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DHAANISH

AHMED

COLLEGE OF ENGINEERINGAn ISO 9001-2008 Certified Institution

(Approved by AICTE, New Delhi & Affiliated to Anna University, Chennai)

Department of Mechanical Engineering

ME2307- DYNAMICS LAB MANUAL

PREPARED BY

Mr.P.PRINCE PACKIARAJ M.Tech,(PhD).Assistant Professor

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TABLETABLE OFOF CCOONTNTEENNTTSS

Sl.No Date of Experiment

Name of the Exper

iment

NoM

arks S

taff

Initial

Remarks

1

2

3

4

5

6

7

Determination of speed andsensitivity for watt governor

Determination of speed andsensitivity for proell governor

Determination of speed andsensitivity for porter governor

Determination of speed andsensitivity for hardnell governor

Determination of moment ofinertia by oscillation method

Cam study model

Determination of whirling speedof shaft

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8

9

10

11

12

13

Balancing of rotating mass

Verification of gyroscopicrelation

Study on balancing ofreciprocating mass

Determination of natural

frequency in vibrating table

Multi degree of freedomsuspension

Determination of naturalfrequency of transverse

vibration

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DATE:

EXP NO:Aim:

DEDETTERMERMIINATIONNATION OOFF SPESPEEEDD AANDND SSEENSNSIITIVITYTIVITY FFOROR

WAWATTTTGOGOVVEERRNNOORR

To determine the speed and sensitivity of the Watt Governor.

Apparatus Required:

1.Watt governor set up.2.tachometer3.dimmer

Formula:

1. Speed, N = (895/h) rpm h-sleeve lift

2. Sensitivity= N/N2-N1 N2-Maximum speed N1-Minimum speed

N-Mean speed

Procedure:

1. The watt governor assembly is mounted over the spindle.2. The motor is started and speed is adjusted. Speed is measured with the help of

tachometer.3. Due to this centrifugal force the sleeve will be rise, the speed and the sleeve height arenoted.4. By using the formula the speed of the governor is calculated.5. The experiment is repeated at different speed and force.

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Tabu lation:

Sl.no Motor speed (rpm) Sleeve lift (h)

(mm)

Governor speed (N)

(rpm)

Calculatio n :

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Result:

At different motor speed the sleeve lift are noted and corresponding governor speed andsensitivity are calculated.

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Date:

Exp No:Aim:


PPRROOELLELL GOGOVVEERRNNOORR

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To determine the speed and sensitivity of the proell Governor.

Apparatus Required:

1.Proell governor.2.Tachometer.

3.Dimmer.

Formula:

N = FM/BM x (m+M/m) x 895/h.

Where,

FM/BM-proell link ratio =0.57. M-mass of the sleeve assembly=2.25kg

m-mass of the ball = 0.092 kg. h-sleeve lift

Sensitivity=N/N2-N1 N2-Maximum speed N1-Minimum speed

N-Mean speed

Procedure:

1. The proell governor assembly is mounted over the spindle.2. The motor is started and speed is adjusted. Speed is measured with the help of

tachometer.3. Due to this centrifugal force the sleeve will be rise, the speed and the sleeve height are

noted.4. By using the formula the speed of the governor is calculated.5. The experiment is repeated at different speed and force.

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Tabu lation:

Sl.NO MOTORSPEED (rpm)

SLEEVE LIFT(h)

(mm)

GOVERNORSPEED( N)

rpm

Calculatio n :

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Result:


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Date:

Exp No:Aim:


PPOORRTETERRGOGOVVEERRNNOORR

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To determine the speed and sensitivity of the porter governor.

Apparatus required:

1. Porter governor.2. Tachometer.3. Dimmer.

Formula:

1. Governor speed n = (m+M/m) * (895/h) rpm.

M-mass of the sleeve assembly =2.25 kg h-sleeve lift

m-mass of the each ball=0.225 kg

2. Sensitivity= N/N2-N1 N-Mean speed N2-Maximum speed

N1-Minimum speed

Procedure:

1. The porter governor assembly is mounted over the spindle.2. The motor is started and speed is adjusted. Speed is measured with the help of


noted.4. By using the formula the speed of the governor is calculated.5. The experiment is repeated at different speed and force.

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Tabu lation:

S.NoMotor Speed (rpm)

Sleeve Lift (h)

(mm)

Governor speed (N)

(rpm)

Calculatio n :

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Result:


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Date:

Exp No:Aim:


HAHARRTTNENELLLL GOVGOVEERRNNOORR

To determine the speed and sensitivity of the Hart Nell governor.

