Design of flywheel

1. DESIGN OF FLYWHEEL

2. Flywheel Application

3. A Flywheel is used to maintain constant angular
velocity of the crankshaft in a reciprocating
engine. In this case, the flywheel—which is
mounted on the crankshaft— stores energy
when torque is exerted on it by a firing piston
and it releases energy to its mechanical loads
when no piston is exerting torque on it.

4. INTRODUCTI
ON
FLYWHEEL
• A flywheel is an inertial energy-storagedevice.
• It absorbs mechanical energy and serves as a reservoir, storing energy
during the period when the supply of energy is more than the requirement
and releases it during the period when the requirement of energy is more
than the supply.

5. FLYWHEELS-FUNCTION NEED
AND OPERATION
•The main function of a fly wheel is to smoothen out variations in the
speed of a shaft caused by torque fluctuations. If the source of the driving
torque or load torque is fluctuating in nature, then a flywheel is usually
called for. Many machines have load patterns that cause the torque time
function to vary over the cycle. Internal combustion engines with one or
two cylinders are a typical example. Piston compressors, punch presses,
rock crushers etc. are the other systems that have fly wheel.
•Flywheel absorbs mechanical energy by increasing its angular velocity
and delivers the stored energy by decreasing itsvelocity.

6. FLYWHEEL MATERIALS
Traditionally, flywheel are made of cast iron. From design consideration, cast
iron flywheel offer the following advantages:-
• Cast iron flywheels are the cheapest.
• Cast iron flywheel can be given any complex shape without involving
machining operations.
• Cast iron flywheel has excellent ability to damp vibrations.
however, cast iron has poor tensile strength compare to steel. The failureof
cast iron is sudden and total. The machinability of cast iron flywheel is
poor compared to steel flywheel.

7. Applications
Providing continuous energy when the energy source is
discontinuous. For example, flywheels are used in
reciprocating engines because the energy source, torque from
the engine, is intermittent.
Delivering energy at rates beyond the ability of a continuous
energy source. This is achieved by collecting energy in the
flywheel over time and then releasing the energy quickly, at
rates that exceed the abilities of the energy source.
Dynamic balancing of rotating elements.
Energy storage in small scale electricity generator sets

8. Advance and Modern Flywheel
Flywheels have also been proposed as a power booster for
electric vehicles. Speeds of 100,000 rpm have been used to
achieve very high power densities.
Modern high energy flywheels use composite rotors made with
carbon-fibre materials. The rotors have a very high strength-to-
density ratio, and rotate at speeds up to 100,000 rpm. in a
vacuum chamber to minimize aerodynamic losses.

9. Benefits in Aerospace
Flywheels are preferred over conventional batteries in many
aerospace applications because of the following benefits:
5 to 10+ times greater specific energy
Lower mass / kW output
Long life. Unaffected by number of charge / discharge
cycles
85-95% round trip efficiency
Fewer regulators / controls needed
Greater peak load capability
Reduced maintenance / life cycle costs

10. Disadvantages
There are safety concerns associated with flywheels due to
their high speed rotor and the possibility of it breaking
loose & releasing all of it's energy in an uncontrolled
manner.
Its Bulkier, adds more weight to the vehicle.

11. Energy stored in a flywheel
Rotational Kinetic Energy, E = ½ Iω2
where,
I - moment of inertia of the flywheel (ability of an
object to resist changes in its rotational velocity)
ω - rotational velocity (Rad / sec)
The moment of inertia, I = kMr 2
where,
M - mass of the flywheel
r - radius of flywheel
k - inertial constant.

12. k depends on the shape of the rotating object.
Shape-factor K for different planar stress geometries
So for a solid disk ; I = Mr 2 /2

13. Co efficient of fluctuation of speed ( Cs )
The difference between the max and min speeds during a cycle is
called the max fluctuation of speed.
The ratio of the max fluctuation of speed to the mean speed is
called coefficient of fluctuation of speed.
Cs = (N1- N2 )/N
= 2( N1-N2 ) / N1 +N2
where N1 = max speed in r.p.m.
N2 = min speed in r.p.m.
N = mean speed in r.p.m.
= (N1 + N2) / 2

14. Permissible values for CS
S.NO Types of machines Coefficient of fluctuation of speed (CS)
1 Engines with belt
transmission
0.030
2 Gear wheel transmission 0.020
3 Crushing machines 0.200
4 Electrical machines 0.003
5 Hammering machines 0.200
6 Pumping machines 0.03-0.05
7 Machine tools 0.030

15. Stresses in a flywheel rim
A flywheel consists of a rim at which the major portion of the
mass or weight of flywheel is concentrated, a boss or hub for
fixing the flywheel on to shaft and a number of arms for
supporting the rim on the hub.
The following stresses are induced in the rim.
Tensile stress due to centrifugal force.
Tensile bending stress caused by the restraint of the arms.

16. Stresses in flywheel arms
The following stresses are induced in the arms of the
flywheel.
Tensile stresses due to centrifugal force acting on the
rim
Bending stress due to the torque transmitted from the
rim to the shaft or from the shaft to the rim.

