Page 364 - Analysis and Design of Machine Elements

Analysis and Design of Machine Elements
342

(a)

(b)
Figure 12.8 Hydrodynamic lubrication in a journal bearing. Source: Adapted from Pu and Ji, 2006.

Holding x constant, integrating twice with respect to y and evaluating constants of
integration by imposing boundary conditions as y = 0, u = 0; and y = h, u = v yields the
expression
v y(y − h) p
u = y + ⋅ (12.6)
h 2 x
This equation gives the velocity distribution of lubricant film as the function of coor-
dinate y and pressure gradient p/ x. The velocity distribution across the film consists
of two terms: a linear distribution due to shear flow and a parabolic distribution due to
pressure flow.