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.
Δ= 64 W R3 n/ Gd 4
R2 = 1.20 R1, d2 = 1.1 d1
l1 = l2
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
∴ l1 = l2 or 2π R1 n1 = 2π R2 n2
But R2 = 1.2 R1 (20% greater)
∴ R2 n1 = 1.2 R1 n2 or n1 / n2 = 1.2
Take the ratio of deflections of two springs
( Δ2/25 ) = 1.20 R1/R1)3 (1/1.20) (d1/1.1d1)4 = ((1.2)2/(1.2)). (1/1/1)4= 0.984
∴ Δ2 = 0.984 × 25 = 24.59 mm