SIMULATION OF AIRCRAFT LANDING GEAR DYNAMICS USING FLEXIBLE MULTIBODY DYNAMICS METHODS IN SIMPACK

Prashant Dilip KhapaneInstitut für Aeroelasticity

DLR - German Aerospace Center

SummaryIn a variety of mechanical systems friction inducedvibrations are a major concern. The aircraft landing gearis by nature a complex multi-degree-of-freedomdynamic system. It may encounter various vibrationmodes which can be induced by brake frictionalcharacteristics and design features. These brake inducedoscillations can lead to very high loads in the landinggear and brake structure which may result in passengerdiscomfort and sometimes in component failure. Alongwith the serious fore and aft oscillations of a landinggear, often referred to as gear walk, chatter, squeal,shimmy and other vibrations in aircraft landing systemsare not only annoying and disconcerting but can alsoaffect the stability of the plane during take-off, landing,and rolling.In this paper, simulation of such an unstable andcomplex phenomenon during aircraft groundmaneuvers is done to detect vibrations in aircraftlanding gear. A commercial multibody simulation toolSIMPACK is used for this purpose. The article is basedon work done in cooperation between DLR andLiebherr Aerospace.

keywords - Landing gear dynamics, Aircraft grounddynamics, Gear walk and other instabilities.

1 Introduction1.1 Landing Gear Dynamics - Problem DefinitionThe term ‘landing gear’ indicates one of the mainfunctions of the gear, namely the containment of thelanding impact but it fails to describe the other mainfunctions, namely the provision of means for the aircraftto maneuver on the ground, taxi and take off [5]. Thepredominant task of an airplane is no doubt to fly withthe best performance achievable. It must not beforgotten, however, that it will spend a good part of itslife on the ground. Landing gear dynamics, especiallyshimmy and brake-induced vibrations, is one of theproblems faced today by the aircraft community.Though they are not catastrophic, can lead to fatalaccidents due to excessive wear. It can also shorten thegear life and cause discomfort to the pilot andpassengers. Structures of modern aircraft becomeincreasingly flexible. The main reasons are slenderfuselages that frequently arise from the stretching ofexisting aircraft, see [16], and the use of new, light-weight structures and materials that influence thevibrational properties of fuselage and wings. Not onlyunsuitable combination of structural stiffness, damping,

and pneumatic tire characteristics but also an unluckycombination of brake system design with the tirephysics can produce a serious vibration problem [18].Shimmy may be caused by a number of conditions suchas low torsional stiffness, excessive free play in thegear, wheel imbalance, or worn parts. Brake-inducedvibration includes conditions known as gear walk,squeal and chatter which are caused by thecharacteristic friction between the brake rotating andnon-rotating parts. This will be explained in details laterin Section 1.3. Although equations for representing various parts of alanding gear are well established, solving the problemsmanually with mathematical programmes can be slowand laborious. Simplifications made to reduce problemsize may introduce inaccuracies such that a designmodification to correct a problem in one area causesunforeseen vibration in other parts of the structure. Inmany cases, vibration problems may not be uncovereduntil physical prototypes are built and tested, addingconsiderable time and expense to the productdevelopment cycle.However, many commercially available computer-aided engineering tools have made it possible to testsome of the problems in the design phase by simulatingthe landing gear impact and rolling. An adequatemodelling of tire and brake dynamics is an importantissue for the analysis of the behavior of an aircraftduring ground maneuvers as potentially unstablephenomenon such as gear walk and shimmy may occurin these phases. At the German Aerospace Center(DLR), simulation of such an unstable and complexphenomenon during aircraft ground maneuvers is doneto detect vibrations in aircraft landing gear. Acommercial multibody simulation tool SIMPACK isused for this purpose. It allows the import of externalmodels from other codes such as Nastran. Landing gearparts modelled in Nastran are used to represent thevibration modes accurately. The goal of this project is tostudy brake and gear interaction and the relatedvibration phenomena including low frequency gearwalk, wheel chatter, and brake squeal.

