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1、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 cups

2、 and stepped rectangular cups is investigated. A common characteristic of these two types of wrinkling is that the wrinkles are found at the draw wall that is relatively unsupported.In the stamping of a tapered square cup, the effect of process parameters, such as the die gap and blank-holder force,

3、 on the occurrence of wrinkling is examined using finiteelement simulations. The simulation 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 that occurred in the stam

4、ping of a stepped rectangular cup, an actual production part that has a similar type of geometry was examined. The wrinkles found at the draw wall are attributed to the unbalanced stretching of the sheet metal between the punch head and the step edge. An optimum die design for the purpose of elimina

5、ting the wrinkles is determined using finite-element analysis. The good agreement between the simulation results and those observed in the wrinkle-free production part validates the accuracy of the finite-element analysis, and demonstrates the advantage of using finite-element analysis for stamping

6、die design.Keywords: Draw-wall wrinkle; Stamping die; Stepped rectangular cup; Tapered square cups1. IntroductionWrinkling is one of the major defects that occur in the sheet metal forming process. For both functional and visual reasons,wrinkles are usually not acceptable in a finished part. There a

7、re three types of wrinkle which frequently occur in the sheet metal forming process: flange wrinkling, wall wrinkling, and elastic buckling of the undeformed area owing to residual elastic compressive stresses. In the forming operation of stamping a complex shape, draw-wall wrinkling means the occur

8、rence of wrinkles in the die cavity. Since the sheet metal in the wall area is relatively unsupported by the tool, the elimination of wall wrinkles is more difficult than the suppression of flange wrinkles. It is well known that additional stretching of the material in the unsupported wall area may

9、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 blank-holder force must lie within a narrow range, above that necessary to suppress wrinkles on the one hand, and belo

10、w that which produces fracture on the other. This narrow range of blank-holder force is difficult to determine. For wrinkles occurring in the central area of a stamped part with a complex shape, a workable range of blank-holder force does not even exist.In order to examine the mechanics of the forma

11、tion of wrinkles, Yoshida et al. 1 developed a test in which a thin plate was non-uniformly stretched along one of its diagonals.They also proposed an approximate theoretical model in which the onset of wrinkling is due to elastic buckling resulting from the compressive lateral stresses developed in

12、 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 according to their theoretical analysis, whereas the experimental results indicated four to six wrinkles. Naray

13、anasamy and Sowerby 4examined the wrinkling of sheet metal when drawing it through a conical die using flat-bottomed and hemispherical-ended punches. They also attempted to rank the properties that appeared to suppress wrinkling.These efforts are focused on the wrinkling problems associated with the

14、 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 forming process made it possible to analyse the wrinkling problem involved in stamping complex shapes. In the present s

15、tudy, the 3D finite-element method was employed to analyse the effects of the process parameters on the metal flow causing wrinkles at the draw wall in the stamping of a tapered square cup, and of a stepped rectangular part.A tapered square cup, as shown in Fig. 1(a), has an inclined draw wall on ea

16、ch side of the cup, similar to that existing in a conical cup. During the stamping process, the sheet metal on the draw wall is relatively unsupported, and is therefore prone to wrinkling. In the present study, the effect of various process parameters on the wrinkling was investigated. In the case o

17、f a stepped rectangular part, as shown in Fig. 1(b),another type of wrinkling is observed. In order to estimate the effectiveness of the analysis, an actual production part with stepped geometry was examined in the present study. The cause of the wrinkling was determined using finite-element analysi

18、s, and an optimum die design was proposed to eliminate the wrinkles. The die design obtained from finite-element analysis was validated by observations on an actual production part.Sketches of (a) a tapered square cup. Sketches of(b) a stepped rectangular cup.Fig. 1.2. Finite-Element ModelThe toolin

19、g geometry, including the punch, die and blankholder,were designed using the CAD program PRO/ENGINEER. Both the 3-node and 4-node shell elements were adopted to generate the mesh systems for the above tooling using the same CAD program. For the finite-element simulation,the tooling is considered to

20、be rigid, and the corresponding meshes are used only to define the tooling geometry and are not for stress analysis. The same CAD program using 4-node shell elements was employed to construct the mesh system for the sheet blank. Figure 2 shows the mesh system for the complete set of tooling and the

21、sheet-blank used in the stamping of a tapered square cup. Owing to the symmetric conditions, only a quarter of the square cup is analysed. In the simulation, the sheet blank is put on the blank-holder and the die is moved down to clamp the sheet blank against the blank-holder. The punch is then move

22、d up to draw the sheet metal into the die cavity.In order to perform an accurate finite-element analysis, the actual stressstrain relationship of the sheet metal is required as part of the input data.In the present study, sheet metal with deep-drawing quality is used in the simulations.A tensile tes

23、t has been conducted for the specimens cut along planes coinciding with the rolling direction (0) and at angles of 45and 90to the rolling direction.The average flow stress ,calculated from the equation =（0+245+90）/4, for each measured true strain,as shown in Fig.3, is used for the simulations for th

24、e stampings of the tapered square cup and also for the stepped rectangular cup. All the simulations performed in the present study were run on an SGI Indigo 2 workstation using the finite-element program PAMFSTAMP. To complete the set of input data required for the simulations, the punch speed is se

