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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. The formability can also be estimate with thenumerical results. The method mainly involves the followingdetailed techniques: 3.1. Intermediate reference surfaceIn the calculation model, most of the intermediate referencesurface can be calculated automatically according to shapefeatures at local forming area. For example, the reference sur-face can be generated at the tangent direction along the borderof forming area. If the forming process is more complicated,the surface can also be generated manually with experience.However, it is difficult to design the intermediate shape of eachstep in the opposite sequence of processing step from finalshape to initial blank shape, especially for complex shape andforming process. When design the shape at current step, thereference surface should be generated from the shape of pre-vious step and the formability should be validated to avoiddefects. Sometimes not only the shape and forming processof current step but also the shapes of previous steps must bemodified.At the design stage of progressive die stamping part, thedesign engineers can generate relatively easily the intermedi-ate reference surface with the CAD software, such as UGNXand CATIA. It is difficult to predict precisely the interme-diate shape on the reference surface. Up to now, althoughthere are many authors try to optimize the shape of theintermediate reference surface with many optimization algo-rithms, the algorithms are only suit to the specific shape partand the optimization time is too long, which is unable tomeet the application requirements. Currently the intermedi-ate reference surface is generated by the designers and theintermediate shape is calculated using IA.3.2. Process conditionsIn the finite element model, many process conditions can beconsidered. For example, the fixed constrains will be addedat the nodes to assume that the relative displacement is verylittle at the connection area. At bending or flanging area, theinfluences of blank-holder force and friction are consideredto simulate the deformation of sheet metal. For large defor-mation at local area, the conditions treatment is differentbetween deep drawing and bulging. If the forming processis bulging, the restraint force or blank-holder force at flang-ing area is very big, the material of sheet metal is almoststiff, even fixed. If the forming process is deep drawing, therestraint force or blank-holder force at flanging area is rela-tively slightly, thematerial can flowat flanging area. InMUSM,the constraint or big blank-holder force should be added on thenodes at flanging area for bulging deformation.And the properblank-holder force will be added to corresponding nodes.3.3. Strain neutral layer offsettingAs shown in Fig. 3, the strain neutral layer (SNL) (Yingping andJun, 2002) will offset from the geometry neutral layer (GNL)to an inner layer along radial direction. Neutral layer offset-ting has a great influence on the blank shape size especiallywhen the rate between the thickness and radius of curvatureis bigger. When considering the SNL offsetting in MSUM, theshape size calculated and the experimental resultwill bemoreclosely.