Abstract
Aircraft landing gears support the aircraft during ground operations, including take-off, landing impact, taxiing, gate handling and maintenance. Mostly for reasons of minimum mass and ground clearance, landing gears are slender structures which exhibit a considerable dynamic response to ground load excitations. As the landing gear is one of the few systems on the aircraft without redundancies, the knowledge of landing gear dynamics is crucial for aircraft design and aircraft safety. Simulation of landing gear dynamics is a cornerstone of aircraft loads analysis, as well for vertical loads resulting from touch-down as for longitudinal and lateral loads resulting from braking, steering and towing. Another important field of interest is landing gear vibrations like gear walk and shimmy. Those phenomena can be brake induced or result from tire spin-up at touch-down or simply from a coupling of dynamics of the running tire and structural mechanics of the landing gear leg. All those effects strongly depend on a number of parameters such as aircraft speed, landing gear vertical deflection, tire pressure and wear of the parts. Many of those parameters can only be estimated and might change during the operation of the aircraft. Numerical investigation is thus a challenging task. Analysis methods exist both in the frequency domain and in the time domain. As stability analysis is straight forward in frequency domain methods, this approach is still often used. However, in many cases nonlinearities are dominant which lead to limit-cycle characteristics of the vibrations. Here, multibody modelling or a mixture of multibody and finite element modelling including time domain simulation is used. In the article, a general outline is given of how vibration problems in landing gears can be treated by numerical analysis methods. The article will start with a classification of typical problems, give a short overview of classical papers, and explain typical approaches. In addition, alternative approaches for stability analysis and for the detection of limit-cycle oscillations as well as state-of-the-art modelling approaches will be presented.
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References
Conway, H.G.: Landing Gear Design. Chapman & Hall, London (1958)
Currey, N.S.: Aircraft Landing Gear Design: Principles and Practices. AIAA Education Series, Washington (1988)
Pazmany, L.: Landing Gear Design for Light Aircraft, vol. 1. Pazmany Aircraft Corp, San Diego (1986)
Roskam, J.: Airplane Design, Part IV: Layout Design of Landing Gear and Systems. Darcoporation, Lawrence, KS, USA (1989)
Raymer, D.: Aircraft Design: A Conceptual Approach, 4th edn. AIAA Education Series, New York (2006)
Tanner, J.A. (ed.): Aircraft Landing Gear Systems; PT-37. Society of Automotive Engineers, Warrendale (1990)
Tanner, J.A., Ulrich, P.C., Medzorian, J.P., Morris, D.L. (eds.): Emerging Technologies in Aircraft Landing Gear; PT-66. Society of Automotive Engineers, Warrendale (1997)
AGARD Conference Proceedings: Landing Gear Design Loads (CP-484). AGARD (1990)
AGARD Report: The Design, Qualification and Maintenance of Vibration-Free Landing Gear (R-800). AGARD (1996)
Hitch, H.P.Y.: Aircraft ground dynamics. Veh. Syst. Dyn. 10, 319–332 (1981)
Krüger, W., Besselink, I., Cowling, D., Doan, D.B., Kortüm, W., Krabacher, W.: Aircraft landing gear dynamics: simulation and control. Veh. Syst. Dyn. 28, 257–289 (1997)
Pritchard, J.: Overview of landing gear dynamics. J. Aircr. 38, 130–137 (2001)
Denti, E., Fanteria, D.: Models of wheel contact dynamics: an analytical study on the in-plane transient responses of a brush model. Veh. Syst. Dyn. 34(3), 199–225 (2000)
Khapane, P.D.: Gear walk instability studies using flexible multibody dynamics simulation methods in SIMPACK. Aerosp. Sci. Technol. 10(1), 19–25 (2006)
