Page - 103 - in Maximum Tire-Road Friction Coefficient Estimation

5 Tire/road friction estimator 3.22). The calculation ofMD,i is discussed in Section 5.5.3. A model for combined longitudinaland lateral forces isusedtoconsider the reduced longitudinal forceavailable when longitudinal and lateral tire forces are present. Thus, lateral tire parameters also have to be known to calculate Fx,i. In total, six parameters each for the longitudinal and lateral tire force characteristics, as well as the nominal tire loadFz,nom and nominal friction potential µ0 have to be known (cf. the tire model described in Section 3.3). TablesD.4andD.3showtheparametersneeded for thevehicleandthe tire, respectively. 5.5. Considerations for the calculation of the longitudinal tire forces Within the rotational equilibrium for the wheels, see Equation 5.10, the horizontal tire force model described in Section 3.3.1 was used to calculateFx,i. The transmittableFx,i is limited when an additional Fy,i is present (cf. the depiction of the Krempel ellipse shown in Figure 2.5). This implies thatFy,i also impacts the calculation ofFx,i due to the combined tire model used. The inputs needed to calculate bothFx,i andFy,i are the longitudinal slip sx,i, the slip angle αi and the tire load Fz,i. As discussed in Section 2.2.2, the treatment of sx,i is the most critical part in most published friction potential estimation algorithms. The calculation ofαi is also not trivial, but fortunately it is not needed with a high accuracy forFx,i(Fy,i). In addition, the results presented in Section 6 focus on longitudinal manoeuvres. Some considerations concerning the estimation of both sx,i andαi are shown in Section 5.5.1 and E.3. Unfortunately, more than ESC sensors were necessary to calculate the longitudinal slipssx,iwith the required accuracy, see Section 5.5.1. For a future application, it is cru- cial to place greater emphasis on the slip determination. Nevertheless, with approaches combined with a global navigation satellite system (GNSS) or radar sensors, it will be possible to achieve the necessary accuracy of the longitudinal slip sx for series applica- tion. Adiscussionof themostpromisingmethodstoestimatesxasproposed in literature is also provided in Section 5.5.1. It also has to be mentioned that the hypotheses of the longitudinal tire forcesFx,i based on the tire model and the particles ofµ max had to be corrected with a linear factor1. The exact origin of the deviation is unclear, but it very likely comes from parameter inaccuracies. A deviation of the parameterµ0 in Equation 1The longitudinal tire forces had to multiplied with 0.8 for the wheels on the front axle and 0.6 on the rear axle, meaning that only 80 % and 60 % of the calculated hypotheses ofFx,i were considered, respectively 103