Nonlinear Damping and Time-Lag Effects in Landing Gear Antishimmy Systems

The damping force generated by the aircraft’s nose gear damper exhibits both linear and nonlinear characteristics, and a certain time delay occurs during its transmission to the strut through the mechanical linkage. These nonlinear damping effects and time delay phenomena significantly influence the shimmy behavior of the landing gear system. In this study, a multi-degree-of-freedom landing gear shimmy model is developed, and bifurcation theory is employed to elucidate the underlying mechanism of the nonlinear damping term on shimmy dynamics. A multidimensional delay differential equation is formulated and solved numerically, enabling an analysis of how time-delay parameters affect shimmy characteristics. The results indicate that the linear damping component directly determines the system’s stability; the quadratic damping term induces periodic oscillations with constant amplitude; and the stability associated with the square root damping term depends on initial conditions. Under the influence of time-delay parameters, the system’s shimmy frequency increases, leading to degraded antishimmy performance of the damper. Finally, it is demonstrated that system stability and damper reliability can be enhanced by compensating for the maximum critical damping coefficient and incorporating time-delay effects at the early design stage.