A Procedure for Determining Tire-Road Friction Characteristics Using a Modification of the Magic Formula Based on Experimental Results

Knowledge of tire-road friction characteristics is essential for the proper performance of most relevant vehicle active safety systems. Therefore, its determination is necessary to improve the effectiveness of these systems and to avoid or reduce the consequences of traffic accidents. For this reason, there is a great deal of literature concerning methods and devices for measuring and modeling tire-road friction. Most of these methods have focused on determining the road friction resistance, taking only road composition and making measurements in wet conditions into account. However, friction forces are also dependent on the tire type, since the contact is established between the tire and the road in real driving conditions. Thus, the type and characteristics of the tire have to be considered in the study of the interaction between the vehicle and the road. The aim of this work is to unify the study of the friction coefficient, taking into consideration the two existing bodies involved in the contact, i.e., the tire and road and the main factors that influence the forces in the contact. To this end, a modification of the Pacejka Magic Formula is proposed to include the effects of the main parameters that influence the contact, such as road composition and its state, tire type, vehicle speed, and slip between the tire and the road. To do so, real tests have been conducted on several roads and with different operating conditions. As a result, a more accurate tire-road friction model has been obtained.