Open coiled helical spring, Mechanical Engineering

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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 R³ n / d ⁴cos α)( (cos² α/G)+(2 sin ² α /E))

= K/ cos α[cos² 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, Δ₂ = K × 0.0125

% Error = ((Δ₁ - Δ₂) / Δ1 )× 100

= (0.0147 - 0.0125/0.0147) × 100 = 14.96%

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