AN ENERGY METHOD ANALYSIS OF CLOSED-DIE FORGING BEING FILLED WITH RIGID-PLASTIC BILLET IN THREE-DIMENSIONS CONDITION

用真实的许用速度场分析模内三维压缩。速度场由三角级数形式的位移函数导出，速度场的级数项的系数由恒体积、模壁边界条件和能量函数最小化的考虑得到。分析定义了三维速度，可以任意绘制笛卡尔和轴对称。用摩擦系数m来表征摩擦，用两种方法来确定模具壁面的约束条件。一种是由接触点的数目决定系数的数目。另一种方法是对坯料挤出模具的体积进行加权，加入能量函数，使能量函数最小化后，用前一种方法计算，引入约束条件。以及变形载荷与变形量关系的实验结果。本文给出了平面应变条件下的充型轮廓和网格畸变的计算结果，并对轴对称问题给出了变形载荷、网格畸变与计算项数高度折减之间关系的计算结果。将载荷和畸变分布与计算结果和实验结果进行了比较，并将平面问题和三维问题的计算结果与实验结果进行了比较，用三维问题的方法引入了约束条件，得到了载荷和畸变分布。

The use of realistic admissible velocity field for analysis of three dimensions compression in the die. The velocity field is derived from displacement functions written in the form of trigonometric series.The coefficients of terms in the series defining the velocity field are obtained from considerations of volume of constancy, boundary condition on the wall of Die and minimization of energy function. Analysis defines the velocity in three dimensions Cartesian and Ax-symmetric can be drawn arbitrary. Friction is identified by a friction factor m.The constrain condition of the wall of Die are introduce by two methods. One is that the number of coefficients are decided by the number of contact points. Other is that weighted the volume of billet is forced out the die, added energy function and after energy function minimize.The calculated, introduced constrain condition by the former method. and experiment results of relation between deformation load. filling billet profile and distortion of grid are shown and compared on the plane strain condition.On Ax-symmetric problems, the calculated results of relation between deformation load, distortion of grid and reduction of height for calculated unmber of terms. The load and distorted profiles are compared to calculated and experiment one.The calculated on plain and three dimensions problems, introduced constrain condition by the later method, and experiment results of the loads and distorted profiles are compared.