Report 5 Landing Gear
Content
Hogeschool van Amsterdam, Technology, Aviation
The 747’s body gear
Project Report
Projectgroup 2A2R
Ivar van Cuyk Jos Frijmann Wytze Hilgers Anouk Lelij Kevin van der Plas Roy van Schagen Roy Wassink Peter van Woudenberg
Projectleader
Sander van der Pijl
Amsterdam, October 2010
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Table of contents
TABLE OF CONTENTS .................................................................................................................... 2 SUMMARY ................................................................................................................................... 4 INTRODUCTION ............................................................................................................................ 5 1 LANDING GEAR ANALYSIS ....................................................................................................... 6 1.1 LANDING GEAR PRINCIPLES ......................................................................................................... 6 1.1.1 FUNCTION LANDING GEAR ................................................................................................................. 6 1.1.2 TYPES ............................................................................................................................................ 6 1.1.3 MAIN LANDING GEAR BOEING 747 .................................................................................................... 8 1.1.4 NOSE GEAR ................................................................................................................................... 10 1.2 BODY GEAR SYSTEMS .............................................................................................................. 12 1.2.1 HYDRAULIC SYSTEM ....................................................................................................................... 13 1.2.2 EXTENSION AND RETRACTION SYSTEM ............................................................................................... 13 1.2.3 ALTERNATE EXTENSION AND SYSTEM ................................................................................................. 15 1.2.4 SHOCK STRUT ................................................................................................................................ 15 1.2.5 BODY GEAR STEERING SYSTEM .......................................................................................................... 16 1.2.6 AIR/GROUND SYSTEM ..................................................................................................................... 17 1.2.7 HYDRAULIC BRAKE SYSTEM .............................................................................................................. 17 1.2.8 BRAKE CONTROL SYSTEM ................................................................................................................. 18 1.3 REGULATIONS ....................................................................................................................... 19 1.3.1 GENERAL REGULATIONS ABOUT THE DESIGN ....................................................................................... 19 1.3.2 DIFFERENT CONDITIONS .................................................................................................................. 20 1.3.3 NOSE WHEEL AND STEERING SYSTEM ................................................................................................. 21 2 DETAILED BODY GEAR DESCRIPTION...................................................................................... 22 2.1 MATERIALS........................................................................................................................... 22 2.1.1 MATERIAL PROPERTIES.................................................................................................................... 22 2.1.2 AVIATION MATERIALS ..................................................................................................................... 23 2.1.3 CHOICE OF THE MANUFACTURER ...................................................................................................... 24 2.2 DIMENSIONS ......................................................................................................................... 24 2.3 CALCULATIONS ...................................................................................................................... 28 2.3.1 CALCULATIONS MAXIMUM SHOCK STRUT ABSORPTION ......................................................................... 28 2.3.2 CALCULATIONS CROSSWIND LANDING ................................................................................................ 31 2.3.3 CALCULATIONS BODY-GEAR MADE WITH MATH-LAB DURING CROSSWIND ............................................... 31 2.3.4 HANDMADE BODY-GEAR CALCULATIONS DURING CROSSWIND ............................................................... 31 2.3.5 INCIDENT CALCULATIONS ................................................................................................................. 32 3 ACCIDENT AND CONCLUSION ................................................................................................ 34 3.1 SYNOPSIS ............................................................................................................................. 34 3.2 MAINTENANCE CONSEQUENCES ................................................................................................. 35 3.2.1 MAINTENANCE CHECKS ................................................................................................................... 35 3.2.2 MAINTENANCE CHANGE .................................................................................................................. 35 3.3 FINANCIAL CONSEQUENCES ....................................................................................................... 36 3.3.1 ADDITIONAL AIRCRAFT COSTS ........................................................................................................... 36 3.3.2 EXTERNAL ADDITIONAL COSTS .......................................................................................................... 36 3.4 THE FINAL CONCLUSION........................................................................................................... 37 Amsterdam Leeuwenburg Airlines Pagina 2
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BIBLIOGRAPHY ........................................................................................................................... 38 APPENDICES ............................................................................................................................... 40
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Summary
The second year Aviation students received an assignment to make an analysis of the landing gear of a modern aircraft. The engineering department of Amsterdam Leeuwenburg Airlines [ALA] wanted the project group to discover any interference in the landing gear of the chosen aircraft. This to make an extension of the fleet possible. The project group has chosen the Boeing 747, this because the landing gear of this aircraft is more complicated. The project group also found a proper incident of the Boeing 747 that could be investigated. First, the project group has made an analysis of the various landing gears. The various landing gears have been described each with its own advantages and disadvantages. The landing gear of the Boeing 747 had been described more precisely after it became clear what kind of landing gear is used on the Boeing 747. The landing gear of the Boeing 747 is called a multi bogey gear. This landing gear consists of a main landing gear and a nose landing gear. The main landing gear of the Boeing 747 contains the body gears and the wing gears, this because the Boeing 747 is an aircraft with a great mass. The body gear consist of two bogeys and is places under the fuselage, the wing gear contains also two bogeys and is placed under the wings of the aircraft. The body gear and the wing gear have, related to each other, a different construction, although almost all components are used in both systems. The nose gear contains one bogey and is placed under the fuselage near the cockpit. There are many laws and requirements, which have to be taken into account when developing a landing gear. The landing gear must be able to deal with great forces that develop in extreme situations. These forces are described and have been taken into account when making calculations of the forces that are acting on the landing gear. The dimensions of the landing gear are needed to make a proper calculation of these forces. The dimensions of the main gear have been described, because during the incident the problem occurred in the main gear of the landing gear. The landing gear must be able to deal with forces acting on it. Therefore, it is necessary to know the properties of the materials used in the landing gear. So the properties of materials that are normally used in aviation are described. There is also described how the properties of the materials can be improved. The calculation is made, after all dimensions and the properties of the used materials are clear. The cause of the problem is made clear by making different calculations of the forces acting on the landing gear. When the cause is made clear the effects of the incident can also be made clear. The financial implications have been examined. Finally a conclusion is made.
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Introduction
The board of ALA is about to buy new aircrafts. The model they are looking for is the Boeing 747. However, an internal discussion about the aircraft is started, due to a recent incident with the landing gear of a Boeing 747. During the retraction of the landing gear after take-off, a gear did not fold-in properly. Wheels hit the aircraft fuselage and got stuck. During the touchdown, the shock absorber of this gear failed. This incident did not cause any human fatalities, but the board of ALA is worried about the possible consequences that this incident may cause. Therefore, the board wants a detailed analysis of the landing gear. The project group examined the landing gear of the Boeing 747. Based on the results of this examination, the board is able to decide whether or not to buy a Boeing 747. The assignment for the investigation is given to project group 2A2R. The members of this group follow the bachelor phase of Aviation Studies. This study is given at the “Hogeschool van Amsterdam”. All members are in their second year, which is in school year 2010-2011. The report is written according to the rules in the dictation of Wentzel. The report will be handed over to the board of ALA on the 14th of October 2010. This report is divided into three chapters: Before the constructions of a landing gear can be understood, the principles of a landing gear are needed to know. With a basic knowledge of a landing gear, the Boeing 747‟s gear can be described. There are rules before a landing gear may be used. A landing gear must gratify to all the regulations in Certification Specification 25. (1) The mechanical analysis includes calculations of forces during different flight phases. The ability to cope with high forces depends on the construction material. It has to be strong, yet elastic and as light as possible. The positions and dimensions of the gears determine the stability and weight distribution of the aircraft. (2) The incident will have an effect to the airworthiness of the Boeing 747. The faulty part may have to be replaced or examined. The maintenance schedule will be adjusted to prevent this incident from happening again. This adjustment will increase the aircraft on ground time, which reduces the profit the aircraft can generate. (3) The main sources of this project are the Boeing 747 Maintenance Manual and the report of the incident of flight JA01KZ. The complete list can be found on page 38.
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1
Landing gear analysis
The construction that the aircraft uses to make contact with the surface is called the landing gear. A landing gear is necessary to make the aircraft manoeuvrable on the surface without damaging the aircraft. To understand a landing gear and its configurations, it is necessary to know the principles of a landing gear (1.1). Because of the problem with the Boeing 747 was a problem with its left body gear, knowledge about the Boeing 747‟s body gear is needed to understand the problem (Error! Reference source not found.). A landing gear may not be used without a certification. The landing gear must gratify to all rules in CS-25 (1.3). Main source of this chapter is chapter 32, Landing Gear, of the Boeing 747‟s manual.
1.1
Landing gear principles
In order to make it possible for an aircraft to manoeuvre when it is not in the air, an aircraft is equipped with a landing gear. A landing gear has multiple functions (1.1.1). The landing gear is performed in several conditions (1.1.2). Because of the landing gear of a Boeing 747 is a multi bogey gear, the multi bogey gear is explained further. The multi bogey gear is divided in the main landing gear (1.1.3) and the nose landing gear (1.1.4).
1.1.1
Function landing gear
The function of a landing gear is to carry the aircraft when it is not in the air. The landing gear makes it possible to make manoeuvres in horizontal directions and to rotate in vertical directions. Another function of a landing gear is to abate the energy that arises during a landing. In this way, a landing is more comfortable, by using a shock absorber. A shock absorber reduces the loads on the other parts of the aircraft When an aircraft is landed, it has to decrease its speed. The only contact with the runway is by the tyres. Therefore, the landing gear is equipped with brakes. The last function of the landing gear system is the aero-dynamical function. When the aircraft is in flight, the landing gear is retracted to create a more aero-dynamical shape of the aircraft. The aircraft has lower drag, which is positive for the fuel consumption.
1.1.2
Types
There are many types of landing gear, each with its own advantages and disadvantages. Mostly wheels are used to make aircraft manoeuvrable on the surface, but skis and floats are also used. The different types of landing gear using wheels to manoeuvre on the surface will be explained (1.1.2.a). Because this type of landing gear is often used in the commercial aviation, instead of the ski‟s and floats. After takeoff, the landing gear is often stored to improve the aerodynamic properties of aircraft. Aircraft designers have devised various ways to store the landing gear as efficient as possible (1.1.2.b).
1.1.2.a
Types of landing gear
Aircraft designers have always been searching for better landing constructions, so there are many types of landing gear. The most used landing gears are: 1. 2. 3. 4. 5. Conventional landing gear Tricycle landing gear Single main wheel Bicycle gear Quadricycle Pagina 6
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The conventional landing system was often used between 1910 and 1950. The conventional landing gear consists of a main landing gear and a tail landing gear, the main landing gear contains two wheels and the tail landing gear one wheel (Appendix I). The tail wheel does not absorb shocks, so the tail wheel can be kept small. The benefits of a small tail wheel are of course less weight and less air resistance. A small tail wheel does also have a couple of disadvantages. Aircraft with a conventional landing gear have an angle with the surface, because the main landing gear wheels are bigger than the tail landing gear wheel. This ensures the pilot has a bad sight when the aircraft is standing on the runway or when the pilot is taxiing on the taxiway. Another disadvantage is ground loop. Ground loop is an effect that occurs when aircraft with a conventional landing gear makes a turn on the runway or taxiway. A destabilizing moment can occur when making a turn (Appendix II). ad 2 Tricycle landing gear
Since 1950 the tricycle landing gear is used often. The tricycle landing gear contains a main landing gear, which had two wheels or bogies and a nose landing gear, which has one wheel or bogey (Appendix I). This construction has many advantages over the conventional landing gear. The pilot has a better view on the runway or taxiway and ground loop cannot occur, because the nose wheel now produces a stabilizing moment (Appendix II). ad 3 Single main wheel
This type contains one main wheel and one small tale wheel (Appendix I). It is a light system because the system is made simple. Because the single main wheel landing gear consists of two wheels the manoeuvrability is not very well. This type of landing gear is often used in aircraft with a small mass. ad 4 Bicycle gear
The bicycle gear has two main landing gear constructions. These are located in the longitudinal (Appendix I). Aircraft with the bicycle gear are not stable because the wheels are placed next to each other, although it was a good construction for aircraft with a narrow fuselage. Mostly auxiliary wheels are used to prevent the wing strikes the surface. ad 5 Quadricycle
This construction consists of four main landing gears (Appendix I). The main landing gear contains wheels, which are located under the fuselage. This is ideal for cargo aircraft because the fuselage is located near the surface, so loading and unloading can be done quickly. The stability of the aircraft is not very well. ad 6 Multi-bogey gear
The multi bogey gear contains a main landing gear and a nose landing gear (Appendix I). The main landing gear consists of two rows of wheels and the nose landing gear mostly of two bogies. The multi-bogey gear is used by aircraft with a large mass.
1.1.2.b
Storage of the landing gear
Mostly the landing gear is stored to improve the aerodynamic characteristics of aircraft. There are several ways to store the landing gear (Appendix III). The landing gear of small aircraft is often stored in the wings or fuselage, or a combination of these places. Big aircraft often use a space, which is called the fuselage-podded. This is a part of the aircraft that strengthened the transition area of the wing and the fuselage. In the fuselage-podded is enough space for storing the landing gear. In some cases, space for the landing gear is
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created under the wings. This is called wing-podded. The landing gear of rotor aircraft is often stored under the engines.
1.1.3
Main Landing Gear Boeing 747
The main landing gear is the principle gear of an aircraft. Which type of a main landing gear is used, depends on the size of the aircraft. The Boeing 747 is a large, heavy aircraft. Therefore is used a complex landing gear, which is composed of a several main gear units (1.1.3.a). The landing gear operates through by a retractable system (1.1.3.b).
1.1.3.a
Construction
The Boeing 747 is equipped with four main gear units, consisting of two body gears, which are attached to the fuselage, and two wing gears, which are placed aft of the rear wing inboard of the engine nacelles. Each of these is featured with four-wheel bogies (Figure 1. ) (Appendix IV).
1. 2. Wing Gear Body Gear
1 2 Figure 1. Boeing 747‟s Main Landing Gear
Through a trunnion and trunnion fork, supported at the forward end by the wing rear spar and at the aft end by the landing gear support beam, is each wing gear attached to the structure. Each body gear is attached to the structure through a trunnion cantilevered from backing on the aft bulkhead of the body gear wheel well. The doors of the landing gear consist of wing gear doors and body gear doors. Both have each wheel well doors and shock strut doors. Wheel well doors operate hydraulically and can be closed when the gear is extended or retracted. These doors are hinged together. The doors of the shock strut are also hinged together. They operate mechanically and are attached by linkage rods. These doors only move when the gear is moved. All doors are of frame construction, with on the inner and outer sides skin panelling. The doors close over all gear openings, and accord with the contour of the fuselage. This provides an aerodynamic smoothness. Several components are used to optimize the using of the landing gear. A shock absorber, or shock strut, is an item, which is used to all current landing gears. The basic function of this component is to absorb the kinetic energy during the landing and taxiing so the accelerations imposed upon the frame will be reduced to an acceptable level. The brakes, in combination with a skid control system, are used to reduce the speed and to stop the aircraft. Brakes can also used to hold an aircraft stationary while it‟s parked, or when the engines are running up, but also to steer the aircraft by differential action or to control speed while the aircraft is taxiing. The skid controls are used to minimize the stopping distance and to reduce the excessive tyre wear and burst tyres by unduly skidding. The available degree of friction coefficient is constantly sensing by the systems, and by controlling brake pressure to supply an almost constant brake force nearly to the skidding point. The anti-skid system is used to prevent a wheel for slipping during braking. This is a lot safer because in a large aircraft, the pilot does not notice the wheels are slipping.
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The „landing gear position indication system‟ shows the position of the landing gear and the doors. The information is delivered to the crew through the display units in the cockpit (EICAS).
1.1.3.b
Operation
The retraction and extension of the landing gear and their doors operates by a hydraulic system. When hydraulic power is available, an electrically powered alternate extension system unlock the gear and doors. This movement is controlled by one action on the panel in the cockpit. When the handle is placed in DN position, the doors open, gear unlocks, gear extends, and then the doors close. UP position is conversely: the gear doors open, the gear retracts and locks, and the doors close. Gear and door operation are controlled by sequence valves. There is one actuator for the extension (Figure 2. ) (1), and two actuators for the retraction of the landing gear (2). Retraction happens during upwind, so there is more strength required to retract.
1. 2 2. Actuators for retraction of the L/G Actuator for extraction of the L/G
1
Figure 2.
Actuators for retraction and extraction
The inner wheels of the Boeing 747 can rotate and are used during towing and taxiing of the aircraft (Figure 3. ). This movement is contrary to the motion of the nose-wheel. For rotating the wheels, two actuators are used (1). The brakes are operated using the hydraulic pipes (2). The possibility of steerable body gear trucks reduce tyre scrubbing, which occurs when an aircraft makes a sharp turn.
1. 2. Actuators for rotating the inner wheels Hydraulic pipes, brakes
2
1
Figure 3.
Actuators on the wheels and hydraulic pipes
Five air-oil shock struts absorb the landing impact. These works in the first place as air springs. The variances in runway and the vibrations of rolling are absorbed by the hydraulic forces within the shock strut.
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A Boeing 747 has eighteen wheels, from which two on the nose gear, eight on the body gear and eight on the wing gear (Appendix IV). Any single wheel of the body gear and wing gear is provided with a brake unit. This is installed on the side nearest the shock strut. The brakes on a Boeing 747 are multidisc brakes, fitted with a combination of automatic adjusters and return springs. These adjusters compensate for the wastage of the brakes. When an aircraft brakes, the anti-skid system automatically operates. The wheel skid is compensated by this system, by control of brake pressure. This happens through the anti-skid valves. A „brake temperature monitoring system‟ displays the brake temperatures and make the cabin crew alert of overheated brakes. The position of the landing gear is showed by proximity switch sensors, which are located on any single landing gear and doors. The sensor signals provide the data of the position to the EICAS display units.
1.1.4
Nose gear
The construction of the nose gear differs from that of the main gear (1.1.4.a). The nose gear is used to support the forward end of the fuselage. The nose gear is also used for controlling the direction of the aircraft while it is moving on the ground (1.1.4.b). The nose gear suffers from vibrations (shimmy) more than the main gear does (1.1.4.c).
1.1.4.a
Construction
Starting from the ground, the nose gear of a Boeing 747 (Figure 4. ) (Appendix IV) has two tyres and wheels (1) that are attached on one axle (2). This axle is connected to the lower end of the shock strut inner cylinder (3). The shock strut is used to absorb the shocks from the landing impacts and rolling over bumps on the ground. Also connected to the shock strut inner cylinder, is the lower end of the lower torsion link (4). The upper end of the upper torsion link (5) is connected to the forward steering collar (6). Aft steering collar (7) attach lugs slip over the forward steering collar attach lugs. Both collars are locked together around the shock strut outer cylinder (8) by actuator attach pins (9). These pins also hold the rod end of the steering actuators (10). The steering actuators, steering collars and torsion links are all parts used in the steering mechanism. At the upper end of the shock strut outer cylinder there is a trunnion (11). When the nose gear extends or retracts it pivots on this trunnion. The trunnion itself rotates in bearings. The trunnion is supported by two side braces (12). The braces extend from the attach lugs at the centre of the shock strut outer cylinder. Besides the side braces, there is also a lower tripod brace (13) connected to the centre of the shock strut outer cylinder. The lower tripod brace is connected to the upper tripod brace (14) that extends forward from the centre of the trunnion. Also connected to the trunnion is the nose gear actuator (15). The nose gear actuator activates the nose gear extension or retraction movement. Between the end of the nose gear actuator and the hinge of both tripod braces there is a drag strut (16). Together with the nose gear lock actuator (17), it holds the nose gear in the up and locked, or down and locked position.
