Enhancement of fatigue life of multi-leaf spring by parameter optimization using RSM

Abstract

The experimental investigation to predict the effect of mechanical processing, strength reduction factors, design, geometric tolerances and material factors on the fatigue life of a leaf spring is costly and time-consuming process. A computer program based on the analytical approach has been developed in FORTRAN, for determination of the fatigue life of a leaf spring of a light commercial vehicle. It takes into account the effect of five factors namely overall strength reduction factor (processing), stiffness (design), span and width (geometry) and ultimate tensile strength (material) on the fatigue life of the leaf spring. The results of the program have been validated experimentally using a full-scale leaf spring testing machine. A mathematical model has also been developed using response surface methodology. The optimal sets of parameters yielding the maximum fatigue life are obtained using the desirability approach. The confirmatory experiments are carried out and the results indicate that the developed model is appropriate for determination of fatigue life within 5 % variation. The interaction effects of the factors affecting fatigue life have also been studied and the overall strength reduction factor is found to be the most significant one.

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Abbreviations

Ca :

No load assembly camber

E :

Young’s modulus of elasticity

N f :

No. of cycles to failure

Nfp :

Predicted fatigue life

ρ :

Density

µ :

Poisson’s ratio

S a :

Alternating stress

σ max :

Maximum stress

S e :

Endurance limit

S e :

Corrected endurance limit

S y :

Yield tensile strength

L:

Span

σ min :

Minimum stress

S m :

Mean Stress

S ae :

Equivalent alternating stress

S ut :

Ultimate tensile strength

K surface :

Surface factor

K load :

Load factor

K temp :

Temperature factor

K size :

Size factor

K reliability :

Reliability factor

S m :

Stress at 103 cycles

References

  1. 1.

    Landgraf RW, Francis RC, (1979) Material and processing effects on fatigue performance of leaf spring. SAE Technical Paper Series, 790407

  2. 2.

    Yamada Y, Watanabe Y (1985) An analysis of heavy duty truck ride. SAE Technical Paper Series, 852240

  3. 3.

    Numazaki I, Yamamoto E, Hamano T (1991) Analysis on the hysteresis loop of the leaf spring. SAE Technical Paper Series, 912715

  4. 4.

    Liu X, Chadda Y, (1993).Automated optimal design of a leaf spring. SAE Technical Paper Series, 933044

  5. 5.

    Konghui G (1991) Development of leaf spring kinematical model and its applications in improvement of truck braking and steering analysis. SAE Technical Paper Series, 912566

  6. 6.

    Fischer G, Streicher M, Grubisic V, (1998) Durability approval of leaf springs under operational loading. SAE Technical Paper Series, 982839

  7. 7.

    Soares E, De Carvalho D, Onusic H, Barreiro J et al (1999).Development of a test bench for static and dynamic tests of a spring leaf for the suspension of commercial vehicles. SAE Technical Paper Series, 01-2990

  8. 8.

    Shokrieh MM, Rezaei D (2003) Analysis and optimization of a composite leaf spring. Compos Struct 60(3):317–325. doi:10.1016/S0263-8223(02)00349-5

    Article  Google Scholar 

  9. 9.

    Sugiyama H, Shabana AA, Omar MA, Loh WY (2006) Development of nonlinear elastic leaf spring model for multibody vehicle systems. Comput Methods Appl Mech Eng 195(50–51):6925–6941. doi:10.1016/j.cma.2005.02.032

    Article  MATH  Google Scholar 

  10. 10.

    Yoo S, Park J, Lim J (2007) Fatigue strength evaluation for the leaf spring of commercial vehicle considering U bolt fixing force. SAE Tech Paper Ser. doi:10.4271/2007-01-0853

    Google Scholar 

  11. 11.

    Guo H, Hao C, Jing D, Wei L (2010) Optimal design and finite element analysis of few-leaf-spring. Int Conf Comp Mech Control Elect Eng. 303–306

  12. 12.

