Page 166 - Tribology in Machine Design

152 Tribology in machine design

4.14.1. Creep of an automobile tyre
An automobile tyre will tend to creep longitudinally if the circumferential
strain in the contact patch is different from that in the unloaded periphery.
In accordance with the theory of the membrane, there is a shortening in the
contact patch of the centre-line of the running surface. This is equal to the
difference between the chord AB and the arc AB (see Fig. 4.48). This leads to
a strain and consequently to a creep given here as a creep ratio:

The silent assumption regarding eqn (4.177) is that the behaviour of the
contact is controlled by the centre-line strain and that there is no strain
outside the contact. The real situation, however, is different.

4.14.2. Transverse tangential forces
Transverse frictional forces and moments are operating when the plane of
the tyre is slightly skewed to the plane of the road. This is usually called
sideslip. Similar conditions arise in the response to spin when turning a
corner. The usual approach to these problems is the same as that for solid
bodies. The analysis starts with the contact being divided into a stick region
at the front edge of the contact patch and a slip region at the rear edge. The
slip region tends to spread forward with the increase in sideslip or spin.
Figure 4.50 shows one-dimensional motion describing the resistance of the
tyre to lateral displacement. This displacement, k, of the equatorial line of
the tyre results in its lateral deformation. The displacement, k is divided into
displacement of the carcass, /c c, and the displacement of tread, /c t. The
carcass is assumed to carry a uniform tension R resulting from the internal
pressure. This tension acts against lateral deflection. The lateral deflection
is also constrained by the walls acting as a spring of stiffness G per unit
length. The tread also acts as an elastic foundation. Surface traction, g(x),
acting in the region — c^x ^ c deforms the tyre. The equilibrium equation
is of the form

Figure 4.50