USE OF FATIGUE ANALYSIS SOFTWARE IN THE OPTIMIZATION OF STRUCTURAL

Transcription

1 USE OF FAIGUE ANALYSIS SOFWARE IN HE OPIMIZAION OF SRUCURAL APPROVAL PROCESS FOR VEHICLE COMPONENS Scozzafave C.C., Ercsson L. G. S., Santana F.A., Wldmann U., Spnell D. M. Mercedes-Benz do Brasl E-mals: ABSRAC hs paper ams to propose a methodology for optmzng the approval process of vehcle components ntroducng the fatgue analyss va software. he case of study used for methodology applcaton was a commercal vehcle suspenson part. he commercal vehcle was modeled n fnte element for statc stress analyss n several load cases. Durablty tests n provng ground wth measurements were also done. he component has faled wthout reachng the track approval crtera. Wth the measurement sgnal of force, a fatgue analyss was done correlatng the obtaned damage wth the covered dstance n test feld untl component falure. A new support proposal was modeled and analyzed usng fnte elements. he optmzaton of structural approval process comes by elmnatng the new verson test at provng ground, approvng t by force measurement correlaton of the frst verson wth the second verson, and new fatgue analyss va software. he optmzaton process reduces the tme and cost durng product development. INRODUCION he modern development process for automotve components ams a reducton of tme n components tests, due the necessty of acceleraton n parts approval process for faster vehcle sgn off delvery. he process becomes challengng because despte of the decrease for test tme, the product qualty and relablty stll has to be ensured. he product development tme reducton can be aded by deeper analyses n component homologaton methods va smulaton, snce t can reduce a sgnfcant tme and cost consumng durng the development process. he present study ams to present a methodology to accelerate a component homologaton va FEA and fatgue analyss. Fatgue s the process of damage and falure due to cyclc loadng, even when ths loadng causes stresses well below a gven materal s ultmate strength, snce the mcroscopc damage can be accumulated untl crack nucleaton leadng to further component falure [1]. he proposed method has ts bass on several topcs that are covered n ths paper, such as: fnte element analyss (FEA), fatgue analyss wth FEA, sgnal measurement, sgnal analyss and accelerated durablty components test. Snce fatgue analyss s the center of the study, an

2 emphass s gven to ths topc, and the state of art for some current fatgue hot topcs are presented, such as: cumulatve damage analyss, local plastfcaton, multaxal fatgue and also crtcal planes approach. Fnally, ths papers follows the same sequence of product development, whch s component desgn, FEA analyss and further durablty test, gong through damage smulaton and correlaton, endng wth new component desgn and approval method descrpton. 1. FEA ANALYSIS o start the component analyss, ts desgn was done and modeled n FEM, as can be seen n fgure 1. For ths frst component verson, sold elements were used n the modelng due the necessty of more refned results. Fgure 1. Component FEA model (frst verson) A full FEA model of the complete vehcle was also modeled; a pcture of the model s presented n fgure 2. he vehcle parts are manly modeled usng shell elements, whch gves a good relatonshp between stress results and smulaton tme consumpton [2]. Only a few parts were modeled n sold elements, such as the component studed. he full vehcle was smulated n the most severe load case for ths component, whch s the vehcle torson. he man stress result that s found n the component s shown n fgure 3. At the most crtcal regon t the torson analyss, the stress reached 100% of the materal lmt. Fgure 2. Full FEA model of the complete vehcle

3 Fgure 3. Stress results for torson load case 2. COMPONEN DURABILIY ES he next step for product homologaton s the durablty test. he complete vehcle, that s showed n fgure 4 s tested on an accelerated durablty provng ground, wth pre-establshed approval crtera for all components of 2940 laps. Fgure 4. Complete vehcle for durablty test In the begnnng of the test, measurement of the load that s appled n the component s done, to make possble the correlaton of the load measured n the torture track wth the FEA load case crtera, as well as, ts stress results and further damage analyss. Fgure 5 shows the component to be mounted n the vehcle and the equpment used to measure the force that s appled n the part durng the vehcle test at provng ground. he vehcle s tested part of the tme loaded and part of the tme unloaded, untl t reaches the approval crtera (2940 laps). Both of the stuatons need to be measured to a better result correlaton. In fgures 6 and 7 t s presented the force measurement for two laps n both cases.

