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              WHAT IS SPRING?

Springs are elastic bodies (generally metal) that can be twisted, pulled, or stretched by some force. They can return to their original shape when the force is released. 

:-In other words it is also termed as a resilient member.

CLASSIFICATION OF SPRINGS

1)  Helical springs:
                1. Tension helical spring
                2.Compression helical spring
                3.Torsion spring
                4.Spiral spring

2) Leaf springs. 
HELICAL SPRING CLASSIFICATION

                1.Open coil helical spring
                2.Closed coil helical spring
                3.Torsion spring
                4.Spiral spring
TENSION HELICAL SPRING (OR) EXTENSION SPRING:

:-It has some means of transferring the load from the support to the body by means of some arrangement.
:-It stretches apart to create load.
:-The gap between the successive coils is small.
:-The wire is coiled in a sequence that the turn is at    right angles to the axis of the spring.
:-The spring is loaded along the axis.
:-By applying load the spring elongates in action.

           EXTENSION SPRINGS AND ITS  END                                    HOOKS

      COMPRESSION HELICAL SPRING

Among the four types, the plain end type is less expensive to manufacture. It tends to bow sideways when applying a compressive load.

:

                   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.

                             

 
                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

                    LEAF SPRING

:Sometimes it is also called as a semi-elliptical spring, as it takes the form of a slender arc shaped length of spring steel of rectangular cross section. :The center of the arc provides the location for the axle,while the tie holes are provided at either end for attaching to the vehicle body.
:Heavy vehicles,leaves are stacked one upon the other to ensure rigidity and strenth.
:It provides dampness and springing function.

                   

 :It can be attached directly to the frame at the both ends or attached directly to one end,usually at the front,with the other end attched through a shackle,a short swinging arm.
 :The shackle takes up the tendency of the leaf spring to elongate when it gets compressed and by which the spring becomes softer.
 :Thus depending upon the load bearing capacity of the vehicle the leaf spring is designed with graduated and Ungraduated leaves.

    FABRICATION STAGES OF A LEAF SPRING

          NIPPING IN LEAF SPRING?

:Because of the difference in the leaf length,different stress will be there at each leaf.To compensate the stress level,prestressing is to be done.Prestressing is achieved by bending the leaves to different radius of curvature before they are assembled with the center clip.
:The radius of curvature decreases with shorter leaves.
:The extra intail gap found between the extra full length leaf and graduated length leaf is called as nip.Such prestressing achieved by a difference in the radius of curvature is known as nipping.
      

 
                         SPRING MATERIALS

The mainly used material for manufacturing the springs are as follows:
1.Hard drawn high carbon steel.          
2.Oil tempered high carbon steel.       
3.Stainless steel
4.Copper or nickel based alloys.

5.Phosphor bronze.
6.Inconel.
7.Monel
8.Titanium 9)Chrome vanadium. 

 10) Chrome silicon.

TERMINOLOGIES IN A COMPRESSION HELICAL SPRING
1)Free length            
2)Pitch                    
3)Endurance limit       
4)Slenderness ratio
5)Pitch       
6)Active coils   
7)Solid length       
8)Pitch angle
9)Hysterisis   
10)Initial tension    11)Permanent set   12)Set

 13)Spring rate        14)Spring index

K equivalent-when springs are in series   Kequivalent-when springs are in parallel PARALLEL(SYMMETRIC DISPLACEMENTCASE)
(Δ1= Δ2)

        










UNSYMMETRICAL DISPLACEMENT(Δ1, Δ2, ΔTOTAL) WHEN THE SPRINGS ARE IN PARALLEL (Δ1≠ Δ2)

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Closed Coiled helical springs subjected to axial loads:

Definition:A spring may be defined as an elastic member whose primary function is to deflect or distort under the action of applied load; it recovers its original shape when load is released.

or

Springs are energy absorbing units whose function is to store energy and to restore it slowly or rapidly depending on the particular application.

