In deep drawing process, if the workpiece is not willing to wrinkle due to small drawing ratio, deep drawing is done without the blank-holder. In present paper, numerical analysis of hot deep drawing for the thick hemispherical head from a plate with the thickness of 63.5 mm which is made of alloy steel HY-100 is presented without using the blank-holder. The drawing process of hemispherical head is studied by using three different geometries of drawing die in three positions as (1) increase in the curvature radius of the die, (2) approximate tractrix and (3) exact tractrix. In this research, Johnson–Cook constitutive model is used in order to explain the flow behavior of the material and the damage model of Johnson–Cook is used for prediction of failure probability in the product. Also, it is assumed that the hot deep drawing is done as isothermal and the strain rate is fixed. The results of numerical analysis show that the probability of damage occurrence in the “exact tractrix” design is lower than the other designs. Also, comparison of the thickness distribution in the wall of hemispherical head shows that the “exact tractrix” design has the least fluctuation of change in the wall thickness. Comparison of drawing force obtained by the numerical analysis show that at the same conditions of blank temperature and friction coefficient, using the “exact tractrix” design can significantly reduce the needed force in order to draw the hemispherical head.

在深冲过程中，如果工件由于低深冲比不愿意起皱，则在没有毛坯夹持器的情况下进行深冲。在本文中，对不使用毛坯支架的，由合金钢HY-100制成的厚度为63.5 mm的厚板半球形头部进行热拉深的数值分析进行了分析。通过在三个位置上使用三种不同的拉拔模具几何形状来研究半球形头部的拉拔过程，这三个方面是：（1）模具曲率半径的增加，（2）近似tractrix和（3）精确tractrix。在这项研究中，约翰逊-库克本构模型用于解释材料的流动行为，约翰逊-库克的损伤模型用于预测产品的失效概率。还，假设热深冲是等温的，并且应变率是固定的。数值分析结果表明，“精确法线”设计中发生损坏的可能性低于其他设计。同样，通过比较半球形头壁中的厚度分布，可以发现“精确字面”设计的壁厚变化波动最小。通过数值分析获得的拉拔力的比较表明，在毛坯温度和摩擦系数相同的条件下，使用“精确法线”设计可以显着减少拉拔半球形头部所需的力。对半球形头部壁厚分布的比较表明，“精确法线”设计壁厚变化的波动最小。通过数值分析获得的拉拔力的比较表明，在毛坯温度和摩擦系数相同的条件下，使用“精确法线”设计可以显着减少拉拔半球形头部所需的力。对半球形头部壁厚分布的比较表明，“精确法线”设计壁厚变化的波动最小。通过数值分析获得的拉拔力的比较表明，在毛坯温度和摩擦系数相同的条件下，使用“精确法线”设计可以显着减少拉拔半球形头部所需的力。