Page - 19 - in Maximum Tire-Road Friction Coefficient Estimation

2 Estimation of the friction potential On a smooth, even, dry road, the adhesion component has the main influence on the friction force, see Figure 2.1 (left). It is caused by molecular bonds between the friction partners and strongly depends on intermediary layers such as water or snow, [Bac98, p.4]. The pressure distribution of rubber material sliding over irregularities caused by the roughness of the road is symmetrical for low sliding speeds vS. With higher sliding speeds, the relaxation of the rubber is not fast enough due to internal damping. Small areas lift from the road surface, which results in an uneven pressure distribution, see Figure 2.1, right. The component of the internal friction forceFF projected to the plane of motion, which is called the hysteresis component (see example of element dFhn in Figure2.1), superposes the friction force in thecontact surface. Inadditiontothesliding speed, it also depends on the geometry of the road and the visco-elastic properties of the rubber. Unlike adhesion, this component is insensitive to the presence of intermediary layers, [Bac96, p.22]. The last two components only occur under certain circumstances. Viscosity components, which are only relevant when thick intermediary liquid layers are present, occur due to shear effects. Cohesion forces appear in cases of abrasion and tire wear. The surface of the rubber material increases, leading to friction loss, [Bac96, p.4]. 2.1.2. Friction potential of the rotating tire Friction-based force transmission requires a relative motion, or the tendency to motion, between the friction partners. In the case of tire road friction, the relevant relative motion is the sliding velocity vS in the contact patch. In the longitudinal direction, it is given byω ·re−vW,xwith the effective tire radius re, the wheel’s rotational speedω and the longitudinal velocity component vW,x in the contact patch. One frequently used value of the longitudinal sliding speed is described by the longitudinal slip sx and reads sx=        ω·re−vW,x |vW,x| vW,x>re ·ω ω·re−vW,x |ω|·re vW,x<re ·ω 0 vW,x= re ·ω. (2.3) In the lateral direction, the relevant sliding velocity is given by the lateral slip angle α= arctan ( vW,y vW,x ) (2.4) which also includes the lateral component vW,y of the velocity in the contact patch. Figure 2.2 shows a graphical explanation of re,ω, vW,x and vW,y and the velocity vC in the wheel centreC. 19