FORMULAS FOR COIL COMPRESSION SPRING 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
Whal factor Kw Wahl factor
Shear stress amplitude τa Spring shear stress amplitude in cycling loading
Midrange shear stress τm Spring midrange shear stress in cycling loading
Torsional rupture
strength
Ssu Torsional rupture strength in mechanical springs
Slope line r Slope line in cyclic loading of springs
Amplitude strength component for infinite life (Shot peened)-(Zimmerli Data) Ssa_zim Ssa = 398 MPa (57.5 kpsi)
Midrange strength component for infinite life (Shot peened)-(Zimmerli Data) Ssm_zim Ssa = 534 MPa (77.5 kpsi)
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
(with Zimmerli Data)
Sse Gerber ordinate intercept with Zimmerli data
Shear stress amplitude limit (According to Gerber failure criteria) Ssa Shear stress amplitude limit for Gerber failure criteria
Shear endurance limit according to Goodman
 (with Zimmerli Data)
Sse Goodman ordinate intercept with Zimmerli data
Shear stress amplitude limit (According to Goodman failure criteria) Ssa Shear stress amplitude limit for Goodman failure criteria
Shear stress amplitude limit (According to Sines failure criteria) Ssa Shear stress amplitude limit for Sines failure criteria
Factor of safety against fatigue fosf Factor of safety against fatigue loading in spring design



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

Reference: