1、Int J Adv Manuf Tech nol (2002) 19:253 592002 Sprin ger-Verlag London LimitedAn Analysis of Draw-Wall Wrinkling in a Stamping Die DesignF.-K. Che n and Y.-C. LiaoDepartme nt of Mecha ni cal Engin eeri ng, Nati onal Taiwa n Un iversity, Taipei, Taiwa nWrinkling that occurs in the stamping of tapered

2、square cups and stepped rectangular cups is in vestigated. A com mon characteristic of these two types of wrin kli ng is that the wrin kles are found at the draw wall that is relatively un supported .In the stamp ing of a tapered square cup, the effect of process parameters, such as the die gap and

3、blank-holder force, on the occurrenee of wrin kli ng is exam ined using fin iteeleme nt simulati ons. The simulati on results show that the larger the die gap, the more severe is the wrinkling, and such wrinkling cannot be suppressed by increasing the blank-holder force. In the analysis of wrinkling

4、 that occurred in the stamping of a stepped recta ngular cup, an actual product ion part that has a similar type of geometry was exam in ed. The wrin kles found at the draw wall are attributed to the un bala needstretch ing of thesheet metal between the punch head and the step edge. An optimum die d

5、esign for the purpose of elim in at ing the wrin kles is determ ined using fin ite-eleme nt an alysis. The good agreeme nt betwee n the simulatio n results and those observed in the wrin kle-free product ion part validates the accuracy of the fin ite-eleme nt an alysis, and dem on strates the adva n

6、tage of using fin ite-eleme nt analysis for stamping die design.Keywords: Draw-wall wrin kle; Stamp ing die; Stepped recta ngular cup; Tapered square cups1. IntroductionWrinkling is one of the major defects that occur in the sheet metal forming process. For both functional and visual reas on s,wri n

7、kles are usually not acceptable in a fini shed part. There are three types of wrin kle which freque ntly occur in the sheet metal forming process: flange wrin kli ng, wall wrinkling, and elastic buckling of the undeformed area owing to residual elastic compressive stresses. In the forming operati on

8、 of stamp ing a complex shape, draw-wall wrin kli ng means the occurrenee of wrinkles in the die cavity. Since the sheet metal in the wall area is relatively un supported by the tool, the elim in ati on of wall wrin kles is more difficult tha n the suppressi on of flange wrin kles. It is well known

9、that additi onal stretch ing of the material in the un supported wall area may prevent wrinkling,and this can be achieved in practice by increasing the blankholder force; but the application of excessive tensile stresses leads to failure by tearing. Hence, the bla nk-holder force must lie with in a

10、narrow ran ge, above that n ecessary to suppress wrin kles on the one hand, and below that which produces fracture on the other. This narrow range of bla nk-holder force is difficult to determ ine. For wrin kles occurri ng in the cen tral area of a stamped part with a complex shape, a workable range

11、 of bla nk-holder force does n ot eve n exist.In order to exam ine the mecha nics of the formatio n of wrin kles, Yoshida et al. 1 developed a test in which a thin plate was non-un iformly stretched along one of its diag on als.They also proposed an approximate theoretical model in which the on set

12、of wrin kli ng is due to elastic buckli ng result ing from the compressive lateral stresses developed in the non-uniform stress field. Yu et al. 2,3 investigated the wrinkling problem both experimentally and analytically. They found that wrinkling could occur having two circumferential waves accordi

13、ng to their theoretical analysis, whereas the experime ntal results in dicated four to six wrin kles. Naraya nasamy and Sowerby 4 exam ined the wrin kli ng of sheet metal whe n draw ing it through a coni cal die using flat-bottomed and hemispherical-ended punches. They also attempted to rank the pro

14、perties that appeared to suppress wrin kli ng.These efforts are focused on the wrinkling problems associated with the forming operations of simple shapes only, such as a circular cup. In the early 1990s, the successful application of the 3D dynamic/explicit finite-element method to the sheetmetal fo

15、rming process made it possible to an alyse the wrin kli ng problem in volved in stamp ing complex shapes. In the prese nt study, the 3D fin ite-eleme nt method was employed to an alyse the effects of the process parameters on the metal flow caus ing wrin kles at the draw wall in the stamp ing of a t

