轴对称多模变薄拉深的上限分析与试验研究

Upper Bound Analysis and Experimental Study of Axisymmetric Ironing Using Stacked Dies

给出一种以非线性流线（除边界流线）描述的轴对称变薄拉深初始流动模型，通过总功率的极小化确定最佳动许可速度场。建立多模变薄拉深任一凹模出口拉应力的一般上限解。提出摩擦因子的试验测试方法并给出其计算公式。凹模出口拉应力和变薄拉深力的理论解与试验结果良好吻合。

The paper presents the basic flow pattern of axisymmetric ironing which is discribed by a non linear flow line(besides bound flow line).The optimum kinematically admisible velocity field can be obtained based on minimizing the total energy dissipation rate.As compared with various engineering solutions based on universally adopted plane strain hypothsis for ironing,the solution is concerned with diametral dimensional changes of cup,smaller diameter to thickness ratio and larger thickness reduction do not exert an influence on precision of the solution.The methods of testing and measuring the friction factors are introduced and the formulas of computing them are given in the paper.The theoretical values of the tension on the outgoing wall and ironing force are in good agreement with experimental values.