Comparison of dynamical behaviours of two motorcycle's' models in the simulation of lowside fall

The study and analysis of motorcycle’s critical driving situations, falls and accidents, are difficult to be described analitically because of the simultaneity of different and complex phenomena which make the dynamics quite elaborate. However, the controllers for active safety systems of motorcycles cannot be synthesized regardless by a suitable analytic model of the vehicle dynamic. In this paper, an analytic model able to describe the strong nonlinearities conveyed by the complex dynamic of a two-wheeled vehicle in curve, is presented. The model takes into account the coupling between the in-plane and out-of-plane dynamics which is accounted for the system nonlinear behaviour, the rear traction and the nonlinear features of the tyres dynamics. The major steps taken to derive such a model are described. Two sets of motion equations with different levels of accuracy have been developed making use of two different linearizations. The first one is obtained as linearization with respect to the roll and the steer angle around the vertical position, while the second is given by the linearization with respect to the steer angle only. A comparison between the two models for a given initial condition have been made by simulating a real scenario representing a critical vehicle condition, the lowside fall. Results show how these two models have no substantial differences in the description of the low side major dynamics making the simpler model a feasible choice for a model-based design of motorcycle’s control system.