A general nonlinear single-track model for curved flat or banked road paths: Identification of the vehicle handling DNA

Abstract

The goal of this work is the development of a general nonlinear single-track model for the cases of curved flat or banked road paths and the identification of the fundamental “handling bricks” or vehicle “DNA”, extending an existing theory for flat road tracks. The handling bricks are related to specific design parameters of the vehicle. It is confirmed (both theoretically and numerically), that two structurally different vehicles, with the same handling bricks, exhibit very similar or identical handling behavior. The current nonlinear model accepts general steering input, and arbitrary axle characteristic functions and can be used for general (flat or banked) road tracks. If necessary, various types of constraints can be easily enforced, linking the dynamic parameters of the model. For example, given a complex steering input, the vehicle's (center of gravity) velocity and (or) the vehicle heading, can be related to the direction of the banked road path. On the other hand, the road path can be given independently of the steering data to check the deviation between the intended and the obtained road paths. An implicit nonlinear Crank-Nicolson time marching technique (with additional internal iterations at each time step), has been developed and implemented for the set of (nonlinear) ordinary differential equations (in a homemade VBA framework). The numerical results, using magic formula-based axle characteristic functions, confirm the robustness of the model formulation.