Omar Al-Mukhtar University Faculty of Engineering, Albeida, Libya
Department of Mechanical Engineering
ME 311 - Theory of machines Laboratory Manual
November'2017
2
Introduction to Theory of Machines Laboratory
An awareness of the machines, mechanisms and how they are operated practically is very essential to
all mechanical Engineering students. In the theoretical course “Theory of machines”, students learn
various fundamental theoretical concepts related to various machine elements lime Governors, Cams,
Flywheels and forces such as centrifugal and centripetal force. But they lack practical knowledge related
to these concepts.
In theory of machines laboratory, students get an opportunity to conduct practical experiments on
various apparatus like Governors, Centripetal force apparatus, Cams, Flywheels and observe the effect
of various forces on the performance of these devices.
Hence it is essential for each student to conduct the experiments, understand the underlying principles
related to each experiment and put in writing the knowledge they have gained in these practical sessions
in the form of a well organized laboratory report. The following section gives guidelines on how to
write a lab report.
Safety Regulations
Safe work rules and procedures are intended to provide students and staff with guidance and direction
to perform their work safely. The elimination or control of hazards inherent to certain tasks is achieved
through the analysis and the detailed description of how the task is to be done. Students and users of
the lab are required to observe the following during all lab sessions in order to ensure their safety.
Specific Safety regulations
The following safety regulations are specific to the experiment concerned.
1. Governor apparatus, Centripetal force apparatus and Cam apparatus contain rotating parts
which rotate at very high rotational speeds. All these apparatus are provided with guards and
they must therefore only be operated with the guards in position. If, for any reason ,the guards
are removed then there is a serious risk of the rotating parts causing the entrapment of loose
clothing, hair, items of the jewellery or parts of the body etc. Hence these equipments must not
be operated without the guards being properly fitted.
2. In the flywheel experiments, care should be taken while releasing the weights to ensure that no
one will be hurt by the weights during the course of their fall.
General Safety regulations
1. Before operating a machine, make sure that the electric connections are properly setup.
2. Work at your assigned station. Do not disturb students working at the other stations.
3. Always use the right tools for the given task.
4. Handle the tools and equipments with extreme care and return the tools to their proper places
(Tool Cabinets).
5. Make sure that you stay away from moving parts of machines.
6. Avoid using neck ties, loose clothing, loose items such as Watches, Wrist bands and similar
items during experiments.
7. Power is to be turned off after completing the experiment
8. Smoking is not allowed inside the Lab.
9. Wear always safety shoes when you operate any machine.
10. Before operating any machine, you must be aware of the following
a. Location of fire extinguishers, fire blanket and the outside exits.
b. To know how the machine operate read instruction manual of the machine before
operating it.
c. How to turn off the machine in case of damages.
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Lab regulations
1. Theory of machines lab is a part of the course Theory of Machines (ME 311). It carries 20
marks and would be counted towards the final score of the course (100 marks). The distribution
of marks is as follows:
Lab activities - 25 %
Lab reports - 25 %
Lab Examination (Written) - 25 %
Lab Examination (Oral) - 25 %
2. The Lab examinations contain the format given below:
Written Exam
In the written examination, each student may be asked to conduct an experiment and write a
report on the results obtained and draw conclusions from the results. To maintain transparency
and avoid partiality students are asked to pick any one experiment on lottery basis. To test the
practical ability, the students may be asked the following type of questions.
1. Conduct an experiment on a given machine and calculate its speed of rotation against
various positions of sleeve. What happens to speed of rotation if the sleeve starts rising?
2. Prepare a table of results and Plot the results on the graph. Write a brief report by
following the guidelines.
3. What are the conclusions that can be drawn from the experiment ?
Oral Exam Hints
The oral exam is an opportunity for the students to demonstrate the following skills
a. Knowledge
b. presentation and speaking skills
c. Ability to communicate.
