• CN:11-2187/TH
  • ISSN:0577-6686

›› 2011, Vol. 47 ›› Issue (24): 20-25.

• 论文 • 上一篇    下一篇



  1. 燕山大学机械工程学院;北京有色金属研究总院有色金属材料制备加工国家重点实验室
  • 发布日期:2011-12-20

Analytical Solution of Stress in Flange Deformation in Axisymmetrical Deep Drawing Process

QIN Siji   

  1. College of Mechanical Engineering, Yanshan University State Key Laboratory for Fabrication and Process of Non-ferrous Metals, Beijing General Research Institute for Non-ferrous Metals
  • Published:2011-12-20

摘要: 在一定的假设条件下,对轴对称拉深成形凸缘变形区的应力进行解析分析,得到以积分形式表示的应力表达式。进行恰当的变量代换后,根据积分函数符合线性变化的规律,分别利用积分中值定理和泰勒级数展开公式,简化得到径向应力的解析表达式。根据简化公式可直接计算得到任一变形瞬间凸缘变形区的应力分布,以及不同变形瞬间的凹模入口处的径向应力。采用两种简化方法计算与以积分计算得到的结果非常接近,给出的算例表明,在拉深过程中,凹模入口处的径向应力最大相对误差小于0.6%,最大应力相对误差小于0.15%。以圆筒形件的拉深成形为例,在考虑板坯在凸缘区和凹模圆角区的摩擦、及板坯在凹模圆角区的弯曲等条件下,采用简化解析公式,计算极限拉深系数,计算结果与试验值吻合较好。

关键词: 板料成形, 积分中值定理, 拉深, 泰勒级数, 应力解

Abstract: The stress expressed in the integral form was obtained based on analytical analysis of the flange for axisymmetrical deep drawing process under certain assumptions. After an appropriate substitution of variable, analytical expressions of radial stress have been simplified by using the integral mean value theorem and Taylor series expansion method respectively according to the linear variation of integral function. The radial stress distributions of the flange at any deformation moments and the stress at the entrance of the die at different moments during the process can be directly calculated by using the simplified formula. The calculated results by using the two simplified methods match well ones by integration. Some given examples show that the maximum relative errors of the radial stress at the entrance of the die during the deep drawing process are less than 0.6%, and relative errors of maximum stress less than 0.15%. In cases of deep drawing of cylindrical cup, the limiting drawing coefficient calculated by the simplified analytical formula was calculated considering friction in the flange area and the die fillet area and sheet metal bending deformation in the die fillet area. The results are in good agreement with the experimental ones.

Key words: Deep drawing, Integral mean value theorem, Sheet metal forming, Stress solution, Taylor series