Daniele Arosio

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

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.

A Fast and Reliable Dynamic Tyre-Road Contact Model for ABS Braking Manoeuvre Simulations

Due to the dimensions of the tyre-road contact area, transients in a tyre last approximately 0.1s. Thus, in the case of abrupt maneuvers such as ABS braking, the use of a steady-state tyre model to predict the vehicle’s behavior would lead to significant errors. Available dynamic tyre models, such as Pacejka’s MF-Tyre model, are based on steady-state formulations and the transient behavior of the tyre is included by introducing a first order differential equation of relevant quantities such as the slip angle and the slippage. In these differential equations the most significant parameter used to describe the transient behavior is the so-called relaxation length, i.e. the distance traveled by the tyre to settle to a new steady–state condition once perturbated. Usually this parameter is assumed to be constant.Copyright