Apparatus Required:

1. Hart Nell governor

2. Tachometer.3. Dimmer.Formula:

1. Governor speed n = (m+M/m) * (895/h) rpm.

M-mass of the sleeve assembly =2.25 kg h-sleeve lift

m-mass of the each ball=0.225 kg

2. Sensitivity= N/N2-N1 N-Mean speed N2-Maximum speedN1-Minimum speed

Procedure:

1. The porter governor assembly is mounted over the spindle.2. The motor is started and speed is adjusted. Speed is measured with the help of


noted.4. By using the formula the speed of the governor is calculated.

5. The experiment is repeated at different speed and force.

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Tabu lation:

Sl.No Motor Speed(rpm)

Sleeve Lift (h)

(mm)

Governor speed (N)

(rpm)

Calculatio n :

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Result:


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Date:

Exp No:Aim:

DEDETTERMERMIINATIONNATION OOFF MOMENTMOMENT OFOF INEINERRTIATIA

BYBY OOSSCCIILLAATTIIOONN

To determine the moment of inertia by oscillation method.

Apparatus Required:

1. Fly wheel 3. Main Frame

2. Chucks 4. Connecting rod.

Formula Used:

1. Polar moment of inertia (J) = /32xd4 m4

d-dia of the connecting rod ends

2. Torsional Rigidity (q) =GJ/l N-M

G-Modulus of rigidity of material=0.79x1011

l-Length of the connecting rod

3. Moment of Inertia (I) =4q/ 2f2 =4qt2p/ 2 kg-m2

Procedure:

1. The connecting rod for which the moment of inertia is to be found is fixed the innerdiameter of the rod is measured by various points.

2. The mean diameter is taken as the diameter of the rod.3. The rod is fixed at both at the top of the chuck and the flywheel and the length

between two points is measured then a small twist is given to the flywheel and isreleased.

4. The time taken for the 5 oscillation is noted in the tabular column.5. The same experiment is repeated for various lengths and at different diameter the

experiment is done by adding the weight of flywheel and the reading are noteddown.

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Tabu lation:

Sl.no Endposition

N T

(sec)

tp =t/n

Length ofrod

(mm)

Diameter ofrod

(mm)

Moment ofinertia

Kg-m2

Calculatio n :

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Result:

Thus the moment of inertia of the given rod is calculated and tabulated.

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Date:

Exp No:

AI

M:

CAMCAM SSTUTUDYDY MMOODDEELL

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To draw the displacement diagram for various cam profile and various followers.

APP A RA T US REQUIRED:

1) Experimental setup 2) Flat, Roller, Knife edge follower 3) Cams

P R O C EDUR E:

1.Taka a paper of size 40cm x 15cm, use scale for x-axis as 1cm = 10 of rotation of cam.2.Take height of lift as10cm.3. Plot displacement diagram for given cam profile.4.Fit graph paper on drum. set 0 as a starting point to lift.5.Give gradual rotation to complot displacement diagram on graph.6.Compare solution obtained by graphical. Do this for other cam profile and follower.

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Tabu lation:

Roller follower Mushroom follower Knife edge follower

Degree Displacement Degree Displacement Degree Displacement

Calculatio n :

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R ESULT:

Thus the displacement diagrams are drawn for the given follower and various cams.

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Date:

Exp No:

DEDETTERMERMIINATIONNATION OOFF WHIRLINGWHIRLING SPESPEEEDD

OFOF TTHHEESSHHAAFTFT

Aim:

To determine the whirling speed of a shaft at various supporting condition.

Apparatus required:

1. Whirling shaft apparatus 2. Various support and bearings.

3. Tachometer 4. Vernier caliper 5. Steel rule

Formula Used:

1. Deflection =h2-h1 cm

h1-minimum deflection, h2-maximum deflection

2. Whirling speed=1/2 g/ rpm

g-gravity 9.81

Procedure:

1. First fixing the arrangement, are selected.

2. The shafts are fixed firmly on the suitable bearing and tighten it.

3. Then the motor is switched on and speed of the motor is increased.

4. The modes of shaft vibration are noted. By using the formula the frequency at variousvibrations calculated.

5. Same procedure repeated using various diameter (4,6 and 8mm) of shaft.

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Tabu lation:

Sl.No Diameter of shaft

(mm)

Lengthof shaft

(cm)

Speed(N)

rpm

Weight of the shaft per unitlength (w) Whirling speed(rpm)

h1

(cm)

h2

(cm)

(cm)

Calcultion:

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Result:

Thus the whirling speed of the various shaft at various end condition are calculated.

