12
Research Article Fatigue Life Assessment of 65Si7 Leaf Springs: A Comparative Study Vinkel Kumar Arora, 1 Gian Bhushan, 2 and M. L. Aggarwal 3 1 Department of Engineering, NIFTEM, HSIIDC, Kundli, Haryana 131028, India 2 Department of Mechanical Engineering, National Institute of Technology, Kurukshetra, Haryana 136019, India 3 Department of Mechanical Engineering, YMCA University of Science & Technology, Faridabad, Haryana 121006, India Correspondence should be addressed to Vinkel Kumar Arora; [email protected] Received 1 July 2014; Revised 28 August 2014; Accepted 28 August 2014; Published 29 October 2014 Academic Editor: T. Y. Kam Copyright © 2014 Vinkel Kumar Arora et al. is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. e experimental fatigue life prediction of leaf springs is a time consuming process. e engineers working in the field of leaf springs always face a challenge to formulate alternate methods of fatigue life assessment. e work presented in this paper provides alternate methods for fatigue life assessment of leaf springs. A 65Si7 light commercial vehicle leaf spring is chosen for this study. e experimental fatigue life and load rate are determined on a full scale leaf spring testing machine. Four alternate methods of fatigue life assessment have been depicted. Firstly by SAE spring design manual approach the fatigue test stroke is established and by the intersection of maximum and initial stress the fatigue life is predicted. e second method constitutes a graphical method based on modified Goodman’s criteria. In the third method codes are written in FORTRAN for fatigue life assessment based on analytical technique. e fourth method consists of computer aided engineering tools. e CAD model of the leaf spring has been prepared in solid works and analyzed using ANSYS. Using CAE tools, ideal type of contact and meshing elements have been proposed. e method which provides fatigue life closer to experimental value and consumes less time is suggested. 1. Introduction In actual practice, the load rate and fatigue life (under specified stress range) are determined experimentally. e process of experimental fatigue life prediction of leaf springs is a time consuming process; that is, for the fatigue life of 100000 cycles, the experimental procedure will consume approximately 2-3 days. For the assessment of experimental fatigue life, a full scale leaf spring testing machine is required. e leaf spring is mounted in the machines simulating the condition of the vehicle, the fatigue test stroke is deter- mined, and the leaf spring is tested from maximum stress to minimum or initial stress. As there are a number of factors responsible for fatigue life enhancement like material processing, loading, surface, size, and environmental factor, it is mandatory that the fatigue life should be determined by considering these factors. e engineers working in the field of leaf springs design are facing a challenge to devise a fatigue life assessment method which is reliable and consumes less time. Although the analytical or simulation techniques pro- vide an approximate fatigue life, the validation of these results through experimental testing is mandatory. Saelem et al. [1] simulated a leaf springs model. An experimental leaf springs model was verified by using a leaf springs test rig that could measure vertical static deflection of leaf springs under static loading condition. e results showed a nonlinear relationship between the applied load and the leaf springs deflection for both directions of loading, in form of a hysteresis loop. Refngah et al. [2] worked on the possibility and capability of replacing the multileaf with the parabolic spring in suspension system. He performed the finite element analysis to analyze the stress distribution and behavior of both the springs. en, time histories service loading data was analyzed and damage area was simulated to predict the fatigue life of the components. e simulation results are compared and validated with the experimental results. Fuentes et al. [3] studied the origin of premature failure analysis procedures, including examining the leaf spring Hindawi Publishing Corporation International Scholarly Research Notices Volume 2014, Article ID 607272, 11 pages http://dx.doi.org/10.1155/2014/607272

Fatigue Life Assessment of 65Si7 Leaf Springs: A Comparative Study

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Page 1: Fatigue Life Assessment of 65Si7 Leaf Springs: A Comparative Study

Research ArticleFatigue Life Assessment of 65Si7 Leaf SpringsA Comparative Study

Vinkel Kumar Arora1 Gian Bhushan2 and M L Aggarwal3

1 Department of Engineering NIFTEM HSIIDC Kundli Haryana 131028 India2Department of Mechanical Engineering National Institute of Technology Kurukshetra Haryana 136019 India3 Department of Mechanical Engineering YMCA University of Science amp Technology Faridabad Haryana 121006 India

Correspondence should be addressed to Vinkel Kumar Arora vinkelaroragmailcom

Received 1 July 2014 Revised 28 August 2014 Accepted 28 August 2014 Published 29 October 2014

Academic Editor T Y Kam

Copyright copy 2014 Vinkel Kumar Arora et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

The experimental fatigue life prediction of leaf springs is a time consuming process The engineers working in the field of leafsprings always face a challenge to formulate alternate methods of fatigue life assessmentThe work presented in this paper providesalternatemethods for fatigue life assessment of leaf springs A 65Si7 light commercial vehicle leaf spring is chosen for this studyTheexperimental fatigue life and load rate are determined on a full scale leaf spring testing machine Four alternate methods of fatiguelife assessment have been depicted Firstly by SAE spring design manual approach the fatigue test stroke is established and by theintersection of maximum and initial stress the fatigue life is predictedThe secondmethod constitutes a graphical method based onmodified Goodmanrsquos criteria In the third method codes are written in FORTRAN for fatigue life assessment based on analyticaltechnique The fourth method consists of computer aided engineering tools The CAD model of the leaf spring has been preparedin solid works and analyzed using ANSYS Using CAE tools ideal type of contact and meshing elements have been proposed Themethod which provides fatigue life closer to experimental value and consumes less time is suggested

1 Introduction

In actual practice the load rate and fatigue life (underspecified stress range) are determined experimentally Theprocess of experimental fatigue life prediction of leaf springsis a time consuming process that is for the fatigue lifeof 100000 cycles the experimental procedure will consumeapproximately 2-3 days For the assessment of experimentalfatigue life a full scale leaf spring testing machine is requiredThe leaf spring is mounted in the machines simulating thecondition of the vehicle the fatigue test stroke is deter-mined and the leaf spring is tested from maximum stressto minimum or initial stress As there are a number offactors responsible for fatigue life enhancement like materialprocessing loading surface size and environmental factorit is mandatory that the fatigue life should be determined byconsidering these factors The engineers working in the fieldof leaf springs design are facing a challenge to devise a fatiguelife assessment method which is reliable and consumes less

time Although the analytical or simulation techniques pro-vide an approximate fatigue life the validation of theseresults through experimental testing is mandatory Saelemet al [1] simulated a leaf springs model An experimentalleaf springs model was verified by using a leaf springstest rig that could measure vertical static deflection of leafsprings under static loading condition The results showed anonlinear relationship between the applied load and the leafsprings deflection for both directions of loading in form ofa hysteresis loop Refngah et al [2] worked on the possibilityand capability of replacing the multileaf with the parabolicspring in suspension system He performed the finite elementanalysis to analyze the stress distribution and behavior ofboth the springs Then time histories service loading datawas analyzed and damage area was simulated to predictthe fatigue life of the components The simulation resultsare compared and validated with the experimental resultsFuentes et al [3] studied the origin of premature failureanalysis procedures including examining the leaf spring

Hindawi Publishing CorporationInternational Scholarly Research NoticesVolume 2014 Article ID 607272 11 pageshttpdxdoiorg1011552014607272

2 International Scholarly Research Notices

Table 1 Mechanical properties of 65Si7

Mechanicalproperty

Youngrsquosmodulus (119864)

MPaBHN Poissonrsquos ratio

(120583)

Ultimate tensilestrength (119878ut)

MPa

Yield tensilestrength (119878

119910)

MPa

Elongation atfracture

(minimum)

Density (120588)kgmm3

Value 200124 380ndash432 0266 1272 10812 7 000000785

history The visual inspection of fractured specimens andsimulation tests on real components were also performedIt was concluded that fracture occurred by a mechanismof mechanical fatigue initiated at the region of the centralhole which suffered the highest tensile stress levels Aggarwalet al [4] evaluated the axial fatigue strength of EN45A springsteel sample experimentally as a function of shot peeningin the circumstances used 119878119873 curves of the samples werecorrelated with leaf springs curve in vehicles Aggarwal et al[5] concluded that influence of high contact pressure andtemperatures resulted in micro weld between the two leafsurfaces The fatigue strength of the leaf springs was studiedas a function of shot peening parameters Patunkar andDolas [6] worked on nonlinear force displacement of eachleaf spring as well as the spring characteristics of a packconsisting of two to four leaves using ANSYS The resultsfrom ANSYS were compared with those from the test whichshowed a fairly good agreement with each other Kumarand Vijayarangan [7] described static and fatigue analysis ofsteel leaf springs and composite multileaf springs made upof glass fibre reinforced polymer using life data analysis Thedimensions of an existing conventional steel leaf spring of alight commercial vehicle were taken and verified by designcalculations Static analysis of 2-D model of conventionalleaf springs was also performed using ANSYS 71 and theresults obtained were compared with experimental resultsSanjurjo et al [8] performed two peening treatments on twodifferent surface conditions It has been confirmed that thesurface finish was the critical factor for the enhancementof the fatigue performance of the reinforced bars It wasconcluded that 90 of the total fatigue enhancement is dueto the removal of surface stress raisers and the enhancementof the product roughness and only 10 is due to the CRSFlayer induced by shot peening Zhuang and Halford [9]proposed a model based on the bauschinger effect and arealistic back-stress based plasticity stress-strain relationThemodel was verified using an advanced finite element modelThe analytical model was used to predict the residual stressrelaxation versus various cyclic loading conditions Effect ofload ratio on residual stress relaxation was also depicted Hesuggested that although the analytical model proposed hereis able to predict the trends of residual stress relaxation anexperimental study on cycle-dependent residual stress relax-ation is also required Savaidis et al [10] developed a finiteelement base model of high strength and high performanceleaf springs He described the mechanical behavior of theleaf spring under damaging driving maneuvers The idealtype of meshing elements and contacts in the leave thicknessis considered to describe the mechanical behavior in anaccurate and time effective manner Experimental results fora serial front axle multileaf spring subjected to vertical and

Datum lineSeat length

Centre boltOpening

Thickness

Fixed end

Clamp lengthInside

diameterof eye

Free end

Width

Length plusmn3998400998400

plusmn6998400998400plusmn6998400998400

plusmn15998400998400

Figure 1 Layout drawing of the leaf spring assembly

braking loads were compared and validatedwith numericallydetermined stress distributions

The objective of the present work is to provide a methodfor precise fatigue life assessment of leaf springs ratherthan experimental testing A LCV leaf spring is taken intoconsideration for this study The experimental fatigue lifeand load deflection are determined on a full scale leaf springtesting machine The loading conditions for the requiredfatigue life are specified by the vehicle manufacturer Fournumbers of specimens with specified geometrical parametersand similar material processing are manufactured and testedfor fatigue life The alternate fatigue life assessment methodcomprises graphical method analytical method (using codesin FORTRAN) SAE spring designmanual method and CAEsolution (using Ansys) The fatigue life by various techniquesis compared and alternate method which gives results closerto experimental is suggested

2 Material

The 65Si7SUP9 grade material is used for the experimentalwork The chemical composition of the material is Mnmdash072 Cmdash053 Smdash0007 Simdash020 Pmdash0019 andCrmdash073 The heat treatment is done at 880∘C and oilquench hardened and it is tempered at 410∘C for 90 minutesto get tempered martensite structure The mechanical prop-erties and parameters of the 65Si7 are shown in Table 1

3 Leaf Spring Design Parameters

To design semielliptical springs the terms like span no loadassembly camber loaded camber stack height opening andseat length are used and these parameters are termed designparameters The layout drawing of the leaf spring assembly isdepicted in Figure 1The line which passes through the centre

International Scholarly Research Notices 3

Table 2 Design parameters of the leaf springs

Span (119871)(mm)

Load rate(119896) (Nmm)

Load (N) No loadcamber(119862119886) (mm)

Seatlength(mm)

Totalnumber ofleaves (119873)

Number offull lengthleaves (119883)

Maximum thickness ofthe individual leaf (119905) timeswidth (119887) (mmtimesmm)

Required fatiguelife (119873

119891) at

(13 plusmn 07 g)Rated(119875119892)

Maximum(119875max)

1150 plusmn 3 15911 plusmn 7 12959 28010 95 plusmn 4 100 12 2 8 times 70 70000 cycles

Figure 2 Leaf spring assembly drawing

of the eyes is termed datum line for the springs with eyesSpan is termed the distance between the centres of the eyes

The distance from the datum line to the point where thecentre bolt or the cup centre intersects the top surface of themain leaf when the spring is not loaded is called free camberor free height This may be either positive or negative Thedistance from the datum line to the point where the centrebolt or the cup centre intersects the top surface of the mainleaf when the spring is loaded is called loaded camber Rideclearance may be termed as the spring travel on the vehiclefrom the design load to the metal to metal contact positionor the deflection from the design load to the metal to metalcontact position Stiffness factor takes into considerationthe leave length and type of end used The various designparameters of the leaf spring assembly of light commercialvehicle are indicated in Table 2 The layout drawing of lightcommercial vehicle (LCV) leaf spring is depicted in Figure 2

31 Manufacturing of Leaf Springs For the fabrication ofhigh strength leaf springs the process comprises shearingpunching heat treatment hot cambering shot peeningscragging and testing for load rate and fatigue life Afterpunching and shearing the raw material is moved to thehardening furnaces for heat treatment The structure of theraw material is partial austenite and after quenching thestructure is martensite but after the tempering process thestructure should be tempered martensite The spring steel ishaving the thickness of 8mm and width of 70mm whichis heated at 880∘C to achieve full austenite structure Hotcambering of the spring is done in this state by passingthrough a finger cambering tools followed by quenching in oilat temperature of 80∘C Tempering is done at a temperature of410∘C for 90min of slow cooling till the tempered martensitestructure is achieved Surface treatment like shot peening andgraphite coating is done on each individual leaf The finalassembly is done by pulling all the leaf with a centre nut andboltThe scragging of the assembly is done and the u clips areattached The assembly is tested for load rate and fatigue life

Hydraulic cylinderLimit switch

Test component

Mounting fixture

Hydraulic cylinderLimit swi htch

Test compponent

Mounting gg fififixture

Figure 3 Full scale leaf spring testing machine in fully laden con-dition

4 Experimental Setup

The 65Si7SUP9 leaf springs assembly consists of two fulllength leaves and ten graduated leaves four rebound clipsof mild steel four shim pipes with four nuts and bolts fourrivets centre nut and bolt and bush of bronzeThemaster leafconsists of upturned berlin eye at both the ends The secondleaf is provided with a military wrapper to avoid accidents incase of master leaf failure at eye section The full scale testingof leaf springs was carried out in an electrohydraulic staticcomponent testing system The laminated leaf springs wereplaced in a fixture simulating the conditions of a vehicle Thesetup consists of a hydraulic power pack to give a hydraulicpressure of 206MPa with a flow rate of 210 liters per minute(lpm) which was sent to a hydraulic actuator to operate ata frequency of 03Hz with the displacement specified by thealternating load This involves applying the axial load onthe leaf springs and measuring the deflection and bendingstress The conventional leaf spring was tested under staticload condition by using hydraulic static load ram for loadapplication Mounting of the leaf spring was done by keepingit in inverted manner on the test bed Two eye ends wereheld in the clamping devices and load was applied from thetop at the center of leaf springs To measure the load dialindicator was used which was located beside the full scaleleaf spring testing machine and deflection was measuredby strain gauges located at the clamping of the test rigThe springs were loaded from unladen load (ie 76 KN) tomaximum load (ie 28 KN) The vertical deflection of thesprings at the unladen load design load flat load rubbertouching load and metal to metal contact or maximum loadwas recorded respectively as per the standard operatingprocedure prescribed [11] Figure 3 shows the full scale leafspring testing machine in static and fully laden condition

4 International Scholarly Research Notices

Table 3 Experimental results for load deflection and bending stresses

Serial number Load type Load (N) Deflection (mm) Bending stress (MPa)1 Unladen load 7661 469 2622 Designrated load 12959 8144 4463 Flat load 15754 99 5404 Rubber touching load 216457 136 7435 Metal to metal contact 28010 176 941

Table 4 Experimental fatigue life of the specimen

Material processing Standardspecified

Alternatingstress level(MPa)

Stress range Fatigue lifeof S-1 (119873

119891)

Fatigue lifeof S-2 (119873

119891)

Fatigue lifeof S-3 (119873

119891)

Fatigue lifeof S-4 (119873

119891)

AverageSD

Normal rollingquenching at 880∘Chardening in oil at 80∘Ctempering at 410∘C for90mins shot peening at18 A intensity BHN380ndash432 and scraggingat 09 of yield stress

06 gndash2 g 269ndash896 627 84212 81961 82226 85656Average83513SD 1518

The leaf springs were tested on a full scale leaf springtesting machine under the unladen rated flat rubber touch-ing load and metal to metal load and the correspondingdeflection and stress values observed are shown in theTable 3The experiments were conducted twice and the mean valueof the results was considered Table 3 depicts the observedvalues of deflection and stress corresponding to the loadsapplied on the shorter leaf by a static hydraulic ram

41 Experimental Fatigue Life Determination To determineexperimental fatigue life four leaf springs specimens (S-1 S-2S-3 and S-4) are manufactured with specified design param-eters Analogous kind of material processing normal rollingquenching at 880∘C hardening in oil at 80∘C tempering at410∘C for 90mins shot peening at 18 A intensity BHN 380ndash432 and scragging at 09 of yield stress was done for allthe specimensThe stress range considered for the specimensis 627MPa 13 plusmn 07 g All the four specimens were testedunder same stress range and fatigue life was determined asdepicted in Table 4 The fatigue life of specimen S-1 is 84212for sample S-2 is 81961 and for samples S-3 and S-4 are 82226and 85685 respectively The mean value that is 83513 of thefatigue life for the four specimens is taken into considerationfor this study As per the requirement specified by the vehiclemanufacturer the leaf springs are to be tested on full scaletesting machine as per 13 plusmn 07 g The maximum load will be2 g and theminimum load will be 06 g Here g represents thedesign load [12]

119878max =119875max lowast 119871119886 lowast 119905

8 lowast sum 119868total= 896MPa

Smin =119875min lowast 119871119886 lowast 119905

8 lowast sum 119868total= 269MPa

(1)

5 SAE Spring Design Manual Approach

Fatigue life is articulated by the number of deflection cyclesthat a spring will withstand without failure or permanentset A leaf spring used in a suspension will undergo a largenumber of cycles of small amplitude near the design loadposition without failure Under the greater amplitude thenumber of cycles without failure will be reduced since themaximum stresses aswell as the stress range are amplified andboth are determining factors in fatigue life of the spring Asper the SAE spring design manual approach [12] the fatiguetest stroke for leaf springs (by considering assembly stress) ispredicted as

(a) deflection at design load = 129591531 = 846mm(b) maximum load on the leaf springs = 28KN(c) metal-to-metal clearance (compression stroke) =

946mm(d) total deflection to maximum load = 1829mm(e) stress at metal-to-metal contact position = 885MPa(f) stress rate = 8851829 = 483MPamm(g) release stroke = 05 times 946 = 473mm(h) fatigue test stoke = 473 + 946 = 1419mm(i) initial stress = 885 minus (1419 times483) = 1996MPa

The maximum stress of 885MPa and initial stress of1996asymp 200MPa are utilized to predict the approximatefatigue life of the leaf spring

51 Fatigue Life Assessment by SAE Spring Design ManualApproach Figure 4 shows a maximum stress versus initialstress plot as per SAE spring design manual approach As perSAE spring design manual this criterion is frequently used

International Scholarly Research Notices 5

400500600700800900

1000110012001300

0 100 200 300 400 500 600 700

Max

imum

stre

ss (M

Pa)

Initial stress (MPa)

= 269MPa= 200MPa

Smax (as specified) = 896MPa

Smax (as per SAE) = 885MPa

Sinitial (as specified)Sinitial (as per SAE)

30000cycles to failure

50000

75000

100000

200000

1000000

cycles to failure

Figure 4Maximum versus initial stress plot (without shot peening)[12]

for determination of approximate fatigue life of the springinitial stress (horizontal scale) and maximum stress (verticalscale) are intersected to estimate the number of cycles thespring will survive The life predicted from this plot does notconsider the effect of shot peening and scragging operationsbut in actual practice processing like shot peening andscragging is performed on the leaf springs which enhancesthe fatigue life by approximately 20

From Figure 4 it is observed that the maximum stressinduced in the leaf springs (by considering the assemblystresses) is 885MPa and the initial stress value is 200MPaThe intersection of 885MPa and 200MPa lies in the zoneof 50000 to 75000 cycles As the point of intersection isnearer to 50000-cycle line it will sustain approximately 58000cycles Due to shot peeing and scragging the fatigue lifeof leaf springs by considering assembly stresses would beapproximately (58000 lowast 12) 69600 cycles

The vehicle manufacture has specified that the maximumstress of 896MPa corresponds to the maximum load of 2 gand the minimum stress of 269MPa corresponds to theminimum load of 06 g where g is the design load Theintersection of 896MPa and 269MPa lies in the zone of 50000to 75000 cycles As the point of intersection is nearer to75000-cycle line approximately it will sustain around 68000cycles Due to shot peeing and scragging the fatigue lifeof leaf springs (by considering assembly stresses) would beapproximately (68000 lowast 12) 81600 cycles

Hence it is observed that with the stress range obtainedfrom SAE spring design approach the fatigue life and asspecified stress range are around 69600 cycles and 81600cycles approximatelyThe stress range specified by the vehiclemanufacturer gives result closer to the experimental results

6 Fatigue Life Estimation byGraphical Method

The graphical method involves determination of effect ofvarious factors like load temperature size and surface on theendurance limit of the 65Si7 Figure 5 shows an alternatingversus number of cycles plot for unfactored endurance limitand factored endurance limit It is observed from Figure 5

0

200

400

600

800

1000

1200

1400

1000 10000 100000 1000000 10000000

S998400e factored curve

Sm = 583MPa

Se unfactored curve

Alte

rnat

ing

stres

sS a

(M

Pa)

NNumber of cycles

Figure 5 Factored and unfactored S-N curve for 65Si7 leaf spring

that the endurance limit is 636MPa without consideringthe various factors affecting the fatigue life It has also beenobserved that the corrected endurance limit is 4019MPaConsidering the design material and processing parameterof the leaf springs the steps involved in the graphicalmethodsare as follows

(a) 119878119906119905 = 1272MPa(b) 119878119910 = 10812MPa

(c) 1198781015840

119890= 05119878119906119905 = 05 times 1272 = 636MPa

(d) 120590min = 269MPa at 06 g load 120590max = 897MPa at 2 gload

(e) 119878119886 = (120590max minus 120590min)2 = (897 minus 269)2 = 314MPa(f) 119878119898 = (120590max + 120590min)2 = (897 + 269)2 = 583MPa(g) 119878119890 = 119870load times 119870surfae times 119870temp times 119870reliability times 119870size times 119878

1015840

119890

(h) 119870load = load factor for bending 119870load = 1(i) 119870surface = 1 (for shot peening treating)(j) 119870temp = 1 if 119879 le 450

∘C(k) 119870reliability = 080 Assuming 99 reliability

(l) 119870size = 1189 lowast (119889eqiv)minus097 for 8mm lt 119889 le 250mm

(m) 119889 eqiv = radic1198609500766 = 6588mm

(n) 11986095 = 005 lowast 119887 lowast ℎ = 3325mm2(o) 119870size = 1189 lowast (119889eqiv)

minus097= 079

(p) 119878119890 = 1 times 1 times 1 times 080 times 079 times 636 = 4019MPa

Figure 6 shows an alternating stress versus mean stress plotfor the LCV leaf spring It has been observed from Figure 6that the intersection of the alternating and mean stress lineslies outside the region AC If the point is within this lineAC the component is designed for infinite life but if thecomponent is outside this region the component is designedfor the finite life Thus from the position of point I it isobserved that the component is designed for the finite lifeThe equivalent alternating stress as determined by joining thepoint of intersection I and ultimate strength point with thealternating stress axis is found to be 578MPa

6 International Scholarly Research Notices

0100200300400500600700800900

100011001200

0 200 400 600 800 1000 1200 1400

Alte

rnat

ing

stres

s (M

Pa)

Mean stress (MPa)

As point I lies outside this region theleaf spring is designed for finite lifeI

C

A

Sa = 314MPa

Sm = 583MPa

Se = 4019MPa

Sae = 578MPa equivalent alternating stress

Figure 6 Alternating stress versus mean stress plot

1400

1200

1000

800

600

400

200

01e + 3 1e + 4 1e + 5 1e + 6 1e + 7 1e + 8

Sae = 578MPa

Se = 4019 MPa

Nf = number of cycles to failure

Alternating stress versus number of cycles

NNumber of cycles

Alte

rnat

ing

stres

sS a

(MPa

)

A

BC

E D

Figure 7 S-N curve for 65Si7

Figure 7 shows the S-N diagram for 65Si7 Point A rep-resents the alternating stress at which the spring will sustain1000 cycles Point D represents the endurance limit that is4019MPa of 65Si7 The line CB represents the equivalentalternating stress The intersection of alternating stress atpoint B will give the number of cycles to fatigue failure

FromFigure 7 S-N plot it is observed thatΔABC is similarto ΔADE

Hence 119860119862119860119864 = 119862119861119863119864

119860119862 = log119860 minus log119862 = 0296

119860119864 = log119860 minus log119864 = 0454

119863119864 = log119863 minus log119864 = log 106minus log 10

3= 3

119862119861 =0296 times 3

0454= 1957

Total 119862119861 = 3 + 197 = 49957

Number of cycles = 104957

= 90763 cycles to failure

(2)

1e + 3 1e + 4 1e + 5 1e + 6 1e + 7 1e + 8

NNumber of cycles

1400

1200

1000

800

600

400

200

0

Alte

rnat

ing

stres

sS a

(MPa

)

N1 cycles at S998400m N2 cycles at Se

= 09(Sut)

Se

A

BC

S998400m

Figure 8 Estimated S-N curve

7 Analytical Method forFatigue Life Prediction

The high cycle fatigue regime is from 103 to 106 and beyondThematerial strength at 103 cycles is called 119878

1015840

119898 which is equal

to 09 Sut The estimated S-N diagram drawn on the log-loggraph is shown in Figure 8 Figure 8 shows that the 119909-axisruns from 103 to 109 or beyond The appropriate 119878

1015840

119898from

the equation for bending load is plotted at N1 = 103 As thematerial exhibits a knee the corrected endurance limit 119878119890 isplotted at N2 = 106 A straight line is drawn between 119878

1015840

119898and

119878119890 The curve is continuous horizontally beyond N2 pointThe equation of the line from 119878

1015840

119898to 119878119890 can be written as

119878 (119873) = 119886119873119887

(taking log on both sides) (3)

log 119878 (119873) = log 119886 + 119887 log119873 (4)

where 119878(119873) is the fatigue strength at any 119873 and 119886 119887 are theconstants defined by the boundary conditions For all theconditions the 119910 intercept is 119878(119873) = 119878

1015840

119898at N = N1 = 103

for endurance limit case 119878(119873) = 119878119890 atN =N2 = 106 Applyingthe boundary condition in the equation we have

log 1198781015840

119898= log 119886 + 119887 log1198731 (5)

log 119878119890 = log 119886 + 119887 log1198732 (6)

log 1198781015840

119898minus log 119878119890 = 119887 (log1198731 minus log1198732) (7)

119885 = (log1198731 minus log1198732) (8)

119887 =1

119885log

1198781015840

119898

119878119890

(9)

log 1198781015840

119898minus 119887 log1198731 = log 119886 (10)

International Scholarly Research Notices 7

As 1198731 = 1000 log101000 = 3

log 1198781015840

119898minus 3119887 = log 119886

119886 =

(1198781015840

119898)2

119878119890

(11)

119873 = (119878119886

119886)

minus1119887

(12)

119878119886119890 = 119886119873119887

119891[13] where119873119891 = number of cycles to failure 119878119886119890 =

equivalent alternating stress 119886 119887 are constantswhich dependson the material properties of 65Si7 The fatigue life is to bepredicted at equivalent alternating stress so 119878119886 is replaced by119878119886119890 The above mentioned equation is used for fatigue lifeestimation and the codes for the analyticalmethod arewrittenin FORTRANThe flowchart is shown in Figure 9

8 Computer Aided Engineering Analysis

The CAD model of the individual leaf is prepared from thestandard drawing of the leaf spring and assembled The leafspring assembly is imported to an analysis software ANSYSfor further processing The different contacts are set andentire model is meshed into small elements The boundaryconditions are applied by taking into consideration the actualloading conditions and the solver gives the solution Thediverse steps involved in CAE analysis are as follows

81 CAD Modeling The CAD modeling of the conventionalleaf springs structure is performed by using solid workssoftware The CAD model of leaf springs consists of total34 different parts which are assembled together in assemblydesign to construct an assemblyThemultileaf springs assem-bly used for analysis is shown in Figure 10

82 Analysis Using ANSYS The CAD model of leaf springshas been imported in the ANSYS solver All the boundaryconditions and material properties have been specified asper the standard specified by the vehicle manufacturer Thematerial used for the leaf springs for analysis is 65Si7 whichis having homogenous and isotropic behaviour The material65Si7 is added in the material library and the engineeringproperties are applied

The process for performing analysis in ANSYS solverinvolves the following

821 Setting the Contact Reign The contact conditions areformed where the components meet The differences inthe contact settings determine how the contacting bodiescan move relative to one another In this assembly the Noseparation contact is used for the analysis It only applies toregion of faces Separation of faces in contact is not allowedbut small amounts of frictionless sliding can occur alongcontact faces In general CONTA174 and TARGE170 areused CONTA174 is used for contact and sliding between3D target surfaces (TARGE170) which is defined by thiselement The element is applicable to 3D structural analysis

