The PAC2002 advanced handling tire model

Abstract

The history of ‘Magic Formula’ tire models is shortly described and the PAC2002 tire model is the latest generation of this type of tire models. PAC2002 is a semi-empirical tire model because it has both the empirical (mathematical formulas) and physical modeling components. The PAC2002 tire model can describe the behavior of tires traveling over relatively smooth road surfaces and its dynamical behavior is valid for frequencies up to 12 Hz. The structure of the model is explained and it is shown what the influences of the different Magic Formula-factors have on the characteristic. The classic tire model input quantities are extended with turn-slip, which is one of two components of tire spin. The functional expressions for steady-state cornering and braking/driving are given. In addition to the stretched-string (first-order relaxation effects) model to describe tire transient behavior, the newly added alternative contact-mass model is explained. The new formula set for tire spin and parking is given, which extends validity of the PAC2002 especially for low speed. Some typical advanced handling applications are given for which the tire model can be used. It is described what measurement program is needed to obtain the tire model parameters. A reduced measurement program can be used that is more cost-effective than and gives comparable accuracy to the full program. It is shown that the additions to PAC2002 (contact-mass transient model, tire spin and parking) result in considerable improvements compared to Magic Formula tire models with the traditional ‘first-order relaxation’ transient tire modeling. Next to the common applications of a Magic Formula tire model, the PAC2002 can be used for analyzing parking behavior, low- and zero-speed applications, changing friction properties as well as in more dynamic analysis such as ABS braking.