Determine the diameter of wire - close coiled helical spring:

A close coiled helical spring has to absorb 100 N-m of energy while compressed to 10 cm. The coil diameter is 10 times the wire diameter. The number of coils is 12. Determine the diameter of wire, mean radius & the maximum shear stress.

Take G = 80 GPa.

Solution

We know

U = (½) W Δ

∴          100 × 10³ = (1 /2 )× W × 100

∴          W = 2000 N

D = 10 d   or   R = 5 d

G = 80 GPa = 80 × 10³ MPa = 80 × 10³ N/mm²

Δ= 64 W R³ n/ Gd ⁴

∴          100 =6 4× 2000 × (5d ) ³ × 12 /  (80 × 10³ ) d ⁴

or         d = 24 mm

R = 5d = 5 × 24 = 120 mm

τ _max = 16 W R / π d ³

= 16 × 2000 × 120/ π (24)³  = 88.4 N/mm²