Determine the diameter of wire - close coiled helical spring, Mechanical Engineering

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

Posted Date: 1/21/2013 1:12:56 AM | Location : United States







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