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BALANCING OF ROTATING MASSDate:

Exp No

Aim:

To verify the balancing using the rotating machine element.

Apparatus required:

1. Balancing rotary system 2. Masses.

Procedure:

1.To order of the basic operation involved with respect to static balancing as following2.Then the mass should be fixed in one side of the stud and its angle to be adjusted with the

help of angular scale and its radil can be corrected with the help of vernier caliper.3.Angular displacement between the masses Is calculated by force diagram through known

value of mass and radil.4.Fix the masses to the calculated angular displacement using angular scale.5.Now switch on the motor.6.By changing the sped of the motor, check it out for vibration for running7.Add by changing the mass with different radil and find out the angular displacement among

the mass for balancing the system

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Tabu lation:

Sl.No Plane A B C D

Mass

Radius

Calculatio n :

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Result:

Thus the Balancing Of Rotating Machine Was Verified.

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Date:

Exp No:

VERIFIVERIFI CACATIONTION OFOF GYROSCOPICGYROSCOPIC RREELLAATTIIOONN

Aim:

To analysis the gyroscopic effect using the test setup and verify the gyroscopic rules ofplane disc.

Apparatus Required:

1. Gyroscopic setup. 2. Weight 3. Tachometer

Technical Data:

1.Rotor diameter (d) = 30 cm.2.Rotor thickness (t) = 8cm.3.Distance of weight pan bolt centre to disc center (l) = 260 mm.4.Weight of the rotor = 7kg.

Formula Used:

1. Precision ratio (wp) = 2 n/60 rad/ sec.2. Angular velocity (w)=d/dt X /180 rad/secd-change in degree dt-time taken in sec

3. Gyroscopic effect (c) = I..P4. Torque, t = wxr

Where,

w = weight of the rotor.

r = distance between weight pan centre to disc centre.5. I = mr2/2 Kg-m2. m-mass of the rotor kg

6. Percentage of error = (T-C)/T X 100.

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Procedure:

1.Switch on the supply.2.Set the require speed of the regulator as constant.3.Add the load as kg, 1kg etc.4.Angle of precision d i.e. Measured.5.Loose the lock screw, start the stop watch and note down.

6.Watch the particular interval and time.7.Take the reading n different load.8.Repeat the equipment maintaining load as constant and varying the speed.9.Do the calculation.

Tabu lation:

Speed Of Disc (rpm) Added weight

(gm)

d

(degree)

dt

(sec)

Angular velocity

rad/sec ()

Applied couple ontachometer (Tact)

Precision ratio

(p) rad/sec

Gyroscopic Effect c

N-m

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Calculatio n :

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Result:

Thus the Gyroscopic relation was verified.

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STUSTUDDYY ONON BBAALALANNCINGCING OFOF RECIRECI PPROCATROCAT IINGNG MASSMASS

Date:

Exp No:

Aim:

To study the behavior of vibration due to the unbalanced mass in reciprocating parts.

Apparatus required:

Balancing of reciprocating mass system masses.

Procedure:

1.Initially all weights and bolts are removed then the motor is started. The speed of the motor isincreased due to the unbalanced masses, the vibration will be created. The vibration Isobserved.

2.The speed is noted down. Now the speed is increased and the vibrations are all so noteddown. The motor is switched off then some weights added on the piston top. The weights

may be added on the piston top. The weights may be added either eccentrically (or) co-axially. Now the motor is started the vibrations are observed at the tested speed noted in theprevious case. If still the vibration are observed. One of the following has to be done toeliminate the unbalance forces

3.Some weights are added in opposites direction of crank and the engine run and the vibration,are observed at the tested speed.

4.Combination of both the above cases. The speeds, the weight added on piston, diameter atwhich the weights are added are noted down at different case.

Result:

The vibrations due the unbalanced forces in the reciprocating masses are studied.

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Date:Exp No:

Aim:

DEDETTERMERMIINATIONNATION OOFFNANATTUURRALAL FFRREQUEEQUENNCYCY

USUSIINNGGVVIIBRBRAATINGTING TATABBLELE

To find natural frequency of free vibration and forced vibration using vibration table.

Apparatus Required:

1) Spring 2) mass 3) damper 4) stopwatch 5) steel rule.

