Page 271 - Machinery Component Maintenance

Balancing of Machinery Components 253

interest, the correct formula for finding it looks as follows (again assum-
ing that there is no influence from bearings and suspension):

d=-+- mr mrjh
W+m Iz-Ix
Where:

d= Displacement of principal inertia axis from shaft axis in plane of
bearing
W= Rotor weight
m= Unbalance mass
r= Radius of unbalance
h= Distance from center-of-gravity to plane of unbalance
J= Distance from center-of-gravity to bearing plane
Ix = Moment of inertia around transverse axis
Iz = Polar moment of inertia around journal axis

Since neither the polar nor the transverse moments of inertia are
known, this formula is impractical. Instead, a widely accepted approxi-
mation may be used.
The approximation lies in the assumption that the unbalance is static
(see Figure 6-12). Total unbalance is thus 20 oz - in. Displacement of the

T
e = 0.01" r = 10" -
I---&--: -- -

.
t-' w * 2000 02

Figure 6-1 2. Symmetric rotor with static unbalance.