Stress Analysis and Optimum Design of Hot Extrusion DiesAbstract/ 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 optimum 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 optimum 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 designIntroduction With the continuous improvement of living standards/ better thermal conductivity of aluminum alloy profiles/ Aluminum components widely used in every aspect of life/ Therefore/ the aluminum alloy extrusion profiles/ profiles of various types of radiators have been widely used in electrical appliances/ machinery/ and other industries/ Variable products and the growing diversity and complexity of high-precision/ the extrusion process is the basis for extrusion die/ It not only determines the shape/ size/ accuracy and surface state/ but also affect the performance of the product/ So extrusion die extrusion technology is the key/ Studies to improve extrusion die quality and prolong its life span usually attempt to simplify 3-D finite element model to 2-D/ but it is only right for simple structural 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 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 The coordinates of the intersection point (P6) between beeline L3 (y = kx+b) and beeline L4 (y =S1) are 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 symmetric about the x-axis/ P8 and P6 are also symmetricabout the x-axis/1/4 Variables in the equations In Eqs/ (1)-(6)/ for points P1 and P2/ and R = R1/ For points P5 and P6/ 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)/ andS2=f6 (z)/ z 0/ H/1/5 Section shape at some height With lines linking P1-P4/ P5-P8/ with circular arc filleting 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/ 1/7 Smooth curved surface Using SKIN command in ANSYS/ smooth curved surfaces were built along the lines/ They are the surfaces of the influence hole/ Using the VA (it generates a volume 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 (6063Al-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 products quality into account/ the working temperature was 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 1200MPa/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/ The bridge collapse often takes place in the die/ And its strength is determined by the height and the distribution 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 (smax) was used as the goal function/The design variable ranges are listed in Table 2/ 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 expected 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/ The initial value of the design variables R1/ R2/ H/ q1/ and q2 were 75/000 mm/ 88/000 mm/ 80/000 mm/ 30/000/ and 30/000/ respectively/ and the maximum equivalent stress smax= 1066/5 MPa/ In the 21 iterations/ the optimum iteration was the eighteenth/ The design variable values were R1=65/048 mm/ R2=80/065 mm/ H = 89/596 mm/ q1=30/642/ q2=20/045/ The maximum equivalent stress smax= 723/1 MPa/ which is 27% less/ The optimum results are shown in Table 4/4 Conclusions 1) Based on ANSYS software/ its second development 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 extrusion die/ The optimal geometric design had 27% lower maximum stress/ A better die will not only reduce die number but also reduce time lost changing dies/ which will greatly heighten productivity/ 3）Die cantilever design of large-scale streaming into false structure Not only is effective to reduce the pressure on the mold to take greater positive die as a result of dangerous sections of the fracture/ greatly extend the life of the die/ but this can not bring streaming bridge structure also more effective to reduce the thickness of the bottom die velocity/ the velocity Extruded ensure a balanced/ stable/ Meanwhile/ the structural design of the extrusion die for the wide disparity in thickness solid Profile Die Design/ opened up a new way of thinking and approach/ References1 Karacs G/ Computer aided methods for die design/ Proceedings of the Conference on Mechanical Engineering/ 1998/ 2/ 463-466/2Mueller G/ Design optimization with the finite element program ANSYS/ International Journal of Computer Applications in Technology/ 1994/ 7/ 271-277/作者： 帅词俊/ 肖刚/ 倪正顺/英文作者： SHUAI Cijun */ XIAO Gang/ NI Zhengshun College of Mechanical and Electronic Engineering/ Central South University/ Changsha/ China/刊名：Tsinghua Science and Technology / 清华大学学报(英文版)/ 编辑部邮箱 2004年 03期查询来源： 中国学术期刊全文数据库查询网址：http//59/69/171/7/kns50/scdbsearch/scdetail/aspx?QueryID=14&CurRec=1热挤压模具的优化设计摘要：热挤压模具立体模型开发利用ANSYS软件及其二次开发语言ANSYS的参数设计，进行有限元分析和优化设计。热挤压模具的三维应力分布很不均匀/悬臂梁有严重的应力集中。获得最佳层面，数据结果表明最佳的高度是89/59630/1+5/6。挤压模分流孔是最佳半径 80/06565/048毫米和毫米，应力集中减少了27%。关键词：三位一体方式，造型，热挤压模具，优化设计引言 随着生活水平的不断提高/由于铝合金型材的导热性能较好，铝零件广泛应用于生活中的每一环节。因此，在铝合金的挤压型材中，各种类型的散热器型材已被广泛地应用在电器、机械等行业中。产品变的日趋多样化、复杂化和高精密度化，挤压模具是基础的挤压工艺。它不仅决定着产品形态、大小、精度和表面状态/而且影响到产品的性能。所以挤压模具是挤压技术的关键。 挤压模具研究改进质量和延长其寿命通常试图将三维有限元模型简化为二维/但只不过是构造简单的结构形状。没有三维有限元分析/其结果不能给制造业提供实际帮助和提供有用的资讯。本文主要介绍铝型材挤压模具优化设计模型。1实体造型 图1主要显示一种平面组合的热挤压模具。其外部直径为227/000毫米/其高度为80/000毫米。其他参数见图1，建模方法如下：1/1坐标P1和P5 直线L(y = kx + b)和圆弧(x2 + y2 =R2)之间的相交点坐标是 1/2坐标P2和P6 直线L1(y = kx + b)和直线L2(y =S1)之间的相交点坐标P2是 直线L3(y = kx + b)和直线L4(y =S1)之间的相交点坐标P6是 1/3 坐标P3/ P4/ P7/ 和 P8 P3和P1是关于Y轴对称。P4和P2也是关于Y轴对称。P7和P5是关于X轴对称。P8和P6也是关于X轴对称。1/4 变量方程 由公式(1)-(6)，得点P1和P2，和R = R1/得点P5和P6，和R = R2。 R1/R2/T1/T2/S1和S2是沿着高度(h)的变化规律来表达模具的功能R1=f1(z)/R2=f2(z)/T1=f3(z)/T2=f4(z)/S1=f5 (z)/和S2=f6(z)/z 0/ H。1/5 在一些高度的部分形状 用直线连接P1-P4/ P5-P8/蘖与圆弧相交于点(P1-P8)/在一些高度获得了部分形状。1/6 在每一高度的部分形状 高度划分为若干界面(微粒)等部分(微粒决定着精密，如果微粒较高的/精度更佳)。在每节高度形状如图2所示。 1/7 光滑曲面 在ANSYS使用表面指挥/顺利沿直线建立曲面，他们是影响面孔。利用VA(它利用现有的面积产生一定容量)指挥/从创立了坚实的表面。1/8 对称性模具 主体和核心的模具画图时用布尔操作增加/减掉等(图3)。对称性模具用于加速计算时使用的有限元分析模型为1/4-实体模型(图4)。 2 计算模型 用挤压铝合金(6063Al-Mg-Si)的一个平面模具来作为例子。铝的液相是6579/Al+Mg2Si的熔体温度是558。考虑到产品质量和挤压压力/工作温度定为450。 模具材料是4Cr5MoSiV1(H13)。下面是450/它的华模和泊松比分别是210GPa和0/25。其屈服强度是1200mpa，摩擦系数是0/3。固92通过免费网用来传送三维实体元素。为了负荷的摩擦力而挤压，表面效应单元154经常被用来生产组合体(图5)。用挤压机为1600吨/挤压强度计算公式为(7)10。其值见列表1。 桥梁倒塌经常是由于挤压，其高度和力量是分布在分流洞。本文中/高度(H)和半径(R1 and R2) 是分流孔的设
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