Identification of Pacejka’s scaling factors from full-scale experimental tests

Abstract

A set of scaling factors has been introduced by Pacejka into his ‘magic formula’ tyre model to take into account the influence of a number of external overall parameters such as road roughness, weather conditions and suspension characteristics. These scaling factors are important for a correct prediction of tyre–road contact forces but are not a function of the tyre itself. From a different point of view, one could say that scaling factors should remain constant for different tyres on the same circuit, with the same weather conditions and with the same car. After having characterized different tyres through indoor tests (which do not consider external overall parameters) and after having identified Pacejka’s coefficients with scaling factors assumed to be one, several outdoor experimental tests have been carried out to determine the influence of vehicle and road surface conditions on scaling factors. These experimental data allowed us to identify, through a minimization approach, the ‘best’ set of Pacejka’s scaling factors for that vehicle and that tyre on that track. Scaling factors for the same track and vehicle but for different tyres were compared to check whether their values remained constant. All experimental data shown in this paper comes from tests carried out within the VERTEC project (vehicle, road, tyre and electronic control systems interaction: increasing active vehicle safety by means of a fully integrated model for behaviour prediction in potentially dangerous situations) (official contract G3RD-CT-2002-00805), a European funded research project that puts together knowledge from vehicle manufacturers (Volvo, Porsche and (CRF)), tyre manufacturers (Pirelli and Nokian Tyres), control logic manufacturers (Lucas Varity GmbH), road maintenance experts (CETE), transport research organizations (TRL) and (VTI) and universities (HUT) and (UNIFI)). The results shown in this paper are obtained by tests performed during tasks 2a (Reference tyre characterizations and tests) and 2b (Development and validation of tyre–pavement interaction model) of VERTEC project. The partners involved in these tasks are Pirelli, Nokian, Porsche, CRF, CETE, VTI, HUT and UNIFI.

Keywords:

• Tyre–road contact forces
• ‘Magic formula’ tyre model
• Pacejka’s scaling factors
• Indoor tyre testing
• Outdoor tyre testing

Acknowledgements

We wish to acknowledge kindly the European Community for having funded this research project and all other partners, especially Mr Mancosu, coordinator of the VERTEC project (official contract G3RD-CT-2002-00805) and the partners involved in task 2a (Reference tyre characterizations and tests) and task 2b (Development and validation of Tyre–Pavement interaction model).

Notes

In this work, MF tyre version 2002 is considered 2.

For low-friction surfaces, such as smooth ice or snow, the dispersion of the scaling factor is smaller since the peak value of the lateral force is reached on the considered slip angle range.