英文翻譯重點 起皺 An Analysis of Draw-Wall Wrinkling in a Stamping Die Design.pdf

Int J Adv Manuf Technol (2002) 19:253259 2002 Springer-Verlag London LimitedAn Analysis of Draw-Wall Wrinkling in a Stamping Die DesignF.-K. Chen and Y.-C. LiaoDepartment of Mechanical Engineering, National Taiwan University, Taipei, TaiwanWrinkling that occurs in the stamping of tapered square cupsand stepped rectangular cups is investigated. A commoncharacteristic of these two types of wrinkling is that thewrinkles are found at the draw wall that is relatively unsup-ported. In the stamping of a tapered square cup, the effect ofprocess parameters, such as the die gap and blank-holderforce, on the occurrence of wrinkling is examined using finite-element simulations. The simulation results show that the largerthe die gap, the more severe is the wrinkling, and suchwrinkling cannot be suppressed by increasing the blank-holderforce. In the analysis of wrinkling that occurred in the stampingof a stepped rectangular cup, an actual production part thathas a similar type of geometry was examined. The wrinklesfound at the draw wall are attributed to the unbalancedstretching of the sheet metal between the punch head and thestep edge. An optimum die design for the purpose of eliminatingthe wrinkles is determined using finite-element analysis. Thegood agreement between the simulation results and thoseobserved in the wrinkle-free production part validates theaccuracy of the finite-element analysis, and demonstrates theadvantage of using finite-element analysis for stamping diedesign.Keywords: Draw-wall wrinkle; Stamping die; Stepped rec-tangular cup; Tapered square cups1. IntroductionWrinkling is one of the major defects that occur in the sheetmetal forming process. For both functional and visual reasons,wrinkles are usually not acceptable in a finished part. Thereare three types of wrinkle which frequently occur in the sheetmetal forming process: flange wrinkling, wall wrinkling, andelastic buckling of the undeformed area owing to residualelastic compressive stresses. In the forming operation of stamp-ing a complex shape, draw-wall wrinkling means the occurrenceCorrespondence and offprint requests to: Professor F.-K. Chen, Depart-ment of Mechanical Engineering, National Taiwan University, No. 1Roosevelt Road, Sec. 4, Taipei, Taiwan 10617. E-mail: fkchenL50560.twof wrinkles in the die cavity. Since the sheet metal in the wallarea is relatively unsupported by the tool, the elimination ofwall wrinkles is more difficult than the suppression of flangewrinkles. It is well known that additional stretching of thematerial in the unsupported wall area may prevent wrinkling,and this can be achieved in practice by increasing the blank-holder force; but the application of excessive tensile stressesleads to failure by tearing. Hence, the blank-holder force mustlie within a narrow range, above that necessary to suppresswrinkles on the one hand, and below that which producesfracture on the other. This narrow range of blank-holder forceis difficult to determine. For wrinkles occurring in the centralarea of a stamped part with a complex shape, a workablerange of blank-holder force does not even exist.In order to examine the mechanics of the formation ofwrinkles, Yoshida et al. 1 developed a test in which a thinplate was non-uniformly stretched along one of its diagonals.They also proposed an approximate theoretical model in whichthe onset of wrinkling is due to elastic buckling resulting fromthe compressive lateral stresses developed in the non-uniformstress field. Yu et al. 2,3 investigated the wrinkling problemboth experimentally and analytically. They found that wrinklingcould occur having two circumferential waves according totheir theoretical analysis, whereas the experimental results indi-cated four to six wrinkles. Narayanasamy and Sowerby 4examined the wrinkling of sheet metal when drawing it througha conical die using flat-bottomed and hemispherical-endedpunches. They also attempted to rank the properties thatappeared to suppress wrinkling.These efforts are focused on the wrinkling problems associa-ted with the forming operations of simple shapes only, suchas a circular cup. In the early 1990s, the successful applicationof the 3D dynamic/explicit finite-element method to the sheet-metal forming process made it possible to analyse the wrinklingproblem involved in stamping complex shapes. In the presentstudy, the 3D finite-element method was employed to analysethe effects of the process parameters on the metal flow causingwrinkles at the draw wall in the stamping of a tapered squarecup, and of a stepped rectangular part.A tapered square cup, as shown in Fig. 1(a), has an inclineddraw wall on each side of the cup, similar to that existing ina conical cup. During the stamping process, the sheet metalon the draw wall is relatively unsupported, and is therefore254 F.