Laboratory Reports
The laboratory report is meant to be a clear and concise record of what was done and observed in the
laboratory. All work, including experimental procedure, related to the experiment has to be written in
the report. The report should include the observations, calculations of results, comparisons, appropriate
explanations of the results and conclusions and recommendations.
It is common for the theoretical calculations to be different from the real world data because they use
simplified equations or models of components. Error is due to the uncertainties associated with the
method of measurement. The objective of the laboratory work is not to obtain results as close as possible
to some ideal theoretical answers. While writing the laboratory report the following points are to be
considered.
Is there any difference between practical and theoretical calculations?
If there is a difference between theoretical and practical results, explain the reason.
After everything is said and done, write the conclusions that can be drawn from the experiment. Also
mention whether you agree with the measurements you obtain. The laboratory report should include
detailed information related to each experiment. The information given under various sections of the
following experiments can be used to prepare the laboratory report. The lab report may be downloaded
from the instructor’s webpage at http://sureshmakkena.webnode.com/documents/teachingnotes
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Experiment No. 1
I. Experiment Title: Experimenting with centripetal apparatus to find the centripetal force at varying
radii of rotating masses.
II. Summary:
Write the summary of experiment in the report. Follow the guidelines given by the instructor.
III. Experiment Objective:
To find the centripetal force, plot graphs of speed of rotation against the radius of rotating masses
and draw theoretical and practical slopes to observe the difference.
IV. Introduction to Experimental setup:
Name of the Apparatus: Centripetal Force apparatus
Draw the diagram of the apparatus: Refer to apparatus manual.
Parts / Elements of the Apparatus
Part 1: Turntable carrying two pairs of masses
Part 2: Radius rods connected to linkages
Part 3: Central carrier
Part 4: Motor with integral power unit containing speed control equipment and electronic
Part 5: tachometer.
V. Experiment Procedure:
i. Set the two masses m₁ and m₂ together at maximum radius position on both sides of the
turntable. Record the values of m₁ , m₂ and r
ii. Calculate the central load, M* g, in Newtons
iii. Switch on the supply and steadily increase the speed until the central load is lifted.
iv. Record the speed N, the masses m₁ , m₂ , M and the mean radius ‘r’ of m₁ and m₂
v. Repeat the experiment for five different values of ‘r’ and tabulate the results
vi. Calculate the centripetal force by using the equation F = 4 ∏² m r N² , where N = rev/sec
vii. Plot graph of N² vertically against 1/r and identify whether this graph is a straight line.
viii. Measure the slope of the above graph
ix. Calculate the slope from theoretical relation F / (4 ∏² m) and compare it with that of
practical value calculated earlier.
x. Observe if there is any error and carryout error analysis.
xi. write conclusions and suggest recommendations
VI. Observations and tabulation of measuring variables
i. Mean radius of rotating masses ‘r’ in mm.
ii. Rotational speed of the masses in R.P.S
iii. Masses of rotating bodies ,m₁ = m₂ = kg , Total mass, m = (m₁ + m₂) = kg
iv. Central load – W in ‘N’ = Mg = * 9.81 = N
Tabulation of values of measuring variables
Table 1 shows the observed values of mean radii of the rotating masses and the rotational
speeds at respective radii.
Table 1: Observed values of sleeve lift, ball radius and governor speed of rotation
S.No Mean radius ‘r’ in m Rotational speed, N in Rev/ sec
1
2
3
4
5
5
VII. Results
The following table 2 shows the results of the experiment.
Table 2: Calculated values of 1/r in m , r/m in meters/kg, N in Rev/ sec and N²
Sl.
No
Mean
radius ‘r’ , m
1/r N,
Rev/Sec
N² Centripetal force, F =
4 ∏² m r N² , N
Central Load
W = m.g , N
Construction of graph, N² (Y axis) vs 1 / r (X axis)
Calculation of Slope of the above graph
Calculation of Theoretical slope, F / (4 ∏² m)
Discussion of results
Compare the Centripetal force with the Central load and find whether there is any relation between
them.
