Page 252 - Tribology in Machine Design

Friction, lubrication and wear in higher kinematic pairs 237

Energy dissipated due to plastic deformations

In the majority of cases, resistance to rolling is dominated by plastic
deformation of one or both contacting bodies. In this case the energy is
dissipated within the solids, at a depth corresponding to the maximum
shear component of the contact stresses, rather than at the interface. With
materials having poor thermal conductivity the release of energy beneath
the surface can lead to high internal temperatures and failure by thermal
stress. Generally metals behave differently than non-metals. The inelastic
properties of metals, and to some extent hard crystalline non-metallic
solids, are governed by the movement of dislocations which, at normal
temperatures, is not significantly influenced either by temperature or by the
rate of deformation.
The rolling friction characteristics of a material which has an elastic
range of stress, followed by rate-independent plastic flow above a sharply
defined yield stress, follow a typical pattern. At low loads the deformation is
predominantly elastic and the rolling resistance is given by the elastic
hysteresis equation (6.8). The hysteresis loss factor as found by experiment
is generally of the order of a few per cent.
At high loads, when the plastic zone is no longer contained, i.e., the
condition of full plasticity is reached, the rolling resistance may be
estimated by the rigid-plastic theory. The onset of full plasticity cannot be
precisely defined but, from the knowledge of the static indentation
behaviour, where full plasticity is reached when W/2a&2.6 and
Ea/YRx 100, it follows that GW/kR&3QQ, where k is the yield stress in
shear of the solid.

Energy dissipated due to surface roughness

It is quite obvious that resistance to the rolling of a wheel is greater on a
rough surface than on a smooth one, but this aspect of the subject has
received little analytical attention. The surface irregularities influence the
rolling friction in two ways. First, they intensify the real contact pressure so
that some local plastic deformation will occur even if the bulk stress level is
within the elastic limit. If the mating surface is hard and smooth the
asperities will be deformed plastically on the first traversal but their
deformation will become progressively more elastic with repeated traver-
sals. A decreasing rolling resistance with repeated rolling contact has been
observed experimentally. The second way in which roughness influences
resistance is through the energy expended in climbing up the irregularities.
It is significant with hard rough surfaces at light loads. The centre-of-mass
of the roller moves up and down in its forward motion which is therefore
unsteady. Measurements of the resistance force show very large, high-
frequency fluctuations. Energy is dissipated in the rapid succession of small
impacts between the surface irregularities. Because the dissipation is by
impact, the resistance due to this cause increases with the rolling speed.