Page - 24 - in Maximum Tire-Road Friction Coefficient Estimation

2 Estimation of the friction potential Friction potential on vehicle level According to Weber, [Web04, p.18-19], the relation of the local friction potentials and the global friction potentials for a vehicle with i= 1, ..,4 wheels in longitudinal and lateral direction is given by µmaxG,x = 1 4∑ i=1 Fz,i · 4∑ i=1 µmaxx,i ·Fz,i, (2.8) µmaxG,y = 1 4∑ i=1 Fz,i · 4∑ i=1 µmaxy,i ·Fz,i. (2.9) Analogously to Equation 2.8, axle-wise values of the friction potential could be defined. One alternative way to calculate the global friction potential µmaxG can also be derived from the vehicle reaction rather than the wheel’s friction potentialsµmaxx,i . Excluding air, rolling and climbing resistance, the global friction potentials can be described by the maximum achievable accelerations ba max x and ba max y . Using the example of the longitu- dinal direction, the friction potential then reads µmaxG,x = ba max x g , (2.10) [Web04, p.28]. This representation directly shows the characteristics also given by the Krempel ellipse in Figure 2.5. Without subscriptsL orG, µmax is used for the friction potential on wheel level. 2.1.3. Overview of relevant influencing factors Several factors influence the friction potential. Bachmann conducted a comprehensive literature review and found the relevant factors shown in Table 2.1, [Bac98, p.7-8]. Most of theseparameters are thoroughlydiscussedwithin theworksof Bachmann, see [Bac96] and [Bac98]. The parameters can be divided into tire, road, intermediary layer and ve- hicle-dependent parameters. 24