DESIGN OF SPRINGS-UNIT4.pptx

DESIGN OF SPRINGS
UNIT-4
30 November 2023 1
Dr. C.GOPINATH
Assistant Professor
St. Joseph college of Engineering

SPRINGS
• Spring is an elastic body whose function is to distort when loaded and to
recover its original shape when the load is removed.
APPLICATION OF SPRINGS
• To apply forces as in brakes, clutches and spring loaded valves.
• To store energy as in watches, toys.
• To measure forces as in spring balance and engine indicators.
• To cushion, absorb or control energy due to either shock or vibration as in
car.
TYPES OF SPRINGS:
30 November 2023 2

HELICAL SPRINGS
30 November 2023 3
 The helical springs are made up of a wire coiled in the form of helix and is
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.
Compression
Helical Spring
Tension Helical Spring

MATERIAL FOR HELICAL SPRINGS
30 November 2023 4
 The material of the spring should have
 high fatigue strength,
 high ductility,
 high resilience and
 creep resistant.
 It largely depends upon the size and service.
 The strength of the wires varies with size, smaller size wires have greater
strength and less ductility, due to the greater degree of cold working.
 Severe service means rapid continuous loading where the ratio of
minimum to maximum load (or stress) is one-half or less, as in automotive
valve springs.
 Average service includes the same stress range as in severe service but
with only intermittent operation, as in engine governor springs and
automobile suspension springs.
 Light service includes springs subjected to loads that are static or very
infrequently varied, as in safety valve springs.
 The springs are mostly made from oil-tempered carbon steel wires
containing 0.60 to 0.70 per cent carbon and 0.60 to 1.0 per cent
manganese.

Material for Helical Springs
 Music wire is used for small springs.
 Non-ferrous materials like phosphor bronze, beryllium copper, monel
metal, brass etc., may be used in special cases to increase fatigue
resistance, temperature resistance and corrosion resistance.
 Table PSGDB 7.105 shows the values of allowable shear stress for various
materials used for springs.
 The helical springs are either cold formed or hot formed depending upon
the size of the wire.
30 November 2023 5
Static Approach to varying Loads
No. of cycles Classification
*Recommended
Design Stress [t]
> 106 Severe service 0.263su
>104 but <106 Average service 0.324su
<104 Light service 0.405su

Terms used in Compression Spring
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Axially loaded helical spring

TERMS USED IN COMPRESSION SPRING
30 November 2023 7
 SOLID LENGTH: 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. Ls = n’.d, where n’ = total number of coils, d =
diameter of the wire
 FREE LENGTH: 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.
 Free length of the spring, LF = n’d+ymax+0.15ymax
 SPRING INDEX: It is defined as the ratio of the mean diameter of the coil
to the diameter of the coil to the diameter of the wire. C=D/d, where
D- mean diameter of coil, d- diameter of wire
 SPRING RATE: It is defined as the load required per unit deflection of the
spring. q=P/y where P- applied load, y- deflection of the spring.
 PITCH: The pitch of the coil is defined as the axial distance between
adjacent coil in uncompressed state.
Pitch length=free length/(n’-1)

30 November 2023 8
Ends for Compression Helical Spring
• In all springs the end coils produce an eccentric application of
the load, increasing the stress on one side of the spring.
• Under certain conditions, especially where the number of coils
is small, this effect must be taken into account.
• The nearest approach to an axial load is secured by squared
and ground ends, where the end turns are squared and then
ground perpendicular to the helix axis.
• It may be noted that part of the coil which is in contact with the
seat does not contribute to spring action and hence are termed
as inactive coils.
• The turns which impact spring action is known as active turns.
• As the load increases, the number of inactive coils also
increased due to seating of the end coils and the amount of
increase varies from 0.5 to 1 turn at usual working loads.

30 November 2023 9
Ends for Compression Helical Spring
PSGDB 7.101

30 November 2023 10
Ends for Tension Helical Spring
• The tensile springs are provided with hooks or loops as shown in
Fig.
• These loops may be made by turning whole coil or half of the coil.
• In a tension spring, large stress concentration is produced at the
loop or other attaching device of tension spring.
• The main disadvantage of tension spring is the failure of the spring
when the wire breaks.
• A compression spring used for carrying a tensile load is shown in
Fig.
• The total number of turns of a tension helical spring must be equal
to the number of turns (n) between the points where the loops start
plus the equivalent turns for the loops.
• It has been found experimentally that half turn should be added for
each loop. Thus for a spring having loops on both ends, the total
number of active turns, n' = n + 1

