Page - 58 - in Maximum Tire-Road Friction Coefficient Estimation

3 Vehicle model wheels read Fz,fl = Fz,f 2 −∆Fz,φ,f, (3.21) Fz,fr = Fz,f 2 +∆Fz,φ,f, Fz,rl = Fz,r 2 −∆Fz,φ,r and Fz,rr = Fz,r 2 +∆Fz,φ,r. 3.2.3. Effective tire radius The position of the instantaneous centre of rotation ICR of the free rolling wheel is characterised by the effective tire radius re. It it is derived from the effective rolling circumferenceUe and given by re= Ue 2pi . (3.22) Both re andUedepend on the tire loadFz and the wheel’s rotational speedωr, as shown in Figure 3.11. According to Hirschberg, the effective tire radius re, which is located r rS re ∆z Fz r r r C ICR ∆z r Fz,nom Figure 3.11.: Relation between effective tire radius re, static tire radius rS radius and unloaded tire radius r0, according to Hirschberg, [HW12, p.17]. between the unloaded tire radius r0 and the static tire radius rS, can be approximated based on physical considerations, [Hir09b]. The result of these considerations is given by Equation 3.23. The influence of Fz is considered in the tire’s vertical deflection ∆z=Fz/cT,z, where cT,z denotes the linear global tire stiffness at the operating point Fz,nom. Thus, the effective tire radius may be approximated by re≈ 1 3 r0 + 2 3 rS= r0− 2 3 ∆z= r0− 2 3 Fz cT,z . (3.23) 58