BL MOLUPE
221043778
PRACTICAL 2:
GOVERNORS
RESULT%
Student number(s):
2
2
1
0
4
3
7
7
8
Surname and initials:
BL MOLUPE
Programme:
BEngTech (Mechanical Engineering)
Module name:
MACHINE OF MECHANIC
M
Module code:
1
Graduate Attribute (GA)
assessment:
2
2
X
Assignment/project number:
Due date:
A
0
0
2
Lecturer:
M
3
4
2
5
1
6
7
8
9
10
X
0
0
2
0
2
5
2
1
LF MONAHENG
DECLARATION OF OWN WORK:
I, BOITUMELO LESEGO MOLUPE student number 221043778, hereby declare that the content of this
assignment/project is my own work, as defined and constituted in the Rules and Regulations of the
Central University of Technology, Free State (Please consult the Programme Guide of the Department).
Signed: BOITUMELO LESEGO MOLUPE
Date:
_____21 May 2022___________________________
Assignment task
Assignment
Weight
Student
Marks
Graduate attributes (GA) indicators
(If a student obtains 50% on assignment task, he or she obtains a
GA). The assignment rubric is described in both practical and learner
guide.
Aim
Sketch of apparatus
Summary of theory
5
10
20
Work is performed within the boundaries of the practice area. (GA2)
Concepts, ideas and theories are communicated (GA 2)
Available literature is searched, and material is critically evaluated for
suitability to the investigation. (GA4)
Obtained GA
are marked
with X
Experimental procedure
5
Data and observation
Calculation and graphs
10
20
Results and discussions
10
Conclusion
Accuracy and neatness
10
10
Investigations and experiments are planned and conducted within an
appropriate discipline. (GA4)
Uncertainty and risk is handled. (GA2)
Theories, principles and laws are used. (GA2)
An appropriate mix of knowledge of mathematics used. (GA2)
Reasoning about and conceptualising engineering materials, components,
systems or processes is performed. (GA2)
Information is analysed, interpreted and derived from available data. (GA4)
Conclusions are drawn from an analysis of all available evidence. (GA2)
The purpose, process and outcomes of the investigation are recorded in a
technical report. (GA2)
Contents
LIST OF FIGURES ............................................................................................................................................ 4
LIST OF TABLES .............................................................................................................................................. 5
LIST OF EQUATIONS ...................................................................................................................................... 6
NOMENCLATURE........................................................................................................................................... 7
AIM OF THE PRACTICAL:] .............................................................................................................................. 9
INTRODUCTION: ............................................................................................................................................ 9
APPARATUS ................................................................................................................................................. 12
EXPERIMENTAL PROCEDURE: ..................................................................................................................... 14
EXPERIMENTAL RESULTS............................................................................................................................. 14
CALCULATIONS AND PLOTTING OF GRAPHS............................................................................................... 15
Sample calculations ............................................................................................................................. 15
RESULTS ...................................................................................................................................................... 16
GRAPHS ....................................................................................................................................................... 17
DISCUSSION AND CONCLUSION .................................................................................................................. 19
References .................................................................................................................................................. 20
LIST OF FIGURES
Figure 1 Porter governor (R.S. KHURMI, 2005) ............................................................................................... 10
Figure 2 Porter governor............................................................................................................................. 13
Figure 3 Diagram of forces for the Porter governor ................................................................................... 15
Figure 4 ....................................................................................................................................................... 17
Figure 5 ....................................................................................................................................................... 17
Figure 6 ....................................................................................................................................................... 18
Figure 7 ....................................................................................................................................................... 18
Figure 8 ....................................................................................................................................................... 19
LIST OF TABLES
Table 1: Experimental rotation speed of the governor ....................................................................................... 14
Table 2 Tabulated Experimental and theoretical results ............................................................................ 16
LIST OF EQUATIONS
2
b
 r = √(BP)2 − (2) + e
 Cos ∝ =
 h=
b
2
 FD =
+
b⁄
2
BP
e
tan ∝
P . L1
L1+L2
g w+(W±FD )
 ω= √ [
h
w
]
NOMENCLATURE
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. 𝜔. 2. 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.
