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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
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Maximum Tire-Road Friction Coefficient Estimation
- Titel
- Maximum Tire-Road Friction Coefficient Estimation
- Autor
- Cornelia Lex
- Verlag
- Verlag der Technischen Universität Graz
- Ort
- Graz
- Datum
- 2015
- Sprache
- englisch
- Lizenz
- CC BY-NC-ND 3.0
- ISBN
- 978-3-85125-423-5
- Abmessungen
- 21.0 x 29.7 cm
- Seiten
- 189
- Kategorie
- Technik