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NASA/TM- 1999-209143
ARL-TR- 1976
An Overview of Landing Gear Dynamics
Jocelyn I. Pritchard U.S. Army Research Laboratory Vehicle Technology Directorate Langley Research Center, Hampton, Virginia
May 1999
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NASA/TM- 1999-209143
ARL-TR- 1976
An Overview of Landing Gear Dynamics
Jocelyn I. Pritchard U.S. Army Research Laboratory Vehicle Technology Directorate Langley Research Center, Hampton, Virginia National Aeronautics and Space Administration Langley Research Center Hampton, Virginia 23681-2199
May 1999
The use of trademarks or names of manufacturers in the report is for accurate reporting and does not constitute an official endorsement, either expressed or implied, of such products or manufacturers by the National Aeronautics and Space Administration or the U.S. Army.
Available from: NASA Center for AeroSpace Information (CASI) National Technical Information Service (NTIS) 7121 Standard Drive 5285 Port Royal Road Hanover, MD 21076-1320 Springfield, VA 22161-2171 (301) 621-0390 (703) 605-6000 An Overview Of Landing Gear Dynamics by Jocelyn Pritchard Abstract One of the problems facing the aircraft community is landing gear dynamics, especially shimmy and brake-induced vibration. Although neither shimmy nor brake-induced vibrations are usually catastrophic, they can lead to accidents due to excessive wear and shortened life of gear parts and contribute to pilot and passenger discomfort. Recently, NASA has initiated an effort to increase the safety of air travel by reducing the number of accidents by a factor of five in ten years. This safety initiative has spurred an increased interest in improving landing gear design to minimize shimmy and brake-induced vibration that are still largely misunderstood phenomena. In order to increase the understanding of these problems, a literature survey was performed. The major focus of the paper is to summarize work documented from the last ten years to highlight the latest efforts in solving these vibration problems. Older publications are included to understand the longevity of the problem and the findings from earlier researchers. The literature survey revealed a variety of analyses, testing, modeling, and simulation of aircraft landing gear.
Experimental validation and characterization of shimmy and brake-induced vibration of aircraft landing gear are also reported. This paper presents an overview of the problem documented in the references together with a history of landing gear dynamic problems and solutions. Based on the assessment of this survey, recommendations of the most critically needed enhancements to the state of the art are given.
Problem Definition Landing gear vibration includes self-induced oscillations referred to as shimmy and brake-induced vibration. Shimmy may be caused by a number of conditions such as low torsional stiffness, excessive freeplay in the gear, wheel imbalance, or worn parts. Brake-induced vibration includes conditions known as gear walk, squeal and chatter which are caused by the characteristics of friction between the brake rotating and nonrotating parts. Squeal refers to the high frequency rotational oscillation of the brake stator assembly whereas chatter and gear walk refer to the low frequency fore and aft motion of the gear.
Shimmy History and Background It is generally acknowledged that the fundamental contributions to understanding shimmy were made by the French whereas the Germans were responsible for much of the subsequent systematic development. In France and Germany shimmy was regarded as a problem that should be dealt with early in the design stages. In the United States, the general tendency was to fix a problem after it had occurred. The U.S. literature is quite extensive but was not considered to be representative of a systematic development.
There were also significant contributions from other countries, including Russia whose papers did not begin to appear in the literature until the 1930's. (Ref. 1) The first fundamental contributions toward understanding the shimmy phenomenon emerged from the automobile industry in France around 1920. Of particular significance was that given by Broulhiet published in 1925. (Ref. 2) His observations on the role of tire mechanics on shimmy behavior are still followed today. While Broulhiet concentrated his attention on the tire, Sensaud de Lavaud (Ref.3) formulated the first fundamental shimmy theory. His theory incorporated a rigid tire that disregarded any effect of ground forces on the tire. Fromm (Ref. 4) also studied wheel shimmy in automobiles and recognized the similarities between the wheel vibration problems in automobiles and aircraft. He was one of the first to identify the vertical elasticity of the tire as the main contribution to the vertical displacement of the vehicle. His earlier investigations on rolling slip of deformable wheels led him to study the effect of sideslip or yaw of the rolling wheel due to lateral forces. Fromm's studies of lateral forces acting on the wheels led to the realization that these forces were coupled with the shimmy oscillation through the moment of the forces about the longitudinal axis. Either damping or build-up of the initial disturbance would occur depending upon the phase shift between the coupled motions. Von Schlippe and Dietrich (Ref. 5) made significant progress in defining the yaw angle and the swivel angle as arbitrary functions of time. Their tire concept was simplified as a thin band with lateral elasticity leading to simple expressions for the forces and moments. This eventually became known as the String Theory.
Some of the earliest investigations of shimmy problems in aircraft took place at Wright Field in Dayton, Ohio. In 1944 (Ref. 6) initial taxi testing of a fighter aircraft (Me 309) exhibited severe shimmy of the nose gear. Design of new piston shimmy dampers in coordination with landing gear manufacturers eliminated shimmy entirely for this aircraft. Other efforts at Wright Field (Ref. 7) included analysis development and validation by test. One such effort utilized a steel drum to perform studies on various airplane tires to correlate lateral deformation and lateral tractive force to banking angle and lateral-load force. In 1950, even though the shimmy problem had been studied for many years it was still a very common occurrence in automobiles, trailers, and aircraft. Physical control of shimmy was available in hardware such as shimmy dampers, but little was known about the cause of shimmy. Wright Air Development Center (WADC) started a program in 1951 to study the problem of shimmy and to learn the deficiencies of earlier efforts to combat the problem. The program included the development of a theory of shimmy, computer studies, experimental research on a laboratory model, and full scale testing. Even though earlier efforts traced the shimmy problem to the mechanical properties of the pneumatic tire, it was during this study that Moreland (Ref. 8) theorized that the tire support flexibility was a more important consideration than the tire mechanics. He contended that a shimmy theory based on the elastic properties of the tire alone was insufficient and that torsional and lateral rigidities, the wheel moment of inertia, and the weight of the strut were also critical in defining system stability. (Ref. 9) Only a fairly complete model of the structure including the tire properties could properly evaluate the stability of the system.
