Spring

A spring is defined as an elastic body, whose function is to distort when loaded and to
recover its original shape when the load is removed.

The various important applications of springs are as follows:

 To cushion, absorb or control energy due to either shock or vibration as in car

springs, railway buffers, air-craft landing gears, shock absorbers and vibration
dampers.
 To apply forces, as in brakes, clutches and spring loaded valves.
 To control motion by maintaining contact between two elements as in cams and
followers.
 To measure forces, as in spring balances and engine indicators.
 To store energy, as in watches, toys, etc.

Types of springs

Though there are many types of the springs, yet the following, according to their shape,
are important from the subject point of view.

Helical springs

 The helical spring are made up of a wire coiled in the form of a helix and is primarily
intended for compressive or tensile loads.
 The cross-section of the wire from which the spring is made may be circular, square or
rectangular. The two forms of helical springs are compression helical spring as shown
in Fig. (a) And tension helical spring as shown in Fig. (b).

 The helical springs are said to be closely coiled when the spring wire is coiled so close
that the plane containing each turn is nearly at right angles to the axis of the helix and the
wire is subjected to torsion.
  In other words, in a closely coiled helical spring, the helix angle is very small; it is
usually less than 10°.
 The major stresses produced in helical springs are shear stresses due to twisting. The load
applied is parallel to or along the axis of the spring.
 In open coiled helical springs, the spring wire is coiled in such a way that there is a gap
between the two consecutive turns, as a result of which the helix angle is large.
 Since the application of open coiled helical springs are limited, therefore our discussion
shall confine to closely coiled helical springs only.

The helical springs have the following advantages:

 These are easy to manufacture.

 These are available in wide range.
 These are reliable.
 These have constant spring rate.
 Their performance can be predicted more accurately.
 Their characteristics can be varied by changing dimensions.

Torsion springs

 Torsion springs may be of helical or spiral type as shown in Fig.

 The helical type may be used only in applications where the load tends to wind up the
spring and are used in various electrical mechanisms.
 The spiral type is also used where the load tends to increase the number of coils and
when made of flat strip are used in watches and clocks.
 The major stresses produced in torsion springs are tensile and compressive due to
bending.

Laminated or leaf springs

  The laminated or leaf spring (also known as flat spring or carriage spring) consists of a
number of flat plates (known as leaves) of varying lengths held together by means of
clamps and bolts, as shown in Fig.
 These are mostly used in automobiles. The major stresses produced in leaf springs are
tensile and compressive stresses.

Disc or Belleville springs

 These springs consist of a number of conical discs held together against slipping by a
central bolt or tube as shown in Fig.

 These springs are used in applications where high spring rates and compact spring units
are required.
 The major stresses produced in disc or Belleville springs are tensile and compressive
stresses.

Special purpose springs

 These springs are air or liquid springs, rubber springs, ring springs etc.
 The fluids (air or liquid) can behave as a compression spring. These springs are used for
special types of application only.

Material for Helical Springs

The material of the spring should have high fatigue strength, high ductility, high
resilience and it should be creep resistant. It largely depends upon the service for which they are
used i.e. severe service, average service or light service.
  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. 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.

Terms used in Compression Springs

The following terms used in connection with compression springs are important from the subject
point of view.
Problems

1. A helical spring is made from a wire of 6 mm diameter and has outside diameter of 75 mm.
If the permissible shear stress is 350 MPa and modulus of rigidity 84 kN/mm 2, find the
axial load which the spring can carry and the deflection per active turn.
2. Design a spring for a balance to measure 0 to 1000 N over a scale of length 80 mm. The
spring is to be enclosed in a casing of 25 mm diameter. The approximate number of turns is
30. The modulus of rigidity is 85 kN/mm2. Also calculate the maximum shear stress
induced.
Solution. Given : W = 1000 N ; δ = 80 mm ; n = 30 ; G = 85 kN/mm2 = 85 × 103 N/mm2
3. Design a helical compression spring for a maximum load of 1000 N for a deflection of 25
mm using the value of spring index as 5. The maximum permissible shear stress for spring
wire is 420 MPa and modulus of rigidity is 84 kN/mm2.
Leaf Springs

 Leaf springs (also known as flat springs) are made out of flat plates.
 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.

