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Tyre characteristics and modelling 253
If we substitute the loaded radius as R l R u z into (5.10) we get
R
e
R
2
3
z
1
(5.11)
5.2.3 Tyre asymmetry
Although it is not intended to address the construction of a tyre in this textbook
a brief mention is needed of two types of tyre asymmetry that can occur,
these being conicity and plysteer. Both types of asymmetry can occur during
tyre fabrication and have the effect of introducing small amounts of lateral
force and aligning moment when a tyre is running at zero slip angle. It will
be seen later in this chapter that these offsets in lateral force or aligning
moment are visible when plotted against slip angle and that representation
in a simulation will depend on the sophistication of the tyre model used.
In a modern vehicle these effects become more important when considering
refinement and the ‘on-centre’ feel of the vehicle, particularly when
driving for long periods at high motorway speeds.
Conicity is an effect that arises due to assuming the tyre to have the shape
of a truncated cone as shown in Figure 5.6.
When considering the effect of conicity it must be realized that incorporation
in a tyre model must take careful account of the tyre axis sytem used.
In Figure 5.6, for example, the tyres shown with exaggerated conicity produce
a force towards the apex of the cone as the vehicle travels on a straight
heading. For the tyre on the left side this is a force that is positive when
referred to the Y SAE -axis. If the same tyre is now switched to the right side
of the vehicle, reversing the direction of rotation, the force is still towards
the apex but is now negative when referred to the Y SAE -axis.
Ply steer is an effect that arises due to a small bias in the positioning of the
cords within the tyre belt layers. This is shown in Figure 5.7 where it is
X SAE
Y SAE
Left
F Y
Direction of travel
F Y
Right
X SAE
Y SAE
Fig. 5.6
Generation of tyre lateral forces due to conicity