During the 1970's many investigators attributed landing gear vibration to wheel and tire imperfections and road surface roughness. References 10 and 11 found that when the frequency of the normal load oscillation was approximately twice the shimmy frequency, a decrease in the shimmy stability would occur. This loss of stability was primarily due to the variations of tire parameters with normal load.
Other investigations found that shimmy motion was large when the frequency of wheel shimmy was close to the frequency of the wheel rotation. This resonance occurred at a particular forward velocity that was a function of the trail of the system. Studies concluded that braking forces tended to increase stability and that traction forces decreased stability even though these effects are small. By 1980 gear designs were having to adapt to increasing gross weight of the aircraft, increasing aircraft flexibility, higher ground roll speeds, and substandard landing fields. By now it was apparent that in order to fully understand the shimmy problem it was necessary to account for airframe flexibility and the coupling between the gear and airframe, and to weigh the effects of free play in gear components and damping devices on the system.
There were many new areas of landing gear design that had emerged and needed attention. For example, ground simulators were being developed for pilot evaluation of steering capabilities that created a need for accuratemathematicalmodelsandflight testing for simulatorverification. Structuraland systemtesting wereperformedboth during andafter the designstageto substantiate the strengthandperformanceof the gear. Tire braking andcorneringdatawerepracticallynon-existentduring this time andoversimplification of many systemparameters madefor inaccuratemodels. Shimmy dampingrequirements often conflicted with good high-speed directionalcontrol. Compositecarbonbrakeswereintroducedand anti-skid systems were being usedto optimize the braking performanceand prevent skids and tire blowouts. Air-over-oil shock struts typically provided shock absorptionwhere the dampingwas a function of the shock strut
stroke.(Ref. 12)
Airframe Flexibility Effects In references 8 and 9 Moreland characterizes shimmy by defining the relationship between a single non-dimensional quantity called the inertia ratio and the dynamics of the airframe. In most cases he studied, when the simplest systems were stable, the higher order systems were not less stable. To precisely describe the system and the shimmy phenomena, the mathematical model required 5 degrees of freedom: tire deflection, swivel angle, strut deflection, damper-linkage strain, and airframe motion. Comparisons of various systems were made with and without tire elasticity. The stability of the gear was influenced by 15 system parameters that were brought together in the shimmy analysis by a seventh order characteristic equation of the model. Routh's stability criterion was applied to the equation to study the effects of changing gear parameters on the stability of the gear. Plots of dimensionless quantities such as velocity ratio, damping ratio, mass ratio, trail ratio, and inertia ratio defined the stability boundaries.
In 1960 at NASA Langley Research Center a simple experimental model of an aircraft was used to study the effects of gear and airframe variables on nose landing gear shimmy behavior. (Ref. 13) A dynamically scaled skeleton model of an aircraft with a single main skid and castering wheel was towed on a moving belt runway at constant speed. The simplicity and size of the model made it relatively easy to vary model parameters for different configurations. This enabled evaluation of the gear through repeated observations of the model's response to varying conditions. Nose wheel steering and forms of shimmy damping were shown to have a stabilizing effect when the wheel was at an angle to the direction of motion.
Another study of the role of airframe dynamics in shimmy analysis is described in reference 14. This report describes the theoretical and experimental study of the F-101 and F-104 nose landing gear shimmy. The dynamic response characteristics of the airplane fuselage were simulated during these tests with a mechanical fixture attached to an overhead platform that served as a mounting structure for landing gear.
Frequency response characteristics were obtained experimentally by applying a periodic input to the fuselage at the nose gear station and recording the resultant bending and torsional motions. A graphical technique was used to fit the theoretical frequency response data to the experimental data to determine the parameters of the simulator from the transfer functions. Fuselage simulators were then designed and used to test the F-101 and F-104 aircraft systems.
Reference 15 presents an analytical method to determine the random vibration response of a flexible aircraft caused by runway irregularities transmitted through the main gear struts. The runway profile is represented as a stationary Gaussian random process. The statistical or power spectral approach yields only an average or root mean square value of the response. This method is useful for estimating fatigue effects in airframes and landing gear and has value for investigating the effect of parameter variations in the average sense. The major drawback of this approach is that in order for the probability distribution to be independent of the position along the length of the runway, the profile has to have the same degree of roughness at all points which is usually not the case. In 1976 a simplified model of the longitudinal vibration of a landing gear strut during landing and spin-up of the wheel was developed. The influence of the lateral forces on the rotating wheelsduring landing was studiedwhile accountingfor the interface betweenthe strut and airframe.(Ref. 16) The elastic forcesproducedin the strut were calculatedfrom landinggearandaircraft fuselagemodes.