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17 15
16
11 14
12 13
A S t a rt in g fr o m
1. 2. 3. 4. 5. 6. 8 7 9 7. 8. 9. 10. 11. 12. 13.
10 6
t 14. h e 15. g 5 16. r 17. See A o 4 S u 1 t n a d 3 rt , 2 in t g h Figure 4. Nose gear fr e o 1.1.4.b Steering operation n m o Both pilots have their own steering tiller that they can use for normal steering operation. One s tiller is on the left of the captain and the is on the right of the first officer. A tiller t other e movement of 90 degrees results in a steering movement of 45 degrees. Tiller movement in h la either direction is transmitted to a steering metering valve by cables (Figure 5. (1). This e n valve directs fluid (oil) with a pressure of 3000 PSI (hydraulic system No. 1) to the nose g di wheel steering actuators (2). When the steering actuators are activated, they transfer their r n power to the attach pins (3). These pins a turning moment to both collars. The o transmit g forward collar (4) transfers the power u to the upper torsion link. The upper torsion link g transfers the power to the lower torsion link. link turns the shock strut inner cylinder to n This e the left or right. This action turns the axle and the axle turns the wheels. The tillers can turn d a the nose wheels around 70 degrees maximum. , r t o h f e a n n o B s o e ei la n n g di 7 n 4 g 7 g h e a a s r t Amsterdam Leeuwenburg Airlines Pagina 11 o w f o a ty n r
Tyre and wheel Axle Shock strut inner cylinder Lower torsion link Upper torsion link Forward steering collar Aft steering collar Shock strut outer cylinder Attach pin Steering actuator Trunnion Side braces Lower tripod brace Upper tripod brace Nose gear actuator Drag strut Nose gear lock actuator
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1. 2. 3. 4.
3
Metering valve assembly Steering actuator Attach pin Forward steering collar
1 4
3
2 Figure 5. Steering operation
Besides the normal steering there is another way to steer the wheels. This is done with the help of the rudder pedals. The nose wheel steering system is connected to the rudder pedals through mechanical linkage and cables. When the nose gear is compressed by the weight of the aircraft, rudder pedal steering is available. The rudder pedals can turn the nose wheels around 10 degrees maximum. When the aircraft is towed, the wheels can turn around 65 degrees maximum without disconnecting the nose gear torsion links.
1.1.4.c
Shimmy
Because of the flexibility of tyre side walls (Appendix V), vibrations known as shimmy are induced into the nose gear. Especially at high speeds, excessive shimmy can cause vibrations throughout the whole aircraft, which is dangerous. Wear of the nose wheel bearings, worn torsion links and uneven tyre pressures all increase the tendency to shimmy. In general these ways are used to reduce shimmy: Provision of a hydraulic lock across the steering jack piston; Fitting a hydraulic damper; Fitting heavy self-centring springs; Double nose wheels; Twin contact wheels. The above mentioned steering metering valve consists of a spring compensator. This spring compensator maintains a pressure of 205 to 325 PSI against the steering actuator pistons to act as a shimmy damper.
1.2
Body Gear Systems
In this paragraph the systems of the Boeing 747‟s body gear is being discussed. The body gear is being discussed because the left body gear of the Boeing 747 was the landing gear that malfunctioned during take-off and causing the Boeing 747 to make an emergency landing at Schiphol Airport. Multiple systems used in the Boeing 747 are using the hydraulic system to support (1.2.1). The extension and retraction system (1.2.2) is one of those systems, because a failure in the hydraulics may not cause the Boeing to be disable to retract the landing gear, there is also a alternate extension and retraction system (1.2.3). When the Boeing 747 touches down with a malfunctioned body gear, the shock struts (0) of the three remaining gears now has to absorb the impact. The body gear of the Boeing 747 is Amsterdam Leeuwenburg Airlines Pagina 12
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also equipped with an Air/Ground system (Error! Reference source not found.), a Body gear steering system (Error! Reference source not found.), a hydraulic braking system (Error! Reference source not found.) and a brake control system (Error! Reference source not found.).
1.2.1
Hydraulic System
The Boeing 747 has a hydraulic system to provide multiple systems in the Boeing 747 to work properly. The hydraulic system is applied in the entire aircraft. In this paragraph only the hydraulics in the body gear (1.2.1.a) and the hydraulic actuator (1.2.1.b) will be discussed.
1.2.1.a
The hydraulic system in the body gear
The hydraulic system of the Boeing 747 is applied to decrease the work pressure of the pilots. It uses a fluid to transport pressure applied by an engine driven pump. The hydraulic system is based on hydrostatic laws, such as Pascal‟s law Sectie 1.01(formula 1). Pascal‟s law tells that the force the pilot applies into the hydraulic system can be increased by decreasing the surface of the applied force. This makes the pilots use a small amount of strength to do heavy tasks, such as, retracting the landing gears. The Boeing 747 has four independent hydraulic systems, so if one fails another can take over. The landing gear relies on the hydraulic systems No.1 and No.4
Pascal‟s law: F = Force A = Surface (formula 1) Units: F in Newton [N] 2 A in square meters [m ]
The hydraulic systems No.1 and No.4 are available for multiple systems applied in the body gear of the Boeing 747. The extension and retraction system, the body gear steering system and the hydraulic brake system use the hydraulic system to increase the force applied by the pilot.
1.2.1.b
Hydraulic actuator
The hydraulic system uses hydraulic actuators (Figure 6. ) to turn the hydraulic pressure into a movement. Actuators are cylinders (1) with two chambers. If the hydraulic pressure increases in one of the chambers the hydraulic the piston will move creating a larger chamber for the high pressure. The piston (2) will move the piston rod (3) which will perform the action that is required. If the hydraulic pressure is increased in the red chamber and the piston rod will move in the direction of the red arrow, if the pressure is increased in the blue chamber, the piston rod will move in to the direction of the blue arrow
1. 2. 3. Cylinder Piston Piston rod
Figure 6.
Hydraulic actuator
1.2.2
Extension and retraction system
The landing gears on Boeing 747 are designed to retract during flight to decrease drag and to increase the aerodynamic stability of the aircraft. This makes the plane use less fuel and a increase manoeuvrability. The body gear will be raised and lowered simultaneous with the Amsterdam Leeuwenburg Airlines Pagina 13
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wing gear and the nose gear by a lever in the cockpit. To raise and lower the landing gear the extension and retraction uses a gear actuator (1.2.2.a) to retract and lower the body gear. The sequence valves make sure all components will retract in correct order (1.2.2.b). The landing gear will be locked into place when raised (1.2.2.c) and when extended (1.2.2.d).
1.2.2.a
Gear actuator
To retract the body gear during flight and extend the body gear for landing the Boeing 747 uses hydraulic powered actuator. The gear actuator will be attached to the aircraft structure and the shock strut of the landing gear (Figure 7. ). Figure 7. When the actuator is retracting (1) the body gear will retract (3). The actuator will turn the shock strut around the trunnion (2) and covers the body gear in the wheel well (Figure 8. ).
1. 2. 3. Gear actuator Trunnion Shock strut
Figure 7.
Retracting body gear
Figure 8.
Retracted body gear
1.2.2.b
Sequence valves
The wheel well doors are linked to the body gear with sequence valves, these valves make sure the wheel well doors are opened before the body gear will be lowered and closed after the body gear is locked into place when retracted. The sequence valves steer the hydraulic fluid from the hydraulic system to the doors actuator, the up lock actuator, the down lock actuator and the body gear actuator. By retracting the landing gear using the landing gear lever, the hydraulic fluid will enter the door sequence valves and goes through a valve to the door actuator. The pressure builds up and the wheel well door will open. When the doors are opened the hydraulic pressure in the sequence valve is also increased and now opens another valve and allows the hydraulic fluid to flow to the lock mechanism, when the body gear is unlocked the hydraulic fluid will now raise the body gear and finally the hydraulic fluid will lock the gear in the up position.
1.2.2.c
Up lock mechanism
To make sure the body gear stays retracted the landing gear will be locked into place, which is done by an up lock mechanism. The body gear of the Boeing 747 is locked by locking a hook around the up lock roller that is attached to the shock strut. The hook will be kept in the locking position by a spring and can be unlocked by a hydraulic actuator or electric actuator to release the body gear or to receive the up lock roller in the hook.
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1.2.2.d
Down lock mechanism
Next to an up lock mechanism there is also a down lock mechanism, to make sure the body gear stays in to place when extended and not retract when touching down at a high impact. The down lock mechanism, that has to lock the body gear into place mechanical, makes sure the Boeing 747 is able to land on its body gear when multiple systems are malfunctioned. The down lock mechanism is an over centre knee joint on the jury strut that is connecting the drag strut with the aircrafts structure (Figure 9. The jury strut will over centre the joint allowing it to take forces in direction of the jury strut, because the jury can only move to the mechanical limit of the knee joint and makes sure the jury strut will not fold and allows the body gear to rise. The joint can be unlocked out of the over centre position by the hydraulic actuator.
Figure 9. Over centre knee joint
1.2.3
Alternate extension and system
Because all the landing gears must be able to extend when the hydraulic system malfunctions, the Boeing 747 is equipped with a alternate extension system. The alternate system will simply electrically unlock the up lock mechanism of the body gear and simultaneous releases the wheel well doors. With some manoeuvring of the aircraft and the gravity the body gear will be lowered and lock into place. The alternate landing gear will be operated by a switch in the cockpit.
1.2.4
Shock strut
The shock strut absorbs most of the impact when the aircraft touches down and when taxiing on the runway. The Boeing 747 is 1. Outer cylinder equipped with Oleo-pneumatic shock 2. Nitrogen valve struts (Figure 10. ). This is a shock 3. Upper chamber absorber that uses both oil (5) and (Nitrogen) compressed nitrogen (3) to absorb 4. Orifice support tube impact. The shock strut has an inner 5. Oil and (11) an outer cylinder (1). The 6. Orifice outer cylinder is attached to the aircraft 7. Upper bearing structure by the trunnion. The inner 8. Metering pin 9. Seal cylinder is attached to the bogie of the 10. Lower bearing body gear. The inner cylinder can 11. Inner cylinder move in and out the outer cylinder to absorb impact. The orifice (6) of the shock strut is a small passage. The oil will be pressed through this passage at impact and controls the absorption of the impact. The metering pen (8) and the orifice support tube (4) allow the shock strut to absorb and control the impact even better. The oil is after compression in the upper chamber and will return to lower chamber. To Figure 10. Oleo-pneumatic Shock strut avoid to oil and the nitrogen to leak Amsterdam Leeuwenburg Airlines Pagina 15
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throw the gap between the inner and outer cylinder, the shock strut has a seal (9) attached to the lower bearing (10) to seal that gap and allows the cylinders to move into each other.
1.2.5
Body gear steering system
The Boeing 747 has a body gear steering system. This system helps the pilots to control the aircraft (1.2.5.a). To get a better view of the body gear steering system, a description of the construction is made (0). When it is clear how the body gear steering system is constructed, its operation can be described (1.2.5.c).
1.2.5.a
Function
Because the Boeing 747 is a heavy aircraft, it needs more gear struts to attach the wheels, which have to resist the great weight of the aircraft on the ground. The Boeing 747 has two body gears under its body. During a turn, these body gears will not follow the radius of the turn as the wing gears do (Figure 11. ). As a result of this, great forces will stress on the wheels and on the strut. Furthermore the body gear wheels will wear faster than normal as a result of tyre scrubbing. Much maintenance on the body gear wheels and struts is necessary to keep the body gear in good condition. To avoid this problem, body gear steering is introduced. Body gear steering allows the body gear of the Boeing 747 to rotate thirteen degrees whether right or left. Now body gear steering has been installed, sharper turns can be made without damaging the wheels or the strut.
Figure 11.
Tyre scrubbing and how to avoid tyre scrubbing
1.2.5.b
Construction
To allow body gear steering, the wheel truck has to rotate in respect to the shock strut. To rotate the wheel truck, the inner cylinder of the shock strut is rotatable. Like at normal gears, the body gear has a torsion link that is linked to the wheel truck and the shock strut. However, instead of an upper torsion link, two steering cylinders were added. These cylinders, connected to each other on the lower torsion link, are connected to the shock strut by a yoke. Now, if one of the cylinders extends, the wheel truck can rotate. The pressure for both cylinders is delivered by hydraulic system 1.
1.2.5.c
Operation
When the nose gear turns in one direction, the body gear turns smaller proportional angles in the other direction. There are some requirements for the body gear steering. To prevent the body gear from damaging during a high speed turn, the body gear steering will switch off when a speed of twenty knots is reached. From that point, it will function as torsion link only. There is also a limit at the angle of rotation. The body gear rotates maximum thirteen degrees whether left or right. The angle of thirteen degrees will be reached when the nose gear is rotated seventy degrees. Furthermore, the body gear may not be tilted and has to be extended and locked. Amsterdam Leeuwenburg Airlines Pagina 16
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1.2.6
Air/ground system
Some systems of the aircraft, like the spoilers, operate different in air than on the ground. This makes it important to know if the aircraft is in the air or on the ground. Therefore, sensors that measure the gear tilt are mounted on the landing gear. Those sensors will send their position data to a Proximity Switch Electronics Unit [PSEU]. The PSEU supplies the position and the control data for primary landing gear sensor and alternate landing gear sensor subsystems. The PSEU will convert the position data to control data before it will send the control data to the air/ground relays. Air/ground relays have the task to tell the aircraft systems when the aircraft is in the air (air mode) and when it is on the ground (ground mode). Some systems do not have enough information when they only know if the landing gear is tilted or not. Many more sensors are mounted on the landing gear, like: up- and down lock sensors and wheel door sensors. However, signals from the landing gear lever switch, body gear steering (body gear has to be centred during in most conditions) are also important. Together, all these subsystems create the air/ground system. Problems can appear in the air/ground system. In case the air/ground system does not get a signal from the sensors after takeoff, the air/ground system will stay in ground mode. When the air/ground system stays in ground mode, some systems in the cockpit will not work, like the autopilot. To continue the flight with this problem, the fuses of the air/ground system can be switched off and then the relays will go to air mode. However, the pilots may not forget to put in the fuses after touch down because the spoilers and brake system will not work properly.
1.2.7
Hydraulic brake system
The hydraulic brake system helps the pilots controlling the aircraft on the ground and in more situations (1.2.7.a). To get a better view of the hydraulic brake system, a description of the construction of this system is made (1.2.7.b). When it is clear how this system is constructed, an explanation of how the system works can be given (1.2.7.c).
1.2.7.a
Function
The hydraulic brake system has the task to slow down the aircraft on the runway when it lands. The brake system also holds the aircraft during parking and engine run up. However, also after take-off the wheels have to be slowed down before they are fully retracted. The brake system also helps with making turns on the ground. There are different kinds of brake systems (drum brakes, single disc brakes and multiple disc brakes). The multiple disc brakes are the most used on airliners. Also the Boeing 747 uses multiple disc brakes. The choice of the brake system depends on how much heat the brakes have to resist.
1.2.7.b
Construction
The multiple disc brakes (Figure 12. ) exists out of four rotor discs (1) and three stator discs (2) that rotate besides each other. The discs are made of carbon and contain a material that creates much friction when the discs are pressed together. The rotor discs have rebated joints (3), which allow the rotor discs to sit still in the wheels. The wheels also have rebated joints. The stator discs are connected to the wheel axis, which cannot rotate (4). Now, if the wheels rotate, the rotor discs will rotate together with the wheels while the stator discs will stay still. Next to the inner rotor disc, a piston housing is mounted (5). This housing contains seven cylinders (6) that press the rotor discs and stator discs together. The cylinders are pressurized by hydraulic system 4. When hydraulic system 4 cannot pressurize the cylinders, hydraulic system 1 will take over this task. If also hydraulic system 1 cannot pressurize the cylinders, than hydraulic system 2 will do pressurize them. The pressure that the brakes need differs from 160 PSI to 3000 PSI. The cylinders that are connected to each other in the piston housing are connected to the hydraulic system by just one hydraulic line (7). To avoid too much pressure on the system, a bleeding valve (8) is mounted on the piston housing. When using the brake system, the brake discs will wear. To check how much the discs are Amsterdam Leeuwenburg Airlines Pagina 17
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worn, two wear indicator pins (9) are used. If these pins are not visible anymore, the brake discs should be replaced.
1 8 6 7 3 2 1. 2. 3. 4. 5. 6. 7. 8. 9. Rotor disc (4x) Stator disc (3x) Rebated joints Wheel axis Piston housing Cylinder (7x) Hydraulic line Bleeding valve Wear indicator pin (2x)
5
9 4
Figure 12.
Multiple disc brake
1.2.7.c
Operation
If one of the pilots creates a force on the ends of the rudder pedals, the brake system will activate. The more force presses on the pedals, the more the brake will slow down the aircraft. Slowing down the aircraft happens when the cylinders in the piston housing extend. When the cylinders extend, the discs will be pressed together. The more the discs are pressed together, the more friction will be created. This will slow down the aircraft. When the cylinders retract, the discs will stay together. To avoid this, small leaf springs are mounted between the discs to create a small space between the discs. When activated, the auto brake system will steer the braking system without any input of the pilots.
1.2.8
Brake control system
The brake control system supplies some functions that help the pilots. These functions are: antiskid protection, automatic braking, and brake torque control. This system also supplies arming logic for the body gear steering system. The automatic braking system will operate when the wheel speed increases to sixty knots or more during touchdown. A selector makes it possible to allow five deceleration levels. Also for a rejected take off there is a deceleration rate. The brake torque control has to prevent the brake from too much torque. When the brake torque control measures too much torque at one of the wheels, it will send a signal to the antiskid system. The antiskid system prevents the aircraft from skid. This is done by sensors that are mounted in each wheel. Those sensors measure the wheel rotation speed. The most effective way of braking is with a wheel speed that is around 85 to 90% of the ground speed. When the wheel speed is much lower than the ground speed, the antiskid system will release the brake at the certain wheel. The brake system will only work when the aircraft is on the ground. Therefore it gets information about the gear tilt from the PSEU. In case this system has been broken, the brake system gets information from the wheels. If they rotate, than the aircraft should be on the ground. This activates the brake system.
