Page 80 - Singiresu S. Rao-Mechanical Vibrations in SI Units, Global Edition-Pearson (2017)

1.9 dampinG elements 77
Area (A)

v

h

FiGure 1.42 Flat plates separated by thin
film of lubricant.

Solution: Since the resisting force (F) can be expressed as F = cv, where c is the damping constant
and v is the velocity, we have
F 400
c = = = 40 N@s>m (E.1)
v 10
By modeling the bearing as a flat-plate-type damper, the damping constant is given by Eq. (E.4) of
Example 1.13:
mA
c = (E.2)
h
Using the known data, Eq. (E.2) gives

10.3445210.12
c = 40 = or h = 0.86125 mm (E.3)
h
■

damping Constant of a Journal bearing
example 1.15
A journal bearing is used to provide lateral support to a rotating shaft as shown in Fig. 1.43. If the
radius of the shaft is R, angular velocity of the shaft is v, radial clearance between the shaft and the
bearing is d, viscosity of the fluid (lubricant) is m, and the length of the bearing is l, derive an expres-
sion for the rotational damping constant of the journal bearing. Assume that the leakage of the fluid
is negligible.

Solution: The damping constant of the journal bearing can be determined using the equation for the
shear stress in viscous fluid. The fluid in contact with the rotating shaft will have a linear velocity
(in tangential direction) of v = Rv, while the fluid in contact with the stationary bearing will have
zero velocity. Assuming a linear variation for the velocity of the fluid in the radial direction, we have
vr rRv
v1r2 = = (E.1)
d d