16、apered square cup, and of a stepped recta ngular part.A tapered square cup, as shown in Fig. 1( a), has an inclined draw wall on each side of the cup, similar to that existi ng in a coni cal cup. During the stamp ing process, the sheet metal on the draw wall is relatively un supported, and is theref

17、ore prone to wrin kli ng. In the prese nt study, the effect of various process parameters on the wrinkling was investigated. In the case of a stepped rectangular part, as shown in Fig. 1( b),another type of wrinkling is observed. In order to estimate the effective ness of the an alysis, an actual pr

18、oducti on part with stepped geometry was exam ined in the present study. The cause of the wrinkling was determined using finite-element analysis, and an optimum die desig n was proposed to elim in ate the wrin kles. The die desig n obta ined from fin ite-eleme nt an alysis was validated by observati

19、o ns on an actual producti on part.Sketches of (a) a tapered square cup.仙）Sketches of(b) a stepped recta ngular cup.Fig. 1.2. Finite-Element ModelThe tooli ng geometry, in cludi ng the pun ch, die and bla nkholder,were desig ned using the CAD program PRO/ENGINEER. Both the 3-node and 4-node shell el

20、eme nts were adopted to gen erate the mesh systems for the above tooling using the same CAD program. For the finite-element simulation,the tooling is considered to be rigid, and the corresponding meshes are used only to defi ne the tooli ng geometry and are not for stress an alysis. The same CAD pro

21、gram using 4-node shell eleme nts was employed to con struct the mesh system for the sheet bla nk. Figure 2 shows the mesh system for the complete set of tooli ng and the sheet-bla nk used in the stamp ing of a tapered square cup. Owing to the symmetric con diti ons, only a quarter of the square cup

22、 is an alysed. In the simulation, the sheet blank is put on the blank-holder and the die is moved down to clamp the sheet bla nk aga inst the bla nk-holder. The punch is the n moved up to draw the sheet metal into the die cavity.In order to perform an accurate fin ite-eleme nt an alysis, the actual

23、stress train relati on ship of the sheet metal is required as part of the in put data .In the prese nt study, sheet metal with deep-draw ing quality is used in the simulati on s.A ten sile test has bee n con ducted for the specime ns cut along pla nes coin cidi ng with the rolli ng direct ion (0

24、76; ) and at an gles of 45° and 90° to the rolli ng direct ion. The average flow stress calculated from the equatio n (r= (0+245+ d 90, for eachmeasured true stra in,as show n in Fig.3, is used for the simulati ons for the stamp ings of the tapered square cup and also for the stepped recta

25、 ngular cup.All the simulati ons performed in the prese nt study were run on an SGI In digo 2 workstati on using the fin ite-eleme nt program PAMFSTAMP. To complete the set of in put data required for the simulati ons, the punch speed is set to 10 m s_1 and a coefficie nt of Coulomb fricti on equal

26、to 0.1 is assumed.Fig. 2. Fin ite-eleme nt mesh.Fig. 3. The stress -stra in relatio nship for the sheet metal.3. Wrinkling in a Tapered Square CupA sketch in dicati ng some releva nt dime nsions of the tapered square cup is show n in Fig. 1(a). Asseen in Fig. 1( a), the length of each side of the sq

27、uare punch head (2 Wp), the die cavity opening (2Wd), and the drawing height (H) are considered as the crucial dimensions that affect the wrinkling.Half of the difference between the dimensions of the die cavity opening and the punch head is termed the die gap ( G) in the present study, i.e. G = Wd-

28、Wp. The extent of the relatively un supported sheet metal at the draw wall is presumably due to the die gap, and the wrin kles are supposed to be suppressed by in creas ing the bla nk-holder force. The effects of both the die gap and the blank-holder force in relation to the occurrence of wrinkling

29、in the stamping of a tapered square cup are in vestigated in the follow ing sect ions.3.1 Effect of Die GapIn order to exam ine the effect of die gap on the wrin kli ng, the stamp ing of a tapered square cup with three different die gaps of 20 mm, 30 mm, and 50 mm was simulated. In each simulation,