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1.3
Regulations
The regulations about the airworthiness on aircrafts are made by the European Aviation Safety Agency [EASA]. The airworthiness requirements are the minimal demands the aircraft has to comply with. These requirements are specified in Certifications Specifications [CS] for large aircraft in particular CS-25. CS-25 describes the minimal standard of the landing gear in general: the mechanical structure, tyres, wheels and steering system (1.3.1). The aircraft has to land in many different conditions such as bad weather or in case of an emergency. For these conditions, special regulations are specified (1.3.2). The regulations are too complicated to describe in detail, therefore the following part contains the most important only. Also the nose gear has to deal with different forces like touchdown and steering (1.3.3).
1.3.1
General regulations about the design
CS-25 has the general rules specified in CS 25.721, these conditions are: “(a) The landing gear system must be designed so that when it fails due to overloads during take-off and landing, the failure mode is not likely to cause spillage of enough fuel to constitute a fire hazard. The overloads must be assumed to act in the upward and aft directions in combination with side loads acting inboard and outboard. In the absence of a more rational analysis, the side loads must be assumed to be up to 20% of the vertical load or 20% of the drag load, whichever is greater. (b) The aircraft must be designed to avoid any rupture leading to the spillage of enough fuel to constitute a fire hazard as a result of a wheels-up landing on a paved runway, under the following minor crash landing conditions (c)For configurations where the engine nacelle is likely to come into contact with the ground, the engine pylon or engine mounting must be designed so that when it fails due to overloads (assuming the overloads to act predominantly in the upward direction and separately predominantly in the aft direction), the failure mode is not likely to cause the spillage of enough fuel to constitute a fire hazard.”1 For safety reasons, the landing gear has to pass a lot of difficult test. These test are designed to make sure that the landing gear complies with all the CS-25 landing gear regulations specified in CS 25.473
1.3.1.a
Retracting mechanism
The rules applied to the retracting mechanism are specified in CS 25.729: (a) Unless there are other means to decelerate the aircraft in flight at this speed, the landing gear, the retracting mechanism, and the aircraft structure (including wheel well doors) must be designed to withstand the flight loads occurring with the landing gear in the extended position at any speed up to 0·67 VC. (b) Landing gear doors, their operating mechanism, and their supporting structures must be designed for the yawing manoeuvres prescribed for the aircraft in addition to the conditions of airspeed and load factor prescribed in sub-paragraphs (a)(1) and (2) of this paragraph. (c) Landing gear lock. There must be positive means to keep the landing gear extended in flight and on the ground. There must be positive means to keep the landing gear and doors in the correct retracted position in flight, unless it can be shown that lowering of the landing gear or doors, or flight with the landing gear or doors extended, at any speed, is not hazardous. Emergency operation. There must be an emergency means for extending the landing gear in the event of – (1) Any reasonably probable failure in the normal retraction system; or (2) The failure of any single source of hydraulic, electric, or equivalent energy supply.”1
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1.3.1.b
Tyres and Wheels
The wheels and tyres must resist many hard forces and wearing. Therefore not every tyre and wheel can be used on an aircraft. The specificities rules are on this subject are described in CS 25.731 and CS 25.733
1.3.2
Different conditions
An aircraft has to deal with many different conditions. When the pilots expect a crosswind landing, the pilots will make a one wheel landing. This landing causes a lot of extra forces on this particular wheel (1.3.2.a). There is also the possibility of an emergency landing, this type causes a lot of extra forces due to a hard landing or broken parts of the aircraft for example the nose wheel, this wheel has to function in all states (1.3.2.b).
1.3.2.a
Normal conditions and ground load
In normal conditions the aircraft has to resist to landing forces but also forces due to taxiing and towing of the aircraft. CS-25 has specified the maximum angels and forces each landing gear in particular has to resist (Figure 13. Figure 13. ). It also shows in which way the nose wheel should be used as tow point.
Figure 13.
Maximum load factor
According to CS-25 the aircraft also has to resist the following forces: “Impact at 1.52 m/s (5 ft/s) vertical velocity, with the aircraft under control, at Maximum Design Landing Weight: - with the landing gear fully retracted and, as separate conditions, - with any other combination of landing gear legs not extended. Sliding on the ground, with: - the landing gear fully retracted and with up to a 20° yaw angle and, as separate conditions, - any other combination of landing gear legs not extended and with 0° yaw angle”1
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1.3.2.b
One gear landing conditions
The one gear landing causes extreme forces on the particular gear. Therefore CS-25 describes the following requirements about the landing. “For the one gear landing conditions, the aircraft is assumed to be in the level attitude and to contact the ground on one main landing gear, in accordance with figure 4 of Appendix A of CS –25. In this attitude – (a) The ground reactions must be the same as those obtained on that side under CS 25.479(d)(1), and (b) Each unbalanced external load must be reacted by aircraft inertia in a rational or conservative manner.”1
1.3.3
Nose wheel and steering system
The nose wheel and also the steering mechanism also has to function in case of an emergency or failure. CS-25 describes the following requirements about this system: “(a) The nose-wheel steering system, unless it is restricted in use to low-speed manoeuvring, must be so designed that exceptional skill is not required for its use during take-off and landing, including the case of cross-wind, and in the event of sudden powerunit failure at any stage during the take- off run. This must be shown by tests. (See AMC 25.745 (a).) (b) It must be shown that, in any practical circumstances, movement of the pilot‟s steering control (including movement during retraction or extension or after retraction of the landing gear) cannot interfere with the correct retraction or extension of the landing gear. (c) Under failure conditions the system must comply with CS 25.1309 (b) and (c). The arrangement of the system must be such that no single failure will result in a nose-wheel position, which will lead to a Hazardous Effect. Where reliance is placed on nose-wheel steering in showing compliance with CS”1
1
This paragraph contains many citations of CS-25 document that is published by EASA, 2010 Amsterdam Leeuwenburg Airlines Pagina 21
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2
Detailed body gear description
This chapter entirely focuses to the mechanical properties of the body gear of the Boeing 747. It is designed to be very strong, yet as light as possible. The choice of materials determines the mechanical properties of the gear (2.1). A landing gear must be stored as efficient as possible. It must be large enough to take the forces, but an enormous landing gear takes a lot of space, which means fewer payloads can be transported (2.2). To be able to find the most critical parts, calculations are made. These calculations include different situations during different flight phases (2.3).
2.1
Materials
A landing gear must be strong enough to operate in different tough conditions. But just adding a lot of material is not the best option to achieve that. Every material has its own specific properties (2.1.1). In aviation, a landing gear can be made from several materials (2.1.2). The manufacturer compares all material properties to choose the best suitable material (2.1.3).
2.1.1
Material properties
A material is chosen by considering its properties. Most pure materials are very weak, so they are alloyed with other elements to increase their strength (2.1.1.a). In aviation, every kilogram of the construction means a kilogram less of payload, so a material with a low density is recommended (2.1.1.b). The stresses on a construction during a landing are very high. A material is needed which is able to cope with these stresses and has a low tendency to yield (2.1.1.c).
2.1.1.a
Alloy
A material in pure condition is usually not very strong. To enhance its properties, it is possible to combine two or more elements and create a stronger material. Commercial steel is a good example: it is iron enforced by carbon. Density, thermal conductivity and reactivity of the alloyed metal don‟t necessarily increase, but engineering properties like strength and elasticity can increase rapidly by adding even small amounts of other elements. Most alloys are created to increase the strength of a metal. The atoms of the two materials are different in size. The larger atoms exert a compressive force on surrounding atoms, while smaller atoms exert a tensile force on the surrounding atoms. This combination of forces helps an alloy to resist deformation.
2.1.1.b
Density
The density is defined as the weight of a homogeneous object divided by its volume. It is a good indication of the strength of the materials. Materials with a high specific volume have more atoms per volume unit. This means that the atoms can resist higher tensions. In aviation, a material is needed that has good properties, but with the lowest specific gravity possible. Building an aircraft of heavy materials means that the plane cannot take much payload.
2.1.1.c
Yield
If an object is subjected to tensions („stresses‟), it will deform. Stiffer materials deform slowly with increasing stress, but when the material is brittle as well, it will not strain a lot before it breaks. The amount of deformation („strain‟) by certain stress levels can be displayed with a stress-strain graph (Figure 14. ). On the vertical axis, the amount of stress is set. The
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horizontal axis shows the amount of strain, which is defined as the change in the object‟s length. This example shows an object which is subjected to tensile stress. 1 5 4 3
1. 2. 3. 4. 5.
Proportionality limit Modulus of elasticity Elastic limit stress Yield point Ultimate strength
2
Figure 14.
Stress-strain curve
In this graph, a number of interesting material properties can be found. When an object is subjected to a force, it will tend to deform. The stress-strain ratio is different for each material. A material with a high ratio does not deform largely with increasing forces. Up to the proportionality limit (1), the stress-strain ratio remains equal. The slope of this line is called the modulus of elasticity (E) (2). If the stress remains lower than a certain point, an object will return to its original shape when the stress is released. The elasticity of a material is limited. If the stress reaches a certain value, the deformations of the object becomes permanently. The stress where this situation occurs is called the elastic limit stress (3). Every material has a different stress-strain curve, but there is a method to compare all materials. From the point on the horizontal axis where the object is 0,2% longer than original, a line with the slope of the modulus of elasticity is drawn. This line hits the graph in the yield point (4). By reading the amount of stress on the vertical axis, the yield strength is known. The value of 0,2% may differ depending on the application. The highest point of the stress-strain curve is called ultimate strength (5). This is the highest amount of stress that an object can take before the object starts to weaken and less stress is needed for increasing strain. A term not shown in the graph is the linear coefficient of expansion. It is the amount of deformation caused by changes in temperature. In aviation, materials with low coefficients of expansion are used, because of the high temperature changes.
2.1.2
Aviation materials
The most common material is aluminium. It is strong, light and very easy to manufacture (Error! Reference source not found.). Composites are making progress in today‟s aviation. It is light and is able to withstand extreme heat and friction (2.1.2.b). Steel is an iron alloy. It is very strong and has a high elasticity (2.1.2.c). Titanium is used where forces are high. It is strong and resistant to corrosion (2.1.2.d).
2.1.2.a
Aluminium
Aluminium is a soft, durable and lightweight material. It is the third most abundant element on earth, after oxygen and silicon. The big advantage of aluminium is its strength compared to its weight. Combined with the fact that it is easy to produce and corrosive resistant, it is an ideal material for aviation. Pure aluminium is very weak: its elastic limit stress is 7-11 MPa. In aviation, aluminium alloy 7075 is the most common alloy. It is therefore called aircraft aluminium. It is not the alloy with the lowest density, but tempered aircraft aluminium has a high elastic limit stress: 475 MPa. Amsterdam Leeuwenburg Airlines Pagina 23
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2.1.2.b
Composites
Composites are gradually more used in aviation. The most popular composite is carbon fibre. Carbon atoms are bonded in microscopic crystals that are aligned parallel to the long axis of the fibre. The alignment makes the fibre very strong for its size and weight. Several thousand fibres are twisted to form a yarn, which will be woven into a fabric. The amount of yarn determines the stiffness of the carbon fibre. However, even a supple carbon fibre is much stiffer than aluminium, which means that it is only usable at place where the risk of bending and stressing is minimal. Carbon fibre can withstand extreme heat and friction, so it‟s mostly used in the brakes.
2.1.2.c
Steel
Steel is an iron-carbon alloy. The amount of carbon differs from 0,2 to 1 percent. Iron can also be alloyed with other elements, but iron-carbon is the most abundant combination. Steel is usable in all kinds of situations, because it is strong yet very elastic. However, it is not really suitable for aviation, because its density is three times higher than aluminium its density.
2.1.2.d
Titanium
Titanium is a very good material considering its mechanical properties. It is corrosion resistant and it has a high strength-to-weight ratio. Titanium its density is sixty percent more than aluminium its density, but it is twice as strong as aircraft aluminium. However, titanium is not as abundant as aluminium. This is because it is hard to machine, which makes it an expansive material. In aviation, titanium is used in the fans of the engines and near the wing root.
2.1.3
Choice of the manufacturer
The best suitable material is chosen after comparing the properties of all possible materials. This material has to be durable, strong and light-weight. The main construction material of the landing gear is aircraft aluminium. This material is the best option because of its natural resistance to corrosion and its high strength-to-weight ratio. Regarding the last property, composite materials would be the best option. The problem with all composites is the extreme stiffness of these materials. When an extreme landing is made, the whole shock strut will bend in the directions it normally would not bend. Aluminium can cope better with extreme bending than composites. Titanium could be a very good material in the future, because it has an even higher strengthto-weight ratio than aluminium. It is naturally corrosion resistant as well. The problem with titanium is that it is difficult to machine. Since aluminium was discovered, steel was completely abandoned from aviation. It may be stronger than aluminium, but it is three times heavier. If forces on a spot on the landing gear are high, it is better to use a bit more aluminium than process the part out of steel.
2.2
Dimensions
Many forces are acting on the aircraft during flight (Figure 15. ) the lift (1) provides an upward force and is created by the wings (2). The upward force ensures that the aircraft is able to fly, but the lift is also causing a rotating force around the centre of gravity (3). The rotating force is caused because the lift is instead of the centre of gravity, acting on the quarter chord point of the wing (4). The quarter chord point is located on the chord line of the wing. All the forces, which are caused by the wing, are acting on this point. The rotating force around the centre of gravity is called a moment and can be defined as the force in Newton times the length of the arm (5) in meters. Another moment in the opposite direction must be created to obviate the rotation around the centre of gravity. The vertical stabilizer (6) on the Amsterdam Leeuwenburg Airlines Pagina 24
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tail of the aircraft is placed to create a moment in the opposite direction. The vertical stabilizer is creating a negative lift force (7) because it is a negative curved wing. Because the lift is negative a rotation in the opposite direction is caused. The negative lift force can be kept small because the arm of the moment in this direction is way bigger than the arm of the positive lift force.
3. 5. 1. 1. Lift 2. Wing 3. Centre of gravity 4. Quarter cord point 5. Arm 6. Vertical stabilizer 7. Negative lift
2. 4.
6.
7.
5. Figure 15. The forces on an aircraft
The dimensions of the landing gear are needed to make a proper calculation of the forces acting on the landing gear (Figure 16. ). The dimension of the nose (1) gear to the wing gear is given, just as the dimension between the wing (2) gear and the body gear (3).
1.
1. Nose gear 2. Wing gear 3. Body gear
3.
2.
Figure 16.
Landing gear configuration
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The dimensions of the construction are needed to make a calculation of the forces acting on the body gear. The dimensions of the nose landing gear construction will not be explained further. The dimensions of the body gear are given as coordinates in the direction of the x, y and z axis. The dimensions of the body gear construction are not given in manual so they are based on the tire size, which can be found in the maintenance manual. The tire size of the main gear tires are (49 inch), which amounts 124,46 centimetres. The dimensions of the other component can be determined in drawings. These drawings show the following coordinates. A(0,0,0), B(-472.91,99.36,Figure 17. Front view body gear 288.925), C(0,0,-288.925), D(0,-195.58,0), E(0,-80.01,0). Point A is located on the point where the most unknown forces are acting on. The axes are drawn from this point because the moments will fall off since there is no arm. Much coordinates are getting clear from the front view of the body gear (Figure 17. ), but there are still e few unknown. The coordinates, which are made clear in the front view (Figure 17. ) are A(0,0,0), B(…,99.36,288.925), C(…,…,…), D(0,-195.58,0), E(0,80.01,0). Other coordinates are clearly, when looking from a different direction to the body gear. The coordinates Cx and Cy will be made clear, when looking to the side view of the body gear (Figure 18. ).
Figure 18. Side view body gear
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Now only the Bx and the Cz coordinate are unknown, so there must be another view of the body gear. (Figure 19. ) shows that the Cz coordinate is equal to the Bz coordinate. This because the fuselage, where both points are fixed to, is parallel to the X axis. Coordinate Cz = Bz = 288,925. The only coordinate, which is not clear, is the Bx coordinate. In drawing three the tire size is also used, but because drawing three is a 3D drawing the tire size must be measured in every used direction. By is known form the previous drawings and is now drawn to scale in drawing three. Because By is along the Y axis the size parallel to the Y axis of the tires is uses to determine the scale along this axis. Along the Y axis is one centimetre in the real life 49.78 centimetres. Drawing one shows that By is in the real life 99, 36 centimetres. So in this drawing By is 99,36 / 49,78 , which is 2 centimetres. Parallel to the X axis a line is drawn. This line is measured and is 9.5 centimetres. The true distance can be found to use the Figure 19. Complete side view of the body gear scale of the X axis, which is calculated the exactly same way as the scale of the Y axis. Only in this case the length of the tires parallel to the X axis is measured instead of the length parallel to the Y axis. The real distance of Bx can now be calculated. Now the coordinates of the body gear are clear. The coordinates of the wing gear are found exactly the same way. Also axis in the X, Y, Z direction are drawn and point A is located on the point where the most unknown forces are act on. The coordinates of the wing gear are A(0,0,0) B(0,-35.56,-244.475) C(0,222.25,177.8) D(-133.35,-288.925,0). Nearly all coordinates became clear from drawing one of wing gear drawings (Figure 20. ). Only the Bx coordinate is not clear. In the second drawing can be seen that the Bx coordinate is zero.
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Figure 20.
Wing gear drawings
2.3
Calculations
During approach and touchdown, different forces work on the aircraft. These forces have to be absorbed during touchdown. With formulas it is possible to calculate the forces in the shock strut and the forces that work on the aircraft during touchdown. The maximum absorption of the shock strut will be determined (2.3.1). By a crosswind landing an extra force component works on the aircraft. The forces are now three dimensional (2.3.2). The forces which work on the gear will be calculated using a computer program (2.3.3Error! Reference source not found.). To verify the results, a handmade calculation is made (2.3.4). During incident the aircraft landed on three main gears instead of four main gears. This has an effect to the distribution of the forces (2.3.5).
2.3.1
Calculations maximum shock strut absorption
The forces on the aircraft during the approach are the lift, drag and the force of gravity (Figure 21. ). There will be no acceleration available in a normal situation. Therefore the following conclusion can be made: . There can also been spoken over an equilibrium.
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V W
Figure 21.
Forces on aircraft during approach
The velocity of the aircraft (Figure 22. ) will change during touchdown, one millisecond before touching down shows a vertical and a horizontal speed component (1) and just after touchdown there is only a horizontal speed component left (2). The vertical and horizontal component of the total landing velocity during the approach can be calculated according to: √ . As described in regulations the maximum admitted ⁄ component during
landing is
Figure 22.
