Springback Reduction in Stamping of Front Side Member with a Response Surface Method
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1 Sprngback Reducton n Stampng of Front Sde Member wth a Response Surface Method Jung-Han Song *, Hoon Huh *, Se-Ho Km **, Sung-Ho Park *** * Department of Mechancal Engneerng, Korea Advanced Insttute of Scence and Technology Scence Town, Daejeon, 35-71, Korea ** School of Automotve, Industry and Mechancal Engneerng, Daegu Unversty 15 Naer, Jllyang, Gyungsan, Gyungbuk, Korea *** POSCO Techncal Research Laboratores, 699 Cumho-dong, Gwangyang-s, Jeonnam, Korea Abstract. Sprngback s a common phenomenon n sheet metal formng snce the elastc recovery of the nternal stresses s nduced after removal of the toolng. The numercal analyss of sprngback s a complcated tme-consumng job and ts result s greatly effected by a type of the yeld functon, fnte elements used and the constrant condton for elmnatng a rgd body moton. In ths paper, optmzaton of the draw-bead force s carred out utlzng the response surface method n order to reduce sprngback and mprove shape accuracy of a deep drawn product. In the optmzaton process, the tendency of sprngback s evaluated qualtatvely wthout sprngback smulaton usually done wth the mplct solvng scheme. Instead of sprngback smulaton, the amount of stress devaton along the thckness drecton n the deep drawn product s used as an ndcator of sprngback. The stampng process s analyzed for a front sde member formed wth advanced hgh strength steel (AHSS) sheets such as DP6. The analyss procedure fully covers the bnderwrap, stampng, trmmng and sprngback processes wth the commercal elasto-plastc fnte element code LS-DYNA 3D. The effect of the restranng force of draw-beads s confrmed wth the decreased stress devaton. The analyss result shown n the fnal sprngback smulaton demonstrates that the present analyss provdes a gudelne for controllng the evoluton of sprngback based on the fnte element smulaton of complcated auto-body members. INTRODUCTION Advanced hgh strength steels (AHSS) such as TRIP and DP gan acceptance recently n the automotve ndustry because ther superor strength to weght rato can lead to mproved fuel effcency and crashworthness assessment of vehcles. The major troubles of the automotve structural members stamped wth hgh strength steel sheets are the tendency of the large amount of sprngback due to the hgh yeld strength and the tensle strength. Sprngback s a common phenomenon n sheet metal formng snce the elastc recovery of the nternal stresses s nduced after removal of the tools. The amount of sprngback s manly nfluenced by a type of the yeld functon and ansotropc model nduced by rollng, toolng geometry, and frcton [1-2]. The dscrepancy of shapes between a deep drawn product and a desgnated one due to sprngback must be compensated at the tool desgn stage n order to guarantee ts functon and assembly wth other parts. It s, however, so dffcult to predct and estmate a compensaton amount for sprngback that the compensaton amount reles on expert engneer s experence and tral and error procedure. The compensaton procedure requres extra try-out tme ncreasng the cost of the development. Recently, the numercal analyss s ntroduced to predct the amount of sprngback and to mprove the shape accuracy pror to tryout stage of press workng. Sprngback s a consequence of the unbalanced stress through the thckness of a sheet undergong bendng. Its reducton s an mportant ssue n the sheet metal formng ndustry. Many researchers have studed the nfluence of the process parameters on the sprngback n order to compensate the sprngback and mprove the shape accuracy of a deep drawn product. Expermental and numercal studes [3-4] have shown 33
2 OPTIMIZATION OF THE BEAD FORCE WITH A RESPONSE SURFACE METHOD FIGURE 1. Shape of the outer panel n front sde member. that sprngback s dependent on several parameters ncludng materal behavor, de shape, frcton and stampng parameters. Gan and Wagoner [5] suggested de desgn scheme wth dsplacement adjustment method for compensatng sprngback. Chou and Hung [6] performed the optmzaton of the de gap and punch radus wth response surface method n channel wall bendng. Lu et al. [7] adopted the varable blank holdng force to reduce the sprngback and Km and Huh [8] optmzed the blank holdng force wth a drect dfferental method n U-draw bendng problem. Altan et al. [9] determned the optmum blank dmenson wth senstvty analyss to compensate sprng back n the flexble formng process. In most of those researches, the amount of sprngback obtaned from the addtonal sprngback analyss s consdered as the objectve functon for optmzaton. However, the numercal analyss