Chapter 6 Governor - Theory of Machine, Mechanical Engineering Mechanical Engineering Notes | EduRev

Mechanical Engineering SSC JE (Technical)

Mechanical Engineering : Chapter 6 Governor - Theory of Machine, Mechanical Engineering Mechanical Engineering Notes | EduRev

The document Chapter 6 Governor - Theory of Machine, Mechanical Engineering Mechanical Engineering Notes | EduRev is a part of the Mechanical Engineering Course Mechanical Engineering SSC JE (Technical).
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Chapter 6

GOVERNOR

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

Chapter 6 Governor - Theory of Machine, Mechanical Engineering Mechanical Engineering Notes | EduRev

  •  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.
 Chapter 6 Governor - Theory of Machine, Mechanical Engineering Mechanical Engineering Notes | EduRev
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
Chapter 6 Governor - Theory of Machine, Mechanical Engineering Mechanical Engineering Notes | EduRev
TYPE OF CENTRIFUGAL GOVERNOR
There are two type of centrifugal governor
(i) Pendulum type – Watt governor
(ii) Loaded type
Chapter 6 Governor - Theory of Machine, Mechanical Engineering Mechanical Engineering Notes | EduRev
Watt Governor
Assumption

  •  Link is massless.
  •  Sleeve is frictionless.

Chapter 6 Governor - Theory of Machine, Mechanical Engineering Mechanical Engineering Notes | EduRev

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
Chapter 6 Governor - Theory of Machine, Mechanical Engineering Mechanical Engineering Notes | EduRev
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

Chapter 6 Governor - Theory of Machine, Mechanical Engineering Mechanical Engineering Notes | EduRev
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,
Chapter 6 Governor - Theory of Machine, Mechanical Engineering Mechanical Engineering Notes | EduRev
By solving it, we get
Chapter 6 Governor - Theory of Machine, Mechanical Engineering Mechanical Engineering Notes | EduRev
Chapter 6 Governor - Theory of Machine, Mechanical Engineering Mechanical Engineering Notes | EduRev
Chapter 6 Governor - Theory of Machine, Mechanical Engineering Mechanical Engineering Notes | EduRev
If k = 1, f = 0
Chapter 6 Governor - Theory of Machine, Mechanical Engineering Mechanical Engineering Notes | EduRev

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.

Chapter 6 Governor - Theory of Machine, Mechanical Engineering Mechanical Engineering Notes | EduRev

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  
Chapter 6 Governor - Theory of Machine, Mechanical Engineering Mechanical Engineering Notes | EduRev
As before, I is the instantaneous centre of the link BAE
Taking moments about I,
Chapter 6 Governor - Theory of Machine, Mechanical Engineering Mechanical Engineering Notes | EduRev
In the position when AE is vertical, i.e., m neglecting its obliquity
Chapter 6 Governor - Theory of Machine, Mechanical Engineering Mechanical Engineering Notes | EduRev
By solving above equation, we get
Chapter 6 Governor - Theory of Machine, Mechanical Engineering Mechanical Engineering Notes | EduRev
If k = 1, f = 0
 Chapter 6 Governor - Theory of Machine, Mechanical Engineering Mechanical Engineering Notes | EduRev
HARTNELL GOVERNOR
In this governor, ball are controlled by a spring.

Chapter 6 Governor - Theory of Machine, Mechanical Engineering Mechanical Engineering Notes | EduRev
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,  
Chapter 6 Governor - Theory of Machine, Mechanical Engineering Mechanical Engineering Notes | EduRev
Neglect obliquity of the arm in that case,
Chapter 6 Governor - Theory of Machine, Mechanical Engineering Mechanical Engineering Notes | EduRev
Now, from above equation
Chapter 6 Governor - Theory of Machine, Mechanical Engineering Mechanical Engineering Notes | EduRev
Also
Chapter 6 Governor - Theory of Machine, Mechanical Engineering Mechanical Engineering Notes | EduRev
SENSITIVENESS OF GOVERNOR
• A governor is said to be sensitive when it readily responds to a small change of speed.
Sensitiveness =
Chapter 6 Governor - Theory of Machine, Mechanical Engineering Mechanical Engineering Notes | EduRev
 Chapter 6 Governor - Theory of Machine, Mechanical Engineering Mechanical Engineering Notes | EduRev
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.

Chapter 6 Governor - Theory of Machine, Mechanical Engineering Mechanical Engineering Notes | EduRev

Controlling force =
Chapter 6 Governor - Theory of Machine, Mechanical Engineering Mechanical Engineering Notes | EduRev
For a Porter governor
Chapter 6 Governor - Theory of Machine, Mechanical Engineering Mechanical Engineering Notes | EduRev
For a Hartnell governor

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