Important types of springs are:

There are various types of springs such as

(i) helical spring: They are made of wire coiled into a helical form, the load being applied along the axis of the helix. In these type of springs the major stresses is torsional shear stress due to twisting. They are both used in tension and compression.

(ii) Spiral springs: They are made of flat strip of metal wound in the form of spiral and loaded in torsion.

In this the major stresses are tensile and compression due to bending.

(iv) Leaf springs:They are composed of flat bars of varying lengths clamped together so as to obtain greater efficiency . Leaf springs may be full elliptic, semi elliptic or cantilever types, In these type of springs the major stresses which come into picture are tensile & compressive.

These type of springs are used in the automobile suspension system.

Uses of springs :

(a) To apply forces and to control motions as in brakes and clutches.

(b) To measure forces as in spring balance.

(c) To store energy as in clock springs.

(d) To reduce the effect of shock or impact loading as in carriage springs.

(e) To change the vibrating characteristics of a member as inflexible mounting of motors.

Derivation of the Formula :

In order to derive a necessary formula which governs the behaviour of springs, consider a closed coiled spring subjected to an axial load W.

Let

W = axial load

D = mean coil diameter

d = diameter of spring wire

n = number of active coils

C = spring index = D / d For circular wires

l = length of spring wire

G = modulus of rigidity

x = deflection of spring

q = Angle of twist

when the spring is being subjected to an axial load to the wire of the spring gets be twisted like a shaft.

If q is the total angle of twist along the wire and x is the deflection of spring under the action of load W along the axis of the coil, so that

x = D / 2 . q

again l = p D n [ consider ,one half turn of a close coiled helical spring ]

Assumptions: (1) The Bending & shear effects may be neglected

             (2) For the purpose of derivation of formula, the helix angle is considered to be so small that it may be neglected.

Any one coil of a such a spring will be assumed to lie in a plane which is nearly ^^r to the axis of the spring. This requires that adjoining coils be close together. With this limitation, a section taken perpendicular to the axis the spring rod becomes nearly vertical. Hence to maintain equilibrium of a segment of the spring, only a shearing force V = F and Torque T = F. r are required at any X – section. In the analysis of springs it is customary to assume that the shearing stresses caused by the direct shear force is uniformly distributed and is negligible

so applying the torsion formula.

Using the torsion formula i.e

SPRING DEFLECTION

Spring striffness: The stiffness is defined as the load per unit deflection therefore

Shear stress

WAHL'S FACTOR :

In order to take into account the effect of direct shear and change in coil curvature a stress factor is defined, which is known as Wahl's factor

K = Wahl' s factor and is defined as

Where C = spring index

                 = D/d

if we take into account the Wahl's factor than the formula for the shear stress becomes

Strain Energy : The strain energy is defined as the energy which is stored within a material when the work has been done on the material.

In the case of a spring the strain energy would be due to bending and the strain energy due to bending is given by the expansion

Example: A close coiled helical spring is to carry a load of 5000N with a deflection of 50 mm and a maximum shearing stress of 400 N/mm² .if the number of active turns or active coils is 8.Estimate the following:

(i) wire diameter

(ii) mean coil diameter

(iii) weight of the spring.

Assume G = 83,000 N/mm² ; r = 7700 kg/m³

solution :

(i) for wire diametre if W is the axial load, then

Futher, deflection is given as

Therefore,

D = .0314 x (13.317)³mm

    =74.15mm

D = 74.15 mm

Weight

Close – coiled helical spring subjected to axial torque T or axial couple.

In this case the material of the spring is subjected to pure bending which tends to reduce Radius R of the coils. In this case the bending moment is constant through out the spring and is equal to the applied axial Torque T. The stresses i.e. maximum bending stress may thus be determined from the bending theory.

Deflection or wind – up angle:

Under the action of an axial torque the deflection of the spring becomes the “wind – up” angle of the spring which is the angle through which one end turns relative to the other. This will be equal to the total change of slope along the wire, according to area – moment theorem

Springs in Series:If two springs of different stiffness are joined endon and carry a common load W, they are said to be connected in series and the combined stiffness and deflection are given by the following equation.

