FORMULAS FOR HELICAL EXTENSION SPRINGS FATIGUE DESIGN




Parameter Symbol Formula
Force amplitude Fa Force amplitude in spring during cycling loading
Midrange force Fm Midrange force in spring during cycling loading
Spring outer diameter OD Spring outer diameter
Spring inner diameter ID Spring inner diameter
Spring index C Spring Index
Spring index -1 C1 Spring index 1 in extension spring
Spring index -2 C2+ Spring index 2 in extension spring
Curvature correction factor for point A KA  Curvature correction factor at point A in extension spring
Stress correction factor for point B KB  Stress correction factor at point B in extension spring
Wahl factor Kw Wahl factor
Torsional rupture
strength
Ssu Torsional rupture strength in mechanical springs
Tensile stress amplitude at point A σA_a Tensile stress amplitude at point A
Midrange tensile stress at point A σA_m Midrange tensile stress at point A
Amplitude strength component for infinite life (Unpeened)-(Zimmerli Data) Ssa_zim Ssa = 241 MPa (35 kpsi)
Midrange strength component for infinite life (Unpeened)-(Zimmerli Data) Ssm_zim Ssa = 379 MPa (55 kpsi)
Shear endurance limit according to Gerber Sse_Gerber Shear endurance limit according to Gerber
Shear endurance limit according to Goodman Sse_Goodman Shear endurance limit according to Goodman
Endurance limit according to Gerber Se_Gerber Endurance limit according to Gerber
Endurance limit according to Goodman Se_Goodman Endurance limit according to Goodman
Factor of safety at point-A according to Gerber fosA_gerber Factor of safety at point-A according to Gerber in extension spring stress analysis
Factor of safety at point-A according to Goodman fosA_goodman Factor of safety at point-A according to Goodman in extension spring stress analysis
Factor of safety at point-B according to Goodman fosB_goodman Factor of safety at point-B according to Gerber in extension spring stress analysis
Factor of safety at point-B according to Goodman fosB_goodman Factor of safety at point-B according to Goodman in extension spring stress analysis
Factor of safety at spring body according to Gerber fosBody_gerber Factor of safety at spring body according to Gerber in extension spring stress analysis
Factor of safety at spring body according to Goodman fosBody_goodman Factor of safety at spring body according to Goodman in extension spring stress analysis

Note 1 : + Recommended practice is to make C2 greater than 4.



List of Parameters
Symbol Definition
Fmax Maximum cyclic force
Fmin Minimum cyclic force (preload)
D Spring mean diameter
d Wire diameter
Sut Ultimate tensile strength of material
Sr Allowable bending strength for the spring end for cycling loading

Reference: