Development of a design verification methodology including strength and fatigue life prediction for...

ORIGINAL ARTICLE

Development of a design verification methodology includingstrength and fatigue life prediction for agricultural tractors

Atayıl Koyuncu & Mustafa İlhan Gökler & Tuna Balkan

Received: 14 October 2010 /Accepted: 9 June 2011 /Published online: 30 August 2011# Springer-Verlag London Limited 2011

Abstract During the operations of an agricultural tractor,front axle and front axle support encounter the worstload conditions of the whole tractor. If the design ofthese components is not verified by systematic engineer-ing approach, the operators of the tractor may face withsudden failures. This paper aims to develop a verificationmethod, which involves testing an agricultural tractor ona special test track and agricultural field and togetherwith the computer aided engineering analysis, in order toprevent such failures in the lifetime of the agriculturaltractor. For this purpose, a strain gage data acquisitionsystem has been designed to measure the strain values onthe component in order to determine maximum principlestresses for the calculation of overload safety on theagricultural field and stress data for the prediction offatigue life on a radial washboard test track. The cyclenumber of these stress data for the fatigue analysis hasbeen established by rainflow cycle counting method.Total fatigue damage for the front axle support has beencalculated considering damage accumulation hypothesisdefined by Miner.

Keywords Agricultural tractor . Strain gages . Dataacquisition . Design verification testing . Fatigue lifeprediction

1 Introduction

Agricultural tractor is in the class of machines that involvesoperation under what are known as “off-road” conditions.Main components of the agricultural tractor are axles, frontaxle support, chassis, transmission, rollover protection andhitch systems. In the agricultural tractor industry, the designof the tractor components and systems is done according topredetermined specifications and requirements. The mostcritical design criteria for the components are determinedregarding the strength requirements, since these compo-nents experience high loads in the application areas ofagricultural tractors. Among the main components, the mostcritical loading conditions occur on the front axle [1], andfront axle support, which is directly subjected to the loadsthat are acting on the front axle. Regarding the loads on thecomponents, it is required that these components should notfail during the operation of the agricultural tractor. Thefailure of the components may happen in two ways: anoverload causes an exceeding stress situation on the criticallocations of the component or a fatigue fracture caused byrepeated loading on the field operations although theoccurring stresses are far below the material’s tensilestrength. Therefore, the strength of the front axle supportagainst overload and fatigue are the requirements that mustbe verified. Figure 1 shows the design verification flowchart of the front axle support.

2 Linear static analysis of the front axle support

The FE model of the front axle support has beenconstructed in order to analyse the front axle support byusing finite element method. The front axle support, which

A. Koyuncu (*) :M. İ. Gökler : T. BalkanDepartment of Mechanical Engineering,Middle East Technical University Ankara,Ankara, Turkeye-mail: [email protected]

Int J Adv Manuf Technol (2012) 60:777–785DOI 10.1007/s00170-011-3590-1

is shown in Fig. 2, is a cantilevered structure that is boltedto the chassis and pivots on the front axle.

One of the load cases has been taken as the front wheelreaction of the tractor acting on the front axle support [2].Since the natural application areas of the agriculturaltractors are fields that have rough terrain characteristics,the tractors experience high dynamic loads. Therefore, aload case named as “3-g loading [2]” has also been takeninto account in addition to front wheel reaction. It isrequired on the field operations that the front axle supportshould resist the load that is three times greater than thefront wheel reaction of the tractor stands on a flat ground.The third load case considers the 3-g loading acting on oneof the front wheels of the tractor. The loads, which exertson the front axle are shown in Fig. 3, where:

Fxl: Longitudinal wheel force on left wheelFyl: Lateral wheel force on left wheelFzl: Vertical wheel force on left wheelFxr: Longitudinal wheel force on right wheelFyr: Lateral wheel force on right wheelFzr: Vertical wheel force on right wheel

Regarding the forces acting on the front axle as shown inFig. 3, the vertical force components acting on both sides ofthe front axle are tabulated in Table 1 according to theselected three load cases.

