Page - 135 - in Maximum Tire-Road Friction Coefficient Estimation

B Tire modelTMsimple and tire dynamics 0 5 10 15 0 0.2 0.4 Slip angle α in degrees F z = 2 kN 0.6 0.8 F z = 4 kN F z = 6 kN F z = 8 kN Figure B.2.: Relaxation length for the tire described in Appendix D with cT,y= 100000 N/m at a transport velocity re ·|ωr|= 60 km/h computed according to Rill, [Ril06]. Tire damping dy is omitted. y e . F y y e c T,y d y W Figure B.3.: Lateral tire deflection ye caused by the lateral forceFy, [Ril06] The relaxation length rα is a function of the wheel loadFz and the slip angleα, as shown in Figure B.2. It increases with higher Fz and decreases with higher α, [dJ00, p.33]. However, since measurements of rα are not available for the investigated tires, the following approach is used to model τ. A lateral tire force acting in the contact patch causes a lateral deflection ye, see Figure B.3. A first order approximation considering ye is given by Rill, [Ril06], and reads FDy ≈Fy+ ∂Fy ∂vy y˙e. (B.5) With the lateral stiffness cT,y and the lateral damping coefficient dy of the tire, the 135