ME-301L MOM AND VIBRATION LAB REPORTS
AZLAL JAMIL -4843
UNIVERSITY OF ENGINEERING AND TECHNOLOGY, PESHAWAR DEPARTMENT OF
MECHANICAL ENGINEERING
CERTIFICATE
Certified that the “MOM AND VIBRATION LAB “work entitled “lab reports” is a
work carried out by:
Name
Reg no
Section
Class no
Subject
:
:
:
:
:
Azlal jamil
20PWMEC4843
M
02
ME-341L MOM AND
VIBRATION LAB
The report has been approved as it satisfies the academic requirements in respect
of mini project work prescribed for the course by teacher.
Subject teacher:
Engr. Kaleem Ullah
Chairman of the Department
prof Dr. Rizwan Mehmood gul
Signature:
Signature:
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ME-301L MOM AND VIBRATION LAB REPORTS
AZLAL JAMIL -4843
Table of Contents
LAB REPORT # 01..................................................................................................................................................................... 4
OBJECTIVES ........................................................................................................................................................................................... 4
THORETICAL BACKGROUND: ................................................................................................................................................................ 4
APPARATUS .......................................................................................................................................................................................... 4
APPARATUS DESCRIPTION: .................................................................................................................................................................. 4
LAB REPORT # 02........................................................................................................................ 10
OBJECTIVES ......................................................................................................................................................................................... 10
THERETICAL BACKGROUND: .............................................................................................................................................................. 10
APPARATUS ........................................................................................................................................................................................ 11
APPARATUS DESCRIPTION: ................................................................................................................................................................ 11
Experimental procedure: ................................................................................................................................................................... 12
observation and calculation:.............................................................................................................................................................. 13
results and conclusion: ....................................................................................................................................................................... 15
precuations: ........................................................................................................................................................................................ 15
LAB REPORT # 03........................................................................................................................ 16
OBJECTIVES ......................................................................................................................................................................................... 16
THORETICAL BACKGROUND: .............................................................................................................................................................. 16
APPARATUS ........................................................................................................................................................................................ 17
APPARATUS DESCRIPTION: ................................................................................................................................................................ 17
Experimental procedure: ................................................................................................................................................................... 18
observation and calculation:.............................................................................................................................................................. 18
results and conclusion: ....................................................................................................................................................................... 19
precautions: ........................................................................................................................................................................................ 19
LAB REPORT # 04........................................................................................................................ 20
OBJECTIVES ......................................................................................................................................................................................... 20
THORETICAL BACKGROUND: .............................................................................................................................................................. 20
APPARATUS ........................................................................................................................................................................................ 21
APPARATUS DESCRIPTION: ................................................................................................................................................................ 21
Experimental procedure: ................................................................................................................................................................... 22
observation and calculation:.............................................................................................................................................................. 23
results and conclusion: ....................................................................................................................................................................... 23
precautions: ........................................................................................................................................................................................ 23
LAB REPORT # 05........................................................................................................................ 24
OBJECTIVES ......................................................................................................................................................................................... 24
THORETICAL BACKGROUND: .............................................................................................................................................................. 24
APPARATUS ........................................................................................................................................................................................ 26
APPARATUS DESCRIPTION: ................................................................................................................................................................ 27
Experimental procedure: ................................................................................................................................................................... 27
observation and calculation:.............................................................................................................................................................. 27
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ME-301L MOM AND VIBRATION LAB REPORTS
AZLAL JAMIL -4843
results and conclusion: ....................................................................................................................................................................... 28
precautions: ........................................................................................................................................................................................ 28
LAB REPORT # 06........................................................................................................................ 29
OBJECTIVES ......................................................................................................................................................................................... 29
THORETICAL BACKGROUND: .............................................................................................................................................................. 29
Equation derivation:........................................................................................................................................................................... 29
APPARATUS ........................................................................................................................................................................................ 31
APPARATUS DESCRIPTION: ................................................................................................................................................................ 32
Experimental procedure: ................................................................................................................................................................... 33
observation and calculation:.............................................................................................................................................................. 33
results and conclusion: ....................................................................................................................................................................... 34
precautions: ........................................................................................................................................................................................ 34
LAB REPORT # 07........................................................................................................................ 35
OBJECTIVES ......................................................................................................................................................................................... 35
THORETICAL BACKGROUND: .............................................................................................................................................................. 35
APPARATUS DESCRIPTION: ................................................................................................................................................................ 37
Experimental procedure: ................................................................................................................................................................... 38
observation and calculation:.............................................................................................................................................................. 38
results and conclusion: ....................................................................................................................................................................... 38
precautions: ........................................................................................................................................................................................ 38
LAB REPORT # 08........................................................................................................................ 39
OBJECTIVES ......................................................................................................................................................................................... 39
THORETICAL BACKGROUND: .............................................................................................................................................................. 39
Mathematical Modelling .................................................................................................................................................................... 39
apparatus description ........................................................................................................................................................................ 40
Experimental procedure: ................................................................................................................................................................... 41
observation and calculation:.............................................................................................................................................................. 42
results and conclusion: ....................................................................................................................................................................... 42
precautions: ........................................................................................................................................................................................ 42
LAB
REPORT # 09 ................................................................................................................................................................... 43
OBJECTIVES ......................................................................................................................................................................................... 43
THORETICAL BACKGROUND: .............................................................................................................................................................. 43
APPARATUS ........................................................................................................................................................................................ 44
APPARATUS DESCRIPTION: ................................................................................................................................................................ 44
Experimental procedure: ................................................................................................................................................................... 45
observation and calculation:.............................................................................................................................................................. 45
results and conclusion: ....................................................................................................................................................................... 46
precautions: ........................................................................................................................................................................................ 46
UNIVERSITY OF ENGINEERING AND TECHNOLOGY, PESHAWAR
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ME-301L MOM AND VIBRATION LAB REPORTS
AZLAL JAMIL -4843
LAB REPORT # 01
TITLE
Introduction to Mechanics of machine and vibration Lab, its Layout and Safety guidelines.
OBJECTIVES
➢
➢
➢
➢
➢
To know about the operational definition of Mechanics of machine and vibration Lab.