Start

Calculate maximum thickness

Estimate the number of leaves width and thickness for required

MOI

Select assembly stresses

Calculate steppingoverhang

If no load assembly camber

Calculate the mass

Calculate fatigue life

End

Calculate Smax

If Kmodified variesmore than 7

Calculate Kmodified

If t gt tmax if MOI estimated gt

MOI required

Required K Pdesign Smax Nf

Calculate required moment ofinertia (MOI) Pmax

Calculate the Smaximum andSinitial stress for fatigue life

If Sas middot t2 = 0

Figure 9 Flowchart for analytical estimation of fatigue life of 65Si7leaf spring

Figure 10 CAD model of the leaf springs

8 International Scholarly Research Notices

Figure 11 Boundary conditions for CAE analysis

TARGE170 is used to represent various 3D target surfaces forthe associated contact elements

822 Meshing In this congregation SOLID187 elementwhich is a standard mechanical element for solids is used forthe result SOLID187 element is a higher order 3-D 10-nodeelement SOLID187 has quadratic displacement behaviourand is well suited to modeling irregular meshes The elementis defined by 10 nodes having three degrees of freedom ateach node translations in the nodal 119909 119910 and 119911 directionsThe number of SOLID187 elements is 6964 and the numberof nodes generated is 16943

823 Static Analysis Module A static structural analysisdetermines the displacements stresses strains and forcesin structures or components caused by loads that do notinduce significant inertia and damping effects Steady loadingand response conditions are assumed that is the loads andthe structurersquos response are assumed to vary slowly withrespect to time Static structure analysis takes into consid-eration some parameters like material properties loadingconditions support conditions and contacts which are to bespecified as the input to the preprocessing of the analysis

824 Applying CAE Boundary Conditions The boundaryconditions are applied by taking into consideration the exper-imental loading conditions The springs have been modelledin flat condition and the loading is done to achieve the initialcondition The total load is divided on the two eyes of themaster leaf and pins The fixed support constitutes the seatlength (on master leaf and last (12th leaf) and the centre boltThe CAE boundary conditions are shown in Figure 11

83 Fatigue Life Assessment Using CAE Tools While leafsprings may work well initially they often fail in service dueto fatigue failure caused by repeated cyclic loadingThe aimoffatigue analysis is characterization of capability of a materialto survive many cycles that a leaf spring may experienceduring its life time In ansys fatigue module twomethods areavailable that is stress life and strain life method For thiswork the stress lifemethod is used to predict the fatigue life ofthe component The static environment is set by applying theboundary conditions by taking into consideration the actualloading conditions After the static analysis the fatigue toolis used for fatigue life estimation In stress life decision treeit is required to make four input decisions to perform a stress

life analysis These decisions affect the outcome of the fatigueanalysis in both predicted life and types of postprocessingavailable Input decisions that are to be considered for fatiguelife estimation are loading typemean stress effectsmultiaxialstress correction and fatigue modification factors

831 Type of Loading Unlike static stress which is analyzedwith calculations for a single stress state fatigue damageoccurs when stress at a point changes over time There areessentially four classes of fatigue loading with the ANSYSfatigue module [14] currently supporting the first three

(i) constant amplitude proportional loading(ii) constant amplitude nonproportional loading(iii) nonconstant amplitude proportional loading(iv) nonconstant amplitude non-proportional loading

Constant amplitude proportional loading is the classic ldquobackof the enveloperdquo calculation describing whether the loadhas a constant maximum value or continually varies withtime Loading is of constant amplitude because only one setof FE stress results along with a loading ratio is requiredto calculate the alternating and mean values The loadingratio is defined as the ratio of the second load to the firstload (LR = L2L1) Loading is proportional since only oneset of FE results are needed (principal stress axes do notchange over time) Common types of constant amplitudeloading are fully reversed (apply a load and then apply anequal and opposite load a load ratio of minus1) and zero-based(apply a load and then remove it a load ratio of 0) Sinceloading is proportional looking at a single set of FE resultscan identify critical fatigue locations Constant amplitudenonproportional loading looks at exactly two load cases thatneed not to be related by a scale factor The loading isof constant amplitude but nonproportional since principalstress or strain axes are free to change between the two loadsets Nonconstant amplitude proportional loading also needsonly one set of FE results But instead of using a single loadratio to calculate alternating and mean values the load ratiovaries over time

832 Mean Stress Correction For stress life if experimen-tal data at different mean stresses or r-ratiorsquos exist meanstress can be accounted for directly through interpolationbetweenmaterial curves If experimental data is not availableseveral empirical options may be chosen including GerberGoodman and Soderberg theories which use static materialproperties yield stress and tensile strength along with S-Ndata to account for any mean stress

833 Multiaxial Stress Correction Factor Experimental testdata is mostly uniaxial whereas finite element results areusually multiaxial At some point stress must be convertedfrom a multiaxial stress state to a uniaxial one Von-Misesstress max shear stress maximum principal stress or any ofthe component stresses can be used for the comparison withthe experimental uniaxial stress value

International Scholarly Research Notices 9

(a) (b)

Figure 12 (a) Fatigue life using CAE tools (b) Equivalent alternating stress

Table 5 CAE results for load deflection and bending stresses

Serial number Load type Load (N) Deflection (mm) Stress (MPa)1 Unladen load 7661 449 270742 Designrated load 12959 7605 4583 Flat load 15754 9245 556834 Rubber touching load 216457 12702 7655 Metal to metal contact 28010 16436 98989

Table 6 Comparison of fatigue life by various approaches

Serial number Method for fatiguelife assessment Alternating stress level Stress range Equivalent alternating stress Fatigue life Variation from

experimental results1 Experimental 269ndash896 627 mdash 83513 mdash

2 SAE spring designmanual approach 200ndash885 685 mdash 69600 166

3 Graphical method 269ndash896 627 578 90763 8684 Analytical method 269ndash896 627 579 90304 8135 CAE method 269ndash896 627 562 82348 239

834 Fatigue Modifications (Value of Infinite Life) Anotheravailable option when conducting a variable amplitudefatigue analysis is the ability to set the value used for infinitelife In constant amplitude loading if the alternating stress islower than the lowest alternating stress on the fatigue curvethe fatigue tool will use the life at the last pointThis providesfor an added level of safety because many materials do notexhibit an endurance limit

The static environment is set and boundary conditions areapplied and the solver gives the solution The deflection andstress results obtained from the specified loads are recorded ina tabular format The CAE results for deflection and bendingstress are shown inTable 5 Figure 12(a) depicts the fatigue lifeof the leaf spring using Ansys solver For prediction of fatiguelife the stress life approach is selected A constant amplitudeload ratio is selected as the loading type The fatigue strengthfactor of 065 is chosen and scale factor is kept as 1 Formean stress theory Goodmanrsquos criteria are selected Lastly formultiaxial stress correction von-mises stress is selected andthe component is designed for finite life It has been observedthat the fatigue life of the leaf spring using CAE tool is 82348

cycles Figure 12(b) depicts the equivalent alternating stressin the leaf spring using Ansys solver

9 Results and Discussion

91 Fatigue Life Comparison by Various Approaches Table 6depicts the comparison of fatigue life by various methodsIt is observed that for the alternating stress level of 896ndash269MPa the experimental fatigue life of the leaf spring is83513 cycles The fatigue life estimated by SAE spring designmanual technique is 69600 cycles for the alternating stresslevel of 885ndash200MPa It is also observed that in the SAEspring design manual approach the maximum stress that is885MPa is less than the specified maximum stress but thestress range is higher than specified stress range Hence thisapproximation provides results within 166 variation Thesame approach with specified stress range gives the fatiguelife of leaf spring to be 81600 For the same alternating stresslevel of 896ndash269MPa the fatigue life is found to be 90763cycles by graphical method and equivalent stress is found to

10 International Scholarly Research Notices

Table 7 Comparison of experimental and CAE results

Load type Load (N) Experimental results CAE results age variation between CAEand Experimental results

Deflection Stress Deflection Stress Deflection StressUnladen load 7661 469 262 449 27074 43 33DesignRated load 12959 8144 446 7605 458 66 27Flat load 15754 99 540 9245 55683 66 31Rubber touching load 216457 136 743 12702 765 66 30Metal to metal contact load 28010 176 941 16436 98989 66 52

be 578MPa In the analytical method the fatigue life is foundto be 90304 cycleswith 813 variation from the experimentalresults The CAE fatigue life is found to be 82348 cycles with239 variation from the experimental results

92 Comparison of Experimental and CAE Results To vali-date the analysis the CAE results have been compared withthe experimental results As the experiments are done ona full scale leaf spring testing machine under the specifiedloads the CAE analysis has been carried out for the sameloads The maximum stress induced in the leaf springs isfound to be 941MPa and 98989MPa using experimental andCAE approach respectively The stress is found to be wellbelow the yield tensile strength which is 10812MPa Thetotal deformation and stress comparison for experimentaland CAE approach also validates the CAE analysis of the leafsprings The results of the comparison have been depicted inthe tabular form in Table 7

From Table 7 it is observed that for the same unladenstatic load conditions deflection in experimental and CAEresults is 469mm and 449mm respectively The deforma-tion observed in CAE results varies by 43 The bendingstress for experimental and CAE results is 262MPa and27074MPa respectively The variation of bending stressobserved in CAE results from experimental is 33 FromTable 7 it is also observed that for the same design loadcondition the deflection found in experimental and CAEis 8144mm and 7605mm respectively The variation inCAE results from experimental is 66The bending stressesunder the design load for experimental and CAE results are446MPa and 458MPa respectivelyThe variation in bendingstress observed in the CAE results is 27 For the maximumload condition the static deflection is 176mm and 16436mmfor experimental and CAE results It has been observedthat when CAE results are compared with experimental thevariation in the deformation varies in between 43 and66 respectively The stress variation lies in the range of27 to 52 It has also been observed that the maximumstress induced in the assembly in both the approaches is wellbelow the yield stress of the material It has been observedthat the CAE results obtained by using SOLID187 meshelements and CONTA172 and TARGE170 (No separation andsliding) contact elements provides the results closer to theexperimental testing

10 Conclusions

The 65Si7 LCV model is taken into consideration fordetermining the fatigue life by experimental and graphicalmethods analytical method (using FORTRAN) SAE springdesign manual approach and CAE (using Ansys) approachThe following conclusions are made

(1) The fatigue life of the leaf spring for same stress rangewill decrease if the magnitude of the initial stressis lower In actual condition the leaf springs willwithstand 15ndash17 more fatigue life than predicted bySAE spring design manual approach

(2) Graphical and analytical methods are time consum-ing and prone to errors but provide results which arewithin 8-9 variation

(3) It is concluded that when CONTA174 TARGE170type of contact and SOLID187 mesh element are usedfor CAE analysis results are closer to the experimen-tal results CAE approach usingAnsys predicts fatiguelife within 2ndash5 of experimental results and can be analternate of experimental and analytical approach

Nomenclature

119862119886 No load assembly camber119864 Youngrsquos modulus of elasticity119873119891 Number of cycles to failure120588 Density120583 Poissonrsquos ratio119878119886 Alternating stress120590max Maximum stress1198781015840

119890 Endurance limit

119878119890 Corrected endurance limit119878119910 Yield tensile strength119871 Span120590min Minimum stress119878119898 Mean stress119878119886119890 Equivalent alternating stress119878119906119905 Ultimate tensile strength119870surface Surface factor119870load Load factor119870temp Temperature factor119870size Size factor119870reliability Reliability factor

International Scholarly Research Notices 11

119889equiv Equivalent diameter of rotating beam spec-imen for any cross section

11986095 Portion of the cross sectional area of non-rounded that is stressed in between 95and 100 of its maximum stress

1198781015840

119898 Stress at 103 cycles

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

The authors would like to acknowledge Mr P S Chawlaand the leaf springs testing division of Friends Auto (India)Ltd whose unconditional support has made this projectsuccessful

References

[1] S Saelem S Chantranuwathana K Panichanun P Preeda-nood P Wichienprakarn and P Kruo-ongarjnukool ldquoExper-imental verification of leaf spring model by using a leaf springtest rigrdquo in Proceedings of the 23rd Conference of the Mechan-ical Engineering Network of Thailand Chiang Mai ThailandNovember 2009

[2] F N A Refngah S Abdullah A Jalar and L B Chua ldquoFatiguelife evaluation of two types of steel leaf springsrdquo InternationalJournal of Mechanical and Materials Engineering vol 4 no 2pp 136ndash140 2009

[3] J J Fuentes H J Aguilar J A Rodrıguez and E J HerreraldquoPremature fracture in automobile leaf springsrdquo EngineeringFailure Analysis vol 16 no 2 pp 648ndash655 2009

[4] M L Aggarwal R A Khan and V P Aggarwal ldquoOptimizationof micro welds used in the leaf springsrdquo International Journal ofEngineering Material and Science vol 28 pp 217ndash220 2006

[5] M L Aggarwal V P Agrawal and R A Khan ldquoA stressapproach model for predictions of fatigue life by shot peeningof EN45A spring steelrdquo International Journal of Fatigue vol 28no 12 pp 1845ndash1853 2006

[6] M M Patunkar and D R Dolas ldquoModelling and analysisof composite leaf spring under the static load condition byusing FEArdquo International Journal of Mechanical amp IndustrialEngineering vol 1 no 1 pp 1ndash4 2011

[7] M S Kumar and S Vijayarangan ldquoAnalytical and experimentalstudies on fatigue life prediction of steel and composite multi-leaf spring for light passenger vehicles using life data analysisrdquoMaterials Science vol 13 no 2 pp 141ndash146 2007

[8] P Sanjurjo C Rodrıguez I F Pariente F J Belzunce and A FCanteli ldquoThe influence of shot peening on the fatigue behaviourof duplex stainless steelsrdquo Procedia Engineering vol 2 no 1 pp1539ndash1546 2010

[9] W Z Zhuang andG RHalford ldquoInvestigation of residual stressrelaxation under cyclic loadrdquo International Journal of Fatiguevol 23 supplement 1 pp S31ndashS37 2001

[10] G Savaidis M Malikoutsakis and A Savaidis ldquoFE simulationof vehicle leaf spring behavior under driving manoeuvresrdquoInternational Journal of Structural Integrity vol 4 no 1 ArticleID 17082873 pp 23ndash32 2013

[11] IS 1135 SpringsmdashLeaf Springs Assembly for Automobiles 1995[12] SAE Spring Design ManualmdashDesign and Application of Leaf

Springs HS-744 AE-11 1990[13] R L Norton Machine DesignmdashAn Integrated Approach Pear-

son Education Asia 2nd edition 2001[14] ldquoAnsys Workbench training manual on fatigue toolrdquo 2014

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Page 2: Fatigue Life Assessment of 65Si7 Leaf Springs: A Comparative Study

2 International Scholarly Research Notices

Table 1 Mechanical properties of 65Si7

Mechanicalproperty

Youngrsquosmodulus (119864)

MPaBHN Poissonrsquos ratio

(120583)

Ultimate tensilestrength (119878ut)

MPa

Yield tensilestrength (119878

119910)

MPa

Elongation atfracture

(minimum)

Density (120588)kgmm3

Value 200124 380ndash432 0266 1272 10812 7 000000785

history The visual inspection of fractured specimens andsimulation tests on real components were also performedIt was concluded that fracture occurred by a mechanismof mechanical fatigue initiated at the region of the centralhole which suffered the highest tensile stress levels Aggarwalet al [4] evaluated the axial fatigue strength of EN45A springsteel sample experimentally as a function of shot peeningin the circumstances used 119878119873 curves of the samples werecorrelated with leaf springs curve in vehicles Aggarwal et al[5] concluded that influence of high contact pressure andtemperatures resulted in micro weld between the two leafsurfaces The fatigue strength of the leaf springs was studiedas a function of shot peening parameters Patunkar andDolas [6] worked on nonlinear force displacement of eachleaf spring as well as the spring characteristics of a packconsisting of two to four leaves using ANSYS The resultsfrom ANSYS were compared with those from the test whichshowed a fairly good agreement with each other Kumarand Vijayarangan [7] described static and fatigue analysis ofsteel leaf springs and composite multileaf springs made upof glass fibre reinforced polymer using life data analysis Thedimensions of an existing conventional steel leaf spring of alight commercial vehicle were taken and verified by designcalculations Static analysis of 2-D model of conventionalleaf springs was also performed using ANSYS 71 and theresults obtained were compared with experimental resultsSanjurjo et al [8] performed two peening treatments on twodifferent surface conditions It has been confirmed that thesurface finish was the critical factor for the enhancementof the fatigue performance of the reinforced bars It wasconcluded that 90 of the total fatigue enhancement is dueto the removal of surface stress raisers and the enhancementof the product roughness and only 10 is due to the CRSFlayer induced by shot peening Zhuang and Halford [9]proposed a model based on the bauschinger effect and arealistic back-stress based plasticity stress-strain relationThemodel was verified using an advanced finite element modelThe analytical model was used to predict the residual stressrelaxation versus various cyclic loading conditions Effect ofload ratio on residual stress relaxation was also depicted Hesuggested that although the analytical model proposed hereis able to predict the trends of residual stress relaxation anexperimental study on cycle-dependent residual stress relax-ation is also required Savaidis et al [10] developed a finiteelement base model of high strength and high performanceleaf springs He described the mechanical behavior of theleaf spring under damaging driving maneuvers The idealtype of meshing elements and contacts in the leave thicknessis considered to describe the mechanical behavior in anaccurate and time effective manner Experimental results fora serial front axle multileaf spring subjected to vertical and

Datum lineSeat length

Centre boltOpening

Thickness

Fixed end

Clamp lengthInside

diameterof eye

Free end

Width

Length plusmn3998400998400

plusmn6998400998400plusmn6998400998400

plusmn15998400998400

Figure 1 Layout drawing of the leaf spring assembly

braking loads were compared and validatedwith numericallydetermined stress distributions

The objective of the present work is to provide a methodfor precise fatigue life assessment of leaf springs ratherthan experimental testing A LCV leaf spring is taken intoconsideration for this study The experimental fatigue lifeand load deflection are determined on a full scale leaf springtesting machine The loading conditions for the requiredfatigue life are specified by the vehicle manufacturer Fournumbers of specimens with specified geometrical parametersand similar material processing are manufactured and testedfor fatigue life The alternate fatigue life assessment methodcomprises graphical method analytical method (using codesin FORTRAN) SAE spring designmanual method and CAEsolution (using Ansys) The fatigue life by various techniquesis compared and alternate method which gives results closerto experimental is suggested

2 Material

The 65Si7SUP9 grade material is used for the experimentalwork The chemical composition of the material is Mnmdash072 Cmdash053 Smdash0007 Simdash020 Pmdash0019 andCrmdash073 The heat treatment is done at 880∘C and oilquench hardened and it is tempered at 410∘C for 90 minutesto get tempered martensite structure The mechanical prop-erties and parameters of the 65Si7 are shown in Table 1

3 Leaf Spring Design Parameters

To design semielliptical springs the terms like span no loadassembly camber loaded camber stack height opening andseat length are used and these parameters are termed designparameters The layout drawing of the leaf spring assembly isdepicted in Figure 1The line which passes through the centre

International Scholarly Research Notices 3

Table 2 Design parameters of the leaf springs

Span (119871)(mm)

Load rate(119896) (Nmm)

Load (N) No loadcamber(119862119886) (mm)

Seatlength(mm)

Totalnumber ofleaves (119873)

Number offull lengthleaves (119883)

Maximum thickness ofthe individual leaf (119905) timeswidth (119887) (mmtimesmm)

Required fatiguelife (119873

119891) at

(13 plusmn 07 g)Rated(119875119892)

Maximum(119875max)

1150 plusmn 3 15911 plusmn 7 12959 28010 95 plusmn 4 100 12 2 8 times 70 70000 cycles

Figure 2 Leaf spring assembly drawing

of the eyes is termed datum line for the springs with eyesSpan is termed the distance between the centres of the eyes

The distance from the datum line to the point where thecentre bolt or the cup centre intersects the top surface of themain leaf when the spring is not loaded is called free camberor free height This may be either positive or negative Thedistance from the datum line to the point where the centrebolt or the cup centre intersects the top surface of the mainleaf when the spring is loaded is called loaded camber Rideclearance may be termed as the spring travel on the vehiclefrom the design load to the metal to metal contact positionor the deflection from the design load to the metal to metalcontact position Stiffness factor takes into considerationthe leave length and type of end used The various designparameters of the leaf spring assembly of light commercialvehicle are indicated in Table 2 The layout drawing of lightcommercial vehicle (LCV) leaf spring is depicted in Figure 2

31 Manufacturing of Leaf Springs For the fabrication ofhigh strength leaf springs the process comprises shearingpunching heat treatment hot cambering shot peeningscragging and testing for load rate and fatigue life Afterpunching and shearing the raw material is moved to thehardening furnaces for heat treatment The structure of theraw material is partial austenite and after quenching thestructure is martensite but after the tempering process thestructure should be tempered martensite The spring steel ishaving the thickness of 8mm and width of 70mm whichis heated at 880∘C to achieve full austenite structure Hotcambering of the spring is done in this state by passingthrough a finger cambering tools followed by quenching in oilat temperature of 80∘C Tempering is done at a temperature of410∘C for 90min of slow cooling till the tempered martensitestructure is achieved Surface treatment like shot peening andgraphite coating is done on each individual leaf The finalassembly is done by pulling all the leaf with a centre nut andboltThe scragging of the assembly is done and the u clips areattached The assembly is tested for load rate and fatigue life

Hydraulic cylinderLimit switch

Test component

Mounting fixture

Hydraulic cylinderLimit swi htch

Test compponent

Mounting gg fififixture

Figure 3 Full scale leaf spring testing machine in fully laden con-dition

4 Experimental Setup

The 65Si7SUP9 leaf springs assembly consists of two fulllength leaves and ten graduated leaves four rebound clipsof mild steel four shim pipes with four nuts and bolts fourrivets centre nut and bolt and bush of bronzeThemaster leafconsists of upturned berlin eye at both the ends The secondleaf is provided with a military wrapper to avoid accidents incase of master leaf failure at eye section The full scale testingof leaf springs was carried out in an electrohydraulic staticcomponent testing system The laminated leaf springs wereplaced in a fixture simulating the conditions of a vehicle Thesetup consists of a hydraulic power pack to give a hydraulicpressure of 206MPa with a flow rate of 210 liters per minute(lpm) which was sent to a hydraulic actuator to operate ata frequency of 03Hz with the displacement specified by thealternating load This involves applying the axial load onthe leaf springs and measuring the deflection and bendingstress The conventional leaf spring was tested under staticload condition by using hydraulic static load ram for loadapplication Mounting of the leaf spring was done by keepingit in inverted manner on the test bed Two eye ends wereheld in the clamping devices and load was applied from thetop at the center of leaf springs To measure the load dialindicator was used which was located beside the full scaleleaf spring testing machine and deflection was measuredby strain gauges located at the clamping of the test rigThe springs were loaded from unladen load (ie 76 KN) tomaximum load (ie 28 KN) The vertical deflection of thesprings at the unladen load design load flat load rubbertouching load and metal to metal contact or maximum loadwas recorded respectively as per the standard operatingprocedure prescribed [11] Figure 3 shows the full scale leafspring testing machine in static and fully laden condition

4 International Scholarly Research Notices

Table 3 Experimental results for load deflection and bending stresses

Serial number Load type Load (N) Deflection (mm) Bending stress (MPa)1 Unladen load 7661 469 2622 Designrated load 12959 8144 4463 Flat load 15754 99 5404 Rubber touching load 216457 136 7435 Metal to metal contact 28010 176 941

Table 4 Experimental fatigue life of the specimen

Material processing Standardspecified

Alternatingstress level(MPa)

Stress range Fatigue lifeof S-1 (119873

119891)

Fatigue lifeof S-2 (119873

119891)

Fatigue lifeof S-3 (119873

119891)

Fatigue lifeof S-4 (119873

119891)

AverageSD

Normal rollingquenching at 880∘Chardening in oil at 80∘Ctempering at 410∘C for90mins shot peening at18 A intensity BHN380ndash432 and scraggingat 09 of yield stress

06 gndash2 g 269ndash896 627 84212 81961 82226 85656Average83513SD 1518

The leaf springs were tested on a full scale leaf springtesting machine under the unladen rated flat rubber touch-ing load and metal to metal load and the correspondingdeflection and stress values observed are shown in theTable 3The experiments were conducted twice and the mean valueof the results was considered Table 3 depicts the observedvalues of deflection and stress corresponding to the loadsapplied on the shorter leaf by a static hydraulic ram

41 Experimental Fatigue Life Determination To determineexperimental fatigue life four leaf springs specimens (S-1 S-2S-3 and S-4) are manufactured with specified design param-eters Analogous kind of material processing normal rollingquenching at 880∘C hardening in oil at 80∘C tempering at410∘C for 90mins shot peening at 18 A intensity BHN 380ndash432 and scragging at 09 of yield stress was done for allthe specimensThe stress range considered for the specimensis 627MPa 13 plusmn 07 g All the four specimens were testedunder same stress range and fatigue life was determined asdepicted in Table 4 The fatigue life of specimen S-1 is 84212for sample S-2 is 81961 and for samples S-3 and S-4 are 82226and 85685 respectively The mean value that is 83513 of thefatigue life for the four specimens is taken into considerationfor this study As per the requirement specified by the vehiclemanufacturer the leaf springs are to be tested on full scaletesting machine as per 13 plusmn 07 g The maximum load will be2 g and theminimum load will be 06 g Here g represents thedesign load [12]

119878max =119875max lowast 119871119886 lowast 119905

8 lowast sum 119868total= 896MPa

Smin =119875min lowast 119871119886 lowast 119905

8 lowast sum 119868total= 269MPa

(1)

5 SAE Spring Design Manual Approach

Fatigue life is articulated by the number of deflection cyclesthat a spring will withstand without failure or permanentset A leaf spring used in a suspension will undergo a largenumber of cycles of small amplitude near the design loadposition without failure Under the greater amplitude thenumber of cycles without failure will be reduced since themaximum stresses aswell as the stress range are amplified andboth are determining factors in fatigue life of the spring Asper the SAE spring design manual approach [12] the fatiguetest stroke for leaf springs (by considering assembly stress) ispredicted as

(a) deflection at design load = 129591531 = 846mm(b) maximum load on the leaf springs = 28KN(c) metal-to-metal clearance (compression stroke) =

946mm(d) total deflection to maximum load = 1829mm(e) stress at metal-to-metal contact position = 885MPa(f) stress rate = 8851829 = 483MPamm(g) release stroke = 05 times 946 = 473mm(h) fatigue test stoke = 473 + 946 = 1419mm(i) initial stress = 885 minus (1419 times483) = 1996MPa

The maximum stress of 885MPa and initial stress of1996asymp 200MPa are utilized to predict the approximatefatigue life of the leaf spring

51 Fatigue Life Assessment by SAE Spring Design ManualApproach Figure 4 shows a maximum stress versus initialstress plot as per SAE spring design manual approach As perSAE spring design manual this criterion is frequently used

International Scholarly Research Notices 5

400500600700800900

1000110012001300

0 100 200 300 400 500 600 700

Max

imum

stre

ss (M

Pa)

Initial stress (MPa)

= 269MPa= 200MPa

Smax (as specified) = 896MPa

Smax (as per SAE) = 885MPa

Sinitial (as specified)Sinitial (as per SAE)

30000cycles to failure

50000

75000

100000

200000

1000000

cycles to failure

Figure 4Maximum versus initial stress plot (without shot peening)[12]

for determination of approximate fatigue life of the springinitial stress (horizontal scale) and maximum stress (verticalscale) are intersected to estimate the number of cycles thespring will survive The life predicted from this plot does notconsider the effect of shot peening and scragging operationsbut in actual practice processing like shot peening andscragging is performed on the leaf springs which enhancesthe fatigue life by approximately 20

From Figure 4 it is observed that the maximum stressinduced in the leaf springs (by considering the assemblystresses) is 885MPa and the initial stress value is 200MPaThe intersection of 885MPa and 200MPa lies in the zoneof 50000 to 75000 cycles As the point of intersection isnearer to 50000-cycle line it will sustain approximately 58000cycles Due to shot peeing and scragging the fatigue lifeof leaf springs by considering assembly stresses would beapproximately (58000 lowast 12) 69600 cycles

The vehicle manufacture has specified that the maximumstress of 896MPa corresponds to the maximum load of 2 gand the minimum stress of 269MPa corresponds to theminimum load of 06 g where g is the design load Theintersection of 896MPa and 269MPa lies in the zone of 50000to 75000 cycles As the point of intersection is nearer to75000-cycle line approximately it will sustain around 68000cycles Due to shot peeing and scragging the fatigue lifeof leaf springs (by considering assembly stresses) would beapproximately (68000 lowast 12) 81600 cycles

Hence it is observed that with the stress range obtainedfrom SAE spring design approach the fatigue life and asspecified stress range are around 69600 cycles and 81600cycles approximatelyThe stress range specified by the vehiclemanufacturer gives result closer to the experimental results

6 Fatigue Life Estimation byGraphical Method

The graphical method involves determination of effect ofvarious factors like load temperature size and surface on theendurance limit of the 65Si7 Figure 5 shows an alternatingversus number of cycles plot for unfactored endurance limitand factored endurance limit It is observed from Figure 5

0

200

400

600

800

1000

1200

1400

1000 10000 100000 1000000 10000000

S998400e factored curve

Sm = 583MPa

Se unfactored curve

Alte

rnat

ing

stres

sS a

(M

Pa)

NNumber of cycles

Figure 5 Factored and unfactored S-N curve for 65Si7 leaf spring

that the endurance limit is 636MPa without consideringthe various factors affecting the fatigue life It has also beenobserved that the corrected endurance limit is 4019MPaConsidering the design material and processing parameterof the leaf springs the steps involved in the graphicalmethodsare as follows

(a) 119878119906119905 = 1272MPa(b) 119878119910 = 10812MPa

(c) 1198781015840

119890= 05119878119906119905 = 05 times 1272 = 636MPa

(d) 120590min = 269MPa at 06 g load 120590max = 897MPa at 2 gload

(e) 119878119886 = (120590max minus 120590min)2 = (897 minus 269)2 = 314MPa(f) 119878119898 = (120590max + 120590min)2 = (897 + 269)2 = 583MPa(g) 119878119890 = 119870load times 119870surfae times 119870temp times 119870reliability times 119870size times 119878