4 Fgure 5. Component frst verson and equpment used to force measurement Fgure 6. Force measurement at loaded condton Fgure 7. Force measurement at unloaded contdon 3. FAIGUE ANALYSIS 3.1. Cumulatve Damage In the fatgue analyss feld, the Mner lnear damage accumulaton hypothess [3] s the most acceptable method for estmatng lfe tme by damage accumulaton Where: D = otal damage D = Damage for each dfferent stress σ

5 n = Number of cycles that a component s subjected n a gven alternatng stressσ. N = Number of cycles to falure atσ, accordng to component materal s Wöhler curve. he ndvdual damage for each dfferent σ are totalzed n the course of the fatgue lfe estmate. When a damage total D = 1 s reached, component falure occurs Plastfcaton n fatgue analyss Whenever the stress exceeds the materal's yeld stress, plastfcaton occurs. he lnear stresscurve s adopted for all stress cycles. he dsplacement of the closed hysteress loops caused by the plastfcaton s then taken nto consderaton. Fgure 8 shows ths procedure. ransformaton of the elastc stress to the elastc-plastc stress s gven by the Neuber rule [4]. Fgure 8. Neuber correcton and plastfcaton effect n cyclc stress 3.3. Multaxal Fatgue Mult-axal loadngs are common n varous components and structures. By the combnaton of mult-axal loadngs, the fatgue analyss goes from unaxal approach to more sophstcated multaxal approach [5]. For components subjected to drect stress and shear, the phase relatonshp between the stresses cannot be constant. In ths case, t s not obvous whch plan experences the most severe combnaton of deformaton and hence greater fatgue damage. he orentaton of a plane s defned by the angle that the normal to the plane makes wth the xyz coordnate system orented along the surface. he plan has an angle Φ of the x-axs towards the y- axs [6]. When loadng s sgnfcantly no proportonal, an analyss by crtcal planes s requred, where stresses and strans are determned for the varous planes of orentaton n the materal durng cyclc loadng, and the stresses and strans actng n the more crtcally loaded s used to predct the damage [6]. An example s shown n fgure 9.

6 3.4. Crtcal plane approach Fgure 9. No proportonal example [6]. Crtcal plane approaches assumes that fatgue damage s essentally drectonal and so consder the damage accumulaton on several planes. he crtcal plane s the plane on whch fatgue strength assessment s to be performed. A range of methods for calculatng damage on a partcular plane s descrbed n the lterature. he method consdered n ths paper conssts of the normal stress use n each plane for fatgue analyss [7]. he crtcal plane crteron method consst of: In each plane a ranflow countng of the normal stress hstory s performed. he resultng stress ampltudes can be used together wth a tenson/compresson S-N curve for the calculaton and lnear summaton of partal damages accordng to Palmgren/Mner. Before damage analyss the S-N curve should be locally modfed accordng to nfluences lke mean stress (whch can be quantfed by means of an Hagh-dagram), notch support effect (whch can be consdered by takng nto account stress gradent [8]), temperature, surface roughness, surface treatments, etc. he plane wth maxmum damage s assumed to be crtcal. he ductlty of the materal has already been taken nto account by scalng of the normal stress or stress tensor [7] Fatgue analyss of the component Sub tems 3.1, 3.2, 3.3 and 3.4 are taken nto account to start the fatgue analyss of the component, because: 1. Varable ampltude of load s encountered, so cumulatve damage analyss s requred. 2. By FEA analyss, hgh stresses can be observed, so a local plastfcaton n the crtcal regon s possble. 3. For the uncertanty of the stress/stran proportonalty at the component, a multaxal fatgue approach has to be used, and the chosen one s the crtcal plane approach. o do the fatgue analyss of the component, a reduced FEA model s created. Snce fgure 6 and 7 represents the real load nput n the component, the torson load case s no more necessary. he torson load case s a statc analyss for maxmum torson, but for a fatgue analyss, a smulaton wth varable load nput s requred. Now, the load from the measurement s drectly nputted n the model, usng the FEA model and post-processor software of fatgue analyss. he reduced model, as well as, the locaton of the load nput s showed n fgure 10..

7 Fgure 10. Reduced model and varable load nput locaton Wth the reduced model and varable load nput showed n fgure 6,7, and 10, the fatgue analyss can be done for ths part verson. he parameters of the analyss, as well as, ts results can be seen n fgure 11. It s mportant to notce that n ths analyss, the 4 laps force measurement s the load nput, and the laps are extrapolated untl theoretcal component falure. Also, the software takes nto account several factors, such as: mean stress, surface roughness, surface treatments, thermal nfluence, statstcal materal data, etc. 4. CORRELAION WIH FAILURE Fgure 11. Fatgue analyss settngs and results After 702 laps at test track, a falure n the regon A was found. As observed n fgure 12, the falure was due crack propagaton. Pont A ndcates the crack ntaton regon, the falure was due fatgue wth multple nucleaton steps. Fgure 12. Falure by crack nucleaton

8 Comparng the damage predcton and the falure encountered, some observatons can be made: 1. he FEA model and fatgue analyss software could represent the crtcal stress pont, snce the falure occurs at the regon A. 2. he total tme to falure s 8,5% hgher than the lfe predcted wth fatgue analyss. he observaton number 2 can be explaned wth the followng equaton: Where: = otal tme to falure = me to crack nucleaton f = + p = me to crack propagaton untl component nspecton Falure n lfe-tme fatgue analyss s defned when a mnmum crack s observed after the component been submtted to a number of cyclc loadng [1]. herefore, the lfe predcted n fgure 11 can be compared only wth the tme f, and not wth the total tme. he tme p can be calculated by the fracture mechancs and crack propagaton approach, whch s not the am of the present study. f p 5. COMPONEN SECOND VERSION DESIGN AND APPROVAL he component frst verson could not be homologated n the torture track due ts falure. hus, new component geometry was made, as showed n fgure 13. It s mportant to notce that the man concept of the part was not changed, as well as, the load nput regon, and only addtonal materal was ntroduced to renforce the component. Fgure 13. Component FEA model (second verson)