To familiarize with the equipment used in Mechanics of machine and vibration Lab
To draw layout of Mechanics of machine and vibration Lab
Detail description of each apparatus in the lab
To get familiar with the safety guidelines.
THORETICAL BACKGROUND:
Mechanics Of Machines & Vibrations:
Branch of Engineering science which deals with the study of relative motion between the various parts of
machine and forces which act on these parts due to constrained motion and vibrations produced is called
mechanics of machines.
Importance of MOM & Vibrations Lab:
This lab enables the students to practically observe the phenomenon of vibrations and to enhance the skills of
the students in the practical field of mechanics of machines and vibration.
APPARATUS
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
Static & dynamic balancing apparatus:
Whirling of shaft apparatus:
Whirling of shaft apparatus:
Gyroscope:
Free vibration apparatus:
Steeped shaft apparatus:
Centrifugal force apparatus:
Cam and follower apparatus:
Static and dynamic balancing apparatus:
Forced vibration apparatus:
APPARATUS DESCRIPTION:
1. STATIC & DYNAMIC BALANCING APPARATUS:
→
→
→
→
This apparatus is designed to carry out an experiment for balancing rotation mass system.
This apparatus enables us to study the phenomena of unbalancing in practical life.
This apparatus is used to experimentally perform the static and dynamic balancing.
This apparatus consists of motor, shaft and rotating discs used to perform balancing
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ME-301L MOM AND VIBRATION LAB REPORTS
AZLAL JAMIL -4843
FIGURE 01: STATIC AND DYNAMIC BALANCING APPARATUS
2. WHIRLING OF SHAFT APPARATUS:
•
•
•
•
This apparatus is used to experimentally study the whirling of rotating shafts and the vibrations that will
be produced during the rotation.
This apparatus is used to find the whirling of the shaft in rotation.
It consists of various components like protective shield, shaft, control panel, nylon bushes and ball
bearings etc.
Shaft is fixed at both the ends and holder by the ball bearings.
FIGURE 02: WHIRLING OF SHAFT APPARATUS
3. GYROSCOPE:
• This apparatus is used for the demonstration of gyroscopic couple. It is based on the principle of the
angular momentum and is used to measure the orientation.
• Gyroscope apparatus consists of two main parts.
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ME-301L MOM AND VIBRATION LAB REPORTS
•
•
AZLAL JAMIL -4843
→ Control panel.
→ Working Panel.
Used to measure gyroscopic torque produced.
Orientation of torque produced can be find out by using thumb rule.
FIGURE 03: GYROSCOPE APPARATUS
4. FREE VIBRATION APPARATUS:
•
•
•
•
•
Free vibration apparatus is used to measure natural vibration in specimen by applying the external force
once. For example, simple pendulum.
It consists of various parts like carriage base, columns, mechanical recorder drum, helical spring etc.
This apparatus is also used to find stiffness of the helical spring.
Do not add force after the initial disturbance so that we get values of free vibrations.
Make the system undamped by removing the damper while calculating values for free vibrations.
FIGURE 04: FREE VIBRATION APPARATUS
5. STEEPED SHAFT APPARATUS:
•
•
•
•
•
•
This apparatus is used to study the relationship between the linear and angular velocities.
Step shaft apparatus consist of three different diameter shafts.
It is used to verify the relation between angular and linear velocity.
A thread is wrapped around the shaft and loads are attached at the other end of the string.
Wrap the string around the shaft carefully so that it does not contain any sag.
Measure the heights of the weights from a fixed point to the ground
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FIGURE 05: STEEPED SHAFT APPARATUS
6. CENTRIFUGAL FORCE APPARATUS:
This apparatus is used to practically demonstrate the centrifugal force that acts on rotating objects.
It is also used to experimentally verify that the centrifugal force is proportional to the square of the speed and
inversely to the radius of rotation.
It consists of two major parts:
→ control panel
→ working unit.
FIGURE 06: CENTRIFUGAL FORCE APPARATUS
7. CAM AND FOLLOWER APPARATUS:
•
•
It is used to convert rotatory motion to reciprocating motion.
Cam and follower apparatus is used to draw the displacement diagram of the rolling follower.
•
This apparatus is used to draw the cam profile of the given cam and follower mechanism.
•
Apparatus consists of following parts .
•
→ Cam
→ Roller Follower
→ Glass bar
Always accurately draw the displacement diagram of the given mechanism.
•
Drawn cam profile should demonstrate the exact motion of the cam and follower mechanism.
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FIGURE 07: CAM FOLLOWER APPARATUS
8. STATIC AND DYNAMIC BALANCING APPARATUS:
•
•
•
•
Static and dynamic balancing apparatus are used to experiment on the rotating mass system and
check their result against accept theory.
This apparatus enables us to study the phenomena of unbalancing I n practical life.
This apparatus is used to experimentally perform the static and dynamic balancing.
This apparatus consists of motor, shaft and rotating discs used to perform balancing
FIGURE 08: CENTRIFUGAL FORCE APPARATU
9. FORCED VIBRATION APPARATUS:
Forced vibration apparatus are used to measure the vibration in a specimen by repeating external force. For
example, oscillation arises in the diesel engine.
FIGURE 09: FORCE VIBRATION APPARATUS
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LAB LAYOUT:
Cam and follower
appratus
STEPPED SHAFT APPARATUS
GYROSCOPE
WHIRLING OF
SHAFT
APPARATUS
CENTRIFUGAL FORCE
APPARATUS
STATIC AND
DYNAMIC
BALANCING
APPARATUS
FORCED
VIBRATION
APPPARATUS
STATIC AND STATIC AND
FREE VIBRATION
APPARATUS
DOOR
UNIVERSITY OF ENGINEERING AND TECHNOLOGY, PESHAWAR
STATIC AND
DYNAMIC
BALANCING
APPARATUS
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ME-301L MOM AND VIBRATION LAB REPORTS
AZLAL JAMIL -4843
LAB REPORT # 02
TITLE
Determine the effect of mass, angular speed and radius on the centrifugal force.
OBJECTIVES
➢ To know about centrifugal force apparatus.
➢ To verify centrifugal force varies directly with
→ Mass of rotating object
→ Radius of rotating object
→ Square of angular speed
THERETICAL BACKGROUND:
•
•
•
•
The time rate of change of velocity is called acceleration.
