Page 554 - Dynamics of Mechanical Systems

0593_C15_fm Page 535 Tuesday, May 7, 2002 7:05 AM

Balancing 535

1 in.
Flywheel (125 lb)
12 in.

FIGURE P15.2.1
A flywheel on a light shaft in nearly
frictionless bearings.

frictionless bearings as represented in Figure P15.2.1. If the flywheel is mounted off-center
by 0.25 in., what weight should be placed on the flywheel rim, opposite to the off-center
offset, so that the flywheel is statically balanced?
P15.2.2: Repeat Problem P15.2.1 if the flywheel mass is 50 kg, with a radius of 30 cm, a
thickness of 2.5 cm, and an off-center mounting of 7 mm.
P15.2.3: See Problem P15.2.1. Suppose the flywheel shaft has frictionless bearings. What
would be the period of small oscillations?
P15.2.4: Repeat Problem P15.2.3 for the data of Problem P15.2.2.
P15.2.5: See Problem P15.2.3. Suppose a slightly unbalanced disk flywheel, supported in
a light shaft with frictionless bearings, is found to oscillate about a static equilibrium
position with a period of 7 sec. How far is the flywheel mass center displaced from the
shaft axis?

Section 15.3 Dynamic Balancing
P15.3.1: A shaft with radius r of 3 in. is rotating with angular speed Ω of 1300 rpm. Particles
P and P , each with weight w of 2 oz. each, are placed on the surface of the shaft as shown
1 2
in Figure P15.3.1. If P and P are separated axially by a distance of 12 in., determine
1 2
the magnitude of the dynamic unbalance.

P
1

Ω
P
2
FIGURE P15.3.1
A rotating shaft with unbalance particles.
P15.3.2: Repeat Problem P15.3.1 if r, w, and have the values r = 7 cm, w = 50 g, and
= 0.333 m.
P15.3.3: See Problem P15.3.1. Suppose the dynamically unbalanced shaft is made of steel
with a density of 489 lb/ft . Suppose further that it is proposed that the shaft be balanced
3
by removing material by drilling short holes on opposite sides of the shaft. Discuss the
feasibility of this suggestion. Specifically, if the holes are to be no more than 0.5 in. in
diameter, no more than 0.5 in. deep, and separated axially by no more than 18 in., suggest
a drilling procedure to balance the shaft. That is, suggest the number, size, and positioning
of the holes.
P15.3.4: Repeat Problem P15.3.3 for the shaft unbalance of Problem P15.3.2 if the mass
density of the shaft is 7800 kg/m .
3