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TSINGHUA SCIENCE AND TECHNOLOGY ISSN 1007-0214 10/24 pp290-293 Volume 9, Number 3, June 2004 Stress Analysis and Optimum Design of Hot Extrusion Dies* SHUAI Cijun (帅词俊)*, XIAO Gang (肖 刚), NI Zhengshun (倪正顺) College of Mechanical and Electronic Engineering, Central South University, Changsha 410083, China Abstract: A three-dimensional model of a hot extrusion die was developed by using ANSYS software and its second development languageANSYS parametric design language. A finite element analysis and op- timum design were carried out. The three-dimensional stress diagram shows that the stress concentration is rather severe in the bridge of the hot extrusion die, and that the stress distribution is very uneven. The opti- mum dimensions are obtained. The results show that the optimum height of the extrusion die is 89.596 mm. The optimum radii of diffluence holes are 65.048 mm and 80.065 mm. The stress concentration is reduced by 27%. Key words: three-dimensional method; modeling; hot extrusion die; optimum design Introduction With the standard of living continuously improving, aluminium parts are widely used in every walk of life. Products are becoming more and more diverse and complicated and precisions are higher and higher1,2. The extrusion die is the basis of the extrusion process. It not only determines product shape, size, precision, and surface state, but also affects product performance. So the extrusion die is the key to extrusion technology. Studies to improve extrusion die quality and prolong its life span usually attempt to simplify 3-D finite ele- ment model to 2-D, but it is only right for simple struc- tural shapes. Without a 3-D finite element analysis, the results cannot give practical manufacturing help and offer useful information3-5. In this paper, aluminium profile extrusion die was modeled to get in optimum design6-8. 1 Solid Modeling Figure 1 shows the male die of a hot extrusion planar combined die. Its external diameter is 227.000 mm, its height is 80.000 mm. Other parameters are shown in Fig. 1. The modeling method is as follows. 1.1 Coordinates of P1 and P5 The coordinates of the point of intersection between the beeline L (y = kx + b) and the circular arc (x2 + y2 = R2) are 2222 1,5 2 ()(1)() 1 kbkbkbR x k + = + (1) 1,51,5 ykxb=+ (2) 1.2 Coordinates of P2 and P6 The coordinates of the intersection point (P2) between beeline L1 (y = kx+b) and beeline L2 (y =S1) are Received: 2003-12-10; selected from Proceedings of the Symposium on Frontiers and Challenges of Mechanical Science and Technology Supported by the Fund for the Doctoral Program of Higher Education of China (No. 20010533010) To whom correspondence should be addressed. E-mail: shuaicijun ; Tel: 86-731-8836858 1 2 Sb x k = (3) y2 = S1 (4) The coordinates of the intersection point (P6) between SHUAI Cijun (帅词俊) et al：Stress Analysis and Optimum Design of Hot Extrusion Dies 291 Fig. 1 Sketch map of the hot extrusion die beeline L3 (y = kx+b) and beeline L4 (y =S1) are x6 = S2 (5) y6 = kx2+b (6) 1.3 Coordinates of P3, P4, P7, and P8 P3 and P1 are symmetric about the y-axis. P4 and P2 are also symmetric about the y-axis. P7 and P5 are sym- metric about the x-axis. P8 and P6 are also symmetric about the x-axis. 1.4 Variables in the equations In Eqs. (1)-(6), for points P1 and P2, b = 2 1 2 1k T k + and R = R1. For points P5 and P6, b = 2 2 2 1k T k + and R = R2. R1, R2, T1, T2, S1, and S2 are the change rule along the height (H) of the die expressed as the functions R1=f1 (z), R2=f2 (z), T1=f3 (z), T2=f4 (z), S1=f5 (z), and S2=f6 (z), z 0, H. 1.5 Section shape at some height With lines linking P1-P4, P5-P8, with circular arc fillet- ing at the point of intersection (P1-P8), the section shape at some height is obtained. 1.6 Section shape at every height H is divided to interfacial number (INUM) equal parts (INUM is decided by the precision, if the INUM is higher, the precision is better). The section shape is drawn at every height as shown in Fig. 2. Fig. 2 Die line diagram 1.7 Smooth curved surface Using SKIN command in ANSYS, smooth curved sur- faces were built along the lines. They are the surfaces of the influence hole. Using the VA (it generates a vol- ume bounded by existing area) command, a solid was created from those surfaces. 1.8 Symmetry of the die The main body and kernel of the die were drawn using the Boolean operations of add, subtract, etc. (Fig. 3). The symmetry of the die was used to accelerate the computations using a 1/4-solid model for the finite element analysis (Fig. 4). 