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accordtng to the explanauon given i the paper. is rather a case of camouflaged gear walk), which vanishes at increased speed presumably due to nonlinearity of tyre circumferential force characteristics. Also in [3] there is descripted a rig test case (virmally rigid) whm tyre and braUantiskid system nonlinurities pmhibit linear treatment. [41 deseribcs a similar phenomenon observed on aim& a& embarks on dcvaloptnsnt of a nonlinear (time domain) model for calculation of tyre longitudinal force. [5] discusses feasibility of linenrimtion in context witb control optimization of a semi-active nose landing gear. Both linear and di differential equations are developd at [61 for tbe wobble (shimmy) of a motorcycle front wheel: nonlinear effects arise from inclusion of wheel unbalance and periodic tyre radial force vpriation. In studying shimmy having occurred in fligh trials, nonlinear efkts were also accounted for by [7l in time domain analyses. Paper [8] p- sents a complete set of nonlinear equations of unsteady tyre dynamics. Paper [9] discusses influence of nonlincarities on shimmy, presenting models for typical nonlincarities as stick-slip friction and freeplay. hxldon of aoaliaearitics in a simulation model of a cantilevered landing gear g.nrrey is prrscntcd at [IO]. From a scan of the sub@ of dities, pvnt author got the impression that there is widespread concern about the reliability of linearized landing gear models. However, increased modelling effm and cost of computation appear to impede application of nonlinear moder8 except in cases when shimmy occurred on existing hardware, notwithstanding cases whcre linearization is imp- PrOpriaD (landing, braking). Interesting enough to present author none of the papers mentioned shimmy under nonsymmetric basic conditions, e.g. a wheel running at a geometrically or elastically induced pre-set slip mgk ('be-in") or tilt angk. co~MRQsuaEs In spite of all effort spem on design of supposedly vibration-free landing gear, the workshop was pmented with some practical e&lmplcs of landing gear shimmy ([2]. [31. [71, [IO]). It was interesting to note that in most c m the 1andiig gem affected cmld not really be cured. Rather in most instances the butden had to be put on maintaining close tolerances w.r.t. fwplay and tyre pressure, on costly early tyrc replacement, on frrsucnt checks of tyre unbalance and out-of-round. and on pilots having to h e spccial openting proccdurcs. In somc instances there has also mass b.en added to tbe lading par, either in form of landing gear reinforcement for increascd stiffness or in form of mass balance for changing vibration modes and/or frequencies. There was not one serious attempt reported to modify geometry of a landing gear affe*ed, for inst~ce to implement a mm suitable idnation and/or mil m. It appurs that volume end form of landing gear bays are being defined to the laat millimeter at a much too early time in the development process. leaving landing gear designers at both airframe and landing gear manufacturers at a loss to re-establish a m ly vibdon-free landing gear. This again empbasiiacs tbc necessity ofprrpsntioa and as mly as possibly application of qualified and commonly accepted methods of design for vibration-free landing gw. ROUND TABLE DISCUSSION Thc Workshop was concluded with a Round Table Discussion kd by Dr. R. Fnymum. The discussion was characterized by deep concern about present state and fum development of "TEE DESIGN, QUALIFICATION AND MAMTENA" OF VIBRATION-FREE LANDING GEAR'. Compared with effort spent on aero- (servo)elaaticity it is obvious that the field of ldinggwrvibrstioas has bccn negkctadbadlyfor a long time. Tbcro was also snse discussion about the reasona therefor. Nowcver, in view of the cost involved in correcting landing gear vibration problems emerging late in the design proms or even not before aircraft delivery to service, diseussion turned to future. It became clear tbat the state of the art of mating leading gear vibrations was not quite up to olber similar subjects and that cooperation was ncGded of expem widely diatributEd across aircraft, landiig gear and tyre industry (the latter was not represented at the workshop), imtitutions, and Sum0ritie.s. Workshop participants did not expect the rapid progress needed. unless there wps a well planned and c- appmtdr to the problem. Unanimously. <strong>AGARD</strong> was identified the only instituhn which bad enough power and wtbority to promote such a cmrdbtcd effatintheinurratofNATOmMnbcrn;ltiear.The format of a Working Group was considered most suitable to acbicve the pmgrcss mmssery within a reasonrbLtim9r.Fnymnrmwasaskcdtoconvey this proposal to tbe appropriate AOARD My. It was conaidemi useful to bave tentative 'Tmms of Rckrena" writt.n for this task. John Olwr of de Havilland. William E. Krabacher of Wright Laboratory, and Amulf Krauss of Daimler-Benz Aerospace were nomid for an informal ''Point of coruct" group.
