07w-landgear

POLITECNICO DI MILANO - DIPARTIMENTO DI INGEGNERIA AEROSPAZIALE AIRCRAFT SYSTEMS – LECTURE NOTES, VERSION 2004 Chapter 7 – Landing gear system

Chapter 7

Landing gear system

These lecture notes are available for the students of the Polytechnic of Milan for free download. No commercialisation allowed. Queste dispense possono essere gratuitamente scaricate da Internet dagli studenti del Politecnico di Milano. E’ vietata la commercializzazione.

7.1


7.1 Introduction The landing gear system includes: • strut; • shock absorber; • extraction/retraction mechanism; • brakes; • wheel; • tyre. Shock absorber and extraction/retraction mechanism may not be present in small airplanes. The landing gear is the interface of airplane to ground, so that all the ground loads are transmitted by it to the aircraft structure. There is then a high influence of the landing gear on the local structure, which must be taken into account since the initial design stage. The landing loads can reach factors of 2.5 for transport aircraft, 4.5 for small general aviation vehicles and higher for combat aircraft. The system must then have considerable mechanical resistance, which means in general that its mass is significant. Depending on aircraft category, this can range from 3 to 7% of the aircraft total mass. The main functions of the landing gear are as follows: 1. energy absorption at landing; 2. braking; 3. taxi control. Landing is the main sizing conditions for the system and its surrounding structure; braking also determines both vertical and horizontal loads that influence structural sizing. Taxi control includes steering and taxi stability.

7.2 General layout and design The layout of the landing gear system determines the load transfer to the structure, ground stability and control. With exception of gliders, which may have just a central fuselage wheel and tailskid, the landing gear arrangement is tricycle, consisting of a main landing gear group

located near the aircraft centre of gravity and a nose or tail landing gear (fig. 7.1). As a matter of fact, the tail element is almost obsolete, because the nose landing gear has a series of unquestioned advantages:

Fig. 7.1 – Nose and tail wheel configurations

• lateral stability in taxiing; • stability in braking; • steady touch down with no risk of

aerodynamic bounce; • high pilot visibility during taxiing; • horizontal floor (occupants’ comfort and

easy freight loading); • low drag during take-off acceleration.

A second observation concerns the number of struts. The most common configuration has double main landing gear and single nose gear. This can apply for


7.2


a wide range of aircraft weights, but normally for airliners beyond 300000 kg of maximum take off mass an additional main landing gear strut is located under the fuselage, or two additional struts are located under wing root area (fig. 7.2).

Fig. 7.2 – Landing gear typical layouts

The longitudinal position of the main landing gear group depends on the centre of gravity position and the tail cone shape. The struts must be aft enough with respect

to the most rear position of the centre of gravity, in such a way that during touch down a nose down moment is generated by the ground forces to the airplane (fig. 7.3), preventing aerodynamic bounce. Moreover the tail cone must not contact the ground, a condition that may easily occur during take-off (in fact a reinforcement or skid is normally

integrated in that part of the structure).

Fig. 7.3 – Main landing gear with respect to aircraft CG position and tail cone shape

TAIL CONE CLEARANCEMAX REAR CG POSITION

The lateral track of the main landing gear gives stability during taxing. The resultant force vector, due to weight and inertial forces, acting on the centre of gravity must fall inside the area delimited by the landing gear ground contact points, to prevent rollover. On the other hand the main wheels should not be too far from the aircraft centre line, to minimise roll and yaw instabilities during non levelled touch down and reduce wing root moment (if the landing gear is wing mounted).

Fig 7.4 – Taxing stability

WHEEL BASE

WHEEL TRACK

AIRCRAFT CG

CG RESULTANT

Fig. 7.5 – Telescopic and articulated leg

As far as the strut design is concerned, two solutions are mainly adopted: the telescopic and articulated leg, shown in fig. 7.5. The telescopic version is always lighter but requires higher ground clearance; then for small aircraft and helicopters the articulated version is more frequently adopted (from the figure it is clear that the piston stroke in the cylinder is lower than the wheel stroke).