2 Computing Model A planar die that extrudes the aluminium alloy (6063 Al-Mg-Si) was used as an example. The liquidoid of Al is 6579, and the melt temperature of Al+Mg2Si is 558. Taking the extrusion pressure and the prod- ucts quality into account, the working temperature was 292 Tsinghua Science and Technology, June 2004, 9(3): 290293 ) determined to be 450. The die material is 4Cr5MoSiV1(H13). Below the 450, its Young modulus and Possion ratio are 210 GPa and 0.25, respectively. Its yield strength is 1200 MPa. The friction coefficient is 0.3. The Solid92 3-D solid element was used to carry through the free mesh. In order to load the frictional force while extruding, the surface effect element Surf154 was used to produce the regular quadrangles (Fig. 5). For the 1600 t extruder, the extrusion intensity was computed using Eq. (7)10. The values are shown in Table 1. 12zztdzzd ()(PPPRTTTRTT=+=+ (7) Fig. 5 Frictional force loaded Table 1 Intensity of each part in the die Fig. 3 Die solid model Fig. 4 One quarter of the solid model (MPa) RzTzTt Td z R z T d T P 83.4227.41222.7219.53 191.80 53.23 14.38 612.54 The bridge collapse often takes place in the die. And its strength is determined by the height and the distri- bution of the diffluence holes. In this paper, the height (H) and the radii (R1 and R2) of the diffluence holes were used as design variables and the maximum equivalent pressure (max) was used as the goal func- tion. The design variable ranges are listed in Table 2. Table 2 Design variable range R1/mm R2/mm H/mm 1/( ) 2/( ) 65.000- 85.000 80.000- 98.000 60.000- 90.000 20.000- 40.000 20.000- 40.000 3 Computed Results Figure 6 is the equivalent stress diagram. From Fig. 6 we can see that the stress is largest at the bridge, as ex- pected 24 maximum equivalent stress values are listed in Table 3 from large to small. The data shows that the nodal maximum equivalent stress is 1066.5 MPa, which is 14.5% higher than the second one (912.0 MPa), and that the stress convergence is very severe in the bridge, this part is apt to produce crack. Fig. 6 Maximum equivalent stress Table 3 Nodes stress values Node code 971 528 719 698 3950714 1156702 727 710 723 700 r / MPa 1066.5 912.0 832.7 811.6 804.4795.3789.9778.8775.8769.0 763.6 763.5 Node code 739 708 706 731 759 1778704 747 690 743 694 696 r / MPa 759.3 756.8 755.9 739.8 739.1736.0734.3715.9706.4700.3 700.1 695.6 SHUAI Cijun (帅词俊) et al：Stress Analysis and Optimum Design of Hot Extrusion Dies 293 The initial value of the design variables R1, R2, H, 1, and 2 were 75.000 mm, 88.000 mm, 80.000 mm, 30.000, and 30.000, respectively, and the maximum equivalent stress max= 1066.5 MPa. In the 21 itera- tions, the optimum iteration was the eighteenth. The design variable values were R1=65.048 mm, R2=80.065 mm, H = 89.596 mm, 1=30.642, 2=20.045. The maximum equivalent stress max= 723.1 MPa, which is 27% less. The optimum results are shown in Table 4. Table 4 Optimization process Iteration times 1 2 3 4 5 6 7 8 9 10 11 R1 / mm 75.000 81.94377.358 80.85567.24980.44167.36565.59165.184 65.17265.067 R2 / mm 88.000 88.22995.261 90.47889.53589.98393.66182.79193.753 80.60480.153 H / mm 80.000 71.64060.100 80.85489.68474.32781.40965.29761.478 84.95588.627 1/( ) 30.000 33.84729.382 21.40032.63336.08531.81637.64439.474 33.86134.052 2/( ) 30.000 30.75126.406 26.94623.01836.72921.26720.32524.740 20.11320.058 max / MPa 1066.5 1167.41323.2 1229.7882.5 1241.7882.4 866.8 943.9 756.0 749.7 Iteration times 12 13 14 15 16 17 18 19 20 21 R1 / mm 65.048 65.04765.048 65.04865.04765.04865.04865.04365.042 65.042 R2 / mm 80.070 80.06393.506 83.63384.98780.07080.06580.04580.044 80.045 H / mm 65.808 85.14188.116 87.94588.97889.59889.59689.86766.840 89.839 1/( ) 30.585 32.45635.414 27.78633.23123.14430.64230.25027.556 31.341 2/( ) 23.479 22.21420.044 35.94120.04620.04520.04520.04220.042 20.042 max / MPa 780.0 769.6 760.4 788.0 769.0 795.8 723.1 741.3 821.3 751.3 4 Conclusions 1) Based on ANSYS software, its second develop- ment language APDL was used to develop a 3-D model of the hot extrusion die that extrudes aluminium profile has been obtained. 2) The 3-D stress distribution was very uneven, with severe stress concentrations in the bridge of the hot ex- trusion die. The optimal geometric design had 27% lower maximum stress, A better die will not only re- duce die number but also reduce time lost changing dies, which will greatly heighten productivity. References 1 Yin Jianhua. Structural adjustment orientation for domestic large-scaled aluminum processing enterprises in terms of import situation of aluminum material in recent years. The World Non-Ferrous Metal, 2001, 10: 37-42. (in Chinese) 2 Li Yi. Forecast on domestic aluminum material consump- tion and advices on optimizing domestic aluminum mate- rial industry constitution. Journal of Southern Institute of Metallurgy, 2002, 4: 305-308. (in Chinese) 3 Yi Miao, Liu Fang. The contributing factors analysis about the life span of the extrusion die. Light Alloy Proces