ACKNOWLEDGEMENTS:
I would like to thank my fellow students who took part in the Experiment with various duties.
Furthermore, I'd also want to express my gratitude to Mr LF MONAHENG, our module lecturer, for his
relentless effort in making our experiment a success.
AIM OF THE PRACTICAL:]
 To determine how the sleeve's vertical movement 𝑦 influences the radius 𝑟 of rotation of the fly
balls
 Investigating the relationship between the rotational speed 𝜔 of the governor and the vertical
displacement 𝑦 of the sleeve
 To investigate if the governor rotational speed 𝜔 varies with the change in height ℎ
INTRODUCTION:
A governor is a device that monitors and controls the speed of a machine, most commonly an engine. In
order to adjust rotational speed, it frequently employs the action of centrifugal forces on weights rotating due
to its shaft. A puller operated by a set of bevel gears, a rotating vertical shaft that drives from above the
governor balls, a governor deadweight, and a main shaft make up the porter governor mechanism. The large
governor deadweight is turned, allowing it to travel freely up and down the main shaft while rotating at the
same speed as the balls (Hasan, 2017). The centrifugal forces acting on the balls rise as rotational speed
increases, allowing them to fly outward, but they are limited by the links connected to the heavy deadweight.
When the centrifugal force exceeds the resistance provided by the deadweight, the imposed weight is lifted
upwards by the centrifugal force (R.S. KHURMI, 2005).
The carburetor controls both air and fuel supply in petrol engines at varied speeds and loads. The governor,
on the other hand, is the device that controls the engine speed in diesel engines. The governor controls the
engine speed by adjusting the fuel flow based on the load (Hasan, 2017). When the load is reduced, the
engine speed tends to overshoot to dangerous levels, and when the load is increased suddenly and
unexpectedly*-, the engine speed tends to drop to dangerous levels (nearly to the point of engine halt). To
avoid such situations, the engine speed is controlled by utilizing an engine governor to regulate the fuel
supply. All injection pumps work together with the governor. The air intake reduces as the engine speed rises,
resulting in more fuel injection (R.S. KHURMI, 2005). The fuel supply, on the other hand, is minimal at idling
speed (no load situations) or when the engine speed is low. To ensure optimum conditions at all speeds and
weights within the given range, a governor is required. Variable speed governors are governors that can
maintain any speed between idle and maximum.
THEORY:
The porter governor is a watt's governor with a central load attached to the sleeve, as shown in Figure 1a.
The load oscillates around the central spindle. This added downward force increases the necessary speed
rotation for the balls to rise to any predetermined level (R.S. KHURMI, 2005).
Consider the forces at work on one-half of the governor, as depicted in the diagram: 1b
Figure 1 Porter governor (R.S. KHURMI, 2005)
Through there are several ways of determining the relation between the height of the governor (h) and the
angular speed of the balls (𝜔), yet the following two method are important from the point view:
 Method of resolution of forces
 Method of resolution of forces
Focusing at method of resolution of forces:
Considering the equilibrium of forces acting at D, we have
𝑊 𝑀. 𝑔
=
2
2
𝑀. 𝑔
𝑇2 =
… … … … … … … … … … … … … … … … … … … … … … … … … … … … . . (𝑖)
2 cos 𝛽
𝑇2 cos 𝛽 =
Or again, considering the equilibrium of forces acting on B. the point B is in equilibrium under the action of
the following forces, as shown in figure 1B (R.S. KHURMI, 2005).
