Page 366 - Analysis and Design of Machine Elements

Analysis and Design of Machine Elements
344
From the derivation in (12.10), similar conditions for establishing hydrodynamic lubri-
cation to the analysis in Section 12.2.4 can be summarized as; an abundant supply of
lubricant with sufficient viscosity, a wedge-shaped space between two relatively moving
plates and lubricant flow from big entrance to small exit.
12.3.2.2 Hydrodynamic Lubrication in a Journal Bearing
Figure 12.8b shows a journal rotating at a constant speed in the clockwise direction,
supported by a film of lubricant of variable thickness h on a fixed bearing. The clearance
between the bearing and the journal is highly exaggerated. The nomenclature and main
design variables of the journal bearing are also illustrated in the figure.
(1) Geometrical relationship of design variables
In Figure 12.8b, the line OO connects journal centre O and bearing centre O . A radial
1 1
clearance is the difference in the radii of bearing and journal, that is,
= R − r (12.11)
Similarly, a diametrical clearance Δ is
Δ= D − d (12.12)

The ratio of diametrical clearance to the journal diameter is defined as relative clear-
ance,
Δ
= = (12.13)
d r

The distance between bearing centre and journal centre is eccentricity e. The dimen-
sionless eccentricity radio is defined as
e
= (12.14)

The minimum film thickness is designated by h min , and it occurs at point D on the line
of centres.
h = − e = (1 − )= r (1 − ) (12.15)
min
In journal bearing design, one of principal objectives is to ensure the minimum film
thickness is sufficiently large to separate the surfaces of journal and bearing completely.
The film thickness at any other point is designated by h; from the triangle OO B in
1
Figure 12.8, we have
2
2
2
R = e +(r + h) − 2e(r + h) cos
Therefore,
√
( ) 2
e
2
r + h = e cos ± R 1 − sin
R
( ) 2
2
Neglecting e sin , the oil film thickness at any position is given by
R
h = (1 + cos )= r (1 + cos ) (12.16)
The film thickness at the highest pressure on point C is
h = (1 + cos ) (12.17)
0 0