Page 81 - Singiresu S. Rao-Mechanical Vibrations in SI Units, Global Edition-Pearson (2017)

78 Chapter 1 Fundamentals oF Vibration
Viscous fluid
(lubricant)

v
Journal
(shaft)

(a)
l

Viscous Bearing
fluid

d
R
R
d
v

(b)
FiGure 1.43 A journal bearing.

The shearing stress 1t2 in the lubricant is given by the product of the radial velocity gradient and the
viscosity of the lubricant:

dv mRv
t = m = (E.2)
dr d
The force required to shear the fluid film is equal to stress times the area. The torque on the shaft (T)
is equal to the force times the lever arm, so that

T = 1tA2R (E.3)
where A = 2pRl is the surface area of the shaft exposed to the lubricant. Thus Eq. (E.3) can be
rewritten as

3
mRv 2pmR lv
T = a b12pRl2R = (E.4)
d d