1015840

119890

(h) 119870load = load factor for bending 119870load = 1(i) 119870surface = 1 (for shot peening treating)(j) 119870temp = 1 if 119879 le 450

∘C(k) 119870reliability = 080 Assuming 99 reliability

(l) 119870size = 1189 lowast (119889eqiv)minus097 for 8mm lt 119889 le 250mm

(m) 119889 eqiv = radic1198609500766 = 6588mm

(n) 11986095 = 005 lowast 119887 lowast ℎ = 3325mm2(o) 119870size = 1189 lowast (119889eqiv)

minus097= 079

(p) 119878119890 = 1 times 1 times 1 times 080 times 079 times 636 = 4019MPa

Figure 6 shows an alternating stress versus mean stress plotfor the LCV leaf spring It has been observed from Figure 6that the intersection of the alternating and mean stress lineslies outside the region AC If the point is within this lineAC the component is designed for infinite life but if thecomponent is outside this region the component is designedfor the finite life Thus from the position of point I it isobserved that the component is designed for the finite lifeThe equivalent alternating stress as determined by joining thepoint of intersection I and ultimate strength point with thealternating stress axis is found to be 578MPa

6 International Scholarly Research Notices

0100200300400500600700800900

100011001200

0 200 400 600 800 1000 1200 1400

Alte

rnat

ing

stres

s (M

Pa)

Mean stress (MPa)

As point I lies outside this region theleaf spring is designed for finite lifeI

C

A

Sa = 314MPa

Sm = 583MPa

Se = 4019MPa

Sae = 578MPa equivalent alternating stress

Figure 6 Alternating stress versus mean stress plot

1400

1200

1000

800

600

400

200

01e + 3 1e + 4 1e + 5 1e + 6 1e + 7 1e + 8

Sae = 578MPa

Se = 4019 MPa

Nf = number of cycles to failure

Alternating stress versus number of cycles

NNumber of cycles

Alte

rnat

ing

stres

sS a

(MPa

)

A

BC

E D

Figure 7 S-N curve for 65Si7

Figure 7 shows the S-N diagram for 65Si7 Point A rep-resents the alternating stress at which the spring will sustain1000 cycles Point D represents the endurance limit that is4019MPa of 65Si7 The line CB represents the equivalentalternating stress The intersection of alternating stress atpoint B will give the number of cycles to fatigue failure

FromFigure 7 S-N plot it is observed thatΔABC is similarto ΔADE

Hence 119860119862119860119864 = 119862119861119863119864

119860119862 = log119860 minus log119862 = 0296

119860119864 = log119860 minus log119864 = 0454

119863119864 = log119863 minus log119864 = log 106minus log 10

3= 3

119862119861 =0296 times 3

0454= 1957

Total 119862119861 = 3 + 197 = 49957

Number of cycles = 104957

= 90763 cycles to failure

(2)

1e + 3 1e + 4 1e + 5 1e + 6 1e + 7 1e + 8

NNumber of cycles

1400

1200

1000

800

600

400

200

0

Alte

rnat

ing

stres

sS a

(MPa

)

N1 cycles at S998400m N2 cycles at Se

= 09(Sut)

Se

A

BC

S998400m

Figure 8 Estimated S-N curve

7 Analytical Method forFatigue Life Prediction

The high cycle fatigue regime is from 103 to 106 and beyondThematerial strength at 103 cycles is called 119878

1015840

119898 which is equal

to 09 Sut The estimated S-N diagram drawn on the log-loggraph is shown in Figure 8 Figure 8 shows that the 119909-axisruns from 103 to 109 or beyond The appropriate 119878

1015840

119898from

the equation for bending load is plotted at N1 = 103 As thematerial exhibits a knee the corrected endurance limit 119878119890 isplotted at N2 = 106 A straight line is drawn between 119878

1015840

119898and

119878119890 The curve is continuous horizontally beyond N2 pointThe equation of the line from 119878

1015840

119898to 119878119890 can be written as

119878 (119873) = 119886119873119887

(taking log on both sides) (3)

log 119878 (119873) = log 119886 + 119887 log119873 (4)

where 119878(119873) is the fatigue strength at any 119873 and 119886 119887 are theconstants defined by the boundary conditions For all theconditions the 119910 intercept is 119878(119873) = 119878

1015840

119898at N = N1 = 103

for endurance limit case 119878(119873) = 119878119890 atN =N2 = 106 Applyingthe boundary condition in the equation we have

log 1198781015840

119898= log 119886 + 119887 log1198731 (5)

log 119878119890 = log 119886 + 119887 log1198732 (6)

log 1198781015840

119898minus log 119878119890 = 119887 (log1198731 minus log1198732) (7)

119885 = (log1198731 minus log1198732) (8)

119887 =1

119885log

1198781015840

119898

119878119890

(9)

log 1198781015840

119898minus 119887 log1198731 = log 119886 (10)

International Scholarly Research Notices 7

As 1198731 = 1000 log101000 = 3

log 1198781015840

119898minus 3119887 = log 119886

119886 =

(1198781015840

119898)2

119878119890

(11)

119873 = (119878119886

119886)

minus1119887

(12)

119878119886119890 = 119886119873119887

119891[13] where119873119891 = number of cycles to failure 119878119886119890 =

equivalent alternating stress 119886 119887 are constantswhich dependson the material properties of 65Si7 The fatigue life is to bepredicted at equivalent alternating stress so 119878119886 is replaced by119878119886119890 The above mentioned equation is used for fatigue lifeestimation and the codes for the analyticalmethod arewrittenin FORTRANThe flowchart is shown in Figure 9

8 Computer Aided Engineering Analysis

The CAD model of the individual leaf is prepared from thestandard drawing of the leaf spring and assembled The leafspring assembly is imported to an analysis software ANSYSfor further processing The different contacts are set andentire model is meshed into small elements The boundaryconditions are applied by taking into consideration the actualloading conditions and the solver gives the solution Thediverse steps involved in CAE analysis are as follows

81 CAD Modeling The CAD modeling of the conventionalleaf springs structure is performed by using solid workssoftware The CAD model of leaf springs consists of total34 different parts which are assembled together in assemblydesign to construct an assemblyThemultileaf springs assem-bly used for analysis is shown in Figure 10

82 Analysis Using ANSYS The CAD model of leaf springshas been imported in the ANSYS solver All the boundaryconditions and material properties have been specified asper the standard specified by the vehicle manufacturer Thematerial used for the leaf springs for analysis is 65Si7 whichis having homogenous and isotropic behaviour The material65Si7 is added in the material library and the engineeringproperties are applied

The process for performing analysis in ANSYS solverinvolves the following

821 Setting the Contact Reign The contact conditions areformed where the components meet The differences inthe contact settings determine how the contacting bodiescan move relative to one another In this assembly the Noseparation contact is used for the analysis It only applies toregion of faces Separation of faces in contact is not allowedbut small amounts of frictionless sliding can occur alongcontact faces In general CONTA174 and TARGE170 areused CONTA174 is used for contact and sliding between3D target surfaces (TARGE170) which is defined by thiselement The element is applicable to 3D structural analysis

Start

Calculate maximum thickness

Estimate the number of leaves width and thickness for required

MOI

Select assembly stresses

Calculate steppingoverhang

If no load assembly camber

Calculate the mass

Calculate fatigue life

End

Calculate Smax

If Kmodified variesmore than 7

Calculate Kmodified

If t gt tmax if MOI estimated gt

MOI required

Required K Pdesign Smax Nf

Calculate required moment ofinertia (MOI) Pmax

Calculate the Smaximum andSinitial stress for fatigue life

If Sas middot t2 = 0

Figure 9 Flowchart for analytical estimation of fatigue life of 65Si7leaf spring

Figure 10 CAD model of the leaf springs

8 International Scholarly Research Notices

Figure 11 Boundary conditions for CAE analysis

TARGE170 is used to represent various 3D target surfaces forthe associated contact elements

822 Meshing In this congregation SOLID187 elementwhich is a standard mechanical element for solids is used forthe result SOLID187 element is a higher order 3-D 10-nodeelement SOLID187 has quadratic displacement behaviourand is well suited to modeling irregular meshes The elementis defined by 10 nodes having three degrees of freedom ateach node translations in the nodal 119909 119910 and 119911 directionsThe number of SOLID187 elements is 6964 and the numberof nodes generated is 16943

823 Static Analysis Module A static structural analysisdetermines the displacements stresses strains and forcesin structures or components caused by loads that do notinduce significant inertia and damping effects Steady loadingand response conditions are assumed that is the loads andthe structurersquos response are assumed to vary slowly withrespect to time Static structure analysis takes into consid-eration some parameters like material properties loadingconditions support conditions and contacts which are to bespecified as the input to the preprocessing of the analysis

824 Applying CAE Boundary Conditions The boundaryconditions are applied by taking into consideration the exper-imental loading conditions The springs have been modelledin flat condition and the loading is done to achieve the initialcondition The total load is divided on the two eyes of themaster leaf and pins The fixed support constitutes the seatlength (on master leaf and last (12th leaf) and the centre boltThe CAE boundary conditions are shown in Figure 11

83 Fatigue Life Assessment Using CAE Tools While leafsprings may work well initially they often fail in service dueto fatigue failure caused by repeated cyclic loadingThe aimoffatigue analysis is characterization of capability of a materialto survive many cycles that a leaf spring may experienceduring its life time In ansys fatigue module twomethods areavailable that is stress life and strain life method For thiswork the stress lifemethod is used to predict the fatigue life ofthe component The static environment is set by applying theboundary conditions by taking into consideration the actualloading conditions After the static analysis the fatigue toolis used for fatigue life estimation In stress life decision treeit is required to make four input decisions to perform a stress

life analysis These decisions affect the outcome of the fatigueanalysis in both predicted life and types of postprocessingavailable Input decisions that are to be considered for fatiguelife estimation are loading typemean stress effectsmultiaxialstress correction and fatigue modification factors

831 Type of Loading Unlike static stress which is analyzedwith calculations for a single stress state fatigue damageoccurs when stress at a point changes over time There areessentially four classes of fatigue loading with the ANSYSfatigue module [14] currently supporting the first three

(i) constant amplitude proportional loading(ii) constant amplitude nonproportional loading(iii) nonconstant amplitude proportional loading(iv) nonconstant amplitude non-proportional loading

Constant amplitude proportional loading is the classic ldquobackof the enveloperdquo calculation describing whether the loadhas a constant maximum value or continually varies withtime Loading is of constant amplitude because only one setof FE stress results along with a loading ratio is requiredto calculate the alternating and mean values The loadingratio is defined as the ratio of the second load to the firstload (LR = L2L1) Loading is proportional since only oneset of FE results are needed (principal stress axes do notchange over time) Common types of constant amplitudeloading are fully reversed (apply a load and then apply anequal and opposite load a load ratio of minus1) and zero-based(apply a load and then remove it a load ratio of 0) Sinceloading is proportional looking at a single set of FE resultscan identify critical fatigue locations Constant amplitudenonproportional loading looks at exactly two load cases thatneed not to be related by a scale factor The loading isof constant amplitude but nonproportional since principalstress or strain axes are free to change between the two loadsets Nonconstant amplitude proportional loading also needsonly one set of FE results But instead of using a single loadratio to calculate alternating and mean values the load ratiovaries over time

832 Mean Stress Correction For stress life if experimen-tal data at different mean stresses or r-ratiorsquos exist meanstress can be accounted for directly through interpolationbetweenmaterial curves If experimental data is not availableseveral empirical options may be chosen including GerberGoodman and Soderberg theories which use static materialproperties yield stress and tensile strength along with S-Ndata to account for any mean stress

833 Multiaxial Stress Correction Factor Experimental testdata is mostly uniaxial whereas finite element results areusually multiaxial At some point stress must be convertedfrom a multiaxial stress state to a uniaxial one Von-Misesstress max shear stress maximum principal stress or any ofthe component stresses can be used for the comparison withthe experimental uniaxial stress value

International Scholarly Research Notices 9

(a) (b)

Figure 12 (a) Fatigue life using CAE tools (b) Equivalent alternating stress

Table 5 CAE results for load deflection and bending stresses

Serial number Load type Load (N) Deflection (mm) Stress (MPa)1 Unladen load 7661 449 270742 Designrated load 12959 7605 4583 Flat load 15754 9245 556834 Rubber touching load 216457 12702 7655 Metal to metal contact 28010 16436 98989

Table 6 Comparison of fatigue life by various approaches

Serial number Method for fatiguelife assessment Alternating stress level Stress range Equivalent alternating stress Fatigue life Variation from

experimental results1 Experimental 269ndash896 627 mdash 83513 mdash

2 SAE spring designmanual approach 200ndash885 685 mdash 69600 166

3 Graphical method 269ndash896 627 578 90763 8684 Analytical method 269ndash896 627 579 90304 8135 CAE method 269ndash896 627 562 82348 239

834 Fatigue Modifications (Value of Infinite Life) Anotheravailable option when conducting a variable amplitudefatigue analysis is the ability to set the value used for infinitelife In constant amplitude loading if the alternating stress islower than the lowest alternating stress on the fatigue curvethe fatigue tool will use the life at the last pointThis providesfor an added level of safety because many materials do notexhibit an endurance limit

The static environment is set and boundary conditions areapplied and the solver gives the solution The deflection andstress results obtained from the specified loads are recorded ina tabular format The CAE results for deflection and bendingstress are shown inTable 5 Figure 12(a) depicts the fatigue lifeof the leaf spring using Ansys solver For prediction of fatiguelife the stress life approach is selected A constant amplitudeload ratio is selected as the loading type The fatigue strengthfactor of 065 is chosen and scale factor is kept as 1 Formean stress theory Goodmanrsquos criteria are selected Lastly formultiaxial stress correction von-mises stress is selected andthe component is designed for finite life It has been observedthat the fatigue life of the leaf spring using CAE tool is 82348

cycles Figure 12(b) depicts the equivalent alternating stressin the leaf spring using Ansys solver

9 Results and Discussion

91 Fatigue Life Comparison by Various Approaches Table 6depicts the comparison of fatigue life by various methodsIt is observed that for the alternating stress level of 896ndash269MPa the experimental fatigue life of the leaf spring is83513 cycles The fatigue life estimated by SAE spring designmanual technique is 69600 cycles for the alternating stresslevel of 885ndash200MPa It is also observed that in the SAEspring design manual approach the maximum stress that is885MPa is less than the specified maximum stress but thestress range is higher than specified stress range Hence thisapproximation provides results within 166 variation Thesame approach with specified stress range gives the fatiguelife of leaf spring to be 81600 For the same alternating stresslevel of 896ndash269MPa the fatigue life is found to be 90763cycles by graphical method and equivalent stress is found to

10 International Scholarly Research Notices

Table 7 Comparison of experimental and CAE results

Load type Load (N) Experimental results CAE results age variation between CAEand Experimental results

Deflection Stress Deflection Stress Deflection StressUnladen load 7661 469 262 449 27074 43 33DesignRated load 12959 8144 446 7605 458 66 27Flat load 15754 99 540 9245 55683 66 31Rubber touching load 216457 136 743 12702 765 66 30Metal to metal contact load 28010 176 941 16436 98989 66 52

be 578MPa In the analytical method the fatigue life is foundto be 90304 cycleswith 813 variation from the experimentalresults The CAE fatigue life is found to be 82348 cycles with239 variation from the experimental results

92 Comparison of Experimental and CAE Results To vali-date the analysis the CAE results have been compared withthe experimental results As the experiments are done ona full scale leaf spring testing machine under the specifiedloads the CAE analysis has been carried out for the sameloads The maximum stress induced in the leaf springs isfound to be 941MPa and 98989MPa using experimental andCAE approach respectively The stress is found to be wellbelow the yield tensile strength which is 10812MPa Thetotal deformation and stress comparison for experimentaland CAE approach also validates the CAE analysis of the leafsprings The results of the comparison have been depicted inthe tabular form in Table 7

From Table 7 it is observed that for the same unladenstatic load conditions deflection in experimental and CAEresults is 469mm and 449mm respectively The deforma-tion observed in CAE results varies by 43 The bendingstress for experimental and CAE results is 262MPa and27074MPa respectively The variation of bending stressobserved in CAE results from experimental is 33 FromTable 7 it is also observed that for the same design loadcondition the deflection found in experimental and CAEis 8144mm and 7605mm respectively The variation inCAE results from experimental is 66The bending stressesunder the design load for experimental and CAE results are446MPa and 458MPa respectivelyThe variation in bendingstress observed in the CAE results is 27 For the maximumload condition the static deflection is 176mm and 16436mmfor experimental and CAE results It has been observedthat when CAE results are compared with experimental thevariation in the deformation varies in between 43 and66 respectively The stress variation lies in the range of27 to 52 It has also been observed that the maximumstress induced in the assembly in both the approaches is wellbelow the yield stress of the material It has been observedthat the CAE results obtained by using SOLID187 meshelements and CONTA172 and TARGE170 (No separation andsliding) contact elements provides the results closer to theexperimental testing

10 Conclusions

The 65Si7 LCV model is taken into consideration fordetermining the fatigue life by experimental and graphicalmethods analytical method (using FORTRAN) SAE springdesign manual approach and CAE (using Ansys) approachThe following conclusions are made

(1) The fatigue life of the leaf spring for same stress rangewill decrease if the magnitude of the initial stressis lower In actual condition the leaf springs willwithstand 15ndash17 more fatigue life than predicted bySAE spring design manual approach

(2) Graphical and analytical methods are time consum-ing and prone to errors but provide results which arewithin 8-9 variation

(3) It is concluded that when CONTA174 TARGE170type of contact and SOLID187 mesh element are usedfor CAE analysis results are closer to the experimen-tal results CAE approach usingAnsys predicts fatiguelife within 2ndash5 of experimental results and can be analternate of experimental and analytical approach

Nomenclature

119862119886 No load assembly camber119864 Youngrsquos modulus of elasticity119873119891 Number of cycles to failure120588 Density120583 Poissonrsquos ratio119878119886 Alternating stress120590max Maximum stress1198781015840

119890 Endurance limit

119878119890 Corrected endurance limit119878119910 Yield tensile strength119871 Span120590min Minimum stress119878119898 Mean stress119878119886119890 Equivalent alternating stress119878119906119905 Ultimate tensile strength119870surface Surface factor119870load Load factor119870temp Temperature factor119870size Size factor119870reliability Reliability factor

International Scholarly Research Notices 11

119889equiv Equivalent diameter of rotating beam spec-imen for any cross section

11986095 Portion of the cross sectional area of non-rounded that is stressed in between 95and 100 of its maximum stress

1198781015840

119898 Stress at 103 cycles

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

The authors would like to acknowledge Mr P S Chawlaand the leaf springs testing division of Friends Auto (India)Ltd whose unconditional support has made this projectsuccessful

References

[1] S Saelem S Chantranuwathana K Panichanun P Preeda-nood P Wichienprakarn and P Kruo-ongarjnukool ldquoExper-imental verification of leaf spring model by using a leaf springtest rigrdquo in Proceedings of the 23rd Conference of the Mechan-ical Engineering Network of Thailand Chiang Mai ThailandNovember 2009

[2] F N A Refngah S Abdullah A Jalar and L B Chua ldquoFatiguelife evaluation of two types of steel leaf springsrdquo InternationalJournal of Mechanical and Materials Engineering vol 4 no 2pp 136ndash140 2009

[3] J J Fuentes H J Aguilar J A Rodrıguez and E J HerreraldquoPremature fracture in automobile leaf springsrdquo EngineeringFailure Analysis vol 16 no 2 pp 648ndash655 2009

[4] M L Aggarwal R A Khan and V P Aggarwal ldquoOptimizationof micro welds used in the leaf springsrdquo International Journal ofEngineering Material and Science vol 28 pp 217ndash220 2006

[5] M L Aggarwal V P Agrawal and R A Khan ldquoA stressapproach model for predictions of fatigue life by shot peeningof EN45A spring steelrdquo International Journal of Fatigue vol 28no 12 pp 1845ndash1853 2006

[6] M M Patunkar and D R Dolas ldquoModelling and analysisof composite leaf spring under the static load condition byusing FEArdquo International Journal of Mechanical amp IndustrialEngineering vol 1 no 1 pp 1ndash4 2011

[7] M S Kumar and S Vijayarangan ldquoAnalytical and experimentalstudies on fatigue life prediction of steel and composite multi-leaf spring for light passenger vehicles using life data analysisrdquoMaterials Science vol 13 no 2 pp 141ndash146 2007

[8] P Sanjurjo C Rodrıguez I F Pariente F J Belzunce and A FCanteli ldquoThe influence of shot peening on the fatigue behaviourof duplex stainless steelsrdquo Procedia Engineering vol 2 no 1 pp1539ndash1546 2010

[9] W Z Zhuang andG RHalford ldquoInvestigation of residual stressrelaxation under cyclic loadrdquo International Journal of Fatiguevol 23 supplement 1 pp S31ndashS37 2001

[10] G Savaidis M Malikoutsakis and A Savaidis ldquoFE simulationof vehicle leaf spring behavior under driving manoeuvresrdquoInternational Journal of Structural Integrity vol 4 no 1 ArticleID 17082873 pp 23ndash32 2013

[11] IS 1135 SpringsmdashLeaf Springs Assembly for Automobiles 1995[12] SAE Spring Design ManualmdashDesign and Application of Leaf

Springs HS-744 AE-11 1990[13] R L Norton Machine DesignmdashAn Integrated Approach Pear-

son Education Asia 2nd edition 2001[14] ldquoAnsys Workbench training manual on fatigue toolrdquo 2014

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Page 3: Fatigue Life Assessment of 65Si7 Leaf Springs: A Comparative Study

International Scholarly Research Notices 3

Table 2 Design parameters of the leaf springs

Span (119871)(mm)

Load rate(119896) (Nmm)

Load (N) No loadcamber(119862119886) (mm)

Seatlength(mm)

Totalnumber ofleaves (119873)

Number offull lengthleaves (119883)

Maximum thickness ofthe individual leaf (119905) timeswidth (119887) (mmtimesmm)

Required fatiguelife (119873

119891) at

(13 plusmn 07 g)Rated(119875119892)

Maximum(119875max)

1150 plusmn 3 15911 plusmn 7 12959 28010 95 plusmn 4 100 12 2 8 times 70 70000 cycles

Figure 2 Leaf spring assembly drawing

of the eyes is termed datum line for the springs with eyesSpan is termed the distance between the centres of the eyes

The distance from the datum line to the point where thecentre bolt or the cup centre intersects the top surface of themain leaf when the spring is not loaded is called free camberor free height This may be either positive or negative Thedistance from the datum line to the point where the centrebolt or the cup centre intersects the top surface of the mainleaf when the spring is loaded is called loaded camber Rideclearance may be termed as the spring travel on the vehiclefrom the design load to the metal to metal contact positionor the deflection from the design load to the metal to metalcontact position Stiffness factor takes into considerationthe leave length and type of end used The various designparameters of the leaf spring assembly of light commercialvehicle are indicated in Table 2 The layout drawing of lightcommercial vehicle (LCV) leaf spring is depicted in Figure 2

31 Manufacturing of Leaf Springs For the fabrication ofhigh strength leaf springs the process comprises shearingpunching heat treatment hot cambering shot peeningscragging and testing for load rate and fatigue life Afterpunching and shearing the raw material is moved to thehardening furnaces for heat treatment The structure of theraw material is partial austenite and after quenching thestructure is martensite but after the tempering process thestructure should be tempered martensite The spring steel ishaving the thickness of 8mm and width of 70mm whichis heated at 880∘C to achieve full austenite structure Hotcambering of the spring is done in this state by passingthrough a finger cambering tools followed by quenching in oilat temperature of 80∘C Tempering is done at a temperature of410∘C for 90min of slow cooling till the tempered martensitestructure is achieved Surface treatment like shot peening andgraphite coating is done on each individual leaf The finalassembly is done by pulling all the leaf with a centre nut andboltThe scragging of the assembly is done and the u clips areattached The assembly is tested for load rate and fatigue life

Hydraulic cylinderLimit switch

Test component

Mounting fixture

Hydraulic cylinderLimit swi htch

Test compponent

Mounting gg fififixture

Figure 3 Full scale leaf spring testing machine in fully laden con-dition

4 Experimental Setup

The 65Si7SUP9 leaf springs assembly consists of two fulllength leaves and ten graduated leaves four rebound clipsof mild steel four shim pipes with four nuts and bolts fourrivets centre nut and bolt and bush of bronzeThemaster leafconsists of upturned berlin eye at both the ends The secondleaf is provided with a military wrapper to avoid accidents incase of master leaf failure at eye section The full scale testingof leaf springs was carried out in an electrohydraulic staticcomponent testing system The laminated leaf springs wereplaced in a fixture simulating the conditions of a vehicle Thesetup consists of a hydraulic power pack to give a hydraulicpressure of 206MPa with a flow rate of 210 liters per minute(lpm) which was sent to a hydraulic actuator to operate ata frequency of 03Hz with the displacement specified by thealternating load This involves applying the axial load onthe leaf springs and measuring the deflection and bendingstress The conventional leaf spring was tested under staticload condition by using hydraulic static load ram for loadapplication Mounting of the leaf spring was done by keepingit in inverted manner on the test bed Two eye ends wereheld in the clamping devices and load was applied from thetop at the center of leaf springs To measure the load dialindicator was used which was located beside the full scaleleaf spring testing machine and deflection was measuredby strain gauges located at the clamping of the test rigThe springs were loaded from unladen load (ie 76 KN) tomaximum load (ie 28 KN) The vertical deflection of thesprings at the unladen load design load flat load rubbertouching load and metal to metal contact or maximum loadwas recorded respectively as per the standard operatingprocedure prescribed [11] Figure 3 shows the full scale leafspring testing machine in static and fully laden condition

4 International Scholarly Research Notices

Table 3 Experimental results for load deflection and bending stresses

Serial number Load type Load (N) Deflection (mm) Bending stress (MPa)1 Unladen load 7661 469 2622 Designrated load 12959 8144 4463 Flat load 15754 99 5404 Rubber touching load 216457 136 7435 Metal to metal contact 28010 176 941

Table 4 Experimental fatigue life of the specimen

Material processing Standardspecified

Alternatingstress level(MPa)

Stress range Fatigue lifeof S-1 (119873

119891)

Fatigue lifeof S-2 (119873

119891)

Fatigue lifeof S-3 (119873

119891)

Fatigue lifeof S-4 (119873

119891)

AverageSD

Normal rollingquenching at 880∘Chardening in oil at 80∘Ctempering at 410∘C for90mins shot peening at18 A intensity BHN380ndash432 and scraggingat 09 of yield stress

06 gndash2 g 269ndash896 627 84212 81961 82226 85656Average83513SD 1518

The leaf springs were tested on a full scale leaf springtesting machine under the unladen rated flat rubber touch-ing load and metal to metal load and the correspondingdeflection and stress values observed are shown in theTable 3The experiments were conducted twice and the mean valueof the results was considered Table 3 depicts the observedvalues of deflection and stress corresponding to the loadsapplied on the shorter leaf by a static hydraulic ram

41 Experimental Fatigue Life Determination To determineexperimental fatigue life four leaf springs specimens (S-1 S-2S-3 and S-4) are manufactured with specified design param-eters Analogous kind of material processing normal rollingquenching at 880∘C hardening in oil at 80∘C tempering at410∘C for 90mins shot peening at 18 A intensity BHN 380ndash432 and scragging at 09 of yield stress was done for allthe specimensThe stress range considered for the specimensis 627MPa 13 plusmn 07 g All the four specimens were testedunder same stress range and fatigue life was determined asdepicted in Table 4 The fatigue life of specimen S-1 is 84212for sample S-2 is 81961 and for samples S-3 and S-4 are 82226and 85685 respectively The mean value that is 83513 of thefatigue life for the four specimens is taken into considerationfor this study As per the requirement specified by the vehiclemanufacturer the leaf springs are to be tested on full scaletesting machine as per 13 plusmn 07 g The maximum load will be2 g and theminimum load will be 06 g Here g represents thedesign load [12]

119878max =119875max lowast 119871119886 lowast 119905

8 lowast sum 119868total= 896MPa

Smin =119875min lowast 119871119886 lowast 119905

8 lowast sum 119868total= 269MPa

(1)

5 SAE Spring Design Manual Approach

Fatigue life is articulated by the number of deflection cyclesthat a spring will withstand without failure or permanentset A leaf spring used in a suspension will undergo a largenumber of cycles of small amplitude near the design loadposition without failure Under the greater amplitude thenumber of cycles without failure will be reduced since themaximum stresses aswell as the stress range are amplified andboth are determining factors in fatigue life of the spring Asper the SAE spring design manual approach [12] the fatiguetest stroke for leaf springs (by considering assembly stress) ispredicted as

(a) deflection at design load = 129591531 = 846mm(b) maximum load on the leaf springs = 28KN(c) metal-to-metal clearance (compression stroke) =

946mm(d) total deflection to maximum load = 1829mm(e) stress at metal-to-metal contact position = 885MPa(f) stress rate = 8851829 = 483MPamm(g) release stroke = 05 times 946 = 473mm(h) fatigue test stoke = 473 + 946 = 1419mm(i) initial stress = 885 minus (1419 times483) = 1996MPa

The maximum stress of 885MPa and initial stress of1996asymp 200MPa are utilized to predict the approximatefatigue life of the leaf spring

51 Fatigue Life Assessment by SAE Spring Design ManualApproach Figure 4 shows a maximum stress versus initialstress plot as per SAE spring design manual approach As perSAE spring design manual this criterion is frequently used

International Scholarly Research Notices 5

400500600700800900

1000110012001300

0 100 200 300 400 500 600 700

Max

imum

stre

ss (M

Pa)

Initial stress (MPa)

