A two step approach has been chosen to derive an approximation from the steady state measurements of tyre characteristics. First, the measurements of the tyre forces in a preprocessed form are normalized with the maximum contact coefficients and the corresponding slip values. Then, with the measurements now forming a very narrow band, a single curve can be used to approximate the whole tyre characteristics. The mutual influences of lateral and longitudinal forces are taken into account with combined slip values, which cover the whole range from locked wheels to heavy spinning wheels including small camber angles. Different surface conditions are considered with three parameters and the sliding coefficient so that the change of original characteristics can be handled easily. The self aligning torque is described by three components: the lateral force times pneumatic trail, the spin-slip torque and the reaction of lateral deflection and longitudinal force. Once again for the approximation of the pneumatic trail a normalization is used leading to a single curve for the whole characteristic. A similar method was applied to get a feasible approximation for the spin-slip torque. Comparisons of calculated and measured characteristics are presented to validate the approximation. Whole characteristics for a tyre moving with lateral and longitudinal slip demonstrate the possible range of application.
Abstract