Open coiled helical spring:
In an open coiled helical spring along with α = 38^{o}, if the inclination of the coil is ignored, determine the percentage by which the axial extension is under estimated.
E = 200 GPa, G = 80 GPa.
Solution
Δ= (64 W R^{3} n / d ^{4 }cos α)( (cos^{2} α/G)+(2 sin ^{2} α /E))
= K/ cos α[cos^{2} α/G +2 sin ^{2} α/E]
α= 38^{o} , Δ = K × (0.115/0.866) × 10^{- 4} = K × 0.0147
If α is neglected,
α= 0, Δ_{2} = K × 0.0125
% Error = ((Δ_{1} - Δ_{2 }) / Δ1 )× 100
= (0.0147 - 0.0125/0.0147) × 100 = 14.96%