17. 1. Tensile stress due to the centrifugal force.
The tensile stress in the rim due to the centrifugal force, assuming
that the rim is unstrained by the arms, is determined in the similar
way as the thin cylinder subjected to internal pressure.
ft = ρ.R2.ω2 = ρ.v2 ( v = R.ω )
When ρ is in kg/m3, v is in m/sec, ft will be in N/m2
where ρ = density of the flywheel material
ω = angular speed of the flywheel
R = mean radius of the flywheel
v = linear velocity of the flywheel

18. 2.Tensile bending stress caused by restraint of arms.
The tensile bending stress in the rim due to the restraint of arms is
based on the assumption that each portion of the rim between a
pair of arms behaves like a beam fixed at both ends and
uniformly loaded, such that length between fixed ends,
L = π.D/n = 2.π.R / n
where n - number of arms

19. The max bending moment,
M =w.l2/12=b.t.ρ.ω2.R/12(2.π.R/n)
Section modulus, Z =1/6 (b.t2)
So bending stress fb =M/Z =b.t.ρ.ω2.R/12(2.π.R/n) *
6 / (b.t2)
Total stress in the rim
f =ft +fb

20. Construction of Flywheel
Flywheels are typically made of steel and rotate on
conventional bearings; these are generally limited to
a revolution rate of a few thousand RPM
The flywheel of smaller size( upto 600 mm dia )are casted in one
piece. The rim and the hub are joined together by means of web.

21. Construction
If flywheel is of larger size (upto 2-5 meters diameter ), then it
is made of arms.
The number of arms depends upon the size of the flywheel and
its speed of rotation. But the flywheels above 2-5 meters are
usually casted in two pieces. Such a flywheel is known as “
split flywheel “.
A split flywheel has the advantage of relieving the shrinkage
stresses in the arms due to unequal rates of cooling of casting.

22. DESIGN APPROACH
There are two stages to the design of a flywheel.
• First, the amount of energy required for the desired degree ofsmoothening
must be found and the (mass) moment of inertia needed to absorb that
energy determined.
• Then flywheel geometry must be defined that caters the required moment
of inertia in a reasonably sized package and is safe against failure at the
designed speeds of operation.
Design Parameters:-
• It depend upon acceptable changes in the speed.
Speed fluctuation:-
• The change in the shaft speed during a cycle is called the speed
fluctuation and it is given by
Fl =ωmax−ωmin

23. DESIGN OF FLYWHEEL
Design
Equation:-
S
I =
𝑬𝒌
𝑪𝒇∗ 𝝎𝒂𝒗𝒈
𝟐
where “Cf”is the co-efficient of speed fluctuation and “Ek”is the kinetic
energy and “𝝎avg” is the average rotational motion.
Torque Variation and Energy:-
The required change in kinetic energy Ek is obtained from the known
torque time relation or curve by integrating it for one cycle and it is
given by
𝜃@
𝜔
𝜃@
𝜔
𝑚 𝑎
𝑥
(𝑇1 −𝑇𝑎𝑣𝑔)d𝜃=Ek

24. GEOMETRY OF FLYWHEEL
• It can be a solid cylindrical disc.
• It can be like conventional wheel design.
But energy requirements and size of the flywheel increases the
geometry changes to disc of central hub and peripheral rimconnected
by webs and to hollow wheels with multiple arms.

25. GEOMETRY OF FLYWHEEL

26. GEOMETRY OF FLYWHEEL
• For a solid disc geometry with inside radius ri and out side radius ro,the
mass moment of inertia I is
• The mass of a hollow circular disc of constant thickness tis
• Combing the two equations we can
write
• Where is material’s weight
density 

27. STRESSES IN FLYWHEEL
• Flywheel being a rotating disc, centrifugal stresses acts upon its distributed
mass and attempts to pull it apart. Its effect is similar to those caused by an
internally pressurized cylinder.
•  = material weight density, ω= angular velocity in rad/sec. ν= Poisson’s
ratio, is the radius to a point of interest, ri and ro are inside and outsideradii
of the solid disc flywheel.

28. ADVANCE AND MODERN
FLYWHEEL
• Advanced flywheels are also now used for protecting against interruptions
to the national electricity grid.
– The flywheel provides power during period between the loss of utility
supplied power and either the return of utility power or the start of a
sufficient back-up power system
• Flywheels have also been proposed as a power booster for electric vehicles.
Speeds of 100,000 rpm have been used to achieve very high power
densities.
• Modern high energy flywheels use composite rotors made with carbon-
fibre materials. The rotors have a very high strength-to-density ratio, and
rotate at speeds up to 100,000 rpm. in a vacuum chamber to minimize
aerodynamic losses.

29. BENEFITS IN AEROSPACE
Flywheelsare preferred over conventional batteries in many
aerospace
applications because of the following benefits:
• 5 to 10+ times greater specific energy
• Lower mass / kW output
• Long life. Unaffected by number of charge / discharge cycles
• 85-95% round trip efficiency
• Fewer regulators / controls needed
• Greater peak load capability
• Reduced maintenance / life cycle costs

30. APPLICATIONS

31. Example 22.1. The turning moment diagram for a petrol engine is drawn to the following
scales: Turning moment, 1 mm = 5 N-m; Crank angle, 1 mm = 1º. The turning moment
diagram repeats itself at every half revolution of the engine and the areas above and below the
mean turning moment line, taken in order are 295, 685, 40, 340, 960, 270 mm2. Determine the
mass of 300 mm diameter flywheel rim when the coefficient of fluctuation of speed is 0.3% and
the engine runs at 1800 r.p.m. Also determine the cross-section of the rim when the width
of the rim is twice of thickness. Assume density of rim material as 7250 kg / m3.