In this paper, finite element method is implemented to model stranded-wire helical springs under different loading conditions. Finite element results are coupled with multiaxial fatigue criteria such as Fatemi–Socie and Kandil–Brown–Miller together with a uniaxial fatigue criterion, Coffin–Manson, to predict fatigue life of the stranded-wire helical springs. It is shown that due to damping effects between wires, stranded-wire helical springs have longer fatigue life compared to their equivalent single-wire helical springs at a similar condition. It is also demonstrated that fatigue life is longer for loadings with higher initial displacement of spring head. As practical examples, fatigue life of stranded-wire helical springs with 9 and 15 wires are estimated and compared. It is shown that the spring with 15 wires gives longer fatigue life. It is also observed that Kandil–Brown–Miller and Fatemi–Socie criteria give the least and the highest fatigue life prediction, respectively.
AmiriMNaderiMKhonsariMM (2011) An experimental approach to evaluate the critical damage. International Journal of Damage Mechanics20: 89–112.
2.
BrownMWMillerKJ (1973) A theory for fatigue under multiaxial stress–strain conditions. Proceedings of Institution of Mechanical Engineers187: 745–755.
3.
ChenXXuSHuangD (1999) Critical plane–strain energy density criterion of multiaxial low-cycle fatigue life under non-proportional loading. Fracture of Engineering Materials and Structures22: 679–686.
4.
ClarkHH (1961) Stranded-wire Helical Springs, Spring Design and Application, 1st ed. New York: McGraw–Hill, pp. 92–96.
5.
CostelloGAPhillipsJW (1979) Static response of stranded wire helical springs. International Journal of Mechanical Sciences21: 171–178.
6.
CruzadoALeenSBUrcheguiMA (2013) Finite element simulation on fretting wear and fatigue in thin steel wires. International Journal of Fatigue55: 7–21.
7.
Del Llano-VizcayaLRubio-GonzálezCMesmacqueG (2006) Multiaxial fatigue and failure analysis of helical compression springs. Engineering Failure Analysis13: 1303–1313.
8.
EyerciogluOWaltonDDeanTA (1997) Comparative bending fatigue strength of precision forged spur gears. Proceedings of Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science211: 293–299.
9.
FatemiASocieDF (1988) A critical plane approach to multiaxial fatigue damage including out-of-phase loading. Fracture of Engineering Materials and Structures11: 149–165.
10.
GlinkaGShenGPlumtreeA (1995) A multiaxial fatigue strain energy density parameter related to the critical plane. Fracture of Engineering Materials and Structures18: 37–46.
11.
HanumannaDNarayananSKrishnamurthyS (2001) Bending fatigue testing of gear teeth under random loading. Proceedings of Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science215: 773–784.
12.
JanMMGaenserHPEichlsedeW (2012) Prediction of the low cycle fatigue regime of the S–N curve with application to an aluminium alloy. Proceedings of Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science226: 1198–1209.
13.
KandilFABrownMWMillerKJ (1982) Biaxial Low-cycle Fatigue Fracture of 316 Stainless Steel at Elevated Temperatures, 1st ed. London: The Metals Society, pp. 203–210.
14.
KimKSParkJC (1999) Shear strain based multiaxial fatigue parameters applied to variable amplitude loading. International Journal of Fatigue21: 475–483.
15.
KimMHKangSW (2008) Testing and analysis of fatigue behaviour in edge details: A comparative study using hot spot and structural stresses. Proceedings of Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science222: 2351–2363.
16.
KunohTLeechCM (1985) Curvature effects on contact position of wire strands. International Journal of Mechanical Sciences27: 465–470.
17.
LeeHJinOMallS (2004) Fretting fatigue behavior of Ti–6Al–4V with dissimilar mating materials. International Journal of Fatigue26: 393–402.
18.
LiJZhangZPSunQ (2009) A new multiaxial fatigue damage model for various metallic materials under the combination of tension and torsion loadings. International Journal of Fatigue31: 776–781.
19.
McDiarmidDL (1994) A shear stress based critical–plane criterion of multiaxial fatigue failure for design and life prediction. Fracture of Engineering Materials and Structures17: 1475–1484.
20.
MachaESonsinoCM (1999) Energy criteria of multiaxial fatigue failure. Fatigue and Fracture of Engineering Materials and Structures22: 1053–1070.
21.
MinJJWangSL (2007) Analysis on dynamic calculation of stranded-wire helical spring. Chinese Journal of Mechanical Engineering43: 199–203.
22.
MuralidharanUMansonSS (1988) A modified universal slops equation for estimation of fatigue. Journal of Engineering Materials and Technology110: 55–58.
23.
NaiduNKSundara RamanSG (2005) Effect of contact pressure on fretting fatigue behavior of Al–Mg–Si alloy AA6061. International Journal of Fatigue27: 283–291.
24.
Navid ChakherlouTAbazadehB (2011) Estimation of fatigue life for plates including pre-treated fastener holes using different multiaxial fatigue criteria. International Journal of Fatigue33: 343–353.
25.
PanWFHungCYChenLL (1999) Fatigue life estimation under multiaxial loading. International Journal of Fatigue21: 3–10.
26.
PapadopoulosIVDavoliPGorlaC (1997) A comparative study of multiaxial high-cycle fatigue criteria for metals. International Journal of Fatigue19: 219–235.
27.
PengYWangSZhouJ (2012) Structural design, numerical simulation and control system of a machine tool for stranded wire helical springs. Journal of Manufacturing Systems31: 34–41.
28.
PhillipsJWCostelloGA (1979) General axial response of stranded wire helical springs. International Journal of Non-Linear Mechanics14: 247–257.
29.
ShariyatM (2010) New multiaxial HCF criteria based on instantaneous fatigue damage tracing in components with complicated geometries and random non-proportional loading conditions. International Journal of Damage Mechanics19: 659–690.
30.
Varvani-FarahaniA (2000) A new energy-critical plane parameter for fatigue life assessment of various metallic materials subjected to in-phase and out-of-phase multiaxial fatigue loading conditions. International Journal of Fatigue22: 295–305.
31.
WangCHBrownMW (1993) A path-independent parameter for fatigue under proportional and non-proportional loading. Fracture of Engineering Materials and Structures16: 1285–1298.
32.
WangSLeiSZhouJ (2010) Mathematical model for determination of strand twist angle and diameter in stranded-wire helical springs. Journal of Mechanical Science and Technology24: 1203–1210.
33.
WangSLZhouJKangL (2008) Dynamic tension of stranded-wire helical spring during reeling. Chinese Journal of Mechanical Engineering44: 36–42.
34.
WangYYYaoWX (2004) Evaluation and comparison of several multiaxial fatigue criteria. International Journal of Fatigue26: 17–25.
35.
WangYYYaoWX (2006) A multiaxial fatigue criterion for various metallic materials under proportional and non-proportional loading. International Journal of Fatigue28: 401–408.
36.
YouBRLeeSB (1996) A critical review on multiaxial fatigue assessments of metals. International Journal of Fatigue18: 235–244.
37.
ZhangYHLiuHHWangDC (1999) Spring Handbook, 1st ed. Beijing: Mechanical industry, pp. 312–329.
