Page - 20 - in Maximum Tire-Road Friction Coefficient Estimation

2 Estimation of the friction potential ω α zi ICR re rs r xi C vC,x vS,xxW,i vW vS W W vS,y y W,i Figure 2.2.: Kinematic wheel quantities of the i-th wheel coordinate system {Oi,xi,yi,zi}with its origin in the wheel centreC according to ISO 8855, [fSI11]; the graphic depiction is based on Hirschberg, [HW12, p.16]. The velocity in the contact pointW between tire and road is described by its components vW,x and vW,y. The components vS,x and vS,y of the sliding ve- locity vS differ from vW byω ·re. The effective tire radius re is the distance between the wheel centreC and the instantaneous centre of rotation ICR. In addition, the unloaded tire radius r0, the static tire radius rS, the wheel speedω and the lateral slip angleα are shown. As shown in Equation 2.3, for forward driving the conditions braking (−1<sx< 0) and accelerating (0<sx<1) have to be distinguished for a slipping tire. As previously mentioned, slip is necessary to transfer friction forces. Longitudinal slip can be divided into twoeffects: slip createdbyslidingof the rubberonthe roadsurfaceandslip thatoc- curs due to the deformation of the tire profile elements when entering the contact patch. For small slip values, deformation slip dominates, whereas with increasing slip, sliding slip outweighs deformation slip. At pure rolling (sx≈ 0), deformation slip is present when tire profile elements enter or exit the contact patch, see next section. For pure sliding (sx∼±1), the effects discussed in Section 2.1.1 dominate. In this condition, the 20