-K. Chen and Y.-C. LiaoFig. 1. Sketches of (a) a tapered square cup and (b) a steppedrectangular ne to wrinkling. In the present study, the effect of variousprocess parameters on the wrinkling was investigated. In thecase of a stepped rectangular part, as shown in Fig. 1(b),another type of wrinkling is observed. In order to estimate theeffectiveness of the analysis, an actual production part withstepped geometry was examined in the present study. Thecause of the wrinkling was determined using finite-elementanalysis, and an optimum die design was proposed to eliminatethe wrinkles. The die design obtained from finite-element analy-sis was validated by observations on an actual production part.2. Finite-Element ModelThe tooling geometry, including the punch, die and blank-holder, were designed using the CAD program PRO/ENGINEER. Both the 3-node and 4-node shell elements wereadopted to generate the mesh systems for the above toolingusing the same CAD program. For the finite-element simul-ation, the tooling is considered to be rigid, and the correspond-ing meshes are used only to define the tooling geometry andFig. 2. Finite-element mesh.are not for stress analysis. The same CAD program using 4-node shell elements was employed to construct the meshsystem for the sheet blank. Figure 2 shows the mesh systemfor the complete set of tooling and the sheet-blank used in thestamping of a tapered square cup. Owing to the symmetricconditions, only a quarter of the square cup is analysed. Inthe simulation, the sheet blank is put on the blank-holder andthe die is moved down to clamp the sheet blank against theblank-holder. The punch is then moved up to draw the sheetmetal into the die cavity.In order to perform an accurate finite-element analysis, theactual stressstrain relationship of the sheet metal is requiredas part of the input data. In the present study, sheet metalwith deep-drawing quality is used in the simulations. A tensiletest has been conducted for the specimens cut along planescoinciding with the rolling direction (0) and at angles of 45and 90 to the rolling direction. The average flow stress H9268,calculated from the equation H9268H11005(H92680H11001 2H926845H11001H926890)/4, for eachmeasured true strain, as shown in Fig. 3, is used for thesimulations for the stampings of the tapered square cup andalso for the stepped rectangular cup.All the simulations performed in the present study were runon an SGI Indigo 2 workstation using the finite-element pro-gram PAMFSTAMP. To complete the set of input data requiredFig. 3. The stressstrain relationship for the sheet metal.Draw-Wall Wrinkling in a Stamping Die Design 255for the simulations, the punch speed is set to 10 m sH110021and acoefficient of Coulomb friction equal to 0.1 is assumed.3. Wrinkling in a Tapered Square CupA sketch indicating some relevant dimensions of the taperedsquare cup is shown in Fig. 1(a). As seen in Fig. 1(a), thelength of each side of the square punch head (2Wp), the diecavity opening (2Wd), and the drawing height (H) are con-sidered as the crucial dimensions that affect the wrinkling.Half of the difference between the dimensions of the die cavityopening and the punch head is termed the die gap (G) in thepresent study, i.e. G H11005 WdH11002 Wp. The extent of the relativelyunsupported sheet metal at the draw wall is presumably dueto the die gap, and the wrinkles are supposed to be suppressedby increasing the blank-holder force. The effects of both thedie gap and the blank-holder force in relation to the occurrenceof wrinkling in the stamping of a tapered square cup areinvestigated in the following sections.3.1 Effect of Die GapIn order to examine the effect of die gap on the wrinkling,the stamping of a tapered square cup with three different diegaps of 20 mm, 30 mm, and 50 mm was simulated. In eachsimulation, the die cavity opening is fixed at 200 mm, and thecup is drawn to the same height of 100 mm. The sheet metalused in all three simulations is a 380 mm H11003 380 mm squaresheet with thickness of 0.7 mm, the stressstrain curve for thematerial is shown in Fig. 3.The simulation results show that wrinkling occurred in allthree tapered square cups, and the simulated shape of thedrawn cup for a die gap of 50 mm is shown in Fig. 4. It isseen in Fig. 4 that the wrinkling is distributed on the drawwall and is particularly obvious at the corner between adjacentwalls. It is suggested that the wrinkling is due to the largeunsupported area at the draw wall during the stamping process,also, the side length of the punch head and the die cavityFig. 