fatigue strength prediction of truck cab by cae

8/6/2019 Fatigue Strength Prediction of Truck Cab by Cae

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1. Introduction

In the conventional vehicle development, the fatiguestrength of a truck cab m ust be evaluated by conduct-ing phy sical tests. This is because in the convention alanalysis, forces acting on t he vehicle body are repre-sented m ainly by such static input s as torsional and ver-tical bendin g forces, and th e analysis results mu st becompared wi th the results of ph ysical tests conductedon prototypes and actual vehicles before the fatiguestrength can be assessed. In order to reduce the devel-opment period and number of prototypes, a technique

is required that depends on so-called virtual proto typesat the drawing stage of developm ent, not on physicalprototypes.

Thanks to recent im provements in com puter perfor-mance and the appearance of m ulti-purpose fatigue lifeanalysis applications on the market, engineers can con-duct fatigue strength analyses that take into accounteven the stress history and m ulti axial stress field, thusmaking predicti ons mor e accurate (1) . The tru ck cab isusually fitted on the frame via four front and rearmounts, through which it receives random inputs, sug-gesting that in or der to predict the fatigue strength, thestress history of com posite inputs in a m ultiaxial stressfield m ust be considered.

As the first step tow ard the ultim ate goal of f atiguestrength prediction based on com puter aided engineer-ing (CAE) assuming rough-road durability test situa-tions, the fatigue strength evaluation m ethod presentedin thi s paper assumes bench durabil ity test situationsand combi nes schemes for predicting cab input l oadsand those for predicting fatigu e strength. The paperalso describes the cases of using the method to investi-gate the causes of cracks in a light-duty truck during thedevelopment stage.

2. Approaches for assessing cab fatiguestrength

2.1 Durability test approachThe fatigue streng th o f the cab is generally assessed

through both rough-road durability t ests (drive tests)and bench durabil ity tests. In a bench durabilit y test,the displacement histor y of a hydrauli c shaker is firstdetermined using, as a target signal, the frame acceler-ation rates obtained throu gh experimental rough -roaddriving, and then oscillation inputs equivalent to thoseexperienced by an actual vehicle are applied by the

shaker using the displacement history t hus determined.In actual bench tests, however, the histo ry is usuallyamplified in ord er to shorten the test tim e. A typical testrigging is shown in Fig. 1 , in whi ch the cab is fitted onthe frame, the suspension and unsprung comp onentsincluding tires are removed, and the end o f each actua-tor on the shaker is attached to the correspondingspring hanger. The shaker generates vertical vibrati onsalong four axes. Altho ugh the shaker cannot generatehorizontal inputs, its functions are considered suffi cientfor evaluating t he cabs fatigue strength since the verti-cal vibration can be regarded as dom inant amon g theeffects the inputs to the cab have on the fatiguestrength.

2.2 CAE simulation approachFig. 2 shows the flow of the CAE method u sed in th is

research for predictin g the cab fatigue strengt h. The fol -lowing two items are not supported by the convention-al analysis but can be support ed by th is CAE methodthat is capable of predictin g the fatigue strength t akingthe history of composite stress inputs through cabmou nts into account.(1) Quantitative history of cab input loads(2) Fatigue life calculation based on stress history

The CAE m ethod com bin es the solv ers and predic-

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Fatigue Strength Prediction of Truck Cab by CAE

Shinichi CHIBA* Kimihiko AOYAMA* Kenji YANABU**Hideo TACHIBANA* * Katsushi MA TSUDA* * Masashi UCHIKURA*** * *

AbstractIn order to accurately predict the fatigue strength of a t ruck cab, it is necessary first to estimate

the input load history from cab mounts, then with the estimated value, to accumulate the damagesfrom the stress time history generated by the input load, and finally to calculate the fatigue life.This paper introduces the method of combining cab input load estimated by multi body simulationand fatigue life estimation by FEM analysis and fatigue life analysis, and one example of the analy-sis of the change mechanism of input mode and fatigue life according to t he changes of test condi-tion.