Besselink, I.J.M.: Shimmy of Aircraft Main Landing Gears, Doctoral Theses. Delft University of Technology, Delft, The Netherlands (2000)
Krüger, W.R.: Design and simulation of semi-active landing gears for transport aircraft. Mech. Struct. Mach. 30(4), 493–526 (2002)
Sateesh, B., Maiti, D.K.: Vibration control of an aircraft nose landing gear due to ground-induced excitation. J. Aerosp. Eng. 224(3), 245–258 (2010)
Thota, P., Krauskopf, B., Lowenberg, M.: Interaction of torsion and lateral bending in aircraft nose landing gear shimmy. Nonlinear. Dyn. 57, 455–467 (2009)
Somieski, G.: Shimmy Analysis of a Simple Aircraft Nose Landing Gear Model Using Different Mathematical Methods. Aerosp. Sci. Technol. 1(8), 545–555 (1997)
Pacejka, H.B.: The wheel shimmy phenomenon. A theoretical and experimental investigation with particular reference to the non-linear problem. Dissertation, Delft University of Technology, Delft (1966)
Somieski, G.: An eigenvalue method for calculation of stability and limit cycles in nonlinear systems. Nonlinear. Dyn. 26(1), 3–22 (2001)
Gülzau, H., Carl, U.B.: Parametric modelling and experimental validation of multi body simulations of elastic flap systems in transport aircraft. In: Proceedings of Workshop on Aircraft System Technologies. Hamburg, Germany, 29–30 March 2007
Ghiringhelli, G.L., Maserati, M., Mantegazza, P., Nixon, M.W.: Multi-body analysis of a tiltrotor configuration. Nonlinear. Dyn. 19, 333–357 (1999)
Arnold, M., Vaculin, O. (eds.): Vehicle system dynamics. Special Issue in Memory of Prof. Willi Kortüm. Veh. Syst. Dyn. 41(5), 35–429 (2004)
Wallrapp, O.: Standardization of flexible body modeling in multibody system codes, part I: definition of standard input data. Mech. Struct. Mach. 22(3), 283–304 (1994)
Krüger, W.R., Spieck, M.: Aeroelastic effects in multibody dynamics. Veh. Syst. Dyn. 41(5), 383–399 (2004)
Arnold, J., Einarsson, G., Krüger, W.R.: Multibody simulation of an oscillating aeroelastic wing model. NAFEMS Int. J. CFD Case Studies 8, 5–18 (2009)
Krüger, W.R.: Multibody dynamics for the coupling of aeroelasticity and flight mechanics of highly flexible structures. In: Proceedings of International Forum of Aeroelasticity and Structural Dynamics (IFASD), Stockholm (2007)
SIMPACK information website. http://www.simpack.com. Accessed 01 March 2011
Neumann, J., Nitzsche, J., Voss, R., Krüger, W.R.: Aeroelastic analysis by coupled non-linear time domain simulation. AVT Specialists’ Meeting on Advanced Methods in Aeroelasticity, RTO-AVT-154, Loen (2008)
Masarati, P., Morandini, M., Quaranta, G., Mantegazza, P.: Open-source multibody analysis software. Multibody Dynamics 2003. In: Proceedings of International Conference on Advances in Computational Multibody Dynamics, Lisboa (2003)
Rook, T., Kumar, S.: Dynamic aircraft landing gear simulation using flexible multibody dynamics methods in ADAMS to guide component design and testing. In: Proceedings of North American MDI User Conference 2001, Novi, MI, USA (2001)
An integrated approach to the dynamic simulation of landing gear systems. LMS Product Brochure. http://www.lmsintl.com/download.asp?id=67B8002C-25DE-4E29-9FCB-E9CFD2FF1285 (2011). Accessed 01 March 2011
Gualdi, S., Morandini, M., Masarati, P.: A deformable slider joint for multibody applications. Proc. XVII Congresso Nazionale A.I.D.A.A., Rome, Italy (2003)
Bauchau, O.A.: On the modelling of prismatic joints in flexible multi-body systems. Comp. Methods. Appl. Mech. Eng. 181, 87–105 (2000)
Lernbeiss, L., Plöchl, M.: Simulation model of an aircraft landing gear considering elastic properties of the shock absorber. J. Multi-body Dyn. 221, 77–86 (2007)
Grossmann, D.T.: F-15 Nose Landing Gear Shimmy, Taxi Tests and Corrective Analyses. SAS Technical Paper 801239 (1980). doi:10.4271/801239
Pacejka, H.B.: Tyre and Vehicle Dynamics, 2nd edn. Butterworth-Heinemann, Oxford (2007). (reprinted 2007)
Schmeitz, A.J.C., Besselink, I.J.M., Jansen, S.T.H.: TNO MF-SWIFT. Veh. Syst. Dyn. 45(Supp. 1), 121–137 (2007)
