Page - 80 - in Maximum Tire-Road Friction Coefficient Estimation
Image of the Page - 80 -
Text of the Page - 80 -
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 ”max for 5
different longitudinal accelerations. The wheel speedsÏfl andÏfr of the driven wheels
showthehighest sensitivity to”max 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 ”max is very small for
values of ”max that are higher than 0.4. This indicates that at these low longitudinal
accelerations, it will not be possible to provide a reliable estimate of”max for”max>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 of”max of 0.9. The wheel speedsÏrl
andÏrr of the non-driven wheels also show a small dependence on” max, especially for
smaller values of”max. Their sensitivities also increase with higher dynamic excitation.
Incontrast, thedependenceof the longitudinalvelocity is small forall”max anddynamic
excitations. This can be explained by the higher inertia and thus the slower response
of the chassis than the wheels to a change in”max. Thus, vx is not likely to contribute
to an estimate of ”max. Due to the high dependence of the sensitivities of the driven
wheelson”max, 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 to”max. 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 on”max 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 ”max vary. Starting at
aboutâ2 m/s2, the wheel speeds already show significant sensitivities for ”max lower
thanâ 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 on” max. As it is a pure
longitudinalmanoeuvre, thesensitivities forboththetwofrontandtherearwheel speeds
80
Maximum Tire-Road Friction Coefficient Estimation
- Title
- Maximum Tire-Road Friction Coefficient Estimation
- Author
- Cornelia Lex
- Publisher
- Verlag der Technischen UniversitÀt Graz
- Location
- Graz
- Date
- 2015
- Language
- English
- License
- CC BY-NC-ND 3.0
- ISBN
- 978-3-85125-423-5
- Size
- 21.0 x 29.7 cm
- Pages
- 189
- Category
- Technik