Acceleration may be produced due to change in magnitude or change in direction.
In circular motion, there is a continuous change in direction of rotating object even if its magnitude is
constant.
Acceleration in circular motion is known as centrifugal acceleration,
Which is given by:
a=
▪
1)
𝒓
According to Newton’s 2nd law: the force due to the acceleration will be:
F=
▪
𝒗𝟐
𝒎𝒗𝟐
𝒓
2)
According to Newton 3rd law of motion, due to this force is centrifugal force:
F=
𝒎𝒗𝟐
𝒓
V=r𝔀
F=
𝒎(𝐫𝔀)𝟐
𝒓
F= mar𝔀𝟐
3)
4)
5)
6)
Relevancy of this experiment to mechanics of machine and vibration lab is that the centrifugal force is the
cause of vibration in unbalancing shaft.
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APPARATUS
Centrifugal force apparatus: The centrifugal force apparatus enables experimental investigation of the centrifugal force F as a function
of the rotating mass m, the distance r of the mass from the centre of rotation and the angular velocity ω,
thus making it possible to confirm the relation F = m·ω2 ·r for the centrifugal force.
FIGURE 2.1: CENTRIFUGAL FORCE APPARATUS
APPARATUS DESCRIPTION:
It consists of the following parts:
• Power on/off
• Speed controller
• Center force shaft
• Center force mass
• Yellow part known as boom
• Small yellow known as lever
• Thrust plate
• Splinter
• Lever arms
• End supports
Lever Mechanism:
Lever mechanism embedded in centrifugal force apparatus is used to take centrifugal force from shafts and
convert it onto the scale that has been calibrated in Newtons which shows resultant centrifugal force. It is
important to remember that the centrifugal force shown on the scale is half of the actual force because
the lever mechanism works upon the 2:1 rule. That means we will have to multiply the obtained scale force
by 2 to get actual centrifugal force.
CF Shafts:
These are the shafts on which we place the loads at a certain radius measured from the center of the thrust
plate.
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Spindle:
This is the main structure on which scale is mounted on which we can see centrifugal force obtained by a
lever.
Boom:
Boom is the foundation of the working unit of CFA on which the whole mechanism has been installed.
FIGURE 2.2: CONTROLLING PANEL OF CENTRIFUGAL FORCE APPARATUS
FIGURE 2.3: WORKING UNIT OF CENTRIFUGAL FORCE APPARATUS
EXPERIMENTAL PROCEDURE:
•
•
•
•
•
•
Setup the centrifugal force apparatus for experiment.
Turn on the electricity supply to centrifugal force apparatus.
Keep one parameter among mass, angular speed or radius as a variable and other two constants to fill
table 1, 2 and 3 to analyze their effect on centrifugal force.
Add masses on both sides of the shafts at a certain radius and switch the conditions upon requirements.
Measure the force on the scale.
Repeat steps 1,2 and 3 for other two parameters to study their effect also.
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•
•
•
•
AZLAL JAMIL -4843
Collect the data and compare actual and theoretical centrifugal forces.
Plot the graphs for force-mass, force-angular speed and force-radius.
After performing the experiment turn off all the switches.
Place the apparatus where it was before.
OBSERVATION AND CALCULATION:
Table -1: Variable - Angular speed (⍵) rev/min
Constants - mass :100g
radius:140mm
speed(rev/min)
Force display(N)
Actual force (N)
Theoretical Force (N)
479
6
12
35.18
308
2
4
14.54
327
4
8
16.39
TABLE 2.1: CENTRIFUGAL FORCE CALCULATION WHEN ANGULAR SPEED IS ONLY VARIABLE
GRAPH 2.1: CENTRIFUGAL FORCE VS ANGULAR SPEED GRAPH
Table -2: Variable - radius
Constants -mass :100g
Speed :306rpm
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radius(mm)
Force display(N)
Actual force (N)
Theoretical Force (N)
140
4
8
14.36
110
2
4
11.28
120
2
4
12.30
TABLE 2.2: CENTRIFUGAL FORCE CALCULATION WHEN RADIUS IS ONLY VARIABLE
GRAPH 2.2: CENTRIFUGAL FORCE VS RADIUS
Table -3: Variable - mass(g)
Constants -speed:305rpm
radius:140mm
mass(kg)
Force display(N)
Actual force (N)
Theoretical Force (N)
100
2
4
14.26
200
6
12
28.53
300
7
16
42.80
TABLE 2.3: CENTRIFUGAL FORCE CALCULATION WHEN RADIUS IS ONLY VARIABLE
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GRAPH 2.3: CENTRIFUGAL FORCE VS MASS
RESULTS AND CONCLUSION:
Hence after performing the experiment, we gain sufficient knowledge about centrifugal force apparatus its
working and different parts functioning. After performing the observation and calculation from the results we
concluded that angular velocity, mass and radius are directly proportional to centrifugal forces. An increase
in any of these variables will increase centrifugal forces and vice versa. As shown in fig 2.1 ,2.2 and 2.3 the
curve is increasing by increasing mass radius or angular speed.
PRECUATIONS:
•
•
•
After performing the experiment turn off the apparatus and place it where before it was placed.
Do not touch the machine while it is operating.
Do not use the machine without lab instructor.
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LAB REPORT # 03
TITLE
To Balance the Unbalanced System both Statically and Dynamically
OBJECTIVES
➢ To know about centrifugal force apparatus.
➢ To balance the unbalanced shaft both statically and dynamically.
➢ To examine the effect the effect of static and dynamic balancing on vibrations.
THORETICAL BACKGROUND:
Unbalancing:
A rotating mass is said to be out of balance when its centre of mass and centre of geometry does not pass
through the same point.
Source Of Unbalancing:
The non-uniform distribution of mass of rotating bodies (shafts) is the source of unbalancing and it produces
vibrations in the machine.
Due to the unbalancing of shafts unbalanced centrifugal forces are produced and that causes the shaft to bend,
Balancing:
Balancing is the technique of eliminating or correcting the unwanted inertia forces or moments in the
reciprocating and rotating bodies like shafts and is achieved by changing the positions of centre of masses.