= 269MPa= 200MPa

Smax (as specified) = 896MPa

Smax (as per SAE) = 885MPa

Sinitial (as specified)Sinitial (as per SAE)

30000cycles to failure

50000

75000

100000

200000

1000000

cycles to failure

Figure 4Maximum versus initial stress plot (without shot peening)[12]

for determination of approximate fatigue life of the springinitial stress (horizontal scale) and maximum stress (verticalscale) are intersected to estimate the number of cycles thespring will survive The life predicted from this plot does notconsider the effect of shot peening and scragging operationsbut in actual practice processing like shot peening andscragging is performed on the leaf springs which enhancesthe fatigue life by approximately 20

From Figure 4 it is observed that the maximum stressinduced in the leaf springs (by considering the assemblystresses) is 885MPa and the initial stress value is 200MPaThe intersection of 885MPa and 200MPa lies in the zoneof 50000 to 75000 cycles As the point of intersection isnearer to 50000-cycle line it will sustain approximately 58000cycles Due to shot peeing and scragging the fatigue lifeof leaf springs by considering assembly stresses would beapproximately (58000 lowast 12) 69600 cycles

The vehicle manufacture has specified that the maximumstress of 896MPa corresponds to the maximum load of 2 gand the minimum stress of 269MPa corresponds to theminimum load of 06 g where g is the design load Theintersection of 896MPa and 269MPa lies in the zone of 50000to 75000 cycles As the point of intersection is nearer to75000-cycle line approximately it will sustain around 68000cycles Due to shot peeing and scragging the fatigue lifeof leaf springs (by considering assembly stresses) would beapproximately (68000 lowast 12) 81600 cycles

Hence it is observed that with the stress range obtainedfrom SAE spring design approach the fatigue life and asspecified stress range are around 69600 cycles and 81600cycles approximatelyThe stress range specified by the vehiclemanufacturer gives result closer to the experimental results

6 Fatigue Life Estimation byGraphical Method

The graphical method involves determination of effect ofvarious factors like load temperature size and surface on theendurance limit of the 65Si7 Figure 5 shows an alternatingversus number of cycles plot for unfactored endurance limitand factored endurance limit It is observed from Figure 5

0

200

400

600

800

1000

1200

1400

1000 10000 100000 1000000 10000000

S998400e factored curve

Sm = 583MPa

Se unfactored curve

Alte

rnat

ing

stres

sS a

(M

Pa)

NNumber of cycles

Figure 5 Factored and unfactored S-N curve for 65Si7 leaf spring

that the endurance limit is 636MPa without consideringthe various factors affecting the fatigue life It has also beenobserved that the corrected endurance limit is 4019MPaConsidering the design material and processing parameterof the leaf springs the steps involved in the graphicalmethodsare as follows

(a) 119878119906119905 = 1272MPa(b) 119878119910 = 10812MPa

(c) 1198781015840

119890= 05119878119906119905 = 05 times 1272 = 636MPa

(d) 120590min = 269MPa at 06 g load 120590max = 897MPa at 2 gload

(e) 119878119886 = (120590max minus 120590min)2 = (897 minus 269)2 = 314MPa(f) 119878119898 = (120590max + 120590min)2 = (897 + 269)2 = 583MPa(g) 119878119890 = 119870load times 119870surfae times 119870temp times 119870reliability times 119870size times 119878

1015840

119890

(h) 119870load = load factor for bending 119870load = 1(i) 119870surface = 1 (for shot peening treating)(j) 119870temp = 1 if 119879 le 450

∘C(k) 119870reliability = 080 Assuming 99 reliability

(l) 119870size = 1189 lowast (119889eqiv)minus097 for 8mm lt 119889 le 250mm

(m) 119889 eqiv = radic1198609500766 = 6588mm

(n) 11986095 = 005 lowast 119887 lowast ℎ = 3325mm2(o) 119870size = 1189 lowast (119889eqiv)

minus097= 079

(p) 119878119890 = 1 times 1 times 1 times 080 times 079 times 636 = 4019MPa

Figure 6 shows an alternating stress versus mean stress plotfor the LCV leaf spring It has been observed from Figure 6that the intersection of the alternating and mean stress lineslies outside the region AC If the point is within this lineAC the component is designed for infinite life but if thecomponent is outside this region the component is designedfor the finite life Thus from the position of point I it isobserved that the component is designed for the finite lifeThe equivalent alternating stress as determined by joining thepoint of intersection I and ultimate strength point with thealternating stress axis is found to be 578MPa

6 International Scholarly Research Notices

0100200300400500600700800900

100011001200

0 200 400 600 800 1000 1200 1400

Alte

rnat

ing

stres

s (M

Pa)

Mean stress (MPa)

As point I lies outside this region theleaf spring is designed for finite lifeI

C

A

Sa = 314MPa

Sm = 583MPa

Se = 4019MPa

Sae = 578MPa equivalent alternating stress

Figure 6 Alternating stress versus mean stress plot

1400

1200

1000

800

600

400

200

01e + 3 1e + 4 1e + 5 1e + 6 1e + 7 1e + 8

Sae = 578MPa

Se = 4019 MPa

Nf = number of cycles to failure

Alternating stress versus number of cycles

NNumber of cycles

Alte

rnat

ing

stres

sS a

(MPa

)

A

BC

E D

Figure 7 S-N curve for 65Si7

Figure 7 shows the S-N diagram for 65Si7 Point A rep-resents the alternating stress at which the spring will sustain1000 cycles Point D represents the endurance limit that is4019MPa of 65Si7 The line CB represents the equivalentalternating stress The intersection of alternating stress atpoint B will give the number of cycles to fatigue failure

FromFigure 7 S-N plot it is observed thatΔABC is similarto ΔADE

Hence 119860119862119860119864 = 119862119861119863119864

119860119862 = log119860 minus log119862 = 0296

119860119864 = log119860 minus log119864 = 0454

119863119864 = log119863 minus log119864 = log 106minus log 10

3= 3

119862119861 =0296 times 3

0454= 1957

Total 119862119861 = 3 + 197 = 49957

Number of cycles = 104957

= 90763 cycles to failure

(2)

1e + 3 1e + 4 1e + 5 1e + 6 1e + 7 1e + 8

NNumber of cycles

1400

1200

1000

800

600

400

200

0

Alte

rnat

ing

stres

sS a

(MPa

)

N1 cycles at S998400m N2 cycles at Se

= 09(Sut)

Se

A

BC

S998400m

Figure 8 Estimated S-N curve

7 Analytical Method forFatigue Life Prediction

The high cycle fatigue regime is from 103 to 106 and beyondThematerial strength at 103 cycles is called 119878

1015840

119898 which is equal

to 09 Sut The estimated S-N diagram drawn on the log-loggraph is shown in Figure 8 Figure 8 shows that the 119909-axisruns from 103 to 109 or beyond The appropriate 119878

1015840

119898from

the equation for bending load is plotted at N1 = 103 As thematerial exhibits a knee the corrected endurance limit 119878119890 isplotted at N2 = 106 A straight line is drawn between 119878

1015840

119898and

119878119890 The curve is continuous horizontally beyond N2 pointThe equation of the line from 119878

1015840

119898to 119878119890 can be written as

119878 (119873) = 119886119873119887

(taking log on both sides) (3)

log 119878 (119873) = log 119886 + 119887 log119873 (4)

where 119878(119873) is the fatigue strength at any 119873 and 119886 119887 are theconstants defined by the boundary conditions For all theconditions the 119910 intercept is 119878(119873) = 119878

1015840

119898at N = N1 = 103

for endurance limit case 119878(119873) = 119878119890 atN =N2 = 106 Applyingthe boundary condition in the equation we have

log 1198781015840

119898= log 119886 + 119887 log1198731 (5)

log 119878119890 = log 119886 + 119887 log1198732 (6)

log 1198781015840

119898minus log 119878119890 = 119887 (log1198731 minus log1198732) (7)

119885 = (log1198731 minus log1198732) (8)

119887 =1

119885log

1198781015840

119898

119878119890

(9)

log 1198781015840

119898minus 119887 log1198731 = log 119886 (10)

International Scholarly Research Notices 7

As 1198731 = 1000 log101000 = 3

log 1198781015840

119898minus 3119887 = log 119886

119886 =

(1198781015840

119898)2

119878119890

(11)

119873 = (119878119886

119886)

minus1119887

(12)

119878119886119890 = 119886119873119887

119891[13] where119873119891 = number of cycles to failure 119878119886119890 =

equivalent alternating stress 119886 119887 are constantswhich dependson the material properties of 65Si7 The fatigue life is to bepredicted at equivalent alternating stress so 119878119886 is replaced by119878119886119890 The above mentioned equation is used for fatigue lifeestimation and the codes for the analyticalmethod arewrittenin FORTRANThe flowchart is shown in Figure 9

8 Computer Aided Engineering Analysis

The CAD model of the individual leaf is prepared from thestandard drawing of the leaf spring and assembled The leafspring assembly is imported to an analysis software ANSYSfor further processing The different contacts are set andentire model is meshed into small elements The boundaryconditions are applied by taking into consideration the actualloading conditions and the solver gives the solution Thediverse steps involved in CAE analysis are as follows

81 CAD Modeling The CAD modeling of the conventionalleaf springs structure is performed by using solid workssoftware The CAD model of leaf springs consists of total34 different parts which are assembled together in assemblydesign to construct an assemblyThemultileaf springs assem-bly used for analysis is shown in Figure 10

82 Analysis Using ANSYS The CAD model of leaf springshas been imported in the ANSYS solver All the boundaryconditions and material properties have been specified asper the standard specified by the vehicle manufacturer Thematerial used for the leaf springs for analysis is 65Si7 whichis having homogenous and isotropic behaviour The material65Si7 is added in the material library and the engineeringproperties are applied

The process for performing analysis in ANSYS solverinvolves the following

821 Setting the Contact Reign The contact conditions areformed where the components meet The differences inthe contact settings determine how the contacting bodiescan move relative to one another In this assembly the Noseparation contact is used for the analysis It only applies toregion of faces Separation of faces in contact is not allowedbut small amounts of frictionless sliding can occur alongcontact faces In general CONTA174 and TARGE170 areused CONTA174 is used for contact and sliding between3D target surfaces (TARGE170) which is defined by thiselement The element is applicable to 3D structural analysis

Start

Calculate maximum thickness

Estimate the number of leaves width and thickness for required

MOI

Select assembly stresses

Calculate steppingoverhang

If no load assembly camber

Calculate the mass

Calculate fatigue life

End

Calculate Smax

If Kmodified variesmore than 7

Calculate Kmodified

If t gt tmax if MOI estimated gt

MOI required

Required K Pdesign Smax Nf

Calculate required moment ofinertia (MOI) Pmax

Calculate the Smaximum andSinitial stress for fatigue life

If Sas middot t2 = 0

Figure 9 Flowchart for analytical estimation of fatigue life of 65Si7leaf spring

Figure 10 CAD model of the leaf springs

8 International Scholarly Research Notices

Figure 11 Boundary conditions for CAE analysis

TARGE170 is used to represent various 3D target surfaces forthe associated contact elements

822 Meshing In this congregation SOLID187 elementwhich is a standard mechanical element for solids is used forthe result SOLID187 element is a higher order 3-D 10-nodeelement SOLID187 has quadratic displacement behaviourand is well suited to modeling irregular meshes The elementis defined by 10 nodes having three degrees of freedom ateach node translations in the nodal 119909 119910 and 119911 directionsThe number of SOLID187 elements is 6964 and the numberof nodes generated is 16943

823 Static Analysis Module A static structural analysisdetermines the displacements stresses strains and forcesin structures or components caused by loads that do notinduce significant inertia and damping effects Steady loadingand response conditions are assumed that is the loads andthe structurersquos response are assumed to vary slowly withrespect to time Static structure analysis takes into consid-eration some parameters like material properties loadingconditions support conditions and contacts which are to bespecified as the input to the preprocessing of the analysis

824 Applying CAE Boundary Conditions The boundaryconditions are applied by taking into consideration the exper-imental loading conditions The springs have been modelledin flat condition and the loading is done to achieve the initialcondition The total load is divided on the two eyes of themaster leaf and pins The fixed support constitutes the seatlength (on master leaf and last (12th leaf) and the centre boltThe CAE boundary conditions are shown in Figure 11

83 Fatigue Life Assessment Using CAE Tools While leafsprings may work well initially they often fail in service dueto fatigue failure caused by repeated cyclic loadingThe aimoffatigue analysis is characterization of capability of a materialto survive many cycles that a leaf spring may experienceduring its life time In ansys fatigue module twomethods areavailable that is stress life and strain life method For thiswork the stress lifemethod is used to predict the fatigue life ofthe component The static environment is set by applying theboundary conditions by taking into consideration the actualloading conditions After the static analysis the fatigue toolis used for fatigue life estimation In stress life decision treeit is required to make four input decisions to perform a stress

life analysis These decisions affect the outcome of the fatigueanalysis in both predicted life and types of postprocessingavailable Input decisions that are to be considered for fatiguelife estimation are loading typemean stress effectsmultiaxialstress correction and fatigue modification factors

831 Type of Loading Unlike static stress which is analyzedwith calculations for a single stress state fatigue damageoccurs when stress at a point changes over time There areessentially four classes of fatigue loading with the ANSYSfatigue module [14] currently supporting the first three

(i) constant amplitude proportional loading(ii) constant amplitude nonproportional loading(iii) nonconstant amplitude proportional loading(iv) nonconstant amplitude non-proportional loading

Constant amplitude proportional loading is the classic ldquobackof the enveloperdquo calculation describing whether the loadhas a constant maximum value or continually varies withtime Loading is of constant amplitude because only one setof FE stress results along with a loading ratio is requiredto calculate the alternating and mean values The loadingratio is defined as the ratio of the second load to the firstload (LR = L2L1) Loading is proportional since only oneset of FE results are needed (principal stress axes do notchange over time) Common types of constant amplitudeloading are fully reversed (apply a load and then apply anequal and opposite load a load ratio of minus1) and zero-based(apply a load and then remove it a load ratio of 0) Sinceloading is proportional looking at a single set of FE resultscan identify critical fatigue locations Constant amplitudenonproportional loading looks at exactly two load cases thatneed not to be related by a scale factor The loading isof constant amplitude but nonproportional since principalstress or strain axes are free to change between the two loadsets Nonconstant amplitude proportional loading also needsonly one set of FE results But instead of using a single loadratio to calculate alternating and mean values the load ratiovaries over time

832 Mean Stress Correction For stress life if experimen-tal data at different mean stresses or r-ratiorsquos exist meanstress can be accounted for directly through interpolationbetweenmaterial curves If experimental data is not availableseveral empirical options may be chosen including GerberGoodman and Soderberg theories which use static materialproperties yield stress and tensile strength along with S-Ndata to account for any mean stress

833 Multiaxial Stress Correction Factor Experimental testdata is mostly uniaxial whereas finite element results areusually multiaxial At some point stress must be convertedfrom a multiaxial stress state to a uniaxial one Von-Misesstress max shear stress maximum principal stress or any ofthe component stresses can be used for the comparison withthe experimental uniaxial stress value

International Scholarly Research Notices 9

(a) (b)

Figure 12 (a) Fatigue life using CAE tools (b) Equivalent alternating stress

Table 5 CAE results for load deflection and bending stresses

Serial number Load type Load (N) Deflection (mm) Stress (MPa)1 Unladen load 7661 449 270742 Designrated load 12959 7605 4583 Flat load 15754 9245 556834 Rubber touching load 216457 12702 7655 Metal to metal contact 28010 16436 98989

Table 6 Comparison of fatigue life by various approaches

Serial number Method for fatiguelife assessment Alternating stress level Stress range Equivalent alternating stress Fatigue life Variation from

experimental results1 Experimental 269ndash896 627 mdash 83513 mdash

2 SAE spring designmanual approach 200ndash885 685 mdash 69600 166

3 Graphical method 269ndash896 627 578 90763 8684 Analytical method 269ndash896 627 579 90304 8135 CAE method 269ndash896 627 562 82348 239

834 Fatigue Modifications (Value of Infinite Life) Anotheravailable option when conducting a variable amplitudefatigue analysis is the ability to set the value used for infinitelife In constant amplitude loading if the alternating stress islower than the lowest alternating stress on the fatigue curvethe fatigue tool will use the life at the last pointThis providesfor an added level of safety because many materials do notexhibit an endurance limit

The static environment is set and boundary conditions areapplied and the solver gives the solution The deflection andstress results obtained from the specified loads are recorded ina tabular format The CAE results for deflection and bendingstress are shown inTable 5 Figure 12(a) depicts the fatigue lifeof the leaf spring using Ansys solver For prediction of fatiguelife the stress life approach is selected A constant amplitudeload ratio is selected as the loading type The fatigue strengthfactor of 065 is chosen and scale factor is kept as 1 Formean stress theory Goodmanrsquos criteria are selected Lastly formultiaxial stress correction von-mises stress is selected andthe component is designed for finite life It has been observedthat the fatigue life of the leaf spring using CAE tool is 82348

cycles Figure 12(b) depicts the equivalent alternating stressin the leaf spring using Ansys solver

9 Results and Discussion

91 Fatigue Life Comparison by Various Approaches Table 6depicts the comparison of fatigue life by various methodsIt is observed that for the alternating stress level of 896ndash269MPa the experimental fatigue life of the leaf spring is83513 cycles The fatigue life estimated by SAE spring designmanual technique is 69600 cycles for the alternating stresslevel of 885ndash200MPa It is also observed that in the SAEspring design manual approach the maximum stress that is885MPa is less than the specified maximum stress but thestress range is higher than specified stress range Hence thisapproximation provides results within 166 variation Thesame approach with specified stress range gives the fatiguelife of leaf spring to be 81600 For the same alternating stresslevel of 896ndash269MPa the fatigue life is found to be 90763cycles by graphical method and equivalent stress is found to

10 International Scholarly Research Notices

Table 7 Comparison of experimental and CAE results

Load type Load (N) Experimental results CAE results age variation between CAEand Experimental results

Deflection Stress Deflection Stress Deflection StressUnladen load 7661 469 262 449 27074 43 33DesignRated load 12959 8144 446 7605 458 66 27Flat load 15754 99 540 9245 55683 66 31Rubber touching load 216457 136 743 12702 765 66 30Metal to metal contact load 28010 176 941 16436 98989 66 52

be 578MPa In the analytical method the fatigue life is foundto be 90304 cycleswith 813 variation from the experimentalresults The CAE fatigue life is found to be 82348 cycles with239 variation from the experimental results

92 Comparison of Experimental and CAE Results To vali-date the analysis the CAE results have been compared withthe experimental results As the experiments are done ona full scale leaf spring testing machine under the specifiedloads the CAE analysis has been carried out for the sameloads The maximum stress induced in the leaf springs isfound to be 941MPa and 98989MPa using experimental andCAE approach respectively The stress is found to be wellbelow the yield tensile strength which is 10812MPa Thetotal deformation and stress comparison for experimentaland CAE approach also validates the CAE analysis of the leafsprings The results of the comparison have been depicted inthe tabular form in Table 7

From Table 7 it is observed that for the same unladenstatic load conditions deflection in experimental and CAEresults is 469mm and 449mm respectively The deforma-tion observed in CAE results varies by 43 The bendingstress for experimental and CAE results is 262MPa and27074MPa respectively The variation of bending stressobserved in CAE results from experimental is 33 FromTable 7 it is also observed that for the same design loadcondition the deflection found in experimental and CAEis 8144mm and 7605mm respectively The variation inCAE results from experimental is 66The bending stressesunder the design load for experimental and CAE results are446MPa and 458MPa respectivelyThe variation in bendingstress observed in the CAE results is 27 For the maximumload condition the static deflection is 176mm and 16436mmfor experimental and CAE results It has been observedthat when CAE results are compared with experimental thevariation in the deformation varies in between 43 and66 respectively The stress variation lies in the range of27 to 52 It has also been observed that the maximumstress induced in the assembly in both the approaches is wellbelow the yield stress of the material It has been observedthat the CAE results obtained by using SOLID187 meshelements and CONTA172 and TARGE170 (No separation andsliding) contact elements provides the results closer to theexperimental testing

10 Conclusions

The 65Si7 LCV model is taken into consideration fordetermining the fatigue life by experimental and graphicalmethods analytical method (using FORTRAN) SAE springdesign manual approach and CAE (using Ansys) approachThe following conclusions are made

(1) The fatigue life of the leaf spring for same stress rangewill decrease if the magnitude of the initial stressis lower In actual condition the leaf springs willwithstand 15ndash17 more fatigue life than predicted bySAE spring design manual approach

(2) Graphical and analytical methods are time consum-ing and prone to errors but provide results which arewithin 8-9 variation

(3) It is concluded that when CONTA174 TARGE170type of contact and SOLID187 mesh element are usedfor CAE analysis results are closer to the experimen-tal results CAE approach usingAnsys predicts fatiguelife within 2ndash5 of experimental results and can be analternate of experimental and analytical approach

Nomenclature

119862119886 No load assembly camber119864 Youngrsquos modulus of elasticity119873119891 Number of cycles to failure120588 Density120583 Poissonrsquos ratio119878119886 Alternating stress120590max Maximum stress1198781015840

119890 Endurance limit

119878119890 Corrected endurance limit119878119910 Yield tensile strength119871 Span120590min Minimum stress119878119898 Mean stress119878119886119890 Equivalent alternating stress119878119906119905 Ultimate tensile strength119870surface Surface factor119870load Load factor119870temp Temperature factor119870size Size factor119870reliability Reliability factor

International Scholarly Research Notices 11

119889equiv Equivalent diameter of rotating beam spec-imen for any cross section

11986095 Portion of the cross sectional area of non-rounded that is stressed in between 95and 100 of its maximum stress

1198781015840

119898 Stress at 103 cycles

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

The authors would like to acknowledge Mr P S Chawlaand the leaf springs testing division of Friends Auto (India)Ltd whose unconditional support has made this projectsuccessful

References

[1] S Saelem S Chantranuwathana K Panichanun P Preeda-nood P Wichienprakarn and P Kruo-ongarjnukool ldquoExper-imental verification of leaf spring model by using a leaf springtest rigrdquo in Proceedings of the 23rd Conference of the Mechan-ical Engineering Network of Thailand Chiang Mai ThailandNovember 2009

[2] F N A Refngah S Abdullah A Jalar and L B Chua ldquoFatiguelife evaluation of two types of steel leaf springsrdquo InternationalJournal of Mechanical and Materials Engineering vol 4 no 2pp 136ndash140 2009

[3] J J Fuentes H J Aguilar J A Rodrıguez and E J HerreraldquoPremature fracture in automobile leaf springsrdquo EngineeringFailure Analysis vol 16 no 2 pp 648ndash655 2009

[4] M L Aggarwal R A Khan and V P Aggarwal ldquoOptimizationof micro welds used in the leaf springsrdquo International Journal ofEngineering Material and Science vol 28 pp 217ndash220 2006

[5] M L Aggarwal V P Agrawal and R A Khan ldquoA stressapproach model for predictions of fatigue life by shot peeningof EN45A spring steelrdquo International Journal of Fatigue vol 28no 12 pp 1845ndash1853 2006

[6] M M Patunkar and D R Dolas ldquoModelling and analysisof composite leaf spring under the static load condition byusing FEArdquo International Journal of Mechanical amp IndustrialEngineering vol 1 no 1 pp 1ndash4 2011

[7] M S Kumar and S Vijayarangan ldquoAnalytical and experimentalstudies on fatigue life prediction of steel and composite multi-leaf spring for light passenger vehicles using life data analysisrdquoMaterials Science vol 13 no 2 pp 141ndash146 2007

[8] P Sanjurjo C Rodrıguez I F Pariente F J Belzunce and A FCanteli ldquoThe influence of shot peening on the fatigue behaviourof duplex stainless steelsrdquo Procedia Engineering vol 2 no 1 pp1539ndash1546 2010

[9] W Z Zhuang andG RHalford ldquoInvestigation of residual stressrelaxation under cyclic loadrdquo International Journal of Fatiguevol 23 supplement 1 pp S31ndashS37 2001

[10] G Savaidis M Malikoutsakis and A Savaidis ldquoFE simulationof vehicle leaf spring behavior under driving manoeuvresrdquoInternational Journal of Structural Integrity vol 4 no 1 ArticleID 17082873 pp 23ndash32 2013

[11] IS 1135 SpringsmdashLeaf Springs Assembly for Automobiles 1995[12] SAE Spring Design ManualmdashDesign and Application of Leaf

Springs HS-744 AE-11 1990[13] R L Norton Machine DesignmdashAn Integrated Approach Pear-

son Education Asia 2nd edition 2001[14] ldquoAnsys Workbench training manual on fatigue toolrdquo 2014

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Page 4: Fatigue Life Assessment of 65Si7 Leaf Springs: A Comparative Study

4 International Scholarly Research Notices

Table 3 Experimental results for load deflection and bending stresses

Serial number Load type Load (N) Deflection (mm) Bending stress (MPa)1 Unladen load 7661 469 2622 Designrated load 12959 8144 4463 Flat load 15754 99 5404 Rubber touching load 216457 136 7435 Metal to metal contact 28010 176 941

Table 4 Experimental fatigue life of the specimen

Material processing Standardspecified

Alternatingstress level(MPa)

Stress range Fatigue lifeof S-1 (119873

119891)

Fatigue lifeof S-2 (119873

119891)

Fatigue lifeof S-3 (119873

119891)

Fatigue lifeof S-4 (119873

119891)

AverageSD

Normal rollingquenching at 880∘Chardening in oil at 80∘Ctempering at 410∘C for90mins shot peening at18 A intensity BHN380ndash432 and scraggingat 09 of yield stress

06 gndash2 g 269ndash896 627 84212 81961 82226 85656Average83513SD 1518

The leaf springs were tested on a full scale leaf springtesting machine under the unladen rated flat rubber touch-ing load and metal to metal load and the correspondingdeflection and stress values observed are shown in theTable 3The experiments were conducted twice and the mean valueof the results was considered Table 3 depicts the observedvalues of deflection and stress corresponding to the loadsapplied on the shorter leaf by a static hydraulic ram

41 Experimental Fatigue Life Determination To determineexperimental fatigue life four leaf springs specimens (S-1 S-2S-3 and S-4) are manufactured with specified design param-eters Analogous kind of material processing normal rollingquenching at 880∘C hardening in oil at 80∘C tempering at410∘C for 90mins shot peening at 18 A intensity BHN 380ndash432 and scragging at 09 of yield stress was done for allthe specimensThe stress range considered for the specimensis 627MPa 13 plusmn 07 g All the four specimens were testedunder same stress range and fatigue life was determined asdepicted in Table 4 The fatigue life of specimen S-1 is 84212for sample S-2 is 81961 and for samples S-3 and S-4 are 82226and 85685 respectively The mean value that is 83513 of thefatigue life for the four specimens is taken into considerationfor this study As per the requirement specified by the vehiclemanufacturer the leaf springs are to be tested on full scaletesting machine as per 13 plusmn 07 g The maximum load will be2 g and theminimum load will be 06 g Here g represents thedesign load [12]

119878max =119875max lowast 119871119886 lowast 119905

8 lowast sum 119868total= 896MPa

Smin =119875min lowast 119871119886 lowast 119905

8 lowast sum 119868total= 269MPa

(1)

5 SAE Spring Design Manual Approach

Fatigue life is articulated by the number of deflection cyclesthat a spring will withstand without failure or permanentset A leaf spring used in a suspension will undergo a largenumber of cycles of small amplitude near the design loadposition without failure Under the greater amplitude thenumber of cycles without failure will be reduced since themaximum stresses aswell as the stress range are amplified andboth are determining factors in fatigue life of the spring Asper the SAE spring design manual approach [12] the fatiguetest stroke for leaf springs (by considering assembly stress) ispredicted as

(a) deflection at design load = 129591531 = 846mm(b) maximum load on the leaf springs = 28KN(c) metal-to-metal clearance (compression stroke) =

946mm(d) total deflection to maximum load = 1829mm(e) stress at metal-to-metal contact position = 885MPa(f) stress rate = 8851829 = 483MPamm(g) release stroke = 05 times 946 = 473mm(h) fatigue test stoke = 473 + 946 = 1419mm(i) initial stress = 885 minus (1419 times483) = 1996MPa

The maximum stress of 885MPa and initial stress of1996asymp 200MPa are utilized to predict the approximatefatigue life of the leaf spring

51 Fatigue Life Assessment by SAE Spring Design ManualApproach Figure 4 shows a maximum stress versus initialstress plot as per SAE spring design manual approach As perSAE spring design manual this criterion is frequently used

International Scholarly Research Notices 5

400500600700800900

1000110012001300

0 100 200 300 400 500 600 700

Max

imum

stre

ss (M

Pa)

Initial stress (MPa)

= 269MPa= 200MPa

Smax (as specified) = 896MPa

Smax (as per SAE) = 885MPa

Sinitial (as specified)Sinitial (as per SAE)

30000cycles to failure

50000

75000

100000

200000

1000000

cycles to failure

Figure 4Maximum versus initial stress plot (without shot peening)[12]

for determination of approximate fatigue life of the springinitial stress (horizontal scale) and maximum stress (verticalscale) are intersected to estimate the number of cycles thespring will survive The life predicted from this plot does notconsider the effect of shot peening and scragging operationsbut in actual practice processing like shot peening andscragging is performed on the leaf springs which enhancesthe fatigue life by approximately 20

From Figure 4 it is observed that the maximum stressinduced in the leaf springs (by considering the assemblystresses) is 885MPa and the initial stress value is 200MPaThe intersection of 885MPa and 200MPa lies in the zoneof 50000 to 75000 cycles As the point of intersection isnearer to 50000-cycle line it will sustain approximately 58000cycles Due to shot peeing and scragging the fatigue lifeof leaf springs by considering assembly stresses would beapproximately (58000 lowast 12) 69600 cycles

