Delay, Nonlinear Oscillations and Shimmying Wheels

The lateral vibration of towed wheels — the so-called shimmy — is a well-known classical example of self-excited nonlinear oscillations. The developments of more and more sophisticated wheel suspension systems and tires in vehicles, as well as the appearance of semi-trailers, caravans, high-speed motorcycles and other large towed vehicle systems require a continuous analysis of this phenomenon. The paper calls the attention for the complexity of the modeling issues and for that of the nonlinear dynamics of the phenomenon strictly from the view-point of the wheel only. This means that the complex dynamics of the vehicle itself is simplified and only those key elements of the mechanical models are considered and analyzed which are related to the wheel-ground connection. The resulting finite and infinite dimensional dynamical systems exhibit a great variety of nonlinear oscillations such as stable and unstable periodic and quasi-periodic oscillations, chaotic and transient chaotic behavior. The infinite dimensional phase space is due to the presence of a special kind of memory, or time delay in the system which is related to the deformed tire contact surface keeping a record of the past motion of the wheel.