板料冲压过程中表面低缺陷的机理外文文献翻译、中英文翻译
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The Mechanism of Surface Low Defect in Sheet Metal Stamping Hongqing Shen1,2 a, Shuhui Li1,2 b and Guanlong Chen1,c 1Auto Body Manufacturing Technology Center, School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai 200240, PR China 2State Key Laboratory of Mechanical System and Vibration, Shanghai 200240, PR China ashenhongqing82, blishuhui, cglchen Keywords: surface low; surface deflection; stamping; sheet metal forming; local buckling. Abstract. In this paper, the mechanism of surface low defect in sheet metal stamping is studied. Firstly, we simulate the forming procedure of a stamping component by Finite Element Method (FEM) to observe the growth of surface low defect. And then, we establish an analytical model and deduce the critical stress for local buckling. Finally, we take advantage of the critical stress to detect local buckling areas in the component. The FE simulation result shows that during springback the non-uniform displacement in the thickness direction forms surface low. Moreover, the detected local buckling area agrees with the experimental surface low area. This indicates that the essence of surface low phenomenon is panels local buckling under the residual compressive stress during springback. Introduction Surface low defects are small local deflections in large flat panels containing sudden shape changes. They have a great influence on automobiles appearance. These defects are strictly detected and controlled in body manufacturing. Liu et al. 1 proposed an optical reflection method to evaluate the surface low defect in pressed automobile panels. Andersson 2 used an optical system, called WMS-system, to detect surface low in a sample stamping panel. In addition he also used stylus measurement in his experiment. Fu et al. 3 used stoning method to detect surface low defects around the corner of an embossment. With the development of finite element method, it becomes possible to predict surface low by numerical analysis. Fukumura et al. 4 simulated surface low defects in an automobile door exterior panel. Park et al. 5 developed a curvature-based algorithm to visualize the surface low defects in simulation. Hu et al. 6 developed a stoning algorithm to visualize the surface low defects in simulation. Andersson 2 adopted a curvature-based visualization algorithm to verify the consistence between experiment result and simulation prediction. Nowadays the mechanism of the surface low defect is of great concern. Based on experiment results, Yang Y.Y. et al. 7 pointed out that the residual compression stress was the mechanics condition of the surface deflection initiation. In Numisheet 2008, Wang Huiping et al. 8 made a study on a surface distortion predictor for sheet metals. They believed that the mechanism of surface distortion was panels local buckling. In this paper, the mechanism of surface low defects in sheet metal forming is further studied. FE Simulation In this study, the experiment by Fu et al. 3 is simulated. In Fig. 1 is the section view of the experimental die setup. The radius of the die bottom surface is 170 mm and the draw depth is 40 mm. The embossment at the die bottom is 150150 10 mm3. A sample panel is shown in Fig. 2. The experimental blank is circular. Its radius is 500 mm. Low carbon steel for the automobile exterior panel is adopted. Detailed characteristics of the material are listed in Table 1. Advanced Materials Research Vols. 538-541 (2012) pp 377-381Online available since 2012/Jun/14 at (2012) Trans Tech