Page - 21 - in Maximum Tire-Road Friction Coefficient Estimation

2 Estimation of the friction potential sliding speed is the same for the whole contact patch. Typical longitudinal and lateral characteristics of the coefficient of frictionµbetween tire and road are shown in Figure 2.3. For small slip variables sx and α, µ increases linearly. With increasing slip,µ increasesdegressivelyup to themaximumµmax which is defined inEquation2.2, until it slightlydecreases andreaches saturation. Innon-critical driving states, vehicles travel in the lower slip regions of Figure 2.3. The difference between the instantaneous or demanded coefficient of frictionµD in the current driving states and the availableµmax can be defined as the safety marginµS. -20 -15 -10 -5 0 5 10 15 20 Slip angle α in degrees -40 -30 -20 -10 0 10 20 30 40 Longitudinal slip s x in % µx+ max µD µx- max µy max µD µ S,x µ S,y Figure 2.3.: Characteristics of utilised longitudinal and lateral coefficients of frictionµx (left) andµy (right) for a constant normal force, longitudinal velocityvC,x, temperature and inflation pressure. The difference between a currently de- mandedµD and the friction potentialµ max is the safety marginµS. Superposition of shear stresses and rolling resistance Thevaluesof the frictionpotentials forbrakingandacceleratingmaydiffer. Instandstill, the tire’s toroid form is flattened under a load, introducing shear stresses in the contact patch. Theysuperposethe longitudinal shearstressescausedbyaccelerationandbraking forces in the contactpatch, seeFigure2.4. Considering theverticalpressuredistribution in the contact patch when the resulting force is before the centre plane of the tire, the friction potential for accelerating is generally higher than that for braking, [Mun12, H2 p.34]. On a rolling tire, the asymmetric pressure distribution in the contact patch also causes a resistance torque, [MW04, p.18], which has to be compensated. 21