Stresses in helical spring with curvature effect
Let us look at a small section of a circular spring, as shown in the figure.
Suppose we hold the section b-c fixed and give a rotation to the section a-d in the anti-clockwise direction as indicated in the figure, then it is observed that line a-d rotates and it takes up another position, say a'-d'.
The inner length a-b being smaller compared to the outer length c-d, the shear strain yi at the inside of the spring will be more than the shear strain yo at the outside of the spring.
Hence, for a given wire diameter, a spring with smaller diameter will experience more difference of shear strain between outside surface and inside surface compared to its larger counterpart. This phenomenon is termed as curvature effect. So more is the spring index (C = D /d) the lesser will be the curvature effect.
For example, the suspensions in the railway carriages use helical springs. These springs have large wire diameter compared to the diameter of the spring itself.
In this case curvature effect will be predominantly high.
To take care of the curvature effect, the earlier equation for maximum shear stress in the spring wire is modified as,
Where, KW is Wahl correction factor, which takes care of both curvature effect and shear stress correction factor and is expressed as,