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

Abstract

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.

Identification of Road-Surface Type Using Deep Neural Networks for Friction Coefficient Estimation

“…These coefficients can be identified solving optimisation task using experimental data [37]. Cabrera et al [38] analysed the friction-slip curve as a function of speed using the Magic formula. After a tyre model is developed, the ABS algorithm is needed.…”

Tire–road friction coefficient estimation based on designed braking pressure pulse

“…The adequacy of the model is examined by comparing the longitudinal force-slip characteristics of the tire obtained from the above relation with those obtained from the widely used Magic Formula (MF) model, 36,37 as seen in Figure 3. The comparisons are illustrated considering three different normal loads (2, 3, and 4 kN) in Figure 3(a), and three different road friction coefficients (0.3, 0.6, and 0.9) in Figure 3(b).…”

Multi-sensor Fusion Road Friction Coefficient Estimation During Steering with Lyapunov Method

“…Vehicle dynamic control systems, such as the ASR (Anti-slip Regulation System), ESC (Electronic Stability Control), and AEB (Autonomous Emergency Brake), are realized by controlling the driving forces or braking forces so that the forces exerted by the road on the tires can be changed to maintain the stability of the wheels and the vehicle. The road friction coefficient is a key parameter for vehicle dynamic control systems [7,8], because it can reflect the dynamic motion limitations to a certain extent [9]. For human-operated vehicles, drivers can estimate the motion limitation of the vehicle and adapt their driving style using experience to prevent the vehicle from driving into critical conditions.…”