Estimated combined steady state tyre slip characteristics

Excessive behaviour of vehicles is often the subject of study, motivated by either the development of active safety systems uch as ESP, or the improvement of vehicle performance such as for racecars. In all of these cases, combined slip needs to be taken into account. In many cases however, the full set of tyre characteristics is not available. Consequently, one needs to work with inaccurate combined slip properties based on estimated slip stifnesses and friction levels. It would be a great advantage if combined slip characteristics could be estimated accurately, especially for truck tyres and racecar tyres, where facilities are rare and testing is very expensive. For passenger cars and light van tyres, about 60% of the testing effort is spent in combined slip. This means time and costs which could be saved by this accurate estimation. Moreover, apart from this reduction of the testing effort, the estimation could be a tool for assessment in testing tyres in combined slip leading to better quality tests results. Anyhow, it will permit to derive combined slip characteristics when no test-data are available. First, some fundamental aspects in tyre modelling are given with the MF-Tyre Model (Magic Formula) treated in detail. Combined slip as described by the MF-Tyre model is discussed with the characteristics derived and compared with different passenger car tyres. In parallel, combined slip is also studied from a more fundamental scope using the physical Brush Model, with special focus on the ratio between tyre forces under pure slip and combined slip conditions (the weighting functions). Various methods to derive these weighting functions based on pure slip characteristics without testing are treated. Among these, two methods lead to satisfactory results, the Slip Circle Sinusoidal Method (SCS) presented by Pottinger and especially the Practical Slip Similarity Method (PSS), derived and developed by the authors. Among others, these methods will be compared with the Magic Formula fits and the experimental results with observed deviations for the PSS-method in shear force with measurement results bounded by 5% for large tyre load and less than 8% for low tyre load. A comparision of the SCS-method and PSS-method with the MF-fits for large slip suggests improvements of the Magic Formula tyre model. Between the various estimations for the prediction of the combined slip based on pure slip characteristics, the Slip Circle Method and the Practical Slip Similarity Method, derived and developed by the authors will lead to a satisfactory prediction with respect to measurement data. In addition, estimated combined slip outside of the measurement range is discussed.