Key words: Fatigue, Body, Nu merical Analysis, CAE

* Engin. Administ rat ion Dept., Research & Dev. Office, MFTBC ** Funct ion Test ing Dept., Research & Dev. Office, MFTBC

* * Cab Design Dept., Research & Dev. Office, M FTBC * * M aterial Engin. Dept., Research & Dev. Office, M FTBC* * *


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tion schemes offered by m ultip le applications, includ-ing static analysis and eigenvalue analysis byNASTRAN, multi-body simulation by ADAMS, andfatigue life analysis by FALANCS. The calculationprocess is as follows:

First, a finit e element m odel of the cab is createdusing CAD data and then an eigenvalue analysis is per-form ed on that model using NASTRAN. The results ofthe eigenvalue analysis are then converted into anADAMSs modal model using ADAM S/FLEX. At thesame ti me, the m ounts and related parts are modeledusing actual measurement data. The m odels thus cre-ated are combined and ADAMSs multi -body simulationis performed on th em to d erive the cab input load hi s-tory. This history is then comb ined with the results ofNASTRANs static analysis to o btain a stress history ,from wh ich the fatigue life of each compo nent is calcu-lated.

This prediction m ethod was developed as part of thedevelopm ent program for a full m odel-change of theMit subishi CANTER light-duty tr ucks, whi ch was com-pleted in June 2002.

3. Analysis of inputs to cab

3.1 Modeling method

3.1.1 Cab mount modelingThe cab is fitted on the frame via cab mou nts. The

cab mounts of the trucks under developm ent were of ahydraulic damping type filled wi th a fluid, which fea-tures high damping force and low spring constant. Fig.3 show s the static characteristi cs and Fig. 4 shows thedynamic characteristics of the hydraulic dampingmou nts, both for the vertical movements of the mounts.The central portion o f the curve in Fig. 3 corresponds tothe characteristic of the fluid-filled section of eachmoun t. When the amount of input is above or belowthe limi ts, the mount comes in contact with a stopperand the spring constant of th e moun t suddenly increas-es. Since the amplitude of inp uts is magnified in bench

durability tests in order to shorten the test time, thespring constant values after making contact with thestopper are signifi cant. The dynamic characteristics ofthe cab mount are expressed by a dy namic spring con-

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Fig. 1 Bench test conditions

Fig. 2 Flowchart of fatigue strength simulation method

Fig. 3 Static characteristics of cab mounts

Fig. 4 Dynamic characteristics of cab mounts


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stant and loss factor f or each vibration fr equency.Fig. 5 is a model of the hydraulic damping m ount

represented by a combination of springs and a dash-pot (2) . The static characterist ics can be expr essed bydirectly substitut ing an actual measurement value forK1 and the dyn amic characteristics can be expressed byadjusting the values of K 2 and C. As show n in Fig. 4 , thecalculated dynamic constant roughly agrees with theactual measurements, whi le the calculated and mea-sured loss factor curves also agree in terms of the reso-nance frequency and peak values although they aresomewhat different in the high vibration frequencyrange. The mo del is therefo re also capable of express-ing the dynamic characteristics.

3.1.2 Input analysis modelRigid structure models have been the most com-

monly used type of model for motion analyses.However, as the trucks cab and fr ame are elastic struc-

tural bodies, elasticity characteristics should be consid-ered when an accurate analysis is expected. The devel-opm ent team therefore used a mod al mod el based onthe constrained mo de method as the structural model.

Fig. 6 shows the fini te element mod els of the cab andframe and the constraint points on them. The constraintpoints on the cab correspond to the four cab m ountlocations; those of the fram e are a total of eight loca-tions consisting of th e four mou nt locations and the fouractuator attaching locations. The num ber of modes tak-

en into account is 30 (including 24 for the constrainedmode) for the cab and 54 (including 48 for the con-strained m ode) for the frame.

The input analysis model is configured by adding tothese cab and frame m odels the m odels that representthe shakers actuators and mounts.

3.2 Verification of simulation resultsThe simu lation was performed by applying th e his-

tory determin ed through experim ents to the actuatorsof the shaker, and the results of the simu lation w ere ver-ified in terms of the cab m ount displacement and theacceleration rates of several parts throu gh com parisonwith the experiment results.