Aircraft movements during landing
To calculate the forces on the aircraft and especially on the landing gear it is generally assumed that all the loss of kinetic energy after and before is transformed into spring energy and eventually dissipated by the shock absorber and transformed into warmth. The momentum in horizontal direction will not change after touching down and will be absorbed by the brakes and not the shock strut. The shock absorber of the aircraft has two functions, reduce the impact of with the ground and absorb the energy of the impact. For the calculations is assumed that the two functions are different components and that the kinetic spring energy of the shock strut is equal to the difference kinetic energy of the aircraft before and after impact. The Figure 23. Spring shock strut will be assumed as a linear spring, so calculations can be made.
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The loss of energy due to the tires and other components is not significant in comparing with the other forces and therefore not needed in the following calculations. An energy balance can be made: The kinetic energy of the vertical speed component (formula 2) is equal to the kinetic energy of the shock strut (formula 3).
(formula 2) = Kinetic energy = Mass = Vertical speed component Units: in Joule in kilogram [ in meters per second
⁄
(formula 3) Units: = Kinetic energy of a spring = Spring stiffness = Spring transformation in Joule in Newton per meter[ in meters
The equation can be reformed to: To calculate the force on the shock strut Hooke‟s law (formula 4) is introduced.
(formula 4) Hooke‟s law = Normal Force of the ground on the aircraft = Spring stiffness = Spring transformation Units: N in Newton in Newton per meter[ in meters
Introduced in the energy balance, the equation can be written as:
To calculate the force on the spring the mass of the aircraft and the spring (shock absorber) is needed. According to Boeing the Maximum Landing Weight [MLW] is 295.742 kg. The maximum on the shock absorber can only determent by a closer examinations or a field-test. Unfortunately are these date not available. it is after several examinations of Boeing 747 landing it is assumed that the . These data results in:
During normal touchdown, the normal force N will be absorbed by four shock struts, therefore the maximum force on each shock strut will be . The difference in time between the body gear and wing gear touchdown is not significant due to the assumptions made. There is also assumed that each shock strut functions as a linear spring, in a real situation the shock absorber doesn‟t absorb the impact linear. When more force is applied on the gas in the shock strut, the more force is needed to compress and at last the gas molecules are almost totally compressed together in the cylinder. Therefore the piston in the cylinder while not reaches the bottom completely. There will always be molecules on the bottom. This problem is a possible fault in the calculation above but not significant to the lot of assumptions made.
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2.3.2
Calculations crosswind landing
During a crosswind landing the aircraft touches down with a slip angle, therefore the wheels that touch down at first the wheels block and slip for a few second on the runway. This slip angle can be calculated according to CS-25: The landing airspeed according to Boeing 158 kts; . This slip causes several extra forces on the structure of the landing gear (Figure 24. ) one of them is friction which can be calculated with the friction coefficient Sectie 1.01(formula 5).There is assumed that each one of the four set wheel carried Figure 24. Top view crosswind landing the same force calculated as in previous paragraph; and that the friction coefficient . Therefore the forces can be calculated:
(formula 5) = Friction = Normal force = friction coefficient Units: in Newton in Newton has no dimension
The structure of the landing gear has to resist the strength of these forces and these can be calculated in each point of the structure. The chapter materials differed the coordinates of each point in the landing gear. These coordinates can be used to draw a picture of the landing gear side, top and front view (2.2). The zero point of the axis of these pictures are chose that the most there are less moments as possible and that the count of unknown factors are the same as the equations.
2.3.3
Calculations body-gear made with math-lab during crosswind
Due to the many unknown factors and the difficulty of equations, the forces on the structure are calculated with math-lab and help of an unreliable source Sander van der Pijl. He uses the coordinated: A(0,0,0), B(-472.91,99.36,-288.925), C(0,0,-288.925), D(0,-195.58,0), E(0,80.01,0) to plot the forces on each point. This result in the following forces: A: x: 586430 N y: -942040 N z: 113990 N B: x: -991640 N y: 376690 N z: -606770 N C: x: 0 N y: -114650 N z: 414010 N
2.3.4
Handmade body-gear calculations during crosswind
The calculations on the body gear can also made by hand with the equation of the moments in point A and de equations of Fx=0 ,Fy=0 and Fz=0 These calculations are shown in (Appendix VI) and results in: A: B: C: x: 581960 N x: -987176 N x: 0 y: -941307 N y: 374993 N y: -113686 N z: 116098 N z: -604801 N z: 409938 N Amsterdam Leeuwenburg Airlines Pagina 31
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2.3.5
Incident calculations
The incident involving the Boeing 747 of Nippon Cargo Airlines causes the Boeing 747 to disable the left body gear. The Boeing 747 had to make a touchdown on one body gear and two wing gears. This will change the forces on the aircraft. The weather conditions were not significant during this landing, so the crosswind component can be considered zero. The maximum force on the shock strut and the maximum impact height of the shock strut is already determined in the calculations of the touchdown limits. The relationship between the vertical touchdown velocity and the mass of the aircraft is now interesting, because an aircraft will not always touches down on MLW and the vertical ⁄ , therefore the equation to calculate the Normal force touchdown velocity is rarely is rewritten to the equation (formula 6) in which the mass is a function of the vertical touchdown velocity
(formula 6) Units: in kilogram [ ] in meters [ ] in Newton [ ] in meters per second [ ⁄ ]
= Mass = Maximum impact height of the shockstrut = Total normal force = Vertical touchdown velocity
Because the incident has lost one point of action for the total normal force can be recalculated by assuming that the Boeing 747 is a rigid body and has a linear spring, because of this the loss of the left body gear causes the Boeing 747 to touchdown with an angle (θ) to the ground and dividing the forces with the same angel ( θ) on the Boeing 747 (Figure 25. ).
Figure 25.
Forces during B747 Incident Landing
With the knowledge that one shock strut can take a maximum force of the maximum of the Boeing 747 with one of the left body gear malfunctioned. The force on the left wing gear shock strut is equal to the maximum force of the shock strut can handle during touchdown, or . With determined there are still three unknown forces. To calculate the other forces the ratio of is determined in which . How the ratio is determined can be find in (Appendix VII). With the ratio known the forces , and are calculated.
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Forces Ratio With be determined as: and the function mass of the vertical touchdown can now
The function is only interesting within the operation limits of the aircraft, for the mass is this between the Operation Empty Weight [OEW] of and the MLW of . The maximum vertical touchdown velocity determined by EASA in CS-25 at a velocity of ⁄ . The function is plotted (Figure 26. ) within the normal operation limits of the Boeing 747 during touchdown. The operation limits with the loss of the left body gear are reduced to the green area in the diagram. A touchdown within the red area will causes the shock strut to fail and the aircraft to crash. The Maximum Vertical Velocity [MVV] is now ⁄ to ⁄ and the maximum mass at MVV from reduced from to .
Figure 26.
Incident landing limits diagram
The reduced operation limits of the Boeing 747 during touchdown with a malfunctioned left body gear have no significant change to the landing procedures. A normal touchdown is the ⁄ and ⁄ and not even near the operation limits. vertical velocity between the
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3
Accident and conclusion
In this chapter all the consequences of the incident with the Boeing 747 will be discussed. Therefore, a better view of the accident is needed (3.1). Because of the damage the incident caused, the landing gear has to be repaired. But also the other parts have to be checked intensively, because it was a mechanical failure that causes the accident (3.2). As a consequence of the maintenance required for repairing and checking the landing gear, the aircraft will not generate benefits. Also the maintenance will generate extra costs. (3.3) At last, a conclusion of the accident with the Boeing 747 and all its mechanical and financial consequences can be made (3.4).
3.1
Synopsis
On September 14th, a serious accident with a Boeing 747, registration number JA01KZ, happened at Amsterdam Schiphol Airport. The cargo flew from Amsterdam Schiphol Airport to Milan Malpensa. When the crew selected „gear up‟ af ter take-off, the Engine Indication and Crew Alerting System [EICAS] displayed the mention ‘gear tilt’, followed by the mention ‘gear disagree’. The left wheel door was not closed, which was confirmed by the gear status on the upper EICAS display. The crew asked the air traffic control permission interrupt the climb, which was permitted. Then the crew verified the items of the non-normal checklist for the ‘gear tilt’ and ‘gear disagree’, but the situation did not change. An attempt to let the gear down, and pull it up, was without any success; the mentions at the EICAS did not disappear. The crew decided to return to the airport, where a smooth landing was made. On the apron, broken seals were visible on the left landing gear. Also the wheel doors and the connection from the landing gear to the aircraft construction were damaged. The shock absorber was found completely depressed, which means that there was no pressure in the shock strut. Also the tires did not reach the ground. The aircraft was delivered in June 2005 to the carrier and was about three months old. The damage was caused by over-extension of the left body gear. During the retraction of the landing gear, the tires of the over-extended gear have hit and damaged the construction of the aircraft. During the landing the shock solver was completely pressed and stayed in this situation. Disassembly revealed that the upper bearing carrier, snubber valve and follower tube were broken or torn. The upper bearing carrier, upper bearing sleeve and snubber valve were found lost in the outer cylinder. This snubber valve was broken on at least eight places whereby the horizontal flange was fully torn. The upper bearing carrier valves were broken close at the lower backpressure. The follower tube had several tear. The inner cylinder was bent and the upper bearing sleeve was damaged at several places. The deformation of the inner cylinder was due to the over-extension and caused by beating down of the upper cylinder sleeve in the lower bearing during the incident landing. Over-extension of the shock absolver occurred when the upper bearing carrier came loose from the inner cylinder. Traces of contact between the steering mechanism and the outer cylinder demonstrate that the extension of the shock absolver was limited by the steering mechanism. Only hampered by the steering mechanism, the shock absolver extended about 12 inches beyond the maximum value. Disassembly showed that the fracture of the upper bearing carrier was the beginning of the damage to the internal shock absorber components and subsequent over-extension. After disassembly of the shock absorber, Boeing received a „Notice of Escapement‟ (NOE) from the manufacturer of the landing gear, with a communication that their supplier had published that a number of upper bearing carriers had not received a correct heat treatment, and were supplied in annealed state. An electrical conductivity test was performed by Boeing Amsterdam Leeuwenburg Airlines Pagina 34
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on the two upper bearing carriers from aircraft JA01KZ. The test confirmed that both upper bearing carriers consist of annealed 2024 aluminium, which corresponded to the NOE of the supplier. All upper bearing carriers which had a faulty heat treatment were identified and the respective airlines where informed by Boeing, which offered support to swap the parts.
3.2
Maintenance consequences
To avoid problems, the aircraft needs maintenance. During maintenance some checks will be done to keep the aircraft in good conditions (3.2.1). In case something happens to the aircraft that has not been remarked during the checks, the maintenance has to be adjusted (3.2.2).
3.2.1
Maintenance checks
According to EASA an aircraft has to undergo some checks during its “life”. These checks are necessary to keep the aircraft in good conditions. There are four types of checks: 1. A-check 2. B-check 3. C-check 4. D-check ad 1 A-Check
After 600 hours of flying, an aircraft has to undergo the A-check. At average use, the check will take place once per month. During this check the most important systems will be checked critical. ad 2 B-Check
When the aircraft has flown for 1800 hours, the B-check has to be done. So this is once per three months. The B-Check is an expansion of the A-check. So the B-check is almost similar to the A-check however the B-Check is more thorough. ad 3 C-Check
Normally the C-Check will be done after one year or one and a half year. During this check all the cockpit panels will be opened and all the wiring will be checked. ad 4 D-Check
The last and most extensive check is the D-check. This check is obliged and has to be done each four or five years. The aircraft will be stripped totally. All the wiring and systems will be checked and replaced when necessary.
3.2.2
Maintenance change
The incident happened to a broken part of the shock strut. This problem could have been avoided if the shock strut was checked critically. In case this is not done, aircraft manufacturers need to rewrite the maintenance manuals. Furthermore it can be necessary to give the personnel more education to recognize problems earlier to avoid these kind of incidents during aircraft operation. In the case of the incident a part of the shock strut was broken. This means that all the Boeing 747‟s need to be investigated to see if the same part is not broken or shows indications of fatigue. In case the part is not reliable. It needs to be replaced, which takes a lot of time. This means that the aircraft will stay on ground for a longer time than normal, which is not desirable.
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3.3
Financial consequences
When an incident happens on board of an aircraft, there are always additional costs to solve the problems that follow on the incident. Most of these costs can be directly linked to the aircraft with the problems (3.3.1). The other part of additional costs may include hiring another aircraft or passenger compensation (3.3.2).
3.3.1
Additional aircraft costs
A lot of things can go wrong with an aircraft, but the costs of these categories will almost certainly rise when an aircraft hits problems: 1. Aircraft on Ground [AOG] 2. Parts 3. Personnel ad 1 Aircraft on Ground
AOG is the term used to tell that an aircraft is not able to generate profits. During AOG-time, aircraft maintenance or inspection will take place. In case of this incident, the whole shock strut of the body gear had to be replaced and all rubber seals of the struts were inspected and replaced if necessary. Replacing a shock strut is not a complex job, but the aircraft has to be lifted to be able to carry out the work safely and properly. ad 2 Parts
When something breaks on an aircraft, it has to be replaced. When looking at this incident, the costs of new parts are high: the whole shocks strut had to be replaced and the damaged aircraft structure, caused during retraction of the landing gear, had to be repaired. ad 3 Personnel
Additional personnel are needed to fix the breakdown. Not all maintenance personnel are qualified to do all repairs. In case of a complex job, an external specialist may be needed. The airliner may want to put extra personnel on the job which means a shorter Aircraft on Ground time. This is a consideration between costs and time.
3.3.2
External additional costs
These costs cannot be directly linked to the aircraft involved with the incident: 1. Another aircraft 2. Passenger compensation ad 1 Another aircraft
The passengers of the broken aircraft have to be transported. Otherwise, the airliner will lose its reputation. An aircraft has to be leased or hired to transport the passengers. Leasing means that an aircraft with personnel is hired. Hiring means just hiring the aircraft without personnel and supplies. Leasing is necessary if the pilots of the original aircraft do not have experience with the leased aircraft. ad 2 Passenger compensation
If the flight delays for more than three hours, passengers have a right to receive compensation. If the flight delays for less than three hours, passengers only have a right to get meals and refreshments.
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3.4
The Final Conclusion
After a closer look to the Boeing 747 landing gear, several calculations on the landing gear and a final analyze of the incident and its consequences, the conclusion can be made. The shock strut on the body gear failed because of a production failure. The lower bearing didn‟t have a heat treatment causing it to brake and allows the nitrogen gas to leak. The shock strut was now unable to absorb the forces of impact. The Boeing 747 without the body gear was able to land safely, because the Boeing 747 without one body gear can easily absorb the forces when touching down with normal procedures. The problem causes the airliner to replace the entire shock strut. All the other Boeing 747 needs to be investigated for lower bearings without a heat treatment and if necessary replace the shock struts lower bearing. The aircraft involving the incident will stay on ground for investigation and to replace the damaged shock strut, making the airliner to lose money on the replacing parts and disallowing the airliner to generates profits To replace the lower bearings of other aircrafts with a lower bearing that didn‟t had a proper heat treatment, the aircraft needs to remain on ground for a period. These aircrafts will also generates no profits when replacing the lower bearing
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Bibliography
Literature Boom, L.C. van den Tabellen en Formules, Werktuigbouwkunde niveau 4 1th druk Baarn, 2000 Van den Brink, R. Technische leergang: Hydrauliek 6th druk Amerongen, 2008 Budinski, K.G; Budinski, M.R Materiaalkunde Technici 2nd edition Schoonhoven, 1999 Callister, William D.; Rethwisch, David G. Materials, Science and Engineering 8th druk Currey, Norman S. Aircraft Landing Gear Design: Principles and Practices Marietta, Georgia, 1988 Lockheed Aeronautical Systems Company Dost, F Construeren Kernboek 1 3th druk Baarn, 2003 Dost, F Construeren Kernboek 2 3th druk Baarn, 2005 Hieminga, Jelle; IJspeert, Simon; van Langen, Pieter Landing Gear Amsterdam, 2010 Hogeschool van Amsterdam Domein Techniek Oxford Aviation Academy Aircraft General Knowledge Oxford, 2010 Pallet Aircraft Instruments and Integrated Systems Essex, 1992 Wentzel, Tilly Opbouw Projectverslag Amsterdam Leeuwenburg Airlines Pagina 38
Aviation Studies Amsterdam, 2009 Hogeschool van Amsterdam Domein Techniek Manuals
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Boeing & KLM Aircraft Maintenance Manual for 747-400 2004 Websites http://www.onderzoeksraad.nl/docs/rapporten/2006039_2005135_JA-01KZ_verkort_rapport.pdf 06-09-2005 http://www.airliners.net Photo’s http://www.boeing.com/commercial/airports/747.htm 12-2002 http://www.boeing.com/commercial/airports/faqs/arcandapproachspeeds.pdf Airport Reference Code and Approach Speeds for Boeing Airplanes 10-10- 2010 http://www.easa.europa.eu/agency-measures/certification-specifications.php EASA CS25 12-08-2010 Presentations Jelle Hieminga
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Appendices
I TYPES OF LANDING GEAR ......................................................................................................... 1 II GROUND LOOP ....................................................................................................................... 3 III LANDING GEAR STORAGE....................................................................................................... 4 IV LOCATION OF THE NOSE GEAR AND THE MAIN GEAR.............................................................. 5 V TYRE REGIONS ........................................................................................................................ 6 VI BODY GEAR CROSSWIND CALCULATIONS ............................................................................... 7 VII INCIDENT LANDING RATIO DETERMINATION ......................................................................... 9 VIII INVESTIGATION REPORT .................................................................................................... 11
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Aviation Studies I Conventional Types of landing gear
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Tricycle
Single main wheel
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Aviation Studies Cycle gear
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Quadricycle
Multi-bogey gear
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Aviation Studies II Ground loop
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Aviation Studies III Landing gear storage.
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Location of the nose gear and the main gear
1 2 3
Nose Gear Wing Gear (main gear) Body Gear (main gear)
1
2 3
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1
Sidewall
1
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Body gear crosswind calculations
Forcec of the croswind: Dx = 405215,7 Dy = 680000 Dz = 78766 Distances: Lady = 1.956 Labx = 4,73 Laby = 0,99 Lacz = 2,89 Labz = Lacz Angles:
X,Y surface: ∑
∑
∑
Y,Z surface: ∑
∑
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Incident landing ratio determination
Figure 27.
Forces during B747 Incident Landing
Determine the ratio of the forces on the shock struts of the B747 can be done by introducing . Using basic mechanics we can produce two equation: ∑ and ∑ . Which will result in: ∑ ∑ There are now two equations and three unknown forces, this means the unknown forces can‟t be determined. To determine the ratio of the three unknown forces a other equation has to be introduced. By assuming that the B747 is a rigid body and has a linear spring, because of this the loss of the left body gear the B747 will touchdown with an angle (θ) to the ground and divides the forces with the same angel (θ) on the B747. Because of the symmetry of the of the two wing gears the force in centre of gravity would be . Also the angel θ can be calculate by . With these two fact we can write as a function of and .
