Torsion Spring Ends

• Torsion Spring Design Resources – Custom Spring End Configurations

In designing ends, it is important to recall that bends, loaded to decrease their radius of curvature, have favorable residual stresses. They can operate at higher applied stress levels than bends that increase the radius by loading. Frequently, spring performance is limited because the sharply bent ends have greater stress than the body.

The equation:

K_BOD = 4C + 1 / 4C + 4

is generally employed to determine maximum bending stress in the ends. Torsion springs are subject to surging and resonance phenomena. The natural frequency (n) for a torsion spring with one end fixed is determined using the following equations:

n = (1.26 x 10³d) / (∏D²N_a) √Eg / ρ; for steel = (2 x 10⁵d) / D²N_a metric

n = d / (8∏D²N_a) √Eg / ρ; for steel = 8040d / D²N_a English

and with both ends fixed:

n = (2.5 x 10³) / (∏D²N_a) d √Eg / ρ; for steel = (4 x 10⁵d) / D²N_a metric

n = d / (4∏D²N_a) √Eg / ρ; for steel = 16080d / D²N_a English

To avoid or minimize resonance phenomena, the natural frequency must be much greater than the operating frequency and/or the spring should contain initial tension.

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