Fig. 7 compares the calculated and experim entallymeasured frame acceleration rates. The simu lationresults are approximately consistent with the experi-ment results. The small disagreements may be primar-ily due to inadequate representation of the elasticitycharacteristics of the connections betw een the frameand shaker. To impr ove the accuracy of the results,therefore, incorporatin g the elasticity characteristics ofthe connections is essential.

Fig. 8 shows the simul ated cab mount displacementcompared with the experimental measurements. The

figure indicates that the simulation outputs are suffi-ciently accurate for practical use, as the amp litud es arealmost equivalent to the experimental m easurementsalthough the history includes some discrepancies.

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Fig. 6 Finite element model and constraint points

Fig. 7 Comparison of frame acceleration betw eenexperiment and simulation

Fig. 5 Hydraulic damping mount modeling


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4. Fatigue life prediction

4.1 Calculation method

4.1.1 Fatigue life prediction incorporating stress his-tory

Stresses that occur in various areas of the cab arecombinations of the follow ing tw o types of stress:1 Static stress, the generation of wh ich depends on

the balance with i nput loads2 Dynami c stress, the generation of w hich depends on

the vibration characteristics of the cabThe following methods can support the stress history incalculation of the fatigue life and applicable to theabove stress types, respectively .1 Linear superpositio n m ethod based on static analy-

sis stress and input loads2 Modal superposition m ethod based on the proper

mod e analysis and m odal displacementSince the experim ental data collected so far show thatstatic inputs such as torsional for ces and vertical bend-ing forces are domi nant among th e inputs to the truckcab, only m ethod 1 was adopt ed in the research. Thismethod is based on the following pri nciple: the stressconditio n at a given tim e can be determi ned by the lin-ear superpositi on of stresses that result fr om t he inputconditio ns, while the history of the stress conditio n isdetermined by m ultipl ying tog ether the stress resultingfrom a unit lo ad and the input load history. The processof predi cting th e fatigue life is as follow s (see also Fig.9):

(1) The value of the stress resulting from a unit loadapplied to each of the four cab mounts is calculated.Since shaking of t he cab is a kind of con straint-freeloading, N ASTRANs inerti a relief analysis prog ram

is used for the calculation.(2) The stress value derived from (1) above is mul tiplied

by the history of cab input load through each mo unt(calculated from multi-body simulation), and thestress value and load are superposed for all theinput cases to create a time history of the stress.

(3) Damage is calculated using rainflow accountingfrom the stress-tim e history created in (2) above andthe fatigue life is calculated using the correctedMin ers rule.

4.1.2 Calculation of stress in spot weldsIn general, a truck cab is formed of a number of

sheets of metal attached by spot weldi ng. Since loadsacting o n the cab are transmitted thr ough th ese weldsto vari ous parts, stress concentrates on the w elds andso they are often the mo st vulnerable points in terms ofstrength.

FALANCS supports the LBF approach which wasproposed by Rupp et al. (3) as a method of analyzing th efatigue life of spot weld s. This appro ach expresses aspot w eld as two sheets of shell elem ents and a beamelement (including rigi d elements and multi-point con-straint s (MPCs)) and calcul ates stresses from elementforces (axial for ce, mo ments, etc.) to deriv e the fatigue

life. Fig. 10 shows how a spot weld is modeled. Themo del is config ured by tw o parallel shell elements anda beam element that join s the shell elements. As to thedistance between the shell elements and the angle of

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Fig. 8 Comparison of cab mount displacement betw eenexperiment and simulation

Fig. 9 Procedure of fat igue life analysis

Fig. 10 Spot-w eld modeling


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the beam element (both are important factors that sig-nificantly influence the element forces), the modelassum es that the shell element is at the mi d-plane ofeach shell and the b eam element is perpendicular to t heshell elements.

4.2 Verification of simulation resultsThe fatigue life sim ulation results were verified by

comparing them with the experimental m easurementson the proto type that was fabricated in the initial stageof development of the vehicle. Since vibratio n inputswithin the evaluation standard range did not causecracks in a sufficient num ber of locations for a signif i-cant comparison, a marginal durability test was con-ducted by applying inputs of m agnitudes beyond thestandard range and a numb er of cracks sufficient for t he

comp arison were prod uced. The evaluation was per-form ed separately on non-w elded panel sections andspot welds.

