Deflection of helical spring of circular cross section wire
Total length of wire = length of one coil x number of active coils
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.
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,