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### Helical Torsion Spring Reaction End Design Calculator and Equations

Helical Torsion Spring Reaction End Design Calculator and Equations

Frequently, the limiting stress value in helical torsion springs is the stress value in the ends. When a helical torsion spring has an eye or bent off end as shown in Figure 1, the stress at the inside of the bend is a tensile stress. The sharp curvature causes the neutral axis to move inward toward the center of the curvature and the tensile stress becomes that of a cantilever multiplied by a constant (K).

Preview Helical Torsion Spring Reaction End Design Calculator

The formula for determining the stress in the bend of the eye in Figure 1 is:

Eq. 1

$S}_{b}=\frac{32PRK}{\pi {d}^{3}$R = mean radius of eye, in

Eq. 2

$R}_{i}=\frac{{I}_{d}+d}{2$Eq. 3

$R}_{o}=\frac{{O}_{d}+d}{2$Eq. 3

$K=\frac{4{C}^{2}-C-1}{4C(C-1)}$Figure 1, Typical Hook End

Where

P = load

R = mean radius of hook

d = diameter of wire or side of square

D = mean coil diameter

C = spring index = D / d

K =
Stress correlation factor for curvature

R_{1} = mean inside radius of hook

R_{o} = mean outside radius of hook

- Bell Helicopter Structural Design Manual, 1977

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