TYPE OF GOVERNOR
1. Centrifugal Governor
2. Inertia Governor
Hence the response of inertia governors is faster than that of centrifugal type.
Let, r = Radial distance OG
v = Tangential velocity of G =ωr
ω = Angular velocity of disc
Centrifugal force of the rotating mass,
F = (radially outwards) mrω2
If the engine shaft is accelerated due to increase in speed, the ball mass does not get accelerated at the same amount on account of its inertia, the inertia force being equal to
TYPE OF CENTRIFUGAL GOVERNOR
There are two type of centrifugal governor
(i) Pendulum type – Watt governor
(ii) Loaded type
Let, m = Mass of each ball
h = Height of each ball
w = Weight of each ball
ω = Angular velocity of the balls, arms and the sleeve
T = Tension in the arm
r = Radial distance of ball-centre from spindle-axis
Weight w (= mg)
centrifugal force mrω2
Tension T in the upper link
Thus equilibrium of the mass gives, height of governor
Let, m = mass of each ball
h = height of governor
w = weight of each ball (= mg)
ω = angular velocity of the balls, arms and the sleeve
T = tension in the arm
r = radial distance of ball-centre from spindle-axis
N = Speed of rotation (rpm)
If the sleeve of a Watt governor is loaded with a heavy mass, it becomes a Porter governor.
Let, M = Mass of the sleeve
m = Mass of each ball
f = Force of friction at the sleeve
h = Height of the governor
r = Distance of the centre of each ball from axis of rotation
q = Angle between arm and spindle axis
b = Angle between link and spindle axis
The instantaneous centre of rotation of the link AB is at I for the given configuration of the governor. It is because the motion of its two points A and B relative to the link is know. The point A oscillates about the point O and B moves in a vertical direction parallel to the axis. Lines perpendicular to the direction of these motions locates the point I.
Considering the equilibrium of the left-hand half of the governor and taking moments about I,
By solving it, we get
If k = 1, f = 0
Considering the equilibrium of the link BAE which is under the action
The weight of the ball, mg
The centrifugal force, mr'ω2
The tension in the link AO
The horizontal reaction of the sleeve
The weight of sleeve and friction
As before, I is the instantaneous centre of the link BAE
Taking moments about I,
In the position when AE is vertical, i.e., m neglecting its obliquity
By solving above equation, we get
If k = 1, f = 0
In this governor, ball are controlled by a spring.
As the speed increases and the balls move away from the spindle axis, the bellcrank levers move on the pivot and lift the sleeve against the spring force. If the speed decreases, the sleeve moves downwards. The movement of the sleeve is communicated to the throttle of the engine. The spring force can be adjusted with
the help of a screw cap.
Let, Centrifugal force (F) = mrω2
Fs = Spring force
Taking moments about the fulcrum A,
Neglect obliquity of the arm in that case,
Now, from above equation
SENSITIVENESS OF GOVERNOR
• A governor is said to be sensitive when it readily responds to a small change of speed.
When, N = Mean speed
N1 = Minimum speed corresponding to full load conditions
N2 = Maximum speed corresponding to no-load conditions
Sensitiveness of a governor is a desirable quality. However, if a governor is too sensitive, it may fluctuate continuously. This phenomenon of fluctuation is pronounced as hunting.
A governor with sensitivity equal to infinity is treated as isochronous governor. For all position of sleeves, governor has same speed.
A governor is said to be stable if it brings the speed of the engine to the required value and there is not much hunting. The ball masses, occupy a definite position for each speed of the engine within the working range. The stability and the sensitivity are two opposite characteristics.
EFFORT OF GOVERNOR
The effort of the governor is the mean force acting on the sleeve to raise or lower it for a given change of speed. At constant speed, the governor is in equilibrium and the resultant force acting on the sleeve is zero. However, when the speed of the governor increases or decreases, a force is exerted on the sleeve which tends to move it. When the sleeve occupies a new steady position, the resultant force acting on it again becomes zero.
POWER OF GOVERNOR
The power of a governor is the work done at the sleeve for a given percentage change of speed.
Power = Effort of governor × displacement
Controlling force is equal and opposite to the centrifugal force and acts readily inward. It is supplied by
Controlling force =
For a Porter governor
For a Hartnell governor