7.3


7.3 Extraction and retraction A retractable landing gear is installed whenever a drag improvement is worthy. This means in all aircraft with exception of agricultural and small general aviation airplanes, where the installation of a movable landing gear would increase the costs beyond the requirements of the aircraft category. Landing gear extraction is a primary operation and always its actuation has high

redundancy. There are different solutions for the mechanism to obtain suitable landing gear movement. Some are schematically shown in fig. 7.6. Many solutions are based on the four bar linkage (cases A to C), where one bar is represented by the aircraft frame. In other solutions (case D) one bar end can slide along a slot. More complex kinematics include three-dimensional motion and the deflection of the bogie, that for the main landing gear of large airplanes is made of double tandem wheels. Actuators, normally of the hydraulic type, control the extraction/retraction operation. In general the mechanism should be designed in such a way that gravity and aerodynamic drag favour extraction; if the conditions on gravity and drag are satisfied, the extraction is possible with no power from the hydraulic system; a diagram reporting piston load vs. stroke will be of the type shown in fig. 7.7, with a constant sign: this means that retraction is obtained by applying a force to contrast drag and movable equipment weight, while extraction can initiate by gravity and be completed by drag. The area under the load line represents the necessary work.

If this is divided by the area of the rectangle defined by the max load and stroke, one obtains the efficiency of the kinematic mechanism, which commonly is in the range 70 – 80 %.

E

D

C

B

A

Fig. 7.6 – Some kinematic patterns

In both extracted and retracted configurations, the mechanism must be blocked (downlock and uplock respectively). A kinematic lock at extraction can be obtained by making the four bar linkage to reach its dead centre at full extraction. In any case a downlock based on a hydraulic or electric device is activated to prevent any movement of the strut when the

a

TNQE

Fig. 7.7 – Piston load-stroke diagram
aircraft is taxiing. An uplock is also
ctivated when the landing gear is fully retracted, to prevent non-intentional

hese lecture notes are available for the students of the Polytechnic of Milan for free download. o commercialisation allowed. ueste dispense possono essere gratuitamente scaricate da Internet dagli studenti del Politecnico di Milano. ’ vietata la commercializzazione.

7.4


extraction during flight, which also could be a dangerous operation at high velocity. Uplocks and downlocks are normally provided for the landing gear doors too.

7.4 Shock absorber layouts The main role of the shock absorber is to zero the vertical component of the airplane velocity during landing, with no rebound and limited load transfer to the vehicle structure (and occupants). Its secondary requirement is to allow a comfortable taxiing. Different types of shock absorbers are available, but when costs and dimensions allow, a hydraulic system is commonly used.

Very small aircraft with fixed landing gear may rely on the elastic properties of the landing gear legs and the damping effect of tyre sideslip on the ground, as schematically shown in fig. 7.8A. A low cost alternative to this method is to use an absorber made of a package of rubber blocks, which are compressed by the landing gear, so that the elastic effects is due to the

rubber compression and damping to hysteresis and local friction.

A) DEFORMABLE LEG B) HYDRAULIC SYSTEMS Fig. 7.8 – Some shock absorber solutions

The hydraulic solution is anyway the mostly adopted one, and fig. 7.8B shows some of the many possible versions. Substantially the system structure is made of a movable piston that, when loaded, compresses a gas (nitrogen) in a cylinder and causes an oil flow through orifices. The system elasticity is due to the gas transformation and the damping effect to the liquid pressure losses. The complexity of the system increases with the requirements. A list of main requirements for an efficient and functional shock absorber follows: • damping characteristics should be different in compression and extension; the

total orifice area can be changed by inserting check valves in some orifices or valves that throttle the orifices in one flow direction;

• during taxiing the absorber should be softer; in this case also controllable orifices can be used; for instance the internal structure of the absorber can be shaped in such a way that, when the leg extension is that of the aircraft is in normal ground operation, the orifices have maximum area;

• for high landing vertical velocities, the shock absorber responds with high reaction forces due to oil viscosity; to attenuate the load transfer to the airplane structure, relief valves may be installed on the absorber, then flattening the reaction curve;

• to increase the energy absorption in crash conditions, multi-stage shock absorbers can be used; the first stage works in normal operation, the second and further stages start compression when a high load is developed; in some application (small aircraft and helicopters), the second stage is a composite cylinder in series with the main stage (crash cartridge).

