Engineering Mechanics

Chapter 29 : Balancing of Rotating Masses „„„„„ 597

or ω = 8·4 rad /s

∴ Speed of the governor,

1

60 60 8·4

80·2 r.p.m.

22

N

ω×

== =

ππ

Ans.

(ii) Speed of the governor when the balls fall by 20 mm

In this case height of governor, h 2 = 159 + 20 = 179 mm = 0·179 m

∴

2

2

9·8

54·7

0·179

g

h

ω= = =

or ω = 7·4 rad /s

∴ Speed of the governor

2

60 60 7·4

70·7 r.p.m.

22

N

ω×

== =

ππ

Ans.

EXERCISE 29·2

1. Three masses A, B and C of 20 kg, 18 kg and 32 kg respectively revolve at radii of 0·4,
   0·5 and 0·2 m respectively, in one plane. The angular positions of B and C are 60° and
   135° respectively from A. Find the magnitude and position of mass D on a radius of 0·6
   m to balance the system. [Ans. 24·5 kg ; 212.9°]


2. In a mechanism, four masses m 1 , m 2 , m 3 and m 4 are 20 kg, 30 kg, 24 kg and 26 kg
   respectively. The corresponding radii of rotation are 200 mm, 150 mm, 250 mm and 300
   mm respectively. The angles between the successive masses are 45°, 75° and 135°
   respectively. Estimate the position and magnitude of the mass, which when attached at a
   radius of 200 mm in the same plane of radiation will balance the system.
   [Ans. 248.7° ; 11·6 kg]


3. In a mechanism, there are four masses, m 1 , m 2 , m 3 and m 4 of 10 kg, 8 kg, 6 kg and 12 kg
   respectively. These masses are attached in an anticlockwise order to a disc or radii of 60
   mm, 120 mm, 150 mm and 90 mm respectively. The angles between m 1 and m 2 is 30°,
   between m 2 and m 3 is 70° and between m 3 and m 4 is 130°. Determine graphically the
   magnitude and directions of fifth mass to be attached to the disc at a radius of 120 mm,
   which will balance the system. [Ans. 6·67 kg ; 227° ]


4. A centrifugal governor is rotating with an angular velocity of 60 r.p.m. find the change,
   in its vertical height when its speed increases to 61 r.p.m. [Ans. 9 mm]

QUESTIONS

1. What is balancing? Discuss its advantages.


2. Describe the procedure for the balancing of rotating bodies.


3. State clearly the difference between (i) balancing of a single rotating body by another
   body in the same plane, and (ii) balancing of a single rotating body by two bodies in two
   different planes.


4. How will you balance several bodies rotating in one plane by a body in the same plane
   analytically?