 The weight of ball (𝜔 = 𝑚𝑔)
 The centrifugal force (𝐹𝑐 )
 The tension in the arm (𝑇1 )
 The tension in the (𝑇2 )
Resolving the forces vertically,
𝑇1 cos 𝛼 = 𝑇2 cos 𝛽 + 𝜔 =
𝑀. 𝑔
+ 𝑚. 𝑔 … … … … … … … … … … … … … . (𝑖𝑖)
2
Resolving the forces horizontally,
𝑇1 sin 𝛼 + 𝑇2 sin 𝛽 = 𝐹𝑐
𝑇1 sin 𝛼 +
𝑀. 𝑔
× sin 𝛽 = 𝐹𝑐
2 cos 𝛽
𝑇1 sin 𝛼 = 𝐹𝑐 −
𝑀.𝑔
2
× tan 𝛼 … … … … … … … … … … … … … … … … … . . (𝑖𝑖)
Dividing equation (iii) by equation (ii),
𝑀. 𝑔
𝐹𝑐 − 2 × tan 𝛽
𝑇1 sin 𝛼
=
𝑀. 𝑔
𝑇1 cos 𝛼
2 + 𝑚. 𝑔
𝑀. 𝑔
𝐹𝑐
𝑀. 𝑔 tan 𝛽
+ 𝑚. 𝑔 =
−
×
2
tan 𝛼
2
tan 𝛽
Substituting
tan 𝛽
tan 𝛼
𝑟
= 𝑞, 𝑎𝑛𝑑 tan 𝛼 = ℎ , 𝑤𝑒 ℎ𝑎𝑣𝑒
𝑀. 𝑔
ℎ 𝑀. 𝑔
+ 𝑚. 𝑔 = 𝑚. 𝜔2 . 𝑟 × −
×𝑞
2
𝑟
2
𝑀
𝑚 + 2 (1 + 𝑞) 𝑔
𝑀. 𝑔
(1 + 𝑞)⌉ =
ℎ = ⌈𝑚. 𝑔 +
× 2 … … … … … … . … … … (𝑖𝑣)
2
𝑚
𝜔
𝑀
𝑀
𝑚 + 2 (1 + 𝑞) 𝑔 60 2 𝑚 + 2 (1 + 𝑞) 895
∴ 𝑁2 =
× ( ) =
×
… … … … … … … … . . (𝑣)
𝑚
ℎ 2𝜋
𝑚
ℎ
𝑇𝑎𝑘𝑖𝑛𝑔 𝑔 = 8.91 𝑚/𝑠 2
NOTES:
 When the length of arms are equal to the length of links and the point P and D lie on same vertical
line, then
tan 𝛼 = tan 𝛽
𝑜𝑟
𝑞=
tan 𝛼
=1
tan 𝛽
Therefore, the equation (v) becomes
𝑁2=
(𝑚+𝑀)
𝑚
=
895
ℎ
 When the loaded sleeve moves up and down the spindle, the frictional force acts on it in a direction
opposite to that of that of the motion of sleeve.
If F= Frictional force acting on the sleeve in newton’s, then the equations (v) and (vi) may be written
as
2
𝑁 =
𝑚.𝑔+(
𝑀.𝑔±𝐹
)(1+𝑞)
2
𝑚.𝑔
×
895
ℎ
… … … … … … … … . . (𝑣𝑖𝑖)
𝑚. 𝑔 + (𝑀. 𝑔 ± 𝐹) 895
×
… … … … … … … … … … … … (𝑣𝑖𝑖𝑖)
𝑚. 𝑔
ℎ
The + sign is used when the sleeve moves upwards or the governor speed increases and negative
sign is used when the sleeve moves downwards or the governor speed decreases (R.S. KHURMI,
2005).
 On comparing the equation (vi) with equation (ii) of watts governor, we find that the mass of the
central load (M) increases the height of the governor in the ratio
𝑚+𝑚
𝑚
(R.S. KHURMI, 2005)
APPARATUS
The porter governor is represented by the arms, fly balls, links and the central dead weight and it is the main
focus of this experiment. The speed adjustment screw allows the operator to change the speed of the electric
motor running the governor. The mass hanger on the left of the governor serves the purpose of adding load
to the governor.
