Determine the deflection of the spring:
A close coiled helical spring deflects 25 mm under a certain axial load. Determine the deflection of the second spring under the similar load if the effective length of the wire is same but the diameter of coils is 20% greater and that of the wire is 10% greater.
Solution
Δ= 64 W R^{3} n/ Gd ^{4}
R_{2} = 1.20 R_{1}, d_{2} = 1.1 d_{1}
l_{1} = l_{2}
G and W are same for two springs.
If we call two springs 1 and 2 then they contain the same length but different coil radius and number of coils
∴ l_{1} = l_{2} or 2π R_{1} n_{1} = 2π R_{2} n_{2}
But R_{2} = 1.2 R_{1} (20% greater)
∴ R_{2} n_{1} = 1.2 R_{1 }n_{2} or n_{1} / n_{2} = 1.2
Take the ratio of deflections of two springs
( Δ_{2}/25 ) = 1.20 R_{1}/R_{1})^{3} (1/1.20) (d_{1}/1.1d_{1})^{4} = ((1.2)^{2}/(1.2)). (1/1/1)^{4}= 0.984
∴ Δ_{2 } = 0.984 × 25 = 24.59 mm