The systems till now described are passive devices, with some hydraulic and mechanical solutions to obtain efficient energy absorption and comfortable taxiing. More advanced solutions, still under development, are based on active control of damping. Since the damping force is function of the orifice geometry and oil


7.5


properties, a control of the damping characteristics of the shock absorber can be obtained in two ways: 1. control of orifices area; 2. control of fluid viscosity. The first solution is possible with the use of micro actuators that throttle the orifices. The second solution is possible with the use of electrorheological or magnetorheological fluids; these oils have properties sensitive to electric or magnetic fields respectively, and their peculiarity is to achieve quasi-plastic behaviour when the field intensity is increased. Generating the field in the orifices sections allows changing significantly the damping behaviour of the shock absorber by controlling the characteristics of a small volume of fluid. Both the systems are controlled on the basis of inputs from sensors of vehicle acceleration and velocity, and shock absorber conditions.

7.5 Shock absorber functioning principles In its most basic configuration, the shock absorber can be depicted as a hydraulic cylinder linked to an accumulator. When the piston moves, the oil from the cylinder passes through an orifice and compresses the gas in the accumulator, as shown schematically in fig. 7.9. According to this approach the reaction R of the shock absorber is function of the piston position and its time derivative, as follows:

Fig. 7.9 – Shock absorber schematic

representation

R

x

( ) 23

0

00

2 xkAAxAV

VpAkQpA &+

⋅−

=⋅+γ

ApR =⋅=

where: p = pressure on piston; A = piston area; pA = accumulator pressure; k = orifice pressure loss coefficient; Q = oil flow rate; p0 = initial accumulator pressure; V0 = initial accumulator gas volume; γ = polytropic exponent; x = piston stroke (x=0 for all extended shock absorber).

The resulting reaction is then the sum of a polytropic transformation, elastic and proportional to the stroke x, and a viscous term, proportional to the stroke derivative . As polytropic index γ, a value of 1.3 – 1.4 can be used, because the process is fast enough to be considered quasi-adiabatic.

x&

Fig. 7.10 shows an indicative plot of the reaction. The final part is related to the piston return to static equilibrium under the aircraft weight, which normally is in the range 60 – 70 % of the maximum stroke ∆.

x

Fig. 7.10 – Shock absorber reaction

RMAX

∆

R

The area under the reaction curve represents the work absorbed by the system. An interesting indication is given by the ratio between this work and the work that could be ideally absorbed with a constant maximum force RMAX and the maximum stroke ∆, called efficiency: These lecture notes are available for the students of the Polytechnic of Milan for free download. No commercialisation allowed. Queste dispense possono essere gratuitamente scaricate da Internet dagli studenti del Politecnico di Milano. E’ vietata la commercializzazione.

7.6


∆⋅

⋅= ∫

∆

MAXR

xdR0η (eq. 7.1)

The ideal absorber (η = 1) is a perfectly stiff-plastic system. A modern hydraulic shock absorber has and efficiency around 0.8 – 0.9.

7.6 Preliminary stroke estimation The max stroke of a landing gear shock absorber can be preliminarily estimated, even if many aircraft and landing gear characteristics are unknown. A simple energy balance, related to the vertical forces during shock absorber compression, can be applied to the landing aircraft considering kinetic and potential energy and the works developed by the shock absorber and lift force, as follows:

∫∫∆∆

⋅+⋅=∆+00

2

21 dxLdxRMgMvZ , (eq. 7.2)

where: M = aircraft mass; vZ = aircraft vertical velocity; g = gravity; ∆ = max shock absorber stroke; x = shock absorber stroke; R=R(x) = function of shock absorber reaction vs. stroke; L=L(x) = function of lift vs. stroke. The contribution of the tyre is not included in this discussion. The equation, as it is written, is not of immediate use, but a number of simplifying considerations can be done. First of all the work absorbed by the landing gear can be written remembering eq. 7.1 and considering the definition of the landing load factor n:

[ ]MgMgR

MgLRn MAXMAX +

≤+

=

then obtaining:

( ) ∆⋅−⋅⋅=⋅∫∆

10

nMgdxR η .

Lift function L(x) can be approximately considered to decrease linearly from its max value Mg to (1/3)Mg, due to the change of trajectory of the airplane during shock absorber compression and consequent decrease of the angle of attack. This allows approximating the integral as follows:

∆⋅⋅=⋅∫∆

MgdxL32

0.