Compare the slopes to find whether there is a difference between theoretical and practical values of
the slope of the graph.
Find the relation between the radius of rotation and the rotation masses.
VIII. Conclusions and recommendations:
Draw useful conclusions from the experiment and write them under this section. Suggest
recommendation to improve the performance of the apparatus and to reduce the error.
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Experiment No. 2
I. Experiment Title: Experimenting with centripetal apparatus to identify variations of centrifugal force with respect to the variations in central load and to compare them.
II. Summary:
Write the summary of experiment in the report. Follow the guidelines given by the
instructor.
III. Experiment Objective: To find the centripetal force at various values of central load and then compare them.
IV. Experiment Procedure:
i. Set the two masses the two masses m₁ and m₂ together at any suitable value of mean radius on both sides of the turn table
ii. Apply a suitable central loading mass M to the central pillar iii. Switch on the supply and steadily increase the speed until the central load is lifted . iv. Record the speed N, the masses m₁ , m₂ , M and the mean radius ‘r’ of m₁ and m₂ v. Stop the machine and add additional load to the central pillar. vi. Repeat the observations for 5 values of ‘M’ and tabulate the results.
V. Observations and tabulation of measuring variables
Observed Measuring Variables
i. Mean radius of rotating masses ‘r’ in mm.
ii. Rotational speed of the masses in R.P.S
iii. Masses of rotating bodies , m₁ = m₂ = kg , Total mass, m = (m₁ + m₂) = kg
iv. Central load – W in ‘N’ = Mg = * 9.81 = N
Tabulation of measuring variables
The following table 1 shows the observations of the experiment.
Table 1: observed values of rotational speed at various values of central masses
S.No Central Mass , ‘M’ in Kg
Mean radius ‘r’ in m
Rotational speed, N in Rev/ sec
1 M₁ =
2 M₂ =
3 M₃ =
4 M₄ =
VI. Results
Table 2 shows the results of the experiment .
Table 2 - Calculated values (experimental values) of central load and N²
S.No Central Mass,Kg
Central load W = Mg , N
Mean radius ‘r’ in m
Speed,N , Rev/ sec
N² Centripetal force,
F = 4 ∏² m r N² , N
1 M₁ =
2 M₂ =
3 M₃ =
4 M₄ =
7
After completing the above table, follow the following steps
i. Plot a graph of F vertically against N²
ii. Measure the slope of the above graph – use your subject knowledge to know what is slope
and how to measure it.
iii. Calculate the slope from theoretical relation (4 ∏² m r)
Discussion of results
Compare the central load with the value of centripetal force calculated about i.e. with F. Compare
them. Also compare the slopes to find whether there is a difference between theoretical and
practical values of the slope of the graph.
Refer to the material given by the instructor to carryout error analysis.
IX. Questions and Answers about the experiment 1. What difference did you notice between theoretical and practical values of slopes of the
graph? What is the reason? 2. What are the effects of varying central load on the speed of rotation? 3.
X. Conclusions and recommendations:
Draw useful conclusions from the experiment and write them under this section. Suggest
recommendation to improve the performance of the apparatus and to reduce the error.
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Experiment No. 3
I. Experiment Title: Experimenting with Porter Governor to find its speed and lift characteristics.
II. Summary:
Write the summary of experiment in the report. Follow the guidelines given by the
instructor.
III. Experiment Objective: To find the rotational speed of porter governor at various sleeve positions both practically and
theoretically and compare their values to draw useful conclusions
IV. Introduction to Experimental setup:
Name of the Apparatus: Governor Apparatus - TM127
Draw the diagram of the apparatus: refer to apparatus manual
Parts / Elements of the Apparatus
Part 1: Base unit containing integrated turn table and E64 MKII Tachometer
Part 2: E 67 combined power supply and speed control
Part 3: Variable speed 12 V D.C Electric motor with front panel
Part 4: Belt
Part 5: Perspex dome
Experimental setup
In the governor apparatus, a motor and belt are used to turn the governor. A speed control unit
(available separately) controls the motor speed. A digital tachometer is used to measure the speed.
