Magic formula tyre model with transient properties

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Magic formula tyre model with transient properties

Pacejka, H.B. / Besselink, I.J.M.

The widely used empirical tyre model, the newest version is presented, is based on the so-called Magic Formula. The development of this model was started in the mid-eighties. In a cooperative effort TU Delft and Volvo developed several next versions, in which the combined slip situation was modelled from a physical view point. In 1993 Michelin introduced a purely empirical method using Magic Formula based functions to describe the tyre horizontal force generation at combined slip. In the previous version of 'Delft Tyre' this approach was adopted and the original description of the aligning torque has been altered to accomodate a relatively simple combined slip extension. The model presented is not restricted to small values of slip and the wheel may run backwards. A full set of equations of the steady state part of the model of the new version 'Delft Tyre 97' is given. The description of transient and oscillatory properties of the tyre-wheel combination has been improved. The dynamic behaviour may be covered by the model as long as the frequency of the wheel motion remains well below the first natural frequencies of the belt with respect to the rim and if the wavelegth of motion and road undulation is sufficiently large with respect to the tyre contact length.