THEORY OF MACHINES & VIBRATIONS

Flywheel

DHEERAJ SARDANA

❖ Teaching Experience: 8+ Years

❖ Qualification: M.Tech. from NIT Bhopal

❖ Achievements:

▪ Cracked GATE Many Times with Good GATE Score & rank

▪ Written Many Research and Review Papers

❖ Area of Expertise: Strength of Materials, Theory of Machines,

Machine Design, Industrial Engineering & Production.

ABOUT ME

Flywheel

1. A horizontal cross compound steam engine develop 300kW at 90 rpm. The fluctuation of speed is to be keptwithin ± 0.5 % of the mean speed and the coefficient offluctuation of energy as found from the turning momentdiagram is to be 0.1. What will be the coefficient ofspeed and the maximum fluctuation of energy of theflywheel ?

A. 0.01,15 kN-m

B. 0.1,30 kN-m

C. 0.01,20 kN-m

D. 0.1,45 kN-m

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2. A punching machine is required to punch 5 holes perminute of 50 mm diameter in 40 mm thick plate. Theultimate shear strength of plate material is 225 MPaThe punch has a stroke of 100 mm. If coefficient offluctuation of energy is 4 % and mean speed of flywheelis 18 m/sec, what will be the mass of the flywheel ?

A. 1820 kg

B. 1396 kg

C. 1690 kg

D. 1745 kg

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3. If CS is the co-efficient of fluctuation of speed, E isthe kinetic energy at mean speed and ΔE is themaximum fluctuation of energy in a flywheel, then

A.

B.

C.

D.

sE E C =

E1

E

=

E2

E

=

s

E2C

E

=

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4. Coefficient of steadiness for flywheel in terms ofspeed is given as

A.

B.

C.

D.

1 2N N

N

−

1 2

N

N N−

1 2

N

N N+

1 2N N

N

+

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5. Common Data

A punching press makes 25 holes of 20 mm diameter perminute in a 15 mm thick plate. This causes variation in thespeed of flywheel attached to press from 240 to 220 rpm. Thepunching operation takes 2 seconds per hole. The 6 N-m ofwork is required to shear 1 mm2 of the area and frictionallosses account for 15 % of the work supplied for punching:

The power required to operate the punching press, is

A. 2.772 kW

B 2.08 kW

C. 5.424 kW

D. 3.47 kW

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6. Common Data

A punching press makes 25 holes of 20 mm diameter perminute in a 15 mm thick plate. This causes variation in thespeed of flywheel attached to press from 240 to 220 rpm. Thepunching operation takes 2 seconds per hole. The 6 N-m ofwork is required to shear 1 mm2 of the area and frictionallosses account for 15 % of the work supplied for punching:

The mass of flywheel with radius of gyration of 0.5 m, is

A. 59 kg

B. 77 kg

C. 88 kg

D. 69 kg

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7. A double-acting steam engine develops 28 kW ofpower at 105 rpm. The maximum and minimumspeeds do not vary more than 1 % of the mean speedand the excess energy is 30 % of the indicated workper stroke. If the radius of gyration of the flywheel is500 mm, the mass of the flywheel is

A. 248 kg

B. 496 kg

C. 744 kg

D. 992 kg

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8. Common data

A mass of flywheel of a steam engine is 2000 kg andhas got a radius of gyration of 76 cm. The startingtorque engine is 1300 N-m and may be assumedconstant.

What will be the angular acceleration of flywheel ?

A. 1.47 rad/sec2

B. 1.125 rad/sec2

C. 1.75 rad/sec2

D. 0.85 rad/sec2

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9. Common data

A mass of flywheel of a steam engine is 2000 kg and hasgot a radius of gyration of 76 cm. The starting torqueengine is 1300 N-m and may be assumed constant.

What will be the speed and kinetic energy of the flywheelafter 10 second ?

