起落架系统的分岔特性与参数耦合影响规律

doi:10.7527/S1000-6893.2025.32725

Abstract

Abstract:

Addressing the frequent occurrence of landing gear shimmy under maneuvering conditions， this paper conducts research on high-fidelity modeling and parameter coupling effects. Based on a delay tire dynamic model， the coupled landing gear—tire shimmy dynamics equations are developed， which incorporate the time-varying tire lateral deformation modes. Utilizing Hopf bifurcation theory， we compute the global dynamic characteristics of the system through multi-dimensional projections， quantitatively revealing the influence patterns and mechanisms of key parameters （such as lateral bending stiffness and torsional stiffness） on the stability of the landing gear system across various taxiing speeds. Comparative results with traditional tire models show consistency of both and limitations of traditional tire models in capturing parameter coupling effects. By employing an enhanced Bayesian optimization method， we optimize the bifurcation characteristics of the landing gear system， resulting in a significant improvement in stability. Based on the parameter optimization results and combined with Sobol global sensitivity analysis， the comparative effects of multi-dimensional parameters on system stability are quantitatively revealed， with the results complementing and validating those from the Hopf bifurcation analysis. The study identifies that when the torsional mode frequency of the landing gear approaches the lateral bending mode frequency， substantial modal coupling occurs， creating a bistable shimmy critical boundary that drastically reduces stability. Low lateral stiffness of the landing gear may trigger shimmy during low-speed taxiing， while greater lateral stiffness at high speeds necessitates matched damping enhancement for shimmy mitigation. Increasing torsional stiffness and decreasing tire lateral stiffness yield notable shimmy suppression effects across the entire speed spectrum， indicating their potential as key control parameters for targeted design and optimization.

Key words: delay tire model, landing gear shimmy, torsional stiffness, lateral bending stiffness, Hopf bifurcation, Gaussian process model

CLC Number:

V216.2⁺.2

Chongchong LIU, Xiaochuan LIU, Yong XU, Xiao LI, Shengli LIU. Bifurcation characteristics and parameter coupling mechanisms of landing gear systems[J]. Acta Aeronautica et Astronautica Sinica, 2026, 47(8): 232725.

Figures/Tables 12

Fig.1

Fig.2

Table 1

Parameter of landing gear and tire

序号	参数	数值
1	$I ψ$ /（ $k g ⋅ m 2$ ）	2.55
2	$C ψ$ /（N·m·s·rad^-1）	80
3	$K ψ$ /（N·m·rad^-1）	85 000
4	$I δ$ /（ $k g ⋅ m 2$ ）	45.26
5	$C δ$ /（N·m·s·rad^-1）	300
6	$K δ$ /（N·m·rad^-1）	1 180 000
7	$l$ /m	0.05
8	$a$ /m	0.08
9	$l g$ /m	1.07
10	$k$ /（N·m^-2）	350 000
11	c/（N·s·m^-2）	300
12	I（kg·m^-2）	0.52
13	R/m	0.22
14	σ/m	0.24