4.2.1 Non-welded panel sectionsFig. 11 compares the calculated and experim entally

measured fatigue lives. In the calculation, the datalength corresponding to one history iteration is regard-ed as one vibr ation cycle. The fatigue-life calculationbased on th e S N analysis p redicted all the cracks thatalso occurred in the physical experiment, but the calcu-lated fatigue life was much shorter than the experimen-

tal result. This discrepancy may be prim arily becausethe calculation did not support th e plastic stress (strain).In fact, the fatigue life calculation that w as perform edbased o n N analysi s using an N curve obtainedby a sim plifi ed method in wh ich the materials tensilestrength and Youngs modulus were used (4) , showedcloser agreement b etween the calculation and physicalexperim ent. This im plies that data on basic materialproperti es mu st be accumulated in th e future for accu-rate prediction of f atigue life by CAE simu lation.

4.2.2 Spot weldsThe fatigue life calculation results were compared

with the results of the experiment conducted for spotwelds on the floor panel. The damage distributi on cal-culated by th e fatigue life simulation is shown in Fig. 12 .The circled points in the figure correspond to the loca-tion s where cracks occurred in the experim ent. The cal-culation result indicates major dam age in many of theselocations. The poin ts indicated by red circles corre-spond to t he locations in w hich cracks were detectedvisually, whil e those indicated by yellow circles corre-spond to t he locations where cracks were found b y cut-ting spot welds after the experim ent. Fig. 13 is a photo-graph showi ng the cross section of a spot weld. Thecrack in the weld has not yet progressed to the surface,so it cannot be detected visually.

There were several location s where cracks actuallyoccurred in the experiment but calculated damage wasrather slight . One possible cause for thi s discrepancy isthat the calculation did not support changes in thestress distribu tion caused by the occurrence of cracksin certain welds, and this mig ht have prevented the sim-ulation from predicting the high stress areas that wouldhave consequentially occurred. Anoth er cause may bethe use of an fix ed value as the coefficient w hen calcu-lating the stress from the separation load and bendingmom ent although this m ethod requires the coefficient

be varied according to the shape of the part around th eweld. Other factors contribut ing of the discrepancy mayinclude the effects of variation in diam eter amo ng spotwelds and the initial stresses resulting from welding

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Fig. 11 Comparison of fatigue life at body panel betw eenexperiment and simulation

Fig. 12 Damage distribution of spot-welds

Fig. 13 Crack initiat ion of spot-w eld


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that were not support ed by this metho d that calculatesthe stress from the beam element forces.

Part A in Fig. 12 is a spot w eld for w hich the simula-tion predicted major dam age but the physical test pro-duced no crack. This weld spot is liabl e to be affectedby contact. The linear-analysis-based simulation, whichcannot support contact, may have created an im practi-cally large damage output.

Many issues remain to be solved before the methodcan be made sufficiently accurate for quantitatively pre-dictin g fatigue life, nevertheless the present stage of thesimulation can predict crack locations with reasonableaccuracy.

5. Application of thesimulation method

The com panys practiceof bench durability tests for

truck cabs includ es, as oneof the standard evaluationitems, the fatigue strengthunder the load of a roofdeck installed on the cab(including the mass of car-go on it). A cab with roofdeck installed is shown inFig. 14 . Physical durabi lit ytests revealed presence oflocations w here cracks didnot occur without a roofdeck but did occur when

the deck was installed. Asimulation was thereforeattempted using themethod presented here toanalyze factors contributingto the decrease in fatiguestrength due to this changein condition.

5.1 Effects of roof deck oninput loads

The team first studiedthe difference in inputloads on the cab between the two condi tions, wit h andwith out the roof deck. Fig. 15 shows the results of ana-lyzing the input load history and the frequency responseat one of the front cab mo unts under the two condition s.The load history graph shows that when the cab isinstalled w ith th e roof deck, the vibration ampli tudeincreases by approx imately 50 % as comp ared with thecase with out t he roof d eck and the frequency responsegraph show s that resonance occurs at aroun d 3 Hz fre-quency.