1.2 Landing Gear Vibrations - State of the ArtBoth civil and military organizations have put greateffort into optimization of the landing gear and itscomponents. Simulation will play an ever increasingrole in further improvement of new aircraft and theintroduction of new ideas and systems [15]. There existsome specific publications in the area of landing geardynamics and simulation. An early overview of

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computer simulation of aircraft and landing gear isgiven by Doyle [7]. Shepherd, Catt, and Cowling [3]describe a program funded by British Aerospace for theanalysis of aircraft-landing gear interaction with a highlevel of detail, including brakes and anti-skid, steeringcontrol, to simulate standard hardware rig test(dynamometer and drop tests) as well as flight testsinvolving ground contact. Barnes and Yager [2] discussthe use of simulators for aircraft research anddevelopment. Two publications of the IAVSD(International Association for Vehicle SystemDynamics), Hitch in 1981 [10] and Krüger et al [15] in1997 and one at NASA Langley Research Center byPritchard [23] are state-of-the-art overviews of aircraftlanding gear dynamics. Modeling tires is a science foritself: In 1941, von Schlippe and Dietrich [25], analyzedthe shimmy motion of an aircraft tire and described theinteraction of tire and landing gear leg stiffness with tireforces analytically. Pacjeka [20] used a similar tiremodel based on the stretched string concept anddeveloped simple derivatives representing first orderlag with a relaxation length and a gyroscopic couplecoefficient as parameters. For the description of steadystate slip characteristics empirical formula have beendeveloped by Bakker and Pacjeka [1], [20] usingtrigonometric functions, this model is known as “MagicFormula”. Recently this formulation has been extendedto include dynamic tire behavior [21]. The performanceof braking system is an important consideration in thedesign of landing gear system. Luber et al [18] haveshown in their experimental work that adjustablecontrol of brake torque is a sensible way to improveaircraft ground handling and performance. Krüger et al[15] also mention the need of a good model of theantilock braking system dynamics. Yager et al [30]under the FAA/NASA friction programme discuss theevalution of friction measurements for different runwaysurfaces. General requirements of a good antiskid brakesystem are described in an SAE paper [32]. Jun [12] inhis paper studies ABS control system for automobileswith different control methods and points out that it isdifficult for one control system to get optimal controlaccuracy and robustness under all kinds of brakingconditions. Tuney [26] has proposed a novel method ofantiskid control for transport aircraft which results insmoother braking and hence improved passengercomfort. One of the early investigations on brake-inducedvibrations was reported by Edman [8]. The reportcontains both experimental and theoretical studiesexplaining the basic phenomena and pointing out theimportance of design considerations. Only linearsolutions were considered in this report, however, it wasrecommended that non-linear friction characteristics beincluded in future theoretical studies. The dynamometertests revealed a connection between the chatterfrequencies and the wheel rotation. Theoretically,decrease in chatter amplitudes were noticed for increasein strut damping, rolling radius, and total mass. Biehl[3] during the development of a digital program to

simulate the DC-9 aircraft main landing gear found outthat brake torque was the primary contributor to chatterand squeal vibrations. J. Enright [9] discusses asimplified technique for laboratory dynamometersimulation of landing gear-brake dynamics whichenable it to be used as a matter of routine to study brakedynamics accurately. Hamzeh et al [11] discuss thefriction induced instabilities in a simplified aircraftbrake model. Denti and Fanteria [6] in their workdiscuss the effects of different tire models and brake onthe longitudinal dynamics of aircraft landing gear. Asfar as simulation of landing gear dynamics is concernedtwo reports from the BF Goodrich Aerospace by Rooket al [24] and H. Vinayak et al [28] are state of the art inthe area.

1.3 Friction Induced Vibrations in Landing GearSystem - BackgroundThe aircraft landing gear, a complex multi-degree-of-freedom dynamic system may encounter vibrationmodes which can be influenced by brake frictionalcharacteristics and design features [9]. As airplane grossweights are increased, the braking performancerequirements have become more severe. Theperformance requirements include normal landing/refused takeoff braking distance limits, thermalrequirements on the landing gear components,durability of friction material and overall weightconsiderations. Due to superior performance of carbon,increasing numbers of airplanes are using carbon brakes[19]. Although carbon has a higher specific heatcapacity, a higher friction coefficient, is lighter inweight and has a better wear rate compared to steel, it ismore prone to vibrations. Brake friction acts in thepitch-plane of the landing gear system, and so affectsthe stability of three pitch-plane modes of vibration asshown in Fig. 1.

Brake Squeal can be defined as torsional vibrations ofnon-rotating components about the axle in thefrequency range of 100-1000 Hz. The root cause of thismode is largely unknown, however, the erratic vibrationphenomenon from flight test suggest that this mode iscaused by the friction characteristics of brake material.it produces very high oscillatory loads on the landinggear/brake structure and can sometimes cause failure.