30、the die cavity opening is fixed at 200 mm, and the cup is drawn to the same height of 100 mm. The sheet metal used in all three simulations is a 380 mm 380 mm square sheet with thickness of 0.7 mm, the stress -strain curve for the material is shown in Fig. 3.Fig. 4. Wrinkling in a tapered square cup

31、 ( G =50 mm).The simulation results show that wrinkling occurred in all three tapered square cups, and the simulated shape of the draw n cup for a die gap of 50 mm is show n in Fig. 4. It is see n in Fig. 4 that the wrinkling is distributed on the draw wall and is particularly obvious at the corner

32、between adjace nt walls. It is suggested that the wrin kli ng is due to the large un supported area at the draw wall during the stamping process,also,the side length of the punch head and the die cavity ope nin gare differe nt owing to the die gap. The sheet metal stretched betwee n the punch head a

33、nd the die cavity shoulder becomes un stable owing to the prese nce of compressive tran sverse stresses. The uncon stra ined stretchi ng of the sheet metal un der compressi on seems to be the main cause for the wrin kli ng at the draw wall. In order to compare the results for the three differe nt di

34、e gaps, the ratio 4 3 of the two principal strains is introduced, 3 being min/ emax, where max and min are the major and the minor prin cipal stra ins, respectively. Hosford and Caddell 5 have show n that if the absolute value of 3 is greater than a critical value, wrinkling is supposed to occur, an

35、d the larger the absolute value of 3 the greater is the possibility of wrinkling.The 3 values along the cross-sect ion M -N at the same draw ing height for the three simulatedshapes with differe nt die gaps, as marked in Fig. 4, are plotted in Fig. 5. It is no ted from Fig. 5 that severe wrinkles ar

36、e located close to the corner and fewer wrinkles occur in the middle of the draw wall for all three differe nt die gaps. It is also no ted that the bigger the die gap, the larger is the absolute value of BCon seque ntly,i ncreas ing the die gap will in crease the possibility of wrin kli ng occurri n

37、g at the draw wall of the tapered square cup.3.2 Effect of the Blank-Holder ForceIt is well known that in creas ing the bla nk-holder force can help to elim in ate wrin kli ng in the stamp ing process. In order to study the effective ness of in creased bla nk-holder force, the stamp ing of a tapered

38、 square cup with die gap of 50 mm,which is associated with severe wrinkling as stated above, was simulated with different values of blank-holder force. The blank-holder force was in creased from 100 kN to 600 kN,which yielded a bla nk-holder pressure of 0.33 MPa and 1.98MPa, respectively. The remain

39、ing simulation conditions are maintained the same as those specified in the previous sect ion. (An in termediate bla nk-holder force of 300 kN was also used in the simulation.)The simulatio n results show that an in crease in the bla nkholder force does not help to elimi nate the wrin kli ng that oc

40、curs at the draw wall.The3 values along the cross-secti on compared with oneano ther for the stamp ing processes with bla nk-holder force of 100 kN and 600 kN. The simulati on results in dicate that the _ values along the cross-sect ion M are almost ide ntical in both cases. In order to exam ine the

41、 differe nee of the wrin kle shape for the two differe nt bla nk-holder forces, five cross-sect ions of thedraw wall at different heights from the bottom to the lineM -N, as marked in Fig. 4, are plotted inFig. 6 for both cases .It is no ted from Fig. 6 that the wavi ness of the cross-sect ions for

42、both cases is similar. This indicates that the blank-holder force does not affect the occurrence of wrinkling in the stamping of a tapered square cup, because the formation of wrinkles is mainly due to the large unsupported area at the draw wall where large compressive transverse stresses exist. The

43、 bla nkholder force has no in flue nce on the in stability mode of the material betwee n the punch head and the die cavity shoulder.Dista nce(mm)Fig. 5. 3-value along the cross-sect ion M -N for differe nt die gaps.Fig. 6. Cross-secti on lines at differe nt heights of the draw wall for different bla

44、nk-holder forces. ( a) 100 kN. ( b) 600 kN.4. Stepped Rectangular CupIn the stamp ing of a stepped recta ngular cup, wrin kli ng occurs at the draw wall even though the die gaps are not so significant.Figure 1( b) shows a sketch of a punch shape used for stamping a stepped rectangular cup in which t

