Design of a Flywheel FLYWHEEL

Transcription

ME 209: Machine Design I
Flywheel
A 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
Design of a Flywheel
Asanga Ratnaweera
Department of Mechanical Engineering
Faculty of Engineering
University of Peradeniya
Manual press
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IC Engines: The basic operation
In 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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Power press
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Power is produced only during the power stroke
Intake
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Combustion engines
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Compression
Power
Exhaust
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IC Engines: Turning Moment
Pressure 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
The torque at the crank shaft or the
turning moment is largely dependent on;
The in-cylinder gas pressure
The inertia force of the reciprocating parts
As explained above the gas pressure
fluctuates over a complete cycle
The acceleration and deceleration of the
piston assembly also changes during the
motion over a cycle
Therefore the Turning Moment also
fluctuates over an engine cycle
IVO - intake valve opens, IVC – intake valve closes
EVO – exhaust valve opens, EVC – exhaust valve closes
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The Fluctuation Turning Moment can be controlled to some extent
by increasing number of cylinders (Multi-cylinder engines)
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There are two common configurations used in multi-cylinder
engines
Inline Engine
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V Engine
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Practically 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 cylinders
A 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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This 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: Procedure

Selection of the engine

Data tables will be provided and select the problem based on the serial
number
Calculation of Turning Moment

Calculation of torque due to inertia forces
TDC
the indicator diagram of the engine will be provided
where M is the mass of the
reciprocating parts
α
Obtain the turning moment and hence find the mean
torque
Calculation of the Moment of Inertia of the Flywheel to
limit the speed fluctuation to given value
Design of the flywheel with the required Moment of
Inertia
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..
The total Inertia force Q = M x
x
calculation of torque due to inertia forces
calculation of torque due to pressure forces

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l=nr
x = l + r − [r cos θ − l cos α ]
x = (n + 1)r − [r cos θ − nr cos α ]
nr sin α = r sin θ
θ
r
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cos α =
(n 2 − sin 2 θ )1/ 2
n
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Calculation of torque due to inertia forces
Design of a Flywheel: Mass

x = (n + 1)r − r cos θ − r (n 2 − sin 2 θ )1/ 2
Mass of the reciprocating parts are largely due to

Mass of the piston
Contribution from the connecting rod
..
cos 2θ ⎤
⎡
x = ω 2 × r ⎢cos θ +
n ⎥⎦
⎣
..
Q=M x
M is the mass of reciprocating parts
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Calculation of the contribution from the connecting
rod

Find the equivalent mass system
m1
B
A
B
A
l2
l
l
Therefore the total mass
M = piston mass + m2
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m 2 x l2 = m 1 x l1
Therefore;
l1
l2
l1
m2
G
G
If the mass of the connecting rod = m
m = m1 + m2
m2 =
l1
m
(l1 + l2 )
Usually for internal combustion
engines;
l2 = 3 x l1
Mass of the con. Rod = 10g/mm
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Calculation of torque due to pressure force

P = S cos α
l=nr
T = Ph
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
θ r
h
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Calculation of resultant torque
P
T = ( P − Q)h
Q
T = Ph − Qh
S
α
Use the Indicator diagram
The pressure force at given
crank angle can be obtained
using the indicator diagram
T = Sh cos α
S
α

Calculation of pressure force (P)

P

θ r
Draw the given indicator diagram on the drawing sheet
Calculate the scale factors for pressure axis and displacement
axis

l=nr
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Consider the given maximum pressure and the stroke of the engine
Draw the configuration diagram to obtain h at each crank
position
Tabulate 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 line
Calculate the maximum fluctuation of energy
h
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Design of a Flywheel: Fluctuation of
Energy
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 flywheel
∆E =
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Design of a Flywheel: Planimeter
The two basic types of flywheels
Disc type
Rim type
Area = Planimeter constant x number of revolutions
Note : Planimeter constant = 10.
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1
1
2
2
× Iω1 − × Iω2
2
2
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Design of a Flywheel: Key and
Keyway

The major components

Arms
Keys are used to transmit torque from a component to
the shaft.
Hub
Shaft
Rim
Key and Keyways
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Keyway

Keyway

Types for Keyways
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Types for Keys
Rectangular keys
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Keyway
Failure modes

A key has two failure mechanisms:

Design of a Flywheel: Shaft
It can sheared off
It can be crushed due to the compressive bearing forces.
The diameter of the shaft should be large enough to
prevent from failure due to the torque on it.
T τ
=
J r
r = distance from the centre
D = diameter of the shaft
τ = shear stress on the shaft at radius r
T = torque on the shaft
J = Polar second moment of area
J=
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Design of a Flywheel: Rim and arms

πD 4
If the speed of rotation is ω;
Centrifugal force on the element
dF = dm × ω 2 ×
R
2
F = 2 ρAR ω
2
2
σ =
The End
F
A
Arms can be designed as specified in Mechanical Engineering Handbooks or
any acceptable standards
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