MSC/Nastran® and Patran®, the general-purpose finiteelement analysis software packages, have been used inconjunction with solid geometry in this study. The finite

element model mesh, which is shown in Fig. 4, has beencreated using solid tetrahedron elements.

The front axle support design is manufactured from greycast iron [3]. For the purpose of solving the finite elementmodel, the values of modulus of elasticity and Poisson’sratio are needed. Since grey cast iron is brittle regarding itsmetallurgical structure, the result evaluations have beendone considering the maximum stress criterion, whichstates that failure occurs when the maximum principalstress reaches either the material’s tensile strength or thecompression strength. Maximum principle stress results foreach of the load case are presented in Figs. 5, 6 and 7. Itcan be stated that the maximum principle stress values havebeen found on the same nodes of the front axle support foreach of the load cases. When comparing the maximumprinciple stress values with the material’s tensile strength ofGG-25, which is 250 MPa, the most critical load case is the3-g loading on one side.

3 Experimental validations

In order to verify the results of the FE analysis of the front axlesupport, an experimental correlation has been done for the FEanalysis results of the load case named “3 g loading on oneside” for the front axle support. The load case has beensimulated in front axle support test unit, which is shown inFig. 8. The front axle beam has been loaded on one side bytwo loading pistons to simulate the loading condition of thesupport. The maximum principle strain at a certain locationhas been measured under static load, for different load levelsfor the purpose of finite element correlation.

Fzl

Fzr

Fyr

Fyl Fxl

Fxr

x z y

Fig. 3 Front axle forces

Load cases

for design

Design of the

Front Axle

Support

FE

Model

Track

and Field

Tests

Overload

safety

factors

and

Fatigue

Fig. 1 Design verification flow chart of the front axle support

Front Axle Support

Front Axle

Pivoting Shaft

Bolt holes

Fig. 2 Front axle support

Table 1 Force components for the load cases

Fzl [N] Fzr [N]

Front wheel reaction 4,905 4,905

3-g Loading 14,715 14,715

3-g Loading on one side 29,430

778 Int J Adv Manuf Technol (2012) 60:777–785

Since the maximum principle stress values regarding theresults of the FE analysis for three load cases have beendetermined on a fillet of the front axle support, HBMRY81-3/350 [4] rosette gage has been mounted near to thatposition, which is shown in Fig. 9.

The principle stress results including the maximumprincipal stress (σmax) and the minimum principal stress(σmin) have been calculated from measured strains, ε1, ε2and ε3, for the three rosette gage grids in Fig. 9a–c, byapplying the Eqs. 1 and 2 [5], which are given as:

smax ¼ E

2

"1 þ "31� u

� �þ 1

1þ u

� � ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi"1 � "3ð Þ2 þ 2"2 � "1 þ "3ð Þ½ �2

q� �

ð1Þ

smin ¼ E

2

"1 þ "31� u

� �� 1

1þ u

� � ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi"1 � "3ð Þ2 þ 2"2 � "1 þ "3ð Þ½ �2

q� �

ð2Þwhere E and υ denote the modulus of elasticity and thePoisson’s ratio of the material, respectively.

Table 2 shows the correlation results. The maximumdifference between the calculated and the measuredmaximum principal stresses at all of the load inputs havebeen found to be 7.7%. The percent error of the stressresults for all load values is within engineering accuracy.This small difference indicates that a good correlation hasbeen found by considering all possible manufacturing andexperimental errors. Since the FEA results and the testresults are close to each other, it may be stated that the FEanalysis method is a reliable way of determining the straingage location on the front axle support part.

4 Field tests

The field measurements have an importance in the designverification process of the front axle support for thedetermination of the local stresses occurring on the criticalsides of the component. In this way the overload safetyfactor of the front axle support may be determinedregarding the measured strains on real operating conditions.

