Development and numerical validation of a reduced-order two-track car model

In this paper we propose a novel reduced-order car model and show how it can be used for parameter fitting and dynamic analysis of complex car vehicles. The proposed two-track model consists of a rigid body interacting with the ground at four contact points and including tire models and load transfer. The model does not include suspension models, thus keeping a reasonable level of complexity. Load transfer (both longitudinal and lateral) is taken into account by explicitly imposing the holonomic constraints (for contact) and computing the reaction forces of the ground at the four contact points. Since the vehicle interacts with the ground at four contact points, it results in a hyper-static structure so that the reaction forces are not uniquely determined. Using the Principle of Least Work, we obtain a compatibility equation, providing for a unique resolution of the forces. The compatibility equation is parametrized by four strain parameters, one for each contact point. These parameters are related to those of the suspension, and provide a means for accounting for some dynamic aspects of the suspension without introducing additional states (and parameters) into the dynamics. We provide numerical computations validating the proposed model with respect to a multi-body virtual prototype on aggressive maneuvers.