When the wire in a compression spring is stressed in torsion, the torsional stress is expressed as:
S = (8PD / ∏d3) KW
Bending stresses are present but can be ignored except when the pitch angle is greater than 15˚ and deflection of each coil is greater than D/4. Under elastic conditions, torsional stress is not uniform around the wire cross section due to coil curvature and a direct shear load. Maximum stress occurs at the inner surfaces of the compression spring and is computed using a stress correction factor. The most widely used stress correction factor KW1 is attributed to Wahl. It is shown below in this formula and in the animation.
KW1 = ((4C – 1) / (4C – 4)) + (0.615 / C)
In some circumstances after yielding occurs, resultant compression spring stresses are distributed more uniformly around the cross section. Then, a stress correction factor KW2 which accounts only for the direct shear component is used.
KW2 = 1 + (0.5/C)
In other circumstances, such a static loading at elevated temperatures, stress distribution tends to become uniform around the cross section and can best be estimated by using no correction factor. Use of different stress correction factors can lead to confusion. In published data, it is essential to know which stress correction factors were used. (The stress correction factor used by a designer must be the same as that used to develop the data.)
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