# Machine Design of Coil Springs

Indian Institute of Technology Madras

Design of Coil Springs

The design of a new spring involves the following considerations:-Space into which the spring must fit and operate. -Values of working forces and deflections. -Accuracy and reliability needed

Design Consideration

The primary consideration in the design of the coil springs are that the induced stresses are below the permissible limits while subjected to or exerting the external force F capable of providing the needed deflection or maintaining the spring rate desired. Stresses In Helical Springs

The flexing of a helical spring creates

torsion in the wire and the force applied

induces a direct stress. The maximum

stress in the wire may be computed by

super position. The result is:

r

max

T t F

J A

= + +

Replacing the terms,

FD d d4 d4 T , r , J and A=

2 2 32 4

π π

= = =

D

F 2

T

F

F

d

T

F

Figure 4.10

Machine Design II Prof. K.Gopinath & Prof. M.M.Mayuram

Indian Institute of Technology Madras

And re-arranging,

K 8FD or K 8FC s 3 s 2 d d

τ = τ =

π π

Where Ks is the shear-stress correction

factor and is defined by the equation:

K 2C 1 s 2C

+

=

(c) combined direct

shear and torsional stress

(a) direct shear

stress distribution

across section

(b) Torsional shear

stress distribution

Figure 4.11

Machine Design II Prof. K.Gopinath & Prof. M.M.Mayuram

Indian Institute of Technology Madras

Curvature Effect

The curvature of the wire increases the

stress on the inside of the spring, an

effect very similar to stress

concentration but due to shifting of the

neutral axis away from the geometric

center, as could be observed in curved

beams. Consequently the stress on the

inside surface of the wire of the spring,

increases but decreases it only slightly

on the outside. The curvature stress is

highly localized that it is very important

only fatigue if is present.

(c) combined direct

(d) effects of stress

concentration

shear and torsional stress

Figure 4.12

This effect can be neglected for static loading, because local yielding with the first application of the load will relieve it. The combined effect of direct shear and curvature correction is accounted by Wahl’s correction factor and is given as: Whal’s correction factor

The combined effect of direct shear and curvature correction is accounted by Wahl’s correction factor and is given as:

K 4C 1 0.615 w 4C 4 C

−

= +

−

Machine Design II Prof. K.Gopinath & Prof. M.M.Mayuram

Indian Institute of Technology Madras

Pre-Setting Or Set Removal

Pre-setting or set removal is a process used in the manufacture of compression springs to induce useful residual stresses. It is done by making the spring longer than needed and compressing it to its solid height. This operation sets the spring to the required final length and, since the torsional yield strength has been exceeded, induces residual stresses opposite in direction to those induced in service. Thus, this set removal increases the strength of the springs and so is especially useful when the spring is used for energy storage purposes. However, this should not be used when springs are subjected to fatigue. Deflection and Stiffness of the spring

A systems strain energy is related to its force deflection behaviour and using the Castigliano’s theorem the deflection of a spring can be estimated using the strain energy stored in it. The total strain energy for a helical spring is composed of torsional component and a shear component. The shear component is quite negligible, and the final equation is,

T2 l F2 l u

2G J 2A G

= +

The spring rate and hence,

D d4 2 T F ; 1 .D.N; J . and A

2 32

d

4

π

= =π =π =

4 F 2 D 3 N F 2D N U

G. d 4 G d 2

= +

Machine Design II Prof. K.Gopinath & Prof. M.M.Mayuram

Indian Institute of Technology Madras

Where N is the number of active coils. The deflection in the spring, using Castigliano’s theorem

U 8FD 3N 4FDN y

F Gd 4...

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