Page - 45 - in Maximum Tire-Road Friction Coefficient Estimation

3 Vehicle model forces, as described in Section 3.3.2. This setup is compared to pure static tire forces, as derived in Section 3.3.1. • Effective tire radius In the reference setup, the effective tire radii are calculated as a function of the tire load. The variation setup uses constant tire radii that correspond to the static tire radius rS in nominal vehicle position. •Dynamic vertical tire load In the reference setup, the input for the horizontal tire contact force model is the dynamic tire load calculated considering the vehicle’s DOF pitch and roll as well as springs and dampers. In the variation setup, the static tire load is used as input for the model of the horizontal tire contact forces. •Wheel moment of inertia The wheel moment of inertia depends on the mass distribution of the wheel, brake disk, and driveline, as well as the engaged gear. Two setups of constant wheel moments of inertias are compared. As a reference, the decoupled wheel moment of inertia as shown in Table D.2 is used. For the second setup, the value of the wheel moment of inertia when the first gear is engaged is used, which represents the highest moment of inertia. 3.1.4. Results for double lane change manoeuvre Figure 3.3a) shows the mean relative deviation ∆ay of the lateral acceleration for the DLC manoeuvre with ARB variation at the front and rear axles. With increasing lon- gitudinal velocity vx, the lateral acceleration bay increases, as does the mean relative deviation ∆ay between the two model settings compared. Nevertheless, ∆ay is within the specified limit of 5 %. For example, the mean relative deviation ∆Fy,rl of the lateral tire forceFy,rl showsasimilar tendency, seeFigure3.3b), butexceeds the specified limits and is thus listed in Table 3.2. Both state variables do not show a dependence on the friction potentialµmax. Table 3.2 shows the maximum mean relative deviations exceeding the limits of 5 % and a phase shift of 0.05 s. The model setups with the highest maximum mean relative deviations are presented in decreasing order. The maximum deviations in Table 3.2 show that lateral tire dynamics, a dynamic tire load distribution, a non-linear steering ratio and anti-roll bars at the front and rear axle have to be considered in the vehicle 45