Brake Chatter is defined as the torsional motion of therotating parts of the brake-wheel-tire assembly aboutthe axle and against the elastic restraint of the tire. It istypically above 50Hz and coupled with the squealmode.

Gear Walk is defined as the cyclic fore and aft motionof the landing gear strut assembly about a normallystatic vertical strut center line. This motion is caused bytire-runway interface friction loads which deflect thelanding gear. It may be sometimes induced by the anti-skid system and could cause passanger discomfort.

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Figure 1: Major Vibration Modes and Frequencies [9]

A valid landing gear simulation is one having the same dynamic response to brake torque as the actual gear.This means that the simulated gear must be designed tohave the same equation of motion in its walk modeunder the action of speed-dependent braking friction[9]. The traditional way to simulate the gear has been touse alternate structure, a dynamometer fixture such thatone of its fundamental modes duplicates the dynamiccharacteristics of the gear walk mode of interest. In thispaper, the flexible multibody dynamics methods areused for the simulation of such an unstable and complexphenomenon during aircraft ground maneuvers to detectfriction-induced vibrations in aircraft landing gear.

2 Modeling Landing Gear System 2.1 Landing Gear as a Rigid Multibody SystemFig. 1 shows the schematic of a simple form of nose

landing gear as a multibody system. In SIMPACK thismultibody system is represented by simple bodyelements such as main fitting, the shock tube, and twoor four wheels, respectively. The shock absorbers (oleo)are located between shock tube and main fitting. Alllanding gears have one translational degree of freedomfor the shock absorber and one rotational degree offreedom for each wheel. The main landing gears include an additional bogieattached to the shock tube with a rotational degree offreedom along the y-axis with 4 wheels attached to it.To model landing gears of large aircraft such as A380main landing gear which has 6 wheels, a bogie, and apitch trimmer in addition can be more complex. To model the system successfully one needs to defineproper force elements to simulate the behavior of thewhole system. SIMPACK has an in-built library ofmany force elements and it is also possible to write theso called user-routines which gives additional freedomto user to model different systems.

2.2 Force ElementsThe force elements describing the landing gearcharacteristics have been modeled in detail for this workby means of so called user-routines in SIMPACK.While the equations of the physical phenomena as suchare valid independently from the exact aircraft type andcan be taken from standard textbooks [5], [22], theparameters for the force elements are usuallyproprietary. The data used in this work are those whichwere prepared for the Flexible Aircraft Project [13].

2.2.1 Hydropnematic OleoFor transport aircraft the main task of vertical energydissipation is almost exclusively taken over by an oleo-pneumatic shock strut. This device combines a gasspring with oil and additional friction damping [15].Damping force is provided by oil flow forced throughan orifice by vertical strut motion. Often the oil flow is“controlled” by means of metering pin.The gas spring is represented by a law of polytropicexpansion [19]

with spring force Ff, pre-stress force F0, oleo stroke s,Figure 1: Schematic of a simple nose landing gear

B_main_fitting

B_shock_strut

B_tir

e

B_tir

e

Isys

F_tire F_tire

J_transl_z

J_rotatoric_y

J_0_DOF

y

x

B_ : body

J_ : joint

F_ : force element

F_oleo

J_3_DOF

Ff F0 1 ssm------

–

n– cκ⋅=

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oleo gas length sm, polytropic coefficient n ( ),and a correction factor ck. The pre-stress force F0 can becalculated from the initial pressure in the fully extendedoleo. The correction factor ck, typically between 0.9 and1.1, allows the adjustment of the curve to measureddata. The minimum and maximum stroke limits aremodeled by stiff springs. A typical function for a oleospring is shown in Fig. 2.

The properties of the passive damper are determined bythe laws describing the flow of a viscous fluid, e.g. oil,through an orifice.

with oleo stroke velocity , oleo damping force Fd, anddamping coefficient d.A typical function for a damper is as shown in Fig. 3.

Stick friction is of great importance especially for themain landing gears. At taxiing, the gears often remain instick mode for several seconds, leaving the tires as theonly flexible suspension element between airframe andrunway. This internal friction force results from frictionof internal seals in the oleo depends on the internal gaspressure and therefore on the oleo spring characteristics.

where is the seal friction force, is the sealfriction coefficient, is the oleo spring force, and isthe oleo stroke.