The cab is suppo rted by m ount s at four l ocations,and so it should b e appropriate to break down the verti-

cal inpu t loads on the cab into four component f orces bouncing, pitching, rolling, and twisting (5) in or der tostudy the causes of the above-menti oned findi ngs. Thefrequency characteristics of each compo nent for ce are

shown in Fig. 16 . The graph indicates that only rolli nginpu ts have a peak frequency of 3 Hz wh en the cab isinstalled wi th the roof d eck although there are no peakfrequencies witho ut the roof deck. There are no othercompon ent forces that have peak frequencies around 3Hz. This means that installing the roof deck signi ficant-ly i ncreases rolling inputs.

5.2 Effects of roof deck on fatigue lifeNext, the team studied the effects the change in

input load discussed above might have on the fatiguelife. The distributio n of damage in a location on the cab

was compared between when the location was underthe roof deck load and when it was free from the load.The results show ed that w hen the deck was installed,the m agnitude of t he largest damage was 20 tim es that

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Fig. 14 Roof deck installation

Fig. 15 Comparison of front mount force betw een roof deckinstalled cab and uninstalled cab

Fig.16 Comparison of component force frequency characteristic betw eenroof deck installed cab and uninstalled cab


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of the cab with n o deck installed ( Fig. 17 ). In order toinvestigate the contribution of t he above-mentioned

component forces to the damage at that location, afatigue life simulation w as conducted for each of theinpu t compon ent forces. The results are shown in Fig.18 . The calculation result ind icates that bouncing inputhas little contribution but rolling input has a significantcontribution to the damage. In other word s, the fatiguestrength of the location is largely influenced by rolli nginputs.

The results of stu dies on t he causes of cracks in acab on which a roof deck is installed are summarized asfollows:(1) Installing t he roof deck significantly increases rolling

inputs.(2) Rolling inputs contribute significantly to the fatigue

strength of t he investigated location.These two facts m ay explain the causes of cracks.

6. Summary

This paper discussed a fatigue strength predictionmethod that was developed to simulate the bench dura-bility test and examined the cases of its application.The results yi elded throu gh the research are summ a-rized below .(1) Mul ti-body sim ulation using an elastic body model

enabled cab input loads to be calculated with suffi-cient accuracy for practical application.

(2) The fatigue life simulation that supported stress

(strain) history allow ed the locations ofcracks to be predicted both in non-welded panel sections and spot w elds,although the prediction w as not suffi-ciently accurate in quantitative termsfor spot welds.(3) The study using the CAE simula-tion method on the effects caused byinstalling on the cab, a roof deck onfatigue life revealed the mechanism o fchanges in the input mode andchanges in the crack life that resultedfrom the difference in the test condi-tion.

In future studies, the team will seekto im prove the accuracy of the fatiguelife simulation, with th e ultimate objec-tive of bui ldin g a CAE simu lation sys-tem that can predict the fatigue

strength u nder rough-road durabilitytest conditions.

References(1) K. Koibuchi: Fatigue Life Prediction

and its Softw are , speech collectionfor JSAE symposium New Proposalsfor Future Fatigue EnduranceEvaluatio n of Vehicle Bodies , JSAE,2000

(2) T. Sakamoto: Development of Engine Rubber Mountwith Hydrauic Damping , Journal of JSAE, Vol. 36, No.12, 1982

(3) A. Rupp, K. Storzel and V. Grubisic: Comput er AidedDimensioning of Spot-Welded Automotive Structures,SAE Technical Paper 95071, 1995

(4) LMS FALANCS Theory Manual Version 2.9(5) Y. Kondo, H. Ono and K. Hamano: Study of Load Applied

to Vehicle Body dur ing Rough-Road Driving , MitsubishiMotors Technical Review, NO. 1, 1988

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Fig. 17 Comparison of damage distribution betw een roof deckinstalled cab and uninstalled cab

Fig. 18 Damage distribut ion by each component force

Sh in ich i CHIBA Ki mi hi ko A OYA MA Ken ji YA NA BU

Hi deo TACHIBA NA Kat su sh i M ATSU DA M asash i UCHIKU RA

fatigue strength prediction of truck cab by cae

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