拉深模设计中拉深壁起皱的分析--外文翻译.doc

毕业设计(论文)外文资料翻译

学院(系)：
专 业：
姓 名：
学 号：
外文出处： Analysis of Draw-Wall Wrinkling
in a Stamping Die Design
附 件： 1.外文资料翻译译文；2.外文原文。

指导教师评语：

签名：
年 月 日
注：请将该封面与附件装订成册。

附件1：外文资料翻译译文
拉深模设计中拉深壁起皱的分析
起皱是金属板料成形中常见的失效形式之一。由于功能和视觉效果的原因，起皱通常是不能为零件制品所能接受的。在金属板料成形加工中通常存在三种类型的起皱现象：法兰起皱；侧壁起皱和由于残余压应力在未变形区产生的弹性变形。在冲压复杂形状的时候，拉深壁起皱就是在模具型腔中形成的褶皱。由于金属板料在拉深壁区域内相对无支撑，因此，消除拉深壁起皱比抑制法兰起皱要难得多。我们知道在不被支撑的拉深壁区域中材料的外力拉深可以防止起皱，这可以在实践中通过增加压边力而实现，但是运用过大的拉深力会引起破裂失效。因此，压边力必须控制在一定的范围内，一方面可以抑制起皱，另一方面也可以防止破裂失效。合适的压边力范围是很难确定的，因为起皱在拉深零件的中心区域以一个复杂的形状形成，甚至根本不存在一个合适的压边力范围。
为了研究起皱的原因，Yoshida et al.发明了一个试验，即：一张薄板延着对角的一个方向进行不均匀拉深。他们还提出了一个近似的理论模型，起皱的初始是由于弹性变形导致横向压力发展成为不均匀的压力场。Yu et al.用试验和理论分析的方法来研究起皱问题。他们发现根据他们的理论分析，起皱发生在两个环形的起伏处，而且试验结果指出了4—6处起皱。Narayanasamy和Sowerby通过圆锥形凸模和半球形凸模的拉深来研究金属板料的起皱。同时，他们也试图整理防止发生起皱的特性参数。
一个有斜度的方形盒，如图1（a）所示，盒形件的每一个倾斜的拉深壁都与圆锥盒形件相似。拉深成形过程中，在拉深壁处的金属板料是相对无支撑的，因此，褶皱是倾斜的。在目前的研究中，各种关于起皱的成型过程参数都被研究。在带有阶梯的方形盒件的研究中，如图1（b）所示，观察到了另一种类型的起皱。在当前的研究中，为了得出分析的效果，实际生产用阶梯形结构的零件来研究。使用有限元方法可以分析出起皱的原因，并且可以使一个最优的模具设计消除起皱现象。有限元分析使得模具设计在实际生产中更为合理化。

（a）带有斜度的方形盒件 （b）带有阶梯的方形盒件
图1
1 有限元模型
模具的几何结构（包括凸模、凹模、压边装置等等），通过使用CAD和PRO/ENGINEER来设计。使用CAD将3个节点或4个节点形成壳形的单体，进而在模型上形成网格体系。使用有限元模拟，模型被视为是刚性的，并且相对应的网格仅仅可以定义模型的几何形状，不能对压力进行分析。使用CAD所建立的4个节点的壳形单体可以为板料创建网格体系。图2给出了模型完全建立时的网格体系和用以成形带有斜度的方形盒件的金属板料。由于对称的原因，仅仅分析了零件的1/4。在模拟过程中，金属板料放在压边装置上，凹模向下移动，夹紧板料。凸模向上移动，拉深板料至模具型腔。
为了精确的完成有限元分析，金属板料的实际压力——拉力的关系需要输入相关的数据。从目前的研究来看，金属板料的深拉深的特性参数已经用于模拟。一个拉深的实验已经用于样品的生产，并且沿着压延方向和与压延方向成45°和90°的方向切断。平均的流动压力σ可以通过公式σ=（σ0+2σ45+σ90）/4，计算出来，进而准确测量出实际拉力，如图2所示，以用于带有斜度的方形盒件和带有阶梯的方形盒件的拉深。