● Process of providing the second mass to counter the effect of an unbalanced mass is known as balancing.
Types Of Balancing:
Following are the 2 types of balancing.
1. Static Balancing
2. Dynamic Balancing
Static Balancing:
System is said to be statically balanced when there are no resultant centrifugal forces and the centre of mass
is on the axis of rotation of the shaft.
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Condition For Static Balancing:
∑F=0
Dynamic Balancing:
System is said to be dynamically balanced when there are no resultant centrifugal forces and no resultant
moments about the shaft axis.
Condition for Dynamically Balancing:
∑F=0
∑M =0
APPARATUS
Static & Dynamic Balancing Apparatus:
Static and dynamic balancing apparatus enables us to study the phenomena of unbalancing in practical life
and we can experimentally perform static and dynamic balancing on the unbalanced shaft.
FIGURE 3.1: STATIC AND DYNAMIC BALANCING APPARATUS
APPARATUS DESCRIPTION:
Rotating Discs:
There are 4 hollow rotating discs are mounted on the shaft on this apparatus on which we can apply different
masses at different angular positions and at different radiuses.
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Shaft:
A shaft is placed in this apparatus on which we have hollow discs that rotate.
Electric Motor:
An electric motor is also installed in this apparatus that gives a
constant rotating speed to the shaft.
EXPERIMENTAL PROCEDURE:
•
•
•
•
•
•
•
•
•
Setup the centrifugal force apparatus for experiment.
Turn on the electricity supply to centrifugal force apparatus.
Make the shaft unbalance and rotate it and check for vibrations.
Now make an arrangement in this way that summation of all the centrifugal forces acting on the shaft
becomes equal to zero.
Thus, by making this arrangement we have statically balanced the system but still there will be vibrations
that are due to the moments produced in that shaft.
So, for the moments now make an arrangement in this way that summation of all moments acting on the
shaft becomes zero.
So now we have done static and dynamic balancing and now there will be no vibrations in the system.
After performing the experiment turn off all the switches.
Place the apparatus where it was before.
OBSERVATION AND CALCULATION:
Distance between plane A and C =285mm
Distance between plane B and D =285mm
planes
mass
radius
force
Moments
Fa
Angular
position(θ)
180
A
ma
ra
B
mb
rb
Fb
0
-Embed
C
mc
rc
Fc
0
Malc
D
md
rd.
Fd
180
-Embed
Malc
TABLE 2.1: CALCULATION OF MOMENTS
According to condition of dynamic balancing
∑M=0
So, the system is dynamically as well as statically balanced.
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RESULTS AND CONCLUSION:
Hence after performing the experiment, we gain sufficient knowledge about static and dynamic balancing
apparatus its working and different parts functioning. And hence, from this experiment we learn how we can
balance the rotating system both statically and dynamically while applying some fundamental equations.
PRECAUTIONS:
● Do not enter the apparatus territory when it is on.
● Always tights the masses before starting the apparatus because loose mass can be dental easily and can
cause damage.
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LAB REPORT # 04
TITLE
To Balance the Unbalanced System both Statically and Dynamically
OBJECTIVES
➢ To know about static and dynamic balancing apparatus.
➢ To balance the unbalanced shaft both statically and dynamically.
➢ To examine the effect of static and dynamic balancing on vibrations.
THORETICAL BACKGROUND:
Unbalancing:
A rotating mass is said to be out of balance when its centre of mass and centre of geometry does not pass
through the same point.
Source Of Unbalancing:
The non-uniform distribution of mass of rotating bodies (shafts) is the source of unbalancing and it produces
vibrations in the machine.
Due to the unbalancing of shafts unbalanced centrifugal forces are produced and that causes the shaft to bend,
Balancing:
Balancing is the technique of eliminating or correcting the unwanted inertia forces or moments in the
reciprocating and rotating bodies like shafts and is achieved by changing the positions of centre of masses.
● Process of providing the second mass to counter the effect of an unbalanced mass is known as balancing.
Types Of Balancing:
Following are the 2 types of balancing.
3. Static Balancing
4. Dynamic Balancing
Static Balancing:
System is said to be statically balanced when there are no resultant centrifugal forces and the centre of mass
is on the axis of rotation of the shaft.
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Condition For Static Balancing:
∑F=0
Dynamic Balancing:
System is said to be dynamically balanced when there are no resultant centrifugal forces and no resultant
moments about the shaft axis.
Condition for Dynamically Balancing:
∑F=0 ∑M =0
APPARATUS
Static & Dynamic Balancing Apparatus:
Static and dynamic balancing apparatus enables us to study the phenomena of unbalancing in practical life
and we can experimentally perform static and dynamic balancing on the unbalanced shaft.
FIGURE 4.1: STATIC AND DYNAMIC BALANCING APPARATUS
APPARATUS DESCRIPTION:
Control Unit:
Control unit in the apparatus is used for changing the angular speed and to on/off the apparatus. In control
unit a motor is installed for which provides togue to the shaft and it rotates.
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Rotating Planes:
There are 4 rotating planes are mounted on the shaft on this apparatus on which we can apply different masses
at different angular positions and at different radiuses.
Shaft:
A shaft is placed in this apparatus on which we have hollow discs that rotate.
Drive Belt:
Drive belt is used to transfer the rotational power from the electric motor to the shaft.
Protective Shield:
To avoid any dismantling of the masses or planes, a shield is used to protect the viewers.
Angular Scale:
An angular scale is used for placing the masses at a particular angular position.
Linear Scale:
A linear scale is used to measure the moment arm for different planes from a reference point.
FIGURE 4.2: DIFFERENT PARTS STATIC AND DYNAMIC BALANCING APPARATUS
EXPERIMENTAL PROCEDURE:
•
•
•
•
•
•
•
•
•
Setup the centrifugal force apparatus for experiment.
Turn on the electricity supply to centrifugal force apparatus.
Make the shaft unbalance and rotate it and check for vibrations.
Now make an arrangement in this way that summation of all the centrifugal forces acting on the
shaft becomes equal to zero.
Thus, by making this arrangement we have statically balanced the system but still there will be
vibrations that are due to the moments produced in that shaft.
So, for the moments now make an arrangement in this way that summation of all moments acting
on the shaft becomes zero.