45、he draw wall C is followed by a step D -E. An actual production part that has this type of geometry was exam ined in the prese nt study. The material used for this product ion part was 0.7 mm thick, and the stress-strain relati on obta ined from ten sile tests is show n in Fig. 3.The procedure in th

46、e press shop for the producti on of this stamp ing part con sists of deep draw ing followed by trimming.In the deep drawing process, no draw bead is employed on the die surface to facilitate the metal flow. However, owing to the small punch corner radius and complex geometry, a split occurred at the

47、 top edge of the punch and wrin kles were found to occur at the draw wall of the actual producti on part,as show n in Fig. 7. It is see n from Fig. 7 that wrin kles are distributed on the draw wall, but are more severe at the corner edges of the step, as marked by A -D and B -E in Fig. 1( b).The met

48、al is torn apart along the whole top edge of the punch,as shown in Fig. 7, to form a split.Fig. 7. Split and wrin kles in the producti on part.Fig. 8. Simulated shape for the product ion part with split and wrin kies.In order to provide a further understanding of the deformation of the sheet-blank d

49、uring the stamp ing process, a fin iteeleme nt an alysis was con ducted. The fin ite-eleme nt simulati on was first performed for the origi nal desig n. The simulated shape of the part is show n from Fig. 8. It is no ted from Fig.8 that the mesh at the top edge of the part is stretched significantly

50、, 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 edge A -B, and the radius of the punch corner A, as marked in Fig.1(b), are con sidered to be the major reas ons for the wall breakage. However, acco

51、rd ing to the results of the finiteelement analysis, splitting can be avoided by increasing the above-mentioned radii. This con cept was validated by the actual product ion part manu factured with larger corner radii.Several attempts were also made to eliminate the wrinkling.First, the blank-holder

52、force was in creased to twice the origi nal value. However, just as for the results obta ined in the previous sect ion for the draw ing of tapered square cup, the effect of bla nk-holder force on the elim in ati on of wrinkling was not found to be significant. The same results are also obtained by i

53、ncreasing the friction or in creas ing the bla nk size. We con clude that this kind of wrin kli ng cannot be suppressed by in creas ing the stretch ing force.Since wrin kles are formed because of excessive metal flow in certa in regi ons, where the sheet is subjected to large compressive stresses, a

54、 straightforward method of elim in ati ng the wrin kles is to add drawbars in the wrinkled area to absorb the redundant material. The drawbars should be added parallel to the direct ion of the wrin kles so that the redundant metal can be absorbed effectively. Based on this con cept, two drawbars are

55、 added to the adjace nt walls, as show n in Fig. 9, to absorb the excessive material. The simulatio n results show that the wrin kles at the corner of the step are absorbed by the drawbars as expected, however some wrin kles still appear at the rema ining wall. This in dicates the n eed to put more

56、drawbars at the draw wall to absorb all the excess material. This is, however,not permissible from considerations of the part design.Fig. 9. Drawbars added to the draw walls.One of the advantages of using finite-element analysis for the stamping process is that the deformed shape of the sheet bla nk

57、 can be mon itored throughout the stamp ing process, which is not possible in the actual product ion process. A close look at the metal flow duri ng the stamp ing process reveals that the sheet bla nk is first draw n into the die cavity by the punch head and the wrinkles are not formed until the she

58、et blank touches the step edge D marked in Fig. 1( b). The wrinkled shape is shown in Fig. 10. This provides valuable information for a possible modification of die desig n.Fig. 10. Wrin kle formed whe n the sheet bla nk touches the steppededge.Fig. 11. Cut-off of the stepped corner.Fig. 12. Simulat

59、ed shape for the modified die desig n.An in itial surmise for the cause of the occurre nee of wrin kli ng is the uneven stretch of the sheet metal between the punch corner radius A and the step corner radius D, as indicated in Fig. 1( b). Therefore a modification of die design was carried out in which the step corner was cut off, as shown in Fig.11, so that the stretch condition is changed favourably, which allows more stretch to be applied by i