图2
目前研究中的所有模拟都在SGI Indigo2工作站使用有限元可调拉深程序完成。完成了用于模拟所需数据的输入（假定凹模速度为10m /s，并且平均摩擦系数为0.1）。
2 带有斜度的方形盒件的起皱
2.1 凸模间隙的影响
为了研究凸模间隙对起皱的影响，现在分别用凸模间隙为20mm，30mm和50mm的带有斜度的方形盒进行拉深模拟。在每次模拟拉深中，凹模口部尺寸为200mm固定不变，并且拉深高度均为100mm。在3次模拟中，均使用尺寸为380mm×380mm的方形板料，且板料厚度均为0.7mm，凹模对板料的压力——拉力关系，如图3所示。

图.3
模拟结果表明：三个有斜度的方形盒均发生了起皱现象，图3给出了凸模间隙为50mm的方形盒的形状。从图3可以看出，起皱分布在拉深壁处，并且拉深壁邻近的拐角处起皱现象尤为严重。经分析，在拉深过程中，起皱是由于拉深壁处存在过大的无支撑区域，而且凸模顶部和凹模口部长度的不同是由于凸模间隙的存在。在凸模顶部与凹模之间的金属板料的延伸变得不稳定，是由于断面压力的存在。在压力作用下，金属板料的无约束拉深是在拉深壁处形成褶皱的主要原因。为了比较三个不同凸模间隙的试验结果，需要引入两个主应力的比值β，β为ε min/ε max, ε min/ε max是主应力相对的最小值和最大值。Hosford和Cadde指出，β值比临界值更重要，如果起皱发生，那么β值越大，起皱现象就可能越严重。如图4和图4的曲线所示，三次不同凸模间隙的拉深模拟，沿M——N截面的相同拉深高度处的β值。从图4可以看出，在3次模拟中位于拉深壁的拐角处起皱比较严重，在拉深壁的中间起皱比较弱。还可以看出，凸模间隙越大，比值β就越大。因此，增加凸模间隙将可能增加带有斜度的方形盒件在拉深壁处起皱的可能性。
2.2 压边力的影响
众所周知，增加压边力可以帮助削弱拉深过程中发生的褶皱。为了研究增加压边力的影响，采用凸模间隙为50mm，不同的压边力数值来对有斜度的方形盒进行拉深起皱的模拟。压边力从100KN增加到600KN，以提供压边力0.33Mpa到1.98Mpa。其他模拟条件和先前的规定保持一致（在模拟当中采用了300KN的压边力）。
模拟结果表明：增加压边力并不能消除拉深壁处起皱现象的发生。如图4所示，在M-N截面处的β值，和压边力分别为100KN、600KN的拉深相比较，模拟结果指出，在M-N截面处的β值都是相同的。为了分析两次不同压边力时出现起皱的不同，从拉深壁顶部到直线M-N处，对5处不同高度截面进行了分析，如图4所示，图5给出了所有情况的曲线。从图5可以看出，几种情况截面处的波度是相似的。这就证明压边力与有斜度的方形盒件拉深中的起皱现象无关，因为褶皱的形成主要是由于拉深壁处大面积无支撑区域存在较大的横断面压力，所以压边力并不影响凸模顶部与凹模肩部之间的制件形状的不稳定状况。

图4 图5 (a )100KN.(b)600KN.
3 带有阶梯的方形盒件
在带有阶梯的方形盒件的拉深中，即使凸模间隙不是这样重要，而在拉深壁处仍然会发生起皱。图1（b）所示为带有阶梯的方形盒件拉深用的凸模，图1（b）给出了拉深壁C和阶梯处D、E。目前，实际生产中一直在研究这种类型的几何结构。生产中，板料的厚度为0.7mm，压力-拉力关系从应力试验中获得。
这种拉深件的生产是通过深拉深和整形两个工序组成的。由于凸模拐角处的小圆角半径和复杂的几何结构，导致在盒形件的顶部边缘发生破裂，在盒形件的拉深壁处发生褶皱，如图6所示。从图6中可以看出，褶皱分布在拉深壁处，尤其在阶梯边缘的拐角处更为严重，如图1（b）所示的A-D和B-E处。金属板料在凸模顶部的边缘开裂，进而形成破裂，如图6所示。

