1、机械行业电子类文献原文英文版机械行业电子类文献原文(英文版) 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 and stepp
2、ed 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, on the oc
3、currence 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 stamping of a
4、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 eliminating the w
5、rinkles 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 die design
6、.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 are three t
7、ypes 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 occurrence of w
8、rinkles 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 prevent wr
9、inkling,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 below that whi
10、ch 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 formation of wr
11、inkles, 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 the non-u
12、niform 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. Narayanasamy an
13、d 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 forming o
14、perations 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 study, the
15、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 each side of
16、 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 of a steppe
17、d 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 analysis, and an
18、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 tooling geometry
19、, 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 be rigid,
20、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 sheet-blan
21、k 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 moved up to dr
22、aw 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 test has been
23、 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 the stampings
24、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 set to 10 m s_
25、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 in Fig. 1(a)
26、, 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 die gap (G) i
27、n 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 relation to
28、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 was simulated.
29、 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. Wrinkling in a
30、 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 particularly obvious
31、 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 between the punch
32、 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 different die ga
33、ps, 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 larger the
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