Fig. 4 FE model mesh of the front axle support

Fig. 7 Max. principle stress plot for “3 g Loading on one Side”

Fig. 6 Max. principle stress plot for “3 g Loading”

Fig. 5 Max. principle stress plot for “Front Wheel Reaction”

Int J Adv Manuf Technol (2012) 60:777–785 779

The field measurements have been done in Sincan,Ankara, on an agricultural field, the soil type of which isclay, since the 60% of the Turkey’s agricultural fields arecomposed of clayey soil [6].

During the measurements, the strain gage data acquisi-tion system, the layout of which is shown in Fig. 10, hasbeen used. The rosette gage grids are connected to thechannels of the National Instruments® (NI) SCC-SG02strain gage modules [7], which are located on NI SC-2345carrier [8]. The SC-2345 carrier is connected to NIDAQCard 6024E [9] using the SHC68-68-EP cable. TheDAQCard 6024E is fitted into the PCMCIA slot of thelaptop computer.

The strain measurements for the three rosette gagechannels and the calculated principle stress results includ-ing driving of the tractor on the field and driving whileploughing at a speed of 4 and 8 km/h are shown in Figs. 11,12, 13, 14, 15, 16, 17 and 18.

The rosette gage has been mounted near to the exactcritical point. It can be pointed out from the results ofthe FE analysis that on the measurement point, a lowerstress result has been expected. Therefore, the measure-ment results have been adjusted by a factor. This factor,in this case, has been determined dividing the finiteelement analysis result for the point, which has themaximum principle stress value, by the stress result onthe point, which the measurements have been done. The

adjustment factors for selected load cases are shown inTable 3.

The adjustment factor (c) can be selected as 2considering the maximum value, which equals to 1.9, inTable 3. The calculated maximum principle stresses frommeasured strains have been multiplied by the adjustmentfactor in order to obtain the adjusted maximum principlestresses, which are the estimated stress values for the exactcritical point. The safety factor values, which are shown inTable 4, can be calculated via dividing the adjustedmaximum stress values that have been recorded in thedifferent operations by the material’s tensile strength value(i.e. 250 MPa).

It is clear that stresses on the measurement point, whenconsidering the material mechanical properties, are belowthe material’s safety stress. The requested overload safetyfactor for the front axle support is 4.5, which has been

Fixed Bolt holes

Front Axle Support

Front Axle Loading Pistons

Fig. 8 Front axle support test unit

Fig. 9 Measurement location

Table 2 Front axle support test results

Load(kN)

Max. principle stressobtained by using strainmeasurements [MPa]

Max. principle stressobtained from MSC/Nastran® [MPa]

% Error

36.0 120.3 123.6 −2.734.2 114.2 117.4 −2.832.4 111.5 111.3 0.2

30.6 104.9 105.1 −0.228.8 100.1 98.9 1.2

27.0 91.1 92.7 −1.825.2 88.1 86.5 1.8

23.4 83.1 80.4 3.2

21.6 77.1 74.2 3.8

19.8 72.1 68.0 5.7

18.0 63.6 61.8 2.8

14.4 53.5 49.4 7.7

0.0 0.0 0.0 0.0

Tractor

Rosette Gage Grids

(Front Axle Support)

SC-2345

Carrier DAQCard

Laptop PC

a

b

c

SCC Strain Gage

Modules 1 2 3

Fig. 10 Layout of the data acquisition system


determined by the Erkunt Agricultural Machinery design-ers. The calculated safety factor values for the fieldoperations are higher than the requested safety factor.Therefore, it is concluded that the front axle support designis safe according to the overload situation. However, it isknown that this part experiences dynamic loads under fieldoperations. Therefore, it is needed to evaluate the designagainst fatigue failure.

5 Fatigue life predictions

There are several ways to predict the fatigue life of atractor component. The simplest method is to test the

agricultural tractor on the determined fields by drivingup to specified kilometres in order to complete itslifetime. Although testing the tractor on the fields issimple, the process is time-consuming and expensive.The second method is to make a laboratory test with thereal data acquired from the fields that a tractor operates.The third method is testing the tractor on a special testtrack. In this way the time duration can be decreased incertain amounts.