Publications, Switzerlanddoi:10.4028/AMR.538-541.377All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of TTP,. (ID: 7, National Cheng Kung University, Tainan, Taiwan-10/01/14,12:02:33) Fig.1 Section view of the experimental die setup. Fig. 2 A sample panel in the experiment. Table 1 Characteristics of the experiment material Thickness mm Youngs Module GPa Poissons ratio Yield strength MPa Ultimate tensile strength MPa Total elongation, L Normal anisotropy, r Strain hardening exponent, n 0.7 207 0.333 157 520 0.4 1.75 0.23 Since the sample is symmetric, we establish only one quarter of the sample and define symmetric boundary conditions on the symmetry axes. In Fig. 3 is the FE model. The FE model simulates the drawing and springback of the panel. The drawing procedure is simulated with ABAQUS Explicit and the springback is simulated with ABAQUS Standard. For simplicity, the material is assumed isotropic. The linear, finite-membrane-strain, reduced-integration, quadrilateral shell element (S4R) is adopted. This element has been proved robust and suitable in sheet metal forming. Meshes around the embossment are carefully refined to describe the small deflection. The minimum elements are about 11 mm2 Fig. 3 FE model of the stamping test. Fig.4 The analytical model. Analytical Model The surface low problem is simplified as a rectangular plate under plane stress condition, shown in Fig. 4. The length of the plate is a, the wide of the plate is b and its thickness is t. The plate is compressed by a uniformly distributed stress,x, in the x direction and tensioned by a uniformly distributed stress, y, in the y direction. The boundary conditions of the plate model are assumed to be simply supported at the four sides. The depth of surface defect is close to the thickness of the sheet, so the deformation of the middle surface is considered. The balance differential equation is 34442222422422(2)212(1)xyxyEtNNNxxyyxyx y+=+ (1) where is the deflection, Nx, Ny and Nxy are membrane stress resultants. In this model, Nx, Ny are assumed uniformly distributed along thickness direction and Nxy equals to zero. So Nx, Ny and Nxy can be expressed as 378Materials Processing Technology II0xxyyxyNtNtN= = (2) According to the boundary condition of the model, the deflection surface of the buckled plate can be represented as 11sinsinmnmnm xnyAab= (3) where mnA represents the amplitude of deflection. Combining equations (1), (2), (3), we can obtain 22222111sinsin0mnxymnmnmnm xn yAttabDabab=+= (4) where D is the bending stiffness, 3212(1)EtD=. When mnA = 0, the equation has a unique solution, 0. This indicates that the plate keeps flat. When mnA 0 and 2222210xymnmnttabDab+= (5) the solution of the equation is not unique. This means the plate buckles. From Eq. (5) we can deduce the buckling compressive stress, 22222222222112(1)BuckleyEtnanaavmbmb=+ . (6) Each pair of n and m represents a buckling mode of the model. The critical compressive stress is the minimum value of all the buckling stresses for all the buckling modes. Since 22200ynamb , (7) we can deduce from Eq. (6) that 22222222222112(1)BuckleyEtnanaavmbmb=+ 22222222112(1)Etnaavmb+ 2222.12(1)Etav (8) So the critical compressive stress can be expressed as: 222212(1)crEtav= (9) Results and Discussion In order to observe the growth of the surface low defect, we measure the displacement in the Z direction (drawing direction) at two representative points. The location of the two measure points are shown in Fig. 5. Point A is around the corner of the embossment, where surface low occurs according Advanced Materials Research Vols. 538-541379to the experimental work by Fu et