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4 Sensitivity Analysis
are used. The side slip angle consists of the side slip angle at small lateral accelerations
close to zero (e.g. occurringwhenenteringacurve), which follows thegeometric relation
β0 =β|bay→0 = lr
R (4.17)
with the distance lr of the vehicle’s COG to the rear axle and the curve radiusR of the
trajectory, [HE11, p.110]. With higher accelerations, the additional angle ∆β adds to
β0. It is not a function ofR, but of bay. Both the characteristic and its maximum value
can be seen in Figure 4.6, which shows a characteristic measured during steady-state
cornering, [fSI04]. For the maximum of β0, the minimum radius, i.e. the turning circle
Rmin of the vehicle, [AG08], is used in Equation 4.17. By rearranging Equation 4.16 for
vx=vy · 1
β0 +∆β , (4.18)
and substituting the components of βwith its maximum values, the normalised lateral
velocity v¯y reads
v¯y= vy
βmax0 +∆β max · 1
vmaxx . (4.19)
Since it is assumedthat∆βmax doesnotdependonµmax whennotat thephysical limits,
the sensitivity of v¯y reads
∂v¯y
∂µ = 1
βmax0 +∆β max · 1
vmaxx · ∂vy
∂µ . (4.20)
Physical equivalence between vx and bωz is gained by normalising bωz and its sensitiv-
-10 -5 0 5 10
-2
0
2
Lateral acceleration
b
a
y in m/s2
Figure 4.6.: Characteristic of side slip angle ∆β (not including the geometric partβ0 at
bay≈ 0 compared to β) measured at steady-state circular driving with an
Audi A4 Avant 1.8 Tfsi
75
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