Figure 2 Porter governor
3. Notations Used
ro = Initial radius of rotation in mm,
r = Radius of rotation in mm,
ho = Initial height of governor in mm,
h = Height of governor in mm,
l = Length of each link in mm,
m = Mass of each fly ball in kg,
M =Dead mass on the Sleeve in kg,
xo = Initial reading on scale in mm,
x = Sleeve displacement in mm,
d = Initial distance of fly ball centre from spindle axis in mm,
α = Angle of inclination of upper arms to the vertical in degrees,
N1 = Minimum spindle speed in RPM,
N2 = Maximum spindle speed in RPM,
N = Mean speed in RPM,
Nexp =Actual speed of Spindle in RPM,
Nthe = Theoretical speed of Spindle in RPM,
Fc = Centrifugal Force in Newton = m r ω2
ω = Governor Spindle speed in rad/s.
EXPERIMENTAL PROCEDURE:
 Additional weight 10N was added onto the hanger
 The electrical motor of the Porter governor was started and we let the speed to increase gradually
until the sleeve with the mass M began to lift from zero.
 The governor speed for that position was recorded. For accurate readings, the speed was kept
constant for at least 10 seconds before the reading was recorded.
 The governor speed was recorded from 0 to 40 mm for each increment of 5 mm of the vertical
movement of the sleeve.
 After the recording of the speed governor for the sleeve lift of 40 mm from zero position, the electrical
motor of the governor was switched off.
EXPERIMENTAL RESULTS
Table 1: Experimental rotation speed of the governor
Sleeve movement
Y(mm)
Additional weight P1 (N)
10N
0
5
10
15
20
25
30
35
40
Governor rotational speed
N(rpm)
217
223
226
229
233
238
242
243
255
Additional weight P2 (N)
20N
Governor rotational speed
N(rpm)
222
227
236
241
246
248
250
251
263
CALCULATIONS AND PLOTTING OF GRAPHS
Figure 3 Diagram of forces for the Porter governor
Sample calculations
Y= 5
@ P=10N
𝐶𝐷 =
𝑟 = √𝑃𝐵 2 −
𝑏 − 𝑌 227,5 − 5
=
= 111,25𝑚𝑚
2
2
𝑏2
= √1252 − 111.252 + 25 = 81.995𝑚𝑚
2
cos 𝛼 =
ℎ=
111,25
→ 𝛼 = 27.126𝑟𝑎𝑑
125
𝑏
𝑒
25
+
= 111,25 +
= 160.049𝑚𝑚
2 𝑡𝑎𝑛𝛼
𝑡𝑎𝑛27,126
FD =
P . L1
10 × 150
=
= 5𝑁
L1 + L2 150 + 150
g w + (W ± FD )
9.81
5 + (25 ± 5)
ω= √ [
×
= 20,714𝑟𝑎𝑑𝑠
]=√
h
w
0,160049
5
𝑁=
Y= 5
𝑤 × 60 20,714 × 60
=
= 199,804𝑟𝑝𝑚
2𝜋
2𝜋
@ P=20N
𝐶𝐷 =
𝑟 = √𝑃𝐵 2 −
𝑏 − 𝑌 227,5 − 5
=
= 111,25𝑚𝑚
2
2
𝑏2
= √1252 − 111.252 + 25 = 81.995𝑚𝑚
2
cos 𝛼 =
ℎ=
111,25
→ 𝛼 = 27.126𝑟𝑎𝑑
125
𝑏
𝑒
25
+
= 111,25 +
= 160.049𝑚𝑚
2 𝑡𝑎𝑛𝛼
𝑡𝑎𝑛27,126
FD =
P . L1
20 × 150
=
= 10𝑁
L1 + L2 150 + 150
g w + (W ± FD )
9.81
5 + (25 ± 10)
ω= √ [
×
= 22,144𝑟𝑎𝑑𝑠
]=√
h
w
0,160049
5
𝑁=
𝑤 × 60 × 60
=
= 211.491𝑟𝑝𝑚
2𝜋
2𝜋
RESULTS
Table 2 Tabulated Experimental and theoretical results
Sleeve
movement
y
(mm)
0
5
10
15
20
25
30
35
40
Radius of Height
rotation
(mm)
(mm)
76,826
81,995
86,631
90,848
94,72
98,304
101,638
104,755
107,679
168,52
160,048
152,862
146,589
144,096
135,781
130,964
126,695
122,097
Additional weight P1 (10 N)
Rotation speed 𝑁 of the
governor (rpm)
Experimental Theoretical
217
223
226
