Page 253 - Tribology in Machine Design

238 Tribology in machine design

6.6. Lubrication of It is generally necessary to use a lubricant to ensure satisfactory operation
cylinders of .engineering surfaces in sliding contact. Even surfaces in nominal rolling
contact, such as ball-bearings, normally experience some micro-slip, which
necessitates lubrication if surface damage and wear are to be avoided. A
lubricating fluid acts in two ways. First, it provides a thin adsorbed film to
the solid surfaces, preventing the adhesion which would otherwise take
place and reducing friction through an interfacial layer of low shear
strength. This is the action known as boundary lubrication. The film is
generally very thin and its behaviour is very dependent upon the physical
and chemical properties of both the lubricant and the solid surfaces. The
lubricant may act in a quite different way. A relatively thick coherent film is
drawn in between the surfaces and sufficient pressure is developed in the
film to support the normal load without solid contact. This action is known
as hydrodynamic lubrication. It depends only upon the geometry of the
contact and the viscous flow properties of the fluid. The way in which a
load-carrying film is generated between two cylinders in rolling and sliding
contact is described in this section. The theory can be applied to the
lubrication of gear teeth, for example, which experience a relative motion
which, as shown in Section 6.2, is instantaneously equivalent to the
combined rolling and sliding contact of two cylinders.
A thin film of an incompressible lubricating fluid, viscosity //, between
two solid surfaces moving with velocities V\ and V 2 is shown in Fig. 6.3.
With thin, nearly parallel films, velocity components perpendicular to the
film are negligible so that the pressure is uniform across the thickness. At a
low Reynolds number, for the case of a thin film and a viscous fluid, the
inertia forces are negligible. Then, for two-dimensional steady flow,
Figure 6.3 equilibrium of the fluid element gives

where v is the stream velocity. Since dp/dx is independent of z, eqn (6.14) can
be integrated with respect to z. Putting v = V 2 and V v at z =0 and h, gives a
parabolic velocity profile, as shown in Fig. 6.3, expressed by

The volume flow rate Q across any section of the film is

For continuity of flow, Q is the same for all cross-sections, i.e.

where h^ is the film thickness at which the pressure gradient dp/dx is zero.