M S and Girish K E (2012), “Stress Analysis and Fatigue Life Prediction for Splice
Joint in an Aircraft Fuselage through an FEM Approach”, International Journal of Engineering and Innovative
Technology (IJEIT), Vol. 1, No. 4, pp. 142-144.
2) Maksimović,S., Boljanović,S. and Maksimović,K.: Improved Numerical Procedure in Fatigue Life
Prediction of Structural Components Under Variable Amplitude Loads, IFC-8-Fatigue 2002, Stocholm, 2–
7.June 2002, Vol.1, pp.675–682.
3) S Sarath, Jason Cherian Issac and K E Girish (2013) “Analysis of the Wingbox with Spliced Skin and
Estimation of the Fatigue Life for the Wingbox” International Journal of Mechanical Engineering and Robotics
Research Vol. 2, No. 2, April 2013 (155-163).
[4] Jaap Schijve (2009), “Fatigue Damage in Aircraft Structures Not Wanted but Tolerated”,
International Journal of Fatigue, Vol. 31, No. 6, pp. 998-1011.
[5] F.H.Darwish, G.M.Atmeh, Z. F. Hasan Design (2012) “Analysis and Modelling of a General Aviation
Aircraft” Volume 6, Number 2, ISSN 1995-6665 Pages 183 – 191.
[6] Michael Bauccio (1993), ASM Metals Reference Book, 3rdEdition, ASM International, Materials Park,
OH.
A Brief Author Biography
Karthik Goud R V – is a PG scholar in machine design at The Oxford college of Engineering, Bangalore.
Trupti P Wani – is Asst.Prof in mechanical department at The Oxford college of Engineering, Bangalore.