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

用实际允许速度场对模具三维压缩进行分析。速度场由以三角级数形式表示的位移函数推导而来。定义速度场的级数中各项的系数分别考虑了恒定体积、模具壁面边界条件和能量函数的最小化。分析定义了三维速度的直角和轴对称可以任意绘制。用摩擦系数m来表示摩擦，用两种方法介绍了模具壁的约束条件。一是系数的数量由接触点的数量决定。另一种是将钢坯的体积加权后强制出模，添加能量函数和后能量函数最小化。采用前一种方法计算，引入约束条件。与试验结果的变形载荷关系。在平面应变条件下，对填充坯料的轮廓和网格变形进行了比较。在轴对称问题上，给出了计算项数下变形荷载、网格变形与高度降低关系的计算结果。将载荷和变形曲线与计算值和实验值进行了比较。对平面和三维问题进行了计算，采用后一种方法引入了约束条件，并对载荷和变形轮廓的实验结果进行了比较。

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.