C.K.PITAHAWAL COLLEGE OF
ENGG. AND TECH.
THEORY OF MACHINES
CREDITS:
BRANCH
DIV.
SEM
YEAR
GROUP
MECHANICAL
B
5
2015
22
NAME
ENROLLMENT NO.
Vohra Mustafa
130090119124
Suthar Dilip
130090119117
Somaiya Milan
130090119114
Ashwin Chauhan
130090119013
WATT AND PORTER GOVERNOR
INTRODUCTION
• The function of a governor is to regulate the
mean speed of an engine, when there are
variations in the load.
• For e.g. :- When the load on an engine increases,
its speed decreases, therefore it becomes
necessary to increase the supply of working fluid.
• On the other hand, when the load on the engine
decreases, its speed increases and thus less
working fluid is required.
• The governor automatically controls the
supply of working fluid to the engine with the
varying load conditions and keeps the mean
speed within certain limits.
• A little consideration will show, that when the
load increases, the configuration of the
governor changes and a valve is moved to
increase the supply of the working fluid.
• Conversely, when the load decreases, the
engine speed increases and the governor
decreases the supply of working fluid.
HOW IS FLYWHEEL DIFFERENT FROM
GOVERNOR?
TYPES OF GOVERNORS
• The governors may, broadly, be classified as
1. Centrifugal governors.
2. Inertia governors.
• The centrifugal governors, may further be classified
as follows :
CENTRIFUGAL GOVERNORS
• The centrifugal governors are based on the balancing of
centrifugal force on the rotating balls by an equal and
opposite radial force, known as the controlling force.
• It consists of two balls of equal mass, which are attached
to the arms.
• These balls are known as governor balls or fly balls.
• The balls revolve with a spindle, which is driven by the
engine through bevel gears.
• The upper ends of the arms are pivoted to the spindle, so
that the balls may rise up or fall down as they revolve
about the vertical axis.
•When the load on the engine
increases, the engine and the
governor speed decreases.
•This results in the decrease of
centrifugal force on the balls.
•Hence the balls move inwards and
the sleeve moves downwards.
•The downward movement of the
sleeve operates a throttle valve at
the other end of the bell crank lever
to increase the supply of working
fluid and thus the engine speed is
increased.
•In this case, the extra power output
is provided to balance the increased
load.
•Conversely, it operates the same
when the load on the engine
decreases.
TERMS USED IN GOVERNORS
• 1. Height of a governor: It is the vertical distance from the centre
of the ball to a point where the axes of the arms (or arms produced)
intersect on the spindle axis. It is usually denoted by h.
• 2. Equilibrium speed: It is the speed at which the governor balls,
arms etc., are in complete equilibrium and the sleeve does not tend
to move upwards or downwards.
• 3. Mean equilibrium speed: It is the speed at the mean position of
the balls or the sleeve.
• 4. Maximum and minimum equilibrium speeds: The speeds at the
maximum and minimum radius of rotation of the balls, without
tending to move either way are known as maximum and minimum
equilibrium speeds respectively.
• Note : There can be many equilibrium speeds between the mean
and the maximum and the mean and the minimum equilibrium
speeds.
• 5. Sleeve lift: It is the vertical distance which the sleeve travels due
to change in equilibrium speed.
WATT GOVERNOR
• The simplest form of a centrifugal governor is a Watt
governor, as shown in Figure.
• It is basically a conical pendulum with links attached
to a sleeve of negligible mass.
• The arms of the governor may be connected to the
spindle in the following three ways :
• 1. The pivot P, may be on the spindle axis as shown in
Figure (a).
• 2. The pivot P, may be offset from the spindle axis
and the arms when produced intersect at O, as
shown in Figure (b)
• 3. The pivot P, may be offset, but the arms cross the
axis at O, as shown in Figure (c).
m = Mass of the ball in kg,
w = Weight of the ball in Newton = m.g,
T = Tension in the arm in Newton,
ω = Angular velocity of the arm and ball about the spindle axis in
rad/s,
r = Radius of the path of rotation of the ball i.e. horizontal
distance from the centre of the ball to the spindle axis in meters,
FC = Centrifugal force acting on the ball in Newton = m.ω2.r, and
h = Height of the governor in meters.
ANALYSIS OF WATT GOVERNOR
1. First method (Resolution of forces
method):
• In this analysis it is assumed that mass of arms,
links, sleeve are negligible in comparison with the
mass of the balls and therefore, neglected in the
analysis.
• Each ball will be in equilibrium under the action
of following forces:
(1) Centrifugal force acting on ball i.e. FC=m.ω2.r
(2) Tension T in upper arm
(3) The weight of the ball W=m.g
• Consider Figure below, applying Lami’s
theorem we get,
• 2. Second method (Instantaneous centre
method):
As shown in fig below
• Since the sleeve B moves up and down it works
as a slider and its velocity is in vertical direction.
It’s centre of rotation lies at line IB in horizontal
direction
• Whereas, A revolves about A and its peripheral
velocity is in direction perpendicular to OA at A.
• Therefore, OAB acts as a single slider crank chain
mechanism with OA as oscillating crank, B as
slider and AB as connecting rod. Hence, I
represents the instantaneous centre of link 3
w.r.t. link 1.
• Taking moment about I,
Therefore, we find that the results obtained by
either method is same.
PORTER GOVERNOR
• To overcome the defects of a Watt Governor, sleeve is loaded
by a dead weight. The load moves up and down the central
spindle.
•
•
•
•
•
•
•
•
•
•
•
•
•
m = Mass of each ball in kg,
w = Weight of each ball in newtons = m.g,
M = Mass of the central load in kg,
W = Weight of the central load in newtons = M.g,
r = Radius of rotation in metres,
h = Height of governor in metres ,
N = Speed of the balls in r.p.m .,
ω = Angular speed of the balls in rad/s= 2 πN/60 rad/s,
FC = Centrifugal force acting on the ball in newtons = m.ω2.r,
T1 = Force in the arm in newtons,
T2 = Force in the link in newtons,
α = Angle of inclination of the arm (or upper link) to the vertical, and
β = Angle of inclination of the link (or lower link) to the vertical.
ANALYSIS OF PORTER GOVERNOR
Instantaneous center method:
• Since the sleeve B moves vertically, its centre of
rotation is along a horizontal from B.
• The point A on link AB which is also the point on
link OA moves in an arc of circle with centre O,
hence the centre of rotation of A on AB is along
the line OA produced.
• Hence, “I” is the point of intersection of
horizontal line at B and the extension of line OA
produced. It represents the instantaneous centre
of link AB.
• Considering the equilibrium of all the forces for
left half of the governor and taking moments
about I, we get,
• If all the arms are equal in length and they
intersect on the axis of spindle then,
• Hence,
• If mass of dead weight M is negligible i.e.
M=0, then above equation reduces to the
equation of Watt Governor.
• The height of governor can be increased by
increasing the mass of dead weight.
• Differentiating above equation with respect to
N gives,
It is clear from above equation that the porter
governor can be made more effective
compared to Watt governor by increasing
M/m ratio.