MOMENT OF INTERTIA OF AFLYWHEEL.

EGERTON UNIVERSITY

FACULTY OF ENGINEERING AND TECHNOLOGY

DEPARTMENT OF INDUSTRIAL AND ENERGY ENGINEERIG

COURSE: B.Sc. MANUFACTURING ENGINEERING.

COURSE TITLE: MACHINE ELEMENTS 11.

COURSE CODE: MENT 223.

TASK: MOMENT OF INERTIA OF A FLYWHEEL.

NAME: KIPROTICH GARISON.

REG NO. B13/14411/16.

DATE OF SUBMISSION: …26/07/2018.

SIGN: ………………………

INSTRUCTOR: ENGR.VINCENT ODHIAMBO.

MOMENT OF INTERTIA OF AFLYWHEEL.

MOMENT OF INERTIA OF FLYWHEEL

Objective

The objective of this experiment is to determine the relationship between the angular

acceleration of flywheel and the torque producing the acceleration.

Theory

Considering a falling mass,

Net force=mg-F

Acceleration=a

Hence ma=mg-ma

F=m(g-a)

Provided that a is much greater than g.

F=mg

For the wheel,

Angular displacement ϴ=2𝜋𝑁[ 𝑟𝑒𝑣. ]

Where N=Number of revolutions.

Average velocity=

1

2

(ϴ+ωN)[rads/s]

Time for N revolution=t seconds.

Therefore,

Angular displacement ϴ=

1

2

ωNt

and ωN=at

hence ϴ=

1

2

at2

from which a=

4𝜋𝑁

𝑡2

According to the second law of motion, torque producing acceleration =

MOMENT OF INTERTIA OF AFLYWHEEL.

Fr=C=K.

4𝜋𝑁

𝑡2

From which K=

𝐶𝑡2

4𝜋𝑁

The constant of proportionality K is called the moment of inertia and may be calculated from the

dimensions and mass of the fly wheel.

K=I=ρπ𝑅2

𝑤°

𝑅2

2

Where R= Radius of fly wheel

w= Width of fly wheel

ρ= Density of the fly wheel = 7850kg/m3

PARAMETERS:

Diameter of disc = 250mm

Diameter of shaft =25mm

Width of disc = 50mm

Density of plate= 7850kg/m3

Procedure

1. Take the load hanger and pulling cord and hook the end loop over the peg on the

flywheel shaft.

2. Wind up a definite number of turns, say 8, from the position where the cord loop falls off

the peg.

3. Wind up the pulling cord 8 turns and hold the flywheel with one hand and a stop watch

with the other. The engraved mark should be by the pointer at this stage. Release the

flywheel and start the watch. Count the revolutions with the aid of the mark, using this to

judge when to stop the watches the set number of revolutions is turned. The load hanger

will fall on to the ground.

4. Repeat the above procedure adding loads by increment of 1Ν. Keep on repeating the

experiment until at least six readings have been obtained.

5. Try retiming one or two of the loads to see what the probable accuracy of the

measurement is.

MOMENT OF INTERTIA OF AFLYWHEEL.

DIAGRAM

RESULTS

Table 1

Acceleration of a flywheel

s/no No. of turns

Ν

Weight (mg) Time (t) s 1/t² Effective

couple

(Nm)

1. 10 0.5 51.0 0.00038

-0.1375

2. 10 1.0 32.0 0.00098 -0.0125

3. 10 1.5 25.0 0.00160 0.1125

4. 10 2.0 21.0 0.00227 0.2375

5. 10 2.5 19.0 0.00277

0.3625

6. 10 3.0 17.0 0.00346

0.4875

7. 10 3.5 16.0 0.00391 0.6125

MOMENT OF INTERTIA OF AFLYWHEEL.

GRAPH ANALYSIS

CALCULATION

CALCULATION OF EFFECTIVE COUPLE.

According to the graph, y-intercept = -1.059

1. 0.05 – 1.5286 =-1.4786*0.25=-0.3697

2. 0.55 – 1.5286 =0.9786*0.25=-0.2447

3. 1.55 – 1.5286 =0.0214*0.25=0.00535

4. 2.55 – 1.5286 =1.044*0.25=0.2554

5. 3.55 – 1.5286 =2.0214*0.25=0.5034

6. 4.55 – 1.5286 =3.044*0.25=0.7554

7. 5.55 – 1.8286 =4.0214*0.25=1.0054

Theoretical calculation of inertia of flywheel is given by;

K=I=ρπ𝑅2

𝑤°

𝑅2

2

= 7850 * π * 0.252 *0.030 *0.0252/2

=0.01445

MOMENT OF INTERTIA OF AFLYWHEEL.

Sources of errors

1.Human errors as the experiment was handled by human measurement instead of machines.

2.Miscalculation and inaccurate counting of the number of rotations.

3.High angular velocity of the wheel rotation.

4.Error in recording the time taken for the desired number of complete revolutions.

5.Energy loss by the apparatus to environment due to friction between the flywheel core and the

cord.

Conclusion

From the experiment, the moment of inertia of flywheel had been studied in which the results are

in the dependency of mass and radius of the wheel.

The experimental values of moment of inertia are found to have huge deviations from the

theoretical one.

The huge deviation is due to sources of errors and the decrease in the efficiency ratio of the

machine in the practical process.

We concluded that the error was done by human mistakes and also might be because of energy

loss due to friction. Thus, it is incomparable with the theoretical one because

REFERENCES

1. Egerton university, industrial and energy engineering department laboratory manual.

2. Bevan T. 1985 “Theory of Machines,”3rd Edition; CBS publishers, Delhi, India.

3. Khurmi, R. 2005 “Theory of Machines,” 4th Edition, S. Chard publishers, New Delhi.

4. Ferd Beer and Russ Johnstone (2005) Vector Mechanics For Engineers; Statics, New Jersey,

McGraw-Hill

5. J.L. Meriam, L.G. Kraige (1998), Engineering Mechanics: Static SI Version, New York, John

Wiley & Sons Inc.

6. R.A. Serway, R. J. Beichner (2000), Physics: For Scientists and Engineers with Modern Physics,

Fifth Edition, Philadelphia, Saunders College Publishing

7. Anthony Bedford, Wallace Fowler, Kenneth M, Liechti, Bedford A. (2003),Statics and mechanics

of materials, Upper Saddle River, New Jersey, Prentice Hall.