25、t to 10 m s_1 and a coefficient of Coulomb friction equal to 0.1 is assumed.Fig. 2. Finite-element mesh.Fig. 3. The stressstrain relationship for the sheet metal.3. Wrinkling in a Tapered Square CupA sketch indicating some relevant dimensions of the tapered square cup is shown in Fig. 1(a). As seen

26、in Fig. 1(a), the length of each side of the square punch head (2Wp), 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 d

27、ie gap (G) in the present study, i.e. G = Wd-Wp. The extent of the relatively unsupported sheet metal at the draw wall is presumably due to the die gap, and the wrinkles are supposed to be suppressed by increasing the blank-holder force. The effects of both the die gap and the blank-holder force in

28、relation to the occurrence of wrinkling in the stamping of a tapered square cup are investigated 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 die gaps of 20 mm, 30 mm, and 50 mm wa

29、s simulated. In each simulation, 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 stressstrain curve for the material is shown in Fig. 3.Fig. 4. Wr

30、inkling in a tapered square cup (G =50 mm).The simulation results show that wrinkling occurred in all three tapered square cups, and the simulated shape of the drawn cup for a die gap of 50 mm is shown in Fig. 4. It is seen in Fig. 4 that the wrinkling is distributed on the draw wall and is particul

31、arly obvious at the corner between adjacent walls. It is suggested that the wrinkling is due to the large unsupported area at the draw wall during the stamping process,also,the side length of the punch head and the die cavity openingare different owing to the die gap. The sheet metal stretched betwe

32、en the punch head and the die cavity shoulder becomes unstable owing to the presence of compressive transverse stresses. The unconstrained stretching of the sheet metal under compression seems to be the main cause for the wrinkling at the draw wall. In order to compare the results for the three diff

33、erent die gaps, the ratio of the two principal strains is introduced, being min/max, where max and min are the major and the minor principal strains, respectively. Hosford and Caddell 5 have shown that if the absolute value of is greater than a critical value, wrinkling is supposed to occur, and the

34、 larger the absolute value of , the greater is the possibility of wrinkling.The values along the cross-section MN at the same drawing height for the three simulated shapes with different die gaps, as marked in Fig. 4, are plotted in Fig. 5. It is noted from Fig. 5 that severe wrinkles are located cl

35、ose to the corner and fewer wrinkles occur in the middle of the draw wall for all three different die gaps. It is also noted that the bigger the die gap, the larger is the absolute value of . Consequently,increasing the die gap will increase the possibility of wrinkling occurring at the draw wall of

36、 the tapered square cup.3.2 Effect of the Blank-Holder ForceIt is well known that increasing the blank-holder force can help to eliminate wrinkling in the stamping process. In order to study the effectiveness of increased blank-holder force, the stamping of a tapered square cup with die gap of 50 mm

37、,which is associated with severe wrinkling as stated above, was simulated with different values of blank-holder force. The blank-holder force was increased from 100 kN to 600 kN,which yielded a blank-holder pressure of 0.33 MPa and 1.98 MPa, respectively. The remaining simulation conditions are main

38、tained the same as those specified in the previous section.（An intermediate blank-holder force of 300 kN was also used in the simulation.）The simulation results show that an increase in the blankholder force does not help to eliminate the wrinkling that occurs at the draw wall.The values along the c

39、ross-section compared with one another for the stamping processes with blank-holder force of 100 kN and 600 kN. The simulation results indicate that the _ values along the cross-section MN are almost identical in both cases. In order to examine the difference of the wrinkle shape for the two differe

40、nt 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-sections for both cases is similar. This indicates that the blank-holder f

41、orce 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 blankholder force has no influence on the instability mode o

42、f the material between the punch head and the die cavity shoulder.Distance(mm)Fig. 5. -value along the cross-section MN for different die gaps.Fig. 6. Cross-section lines at different heights of the draw wall fordifferent blank-holder forces. (a) 100 kN. (b) 600 kN.4. Stepped Rectangular CupIn the s

43、tamping of a stepped rectangular cup, wrinkling 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 the draw wall C is followed by a step DE. An actual production part that has this t

44、ype of geometry was examined in the present study. The material used 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 this stamping part consists of deep drawing followed by t

45、rimming.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 top edge of the punch and wrinkles were found to occur at the draw wall of the actual productio

46、n part,as shown in Fig. 7. It is seen from Fig. 7 that wrinkles are distributed on the draw wall, but are more severe at the corner edges 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.Fig. 7. Split a

47、nd wrinkles in the production part.Fig. 8. Simulated shape for the production part with split and wrinkles.In order to provide a further understanding of the deformation of the sheet-blank during the stamping process, a finiteelement analysis was conducted. The finite-element simulation was first pe

48、rformed for the original design. The simulated shape 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 stretched significantly, and that wrinkles are distributed at the draw wall,similar to those observed in the actual part.The small punch radius,

49、such as the radius along the edge AB, and the radius of the punch corner A, as marked in Fig.1(b), are considered to be the major reasons for the wall breakage. However, according to the results of the finiteelement analysis, splitting can be avoided by increasing the above-mentioned radii. This concept was validated by the actual production part manufactured with larger corner radii.Several attempts were also made to eliminate the wrinkling