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ME 209: Machine Design I

Design of a Flywheel

Asanga RatnaweeraDepartment of Mechanical Engineering

Faculty of Engineering University of Peradeniya

2/14/2006 ACR/ME209/2006

FlywheelA flywheel acts as an energy reservoir, which stores energy during the period when the supply of energy is more than the requirement and releases energy during the period when the requirement is more than the supply.

FLYWHEEL

Manual press Combustion engines Power press

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IC Engines: The basic operationIn internal combustion engines, the energy is developed during the power (expansion) stroke and the engine runs for the whole cycle on the energy supplied during that stroke.

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IC Engines: The basic operationPower is produced only during the power stroke

Intake Compression Power Exhaust

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IC Engines: The basic operationPressure and temperature rapidly increases during the combustion and hence the piston is pushed down. Therefore, there is a significant fluctuation of energy during once engine cycle

IVO - intake valve opens, IVC – intake valve closesEVO – exhaust valve opens, EVC – exhaust valve closes

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IC Engines: Turning Moment

The torque at the crank shaft or the turning moment is largely dependent on;

The in-cylinder gas pressureThe inertia force of the reciprocating parts

As explained above the gas pressure fluctuates over a complete cycleThe acceleration and deceleration of the piston assembly also changes during the motion over a cycleTherefore the Turning Moment also fluctuates over an engine cycle

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IC Engines: Turning MomentThe Fluctuation Turning Moment can be controlled to some extent by increasing number of cylinders (Multi-cylinder engines)

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IC Engines: Turning MomentThere are two common configurations used in multi-cylinder engines

Inline Engine V Engine

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IC Engines: Turning MomentPractically it is not possible to build engines with cylinders beyond a certain number. (depends on the capacity)Therefore, a complete smoothness can not be achieved by only increasing the number of cylindersA flywheel is usually coupled to the crank shaft to limit the fluctuation of turning moment and hence the fluctuation of speed.

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Design of a FlywheelThis design exercise deals with the design of a flywheel to bring the fluctuation of the engine speed to a required limit.

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Design of a Flywheel: ProcedureSelection of the engine

Data tables will be provided and select the problem based on the serial number

Calculation of Turning Momentcalculation of torque due to inertia forcescalculation of torque due to pressure forces

the indicator diagram of the engine will be providedObtain the turning moment and hence find the mean torqueCalculation of the Moment of Inertia of the Flywheel to limit the speed fluctuation to given valueDesign of the flywheel with the required Moment of Inertia

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Design of a Flywheel: ProcedureCalculation of torque due to inertia forces

[ ]αθ coscos)1( nrrrnx −−+=

r

l=nr

θ

α

x

TDC

[ ]αθ coscos lrrlx −−+=

θα sinsin rnr =

nn 2/122 )sin(cos θα −

=

The total Inertia force where M is the mass of the reciprocating parts

..xMQ =

4

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Design of a Flywheel: ProcedureCalculation of torque due to inertia forces

2/122 )sin(cos)1( θθ −−−+= nrrrnx

⎥⎦⎤

⎢⎣⎡ +×=

nrx θθω 2coscos2

..

..xMQ =

M is the mass of reciprocating parts

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Design of a Flywheel: Mass

Mass of the reciprocating parts are largely due toMass of the pistonContribution from the connecting rod

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Design of a Flywheel: Mass

Calculation of the contribution from the connecting rod

l

l2l1

G

A B

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Design of a Flywheel: Mass

Find the equivalent mass system

l

l2l1

G

AB

m1 m2

If the mass of the connecting rod = mm = m1 + m2

m2 x l2 = m1 x l1

Therefore;

Usually for internal combustion engines;

l2 = 3 x l1Mass of the con. Rod = 10g/mm

mll

lm)( 21

12 +=

Therefore the total mass M = piston mass + m2

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Design of a Flywheel: ProcedureCalculation of torque due to pressure force

r

l=nr

θ

α

h

P

S

αcosSP =

αcosShT =

PhT =

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Design of a Flywheel: ProcedureCalculation of pressure force (P)

Use the Indicator diagram

The pressure force at given crank angle can be obtained using the indicator diagram

The indicator diagram of an engine can experimentally be obtained by measuring the in-cylinder gas pressure and plotting the variation of pressure against the volume over one cycle

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Design of a Flywheel: ProcedureCalculation of resultant torque

r

l=nr

θ

α

h

P

S

hQPT )( −=Q QhPhT −=

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Design of a Flywheel: Procedure

Draw the given indicator diagram on the drawing sheetCalculate the scale factors for pressure axis and displacement axis

Consider the given maximum pressure and the stroke of the engineDraw the configuration diagram to obtain h at each crank positionTabulate the pressure and the value of h at each crank position.Tabulate the gas torque, inertia torque and the total torque at each crank position.Draw the Turning Moment diagram and the mean torque lineCalculate the maximum fluctuation of energy

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Design of a Flywheel: Fluctuation of Energy

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Design of a Flywheel: Fluctuation of Energy

Use the Planimeter to calculate the area hence the energy fluctuation

Then calculate the moment of inertia of the flywheel22

21 2

121 ωω IIE ×−×=∆

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Design of a Flywheel: Planimeter

Area = Planimeter constant x number of revolutionsNote : Planimeter constant = 10.

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Design of a FlywheelThe two basic types of flywheels

Rim type Disc type

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Design of a Flywheel

The major components

Rim

ArmsHub

Key and Keyways

Shaft

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Design of a Flywheel: Key and Keyway

Keys are used to transmit torque from a component to the shaft.

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Design of a Flywheel: Key and Keyway

Types for Keyways

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Design of a Flywheel: Key and Keyway

Types for Keys

Rectangular keys

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Design of a Flywheel: Key and Keyway

Failure modesA key has two failure mechanisms:

It can sheared offIt can be crushed due to the compressive bearing forces.

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Design of a Flywheel: Shaft

The diameter of the shaft should be large enough to prevent from failure due to the torque on it.

rJT τ=

T = torque on the shaftJ = Polar second moment of area

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4DJ π=

r = distance from the centreD = diameter of the shaftτ = shear stress on the shaft at radius r

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Design of a Flywheel: Rim and arms

If the speed of rotation is ω;Centrifugal force on the element

2dmdF 2 R

××= ω

222F ωρAR=

AF

=σ

Arms can be designed as specified in Mechanical Engineering Handbooks or any acceptable standards

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Design of a Flywheel

The End