Governors Notes | Study Mechanical Engineering SSC JE (Technical) - Mechanical Engineering

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FUNCTION/GENERAL WORKING

  •  The function of a Governor is to maintain speed of an engine within specified limits whenever there is a variation of load.
  •  If the load on the shaft increases, the speed of the engine decrease unless the supply of fuel is increased by opening the throttle valve. On the other hand, if the load on the shaft decreases, the speed of the engine increases unless the fuel supply is decreased by closing the valve sufficient to slow the engine to its original speed. The throttle valve is operated by the governor through a mechanism for the purpose.


TYPE OF GOVERNOR
1. Centrifugal Governor

Governors Notes | Study Mechanical Engineering SSC JE (Technical) - Mechanical Engineering

  •  Its action depends on the change of speed and centrifugal effect produced by the masses, known as governor balls, which rotate at a distance from the axis of rotation.
  •  The action of the governor depends upon the centrifugal effects produced by the masses of the two balls. With the increase in the speed, the balls tend to rotate at a greater radius from the axis. This causes the sleeve to slide up on the spindle and this movement of the sleeve in communicated to the throttle through a bell crank  lever. This closes the throttle valve to the required extent. When the speed decreases, the balls rotate at a smaller radius and the valve is opened according to the requirement.

2. Inertia Governor

  •  The positions of the balls are affected by the forces set up by an angular acceleration or deceleration of the given spindle, in addition to centrifugal forces on the balls.
  • The balls are operated by the rate of change of speed in case of inertia governors.

Hence the response of inertia governors is faster than that of centrifugal type.
 Governors Notes | Study Mechanical Engineering SSC JE (Technical) - Mechanical Engineering
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
Governors Notes | Study Mechanical Engineering SSC JE (Technical) - Mechanical Engineering
TYPE OF CENTRIFUGAL GOVERNOR
There are two type of centrifugal governor
(i) Pendulum type – Watt governor
(ii) Loaded type
Governors Notes | Study Mechanical Engineering SSC JE (Technical) - Mechanical Engineering
Watt Governor
Assumption

  •  Link is massless.
  •  Sleeve is frictionless.

Governors Notes | Study Mechanical Engineering SSC JE (Technical) - Mechanical Engineering

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

  •  The mass m at A is in static equilibrium under the action of

Weight w (= mg)
centrifugal force mrω2
Tension T in the upper link
Thus equilibrium of the mass gives, height of governor
Governors Notes | Study Mechanical Engineering SSC JE (Technical) - Mechanical Engineering
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)

PORTER GOVERNOR
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

Governors Notes | Study Mechanical Engineering SSC JE (Technical) - Mechanical Engineering
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,
Governors Notes | Study Mechanical Engineering SSC JE (Technical) - Mechanical Engineering
By solving it, we get
Governors Notes | Study Mechanical Engineering SSC JE (Technical) - Mechanical Engineering
Governors Notes | Study Mechanical Engineering SSC JE (Technical) - Mechanical Engineering
Governors Notes | Study Mechanical Engineering SSC JE (Technical) - Mechanical Engineering
If k = 1, f = 0
Governors Notes | Study Mechanical Engineering SSC JE (Technical) - Mechanical Engineering

PROELL GOVERNOR

  •  A Proell Governor is known as a Proell Governor if the two balls (masses) are fixed on the upward extensions of the lower links which are in the form of bent links BAE and CDF shown in the below figure.

Governors Notes | Study Mechanical Engineering SSC JE (Technical) - Mechanical Engineering

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  
Governors Notes | Study Mechanical Engineering SSC JE (Technical) - Mechanical Engineering
As before, I is the instantaneous centre of the link BAE
Taking moments about I,
Governors Notes | Study Mechanical Engineering SSC JE (Technical) - Mechanical Engineering
In the position when AE is vertical, i.e., m neglecting its obliquity
Governors Notes | Study Mechanical Engineering SSC JE (Technical) - Mechanical Engineering
By solving above equation, we get
Governors Notes | Study Mechanical Engineering SSC JE (Technical) - Mechanical Engineering
If k = 1, f = 0
 Governors Notes | Study Mechanical Engineering SSC JE (Technical) - Mechanical Engineering
HARTNELL GOVERNOR
In this governor, ball are controlled by a spring.

Governors Notes | Study Mechanical Engineering SSC JE (Technical) - Mechanical Engineering
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,  
Governors Notes | Study Mechanical Engineering SSC JE (Technical) - Mechanical Engineering
Neglect obliquity of the arm in that case,
Governors Notes | Study Mechanical Engineering SSC JE (Technical) - Mechanical Engineering
Now, from above equation
Governors Notes | Study Mechanical Engineering SSC JE (Technical) - Mechanical Engineering
Also
Governors Notes | Study Mechanical Engineering SSC JE (Technical) - Mechanical Engineering
SENSITIVENESS OF GOVERNOR
• A governor is said to be sensitive when it readily responds to a small change of speed.
Sensitiveness =
Governors Notes | Study Mechanical Engineering SSC JE (Technical) - Mechanical Engineering
 Governors Notes | Study Mechanical Engineering SSC JE (Technical) - Mechanical Engineering
When, N = Mean speed
N= Minimum speed corresponding to full load conditions
N2 = Maximum speed corresponding to no-load conditions

HUNTING
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.

ISOCHRONISM
A governor with sensitivity equal to infinity is treated as isochronous governor. For all position of sleeves, governor has same speed.

STABILITY 
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
Controlling force is equal and opposite to the centrifugal force and acts readily inward. It is supplied by

  •  Gravity of mass of ball in case of watt governor.
  •  Gravity of mass of ball and dead weight of sleeve in case of porter and porter governor.
  •  Gravity of ball masses and spring force in hartnell and hartung governs.
  •  Controlling force curve for spring loaded governor.

Governors Notes | Study Mechanical Engineering SSC JE (Technical) - Mechanical Engineering

Controlling force =
Governors Notes | Study Mechanical Engineering SSC JE (Technical) - Mechanical Engineering
For a Porter governor
Governors Notes | Study Mechanical Engineering SSC JE (Technical) - Mechanical Engineering
For a Hartnell governor

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