al. 3. Point B is near Point A, but surface low does not occur at this point. The difference of the displacement in the Z direction, Z=ZA-ZB, represents the surface deflection of the local area. Fig. 5 The selected measure points. Fig. 6 The history of surface deflection In Fig. 6 is the history of surface deflection during the entire forming process. During the drawing procedure, the surface deflection fluctuates about the zero value within 0.1mm. At the end of drawing, the surface deflection is only 0.01 mm. During springback, the absolute value of surface deflection increases dramatically. At the end of springback, the absolute value of surface deflection increases from 0.01 to 0.1 mm (negative value means concave and positive value means convex), 10 times the original value. This indicates that the panel trembles during drawing, but surface low does not grow in this stage. It is during springback that the non-uniform displacement in thickness direction forms surface low. local buckling surface low (stoning) Fig. 7 Minor stress distribution. Fig. 8 The surface low areas and the local buckling areas. In Fig. 7 is the minor stress distribution around the embossment corner. Different from other areas, the minor stress in the surface low area is negative. This indicates that the surface low area is under a plane stress status of compression and tension. According to the analytical model in Fig. 4, buckling may happen if the local compressive stress is larger than the critical value. Table 2 Calculation of the critical stress Sub-domain Compressive stress x (MPa) The compressive length, a (mm) The critical stress, cr (MPa) Buckle or not 1 234 12 645 No 2 210 15 412 No 3 190 18 286 No 4 170 22 191 No 5 150 26 137 Yes 6 100 27 127 No 7 50 34 80 No 380Materials Processing Technology IIAccording to the stress distribution in Fig. 7 and Eq. (9), we can calculate the critical stress for the sub-domains divided by the compressive stress level (shown in Table 2). According the results, buckling occurs in the sub-domain 5 whose boundary compressive stress is 150 MPa. Fig. 8 shows the predicted local buckling area and compares it with the experiment results by Fu et al. 3. It is obvious that the local buckling area agrees with the detected surface low area. This indicates that the essence of surface low phenomenon is panels local buckling under the compressive residual stress during springback. Conclusion Our work in this paper focuses on the mechanism of surface low defect in sheet metal stamping. Based on the finite element simulation results, theoretical analysis and the referred experiment result, the following conclusions apply: ? The stamping panel trembles during drawing, but surface low does not grow in this stage. It is during springback that the non-uniform displacement in thickness direction forms surface low. ? The panel local buckling under the compressive residual stress during springback is one of the major reasons for surface low in sheet metal stamping. Acknowledgements The authors acknowledge the support from Research Project of State Key Laboratory of Mechanical System and Vibration MSVMS201101, Doctoral Fund of Ministry of Education of China 20100073110034 and Shu Guang project supported by Shanghai Municipal Education Commission and Shanghai Education Development Foundation 10SG13. References 1 Liu L., Sawada T., Sakamoto M.: Journal of Materials Processing Technology 103, 280-287. 2 Andersson A.: Journal of Materials Processing Technology 209, 821-837. 3 Fu Zhengchun, Hu Ping, Wang Huiping, Zhao Kunmin. Research on experiment and simulation of automobile panel redrawing character. Numisheet 2008,Sep. 1-5,2008-Interlaken, Switzerland. 