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•The example part, A, with a height of 19 mm was manufactured using six forming stages. Since the height of part B is 80 mm, we assumed that this part would require more than six forming stages.
3 Process Sequence Design：
The design guidelines discussed above and others obtained from die design handbooks (8) were applied in the design of progressive die sequence for part B. Figure 4 shows the flow chart of the steps conducted to determine the parameters of the first forming stage for part B using FEM.
3.1 Simulation Model：
The simulation model used is shown in Fig. 5. The geometry was modeled over a unit radian about the Z axis due to axisymmetric deformation mode. The sheet was meshed with axisymmetric quadrilateral element with eight elements along the thickness to capture thickness distribution. The dies were modeled to be rigid and the stress strain relation for the deforming material was σ¯=657ε¯0.24MPa. A Coulomb friction coefficient, μ=0.1, was selected as the thinning distribution from FEM simulation using this value that matched experimental results for the example part A. The initial blank diameter, db, was determined to be 165 mm through volume constancy using the part dimensions given in Fig. 2. The punch velocity of 150 mm/s was used in the simulations.
3.2 Blank-Holder Force for the First Stage：
The blank holder force for the first stage was determined by performing simulations with different blank-holder forces. If the blank-holder force is insufficient, the FEM simulation shows that the blank holder will move upwards (Fig. 5) resulting in flange wrinkling. In the first forming stage the minimum blank holder force of 50 kN was selected to prevent wrinkling, i.e., the upward movement of the blank holder. A similar strategy was used to determine the blank holder forces in subsequent forming stages.
3.3 Punch Diameter, Die Diameter and Drawing Depth for the First Stage：
The punch diameter and the drawing depth have maximum influence on wall thinning. The maximum wall thinning was constrained to be less than 4% in the first stage. Moreover, in the first stage, the cup is drawn completely without flange to put more material into the die cavity. Table 1 shows the simulation matrix used to determine the optimum (dimensions to constrain the wall thinning below 4% and minimize the number of forming stages) punch diameter for the first stage. The draw ratios of 1.65, 1.6 and 1.55 were obtained from die design handbook (8) for the initial determination of punch diameters. The punch diameters of 100, 97, and 95 mm were calculated from these ratios. The die clearance was taken as 1.1t0 while t0 is the initial sheet thickness. The last column in Table 1 shows the maximum wall thinning obtained from FEM. The maximum wall thinning is less than 4% for punch diameters of 97 and 100 mm. In order to reduce the number of forming stages, the punch diameter of 97 mm was selected.
The most important output from FEM simulations is the location of the maximum thinning in the part. Design engineers can use this information to select the punch diameters for subsequent stages. The punch radius for the first stage was selected to be 48.5 mm. After the first stage drawing, the maximum wall thinning of 3.72% is observed in the part at a distance of 43.7 mm from the center line (Fig. 6). Hence any punch radius equal to or more than 43.7 mm in the second stage will hit the maximum thinning area which would result in significant wall thinning. Therefore, the second stage punch radius should be smaller than 43.7 mm. The FEM simulations thus gave the upper limit for the next stage punch diameter. Simulations were then carried out to determine the optimum punch diameter for the subsequent stages. Cups were completely drawn for the first four stages and the maximum thinning was restricted below 6%.