of sprngback s greatly effected by a type of the yeld functon, shell element used, contact parameters etc. Moreover, sprngback analyss of complcated auto-body panels s a complcated tmeconsumng job due to ts convergent problem n an mplct solvng scheme. In ths paper, optmzaton of the draw-bead force s performed wth the response surface method n order to reduce sprngback n an outer panel of front sde member. In the optmzaton procedure, the tendency of sprngback s evaluated qualtatvely wthout sprng back smulaton. Instead of performng sprngback smulaton, the amount of stress devaton along the thckness drecton s drectly obtaned from the fnte element stampng analyss and utlzed as an ndcator of sprngback. The stampng process s analyzed for the outer panel formed wth advanced hgh strength steel (AHSS) sheet such as DP6. The analyss procedure fully covers the bnder-wrap, stampng and trmmng processes. After the optmzaton, the effect of the optmum restranng force of draw-bead s confrmed wth the decreased stress devaton along the thckness drecton. The analyss result shown n the fnal sprngback smulaton wth the optmum draw-bead forces demonstrate that the present analyss provdes a gudelne for controllng the evoluton of sprngback based on the fnte element smulaton of complcated auto-body members. The stress devaton along the thckness drecton s selected as an objectve functon for optmzaton. A response surface method s utlzed to calculate the mnmzaton of the objectve functon. At each desgn pont, fnte element stampng smulaton of the outer panel s carred out and constructon of the response surface of the objectve functon s followed to mnmze the error between the response surface and desgn ponts. A commercal explct fnte element code, LS-DYNA 3D [1], s employed n stampng smulaton. Constructon of the response surface of the objectve functon for optmzaton s carred out wth the help of HyperStudy []. Optmzaton Procedure The optmum desgn procedure wth respect to a desgn varable p can be defned by mnmzaton of an objectve functon as follows: m n.φ( p) (1-a) subject to ( p) = 1,2, Kn (1-b) g where p s a desgn varable such as the draw-bead force. Φ ( p) and g ( p) are the objectve functon and constrant condtons, resp ㅁ ectvely. For the purpose of reducng sprngback, the amount of stress devaton along the thckness drecton whch s drectly obtaned from the fnte element smulaton s utlzed as the objectve functon rather than calculatng the amount of sprngback. Constrant condtons are assgned so that the prncpal strans should be located under the formng lmt and thckness reducton should be less than 2 % for preventng the fracture n a blank. The objectve functon and constrant condtons are as follows: 2 m n. Φ = ( σ ~ σ dω (2-a) Ω opt ) subject to g = ε ) n Ω (2-b) 1 ( 1, max ε1 C where σ s the longtudnal stress component accordng to local element coordnates, ~σ s a desred value of stress component, ε s major prncpal stran 1 and ε s a lmt stran on the formng lmt dagram 1C respectvely. The desred value, ~σ, expressed n 34
3 equaton (3) represents the averaged value of σ at the ntegraton ponts along the thckness drecton. ~ σ dzˆ ΩE σ = (3) dzˆ ΩE The response surface method s a methodology to construct global approxmaton of the system behavor based on results calculated at varous ponts n the optmzaton problem [12]. It s wdely utlzed because the constructed response surface contans only the polynomal terms so that the global maxmum and mnmum ponts are easly obtaned. The approxmaton functon Φ a ( p) of the response surface functon Φ( p) s assumed to be a summaton of bass functons: Procedure for the optmzaton of the draw-bead force can be summarzed as shown n Fg. 2. Frst, the geometry and state varables such as devaton of the longtudnal stress for gven process parameters and desgn varables such as the draw-bead forces are determned by the fnte element analyss. Secondly, the objectve functon and constrant condtons are calculated from these results. Fnally, the optmum draw-bead forces are sought by the response surface method when the change of the objectve functon becomes suffcently small. L Φ ( p) = Ψ (4) a a = where L s the number of bass functons, and Ψ are the bass functons that consttute model. The constants, a, are obtaned to mnmze the least square value: L = L 2 2 [ Φ( p ) Φ ( p )] = [ Φ( p ) a Ψ ] (5) a = A choce of the bass functons, Ψ, nfluences the accuracy of approxmaton. Quadratc bass functons are used to construct the objectve functon of longtudnal stress devaton and constrant condton of the prncpal stran. Fnte Element Analyss Input: Process Parameter Constructon of Response Surface: Objectve functon and Constrant Calculaton: Optmum Searchng of RSM Φ < tolerance YES FIGURE 2. Schematc dagram of the optmzaton procedure wth response surface method. No FIGURE 3. Intal settng for tools and blank for the formng analyss of outer panel. Optmzaton of the Draw-bead Force The optmzaton of the draw-bead force for reducng sprngback was carred out wth the help of a commercal fnte element code, LS-DYNA, and an optmzaton program, HyperStudy. Fgure 3 shows the toolng system for the analyss of an outer panel. The materal of the blank used s the DP 6 whose flow stress s express as σ = 123.7(.126+ ε ). 