In this study a radial washboard test track, which wasconstructed in Erkunt Agricultural Machinery for validatingthe durability performance of the tractor, has been used.The schematic diagram of the track is shown in Fig. 19.The radial washboard track was designed to match the

0 50 100 150 200 250 300 350-150

-100

-50

0

50

100

150

200

Time (s)

Str

ain

(m

icro

stra

in)

Channel 1Channel 2Channel 3

Fig. 11 Field strain data acquired from rosette gage channels at atractor speed of 4 km/h

0 50 100 150 200 250 300 350-20

-15

-10

-5

0

5

10

15

20

25

Time (s)

Pri

nci

ple

Str

esse

s (M

Pa)

Sigma (max.)Sigma (min.)

Fig. 14 Principle stress data calculated from strain data at a tractorspeed of 4 km/h during ploughing

0 50 100 150 200 250 300 350-150

-100

-50

0

50

100

150

200

Time (s)

Str

ain

(m

icro

stra

in)


Fig. 13 Field strain data acquired from rosette gage channels at atractor speed of 4 km/h during ploughing

0 50 100 150 200 250 300 350-25

-20

-15

-10

-5

0

5

10

15

20

25

Time (s)

Pri

nci

ple

Str

esse

s (M

Pa)


Fig. 12 Principle stress data calculated from strain data at a tractorspeed of 4 km/h


fatigue damage generated during the lifetime of the tractorby simulating compressed testing cycles. This test track hasbeen constructed with 12 obstacles, the 6 of which haveheights of 100 mm (A) and the remaining has 50 mm (B)heights. The goal is to achieve the full 1,000,000 cycleswithout any cracks in the major components of the vehicle.

The test tractor has to be driven 33 days at a tractorspeed of 7 km/h in order to reach 1,000,000 cycles on theradial washboard test track. The duration is even long whenconsidering the competitive market in the automotiveindustry. However, acquiring the strain data, which can beutilized for the fatigue life prediction of the component,reduces the duration of the test. Since the test track repeatsitself in every cycle, the test duration can be decreased from

1,000,000 cycles to 1 cycle, and the acquired test data hasbeen repeated 1,000,000 times for the fatigue life analysis.

The acquired strain data, which are shown in Fig. 20, asexpected, have local peaks while the wheels are crossingover the obstacles.

FEMFAT®, which has FEMFAT®-STRAIN module forcalculating the fatigue behaviour at strain gages applied onthe real structure based on measured strain–time histories,has been used for this study. Complex loads are exerted andthe directions of the principle stresses are changingpermanently on front axle support, while the tractor isoperating. Therefore, classic damage criteria like maximumprinciple stress or von Mises stress is not applicable formultiaxial fatigue analysis. For non-proportional loadings

0 20 40 60 80 100 120 140 160 180 200-100

-50

0

50

100

150

200

Time (s)

Str

ain

(m

icro

stra

in)


Fig. 15 Field strain data acquired from rosette gage channels at atractor speed of 8 km/h

0 20 40 60 80 100 120 140 160 180 200-15

-10

-5

0

5

10

15

20

25

Time (s)

Pri

nci

ple

Str

esse

s (M

Pa)

Sigma (max.)Sigma (min)

Fig. 18 principle stress data calculated from strain data at channels ata tractor speed of 8 km/h during ploughing

0 20 40 60 80 100 120 140 160 180 200-100

-50

0

50

100

150

200

Time (s)

Str

ain

(m

icro

stra

in)


Fig. 17 Field strain data acquired from Rosette gage tractor speed of8 km/h during ploughing

0 20 40 60 80 100 120 140 160 180 200-25

-20

-15

-10

-5

0

5

10

15

20

25

Time (s)

Pri

nci

ple

Str

esse

s (M

Pa)


Fig. 16 Principle stress data calculated from strain data at a tractorspeed of 8 km/h


and multiaxial stress states with rotating principal stressdirections, the critical plane criterion is a widely appliedand commonly accepted concept. The principle is rathersimple: In each plane a rainflow counting of the normalstress history is performed. The resulting stress amplitudescan be used together with a tension/compression S–N curvefor the calculation and linear summation of partial damagesaccording to Palmgren/Miner. The plane with maximumdamage is assumed to be critical [10].