Therehavebeenrecentefforts to approach the landing gearshimmyproblemas a "flexible landing
gearinteractionwith flexible aircraft" problem as in reference17. This paperpresentstheir approachto integratingthe flexible propertiesof the aircraft into the shimmyinvestigationof noselanding gearduring the development phaseof a fighter aircraft.Taxi testsof theprototypeindicateda severe shimmyoscillation at a frequencyof 25.7 Hz. After consideringseveralpotential fixes, it was found that increasingthe pressure level in the nosegeartire removedthe oscillation. Higher ordermodelsof landinggearlegswere usedto includeall the featuresthat areneededto representthe interactionswith other subsystems during groundroll andlandingsimulations. The mostimportantparameters in this shimmyinvestigationwerethe relaxationlength or length of the groundcontact areaof the tire and the damping(friction) of the piston againstthe cylinder. The elastic fuselagemodeswere not consideredto be important if the leg mode frequencies werewell separated from the aircraftmodefrequencies.
Role of Tire Theories
As previouslymentioned,tire mechanics areintimatelyrelatedto the shimmyproblem. Tire models werevery difficult to define dueto the influenceof the groundforceson tire behavior.Sincethe problemof shimmyand self-excitedvibration of landing gearhasexistedfor sucha long time, many theorieson the elastic deformationof tires had been proposed. There was much controversyover the advantages and disadvantages of thesetheoriesdueto erroneous conclusions presented in previouspaperson tire mechanics and shimmy. (Ref. 18) The tire theorieswere categorizedinto two basic groups.(Ref. 19) The major differencebetweenthe two groupsis the numberof coordinates usedto describethe tire deformation. The first group yielded the simplesttheory becausethere was no tangible model. The tire was taken into accountby consideringits kinematicalbehaviorin the overall system. This group includesMoreland's point contacttheory that assumed the interactionbetweenthe ground and the tire could be treatedas a singlepoint. (Ref. 8) This theory accountsfor the effect of sideforce on the yaw angleof the tire and a time delaybetweenthe applicationof the sideforce andthe steadystateyaw. (Ref. 18) The secondgroup utilizes a physicalmodel of the tire. The mostrenownedexampleof this group is the stringmodel.(Ref.5) In this theory,the tire is approximated by anelasticstring stretched aroundthe outeredgeof the wheeland attached by elasticsprings. The elasticrestoringeffect of the tire is basedon a linear principle that the deviationfrom the original swivel angleis proportionalto the lateral deflectionof the tire. The tire force andmomentare found by integratingthe infinitesimal effects of the deformations.(Ref. 18) This theory assumes purerolling of the tire. Pacejka(Ref. 20) improvedthis approximationby using multiple stretched stringsto simulatethe width of the tire andnonstationary propertiesof the rolling tire are included. Most theoriesarelinear which meantonly small perturbationsandno sliding in the contactareaof the tire are addressed. Thesemethodsareconsidered to be effective for low frequencyapplications.Pacejka'smethod is particularlyapplicableto vibrationproblemsof steeringandsuspension systems of vehiclesathigh speed and frequency. Simple equationsare derived that relate inertial forces to dynamic displacements and externalgroundforcesto staticdisplacements of the tire centerplane.His analyticalresultscomparedwell with experimental data.
In 1957Smiley (Ref.21) developeda summarytheorythat combinedmany featuresof the existing
theoriesandincludedcomparisons with experimental data.The summarytheoryis a minor modificationof the basictheory of Von SchlippeandDietrich (Ref. 5) that includestilting of the tire in moredetail while omittingPacejka'srefinements necessary for wide tires. The kinematicrelationsof thelateral deflectionof the tire ground-contact centerpoint with the corresponding wheelcoordinatesof lateral deflection,swivel angle,andtilt anglearegiven for a rolling tire. Informationabouttire distortion is utilized in the derivation of thesekinematic relations. Equationsfor the forces and moments on the wheel together with the kinematicrelationsestablishthe equationsof motion for a rolling wheel. The theory wasnot validatedfor full-scale conditionsandthere wasno reliable methodat that time to predict the elasticcharacteristics of tires that wereneededfor shimmy analysis.Discrepancies werecontributedto tire hysteresiseffects and othernonlinearinfluenceshowever,therewereno strongindicatorsthat nonlineartheory wasnecessary to predict stability boundaries. References18 and 19provide comparisons of the two basictheoriesfrom a validation standpointas well as from computationaland clarity aspects. It was found that both of these fundamental linear theoriespredictedshimmycharacteristics of landinggearsystems if the inputparameters wereproperlychosen.
Brake-induced Vibration Technological advances in aircraft led to smaller brakes with more energy to dissipate, lighter shock struts with higher strength materials, and increased flexibility all of which increased the likelihood of vibrations of landing gear due to braking action. Brake-induced vibrations in landing gear may be induced for several reasons. The self-excitation of modes due to negative damping arises from variations in the coefficient of friction with instantaneous slip velocity. Forced oscillations are due to irregularities in the friction surfaces. Self-excited whirl vibration is caused by eccentricity of rotating and non-rotating brake parts. The Information Report on brake dynamics of the SAE Committee A5 in 1997 (Ref. 22) categorized these landing gear dynamic vibration problems. A uniform method of classifying brake characteristics was given in terms of coefficient of friction, dynamic variation of friction coefficient, wear variation, and torque versus pressure characteristics. Self-excitation may be induced by large variations in the stiffness of brake components, poorly phased feedback in the anti-skid system, and tire lock-up corresponding to maximum drag. Solutions to these vibration problems included provision of basic aircraft parametric data from airframe manufacturers for analysis and testing. Data collection from flight testing is needed for skid control on wet and dry surfaces at shimmy speeds. Brake history and frequency and amplitude of vibration are desirable in order to characterize a pattern.
