When a tire operates at a side slip level above peak friction, large vibrations in the produced forces and moments are observed. In the lateral direction, these vibrations are typically centered at frequencies close to 50 Hz and significantly affect the force that is produced by the tire. As an example, high dynamics vehicle maneuvers with an electronic stability program control system in the loop can be affected by this behavior. To accurately reproduce the tire response in these operating conditions, it is important to employ a model that can capture this phenomenon.
Based on analysis of nonlinear, unstable systems and limit cycle phenomenon, a theory is presented that provides a physical background for the source of vibrations. The theory also gives insight in how the frequency and amplitude of the vibrations are influenced by the tire physical characteristics and the operating conditions. It is found that the most dominant characteristics are the shape of the steady-state force response of the tire around peak friction, the contact patch mass, the carcass damping and stiffness. Simulations with physical models of different complexity levels, as well as with the commercial Simcenter Tire MF-Tyre/MF-Swift tire software model, validate the theory and demonstrate how the vibrations can be reproduced in a simulation environment. The simulation results are compared with tire measurements in different operating conditions, validating the exposed theory and employed models.