T-4 PAPERS PRESENTED AT "HE WORKSHOP m "Preliminary Design Optimization of Carrier and Land Based Fightcr Landing Gears", B. M. Crenshaw and Susan C. Brown. Lockheed Martin Aeronautical Systems. 86 South Cohb Drive, Marietta Ge 38063 USA "A Review of Aircraft Landing Gear Dynamics", William E. Krabacher. WLIFIVMA, Wright Laboratory, Wright plncrsoa AFB. obi 45433 USA "Self-Induced Oscillatim of Landing Gear as an Integral LMding Gear Aircraft System Problem". W. Luber, G. Kempf, A. Krauss, Daimler-Eenz Aerospace AG, Military Aircraft LME24, D-81663 Munich. -Y "Analysis and Control of the Flexible Dynamics of Landiig Gear in the Presence of Antiskid Control Systems", E. Denti and D. Fantsria. Dipmimento di lngegneria Aerospaziale, Univerriti di Pisa. Via Diotisahri 2,56126 Pisa. Italy 'Tuselage Vibration Control Using Semi- Active Front Gear", H. Wentscher. W. Kortiim. W. R. Krliger, DLR - Deutsche Forsehungsanstalt for Luft- und Raumfdut, Insaitut fiir Robot* und Sys~mdynamik. D 82234 Wcssliig. Germany "Dynamic Behaviour of Motorbikes", F. BOhm and H. P. Willumeit, Department of Traffic Engineering and Applied Mechanics, Technical University Berlin, Germany. Paper was presented by P. Banaarie "Landing Gear Shimmy - DE HAVILLAND's Experience", John Glaser and George Hrycko. Structural Dynamics Group, de Havilland Inc.. 123 Garratt Blvd., Downsview. Ontario, M3KIY5, Canada "Unsteady Tire Dynamics and the Application Thereof to Shimmy and Landing Load Computations", Klaus Kanig, Daimler-Benz Aerospace Airbus GmbH, HiinefeldsuaSc 1-5, Bremen, -Y [9] 'Tnfluence arity on the Shimmy g,Gear". P. Wocrner Dowty S.A., VClizy. for Landing Gear lications to the as F/A-l8A", Jeff ngincer, Structural
Page 1: 336853 AQARD-U-800 A\ T ADVISORY GR
Page 4 and 5: The Mission of AGARD According to i
Page 6 and 7: L’etude, l’homologation et la m
Page 8 and 9: Preface Fully reliable procedures f
Page 10 and 11: INTRODUCTION Landing gear is an inv
Page 14 and 15: - SUMMARY The differences in requir
Page 16 and 17: Once preliminary stroke values are
Page 18 and 19: increased inflation pressures and l
Page 20 and 21: Figure 1. Stroke Requirements as a
Page 22 and 23: Maximum Weight ~ Landing Weight Lan
Page 24 and 25: SPACER \ METERING PIN UPPER BEARING
Page 26 and 27: .!2 w 2 1.2e+5 1.0~5 8.0e+4 o 6.0~4
Page 28: 400 350 i 300 P 250 d 200 $ W f 150
Page 31 and 32: 2-2 K,, - Torsional Spring Rate of
Page 33 and 34: 2-4 Q - Tire Roll Rotation about th
Page 35 and 36: 2-6 landing gear shimmy analysis da
Page 37 and 38: : 1 .I FIGURE 7 FIGURE 8 I - + I Y
Page 39 and 40: 2-10 these models uses the Moreland
Page 41 and 42: 2-12 KT TORSIONALSPRING RATE 8- 0 0
Page 43 and 44: 3-2 therefore based on the requirem
Page 45 and 46: 3-4 pistons within fractions of a s
Page 47 and 48: 3-6 deceleration during brake initi
Page 49 and 50: 3-8 Through interference of aerodyn
Page 51 and 52: 3-10 STA 144.40 Fig. 2-1 Advanced T
Page 53 and 54: 3-12 ............... X 1 Fig. 2 - 5
Page 55 and 56: 200. 100. 0 W. 0.5 Fig. 3-5 Histogr
Page 58 and 59: ANALYSIS AND CONTROL OF THE FLEXIBL
Page 60 and 61: ~ - . govern the dynamic generation
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tyre model Is .en orooosed I . in I
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nm.1.1 Fig. 5.3-2 Transient respons
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0.012 0.014 0.01s Time ($1 Fig. 5.3
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1.2 I f ltlt I 1 .,( ~ ............
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- - .. H.Tsukinoki, Antilock Brake
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5-2 NAsTRAN \ 7 1 A CAD I I I I Pro
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5-4 tion time actuator. The possibl
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5-6 Fed with this data, the BEAM pr
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5-8 given used for the excitation o
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5-10 5.2 Quasistochastic Excitation
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5-12 whole frequency range of inter
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6-2 The associated lateral spring c
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The expansion of this gives: 2.1 Th
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6-6 where MR represents the frictio
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6-8 The reaction force coming from
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6-10 Although the solution of the M
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6-12 brake force and self aligning
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6-14 For simulation respectively pr
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6-16 10 1 LMPLITUDE (l/degree) 0.1
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6-18 Massfactor MR [Nms2/degr.] 0,0
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6-20 5 Numerical method of investig
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6-22 numerical procedure, however,
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6-24 [Will871 [ W ill8 91 (Will951
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1-2 These examples occurred over IO
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5. DASH 8 MAIN LANDING GEAR SHIMMY
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develop the equations of motion. Th
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E 9
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7-10 .
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7-12 I 1% 6 !I i 3 > t a a 5? Y
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8-2 For larger deformations as they
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8-4 6. COMPUTATION OF THE LANDING I
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8-6 total tire loads at the centre
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8-8 E 30 s - 10 g 20 0 unstable . .
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- INFLUENCE OF NONLINEARITY ON THE
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- The solution is of the form : X =
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Frequency responses ofwtion model f
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(% These 4 integdons can be compute
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5.1.2 Structural description of lan
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o.O(r . 1 J/! ,....... ' ..........
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10-2 MSD = steering damper exponent
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10-4 TABLE 1 - Degrees of Freedom S
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10-6 A total of three degrees of fr
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10-8 3.1.3. Translational Kinematic
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10-10 FIXED ADAPTER Fig. 7. Steerin
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10-12 0 - o.5oot+oo 0.000E+00 . 0 -
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