The vehicle manufacture has specified that the maximumstress of 896MPa corresponds to the maximum load of 2 gand the minimum stress of 269MPa corresponds to theminimum load of 06 g where g is the design load Theintersection of 896MPa and 269MPa lies in the zone of 50000to 75000 cycles As the point of intersection is nearer to75000-cycle line approximately it will sustain around 68000cycles Due to shot peeing and scragging the fatigue lifeof leaf springs (by considering assembly stresses) would beapproximately (68000 lowast 12) 81600 cycles

Hence it is observed that with the stress range obtainedfrom SAE spring design approach the fatigue life and asspecified stress range are around 69600 cycles and 81600cycles approximatelyThe stress range specified by the vehiclemanufacturer gives result closer to the experimental results

6 Fatigue Life Estimation byGraphical Method

The graphical method involves determination of effect ofvarious factors like load temperature size and surface on theendurance limit of the 65Si7 Figure 5 shows an alternatingversus number of cycles plot for unfactored endurance limitand factored endurance limit It is observed from Figure 5

0

200

400

600

800

1000

1200

1400

1000 10000 100000 1000000 10000000

S998400e factored curve

Sm = 583MPa

Se unfactored curve

Alte

rnat

ing

stres

sS a

(M

Pa)

NNumber of cycles

Figure 5 Factored and unfactored S-N curve for 65Si7 leaf spring

that the endurance limit is 636MPa without consideringthe various factors affecting the fatigue life It has also beenobserved that the corrected endurance limit is 4019MPaConsidering the design material and processing parameterof the leaf springs the steps involved in the graphicalmethodsare as follows

(a) 119878119906119905 = 1272MPa(b) 119878119910 = 10812MPa

(c) 1198781015840

119890= 05119878119906119905 = 05 times 1272 = 636MPa

(d) 120590min = 269MPa at 06 g load 120590max = 897MPa at 2 gload

(e) 119878119886 = (120590max minus 120590min)2 = (897 minus 269)2 = 314MPa(f) 119878119898 = (120590max + 120590min)2 = (897 + 269)2 = 583MPa(g) 119878119890 = 119870load times 119870surfae times 119870temp times 119870reliability times 119870size times 119878

1015840

119890

(h) 119870load = load factor for bending 119870load = 1(i) 119870surface = 1 (for shot peening treating)(j) 119870temp = 1 if 119879 le 450

∘C(k) 119870reliability = 080 Assuming 99 reliability

(l) 119870size = 1189 lowast (119889eqiv)minus097 for 8mm lt 119889 le 250mm

(m) 119889 eqiv = radic1198609500766 = 6588mm

(n) 11986095 = 005 lowast 119887 lowast ℎ = 3325mm2(o) 119870size = 1189 lowast (119889eqiv)

minus097= 079

(p) 119878119890 = 1 times 1 times 1 times 080 times 079 times 636 = 4019MPa

Figure 6 shows an alternating stress versus mean stress plotfor the LCV leaf spring It has been observed from Figure 6that the intersection of the alternating and mean stress lineslies outside the region AC If the point is within this lineAC the component is designed for infinite life but if thecomponent is outside this region the component is designedfor the finite life Thus from the position of point I it isobserved that the component is designed for the finite lifeThe equivalent alternating stress as determined by joining thepoint of intersection I and ultimate strength point with thealternating stress axis is found to be 578MPa

6 International Scholarly Research Notices

0100200300400500600700800900

100011001200

0 200 400 600 800 1000 1200 1400

Alte

rnat

ing

stres

s (M

Pa)

Mean stress (MPa)

As point I lies outside this region theleaf spring is designed for finite lifeI

C

A

Sa = 314MPa

Sm = 583MPa

Se = 4019MPa

Sae = 578MPa equivalent alternating stress

Figure 6 Alternating stress versus mean stress plot

1400

1200

1000

800

600

400

200

01e + 3 1e + 4 1e + 5 1e + 6 1e + 7 1e + 8

Sae = 578MPa

Se = 4019 MPa

Nf = number of cycles to failure

Alternating stress versus number of cycles

NNumber of cycles

Alte

rnat

ing

stres

sS a

(MPa

)

A

BC

E D

Figure 7 S-N curve for 65Si7

Figure 7 shows the S-N diagram for 65Si7 Point A rep-resents the alternating stress at which the spring will sustain1000 cycles Point D represents the endurance limit that is4019MPa of 65Si7 The line CB represents the equivalentalternating stress The intersection of alternating stress atpoint B will give the number of cycles to fatigue failure

FromFigure 7 S-N plot it is observed thatΔABC is similarto ΔADE

Hence 119860119862119860119864 = 119862119861119863119864

119860119862 = log119860 minus log119862 = 0296

119860119864 = log119860 minus log119864 = 0454

119863119864 = log119863 minus log119864 = log 106minus log 10

3= 3

119862119861 =0296 times 3

0454= 1957

Total 119862119861 = 3 + 197 = 49957

Number of cycles = 104957

= 90763 cycles to failure

(2)

1e + 3 1e + 4 1e + 5 1e + 6 1e + 7 1e + 8

NNumber of cycles

1400

1200

1000

800

600

400

200

0

Alte

rnat

ing

stres

sS a

(MPa

)

N1 cycles at S998400m N2 cycles at Se

= 09(Sut)

Se

A

BC

S998400m

Figure 8 Estimated S-N curve

7 Analytical Method forFatigue Life Prediction

The high cycle fatigue regime is from 103 to 106 and beyondThematerial strength at 103 cycles is called 119878

1015840

119898 which is equal

to 09 Sut The estimated S-N diagram drawn on the log-loggraph is shown in Figure 8 Figure 8 shows that the 119909-axisruns from 103 to 109 or beyond The appropriate 119878

1015840

119898from

the equation for bending load is plotted at N1 = 103 As thematerial exhibits a knee the corrected endurance limit 119878119890 isplotted at N2 = 106 A straight line is drawn between 119878

1015840

119898and

119878119890 The curve is continuous horizontally beyond N2 pointThe equation of the line from 119878

1015840

119898to 119878119890 can be written as

119878 (119873) = 119886119873119887

(taking log on both sides) (3)

log 119878 (119873) = log 119886 + 119887 log119873 (4)

where 119878(119873) is the fatigue strength at any 119873 and 119886 119887 are theconstants defined by the boundary conditions For all theconditions the 119910 intercept is 119878(119873) = 119878

1015840

119898at N = N1 = 103

for endurance limit case 119878(119873) = 119878119890 atN =N2 = 106 Applyingthe boundary condition in the equation we have

log 1198781015840

119898= log 119886 + 119887 log1198731 (5)

log 119878119890 = log 119886 + 119887 log1198732 (6)

log 1198781015840

119898minus log 119878119890 = 119887 (log1198731 minus log1198732) (7)

119885 = (log1198731 minus log1198732) (8)

119887 =1

119885log

1198781015840

119898

119878119890

(9)

log 1198781015840

119898minus 119887 log1198731 = log 119886 (10)

International Scholarly Research Notices 7

As 1198731 = 1000 log101000 = 3

log 1198781015840

119898minus 3119887 = log 119886

119886 =

(1198781015840

119898)2

119878119890

(11)

119873 = (119878119886

119886)

minus1119887

(12)

119878119886119890 = 119886119873119887

119891[13] where119873119891 = number of cycles to failure 119878119886119890 =

equivalent alternating stress 119886 119887 are constantswhich dependson the material properties of 65Si7 The fatigue life is to bepredicted at equivalent alternating stress so 119878119886 is replaced by119878119886119890 The above mentioned equation is used for fatigue lifeestimation and the codes for the analyticalmethod arewrittenin FORTRANThe flowchart is shown in Figure 9

8 Computer Aided Engineering Analysis

The CAD model of the individual leaf is prepared from thestandard drawing of the leaf spring and assembled The leafspring assembly is imported to an analysis software ANSYSfor further processing The different contacts are set andentire model is meshed into small elements The boundaryconditions are applied by taking into consideration the actualloading conditions and the solver gives the solution Thediverse steps involved in CAE analysis are as follows

81 CAD Modeling The CAD modeling of the conventionalleaf springs structure is performed by using solid workssoftware The CAD model of leaf springs consists of total34 different parts which are assembled together in assemblydesign to construct an assemblyThemultileaf springs assem-bly used for analysis is shown in Figure 10

82 Analysis Using ANSYS The CAD model of leaf springshas been imported in the ANSYS solver All the boundaryconditions and material properties have been specified asper the standard specified by the vehicle manufacturer Thematerial used for the leaf springs for analysis is 65Si7 whichis having homogenous and isotropic behaviour The material65Si7 is added in the material library and the engineeringproperties are applied

The process for performing analysis in ANSYS solverinvolves the following

821 Setting the Contact Reign The contact conditions areformed where the components meet The differences inthe contact settings determine how the contacting bodiescan move relative to one another In this assembly the Noseparation contact is used for the analysis It only applies toregion of faces Separation of faces in contact is not allowedbut small amounts of frictionless sliding can occur alongcontact faces In general CONTA174 and TARGE170 areused CONTA174 is used for contact and sliding between3D target surfaces (TARGE170) which is defined by thiselement The element is applicable to 3D structural analysis

Start

Calculate maximum thickness

Estimate the number of leaves width and thickness for required

MOI

Select assembly stresses

Calculate steppingoverhang

If no load assembly camber

Calculate the mass

Calculate fatigue life

End

Calculate Smax

If Kmodified variesmore than 7

Calculate Kmodified

If t gt tmax if MOI estimated gt

MOI required

Required K Pdesign Smax Nf

Calculate required moment ofinertia (MOI) Pmax

Calculate the Smaximum andSinitial stress for fatigue life

If Sas middot t2 = 0

Figure 9 Flowchart for analytical estimation of fatigue life of 65Si7leaf spring

Figure 10 CAD model of the leaf springs

8 International Scholarly Research Notices

Figure 11 Boundary conditions for CAE analysis

TARGE170 is used to represent various 3D target surfaces forthe associated contact elements

822 Meshing In this congregation SOLID187 elementwhich is a standard mechanical element for solids is used forthe result SOLID187 element is a higher order 3-D 10-nodeelement SOLID187 has quadratic displacement behaviourand is well suited to modeling irregular meshes The elementis defined by 10 nodes having three degrees of freedom ateach node translations in the nodal 119909 119910 and 119911 directionsThe number of SOLID187 elements is 6964 and the numberof nodes generated is 16943

823 Static Analysis Module A static structural analysisdetermines the displacements stresses strains and forcesin structures or components caused by loads that do notinduce significant inertia and damping effects Steady loadingand response conditions are assumed that is the loads andthe structurersquos response are assumed to vary slowly withrespect to time Static structure analysis takes into consid-eration some parameters like material properties loadingconditions support conditions and contacts which are to bespecified as the input to the preprocessing of the analysis

824 Applying CAE Boundary Conditions The boundaryconditions are applied by taking into consideration the exper-imental loading conditions The springs have been modelledin flat condition and the loading is done to achieve the initialcondition The total load is divided on the two eyes of themaster leaf and pins The fixed support constitutes the seatlength (on master leaf and last (12th leaf) and the centre boltThe CAE boundary conditions are shown in Figure 11

83 Fatigue Life Assessment Using CAE Tools While leafsprings may work well initially they often fail in service dueto fatigue failure caused by repeated cyclic loadingThe aimoffatigue analysis is characterization of capability of a materialto survive many cycles that a leaf spring may experienceduring its life time In ansys fatigue module twomethods areavailable that is stress life and strain life method For thiswork the stress lifemethod is used to predict the fatigue life ofthe component The static environment is set by applying theboundary conditions by taking into consideration the actualloading conditions After the static analysis the fatigue toolis used for fatigue life estimation In stress life decision treeit is required to make four input decisions to perform a stress

life analysis These decisions affect the outcome of the fatigueanalysis in both predicted life and types of postprocessingavailable Input decisions that are to be considered for fatiguelife estimation are loading typemean stress effectsmultiaxialstress correction and fatigue modification factors

831 Type of Loading Unlike static stress which is analyzedwith calculations for a single stress state fatigue damageoccurs when stress at a point changes over time There areessentially four classes of fatigue loading with the ANSYSfatigue module [14] currently supporting the first three

(i) constant amplitude proportional loading(ii) constant amplitude nonproportional loading(iii) nonconstant amplitude proportional loading(iv) nonconstant amplitude non-proportional loading

Constant amplitude proportional loading is the classic ldquobackof the enveloperdquo calculation describing whether the loadhas a constant maximum value or continually varies withtime Loading is of constant amplitude because only one setof FE stress results along with a loading ratio is requiredto calculate the alternating and mean values The loadingratio is defined as the ratio of the second load to the firstload (LR = L2L1) Loading is proportional since only oneset of FE results are needed (principal stress axes do notchange over time) Common types of constant amplitudeloading are fully reversed (apply a load and then apply anequal and opposite load a load ratio of minus1) and zero-based(apply a load and then remove it a load ratio of 0) Sinceloading is proportional looking at a single set of FE resultscan identify critical fatigue locations Constant amplitudenonproportional loading looks at exactly two load cases thatneed not to be related by a scale factor The loading isof constant amplitude but nonproportional since principalstress or strain axes are free to change between the two loadsets Nonconstant amplitude proportional loading also needsonly one set of FE results But instead of using a single loadratio to calculate alternating and mean values the load ratiovaries over time

832 Mean Stress Correction For stress life if experimen-tal data at different mean stresses or r-ratiorsquos exist meanstress can be accounted for directly through interpolationbetweenmaterial curves If experimental data is not availableseveral empirical options may be chosen including GerberGoodman and Soderberg theories which use static materialproperties yield stress and tensile strength along with S-Ndata to account for any mean stress

833 Multiaxial Stress Correction Factor Experimental testdata is mostly uniaxial whereas finite element results areusually multiaxial At some point stress must be convertedfrom a multiaxial stress state to a uniaxial one Von-Misesstress max shear stress maximum principal stress or any ofthe component stresses can be used for the comparison withthe experimental uniaxial stress value

International Scholarly Research Notices 9

(a) (b)

Figure 12 (a) Fatigue life using CAE tools (b) Equivalent alternating stress

Table 5 CAE results for load deflection and bending stresses

Serial number Load type Load (N) Deflection (mm) Stress (MPa)1 Unladen load 7661 449 270742 Designrated load 12959 7605 4583 Flat load 15754 9245 556834 Rubber touching load 216457 12702 7655 Metal to metal contact 28010 16436 98989

Table 6 Comparison of fatigue life by various approaches

Serial number Method for fatiguelife assessment Alternating stress level Stress range Equivalent alternating stress Fatigue life Variation from

experimental results1 Experimental 269ndash896 627 mdash 83513 mdash

2 SAE spring designmanual approach 200ndash885 685 mdash 69600 166

3 Graphical method 269ndash896 627 578 90763 8684 Analytical method 269ndash896 627 579 90304 8135 CAE method 269ndash896 627 562 82348 239

834 Fatigue Modifications (Value of Infinite Life) Anotheravailable option when conducting a variable amplitudefatigue analysis is the ability to set the value used for infinitelife In constant amplitude loading if the alternating stress islower than the lowest alternating stress on the fatigue curvethe fatigue tool will use the life at the last pointThis providesfor an added level of safety because many materials do notexhibit an endurance limit

The static environment is set and boundary conditions areapplied and the solver gives the solution The deflection andstress results obtained from the specified loads are recorded ina tabular format The CAE results for deflection and bendingstress are shown inTable 5 Figure 12(a) depicts the fatigue lifeof the leaf spring using Ansys solver For prediction of fatiguelife the stress life approach is selected A constant amplitudeload ratio is selected as the loading type The fatigue strengthfactor of 065 is chosen and scale factor is kept as 1 Formean stress theory Goodmanrsquos criteria are selected Lastly formultiaxial stress correction von-mises stress is selected andthe component is designed for finite life It has been observedthat the fatigue life of the leaf spring using CAE tool is 82348

cycles Figure 12(b) depicts the equivalent alternating stressin the leaf spring using Ansys solver

9 Results and Discussion

91 Fatigue Life Comparison by Various Approaches Table 6depicts the comparison of fatigue life by various methodsIt is observed that for the alternating stress level of 896ndash269MPa the experimental fatigue life of the leaf spring is83513 cycles The fatigue life estimated by SAE spring designmanual technique is 69600 cycles for the alternating stresslevel of 885ndash200MPa It is also observed that in the SAEspring design manual approach the maximum stress that is885MPa is less than the specified maximum stress but thestress range is higher than specified stress range Hence thisapproximation provides results within 166 variation Thesame approach with specified stress range gives the fatiguelife of leaf spring to be 81600 For the same alternating stresslevel of 896ndash269MPa the fatigue life is found to be 90763cycles by graphical method and equivalent stress is found to

10 International Scholarly Research Notices

Table 7 Comparison of experimental and CAE results

Load type Load (N) Experimental results CAE results age variation between CAEand Experimental results

Deflection Stress Deflection Stress Deflection StressUnladen load 7661 469 262 449 27074 43 33DesignRated load 12959 8144 446 7605 458 66 27Flat load 15754 99 540 9245 55683 66 31Rubber touching load 216457 136 743 12702 765 66 30Metal to metal contact load 28010 176 941 16436 98989 66 52

be 578MPa In the analytical method the fatigue life is foundto be 90304 cycleswith 813 variation from the experimentalresults The CAE fatigue life is found to be 82348 cycles with239 variation from the experimental results

92 Comparison of Experimental and CAE Results To vali-date the analysis the CAE results have been compared withthe experimental results As the experiments are done ona full scale leaf spring testing machine under the specifiedloads the CAE analysis has been carried out for the sameloads The maximum stress induced in the leaf springs isfound to be 941MPa and 98989MPa using experimental andCAE approach respectively The stress is found to be wellbelow the yield tensile strength which is 10812MPa Thetotal deformation and stress comparison for experimentaland CAE approach also validates the CAE analysis of the leafsprings The results of the comparison have been depicted inthe tabular form in Table 7

From Table 7 it is observed that for the same unladenstatic load conditions deflection in experimental and CAEresults is 469mm and 449mm respectively The deforma-tion observed in CAE results varies by 43 The bendingstress for experimental and CAE results is 262MPa and27074MPa respectively The variation of bending stressobserved in CAE results from experimental is 33 FromTable 7 it is also observed that for the same design loadcondition the deflection found in experimental and CAEis 8144mm and 7605mm respectively The variation inCAE results from experimental is 66The bending stressesunder the design load for experimental and CAE results are446MPa and 458MPa respectivelyThe variation in bendingstress observed in the CAE results is 27 For the maximumload condition the static deflection is 176mm and 16436mmfor experimental and CAE results It has been observedthat when CAE results are compared with experimental thevariation in the deformation varies in between 43 and66 respectively The stress variation lies in the range of27 to 52 It has also been observed that the maximumstress induced in the assembly in both the approaches is wellbelow the yield stress of the material It has been observedthat the CAE results obtained by using SOLID187 meshelements and CONTA172 and TARGE170 (No separation andsliding) contact elements provides the results closer to theexperimental testing

10 Conclusions

The 65Si7 LCV model is taken into consideration fordetermining the fatigue life by experimental and graphicalmethods analytical method (using FORTRAN) SAE springdesign manual approach and CAE (using Ansys) approachThe following conclusions are made

(1) The fatigue life of the leaf spring for same stress rangewill decrease if the magnitude of the initial stressis lower In actual condition the leaf springs willwithstand 15ndash17 more fatigue life than predicted bySAE spring design manual approach

(2) Graphical and analytical methods are time consum-ing and prone to errors but provide results which arewithin 8-9 variation

(3) It is concluded that when CONTA174 TARGE170type of contact and SOLID187 mesh element are usedfor CAE analysis results are closer to the experimen-tal results CAE approach usingAnsys predicts fatiguelife within 2ndash5 of experimental results and can be analternate of experimental and analytical approach

Nomenclature

119862119886 No load assembly camber119864 Youngrsquos modulus of elasticity119873119891 Number of cycles to failure120588 Density120583 Poissonrsquos ratio119878119886 Alternating stress120590max Maximum stress1198781015840

119890 Endurance limit

119878119890 Corrected endurance limit119878119910 Yield tensile strength119871 Span120590min Minimum stress119878119898 Mean stress119878119886119890 Equivalent alternating stress119878119906119905 Ultimate tensile strength119870surface Surface factor119870load Load factor119870temp Temperature factor119870size Size factor119870reliability Reliability factor

International Scholarly Research Notices 11

119889equiv Equivalent diameter of rotating beam spec-imen for any cross section

11986095 Portion of the cross sectional area of non-rounded that is stressed in between 95and 100 of its maximum stress

1198781015840

119898 Stress at 103 cycles

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

The authors would like to acknowledge Mr P S Chawlaand the leaf springs testing division of Friends Auto (India)Ltd whose unconditional support has made this projectsuccessful

References

[1] S Saelem S Chantranuwathana K Panichanun P Preeda-nood P Wichienprakarn and P Kruo-ongarjnukool ldquoExper-imental verification of leaf spring model by using a leaf springtest rigrdquo in Proceedings of the 23rd Conference of the Mechan-ical Engineering Network of Thailand Chiang Mai ThailandNovember 2009

[2] F N A Refngah S Abdullah A Jalar and L B Chua ldquoFatiguelife evaluation of two types of steel leaf springsrdquo InternationalJournal of Mechanical and Materials Engineering vol 4 no 2pp 136ndash140 2009

[3] J J Fuentes H J Aguilar J A Rodrıguez and E J HerreraldquoPremature fracture in automobile leaf springsrdquo EngineeringFailure Analysis vol 16 no 2 pp 648ndash655 2009

[4] M L Aggarwal R A Khan and V P Aggarwal ldquoOptimizationof micro welds used in the leaf springsrdquo International Journal ofEngineering Material and Science vol 28 pp 217ndash220 2006

[5] M L Aggarwal V P Agrawal and R A Khan ldquoA stressapproach model for predictions of fatigue life by shot peeningof EN45A spring steelrdquo International Journal of Fatigue vol 28no 12 pp 1845ndash1853 2006

[6] M M Patunkar and D R Dolas ldquoModelling and analysisof composite leaf spring under the static load condition byusing FEArdquo International Journal of Mechanical amp IndustrialEngineering vol 1 no 1 pp 1ndash4 2011

[7] M S Kumar and S Vijayarangan ldquoAnalytical and experimentalstudies on fatigue life prediction of steel and composite multi-leaf spring for light passenger vehicles using life data analysisrdquoMaterials Science vol 13 no 2 pp 141ndash146 2007

[8] P Sanjurjo C Rodrıguez I F Pariente F J Belzunce and A FCanteli ldquoThe influence of shot peening on the fatigue behaviourof duplex stainless steelsrdquo Procedia Engineering vol 2 no 1 pp1539ndash1546 2010

[9] W Z Zhuang andG RHalford ldquoInvestigation of residual stressrelaxation under cyclic loadrdquo International Journal of Fatiguevol 23 supplement 1 pp S31ndashS37 2001

[10] G Savaidis M Malikoutsakis and A Savaidis ldquoFE simulationof vehicle leaf spring behavior under driving manoeuvresrdquoInternational Journal of Structural Integrity vol 4 no 1 ArticleID 17082873 pp 23ndash32 2013

[11] IS 1135 SpringsmdashLeaf Springs Assembly for Automobiles 1995[12] SAE Spring Design ManualmdashDesign and Application of Leaf

Springs HS-744 AE-11 1990[13] R L Norton Machine DesignmdashAn Integrated Approach Pear-

son Education Asia 2nd edition 2001[14] ldquoAnsys Workbench training manual on fatigue toolrdquo 2014

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Page 5: Fatigue Life Assessment of 65Si7 Leaf Springs: A Comparative Study

International Scholarly Research Notices 5

400500600700800900

1000110012001300

0 100 200 300 400 500 600 700

Max

imum

stre

ss (M

Pa)

Initial stress (MPa)

= 269MPa= 200MPa

Smax (as specified) = 896MPa

Smax (as per SAE) = 885MPa

Sinitial (as specified)Sinitial (as per SAE)

30000cycles to failure

50000

75000

100000

200000

1000000

cycles to failure

Figure 4Maximum versus initial stress plot (without shot peening)[12]

for determination of approximate fatigue life of the springinitial stress (horizontal scale) and maximum stress (verticalscale) are intersected to estimate the number of cycles thespring will survive The life predicted from this plot does notconsider the effect of shot peening and scragging operationsbut in actual practice processing like shot peening andscragging is performed on the leaf springs which enhancesthe fatigue life by approximately 20

From Figure 4 it is observed that the maximum stressinduced in the leaf springs (by considering the assemblystresses) is 885MPa and the initial stress value is 200MPaThe intersection of 885MPa and 200MPa lies in the zoneof 50000 to 75000 cycles As the point of intersection isnearer to 50000-cycle line it will sustain approximately 58000cycles Due to shot peeing and scragging the fatigue lifeof leaf springs by considering assembly stresses would beapproximately (58000 lowast 12) 69600 cycles

The vehicle manufacture has specified that the maximumstress of 896MPa corresponds to the maximum load of 2 gand the minimum stress of 269MPa corresponds to theminimum load of 06 g where g is the design load Theintersection of 896MPa and 269MPa lies in the zone of 50000to 75000 cycles As the point of intersection is nearer to75000-cycle line approximately it will sustain around 68000cycles Due to shot peeing and scragging the fatigue lifeof leaf springs (by considering assembly stresses) would beapproximately (68000 lowast 12) 81600 cycles

Hence it is observed that with the stress range obtainedfrom SAE spring design approach the fatigue life and asspecified stress range are around 69600 cycles and 81600cycles approximatelyThe stress range specified by the vehiclemanufacturer gives result closer to the experimental results

6 Fatigue Life Estimation byGraphical Method

The graphical method involves determination of effect ofvarious factors like load temperature size and surface on theendurance limit of the 65Si7 Figure 5 shows an alternatingversus number of cycles plot for unfactored endurance limitand factored endurance limit It is observed from Figure 5

0

200

400

600

800

1000

1200

1400

1000 10000 100000 1000000 10000000

S998400e factored curve

Sm = 583MPa

Se unfactored curve

Alte

rnat

ing

stres

sS a

(M

Pa)

NNumber of cycles

Figure 5 Factored and unfactored S-N curve for 65Si7 leaf spring

that the endurance limit is 636MPa without consideringthe various factors affecting the fatigue life It has also beenobserved that the corrected endurance limit is 4019MPaConsidering the design material and processing parameterof the leaf springs the steps involved in the graphicalmethodsare as follows

(a) 119878119906119905 = 1272MPa(b) 119878119910 = 10812MPa

(c) 1198781015840

119890= 05119878119906119905 = 05 times 1272 = 636MPa

(d) 120590min = 269MPa at 06 g load 120590max = 897MPa at 2 gload

(e) 119878119886 = (120590max minus 120590min)2 = (897 minus 269)2 = 314MPa(f) 119878119898 = (120590max + 120590min)2 = (897 + 269)2 = 583MPa(g) 119878119890 = 119870load times 119870surfae times 119870temp times 119870reliability times 119870size times 119878

1015840

119890

(h) 119870load = load factor for bending 119870load = 1(i) 119870surface = 1 (for shot peening treating)(j) 119870temp = 1 if 119879 le 450

∘C(k) 119870reliability = 080 Assuming 99 reliability

(l) 119870size = 1189 lowast (119889eqiv)minus097 for 8mm lt 119889 le 250mm

(m) 119889 eqiv = radic1198609500766 = 6588mm

(n) 11986095 = 005 lowast 119887 lowast ℎ = 3325mm2(o) 119870size = 1189 lowast (119889eqiv)

minus097= 079

(p) 119878119890 = 1 times 1 times 1 times 080 times 079 times 636 = 4019MPa

Figure 6 shows an alternating stress versus mean stress plotfor the LCV leaf spring It has been observed from Figure 6that the intersection of the alternating and mean stress lineslies outside the region AC If the point is within this lineAC the component is designed for infinite life but if thecomponent is outside this region the component is designedfor the finite life Thus from the position of point I it isobserved that the component is designed for the finite lifeThe equivalent alternating stress as determined by joining thepoint of intersection I and ultimate strength point with thealternating stress axis is found to be 578MPa

6 International Scholarly Research Notices

0100200300400500600700800900

100011001200

0 200 400 600 800 1000 1200 1400

Alte

rnat

ing

stres

s (M

Pa)

Mean stress (MPa)

As point I lies outside this region theleaf spring is designed for finite lifeI

C

A

Sa = 314MPa

Sm = 583MPa

Se = 4019MPa

Sae = 578MPa equivalent alternating stress

Figure 6 Alternating stress versus mean stress plot

1400

1200

1000

800

600

400

200

01e + 3 1e + 4 1e + 5 1e + 6 1e + 7 1e + 8

Sae = 578MPa

Se = 4019 MPa

Nf = number of cycles to failure

Alternating stress versus number of cycles

NNumber of cycles

Alte

rnat

ing

stres

sS a

(MPa

)

A

BC

E D

Figure 7 S-N curve for 65Si7

Figure 7 shows the S-N diagram for 65Si7 Point A rep-resents the alternating stress at which the spring will sustain1000 cycles Point D represents the endurance limit that is4019MPa of 65Si7 The line CB represents the equivalentalternating stress The intersection of alternating stress atpoint B will give the number of cycles to fatigue failure

FromFigure 7 S-N plot it is observed thatΔABC is similarto ΔADE

Hence 119860119862119860119864 = 119862119861119863119864

119860119862 = log119860 minus log119862 = 0296

119860119864 = log119860 minus log119864 = 0454

119863119864 = log119863 minus log119864 = log 106minus log 10

3= 3

119862119861 =0296 times 3

0454= 1957

Total 119862119861 = 3 + 197 = 49957

Number of cycles = 104957

= 90763 cycles to failure

(2)

1e + 3 1e + 4 1e + 5 1e + 6 1e + 7 1e + 8

NNumber of cycles

1400

1200

1000

800

600

400

200

0

Alte

rnat

ing

stres

sS a

(MPa

)

N1 cycles at S998400m N2 cycles at Se

= 09(Sut)

