Fig. 13.  Geometry morphing algorithms  The surface morphing algorithm is implemented in UG-NX platform (Fig. 14). The interface consists of a main window W1 for viewing the CAD model and a sub window W2 for modifying model. In W2, the interface allows the user to define the surface low/distortion outer profile (user selected or customized), the mesh sizes and morphing function type. In W1, the surface can be modified by selecting the control scalar and moving it in normal direction (the remaining scalars move accordingly). As the user press the button “Preview”, the modified surface is immediately shown in W1. Press “Apply”, the desirable surface is generated and the  result can be conveniently stored by these control scalars. The surface low/distortion profile and magnitude found in the previous section are guideline for this operation.  Fig. 14.  Surface morphing based on UG-NX platform   The die face is over-crowned in the area where surface low/distortion occurs (Fig. 15) according to the morphed result. A caulking material is used to over-crown the experimental die. The caulking material sticks to the die and is hard enough for  a number of stamping. Over-crowning a production die requires welding and CNC machining.   
Fig. 15.  Morphed low die (four corners)   4  Experimental Results  To verify the validity of die morphing algorithm, experimental studies are performed using the specimen with plan view angle () of 90°, plan view radius (R) of 20 mm and reverse draw depth (H) of 10 mm. For the experiments, CR5 steel is used. The validity of the die morphing is verified by comparing the results of the surface low/distortion of specimens that were stamped by dies under good bearing, blank with holds and die morphing condition. The stamping lasers scanned result with the holding pad method and with holes in specimen are showed in Fig. 16 and Fig. 17, respectively. Although the magnitudes are both reduced, there is still micro-distortion on the die cannot be ignored. The surface low/distortion of a specimen with holes reduced more. However, the position and size of a hole are case dependent and need a lot of trial and error. Sometimes, the hole makes the forming unstable.  Fig. 16.   Surface distortion under good bearing condition   Fig. 17.    Surface distortion under blank with holes condition  Specimens stamped by the over-crowned die are laser scanned and the results are presented in Fig. 18. The magnitude is hard to detect by bare eyes. Only the right corner of the specimen shows 0.05 mm geometry deviation. Table 2 lists the maximum and the average surface low/distortion magnitudes of all scenarios. Compared with the experiment results of three correction methods, it approves that this die face morphing is more efficient.   Fig. 18.  Surface contour of specimen stamped by our method  Table 2.  Comparison of surface low/distortion magnitudes Correct method Maximum low/distortion magnitude max/mm Average low/distortion magnitude a/mm Uncorrected  0.211 2 0.168 7 Good bearing 0.152 0 0.135 0 Blank with holes 0.135 5 0.100 7 The proposed method 0.052 5 0.052 5  5  Conclusions  (1) Good die bearing can ensure contact of sheet metal with upper and lower die at the end of forming, there is still micro-distortion on the die cannot be ignored although the low/distortion magnitude is reduced. (2) A hole in blank changes the material flow during forming. However, the position and size of a hole are case dependent and need a lot of trial and error. Sometimes, the hole makes the forming unstable. (3) Die face morphing guided by the geometry-based criteria shows the better result in reducing the surface low/distortion magnitude and proves a practical method for correcting surface low/distortion.  Acknowledgements  The authors are grateful to Dr. JIN Chunning,
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