Each governor uses rotating weights (masses) and levers to raise a sleeve against the action of
gravity or a spring. Graduations show the position of the sleeve as it rises. The Porter governor
includes small containers to hold steel balls to vary the mass of the sleeve. A clear safety ‘dome’
covers the moving parts for safety.
V. Experiment Procedure:
Write the entire procedure to conduct the experiment here.
Refer to the section 4.2 in the pages 4-1, 4-2 and 4-3 of apparatus manual to gather useful
information
Steps to be followed to complete the experiment
In order to achieve the experiment’s objective and draw useful conclusions, the following steps
are to be followed in the laboratory
1. Step 1: Conduct an experiment on porter governor to determine the speed of rotation of
porter governor at various sleeve positions for both sleeve rising and sleeve falling.
2. Step 2: Compute the theoretical speed of rotation at various sleeve positions.
3. Step 3: Draw Characteristic curves of speed of rotation of Porter governor against various
sleeve positions for both sleeve rising and sleeve falling.
4. Step 4: Draw Characteristic curves of theoretical speed of rotation of Porter governor
against various sleeve position on the same graph of experimental speed of rotation.
5. Step 5: Find the difference between practical and theoretical values. Carryout error analysis
and find the reasons for the presence of errors.
VI. Observations and tabulation of measuring variables
Step 1: Conduct an experiment on porter governor to determine the speed of rotation of porter governor
at various sleeve positions for both sleeve rising and sleeve falling.
Observed Measuring Variables
i. Sleeve Lift
ii. Speed in R.P.M
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Tabulation of values of measuring variables
Sleeve mass, M = 300 g
Mass of each ball, m = 200g
Table 1 given below shows the observed tachometer readings at various sleeve positions for both sleeve
rising and sleeve falling
Table 1: Observed tachometer readings at various sleeve positions
Sl.
No
Sleeve Lift
In mm
Tachometer reading – (x)
Sleeve Rising Sleeve Falling
1 4
2 8
3 12
4 16
5 20
6 24
VII. Results and Discussion
Calculation and Tabulation of Results:
Table 2 shows the calculated values of speed of rotation (experimental values) of porter governor
at various sleeve positions for both sleeve rising and sleeve falling
Table 2: Experimental values of rotational speed at various sleeve positions
Sl.
No
Sleeve Lift
In mm
Sleeve Rising Sleeve Falling
Tachometer
reading – (x)
Speed in RPM
N = (x)*0.3*1000
Tachometer
reading – (x)
Speed in RPM
N = (x)*0.3*1000
1 4
2 8
3 12
4 16
5 20
6 24
Step 2: Compute the theoretical speed of rotation at various sleeve positions.
Refer to page 3-3, page 4-6 and figure 3.2 to find theoretical speed of rotation at various sleeve
positions.
Draw figure 3.2 and find the radius of governor ball at each sleeve position theoretically with the
help of the ruler.
Find the angles of upper and lower arms of the governor with respect governor axis, i.e., find ‘Ѳ’ and ‘ф’ at various sleeve positions - refer to the equations given in page 4-6. Find values of governor height ‘h’ at various sleeve positions - refer to the equation in page 4-6. Find ‘ω’ and ‘N’ at various sleeve positions - - refer to page 2-4 and equation 2.6 in page 2-4.
Tabulation of theoretical speed of rotation at various sleeve positions.
Table 3 given below shows the theoretical angular velocities and rotational speeds at various sleeve
positions
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Table 3: Theoretic readings at various sleeve positions
Sl.
No
Sleeve Lift
In mm
Theoretical Angular
velocity ‘ω’ in rad/sec
Theoretical
Rotational speed ‘N’ in RPM
1 4
2 8
3 12
4 16
5 20
6 24
Step 3: Draw Characteristic curves of speed of rotation of Porter governor against various sleeve
position for both sleeve rising and sleeve falling.