Se

A

BC

S998400m

Figure 8 Estimated S-N curve

7 Analytical Method forFatigue Life Prediction

The high cycle fatigue regime is from 103 to 106 and beyondThematerial strength at 103 cycles is called 119878

1015840

119898 which is equal

to 09 Sut The estimated S-N diagram drawn on the log-loggraph is shown in Figure 8 Figure 8 shows that the 119909-axisruns from 103 to 109 or beyond The appropriate 119878

1015840

119898from

the equation for bending load is plotted at N1 = 103 As thematerial exhibits a knee the corrected endurance limit 119878119890 isplotted at N2 = 106 A straight line is drawn between 119878

1015840

119898and

119878119890 The curve is continuous horizontally beyond N2 pointThe equation of the line from 119878

1015840

119898to 119878119890 can be written as

119878 (119873) = 119886119873119887

(taking log on both sides) (3)

log 119878 (119873) = log 119886 + 119887 log119873 (4)

where 119878(119873) is the fatigue strength at any 119873 and 119886 119887 are theconstants defined by the boundary conditions For all theconditions the 119910 intercept is 119878(119873) = 119878

1015840

119898at N = N1 = 103

for endurance limit case 119878(119873) = 119878119890 atN =N2 = 106 Applyingthe boundary condition in the equation we have

log 1198781015840

119898= log 119886 + 119887 log1198731 (5)

log 119878119890 = log 119886 + 119887 log1198732 (6)

log 1198781015840

119898minus log 119878119890 = 119887 (log1198731 minus log1198732) (7)

119885 = (log1198731 minus log1198732) (8)

119887 =1

119885log

1198781015840

119898

119878119890

(9)

log 1198781015840

119898minus 119887 log1198731 = log 119886 (10)

International Scholarly Research Notices 7

As 1198731 = 1000 log101000 = 3

log 1198781015840

119898minus 3119887 = log 119886

119886 =

(1198781015840

119898)2

119878119890

(11)

119873 = (119878119886

119886)

minus1119887

(12)

119878119886119890 = 119886119873119887

119891[13] where119873119891 = number of cycles to failure 119878119886119890 =

equivalent alternating stress 119886 119887 are constantswhich dependson the material properties of 65Si7 The fatigue life is to bepredicted at equivalent alternating stress so 119878119886 is replaced by119878119886119890 The above mentioned equation is used for fatigue lifeestimation and the codes for the analyticalmethod arewrittenin FORTRANThe flowchart is shown in Figure 9

8 Computer Aided Engineering Analysis

The CAD model of the individual leaf is prepared from thestandard drawing of the leaf spring and assembled The leafspring assembly is imported to an analysis software ANSYSfor further processing The different contacts are set andentire model is meshed into small elements The boundaryconditions are applied by taking into consideration the actualloading conditions and the solver gives the solution Thediverse steps involved in CAE analysis are as follows

81 CAD Modeling The CAD modeling of the conventionalleaf springs structure is performed by using solid workssoftware The CAD model of leaf springs consists of total34 different parts which are assembled together in assemblydesign to construct an assemblyThemultileaf springs assem-bly used for analysis is shown in Figure 10

82 Analysis Using ANSYS The CAD model of leaf springshas been imported in the ANSYS solver All the boundaryconditions and material properties have been specified asper the standard specified by the vehicle manufacturer Thematerial used for the leaf springs for analysis is 65Si7 whichis having homogenous and isotropic behaviour The material65Si7 is added in the material library and the engineeringproperties are applied

The process for performing analysis in ANSYS solverinvolves the following

821 Setting the Contact Reign The contact conditions areformed where the components meet The differences inthe contact settings determine how the contacting bodiescan move relative to one another In this assembly the Noseparation contact is used for the analysis It only applies toregion of faces Separation of faces in contact is not allowedbut small amounts of frictionless sliding can occur alongcontact faces In general CONTA174 and TARGE170 areused CONTA174 is used for contact and sliding between3D target surfaces (TARGE170) which is defined by thiselement The element is applicable to 3D structural analysis

Start

Calculate maximum thickness

Estimate the number of leaves width and thickness for required

MOI

Select assembly stresses

Calculate steppingoverhang

If no load assembly camber

Calculate the mass

Calculate fatigue life

End

Calculate Smax

If Kmodified variesmore than 7

Calculate Kmodified

If t gt tmax if MOI estimated gt

MOI required

Required K Pdesign Smax Nf

Calculate required moment ofinertia (MOI) Pmax

Calculate the Smaximum andSinitial stress for fatigue life

If Sas middot t2 = 0

Figure 9 Flowchart for analytical estimation of fatigue life of 65Si7leaf spring

Figure 10 CAD model of the leaf springs

8 International Scholarly Research Notices

Figure 11 Boundary conditions for CAE analysis

TARGE170 is used to represent various 3D target surfaces forthe associated contact elements

822 Meshing In this congregation SOLID187 elementwhich is a standard mechanical element for solids is used forthe result SOLID187 element is a higher order 3-D 10-nodeelement SOLID187 has quadratic displacement behaviourand is well suited to modeling irregular meshes The elementis defined by 10 nodes having three degrees of freedom ateach node translations in the nodal 119909 119910 and 119911 directionsThe number of SOLID187 elements is 6964 and the numberof nodes generated is 16943

823 Static Analysis Module A static structural analysisdetermines the displacements stresses strains and forcesin structures or components caused by loads that do notinduce significant inertia and damping effects Steady loadingand response conditions are assumed that is the loads andthe structurersquos response are assumed to vary slowly withrespect to time Static structure analysis takes into consid-eration some parameters like material properties loadingconditions support conditions and contacts which are to bespecified as the input to the preprocessing of the analysis

824 Applying CAE Boundary Conditions The boundaryconditions are applied by taking into consideration the exper-imental loading conditions The springs have been modelledin flat condition and the loading is done to achieve the initialcondition The total load is divided on the two eyes of themaster leaf and pins The fixed support constitutes the seatlength (on master leaf and last (12th leaf) and the centre boltThe CAE boundary conditions are shown in Figure 11

83 Fatigue Life Assessment Using CAE Tools While leafsprings may work well initially they often fail in service dueto fatigue failure caused by repeated cyclic loadingThe aimoffatigue analysis is characterization of capability of a materialto survive many cycles that a leaf spring may experienceduring its life time In ansys fatigue module twomethods areavailable that is stress life and strain life method For thiswork the stress lifemethod is used to predict the fatigue life ofthe component The static environment is set by applying theboundary conditions by taking into consideration the actualloading conditions After the static analysis the fatigue toolis used for fatigue life estimation In stress life decision treeit is required to make four input decisions to perform a stress

life analysis These decisions affect the outcome of the fatigueanalysis in both predicted life and types of postprocessingavailable Input decisions that are to be considered for fatiguelife estimation are loading typemean stress effectsmultiaxialstress correction and fatigue modification factors

831 Type of Loading Unlike static stress which is analyzedwith calculations for a single stress state fatigue damageoccurs when stress at a point changes over time There areessentially four classes of fatigue loading with the ANSYSfatigue module [14] currently supporting the first three

(i) constant amplitude proportional loading(ii) constant amplitude nonproportional loading(iii) nonconstant amplitude proportional loading(iv) nonconstant amplitude non-proportional loading

Constant amplitude proportional loading is the classic ldquobackof the enveloperdquo calculation describing whether the loadhas a constant maximum value or continually varies withtime Loading is of constant amplitude because only one setof FE stress results along with a loading ratio is requiredto calculate the alternating and mean values The loadingratio is defined as the ratio of the second load to the firstload (LR = L2L1) Loading is proportional since only oneset of FE results are needed (principal stress axes do notchange over time) Common types of constant amplitudeloading are fully reversed (apply a load and then apply anequal and opposite load a load ratio of minus1) and zero-based(apply a load and then remove it a load ratio of 0) Sinceloading is proportional looking at a single set of FE resultscan identify critical fatigue locations Constant amplitudenonproportional loading looks at exactly two load cases thatneed not to be related by a scale factor The loading isof constant amplitude but nonproportional since principalstress or strain axes are free to change between the two loadsets Nonconstant amplitude proportional loading also needsonly one set of FE results But instead of using a single loadratio to calculate alternating and mean values the load ratiovaries over time

832 Mean Stress Correction For stress life if experimen-tal data at different mean stresses or r-ratiorsquos exist meanstress can be accounted for directly through interpolationbetweenmaterial curves If experimental data is not availableseveral empirical options may be chosen including GerberGoodman and Soderberg theories which use static materialproperties yield stress and tensile strength along with S-Ndata to account for any mean stress

833 Multiaxial Stress Correction Factor Experimental testdata is mostly uniaxial whereas finite element results areusually multiaxial At some point stress must be convertedfrom a multiaxial stress state to a uniaxial one Von-Misesstress max shear stress maximum principal stress or any ofthe component stresses can be used for the comparison withthe experimental uniaxial stress value

International Scholarly Research Notices 9

(a) (b)

Figure 12 (a) Fatigue life using CAE tools (b) Equivalent alternating stress

Table 5 CAE results for load deflection and bending stresses

Serial number Load type Load (N) Deflection (mm) Stress (MPa)1 Unladen load 7661 449 270742 Designrated load 12959 7605 4583 Flat load 15754 9245 556834 Rubber touching load 216457 12702 7655 Metal to metal contact 28010 16436 98989

Table 6 Comparison of fatigue life by various approaches

Serial number Method for fatiguelife assessment Alternating stress level Stress range Equivalent alternating stress Fatigue life Variation from

experimental results1 Experimental 269ndash896 627 mdash 83513 mdash

2 SAE spring designmanual approach 200ndash885 685 mdash 69600 166

3 Graphical method 269ndash896 627 578 90763 8684 Analytical method 269ndash896 627 579 90304 8135 CAE method 269ndash896 627 562 82348 239

834 Fatigue Modifications (Value of Infinite Life) Anotheravailable option when conducting a variable amplitudefatigue analysis is the ability to set the value used for infinitelife In constant amplitude loading if the alternating stress islower than the lowest alternating stress on the fatigue curvethe fatigue tool will use the life at the last pointThis providesfor an added level of safety because many materials do notexhibit an endurance limit

The static environment is set and boundary conditions areapplied and the solver gives the solution The deflection andstress results obtained from the specified loads are recorded ina tabular format The CAE results for deflection and bendingstress are shown inTable 5 Figure 12(a) depicts the fatigue lifeof the leaf spring using Ansys solver For prediction of fatiguelife the stress life approach is selected A constant amplitudeload ratio is selected as the loading type The fatigue strengthfactor of 065 is chosen and scale factor is kept as 1 Formean stress theory Goodmanrsquos criteria are selected Lastly formultiaxial stress correction von-mises stress is selected andthe component is designed for finite life It has been observedthat the fatigue life of the leaf spring using CAE tool is 82348

cycles Figure 12(b) depicts the equivalent alternating stressin the leaf spring using Ansys solver

9 Results and Discussion

91 Fatigue Life Comparison by Various Approaches Table 6depicts the comparison of fatigue life by various methodsIt is observed that for the alternating stress level of 896ndash269MPa the experimental fatigue life of the leaf spring is83513 cycles The fatigue life estimated by SAE spring designmanual technique is 69600 cycles for the alternating stresslevel of 885ndash200MPa It is also observed that in the SAEspring design manual approach the maximum stress that is885MPa is less than the specified maximum stress but thestress range is higher than specified stress range Hence thisapproximation provides results within 166 variation Thesame approach with specified stress range gives the fatiguelife of leaf spring to be 81600 For the same alternating stresslevel of 896ndash269MPa the fatigue life is found to be 90763cycles by graphical method and equivalent stress is found to

10 International Scholarly Research Notices

Table 7 Comparison of experimental and CAE results

Load type Load (N) Experimental results CAE results age variation between CAEand Experimental results

Deflection Stress Deflection Stress Deflection StressUnladen load 7661 469 262 449 27074 43 33DesignRated load 12959 8144 446 7605 458 66 27Flat load 15754 99 540 9245 55683 66 31Rubber touching load 216457 136 743 12702 765 66 30Metal to metal contact load 28010 176 941 16436 98989 66 52

be 578MPa In the analytical method the fatigue life is foundto be 90304 cycleswith 813 variation from the experimentalresults The CAE fatigue life is found to be 82348 cycles with239 variation from the experimental results

92 Comparison of Experimental and CAE Results To vali-date the analysis the CAE results have been compared withthe experimental results As the experiments are done ona full scale leaf spring testing machine under the specifiedloads the CAE analysis has been carried out for the sameloads The maximum stress induced in the leaf springs isfound to be 941MPa and 98989MPa using experimental andCAE approach respectively The stress is found to be wellbelow the yield tensile strength which is 10812MPa Thetotal deformation and stress comparison for experimentaland CAE approach also validates the CAE analysis of the leafsprings The results of the comparison have been depicted inthe tabular form in Table 7

From Table 7 it is observed that for the same unladenstatic load conditions deflection in experimental and CAEresults is 469mm and 449mm respectively The deforma-tion observed in CAE results varies by 43 The bendingstress for experimental and CAE results is 262MPa and27074MPa respectively The variation of bending stressobserved in CAE results from experimental is 33 FromTable 7 it is also observed that for the same design loadcondition the deflection found in experimental and CAEis 8144mm and 7605mm respectively The variation inCAE results from experimental is 66The bending stressesunder the design load for experimental and CAE results are446MPa and 458MPa respectivelyThe variation in bendingstress observed in the CAE results is 27 For the maximumload condition the static deflection is 176mm and 16436mmfor experimental and CAE results It has been observedthat when CAE results are compared with experimental thevariation in the deformation varies in between 43 and66 respectively The stress variation lies in the range of27 to 52 It has also been observed that the maximumstress induced in the assembly in both the approaches is wellbelow the yield stress of the material It has been observedthat the CAE results obtained by using SOLID187 meshelements and CONTA172 and TARGE170 (No separation andsliding) contact elements provides the results closer to theexperimental testing

10 Conclusions

The 65Si7 LCV model is taken into consideration fordetermining the fatigue life by experimental and graphicalmethods analytical method (using FORTRAN) SAE springdesign manual approach and CAE (using Ansys) approachThe following conclusions are made

(1) The fatigue life of the leaf spring for same stress rangewill decrease if the magnitude of the initial stressis lower In actual condition the leaf springs willwithstand 15ndash17 more fatigue life than predicted bySAE spring design manual approach

(2) Graphical and analytical methods are time consum-ing and prone to errors but provide results which arewithin 8-9 variation

(3) It is concluded that when CONTA174 TARGE170type of contact and SOLID187 mesh element are usedfor CAE analysis results are closer to the experimen-tal results CAE approach usingAnsys predicts fatiguelife within 2ndash5 of experimental results and can be analternate of experimental and analytical approach

Nomenclature

119862119886 No load assembly camber119864 Youngrsquos modulus of elasticity119873119891 Number of cycles to failure120588 Density120583 Poissonrsquos ratio119878119886 Alternating stress120590max Maximum stress1198781015840

119890 Endurance limit

119878119890 Corrected endurance limit119878119910 Yield tensile strength119871 Span120590min Minimum stress119878119898 Mean stress119878119886119890 Equivalent alternating stress119878119906119905 Ultimate tensile strength119870surface Surface factor119870load Load factor119870temp Temperature factor119870size Size factor119870reliability Reliability factor

International Scholarly Research Notices 11

119889equiv Equivalent diameter of rotating beam spec-imen for any cross section

11986095 Portion of the cross sectional area of non-rounded that is stressed in between 95and 100 of its maximum stress

1198781015840

119898 Stress at 103 cycles

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

The authors would like to acknowledge Mr P S Chawlaand the leaf springs testing division of Friends Auto (India)Ltd whose unconditional support has made this projectsuccessful

References

[1] S Saelem S Chantranuwathana K Panichanun P Preeda-nood P Wichienprakarn and P Kruo-ongarjnukool ldquoExper-imental verification of leaf spring model by using a leaf springtest rigrdquo in Proceedings of the 23rd Conference of the Mechan-ical Engineering Network of Thailand Chiang Mai ThailandNovember 2009

[2] F N A Refngah S Abdullah A Jalar and L B Chua ldquoFatiguelife evaluation of two types of steel leaf springsrdquo InternationalJournal of Mechanical and Materials Engineering vol 4 no 2pp 136ndash140 2009

[3] J J Fuentes H J Aguilar J A Rodrıguez and E J HerreraldquoPremature fracture in automobile leaf springsrdquo EngineeringFailure Analysis vol 16 no 2 pp 648ndash655 2009

[4] M L Aggarwal R A Khan and V P Aggarwal ldquoOptimizationof micro welds used in the leaf springsrdquo International Journal ofEngineering Material and Science vol 28 pp 217ndash220 2006

[5] M L Aggarwal V P Agrawal and R A Khan ldquoA stressapproach model for predictions of fatigue life by shot peeningof EN45A spring steelrdquo International Journal of Fatigue vol 28no 12 pp 1845ndash1853 2006

[6] M M Patunkar and D R Dolas ldquoModelling and analysisof composite leaf spring under the static load condition byusing FEArdquo International Journal of Mechanical amp IndustrialEngineering vol 1 no 1 pp 1ndash4 2011

[7] M S Kumar and S Vijayarangan ldquoAnalytical and experimentalstudies on fatigue life prediction of steel and composite multi-leaf spring for light passenger vehicles using life data analysisrdquoMaterials Science vol 13 no 2 pp 141ndash146 2007

[8] P Sanjurjo C Rodrıguez I F Pariente F J Belzunce and A FCanteli ldquoThe influence of shot peening on the fatigue behaviourof duplex stainless steelsrdquo Procedia Engineering vol 2 no 1 pp1539ndash1546 2010

[9] W Z Zhuang andG RHalford ldquoInvestigation of residual stressrelaxation under cyclic loadrdquo International Journal of Fatiguevol 23 supplement 1 pp S31ndashS37 2001

[10] G Savaidis M Malikoutsakis and A Savaidis ldquoFE simulationof vehicle leaf spring behavior under driving manoeuvresrdquoInternational Journal of Structural Integrity vol 4 no 1 ArticleID 17082873 pp 23ndash32 2013

[11] IS 1135 SpringsmdashLeaf Springs Assembly for Automobiles 1995[12] SAE Spring Design ManualmdashDesign and Application of Leaf

Springs HS-744 AE-11 1990[13] R L Norton Machine DesignmdashAn Integrated Approach Pear-

son Education Asia 2nd edition 2001[14] ldquoAnsys Workbench training manual on fatigue toolrdquo 2014

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Page 6: Fatigue Life Assessment of 65Si7 Leaf Springs: A Comparative Study

6 International Scholarly Research Notices

0100200300400500600700800900

100011001200

0 200 400 600 800 1000 1200 1400

Alte

rnat

ing

stres

s (M

Pa)

Mean stress (MPa)

As point I lies outside this region theleaf spring is designed for finite lifeI

C

A

Sa = 314MPa

Sm = 583MPa

Se = 4019MPa

Sae = 578MPa equivalent alternating stress

Figure 6 Alternating stress versus mean stress plot

1400

1200

1000

800

600

400

200

01e + 3 1e + 4 1e + 5 1e + 6 1e + 7 1e + 8

Sae = 578MPa

Se = 4019 MPa

Nf = number of cycles to failure

Alternating stress versus number of cycles

NNumber of cycles

Alte

rnat

ing

stres

sS a

(MPa

)

A

BC

E D

Figure 7 S-N curve for 65Si7

Figure 7 shows the S-N diagram for 65Si7 Point A rep-resents the alternating stress at which the spring will sustain1000 cycles Point D represents the endurance limit that is4019MPa of 65Si7 The line CB represents the equivalentalternating stress The intersection of alternating stress atpoint B will give the number of cycles to fatigue failure

FromFigure 7 S-N plot it is observed thatΔABC is similarto ΔADE

Hence 119860119862119860119864 = 119862119861119863119864

119860119862 = log119860 minus log119862 = 0296

119860119864 = log119860 minus log119864 = 0454

119863119864 = log119863 minus log119864 = log 106minus log 10

3= 3

119862119861 =0296 times 3

0454= 1957

Total 119862119861 = 3 + 197 = 49957

Number of cycles = 104957

= 90763 cycles to failure

(2)

1e + 3 1e + 4 1e + 5 1e + 6 1e + 7 1e + 8

NNumber of cycles

1400

1200

1000

800

600

400

200

0

Alte

rnat

ing

stres

sS a

(MPa

)

N1 cycles at S998400m N2 cycles at Se

= 09(Sut)

Se

A

BC

S998400m

Figure 8 Estimated S-N curve

7 Analytical Method forFatigue Life Prediction

The high cycle fatigue regime is from 103 to 106 and beyondThematerial strength at 103 cycles is called 119878

1015840

119898 which is equal

to 09 Sut The estimated S-N diagram drawn on the log-loggraph is shown in Figure 8 Figure 8 shows that the 119909-axisruns from 103 to 109 or beyond The appropriate 119878

1015840

119898from

the equation for bending load is plotted at N1 = 103 As thematerial exhibits a knee the corrected endurance limit 119878119890 isplotted at N2 = 106 A straight line is drawn between 119878

1015840

119898and

119878119890 The curve is continuous horizontally beyond N2 pointThe equation of the line from 119878

1015840

119898to 119878119890 can be written as

119878 (119873) = 119886119873119887

(taking log on both sides) (3)

log 119878 (119873) = log 119886 + 119887 log119873 (4)

where 119878(119873) is the fatigue strength at any 119873 and 119886 119887 are theconstants defined by the boundary conditions For all theconditions the 119910 intercept is 119878(119873) = 119878

1015840

119898at N = N1 = 103

for endurance limit case 119878(119873) = 119878119890 atN =N2 = 106 Applyingthe boundary condition in the equation we have

log 1198781015840

119898= log 119886 + 119887 log1198731 (5)

log 119878119890 = log 119886 + 119887 log1198732 (6)

log 1198781015840

119898minus log 119878119890 = 119887 (log1198731 minus log1198732) (7)

119885 = (log1198731 minus log1198732) (8)

119887 =1

119885log

1198781015840

119898

119878119890

(9)

log 1198781015840

119898minus 119887 log1198731 = log 119886 (10)

International Scholarly Research Notices 7

As 1198731 = 1000 log101000 = 3

log 1198781015840

119898minus 3119887 = log 119886

119886 =

(1198781015840

119898)2

119878119890

(11)

119873 = (119878119886

119886)

minus1119887

(12)

119878119886119890 = 119886119873119887

119891[13] where119873119891 = number of cycles to failure 119878119886119890 =

equivalent alternating stress 119886 119887 are constantswhich dependson the material properties of 65Si7 The fatigue life is to bepredicted at equivalent alternating stress so 119878119886 is replaced by119878119886119890 The above mentioned equation is used for fatigue lifeestimation and the codes for the analyticalmethod arewrittenin FORTRANThe flowchart is shown in Figure 9

8 Computer Aided Engineering Analysis

The CAD model of the individual leaf is prepared from thestandard drawing of the leaf spring and assembled The leafspring assembly is imported to an analysis software ANSYSfor further processing The different contacts are set andentire model is meshed into small elements The boundaryconditions are applied by taking into consideration the actualloading conditions and the solver gives the solution Thediverse steps involved in CAE analysis are as follows

81 CAD Modeling The CAD modeling of the conventionalleaf springs structure is performed by using solid workssoftware The CAD model of leaf springs consists of total34 different parts which are assembled together in assemblydesign to construct an assemblyThemultileaf springs assem-bly used for analysis is shown in Figure 10

82 Analysis Using ANSYS The CAD model of leaf springshas been imported in the ANSYS solver All the boundaryconditions and material properties have been specified asper the standard specified by the vehicle manufacturer Thematerial used for the leaf springs for analysis is 65Si7 whichis having homogenous and isotropic behaviour The material65Si7 is added in the material library and the engineeringproperties are applied

The process for performing analysis in ANSYS solverinvolves the following

821 Setting the Contact Reign The contact conditions areformed where the components meet The differences inthe contact settings determine how the contacting bodiescan move relative to one another In this assembly the Noseparation contact is used for the analysis It only applies toregion of faces Separation of faces in contact is not allowedbut small amounts of frictionless sliding can occur alongcontact faces In general CONTA174 and TARGE170 areused CONTA174 is used for contact and sliding between3D target surfaces (TARGE170) which is defined by thiselement The element is applicable to 3D structural analysis

Start

Calculate maximum thickness

Estimate the number of leaves width and thickness for required

MOI

Select assembly stresses

Calculate steppingoverhang

If no load assembly camber

Calculate the mass

Calculate fatigue life

End

Calculate Smax

If Kmodified variesmore than 7

Calculate Kmodified

If t gt tmax if MOI estimated gt

MOI required

Required K Pdesign Smax Nf

Calculate required moment ofinertia (MOI) Pmax

Calculate the Smaximum andSinitial stress for fatigue life

If Sas middot t2 = 0

Figure 9 Flowchart for analytical estimation of fatigue life of 65Si7leaf spring

Figure 10 CAD model of the leaf springs

8 International Scholarly Research Notices

Figure 11 Boundary conditions for CAE analysis

TARGE170 is used to represent various 3D target surfaces forthe associated contact elements

822 Meshing In this congregation SOLID187 elementwhich is a standard mechanical element for solids is used forthe result SOLID187 element is a higher order 3-D 10-nodeelement SOLID187 has quadratic displacement behaviourand is well suited to modeling irregular meshes The elementis defined by 10 nodes having three degrees of freedom ateach node translations in the nodal 119909 119910 and 119911 directionsThe number of SOLID187 elements is 6964 and the numberof nodes generated is 16943

823 Static Analysis Module A static structural analysisdetermines the displacements stresses strains and forcesin structures or components caused by loads that do notinduce significant inertia and damping effects Steady loadingand response conditions are assumed that is the loads andthe structurersquos response are assumed to vary slowly withrespect to time Static structure analysis takes into consid-eration some parameters like material properties loadingconditions support conditions and contacts which are to bespecified as the input to the preprocessing of the analysis

824 Applying CAE Boundary Conditions The boundaryconditions are applied by taking into consideration the exper-imental loading conditions The springs have been modelledin flat condition and the loading is done to achieve the initialcondition The total load is divided on the two eyes of themaster leaf and pins The fixed support constitutes the seatlength (on master leaf and last (12th leaf) and the centre boltThe CAE boundary conditions are shown in Figure 11

83 Fatigue Life Assessment Using CAE Tools While leafsprings may work well initially they often fail in service dueto fatigue failure caused by repeated cyclic loadingThe aimoffatigue analysis is characterization of capability of a materialto survive many cycles that a leaf spring may experienceduring its life time In ansys fatigue module twomethods areavailable that is stress life and strain life method For thiswork the stress lifemethod is used to predict the fatigue life ofthe component The static environment is set by applying theboundary conditions by taking into consideration the actualloading conditions After the static analysis the fatigue toolis used for fatigue life estimation In stress life decision treeit is required to make four input decisions to perform a stress

life analysis These decisions affect the outcome of the fatigueanalysis in both predicted life and types of postprocessingavailable Input decisions that are to be considered for fatiguelife estimation are loading typemean stress effectsmultiaxialstress correction and fatigue modification factors

831 Type of Loading Unlike static stress which is analyzedwith calculations for a single stress state fatigue damageoccurs when stress at a point changes over time There areessentially four classes of fatigue loading with the ANSYSfatigue module [14] currently supporting the first three

(i) constant amplitude proportional loading(ii) constant amplitude nonproportional loading(iii) nonconstant amplitude proportional loading(iv) nonconstant amplitude non-proportional loading

Constant amplitude proportional loading is the classic ldquobackof the enveloperdquo calculation describing whether the loadhas a constant maximum value or continually varies withtime Loading is of constant amplitude because only one setof FE stress results along with a loading ratio is requiredto calculate the alternating and mean values The loadingratio is defined as the ratio of the second load to the firstload (LR = L2L1) Loading is proportional since only oneset of FE results are needed (principal stress axes do notchange over time) Common types of constant amplitudeloading are fully reversed (apply a load and then apply anequal and opposite load a load ratio of minus1) and zero-based(apply a load and then remove it a load ratio of 0) Sinceloading is proportional looking at a single set of FE resultscan identify critical fatigue locations Constant amplitudenonproportional loading looks at exactly two load cases thatneed not to be related by a scale factor The loading isof constant amplitude but nonproportional since principalstress or strain axes are free to change between the two loadsets Nonconstant amplitude proportional loading also needsonly one set of FE results But instead of using a single loadratio to calculate alternating and mean values the load ratiovaries over time

832 Mean Stress Correction For stress life if experimen-tal data at different mean stresses or r-ratiorsquos exist meanstress can be accounted for directly through interpolationbetweenmaterial curves If experimental data is not availableseveral empirical options may be chosen including GerberGoodman and Soderberg theories which use static materialproperties yield stress and tensile strength along with S-Ndata to account for any mean stress

833 Multiaxial Stress Correction Factor Experimental testdata is mostly uniaxial whereas finite element results areusually multiaxial At some point stress must be convertedfrom a multiaxial stress state to a uniaxial one Von-Misesstress max shear stress maximum principal stress or any ofthe component stresses can be used for the comparison withthe experimental uniaxial stress value

International Scholarly Research Notices 9

(a) (b)

Figure 12 (a) Fatigue life using CAE tools (b) Equivalent alternating stress

Table 5 CAE results for load deflection and bending stresses

Serial number Load type Load (N) Deflection (mm) Stress (MPa)1 Unladen load 7661 449 270742 Designrated load 12959 7605 4583 Flat load 15754 9245 556834 Rubber touching load 216457 12702 7655 Metal to metal contact 28010 16436 98989

Table 6 Comparison of fatigue life by various approaches

Serial number Method for fatiguelife assessment Alternating stress level Stress range Equivalent alternating stress Fatigue life Variation from

experimental results1 Experimental 269ndash896 627 mdash 83513 mdash

2 SAE spring designmanual approach 200ndash885 685 mdash 69600 166

3 Graphical method 269ndash896 627 578 90763 8684 Analytical method 269ndash896 627 579 90304 8135 CAE method 269ndash896 627 562 82348 239

