Page - 22 - in Maximum Tire-Road Friction Coefficient Estimation

2 Estimation of the friction potential I III II I III II τ x v x acceleration deceleration τ x L L τ x L tread elements entering contact patch tread elements leaving contact patch Figure 2.4.: Longitudinal shear stress τx in the contactpatchbetween tire and roadwith lengthL due to: I. toroid flattening, II. acceleration/deceleration and III. superposition of both conditions, based on Mundl, [Mun12, H2 p.34] Combined friction potential Figure 2.5 shows a representation of the friction potential for combined slip basedon the Krempeldiagram. IntheKrempeldiagram, the lateral tire forcesare shownwithrespect to the longitudinal tire forces for a constant normal force, [HE11, p.62]. The combined friction potential consists of the maximum combined tire forces (i.e. the outer limits of the Krempel diagram) divided by the normal force. This representation is connected to Kamm’s circle for µmaxx = µ max y , but also considers different friction potentials for braking, accelerating and cornering. Figure 2.5 shows that in the case of combined horizontal tire forces acting on the contact patch, the available friction potential only decreases in either the longitudinal or the lateral direction. Friction potential on wheel level The effects mentioned for sliding and slipping rubber are local effects in the contact patch. According to Roth, [Rot92, p.8-10,13], the behaviour of the overall system can be described as the sum of these local effects, i.e. the integral of the local effects over the 22