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.
KBOD = 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) / (∏D2Na) √Eg / ρ; for steel = (2 x 105d) / D2Na metric
n = d / (8∏D2Na) √Eg / ρ; for steel = 8040d / D2Na English
and with both ends fixed:
n = (2.5 x 103) / (∏D2Na) d √Eg / ρ; for steel = (4 x 105d) / D2Na metric
n = d / (4∏D2Na) √Eg / ρ; for steel = 16080d / D2Na 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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