Types of governors; force analysis of Porter and Hartnell governors. Controlling force, stability, sensitiveness, isochronism, effort and power.

1. Department of Robotics & Automation
JSS Academy of Technical Education, Bangalore-560060
Robot Kinetics, Dynamics & Control
(Course Code:21RA44)

2. Robot Kinetics & Dynamics
Module 4: Governors

3. Governors: Types of governors; force analysis of Porter and Hartnell governors.
Controlling force, stability, sensitiveness, isochronism, effort and power.
CONTENTS

4. Introduction
• Governor is a device, used in an engine to maintain the mean speed of the
engine by controlling the flow of fuel with respect to load on the engine.
• Mainly used in Generators, not in ordinary vehicles

5. Introduction
• The function of a governor is to regulate the mean speed of an engine, when
there are variations in the load.
• When the load on an engine increases, its speed decreases, it becomes
necessary to increase the supply of working fluid.
• When the load on the engine decreases, its speed increases and less working
fluid is required.
• The governor controls the supply of working fluid to the engine with the varying
load conditions and keeps the mean speed within certain limits

6. Types of Governors
The governors may, broadly, be classified as;
1. Centrifugal governors
2. Inertia governors
• The Inertia governor is more sensitive & balancing of the revolving parts of the
inertia governor is complicated. Hence centrifugal governors are widely used.

7. Types of Governors
The governors may, broadly, be classified as
1. Centrifugal governors
2. Inertia governors

8. Types of Governors
Centrifugal Governors
Engine Crankshaft

9. • 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 (fly balls) of equal mass, which are attached to the arms as shown in fig.
• The spindle is connected to crankshaft through bevel gears.
• The arms are connected to a sleeve, which is keyed to the spindle.
• Sleeve revolves with the spindle; but can slide up and down.
• Two stops S,S are provided on the spindle to limit the travel of the sleeve in upward and downward directions.
• The sleeve is connected by a bell crank lever to a throttle valve.
• The balls and the sleeve rises when the spindle speed increases, and falls when the speed decreases.
Construction
Centrifugal Governors

10. • When the load on the engine increases, the speed of the engine and
the governor decreases, results in the decrease of centrifugal force
on the balls & the balls move inwards and the sleeve moves
downwards. The downward movement of the sleeve operates a
throttle valve to increase the supply of working fluid and thus the
engine speed is increased.
• When the load on the engine decreases, the engine and the
governor speed increases, results in the increase of centrifugal force
on the balls. The balls move outwards and the sleeve rises upwards.
This upward movement of the sleeve reduces the supply of the
working fluid and hence the speed is decreased.
Working

11. 1. Height of a governor (h). The vertical distance from the centre of the
ball to a point where the axes of the arms intersect on the spindle axis.
2. Equilibrium speed. Speed at which the balls, arms etc., are in
complete equilibrium and the sleeve does not move upwards or
downwards.
3. Mean equilibrium speed. Speed at the mean position of the balls or
the sleeve.
4. Max. & Min. equilibrium speeds: Speeds at the maximum and
minimum radius of rotation of the balls, without tending to move either
way.
5. Sleeve lift: The vertical distance which the sleeve travels due to
change in equilibrium speed.
Terms Used in Governors

12. Porter Governor

13. Porter Governor
• Type of centrifugal governor with a dead weight attached onto
the sleeve.
• Invented to overcome the disadvantage of the watt governor,
since the watt governor is not suitable for high-speed engines.
In watt governor, it becomes difficult to adjust the fuel supply at
a higher speed.
• Because of the dead weight attached to the sleeve, the flyball
requires more effort to lift the sleeve. After attaining the required
speed of the engine sleeve starts to slide onto the spindle.
• Invented by Charles T. Porter in 1858 to control the speed of the
steam engines.

14. Porter Governor
Case- I :- When load on engine increases
• When load on engine increases, the speed of engine decreases.
• Because of decrease in rotational speed, the centrifugal force on
flyballs decreases and flyballs moves inwards.
• Hence radius of rotation of flyballs decreases & sleeve will move
in downward direction.
• This movement of sleeve operates the opening of throttle valve
by means of bell crank lever.
• As the sleeve moves downwards, the opening of the throttle
valve increases hence the excess fuel will be supplied to the
engine.

