Virtual tires in the early vehicle development phase

Pacejka’s Magic Formula (MF), a semiempirical tire model, is nowadays the worldwide standard for vehicle dynamic simulations [1]. In the past, various measuring methods have been developed to parameterize Pacejka’s tire model; the most famous one is the TIME procedure [2]. All of them use several measuring points within the tire’s operating area. After having fitted the MFparameters to these measuring points the tire model can be used for vehicle dynamic simulations. However, in the early vehicle design phase real tires are often not available. Furthermore, cost and time pressure raises the demand for new virtual methods. The goal is to develop virtually the tire in conjunction with the vehicle. This extends the possibilities of the designers. This article presents a new parameterization method for the MF-tire model. The base concept is to define characteristic values (CVs) that fully describe the properties of a tire. They can be set either according to a simple measurement on a tire test rig, or to the specification of the user. These tire CVs are then used to generate a MFparameter file. A genetic algorithm achieves the best fitting results. Possible applications are the modification of specific tire characteristics, a global sensitivity analysis (between tyre CVs and the vehicle behaviour) and a new concept of a tire measurement procedure. Keywords—Magic Formula, optimisation, sensitivity, vehicle dynamics.