30 November 2023 11
Ends for Tension Helical Spring

30 November 2023 12
Stresses in Helical Spring
• Figure a shows a round-wire helical compression
spring Loaded by the axial force P.
• Designate D as the mean coil diameter and d as the
wire diameter.
• Now imagine that the spring is cut at some point
(Fig. b), a portion of it removed, and the effect of the
removed portion replaced by the net internal
reactions.
• Then, as shown in the figure, from equilibrium the cut
portion would contain a direct shear force P and a
torsion Mt = PD/2.
• The flexing of a helical spring creates a torsion in the
wire.
• The maximum stress in the wire may be computed by
superposition of the direct shear stress and the
torsional shear stress

30 November 2023 13
• The resultant stress consists of superimposition of torsional
shear stress, direct shear stress and additional stresses due to
the curvature of the coil.
• The stresses in the spring wire on account of these factors are
shown in Fig.
• When the bar is bent in the form of coil, the length of the
inside fibre is less than the length of the outside fibre. This
results in stress concentration at the inside fibre of the coil.
• AM Wahl1 derived the equation for resultant stress, which
includes torsional shear stress, direct shear stress and stress
concentration due to curvature.
• This equation is given by,
where K is called the stress factor or Wahl factor.
• The Wahl factor is given by,

30 November 2023 14

30 November 2023 15
(a) Helical Spring (b) Helical Spring-unbent
• The Wahl factor provides a simple method to find out
resultant stresses in the spring.
• The resultant shear stress is maximum at the inside radius
of the coil.
• In normal applications, the spring is designed by using the
Wahl factor.

30 November 2023 16
• The load-deflection equation of the spring is given by
• The rate of spring (q) is given
by, q = P/y
• Then stiffness of the spring is
given by,
• Strain energy stored in the spring

30 November 2023 17
• The basic procedure for the design of helical spring consists of
the following steps:
1) For the given application, estimate the maximum spring force
(P) and the corresponding required deflection (y) of the
spring. In some cases, maximum spring force (P) and stiffness
q, which is (P/d), are specified.
2) Select a suitable spring material and find out ultimate tensile
strength (σut) from the data.
3) Calculate the permissible shear stress for the spring wire by
following relationship: τ = 0.30 σut or 0.50 σut
4) Assume a suitable value for the spring index (C). For
industrial applications, the spring index varies from 8 to 10. A
spring index of 8 is considered as a good value. The spring
index for springs in valves and clutches is 5. The spring index
should never be less than 3.
5) Calculate the Wahl factor using the equation in PSGDB 7.100
Design Procedure of Helical Spring

30 November 2023 18
6) Determine wire diameter (d) by using the stress Eq. PSGDB
7.100.
7) Determine mean coil diameter (D) by the following
relationship: D = Cd
8) Determine the number of active coils (n) by using deflection
Eq. PSGDB 7.100. The modulus of rigidity (G) for steel wires
is 81370 MPa.
9) Decide the style of ends for the spring depending upon the
configuration of the application. Determine the number of
inactive coils. Adding active and inactive coils, find out the
total number of coils (n').
10)Determine the solid length of the spring by the following
relationship: Solid length = n‘d
Design procedure of Helical Spring

30 November 2023 19
11)Determine the maximum deflection of the spring by Eq.
PSGDB 7.100.
12)Assume a gap of 0.5 to 2 mm between adjacent coils, when
the spring is under the action of maximum load. The total
axial gap between coils is given by,
total gap = (n'–1) × gap between two adjacent coils
11)In some cases, the total axial gap is taken as 15% of the
maximum deflection:
12)Determine the free length of the spring by the following
relationship: Free length = Solid length + Total gap + ymax
13)Determine the pitch of the coil by using the equations in
PSGDB 7.101
14)Determine the rate of spring by stiffness Eq. PSGDB 7.100
15)Prepare a list of spring specifications.
Design procedure of Helical Spring

30 November 2023 20
• It has been found experimentally that when the free length of
the spring (LF) is more than three times the mean or pitch
diameter (D), then the spring behaves like a column and may
fail by buckling at a comparatively low load as shown in Fig
• The spring should be preferably designed as buckle-proof.
Compression springs, which cannot be designed buckle-proof,
must be guided in a sleeve or over an arbor.
• The thumb rules for provision of guide are as follows:
Buckling of compression springs
• Lf/D < 3,
• for Lf/D > 3 the spring must be
suitably guided

30 November 2023 21
• 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.
• In the beginning, the end coils of the spring in contact with the
applied load takes up whole of the deflection and then it
transmits a large part of its deflection to the adjacent coils.
• In this way, a wave of compression propagates through the
coils to the supported end from where it is reflected back to
the deflected end.
• This wave of compression travels along the spring indefinitely.
• 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.
Surge in springs

30 November 2023 22
• 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.
• It has been found that the natural frequency of spring should be atleast
twelve times the frequency of application of a periodic load in order to
avoid resonance.
• The natural frequency for springs clamped between two plates is given by
Surge in springs
• Check for surging : f > 12 fn
• 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

