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 =

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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