Page 307 - Automotive Engineering Powertrain Chassis System and Vehicle Body

CHAP TER 1 0. 1 Tyres and wheels

The following data can provide an example: due to a change to track width;
in the case of deviations in zero toe-in around 1% per
0
d ¼ 10 or v ¼ 1 mm;
Front axle force F Z;V;f ¼ 7kN; m Y;W ¼ 0:7 on uneven ground.
ðasphalted roadÞ
Tyres 155 R 13 78 S p T ¼ 1:8 bar; v 120 km h
In general it can be said that the ratio i R (see Fig. 10.1-31)
will take the following values:
In accordance with Equation 10.1.11 related to one wheel:
around 1.5 on cobbles
around 3 on potholed roads
F Y;W;f ¼ m Y;W F Z;W;f ¼ m Y;W F Z;V;f =2 ¼ 0:7 3:5kN around 4 on compacted sand
F Y;W;f ¼ 2:45 kN
up to 20 on loose sand.

The slip angle read off at F Y,W,f in Fig. 10.1-44 is 4 and
corresponds to the values in Fig. 10.1-43. 10.1.7 Rolling force coefficients
However, the dynamic wheel load transfer seen in and sliding friction
Fig. 10.1-5 plays a role during cornering, leading to
a greater slip angle on the wheel on the outside of the 10.1.7.1 Slip
curve (and thus also on the inner wheel), than resulted
from test rig measurements. On ‘82’ series tyres, a is If a tyre transfers drive or braking forces, a relative

about 5 , in accordance with Fig. 10.1-38:
movement occurs between the road and tyre, i.e. the
rolling speed of the wheel is greater or less than the
a z 7 m Y;W (10.1.4c) vehicle speed (see Equation 10.1.1b). The ratio of the
two speeds goes almost to N when the wheel is spinning,

With sin 5 in accordance with Equation 10.1.4b there is and is 0 when it locks. Slip is usually given as a percent-
an increase of age. The following equation applies during braking:

Dk R z 0:7 0:087 ¼ 0:061 vehicle speed circumferential speed of wheel
S X;W;b ¼
vehicle speed
Assuming a value of k R,0 ¼ 0.012, in accordance with
Equation 10.1.4a, on asphalted road S ¼ v v W 100 ð%Þ (10.1.4e)
X;W;b
v
k R ¼ i R k R;0 ¼ 1:2 0:010 ¼ 0:012 Drive slip is governed by:

and therefore the rolling resistance during cornering is v W v
S X;W;a ¼ 100 ð%Þ (10.1.4f)
v W
k R;co ¼ 0:012 þ 0:061 z 0:073
The different expressions have the advantage that, in
In the case of the understeering vehicles (Fig. 10.1-41) both cases where the wheel is spinning or locked, the
k R , co increases as a result of the additional steering input value is 100% and is positive.
and – if the wheels are driven – m rsl should be inserted for Further details can be found in Section 10.1.2.8,
m Y,W (see Equation 10.1.18); the slip angle increases Section 8.1.2 Chapter 8.1 and Section 10.1.2.
further. ‘65 Series’ tyres, on the other hand, require
a smaller steering input and thus make the vehicle easier 10.1.7.2 Friction coefficients and factors
to handle:
The higher the braking force or traction to be trans-

a ¼ 3 m Y;W (10.1.4d) mitted, the greater the slip becomes. Depending on the
road condition, the transferable longitudinal force
reaches its highest value between 10% and 30% slip and
then reduces until the wheel locks (100% slip). The
10.1.6.3 Other influencing variables quotient from longitudinal force F x and vertical force

F Z,W is the coefficient of friction, also known as the cir-
The rolling resistance increases in certain situations:
cumferential force coefficient
in the case of a large negative or positive camber

(the influence can be ignored up to 2 ); m X;W ¼ F X;W =F Z;W (10.1.5)

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