Page 53 - Tribology in Machine Design

40 Tribology in machine design

2.11.6. Fatigue wear equation
It is known that conforming and nonconforming surfaces can be lubricated
hydrodynamically and that if the surfaces are smooth enough they will not
touch. Wear is not then expected unless the loads are large enough to bring
about failure by fatigue. For real surface contact the point of maximum
shear stress lies beneath the surface. The size of the region where flow occurs
increases with load, and reaches the surface at about twice the load at which
flow begins, if yielding does not modify the stresses. Thus, for a friction
coefficient of 0.5 the load required to induce plastic flow is reduced by a
factor of 3 and the point of maximum shear stress rises to the surface. The
existence of tensile stresses is important with respect to the fatigue wear of
metals. The fact, that there is a range of loads under which plastic flow can
occur without extending to the surface, implies that under such conditions,
protective films such as the lubricant boundary layers will remain intact.
Thus, the obvious question is, how can wear occur when asperities are
always separated by intact lubricant layers. The answer to this question
appears to lie in the fact that some wear processes can occur in the presence
of surface films. Surface films protect the substrate materials from damage
in depth but they do not prevent subsurface deformation caused by
repeated asperity contact. Each asperity contact is associated with a wave
of deformation. Each cross-section of the rubbing surfaces is therefore
successively subjected to compressive and tensile stresses. Assuming that
adhesive wear takes place in the metal-metal contact area, A m, it is logical
to conclude that fatigue wear takes place on the remaining part, that is
(A T-A m), of the real contact area. Repeated stresses through the thin
adsorbed lubricant film existing on these micro-areas are expected to cause
fatigue wear. To calculate the amount of fatigue wear in a lubricated
contact, an engineering wear model, developed at IBM, can be adopted.
The basic assumptions of the non-zero wear model are consistent with the
Palmgren function, since the coefficient of friction is assumed to be constant
for any given combination of materials irrespective of load and geometry.
Thus the model has the correct dimensional relationship for fatigue wear.
Non-zero wear is a change in the contour which is more marked than the
surface finish. The basic measure of wear is the cross-sectional area, Q, of a
scar taken in a plane perpendicular to the direction of motion. The model
for non-zero wear is formulated on the assumption that wear can be related to
a certain portion, U, of the energy expanded in sliding and to the number N of
passes, by means of a differential equation of the type

For fatigue wear an equation can be developed from eqn (2.88);

where C" is a parameter which is independent of N, S is the maximum