Page 190 - Tribology in Machine Design

Sliding-element bearings 175
Figure 5.1
developing pressure and forcing fluid to flow outward through the
narrow space between the parallel surfaces. This is called a hydrostatic
lubrication or an externally pressurized lubrication;
(ii) one surface rapidly moves normal to the other, with viscous resistance
to the displacement of the oil. This is a squeeze-film lubrication;
(iii) by positioning one surface so that it is slightly inclined to the other,
then by relative sliding motion of the surfaces, lubricant is dragged into
the converging space between them. It is a wedge-film lubrication and
the type generally meant when the word hydrodynamic lubrication is
used.
Positioning of the surfaces usually occurs automatically when the load is
applied if the surfaces are free of certain constraints. Under dynamic loads
the action of a bearing may be a combination of the foregoing and hence
general equations are going to be derived and used to illustrate the
preceding three methods.
Let a thin film exist between the two moving bearing surfaces 1 and 2, the
former flat and lying in the X-Z plane, the latter curved and inclined, as
illustrated in Fig. 5.1. Component velocities u, v and w exist in directions X,
Y and Z, respectively. At any instant, two points having the same x, z
coordinates and separated by a distance h will have absolute velocities
which give the following set of boundary conditions
The pressure gradients, dp/dx and dp/dz in the X and Z directions are
independent of y in a thin film, and dp/8y=Q.
Recalling the fundamental relationship between pressure and velocity as
would be discussed in a fluid mechanics course
and integrating it with respect to y gives
and from the conditions of eqn (5.1)
Thus
Similarly