2.2.2 Tire The tire model developed at the DLR takes vertical,longitudinal, and lateral effects into account. The tireconnects the wheel to the runway when the aircraft is onthe ground. The simulation force element measures theheight of the wheel axis with respect to the excitation.This rolling radius rr is subtracted from the nominal tireradius rnom to determine the tire deflection dz

The wheel is modeled as a separate body with arotational degree of freedom. The longitudinal andlateral motion of the body with respect to the runway isused to calculate tire slip and torque on the wheel.The vertical force Fz is calculated first. It is a functionof the tire deflection dz. Using a third-order polynomialwe find

where c1, c2, and c3 are selected to match measured tiredata. A linear spring can be simulated by setting c2 andc3 equal to zero and providing the spring coefficient inc1. For longitudinal forces the slip calculated in the maintire element is used. It is defined as the ratio between thehorizontal velocity of the wheel contact point and theaxle forward velocity,

where W denotes wheel spin and vx the wheel axleforward velocity. The friction coefficient mRW of the runway is a functionof slip. An approximation of the functional relationbetween mRW and slip is displayed in Fig. 4

Typical values for m1 and m2 range from 0.4 to 0.9 fordry runways, depending on the runway type.The friction coefficient mRW is needed to calculate thelongitudinal tire force Fx which is a function of thevertical tire force Fz and mRW

The resulting torque Ty on the wheel is calculated usingthe effective rolling radius rr,eff which can be set to a

Figure 2: A typical curve set for oleo spring

Figure 3: A typical curve set for oleo damper

1 n κ≤ ≤

0

200

400

600

800

1000

1200

1400

1600

-0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Air-

sprin

g fo

rce (

KN

)

Oleo stroke (m)

Oleo-spring force

Fd s·( )sgn d s·2⋅ ⋅=

s·

-600

-400

-200

0

200

400

600

800

-1 -0.5 0 0.5 1

Dm

aper

forc

e (K

N)

Oleo stroke velocity (m/s)

Oleo-damper force

Fsf µsf Fs s( )sign dsdt-----

⋅ ⋅–=

Fsf µsfFs s

Figure 4: Functional relation between friction coefficient and slip

dz rnom r–r

=

Fz c1dz c2dz2 c3dz

3+ +=

sliplongitudinalvx rrΩ–

vx--------------------=

µRW

slips1 s2

µ1

µ2

Fx µRW Fz⋅=

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constant value or, if desired, can be calculated duringthe simulation using the equation

The torque Ty is then

For the asymmetric landing and ground maneuversimulations it becomes necessary to calculate the lateralforces and aligning torque coming on the tires. They arefunctions of lateral slip. The lateral slip is calculated bythe following equation [20],

The lateral force can be calculated by means of an inputfunction which is a function of the lateral slip and in turnthe yaw angle or slip angle. Lateral force and aligningtorque as a function of yaw angle is shown in Fig. 5.

2.3 Modelling Flexible Landing Gear

2.3.1 FEA InterfaceElastic bodies are transferred into SIMPACK using themodal approach. An elastic body is set up in a FEA tooland is there subject to an eigen value/ eigen vectoranalysis. Mode shapes and nodes are transferred into theMBS model. The resulting deformation is a linearsuperposition of the mode shapes, Fig. 6. The spacial motion of an elastic body is divided into aglobal motion, characterized by the movements of thebody reference frame, and its elastic deformation whichis expressed by the displacements of all (infinite) bodypoints in relation to the body reference frame, Fig. 7.The global motion equals the rigid body motion of aclassical rigid MBS body. The location and time

dependent body deformation vector u(r,t) is split by aseparation function often referred to as “Ritz approach”into a location dependent displacement matrix F(r) andthe corresponding time dependent so-called elasticstates q(t):

.Each element of the vector q represents the influence ofone eigen mode on the total response. The displacementmatrix consists of mode shapes of eigen value and staticload analyses. The eigen- and static modes as well as thestiffness matrix are computed in FEA; additionally,geometric stiffening effects, e.g. due to centrifugalforces, can be included. Depending on the application often a relatively smallnumber of low frequency modes are sufficient torepresent, e.g., a static bending shape of an elastic bodywith sufficient accuracy. During the transfer toSIMPACK, the user is enabled to select only thosemodes which are necessary to describe the bodyflexibility for the individual load case. Thus, the fullFEA model of system is replaced by a relatively smallset of linear equations.The interface has been implemented for the FEA codes

