Page - 48 - in Maximum Tire-Road Friction Coefficient Estimation

3 Vehicle model Table 3.4.: Mean relative deviations of braking manoeuvre for model setups with a devi- ation higher than 5 % and phase shifts higher than 0.05 s in decreasing order for the investigated variables Variable Highest influence Second highest influence Wheel speeds (front) effective tire radius wheel moment of inertia 15.71 % 11.46 % Wheel speeds (rear) effective tire radius wheel moment of inertia 15.57 % 11.45 % Tire loads tire load - 15.6 % Longitudinal tire forces tire load - 16.07 % longitudinal control cannot follow the speed profile properly at highµmax when not con- sidering tire force dynamics. A similar effect occurred in the braking manoeuvre, where somecombinationsofµmax andthe longitudinalvehicle speedcouldnotbe reachedwith- out tire-force dynamics. This is a controller-specific problem and is not related to the evaluation problem. Therefore, these combinations were not considered in Table 3.4. It is possible that the maximum mean relative deviations of the few cases of simulation without tire force dynamics and near the physical limits are slightly higher than those presented in Table 3.4. Nevertheless, it is unlikely that it exceed the 5 %, as all model variations not listed have mean relative deviations below 1 %. According to the results presented in Table 3.3 and Table 3.4, the dynamic tire load distribution, effective tire radii dependent on the dynamic tire loads, varying wheel moment of inertia for the driven axles, and the longitudinal tire dynamics have to be considered. The effort to include varying tire loads and an effective tire radii depending on the dynamic load is relatively low. It is also necessary to include a varying tire load for accurate simulation of lateral manoeuvres, see Section 3.1.4. Since the maximum deviation is slightlyabovethe limitof5%, longitudinal tiredynamicsarenotconsidered, despite causing a phase shift on longitudinal velocity and wheel rotational speeds. This is acceptable because the tire’s longitudinal stiffness cT,x>cT,y, and thus the influence of the longitudinal tire dynamics is smaller than that of the lateral tire dynamics, as shown in Section 3.2, [Hir09b]. The variation of the wheel moment of inertia impacts thewheel rotational speeds, seeTable3.3andTable3.4. Duringbraking, thegearbox is simulated as fully decoupled, and only the wheel’s moment of inertia is relevant. During 48