9 Followng the same desgn process for ths second verson, the same FEA analyss s made, wth the same torson load case at the complete vehcle, but changng the component geometry. he new result s observed n fgure 14. Fgure 14. Stress results for torson load case At ths step of the development process, another round of test n the accelerated durablty provng ground should be necessary to approve the new component verson. he present study ams to homologate the component second verson wthout the extra round of test, approvng t va FEA analyss, fatgue analyss and force measurement correlaton. o make t possble, some assumptons have to be adopted: 1. he new geometry follows the same concept from the prevous one,.e. the crtcal ponts does not change. 2. he component load nput drecton and value cannot change between the frst and second verson. he part studed n ths paper follows the 2 assumptons prevously descrbed: 1. he frst verson concept s followed, shown n fgure 13 and the crtcal ponts reman the same as shown n fgure able 1 shows a comparson between the load nput at torson load case for each verson. Snce the mechansm that nput the load nto the component does not change, and the new geometry follows the same concept from the prevous one, nether the value nor the drecton of load has to have sgnfcant changes. Frst verson load nput (kgf) 2294 Second verson load nput (kgf) 2310 able 1. Comparson between the load nputs at FEA analyss (torson load case) for each verson

10 Snce the assumptons are vald, the same FEA and further fatgue analyss showed n fgure 10 can be done, mantanng the reduced FEA model, the prevous load measurement but now usng the component second verson. he parameters of the analyss, as well as, ts results can be seen n fgure 15. Fgure 15. Fatgue analyss settngs and results By analyzng the second verson part smulated lfe tme t can be observed that t fulflls the approval crtera requred to ths torture track (2940 laps), wth a safety factor of 15. herefore, the component second verson does not need a second round of testng, and t s approved by fatgue smulaton correlated wth load measurement from former part verson. CONCLUSION he presented study has covered the man steps of product development, gvng a focus to tme reducton durng the component homologaton aded by FEA analyss, force measurement correlaton and fatgue analyss. herefore, the followng conclusons can be made: 1. he vehcle FEA has good correlaton wth realty, snce t ponted the falure regon as the component hghest stress regon. 2. he lfe tme analyss has led to a good correlaton between smulaton and realty, t contrbutes to the parameter analyss assertveness, such as the crtcal plane approach and fatgue analyss settngs. But t s mportant to state that only one component falure was studed. 3. he good correlaton rate between smulaton and realty proves a satsfactory use of the load measurement extrapolaton for fatgue analyss. 4. o mprove the correlaton, a fracture mechancs model could have been ntegrated to the fatgue analyss, ths would cover the crack nucleaton and propagaton tme. 5. o ensure the methodology effectveness several assumptons have to be satsfed, such as: the new geometry has to follow the same concept from the prevous one and the component load nput drecton and value cannot change between the versons.

11 REFERENCES [1] DOWLING, N. E. Mechancal Behavor of Materals, 3rd edton. Englewood Clffs: Prentce Hall, [2] QUEK, S. S.; LIU, G. R. Fnte Element Method: A Practcal Course. Oxford: Butterworth-Henemann, [3] Mner, M. A. Cumulatve Damage n Fatgue. Journal of Appled Mechancs, v.12, p , [4] NEUBER, H. heory of Stress Concentraton for Shear-Straned Prsmatcal Bodes wth Arbtrary Nonlnear Stress-Stran Law. Journal of Appled Mechancs, v.28, p , [5] FAEMI, A.; SHAMSAEI, N. Multaxal Fatgue: An overvew and some approxmaton models for lfe estmaton. Internatonal Journal of Fatgue, v.33, p , [6] SPINELLI, D. M. Lean development methodology for structural components development supported by desgn tools, manufacturng process and materals testng. São Carlos: Doctor hess - Escola de Engenhara de São Carlos, Unversdade de São Paulo, [7] Gaer, C.; Dannbauer H. A Multaxal Fatgue Analyss Method For Ductle, Sem-Ductle, And Brttle Materals. he Araban Journal for Scence and Engneerng, v.33, p , [8] FKM-Gudelne. Analytcal Strength Assessment, Frankfurt am Man: Forschungskuratorum Maschnenbau, DEFINIIONS D = otal damage D = Damage for each dfferent stress σ n = Number of cycles that a component s subjected n a gven alternatng stressσ. N = Number of cycles to falure atσ, accordng to component materal s Wöhler curve. = otal tme to falure = me to crack nucleaton f p = me to crack propagaton untl component nspecton