Page 80 - Mechanical Engineer's Data Handbook

APPLIED MECHANICS 69

Dynamic unbalance, forces in several planes

For a force mrw2 acting at x from bearing A, the
moment of the force about the bearing is mrw2x. This
has components:
mrdx sin 8 vertically
mrw2xcos 6 horizontally
For several forces:

Total vertical moment M,=mlrlw2x, sin 6, -+m,r,w2x, sin 8,
Several out of balance masses in one plane Total horizontal moment M,=m,r,w2x, cos8,
+m,r,w2x,ws82 . . .
The forces are: m1r102, m2r2w2, etc. These are re-
solved into vertical and horizontal components:
Fv=m,r,w2sin8, +m,r202sin8,+. . .
F,=m,r,02cos8,+m2r2w2cos8,+. . .
Resultant force F, = d m

at an angle to horizontal axis 6, =tan -

Resultant moment ,M, = ,/=

acting at ob = tan- *

.M
The reaction at B is: Rb=L
L
where: L=span.
The process is repeated, by taking moments about
end B, and R, found.
Method of balancing Complete 'dynamic balance' is
-- m achieved by introducing forces equal and opposite to
R, and R,. In practice, balancing is carried out at
planes a short distance from the bearings.

mr c-? cos0

\
To balance a mass mb at rb such that mbrb=i Fr
w
is required at an angle e,+ 180".