Page 65 - Tribology in Machine Design

52 Tribology in machine design

properly lubricated bearings is very small and is almost negligible. On the
basis of these observations Reynolds drew the following conclusions:
(i) friction is due to shearing of the lubricant;
(ii) viscosity governs the load carrying capacity as well as friction;
(iii) the bearing is entirely supported by the oil film.
He assumed the film thickness to be such as to justify its treatment by the
theory of viscous flow, taking the bearing to be of infinite length and the
coefficient of viscosity of the oil as constant. Let

r = the radius of the journal,
/=the virtual coefficient of friction,
F = the tangential resisting force at radius, r,
P = the total load carried by the bearing.

Again, if
,4= the area wetted by the lubricant,
F = the peripheral velocity of the journal,
c=the clearance between the bearing and the shaft, when the shj
is placed centrally,

then using eqn (2.121)

This result, given by Petroff in 1883, was the first attempt to relate bearing
friction with the viscosity of the lubricant.
In 1886 Osborne Reynolds, without any knowledge of the work of
Petroff, published his treatise, which gave a deeper insight into the
hydrodynamic theory of lubrication. Reynolds recognized that the journal
cannot take up a central position in the bearing, but must so find a position
according to its speed and load, that the conditions for equilibrium are
satisfied. At high speeds the eccentricity of the journal in the bearing
decreases, but at low speeds it increases. Theoretically the journal takes up a
position, such that the point of nearest approach of the surfaces is in
advance of the point of maximum pressure, measured in the direction of
rotation. Thus the lubricant, after being under pressure, has to force its way
through the narrow gap between the journal and the bearing, so that
friction is increased. Two particular cases of the Reynolds theory will be
discussed separately.