Figure 5: Lateral Force and aligning torque as a function of slip angle respectively

rr eff, rnom dz 3⁄( )–=

Ty rr eff, Fx⋅=

Sliplateralvyvx-----=

Fy

Yaw angle

Yaw angle

Mz

Figure 6: Elastic bodies in SIMPACK

Figure 7: Definition of an elastic body in SIMPACK

FEMBS- Modal reduction:

Selection of significant

- Marker set-up:Determination of nodes

- Calculation of

Large body motions and

eigen- and static modes

adopted as MBS-markers

small elastic deformations

MBS-Model

coupling terms:

MBS-Simulation

FEA-Results

FEA-Model

FEA-Calculation

e.g.inertial

undeformed

deformed body

r P(t=0)

P(t)u(r,t)s(t)

body fixed reference system

system

body

u r t,( ) Φ r( )q t( )=

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NASTRAN, ANSYS, ABAQUS and MARC [17], [29].

2.3.2 Modelling Flexible Main Landing Gear forEbraer190The landing gear model is prepared in Nastran as abeam model with the help of data exchanged with theindustry partner Liebherr for a newly developedregional aircraft. The landing gear is modelled fordifferent strokes and the results of the modal analysisare compared to the model received from the Liebherrand fine tuned to get similar eigen shapes and eigenfrequencies.

Figure 8: Beam model representation

To create the model in Nastran following data given inTable 1 is used.

The wheel axle is attached with the rotational degree offreedom around the y-axis at the end of beam numbertwo. The wheels are represented by condensed masses.The results of the modal analysis for zero stroke are

given in Table 2.The nastran model is then imported in SIMPACK asexplained in the Section 2.3.1

3 Aircraft Braking Stopping of the aircraft being their primary task, brakesare also used to control speed while taxiing, to steer theaircraft through differential action, and to hold theaircraft stationary when parked and during engine run-up. They are generally fixed to the main gears only andadd substantial weight to them. Most airplanes use diskbrakes in conjunction with an advanced anti-skidcontrol system. In the work done related to the Flexair project at theDLR, two different braking algorithms have beenimplemented and tested for different rolling cases.

3.1 Dynamic BrakingConsider the forces and torques on one of the landinggear wheels, as shown in the Fig. 9.

where Fn is the normal force on the tire, Va is theforward velocity, and Tb is the braking torque. If wewrite down the general form of force equations they willlook like this

where is the braking force coefficient [13], , are the forces in x and y direction respectively, isthe moment in y direction, is the yaw angle, is thedeformed tire radius. According to JAR standards [31]for dynamic braking the following curve shown inFig. 10 is used as a constant torque acting between theaxle and the inertial system.

3.2 Antilock Braking SystemAn approximation of functional relation betweenfriction coefficient and the slip ratio is as shown inFig. 11 [26] which is similar to Fig. 4.This coefficient depends mainly on the slip ratio,