One of the early investigations on brake vibration was reported in reference 23 where a study of landing gear vibration due to brake chatter and squeal during taxi and landing was performed. The report contains both experimental (static, dynamic, and taxi tests) and theoretical studies explaining the basic phenomena and pointing out the important design considerations. Static tests were conducted to determine parameters such as weight and mass moments of inertia, damping ratios, and spring rates that were needed for analytical studies. Dynamic tests included brake and strut dynamometer testing that measured drag loads, brake pressure, wheel speed, side force, fore and aft motion of the axle, and angular acceleration of the axle. Taxi tests involved a number of relatively uncontrollable variables which is why it is difficult to achieve the same results with the dynamometer tests. Systems of individual masses, springs, and dampers were used to represent the landing gear to aid in studying the effects of friction characteristics of the brake on the dynamic stability of the gear. Only linear solutions were considered in this report, however, it was recommended that non-linear friction characteristics be included in future theoretical studies. The dynamometer tests revealed a connection between the chatter frequencies and the wheel rotation.
Theoretically, decreases in chatter amplitudes were noticed for increases in strut damping, rolling radius, and total mass. Another effort to study landing gear chatter and brake squeal vibrations was at the Naval Research Laboratory during the development of a digital program to simulate the DC-9 aircraft main gear slowing to a stop. (Ref. 24) The analytical model represented the fore and aft motion of the gear with accompanying rotationalmotion at the gearaxle. Comparisonof computedresponses andmeasured data indicated reasonablesimulation accuracy. The analysis showed that brake torque was the primary contributor to chatterand squealvibration. Increasingthe braketorquein combinationwith diminishing brakerotor to statorangularvelocity instigatedthe vibration. This functioneffectively produceda negative dampingthat sustained or increased the vibration amplitudes.Attenuationmethodsincludedusing a mix in the brakelining that ensureda flat braketorquefunction. Vibration absorberswere also suggested even thoughanexcessive weightpenaltyexistedfor chattervibration absorbers.
At Wright PattersonAFB dynamometer testswereperformedto simulatenormal serviceconditions
experienced by the brake on the T-38A aircraft for the purposeof investigatingthe brakecharacteristics (Ref. 25). Brake torque, hydraulic pressure,dynamometerflywheel speed,and test wheel speedwere measured during dynamometer testsperformedon a B. F. Goodrich2-727 brakeassembly at threedifferent decelerationand brakeinitiation speeds to determinethe kinetic friction and relative rubbing velocities.
The experimentaldata and the analysisboth indicatedthat the systemwas stable. Dynamometertest temperatures wereusedto investigatethe temperature response of the brakerotor andstatorduringbraking.
A comparison to the analyticalmodel showedgoodreliability for predictingrubbing surfacetemperatures.
Predictingthesetemperatures accuratelyis advantageous to designers due to the potentialfor strut chatter andmetallurgicaldesigncriteria. All testswereconductedon new brakes,however,it was suggested that thesetestsandanalyses shouldalsobe performedon worn brakesto observeany differencesin the results.
More recentinvestigations emphasized the effect of the variation of friction coefficientwith slip velocity betweenrotors andstatorsasin reference 26. This report alsogivesan overviewof the stability andmodal interactionscausedby nonlinearnegativedampingat the brake friction interface.It was emphasized in reference27 that the braking systemshould be analyzedas a global systemrather than as separate components dueto the couplingbetweenthe parts.Nonlinearmodelingof aircraft landinggearbrakewhirl andsquealwasdiscussed in references 28-30.Thesestudiesfound that systemstability could be alteredby changes in the brakefriction coefficient,pressure, stiffness,geometry,andvariousbrakedesignparameters.
Modeling and Simulation
Traditionally the emphasisin analytical prediction capability was on landing impact loads since thesewere consideredto be the largest that the aircraft would experience. The oscillatory loads from taxiing weredeemedas secondary.The emphasiseventuallyincludedthe requirementto more accurately model the gear to improve the dynamic response predictions.The state-of-the-art in modeling techniques for landing gear prior to 1980 was summarizedin reference31. There was a need for experimental verification of the details of the gascompression processanddeterminationof the parameters that affect this processsuchashydraulicfluid compressibility,fluid-gasmixing, anddeformationof the gearchamber.
The orifice coefficientswereconsidered extremelyimportantfor calculatingthe responseof the gear and very accurate procedures wereneededto determinethesevaluesfor hydraulic damping. Sincethe orifice flow is highly unsteady,problems arosewhen steadyflow hydraulic force models were used in taxi simulations.Most modelsincludedfriction asdry or Coulombfriction but frictional forcesweresometimes left out of the analysisbecause a good methodfor measuringtheseforceswas not known. Normal forces on thebearingsthatcreatefriction forcesweredependent on the geargeometryandthe wheel loading. For flexible modelswherethe deformationof the gearwasincludedin the analysis,determination of the normal forces becamevery complex.The tire was modeledas a simple spring (linear andnonlinear) with point contactwith the groundandlinearviscousdamping. Tire stiffnesswasrepresented by staticload deflection curves either provided from experimentor manufacturer.The tire interface with the ground and the geometryof the tire footprint wasan areathatneededmoreattention. Numericalsimulationscouldbe used with someconfidenceto predictfatigueandpeakloadsif the analysishadbeenevaluated with taxi or drop testdata. Modeling andsimulationefforts over the pastten yearshavebecomefairly sophisticated as input data hasbeen carefully scrutinizedand experimentsare conductedto validate models.Efforts to model nonlinearities such as damping and friction characteristicswere becoming more prevalent. Several examplesof modelinggearsystems aregivenbelow.
