Design a helical valve spring for an operating load range of $600N$ to $1200N$. the compression at the maximum load is $25mm$. take the spring index 6 and permissible endurance shear stress for the spring material as $480Mpa$ and yield stress in shear is 960Mpa and $G = 80N/mm^2$.

Subject :- Machine Design -I

Topic :- Spring

Difficulty :- Medium

Given: P=600N to 1200N , $\delta$=25mm, C=6, $\tau$=480MPa, $\sigma_y$=960MPa, G=80 Kn/$mm^2$

1. Wire diameter(d):

$\tau=K\frac{8PC}{\pi d^2}$

$480=1.3105\frac{8(1200)(6)}{\pi d^2}$

$d=7.08=8mm$

1. Coil diameter(D):

$D=C*d=6*8=48mm$

1. No. of active coil(N):

$\delta=\frac{8PD^3N}{Gd^4}$

$25=\frac{8(1200-600)48^3N}{80000*8^4}$

$N=15.43=16 coils$

1. Total no. of coils($N_t$):

For, plain ends $N_t$=N; Plain end ground $N_t$=N-$\frac{1}{2}$; Square end $N_t$=N-1

We assume spring is square end, therefor $N_\gamma$d=148=112mm

1. Free length of spring:

Free length of spring=Solid length+Axial gap+$\delta$

But, axial gap = $(14-1)*0.5 = 6.5mm$

Free length of spring = $112+6.5+25 = 143.5 = 144mm$