2025年机械行业电子类文献原文英文版.docx

该【2025年机械行业电子类文献原文英文版 】是由【梅花书斋】上传分享，文档一共【12】页，该文档可以免费在线阅读，需要了解更多关于【2025年机械行业电子类文献原文英文版 】的内容，可以使用淘豆网的站内搜索功能，选择自己适合的文档，以下文字是截取该文章内的部分文字，如需要获得完整电子版，请下载此文档到您的设备，方便您编辑和打印。编号：
时间：x月x曰
书山有路勤为径，学海无涯苦作舟
页码：

Int J Adv Manuf Technol () 19:253–259
 Springer-Verlag London Limited
An Analysis of Draw-Wall Wrinkling in a Stamping Die Design
F.-K. Chen and Y.-C. Liao
Department of Mechanical Engineering, National Taiwan University, Taipei, Taiwan
Wrinkling that occurs in the stamping of tapered square cups 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 the stamping of a tapered square cup, the effect of process parameters, such as the die gap and blank-holder force, 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 stamping 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 eliminating 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 die design.
Keywords: Draw-wall wrinkle; Stamping die; Stepped rectangular cup; Tapered square cups
1. Introduction
Wrinkling 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 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 occurrence 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 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 below 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 formation of wrinkles, Yoshida et al. [1] developed a test in which a thin plate was non-uniformly stretched along one of its 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-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. Narayanasamy and Sowerby [4]
examined the wrinkling of sheet metal when drawing it through a conical die using flat-bottomed and hemispherical-ended
编号：
时间：x月x曰
书山有路勤为径，学海无涯苦作舟
页码：

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 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 study, 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 each 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 of 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 analysis, 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.
编号：
时间：x月x曰
书山有路勤为径，学海无涯苦作舟
页码：

Sketches of(b) a stepped rectangular cup.
Fig. 1.
2. Finite-Element Model
The tooling 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 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 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 moved up to draw the sheet metal into the die cavity.
In order to perform an accurate finite-element analysis, the actual stress–strain relationship of the sheet metal is required as part of the input the present study, sheet metal with deep-drawing quality is used in the tensile test has been conducted for the specimens cut along planes coinciding with the rolling direction (0°) and at angles of 45°and 90°to the rolling average flow stress σ,calculated from the equation σ=（σ0+2σ45+σ90）/4, for each measured true strain,as shown in , is used for the simulations for the 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 set to 10 m s_1 and a coefficient of Coulomb friction equal to is assumed.
Fig. 2. Finite-element mesh.
编号：
时间：x月x曰
书山有路勤为径，学海无涯苦作舟
页码：

Fig. 3. The stress–strain relationship for the sheet metal.
3. Wrinkling in a Tapered Square Cup
A sketch indicating some relevant dimensions of the tapered square cup is shown in Fig. 1(a). As seen 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 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, . 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 the occurrence of wrinkling in the stamping of a tapered square cup are investigated in the following sections.
Effect of Die Gap
In 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. 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 mm, the stress–strain curve for the material is shown in Fig. 3.
Fig. 4. Wrinkling 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 particularly 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 between the punch head and the die cavity shoulder
编号：
时间：x月x曰
书山有路勤为径，学海无涯苦作舟
页码：

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 gaps, the ratio 5β of the two principal strains is introduced, β being εmin/εmax, where εmax and εmin are the major and the minor principal strains, respectively. Hosford and Caddell [5] have shown that if the absolute value of β is greater than a critical value, wrinkling is supposed to occur, and the larger the absolute value of β, the greater is the possibility of wrinkling.
The β values along the cross-section M–N 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 close 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 β. Consequently,increasing the die gap will increase the possibility of wrinkling occurring at the draw wall of the tapered square cup.
Effect of the Blank-Holder Force
It 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,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 MPa and MPa, respectively. The remaining simulation conditions are maintained 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 β values along the cross-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 a