This document provides information about springs and flywheels. It defines springs as elastic bodies that distort under load and recover their original shape when unloaded. Common types of springs discussed include helical, leaf, and Belleville springs. Terminology used in helical springs like wire diameter, coil diameter, and spring index are defined. The document also discusses flywheels, their purpose of storing energy from the power source and releasing it more uniformly. Equations for coefficient of fluctuation of speed and energy, work done per cycle, and energy stored in a flywheel are provided.

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DEPARTMENT OF MECHANICAL ENGINEERING
ME 6503 : DESIGN OF MACHINE ELEMENTS
UNIT -4 : DESIGN OF ENERGY STORING ELEMENTS AND ENGINE COMPONENTS
By
Mr. B.Balavairavan
Assistant Professor
Mechanical Engineering
Kamaraj College of Engg and Tech
Virudhunagar

2. Spring
Spring is an elastic body whose function is
to distort when loaded and to recover its
original shape when the load is removed.
Mechanical springs are
used in machines and other
applications mainly
• to exert force,
• to provide flexibility
• to store or absorb energy.
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3. Application of springs
1. To apply forces as in brakes, clutches and
spring loaded valves.
2. To store energy as in watches, toys.
3. To measure forces as in spring balance and
engine indicators.
4. To cushion, absorb or control energy due to
either shock or vibration as in car.
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4. The most common types of springs are as follows
1. Helical Spring
2. Leaf Spring
3. Disc Spring or Belleville Spring
Types of spring
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5. Types of spring – Helical spring
The helical springs are made up of a wire coiled in the
form of helix and are primarily intended for tensile or
compressive loads. The cross section of the wire from which
the spring made may be circular, square or rectangular. The
two forms of helical springs are compression spring and
helical tension springs.
Helical springs - Classification
a) Open coiled or Compression helical spring
b) Closed coiled or Tension helical spring
c) Torsion spring
d) Spiral spring
e) Concentric spring
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6. Types of spring – Helical spring
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(a) Open coiled or Compression helical spring
The springs which are sustain compressive force along the
axis are called compression helical or open coil springs. These
springs have helix angle more than 100
(b) Closed coiled or Tension helical spring
The springs which are sustain tensile force along the axis
are called tension helical or closed coil springs. These springs
have helix angle less than 100.

7. (c) Torsion Spring
It is also a form of helical spring, but it rotates about an
axis to create load. It releases the load in an arc around the
axis. Mainly used for torque transmission. The ends of the
spring are attached to other application objects, so that if the
object rotates around the center of the spring, it tends to push
the spring to retrieve its normal position.
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Types of spring – Helical spring

8. Types of spring – Helical spring
(d) Spiral Spring
It is made of a band of steel wrapped around itself a
number of times to create a geometric shape. Its inner end is
attached to an arbor and outer end is attached to a retaining
drum. It has a few rotations and also contains a thicker band of
steel. It releases power when it unwinds.
D.M.E - B.B 8

9. Types of spring – Concentric spring
• Concentric helical springs are used to obtain a greater spring
force in a given space and to ensure the operation of a
mechanism in the event that one spring will break.
• To obtain the above conditions, either a two- spring nest or a
three-spring nest may be used.
• Fig. Shows the two concentric springs have the same free
length and arc compressed equally. Such springs are used for
automobile clutches and railway clutches.
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10. Terminologies used in Helical spring
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11. Terminologies used in Helical spring
• Coil Diameter (D)
The mean diameter of the helix.
D = (D outer + Dinner)/2.
• Wire Diameter (d)
The diameter of the wire that is wound into a helix.
• Spring Index (C)
The ratio of mean coil diameter to wire diameter.
C = D/d
• Spring Stiffness or Spring rate (q)
The ratio of load required per unit deflection.
q = P/y
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12. Terminologies used in Helical spring
• Active Coils (Na or n)
The number of coils which actually deform when the
spring is loaded.
• Inactive Coils
The coils which do not take part in deflection of the
spring are known as inactive coils.
• Total Coils (Nt)
The number of coils or turns in the spring.
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13. Terminologies used in Helical spring
• Solid Length (La)
When the compression spring is compressed until the
coils come in contact with each other the spring is said to be
solid. The solid length of a spring is the product of total
number of coils and the diameter of the wire.
• Free Length (Lf)
It is the length of the spring in the free or unloaded
condition. It is equal to the solid length plus the maximum
deflection or compression of the spring and the clearance
between the adjacent coils.
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14. End conditions of Helical spring
Generally, the following four end conditions are used.
1. Plain end
2. Plain and Ground
3. Squared end
4. Squared and Ground end
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15. TERMINOLOGIES USED IN
HELICAL SPRING
• Pitch (p)
The pitch of the coil is defined as the axial distance
between any two adjacent coil in uncompressed state.
• Helix angle or Coil angle or pitch angle (α)
The angle between the coils and the base of the spring.
The pitch angle is calculated from the equation
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16. Terminologies used in Helical spring
• Wahl’s Stress Concentration factor
A factor to correct stress in helical springs effects of
curvatures and direct shear.
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17. Surge in Springs
• When one end of a helical spring is resting on a rigid support
and the other end is loaded suddenly, then all the coils of the
spring will not suddenly deflect equally, because some time is
required for the propagation of stress along the spring wire.
• If the applied load is of fluctuating type as in the case of valve
spring in internal combustion engines and if the time interval
between the load applications is equal to the time required for
the wave to travel from one end to the other end, then
resonance will occur.
• This results in very large deflections of the coils and
correspondingly very high stresses. Under these conditions, it
is just possible that the spring may fail. This phenomenon is
called surge. D.M.E - B.B 17