15. Porter Governor
Case-I :- When load on engine decreases
• When the load on engine decreases, the speed of engine
increases.
• Because of increase in rotational speed, the centrifugal force on
flyball increases & flyballs are pushed outwards.
• Hence radius of rotation of flyball increases & sleeve will move in
upward direction.
• As the sleeve moves upwards, the throttle valve opening is
decreases and the supply of excess fuel is lowered.

16. Porter Governor Let, 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 = 2πN/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
β = Angle of inclination of the link (or lower link) to the vertical

17. Porter Governor Instantaneous centre method

18. Porter Governor Instantaneous centre method
Taking moments about the point I
(CW moments +ve & CCW moment –ve)
Fc × BM = w × IM +
W
2
x ID
Fc × BM = m.g x IM +
W
2
x ID
Fc = m.g x
IM
BM
+
M .g
2
x
ID
BM
Fc = m.g x
IM
BM
+
M .g
2
x (
I𝑀
BM
+
𝑀𝐷
BM
)

19. Porter Governor Instantaneous centre method
B
I M
α
B
M D
IM
BM
= tanα MD
BM
= tanβ
Dividing throughout by tan α
Fc = m.g x
IM
BM
+
M .g
2
x (
I𝑀
BM
+
𝑀𝐷
BM
)
Fc = m.g x tanα +
M .g
2
x (tanα + tanβ)
β

20. Porter Governor Instantaneous centre method
Dividing throughout by tan α
Fc = m.g x
IM
BM
+
M .g
2
x (
I𝑀
BM
+
𝑀𝐷
BM
)
Fc = m.g x tanα +
M .g
2
x (tanα + tanβ)
Fc
tanα
= m.g +
M .g
2
x (1 +
𝑡𝑎𝑛β
tanα
)
α
r
h
P
B
tanα =
r
ℎ

21. Porter Governor Instantaneous centre method
Fc
tanα
= m.g +
M .g
2
x (1 +
𝑡𝑎𝑛β
tanα
)
( tanα =
r
ℎ
FC = m.ω2.r )
& Also,
𝑡𝑎𝑛β
tanα
= q
m.ω2.r
ℎ
𝑟
= m.g +
M .g
2
x (1 +q)
h

22. Hartnell Governor

23. Hartnell Governor

24. Hartnell Governor
• Hartnell governor is a spring-loaded centrifugal
governor.
• It consists of two bell crank levers pivoted at the points
to the frame
• The frame is attached to the governor spindle and
therefore rotates with it.
• Each lever carries a ball at the end of the vertical arm
and a roller at the end of the horizontal arm.
• A helical spring in compression provides equal
downward force on the sleeve.
• The spring force may be adjusted by the nut on the
frame.

25. Hartnell Governor
• As it is spring-loaded, It doesn’t require gravitational force to return to the initial position after lowering
of speed. Hence it is possible to mount it in an inclined or horizontal position.

26. Hartnell Governor
Case 1: When the load on the engine decreases
• When the load on the engine decreases, the speed of
the engine increases.
• Because of the increase in engine speed, centrifugal
force on flyball increases. And flyballs are moved
outside. Hence load on spring increases and the spring
compresses
• Results in the upward movement of the sleeve on the
spindle, hence the supply of fuel to the engine
decreases, and the speed of the engine decreases to
the mean speed.

27. Hartnell Governor
Case 2: When the load on the engine increases
• When the load on the engine increases, the speed of the
engine decreases.
• As decrease in engine speed, centrifugal force on flyball
decreases & flyballs move inwards. Hence load on
spring decreases and the spring extends.
• Results in lowering of the sleeve on the spindle (due to
spring force), hence the supply of fuel to the engine
increases, and the speed of the engine increases to the
mean speed.

28. Hartnell Governor Expression for Speed of a Hartnell Governor
h = sleeve movement
Max. Position
Min. Position

29. Hartnell Governor
Let m = Mass of each ball in kg
M = Mass of sleeve in kg
r1 = Minimum radius of rotation in m
r2 = Maximum radius of rotation in m
1 = Angular speed of the governor at minimum radius in rad/s
2 = Angular speed of the governor at maximum radius in rad/s
FS1 = Spring force exerted on the sleeve at 1 in N
FS2 = Spring force exerted on the sleeve at 2 in N
F1 = Centrifugal force at 1 in newtons = m (1)2 r1
F2 = Centrifugal force at 2 in newtons = m (2) 2 r2
K = Stiffness of the spring
c = Length of the vertical or ball arm of the lever in m
b = Length of the horizontal or sleeve arm of the lever in m
r = Distance of fulcrum O from the governor axis or the radius of rotation when the governor is in mid-position, in metres