In reference32 an analysisof fatigue of light aircraft landing gear using randompropertiesand surfaceprofiles wasdeveloped.The systemwasmodeledasa linear, 1DOF nonstationary vibrating system referredto asa randomparametric vibration problemthatusesa recentlydeveloped randommatrix method.
Reference33 is a follow up to the work described in reference3 with nonstationary dampingandrandom nonstationaryloadsincluded. The random matrix methodwas shownto be better suitedfor this type of problem than a hybrid Monte Carlo technique. In reference34 modeling andparameteridentification of singledegreeof freedomstructuralsystemsare investigated.Experimentswere conductedto measure the free response of thesestructuralsystemsandthe measurements wereusedto formulatesystemmodelsand parameters. Models include a linear, dampedoscillator and a nonlinear shock strut with and without friction forces. Resultsshowedthat it is possibleto model and identify a physical structuresuch as a dampedoscillatorwith dampingeffects. Comparisons betweenthe response predictedby the modelandthe response measured experimentallyagreedfor the first few seconds of motion but then deteriorated in later stages. This was duein part to ill-conditioning of the equationseventhough experimentalmeasurements wereusedto identify the model parameters of the system. Models developedin references 35-39 include the effects of linkage dynamics,dampermounting characteristics, Coulomb friction, nonlinear tire, air spring, oleo dampingforces, torsional freeplay, and spring hardeningeffects of bending and torsional stiffness.
An example of non-linear modeling involved an A-6 Intruder nose gear. The model included
nonlinear effects in the pneumatic air spring, stick-slip friction, velocity squareddamping, geometry governeddischargecoefficients,andtire model. Analytical resultswere in excellentagreement with test data that was acquiredat NASA Langley ResearchCenter.(Ref. 40) Reference41 describeslinear and nonlinearanalysismethodsappliedto investigatethe shimmy of a simplenosegearmodel.The nonlinear shimmymodelconsisted of torsionaldynamicsof the gear,the forces,moments, andlateralelasticityof the tire using elastic string theory. Resultsshowedthat the occurrenceof shimmyincreaseswith increasing velocity, lower torsionaldamping,andincreasingvertical force. The numericalsimulationresultsconfirm the stability of the linear systemand provided additional information concerningthe nonlinear regions.
Reference42 is an exampleof a model that includesan error feedbackcontrol law for anti-skid braking simulationusedin determiningthe effectsof structuralparameters on gearwalk instability. The effect of longitudinal stiffnessof the tire, the vertical dampingof the tire, and the inclination angleof the strut on gearwalk stabilitywereinvestigated.
There were also efforts to study and comparemodeling techniques. Reference43 developed
simulationsand analysesof conventionaloleo-pneumaticlanding gear during taxi and landing impact.
Simplification of the model andthe effect of certainelementomissionson the model fidelity werepointed out. For example,constantspring anddampingcoefficientswill not provide a realistic simulationeffect.
The hydraulicforce is a function of meteringpin andstrutclosureandthereforecannotberepresented by a singleforce closurerate. This curve is different for acceleration anddecelerationphases. Reference44 gives a review of two landinggearshimmymodelsdemonstrating the use of the Morelandtire model and the Von Schlippe-Dietrich tire model. The modelswereusedto perform a parametricstudyof theeffect of numericalvariation of severalinput parameters on the stability of the gear. A comparisonis madeof the analyticalresults to experimentaldata showinggood agreementof the limit cycle oscillation frequency.
Both analyses wereconsidered to be successful in determiningthe stability characteristics of landing gear.
The resultssuggested thatdynamic modelingof the gearwould significantly improve the accuracyof the analyticalpredictions. It was discoveredthat the spring stiffnessvalueswere stability critical parameters and if the fuselageflexibility effects are not taken into account,the measuredvalues of the stiffness parameters maybe in errorby asmuchas3 timesthe actualvalues.
General-purpose computerprogramswere alsobeing developedto model completelanding gear
systems.An exampleof this type of modelingis describedin reference45 wherethe Dynamic Analysis and Design System(DADS) program is used to model the responseof two types of landing gear on damagedand repairedrunways during landing, taxiing, and take off. Both the cantileveredand the articulatedmodelsincluded nonlineareffects suchas the hydraulic orifice damping,pneumaticair spring, bearingfriction forces in the strut, anda tire-load deflectioncurve. Thesemodelscould be usedas stand alonegearon a runway surfaceor combinedtogetherto simulatean entireaircraft. The dynamicanalysis andsimulationshowresultssuchas strutloadsand strokefor different runwayprofiles. The plots indicate stickmotion of the strut andthe animationcapabilityin DADS givesan advantageous view of the response of thegearrolling over a runway.
Finite Element Modeling
Finite elementmodelinghasbecomea useful tool for studyingdynamic stability issuesof landing gear. Reference27 describes finite elementmodelingof the whirl and squealmodesof landing gearand braking systems. Correlationbetweenthe analysisand various systemcomponenttests as well as the performanceof the completemodel and actual systemduring operationare performed. Models include landing gear, wheels,brakes,and tires. Design sensitivity studiesare also used to evaluatecomponent changes duringthe designprocess.A feasibility study of computingnonlinearfinite elementsimulationsof whirl andsquealdynamicsis discussed in reference28. DYNA3D is an explicit finite elementcodethat usesthe centraldifferencemethodto integratethe equationsof motion in time. The model includesthe aircraft inertia andtire flexibility effectswithout addingextensivecomputationalexpense. Advantages of using this method over more commonly used linear complex finite elementanalysisare evident in the nonlinear transient analysiscapability, the ability to model nonlinear stiffnessand damping effects of hydraulicfluid, modelingwhirl andsquealinstabilitieswith negativedamping,andprovisionfor modeling a sliding interface.