4 Fukumura Masaru, Yamasaki Yuji, Inage Daisuke, Fujita Takashi. Finite Element Simulation of Surface defects in the automobile door outer panel.CP712, Materials Processing and Design: Modeling, Simulation and Application, NUMIFORM 2004. 5 Park C.D., Chung W.J., Kim B.M.: Journal of Materials Processing Technology 187-188, 99-102. 6 Hu Yang, Zhu Xinhai, Lee Wing. Surface low prediction using ls-dyna and dynaform.Numisheet 2008,Sep. 1-5, 2008-Interlaken, Switzerland. 7 Yang Y.Y., Zhao L.H., Sun Z.Z.: Journal of Materials Processing Technology 187-188, 145-149. 8 Wang Huiping, Xu Siguang, Cao Jian, Chen Wayne, Cheng Hang S., Wang Chuan-Tao. Prelimilary study on a surface distortion predictor for sheet metals: validation in Yoshida buckling problems.Numisheet 2008, Sep. 1-5, 2008-Interlaken, Switzerland. Advanced Materials Research Vols. 538-541381Materials Processing Technology II 10.4028/AMR.538-541 The Mechanism of Surface Low Defect in Sheet Metal Stamping 10.4028/AMR.538-541.377 译文出处：Advanced Materials Rearch Vols.602-604(2013)pp 1903-1909板料冲压过程中表面低缺陷的机理Hongqing Shen1,2,a,Shuhui Li1,2,band Guanlong Chen1,c1中国上海交通大学机械工程学院汽车车身制造中心2中国上海交通大学机械系统与振动国家重点实验室aShenhongqing82,blishuhui,cglchen摘要：在本文中，我们研究的是板料冲压过程中表面缺陷的形成机理。首先，我们通过有限元法（FEM）模拟了一个冲压件的形成过程，并观察冲压件表面缺陷的形成过程。接着，我们建立一个分析模型，通过分析模型推导出局部弯曲的临界压力。最后，我们利用临界压力来检测冲压件的弯曲面积。有限元法仿真结果显示在弯曲回弹过程中，厚度方向的不统一变形导致了表面缺陷的形成。而且，仿真得到的局部弯曲面积与实验得到的表面缺陷的面积相同。这表明，表面缺陷现象产生的实质是在表面回弹中残余应力导致的面板局部弯曲。关键字：低表面；表面缺陷；冲压；板料成形；局部弯曲；1. 引言: 表面缺陷是在包含有突然的形变的大平板上的小的局部挠度。它们在汽车外观上有很大的影响。这些缺陷在人工制造中应该受到严格的检测和限制。Liu et al1提出了用光反射法来检测汽车面板成形中的表面缺陷。Andersson2使用称为WMS光反射系统来检测简单冲压面板的表面缺陷。同时在他的实验中使用探针测量技术。Fu et al3使用石刻法检测位于凸模边角周围的表面缺陷。随着有限元法的发展，使数值分析来预测表面缺陷成为可能。Fukumura et al4模拟了汽车门外部面板表面缺陷。Park et al5开发了一种曲率算法在模拟表面缺陷过程中使其可视化。Hu et al6开发了一种石刻算法在模拟表面缺陷过程中使其可视化。Andersson2采用了一种基于曲率可视化算法来验证实验结果和仿真预测之间的一致性。如今，表面缺陷的形成机理备受关注。基于实验的结果，Yang Y.Y.et al.7指出残余压应力是临界表面挠度的力学条件。在2008年的成形数值模拟会议，Wang Huiping et al.8做了一个关于板料表面变形预测的研究。他们认为表面变形的机理是面板的局部弯曲。在本文中，板料成形中表面缺陷的形成机理将得到进一步研究。有限元模拟 在这项研究中，Fu et al3进行了实验的模拟。图1是实验模具设备的截面图。模具底部表面的半径是170mm，拉深深度是40mm，模具底部凸模的体积是150150150mm3。图2为一个简单的面板。实验毛坯是可循环使用，它的半径是500mm。汽车外部面板材料采用的是低碳钢，材料的具体特性如下表1。 图1.实验模具设备的截面图 图2.简单面板 表1.材料的具体特性厚度mm杨氏模量GPa泊松比屈服强度MPa极限抗拉强度MPa总延伸量L厚向异性r应变硬化指数n0.72070.3331575200.41.750.23 因为样品是对称的，故我们只需建立四分之一的样品模型并在对称轴上建立对称边界条件。有限元模型如图3。有限元模型仿真了面板的拉伸和回弹过程。拉伸过程是通过ABAQUS显示模块来仿真完成的，回弹过程是通过ABAQUS标准模块来仿真完成的。为了简单起见，假设材料是各向同性的。应用了线性，有限薄膜拉力、缩减积分、四边形壳单元（S4R）。在板料成形过程中这个元素已经被证明是有效的和合适的。细化凸模周围的网格使能更准确的表示小的挠度。最小的元素是11mm2。 图3.冲压的有限元模型 图4.分析模型分析模型 表面缺陷简化为平面应力条件下的矩形板，如图4所示。板的长为a，宽度为b，厚度为t。板受到沿X方向均匀分布的压应力x作用，受到沿Y轴均匀分布的拉应力y作用。板模型的边界条件假设只是受到四个方向的力的作用。表面缺陷的深度接近于板料的厚度，那么只用考虑中间表面的变形。平衡微分方程为：（1）W是挠度，Nx,Ny和Nxy是合模压力。在这个模型中，假设Nx,Ny是沿厚度方向均与分布的，Nxy等于零。则Nx,Ny和Nxy可表示为： (2)根据模型的边界条件，屈曲薄板的表面挠度可以表示：（3）Amn代表偏转振幅。联立等式（1）、（2）、（3）得：(4)。D是抗弯刚度，。当Amn=0时，等式有一个唯一解，W=0。这表明板料没有弯曲。当Amn0且，（5）方程的解不唯一。这表明板料弯曲。由（5）我们可以得到弯曲压应力， （6）每一对n和m代表模型的屈曲模式。主要的压应力是所有的屈曲模式的屈曲应力的最小值。因此，从（6）式可得:(8)所以主要的压应力可以表示为： (9)实验结果和结论 为了观察表面缺陷的生长，我们测量了Z轴方向（拉伸方向）两个点的移位。两个点的位置如图5所示。点A位于凸模的拐角处，根据Fu et al3的实验结果，此处易发生表面缺陷。点B位于点A的附近，此处不易发生表面缺陷。Z方向偏移的不同代表不同的变形区域。 图5.选择测量的点 图6.表面缺陷的历程 图6是在整个成形过程中表面缺陷的历程。在拉伸过程中，表面弯曲在00.1mm范围内波动。在拉伸的最后阶段，表面弯曲仅有0.01mm。在回弹中，表面弯曲的绝对值急剧增加。在回弹最后阶段，表面弯曲的绝对值从0.01mm增至0.1mm（负值表示凹陷，正值表示凸起），是原来数值的10倍。这表明在拉伸过程中板料发生颤动但不发生缺陷。而在回弹中，因板料厚度方向的变形不一致导致了缺陷的产生。 局部弯曲 表面缺陷（探针）图7.较小的应力分布 图8.表面缺陷的面积和弯曲的面积 图7为凸模边角较小的应力分布。与其他的区域不同，在表面缺陷的区域较小的应力值是负的。这表明表面缺陷区域处在一个压力和拉力共同作用的平面应力状态。根据图4的分析模型，如果区域的压应力大于平均值，板料弯曲就可能发生。 表2.临界压力的计算值网格序号压应力x（MPa）压缩长度a（mm）平均应力cr(MPa)弯曲与否1234567234210190170150100
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