Springs in parallel: If the two spring are joined in such a way that they have a common deflection ‘x' ; then they are said to be connected in parallel.In this care the load carried is shared between the two springs and total load W = W₁ + W₂

edu-spring

INTRODUCTION

A helical spring is a spiral wound wire with a constant coil diameter and uniform pitch.   The most common form of helical spring is the compression spring but tension springs are also widely used. .   Helical springs are generally made from round wire... it is comparatively rare for springs to be made from square or rectangular sections.  The strength of the steel used is one of the most important criteria to consider in designing springs.  Most helical springs are mass produced by specialists organisations.  It is not recommended that springs are made specifically for applications if off-the-shelf springs can be obtained to the job.

Note: Excelcals has produced a set of excel based calculations which contain much of the content found on this page. Excelcalcs - Helical springs

Compression Springs

Tension Springs

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Nomenclature

C = Spring Index D/d d = wire diameter (m) D = Spring diameter = (Di+Do)/2 (m) Di = Spring inside diameter (m) Do = Spring outside diameter (m) Dil = Spring inside diameter (loaded ) (m) E = Young's Modulus (N/m2) F = Axial Force (N) Fi = Initial Axial Force (N)      (close coiled tension spring) G = Modulus of Rigidity (N/m2) K d = Traverse Shear Factor = (C + 0,5)/C K W = Wahl Factor = (4C-1)/(4C-4)+ (0,615/C) L = length (m)

L 0 = Free Length (m) L s = Solid Length (m) n t = Total number of coils n = Number of active coils p = pitch (m) y = distance from neutral axis to outer fibre of wire (m) τ = shear stress (N/m2) τ i = initial spring stress (N/m2) τ max = Max shear stress (N/m2) θ = Deflection (radians) δ = linear deflection (mm)

Note: metres (m) have been shown as the units of length in all of the variables above for consistency.   In most practical calculations milli-metres will be more convenient.

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Spring Index

The spring index (C) for helical springs in a measure of coil curvature ..

For most helical springs C is between 3 and 12

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Spring Rate

Generally springs are designed to have a deflection proportional to the applied load (or torque -for torsion springs).   The "Spring Rate" is the Load per unit deflection.... Rate (N/mm) = F(N) / δ _e(deflection=mm)

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Spring Stress Values

For General purpose springs a maximum stress value of 40% of the steel tensile stress may be used. However the stress levels are related to the duty and material condition (ref to relevant Code/standard). Reference Webpage Spring Materials

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Compression Springs- Formulae

a)   Stress

A typical compression spring is shown below

Consider a compression spring under an axial force F.   If a section through a single wire is taken it can be seen that, to maintain equilibrium of forces, the wire is transmits a pure shear load F and also to a torque of Fr.  

The stress in the wire due to the applied load =

This equation is simplified by using a traverse shear distribution factor K _d = (C+0,5)/C.... The above equation now becomes.

The curvature of the helical spring actually results in higher shear stresses on the inner surfaces of the spring than indicated by the formula above.  A curvature correction factor has been determined ( attributed to A.M.Wahl). This (Wahl) factor K _w is shown as follows.

This factor includes the traverse shear distribution factor K _d.. The formula for maximum shear stress now becomes.

A table relating K_W to C is provided below

C	3	4	5	6	7	8	9	10	11	12	13	14	15	16
Kw	1,58	1,4	1,31	1,25	1,21	1,18	1,16	1,14	1,13	1,12	1,11	1,1	1,1	1,09

b)   Deflection

The spring axial deflection is obtained as follows.

The force deflection relationship is most conventiently obtained using Castigliano's theorem. Which is stated as ... When forces act on elastic systems subject to small displacements, the displacement corresponding to any force collinear with the force is equal to the partial derivative to the total strain energy with respect to that force.