Software Development
Reference46 usesa library of componentsbasedon finite element methodswhich range from
beamsand springs to very specific landing gear elementssuch as shock absorbers,actuators,flexible sliders,and flexible wheel elements. Customizationof elementsis also availablethrough user defined elements.Resultspresented includesimulationof a droptest, taxiing on repairedrunway,tire burstduring rollout, and shimmy of a two-wheeledcantilevergear. Reference47 developeda very comprehensive landinggearmodel andsimulationsoftwarecapabilitythatintegrates landinggearandbrakingsystems with an aircraft for the purposeof parametricdesign. The softwarecan be usedduring the conceptualdesign stageor to evaluateproposedmodificationsfor an existing configuration. All phasesof aircraft landing geardynamicshavebeenincludedto a fairly high level of detail including take-off, landing,steering,and taxiing. Also flexibility of the strut andbogie weremodeled. The softwareis composedof modulesthat correspond to different subsystems or components suchthata wide rangeof configurationscanbe modeled from a singlelanding gearstrut to a whole aircraft with multiple gear. The softwarehasthe capability of modeling the aircraft as a flexible body that may be importantin configurationsthat havemore than two maingearacrossthe fuselage.A finite elementmodel is usedfor the strut component of the gear.Sincethe frequencies andmodeshapes changeasthegearis extendedor compressed the modelis evaluated at several different positionsandinterpolatedin between. A modal reductionroutine is usedfor removingunwanted modesin order to preservethe efficiency of the software. The oleo, bogie, brakesand wheels,braking servo,steeringactuation,control systems,tires, andrunway profile are alsoincluded in the model. The softwarehasbeenvalidatedwith testdataandanexampleof a droptestis givenin thepaper.
Sensitivity Analysis and System Studies With the development of more accurate models for analyzing gear vibration problems, system sensitivity studies became feasible and valuable in the design and evaluation of landing gear dynamics. Ref 14 describes a sensitivity study of several service variables on the dynamic stability of the F-101 and F-104 landing gear systems. Among the studies are the effects of wear, manufacturing tolerances, and normal maintenance procedures on the nominal gear. These studies were helpful in determining if optimum performance of the gear could be achieved by changing the values of the nominal service variables. Also, it was important to establish guidelines that stated if any deviations in these service variables from their nominal values would be detrimental to the performance of the aircraft. Torsional free play of the F-104 gear was found to have the most profound effect on the stability of the gear, particularly for fully extended operation. Tire unbalance reduced the dynamic stability of the gear when adverse values of other service variables were present such as air in the steer-damp unit or excessive torsional free play. For the F-101 gear, tire unbalance was shown to have a severe effect on the stability. Reference 48 describes an analytical method of determining the sensitivity of various parameters of the landing gear and the braking system on the landing gear dynamics during landing. The differential equations of motion of an 11 degree of freedom system in generalized coordinates are written using Lagrange equations which are solved with variations of the parameters. During the design modifications of the F-15 reported in reference 49, landing gear shimmy tests were performed using a dynamometer facility and prototype landing gear. Several instances of shimmy were encountered during testing and the results indicated that shimmy speed was a function of strut torsional free play. Nonlinear analyses showed the sensitivity of shimmy speed to changes in tire parameter values and frictional coefficients. The sensitivity analysis reported in reference 50 showed that forward speed, vertical velocity, pitch attitude, and damping coefficients of the landing gear have the largest effect on the g loads at touchdown. The nonlinear model described in reference 37 varied system parameters to study the dynamic behavior of a dual wheel nose-gear system. The study included parameters such as wheel span and cant angle, mass of the torque arms and its relative position to the shock strut, torque arm stiffness, damper stiffness, wheel size and mass, and tire vertical and lateral stiffness.
Messier-Dowty has studied shimmy phenomena in order to improve the prediction of the dynamic behavior of landing gear systems. In reference 51 they have developed several models with many input parameters, particularly non-linear parameters and made comparisons to test data. Simulations show sensitivities of shimmy stability to variations in these parameters and reinforce the need for taking nonlinearities into account. The effects of longitudinal tire stiffness, vertical damping, and inclination angle of the strut on gear walk stability are investigated in reference 42. The analytical model was developed to study the behavior of main landing gear during taxi and braking. The model includes an error feedback control law for anti-skid braking simulation. In Reference 52 system studies were performed for landing impact and taxi for three types of dual-chamber shock struts to aid in the selection process when designing landing gear for different applications. The strut behavior was calculated for the design energy conditions of a transport aircraft. No validation of the equations and results was performed. Reference 53 gives an example of a shock strut model for an articulated landing gear that was used for the purpose of comparing different linkage system configurations. Linkage mechanisms are important for achieving mechanical advantages and other improvements in weight, reduced friction, and steering. The strut model included hydraulic damping and pneumatic spring forces, but seal and bearing friction were neglected during landing conditions. The tire model was relatively simple having empirical coefficients obtained from static testing. The simulation also included aerodynamics, engine model, and ground effects.
Reference 54 developed a numerical to study the advantages and disadvantages of decreasing the initial charge pressure of the air-oil chamber in the strut. The analysis was performed with and without the effects of the relaxation properties of the tire which influences the maximum load point in the lower part of the strut but does not affect the upper part of strut or fuselage. The advantage of shortening the strut did not outweigh the disadvantage of increasing the stiffness of the strut both caused by "soft-filling".