    Qin-man F 2011 Multi-objective optimization design for gradient stiffness leaf spring multi-objective optimization design for gradient stiffness leaf spring. Information and Computing (ICIC) pp. 354–357

  13. 13.

    Kanbolat A, Soner M, Karaagac M, Erdogus T (2011) Parabolic leaf spring optimization and fatigue strength evaluation on the base of road load data, endurance rig tests and non linear finite element analysis. In: SAE Technical Paper Series, 01-0438 (pp. 1–8). doi:10.4271/2011-01-0438

  14. 14.

    Gonzalez RA, Chacon JM, Donoso A, Gonzalez RAG (2011) Design of an adjustable-stiffness spring: mathematical modeling and simulation, fabrication and experimental validation. Mech Mach Theory 43(12):1970–1979

    Article  Google Scholar 

  15. 15.

    Refngah Ahmad F, SA N (2009) Fatigue life evaluation of two types of steel leaf springs. Int J Mech Mat Eng 4(2):136–140

    Google Scholar 

  16. 16.

    Zhuang WZ, Halford GR (2001) Investigation of residual stress relaxation under cyclic load. Int J Fatigue 23:31–37. doi:10.1016/S0142-1123(01)00132-3

    Article  Google Scholar 

  17. 17.

    Ekbote T, Sadashivappa KS, Abdul Budan D (2012) Optimal design and analysis of mono leaf composite spring by finite element analysis. Advances in Engineering, Science and Management (ICAESM), pp 41–46

    Google Scholar 

  18. 18.

    Singh Simran J, Gupta M (2013) Comparison of particle swarm optimization and simulated annealing for weight optimization of composite leaf spring. Int J Comput Eng Manag 16(4):162–169

  19. 19.

    Arora Vinkel K, Bhushan G, Aggarwal ML (2014) Effect of assembly stresses on fatigue life of symmetrical 65Si7 leaf springs. Int Scholarly Res Not 762561:10

  20. 20.

    Arora Vinkel K, Bhushan G, Aggarwal ML (2014) Fatigue life assessment of 65si7 leaf springs: a comparative study. Int Scholarly Res Not 2014 607272:11

  21. 21.

    Park JH, Kim KJ, Lee JW, Yoon J (2015) Light-weight design of automotive suspension link based on design of experiment. Int J Automotive Technol 16(1):66–71

    Google Scholar 

  22. 22.

    Sendra Juan M, Bosque Pescarolo Stefania, Ana Rodriguez Luis Cuadros Campana, Garcia M, Lopez Eva M (2001) Optimizing analytical methods using sequential response surface methodology. Application to pararosaniline determination of formaldehyde. Fresenius J Anal Chem 369:715–718

    Article  Google Scholar 

  23. 23.

    Derringer G, Suich R (1980) Simultaneous optimization of several response variables. J Quality Technol 12(9):214–219

    Google Scholar 

  24. 24.

    Norton RL (2001) Machine design—an integrated approach. 2nd ed. pp. 366–383, (2 ed.). Pearson Education, Asia

  25. 25.

    IS 1135.(1995). Springs—Leaf Springs Assembly for Automobiles

  26. 26.

    Eudd JH (1995) Spring Design Manual-Design and application of leaf springs HS-744, AE-11. Society of Automotive Engineers

  27. 27.

    Myer RH, Montgomery DC (1995) Response surface methodology. Wiley, New York

    Google Scholar 

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Acknowledgments

The authors would like to acknowledge Mr. P S Chawla and the leaf springs testing division of Friends Auto (India) Ltd, whose unconditional support have made this project successful.

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Correspondence to Vinkel Kumar Arora.

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Technical Editor: Fernando Antonio Forcellini.

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Arora, V.K., Bhushan, G. & Aggarwal, M.L. Enhancement of fatigue life of multi-leaf spring by parameter optimization using RSM. J Braz. Soc. Mech. Sci. Eng. 39, 1333–1349 (2017). https://doi.org/10.1007/s40430-016-0638-z

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Keywords

  • Leaf spring
  • Fatigue life
  • Design factor
  • Geometry factor
  • Strength reduction factor
  • Material factor