16 MPa. The ntal sheet thckness s 2.5 mm. The blank holdng force of 75 ton s mposed on the bnder. The coulomb frcton coeffcent s.15 between the sheet and tools. In the explct smulaton, the step sze for the analyss s determned from the elastc modulus, the densty and the mesh sze of the blank. A mass scalng scheme s used to ncrease the densty of the blank to ten tmes of the orgnal densty, whch ncreases the tme step sze about 3.3 tmes. The mass scalng scheme satsfes the statc condton and produces no problem of the excessve knetc energy durng the smulaton. The punch speed s fxed to 2 m/s. The stampng analyss s carred out untl the blank s fully drawn from the bnder and then trmmng analyss s performed. The restranng force of draw-beads s used as the desgn varable for sprngback reducton. Total of eght desgn varables are selected consderng the shape change of the outer panel n front sde member. The 35
4 FIGURE 4. Locaton of draw-beads and selecton of desgn varable. locaton of each desgn varable s expressed n Fg. 4 wth curved lnes on the blank holder. Accordng to the locaton of desgn varables, desgn regons are dvded nto four and t s assumed that, n each desgn regon, only two correspondng varables are manly effected and co-relaton of another desgn varable s relatvely small. For the constructon of the ntal approxmated response surface, fnte element smulatons are carred out as the ntal guesses when the constant bead force such as 5 N/mm s mposed. Factoral desgn technques are utlzed n the selecton of desgn ponts. Lnear bass functons are used for global searchng of optmum ponts whle quadratc functons are used for local searchng. Durng the optmzaton process, the varaton of the objectve functon, constrants and desgn varables s depcted n Fg. 5. As the step goes on, the drawbead force s ncreased ntally and has a steady value not to volate the constrant condton. The optmum values are determned when the change of the objectve functon becomes suffcently small. The optmum (a) FLD curve of DP 6 Constrant lne Result Major Stran (%) Mnor Stran (%) (b) FIGURE 5. Thckness and prncpal stran dstrbuton after the optmzaton: (a) thckness; (b) FLD and prncpal stran. values are shown n Table 1. The stampng and trmmng analyss of the outer panel n front sde member s performed wth those optmum values. Dstrbuton of the thckness and the prncpal strans are shown n Fg. 6. The dstrbuton of the prncpal strans on the formng lmt dagram ndcates that the constrant condtons are satsfed and the fracture s Objectve functon( x1 9 N 2 /mm) Objectve Constrant Constrant Value g Optmzaton step Optmzaton step (a) (b) FIGURE 6. Varaton of varables durng the optmzaton process on the desgn regon 1: (a) objectve functon and constrant; (b) desgn varables. TABLE 1. Optmum restranng force of draw-bead obtaned from the response surface method Draw-bead Force (N/mm) varable 1 varable 2 Desgn Varable DV1 DV2 DV3 DV4 DV5 DV6 DV7 DV8 Restranng Force (N/mm)
5 Longtudnal Stress (MPa) Dstance along the secton (mm) pt= pt= pt=. pt=.5385 pt=.962 Longtudnal Stress (MPa) pt= pt= pt=. pt=.5385 pt= Dstance along the secton (mm) (a) (b) (c) FIGURE 7. Comparson of the stress devaton through the thckness ntegraton pont along the desgnate secton: (a) desgnate secton; (b) before the optmzaton (ntal); (c) after the optmzaton. not occurred n the formng analyss wth the optmum bead forces. The stress devaton through the thckness s examned along the desgnate secton n order to nvestgate the effect of the optmum bead force. After mnmzaton of the objectve functon, the devaton of the longtudnal stress through the thckness s changed from the ntal state to the optmum state as shown n Fg. 7. It s because the blank s adequately tensoned due to the restranng force of draw-bead so that the stress devaton s drastcally decreased along the desgnate secton. FIGURE 8. Mesh coarsenng for sprngback analyss. VERIFICATION WITH THE SPRINGBACK ANALYSIS In the prevous optmzaton, the tendency of sprng back was evaluated qualtatvely wthout sprngback smulaton. Instead of performng sprngback smulaton, the amount of stress devaton along the thckness