This equation can be written as:
With the three functions determined the ratio of the unknown forces can be calculated, this is done by using the matrix‟s.
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The ratio of the unknown forces can now be determined:
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Aviation Studies VIII Investigation report
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The 747’s body gear
Project Report
Projectgroup 2A2R
Ivar van Cuyk Jos Frijmann Wytze Hilgers Anouk Lelij Kevin van der Plas Roy van Schagen Roy Wassink Peter van Woudenberg
Projectleader
Sander van der Pijl
Amsterdam, October 2010
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Table of contents
TABLE OF CONTENTS .................................................................................................................... 2 SUMMARY ................................................................................................................................... 4 INTRODUCTION ............................................................................................................................ 5 1 LANDING GEAR ANALYSIS ....................................................................................................... 6 1.1 LANDING GEAR PRINCIPLES ......................................................................................................... 6 1.1.1 FUNCTION LANDING GEAR ................................................................................................................. 6 1.1.2 TYPES ............................................................................................................................................ 6 1.1.3 MAIN LANDING GEAR BOEING 747 .................................................................................................... 8 1.1.4 NOSE GEAR ................................................................................................................................... 10 1.2 BODY GEAR SYSTEMS .............................................................................................................. 12 1.2.1 HYDRAULIC SYSTEM ....................................................................................................................... 13 1.2.2 EXTENSION AND RETRACTION SYSTEM ............................................................................................... 13 1.2.3 ALTERNATE EXTENSION AND SYSTEM ................................................................................................. 15 1.2.4 SHOCK STRUT ................................................................................................................................ 15 1.2.5 BODY GEAR STEERING SYSTEM .......................................................................................................... 16 1.2.6 AIR/GROUND SYSTEM ..................................................................................................................... 17 1.2.7 HYDRAULIC BRAKE SYSTEM .............................................................................................................. 17 1.2.8 BRAKE CONTROL SYSTEM ................................................................................................................. 18 1.3 REGULATIONS ....................................................................................................................... 19 1.3.1 GENERAL REGULATIONS ABOUT THE DESIGN ....................................................................................... 19 1.3.2 DIFFERENT CONDITIONS .................................................................................................................. 20 1.3.3 NOSE WHEEL AND STEERING SYSTEM ................................................................................................. 21 2 DETAILED BODY GEAR DESCRIPTION...................................................................................... 22 2.1 MATERIALS........................................................................................................................... 22 2.1.1 MATERIAL PROPERTIES.................................................................................................................... 22 2.1.2 AVIATION MATERIALS ..................................................................................................................... 23 2.1.3 CHOICE OF THE MANUFACTURER ...................................................................................................... 24 2.2 DIMENSIONS ......................................................................................................................... 24 2.3 CALCULATIONS ...................................................................................................................... 28 2.3.1 CALCULATIONS MAXIMUM SHOCK STRUT ABSORPTION ......................................................................... 28 2.3.2 CALCULATIONS CROSSWIND LANDING ................................................................................................ 31 2.3.3 CALCULATIONS BODY-GEAR MADE WITH MATH-LAB DURING CROSSWIND ............................................... 31 2.3.4 HANDMADE BODY-GEAR CALCULATIONS DURING CROSSWIND ............................................................... 31 2.3.5 INCIDENT CALCULATIONS ................................................................................................................. 32 3 ACCIDENT AND CONCLUSION ................................................................................................ 34 3.1 SYNOPSIS ............................................................................................................................. 34 3.2 MAINTENANCE CONSEQUENCES ................................................................................................. 35 3.2.1 MAINTENANCE CHECKS ................................................................................................................... 35 3.2.2 MAINTENANCE CHANGE .................................................................................................................. 35 3.3 FINANCIAL CONSEQUENCES ....................................................................................................... 36 3.3.1 ADDITIONAL AIRCRAFT COSTS ........................................................................................................... 36 3.3.2 EXTERNAL ADDITIONAL COSTS .......................................................................................................... 36 3.4 THE FINAL CONCLUSION........................................................................................................... 37 Amsterdam Leeuwenburg Airlines Pagina 2
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BIBLIOGRAPHY ........................................................................................................................... 38 APPENDICES ............................................................................................................................... 40
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Summary
The second year Aviation students received an assignment to make an analysis of the landing gear of a modern aircraft. The engineering department of Amsterdam Leeuwenburg Airlines [ALA] wanted the project group to discover any interference in the landing gear of the chosen aircraft. This to make an extension of the fleet possible. The project group has chosen the Boeing 747, this because the landing gear of this aircraft is more complicated. The project group also found a proper incident of the Boeing 747 that could be investigated. First, the project group has made an analysis of the various landing gears. The various landing gears have been described each with its own advantages and disadvantages. The landing gear of the Boeing 747 had been described more precisely after it became clear what kind of landing gear is used on the Boeing 747. The landing gear of the Boeing 747 is called a multi bogey gear. This landing gear consists of a main landing gear and a nose landing gear. The main landing gear of the Boeing 747 contains the body gears and the wing gears, this because the Boeing 747 is an aircraft with a great mass. The body gear consist of two bogeys and is places under the fuselage, the wing gear contains also two bogeys and is placed under the wings of the aircraft. The body gear and the wing gear have, related to each other, a different construction, although almost all components are used in both systems. The nose gear contains one bogey and is placed under the fuselage near the cockpit. There are many laws and requirements, which have to be taken into account when developing a landing gear. The landing gear must be able to deal with great forces that develop in extreme situations. These forces are described and have been taken into account when making calculations of the forces that are acting on the landing gear. The dimensions of the landing gear are needed to make a proper calculation of these forces. The dimensions of the main gear have been described, because during the incident the problem occurred in the main gear of the landing gear. The landing gear must be able to deal with forces acting on it. Therefore, it is necessary to know the properties of the materials used in the landing gear. So the properties of materials that are normally used in aviation are described. There is also described how the properties of the materials can be improved. The calculation is made, after all dimensions and the properties of the used materials are clear. The cause of the problem is made clear by making different calculations of the forces acting on the landing gear. When the cause is made clear the effects of the incident can also be made clear. The financial implications have been examined. Finally a conclusion is made.
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Introduction
The board of ALA is about to buy new aircrafts. The model they are looking for is the Boeing 747. However, an internal discussion about the aircraft is started, due to a recent incident with the landing gear of a Boeing 747. During the retraction of the landing gear after take-off, a gear did not fold-in properly. Wheels hit the aircraft fuselage and got stuck. During the touchdown, the shock absorber of this gear failed. This incident did not cause any human fatalities, but the board of ALA is worried about the possible consequences that this incident may cause. Therefore, the board wants a detailed analysis of the landing gear. The project group examined the landing gear of the Boeing 747. Based on the results of this examination, the board is able to decide whether or not to buy a Boeing 747. The assignment for the investigation is given to project group 2A2R. The members of this group follow the bachelor phase of Aviation Studies. This study is given at the “Hogeschool van Amsterdam”. All members are in their second year, which is in school year 2010-2011. The report is written according to the rules in the dictation of Wentzel. The report will be handed over to the board of ALA on the 14th of October 2010. This report is divided into three chapters: Before the constructions of a landing gear can be understood, the principles of a landing gear are needed to know. With a basic knowledge of a landing gear, the Boeing 747‟s gear can be described. There are rules before a landing gear may be used. A landing gear must gratify to all the regulations in Certification Specification 25. (1) The mechanical analysis includes calculations of forces during different flight phases. The ability to cope with high forces depends on the construction material. It has to be strong, yet elastic and as light as possible. The positions and dimensions of the gears determine the stability and weight distribution of the aircraft. (2) The incident will have an effect to the airworthiness of the Boeing 747. The faulty part may have to be replaced or examined. The maintenance schedule will be adjusted to prevent this incident from happening again. This adjustment will increase the aircraft on ground time, which reduces the profit the aircraft can generate. (3) The main sources of this project are the Boeing 747 Maintenance Manual and the report of the incident of flight JA01KZ. The complete list can be found on page 38.
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1
Landing gear analysis
The construction that the aircraft uses to make contact with the surface is called the landing gear. A landing gear is necessary to make the aircraft manoeuvrable on the surface without damaging the aircraft. To understand a landing gear and its configurations, it is necessary to know the principles of a landing gear (1.1). Because of the problem with the Boeing 747 was a problem with its left body gear, knowledge about the Boeing 747‟s body gear is needed to understand the problem (Error! Reference source not found.). A landing gear may not be used without a certification. The landing gear must gratify to all rules in CS-25 (1.3). Main source of this chapter is chapter 32, Landing Gear, of the Boeing 747‟s manual.
1.1
Landing gear principles
In order to make it possible for an aircraft to manoeuvre when it is not in the air, an aircraft is equipped with a landing gear. A landing gear has multiple functions (1.1.1). The landing gear is performed in several conditions (1.1.2). Because of the landing gear of a Boeing 747 is a multi bogey gear, the multi bogey gear is explained further. The multi bogey gear is divided in the main landing gear (1.1.3) and the nose landing gear (1.1.4).
1.1.1
Function landing gear
The function of a landing gear is to carry the aircraft when it is not in the air. The landing gear makes it possible to make manoeuvres in horizontal directions and to rotate in vertical directions. Another function of a landing gear is to abate the energy that arises during a landing. In this way, a landing is more comfortable, by using a shock absorber. A shock absorber reduces the loads on the other parts of the aircraft When an aircraft is landed, it has to decrease its speed. The only contact with the runway is by the tyres. Therefore, the landing gear is equipped with brakes. The last function of the landing gear system is the aero-dynamical function. When the aircraft is in flight, the landing gear is retracted to create a more aero-dynamical shape of the aircraft. The aircraft has lower drag, which is positive for the fuel consumption.
1.1.2
Types
There are many types of landing gear, each with its own advantages and disadvantages. Mostly wheels are used to make aircraft manoeuvrable on the surface, but skis and floats are also used. The different types of landing gear using wheels to manoeuvre on the surface will be explained (1.1.2.a). Because this type of landing gear is often used in the commercial aviation, instead of the ski‟s and floats. After takeoff, the landing gear is often stored to improve the aerodynamic properties of aircraft. Aircraft designers have devised various ways to store the landing gear as efficient as possible (1.1.2.b).
1.1.2.a
Types of landing gear
Aircraft designers have always been searching for better landing constructions, so there are many types of landing gear. The most used landing gears are: 1. 2. 3. 4. 5. Conventional landing gear Tricycle landing gear Single main wheel Bicycle gear Quadricycle Pagina 6
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The conventional landing system was often used between 1910 and 1950. The conventional landing gear consists of a main landing gear and a tail landing gear, the main landing gear contains two wheels and the tail landing gear one wheel (Appendix I). The tail wheel does not absorb shocks, so the tail wheel can be kept small. The benefits of a small tail wheel are of course less weight and less air resistance. A small tail wheel does also have a couple of disadvantages. Aircraft with a conventional landing gear have an angle with the surface, because the main landing gear wheels are bigger than the tail landing gear wheel. This ensures the pilot has a bad sight when the aircraft is standing on the runway or when the pilot is taxiing on the taxiway. Another disadvantage is ground loop. Ground loop is an effect that occurs when aircraft with a conventional landing gear makes a turn on the runway or taxiway. A destabilizing moment can occur when making a turn (Appendix II). ad 2 Tricycle landing gear
Since 1950 the tricycle landing gear is used often. The tricycle landing gear contains a main landing gear, which had two wheels or bogies and a nose landing gear, which has one wheel or bogey (Appendix I). This construction has many advantages over the conventional landing gear. The pilot has a better view on the runway or taxiway and ground loop cannot occur, because the nose wheel now produces a stabilizing moment (Appendix II). ad 3 Single main wheel
This type contains one main wheel and one small tale wheel (Appendix I). It is a light system because the system is made simple. Because the single main wheel landing gear consists of two wheels the manoeuvrability is not very well. This type of landing gear is often used in aircraft with a small mass. ad 4 Bicycle gear
The bicycle gear has two main landing gear constructions. These are located in the longitudinal (Appendix I). Aircraft with the bicycle gear are not stable because the wheels are placed next to each other, although it was a good construction for aircraft with a narrow fuselage. Mostly auxiliary wheels are used to prevent the wing strikes the surface. ad 5 Quadricycle
This construction consists of four main landing gears (Appendix I). The main landing gear contains wheels, which are located under the fuselage. This is ideal for cargo aircraft because the fuselage is located near the surface, so loading and unloading can be done quickly. The stability of the aircraft is not very well. ad 6 Multi-bogey gear
The multi bogey gear contains a main landing gear and a nose landing gear (Appendix I). The main landing gear consists of two rows of wheels and the nose landing gear mostly of two bogies. The multi-bogey gear is used by aircraft with a large mass.
1.1.2.b
Storage of the landing gear
Mostly the landing gear is stored to improve the aerodynamic characteristics of aircraft. There are several ways to store the landing gear (Appendix III). The landing gear of small aircraft is often stored in the wings or fuselage, or a combination of these places. Big aircraft often use a space, which is called the fuselage-podded. This is a part of the aircraft that strengthened the transition area of the wing and the fuselage. In the fuselage-podded is enough space for storing the landing gear. In some cases, space for the landing gear is
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created under the wings. This is called wing-podded. The landing gear of rotor aircraft is often stored under the engines.
1.1.3
Main Landing Gear Boeing 747
The main landing gear is the principle gear of an aircraft. Which type of a main landing gear is used, depends on the size of the aircraft. The Boeing 747 is a large, heavy aircraft. Therefore is used a complex landing gear, which is composed of a several main gear units (1.1.3.a). The landing gear operates through by a retractable system (1.1.3.b).
1.1.3.a
Construction
The Boeing 747 is equipped with four main gear units, consisting of two body gears, which are attached to the fuselage, and two wing gears, which are placed aft of the rear wing inboard of the engine nacelles. Each of these is featured with four-wheel bogies (Figure 1. ) (Appendix IV).
1. 2. Wing Gear Body Gear
1 2 Figure 1. Boeing 747‟s Main Landing Gear
Through a trunnion and trunnion fork, supported at the forward end by the wing rear spar and at the aft end by the landing gear support beam, is each wing gear attached to the structure. Each body gear is attached to the structure through a trunnion cantilevered from backing on the aft bulkhead of the body gear wheel well. The doors of the landing gear consist of wing gear doors and body gear doors. Both have each wheel well doors and shock strut doors. Wheel well doors operate hydraulically and can be closed when the gear is extended or retracted. These doors are hinged together. The doors of the shock strut are also hinged together. They operate mechanically and are attached by linkage rods. These doors only move when the gear is moved. All doors are of frame construction, with on the inner and outer sides skin panelling. The doors close over all gear openings, and accord with the contour of the fuselage. This provides an aerodynamic smoothness. Several components are used to optimize the using of the landing gear. A shock absorber, or shock strut, is an item, which is used to all current landing gears. The basic function of this component is to absorb the kinetic energy during the landing and taxiing so the accelerations imposed upon the frame will be reduced to an acceptable level. The brakes, in combination with a skid control system, are used to reduce the speed and to stop the aircraft. Brakes can also used to hold an aircraft stationary while it‟s parked, or when the engines are running up, but also to steer the aircraft by differential action or to control speed while the aircraft is taxiing. The skid controls are used to minimize the stopping distance and to reduce the excessive tyre wear and burst tyres by unduly skidding. The available degree of friction coefficient is constantly sensing by the systems, and by controlling brake pressure to supply an almost constant brake force nearly to the skidding point. The anti-skid system is used to prevent a wheel for slipping during braking. This is a lot safer because in a large aircraft, the pilot does not notice the wheels are slipping.
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The „landing gear position indication system‟ shows the position of the landing gear and the doors. The information is delivered to the crew through the display units in the cockpit (EICAS).
1.1.3.b
Operation
The retraction and extension of the landing gear and their doors operates by a hydraulic system. When hydraulic power is available, an electrically powered alternate extension system unlock the gear and doors. This movement is controlled by one action on the panel in the cockpit. When the handle is placed in DN position, the doors open, gear unlocks, gear extends, and then the doors close. UP position is conversely: the gear doors open, the gear retracts and locks, and the doors close. Gear and door operation are controlled by sequence valves. There is one actuator for the extension (Figure 2. ) (1), and two actuators for the retraction of the landing gear (2). Retraction happens during upwind, so there is more strength required to retract.
1. 2 2. Actuators for retraction of the L/G Actuator for extraction of the L/G
1
Figure 2.
Actuators for retraction and extraction
The inner wheels of the Boeing 747 can rotate and are used during towing and taxiing of the aircraft (Figure 3. ). This movement is contrary to the motion of the nose-wheel. For rotating the wheels, two actuators are used (1). The brakes are operated using the hydraulic pipes (2). The possibility of steerable body gear trucks reduce tyre scrubbing, which occurs when an aircraft makes a sharp turn.
1. 2. Actuators for rotating the inner wheels Hydraulic pipes, brakes
2
1
Figure 3.
Actuators on the wheels and hydraulic pipes
Five air-oil shock struts absorb the landing impact. These works in the first place as air springs. The variances in runway and the vibrations of rolling are absorbed by the hydraulic forces within the shock strut.
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A Boeing 747 has eighteen wheels, from which two on the nose gear, eight on the body gear and eight on the wing gear (Appendix IV). Any single wheel of the body gear and wing gear is provided with a brake unit. This is installed on the side nearest the shock strut. The brakes on a Boeing 747 are multidisc brakes, fitted with a combination of automatic adjusters and return springs. These adjusters compensate for the wastage of the brakes. When an aircraft brakes, the anti-skid system automatically operates. The wheel skid is compensated by this system, by control of brake pressure. This happens through the anti-skid valves. A „brake temperature monitoring system‟ displays the brake temperatures and make the cabin crew alert of overheated brakes. The position of the landing gear is showed by proximity switch sensors, which are located on any single landing gear and doors. The sensor signals provide the data of the position to the EICAS display units.
1.1.4
Nose gear
The construction of the nose gear differs from that of the main gear (1.1.4.a). The nose gear is used to support the forward end of the fuselage. The nose gear is also used for controlling the direction of the aircraft while it is moving on the ground (1.1.4.b). The nose gear suffers from vibrations (shimmy) more than the main gear does (1.1.4.c).
