Helical Torsion Spring Reaction End Design Calculator and Equations

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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).

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

Eq. 1

S_{b} = \frac{32 P R K}{π 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}{4 C (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
R₁ = mean inside radius of hook
R_o = mean outside radius of hook

Bell Helicopter Structural Design Manual, 1977