229
233
238
242
247
252
192,495
197,831
202,388
206,685
208,528
214,751
218,659
222,317
226,466
Additional weight P2 (N)
Rotation speed 𝑁 of the
governor (rpm)
Experimental Theoretical
222
227
236
241
246
248
250
251
263
205,782
211,491
216,371
220,953
222,877
229,579
233.765
233.763
242.1
GRAPHS
Radius and Height vs Y movement
180,000
160,000
radius,height
140,000
y = -5377.2x + 164089
120,000
100,000
y = 3819.4x + 74614
80,000
60,000
40,000
20,000
0
5
10
15
20
25
30
35
40
Y movement
Radiud
Height
Figure 4
radius vs Rotational speeds(N)
250,000
y = 4165.8x + 189184
speed(rpm)
200,000
150,000
100,000
y = 3819.4x + 74614
50,000
0
76,826 81,995 86,631 90,848 94,721 98,304 101,638 104,755 107,679
Radius
N-Experimental
Figure 5
N-theoretical
Height vc P1 Rotational speeds(N)
Rotational speeds
250,000
200,000
y = 4165.8x + 189184
150,000
y = -5377.2x + 164089
100,000
50,000
0
168,52 160,048 152,862 146,589 144,096 135,781 130,964 126,695 122,097
Height
N- EXPERIMENTAL
N-theorectical
Figure 6
Radius vs P2 Rotational speeds(N)
Rotational speeds
250,000
y = 4152.2x + 203138
200,000
150,000
100,000
y = 3819.4x + 74614
50,000
0
76,826 81,995 86,631 90,848 94,721 98,304 101,638 104,755 107,679
Radius
N- Theoretical
Figure 7
N- EXPERIMENTAL
height vs P2 rotational speeds(N)
rotational speeds
250,000
y = 4152.2x + 203138
200,000
150,000
y = -5377.2x + 164089
100,000
50,000
0
168,52 160,048 152,862 146,589 144,096 135,781 130,964 126,695
height
N- Experimental
N - theoretical
Figure 8
DISCUSSION AND CONCLUSION
The first step of rotational speed vs fly ball radius graphs reveals directly proportional relationship which is
right according to the theory summary as the fly ball radius increases with the governor’s rising rotational
speed. Again in this case, the theoretical and experimental graphs were mostly parallel to each other and
this validates the theoretical formulae.
The second set of rotational vs governor height graphs demonstrates that these two variables are inversely
proportional. According to the radius and height graph against vertical movement, as the y movement
increases the height decreases and the radius increases, this is due to the fact that as the y movement
increases the fly-balls are pulled further apart from the center and in this case the radius increases while the
height decreases.
For the radius against rotational speed, the increase in rotational speed is due to the increase in the y
movement therefore as the increase in the y movement is directly proportional to the increase In rotation
speed, we can then see according to graph 1 and graph 2 that they are both directly proportional to the
radius.
References
Hasan, A., 2017. iopscience.. [Online]
Available at: https://iopscience.iop.org/article/10.1088/1742-6596/1950/1/012031/pdf
[Accessed 21 may 2022].
R.S. KHURMI, J. G., 2005. Theory of machines. 14th ed. NEW DEHLI: S. CHAND TECHNICAL.