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10. FLYWHEELS

A flywheel is an energy-storage device which acts as asmoothing element in a dynamical power transmission circuit.

A flywheel is a power filtering device, which stores excessenergy and delivers the excess energy when required.

10.1. FLYWHEEL SIZE

Fig 1 shows a flat circular disk type flywheel attached to a motor

shaft.

)1(2

1 2IE

1

Energy is stored in a flywheelby speeding it up or energy isdelivered by a flywheel byslowing it down.

The kinetic energy of aflywheel which rotates at rad/s is

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Energy stored is linearly dependent on the flywheel massmoment of inertiaI, and quadratically dependent on angularvelocity .

Flywheel must change its velocity in-order to store or deliverenergy.

Hence, the relation between the energy change and the velocitychange is:

where the subscript 1 and 2 designate the minimum and maximum

conditions, respectively.

The average speed of the flywheel, designated byav

, is

Defining the coefficient of speed fluctuation as

)2(22

1

2

212 I

EEE

)3(2

12 av

)4(12

av

sC

2

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The energy change is now written as

Substituting for 2-

1in terms of av, the energy change is givento be

In many practical applications, the required torque is time-dependent with a peak-torque requirement only for a very short

duration. Eg. Punch presses, molding machines, etc. in such applications, it is a waste to provide motors that deliver the

peak-torque requirement. better to use motors of smaller capacity by using flywheels

alongside.

)5(2

2

12

1212

2

1

2

212

avI

I

IEEE

)6(2

12 avsICEE

3

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10.2. ENERGY OUTPUT TORQUE

An engine shaft output torque variation, in four stroke engines,for 720o of the crank angle is shown in fig 2 below.

The resisting torque which the engine is driving is representedby Tavwhere Tav = TL, TL being the load torque.

The shaded area under the T-curve represents the work whicheither increases or decreases the kinetic energy of the systemby causing decrease or increase in the crank shaft speed.

4

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The increase or decrease of the speed depends upon the inertiaof the system which is mainly due to mass of the flywheel.

Control of the crankshaft speed is obtained from the flywheel.

For a flywheel mounted on the drive shaft or crankshaft asshown in fig 2, from Newtons law of motion

where I is the moment of inertia of the flywheel, and

T-TL is the excess torque available in case ofT>TL, or torque to be supplied by the

flywheel in case T < TL. Noting that

)8(

,

)7(

ITT

or

IT

L

)9( dd

5

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Equation (8) can be written as

Integrating between certain limits 1 and2 , we obtain

The term represents the shaded area under the T-curve which is normally evaluated graphically.

Positive area of the torque versus crank angle diagramrepresent regions in the engine cycle where work is done toincrease flywheel speed, and negative areas represent theenergy taken away from the flywheel thereby decreasing thespeed of the flywheel.

)11(

)10(

dIdTT

ord

dITT

L

L

)12(2

2

1

2

2

2

1

IdTT L

dTT L 2

1

6

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The locations of the maximum and minimum speeds, 2and1respectively, can be determined by inspection from the torquediagram.

That is between the end of the first loop and the beginning ofseventh loop.

Between which positions the value of (T-TL) is maximum.

From the T-diagram we have

where A is the area under the T- curve between 1 and2.

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,

)13(2

2

2

1

2

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avs ICA

or

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Representing the crankshaft speed in rpm,

for a given average speed of the flywheel in rpm, the inertia ofthe flywheel is determined from

Flywheels are usually of two types: disc and rim type.

For the disc type flywheel,

where W = mg, and d = 2r.

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160

4

2

2

22

nIC

nICA

s

s

)16(91

2nC

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s

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1 22Wd

gmrI

8

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For the rim type flywheel,

where, k is the radius of gyration of the rim.

Usually, kcan be taken as the mean radius of the flywheel rim,in which case

)18(2

mkI

)19(4

222

g

WdmrmkI mm

9