Table 1

Fig.3

Fig.4

Fig.5

Fig.6

Fig.7

Fig.8

Fig.9

Fig.10

Fig.11

References 36

[1]	JENKINS A. Self-oscillation［J］. Physics Reports， 2013， 525（2）： 167-222.
[2]	DING W J. Self-excited vibration： Theory， paradigms， and research methods［M］. Beijing： Tsinghua University Press， 2011：1-20 （in Chinese）.
[3]	SANCHES L， GUIMARÃES T A M， MARQUES F D. Nonlinear energy sink to enhance the landing gear shimmy performance［J］. Acta Mechanica， 2021， 232（7）： 2605-2622.
[4]	阮爽，张明，聂宏. 结构间隙对起落架地面滑跑摆振特性影响分析［J］. 振动与冲击， 2024， 43（2）： 234-243.
	RUAN S， ZHANG M， NIE H. Influence of the structural clearance on the shimmy characteristics of the landing gear during ground taxiing［J］. Journal of Vibration and Shock， 2024， 43（2）： 234-243 （in Chinese）.
[5]	刘小川，刘冲冲，牟让科. 飞机起落架系统摆振动力学研究进展［J］. 航空学报， 2022， 43（6）： 527063.
	LIU X C， LIU C C， MOU R K. Research progress on shimmy dynamics of aircraft landing gear systems［J］. Acta Aeronautica et Astronautica Sinica， 2022， 43（6）： 527063 （in Chinese）.
[6]	刘胜利，刘小川，崔荣耀，等. 机体连接处局部刚度对轻型飞机起落架摆振稳定性的影响研究［J］. 振动工程学报， 2017， 30（2）： 249-254.
	LIU S L， LIU X C， CUI R Y， et al. The influence of the fuselage joint local stiffness on landing gear shimmy stabilization of the light aircraft［J］. Journal of Vibration Engineering， 2017， 30（2）： 249-254 （in Chinese）.
[7]	刘冲冲，刘胜利，崔荣耀. 考虑机体局部刚度影响的前起落架摆振分析［J］. 机械科学与技术， 2017， 36（5）： 811-815.
	LIU C C， LIU S L， CUI R Y. Nose landing gear shimmy analysis considering fuselage local stifness［J］. Mechanical Science and Technology for Aerospace Engineering， 2017， 36（5）： 811-815 （in Chinese）.
[8]	FENG F， NIE H， ZHANG M， et al. Effect of torsional damping on aircraft nose landing-gear shimmy［J］. Journal of Aircraft， 2014， 52（2）： 561-568.
[9]	RUAN S， ZHANG M， YANG S F， et al. Research on the stability and bifurcation characteristics of a landing gear shimming dynamics system［J］. Aerospace， 2024， 11（2）： 104.
[10]	THOTA P， KRAUSKOPF B， LOWENBERG M. Multi-parameter bifurcation study of shimmy oscillations in a dual-wheel aircraft nose landing gear［J］. Nonlinear Dynamics， 2012， 70（2）： 1675-1688.
[11]	BESSELINK I J M. Shimmy of aircraft main landing gears［D］. Delft： Delft University of Technology， 2000：2-21.
[12]	BEREGI S， TAKACS D， GYEBROSZKI G， et al. Theoretical and experimental study on the nonlinear dynamics of wheel-shimmy［J］. Nonlinear Dynamics， 2019， 98（4）： 2581-2593.
[13]	DU X L， XU Y， LIU Q， et al. Shimmy dynamics in a dual-wheel nose landing gear with freeplay under stochastic wind disturbances［J］. Nonlinear Dynamics， 2024， 112（4）： 2477-2499.
[14]	聂宏，魏小辉，张明，等. 飞机起降系统非线性动力学稳定性研究进展［J］. 航空学报， 2025， 46（5）： 531229.
	NIE H， WEI X H， ZHANG M， et al. Research progress on nonlinear dynamic stability of aircraft landing system［J］. Acta Aeronautica et Astronautica Sinica， 2025， 46（5）： 531229 （in Chinese）.
[15]	DAUGHTERTY R H. A study of the mechanical properties of modern radial aircraft tires［R］. Washington， D.C.： NASA， Langley Research Center， 2003.
[16]	PACEJKA H. Tyre and vehicle dynamics［M］. Amsterdam：Elsevier， 2005： 364-426.
[17]	PACEJKA H B. The wheel shimmy phenomenon［D］. Delft： Delft University of Technology， 1966： 5-54.
[18]	COLLINS R L. Frequency response of tires using the point contact theory［J］. Journal of Aircraft， 1972， 9（6）： 427-432.
[19]	RAN S H， BESSELINK I J M， NIJMEIJER H. Energy analysis of the Von Schlippe tyre model with application to shimmy［J］. Vehicle System Dynamics， 2015， 53（12）： 1795-1810.
[20]	LIU C C， LIU X C， XU Y， et al. An updating method of aero tyre model by shimmy test［C］∥Proceedings of the 6th China Aeronautical Science and Technology Conference. Singapore： Springer， 2024： 547-564.
[21]	LAX P， WENDROFF B. Systems of conservation laws［J］. Communications on Pure and Applied Mathematics， 1960， 13（2）： 217-237.
[22]	TAKÁCS D， OROSZ G， STÉPÁN G. Delay effects in shimmy dynamics of wheels with stretched string-like tyres［J］. European Journal of Mechanics-A， 2009， 28（3）： 516-525.
[23]	STÉPÁN G. Delay， nonlinear oscillations and shimmying wheels［C］∥IUTAM Symposium on New Applications of Nonlinear and Chaotic Dynamics in Mechanics. Dordrecht： Springer， 1999： 373-386.
[24]	刘冲冲，刘小川，许勇，等. 考虑轮胎时滞效应的起落架摆振分析［J］. 振动工程学报， 2025， 38（8）： 1645-1654.
	LIU C C， LIU X C， XU Y， et al. Analysis of landing gear shimmy considering tire time delay effect［J］. Journal of Vibration Engineering， 2025， 38（8）： 1645-1654 （in Chinese）.
[25]	SOMIESKI G. Shimmy analysis of a simple aircraft nose landing gear model using different mathematical methods［J］. Aerospace Science and Technology， 1997， 1（8）： 545-555.
[26]	THOTA P， KRAUSKOPF B， LOWENBERG M. Interaction of torsion and lateral bending inaircraft nose landing gear shimmy［J］. Nonlinear Dynamics， 2009， 57（3）： 455-467.
[27]	SMILEY R F. Some considerations of hysteresis effects on tire motion and wheel shimmy： Technical Note 4198 ［R］. Washington，D.C.： NACA， 1957.
[28]	MI T， STEPAN G， TAKACS D， et al. Vehicle shimmy modeling with pacejka’s magic formula and the delayed tire model［J］. Journal of Computational and Nonlinear Dynamics， 2020， 15（3）： 031005.
[29]	STÉPÁN G. Delay， nonlinear oscillations and shimmying wheels［C］∥IUTAM Symposium on New Applications of Nonlinear and Chaotic Dynamics in Mechanics. Dordrecht： Springer， 1999： 373-386.
[30]	BACHRATHY D， STÉPÁN G. Bisection method in higher dimensions and the efficiency number［J］. Periodica Polytechnica Mechanical Engineering， 2012， 56（2）： 81.
[31]	刘冲冲，刘小川，刘胜利，等. 轮胎刚度智能预测及在起落架摆振分析中的应用［J］. 振动工程学报， 2023， 36（4）： 903-908.
	LIU C C， LIU X C， LIU S L， et al. Intelligent prediction of tire stiffness and application in landing gear shimmy analysis［J］. Journal of Vibration Engineering， 2023， 36（4）： 903-908 （in Chinese）.
[32]	ZHURAVLEV V P， KLIMOV D M， PLOTNIKOV P K. A new model of shimmy［J］. Mechanics of Solids， 2013， 48（5）： 490-499.
[33]	PADMANABHAN M A， DOWELL E H. Study of nonlinear stiffness and damping effects on shimmy and flutter［J］. Journal of Aircraft， 2023， 60（6）： 1976-1985.
[34]	SHAHRIARI B， SWERSKY K， WANG Z Y， et al. Taking the human out of the loop： A review of Bayesian optimization［J］. Proceedings of the IEEE， 2016， 104（1）： 148-175.
[35]	GHOREISHI S F， ALLAIRE D. Multi-information source constrained Bayesian optimization［J］. Structural and Multidisciplinary Optimization， 2019， 59（3）： 977-991.
[36]	SALTELLI A， RATTO M， ANDRES T， et al. Global sensitivity analysis. The primer［M］. New York： Wiley， 2007： 150-163.