30. Taking moment about O1 & O2
F1 x C1 = mg x a1 + (
𝑀𝑔+𝐹𝑆1
2
) b1
F2 x C2 = mg x a2 + (
𝑀𝑔+𝐹𝑆2
2
) b2
For Equilibrium condition
a1 = a2 = 0
c1 = c2 = c
b1 = b2 = b
…(1)
…(2)
…(3)
F1 x C = (
𝑀𝑔+𝐹𝑆1
2
) b
F2 x C = (
𝑀𝑔+𝐹𝑆2
2
) b
…(4)
…(5)

31. Eq. 5 – Eq. 4
F1 x C = (
𝑀𝑔+𝐹𝑆1
2
) b
F2 x C = (
𝑀𝑔+𝐹𝑆2
2
) b
(F2 - F1 ) C = [(
𝑀𝑔+𝐹𝑆2
2
) - (
𝑀𝑔+𝐹𝑆1
2
)] b
(F2 - F1 ) C = [(
𝐹𝑆2
2
) - (
𝐹𝑆1
2
) ]b
…(4)
…(5)
2 (F2 - F1 )
𝒄
𝒃
= Fs2 - Fs1
Spring stiffness K =
Spring Force
Deflection
=
Fs2 − Fs1
h
h = b x 
…(6)
=
r2
−r1
c
h = b x (
r2
−r1
c
)
…(7)
K =
Fs2 − Fs1
𝒓𝟐−𝒓𝟏(
𝑏
𝑐
)
K = (
𝑐
𝑏
)
Fs2 − Fs1
(𝒓𝟐−𝒓𝟏)
…(8)
…(9)
From Eq. 6 – Eq. 9
K = 2 (
𝒄
𝒃
)
^𝟐 (F2 − F1)
(𝒓𝟐−𝒓𝟏)
h

32. 1. Controlling Force
• When a body rotates in a circular path, an inward radial or centripetal
force acts opposite to the centrifugal force.
• Inward force acting on the rotating balls is known as controlling force.
• It is equal and opposite to the centrifugal force
• ∴ Controlling force, FC = m.ω2.r
• The controlling force is provided by the weight of the sleeve and balls
as in Porter governor and by the spring and weight as in Hartnell
governor.

33. 2. Stability of Governors
• A governor is said to be stable when for every speed within the working range there is a definite
configuration i.e. there is only one radius of rotation of the governor balls at which the governor is in
equilibrium.
• For a stable governor, if the equilibrium speed increases, the radius of governor balls must also
increase.

34. 3. Sensitiveness of Governors
• A governor is said to be sensitive when it quick responds to a small change of speed.
• The movement of the sleeve for a small change of speed is measure of sensitivity
• Sensitiveness is defined as the ratio of the difference between the maximum and minimum equilibrium
speeds to the mean equilibrium speed.

35. Isochronous Governors
• When the equilibrium speed of governor is constant for all radii of rotation of the balls, within
the working range, known as isochronous governor.
• For isochronism, range of speed should be zero i.e. N2 – N1 = 0 or N2 = N1.
• h1 = h2, which is impossible in the case of a Porter governor. Hence a Porter governor cannot be isochronous.
Porter Governor

36. Isochronous Governors
Hartnell Governor
Consider the case of a Hartnell governor running at speeds N1 and N2 r.p.m.
F1 x C = (
𝑀𝑔+𝐹𝑆1
2
) b
F2 x C = (
𝑀𝑔+𝐹𝑆2
2
) b
…(4)
…(5)
For isochronism, N2 = N1
(
𝑀𝑔+𝐹𝑆1
𝑀𝑔+𝐹𝑠2
) =
𝑟1
𝑟2
• The isochronous governor is not of practical use because the sleeve will move to one of its extreme positions
immediately the speed deviates from the isochronous speed.

37. Effort of Governor
The effort of a governor is the mean force exerted at the sleeve for a given percentage change of
speed* (or lift of the sleeve).
• When the governor is running steadily, there is no force at the sleeve.
• When the speed changes, there is a resistance at the sleeve which opposes its motion.

38. Power of Governor
• The power of a governor is the work done at the sleeve for a given percentage change of
speed.
• It is the product of the mean value of the effort and the distance through which the sleeve
moves.
Mathematically,
Power = Mean effort × lift of sleeve

39. End of Module