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A multi-step unfolding method (MSUM) is developed for blank design and formability pre-diction of complicated progressive die stamping part. In themethod, a finite elementmodelof the inverse approach (IA) is developed at a local area according to the stamping process,and the intermediate shape is unfolded on a reference surface at the local area. Not onlythe influence of the connection, blank-holder force and the friction, but also the influenceof the offsetting of the strain neutral layer with different radius of curvature at local area,are considered in the model, which improves the calculation precision of the blank shapeat each step. The key intermediate blank shapes and initial blank shape can be generatedusing the method with many times in an inverse sequence. The optimum blank shape alsocan be designed according to the formability of the forming part. The MSUM is illustratedto the blank design of a progressive die stamping part, and a benchmark test is comparedwith experimental and other numerical results.57650
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1. IntroductionA large number of parts on automobile body are deformedby stamping, and sometimes the features of the stampingparts are very complicated. In order to improve the qualityand the efficiency of products, many parts are formed usingprogressive die process. Comparing with simple press tool,progressive die has the advantages of high quality and effi-ciency of product, which is especially suitable for large-lotproduction in a short delivery time. However, it is very dif-ficult to design strip layout in progressive die design, and onlythe rich experience and technical engineers are competent todo it well.In the strip layout design, firstly, the stamping processsequence is designed according to the part featureswith expe- rience and simple theoretical formula. Secondly, the shape ateach step is designedwith the process sequence and all shapesare assembled into a strip. After finishing the die structuredesign with strip layout, it is very important to validate thedesign of strip layout and the die structure in a real produc-tion condition to find out potential defects. It is necessary tomodify the design of strip layout and the die structure untilthe defects is removed. So it is a rather difficult task to obtainan optimum strip layout. If the optimal blank shape and sizeat each step and the formability are predicted at the designstage, which will greatly reduce the trial and error time of thewhole progressive die design.However, at the design stage of strip layout, intermediateshape and boundary conditions of process are unknown. It isimpossible to use finite element incremental approach to sim- ulate the sheet metal forming at each step (Jian et al., 2002).And the most important thing for the designer is to calcu-late the intermediate shapes and to predict the formabilityof each step from the final shape of the part to initial blank.Up to now, the inverse approach (IA) (Guo et al., 1990, 2000,2001; Naceur et al., 2001) or one step (Lee and Huh, 1998)isabetter solution for the problem. But the inverse approach canonly calculate the initial shape from the final shape withouttaking into account intermediate forming process, and some-times there is a big error evenwrong result for complex shape,especially at upright wall or undercut conditions.Many authors used the IA to predict the initial blank shapeof the complete part, and it is an effective method for manystamping part with simple process. But for complicated form-ing parts or progressive die stamping parts, the intermediateforming process has great effect on the initial blank shape, andit is difficult to set the boundary conditions for different localforming areas with complete unfolding.
It is feasible methodto calculate inversely the local forming area according to thepractical forming processes step by step, and the upright wallor undercut conditions can be avoided to some extent.In the sheet metal forming simulation system, FASTAMP(Yuqi et al., 2004), a multi-step unfolding method (MSUM) isdeveloped to assist the progressive die design. Firstly, a finiteelementmodel of the inverse approach is developed at a localarea according to the stamping process, and the intermediateshape is unfolded inversely from final shape to initial shapeon a reference surface at each step. In calculation model, thereference surface may be generated according to the processand feature surface. The influences of stamping process suchas the connection, blank-holder force, the friction and theoffsetting of the strain neutral layer with different radius ofcurvature at local area, are also considered. Then these shapesare assembled into a strip layout. The forming defects can bepredicted with the numerical results and the optimum blankshape also can be generated using the unfolding method.In this paper, some finite element aspects in the IA arerecalled firstly. One example is illustrated to the blank designof a progressive die stamping part, and the initial shape ofanother example is compared with experimental and othernumerical results.2. Some finite element aspects in MSUMThe finite element model of MSUM is based on IA. The detailsof the finite element formulation can be found in the papers(Guo et al., 1990, 2000; Naceur et al., 2001).The mixed element types of DKT (Batoz et al., 1980) andDKQ (Batoz et al., 2000) with bending effect are used in theanalytical model to improve the calculation precision. Thetreatments (Yuqi and Junhua, 2006) of the boundary condi-tions such as displacement constraint and external nodalforce transformed from blank-holder force, friction force andthe total restraining force of drawbead are introduced toimprove the conditioning of the tangent stiffness matrix.Using MSUM at the local area, the upright wall or undercutconditions will become weak with practical stamping direc-tion, the conditioning of tangent matrix will be increased andthe convergence speed is improved. 3. The procedure of MSUMA typical progressive die part (Fig. 1) and the strip layout (Fig. 2)are designed with the progressive die wizard (PDW) in UG NXsoftware. At the process design stage, only the final shapeis known and the intermediate shape should be designedaccording to the process requirements and shape features.For example, it is necessary to cut the sheet on the interme-diate reference surface and then to flange it at the flangingdesign process. If there is a large deformation at flanging area,it is necessary to calculate the cutting line precisely and pre-viously. Moreover, if there will be a large deformation at localarea, such as drawing, flanging or bulging, it is very useful toestimate formability and check process conditions in advance,which is helpful to avoid forming defects, such as rupture andseverewrinkling. Therefore, progressive die design process is adifficult and complex task even for rich experienced engineers.AMSUMbased on the inverse approach is proposed againstthe difficulty of progressive die design. The intermediateshape and cutting lines are calculated with process andshape features.