Using continuation analysis to identify shimmy-suppression devices for an aircraft main landing gear

Abstract This paper considers several passive shimmy-suppression devices for a dual-wheel main landing gear (MLG) and proposes a method of selecting the device parameter values for which no shimmy occurs. Two of these devices include an inerter, a novel mechanical element with the property that the applied force is proportional to the relative acceleration between its terminals. A nonlinear mathematical model is developed to represent the MLG dynamics. A bifurcation study is then carried out to investigate the effects of the shimmy-suppression devices on the gear steady-state response. The aircraft forward speed and the device damping are chosen as the continuation parameters. A range of device parameter values that ensure the aircraft is free from shimmy instability for any forward speed within its operating region are identified. It is shown that the use of a proposed spring-damper configuration can result in a more robust device in terms of the device damping over that of a conventional shimmy damper. Two inerter-based shimmy-suppression devices are then considered and yield further benefits on expanding the zero-shimmy regions in the two-parameter bifurcation diagrams.

[1]  Zhan Shu,et al.  Passive vehicle suspensions employing inerters with multiple performance requirements , 2014 .

[2]  Fu-Cheng Wang,et al.  The performance improvements of train suspension systems with mechanical networks employing inerters , 2009 .

[3]  H. P. Y. Hitch.  Aircraft Ground Dynamics , 1981 .

[4]  Ijm Igo Besselink.  Shimmy of Aircraft Main Landing Gears , 2000 .

[5]  Jinxiong Zhou,et al.  Incremental harmonic balance method for predicting amplitudes of a multi-d.o.f. non-linear wheel shimmy system with combined Coulomb and quadratic damping , 2005 .

[6]  Fu-Cheng Wang,et al.  Performance analyses of building suspension control with inerters , 2007, 2007 46th IEEE Conference on Decision and Control.

[7]  H. Tourajizadeh,et al.  Robust and optimal control of shimmy vibration in aircraft nose landing gear , 2016 .

[8]  J.Z. Jiang,et al.  Experimental testing and modelling of a mechanical steering compensator , 2008, 2008 3rd International Symposium on Communications, Control and Signal Processing.

[9]  G. Somieski,et al.  Shimmy analysis of a simple aircraft nose landing gear model using different mathematical methods , 1997 .

[11]  Simos A. Evangelou,et al.  An H∞ loop-shaping approach to steering control for high-performance motorcycles , 2006 .

[12]  Simon A Neild,et al.  Optimal configurations for a linear vibration suppression device in a multi‐storey building , 2017 .

[13]  J. A. Kuznecov.  Elements of applied bifurcation theory , 1998 .

[14]  Bernd Krauskopf,et al.  Numerical continuation and bifurcation analysis in aircraft design: an industrial perspective , 2015, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[15]  Bernd Krauskopf,et al.  Influence of Variable Side-Stay Geometry on the Shimmy Dynamics of an Aircraft Dual-Wheel Main Landing Gear , 2013, SIAM J. Appl. Dyn. Syst..

[16]  Mark H Lowenberg,et al.  The Dynamical Systems Toolbox: Integrating AUTO into MATLAB , 2010 .

[17]  David J. Wagg,et al.  Using an inerter‐based device for structural vibration suppression , 2014 .

[18]  H. B. Keller,et al.  NUMERICAL ANALYSIS AND CONTROL OF BIFURCATION PROBLEMS (II): BIFURCATION IN INFINITE DIMENSIONS , 1991 .

[19]  Malcolm C. Smith.  Synthesis of mechanical networks: the inerter , 2002, IEEE Trans. Autom. Control..

[20]  W. Kortüm,et al.  Aircraft Landing Gear Dynamics: Simulation and Control , 1997 .

[21]  Fu-Cheng Wang,et al.  Performance benefits in passive vehicle suspensions employing inerters , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[22]  Long Chen,et al.  Improved design of dynamic vibration absorber by using the inerter and its application in vehicle suspension , 2016 .

[23]  Mikhail Goman,et al.  Application of bifurcation methods to nonlinear flight dynamics problems , 1997 .

[24]  Hans B. Pacejka,et al.  An Analysis of a Civil Aircraft Main Gear Shimmy Failure , 1993 .

[25]  Michael Z. Q. Chen,et al.  Application of inerter to aircraft landing gear suspension , 2015, 2015 34th Chinese Control Conference (CCC).

[26]  L. Segel,et al.  Force and Moment Response of Pneumatic Tires to Lateral Motion Inputs , 1966 .

[27]  Roger M. Goodall,et al.  Passive suspensions incorporating inerters for railway vehicles , 2012 .

[28]  Mark H Lowenberg,et al.  Interaction of torsion and lateral bending in aircraft nose landing gear shimmy , 2009 .

[29]  Simon A Neild,et al.  Inerter-Based Configurations for Main-Landing-Gear Shimmy Suppression , 2017 .

[30]  Roger M. Goodall,et al.  Passive suspensions for ride quality improvement of two-axle railway vehicles , 2015 .

[31]  James T. Gordon,et al.  An Asymptotic Method for Predicting Amplitudes of Nonlinear Wheel Shimmy , 1977 .

[32]  John Kennedy,et al.  Effect of noise reducing components on nose landing gear stability for a mid-size aircraft coupled with vortex shedding and freeplay , 2015 .

[33]  Michel Basset,et al.  Indirect Fuzzy Adaptive Control for Active Shimmy Damping , 2008 .

[34]  Ibrahim Ozkol,et al.  Application of a magnetorheological damper modeled using the current–dependent Bouc–Wen model for shimmy suppression in a torsional nose landing gear with and without freeplay , 2014 .

[35]  Niranjan K. Sura,et al.  Lateral Response of Nonlinear Nose Wheel Landing Gear Models with Torsional Free-play , 2007 .

[36]  Kohju Ikago,et al.  Seismic control of single‐degree‐of‐freedom structure using tuned viscous mass damper , 2012 .

[37]  Kamran Behdinan,et al.  Linear Stability Analysis and Dynamic Response of Shimmy Dampers for Main Landing Gears , 2016 .

[38]  Mark H Lowenberg,et al.  Bifurcation Analysis of a Coupled Nose Landing Gear-Fuselage System , 2012 .

[39]  Dénes Takács.  Dynamics of towed wheels: nonlinear theory and experiments , 2010 .

[40]  Rajendra Singh,et al.  Analysis of periodically excited non-linear systems by a parametric continuation technique , 1995 .

[41]  Dénes Takács,et al.  Experiments on Quasiperiodic Wheel Shimmy , 2009 .

[42]  Mark H Lowenberg,et al.  Shimmy in a nonlinear model of an aircraft nose landing gear with non-zero rake angle , 2008 .