Sophisticated but quite simple contact calculation for handling tire models

Handling tire models like Pacejka (Tire and Vehicle Dynamics, 3rd edn., Elsevier, Amsterdam, 2012) or TMeasy (Rill in Proc. of the XV Int. Symp. on Dynamic Problems of Mechanics, Buzios, RJ, Brazil, 2013) consider the contact patch as one coherent plane. As a consequence, the irregularities of a rough road profile must be approximated by an appropriate local road plane that serves as an effective road plane in order to calculate the geometric contact point and the corresponding contact velocities. The Pacejka/SWIFT tire model employs a road enveloping model that generates the effective height and slope by elliptical cams. TMeasy just uses four representative road points for that purpose. In addition, TMeasy replaces the geometric contact point by the static contact point and shifts it finally to the dynamic contact point that represents the point where the contact forces are applied. In doing so, a rather sophisticated but still simple contact calculation is possible. Simulations obtained with a virtual tire test rig and fully nonlinear three-dimensional multibody system models of a motor-scooter and a passenger car demonstrate the potential of this contact approach.