Page - 75 - in Maximum Tire-Road Friction Coefficient Estimation

4 Sensitivity Analysis are used. The side slip angle consists of the side slip angle at small lateral accelerations close to zero (e.g. occurringwhenenteringacurve), which follows thegeometric relation β0 =β|bay→0 = lr R (4.17) with the distance lr of the vehicle’s COG to the rear axle and the curve radiusR of the trajectory, [HE11, p.110]. With higher accelerations, the additional angle ∆β adds to β0. It is not a function ofR, but of bay. Both the characteristic and its maximum value can be seen in Figure 4.6, which shows a characteristic measured during steady-state cornering, [fSI04]. For the maximum of β0, the minimum radius, i.e. the turning circle Rmin of the vehicle, [AG08], is used in Equation 4.17. By rearranging Equation 4.16 for vx=vy · 1 β0 +∆β , (4.18) and substituting the components of βwith its maximum values, the normalised lateral velocity v¯y reads v¯y= vy βmax0 +∆β max · 1 vmaxx . (4.19) Since it is assumedthat∆βmax doesnotdependonµmax whennotat thephysical limits, the sensitivity of v¯y reads ∂v¯y ∂µ = 1 βmax0 +∆β max · 1 vmaxx · ∂vy ∂µ . (4.20) Physical equivalence between vx and bωz is gained by normalising bωz and its sensitiv- -10 -5 0 5 10 -2 0 2 Lateral acceleration b a y in m/s2 Figure 4.6.: Characteristic of side slip angle ∆β (not including the geometric partβ0 at bay≈ 0 compared to β) measured at steady-state circular driving with an Audi A4 Avant 1.8 Tfsi 75