Refer to page 4-8 and 4-10 of the manual
Step 4: Draw Characteristic curves of theoretical speed of rotation of Porter governor against
various sleeve position on the same graph of experimental speed of rotation.
Refer to page 4-10 of the manual
Discussion of results
Step 5: Find the difference between practical and theoretical values. Carryout error analysis and find
the reasons for the presence of errors.
Refer to the material given by the instructor to carryout error analysis.
VIII. Questions and Answers about the experiment 1. Is there any difference between theoretical speed of rotation and experimental speed of
rotation? What is the reason? 2. What are the important parts of the experimental apparatus? 3. Is it possible to eliminate friction and get an ideal condition at which the speed of rotation is
same at both instances of sleeve rising and sleeve falling? 4. If the sleeve is rising, direction of frictional force coincides with the direction of action of
sleeve weight. Do you agree with this statement? Explain the reason. 5. If the sleeve is falling, direction of frictional force becomes opposite to the direction of action
of sleeve weight. Do you agree with this statement? Explain the reason.
IX. Conclusions and recommendations:
Draw useful conclusions from the experiment and write them under this section. Suggest
recommendation to improve the performance of the apparatus and to reduce the error.
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Experiment No 4
I. Experiment Title: Experimenting with flywheel apparatus to find its useful properties.
II. Summary: Using the guidelines, write the summary of experiment in the report.
III. Experiment Objective:
To evaluate maximum velocity, energy delivered, energy content at unit speed , Moment of
Inertia and the radius of gyration of flywheel.
IV. Introduction Introduce the experiment; explain the significance of experiment and its results.
V. Apparatus Description
Name of the Apparatus: Flywheel Apparatus
Describe the apparatus and its parts. Observe the sketches given in page 6 of flywheel manual and
draw them. Ensure that all parts shown in the figure are explained. The figure has to be numbered
and to be referred in the text as per the given guidelines.
VI. Theory
Explain the theoretical principles and the assumptions that are used in the experiment. Write all the
equations used to find the following. Explain all the symbols used in these equations. Refer to the
equations given in page 7 and 9 of manual
1. Maximum velocity of the flywheel ( Final velocity of descending mass)
2. Maximum rotational speed of the flywheel
3. Energy delivered to the flywheel ( The maximum energy content of the flywheel)
4. Energy content at unit speed ( i.e. Energy stored when rotating at unit speed)
5. Moment of Inertia of flywheel -
To find the friction torque factor ‘f’, the flywheel is to be allowed to come to rest . When
the flywheel is allowed to come to rest, it will rotate a further ‘n’ revolutions and in doing
so it will dissipate the KE by friction work. This value of ‘n’ has to be identified and
substituted in the above equation.
6. Radius of gyration of flywheel
VII. Experiment Procedure:
i. First spin the flywheel by hand for a few minutes to warm the bearings and stabilize viscous
friction.
ii. Attach the cord to the axle by a loop and adjust the length so that it is released at the instant
the weights touch the floor.
iii. Commence the experiment by attaching a mass of about 0.5 kg on the cord
iv. Turn the flywheel until the lower edge of the weight is a convenient height H as measured
with the tape or rule.
v. Record the values of m, H and r
vi. Allow the weight to fall and observe the time t in seconds to reach the floor and record t
vii. Repeat step vi three times to find mean value of t.
viii. Increase the value of m in steps of suitable weights (for example 0.5 kg) and repeat steps v
and vi.
ix. Complete the table of observations and calculate results using the equations mentioned in
the theory section.
x. To find Moment of Inertia, detach the loop from the axle, count the number of revolutions
‘n’ until the flywheel comes to rest. Record ‘n’.
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VIII. Observations and tabulation of measuring variables
Observed Measuring Variables
Various useful parameters of the falling weight are observed and presented in the following table
1. These parameters include mass of falling weight, height of it from the floor, radius of the
flywheel, Mass of flywheel, three observations of time taken by each mass to reach the floor.