Table 1 Geometrical data used for the Landing Gear Nastran model

BEAM #1 BEAM #2

D1 0.09 0.008

L1 1.469 1.188

t1 0.008 0.008

E1 2.1E+11 2.1E+11

Table 2 Results of modal analysis in Nastran

MODE NUMBER

EIGEN-FREUENIES HZ

EIGENSHAPE

1 10.10 Torsion, Lateral

2 11.22 Fore-aft, Side stay tangential

3 13.25 Torsion, Side stay radial

4 45.69 Second Lateral

5 62.31 vertical mode of the wheels

Figure 9: Schematic of one wheel during braking

Tb

Va Fuselage

Strut

Fn

Fb

Fx Fl ζ( )cos× F2 ζ( )sin×– µb abs Fn( )× ζ( )cos×–=

Fy Fl ζ( )sin× F2 ζ( )cos× µb abs Fn( )× ζ( )sin×+ +=

My Fl rz× µb abs Fn( )× rz×–=

µb Fx FyMy

ζ rz

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normal force, forward velocity, and runway conditions(damp, rain, ice, snow). The nature of this dependenceis not well understood even after numerousexperiments. If we assume that other factors are fixedthe friction coefficient can be represented as a functionof slip ratio as shown in Fig. 11 and has a uniquemaximum. During braking it is possible that the wheelsget locked. This occurs when the applied braking torqueexceeds the friction torque between the tire and thesurface, reducing the wheel angular speed to zero, i.e.the slip ratio becomes equal to one. In such a case theairplane should be equipped with an Antilock BrakingSystem which prevents wheel locking. In addition itshould also try to maximize the friction coefficientbetween the tire and the runway surface, in order tominimize the stopping distance. Achieving a shorterstopping distance becomes critical on wet or icyrunways and during rejected take-offs (RTO). It mayalso be designed to enhance passenger comfort throughreducing strut vibrations and improving tire wearthrough smoother braking, as secondary objectives [26]. For this purpose a simple and somewhat idealized anti-lock braking algorithm has been implemented at theDLR which works as follows:A sensor at the landing gear wheels measures the actualspeed and the slip which is fed to the control systemalong with the desired velocity and the desired slip. Ifthe actual velocity is greater than the desired velocityand the actual slip is not equal to the desired slip thenthe antilock braking system is activated. There is a bangbang controller which brings ABS into action when the

slip falls below the desired level and releases the brakeswhen the slip increases. Fig. 12 shows the schematic ofan ABS algorithm where v_a and slip_a are actual speed

and slip respectively, v_d and slip_d are desired speedand slip respectively, om_a is actual rotational speed ofa wheel, and r is the radius of the wheel.

4 Main ResultsEngineers designing one of the most critical system ofan aircraft, the landing gear system, face the dauntingtask of tracking down and correcting vibration sourcesin it. In the last decade or so OEMs have cut down thetime to deliver the aircraft. So they do not have theluxury of iteratively refine the design by means ofexperimental testing of the prototype. Dynamicsimulation of the entire landing gear system is a fasterand very accurate way, thanks to the CAE tools that areavailable today. It can also be used quickly for differentaircraft system as the basic modelling tasks such asbrake-algorithm and tire model are ready to use oncefinished. To understand the aircraft ground dynamics and todetermine realistic ground loads a simulation ofoperational cases with an accurate model is thusnecessary.In this paper, a ground handling scheme has beenexamined and has been evaluated by means of variousimportant ground maneuvers. Different modelling tasksincluded development of a tire model with lateraldynamics to calculate the cornering forces during acurved run, braking system with an ABS algorithm andits effect on the aircraft performance in terms ofstopping distance and passenger comfort. The goal ofthe project is also to study landing gear and brakeinteraction and the related friction induced vibration. A

Figure 10: A typical dynamic braking torque curve

Figure 11: Friction coefficient as a function of slip ratio

Tb

Time

Slip Ratio = 10 1

µ-peak

µrw

Wheel Locking

Slip RatioFigure 12: Schematic of an ABS algorithm

Aircraft statespace model

v_aom_ar

Determine slip

slip_d

(slip_a)

v_d v_a > v_d

No brakes

Hydraulic lag

v_a,slip_a

slip_a < slip_d

Bang-bang controller

Friction element

Braking torque

appliedbrakingtorque

Nobraketorque

No

Yes

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flexible landing gear was also modelled for thatpurpose.

4.1 Simulation CasesFor simulating the performance of different brakingalgorithm complete MBS model of the aircraft and mainlanding gear are used. The different simulation cases areshown in Table 3.

4.2 BrakingA good ABS algorithm should avoid locking of thewheel and at the same time maximize the frictioncoefficient between the tire and runway surface, thusminimizing the stopping distance. It may also takepassenger comfort as a secondary objective intoconsideration. As explained in the Section 3.2, the ABSalgorithm implemented in SIMPACK is used for theoptimization of the slip value while braking. Fig. 13 shows how the slip is optimized to get the

maximum amount of braking possible without thewheel skidding or locking. As explained in Section 3.1, dynamic braking has alsobeen examined in the project as an alternative brakingalgorithm. The following results clearly show that theABS algorithm is a better alternative for braking as itprovides better passenger comfort and reduced friction-induced vibration, and is stable.Along with the shorter braking distance, as a secondaryobjective the ABS system may also be designed toimprove the passenger comfort. Fig. 14 shows howABS algorithm reduced forces in x direction at the main

landing gear attachment and is stable when it comes toacceleration at the attachment point. It shows that withthe ABS algorithm smooth braking is achieved with thereduced strut vibrations and in turn the better passengercomfort.

