Page - 80 - in Maximum Tire-Road Friction Coefficient Estimation

4 Sensitivity Analysis Region 1 (accelerating) The first region examined comprises the area with positive longitudinal accelerations. Figure 4.11 shows the characteristics of the normalised sensitivities versus µmax for 5 different longitudinal accelerations. The wheel speedsωfl andωfr of the driven wheels showthehighest sensitivity toµmax byaconsiderablemargin. Asexpected, theabsolute values of the sensitivities increase with higher dynamic excitation. For a longitudinal acceleration of about 0.4 m/s2, the change of sensitivity versus µmax is very small for values of µmax that are higher than 0.4. This indicates that at these low longitudinal accelerations, it will not be possible to provide a reliable estimate ofµmax forµmax>0.4 using solely the vehicle-dynamics-based method presented in this work. Nevertheless, at a longitudinal excitation of about 1.4 m/s2, the sensitivities of the wheel speeds already show a distinguishable characteristic up to a value ofµmax of 0.9. The wheel speedsωrl andωrr of the non-driven wheels also show a small dependence onµ max, especially for smaller values ofµmax. Their sensitivities also increase with higher dynamic excitation. Incontrast, thedependenceof the longitudinalvelocity is small forallµmax anddynamic excitations. This can be explained by the higher inertia and thus the slower response of the chassis than the wheels to a change inµmax. Thus, vx is not likely to contribute to an estimate of µmax. Due to the high dependence of the sensitivities of the driven wheelsonµmax, anall-wheeldrive(AWD)configurationwasalsosimulatedwithatorque distribution of 50% each on the front and rear axles, see Section 4.5.2. Region 2 (braking) Theresultingsensitivitiesof theareaofnegative bax (Region 2)areshowninFigure4.12, which shows the five selected data points of bax. Since, in contrast to the front-wheel drive configuration in Region 1, wheel torque is now applied to all four wheels, the rear wheel speedsalso showahigher sensitivity toµmax. Thebrakedistribution is set to60% on the front axle and 40 % on the rear axle for these simulations. The sensitivities of the wheel speeds show a very high dependence onµmax and on the longitudinal acceleration. The tendencies are similar for all acceleration points, but the absolute values vary as the wheel slips, and thus the longitudinal forces depending on µmax vary. Starting at about−2 m/s2, the wheel speeds already show significant sensitivities for µmax lower than≈ 1 at the simulated initial vx,0. This indicates that starting at this longitudinal acceleration, a distinction of these road or tire conditions may be feasible. Similar to Region 1, the sensitivity of vx,0 shows a negligible dependence onµ max. As it is a pure longitudinalmanoeuvre, thesensitivities forboththetwofrontandtherearwheel speeds 80