Substituting into eq. 7.2 and solving with respect to ∆ brings to:


7.7


( )[ ] gnvZ

2311

2

⋅−−⋅=∆

η.

The procedure above explained is still used at preliminary stage for the evaluation of the max shock absorber stroke, but contains a series of approximations that cannot be accepted in further development stages of the aircraft design. A more detailed evaluation can be performed by a rough two rigid body model, where one rigid body is the aircraft and the other is the landing gear (legs, pistons, wheels, brakes and all parts connected to the moving equipment). Then, following the indications in fig. 7.11, a system of two differential equations can be written, as follows:

( ) ( ) ( )( ) ( ) ( ) (yFyFyxFyxFmgym

xLyxFyxFMgxM

TT &&&&&

&&&&&

2121

21

−−−+−+−= )+−−−−−=

,

where: M = aircraft mass less landing gear mass; m = landing gear mass; g = gravity;

( )yxF −1 = shock absorber polytropic function; ( )yxF && −2 = shock absorber viscous function; ( )yFT1 = tyre elastic reaction function; ( )yFT &2 = tyre viscous reaction function;

( )xL & = lift function. It is easy to find out that lift can be expressed as a function of the time derivative of x; in fact lift, in its

classic formula, is given by:

Fig. 7.11 – Multi-body representation

of aircraft and landing gear

x

y

FT2FT1

F2 F1

m

M

αα

ρ∂∂

= LCSvL 2

21

,

where: ρ = air density; v = aircraft velocity; S = aircraft reference surface; CL = aircraft lift coefficient; α = aircraft angle of attack. All the components of lift are constant during landing gear compression, with exception of α (and, in a very minor extent, of v); the angle of attack α, as shown of the aircraft pitch orientation αA with respectrajectory αT with respect to the horizon, and vertical velocity:

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Fig. 7.12 – Aircraft trajectory during landing

in fig. 7.12, is clearly given by the sum t to the horizon and the angle of its this last one is easily related to the

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7.8


vx

ATA&

+=+= αααα .

The above written system of differential equations must be numerically solved; a parametric analysis can be done by changing the shock absorber geometrical and mechanical characteristics and evaluating their influence on the load factor, stroke, etc.

7.7 Brakes Most airplanes are equipped with disc brakes, with a functioning principle similar to that of the automotive systems, but based on different sizing principles. Drum brakes are almost obsolete. The main components of a disc brake, which is usually powered by the hydraulic system, are as follows (fig. 7.13): • pressure plate; • stator discs; • rotor discs; • back plate. The complete equipment is housed inside the wheel, then occupying a large part of the room between the axle and the wheel. The stator discs are keyed to the axle, or anyway constrained in such a way to be only free to move along its axis. They bring, on the two flat surfaces, lining blocks, or pads, made of a mixture of metallic and ceramic materials. The rotor discs are keyed to the wheel, rotating then with it and being free to move along its axis. They are alternated to the stator discs, so that the assembly results a sandwich of rotor discs and stator discs packed together. The stator disc at one extremity, or back plate, is fully constrained to the axle and brings lining blocks on one side only.

ROTOR

STATOR

CYLINDERS

PRESSURE PLATE

BACK PLATE

AXLE

WHEEL KEY

WHEELBRAKE ASSEMBLY

Fig 7.13 – Disc brake

KEY SLOTS TO AXLE

KEY SLOTS TO WHEEL

STATOR DISCROTOR DISC

LINING BLOCKS

The stator disc at the opposite extremity, or pressure plate, brings lining blocks on one side only and, during braking, is pushed against the first rotor disc of the assembly by a series of hydraulic pistons. This action compresses the entire disc package, because rotor and stator parts are all free to move along the wheel axis, with exception of the back plate at one extremity, which contrasts the pressure.


7.9

Since the rotor and stator discs are in relative rotation, the contact between the lining blocks and the rotor discs will generate a tangential friction, responsible for braking. The higher the hydraulic pressure, the higher the normal contact force and then the friction force. When pressure is reduced, the discs are released by a series of springs.


