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


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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Ca :

No load assembly camber

E :

Young’s modulus of elasticity

N f :

No. of cycles to failure

Nfp :

Predicted fatigue life

ρ :


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



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


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