1.1.4.a
Construction
Starting from the ground, the nose gear of a Boeing 747 (Figure 4. ) (Appendix IV) has two tyres and wheels (1) that are attached on one axle (2). This axle is connected to the lower end of the shock strut inner cylinder (3). The shock strut is used to absorb the shocks from the landing impacts and rolling over bumps on the ground. Also connected to the shock strut inner cylinder, is the lower end of the lower torsion link (4). The upper end of the upper torsion link (5) is connected to the forward steering collar (6). Aft steering collar (7) attach lugs slip over the forward steering collar attach lugs. Both collars are locked together around the shock strut outer cylinder (8) by actuator attach pins (9). These pins also hold the rod end of the steering actuators (10). The steering actuators, steering collars and torsion links are all parts used in the steering mechanism. At the upper end of the shock strut outer cylinder there is a trunnion (11). When the nose gear extends or retracts it pivots on this trunnion. The trunnion itself rotates in bearings. The trunnion is supported by two side braces (12). The braces extend from the attach lugs at the centre of the shock strut outer cylinder. Besides the side braces, there is also a lower tripod brace (13) connected to the centre of the shock strut outer cylinder. The lower tripod brace is connected to the upper tripod brace (14) that extends forward from the centre of the trunnion. Also connected to the trunnion is the nose gear actuator (15). The nose gear actuator activates the nose gear extension or retraction movement. Between the end of the nose gear actuator and the hinge of both tripod braces there is a drag strut (16). Together with the nose gear lock actuator (17), it holds the nose gear in the up and locked, or down and locked position.
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17 15
16
11 14
12 13
A S t a rt in g fr o m
1. 2. 3. 4. 5. 6. 8 7 9 7. 8. 9. 10. 11. 12. 13.
10 6
t 14. h e 15. g 5 16. r 17. See A o 4 S u 1 t n a d 3 rt , 2 in t g h Figure 4. Nose gear fr e o 1.1.4.b Steering operation n m o Both pilots have their own steering tiller that they can use for normal steering operation. One s tiller is on the left of the captain and the is on the right of the first officer. A tiller t other e movement of 90 degrees results in a steering movement of 45 degrees. Tiller movement in h la either direction is transmitted to a steering metering valve by cables (Figure 5. (1). This e n valve directs fluid (oil) with a pressure of 3000 PSI (hydraulic system No. 1) to the nose g di wheel steering actuators (2). When the steering actuators are activated, they transfer their r n power to the attach pins (3). These pins a turning moment to both collars. The o transmit g forward collar (4) transfers the power u to the upper torsion link. The upper torsion link g transfers the power to the lower torsion link. link turns the shock strut inner cylinder to n This e the left or right. This action turns the axle and the axle turns the wheels. The tillers can turn d a the nose wheels around 70 degrees maximum. , r t o h f e a n n o B s o e ei la n n g di 7 n 4 g 7 g h e a a s r t Amsterdam Leeuwenburg Airlines Pagina 11 o w f o a ty n r
Tyre and wheel Axle Shock strut inner cylinder Lower torsion link Upper torsion link Forward steering collar Aft steering collar Shock strut outer cylinder Attach pin Steering actuator Trunnion Side braces Lower tripod brace Upper tripod brace Nose gear actuator Drag strut Nose gear lock actuator
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1. 2. 3. 4.
3
Metering valve assembly Steering actuator Attach pin Forward steering collar
1 4
3
2 Figure 5. Steering operation
Besides the normal steering there is another way to steer the wheels. This is done with the help of the rudder pedals. The nose wheel steering system is connected to the rudder pedals through mechanical linkage and cables. When the nose gear is compressed by the weight of the aircraft, rudder pedal steering is available. The rudder pedals can turn the nose wheels around 10 degrees maximum. When the aircraft is towed, the wheels can turn around 65 degrees maximum without disconnecting the nose gear torsion links.
1.1.4.c
Shimmy
Because of the flexibility of tyre side walls (Appendix V), vibrations known as shimmy are induced into the nose gear. Especially at high speeds, excessive shimmy can cause vibrations throughout the whole aircraft, which is dangerous. Wear of the nose wheel bearings, worn torsion links and uneven tyre pressures all increase the tendency to shimmy. In general these ways are used to reduce shimmy: Provision of a hydraulic lock across the steering jack piston; Fitting a hydraulic damper; Fitting heavy self-centring springs; Double nose wheels; Twin contact wheels. The above mentioned steering metering valve consists of a spring compensator. This spring compensator maintains a pressure of 205 to 325 PSI against the steering actuator pistons to act as a shimmy damper.
1.2
Body Gear Systems
In this paragraph the systems of the Boeing 747‟s body gear is being discussed. The body gear is being discussed because the left body gear of the Boeing 747 was the landing gear that malfunctioned during take-off and causing the Boeing 747 to make an emergency landing at Schiphol Airport. Multiple systems used in the Boeing 747 are using the hydraulic system to support (1.2.1). The extension and retraction system (1.2.2) is one of those systems, because a failure in the hydraulics may not cause the Boeing to be disable to retract the landing gear, there is also a alternate extension and retraction system (1.2.3). When the Boeing 747 touches down with a malfunctioned body gear, the shock struts (0) of the three remaining gears now has to absorb the impact. The body gear of the Boeing 747 is Amsterdam Leeuwenburg Airlines Pagina 12
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also equipped with an Air/Ground system (Error! Reference source not found.), a Body gear steering system (Error! Reference source not found.), a hydraulic braking system (Error! Reference source not found.) and a brake control system (Error! Reference source not found.).
1.2.1
Hydraulic System
The Boeing 747 has a hydraulic system to provide multiple systems in the Boeing 747 to work properly. The hydraulic system is applied in the entire aircraft. In this paragraph only the hydraulics in the body gear (1.2.1.a) and the hydraulic actuator (1.2.1.b) will be discussed.
1.2.1.a
The hydraulic system in the body gear
The hydraulic system of the Boeing 747 is applied to decrease the work pressure of the pilots. It uses a fluid to transport pressure applied by an engine driven pump. The hydraulic system is based on hydrostatic laws, such as Pascal‟s law Sectie 1.01(formula 1). Pascal‟s law tells that the force the pilot applies into the hydraulic system can be increased by decreasing the surface of the applied force. This makes the pilots use a small amount of strength to do heavy tasks, such as, retracting the landing gears. The Boeing 747 has four independent hydraulic systems, so if one fails another can take over. The landing gear relies on the hydraulic systems No.1 and No.4
Pascal‟s law: F = Force A = Surface (formula 1) Units: F in Newton [N] 2 A in square meters [m ]
The hydraulic systems No.1 and No.4 are available for multiple systems applied in the body gear of the Boeing 747. The extension and retraction system, the body gear steering system and the hydraulic brake system use the hydraulic system to increase the force applied by the pilot.
1.2.1.b
Hydraulic actuator
The hydraulic system uses hydraulic actuators (Figure 6. ) to turn the hydraulic pressure into a movement. Actuators are cylinders (1) with two chambers. If the hydraulic pressure increases in one of the chambers the hydraulic the piston will move creating a larger chamber for the high pressure. The piston (2) will move the piston rod (3) which will perform the action that is required. If the hydraulic pressure is increased in the red chamber and the piston rod will move in the direction of the red arrow, if the pressure is increased in the blue chamber, the piston rod will move in to the direction of the blue arrow
1. 2. 3. Cylinder Piston Piston rod
Figure 6.
Hydraulic actuator
1.2.2
Extension and retraction system
The landing gears on Boeing 747 are designed to retract during flight to decrease drag and to increase the aerodynamic stability of the aircraft. This makes the plane use less fuel and a increase manoeuvrability. The body gear will be raised and lowered simultaneous with the Amsterdam Leeuwenburg Airlines Pagina 13
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wing gear and the nose gear by a lever in the cockpit. To raise and lower the landing gear the extension and retraction uses a gear actuator (1.2.2.a) to retract and lower the body gear. The sequence valves make sure all components will retract in correct order (1.2.2.b). The landing gear will be locked into place when raised (1.2.2.c) and when extended (1.2.2.d).
1.2.2.a
Gear actuator
To retract the body gear during flight and extend the body gear for landing the Boeing 747 uses hydraulic powered actuator. The gear actuator will be attached to the aircraft structure and the shock strut of the landing gear (Figure 7. ). Figure 7. When the actuator is retracting (1) the body gear will retract (3). The actuator will turn the shock strut around the trunnion (2) and covers the body gear in the wheel well (Figure 8. ).
1. 2. 3. Gear actuator Trunnion Shock strut
Figure 7.
Retracting body gear
Figure 8.
Retracted body gear
1.2.2.b
Sequence valves
The wheel well doors are linked to the body gear with sequence valves, these valves make sure the wheel well doors are opened before the body gear will be lowered and closed after the body gear is locked into place when retracted. The sequence valves steer the hydraulic fluid from the hydraulic system to the doors actuator, the up lock actuator, the down lock actuator and the body gear actuator. By retracting the landing gear using the landing gear lever, the hydraulic fluid will enter the door sequence valves and goes through a valve to the door actuator. The pressure builds up and the wheel well door will open. When the doors are opened the hydraulic pressure in the sequence valve is also increased and now opens another valve and allows the hydraulic fluid to flow to the lock mechanism, when the body gear is unlocked the hydraulic fluid will now raise the body gear and finally the hydraulic fluid will lock the gear in the up position.
1.2.2.c
Up lock mechanism
To make sure the body gear stays retracted the landing gear will be locked into place, which is done by an up lock mechanism. The body gear of the Boeing 747 is locked by locking a hook around the up lock roller that is attached to the shock strut. The hook will be kept in the locking position by a spring and can be unlocked by a hydraulic actuator or electric actuator to release the body gear or to receive the up lock roller in the hook.
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1.2.2.d
Down lock mechanism
Next to an up lock mechanism there is also a down lock mechanism, to make sure the body gear stays in to place when extended and not retract when touching down at a high impact. The down lock mechanism, that has to lock the body gear into place mechanical, makes sure the Boeing 747 is able to land on its body gear when multiple systems are malfunctioned. The down lock mechanism is an over centre knee joint on the jury strut that is connecting the drag strut with the aircrafts structure (Figure 9. The jury strut will over centre the joint allowing it to take forces in direction of the jury strut, because the jury can only move to the mechanical limit of the knee joint and makes sure the jury strut will not fold and allows the body gear to rise. The joint can be unlocked out of the over centre position by the hydraulic actuator.
Figure 9. Over centre knee joint
1.2.3
Alternate extension and system
Because all the landing gears must be able to extend when the hydraulic system malfunctions, the Boeing 747 is equipped with a alternate extension system. The alternate system will simply electrically unlock the up lock mechanism of the body gear and simultaneous releases the wheel well doors. With some manoeuvring of the aircraft and the gravity the body gear will be lowered and lock into place. The alternate landing gear will be operated by a switch in the cockpit.
1.2.4
Shock strut
The shock strut absorbs most of the impact when the aircraft touches down and when taxiing on the runway. The Boeing 747 is 1. Outer cylinder equipped with Oleo-pneumatic shock 2. Nitrogen valve struts (Figure 10. ). This is a shock 3. Upper chamber absorber that uses both oil (5) and (Nitrogen) compressed nitrogen (3) to absorb 4. Orifice support tube impact. The shock strut has an inner 5. Oil and (11) an outer cylinder (1). The 6. Orifice outer cylinder is attached to the aircraft 7. Upper bearing structure by the trunnion. The inner 8. Metering pin 9. Seal cylinder is attached to the bogie of the 10. Lower bearing body gear. The inner cylinder can 11. Inner cylinder move in and out the outer cylinder to absorb impact. The orifice (6) of the shock strut is a small passage. The oil will be pressed through this passage at impact and controls the absorption of the impact. The metering pen (8) and the orifice support tube (4) allow the shock strut to absorb and control the impact even better. The oil is after compression in the upper chamber and will return to lower chamber. To Figure 10. Oleo-pneumatic Shock strut avoid to oil and the nitrogen to leak Amsterdam Leeuwenburg Airlines Pagina 15
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throw the gap between the inner and outer cylinder, the shock strut has a seal (9) attached to the lower bearing (10) to seal that gap and allows the cylinders to move into each other.
1.2.5
Body gear steering system
The Boeing 747 has a body gear steering system. This system helps the pilots to control the aircraft (1.2.5.a). To get a better view of the body gear steering system, a description of the construction is made (0). When it is clear how the body gear steering system is constructed, its operation can be described (1.2.5.c).
1.2.5.a
Function
Because the Boeing 747 is a heavy aircraft, it needs more gear struts to attach the wheels, which have to resist the great weight of the aircraft on the ground. The Boeing 747 has two body gears under its body. During a turn, these body gears will not follow the radius of the turn as the wing gears do (Figure 11. ). As a result of this, great forces will stress on the wheels and on the strut. Furthermore the body gear wheels will wear faster than normal as a result of tyre scrubbing. Much maintenance on the body gear wheels and struts is necessary to keep the body gear in good condition. To avoid this problem, body gear steering is introduced. Body gear steering allows the body gear of the Boeing 747 to rotate thirteen degrees whether right or left. Now body gear steering has been installed, sharper turns can be made without damaging the wheels or the strut.
Figure 11.
Tyre scrubbing and how to avoid tyre scrubbing
1.2.5.b
Construction
To allow body gear steering, the wheel truck has to rotate in respect to the shock strut. To rotate the wheel truck, the inner cylinder of the shock strut is rotatable. Like at normal gears, the body gear has a torsion link that is linked to the wheel truck and the shock strut. However, instead of an upper torsion link, two steering cylinders were added. These cylinders, connected to each other on the lower torsion link, are connected to the shock strut by a yoke. Now, if one of the cylinders extends, the wheel truck can rotate. The pressure for both cylinders is delivered by hydraulic system 1.
1.2.5.c
Operation
When the nose gear turns in one direction, the body gear turns smaller proportional angles in the other direction. There are some requirements for the body gear steering. To prevent the body gear from damaging during a high speed turn, the body gear steering will switch off when a speed of twenty knots is reached. From that point, it will function as torsion link only. There is also a limit at the angle of rotation. The body gear rotates maximum thirteen degrees whether left or right. The angle of thirteen degrees will be reached when the nose gear is rotated seventy degrees. Furthermore, the body gear may not be tilted and has to be extended and locked. Amsterdam Leeuwenburg Airlines Pagina 16
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1.2.6
Air/ground system
Some systems of the aircraft, like the spoilers, operate different in air than on the ground. This makes it important to know if the aircraft is in the air or on the ground. Therefore, sensors that measure the gear tilt are mounted on the landing gear. Those sensors will send their position data to a Proximity Switch Electronics Unit [PSEU]. The PSEU supplies the position and the control data for primary landing gear sensor and alternate landing gear sensor subsystems. The PSEU will convert the position data to control data before it will send the control data to the air/ground relays. Air/ground relays have the task to tell the aircraft systems when the aircraft is in the air (air mode) and when it is on the ground (ground mode). Some systems do not have enough information when they only know if the landing gear is tilted or not. Many more sensors are mounted on the landing gear, like: up- and down lock sensors and wheel door sensors. However, signals from the landing gear lever switch, body gear steering (body gear has to be centred during in most conditions) are also important. Together, all these subsystems create the air/ground system. Problems can appear in the air/ground system. In case the air/ground system does not get a signal from the sensors after takeoff, the air/ground system will stay in ground mode. When the air/ground system stays in ground mode, some systems in the cockpit will not work, like the autopilot. To continue the flight with this problem, the fuses of the air/ground system can be switched off and then the relays will go to air mode. However, the pilots may not forget to put in the fuses after touch down because the spoilers and brake system will not work properly.
1.2.7
Hydraulic brake system
The hydraulic brake system helps the pilots controlling the aircraft on the ground and in more situations (1.2.7.a). To get a better view of the hydraulic brake system, a description of the construction of this system is made (1.2.7.b). When it is clear how this system is constructed, an explanation of how the system works can be given (1.2.7.c).
1.2.7.a
Function
The hydraulic brake system has the task to slow down the aircraft on the runway when it lands. The brake system also holds the aircraft during parking and engine run up. However, also after take-off the wheels have to be slowed down before they are fully retracted. The brake system also helps with making turns on the ground. There are different kinds of brake systems (drum brakes, single disc brakes and multiple disc brakes). The multiple disc brakes are the most used on airliners. Also the Boeing 747 uses multiple disc brakes. The choice of the brake system depends on how much heat the brakes have to resist.
1.2.7.b
Construction
The multiple disc brakes (Figure 12. ) exists out of four rotor discs (1) and three stator discs (2) that rotate besides each other. The discs are made of carbon and contain a material that creates much friction when the discs are pressed together. The rotor discs have rebated joints (3), which allow the rotor discs to sit still in the wheels. The wheels also have rebated joints. The stator discs are connected to the wheel axis, which cannot rotate (4). Now, if the wheels rotate, the rotor discs will rotate together with the wheels while the stator discs will stay still. Next to the inner rotor disc, a piston housing is mounted (5). This housing contains seven cylinders (6) that press the rotor discs and stator discs together. The cylinders are pressurized by hydraulic system 4. When hydraulic system 4 cannot pressurize the cylinders, hydraulic system 1 will take over this task. If also hydraulic system 1 cannot pressurize the cylinders, than hydraulic system 2 will do pressurize them. The pressure that the brakes need differs from 160 PSI to 3000 PSI. The cylinders that are connected to each other in the piston housing are connected to the hydraulic system by just one hydraulic line (7). To avoid too much pressure on the system, a bleeding valve (8) is mounted on the piston housing. When using the brake system, the brake discs will wear. To check how much the discs are Amsterdam Leeuwenburg Airlines Pagina 17
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worn, two wear indicator pins (9) are used. If these pins are not visible anymore, the brake discs should be replaced.
1 8 6 7 3 2 1. 2. 3. 4. 5. 6. 7. 8. 9. Rotor disc (4x) Stator disc (3x) Rebated joints Wheel axis Piston housing Cylinder (7x) Hydraulic line Bleeding valve Wear indicator pin (2x)
5
9 4
Figure 12.
Multiple disc brake
1.2.7.c
Operation
If one of the pilots creates a force on the ends of the rudder pedals, the brake system will activate. The more force presses on the pedals, the more the brake will slow down the aircraft. Slowing down the aircraft happens when the cylinders in the piston housing extend. When the cylinders extend, the discs will be pressed together. The more the discs are pressed together, the more friction will be created. This will slow down the aircraft. When the cylinders retract, the discs will stay together. To avoid this, small leaf springs are mounted between the discs to create a small space between the discs. When activated, the auto brake system will steer the braking system without any input of the pilots.
1.2.8
Brake control system
The brake control system supplies some functions that help the pilots. These functions are: antiskid protection, automatic braking, and brake torque control. This system also supplies arming logic for the body gear steering system. The automatic braking system will operate when the wheel speed increases to sixty knots or more during touchdown. A selector makes it possible to allow five deceleration levels. Also for a rejected take off there is a deceleration rate. The brake torque control has to prevent the brake from too much torque. When the brake torque control measures too much torque at one of the wheels, it will send a signal to the antiskid system. The antiskid system prevents the aircraft from skid. This is done by sensors that are mounted in each wheel. Those sensors measure the wheel rotation speed. The most effective way of braking is with a wheel speed that is around 85 to 90% of the ground speed. When the wheel speed is much lower than the ground speed, the antiskid system will release the brake at the certain wheel. The brake system will only work when the aircraft is on the ground. Therefore it gets information about the gear tilt from the PSEU. In case this system has been broken, the brake system gets information from the wheels. If they rotate, than the aircraft should be on the ground. This activates the brake system.