Construction of Leaf Spring

 A leaf spring commonly used in automobiles is of semi-elliptical form as shown in Fig.

 It is built up of a number of plates (known as leaves).

 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 centre or by a
bolt passing through the centre.
 Since the band exerts stiffening and strengthening effect, therefore the effective length of
the spring for bending will be overall length of the spring minus width of band.
 In case of a centre bolt, two-third distance between centers of U-bolt should be subtracted
from the overall length of the spring in order to find effective length.
 The spring is clamped to the axle housing by means of U-bolts.

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:
 For automobiles : 50 Cr 1, 50 Cr 1 V 23, and 55 Si 2 Mn 90 all used in hardened
and tempered state.
 For rail road springs: C 55 (water-hardened), C 75 (oil-hardened), 40 Si 2 Mn 90
(water hardened) and 55 Si 2 Mn 90 (oil-hardened).
 The physical properties of some of these materials are given in the following
table. All values are for oil quenched condition and for single heat only

Problems
1. Design a leaf spring for the following specifications: Total load = 140 kN; Number of
springs supporting the load = 4; Maximum number of leaves = 10; Span of the spring =
1000 mm; Permissible deflection = 80 mm.

Take Young’s modulus, E = 200 kN/mm2 and allowable stress in spring material as 600 MPa.
2. A truck spring has 12 numbers of leaves, two of which are full length leaves. The spring
supports are 1.05 m apart and the central band is 85 mm wide. The central load is to be
5.4 kN with a permissible stress of 280 MPa. Determine the thickness and width of the
steel spring leaves. The ratio of the total depth to the width of the spring is 3. Also
determine the deflection of the spring.
Energy Stored in Helical Springs of Circular Wire

A rail wagon of mass 20 tones is moving with a velocity of 2 m/s. It is brought to rest by two
buffers with springs of 300 mm diameter. The maximum deflection of springs is 250 mm. The
allowable shear stress in the spring material is 600 MPa. Design the spring for the buffers.
Given: m = 20 t = 20 000 kg; v = 2 m/s; D = 300 mm;  = 250 mm; = 600 MPa = 600 N/mm2

1. Diameter of the spring wire

Let d =Diameter of the spring wire.

We know that kinetic energy of the wagon

A closely coiled helical spring is made of 10 mm diameter steel wire, the coil consisting of 10
complete turns with a mean diameter of 120 mm. The spring carries an axial pull of 200 N.
Determine the shear stress induced in the spring neglecting the effect of stress concentration.
Determine also the deflection in the spring, its stiffness and strain energy stored by it if the
modulus of rigidity of the material is 80 kN/mm2.

Helical Torsion Springs

The helical torsion springs as shown in Fig. 23.23, may be made from round, rectangular or
square wire. These are wound in a similar manner as helical compression or tension springs but
the ends are shaped to transmit torque. The primary stress in helical torsion springs is bending
stress whereas in compression or tension springs, the stresses are torsional shear stresses.

The helical torsion springs are widely used for transmitting small torques as in door
hinges, brush holders in electric motors, automobile starters etc.
A helical torsion spring of mean diameter 60 mm is made of a round wire of 6 mm diameter. If a
torque of 6 N-m is applied on the spring, find the bending stress induced and the angular
deflection of the spring in degrees. The spring index is 10 and modulus of elasticity for the
spring material is 200 kN/mm2. The number of effective turns may be taken as 5.5.

Helical Springs Subjected to Fatigue Loading:

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, therefore a modified Soderberg diagram is used for springs.

Problem

A helical compression spring made of oil tempered carbon steel, is subjected to a load
which varies from 400 N to 1000 N. The spring index is 6 and the design factor of safety is 1.25.
If the yield stress in shear is 770 MPa and endurance stress in shear is 350 MPa, find : 1. Size of
the spring wire, 2. Diameters of the spring, 3. Number of turns of the spring, and 4. Free length
of the spring.

The compression of the spring at the maximum load is 30 mm. The modulus of rigidity
for the spring material may be taken as 80 kN/mm2.