A helical compression spring is made with oil-tempered wire with wire diameter of 0.2 in, mean coil diameter of 2 in, a total of 12 coils, a free length of 5 in, with squared ends. (a) Find the solid length. (b) Find the force necessary to deflect the spring to its solid length. (c) Find the factor of safety guarding against yielding when the spring is compressed to its solid length.

a. Solid length Ls = 2.6 in

b. Force necessary for deflection Fs = 67.2Ibf

Factor of safety FOS = 2.04

Explanation:

Given details

Oil-tempered wire,

d = 0.2 in,

D = 2 in,

n = 12 coils,

Lo = 5 in

(a) Find the solid length

Ls = d (n + 1)

= 0.2 (12 + 1) = 2.6 in Ans

(b) Find the force necessary to deflect the spring to its solid length.

N = n - 2 = 12 - 2 = 10 coils

Take G = 11.2 Mpsi

K = (d^4*G) / (8D^3N)

K = (0.2^4*11.2) / (8*2^3*10) = 28Ibf/in

Fs = k*Ys = k (Lo - Ls)

= 28 (5 - 2.6) = 67.2 lbf Ans.

c) Find the factor of safety guarding against yielding when the spring is compressed to its solid length.

For C = D/d = 2/0.2 = 10

Kb = (4C + 2) / (4C - 3)

= (4*10 + 2) / (4*10 - 3) = 1.135

Tau ts = Kb { (8FD) / (Πd^3) }

= 1.135 { (8*67.2*2) / (Π*2^3) }

= 48.56 * 10^6 psi

Let m = 0.187,

A = 147 kpsi. inm^3

Sut = A/d^3 = 147/0.2^3 = 198.6 kpsi

Ssy = 0.50 Sut

= 0.50 (198.6) = 99.3 kpsi

FOS = Ssy/ts

= 99.3/48.56 = 2.04 Ans.