4.3 Friction-induced Vibrations Gear walk, as explained in the Section 1.3, is cyclicfore-aft motion of the landing gear assembly about anormally static vertical strut-center line. Gear walkinstability is illustrated by the time histories of gear-deflection, brake torque, and wheel-tire footprint(speed) as shown in Fig. 15.

Table 3 Different Simulation Cases

SIMULATIONS IMPORTANT RESULTS

Braking slip optimization, passanger comfort, and stability

Friction-induced vibrations

friction-induced vibrations study, passanger comfort, and stability

Figure 13: Slip optimization with ABS algorithm

-0.10

-0.05

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.00 2.00 4.00 6.00 8.00 10.00 12.00

Time (s)

Slip

Rat

io

Actual SlipDesired Slip

Figure 14: Comparison of ABS and dynamic braking algorithm

-0.25

-0.20

-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

0.00 1.00 2.00 3.00 4.00 5.00 6.00

Time (s)

Def

lect

ion

at th

e G

ear

Wal

k Se

nsor

(m)

ABSDyn Braking

-20.00

-10.00

0.00

10.00

20.00

30.00

40.00

50.00

0.00 1.00 2.00 3.00 4.00 5.00 6.00

Time (s)

Acc

eler

atio

n A

F A

ttach

men

t Sen

sor

(m/s^

2)ABSDyn Braking

-400.00

-300.00

-200.00

-100.00

0.00

100.00

200.00

300.00

0.00 1.00 2.00 3.00 4.00 5.00 6.00

Time (s)

Forc

e ac

ting

at th

e LG

Atta

chm

ent (

KN

)

Dyn BrakingABS

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For this multibody simulation a full aircraft model withflexible landing gear at the attachment point is used.Braking action is initiated at the end of 2 second rollingin forward direction untill the desired speed is achieved.Though initially the gear deflection increases whenbrakes are applied the amplitude is does not grow ascompared to the dynamic braking due to the slip-optimization principle behind the anti-skid algorithm.Once the desired speed is achieved the deflectionreduces very fast and is almost zero.

5 ConclusionsIn order to simulate important aircraft groundmaneuvers and brake-gear interaction different toolssuch as a tire model with lateral dynamics effects, asimple but effective ABS algorithm are implemented inthe commercial multibody simulation code SIMPACK.The simulation comparison shows that antiskidalgorithm is more effective in terms passanger comfort,the gear vibrations, and the stability. A flexible landinggear model was developed in order to study the friction-induced vibrations in the landing gear. In future, usingthe work done as a base, brake gear interaction will besubject to closer studies.

ACKNOWLEDGEMENT

I would like to thank Dr. Krüger for his help andconstructive remarks, his expertise with the landinggear dynamics made the work presented in the paperpossible. I would also like to thank Mr. Grapherr andMr. Thorn at the Liebherr Aerospace for their inputs.

6 References[1] E. Bakker, L. Nyborg, H.B. Pacejka: A New Tyre

Model With an Application in Vehicle DynamicsStudies. SAE 890087, 1989.

[2] A.G. Barnes, T.Y. Yager: Simulation of AircraftBehavior On and Close To the Ground,AGARDOgraph AG333;1998.

[3] F.A. Biehl: Aircraft Landing Gear Brake Squealand Strut Chatter Investigation, The Shock andVibration Bulletin, Naval Research Laboratory,Washington, D.C., January 1969.

[4] T. Catt, D. Cowling and A. Shepherd: ActiveLanding Gear Control for Improved Ride Qualityduring Ground Roll. Smart Structures for Aircraftand Spacecraft (AGARD CP 531), StirlingDynamics Ltd., Bristol, 1993

[5] N.S. Currey: Aircraft Landing Gear Design: Prin-ciples and Practices, AIAA Education Series,Washington, 1988.

[6] E. Denti, D. Fanteria: Effects of Different Modelsof Tire and Brake On the Aircraft Landing Gear,IFASD 2003.

[7] G.A. Doyle: A Review of Computer Simulationsfor Aircraft-surface Dynamics. Journal of Air-craft, 23 (4), 1986.

[8] J.L.Edman: Aircraft Vibrations Due To BrakeChatter and Squeal, WADC Technical Report 55-326, Wright Air Development Center, AirResearch and Development Command, USAF,Wright Patterson Air Force Base, OH, October1955.

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Figure 15: Gear Walk Instability

-0.12

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