The stress cycles as shown in Fig. 21 have been establishedin FEMFAT® by the rainflow cycle counting method [11].

Every stress cycle is composed of an amplitude stressand mean stress. FEMFAT®-STRAIN program has calcu-lated a damage value for each of the stress cycle that hasbeen determined from the rainflow cycle counting algo-rithm for the washboard test track.

The prediction of the fatigue life in this study is based onthe procedure of influence factors for the criterion of failure.The S/N diagram of the material, which is shown in Fig. 22, ismainly influenced from notches, mean stress, surfaceroughness, state of hardening and tempering and technolog-ical treatment of the surface [12]. The ordinate of the S/Ndiagram is called the stress amplitude, and this amplitudemust always be accompanied by the number of cycles N towhich it corresponds. When using a log–log plot, S/Ndiagram is described by endurance stress limit, endurancecycle limit and S/N curve inclination (k). Endurance stresslimit is the stress amplitude for which the fatigue life goes toinfinity and the corresponding number of cycle is theendurance cycle limit. S/N curve inclination (k) is the inverse

of the slope of the S/N curve before the endurance cyclelimit. The main purpose of the method of influence factors isto determine these three parameters according to the localconditions of the component.

The following influence factors have been considered inthe fatigue life prediction process of the front axle support:

– Influence of the mean stress on the endurance stresslimit

– Influence of the mean stress on the inclination ofthe S/N curve

– Influence of the surface roughness on the endurancestress limit

– Influence of the surface roughness on the inclination ofthe S/N curve

– Influence of the surface roughness on the endurancecycle limit of the S/N curve

Table 3 Factor comparisons regarding the FE analysis results for theselected load cases

Stress on measurementpoint [MPa]

Stress on exactpoint [MPa]

Adjustmentfactor (c)

Front wheelreaction

9 15 1.7

3-g Loading 27 45 1.7

3-g Loading onone side

103 203 1.9

Table 4 Measurements Results and Safety Factors

Measured Max.Principle Stress[MPa]

Adjusted Max.Principle Stress[MPa]

SafetyFactor

Field (4 km/h) 20.1 40.2 6.2

Field during ploughing(4 km/h)

23.3 46.6 5.4

Field (8 km/h) 21.3 42.6 5.9

Field during ploughing(8 km/h)

24.6 49.2 5.2

Fig. 19 Radial washboard test track

0 5 10 15 20 25 30 35 40 45 50-150

-100

-50

0

50

100

150

200

250

300

Time (s)

Str

ain

(m

icro

stra

in)


Local Peak Due to

Engine Start

Cycle Starts Cycle Ends

Fig. 20 Strain data acquired from rosette gage channels on thewashboard test track


The linear hypothesis of damage accumulation by Miner[13] is the basis of nearly all known methods of predictingthe fatigue life in engineering purposes. According to thisrule applying n1 cycles with stress amplitude of A1 andcorresponding fatigue life endurance N1 as shown inFig. 23, is equivalent to consuming n1/N1 of the fatigueresistance. The same assumptions apply to any subsequentblock of load cycles. Failure occurs if the fatigue resistanceis fully consumed.

