find out the proof load in close coiled helical

Question

Find out the proof load in close coiled helical spring:

A close coiled helical spring is built of 6 mm diameter wire. The coil diameter is equal to 80 mm, number of coil is 10. If the maximum stress in the spring is not to exceed 180 MPa, find out

1. the proof load,

2. the extension of spring.

Take G = 80 GPa.

Solution

Proof load is the load equivalent to maximum shearing stress in spring wire.

d = 6 mm, D = 80 mm, R = D/2 = 40 mm , n = 10, τ_max = 180 N/mm² , G = 80 GPa

Check

 d /2 D  = 6/ (2 × 180) = 0.0167

Therefore,       K = 1

 (a)       Proof load, W = τ_max . π d ³ /16 R

= 180 × (π (6)³/ (16 × 40) = 191 N

 (b)       Extension, Δ= 64 W R³ n/ Gd ⁴

=64 × 191 × 40³ × 10 / 80 × 10³ × 6⁴

= 75.5 mm