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1.3
Regulations
The regulations about the airworthiness on aircrafts are made by the European Aviation Safety Agency [EASA]. The airworthiness requirements are the minimal demands the aircraft has to comply with. These requirements are specified in Certifications Specifications [CS] for large aircraft in particular CS-25. CS-25 describes the minimal standard of the landing gear in general: the mechanical structure, tyres, wheels and steering system (1.3.1). The aircraft has to land in many different conditions such as bad weather or in case of an emergency. For these conditions, special regulations are specified (1.3.2). The regulations are too complicated to describe in detail, therefore the following part contains the most important only. Also the nose gear has to deal with different forces like touchdown and steering (1.3.3).
1.3.1
General regulations about the design
CS-25 has the general rules specified in CS 25.721, these conditions are: “(a) The landing gear system must be designed so that when it fails due to overloads during take-off and landing, the failure mode is not likely to cause spillage of enough fuel to constitute a fire hazard. The overloads must be assumed to act in the upward and aft directions in combination with side loads acting inboard and outboard. In the absence of a more rational analysis, the side loads must be assumed to be up to 20% of the vertical load or 20% of the drag load, whichever is greater. (b) The aircraft must be designed to avoid any rupture leading to the spillage of enough fuel to constitute a fire hazard as a result of a wheels-up landing on a paved runway, under the following minor crash landing conditions (c)For configurations where the engine nacelle is likely to come into contact with the ground, the engine pylon or engine mounting must be designed so that when it fails due to overloads (assuming the overloads to act predominantly in the upward direction and separately predominantly in the aft direction), the failure mode is not likely to cause the spillage of enough fuel to constitute a fire hazard.”1 For safety reasons, the landing gear has to pass a lot of difficult test. These test are designed to make sure that the landing gear complies with all the CS-25 landing gear regulations specified in CS 25.473
1.3.1.a
Retracting mechanism
The rules applied to the retracting mechanism are specified in CS 25.729: (a) Unless there are other means to decelerate the aircraft in flight at this speed, the landing gear, the retracting mechanism, and the aircraft structure (including wheel well doors) must be designed to withstand the flight loads occurring with the landing gear in the extended position at any speed up to 0·67 VC. (b) Landing gear doors, their operating mechanism, and their supporting structures must be designed for the yawing manoeuvres prescribed for the aircraft in addition to the conditions of airspeed and load factor prescribed in sub-paragraphs (a)(1) and (2) of this paragraph. (c) Landing gear lock. There must be positive means to keep the landing gear extended in flight and on the ground. There must be positive means to keep the landing gear and doors in the correct retracted position in flight, unless it can be shown that lowering of the landing gear or doors, or flight with the landing gear or doors extended, at any speed, is not hazardous. Emergency operation. There must be an emergency means for extending the landing gear in the event of – (1) Any reasonably probable failure in the normal retraction system; or (2) The failure of any single source of hydraulic, electric, or equivalent energy supply.”1
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1.3.1.b
Tyres and Wheels
The wheels and tyres must resist many hard forces and wearing. Therefore not every tyre and wheel can be used on an aircraft. The specificities rules are on this subject are described in CS 25.731 and CS 25.733
1.3.2
Different conditions
An aircraft has to deal with many different conditions. When the pilots expect a crosswind landing, the pilots will make a one wheel landing. This landing causes a lot of extra forces on this particular wheel (1.3.2.a). There is also the possibility of an emergency landing, this type causes a lot of extra forces due to a hard landing or broken parts of the aircraft for example the nose wheel, this wheel has to function in all states (1.3.2.b).
1.3.2.a
Normal conditions and ground load
In normal conditions the aircraft has to resist to landing forces but also forces due to taxiing and towing of the aircraft. CS-25 has specified the maximum angels and forces each landing gear in particular has to resist (Figure 13. Figure 13. ). It also shows in which way the nose wheel should be used as tow point.
Figure 13.
Maximum load factor
According to CS-25 the aircraft also has to resist the following forces: “Impact at 1.52 m/s (5 ft/s) vertical velocity, with the aircraft under control, at Maximum Design Landing Weight: - with the landing gear fully retracted and, as separate conditions, - with any other combination of landing gear legs not extended. Sliding on the ground, with: - the landing gear fully retracted and with up to a 20° yaw angle and, as separate conditions, - any other combination of landing gear legs not extended and with 0° yaw angle”1
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1.3.2.b
One gear landing conditions
The one gear landing causes extreme forces on the particular gear. Therefore CS-25 describes the following requirements about the landing. “For the one gear landing conditions, the aircraft is assumed to be in the level attitude and to contact the ground on one main landing gear, in accordance with figure 4 of Appendix A of CS –25. In this attitude – (a) The ground reactions must be the same as those obtained on that side under CS 25.479(d)(1), and (b) Each unbalanced external load must be reacted by aircraft inertia in a rational or conservative manner.”1
1.3.3
Nose wheel and steering system
The nose wheel and also the steering mechanism also has to function in case of an emergency or failure. CS-25 describes the following requirements about this system: “(a) The nose-wheel steering system, unless it is restricted in use to low-speed manoeuvring, must be so designed that exceptional skill is not required for its use during take-off and landing, including the case of cross-wind, and in the event of sudden powerunit failure at any stage during the take- off run. This must be shown by tests. (See AMC 25.745 (a).) (b) It must be shown that, in any practical circumstances, movement of the pilot‟s steering control (including movement during retraction or extension or after retraction of the landing gear) cannot interfere with the correct retraction or extension of the landing gear. (c) Under failure conditions the system must comply with CS 25.1309 (b) and (c). The arrangement of the system must be such that no single failure will result in a nose-wheel position, which will lead to a Hazardous Effect. Where reliance is placed on nose-wheel steering in showing compliance with CS”1
1
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2
Detailed body gear description
This chapter entirely focuses to the mechanical properties of the body gear of the Boeing 747. It is designed to be very strong, yet as light as possible. The choice of materials determines the mechanical properties of the gear (2.1). A landing gear must be stored as efficient as possible. It must be large enough to take the forces, but an enormous landing gear takes a lot of space, which means fewer payloads can be transported (2.2). To be able to find the most critical parts, calculations are made. These calculations include different situations during different flight phases (2.3).
2.1
Materials
A landing gear must be strong enough to operate in different tough conditions. But just adding a lot of material is not the best option to achieve that. Every material has its own specific properties (2.1.1). In aviation, a landing gear can be made from several materials (2.1.2). The manufacturer compares all material properties to choose the best suitable material (2.1.3).
2.1.1
Material properties
A material is chosen by considering its properties. Most pure materials are very weak, so they are alloyed with other elements to increase their strength (2.1.1.a). In aviation, every kilogram of the construction means a kilogram less of payload, so a material with a low density is recommended (2.1.1.b). The stresses on a construction during a landing are very high. A material is needed which is able to cope with these stresses and has a low tendency to yield (2.1.1.c).
2.1.1.a
Alloy
A material in pure condition is usually not very strong. To enhance its properties, it is possible to combine two or more elements and create a stronger material. Commercial steel is a good example: it is iron enforced by carbon. Density, thermal conductivity and reactivity of the alloyed metal don‟t necessarily increase, but engineering properties like strength and elasticity can increase rapidly by adding even small amounts of other elements. Most alloys are created to increase the strength of a metal. The atoms of the two materials are different in size. The larger atoms exert a compressive force on surrounding atoms, while smaller atoms exert a tensile force on the surrounding atoms. This combination of forces helps an alloy to resist deformation.
2.1.1.b
Density
The density is defined as the weight of a homogeneous object divided by its volume. It is a good indication of the strength of the materials. Materials with a high specific volume have more atoms per volume unit. This means that the atoms can resist higher tensions. In aviation, a material is needed that has good properties, but with the lowest specific gravity possible. Building an aircraft of heavy materials means that the plane cannot take much payload.
2.1.1.c
Yield
If an object is subjected to tensions („stresses‟), it will deform. Stiffer materials deform slowly with increasing stress, but when the material is brittle as well, it will not strain a lot before it breaks. The amount of deformation („strain‟) by certain stress levels can be displayed with a stress-strain graph (Figure 14. ). On the vertical axis, the amount of stress is set. The
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horizontal axis shows the amount of strain, which is defined as the change in the object‟s length. This example shows an object which is subjected to tensile stress. 1 5 4 3
1. 2. 3. 4. 5.
Proportionality limit Modulus of elasticity Elastic limit stress Yield point Ultimate strength
2
Figure 14.
Stress-strain curve
In this graph, a number of interesting material properties can be found. When an object is subjected to a force, it will tend to deform. The stress-strain ratio is different for each material. A material with a high ratio does not deform largely with increasing forces. Up to the proportionality limit (1), the stress-strain ratio remains equal. The slope of this line is called the modulus of elasticity (E) (2). If the stress remains lower than a certain point, an object will return to its original shape when the stress is released. The elasticity of a material is limited. If the stress reaches a certain value, the deformations of the object becomes permanently. The stress where this situation occurs is called the elastic limit stress (3). Every material has a different stress-strain curve, but there is a method to compare all materials. From the point on the horizontal axis where the object is 0,2% longer than original, a line with the slope of the modulus of elasticity is drawn. This line hits the graph in the yield point (4). By reading the amount of stress on the vertical axis, the yield strength is known. The value of 0,2% may differ depending on the application. The highest point of the stress-strain curve is called ultimate strength (5). This is the highest amount of stress that an object can take before the object starts to weaken and less stress is needed for increasing strain. A term not shown in the graph is the linear coefficient of expansion. It is the amount of deformation caused by changes in temperature. In aviation, materials with low coefficients of expansion are used, because of the high temperature changes.
2.1.2
Aviation materials
The most common material is aluminium. It is strong, light and very easy to manufacture (Error! Reference source not found.). Composites are making progress in today‟s aviation. It is light and is able to withstand extreme heat and friction (2.1.2.b). Steel is an iron alloy. It is very strong and has a high elasticity (2.1.2.c). Titanium is used where forces are high. It is strong and resistant to corrosion (2.1.2.d).
2.1.2.a
Aluminium
Aluminium is a soft, durable and lightweight material. It is the third most abundant element on earth, after oxygen and silicon. The big advantage of aluminium is its strength compared to its weight. Combined with the fact that it is easy to produce and corrosive resistant, it is an ideal material for aviation. Pure aluminium is very weak: its elastic limit stress is 7-11 MPa. In aviation, aluminium alloy 7075 is the most common alloy. It is therefore called aircraft aluminium. It is not the alloy with the lowest density, but tempered aircraft aluminium has a high elastic limit stress: 475 MPa. Amsterdam Leeuwenburg Airlines Pagina 23
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2.1.2.b
Composites
Composites are gradually more used in aviation. The most popular composite is carbon fibre. Carbon atoms are bonded in microscopic crystals that are aligned parallel to the long axis of the fibre. The alignment makes the fibre very strong for its size and weight. Several thousand fibres are twisted to form a yarn, which will be woven into a fabric. The amount of yarn determines the stiffness of the carbon fibre. However, even a supple carbon fibre is much stiffer than aluminium, which means that it is only usable at place where the risk of bending and stressing is minimal. Carbon fibre can withstand extreme heat and friction, so it‟s mostly used in the brakes.
2.1.2.c
Steel
Steel is an iron-carbon alloy. The amount of carbon differs from 0,2 to 1 percent. Iron can also be alloyed with other elements, but iron-carbon is the most abundant combination. Steel is usable in all kinds of situations, because it is strong yet very elastic. However, it is not really suitable for aviation, because its density is three times higher than aluminium its density.
2.1.2.d
Titanium
Titanium is a very good material considering its mechanical properties. It is corrosion resistant and it has a high strength-to-weight ratio. Titanium its density is sixty percent more than aluminium its density, but it is twice as strong as aircraft aluminium. However, titanium is not as abundant as aluminium. This is because it is hard to machine, which makes it an expansive material. In aviation, titanium is used in the fans of the engines and near the wing root.
2.1.3
Choice of the manufacturer
The best suitable material is chosen after comparing the properties of all possible materials. This material has to be durable, strong and light-weight. The main construction material of the landing gear is aircraft aluminium. This material is the best option because of its natural resistance to corrosion and its high strength-to-weight ratio. Regarding the last property, composite materials would be the best option. The problem with all composites is the extreme stiffness of these materials. When an extreme landing is made, the whole shock strut will bend in the directions it normally would not bend. Aluminium can cope better with extreme bending than composites. Titanium could be a very good material in the future, because it has an even higher strengthto-weight ratio than aluminium. It is naturally corrosion resistant as well. The problem with titanium is that it is difficult to machine. Since aluminium was discovered, steel was completely abandoned from aviation. It may be stronger than aluminium, but it is three times heavier. If forces on a spot on the landing gear are high, it is better to use a bit more aluminium than process the part out of steel.
2.2
Dimensions
Many forces are acting on the aircraft during flight (Figure 15. ) the lift (1) provides an upward force and is created by the wings (2). The upward force ensures that the aircraft is able to fly, but the lift is also causing a rotating force around the centre of gravity (3). The rotating force is caused because the lift is instead of the centre of gravity, acting on the quarter chord point of the wing (4). The quarter chord point is located on the chord line of the wing. All the forces, which are caused by the wing, are acting on this point. The rotating force around the centre of gravity is called a moment and can be defined as the force in Newton times the length of the arm (5) in meters. Another moment in the opposite direction must be created to obviate the rotation around the centre of gravity. The vertical stabilizer (6) on the Amsterdam Leeuwenburg Airlines Pagina 24
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tail of the aircraft is placed to create a moment in the opposite direction. The vertical stabilizer is creating a negative lift force (7) because it is a negative curved wing. Because the lift is negative a rotation in the opposite direction is caused. The negative lift force can be kept small because the arm of the moment in this direction is way bigger than the arm of the positive lift force.
3. 5. 1. 1. Lift 2. Wing 3. Centre of gravity 4. Quarter cord point 5. Arm 6. Vertical stabilizer 7. Negative lift
2. 4.
6.
7.
5. Figure 15. The forces on an aircraft
The dimensions of the landing gear are needed to make a proper calculation of the forces acting on the landing gear (Figure 16. ). The dimension of the nose (1) gear to the wing gear is given, just as the dimension between the wing (2) gear and the body gear (3).
1.
1. Nose gear 2. Wing gear 3. Body gear
3.
2.
Figure 16.
Landing gear configuration
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The dimensions of the construction are needed to make a calculation of the forces acting on the body gear. The dimensions of the nose landing gear construction will not be explained further. The dimensions of the body gear are given as coordinates in the direction of the x, y and z axis. The dimensions of the body gear construction are not given in manual so they are based on the tire size, which can be found in the maintenance manual. The tire size of the main gear tires are (49 inch), which amounts 124,46 centimetres. The dimensions of the other component can be determined in drawings. These drawings show the following coordinates. A(0,0,0), B(-472.91,99.36,Figure 17. Front view body gear 288.925), C(0,0,-288.925), D(0,-195.58,0), E(0,-80.01,0). Point A is located on the point where the most unknown forces are acting on. The axes are drawn from this point because the moments will fall off since there is no arm. Much coordinates are getting clear from the front view of the body gear (Figure 17. ), but there are still e few unknown. The coordinates, which are made clear in the front view (Figure 17. ) are A(0,0,0), B(…,99.36,288.925), C(…,…,…), D(0,-195.58,0), E(0,80.01,0). Other coordinates are clearly, when looking from a different direction to the body gear. The coordinates Cx and Cy will be made clear, when looking to the side view of the body gear (Figure 18. ).
Figure 18. Side view body gear
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Now only the Bx and the Cz coordinate are unknown, so there must be another view of the body gear. (Figure 19. ) shows that the Cz coordinate is equal to the Bz coordinate. This because the fuselage, where both points are fixed to, is parallel to the X axis. Coordinate Cz = Bz = 288,925. The only coordinate, which is not clear, is the Bx coordinate. In drawing three the tire size is also used, but because drawing three is a 3D drawing the tire size must be measured in every used direction. By is known form the previous drawings and is now drawn to scale in drawing three. Because By is along the Y axis the size parallel to the Y axis of the tires is uses to determine the scale along this axis. Along the Y axis is one centimetre in the real life 49.78 centimetres. Drawing one shows that By is in the real life 99, 36 centimetres. So in this drawing By is 99,36 / 49,78 , which is 2 centimetres. Parallel to the X axis a line is drawn. This line is measured and is 9.5 centimetres. The true distance can be found to use the Figure 19. Complete side view of the body gear scale of the X axis, which is calculated the exactly same way as the scale of the Y axis. Only in this case the length of the tires parallel to the X axis is measured instead of the length parallel to the Y axis. The real distance of Bx can now be calculated. Now the coordinates of the body gear are clear. The coordinates of the wing gear are found exactly the same way. Also axis in the X, Y, Z direction are drawn and point A is located on the point where the most unknown forces are act on. The coordinates of the wing gear are A(0,0,0) B(0,-35.56,-244.475) C(0,222.25,177.8) D(-133.35,-288.925,0). Nearly all coordinates became clear from drawing one of wing gear drawings (Figure 20. ). Only the Bx coordinate is not clear. In the second drawing can be seen that the Bx coordinate is zero.
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Figure 20.
Wing gear drawings
2.3
Calculations
During approach and touchdown, different forces work on the aircraft. These forces have to be absorbed during touchdown. With formulas it is possible to calculate the forces in the shock strut and the forces that work on the aircraft during touchdown. The maximum absorption of the shock strut will be determined (2.3.1). By a crosswind landing an extra force component works on the aircraft. The forces are now three dimensional (2.3.2). The forces which work on the gear will be calculated using a computer program (2.3.3Error! Reference source not found.). To verify the results, a handmade calculation is made (2.3.4). During incident the aircraft landed on three main gears instead of four main gears. This has an effect to the distribution of the forces (2.3.5).
2.3.1
Calculations maximum shock strut absorption
The forces on the aircraft during the approach are the lift, drag and the force of gravity (Figure 21. ). There will be no acceleration available in a normal situation. Therefore the following conclusion can be made: . There can also been spoken over an equilibrium.
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V W
Figure 21.
Forces on aircraft during approach
The velocity of the aircraft (Figure 22. ) will change during touchdown, one millisecond before touching down shows a vertical and a horizontal speed component (1) and just after touchdown there is only a horizontal speed component left (2). The vertical and horizontal component of the total landing velocity during the approach can be calculated according to: √ . As described in regulations the maximum admitted ⁄ component during
landing is
Figure 22.
Aircraft movements during landing
To calculate the forces on the aircraft and especially on the landing gear it is generally assumed that all the loss of kinetic energy after and before is transformed into spring energy and eventually dissipated by the shock absorber and transformed into warmth. The momentum in horizontal direction will not change after touching down and will be absorbed by the brakes and not the shock strut. The shock absorber of the aircraft has two functions, reduce the impact of with the ground and absorb the energy of the impact. For the calculations is assumed that the two functions are different components and that the kinetic spring energy of the shock strut is equal to the difference kinetic energy of the aircraft before and after impact. The Figure 23. Spring shock strut will be assumed as a linear spring, so calculations can be made.