Formula Used:

Natural Frequency fn=N/T Hz

N-No of oscillation T=Time period of 5 oscillations in sec

Procedure:

Free Vibration:1) Remove the damper from the experimental setup.2) Then strike the beam by taken 5 oscillation time required.

3) Repeat the procedure for different length of beam to adjust the beamForced Vibration: set up.1) Fit the spring, mass damper in proper position note down the spring stiffness, mass ofthe beam, length of the beam from one tunion point and measure the exciter mass.

2) The electrical motor is switched ON, using stop watch note down 5 oscillation time

for small jerk.3) Then repeat the procedure for different length of beam.

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Tabu lation:

Free vibration:

Sl.No Vibration

Exciterposition

No ofoscillation

Time required tocomplete one set ofoscillation

(sec)

Timeperiod

T

Frequency

(Hz)

Forced Vibration:

S.No Vibration Exciter position

No ofoscillation

Time

period(T)(sec)

Frequency (Hz) Speed(rpm)

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Calculatio n :

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Result:

Thus the natural frequency of free and forced vibration using vibrating tale was found.

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Exp No:

MULTIMULTI DEDEGREEGREE OFOF FREFREEEDOMDOM SUSSUSPPEENNSSOONN

Aim:

To find out the mass moment of inertia of any irregular section.

Apparatus required:

1) Bifilar and trifler setup 2) stopwatch

3) Different weight of cycle 4) steel rule

Formula Used:

Bi f ille r :

1) Natural Frequency fn=N/T Hz

2) Radius of Gyration k=1/2 fnxg.ab/l

3) Moment of Inertia I=mk2 kg-m2

Where,

N-No of oscillation ab-Distance between two nodes

Fn-Natural Frequency in Hz l-length of the thread

T-Time taken for 5 oscillations in sec k-Radius of gyration

M-mass of the bifiller plate

Tri f il ler:

1) Radius of gyration k=1/2 fnxg.r2/l

2) Moment of inertia I=mk2 kg-m2

Where,

r-Radius of the Trifiller m-mass of the trifiller g-Gravity (9.81)

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Procedure:

1) Select either of bifilar (or) trifler plates.

2) With the help of spring chucks lighter at tops.

3) Adjust the length of spring to descry the value (or) measure length on it.4) Give small horizontal twist at the same time start the stop watch and note down timerequired for five (or) ten oscillation.

5) Repeat the experiment by adding weight and checking length.

Tabu lation:

S.NO Types of Suspensio

n

Selfweight

(kg)

No. ofoscilla

tion

TimeTaken

sec

weightadded

(gm)

Radiusof

gyration

K(m)

Naturalfrequency

(fn)

Hz

Momentof Inertia

I

(Kg-m2)

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Calculatio n :

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Result:

Thus the MI of irregular section find out.

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DEDETTERMERMIINATIONNATION OOFFNANATTUURRALAL FFRREQUEEQUENNCYCY OOFF TRTRAANSNSVVEREERE VVIIBBRRAATTIIOONN

Date:

Exp No:

Aim:

To determine the natural frequency of free transverse vibration due to uniformly distrusted loadand concentrated load over a simply supported shaft.

Apparatus Required:

1. Shaft 2. Stop watch 3. Weight 4. Transverse vibration system.

Formula Used:

Si m ply sup p orted Bea m :

1. Uniform Distributed Load Frequency (fn) =0.571/2. Point load Frequency (fn) =0.4985/3. Varying load Frequency (fn) =0.4985/

Cantile v er B ea m :

1. Cantilever Beam Frequency (fn) = (1/2) xg/

g-Gravity -Deflection.

Procedure:

1. First proper lubrication is done for the bearing.2. The given beam is fitted into the slots of Turn ion bearings and they are tightened.3. The weight is added according to the condition of loading whether is to be loaded

uniformly or concentrated.Then the beam is given a swing and starts oscillating.

4. The time taken for five oscillations noted down.5. The experiment is repeated for various types of loads and the types of beams.

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Tabu lation:

BEAM

FREQUENCY(fn) Hz

UDL POINT LOAD

VARIYINGLOAD U

DL

POINTLOAD

VARIYING

LOAD

DEFLECTION

(cm)

TIME

(sec)

DEFLECTION

(cm)

TIM E

(sec)

DEFLECTION

(cm)

TIME

(sec)

Observa tio n:

1) Mass of the each weight (m)=158 gm

2) Length of the cantilever beam=235mm

Calculatio n :

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