18. Surge in Springs
The surge in springs may be eliminated by using the following
methods :
1. By using friction dampers on the centre coils so that the wave
propagation dies out.
2. By using springs of high natural frequency.
3. By using springs having pitch of the coils near the ends
different than at the centre to have different natural
frequencies.
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19. Buckling of springs
The helical compression spring behaves
like a column and buckles at a comparative
small load when the length of the spring is
more than 4 times the mean coil diameter.
Surge in springs
The material is subjected to higher stresses,
which may cause early fatigue failure. This
effect is called as spring surge.
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20. Springs in series
• When two or more springs are arranged in
series and subjected to load P as shown in
figure.
• Their equivalent stiffness is given by
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21. Springs in parallel
• When two or more springs are arranged in
parallel and subjected to load P as shown in
figure.
• Their equivalent stiffness is given by
q = q1 + q2
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22. The laminated or leaf spring consists of a number of flat
plates of varying lengths held together by means of clamps and
bolts. These are mostly used in automobiles.
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TYPES OF SPRING – Leaf Spring

23. Nipping in leaf spring
Stress in the full length leaves is 50% greater than the
stress in the graduated leaves. When the load is gradually
applied to the spring, the full length leaf is relieved of the
initial stress and then stressed in opposite direction. Such a pre
stressing obtained by a difference of radii of curvature is
known as nipping.
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24. Materials for Leaf Springs
The material used for leaf springs is usually a plain carbon
steel having 0.90 to 1.0% carbon. The leaves are heat treated
after the forming process. The heat treatment of spring steel
produces greater strength and therefore greater load capacity,
greater range of deflection and better fatigue properties.
According to Indian standards, the recommended materials are
• 1. For automobiles : 50 Cr 1, 50 Cr 1 V 23, and 55 Si 2 Mn 90
all used in hardened and tempered state.
• 2. For rail road springs : C 55 (water-hardened), C 75 (oil-
hardened), 40 Si 2 Mn 90 (waterhardened) and 55 Si 2 Mn 90
(oil-hardened).
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25. TYPES OF SPRING – Belleville
Spring
• Belleville springs or Disc springs are used where space
limitations require high capacity units i.e. Applications
requiring high spring stiffness and compact spring units. This
is obtained at the expense of thickly non-uniform stress
distribution across the section. High Stresses are used in the
design of Belleville springs. Each spring consists of several
annular discs that arc dished to a conical shape as in fig (a).
There are staked up one on top of another as in fig. (b) In order
to increase the deflection.
• The unit may be held in alignment by a central bolt or a tube.
The springs placed in series as shown in fig. (c) and the
deflection is proportional to the number of discs.
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26. TYPES OF SPRING – Belleville
Spring
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27. Flywheel
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28. Flywheel
A flywheel used in machines serves as a
reservoir, which stores 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.
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29. Coefficient of Fluctuation of Speed
The difference between the maximum and
minimum speeds during a cycle is called the
maximum fluctuation of speed. The ratio of the
maximum fluctuation of speed to the mean speed is
called the coefficient of fluctuation of speed.
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30. Turning moment diagram
The turning moment diagram (also known
as crank effort diagram) is the graphical
representation of the turning moment or crank-
effort for various positions of the crank. It is
plotted on cartesian co-ordinates, in which the
turning moment is taken as the ordinate and
crank angle as abscissa.
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31. Turning moment diagram – Single
cylinder engine
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32. Turning moment diagram – Multi
cylinder engine
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33. Turning moment diagram – IC engine
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34. Fluctuation of Energy
The variations of energy above and below the
mean resisting torque line are called fluctuations of
energy.
The difference between the maximum and the
minimum energies is known as maximum fluctuation
of energy.
Maximum fluctuation of energy, E =
Maximum energy – Minimum energy
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35. Coefficient of Fluctuation of Energy
It may be defined as the ratio of the
maximum fluctuation of energy to the work
done per cycle.
CE= Maximum fluctuation of energy /
Work done per cycle
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36. Work done per cycle
The work done per cycle (in N-m or joules)
may be obtained by using the following two
relations :
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37. Work done per cycle
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38. Energy Stored in a Flywheel
Energy stored, E = mk2ω2CS = mv2CS
m = Mass of the flywheel in kg,
k = Radius of gyration of the flywheel in metres
ω = angular speed in rad/s2
Cs = Coefficient of Fluctuation of Speed
v = Mean linear velocity
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39. Dimensions of the Flywheel Rim
Tensile stress or hoop stress,σ = ρR2ω2 = ρv2
ρ = Density of rim material in kg/m3,
N = Speed of the flywheel in r.p.m.,
ω = Angular velocity of the flywheel in rad/s,
v = Linear velocity at the mean radius in m/s
= ω R = DN/60
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40. Mass of the rim, m = Volume × density = ρ DA
If the cross-section of the rim is a
rectangular, then
A = b × t
where b = Width of the rim, and
t = Thickness of the rim.
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Dimensions of the Flywheel Rim

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