Engineering Mechanics

Chapter 29 : Balancing of Rotating Masses „„„„„ 595

Fig. 29.7. Centrifugal governor

Magnitude and angular position of the balancing mass

1. First of all, draw the space diagram, with the given masses and their positions as shown in
   Fig. 29·6 (a).


2. Take some convenient point a and draw ab equal to m 1 × r 1 = 2·5 × 250 = 625 to some
   scale and parallel to the 2·5 kg mass.


3. Through b, draw bc equal to m 2 × r 2 = 3·5 × 300 = 1050 to scale and parallel to the 3·5 kg
   mass.


4. Similarly, through c draw cd equal to m 3 × r 3 = 5 × 225 = 1125 to scale and parallel to the
   5 kg mass.


5. Join da, which represents the magnitude and direction of the assumed resultant force.
   Now the assumed balancing force will be given by ad to the scale.


6. Measuring ad to scale, we find that ad = 1575.


7. Therefore m × 262·5 = 1575

or

1575

6kg

262·5

m==Ans.

8. Now measuring the inclination of da with respect to Y-Y, we find that
   θ = 263º Ans.

Unbalanced force on the spindle

We know that angular velocity of the spindle,

2 2 240

8rad/s

60 60

ππ×N

ω= = = π

and the unbalanced force on the spindle,

P = mω^2 r = 6(8π)^2 0.2625 = 995 N Ans.

29·10. CENTRIFUGAL GOVERNOR

A centrifugal governor is a device to keep the engine speed, more or less, uniform at all the
load conditions. It is based on the principle of balancing of rotating masses. A centrifugal governor,
in its simplest form, consists of two heavy balls (known as fly
balls or governor) of equal mass attached to the arms as shown in
Fig. 29·7.

The arms are pivoted at their upper ends to a rotating shaft
known as spindle. The flyballs are also connected to a sleeve
through the links. The sleeve revolves with the spindle and can
also slide up and down on the rotating shaft. The spindle (or the
centrifugal governor) is driven by the shaft of an engine either by
a belt or gear arrangement. The sleeve, with its upward or
downward movement, controls a throttle valve through levers.
This valve, in turn, controls the supply of oil in the engine.

When the engine is running at its normal speed, the posi-
tion of control valve, flyballs and sleeve will be in their normal
positions. Now, if load on the engine increases, it will decrease the
speed of the engine shaft. The decrease in the speed of engine
shaft will decrease the speed of centrifugal governor (or more accurately spindle of the governor) as
a result of which the flyballs will come down due to decreased centrifugal force.