drecton s used as an ndcator of sprngback. In order to demonstrate the valdty of the optmzaton procedure and selecton of the objectve functon, sprngback analyss s carred out wth LS-DYNA 3D mplct solvng scheme. Hughes-Lu shell element s used and total of fve ntegraton ponts through the thckness were selected for precse consderaton of stress devaton. In an mplct solvng scheme, total number of element s drectly effected to the calculaton tme. Mesh coarsenng scheme s utlzed so that ntally elements are decreased to as shown n Fg. 8. All statc smulatons, ncludng the sprngback analyss, requre that the rgd body motons be elmnated by defnng constrans. The constrants are mposed at three nodal ponts shown n Fg. 9 consderng the assembly wth another part. Wth the results of the draw-bead force obtaned dy=dz= FIGURE 9. Boundary condton for sprngback analyss. from each optmzaton step, the sprngback analyss s performed and deformed shapes are compared n Fg. 1. The fgure shows that sprngback s gettng on the decrease as optmzaton step goes on and when the optmum bead force s appled, deformed shape after sprngback s close concdence wth ts orgnal shape. Especally, the tendency of sprngback reducton s dstnctly detected along the longtudnal drecton. It s consequence from the mnmzaton of the unbalanced stress through the thckness as shown n Fg. 7. The result shown n the sprngback smulaton demonstrates that the present analyss s approprate and effcent for controllng the evoluton of sprngback and t provdes a gudelne to mprove the shape accuracy n the desgn stage of the complcated parts n auto-body members. 37
6 Y-Coordnate (mm) Orgnal Shape Intal guess Optmzaton step 1 Optmzaton step 2 Fnal result X-coordnate (mm) Y-Coordnate (mm) Orgnal Shape Intal guess Optmzaton step 1 Optmzaton step 2 Fnal result Z-coordnate (mm) (a) (b) (c) FIGURE 1. Comparson of the sprngback along the desgnate secton wth respect to the optmzaton step: (a) desgnate secton; (b) longtudnal secton; (c) cross secton. CONCLUSION Ths paper s concerned wth optmzaton of the draw-bead force for reducng sprngback n an outer panel of front sde member. The objectve functon s assgned as the amount of stress devaton along the thckness drecton whch s drectly obtaned from the fnte element stampng smulaton, nstead of sprng back angle. The prncpal strans should be located under the formng lmt as the constrant condton n order to prevent the fracture n a blank. A response surface method s utlzed n the optmzaton process. After the optmzaton, the effect of the restranng force of draw-beads s confrmed wth the decreased stress devaton along the thckness drecton. Sprngback analyss s carred out wth the obtaned optmal restranng force of draw-beads. The results shown n sprngback smulaton fully demonstrate that the present analyss provdes a gudelne for controllng the evoluton of sprngback based on the fnte element smulaton of complcated auto-body members. REFERENCES 1. Chnn, B. K., Km, H. Y. and Lee, J. K., Modelng the Bauschnger Effect for Sheet Metals, Part II: applcatons, Int. J. Plastcty, 18, (22). 2. Gau, J. T., and Knzel, G. L., A New Model for Sprng back Predcton n whch the Bauschnger Effect s Consdered, Int. J. Mech. Sc., 43, (21). 3. Xu, W. L., Ma, C. H., L, C. H. and Feng W. J., Senstve Factors n Sprngback Smulaton for Sheet Metal Formng, J. Mater. Process. Technol., 151, (24). 4. Samuel, M, Expermental and Numercal Predcton of Sprngback and Sde Wall Curl n U-Bendng of Ansotropc Sheet Metals, J. Mater. Process. Technol,, 15, (2). 5. Gan, W. and Wagoner, R. H., De Desgn Method for Sheet Sprngback, Int. J. Mech. Sc., 46, (24). 6. Chou, C. H. and Hung, I. N., Fnte Element Analyss and Optmzaton on Sprngback Reducton, Int. J. Mach. Tool. Manu., 39, (1999). 7. Lu, G., Ln, Z., Xu, W. and Bao, Y., Varable Blankholder Force n U-shaped Part Formng for Elmnatng Sprngback Error J. Mater. Process. Technol,, 12, (22). 8. Km, S. H. and Huh, H., Desgn Senstvty Analyss of Sheet Metal Formng Processes wth a Drect Dfferentaton method, J. Mater. Process. Technol., , (22). 9. Palanswamy, H., Ngale, G. and T. Altan, Optmzaton of Blank Dmensons to Reduce Sprngback n the Flexformng Process, J. Mater. Process. Techno.,. 146, (24). 1. LS-DYNA 3D Keyword Manual, Lvermore Software Technology Cooperaton.. HyperStudy 7. User s Manual, Altar Engneerng. 12. Huh, H. and Km, S. H. Optmum Process Desgn n Sheet-Metal Formng wth Fnte Element Analyss, Trans. ASME, J. Eng. Mater. Technol., 123, (21). 12. Huh, H., Song, J. H., Km, K. S. and Km, K. S., Effect of Draw-bead and Blank Holdng Force on Sheet Metal Formng Process Proc. NUMIFORM 24, 21, N78. 38
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