834 Fatigue Modifications (Value of Infinite Life) Anotheravailable option when conducting a variable amplitudefatigue analysis is the ability to set the value used for infinitelife In constant amplitude loading if the alternating stress islower than the lowest alternating stress on the fatigue curvethe fatigue tool will use the life at the last pointThis providesfor an added level of safety because many materials do notexhibit an endurance limit

The static environment is set and boundary conditions areapplied and the solver gives the solution The deflection andstress results obtained from the specified loads are recorded ina tabular format The CAE results for deflection and bendingstress are shown inTable 5 Figure 12(a) depicts the fatigue lifeof the leaf spring using Ansys solver For prediction of fatiguelife the stress life approach is selected A constant amplitudeload ratio is selected as the loading type The fatigue strengthfactor of 065 is chosen and scale factor is kept as 1 Formean stress theory Goodmanrsquos criteria are selected Lastly formultiaxial stress correction von-mises stress is selected andthe component is designed for finite life It has been observedthat the fatigue life of the leaf spring using CAE tool is 82348

cycles Figure 12(b) depicts the equivalent alternating stressin the leaf spring using Ansys solver

9 Results and Discussion

91 Fatigue Life Comparison by Various Approaches Table 6depicts the comparison of fatigue life by various methodsIt is observed that for the alternating stress level of 896ndash269MPa the experimental fatigue life of the leaf spring is83513 cycles The fatigue life estimated by SAE spring designmanual technique is 69600 cycles for the alternating stresslevel of 885ndash200MPa It is also observed that in the SAEspring design manual approach the maximum stress that is885MPa is less than the specified maximum stress but thestress range is higher than specified stress range Hence thisapproximation provides results within 166 variation Thesame approach with specified stress range gives the fatiguelife of leaf spring to be 81600 For the same alternating stresslevel of 896ndash269MPa the fatigue life is found to be 90763cycles by graphical method and equivalent stress is found to

10 International Scholarly Research Notices

Table 7 Comparison of experimental and CAE results

Load type Load (N) Experimental results CAE results age variation between CAEand Experimental results

Deflection Stress Deflection Stress Deflection StressUnladen load 7661 469 262 449 27074 43 33DesignRated load 12959 8144 446 7605 458 66 27Flat load 15754 99 540 9245 55683 66 31Rubber touching load 216457 136 743 12702 765 66 30Metal to metal contact load 28010 176 941 16436 98989 66 52

be 578MPa In the analytical method the fatigue life is foundto be 90304 cycleswith 813 variation from the experimentalresults The CAE fatigue life is found to be 82348 cycles with239 variation from the experimental results

92 Comparison of Experimental and CAE Results To vali-date the analysis the CAE results have been compared withthe experimental results As the experiments are done ona full scale leaf spring testing machine under the specifiedloads the CAE analysis has been carried out for the sameloads The maximum stress induced in the leaf springs isfound to be 941MPa and 98989MPa using experimental andCAE approach respectively The stress is found to be wellbelow the yield tensile strength which is 10812MPa Thetotal deformation and stress comparison for experimentaland CAE approach also validates the CAE analysis of the leafsprings The results of the comparison have been depicted inthe tabular form in Table 7

From Table 7 it is observed that for the same unladenstatic load conditions deflection in experimental and CAEresults is 469mm and 449mm respectively The deforma-tion observed in CAE results varies by 43 The bendingstress for experimental and CAE results is 262MPa and27074MPa respectively The variation of bending stressobserved in CAE results from experimental is 33 FromTable 7 it is also observed that for the same design loadcondition the deflection found in experimental and CAEis 8144mm and 7605mm respectively The variation inCAE results from experimental is 66The bending stressesunder the design load for experimental and CAE results are446MPa and 458MPa respectivelyThe variation in bendingstress observed in the CAE results is 27 For the maximumload condition the static deflection is 176mm and 16436mmfor experimental and CAE results It has been observedthat when CAE results are compared with experimental thevariation in the deformation varies in between 43 and66 respectively The stress variation lies in the range of27 to 52 It has also been observed that the maximumstress induced in the assembly in both the approaches is wellbelow the yield stress of the material It has been observedthat the CAE results obtained by using SOLID187 meshelements and CONTA172 and TARGE170 (No separation andsliding) contact elements provides the results closer to theexperimental testing

10 Conclusions

The 65Si7 LCV model is taken into consideration fordetermining the fatigue life by experimental and graphicalmethods analytical method (using FORTRAN) SAE springdesign manual approach and CAE (using Ansys) approachThe following conclusions are made

(1) The fatigue life of the leaf spring for same stress rangewill decrease if the magnitude of the initial stressis lower In actual condition the leaf springs willwithstand 15ndash17 more fatigue life than predicted bySAE spring design manual approach

(2) Graphical and analytical methods are time consum-ing and prone to errors but provide results which arewithin 8-9 variation

(3) It is concluded that when CONTA174 TARGE170type of contact and SOLID187 mesh element are usedfor CAE analysis results are closer to the experimen-tal results CAE approach usingAnsys predicts fatiguelife within 2ndash5 of experimental results and can be analternate of experimental and analytical approach

Nomenclature

119862119886 No load assembly camber119864 Youngrsquos modulus of elasticity119873119891 Number of cycles to failure120588 Density120583 Poissonrsquos ratio119878119886 Alternating stress120590max Maximum stress1198781015840

119890 Endurance limit

119878119890 Corrected endurance limit119878119910 Yield tensile strength119871 Span120590min Minimum stress119878119898 Mean stress119878119886119890 Equivalent alternating stress119878119906119905 Ultimate tensile strength119870surface Surface factor119870load Load factor119870temp Temperature factor119870size Size factor119870reliability Reliability factor

International Scholarly Research Notices 11

119889equiv Equivalent diameter of rotating beam spec-imen for any cross section

11986095 Portion of the cross sectional area of non-rounded that is stressed in between 95and 100 of its maximum stress

1198781015840

119898 Stress at 103 cycles

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

The authors would like to acknowledge Mr P S Chawlaand the leaf springs testing division of Friends Auto (India)Ltd whose unconditional support has made this projectsuccessful

References

[1] S Saelem S Chantranuwathana K Panichanun P Preeda-nood P Wichienprakarn and P Kruo-ongarjnukool ldquoExper-imental verification of leaf spring model by using a leaf springtest rigrdquo in Proceedings of the 23rd Conference of the Mechan-ical Engineering Network of Thailand Chiang Mai ThailandNovember 2009

[2] F N A Refngah S Abdullah A Jalar and L B Chua ldquoFatiguelife evaluation of two types of steel leaf springsrdquo InternationalJournal of Mechanical and Materials Engineering vol 4 no 2pp 136ndash140 2009

[3] J J Fuentes H J Aguilar J A Rodrıguez and E J HerreraldquoPremature fracture in automobile leaf springsrdquo EngineeringFailure Analysis vol 16 no 2 pp 648ndash655 2009

[4] M L Aggarwal R A Khan and V P Aggarwal ldquoOptimizationof micro welds used in the leaf springsrdquo International Journal ofEngineering Material and Science vol 28 pp 217ndash220 2006

[5] M L Aggarwal V P Agrawal and R A Khan ldquoA stressapproach model for predictions of fatigue life by shot peeningof EN45A spring steelrdquo International Journal of Fatigue vol 28no 12 pp 1845ndash1853 2006

[6] M M Patunkar and D R Dolas ldquoModelling and analysisof composite leaf spring under the static load condition byusing FEArdquo International Journal of Mechanical amp IndustrialEngineering vol 1 no 1 pp 1ndash4 2011

[7] M S Kumar and S Vijayarangan ldquoAnalytical and experimentalstudies on fatigue life prediction of steel and composite multi-leaf spring for light passenger vehicles using life data analysisrdquoMaterials Science vol 13 no 2 pp 141ndash146 2007

[8] P Sanjurjo C Rodrıguez I F Pariente F J Belzunce and A FCanteli ldquoThe influence of shot peening on the fatigue behaviourof duplex stainless steelsrdquo Procedia Engineering vol 2 no 1 pp1539ndash1546 2010

[9] W Z Zhuang andG RHalford ldquoInvestigation of residual stressrelaxation under cyclic loadrdquo International Journal of Fatiguevol 23 supplement 1 pp S31ndashS37 2001

[10] G Savaidis M Malikoutsakis and A Savaidis ldquoFE simulationof vehicle leaf spring behavior under driving manoeuvresrdquoInternational Journal of Structural Integrity vol 4 no 1 ArticleID 17082873 pp 23ndash32 2013

[11] IS 1135 SpringsmdashLeaf Springs Assembly for Automobiles 1995[12] SAE Spring Design ManualmdashDesign and Application of Leaf

Springs HS-744 AE-11 1990[13] R L Norton Machine DesignmdashAn Integrated Approach Pear-

son Education Asia 2nd edition 2001[14] ldquoAnsys Workbench training manual on fatigue toolrdquo 2014

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International Journal of

Page 7: Fatigue Life Assessment of 65Si7 Leaf Springs: A Comparative Study

International Scholarly Research Notices 7

As 1198731 = 1000 log101000 = 3

log 1198781015840

119898minus 3119887 = log 119886

119886 =

(1198781015840

119898)2

119878119890

(11)

119873 = (119878119886

119886)

minus1119887

(12)

119878119886119890 = 119886119873119887

119891[13] where119873119891 = number of cycles to failure 119878119886119890 =

equivalent alternating stress 119886 119887 are constantswhich dependson the material properties of 65Si7 The fatigue life is to bepredicted at equivalent alternating stress so 119878119886 is replaced by119878119886119890 The above mentioned equation is used for fatigue lifeestimation and the codes for the analyticalmethod arewrittenin FORTRANThe flowchart is shown in Figure 9

8 Computer Aided Engineering Analysis

The CAD model of the individual leaf is prepared from thestandard drawing of the leaf spring and assembled The leafspring assembly is imported to an analysis software ANSYSfor further processing The different contacts are set andentire model is meshed into small elements The boundaryconditions are applied by taking into consideration the actualloading conditions and the solver gives the solution Thediverse steps involved in CAE analysis are as follows

81 CAD Modeling The CAD modeling of the conventionalleaf springs structure is performed by using solid workssoftware The CAD model of leaf springs consists of total34 different parts which are assembled together in assemblydesign to construct an assemblyThemultileaf springs assem-bly used for analysis is shown in Figure 10

82 Analysis Using ANSYS The CAD model of leaf springshas been imported in the ANSYS solver All the boundaryconditions and material properties have been specified asper the standard specified by the vehicle manufacturer Thematerial used for the leaf springs for analysis is 65Si7 whichis having homogenous and isotropic behaviour The material65Si7 is added in the material library and the engineeringproperties are applied

The process for performing analysis in ANSYS solverinvolves the following

821 Setting the Contact Reign The contact conditions areformed where the components meet The differences inthe contact settings determine how the contacting bodiescan move relative to one another In this assembly the Noseparation contact is used for the analysis It only applies toregion of faces Separation of faces in contact is not allowedbut small amounts of frictionless sliding can occur alongcontact faces In general CONTA174 and TARGE170 areused CONTA174 is used for contact and sliding between3D target surfaces (TARGE170) which is defined by thiselement The element is applicable to 3D structural analysis

Start

Calculate maximum thickness

Estimate the number of leaves width and thickness for required

MOI

Select assembly stresses

Calculate steppingoverhang

If no load assembly camber

Calculate the mass

Calculate fatigue life

End

Calculate Smax

If Kmodified variesmore than 7

Calculate Kmodified

If t gt tmax if MOI estimated gt

MOI required

Required K Pdesign Smax Nf

Calculate required moment ofinertia (MOI) Pmax

Calculate the Smaximum andSinitial stress for fatigue life

If Sas middot t2 = 0

Figure 9 Flowchart for analytical estimation of fatigue life of 65Si7leaf spring

Figure 10 CAD model of the leaf springs

8 International Scholarly Research Notices

Figure 11 Boundary conditions for CAE analysis

TARGE170 is used to represent various 3D target surfaces forthe associated contact elements

822 Meshing In this congregation SOLID187 elementwhich is a standard mechanical element for solids is used forthe result SOLID187 element is a higher order 3-D 10-nodeelement SOLID187 has quadratic displacement behaviourand is well suited to modeling irregular meshes The elementis defined by 10 nodes having three degrees of freedom ateach node translations in the nodal 119909 119910 and 119911 directionsThe number of SOLID187 elements is 6964 and the numberof nodes generated is 16943

823 Static Analysis Module A static structural analysisdetermines the displacements stresses strains and forcesin structures or components caused by loads that do notinduce significant inertia and damping effects Steady loadingand response conditions are assumed that is the loads andthe structurersquos response are assumed to vary slowly withrespect to time Static structure analysis takes into consid-eration some parameters like material properties loadingconditions support conditions and contacts which are to bespecified as the input to the preprocessing of the analysis

824 Applying CAE Boundary Conditions The boundaryconditions are applied by taking into consideration the exper-imental loading conditions The springs have been modelledin flat condition and the loading is done to achieve the initialcondition The total load is divided on the two eyes of themaster leaf and pins The fixed support constitutes the seatlength (on master leaf and last (12th leaf) and the centre boltThe CAE boundary conditions are shown in Figure 11

83 Fatigue Life Assessment Using CAE Tools While leafsprings may work well initially they often fail in service dueto fatigue failure caused by repeated cyclic loadingThe aimoffatigue analysis is characterization of capability of a materialto survive many cycles that a leaf spring may experienceduring its life time In ansys fatigue module twomethods areavailable that is stress life and strain life method For thiswork the stress lifemethod is used to predict the fatigue life ofthe component The static environment is set by applying theboundary conditions by taking into consideration the actualloading conditions After the static analysis the fatigue toolis used for fatigue life estimation In stress life decision treeit is required to make four input decisions to perform a stress

life analysis These decisions affect the outcome of the fatigueanalysis in both predicted life and types of postprocessingavailable Input decisions that are to be considered for fatiguelife estimation are loading typemean stress effectsmultiaxialstress correction and fatigue modification factors

831 Type of Loading Unlike static stress which is analyzedwith calculations for a single stress state fatigue damageoccurs when stress at a point changes over time There areessentially four classes of fatigue loading with the ANSYSfatigue module [14] currently supporting the first three

(i) constant amplitude proportional loading(ii) constant amplitude nonproportional loading(iii) nonconstant amplitude proportional loading(iv) nonconstant amplitude non-proportional loading

Constant amplitude proportional loading is the classic ldquobackof the enveloperdquo calculation describing whether the loadhas a constant maximum value or continually varies withtime Loading is of constant amplitude because only one setof FE stress results along with a loading ratio is requiredto calculate the alternating and mean values The loadingratio is defined as the ratio of the second load to the firstload (LR = L2L1) Loading is proportional since only oneset of FE results are needed (principal stress axes do notchange over time) Common types of constant amplitudeloading are fully reversed (apply a load and then apply anequal and opposite load a load ratio of minus1) and zero-based(apply a load and then remove it a load ratio of 0) Sinceloading is proportional looking at a single set of FE resultscan identify critical fatigue locations Constant amplitudenonproportional loading looks at exactly two load cases thatneed not to be related by a scale factor The loading isof constant amplitude but nonproportional since principalstress or strain axes are free to change between the two loadsets Nonconstant amplitude proportional loading also needsonly one set of FE results But instead of using a single loadratio to calculate alternating and mean values the load ratiovaries over time

832 Mean Stress Correction For stress life if experimen-tal data at different mean stresses or r-ratiorsquos exist meanstress can be accounted for directly through interpolationbetweenmaterial curves If experimental data is not availableseveral empirical options may be chosen including GerberGoodman and Soderberg theories which use static materialproperties yield stress and tensile strength along with S-Ndata to account for any mean stress

833 Multiaxial Stress Correction Factor Experimental testdata is mostly uniaxial whereas finite element results areusually multiaxial At some point stress must be convertedfrom a multiaxial stress state to a uniaxial one Von-Misesstress max shear stress maximum principal stress or any ofthe component stresses can be used for the comparison withthe experimental uniaxial stress value

International Scholarly Research Notices 9

(a) (b)

Figure 12 (a) Fatigue life using CAE tools (b) Equivalent alternating stress

Table 5 CAE results for load deflection and bending stresses

Serial number Load type Load (N) Deflection (mm) Stress (MPa)1 Unladen load 7661 449 270742 Designrated load 12959 7605 4583 Flat load 15754 9245 556834 Rubber touching load 216457 12702 7655 Metal to metal contact 28010 16436 98989

Table 6 Comparison of fatigue life by various approaches

Serial number Method for fatiguelife assessment Alternating stress level Stress range Equivalent alternating stress Fatigue life Variation from

experimental results1 Experimental 269ndash896 627 mdash 83513 mdash

2 SAE spring designmanual approach 200ndash885 685 mdash 69600 166

3 Graphical method 269ndash896 627 578 90763 8684 Analytical method 269ndash896 627 579 90304 8135 CAE method 269ndash896 627 562 82348 239

834 Fatigue Modifications (Value of Infinite Life) Anotheravailable option when conducting a variable amplitudefatigue analysis is the ability to set the value used for infinitelife In constant amplitude loading if the alternating stress islower than the lowest alternating stress on the fatigue curvethe fatigue tool will use the life at the last pointThis providesfor an added level of safety because many materials do notexhibit an endurance limit

The static environment is set and boundary conditions areapplied and the solver gives the solution The deflection andstress results obtained from the specified loads are recorded ina tabular format The CAE results for deflection and bendingstress are shown inTable 5 Figure 12(a) depicts the fatigue lifeof the leaf spring using Ansys solver For prediction of fatiguelife the stress life approach is selected A constant amplitudeload ratio is selected as the loading type The fatigue strengthfactor of 065 is chosen and scale factor is kept as 1 Formean stress theory Goodmanrsquos criteria are selected Lastly formultiaxial stress correction von-mises stress is selected andthe component is designed for finite life It has been observedthat the fatigue life of the leaf spring using CAE tool is 82348

cycles Figure 12(b) depicts the equivalent alternating stressin the leaf spring using Ansys solver

9 Results and Discussion

91 Fatigue Life Comparison by Various Approaches Table 6depicts the comparison of fatigue life by various methodsIt is observed that for the alternating stress level of 896ndash269MPa the experimental fatigue life of the leaf spring is83513 cycles The fatigue life estimated by SAE spring designmanual technique is 69600 cycles for the alternating stresslevel of 885ndash200MPa It is also observed that in the SAEspring design manual approach the maximum stress that is885MPa is less than the specified maximum stress but thestress range is higher than specified stress range Hence thisapproximation provides results within 166 variation Thesame approach with specified stress range gives the fatiguelife of leaf spring to be 81600 For the same alternating stresslevel of 896ndash269MPa the fatigue life is found to be 90763cycles by graphical method and equivalent stress is found to

10 International Scholarly Research Notices

Table 7 Comparison of experimental and CAE results

Load type Load (N) Experimental results CAE results age variation between CAEand Experimental results

Deflection Stress Deflection Stress Deflection StressUnladen load 7661 469 262 449 27074 43 33DesignRated load 12959 8144 446 7605 458 66 27Flat load 15754 99 540 9245 55683 66 31Rubber touching load 216457 136 743 12702 765 66 30Metal to metal contact load 28010 176 941 16436 98989 66 52

be 578MPa In the analytical method the fatigue life is foundto be 90304 cycleswith 813 variation from the experimentalresults The CAE fatigue life is found to be 82348 cycles with239 variation from the experimental results

92 Comparison of Experimental and CAE Results To vali-date the analysis the CAE results have been compared withthe experimental results As the experiments are done ona full scale leaf spring testing machine under the specifiedloads the CAE analysis has been carried out for the sameloads The maximum stress induced in the leaf springs isfound to be 941MPa and 98989MPa using experimental andCAE approach respectively The stress is found to be wellbelow the yield tensile strength which is 10812MPa Thetotal deformation and stress comparison for experimentaland CAE approach also validates the CAE analysis of the leafsprings The results of the comparison have been depicted inthe tabular form in Table 7

From Table 7 it is observed that for the same unladenstatic load conditions deflection in experimental and CAEresults is 469mm and 449mm respectively The deforma-tion observed in CAE results varies by 43 The bendingstress for experimental and CAE results is 262MPa and27074MPa respectively The variation of bending stressobserved in CAE results from experimental is 33 FromTable 7 it is also observed that for the same design loadcondition the deflection found in experimental and CAEis 8144mm and 7605mm respectively The variation inCAE results from experimental is 66The bending stressesunder the design load for experimental and CAE results are446MPa and 458MPa respectivelyThe variation in bendingstress observed in the CAE results is 27 For the maximumload condition the static deflection is 176mm and 16436mmfor experimental and CAE results It has been observedthat when CAE results are compared with experimental thevariation in the deformation varies in between 43 and66 respectively The stress variation lies in the range of27 to 52 It has also been observed that the maximumstress induced in the assembly in both the approaches is wellbelow the yield stress of the material It has been observedthat the CAE results obtained by using SOLID187 meshelements and CONTA172 and TARGE170 (No separation andsliding) contact elements provides the results closer to theexperimental testing

10 Conclusions

The 65Si7 LCV model is taken into consideration fordetermining the fatigue life by experimental and graphicalmethods analytical method (using FORTRAN) SAE springdesign manual approach and CAE (using Ansys) approachThe following conclusions are made

(1) The fatigue life of the leaf spring for same stress rangewill decrease if the magnitude of the initial stressis lower In actual condition the leaf springs willwithstand 15ndash17 more fatigue life than predicted bySAE spring design manual approach

(2) Graphical and analytical methods are time consum-ing and prone to errors but provide results which arewithin 8-9 variation

(3) It is concluded that when CONTA174 TARGE170type of contact and SOLID187 mesh element are usedfor CAE analysis results are closer to the experimen-tal results CAE approach usingAnsys predicts fatiguelife within 2ndash5 of experimental results and can be analternate of experimental and analytical approach

Nomenclature

119862119886 No load assembly camber119864 Youngrsquos modulus of elasticity119873119891 Number of cycles to failure120588 Density120583 Poissonrsquos ratio119878119886 Alternating stress120590max Maximum stress1198781015840

119890 Endurance limit

119878119890 Corrected endurance limit119878119910 Yield tensile strength119871 Span120590min Minimum stress119878119898 Mean stress119878119886119890 Equivalent alternating stress119878119906119905 Ultimate tensile strength119870surface Surface factor119870load Load factor119870temp Temperature factor119870size Size factor119870reliability Reliability factor

International Scholarly Research Notices 11

119889equiv Equivalent diameter of rotating beam spec-imen for any cross section

11986095 Portion of the cross sectional area of non-rounded that is stressed in between 95and 100 of its maximum stress

1198781015840

119898 Stress at 103 cycles

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

The authors would like to acknowledge Mr P S Chawlaand the leaf springs testing division of Friends Auto (India)Ltd whose unconditional support has made this projectsuccessful

References

[1] S Saelem S Chantranuwathana K Panichanun P Preeda-nood P Wichienprakarn and P Kruo-ongarjnukool ldquoExper-imental verification of leaf spring model by using a leaf springtest rigrdquo in Proceedings of the 23rd Conference of the Mechan-ical Engineering Network of Thailand Chiang Mai ThailandNovember 2009

[2] F N A Refngah S Abdullah A Jalar and L B Chua ldquoFatiguelife evaluation of two types of steel leaf springsrdquo InternationalJournal of Mechanical and Materials Engineering vol 4 no 2pp 136ndash140 2009

[3] J J Fuentes H J Aguilar J A Rodrıguez and E J HerreraldquoPremature fracture in automobile leaf springsrdquo EngineeringFailure Analysis vol 16 no 2 pp 648ndash655 2009

[4] M L Aggarwal R A Khan and V P Aggarwal ldquoOptimizationof micro welds used in the leaf springsrdquo International Journal ofEngineering Material and Science vol 28 pp 217ndash220 2006

[5] M L Aggarwal V P Agrawal and R A Khan ldquoA stressapproach model for predictions of fatigue life by shot peeningof EN45A spring steelrdquo International Journal of Fatigue vol 28no 12 pp 1845ndash1853 2006

[6] M M Patunkar and D R Dolas ldquoModelling and analysisof composite leaf spring under the static load condition byusing FEArdquo International Journal of Mechanical amp IndustrialEngineering vol 1 no 1 pp 1ndash4 2011

[7] M S Kumar and S Vijayarangan ldquoAnalytical and experimentalstudies on fatigue life prediction of steel and composite multi-leaf spring for light passenger vehicles using life data analysisrdquoMaterials Science vol 13 no 2 pp 141ndash146 2007

[8] P Sanjurjo C Rodrıguez I F Pariente F J Belzunce and A FCanteli ldquoThe influence of shot peening on the fatigue behaviourof duplex stainless steelsrdquo Procedia Engineering vol 2 no 1 pp1539ndash1546 2010

[9] W Z Zhuang andG RHalford ldquoInvestigation of residual stressrelaxation under cyclic loadrdquo International Journal of Fatiguevol 23 supplement 1 pp S31ndashS37 2001

[10] G Savaidis M Malikoutsakis and A Savaidis ldquoFE simulationof vehicle leaf spring behavior under driving manoeuvresrdquoInternational Journal of Structural Integrity vol 4 no 1 ArticleID 17082873 pp 23ndash32 2013

[11] IS 1135 SpringsmdashLeaf Springs Assembly for Automobiles 1995[12] SAE Spring Design ManualmdashDesign and Application of Leaf

Springs HS-744 AE-11 1990[13] R L Norton Machine DesignmdashAn Integrated Approach Pear-

son Education Asia 2nd edition 2001[14] ldquoAnsys Workbench training manual on fatigue toolrdquo 2014

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Page 8: Fatigue Life Assessment of 65Si7 Leaf Springs: A Comparative Study

8 International Scholarly Research Notices

Figure 11 Boundary conditions for CAE analysis

TARGE170 is used to represent various 3D target surfaces forthe associated contact elements

822 Meshing In this congregation SOLID187 elementwhich is a standard mechanical element for solids is used forthe result SOLID187 element is a higher order 3-D 10-nodeelement SOLID187 has quadratic displacement behaviourand is well suited to modeling irregular meshes The elementis defined by 10 nodes having three degrees of freedom ateach node translations in the nodal 119909 119910 and 119911 directionsThe number of SOLID187 elements is 6964 and the numberof nodes generated is 16943

823 Static Analysis Module A static structural analysisdetermines the displacements stresses strains and forcesin structures or components caused by loads that do notinduce significant inertia and damping effects Steady loadingand response conditions are assumed that is the loads andthe structurersquos response are assumed to vary slowly withrespect to time Static structure analysis takes into consid-eration some parameters like material properties loadingconditions support conditions and contacts which are to bespecified as the input to the preprocessing of the analysis

824 Applying CAE Boundary Conditions The boundaryconditions are applied by taking into consideration the exper-imental loading conditions The springs have been modelledin flat condition and the loading is done to achieve the initialcondition The total load is divided on the two eyes of themaster leaf and pins The fixed support constitutes the seatlength (on master leaf and last (12th leaf) and the centre boltThe CAE boundary conditions are shown in Figure 11

83 Fatigue Life Assessment Using CAE Tools While leafsprings may work well initially they often fail in service dueto fatigue failure caused by repeated cyclic loadingThe aimoffatigue analysis is characterization of capability of a materialto survive many cycles that a leaf spring may experienceduring its life time In ansys fatigue module twomethods areavailable that is stress life and strain life method For thiswork the stress lifemethod is used to predict the fatigue life ofthe component The static environment is set by applying theboundary conditions by taking into consideration the actualloading conditions After the static analysis the fatigue toolis used for fatigue life estimation In stress life decision treeit is required to make four input decisions to perform a stress

life analysis These decisions affect the outcome of the fatigueanalysis in both predicted life and types of postprocessingavailable Input decisions that are to be considered for fatiguelife estimation are loading typemean stress effectsmultiaxialstress correction and fatigue modification factors

831 Type of Loading Unlike static stress which is analyzedwith calculations for a single stress state fatigue damageoccurs when stress at a point changes over time There areessentially four classes of fatigue loading with the ANSYSfatigue module [14] currently supporting the first three

(i) constant amplitude proportional loading(ii) constant amplitude nonproportional loading(iii) nonconstant amplitude proportional loading(iv) nonconstant amplitude non-proportional loading

Constant amplitude proportional loading is the classic ldquobackof the enveloperdquo calculation describing whether the loadhas a constant maximum value or continually varies withtime Loading is of constant amplitude because only one setof FE stress results along with a loading ratio is requiredto calculate the alternating and mean values The loadingratio is defined as the ratio of the second load to the firstload (LR = L2L1) Loading is proportional since only oneset of FE results are needed (principal stress axes do notchange over time) Common types of constant amplitudeloading are fully reversed (apply a load and then apply anequal and opposite load a load ratio of minus1) and zero-based(apply a load and then remove it a load ratio of 0) Sinceloading is proportional looking at a single set of FE resultscan identify critical fatigue locations Constant amplitudenonproportional loading looks at exactly two load cases thatneed not to be related by a scale factor The loading isof constant amplitude but nonproportional since principalstress or strain axes are free to change between the two loadsets Nonconstant amplitude proportional loading also needsonly one set of FE results But instead of using a single loadratio to calculate alternating and mean values the load ratiovaries over time

832 Mean Stress Correction For stress life if experimen-tal data at different mean stresses or r-ratiorsquos exist meanstress can be accounted for directly through interpolationbetweenmaterial curves If experimental data is not availableseveral empirical options may be chosen including GerberGoodman and Soderberg theories which use static materialproperties yield stress and tensile strength along with S-Ndata to account for any mean stress

833 Multiaxial Stress Correction Factor Experimental testdata is mostly uniaxial whereas finite element results areusually multiaxial At some point stress must be convertedfrom a multiaxial stress state to a uniaxial one Von-Misesstress max shear stress maximum principal stress or any ofthe component stresses can be used for the comparison withthe experimental uniaxial stress value

