Page 167 - Tribology in Machine Design

Friction, lubrication and wear in lower kinematic pairs 153

where G t is called the tread stiffness. The velocity of lateral slip in the
contact zone (rigid ground, /c g =0 and one-dimensional motion) is de-
scribed by

It should also be remembered that in a stick regime, s =0. It seems that the
propositions to assume a rigid carcass and allow only for the deformation of
the tread are not realistic. A more practical model is to neglect the tread
deflection and only consider carcass deformation, i.e. k = k c. With this
assumption, eqn (4.178) becomes

where y = (R/G C)* is the relaxation length. Assuming further that s =0 in the
entire contact zone, the displacement within the contact zone for a case of
slideslip is given by

where k is the displacement at the entry to the contact zone. Outside the
contact zone g(x)=Q, therefore eqn (4.180) yields
in front of the contact

at the rear of the contact

At the leading edge, the displacement gradient is continuous and therefore
k= — JK. Figure 4.51 shows the equatorial line in a deflected state. In the
contact zone

Figure 4.51

which corresponds to a force Q' = — 2G cc(y + c).
At the rear of the contact zone, there is a discontinuity in dk/dx which
gives rise to an infinite traction q"(c) corresponding to a force