Table 1 – Observed parameters of falling mass
Sl.
No
Mass of
falling weight
, kg
Height of
mass from
floor, m
Radius of
flywheel, r
Mass of
flywheel,
kg
Time taken by
falling mass
to reach floor,
sec
1
m₁ = 0.5
t₁ =
t₂=
t₃=
2
m₂ =
t₁ =
t₂=
t₃=
3
m₃ =
t₁ =
t₂=
t₃=
4
m₄=
t₁ =
t₂=
t₃=
Value of ‘n’ = , Flywheel mass , M = Kg
IX. Results and Discussion
The mean time for each mass, values of 1/m and t² have been calculated as shown in the following
table 2
Table 2: Mean values of time for the various falling weights.
Sl.No Mass ,m, kg 1/m , 1/kg Mean time , t =(t₁ + t₂ + t₃) / 3, s t², s²
1 m₁ = 0.5
2 m₂ =
3 m₃ =
4 m₄=
Calculate the following for each observation of Table 2.
1. Maximum velocity of the flywheel and Maximum rotational speed of the flywheel
2. Energy delivered to the flywheel and Energy content at unit speed
3. Moment of Inertia of flywheel and Radius of gyration of flywheel
Plot a graph of 1/m against ‘t²’ , using the values given in table 2.
X. Conclusions and Recommendations
XI. References
XII. Questions
1. From the above experiment what is your comment about Variation of maximum velocity
‘V’ when compared to mass ‘m’
2. From the results of the above experiment, when mass increases what happens to the
maximum rotational speed, energy delivered to the flywheel?
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Experiment No. 5
I. Experiment Title: Experimenting with Cam apparatus to draw profile of the cam.
II. Summary: Using the guidelines, write the summary of experiment in the report.
III. Experiment Objective:
To draw the cam profile using the displacement diagram traced by the pencil attached to the cam
apparatus and it with that of original cam profile.
IV. Introduction Introduce the experiment; explain the significance of experiment and its results.
V. Apparatus Description
Name of the Apparatus: Cam Apparatus
Describe the apparatus and its parts.
The main part of the product is a geared motor coupled to an extension shaft with a
tapered end that carries a cam. A vertical compression spring pushes a cam follower
onto the cam face. A nut adjusts the spring tension. A timing belt from the cam shaft
drives a cylindrical drum carrying chart paper. A pen traces a record of the cam
follower amplitude.. A heavy flywheel reduces any speed fluctuations. A motor speed
control (included) varies the speed of the cam shaft and the direction of rotation. A
guard covers the moving parts to protect the user.
Observe the sketches given in the manual and draw them. Ensure that all parts shown in the figure
are explained. The figure has to be numbered and to be referred in the text as per the given
guidelines.
VI. Theory
Explain the theoretical principles and the assumptions that are used in the experiment. Explain how
the accuracy of the cam profile that you draw can be tested. .
VII. Experiment Procedure:
i. Arrange the paper and pencil on the cylindrical disk of the apparatus and tighten the pencil
holder to the required level.
ii. Properly tighten all the nuts involving cam, follower , safety dome
iii. Slowly increase the speed of rotation of cam and observe the trace of displacement diagram
that is being drawn by the pencil.
iv. After ensuring that the displacement diagram is properly drawn, remove the apparatus and
takeout the paper on which displacement diagram is drawn.
v. Draw the cam profile of roller follower by taking the displacement diagram as reference.
vi. Compare the drawn profile with the original profile and give your comments.
VIII. Observations and tabulation of measuring variables
Observed Measuring Variables
Radius of the roller = cm
Observe the displacement diagram that is being drawn by the apparatus and note the starting and
end points of the diagram.
Length of displacement diagram = cm
IX. Results and Discussion
Find the radius of base circle – Use your subject knowledge to find it
Draw cam profile for roller follower using the displacement diagram .
Find if there is any error between the drawn profile and original profile.
X. Conclusions and Recommendations
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