So now we have done static and dynamic balancing and now there will be no vibrations in the
system.
After performing the experiment turn off all the switches.
Place the apparatus where it was before.
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OBSERVATION AND CALCULATION:
Position Of Plane A from Reference point=3cm
Position Of Plane B from Reference point=9cm
Position Of Plane C from Reference point=12cm
Position Of Plane D from Reference point=18cm
Distance between Plan A and Plan C =9cm
Distance between Plan B and Plan D =9cm
masses
(g)
Planes
Angle
Force
Moment arm(cm)
A
37
0
37
3
B
37
180
-37
9
C
37
180
-37
12
D
37
0
37
18
According to condition of dynamic balancing
∑M=0
Macomb=0
37*9-37*9=0
RESULTS AND CONCLUSION:
Hence after performing the experiment, we gain sufficient knowledge about static and dynamic balancing
apparatus its working and different parts functioning. So, from this experiment we learn how we can balance
the rotating system both statically and dynamically while applying some fundamental equations.
PRECAUTIONS:
●
Do not enter the apparatus territory when it is on.
●
Always put the protective shield on the apparatus before starting the apparatus.
●
Always tights the masses before starting the apparatus because loose mass can be dental easily and can
cause damage.
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LAB REPORT # 05
TITLE
Draw a cam profile for given cam and follower mechanism
OBJECTIVES
➢ To know about cam and follower apparatus.
➢ To draw the displacement curve for a given cam and follower mechanism.
➢ To draw the cam profile from the displacement diagram.
THORETICAL BACKGROUND:
CAM AND FOLLOWER:
A cam is a rotating machine element which gives reciprocating or oscillating motion to another element
known as follower.
Example:
Cam lobe of the camshaft is used to open engine valves.
CLASSIFICATION OF CAMS:
Cams are classified according to
→ Shapes
→ Manner of constraint of the follower
→ Cam mechanism (I/p and O/P motion)
According To Shapes:
●
Radial or disc cam
●
Cylindrical cam
●
End cam
●
Wedge Cam
●
Spiral Cam
●
Spherical cam
●
Glenoidal cam
According to Manner of Constraint of Follower:
●
Preloaded spring cam
●
Positive drive cam
●
Gravity cam
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According To Cam Mechanism:
●
Rotating cam-translating follower
●
Rotating follower-oscillating follower
●
Reciprocating cam-Translating follower
Classification Of Follower:
Followers are classified according to
●
According to surface of contact
●
According to path of motion of follower
●
According to motion of follower
According to surface of contact:
●
Knife edge follower
●
Roller follower
●
Flat faced follower
●
Spherical faced follower
According to path of motion of follower:
●
Radial follower’
●
Offset follower
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According to motion of follower:
●
Reciprocating follower
●
Oscillating follower
APPARATUS
Cam and follower apparatus.
FIGURE 5.1: CAM AND FOLLOWER APPARATUS
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APPARATUS DESCRIPTION:
Follower Specifications:
The follower in our lab has the following specifications.
● Reciprocating Follower
● Radial Follower
● Roller Follower
Mechanism Description:
Cam is mounted on rack and pinion. A glass bar is located on the mechanism on which we can track the
location of follower by using pencil and white paper.
EXPERIMENTAL PROCEDURE:
•
•
•
•
•
•
•
•
•
Setup the centrifugal force apparatus for experiment.
Turn on the electricity supply to centrifugal force apparatus.
Put a graph paper on glass slide
Slowly rotate the cam
The follower will reciprocate
And the displacement curve will be drawn on paper by mean of pencil being clamped
With the help of curve, we draw cam profile
After performing the experiment turn off all the switches.
Place the apparatus where it was before.
OBSERVATION AND CALCULATION:
→ Radius (Basic circle) =8cm
→ Circumference=𝟐𝝅𝒓
→ C =50.24cm
→ 50.24cm=360°
→ 1cm=7.17°
→ “x” dwell=31cm
→ 31cm=7.17°ˣ31
→ Dwell= 222.7°
→ Rise +fall=𝟑𝟔𝟎° − 𝟐𝟐𝟐. 𝟕°
→ rise=fall=
𝟑𝟔𝟎°−𝟐𝟐𝟐.𝟕°
𝟐
→ rise= fall =68.8°
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RESULTS AND CONCLUSION:
Hence after performing the experiment, we gain sufficient knowledge about cam and follower apparatus its
working and different parts functioning. So, from this experiment we learn how we can balance the rotating
system both statically and dynamically while applying some fundamental equations.
PRECAUTIONS:
●
Do not enter the apparatus territory when it is moving.
●
Turned off the machine when procedure is completed.
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LAB REPORT # 06
TITLE
Measure the gyroscopic torque using gyroscope.
OBJECTIVES
➢ To know about gyroscope.
➢ To understand what a gyroscopic effect is.
➢ To calculate a gyroscopic couple.
THORETICAL BACKGROUND:
GYROSCOPIC PHENOMENA:
When a spinning object is forced to change its orientation, that spinning object
experiences a torque in response to the change in orientation. This phenomenon is known
as gyroscopic phenomena.
PRECESSION OF GYRO:
Change in the spinning axis orientation is known as precession of gyro.
PRECESSION AXIS:
Axis through which the orientation of gyro changes is called the precession axis
FIGURE 6.1:
EQUATION DERIVATION:
Angular momentum=L= mar
△𝑳 △𝒎𝒗𝒓
=
△𝒕
∆𝒕
Change in angular momentum with time =
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As:
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△𝑚𝑣
=F
∆𝑡
Newton 2nd law:
So:
△𝐿
=F.