Testing and Validation The literature was reviewed for examples of testing for verification of analytical models, accurate parameter identification for input into analytical models, and determining the stability of gear designs.
Reference 55 describes analytical and experimental studies of shimmy for the DASH 7 and DASH 8 aircraft to understand nose gear shimmy and to aid in the development of analysis methods for predicting shimmy.
Shimmy occurred during service of the DASH 7 nose gear and was predicted during the design of the DASH 8 main gear. Aircraft ground testing of a DASH 7 nose gear investigated variables such as free-play in the scissors, effects of spin-up transient oscillations, and time-delay steering mechanism. The analysis model used represents backlash, bearing friction, scissors stiffness and free play, and fuselage torsional stiffness and free play. The frequencies predicted were 20% higher than the values measured and was attributed to mass and stiffness modeling inaccuracies. Effects of free play and mass balance on stability were investigated. The main landing gear of the DASH 8 was prone to shimmy due to its long flexible design. Analytical results showed that increasing torsional stiffness and side bending stiffness of the gear would increase stability. Mechanical trail was increased to the maximum to improve stability also. The DASH 7 nose landing gear shimmy problem was contained at the expense of increased maintenance cost, pilot workload, and in some cases airplane weight. In the case of the DASH 8, all 400 airplanes in service are shimmy free but at the expense of increased time and effort to establish the final design with a weight penalty.
There are different approaches to testing landing gear. Test results may therefore differ as discussed in reference 56. Large differences still exist between dynamometer and airplane test results. Although it is possible to predict the dynamometer results with an analytical model of the dynamometer test setup if the dynamics of the overhead rig are included, the dynamometer predicts much more stable behavior than the actual landing gear on the aircraft. The lack of complete simulation of the torsional squeal modes interaction with the rest of the landing gear structure, and the lack of simulation of low frequency modes can result in significant differences between the stability of important modes in the lab as compared to the actual aircraft. Another large difference between the dynamometer and the aircraft landing gear is the modal density in the low frequency range between 0 and 50 Hz. For the example discussed in the reference the main landing gear had fifteen modes in this range where the simulator of the gear had only two. The lack of simulation of the low frequency modes of the landing gear system can result in significant differences between the stability of important modes in the laboratory as compared to the aircraft. The author states that a simulator of this type can be used to predict airplane performance only if it is used in conjunction with a detailed analytical model of the complete landing gear system. Reference 57 gives a brief overview of a 1993 NASA test program to study aircraft nose gear shimmy. The parameters were torsional stiffness, torsional freeplay, wheel balancing, and worn parts. Steerable nose wheels were lO particularly susceptible to shimmy problems. Test results of the Shuttle nose landing gear compared with that of a steel dynamometer showed little difference except in the case of a simulated flat tire test. This test was shown to be significant only in the dynamometer data. Basically vertical load had little effect on maximum steering collar rotation, maximum axle acceleration and maximum wheel swivel acceleration for the shuttle nose gear tests which also confirmed earlier dynamometer data that shimmy did not appear to be a problem. Reference 58 describes methodology to measure nose landing gear shimmy parameters using T- 46 static test article and static force-deflection measurements. The shimmy stiffness and torsional freeplay parameters were then input into a shimmy analysis that incorporated the Moreland tire model. Stability was predicted over a speed range of 20 to 140 knots. The prediction was validated through taxi tests of the T- 46. In reference 59 a mathematical model was developed to analyze the stability of the F-28 and other similar gear and then validated through ground vibration tests and aircraft taxi tests. It was found that this gear was basically unstable. An examination of the modes of the gear model found that the torsional-yaw mode had negative damping for velocities above 70 m/s at a .25 m vertical deflection of the shock absorber.
A shimmy damper was included at the apex of the torque links that proved to be stabilizing in the analysis as well as subsequent flight tests. Eventually experimental testing in landing gear systems and components was performed to determine critical input parameters for improving analytical methods. Taxi tests of the airplane were not conducive to developmental work on the gear or for broad investigations of the effects of system parameters, therefore laboratory tests were the most cost-effective way to investigate the stability of the gear.
Stability characteristics have been examined in the laboratory over the complete range of speed, vertical load, and service parameter changes. Reference 60 examines several major differences between laboratory tests and airplane tests. The mounting structure to which the landing gear is attached affects the frequency and damping. The curvature of the flywheel surface affects the rolling dynamics of the tire such as cornering power, relaxation length, and tire lateral spring rate. The melted rubber on the flywheel surface will change the friction between the tire and the flywheel surface causing the gear to be more stable than the actual. Landing gear exhibit non-linear characteristics such as friction and damping that are dependent on the level of excitation. Lab testing usually involves gear in new condition that is non-typical of actual landing gear systems. Because of these differences, the predictions are carried out by an experimentally verified analysis rather than directly from lab test results. Reference 60 describes one such effort to examine shimmy instability analytically during the design stages and by experimental testing. The critical input parameters for the analytical study were flexibility coefficients, damping and steering characteristics, fuselage frequency response, frictional torques, deadband values, and tire parameters which were determined in lab tests. Correlation between the lab tests and the analysis was very good. The complete landing gear was then tested either in laboratory simulation or taxi tests on the actual airplane.
Assessment and Recommendations for Future Work Significant improvements in analytical predictions can be made if gear and tire parameters such as stiffness, damping, and friction are known as functions of load on the gear or aircraft ground speed. (Ref.
