Page 210 - Tribology in Machine Design

Sliding-element bearings 195

with eqn (5.42), the flow is seen to be

or

where c d is the diametral clearance. Although it is not directly evident from
Figure 5.16
this simple result, the flow is an increasing function of the load and a
decreasing function of viscosity, indicated by the eccentricity term e. At the
ends of the diverging space in the bearing, negative pressure may draw in
some of the oil previously forced out. However, if a pump supplies oil and
distribution grooves keep the space filled and under pressure, there is an
outward flow. This occurs through a cylindrical slot of varying thickness,
which is a function of the eccentricity. The flow is not caused by journal or
bearing motion, and it is designated film flow Q {. It is readily determined
whether a central source of uniform pressure p 0 may be assumed, as from a
pump-fed partial annular groove. Instead of starting with eqn (5.56), an
elemental flow q z from one end may be obtained from the flat slot, eqn
(5.17), by writing r d® for b and (/ - a)/2 for /, where the new / is the bearing
€>2
q z, where
i=>i
©! and 0 2 define the appropriate angular positions, such as n and 2n
respectively. Additional flow may occur through the short slots which close
the ends of an axial groove or through a small triangular slot formed by
chamfering the plane surfaces at the joint in a split bearing.
Oil flow and torque are closely related to bearing and film temperature
and, thereby, to oil viscosity, which in turn affects the torque. Oil
temperature may be predicted by establishing a heat balance between the
heat generated and the heat rejected. Heat H % is generated by the shearing
action on the oil, heat H 0 is carried away in oil flowing out of the ends of the
bearing, and by radiation and convection, heat H b is dissipated from the
bearing housing and attached parts, and heat H s from the rotating shaft. In
equation form

The heat generation rate H g is the work done by the rotating member per
unit time (power loss). Thus, if torque T r is in Nm and n' in r.p.s., the heat
generation rate is

3
3
Now, T r and T 0 vary as d and n'. Therefore, # g varies as d and
2
approximately as (n') . Hence a large diameter and high speed bearings
generally require a large amount of cooling, which may be obtained by a
liberal flow of oil through the space between the bearing and the journal.
Flowing out of the ends of the bearing, the oil is caught and returned to a