圆锥模拉拔问题的下限解析解

Lower Bound Analytic Solution to the Drawing through Circular Cone Dies

金属材料通过阴模拉拔加工,因速度场方法的数学分析较为简单,所以常用其求解拉拔加工问题.基于材料的物理非线性,求解其平衡微分方程数学难度较大,较少采用应力法求解.文中忽略较小剪应力对材料屈服的影响,求解出圆锥模拉拔问题的下限应力解.算例的结果介于速度场上限解析解和应力场近似解之间,表明文中的应力解析解更为合理,可供塑性拉拔加工工程参考.

Due to the simplicity of the velocity field method in mathematical analysis, the method of velocity field is generally adopted to solve the equation of drawing metal material. Owing to the physical nonlinearity of material, it is difficult to solve stress differential equation, so the stress method is seldom adopted. Neglecting small effect of shear stress on the yield criterion, the lower bound of stress analytic solution to the drawing through dies of circular cone is obtained. The calculation result is in the range of the upper bound analytic solution of velocity field and approximate solution of stress field, showing that this method is more reasonable, may serve as a reference for the plastic processing of drawing.