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Engineering Dynamics (ME-123L) Lab Manual

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Department of Mechanical Engineering

Quaid-e-Azam College of Engineering & Technology Sahiwal

ME 123L EGINEERING DYNAMICS LAB MANUAL

Exp. Date Name of the Experiment Page No.

Signature of

No. the Staff

1 FLYWHEEL AND AXLE SYSTEM

2

GYROSCOPE – TO MEASURE GYROSCOPE COUPLE

3

DETERMINATION OF SPEED AND SENSITIVITY OF WATT GOVERNOR

4

DETERMINATION OF SPEED AND SENSITIVITY OF PORTER GOVERNOR

5 DETERMINATION OF SPEED AND SENSITIVITY OF PORELL GOVERNOR

DETERMINATION OF SPEED AND 6 SENSITIVITY OF HARTNELL GOVERNOR

7 a.

CAM PROFILE DRAWING, MOTION CURVES

7 b. CAM JUMP PHENOMENON

8

SINGLE DEGREE OF FREEDOM – SPRING MASS SYSTEM

EXPERIMENTAL PROCEDURE

1. Determine period of oscillation without object, t 1
2. I 1 = (t 1 / 2π)

2 X m 1 X g X L 1 , kg.m

2

3. Fix object whose CG consider with CG of beam
4. Determine period of oscillation t 2
5. Calculate I 2 = {(t 1 / 2π)

2 X (m 1 + m2) g X L 1 } - I 1 kg.m

2

TABULATION

Object Masss Time Taken for one oscillation Mass moment of inertia of object about pivot point I 2 Without object With object T 1 in sec T 2 in sec

Model Calculation

Ex. No. 02 VERIFICATION OF GYROSCOPIC RELATION Date:

AIM

To analysis the gyroscopic effect using the test setup and verify the gyroscopic rules of

plane disc.

APPARATUS REQUIRED

1. Gyroscopic setup.
2. Weight
3. Tachometer

FORMULA

1. Precision ratio (ωP) = (dØ/dt) X 1/180 rad/sec dØ- change in degree dt- time taken in sec
2. Angular velocity (ω) = 2π N / 60 rad/ sec.
3. Gyroscopic effect (C) = I.ω.ωP
4. Torque, T = w X r Where w = weight of the rotor.

r = distance between weight pan centre to disc centre.

5. I = mr

2 /2 Kg-m

2

. (^) m - mass of the rotor kg

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

SPECIFICATION

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.

EXPERIMENTAL PROCEDURE

1. Switch on the supply.
2. Set the require speed of the regulator as constant.
3. Add the load as ½ kg, 1kg etc.
4. Angle of precision 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.

Ex. No. 03 DETERMINATION OF SPEED AND SENSITIVITY Date: FOR WATT GOVERNOR

AIM

To determine the speed and sensitivity of the Watt Governor

APPARATUS REQUIRED

1. Watt governor set up.
2. tachometer

FORMULA

1. Height h = h 0 – (x / 2) in m

2. α = cos

   (h / 2) in deg 

3. Speed of Governor, N = √(895/h) rpm
4. Angular velocity, ω = (2πN / 60) in rad/s
5. Force F = (w/g) X ω

2 X r (kg.f)

KEYWORDS AND NOTATION

Length of each unit, L in m Initial height of governor, h 0 in m Initial radius of rotation r 0 in m Radius of rotation, r in m Weight of each ball, w = 0.6 kg h - Sleeve lift in m N2-Maximum speed in rpm N1-Minimum speed in rpm N-Mean speed in rpm

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

TABULATION

Speed of Motor Rpm

Starting Height h 0

Sleeve

Radius Angular Force Height of α in displacement Velocity F in h in m rotation deg x in m ω kg.f r in m

Model Calculation

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.

TABULATION

Speed Starting height h 0 Sleeve

Radius Angular Force Sl. of Height of α in displacement Velocity F in No. Motor h in m rotation deg x in m ω kg.f rpm r in m

Model Calculation

Ex. No. 05 Date:

DETERMINATION OF SPEED AND SENSITIVITY FOR

PORTER GOVERNOR

AIM

To determine the speed and sensitivity of the porter governor.

APPARATUS REQUIRED

1. Porter governor.
2. Tachometer.
3. Weight.

FORMULA

1. 1 Height h = h 0 – (x / 2) in m

2. α = cos

   (h / 2) in deg 

3. Angular velocity, ω = (2πN / 60) in rad/s
4. Speed of Governor, N = √ FM/BM x (m+M/m) x 895/h.
5. Force F = (w/g) X ω

2 X r (kg.f)

KEYWORDS AND NOTATION

Length of each unit, L in m Initial height of governor, h 0 in m Initial radius of rotation r 0 in m Radius of rotation, r in m Weight of each ball, w = 0.6 kg h - Sleeve lift in m N2-Maximum speed in rpm N1-Minimum speed in rpm N-Mean speed in rpm

SPECIFICATION

FM/BM = 0.