The rotor discs usually have radial slots, to minimise disc deformation during heat up. The discs can be made of steel but, when affordable, carbon discs allow lower weight. For a short period in the 60’s they were made of beryllium, but its manufacturing costs and difficulties excluded it from standard use. The stator disc is usually made of steel. The lining is fragmented into sector blocks because it is made of a brittle compressed mixture of metals and ceramics, that may be broken if the pressure is not distributed uniformly on the entire surface. Brake sizing is based on heating during a single landing, considering that ventilation has a limited effect and neglecting the contribution of possible thrust reverse, flaps and spoilers. This means that a high part of the kinetic energy at landing will be converted into brakes heating; the part of brakes that is involved is often referred to as heat sink. This event can be expressed by a simple formula of energy balance:

TcmMvk v ∆⋅⋅=⋅ 2

21

,

where: k = fraction of energy converted to brake heat; M = aircraft mass; v = landing velocity; m = total heat sink mass; cv = heat sink specific heat; ∆T = temperature increment during braking. Considering that anyway there is a drag contribution to braking, k may often be approximated to 0.8. For sizing, M should be the max landing mass, v the max landing velocity and ∆T the difference between the allowable disc material temperature and the highest possible initial temperature. Materials with high specific heat and high operating temperature are of course preferred, because they allow a reduced total disc mass. Usually brakes are located in all the main landing gear wheels: the above-mentioned mass m is then related to all the brakes located in the wheels. Large aircraft may have braking nose wheels. A multiple disc brake is used whenever a high braking power is necessary, because the lining friction surface increases with the number of discs. Moreover a thick disc would not allow a suitable temperature distribution, but would be rather cold at the core and overheat in periphery. On the other hand, discs must be sized in such a way to withstand the high tangential stress that is generated by friction.

RR

RB

NM TM

Fig. 7.14 – Evaluation of the braking intensity

NN TM

NM


7.10


The braking intensity is a function of the brake geometry and, in a minor extent, of the aircraft geometry. From fig. 7.14 the braking torque C can be easily evaluated as a function of the hydraulic pressure and discs geometry, as follows:

BRApC ⋅⋅⋅= µ , (eq. 7.3) where: p = hydraulic pressure; A = total lining friction area; µ = disc friction coefficient, normally around 0.3; RB = radius of the lining block centroids. The braking force TM will be then given by:

RM R

CT = ,

where RR is the rolling radius (that depends on the normal reaction NM, tyre pressure and tyre geometry). Of course the braking force cannot increase indefinitely with pressure, but is limited by the tyre grip; this is defined by a factor µG that ranges from 0.9 for dry runway and tyre and asphalt in good conditions to 0.5 in case of wet runway and down to 0.1 for iced runway. Then TM is limited by:

MGMAXM NT ⋅= µ , (eq. 7.4)

where NM is the normal reaction of the main landing gear. In static conditions (airplane at rest) NM will be equal more or less to 90% of the aircraft weight, due to the conventional position of the aircraft centre of gravity. In braking conditions NM is lower and the inertia forces overload the nose landing gear. Depending on the longitudinal and vertical position of the centre of gravity, a simple algebraic system in the two unknowns NM and T can be set up and solved if any drag contribution is neglected.

MAXM

7.8 Anti-skid and auto-braking systems Deceleration is obtained through the friction between the braking wheels and ground. By increasing the braking system pressure, the braking torque increases according to eq. 7.3, and then also the tangential force between wheel and runway. The pilot controls the system pressure through the pedals. If this tangential force exceeds the limit indicated in eq. 7.4, the wheel tends to block, the wheel to ground friction coefficient switches from static to dynamic and decreases. Three effects result from the wheel blocking: 1. an increase of the stopping distance, due to reduction of the friction coefficient; 2. a loss of guidance control, due to the loss of tyre grip. 3. risk of tyre explosion. The anti-skid braking systems, which were developed after the Second World War, avoid wheel blocking by modulating the braking system pressure. The wheels are equipped with speed sensors and their signal is transmitted to a processing unit (the older systems were of course based on analogue technology, but worked on the same principle). The speed decrease of all braking wheels is monitored and compared to each other and with predetermined deceleration patterns. If one wheel These lecture notes are available for the students of the Polytechnic of Milan for free download. No commercialisation allowed. Queste dispense possono essere gratuitamente scaricate da Internet dagli studenti del Politecnico di Milano. E’ vietata la commercializzazione.

