Vehicle drifting dynamics: discovery of new equilibria
Sina Milani, Hormoz Marzbani, Reza N. Jazar
Abstract
This study deals with drifting as one of the most important nonlinearities in vehicle dynamics. A four-wheel vehicle model is used to calculate the equilibria in planar motion, numerically, by introducing an assumption on constant longitudinal tyre slips. Other than the unstable drifting points that were reported by previous researchers, a new pair of drifting equilibria are identified and the difference between the two types is studied. The phase portrait approach is used to identify the type of these equilibria, and they reveal the type of instability in the primary and the secondary drifting points, and provide control suggestions to stabilise the drifting equilibria. It is observed that the rear-wheel-drive vehicles have primary drifting equilibria, while the four-wheel-drive vehicles have secondary drifting equilibria. There is a transition point between the primary and the secondary drifting types when the front longitudinal tyre slips increase from zero to saturation. It is further shown that primary drifting becomes stable by regulating the yaw rate at the equilibrium value; whereas the secondary drifting may be stabilised through a constant forward velocity. The stabilisation methods are applied through control designs and validated in simulations.