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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
Maximum Tire-Road Friction Coefficient Estimation
- Title
- Maximum Tire-Road Friction Coefficient Estimation
- Author
- Cornelia Lex
- Publisher
- Verlag der Technischen Universität 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