∆𝑡
△𝐿
=T
∆𝑡
r
put in equ: 1)
△𝒎𝒗𝒓
=T 1)
∆𝒕
As: V=r 𝜔
So:
△𝑚𝑟 2 𝜔
=
∆𝑡
𝑇
△ 𝐼𝜔
=𝑇
∆𝑡
𝑻=𝑰𝜶
2)
𝐼 = 𝑖𝑛𝑒𝑟𝑡𝑖𝑎 𝑜𝑓 𝑠𝑝𝑖𝑛𝑛𝑖𝑛𝑔 𝑜𝑏𝑗𝑒𝑐𝑡
Where
𝛼 = 𝑎𝑛𝑔𝑢𝑙𝑎𝑟 𝑎𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛
Sin 𝛿𝜃 =
⃗⃗⃗⃗
𝑟𝑏
𝛼= 𝜔 =
⃗⃗⃗⃗
𝑟𝑏
𝜔
𝜔Sin 𝛿𝜃
∆𝑡
For small 𝛿𝜃:
Sin 𝛿𝜃 = 𝛿𝜃
So:
𝛼=
𝜔 𝛿𝜃
∆𝑡
𝜶= 𝝎𝝎𝒑
3)
Put equal: 3) in equal: 2)
𝑇 = 𝑀𝑔 = 𝐼 𝜔𝜔𝑝
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APPARATUS
Gyroscope
FIGURE 6.1: GYROSCOPE
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APPARATUS DESCRIPTION:
It consists of two major parts.
1. Control panel
2. Working Panel
CONTROL PANEL:
CONTROL PANEL CONSISTS OF
power on / off buttons. It shows rotational speed (⍵) as well as precession speed of gyro (⍵p).
FIGURE 6.2: CONTROL PANEL
WORKING PANEL:
Working panel consists of
● Spinning body
● Sliding bar
● Slider mass
● Stopping limits
● Centrifugal mass
/Gyro
● Precession mass
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FIGURE 6.3: WORKING PARTS
EXPERIMENTAL PROCEDURE:
•
Put the safety cover on the apparatus and turn it on.
● Now observe whether the rod is in a horizontal plane or not.
● Depending upon the siltation of the rod increase or decrease the speed of spinning
mass so that the rod is in a horizontal plane.
● Now increase the rotational speed of the rod, this again makes the rod unbalance.
● Adjust again the speed on the spinning wheel i.e., precision to make the rod
balanced once again.
● Repeat the process several times for different values.
● Now calculate the gyro moment and torque and compare the result.
OBSERVATION AND CALCULATION:
Mass of spinning mass =m=0.0656kg
Moment of inertia of gyro =Ig=0.0000375
⍵=rev/min
⍵= (2* 3,14/60) *(2*3,14/60) ⍵. ⍵p rad/sec
M⍵=mgr. (Nm.)
M⍵=0.0656*9.81*r
Mk=I. (2* 3,14/60) *(2*3,14/60) ⍵. ⍵p
Mk=0.00000041. ⍵. ⍵p (Nm.)
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s.no
r(m)
𝝎 (rad/sec)
𝝎𝒑 (rad/sec)
Mw (Nm.)
Mg (Nm.)
%𝐞𝐫𝐫𝐨𝐫
1.
0.026
351.4
1.09
0.0167
0.0167
14%
2.
0.046
429.3
1.65
0.0265
0.0296
10%
3.
0.059
367
2.634
0.0362
0.0379
4%
RESULTS AND CONCLUSION:
Hence after performing the experiment, we gain sufficient knowledge about gyroscope its working and
different parts functioning.So, by performing this lab we practically learn the laws of gyroscopes.
PRECAUTIONS:
• Do not enter the apparatus territory when it is on.
● Always put the protective shield on the apparatus before starting the apparatus
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LAB REPORT # 07
TITLE
Determine Natural Theoretical Frequency & Time Period Of Free Vibrating Spring &
Compare with Experimental Values
OBJECTIVES
➢ To know about free vibration apparatus.
➢ To calculate natural frequency and time period theoretically and experimentally.
THORETICAL BACKGROUND:
VIBRATION :
To and fro motion of a body about any mean position is called vibration .
Classification Of Vibration :
Free Vibration :
Vibration in which no external force acts on a vibrating body after initial disturbance is called free vibration
TYPES OF FREE VIBRATIONS :
● Longitudinal vibration
● Transverse vibration
● Torsional vibration
FORCED VIBRATION :
When a vibrating body vibrates under the influence of an external force that phenomena is called forced
vibration .
● Resonance phenomena occurred in forced vibrations when system 's natural frequency coincides
with the forcing frequency .
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DAMPED VIBRATION :
Reduction in the amplitude of vibrations over every cycle ,such vibration is called damped vibrations .
MATHEMATICAL MODELLING OF MASS-SPRING SYSTEM
𝑤=𝑘Δ
𝑚𝑔 = 𝑘 Δ
𝑘 − 𝑚𝑔 / Δ Also
Restoring Force equals
to : 𝑤 − 𝑘 ( Δ + 𝑥 )
∑ 𝐹 = 𝑚𝑎
𝑚𝑎 = 𝑚𝑔 − 𝑘 Δ − 𝑘𝑥
As 𝑚𝑔 = 𝑘 Δ
So Above equation becomes
𝑚𝑎 + 𝑘𝑥 = 0
𝑎=𝑘. 𝑥/ 𝑚
So natural frequency of mass spring free vibration system is given by
𝞈𝑛=√𝑘/𝑚
(red/sec)
𝑓𝑛 = 1/2𝜋 . √ 𝑘 / 𝑚
𝑇𝑛 = 2 𝜋 . √ 𝑚 / 𝑘
( cycles /sec )
(sec)
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APPARATUS DESCRIPTION:
Step shaft apparatus is present in the department of Mechanical Engineering, UET Peshawar. Step shaft
consists of three different diameters of shaft 25mm,50mm,75mm respectively. A thread is wrapped around
the shafts and loads are attached to the other end of threads. Stopping screw is used to threads. encounter
unwanted rotations of the shafts
Free Vibration Apparatus :
Free vibration apparatus is present in MOM & Vibration lab M.E.D U.E.T Peshawar .
It consists of the following main components .
● Base :
It is the foundation of the apparatus and all other components are placed on it .
● Guide Columns :
Provide support to the whole structure .
● Carriage :
Rods that move in vertical direction upon the loading and unloading of the masses .
● Guide Rollers :
Moves in vertical direction as spring stretches and compresses on the application of load .
● Damper :
Viscous damper has been placed in the apparatus and air
has been used as a damper .
● Helical Spring :
Helical extension spring is used in this apparatus and used to find time period and frequency of the
systems .