61) Obtaining these parameters can be very labor intensive. Some landing gear dynamicists are of the opinion that there is a need for standardized analytical modeling capabilities that are comprehensive and accurate but not cumbersome or computer intensive. These tools should be versatile enough to handle different types of gear as well as wheel/tire configurations and should be well maintained and documented.
A database of predictions of aircraft contributions to the gear parameters would eliminate the need for labor intensive measurements on the aircraft. The need for a better understanding of damping and friction in the gear still exists today. Reference 62 gives an overview of the needs for improvements in analytical modeling andtesting. They contendthat simulationmodelscan be usedin parametricstudiesto improve shimmystability of geardesigns, however,a total assessment of the systemstabilityrequiresanalyzingthe entire operatingrange of the aircraft andcan be difficult to obtain in this manner. In the openliterature they found few publicationsthat dealt with model simulationshaving significant impact on landing gear design. Still simulationcanprovide a lessexpensivealternativeto full scaletesting. Testfindings indicate that torsional freeplay tends to destabilizethe systemwhereasfriction forces have a stabilizing effect.
Separation of lateral andtorsionalfrequencies through lateral andtorsionalstiffnessmodifications,adding negativeor large positive mechanicaltrail, massbalanceappliedto the wheel axle, steeringsystems,and shimmydampers are all methodsfor improving shimmystability accordingto the references cited. Worn parts,tire wear,andtire inflation alsoadverselyaffectshimmystability.
Landing dynamicsissues havebeenthe focusof the Aircraft Landing DynamicsFacility (ALDF) at
NASA Langley ResearchCenter sinceits inception in 1956. Landing gear vibration could be studied further in this facility. In January1998a workshopwasheld at NASA Langleywherethe aircraft landing gear community was invited to discuss vibration problems. Landing gear and tire manufacturers, commercialairline and generalaviation personnel,FAA, and WPAFB were in attendance. The overall consensus wasthatanalyticaltoolswere availableto predict shimmyandbrake-induced vibration,but there was a needfor accuratetire characterization to provide input for the models. They requestedanupdateto the NASA Technical Report R-64 cataloging mechanicalpropertiesof aircraft tires including dynamic propertiesof radial and advancedbias-ply tires. Since the data for the original R-64 documentwere acquiredat the ALDF it seemed appropriate to perform the updateactivity thereaswell. The testplan and schedule hasbeeninitiated andtestingis projectedto startin the summerof 1999.
Concluding Remarks
In order to increase understanding of landing gear shimmy and brake-induced vibration problems, a literature survey on landing gear dynamics was performed. The major focus of the paper was to summarize work documented from the last ten years to highlight the latest efforts in solving these vibration problems.
Older publications are included to understand the longevity of the problem and the findings from earlier researchers. The literature survey revealed a variety of analyses, testing, modeling, and simulation of aircraft landing gear. Experimental validation and characterization of shimmy and brake-induced vibration of aircraft landing gear were also reported. This paper presented an overview of the problem documented in the references together with a history of landing gear dynamic problems and solutions. Based on the assessment of this survey, recommendations of the most critically needed enhancements to the state of the art were given.
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3. REPORT TYPE AND DATES COVERED 1. AGENCY USE ONLY (Leave blank) 2. REPORT DATE Technical Memorandum May 1999 4. TITLE AND SUBTITLE 5. FUNDING NUMBERS An Overview of Landing Gear Dynamics WU 522-18-11-04 6. AUTHOR(S) Jocelyn I. Pritchard 8. PERFORMING ORGANIZATION 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) REPORT NUMBER NASA Langley Research Center U.S. Army Research Laboratory Hampton, VA 23681-2199 Vehicle Technology Directorate NASA Langley Research Center L-17840 Hampton, VA 23681-2199 IO. SPONSORING/MONITORING 9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) AGENCY REPORT NUMBER National Aeronautics and Space Administration Washington, DC 20546-0001 NASA/TM-1999-209143 and ARL-TR-1976 U.S. Army Research Laboratory Adelphi, MD 20783-1145 11. SUPPLEMENTARY NOTES 12a. DISTRIBUTION/AVAILABILITY STATEMENT 12b. DISTRIBUTION CODE Unclassified-Unlimited Subject Category 05 Distribution: Standard Availability: NASA CASI (301) 621-0390 13. ABSTRACT (Maximum 200 words) One of the problems facing the aircraft community is landing gear dynamics, especially shimmy and brake- induced vibration. Shimmy and brake-induced vibrations can lead to accidents due to excessive wear and shortened life of gear parts and contribute to pilot and passenger discomfort. To increase understanding of these problems, a literature survey was performed. The major focus is on work from the last ten years. Some older publications are included to understand the longevity of the problem and the background from earlier researchers. The literature survey includes analyses, testing, modeling, and simulation of aircraft landing gear; and experimental validation and characterization of shimmy and brake-induced vibration of aircraft landing gear.
The paper presents an overview of the problem, background information, and a history of landing gear dynamics problems and solutions. Based on the survey an assessment and recommendations of the most critically needed enhancements to the state of the art will be presented. The status of Langley work contributing to this activity will be given.
14. SUBJECT TERMS 15. NUMBER OF PAGES 2O vibration, landing gear dynamics, shimmy 16. PRICE CODE A03 17. SECURITY CLASSIFICATION 18. SECURITY CLASSIFICATION 19. SECURITY CLASSIFICATION 20. LIMITATION OF REPORT OF THIS PAGE OF ABSTRACT OF ABSTRACT Unclassified Unclassified Unclassified UL NSN 7540-01-280-5500 Standard Form 298 (Rev. 2-89) Prescribed by ANSI Std. Z-39-18 298-102