30 November 2023 23
Design against Fluctuating Load
• In many applications, the force acting on the spring is not
constant but varies in magnitude with time.
• The valve spring of an automotive engine is subjected to
millions of stress cycles during its lifetime.
• On the other hand, the springs in linkages and mechanisms
are subjected to comparatively less number of stress cycles.
• The springs subjected to fluctuating stresses are designed
on the basis of two criteria—design for infinite life and
design for finite life.
• Let us consider a spring subjected to an external fluctuating
force, which changes its magnitude from Pmax to Pmin in the
load cycle.
• The mean force Pm and the force amplitude Pa are given by,

30 November 2023 24
Design against fluctuating load
• The mean stress (τm) is calculated from mean force (Pm) by using shear
stress correction factor (Ks). It is given by,
• Ksh is the correction factor for direct shear stress and it is applicable to
mean stress only. ks = ksh.kc
• kc - curvature factor
• For torsional stress amplitude (τa), it is necessary to also consider the
effect of stress concentration due to curvature (ks )in addition to direct
shear stress. Therefore,
• For Patented and cold-drawn steel wires (Grade-1 to 4), τ-1 = 0.21 σu
and τy = 0.42 σu
• For oil-hardened and tempered steel wires (SW and VW grade),
τ-1 = 0.22 σu and τy = 0.45 σu
Curvature factor kc
C 3 4 6 7 8 9 10
kc 1.35 1.25 1.15 1.13 1.11 1.1 1.09

30 November 2023 25
Design against fluctuating load
• The helical springs subjected to fatigue loading are
designed by using the Soderberg line method.
• The spring materials are usually tested for torsional
endurance strength under a repeated stress that varies
from zero to a maximum.
• Since the springs are ordinarily loaded in one direction
only (the load in springs is never reversed in nature),
therefore a modified Soderberg line is used for springs,

30 November 2023 26
Concentric or Composite Springs
• A concentric or composite spring is used for one of the
following purposes :
• To obtain greater spring force within a given space.
• To insure the operation of a mechanism in the event
of failure of one of the springs.
• Concentric spring is also called a ‘nested’ spring.
• The concentric springs for the above two purposes may
have two or more springs and have the same free lengths
as shown in Fig. and are compressed equally.
• Such springs are used in automobile clutches, valve
springs in aircraft, heavy duty diesel engines and
rail-road car suspension systems.
• The adjacent coils of the concentric spring are wound in
opposite directions to eliminate any tendency to bind.
• If the same material is used, the concentric springs are
designed for the same stress.
• In order to get the same stress factor (K), it is desirable
to have the same spring index (C ).

30 November 2023 27
• Assuming that both the springs are made of same material, then
the maximum shear stress induced in both the springs is
approximately same, i.e. τ1 = τ2
• If both the springs are effective throughout their working range,
then their free length and deflection are equal, i.e. y1 =y2
• The following relations are used for designing Concentric
springs.
• τ1 = τ2 < [τ]
• D1/d1 = D2/d2 =C
• P1/P2 =2(C/(C-2))
• d1< (D1-D2)/2
Concentric or Composite Springs

30 November 2023 28
• When extension springs are made with coils in contact with one another,
they are said to be close-wound.
• Spring manufacturers prefer some initial tension in close-wound springs
in order to hold the free length more accurately.
• The deflection y is the extension of the spring beyond the free length Lf
and Pi is the initial tension in the spring that must be exceeded before
the spring deflects.
• The load-deflection relation is then P = Pi + qy where q is the spring
rate.
Extension Springs

30 November 2023 29
Helical Torsion Springs
• A helical torsion spring is a device used to transmit the torque to a
particular component of a machine or mechanism.
• It is widely used in door hinges, brush holders, automobile starters and
door locks.
• The ends are formed in such a way that the spring is loaded by a torque
about the axis of the coils.
• The helical torsion spring resists the bending moment (P x r), which
tends to wind up the spring.
• The wire of the spring is subjected to bending stresses.
• Each individual section of the torsion spring is, in effect, a portion of a
curved beam.
• The bending stress induced in the
spring wire
• The deflection or angular deformation
of the spring

30 November 2023 30
Leaf Spring
• The laminated or leaf spring consists of a number of flat plates of
varying lengths held together by means of clamps and bolts..
• The advantage of leaf spring over helical spring is that the ends of the
spring may be guided along a definite path as it deflects to act as a
structural member in addition to energy absorbing device.
• Thus the leaf springs may carry lateral loads, brake torque, driving
torque etc., in addition to shocks.
• These are mostly used in automobiles.
• A leaf spring commonly used in automobiles is of semielliptical form.
• It is built up of a number of plates.