● Mechanical Recorder Drum :
This is used to record amplitude of vibration on a graph paper using graph paper and marker .
FIGURE 7.1: FREE VIBRATION APPARATUS
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EXPERIMENTAL PROCEDURE:
● First of all, find the natural frequency and time period theoretically .
● For this measure the initial length of the spring and attach masses that will produce elongation in the
spring .
● Measure the final length of the spring after elongation and find stiffness using
●
●
●
●
●
𝑘 = 𝑚𝑔 /Δ .
Find natural frequency and time period theoretically .
Now give some initial disturbance to the spring and it will vibrate freely .
Measure the amplitude with respect to time on graph paper using a mechanical recorder drum .
Now using equation 𝑠 = 𝑣𝑡 . λ = 𝑣. 𝑡
Where t is time period and from time period calculate frequency using 𝑓 = 1 / 𝑇 .
OBSERVATION AND CALCULATION:
Initial Length =0.0215m
Final Length after load applied =0.0235m
Mass added =3.5kg
𝑘 = 𝑚𝑔 /Δ
𝑘 = 3. 5 * 9. 8 /0. 0235 − 0. 0215
K=1716.15 𝑁 / 𝑚 Natural
Frequency :
𝑓𝑛 = 1/2𝜋 . √ 𝑘 / 𝑚
𝑓𝑛 = 1/2 * 3. 14 . √1716. 15/3. 5
𝑓𝑛 = 3. 5 𝐻𝑧
Time Period :
𝑇𝑛 = 2𝜋 . √ 𝑚 / 𝑘
𝑇𝑛 = 2 * 3. 14. √3. 5/1716. 15
𝑇𝑛 = 0. 28 𝑠𝑒𝑐
RESULTS AND CONCLUSION:
So from doing this lab we learn to measure frequency and time period of the mass spring system using free
vibration apparatus and compare experimentally and theoretical value .
PRECAUTIONS:
● Do not add force on the system after initial disturbance so that we get accurate readings .
● Make the system undamped by removing the damper otherwise we will get the calculations about
damped free vibrations .
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LAB REPORT # 08
TITLE
Analysis Of Forced Vibration Using Forced vibration Apparatus
OBJECTIVES
● To estimate the natural frequency of a vibrating beam .
● To verify resonance conditions .
THORETICAL BACKGROUND:
FORCED VIBRATION :
When external force acts on the vibrating object, vibration of that object is said to be forced vibrations .
RESONANCE PHENOMENA :
In forced vibration when frequency of external applied force becomes equal to the natural frequency of the
vibrating body then phenomena of resonance occur .
Amplitude of the vibrating body at this moment will be maximum .
That is
𝐹 ( 𝑛𝑎𝑡𝑢𝑟𝑎𝑙 ) = 𝐹 ( 𝑒𝑥𝑡𝑒𝑟𝑛𝑎𝑙 𝑓𝑜𝑟𝑐𝑒 )
MATHEMATICAL MODELLING
Consider a system shown in the following figure
As arc is subtended by angle 𝛉 is given by 𝑥 = 𝑎 𝛉 .
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∑ 𝑀𝑜 = 0 ………(1)
𝐼 𝝰 + 𝐹𝑠 ( 𝑎 ) = 0
𝐼 𝝰 + 𝑘𝑥 ( 𝑎 ) = 0
𝑥=𝑎𝛉
2
So
𝐼 𝝰 + 𝐾𝑎 𝛉 = 0
2
𝝰 + 𝐾 𝑎 𝛉/ 𝐼 = 0
As
2
𝑘𝑎 /𝐼
⍵=
So
3
As moment of inertia for cantilever beam is given by 𝐼 = 𝑚 𝑙 /3
𝐹
= 1/2𝞹
3𝑘 𝑎 / 𝑚 𝑙 ……..(2)
l=length of the beam .
Now for forced Vibration :
2
𝐼 𝝰 + 𝑘 𝑎 𝛉 = 𝑘𝑥𝑎
𝑥 = 𝑟𝑠𝑖𝑛 ⍵ 𝑡 𝑓 2
𝐼 𝝰 + 𝑘 𝑎 𝛉 = 𝑘𝑎𝑟𝑠𝑖𝑛 ⍵ 𝑡 𝑓 2
𝝰 + 𝑘 𝑎 𝛉/ 𝐼 = 𝑘𝑎𝑟𝑠𝑖𝑛 ⍵ 𝑡 / 𝐼 𝑓 2
Let 𝑘 𝑎 / 𝐼 = 𝑏
𝑎𝑛𝑑
𝑘𝑎𝑟 / 𝐼 = 𝐴
So then above equation becomes 𝛉 = 𝐴𝑠𝑖𝑛 𝑤 𝑡 / 𝑏 − ⍵
For Resonance :
𝛉
= 𝐴/ 𝑏 − ⍵
Here 𝑏 − ⍵ = 0
So
⍵=
2
𝑘𝑎/ 𝐼
APPARATUS DESCRIPTION
Forced Vibration Apparatus :
Control Panel :
Control panel includes speed dials that are used to give speed to the oscillator .
Cantilever Beam :
Cantilever beam is used to calculate frequencies of force applied .
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Damper :
Viscous damper is used to induce the phenomena of damping .
Mechanical Recorder Drum :
This is used to record amplitude of vibration on a graph paper using graph paper and marker .
Helical Spring :
Helical extension spring is used in this appartusand used to find time period and frequency of the forced
vibrations .
Guide Columns :
Provide support to the whole structure .
FIGURE 8.1: FORCED VIBRATION APPARATUS
EXPERIMENTAL PROCEDURE:
● First of all we will find out the natural frequency of the forced vibration apparatus .
● After that we increase frequency and force acting on the spring .
● At first amplitude was low and increased with frequency increment .
● But at some interval the amplitude of vibration decreased .
● With increase in force amplitude this is because as spring moves upward impact of force is given
which does not show its effect perfectly .
● Record the vibrations on the graph paper using a mechanical recorder drum .