A. 108 rpm, 73.1 kN-m

B. 81 rpm, 54.8 kN-m

C. 135 rpm, 94.1 kN-m

D. 162 rpm, 109.6 kN-m

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10. Punching machine does 600 J of work per squarecm of sheared area when punch 3.8 cm diameterholes in a 3.2 cm thick plate. The punch has a strokeof 10.2 cm and punches 6 holes per minute. Themaximum speed of the flywheel at its radius ofgyration is 27.5 m/s. If its speed at the same radiusdoes not fall below 24.5 m/s, the mass of theflywheel and the power of the motor driving thismachine, respectively are

A. 186 kg, 1.7 kW

B. 310 kg, 2.8 kW

C. 248 kg, 2.3 kW

D. 372 kg, 3.45 kW

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11. A Punching press is driven by a constant torqueelectric motor. The press is provided with aflywheel that rotates at maximum speed of 225rpm. The press punches 720 holes per hour, eachpunching operation takes 2 second and requires 15kN-m of energy. If speed of the same is not to fallbelow 200 rpm, what will be the motor power andflywheel inertia ?

A. 2.7 kW, 138.9 kg-m2

B. 3 kW, 154.4 kg-m2

C. 3.75 kW, 193 kg-m2

D. 2.25 kW, 115.8 kg-m2

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12. A riveting machine of 3 kW takes 1.5 seconds tocomplete one riveting operation and it absorbs 12kN-m of energy. The moving parts including theflywheel are equivalent to 220 kg at 0.5 m radius.What will be the speed of the flywheel immediatelyafter riveting if it is 360 rpm before riveting ?

A. 243 rpm

B. 567 rpm

C. 405 rpm

D. 324 rpm

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13. The table below gives mean pressure during variousstrokes of a 25 cm diameter and 40 cm strokeengine working on four stroke cycle –

Stroke Mean pressure above atmosphere in kg per square cm

Suction 0.05

Compression 2.00

Expansion 7.00

Exhaust 0.15

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14. The resistance is uniform and the maximum andminimum speeds occur at the end and commencementof expansion stroke, respectively. The total fluctuationof speed will not allow to exceed 1.5 percent of meanwhich is 220 rpm. What will be the moment of inertia inkg-m2 on a flywheel ?

A. 1543 kg-m2

B. 1052 kg-m2

C. 1403 kg-m2

D. 1263 kg-m2

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15. A single cylinder double acting steam enginedevelops 150 kW at a mean speed of 80 rpm. Thecoefficient of fluctuation of energy is 0.1 and thefluctuation of speed is ± 2 % of mean speed. Ifflywheel has the mass of 3787 kg and the hub andspokes provide 5 % of the rotational inertia of theflywheel, the radius of gyration of the flywheel is

A. 1 m

B. 2 m

C. 1.5 m

D. 1.25 m

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16. A cast iron flywheel is required to absorb 25000 N-m of energy as speed is increased from 120 rpm to125 rpm. If the flywheel is to be solid disc having adiameter 8 times its thickness and the density ofcast iron is 7200 kg /m3, the diameter of flywheel is

A. 2.2 m

B. 1.65 m

C. 1.4 m

D. 2.75 m

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17. Common DataTurning moment curve for one revolution of a multi-cylinder engineabove and below the line of mean resisting torque are given by – 0.32,+4.06, –2.71, + 3.29, –3.16, + 2.32, – 3.74, + 2.71 and –2.45 cm2.The vertical and horizontal scales are 1 cm = 60000 kg-cm, and 1 cm =24° respectively. The fluctuation of speed is limited to ± 1.5 percent ofmean speed which is 250 rpm. The hoop stress in rim material is limitedto 56 kg/cm2 and density of rim material is 0.0072 kg per cubic cm.

What will be the suitable diameter of rim when effect of boss and armsis neglected ?A. 2.6 mB. 1.6 mC. 3.1 mD. 2.1 m

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18. Common DataTurning moment curve for one revolution of a multi-cylinder engineabove and below the line of mean resisting torque are given by –0.32,+4.06, –2.71, + 3.29, –3.16, + 2.32, – 3.74, + 2.71 and –2.45 cm2.The vertical and horizontal scales are 1 cm = 60000 kg-cm, and 1 cm =24° respectively. The fluctuation of speed is limited to ± 1.5 percent ofmean speed which is 250 rpm. The hoop stress in rim material is limitedto 56 kg/cm2 and density of rim material is 0.0072 kg per cubic cm.

If width of rim equal to four times its thickness, what will be the cross-section of flywheel rim ?A. 133.1 cm2

B. 106.5 cm2

C. 95.8 cm2

D. 79.8 cm2

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19. The mass of the flywheel is concentrated in the rim,because then it will;

A. store much energy

B. store less energy

C. store zero energy

D. make the flywheel stronger

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