As shown in Figure 4(a), the nodes on the top surface of the die were con- strained (stationary surface) and the measured load of 356 kN was equally distributed on the contact nodes at the workpiece die interface. Similar boundary con- ditions for the punch are shown in Figure 4(b). It is noticeable that fewer nodes are in contact with the sheet metal due to the die tilt for the asymmetric load- ing case as shown in Figure 4(c). In real practice, the pressure actually varies along the die contact surface. Since the actual distribution was not known, uniform distribution was considered in the present analysis. DISCUSSION OF RESULTS As described in the earlier section, the numerical analysis of die Station 4 (both the die and punch) was performed using the code MSC/NASTRAN. Two cases were considered, namely: (a) symmetric loading and (b) asymmetric loading. Symmetric Loading Numerical analysis of the die was carried out for a measured load of 356 kN as distributed equally in Figure 4(a). The major displacements in the loading direction are shown in Figure 5(a). These displace- ment contours can be shown in various colors to rep- resent different magnitudes. The maximum displace- ment value is 0.01 mm for a uniformly distributed load of 356 kN. The corresponding critical stress is very small, 8.4 MPa in the y direction and 30 MPa in the x direction. The calculated displacements and stresses at the surrounding elements and nodes were of the same order, but they decreased in magnitude at the nodes away from this critical region. Thus, the die was considered very rigid under this loading con- dition. Symmetric loading was applied to the punch and the numerical analysis was carried out separately. The displacement values in the protruding region of the punch were high compared to the die. The maximum displacement was 0.08 mm. It should be noted that the displacement values in this critical range of the punch were of the same order ranging from 0.05 mm to 0.08 ram. Although the load acting on the punch (bottom half) was the same as the die (upper half), that is, 356 kN, the values of displacements and stresses were higher in the punch because of the differences in the geometry. This is especially true for the pro- truding part of the punch. The corresponding maxi- mum stress was 232 MPa. This part of the punch is still in the elastic range as the yield strength of tool steel is approximately 1034 MPa. The critical stress value might be varied for different load distributions. Since the actual distribution of the load was not known, the load was distributed equally on all nodes. As the die (upper half) is operating in a region which is ex- tremely safe, a change in the load distribution may not produce any high critical stresses in the die. Al- though higher loads are applied at other die stations (see Table 1), it is concluded that the critical stresses are not going to be significantly higher due to the ap- propriate changes in the die geometries. Asymmetric Loading For the purpose of analysis, an asymmetric loading situation was created by tilting the die. Thus, only 15 nodes were in contact with the workpiece compared to 40 nodes for the symmetric loading case. As shown in Figure 4(c), a 356 kN load was uniformly distrib- uted over the 15 nodes that were in contact with the workpiece. Although the pressure was high, because of the geometry at the location where the load was acting, the critical values of displacement and stress were found to be similar to the symmetric case. The predicted displacement and stress values were not sig- R.S. Rao  

9 Stamping Die Stress Analysis nificantly higher than the values predicted for the symmetric case. CONCLUSIONS In this preliminary study, we have demonstrated the capabilities of the computational procedure, based on finite element method, to evaluate the stresses and de- flections within the stamping dies for the measured loads. The dies were found to be within the tolerable elastic limits for both symmetric and asymmetric loading conditions. Thus the computational procedure can be used to study the tilt and alignment character- istics of stamping dies. In general, the die load mon- itors are very useful not only for analysis but also for on-line tonnage control. Future research involves the integration of the structural analysis of stamping dies with that of the transfer press as a total system. ACKNOWLEDGMENTS Professor J.G. Eisley, W.J. Anderson, and Mr. D. Londhe are thanked for their comments on this paper. REFERENCES 1. R.S. Rao and A. Bhattacharya, "Transfer Process De- flection, Parallelism, and Alignment Characteristics," Technical Report, January 1988, Department of Me- chanical Engineering and Applied Mechanics, the Uni- versity of Michigan, Ann Arbor. 2. Editors of American Machinist, "Metalforming: Modem Machines, Methods, and Tooling for Engineers and Op- erating Personnel," McGraw-Hill, Inc., 1982, pp. 47- 50. 3. W.J. Anderson, J.G. Eisley, and M.A. Tessmer, "Transfer Press Deflection, Parallelism, and Alignment Characteristics," Technical Report, January 1988, De- partment of Aerospace Engineering, the University of Michigan, Ann Arbor. 4. B.B. Yoon, R.S. Rao, and N. Kikuchi, "Sheet Stretch- ing: A Theoretical Experimental Comparison," Inter- national Journal of Mechanical Sciences, Vol. 31, No. 8, pp. 579-590, 1989. 5. B.B. Yoon, R.S. Rao, and N. Kikuchi, "Experimental and Numerical Comparisons of Sheet Stretching Using a New Friction Model," ASME Journal of Engineering Materials and Technology, in press. 6. MSX/NASTRAN, McNeal Schwendler Corporation. 冲压模具的应力分析英文文献和中文翻译(2):http://www.751com.cn/fanyi/lunwen_41802.html