Regenerative Effect of Tire Carcass in Simple Shimmy Models

A simple mechanical model of the towed elastic wheel is constructed and analyzed. The lateral deformation of the tire is described by the time delayed tire model, which considers the memory effect of the contact patch. The deformation outside the contact patch is also modeled with the help of the brush model in order to take into account the effect of the deformation waves that propagate along the circumference of the tire. The mathematical model for small oscillations is composed in the form of a functional differential equation of the neutral type. The linear stability of the towed wheel is analyzed via the construction of stability charts in the plane of the relevant engineering parameters. Simulations are also presented to illustrate the regenerative effect of the tire carcass.