Machine Design: Design of Coil Springs

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