For the helical spring the strain energy includes that due to shear and that due to torsion.
Referring to notes on strain energy Strain Energy

Replacing T= FD/2, l = πDn, A = πd² /4 The formula becomes.

Using Castiglianos theorem to find the total strain energy....

Substituting the spring index C for D/d The formula becomes....

In practice the term (1 + 0,5/C²) which approximates to 1 can be ignored

c)  Spring Rate

The spring rate = Axial Force /Axial deflection

In practice the term (C² /(C² + 0,5)) which approximates to 1 can be ignored

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Compression Spring End Designs

The figure below shows various end designs with different handing.   Each end design can be associated with any end design.  The plain ends are not desirable for springs which are highly loaded or for precise duties.

The table below shows some equations affected by the end designs...

Note: The results from these equations is not necessarily integers and the equations are not accurate.   The springmaking process involves a degree of variation...

Term	Plain	Plain and Ground	Closed	Closed and Ground
End Coils (n e )	0	1	2	2
Total Coils (n t )	n	n+1	n+2	n+2
Free Length (L 0 )	pn+d	p(n+1)	pn +3d	pn +2d
Solid Length (L s )	d(n t +1)	dn t	d(n t +1	dn t
Pitch(p )	(L 0-d)/n	L 0/(n +1)	(L 0-3d)/n	(L 0-2d)/n

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Helical Extension Springs

The formulae provided for the compression springs generally also apply to extension springs.

An important design consideration for helical extensions springs is the shape of the ends which transfers the load to the the spring body.  These must be designed to transfer the load with minimum local stress concentration values caused by sharp bends.   The figures below show some end designs.. The third design C) design has relatively low stress concentration factors.

Extension Spring Initial Tension

An Extension spring is sometimes tightly wound such that it is prestressed with an initial stress τ _i . This results in the spring having a property of an initial tension which must be exceeded before any deflection can take place.   When the load exceeds the initial tension the spring behaves according the the formulae above.  This relationship is illustrated in the figure below

>

The initial tension load can be calculated from the formula.... T _i = π τ _i d ³/ ( 8 D)

Best range of of Initial Stress (τ _i) for a spring related to the Spring Index C = (D/d)

C = D/d	Best Initial Tension Stress range = τ i
	(N/mm 2 )
3	140	205
4	120	185
5	110	165
6	95	150
7	90	140
8	80	125
9	70	110
10	60	100
11	55	90
12	45	85
13	40	75
14	35	65
15	30	60
16	25	55

If the coils in a tension spring are not tightly wound, there is no initial tension and the relevant equations are identical to those for the spring under compression as identified above.

The equations for tension springs with initial tension are provided below

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Helical Compression Springs (Rectangular Wire)

Spring Rate and Stress

Rate (N/mm) = K 2 G b t 3/ (n D 3)

Stress (N/mm 2) = K W .K 1 F D /( b t 2 )

D = Mean Diameter of spring(mm) b = Largest section dimension(mm) t = Smallest Section dimension(mm) n = Number of Active turns F = Axial Force on Spring K 1 = Shape Factor (see table) K 2 = Shape Factor (see table) K W = Wahl Factor (see table) C = Spring Index = D/(radial dimension = b or t)

b/t	1.0	1.5	1.75	2.0	2.5	3.0	4.0	6.0	8.0	10.0
K 1	2.41	2.16	2.09	2.04	1.94	1.87	1.77	1.67	1.63	1.60
K 2	0.18	0.25	0.272	0.292	0.317	0.335	0.385	0.381	0.391	0.399

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Conical Helical Compression Springs

These are helical springs with coils progressively change in diameter to give increasing stiffness with increasing load.  This type of spring has the advantage that its compressed height can be relatively small.  A major user of conical springs is the upholstery industry for beds and settees.

D1 = Smaller Diameter D2 = Larger Diameter

Allowable Force on Spring...
F_a = allowable force (N)..τ = allowable shear stress (N/m²)

Stiffness of Spring...