Bifurcation characteristics and parameter coupling mechanisms of landing gear systems

RichHTML

PDF (PC)

Knowledge

Abstract

Cite this article

share this article

Figures/Tables 12

References 36

Related Articles 7

Recommended Articles

Metrics

Comments

[1]	Jingkui ZHANG, Jiapeng CHANG, Miao CUI, Qifen LI, Hongbo REN, Yongwen YANG. First Hopf bifurcation of conducting fluid in three-dimensional square cavity [J]. Acta Aeronautica et Astronautica Sinica, 2023, 44(18): 128328-128328.
[2]	ZHANG Ji-kui;LI Zheng-neng;KOU Chang-he. Structural Design of High Aspect Ratio Composite Material Wing [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2005, 26(4): 450-453.
[3]	LIANG Su-nan;ZHANG Shu-guang. Topological Analysis on the Effects of Unsteady Aerodynamics on Motion of Aircraft [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2003, 24(6): 495-498.
[4]	LI Kang;FANG Zhen-ping. Application of Bifurcation Analysis to Control Law Design at High Angles of Attack [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2003, 24(4): 289-292.
[5]	GU Hong-bin;DING Yun-liang;YAO Zhi;ZHANG Jian-hua;XIONG Mei;GONG Liang-guo. SIMULATION OF AIRCRAFT WHEEL SHIMMY [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2001, 22(4): 362-365.
[6]	Guo Qlanrong. AN INFINITE DIMENSIONAL NONLINEAR ANALYSIS OF ACTIVE SUPPRESSING PANEL FLUTTER [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 1990, 11(7): 389-393.
[7]	Xu Zhong;Zou Zhemin;Fan Weixun. CALCULATION OF TORSIONAL STIFFNESS FOR CROSS SECTIONS OF COMPOSITE ROTOR BLADES [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 1988, 10(10): 506-509.