Page - 23 - in Maximum Tire-Road Friction Coefficient Estimation

2 Estimation of the friction potential µ x µ y µmax µ D µ x+ maxµ x- max µ y max µ y max µ S Figure 2.5.: Schematic representation of the combined friction potential based on the outer limits of a Krempel diagram, based on Heißing et al., [HE11, p.62]. The absolute value ofµmaxx− is higher than that ofµmaxx+ when considering the vehicle’s different braking, acceleration and cornering capabilities. effective surface. This consideration applies to local views of the contact patch as well as to global views of one wheel, one axle or a vehicle. The smallest level of scale concerning friction-based force transmission within this thesis are local effects in the contact patch, which are related to the local shear stresses τx and τy and the normal stress σz acting in vertical direction by µL,x= τx σz and µL,y= τy σz , (2.5) cf. [Rot92,p.13]. These local coefficientsof frictionµL,x andµL,y are relatedtoa friction coefficientµxmeasurable for awholewheelby the effective frictionareaAe. The friction coefficientµ and the friction potentialµmax for one whole wheel are given by µx = Fx Fz , (2.6) µmaxx = Fmaxx Fz (2.7) with the longitudinal tire forceFx and the vertical tire forceFz. Accordingly, the coeffi- cient of frictionµy in the lateral direction and its friction potentialµ max y are calculated with the lateral tire forceFy. Nevertheless, even on a free rolling wheel, there are local friction forces due to the shear stresses resulting from the effect shown in Figure 2.4. Thus, although the whole wheel is not yet transmitting forces, the local coefficient of friction is partially utilized (µL>0 atµ= 0), [Rot92, p.13]. 23