4. Wrinkling in a tapered square cup (G H11005 50 mm).opening are different owing to the die gap. The sheet metalstretched between the punch head and the die cavity shoulderbecomes unstable owing to the presence of compressive trans-verse stresses. The unconstrained stretching of the sheet metalunder compression seems to be the main cause for the wrink-ling at the draw wall. In order to compare the results for thethree different die gaps, the ratio H9252 of the two principal strainsis introduced, H9252 being H9280min/H9280max, where H9280maxand H9280minare themajor and the minor principal strains, respectively. Hosfordand Caddell 5 have shown that if the absolute value of H9252 isgreater than a critical value, wrinkling is supposed to occur,and the larger the absolute value of H9252, the greater is thepossibility of wrinkling.The H9252 values along the cross-section MN at the samedrawing height for the three simulated shapes with differentdie gaps, as marked in Fig. 4, are plotted in Fig. 5. It is notedfrom Fig. 5 that severe wrinkles are located close to the cornerand fewer wrinkles occur in the middle of the draw wall forall three different die gaps. It is also noted that the bigger thedie gap, the larger is the absolute value of H9252. Consequently,increasing the die gap will increase the possibility of wrinklingoccurring at the draw wall of the tapered square cup.3.2 Effect of the Blank-Holder ForceIt is well known that increasing the blank-holder force canhelp to eliminate wrinkling in the stamping process. In orderto study the effectiveness of increased blank-holder force, thestamping of a tapered square cup with die gap of 50 mm,which is associated with severe wrinkling as stated above, wassimulated with different values of blank-holder force. Theblank-holder force was increased from 100 kN to 600 kN,which yielded a blank-holder pressure of 0.33 MPa and 1.98MPa, respectively. The remaining simulation conditions aremaintained the same as those specified in the previous section.An intermediate blank-holder force of 300 kN was also usedin the simulation.The simulation results show that an increase in the blank-holder force does not help to eliminate the wrinkling thatoccurs at the draw wall. The H9252 values along the cross-sectionFig. 5. H9252-value along the cross-section MN for different die gaps.256 F.-K. Chen and Y.-C. LiaoMN, as marked in Fig. 4, are compared with one another forthe stamping processes with blank-holder force of 100 kN and600 kN. The simulation results indicate that the H9252 values alongthe cross-section MN are almost identical in both cases. Inorder to examine the difference of the wrinkle shape for thetwo different blank-holder forces, five cross-sections of thedraw wall at different heights from the bottom to the line MN, as marked in Fig. 4, are plotted in Fig. 6 for both cases.It is noted from Fig. 6 that the waviness of the cross-sectionsfor both cases is similar. This indicates that the blank-holderforce does not affect the occurrence of wrinkling in the stamp-ing of a tapered square cup, because the formation of wrinklesis mainly due to the large unsupported area at the draw wallwhere large compressive transverse stresses exist. The blank-holder force has no influence on the instability mode of thematerial between the punch head and the die cavity shoulder.4. Stepped Rectangular CupIn the stamping of a stepped rectangular cup, wrinkling occursat the draw wall even though the die gaps are not so significant.Figure 1(b) shows a sketch of a punch shape used for stampinga stepped rectangular cup in which the draw wall C is followedby a step DE. An actual production part that has this typeof geometry was examined in the present study. The materialused for this production part was 0.7 mm thick, and the stressstrain relation obtained from tensile tests is shown in Fig. 3.The procedure in the press shop for the production of thisstamping part consists of deep drawing followed by trimming.In the deep drawing