图6 图7
为了对拉深过程中金属板料出现的变形现象有更进一步的了解，生产中仍然采用了有限元分析方法。最初的设计已经用有限元模拟完成。模拟的盒形件外形如图7所示。从图7可以看出，盒形件顶部边缘的网络拉深比较严重，褶皱分布在拉深壁处，这与实际生产中的状况是一致的。
小的凸模圆角，例如A-B边缘的圆角和凸模拐角A处的圆角，如图1（b）所示，是拉深壁处破裂的主要原因。然而，根据有限元分析的结果，通过加大上述两处圆角可以避免破裂的产生。较大的拐角圆角这种想法通过实际生产加工被验证是可行的。
在拉深工序中采用有限元分析的优点之一就是可以通过拉深模拟来监视、控制金属板料的形状变形，而这些在实际生产中是不可能做到的。在拉深过程中，仔细地看金属板料的流动，可以看出金属板料首先由凸模拉深进凹模腔内，直到金属板料到阶梯边缘D——E处时，褶皱才开始形成。褶皱的形状如图8所示。有限元分析还可以为模具设计的改进提供相关的数据信息。、

图8
4 简要论点及结束语
在拉深过程中发生的两种类型的褶皱通过有限元分析研究以及对起皱原因做的试验，最终发现了抑制起皱的方法。
第一种类型的起皱出现在带有斜度的方形盒件的拉深壁处。在凹模口部的高度尺寸和凸模顶部的高度尺寸等因素中，起皱的发生归因于较大的凸模间隙。较大的凸模间隙会导致拉深到凸模顶部与凹模肩部的金属板料处产生较大的无支撑区域，而金属板料较大的无支撑区域是形成起皱的最终原因。有限元模拟表明这种类型的起皱是不能通过增加压边力而抑制的。
另一种类型的起皱发生在实际生产中带有阶梯的几何结构的方形盒件中。研究发现即使凸模间隙影响不是很重要，起皱还是会发生在阶梯上面的拉深壁处。根据有限元分析，起皱的原因主要是由于凸模顶部和台阶边缘之间的不均匀拉深造成的。为了避免起皱，在模具设计中使用有限元模拟做了一些试验，试验最终确定的最优设计就是将阶梯去除。修改后的模具设计生产出了无缺陷的盒形零件。模具分析的结果和实际生产所获得的结论证明了有限元分析的准确性和使用有限元模拟的有效性。因此，可以说：有限元方法可以取代传统的实际生产试验的昂贵的方法。
附件2：外文原文
An Analysis of Draw-Wall Wrinkling in a Stamping Die Design
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 blank-holder 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 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-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 punches. They also attempted to rank the properties that appeared to suppress wrinkling.
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.

Fig.1
1. Finite-Element Model
The 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 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 data. In the present study, sheet metal with deep-drawing quality is used in the simulations. A 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 direction. The average flow stress, calculated from the equation σ=（σ0+2σ45+σ90）/4, for each measured true strain, as shown in Fig. 2, is used for the simulations for the stampings of the tapered square cup and also for the stepped rectangular cup.

Fig.2
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 10m /s and a coefficient of Coulomb friction equal to 0.1 is assumed.
2. Wrinkling in a Tapered Square Cup
2.1 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 0.7 mm, the stress–strain curve for the material is shown in Fig. 3.

Fig 3
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 opening are different owing to the die gap. The sheet metal stretched between 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 different 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 larger the absolute value of _, the greater is the possibility of wrinkling．
The _ 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 _. Consequently,　increasing the die gap will increase the possibility of wrinkling　occurring at the draw wall of the tapered square cup.
2.2 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 0.33 MPa and 1.98　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 wall. The _ values along the cross-section　M–N, as marked in Fig. 4, are 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 M–N are almost identical in both cases. In　order to examine the difference of the wrinkle shape for the　two different blank-holder forces, five cross-sections of the　draw wall at different heights from the bottom to the line M–N, as marked in Fig. 4, are plotted in Fig. 5 for both cases.　It is noted from Fig. 5 that the waviness of the cross-sections　for 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 blank-holder　force has no influence on the instability mode of the material between the punch head and the die cavity shoulder.

Fig 4 Fig 5

3. Stepped Rectangular Cup
In the stamping 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 D–E. An actual production part that has this type of geometry was examined in the present study. The material used for this production part was 0.7 mm thick, and the stress–strain relation obtained from tensile tests .
The procedure in the press shop for the production of this stamping part consists of deep drawing 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 top edge of the punch and wrinkles were found to occur at the draw wall of the actual production part, as shown in Fig. 6. It is seen from Fig. 6 that wrinkles 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 metal is torn apart along the whole top edge of the punch