30 November 2023 31
Multi-leaf spring
• The leaves are usually given an initial curvature or cambered so that
they will tend to straighten under the load.
• The leaves are held together by means of a band shrunk around them
at the center or by a bolt passing through the center.
• Since the band exerts stiffening and strengthening effect, therefore the
effective length of the spring for bending will be overall length of spring
minus width of band.
• The spring is clamped to the axle housing by means of U bolts.
• The longest leaf known as main leaf or master leaf has its ends formed
in the shape of an eye through which the bolts are passed to secure the
spring to its support.
• Usually the eyes through which the spring is attached to the hanger or
shackle, are provided with bushings of some antifriction materials such
as bronze or rubber.
• The other leaves of the springs are known as graduated leaves.
• Rebound clips are located at intermediate positions in the length of the
spring so that the graduated leaves also share the stress induced in the
full length of leaves when the spring rebounds.

30 November 2023 32
Multi-leaf spring - construction
Flat spring (cantilever
type).
Flat spring (simply supported
beam type).
Cantilever is cut into a
series of n strips
• Treating the spring as a cantilever beam of uniform strength,
• The bending stress induced in the spring
• The deflection of the spring
• The above relations give the stress and deflection of a leaf spring of
uniform cross-section in the form of simply supported beam.
• The stress at such a spring is maximum at the support.

30 November 2023 33
Multi-leaf spring
• If a triangular plate is used as shown in Fig. (a), the stress will be
uniform throughout.
• If this triangular plate is cut into strips of uniform width and placed one
below the other, as shown in Fig. (b) to form a graduated or laminated
leaf spring, then the above arrangement, the spring becomes compact so
that the space occupied by the spring is considerably reduced.
• The bending stress
induced in the spring
• The deflection of the
spring

30 November 2023 34
Multi-leaf spring
• When bending stress alone is considered, the graduated leaves may
have zero width at the loaded end.
• But sufficient metal must be provided to support the shear.
• Therefore, it becomes necessary to have one or more leaves of
uniform cross-section extending clear to the end.
• From the above equations that for the same deflection, the stress in the
uniform cross-section leaves (i.e. full length leaves) is 50% greater
than in the graduated leaves, assuming that each spring element
deflects according to its own elastic curve
• The maximum stress or bending stress for Full length leaves,
• The maximum stress or bending stress for graduated leaves
• The deflection in the full length and graduated leave

30 November 2023 35
LEAF SPRING - Equalized Stress in Spring Leaves (Nipping)
• The stresses in extra full-length leaves are 50% more than the stresses
in graduated-length leaves.
• One of the methods of equalizing the stresses in different leaves is to
pre-stress the spring.
• The pre-stressing is achieved by bending the leaves to different radii of
curvature, before they are assembled with the centre clip.
• As shown in Fig., the full-length leaf is given a greater radius of
curvature than the adjacent leaf.
• The radius of curvature decreases with shorter leaves.
• The initial gap C between the extra full-length leaf and the graduated-
length leaf before the assembly, is called a ‘nip’.
• Such pre-stressing, achieved by a difference in radii of curvature, is
known as ‘nipping’.
• Nipping is common in automobile suspension springs.

30 November 2023 36
• Initial gap (or) Nip
• Load on the bolt to close the nip
Leaf spring
• Let 2L1- length of span (or) overall length of spring,
• l = Width of band or distance between centres of U-bolts. It is the
ineffective length of the spring,
• ne = Number of full length leaves,
• ng = Number of graduated leaves, and
• n = Total number of leaves = ne + ng
• The effective length of the spring, 2L = 2L1 – l

30 November 2023 37
• A Belleville spring consists of a coned disk as shown in
Fig.
• This type of spring is also called ‘coned disk’ spring.
• It is called Belleville spring because it was invented by
Julian Belleville, who patented its design in France in
1867.
• In the Belleville spring, (h/t) ratio is reduced to 2.1 the
load is constant for this range of deflection.
• This is useful for engaging or disengaging the clutch, when
the Belleville spring is used as a clutch spring.
• The Belleville spring offers the following advantages:
• It is simple in construction and easy to manufacture.
• The Belleville spring is a compact spring unit.
• It is especially useful where very large force is desired
for small deflection of the spring.
• It provides a wide range of spring constants making it
versatile.
• It can provide any linear or non-linear load deflection
characteristic.
Belleville Springs

30 November 2023 38
Belleville springs
Let
P = axial force on the spring (N)
y = deflection of spring (m)
t = thickness of disc or washer (m)
h = free height minus thickness (m)
E = modulus of elasticity (N/m2)
σ = stress at the inside circumference
(N/m2)
d0 = outer diameter of washer (m)
di = inner diameter of washer (m)
ν = Poisson’s ratio ( 0.3 for steel)
M, C1, C2 = Constants

DESIGN OF SPRINGS-UNIT4.pptx

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