Gipser, M.: FTire Info & Download. http://www.ftire.com (2011). Accessed 01 March 2011
van Slagmaata, M.T.P.: Tire models in aircraft landing gear simulation. Veh. Syst. Dyn. 21(1), 108–115 (1992)
Moreland, W.: The story of shimmy. J. Aeronaut. Sci. 21, 793–808 (1954)
Smiley, R. F., Horne, W. B.: Mechanical properties of pneumatic tires with special reference to modern aircraft tires. NACA TR-R-64, 1960
Blundell, M., Harty, D.: The multibody systems approach to vehicle dynamics. Elsevier LTD, Oxford (2004)
Zegelaar, P., Pacejka, H.: Dynamic tyre responses to brake torque variations. Veh. Syst. Dyn. Suppl. 27, 65–79 (1997)
Zegelaar, P.: The Dynamic Response of Tyres to Brake Torque Variations and Road Unevennesses. Doctoral Thesis, TU Delft, Delft (1998)
Canudas-de-Wit, C., Tsiotras, P., Velenis, E., Basset, M., Gissinger, G.: Dynamic friction models for road/tire longitudinal interaction. Veh. Syst. Dyn. 39(3), 189–226 (2003)
Hall, W., Mottram, J.T., Jones, R.P.: Finite element simulation of a rolling automobile tyre to understand its transient macroscopic behaviour. J. Automob. Eng. 218(12), 1393–1408 (2004)
Gibbesch, A.: High-Speed Tyre-Soil Interaction of Aircraft on Soft Runways. AVT Symposium on Habitability of Combat and Transport Vehicles: Noise, Vibration and Motion. RTO-MP-AVT-110, Prague (2004)
Armstrong-Helouvry, B., Dupont, P., Canudas-de-Wit, C.: A survey of models, analysis tools and compensation methods for the control of machines with friction. Automatica 30(7), 1083–1138 (1994)
Pennestrì, E., Valentini, P., Vita, L.: Multibody dynamics simulation of planar linkages with Dahl friction. Multibody Syst. Dyn. 17, 321–347 (2007)
Dahl, P.R.: Solid friction damping of mechanical vibrations. AIAA J. 14(12), 1675–1682 (1976)
Dupont, P., Hayward, V., Armstrong, B., Altpeter, F.: Single state elastoplastic friction models. IEEE Trans. Autom. Control 47(5), 787–792 (2002)
Faraz, A., Payandeh, S.: Towards approximate models of coulomb frictional moments in: (i) revolute pin joints and (ii) spherical-socket ball joints. J. Eng. Math. 40, 283–296 (2001)
Jategaonkar, R., Behr, R., Gockel, W., Zorn, C.: Data Analysis of Phoenix Reusable Launch Vehicle Demonstrator Flight Test. J. Airc. 43(6), 1732–1737 (2006)
Gualdi, S., et al.: Anti-skid induced aircraft landing gear instability. Aerosp. Sci. Technol. 12(8), 627–637 (2002)
Krüger, W.R., Morandini, M.: Numerical simulation of landing gear dynamics: state-of-the-art and recent developments. In: Proceedings of Limit Cycle Oscillation and Other Amplitude-Limited Self Excited Vibrations, RTO-MP-AVT-152, Loen, Norway (2008)
Acknowledgments
All examples used in the paper originate from the work performed at the DLR Institute of Aeroelasticity in Göttingen and the former Department of Vehicle System Dynamics of DLR in Oberpfaffenhofen, Germany, as well as at the Department of Aerospace Engineering of the Politecnico Di Milano, Italy. The article is based on a contribution of the authors to the RTO-AVT Symposium on Limit Cycle Oscillation and Other Amplitude-Limited Self Excited Vibrations in Loen, Norway [57]. The authors would like to acknowledge the work of G. Somieski, who set up the theoretical background and software for quasi-linear analysis of landing gear dynamics, Sect. 2, and the work of P. Khapane, who modelled and analyzed the dynamics of brake-gear interaction. Figure 1 originates from the unpublished Master’s Thesis of L. Lernbeiss. The work presented in Sect. 4.2 was performed with the help of S. Gualdi and G.L. Ghiringhelli.
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Krüger, W.R., Morandini, M. Recent developments at the numerical simulation of landing gear dynamics. CEAS Aeronaut J 1, 55–68 (2011). https://doi.org/10.1007/s13272-011-0003-y
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DOI: https://doi.org/10.1007/s13272-011-0003-y