7.11


is decelerating more intensively than the others, or outside a predetermined boundary, the event is interpreted as incipient wheel locking. A servo-valve then releases the braking pressure of that specific wheel, by allowing it to spin-up to the speed level sampled prior to slippage deceleration, and then the control system starts to find the new modulating pressure. Older systems were actually on-off control systems, because they operated an intense reduction and increase of pressure; current systems have a smooth and refined control, capable of maintaining the wheel speed at a limited skidding level that maximises the ground friction. The automatic braking system is often associated with anti-skid system. In auto-braking the pilot does not need to use the pedals to brake, because a pre-set braking deceleration is automatically applied. With the auto-braking armed in landing mode, brakes will be automatically activated a few seconds after touch down, or at spoiler extension, then providing a constant deceleration; the intensity is pre-set by the crew before landing. The system works also in take-off mode: if the pilot makes any operation typical of a rejected take-off (extends the spoilers, or moves the thrust lever back to idle, or operates the thrust reversers), auto-braking is triggered at maximum level. In any case the pilot can overcome the auto-braking by pressing the pedals beyond a predetermined excursion. The anti-skid system is always operating, also during automatic braking.

7.9 Tyres and wheels The tyres are the aircraft-to-ground interface and are then the regions where braking and steering forces are generated, also contributing in a minor extent to shock absorption. The normal force N is generated by the tyre pressure p and the intersection area A between tyre and ground:

ApN ⋅= Braking force was already considered in the previous paragraph; its max value is given by the normal force and the ground-tyre grip factor as indicated in eq. 7.4. Now, if one defines the ground friction factor as the ratio between the longitudinal braking force and the normal force, this depends on different factors: tyre material

and conditions, ground material and conditions, longitudinal slip and vehicle velocity. The longitudinal slip k is given by the ratio between the sliding speed vSL and the vehicle speed v:

vRv

vv

k RSL ⋅−==

ω

where ω is the wheel rotational speed and RR the already

mentioned rolling radius. As shown in fig. 7.15, the maximum value of the friction factor is obtained around a 10% longitudinal slip and the friction factor decreases when the vehicle velocity increases.

Fig. 7.15 –Friction factor vs. longitudinal slip and vehicle velocity


7.12


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A lateral force arises when the tyre has a slip angle with respect to ground: this is responsible for steering. A law similar to eq. 7.4, given by the normal force and a side friction coefficient, can approximate this force:

Fig. 7.16 – Side friction coefficient

β

λ

10 5

1.0

0.5

NS ⋅= λ .

This coefficient, λ, is a function of the slip angle β and is linear for angles lower than 5°, then tending rather rapidly to the ground friction factor µG, as indicated in fig. 7.16.

Aircraft tyres can be both with internal tube or tubeless. Fig. 7.17 shows some details of the tyre structure. The external layer in contact with the ground is the tread, made of rubber, thicker than the automotive version, because it is subject to severe wearing during spin up at landing. The side external layer, from the tread to the beads, is the sidewall, still made of rubber but smooth. The internal multiple layer structure is the cord body. Each layer may be considered a composite structure, made of parallel nylon cords imbedded in rubber. Since the cords are capable to withstand only tensile loads, adjacent layers have orthogonal cord directions, which give the body a uniform stiffness and strength.

TREAD

Fig. 7.17 – Tyre section

BEAD TOE

CORD LAYERS

BEAD WIRES

SIDEWALL

CORD BODY

The beads are the edges of the tyre, connected to the wheel rim. They contain a ring of high strength steel wires covered by the rubber and by chafing strips for reinforcement; the wires also serve as anchoring line of the cords. Tyre designation follows one of the two rules as follows: AxB and AxB-C, where A, B and C represent respectively the overall outside diameter, cross sectional width and rim diameter; measures are in inches. The wheels have the double function to carry the tyre and, in many cases, house the brakes. Aircraft wheels are made of aluminium or magnesium alloys. There are substantially two types of wheels: split wheel and demountable flange wheel. The first one is made of two halves bolted together and with the connection line sealed by an o-ring. The second one is made of a main wheel body closed on one side by a bolted flange. The wheel is then mounted on the axle by tapered roller bearing, capable to withstand high radial and lateral loads. These are the wheel parts that mostly require maintenance, basically consisting in cleaning and lubrication. Some wheels for military aircraft are equipped with fusible plugs, or pressure relief valves, activated by the overheating that may occur during the spin up in high velocity landing conditions.

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07w-landgear

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