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4. Examples4.1. Example 1: Aided design of strip layoutAs shown in Fig. 4(a), the dominating forming process of a pro-gressive die forming part involves bulging, bending, flangingand restriking. The strip layout is assembledwith six key inter-mediate shapes (Fig. 2) and other auxiliary shapes. As shown step in strip layout. Before bending at this local area, the cut-ting line will be calculated and then to bend the sheet metal.So, when unfolding the local bending area, the intermediateshapewill be projected on the reference surface (plane surfaceat current step) at the previous step. The offsetting of strainneutral layer is calculated.At the local area, the bending radiusis 1.5mm, the offsetting size is 0.03mm with the theoreticalformula (Shuobeng et al., 2002). The error between the sizeof cutting line with offsetting and the experimental result isrelatively little.2nd step. As shown in Fig. 4(c), the flanging area (Fig. 4(a),C and E area) will be unfolded. The counterpart shape is the13th step in strip layout.When unfolding the flanging area, thereference surface is calculated automatically with the featuresurface of previous unfolding shape. Generally, the referencesurface is extruded fromthe boundary curves (feature curves)in the tangent direction of the feature surface. As shown inFig. 5, the flanging contains compression deformation andstretch forming, and it is difficult to determine the cutting lineon the 3D reference surface with experience.Many physical quantities can be obtained with the result,such as the distribution of stress, strain, thickness and form-ing limited diagram (FLD). As shown in Fig. 6, the distributionof thickness strain show that the larger thickness thinning is 10.7% at the stretch deformation area with good formability,and the larger thickness strain is 10.7% at the compressiondeformation area with a little of wrinkle risk.3rd step. As shown in Fig. 4(d), the bending area (Fig. 4(a),F area) will be unfolded. The counterpart shape is the 11thstep in strip layout. The unfolding operation is similar withthe first step. However, due to the larger rate of the bendingradius of curvature and thickness at the bending area, wherethe bending radius is 63.5mm, the offsetting of neutral layercan be ignored.4th step. As shown in Fig. 4(e), the bending area (Fig. 4(a), Barea)will be unfolded. The counterpart shape is the 9th step in strip layout. The unfolding operation is similar with the thirdstep and the offsetting is ignored.5th step. As shown in Fig. 4(f), the bulging area (Fig. 4(a),G area) will be unfolded. The counterpart shape is the 2nd step in strip layout and the reference surface is plane. Forthe bulging process is after cutting, the deformation is only atlocal area under the blank-holder force and friction force. Inthe finite element model, the nodes around the bulging areaare added with blank-holder force and friction force. At therelatively far area, the nodes are added fixed constraints. Asshown in Fig. 7, the largest thickness thinning reaches morethan 30% with over thinning and rupture risk. It may be agood choice to reduce the blank-holder force to avoid rupturerisk.6th step. As shown in Fig. 4(g), the bulging area (Fig. 4(a), Aarea) will be unfolded. The counterpart shape is the 1st stepin strip layout. The unfolding operation is similar with the 5thstep. As shown in Fig. 8, the largest thickness thinning is about20% with good formability.With the shapes of previous six steps, the key blank shapeof 15, 13, 11, 9, 2 and 1 can be designed with presumptivestamping process. The remaining step involves cutting andrestriking process, which are independent to blank design.4.2. Example 2: Numerical verification withexperimental resultAs shown in Fig. 9, a progressive die part of automobile isunfolded usingMSUM. The unfolding operation is similarwiththe Example 1.As shown in Fig. 10(a), comparing the outline of the initialshape usingMSUMin FASTAMP software with the experimen-tal result and the numerical result in FASTFORM 3D software,there are little differences in details at the local area (Fig. 10(b),C area).5. ConclusionsAmulti-step unfoldingmethod (MSUM) is developed for blankdesign and formability prediction of complicated progressivedie stamping part to assist the process design. In the method,a finite elementmodel of the inverse approach is developed ata local area according to the stamping process. The interme-diate shapewill be unfolded on a reference surface at the localarea, and the surface can be generated automatically with thefeature surface and stamping process. Not only the influence of the connection, blank-holder force and the friction, but alsothe influence of the offsetting of the strain neutral layer withdifferent radius of curvature, are considered in the numericalmodel, which improves the calculation precision of the blankshape at each step.