Research on the Stability and Bifurcation Characteristics of a Landing Gear Shimming Dynamics System

Abstract

A dynamic model is established to investigate the shimmy instability of a landing gear system, considering the influence of nonlinear damping. The stability criterion is utilized to determine the critical speed at which the landing gear system becomes unstable. The central manifold theorem and canonical method are employed to simplify the dynamic model of the landing gear. The first Lyapunov coefficient of the system is theoretically derived and verified using numerical simulation. Further investigation on the Hopf bifurcation characteristics and stability of the shimmy in the landing gear system is conducted. The results indicate that above a certain threshold speed, with a tire stability distance greater than half the tire length in contact with the ground plus the slack length, the aircraft remains stable during taxiing. At critical speeds, a shimmy system with higher-order nonlinear damping will undergo supercritical Hopf bifurcation. Quantitative analysis suggests an increase in the linear damping coefficient within a range that ensures a stability margin to mitigate undesired oscillation, while the nonlinear damping coefficient should be designed within a reasonable range to decrease the amplitude of the limit cycle.