Abstract
Aircraft landing gear assemblies comprise of various subsystems working in unison to enable functionalities such as taxiing, take-off and landing. As development cycles and prototy** iterations begin to shorten, it is important to develop and improve practical methodologies to meet certain design metrics. This paper presents an efficient methodology that applies high-fidelity multi-disciplinary design optimization techniques to commercial landing gear assemblies, for weight, cost, and structural performance by considering both structural and dynamic behaviours. First, a simplified landing gear assembly model was created to complement with an accurate slave link subassembly, generated based of drawings supplied from the industrial partner, Safran Landing Systems. Second, a Multi-Body Dynamic (MBD) analysis was performed using realistic input motion signals to replicate the dynamic behaviour of the physical system. The third stage involved performing topology optimization with results from the MBD analysis; this can be achieved through the utilization of the Equivalent Static Load Method (ESLM). Lastly, topology results were generated and design interpretation was performed to generate two designs of different approaches. The first design involved trying to closely match the topology results and resulted in a design with an overall weight savings of 67%, peak stress increase of 74%, and no apparent cost savings due to complex features. The second design focused on manufacturability and achieved overall weight saving of 36%, peak stress increase of 6%, and an estimated 60% in cost savings.
Similar content being viewed by others
References
AGARD Report (1995) The design, qualification and maintenance of vibration-free landing gear (R-800)
Altair OptiStruct (2015a) OptiStruct 14.0 Reference Guide. Altair Engineering, Inc., Troy
Altair OptiStruct (2015b) MotionSolve 14.0 reference guide. Altair Engineering, Inc., Troy
Bauchau OA (2011) Flexible Multibody Dynamics. Springer Netherlands, Atlanta, GA
Bendsøe MP, Sigmund O (1999) Material interpolation schemes in topology optimization. Arch Appl Mech 69:635–654. https://doi.org/10.1007/s004190050248
Besselink IJM (2000) Shimmy of Aircraft Main Landing Gears. Delft University of Technology, Delft, Netherlands
Brenan KE, Campbell SLV, Petzold LR (1996) Numerical solution of initial-value problems in differential-algebraic equations. Book 256
Cardona A (2000) Superelements modelling in flexible multibody dynamics. Multibody Syst Dyn 4:245–266. https://doi.org/10.1023/A:1009875930
Choi WS, Park KB, Park GJ (2005) Calculation of equivalent static loads and its application. Nucl Eng Des 235:2337–2348. https://doi.org/10.1016/j.nucengdes.2005.05.030
Craig RR, Bampton MCC (1968) Coupling of substructure for dynamic analyses. AIAA J 6:1313–1319
Denti E, Fanteria D (2010) Models of Wheel Contact Dynamics : An Analytical Study on the In-Plane Transient Responses of a Brush Model. Veh Syst Dyn 34:37–41
Deveau S (2013) Transportation - should Airlines start charging by the pound. Financ. Post
DuPont (2016) Acetal Resin DuPont™ Delrin ® 100 NC010
Engineering A (2008) Multi-disciplinary design of an aircraft landing gear with altair hyperworks altair engineering, October 2008
Gowda AC, Basha N (2014) Trends in mechanical engineering & technology linear static and fatigue analysis of nose landing gear for trainer aircraft. 4:1–10
Hitch HPY (1981) Aircraft ground dynamics. Veh Syst Dyn 10:319–332. https://doi.org/10.1080/00423118108968681
International Air Transport Association (2016a) IATA forecasts passenger demand to double over 20 Years. IATA Press Release No 59 18–22
International Air Transport Association (2016b) Fact Sheet : Climate Change. IATA Environ. Policy 1–3
Kang BS, Choi WS, Park GJ (2001) Structural optimization under equivalent static loads transformed from dynamic loads based on displacement. Comput Struct 79:145–154. https://doi.org/10.1016/S0045-7949(00)00127-9