In Fig. 23, it implies failure at the moment as implied inEq. 3, which is given as:

n1N1

þ n2N2

þ n3N3

¼ 1 ð3Þ

If more than three blocks are applied, this equation isgeneralized as:X ni

Ni¼ 1 ð4Þ

When the Eqs. 3 and 4 satisfy, a destruction of thecomponent occurs. If fatigue life predictions are made with

the Miner’s rule, it should be realized that the results areassociated with uncertainties of the reliability of the rule. Ifthe rule is used, extrapolation of S–N curves below thefatigue limit is recommended in order to allocate fatiguedamage contributions to small cycles below the fatiguelimit. The following modifications to the original Miner’srule can be associated in order to deal with the damagingeffects of oscillating stresses, which lie beyond theendurance stress limit (σEndurance) of the component S/Ncurve, which is shown in Fig. 24:

– The elementary Miner’s rule is: The S/N curve with theinclination k is lengthened until the stress amplitude(σA) reaches zero.

– The modified Miner’s rule, suggested by Haibach [14],is as follows: Endurance strength inclination is 2k°−°1.

The fatigue analysis has been done considering the threeversions of the Miner’s rule. The results, which are shownin Table 5, indicate that the most conservative version is asexpected the elementary rule, which considers the stressesdown to zero amplitude when calculating the damageresults.

Since the damage result for elementary Miner’s rule isless than unity, which is the critical value for failure, it can

Fig. 22 S/N curve parameters [11]

Fig. 21 Stress cycles in 106-cycles washboard track strain DataFig. 23 Damage accumulation [12]

Fig. 24 Miner’s rule versions [12]


be concluded that, on the washboard track the failure of thecomponent would not occur in 1,000,000 cycles.

6 Conclusions

Verification tests in this study have been done on the radialwashboard test track to simulate compressed testing cycles, andon an agricultural field in Turkey, aiming to represent the realworld situations that the product can face. It may be stated fromthe safety factors against overload situation and the fatiguedamage results that the front axle support would not fail in thelifetime of a tractor. By achieving these results, the designspecifications for the front axle support have been met and thedesign has been verified regarding the design requirements.

Acknowledgments The authors would like to thank Erkunt Agri-cultural Machinery Ind. Inc. for funding this study.

References

1. Mahanty DK, Manohar V, Khomane BS, Nayak S (1995)Analysis and weight reduction of a tractor’s front axle. TataConsultancy Service, India

2. MSC/WORLD (1994) Eicher tractor puts FEA to work in valueengineering, volume IV

3. TGL (Technische Güte und Lieferbedingungen) (TGL 14400),DIN (GG-25), Material data for cyclic loading, 1955

4. Strain Gages and Accessories Catalogue, HBM (HottingerBaldwin Messtechnik) GMBH, 2005

5. Borden Jeffrey W (1997) Static stress analysis of industrialconveyor pulleys using finite element analysis with experimentalverification. University of Louisville

6. Çevre Envanteri Dairesi Başkanlığı (2004) “Türkiye ÇevreAtlası”, T.C. Çevre ve Orman Bakanlığı,

7. National Instruments Corporation (2004) SCC-SG Series straingage modules. User Guide

8. National Instruments Products and Services, web site: http://sine.ni.com/nips/cds/view/p/lang/en/nid/12310.

9. National Instruments Products and Services, web site: http://sine.ni.com/nips/cds/view/p/lang/en/nid/10778.

10. Gaier C, Dannbauer H (2006) An efficient critical plane methodfor ductile, semi-ductile and brittle materials. Magna Powertrain,Engineering Center Steyr, Austria

11. Murakami Y (1992) The rainflow method in fatigue. The TatsuoEndo Memorial Volume

12. FEMFAT theory basic user’s manual, 200013. Miner MA (1945) Cumulative damage in fatigue. ASME

Journal of Applied Mechanics, S.A159–A164.American Society ofMechanical Engineers (ASME), New York

14. Haibach E (1989) Betriebsfestigkeit-Verfahren und Daten zurBauteilberechnung. VDI Verlag, Düsseldorf

Table 5 FEMFAT®-STRAIN damage results

Miner’s ruleversions

Total damage (c=1)a Total damage (c=2)*(1,000,000 cycles) (1,000,000 cycles)

Original 0 0.71

Modified 2.0×10−5 0.79

Elementary 1.8×10−3 0.91

a c is the adjustment factor for the stress results


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