Determine the deflection of the spring, Mechanical Engineering

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 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

2332_Determine the deflection of the spring.png

 ( 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

Posted Date: 1/21/2013 1:16:16 AM | Location : United States







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