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The loss of energy due to the tires and other components is not significant in comparing with the other forces and therefore not needed in the following calculations. An energy balance can be made: The kinetic energy of the vertical speed component (formula 2) is equal to the kinetic energy of the shock strut (formula 3).
(formula 2) = Kinetic energy = Mass = Vertical speed component Units: in Joule in kilogram [ in meters per second
⁄
(formula 3) Units: = Kinetic energy of a spring = Spring stiffness = Spring transformation in Joule in Newton per meter[ in meters
The equation can be reformed to: To calculate the force on the shock strut Hooke‟s law (formula 4) is introduced.
(formula 4) Hooke‟s law = Normal Force of the ground on the aircraft = Spring stiffness = Spring transformation Units: N in Newton in Newton per meter[ in meters
Introduced in the energy balance, the equation can be written as:
To calculate the force on the spring the mass of the aircraft and the spring (shock absorber) is needed. According to Boeing the Maximum Landing Weight [MLW] is 295.742 kg. The maximum on the shock absorber can only determent by a closer examinations or a field-test. Unfortunately are these date not available. it is after several examinations of Boeing 747 landing it is assumed that the . These data results in:
During normal touchdown, the normal force N will be absorbed by four shock struts, therefore the maximum force on each shock strut will be . The difference in time between the body gear and wing gear touchdown is not significant due to the assumptions made. There is also assumed that each shock strut functions as a linear spring, in a real situation the shock absorber doesn‟t absorb the impact linear. When more force is applied on the gas in the shock strut, the more force is needed to compress and at last the gas molecules are almost totally compressed together in the cylinder. Therefore the piston in the cylinder while not reaches the bottom completely. There will always be molecules on the bottom. This problem is a possible fault in the calculation above but not significant to the lot of assumptions made.
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2.3.2
Calculations crosswind landing
During a crosswind landing the aircraft touches down with a slip angle, therefore the wheels that touch down at first the wheels block and slip for a few second on the runway. This slip angle can be calculated according to CS-25: The landing airspeed according to Boeing 158 kts; . This slip causes several extra forces on the structure of the landing gear (Figure 24. ) one of them is friction which can be calculated with the friction coefficient Sectie 1.01(formula 5).There is assumed that each one of the four set wheel carried Figure 24. Top view crosswind landing the same force calculated as in previous paragraph; and that the friction coefficient . Therefore the forces can be calculated:
(formula 5) = Friction = Normal force = friction coefficient Units: in Newton in Newton has no dimension
The structure of the landing gear has to resist the strength of these forces and these can be calculated in each point of the structure. The chapter materials differed the coordinates of each point in the landing gear. These coordinates can be used to draw a picture of the landing gear side, top and front view (2.2). The zero point of the axis of these pictures are chose that the most there are less moments as possible and that the count of unknown factors are the same as the equations.
2.3.3
Calculations body-gear made with math-lab during crosswind
Due to the many unknown factors and the difficulty of equations, the forces on the structure are calculated with math-lab and help of an unreliable source Sander van der Pijl. He uses the coordinated: A(0,0,0), B(-472.91,99.36,-288.925), C(0,0,-288.925), D(0,-195.58,0), E(0,80.01,0) to plot the forces on each point. This result in the following forces: A: x: 586430 N y: -942040 N z: 113990 N B: x: -991640 N y: 376690 N z: -606770 N C: x: 0 N y: -114650 N z: 414010 N
2.3.4
Handmade body-gear calculations during crosswind
The calculations on the body gear can also made by hand with the equation of the moments in point A and de equations of Fx=0 ,Fy=0 and Fz=0 These calculations are shown in (Appendix VI) and results in: A: B: C: x: 581960 N x: -987176 N x: 0 y: -941307 N y: 374993 N y: -113686 N z: 116098 N z: -604801 N z: 409938 N Amsterdam Leeuwenburg Airlines Pagina 31
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2.3.5
Incident calculations
The incident involving the Boeing 747 of Nippon Cargo Airlines causes the Boeing 747 to disable the left body gear. The Boeing 747 had to make a touchdown on one body gear and two wing gears. This will change the forces on the aircraft. The weather conditions were not significant during this landing, so the crosswind component can be considered zero. The maximum force on the shock strut and the maximum impact height of the shock strut is already determined in the calculations of the touchdown limits. The relationship between the vertical touchdown velocity and the mass of the aircraft is now interesting, because an aircraft will not always touches down on MLW and the vertical ⁄ , therefore the equation to calculate the Normal force touchdown velocity is rarely is rewritten to the equation (formula 6) in which the mass is a function of the vertical touchdown velocity
(formula 6) Units: in kilogram [ ] in meters [ ] in Newton [ ] in meters per second [ ⁄ ]
= Mass = Maximum impact height of the shockstrut = Total normal force = Vertical touchdown velocity
Because the incident has lost one point of action for the total normal force can be recalculated by assuming that the Boeing 747 is a rigid body and has a linear spring, because of this the loss of the left body gear causes the Boeing 747 to touchdown with an angle (θ) to the ground and dividing the forces with the same angel ( θ) on the Boeing 747 (Figure 25. ).
Figure 25.
Forces during B747 Incident Landing
With the knowledge that one shock strut can take a maximum force of the maximum of the Boeing 747 with one of the left body gear malfunctioned. The force on the left wing gear shock strut is equal to the maximum force of the shock strut can handle during touchdown, or . With determined there are still three unknown forces. To calculate the other forces the ratio of is determined in which . How the ratio is determined can be find in (Appendix VII). With the ratio known the forces , and are calculated.
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Forces Ratio With be determined as: and the function mass of the vertical touchdown can now
The function is only interesting within the operation limits of the aircraft, for the mass is this between the Operation Empty Weight [OEW] of and the MLW of . The maximum vertical touchdown velocity determined by EASA in CS-25 at a velocity of ⁄ . The function is plotted (Figure 26. ) within the normal operation limits of the Boeing 747 during touchdown. The operation limits with the loss of the left body gear are reduced to the green area in the diagram. A touchdown within the red area will causes the shock strut to fail and the aircraft to crash. The Maximum Vertical Velocity [MVV] is now ⁄ to ⁄ and the maximum mass at MVV from reduced from to .
Figure 26.
Incident landing limits diagram
The reduced operation limits of the Boeing 747 during touchdown with a malfunctioned left body gear have no significant change to the landing procedures. A normal touchdown is the ⁄ and ⁄ and not even near the operation limits. vertical velocity between the
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3
Accident and conclusion
In this chapter all the consequences of the incident with the Boeing 747 will be discussed. Therefore, a better view of the accident is needed (3.1). Because of the damage the incident caused, the landing gear has to be repaired. But also the other parts have to be checked intensively, because it was a mechanical failure that causes the accident (3.2). As a consequence of the maintenance required for repairing and checking the landing gear, the aircraft will not generate benefits. Also the maintenance will generate extra costs. (3.3) At last, a conclusion of the accident with the Boeing 747 and all its mechanical and financial consequences can be made (3.4).
3.1
Synopsis
On September 14th, a serious accident with a Boeing 747, registration number JA01KZ, happened at Amsterdam Schiphol Airport. The cargo flew from Amsterdam Schiphol Airport to Milan Malpensa. When the crew selected „gear up‟ af ter take-off, the Engine Indication and Crew Alerting System [EICAS] displayed the mention ‘gear tilt’, followed by the mention ‘gear disagree’. The left wheel door was not closed, which was confirmed by the gear status on the upper EICAS display. The crew asked the air traffic control permission interrupt the climb, which was permitted. Then the crew verified the items of the non-normal checklist for the ‘gear tilt’ and ‘gear disagree’, but the situation did not change. An attempt to let the gear down, and pull it up, was without any success; the mentions at the EICAS did not disappear. The crew decided to return to the airport, where a smooth landing was made. On the apron, broken seals were visible on the left landing gear. Also the wheel doors and the connection from the landing gear to the aircraft construction were damaged. The shock absorber was found completely depressed, which means that there was no pressure in the shock strut. Also the tires did not reach the ground. The aircraft was delivered in June 2005 to the carrier and was about three months old. The damage was caused by over-extension of the left body gear. During the retraction of the landing gear, the tires of the over-extended gear have hit and damaged the construction of the aircraft. During the landing the shock solver was completely pressed and stayed in this situation. Disassembly revealed that the upper bearing carrier, snubber valve and follower tube were broken or torn. The upper bearing carrier, upper bearing sleeve and snubber valve were found lost in the outer cylinder. This snubber valve was broken on at least eight places whereby the horizontal flange was fully torn. The upper bearing carrier valves were broken close at the lower backpressure. The follower tube had several tear. The inner cylinder was bent and the upper bearing sleeve was damaged at several places. The deformation of the inner cylinder was due to the over-extension and caused by beating down of the upper cylinder sleeve in the lower bearing during the incident landing. Over-extension of the shock absolver occurred when the upper bearing carrier came loose from the inner cylinder. Traces of contact between the steering mechanism and the outer cylinder demonstrate that the extension of the shock absolver was limited by the steering mechanism. Only hampered by the steering mechanism, the shock absolver extended about 12 inches beyond the maximum value. Disassembly showed that the fracture of the upper bearing carrier was the beginning of the damage to the internal shock absorber components and subsequent over-extension. After disassembly of the shock absorber, Boeing received a „Notice of Escapement‟ (NOE) from the manufacturer of the landing gear, with a communication that their supplier had published that a number of upper bearing carriers had not received a correct heat treatment, and were supplied in annealed state. An electrical conductivity test was performed by Boeing Amsterdam Leeuwenburg Airlines Pagina 34
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on the two upper bearing carriers from aircraft JA01KZ. The test confirmed that both upper bearing carriers consist of annealed 2024 aluminium, which corresponded to the NOE of the supplier. All upper bearing carriers which had a faulty heat treatment were identified and the respective airlines where informed by Boeing, which offered support to swap the parts.
3.2
Maintenance consequences
To avoid problems, the aircraft needs maintenance. During maintenance some checks will be done to keep the aircraft in good conditions (3.2.1). In case something happens to the aircraft that has not been remarked during the checks, the maintenance has to be adjusted (3.2.2).
3.2.1
Maintenance checks
According to EASA an aircraft has to undergo some checks during its “life”. These checks are necessary to keep the aircraft in good conditions. There are four types of checks: 1. A-check 2. B-check 3. C-check 4. D-check ad 1 A-Check
After 600 hours of flying, an aircraft has to undergo the A-check. At average use, the check will take place once per month. During this check the most important systems will be checked critical. ad 2 B-Check
When the aircraft has flown for 1800 hours, the B-check has to be done. So this is once per three months. The B-Check is an expansion of the A-check. So the B-check is almost similar to the A-check however the B-Check is more thorough. ad 3 C-Check
Normally the C-Check will be done after one year or one and a half year. During this check all the cockpit panels will be opened and all the wiring will be checked. ad 4 D-Check
The last and most extensive check is the D-check. This check is obliged and has to be done each four or five years. The aircraft will be stripped totally. All the wiring and systems will be checked and replaced when necessary.
3.2.2
Maintenance change
The incident happened to a broken part of the shock strut. This problem could have been avoided if the shock strut was checked critically. In case this is not done, aircraft manufacturers need to rewrite the maintenance manuals. Furthermore it can be necessary to give the personnel more education to recognize problems earlier to avoid these kind of incidents during aircraft operation. In the case of the incident a part of the shock strut was broken. This means that all the Boeing 747‟s need to be investigated to see if the same part is not broken or shows indications of fatigue. In case the part is not reliable. It needs to be replaced, which takes a lot of time. This means that the aircraft will stay on ground for a longer time than normal, which is not desirable.
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3.3
Financial consequences
When an incident happens on board of an aircraft, there are always additional costs to solve the problems that follow on the incident. Most of these costs can be directly linked to the aircraft with the problems (3.3.1). The other part of additional costs may include hiring another aircraft or passenger compensation (3.3.2).
3.3.1
Additional aircraft costs
A lot of things can go wrong with an aircraft, but the costs of these categories will almost certainly rise when an aircraft hits problems: 1. Aircraft on Ground [AOG] 2. Parts 3. Personnel ad 1 Aircraft on Ground
AOG is the term used to tell that an aircraft is not able to generate profits. During AOG-time, aircraft maintenance or inspection will take place. In case of this incident, the whole shock strut of the body gear had to be replaced and all rubber seals of the struts were inspected and replaced if necessary. Replacing a shock strut is not a complex job, but the aircraft has to be lifted to be able to carry out the work safely and properly. ad 2 Parts
When something breaks on an aircraft, it has to be replaced. When looking at this incident, the costs of new parts are high: the whole shocks strut had to be replaced and the damaged aircraft structure, caused during retraction of the landing gear, had to be repaired. ad 3 Personnel
Additional personnel are needed to fix the breakdown. Not all maintenance personnel are qualified to do all repairs. In case of a complex job, an external specialist may be needed. The airliner may want to put extra personnel on the job which means a shorter Aircraft on Ground time. This is a consideration between costs and time.
3.3.2
External additional costs
These costs cannot be directly linked to the aircraft involved with the incident: 1. Another aircraft 2. Passenger compensation ad 1 Another aircraft
The passengers of the broken aircraft have to be transported. Otherwise, the airliner will lose its reputation. An aircraft has to be leased or hired to transport the passengers. Leasing means that an aircraft with personnel is hired. Hiring means just hiring the aircraft without personnel and supplies. Leasing is necessary if the pilots of the original aircraft do not have experience with the leased aircraft. ad 2 Passenger compensation
If the flight delays for more than three hours, passengers have a right to receive compensation. If the flight delays for less than three hours, passengers only have a right to get meals and refreshments.
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3.4
The Final Conclusion
After a closer look to the Boeing 747 landing gear, several calculations on the landing gear and a final analyze of the incident and its consequences, the conclusion can be made. The shock strut on the body gear failed because of a production failure. The lower bearing didn‟t have a heat treatment causing it to brake and allows the nitrogen gas to leak. The shock strut was now unable to absorb the forces of impact. The Boeing 747 without the body gear was able to land safely, because the Boeing 747 without one body gear can easily absorb the forces when touching down with normal procedures. The problem causes the airliner to replace the entire shock strut. All the other Boeing 747 needs to be investigated for lower bearings without a heat treatment and if necessary replace the shock struts lower bearing. The aircraft involving the incident will stay on ground for investigation and to replace the damaged shock strut, making the airliner to lose money on the replacing parts and disallowing the airliner to generates profits To replace the lower bearings of other aircrafts with a lower bearing that didn‟t had a proper heat treatment, the aircraft needs to remain on ground for a period. These aircrafts will also generates no profits when replacing the lower bearing
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Bibliography
Literature Boom, L.C. van den Tabellen en Formules, Werktuigbouwkunde niveau 4 1th druk Baarn, 2000 Van den Brink, R. Technische leergang: Hydrauliek 6th druk Amerongen, 2008 Budinski, K.G; Budinski, M.R Materiaalkunde Technici 2nd edition Schoonhoven, 1999 Callister, William D.; Rethwisch, David G. Materials, Science and Engineering 8th druk Currey, Norman S. Aircraft Landing Gear Design: Principles and Practices Marietta, Georgia, 1988 Lockheed Aeronautical Systems Company Dost, F Construeren Kernboek 1 3th druk Baarn, 2003 Dost, F Construeren Kernboek 2 3th druk Baarn, 2005 Hieminga, Jelle; IJspeert, Simon; van Langen, Pieter Landing Gear Amsterdam, 2010 Hogeschool van Amsterdam Domein Techniek Oxford Aviation Academy Aircraft General Knowledge Oxford, 2010 Pallet Aircraft Instruments and Integrated Systems Essex, 1992 Wentzel, Tilly Opbouw Projectverslag Amsterdam Leeuwenburg Airlines Pagina 38
Aviation Studies Amsterdam, 2009 Hogeschool van Amsterdam Domein Techniek Manuals
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Boeing & KLM Aircraft Maintenance Manual for 747-400 2004 Websites http://www.onderzoeksraad.nl/docs/rapporten/2006039_2005135_JA-01KZ_verkort_rapport.pdf 06-09-2005 http://www.airliners.net Photo’s http://www.boeing.com/commercial/airports/747.htm 12-2002 http://www.boeing.com/commercial/airports/faqs/arcandapproachspeeds.pdf Airport Reference Code and Approach Speeds for Boeing Airplanes 10-10- 2010 http://www.easa.europa.eu/agency-measures/certification-specifications.php EASA CS25 12-08-2010 Presentations Jelle Hieminga
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Appendices
I TYPES OF LANDING GEAR ......................................................................................................... 1 II GROUND LOOP ....................................................................................................................... 3 III LANDING GEAR STORAGE....................................................................................................... 4 IV LOCATION OF THE NOSE GEAR AND THE MAIN GEAR.............................................................. 5 V TYRE REGIONS ........................................................................................................................ 6 VI BODY GEAR CROSSWIND CALCULATIONS ............................................................................... 7 VII INCIDENT LANDING RATIO DETERMINATION ......................................................................... 9 VIII INVESTIGATION REPORT .................................................................................................... 11
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Aviation Studies I Conventional Types of landing gear
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Tricycle
Single main wheel
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Quadricycle
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Aviation Studies II Ground loop
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Aviation Studies III Landing gear storage.
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Location of the nose gear and the main gear
1 2 3
Nose Gear Wing Gear (main gear) Body Gear (main gear)
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Body gear crosswind calculations
Forcec of the croswind: Dx = 405215,7 Dy = 680000 Dz = 78766 Distances: Lady = 1.956 Labx = 4,73 Laby = 0,99 Lacz = 2,89 Labz = Lacz Angles:
X,Y surface: ∑
∑
∑
Y,Z surface: ∑
∑
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Incident landing ratio determination
Figure 27.
Forces during B747 Incident Landing
Determine the ratio of the forces on the shock struts of the B747 can be done by introducing . Using basic mechanics we can produce two equation: ∑ and ∑ . Which will result in: ∑ ∑ There are now two equations and three unknown forces, this means the unknown forces can‟t be determined. To determine the ratio of the three unknown forces a other equation has to be introduced. By assuming that the B747 is a rigid body and has a linear spring, because of this the loss of the left body gear the B747 will touchdown with an angle (θ) to the ground and divides the forces with the same angel (θ) on the B747. Because of the symmetry of the of the two wing gears the force in centre of gravity would be . Also the angel θ can be calculate by . With these two fact we can write as a function of and .
This equation can be written as:
With the three functions determined the ratio of the unknown forces can be calculated, this is done by using the matrix‟s.
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The ratio of the unknown forces can now be determined:
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