Page - 81 - in Maximum Tire-Road Friction Coefficient Estimation

4 Sensitivity Analysis 0.2 0.6 -40 -35 -30 -25 -20 -15 -10 -5 0 µmax b a x =0.4, b a y =0 b a x =1.4, b a y =0 b a x =2.4, b a y =0 b a x =3.4, b a y =0 b a x =4.4, b a y =0 1.0 v x w fl , w fr w rl , w rr 0.2 0.6 µmax 1.0 0.2 0.6 µmax 1.0 0.2 0.6 µmax 1.00.2 0.6 µmax 1.0 Figure 4.11.: Normalised sensitivities for all state variables except vy and bωz, which are zero within this region, for selected acceleration data points in Region 1 (positive longitudinal excitation). Note: High values of bax and bay cannot be reached at lowµmax, thus not allµmax are shown for all data points. are congruent. For most of the longitudinal acceleration data points, the front wheel speeds show a higher sensitivity toµmax due to the higher braking torque applied on the front axle. At a longitudinal acceleration of about−6 m/s2 and higher, the sensitivities of the rear wheels exceed those of the front wheels for the simulated initial vx,0. Due to the higher wheel load on the front axle during braking, the rear wheels are relieved, and wi increases more rapidly than on the front axle. The high dependency of the sensitivities of the wheel speeds onµmax and the applied brake torque on the front and rearaxles is comparable to the results fromthecomparisonofAWDandFWDin Region 1. Thus, a theoretical configuration with brake torque only applied to the front wheels was also simulated, see Section 4.5.3. Region 3 (pure cornering) Similar to the results from Region 1 and Region 2, the wheel speeds show the highest sensitivity for driving states with purely lateral excitation in Region 3. as shown in Figure 4.13. A left turn is made during this manoeuvre. With increasing lateral ac- celerations, the tire loadFz,fl decreases, which at first causes the absolute value of the sensitivityof thewheel speedωfl to increase faster comparedto thatofωfr. Atacertain point, the sensitivity ofωfr exceeds that ofωfl, due to the influence ofµ max within the 81