# Balancing of machines A fan (as shown in the figur...

Balancing of machines
A fan (as shown in the figure below) needs to be balanced. Theblades are attached to both the hub and outer cylinder. Correctionweights can only be added to the front and rear edges of the outercylinder. The fan shown below has a diameter of 2000 mm and a depthof 300 mm long. An unbalance of 0.08 kg.m is located 700 mm radiusin a plane 50 mm from the front face end. Determine the size of thecorrection masses to be added to the two edges of the outercylinder in order to balance the fan.
(Hint: Choose a radius and determine the mass required noting itsangular position.)

==============================================

1. This is not much more than a guess but consider the unbalancepoint as a fixed mass m
on a thin rod attached to the axis as specified. What needsto be balanced is the moment
of that inertia of that mass. Let the x-axis be the fan axis.First balance the mass along
the x-axis. M*d^2 = m*x^2 where you're solving for M in termsx for the unbalance point
and whatever d is for the point that you wish to attach themass M - I'm not too clear
about that diagram. Now let y be the radial direction of theunbalance point. Then, since
you're allowed to choose a radius let M*R^2 = m*r^2 where requals the distance of
the unbalance point from the axis of the fan. Now solve for R,the radius that you're
allowed to choose. I think that a single mass M at R and dwould balance the fan.
No guarantees - good luck!!
8/18 There is an additional consideration not discussedabove. The fan may not be in
static balance which could cause minor vibration. Thiscan be corrected by splitting
themass M into 2 parts M1 and M2 and placing them at either end of thex-axis.
Theymust, of course, be 180 degrees from the mass at the unbalancepoint.
Theywould have to satify the condition that the center mass of these 2masses
alongwith the unbalance mass of would lie at the center of the fan bladeaxis
which wouldbe at x = 0. Thus M1 * L/2 - M2 * L/2 + .08kg * .05m = 0 where L
is thelength of the outer cylinder. From this you can get the ratio forsplitting
M andobtaining static balance for the fan.