International Scholarly Research Notices 9

(a) (b)

Figure 12 (a) Fatigue life using CAE tools (b) Equivalent alternating stress

Table 5 CAE results for load deflection and bending stresses

Serial number Load type Load (N) Deflection (mm) Stress (MPa)1 Unladen load 7661 449 270742 Designrated load 12959 7605 4583 Flat load 15754 9245 556834 Rubber touching load 216457 12702 7655 Metal to metal contact 28010 16436 98989

Table 6 Comparison of fatigue life by various approaches

Serial number Method for fatiguelife assessment Alternating stress level Stress range Equivalent alternating stress Fatigue life Variation from

experimental results1 Experimental 269ndash896 627 mdash 83513 mdash

2 SAE spring designmanual approach 200ndash885 685 mdash 69600 166

3 Graphical method 269ndash896 627 578 90763 8684 Analytical method 269ndash896 627 579 90304 8135 CAE method 269ndash896 627 562 82348 239

834 Fatigue Modifications (Value of Infinite Life) Anotheravailable option when conducting a variable amplitudefatigue analysis is the ability to set the value used for infinitelife In constant amplitude loading if the alternating stress islower than the lowest alternating stress on the fatigue curvethe fatigue tool will use the life at the last pointThis providesfor an added level of safety because many materials do notexhibit an endurance limit

The static environment is set and boundary conditions areapplied and the solver gives the solution The deflection andstress results obtained from the specified loads are recorded ina tabular format The CAE results for deflection and bendingstress are shown inTable 5 Figure 12(a) depicts the fatigue lifeof the leaf spring using Ansys solver For prediction of fatiguelife the stress life approach is selected A constant amplitudeload ratio is selected as the loading type The fatigue strengthfactor of 065 is chosen and scale factor is kept as 1 Formean stress theory Goodmanrsquos criteria are selected Lastly formultiaxial stress correction von-mises stress is selected andthe component is designed for finite life It has been observedthat the fatigue life of the leaf spring using CAE tool is 82348

cycles Figure 12(b) depicts the equivalent alternating stressin the leaf spring using Ansys solver

9 Results and Discussion

91 Fatigue Life Comparison by Various Approaches Table 6depicts the comparison of fatigue life by various methodsIt is observed that for the alternating stress level of 896ndash269MPa the experimental fatigue life of the leaf spring is83513 cycles The fatigue life estimated by SAE spring designmanual technique is 69600 cycles for the alternating stresslevel of 885ndash200MPa It is also observed that in the SAEspring design manual approach the maximum stress that is885MPa is less than the specified maximum stress but thestress range is higher than specified stress range Hence thisapproximation provides results within 166 variation Thesame approach with specified stress range gives the fatiguelife of leaf spring to be 81600 For the same alternating stresslevel of 896ndash269MPa the fatigue life is found to be 90763cycles by graphical method and equivalent stress is found to

10 International Scholarly Research Notices

Table 7 Comparison of experimental and CAE results

Load type Load (N) Experimental results CAE results age variation between CAEand Experimental results

Deflection Stress Deflection Stress Deflection StressUnladen load 7661 469 262 449 27074 43 33DesignRated load 12959 8144 446 7605 458 66 27Flat load 15754 99 540 9245 55683 66 31Rubber touching load 216457 136 743 12702 765 66 30Metal to metal contact load 28010 176 941 16436 98989 66 52

be 578MPa In the analytical method the fatigue life is foundto be 90304 cycleswith 813 variation from the experimentalresults The CAE fatigue life is found to be 82348 cycles with239 variation from the experimental results

92 Comparison of Experimental and CAE Results To vali-date the analysis the CAE results have been compared withthe experimental results As the experiments are done ona full scale leaf spring testing machine under the specifiedloads the CAE analysis has been carried out for the sameloads The maximum stress induced in the leaf springs isfound to be 941MPa and 98989MPa using experimental andCAE approach respectively The stress is found to be wellbelow the yield tensile strength which is 10812MPa Thetotal deformation and stress comparison for experimentaland CAE approach also validates the CAE analysis of the leafsprings The results of the comparison have been depicted inthe tabular form in Table 7

From Table 7 it is observed that for the same unladenstatic load conditions deflection in experimental and CAEresults is 469mm and 449mm respectively The deforma-tion observed in CAE results varies by 43 The bendingstress for experimental and CAE results is 262MPa and27074MPa respectively The variation of bending stressobserved in CAE results from experimental is 33 FromTable 7 it is also observed that for the same design loadcondition the deflection found in experimental and CAEis 8144mm and 7605mm respectively The variation inCAE results from experimental is 66The bending stressesunder the design load for experimental and CAE results are446MPa and 458MPa respectivelyThe variation in bendingstress observed in the CAE results is 27 For the maximumload condition the static deflection is 176mm and 16436mmfor experimental and CAE results It has been observedthat when CAE results are compared with experimental thevariation in the deformation varies in between 43 and66 respectively The stress variation lies in the range of27 to 52 It has also been observed that the maximumstress induced in the assembly in both the approaches is wellbelow the yield stress of the material It has been observedthat the CAE results obtained by using SOLID187 meshelements and CONTA172 and TARGE170 (No separation andsliding) contact elements provides the results closer to theexperimental testing

10 Conclusions

The 65Si7 LCV model is taken into consideration fordetermining the fatigue life by experimental and graphicalmethods analytical method (using FORTRAN) SAE springdesign manual approach and CAE (using Ansys) approachThe following conclusions are made

(1) The fatigue life of the leaf spring for same stress rangewill decrease if the magnitude of the initial stressis lower In actual condition the leaf springs willwithstand 15ndash17 more fatigue life than predicted bySAE spring design manual approach

(2) Graphical and analytical methods are time consum-ing and prone to errors but provide results which arewithin 8-9 variation

(3) It is concluded that when CONTA174 TARGE170type of contact and SOLID187 mesh element are usedfor CAE analysis results are closer to the experimen-tal results CAE approach usingAnsys predicts fatiguelife within 2ndash5 of experimental results and can be analternate of experimental and analytical approach

Nomenclature

119862119886 No load assembly camber119864 Youngrsquos modulus of elasticity119873119891 Number of cycles to failure120588 Density120583 Poissonrsquos ratio119878119886 Alternating stress120590max Maximum stress1198781015840

119890 Endurance limit

119878119890 Corrected endurance limit119878119910 Yield tensile strength119871 Span120590min Minimum stress119878119898 Mean stress119878119886119890 Equivalent alternating stress119878119906119905 Ultimate tensile strength119870surface Surface factor119870load Load factor119870temp Temperature factor119870size Size factor119870reliability Reliability factor

International Scholarly Research Notices 11

119889equiv Equivalent diameter of rotating beam spec-imen for any cross section

11986095 Portion of the cross sectional area of non-rounded that is stressed in between 95and 100 of its maximum stress

1198781015840

119898 Stress at 103 cycles

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

The authors would like to acknowledge Mr P S Chawlaand the leaf springs testing division of Friends Auto (India)Ltd whose unconditional support has made this projectsuccessful

References

[1] S Saelem S Chantranuwathana K Panichanun P Preeda-nood P Wichienprakarn and P Kruo-ongarjnukool ldquoExper-imental verification of leaf spring model by using a leaf springtest rigrdquo in Proceedings of the 23rd Conference of the Mechan-ical Engineering Network of Thailand Chiang Mai ThailandNovember 2009

[2] F N A Refngah S Abdullah A Jalar and L B Chua ldquoFatiguelife evaluation of two types of steel leaf springsrdquo InternationalJournal of Mechanical and Materials Engineering vol 4 no 2pp 136ndash140 2009

[3] J J Fuentes H J Aguilar J A Rodrıguez and E J HerreraldquoPremature fracture in automobile leaf springsrdquo EngineeringFailure Analysis vol 16 no 2 pp 648ndash655 2009

[4] M L Aggarwal R A Khan and V P Aggarwal ldquoOptimizationof micro welds used in the leaf springsrdquo International Journal ofEngineering Material and Science vol 28 pp 217ndash220 2006

[5] M L Aggarwal V P Agrawal and R A Khan ldquoA stressapproach model for predictions of fatigue life by shot peeningof EN45A spring steelrdquo International Journal of Fatigue vol 28no 12 pp 1845ndash1853 2006

[6] M M Patunkar and D R Dolas ldquoModelling and analysisof composite leaf spring under the static load condition byusing FEArdquo International Journal of Mechanical amp IndustrialEngineering vol 1 no 1 pp 1ndash4 2011

[7] M S Kumar and S Vijayarangan ldquoAnalytical and experimentalstudies on fatigue life prediction of steel and composite multi-leaf spring for light passenger vehicles using life data analysisrdquoMaterials Science vol 13 no 2 pp 141ndash146 2007

[8] P Sanjurjo C Rodrıguez I F Pariente F J Belzunce and A FCanteli ldquoThe influence of shot peening on the fatigue behaviourof duplex stainless steelsrdquo Procedia Engineering vol 2 no 1 pp1539ndash1546 2010

[9] W Z Zhuang andG RHalford ldquoInvestigation of residual stressrelaxation under cyclic loadrdquo International Journal of Fatiguevol 23 supplement 1 pp S31ndashS37 2001

[10] G Savaidis M Malikoutsakis and A Savaidis ldquoFE simulationof vehicle leaf spring behavior under driving manoeuvresrdquoInternational Journal of Structural Integrity vol 4 no 1 ArticleID 17082873 pp 23ndash32 2013

[11] IS 1135 SpringsmdashLeaf Springs Assembly for Automobiles 1995[12] SAE Spring Design ManualmdashDesign and Application of Leaf

Springs HS-744 AE-11 1990[13] R L Norton Machine DesignmdashAn Integrated Approach Pear-

son Education Asia 2nd edition 2001[14] ldquoAnsys Workbench training manual on fatigue toolrdquo 2014

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Page 9: Fatigue Life Assessment of 65Si7 Leaf Springs: A Comparative Study

International Scholarly Research Notices 9

(a) (b)

Figure 12 (a) Fatigue life using CAE tools (b) Equivalent alternating stress

Table 5 CAE results for load deflection and bending stresses

Serial number Load type Load (N) Deflection (mm) Stress (MPa)1 Unladen load 7661 449 270742 Designrated load 12959 7605 4583 Flat load 15754 9245 556834 Rubber touching load 216457 12702 7655 Metal to metal contact 28010 16436 98989

Table 6 Comparison of fatigue life by various approaches

Serial number Method for fatiguelife assessment Alternating stress level Stress range Equivalent alternating stress Fatigue life Variation from

experimental results1 Experimental 269ndash896 627 mdash 83513 mdash

2 SAE spring designmanual approach 200ndash885 685 mdash 69600 166

3 Graphical method 269ndash896 627 578 90763 8684 Analytical method 269ndash896 627 579 90304 8135 CAE method 269ndash896 627 562 82348 239

834 Fatigue Modifications (Value of Infinite Life) Anotheravailable option when conducting a variable amplitudefatigue analysis is the ability to set the value used for infinitelife In constant amplitude loading if the alternating stress islower than the lowest alternating stress on the fatigue curvethe fatigue tool will use the life at the last pointThis providesfor an added level of safety because many materials do notexhibit an endurance limit

The static environment is set and boundary conditions areapplied and the solver gives the solution The deflection andstress results obtained from the specified loads are recorded ina tabular format The CAE results for deflection and bendingstress are shown inTable 5 Figure 12(a) depicts the fatigue lifeof the leaf spring using Ansys solver For prediction of fatiguelife the stress life approach is selected A constant amplitudeload ratio is selected as the loading type The fatigue strengthfactor of 065 is chosen and scale factor is kept as 1 Formean stress theory Goodmanrsquos criteria are selected Lastly formultiaxial stress correction von-mises stress is selected andthe component is designed for finite life It has been observedthat the fatigue life of the leaf spring using CAE tool is 82348

cycles Figure 12(b) depicts the equivalent alternating stressin the leaf spring using Ansys solver

9 Results and Discussion

91 Fatigue Life Comparison by Various Approaches Table 6depicts the comparison of fatigue life by various methodsIt is observed that for the alternating stress level of 896ndash269MPa the experimental fatigue life of the leaf spring is83513 cycles The fatigue life estimated by SAE spring designmanual technique is 69600 cycles for the alternating stresslevel of 885ndash200MPa It is also observed that in the SAEspring design manual approach the maximum stress that is885MPa is less than the specified maximum stress but thestress range is higher than specified stress range Hence thisapproximation provides results within 166 variation Thesame approach with specified stress range gives the fatiguelife of leaf spring to be 81600 For the same alternating stresslevel of 896ndash269MPa the fatigue life is found to be 90763cycles by graphical method and equivalent stress is found to

10 International Scholarly Research Notices

Table 7 Comparison of experimental and CAE results

Load type Load (N) Experimental results CAE results age variation between CAEand Experimental results

Deflection Stress Deflection Stress Deflection StressUnladen load 7661 469 262 449 27074 43 33DesignRated load 12959 8144 446 7605 458 66 27Flat load 15754 99 540 9245 55683 66 31Rubber touching load 216457 136 743 12702 765 66 30Metal to metal contact load 28010 176 941 16436 98989 66 52

be 578MPa In the analytical method the fatigue life is foundto be 90304 cycleswith 813 variation from the experimentalresults The CAE fatigue life is found to be 82348 cycles with239 variation from the experimental results

92 Comparison of Experimental and CAE Results To vali-date the analysis the CAE results have been compared withthe experimental results As the experiments are done ona full scale leaf spring testing machine under the specifiedloads the CAE analysis has been carried out for the sameloads The maximum stress induced in the leaf springs isfound to be 941MPa and 98989MPa using experimental andCAE approach respectively The stress is found to be wellbelow the yield tensile strength which is 10812MPa Thetotal deformation and stress comparison for experimentaland CAE approach also validates the CAE analysis of the leafsprings The results of the comparison have been depicted inthe tabular form in Table 7

From Table 7 it is observed that for the same unladenstatic load conditions deflection in experimental and CAEresults is 469mm and 449mm respectively The deforma-tion observed in CAE results varies by 43 The bendingstress for experimental and CAE results is 262MPa and27074MPa respectively The variation of bending stressobserved in CAE results from experimental is 33 FromTable 7 it is also observed that for the same design loadcondition the deflection found in experimental and CAEis 8144mm and 7605mm respectively The variation inCAE results from experimental is 66The bending stressesunder the design load for experimental and CAE results are446MPa and 458MPa respectivelyThe variation in bendingstress observed in the CAE results is 27 For the maximumload condition the static deflection is 176mm and 16436mmfor experimental and CAE results It has been observedthat when CAE results are compared with experimental thevariation in the deformation varies in between 43 and66 respectively The stress variation lies in the range of27 to 52 It has also been observed that the maximumstress induced in the assembly in both the approaches is wellbelow the yield stress of the material It has been observedthat the CAE results obtained by using SOLID187 meshelements and CONTA172 and TARGE170 (No separation andsliding) contact elements provides the results closer to theexperimental testing

10 Conclusions

The 65Si7 LCV model is taken into consideration fordetermining the fatigue life by experimental and graphicalmethods analytical method (using FORTRAN) SAE springdesign manual approach and CAE (using Ansys) approachThe following conclusions are made

(1) The fatigue life of the leaf spring for same stress rangewill decrease if the magnitude of the initial stressis lower In actual condition the leaf springs willwithstand 15ndash17 more fatigue life than predicted bySAE spring design manual approach

(2) Graphical and analytical methods are time consum-ing and prone to errors but provide results which arewithin 8-9 variation

(3) It is concluded that when CONTA174 TARGE170type of contact and SOLID187 mesh element are usedfor CAE analysis results are closer to the experimen-tal results CAE approach usingAnsys predicts fatiguelife within 2ndash5 of experimental results and can be analternate of experimental and analytical approach

Nomenclature

119862119886 No load assembly camber119864 Youngrsquos modulus of elasticity119873119891 Number of cycles to failure120588 Density120583 Poissonrsquos ratio119878119886 Alternating stress120590max Maximum stress1198781015840

119890 Endurance limit

119878119890 Corrected endurance limit119878119910 Yield tensile strength119871 Span120590min Minimum stress119878119898 Mean stress119878119886119890 Equivalent alternating stress119878119906119905 Ultimate tensile strength119870surface Surface factor119870load Load factor119870temp Temperature factor119870size Size factor119870reliability Reliability factor

International Scholarly Research Notices 11

119889equiv Equivalent diameter of rotating beam spec-imen for any cross section

11986095 Portion of the cross sectional area of non-rounded that is stressed in between 95and 100 of its maximum stress

1198781015840

119898 Stress at 103 cycles

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

The authors would like to acknowledge Mr P S Chawlaand the leaf springs testing division of Friends Auto (India)Ltd whose unconditional support has made this projectsuccessful

References

[1] S Saelem S Chantranuwathana K Panichanun P Preeda-nood P Wichienprakarn and P Kruo-ongarjnukool ldquoExper-imental verification of leaf spring model by using a leaf springtest rigrdquo in Proceedings of the 23rd Conference of the Mechan-ical Engineering Network of Thailand Chiang Mai ThailandNovember 2009

[2] F N A Refngah S Abdullah A Jalar and L B Chua ldquoFatiguelife evaluation of two types of steel leaf springsrdquo InternationalJournal of Mechanical and Materials Engineering vol 4 no 2pp 136ndash140 2009

[3] J J Fuentes H J Aguilar J A Rodrıguez and E J HerreraldquoPremature fracture in automobile leaf springsrdquo EngineeringFailure Analysis vol 16 no 2 pp 648ndash655 2009

[4] M L Aggarwal R A Khan and V P Aggarwal ldquoOptimizationof micro welds used in the leaf springsrdquo International Journal ofEngineering Material and Science vol 28 pp 217ndash220 2006

[5] M L Aggarwal V P Agrawal and R A Khan ldquoA stressapproach model for predictions of fatigue life by shot peeningof EN45A spring steelrdquo International Journal of Fatigue vol 28no 12 pp 1845ndash1853 2006

[6] M M Patunkar and D R Dolas ldquoModelling and analysisof composite leaf spring under the static load condition byusing FEArdquo International Journal of Mechanical amp IndustrialEngineering vol 1 no 1 pp 1ndash4 2011

[7] M S Kumar and S Vijayarangan ldquoAnalytical and experimentalstudies on fatigue life prediction of steel and composite multi-leaf spring for light passenger vehicles using life data analysisrdquoMaterials Science vol 13 no 2 pp 141ndash146 2007

[8] P Sanjurjo C Rodrıguez I F Pariente F J Belzunce and A FCanteli ldquoThe influence of shot peening on the fatigue behaviourof duplex stainless steelsrdquo Procedia Engineering vol 2 no 1 pp1539ndash1546 2010

[9] W Z Zhuang andG RHalford ldquoInvestigation of residual stressrelaxation under cyclic loadrdquo International Journal of Fatiguevol 23 supplement 1 pp S31ndashS37 2001

[10] G Savaidis M Malikoutsakis and A Savaidis ldquoFE simulationof vehicle leaf spring behavior under driving manoeuvresrdquoInternational Journal of Structural Integrity vol 4 no 1 ArticleID 17082873 pp 23ndash32 2013

[11] IS 1135 SpringsmdashLeaf Springs Assembly for Automobiles 1995[12] SAE Spring Design ManualmdashDesign and Application of Leaf

Springs HS-744 AE-11 1990[13] R L Norton Machine DesignmdashAn Integrated Approach Pear-

son Education Asia 2nd edition 2001[14] ldquoAnsys Workbench training manual on fatigue toolrdquo 2014

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Page 10: Fatigue Life Assessment of 65Si7 Leaf Springs: A Comparative Study

10 International Scholarly Research Notices

Table 7 Comparison of experimental and CAE results

Load type Load (N) Experimental results CAE results age variation between CAEand Experimental results

Deflection Stress Deflection Stress Deflection StressUnladen load 7661 469 262 449 27074 43 33DesignRated load 12959 8144 446 7605 458 66 27Flat load 15754 99 540 9245 55683 66 31Rubber touching load 216457 136 743 12702 765 66 30Metal to metal contact load 28010 176 941 16436 98989 66 52

be 578MPa In the analytical method the fatigue life is foundto be 90304 cycleswith 813 variation from the experimentalresults The CAE fatigue life is found to be 82348 cycles with239 variation from the experimental results

92 Comparison of Experimental and CAE Results To vali-date the analysis the CAE results have been compared withthe experimental results As the experiments are done ona full scale leaf spring testing machine under the specifiedloads the CAE analysis has been carried out for the sameloads The maximum stress induced in the leaf springs isfound to be 941MPa and 98989MPa using experimental andCAE approach respectively The stress is found to be wellbelow the yield tensile strength which is 10812MPa Thetotal deformation and stress comparison for experimentaland CAE approach also validates the CAE analysis of the leafsprings The results of the comparison have been depicted inthe tabular form in Table 7

From Table 7 it is observed that for the same unladenstatic load conditions deflection in experimental and CAEresults is 469mm and 449mm respectively The deforma-tion observed in CAE results varies by 43 The bendingstress for experimental and CAE results is 262MPa and27074MPa respectively The variation of bending stressobserved in CAE results from experimental is 33 FromTable 7 it is also observed that for the same design loadcondition the deflection found in experimental and CAEis 8144mm and 7605mm respectively The variation inCAE results from experimental is 66The bending stressesunder the design load for experimental and CAE results are446MPa and 458MPa respectivelyThe variation in bendingstress observed in the CAE results is 27 For the maximumload condition the static deflection is 176mm and 16436mmfor experimental and CAE results It has been observedthat when CAE results are compared with experimental thevariation in the deformation varies in between 43 and66 respectively The stress variation lies in the range of27 to 52 It has also been observed that the maximumstress induced in the assembly in both the approaches is wellbelow the yield stress of the material It has been observedthat the CAE results obtained by using SOLID187 meshelements and CONTA172 and TARGE170 (No separation andsliding) contact elements provides the results closer to theexperimental testing

10 Conclusions

The 65Si7 LCV model is taken into consideration fordetermining the fatigue life by experimental and graphicalmethods analytical method (using FORTRAN) SAE springdesign manual approach and CAE (using Ansys) approachThe following conclusions are made

(1) The fatigue life of the leaf spring for same stress rangewill decrease if the magnitude of the initial stressis lower In actual condition the leaf springs willwithstand 15ndash17 more fatigue life than predicted bySAE spring design manual approach

(2) Graphical and analytical methods are time consum-ing and prone to errors but provide results which arewithin 8-9 variation

(3) It is concluded that when CONTA174 TARGE170type of contact and SOLID187 mesh element are usedfor CAE analysis results are closer to the experimen-tal results CAE approach usingAnsys predicts fatiguelife within 2ndash5 of experimental results and can be analternate of experimental and analytical approach

Nomenclature

119862119886 No load assembly camber119864 Youngrsquos modulus of elasticity119873119891 Number of cycles to failure120588 Density120583 Poissonrsquos ratio119878119886 Alternating stress120590max Maximum stress1198781015840

119890 Endurance limit

119878119890 Corrected endurance limit119878119910 Yield tensile strength119871 Span120590min Minimum stress119878119898 Mean stress119878119886119890 Equivalent alternating stress119878119906119905 Ultimate tensile strength119870surface Surface factor119870load Load factor119870temp Temperature factor119870size Size factor119870reliability Reliability factor

International Scholarly Research Notices 11

119889equiv Equivalent diameter of rotating beam spec-imen for any cross section

11986095 Portion of the cross sectional area of non-rounded that is stressed in between 95and 100 of its maximum stress

1198781015840

119898 Stress at 103 cycles

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

The authors would like to acknowledge Mr P S Chawlaand the leaf springs testing division of Friends Auto (India)Ltd whose unconditional support has made this projectsuccessful

References

[1] S Saelem S Chantranuwathana K Panichanun P Preeda-nood P Wichienprakarn and P Kruo-ongarjnukool ldquoExper-imental verification of leaf spring model by using a leaf springtest rigrdquo in Proceedings of the 23rd Conference of the Mechan-ical Engineering Network of Thailand Chiang Mai ThailandNovember 2009

[2] F N A Refngah S Abdullah A Jalar and L B Chua ldquoFatiguelife evaluation of two types of steel leaf springsrdquo InternationalJournal of Mechanical and Materials Engineering vol 4 no 2pp 136ndash140 2009

[3] J J Fuentes H J Aguilar J A Rodrıguez and E J HerreraldquoPremature fracture in automobile leaf springsrdquo EngineeringFailure Analysis vol 16 no 2 pp 648ndash655 2009

[4] M L Aggarwal R A Khan and V P Aggarwal ldquoOptimizationof micro welds used in the leaf springsrdquo International Journal ofEngineering Material and Science vol 28 pp 217ndash220 2006

[5] M L Aggarwal V P Agrawal and R A Khan ldquoA stressapproach model for predictions of fatigue life by shot peeningof EN45A spring steelrdquo International Journal of Fatigue vol 28no 12 pp 1845ndash1853 2006

[6] M M Patunkar and D R Dolas ldquoModelling and analysisof composite leaf spring under the static load condition byusing FEArdquo International Journal of Mechanical amp IndustrialEngineering vol 1 no 1 pp 1ndash4 2011

[7] M S Kumar and S Vijayarangan ldquoAnalytical and experimentalstudies on fatigue life prediction of steel and composite multi-leaf spring for light passenger vehicles using life data analysisrdquoMaterials Science vol 13 no 2 pp 141ndash146 2007

[8] P Sanjurjo C Rodrıguez I F Pariente F J Belzunce and A FCanteli ldquoThe influence of shot peening on the fatigue behaviourof duplex stainless steelsrdquo Procedia Engineering vol 2 no 1 pp1539ndash1546 2010

[9] W Z Zhuang andG RHalford ldquoInvestigation of residual stressrelaxation under cyclic loadrdquo International Journal of Fatiguevol 23 supplement 1 pp S31ndashS37 2001

[10] G Savaidis M Malikoutsakis and A Savaidis ldquoFE simulationof vehicle leaf spring behavior under driving manoeuvresrdquoInternational Journal of Structural Integrity vol 4 no 1 ArticleID 17082873 pp 23ndash32 2013

[11] IS 1135 SpringsmdashLeaf Springs Assembly for Automobiles 1995[12] SAE Spring Design ManualmdashDesign and Application of Leaf

Springs HS-744 AE-11 1990[13] R L Norton Machine DesignmdashAn Integrated Approach Pear-

son Education Asia 2nd edition 2001[14] ldquoAnsys Workbench training manual on fatigue toolrdquo 2014

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Page 11: Fatigue Life Assessment of 65Si7 Leaf Springs: A Comparative Study

International Scholarly Research Notices 11

119889equiv Equivalent diameter of rotating beam spec-imen for any cross section

11986095 Portion of the cross sectional area of non-rounded that is stressed in between 95and 100 of its maximum stress

1198781015840

119898 Stress at 103 cycles

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

The authors would like to acknowledge Mr P S Chawlaand the leaf springs testing division of Friends Auto (India)Ltd whose unconditional support has made this projectsuccessful

References

[1] S Saelem S Chantranuwathana K Panichanun P Preeda-nood P Wichienprakarn and P Kruo-ongarjnukool ldquoExper-imental verification of leaf spring model by using a leaf springtest rigrdquo in Proceedings of the 23rd Conference of the Mechan-ical Engineering Network of Thailand Chiang Mai ThailandNovember 2009

[2] F N A Refngah S Abdullah A Jalar and L B Chua ldquoFatiguelife evaluation of two types of steel leaf springsrdquo InternationalJournal of Mechanical and Materials Engineering vol 4 no 2pp 136ndash140 2009

[3] J J Fuentes H J Aguilar J A Rodrıguez and E J HerreraldquoPremature fracture in automobile leaf springsrdquo EngineeringFailure Analysis vol 16 no 2 pp 648ndash655 2009

[4] M L Aggarwal R A Khan and V P Aggarwal ldquoOptimizationof micro welds used in the leaf springsrdquo International Journal ofEngineering Material and Science vol 28 pp 217ndash220 2006

[5] M L Aggarwal V P Agrawal and R A Khan ldquoA stressapproach model for predictions of fatigue life by shot peeningof EN45A spring steelrdquo International Journal of Fatigue vol 28no 12 pp 1845ndash1853 2006

[6] M M Patunkar and D R Dolas ldquoModelling and analysisof composite leaf spring under the static load condition byusing FEArdquo International Journal of Mechanical amp IndustrialEngineering vol 1 no 1 pp 1ndash4 2011

[7] M S Kumar and S Vijayarangan ldquoAnalytical and experimentalstudies on fatigue life prediction of steel and composite multi-leaf spring for light passenger vehicles using life data analysisrdquoMaterials Science vol 13 no 2 pp 141ndash146 2007

[8] P Sanjurjo C Rodrıguez I F Pariente F J Belzunce and A FCanteli ldquoThe influence of shot peening on the fatigue behaviourof duplex stainless steelsrdquo Procedia Engineering vol 2 no 1 pp1539ndash1546 2010

[9] W Z Zhuang andG RHalford ldquoInvestigation of residual stressrelaxation under cyclic loadrdquo International Journal of Fatiguevol 23 supplement 1 pp S31ndashS37 2001

[10] G Savaidis M Malikoutsakis and A Savaidis ldquoFE simulationof vehicle leaf spring behavior under driving manoeuvresrdquoInternational Journal of Structural Integrity vol 4 no 1 ArticleID 17082873 pp 23ndash32 2013

[11] IS 1135 SpringsmdashLeaf Springs Assembly for Automobiles 1995[12] SAE Spring Design ManualmdashDesign and Application of Leaf

Springs HS-744 AE-11 1990[13] R L Norton Machine DesignmdashAn Integrated Approach Pear-

son Education Asia 2nd edition 2001[14] ldquoAnsys Workbench training manual on fatigue toolrdquo 2014

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Page 12: Fatigue Life Assessment of 65Si7 Leaf Springs: A Comparative Study

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of