Page 305 - Automotive Engineering Powertrain Chassis System and Vehicle Body

CHAP TER 1 0. 1 Tyres and wheels

road surface. The more softly sprung the vehicle, the
more the variations in radial force in the tyre make
themselves felt.
The lateral force variations of the tyre influence the
straight-running ability of the vehicle. Even with a tyre
that is running straight, i.e. where the slip angle is zero,
lateral forces occur, which also depend on the direction
of travel.
The variations in longitudinal force that occur must be
absorbed on the chassis side by the rubber bearings.
The ply steer force dependent on the rolling angle
results from the belt design because of the lateral drift of
Fig. 10.1-30 The tyre spring rate can fluctuate depending on the the tyre contact area as a consequence of flat spotting. In
manufacturing process, shown as c 1 to c 8 .
contrast, the conicity force, resulting from a change in
diameter across the width of the tyre, is not dependent
on the rolling angle. Both forces disturb the straight
175 R 14 88 S steel radial tyre, loaded at F Z,W ¼ 4.5 kN
and pressurized to p T ¼1.9 bar. Assuming this had a mean running of the vehicle.
1
spring rate c T ¼ 186 N m , which fluctuates by 5%,
the upper limit would be c T,max ¼ 195 N mm 1 and the
1
lower limit would be c T,min ¼ 177 N mm . Under ver- 10.1.6 Rolling resistance
tical force F Z,W ¼ 4.5 kN ¼ 4500 N the tyre would,
according to Equation 10.1.3a, have as its smallest jounce
travel: 10.1.6.1 Rolling resistance in straight-line
driving
F Z;W 4500
s T;min ¼ ¼ ; s T;min ¼ 23:1mm Rolling resistance is a result of energy loss in the tyre,
C T;max 195
which can be traced back to the deformation of the area
(10.1.3a) of tyre contact and the damping properties of the rubber.
These lead to the transformation of mechanical into
and
thermal energy, contributing to warming of the tyre.
s T;max ¼ 25:4mm Sixty to 70% of the rolling resistance is generated in
the running tread (Fig. 10.1-5) and its level is mainly
as the greatest travel. The difference is: dependent on the rubber mixture. Low damping running
tread mixtures improve the rolling resistance, but at the
Ds T ¼ s T;max s T;min ¼ 2:3mm
same time reduce the coefficient of friction on a wet road
ThisdifferenceinthedynamicrollingradiusofDs T ¼ 2.3mm surface. It can be said that the ratio is approximately 1:1,
would cause variations in vertical force DF z,w , which never- which means a 10% reduction in the rolling resistance
theless is still smaller than the friction in the wheel leads to a 10% longer braking distance on a wet road
suspension bearings. At a speed of perhaps 120 km/h and surface. The use of new combinations of materials in the
travelling on a completely smooth road surface, this running tread (use of silica) has led to partial reduction of
would nevertheless lead to vibration that would be par- the conflict between these aims.
ticularly noticeable on the front axle. Rolling resistance is either expressed as a rolling
The vehicle used as an example should have a body resistance force F R or as the rolling resistance factor k R –
spring rate of c f ¼ 15 N/mm per front axle side. The also known as the coefficient of rolling resistance:
travel Ds T would then give a vertical force difference of:
F R ¼ k R F Z;W ðNÞ (10.1.4)
DF Z;W;f ¼ c Ds T ¼ 15 2:3; DF Z;W;f ¼ 34:5N
f
The factor k R is important for calculating the driving
performance diagram and depends on the vertical force
The friction per front axle side is, however, not generally
below F Z,W and the tyre pressure p T . Figure 10.1-31 shows the
theoretical k R curve of tyres of different speed classes as
F fr ¼ 100 N a function of the speed. Although the coefficient of
rolling friction of the T tyre increases disproportionally
1
so it can only be overcome if greater variations in ver- from around 120 km h , this increase does not occur in
1
tical force occur as a result of non-uniformity in the H and V tyres until 160 to 170 km h . The reason for

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