M - mass of the sleeve assembly =2.25 kg m - mass of the each ball=0.225 kg

EXPERIMENTAL 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 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.

Ex. No. 06 Date:

DETERMINATION OF SPEED AND SENSITIVITY FOR

HART NELL GOVERNOR

AIM

To determine the speed and sensitivity of the porter governor.

APPARATUS REQUIRED

1. Hartnell governor.
2. Tachometer.
3. Weight.

FORMULA

1. 1. 1 Height h = h 0 – (x / 2) in m

2. α = cos

   (h / 2) in deg 

3. Angular velocity, ω = (2πN / 60) in rad/s
4. Speed of Governor, N = √ FM/BM x (m+M/m) x 895/h.
5. Force F = (w/g) X ω

2 X r (kg.f)

KEYWORDS AND NOTATION

Length of each unit, L in m Initial height of governor, h 0 in m Initial radius of rotation r 0 in m Radius of rotation, r in m Weight of each ball, w = 0.6 kg h - Sleeve lift in m N2-Maximum speed in rpm N1-Minimum speed in rpm N-Mean speed in rpm

SPECIFICATION

M - mass of the sleeve assembly =2.25 kg m - mass of the each ball=0.225 kg

EXPERIMENTAL 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 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.

TABULATION

Speed Starting Height h 0

Sleeve

Radius Angular Force Sl. of Height of α in displacement Velocity F in No. Motor h in m rotation deg x in m ω kg.f rpm r in m

Model Calculation

TABULATION

Angle of Lift x in Displacement Velocity V

Angular Acceleration Sl. No. rotation in a in mm / sec

2

θ Mm^ D in mm^ in mm/sec

Model Calculation

Ex. No. 07 (b) CAM JUMP PHENOMENON Date:

AIM

To determine the speed at which cam jump occur for various spring loading condition.

APPARATUS REQUIRED

1. Experimental setup
2. Spring

FORMULA

Cam jump speed, N = > (60 / 2π) X √ {(1/e) X ({(K X δ)/m} + g)}

KEYWORDS AND NOTATION

∆ is compression length of spring,= c + lift = c + (2 X e) c is initial compression, in mm e is eccentricity of cam, in mm k

is spring stiffness

SPECIFICATION

g = 9.81 N

e = 0.006m

K = (Gd

4 ) / (8D

3 n)

G = 0.8 X 10

5 N/mm

2 , Coil dia (d) = 1.5 mm, D = 26 mm, number of coil n = 18

EXPERIMENTAL PROCEDURE

TABULATION

Sl No. C ∆ = c+(2 x e) Observed speed Calculated speed

Ex. No. 08 Date:

SINGLE DEGREE OF FREEDOM SYSTEM

AIM

To determine the natural frequency of spring mass system, damping factor and

damping coefficient.

APPARATUS REQUIRED

1. Experimental Setup
2. Electronic timer
3. Spring mass

FORMULA

Stiffness of spring, K = Gd

4 / 8D

3 n

Natural frequency ωn = √(K/m)

Damping frequency ωd = 2π / td

Damping factor ξ = √1 – ( ωd / ωn)

2

Influence coefficient c = 2 X ξ X m X ωn

KEYWORDS AND NOTATION

Stiffness of spring, K

Rigidity modulus, G = 0.8 X 105 kg/mm

Coil diameter, d = 20 mm Outer dia = 58 mm

Mean diameter of coil, D = outer diameter – coil d iameter = 38 mm

Number of turns, n

Natural frequency ωn

Mass attached, m in kg

Damping frequency, ωd

Time taken for one oscillation of mass, td

Damping factor, ξ

Damping coefficient, c

EXPERIMENTAL PROCEDURE

1. Keep one spring and mass only
2. Keep proximity switch at equilibrium position of masss
3. Give 50 mm deflection to mass
4. Measure cycle time for vibration, td calculate ωd = 2π / td
5. Calculate K = Gd

4 / 8D

3 n

6. Find natural frequency of spring for mass ‘m’ , ωn = √(K/m)
7. Find damping factor ξ = √1 – ( ωd / ωn)

2

8. Do the above for other spring also.

TABULATION

Sl

Weight Time taken for Damping Natural Damping Damping

Added one oscillation frequen c y Frequency Factor coefficient No. kg T ωd ωn ξ c

Model Calculation