Knowles JAC, Krauskopf B, Lowenberg M (2013) Numerical continuation analysis of a three-dimensional aircraft main landing gear mechanism. Nonlinear Dyn 71:331–352. https://doi.org/10.1007/s11071-012-0664-z
Krüger WR, Morandini M (2014) Recent developments at the numerical simulation of landing gear dynamics. CEAS Aeronaut J 1:55–68. https://doi.org/10.1007/s13272-011-0003-y
Krüger WR, Besselink IJM, Cowling D et al (1997) Aircraft landing gear dynamics: simulation and control. Veh Syst Dyn 28:119–158. https://doi.org/10.1080/00423119708969352
Lee HA, Park GJ (2012) Topology optimization for structures with nonlinear behavior using the equivalent static loads method. J Mech Des 134:14. https://doi.org/10.1115/1.4005600
Li M, Tang W, Yuan M (2014) Structural dynamic topology optimization based on dynamic reliability using equivalent static loads. Struct Multidiscip Optim 49:121–129. https://doi.org/10.1007/s00158-013-0965-y
Nguyen T, Schonning A, Eason P, Nicholson D (2012) Methods for analyzing nose gear during landing using structural finite element analysis. J Aircr 49:275–280. https://doi.org/10.2514/1.C031519
Oh SH (2014) A study on development of dual locking linkage for landing gear for the application to UAV. 7:41–48
Park GJ (2011) Technical overview of the equivalent static loads method for non-linear static response structural optimization. Struct Multidiscip Optim 43:319–337. https://doi.org/10.1007/s00158-010-0530-x
Park GJ, Kang BS (2003) Validation of a structural optimization algorithm transforming dynamic loads into equivalent static loads. J Optim Theory Appl 118:191–200. https://doi.org/10.1023/A:1024799727258
Pritchard J (2001) Overview of landing gear dynamics. J Aircr 38:130–137. https://doi.org/10.2514/2.2744
Schmidt M, Rohrbach K (1990) ASM handbook, volume 1: properties and selection: irons, steels, and high-performance alloys. Met Handb 1:793–800. https://doi.org/10.1361/asmhba0001
Shabana AA (1997) Flexible multibody dynamics: review of past and recent developments. Multibody Syst Dyn 1:189–222. https://doi.org/10.1023/A1009773505418
Sun J, Tian Q, Hu H (2016) Structural optimization of flexible components in a flexible multibody system modeled via ANCF. Mech Mach Theory 104:59–80. https://doi.org/10.1016/j.mechmachtheory.2016.05.008
Tadeusz N, Jerzy M, Adam B (2006) Numerical analysis of a front support landing gear dynamics. 3–10
Tanaka K, Matsuoka S, Kimura M (1984) Fatigue Strength of 7075-T6 Aluminium Alloy Under Combined Axial Loading and Torsion. Fatigue Fract Eng Mater Struct 7:195–211. https://doi.org/10.1111/j.1460-2695.1984.tb00189.x
Vatanabe SL, Lippi TN, de Lima CR et al (2016) Topology optimization with manufacturing constraints: a unified projection-based approach. Adv Eng Softw 100:97–112. https://doi.org/10.1016/j.advengsoft.2016.07.002
**ngguo M, **aomei Y, Bangchun W (2007) Multi-body dynamics simulation on flexible crankshaft system. 12th IFTOMM World Congr World Congr 3–5
Zhou M, Shyy YK, Thomas HL (2001) Checkerboard and minimum member size control in topology optimization. Struct Multidiscip Optim 21:152–158. https://doi.org/10.1007/s001580050179
Acknowledgements
The authors would like to express their gratitude to Joseph Lan and James Ning at Safran Landing Systems Canada for their expertise and guidance throughout the course of this research. This research was supported by the National Science and Engineering Research Council of Canada and Safran Landing Systems Canada. The contributions made are greatly appreciated.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Wong, J., Ryan, L. & Kim, I.Y. Design optimization of aircraft landing gear assembly under dynamic loading. Struct Multidisc Optim 57, 1357–1375 (2018). https://doi.org/10.1007/s00158-017-1817-y
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00158-017-1817-y