process, no draw bead is employed onthe die surface to facilitate the metal flow. However, owingto the small punch corner radius and complex geometry, asplit occurred at the top edge of the punch and wrinkles werefound to occur at the draw wall of the actual production part,as shown in Fig. 7. It is seen from Fig. 7 that wrinkles aredistributed on the draw wall, but are more severe at the corneredges of the step, as marked by AD and BE in Fig. 1(b).The metal is torn apart along the whole top edge of the punch,as shown in Fig. 7, to form a split.In order to provide a further understanding of the defor-mation of the sheet-blank during the stamping process, a finite-element analysis was conducted. The finite-element simulationwas first performed for the original design. The simulatedshape of the part is shown from Fig. 8. It is noted from Fig.8 that the mesh at the top edge of the part is stretchedFig. 6. Cross-section lines at different heights of the draw wall fordifferent blank-holder forces. (a) 100 kN. (b) 600 kN.Fig. 7. Split and wrinkles in the production part.Fig. 8. Simulated shape for the production part with split and wrinkles.significantly, and that wrinkles are distributed at the draw wall,similar to those observed in the actual part.The small punch radius, such as the radius along the edgeAB, and the radius of the punch corner A, as marked in Fig.1(b), are considered to be the major reasons for the wallbreakage. However, according to the results of the finite-element analysis, splitting can be avoided by increasing theabove-mentioned radii. This concept was validated by theactual production part manufactured with larger corner radii.Several attempts were also made to eliminate the wrinkling.First, the blank-holder force was increased to twice the originalvalue. However, just as for the results obtained in the previoussection for the drawing of tapered square cup, the effect ofblank-holder force on the elimination of wrinkling was notfound to be significant. The same results are also obtained byincreasing the friction or increasing the blank size. We concludethat this kind of wrinkling cannot be suppressed by increasingthe stretching force.Since wrinkles are formed because of excessive metal flowin certain regions, where the sheet is subjected to large com-pressive stresses, a straightforward method of eliminating thewrinkles is to add drawbars in the wrinkled area to absorb theredundant material. The drawbars should be added parallel tothe direction of the wrinkles so that the redundant metal canbe absorbed effectively. Based on this concept, two drawbarsare added to the adjacent walls, as shown in Fig. 9, to absorbthe excessive material. The simulation results show that theDraw-Wall Wrinkling in a Stamping Die Design 257Fig. 9. Drawbars added to the draw walls.wrinkles at the corner of the step are absorbed by the drawbarsas expected, however some wrinkles still appear at the remain-ing wall. This indicates the need to put more drawbars at thedraw wall to absorb all the excess material. This is, however,not permissible from considerations of the part design.One of the advantages of using finite-element analysis forthe stamping process is that the deformed shape of the sheetblank can be monitored throughout the stamping process, whichis not possible in the actual production process. A close lookat the metal flow during the stamping process reveals that thesheet blank is first drawn into the die cavity by the punchhead and the wrinkles are not formed until the sheet blanktouches the step edge DE marked in Fig. 1(b). The wrinkledshape is shown in Fig. 10. This provides valuable informationfor a possible modification of die design.An initial surmise for the cause of the occurrence of wrink-ling is the uneven stretch of the sheet metal between the punchcorner radius A and the step corner radius D, as indicated inFig. 1(b). Therefore a modification of die design was carriedout in which the step corner was cut off, as shown in Fig.11, so that the stretch condition is changed favourably, whichallows more stretch to be applied by increasing the step edges.However, wrinkles were still found at the draw wall of thecup. This result implies that wrinkles are introduced becauseof the uneven stretch between the whole punch head edge andthe whole step edge, not merely between the punch corner andFig. 10. Wrinkle formed when the sheet blank touches the steppededge.Fig. 11. Cut-off of the stepped corner.the step corner. In order