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OBSERVATION AND CALCULATION:
Mass of the beam ,m=1.68kg
Length of the beam ,L=0.730m
Speed of mechanical recorder drum ,V=0.02m/sec
Wavelength ,𝝀=0.06m
𝐴𝑠 𝐾 = 𝑚𝑔 /ẟ
Here ẟ = 8. 3 − 7. 3 = 1 𝑐𝑚 = 0. 01 𝑚 Mass that bring
this deflection ,M=1kg
2
K=1*9.81/0.01=981N/ 𝑚
Distance of spring from pivot point ,a=0.55m
𝐹
= 1 /2𝞹
𝑛𝑎𝑡𝑢𝑟𝑎𝑙
𝐹
𝑛𝑎𝑡𝑢𝑟𝑎𝑙
2
3
* 0. 55 / 1. 68 * 0. 730
= 1/2𝞹 3 * 981
𝐹
2
3
3 𝑘𝑎 /𝑚𝑙
= 5 . 87 𝐻𝑧
𝑛𝑎𝑡𝑢𝑟𝑎𝑙
Experimental Frequency is given by 𝑉 = 𝝀. 𝑡…….(3) 𝑡 = 0.
06/0. 02
𝑡 = 3 𝐻𝑧
𝐹
=1/𝑡
𝑒𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡𝑎𝑙
𝐹
= 1/3
𝑒𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡𝑎𝑙
𝐹
= 0. 33 𝐻𝑧
𝑒𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡𝑎𝑙
RESULTS AND CONCLUSION:
So from the results we concluded that experimental frequency is less than theoretical value . As we are not
considering the damping effect but air friction acting as a damper so its amplitude decreases .
PRECAUTIONS:
•
Do not enter the apparatus territory when it is on.
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LAB REPORT # 09
TITLE
Verification of relation between angular and linear displacement.
OBJECTIVES
➢ To know about step shaft apparatus.
➢ To verify the relation between linear and angular displacement. 𝑆 = 𝑟 𝚯
THORETICAL BACKGROUND:
Displacement:
position of a body due to external actions both rotational or translational applied to it.
● Linear Displacement
● Angular displacement Explanation:
When somebody is rotating, they also cover some linear displacement. We observe this in our daily life so
there is an association between angular and linear displacement according to mathematical equations.
𝑉 = 𝑟𝑤
𝑉 = 𝑟. 𝚯/ 𝑡
𝑣. 𝑡 = 𝑟. 𝚯
As 𝑆 = 𝑣. 𝑡
𝑠 = 𝑟. 𝚯
Where 𝚯 must be in radian.
For 1 rev:
𝚯 = 2. 𝝅
For N revolutions
𝚯 𝑛 = 2. 𝝅. 𝑁
So, distance covered in N revolutions
𝑆𝑛 = 𝑟. 𝚯 𝑛
𝑆𝑛 = 𝑟. 2. 𝝅. 𝑁
Distance covered in 1 revolution
𝑆𝑛 / 𝑁 = 2𝝅 𝑟
𝑆𝑛 / 𝑁 = 𝝅 𝑑
𝑆𝑛 / 𝑁𝑑 = 𝝅
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APPARATUS
Step pulley/shaft apparatus
FIGURE 9.1: STEP SHAFT APPARATUS
APPARATUS DESCRIPTION:
Step shaft apparatus is present in the department of Mechanical Engineering, UET Peshawar. Step shaft
consists of three different diameters of shaft 25mm,50mm,75mm respectively. A thread is wrapped around
the shafts and loads are attached to the other end of threads. Stopping screw is used to threads. encounter
unwanted rotations of the shafts
FIGURE 9.2: STEP SHAFT APPARATUS
UNIVERSITY OF ENGINEERING AND TECHNOLOGY, PESHAWAR
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ME-301L MOM AND VIBRATION LAB REPORTS
AZLAL JAMIL -4843
EXPERIMENTAL PROCEDURE:
● First of all, wrap all the thread around the shafts to a maximum extent and then balance the three
hanging loads and then measure the height of the loads from the ground.
● Then rotate the shaft for 1 complete revolution and then measure the heights from the ground for all
three masses.
● Then give the shaft a 2nd revolution and then again measure the heights from the grounds for all three
masses.
● Repeat the experiment to get different values.
OBSERVATION AND CALCULATION:
Shaft 1 Diameter =2.5cm
Shaft 2 Diameter =5cm,
Shaft 3 Diameter=7.5cm
No. of turns
Shaft 1
Shaft 2
Shaft 3
Height
from
ground
(cm)
Distance
Moved
Height
from
ground
(cm)
Distance
Moved
Height
from
ground
(cm)
Distance
Moved
0
81
-
81
-
81
-
1
72.9
8.1
65.2
15.8
57.1
23.9
2
64.5
16.5
48
33
32.5
48.5
SHAFT 1:
No of turn 1: S=81-72.9=8.1
𝑆𝑛 / 𝑁𝑑 = 𝝅
8. 1/1 * 2. 5 = 3. 24
No of turn 2: S=81-64.5=16.5
𝑆𝑛 / 𝑁𝑑 = 𝝅
16. 5/2 * 2. 5 = 3. 3
UNIVERSITY OF ENGINEERING AND TECHNOLOGY, PESHAWAR
45 | PAGE
ME-301L MOM AND VIBRATION LAB REPORTS
AZLAL JAMIL -4843
SHAFT 2:
No of turn 1: S=81-65.2=15.8
𝑆𝑛 / 𝑁𝑑 = 𝝅
15. 8/1 * 5 = 3. 16
No of turn 2: S=81-48=33
𝑆𝑛 / 𝑁𝑑 = 𝝅
33/2 * 5 = 3. 3
SHAFT 3:
No of turn 1: S=81-57.1=23.9
𝑆𝑛 / 𝑁𝑑 = 𝝅
23. 9/1 * 7. 5 = 3. 18
No of turn 2: S=81-32.5=48.5
𝑆𝑛 / 𝑁𝑑 = 𝝅
48. 5/2 * 7. 5 = 3. 23
RESULTS AND CONCLUSION:
So, from our calculations we found that our calculations were approximately equal to pi that 3.14 so by doing
this lab we practically proved the relation between angular and linear displacement.
PRECAUTIONS:
•
Do not enter the apparatus territory when it is on.
UNIVERSITY OF ENGINEERING AND TECHNOLOGY, PESHAWAR
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