圆锥形件拉深成形应力应变的直接积分解法

A Direct Integral Method to Solve Stress and Strain of Conical Parts in Deep Drawing Process

针对圆锥形件的拉深成形,在平面应力和比例加载条件下,采用参数方程的方法分析得到了变形区应变的微分方程。可在圆锥形件的凸缘区、凹模圆角区及锥壁区分别根据应变微分方程,代入相应的边界条件,采用直接积分得到应力、应变解,将应用于轴对称平面内的积分解法推广至分析圆锥形件的拉深成形问题。在凸缘区,锥角等于0;在锥壁区,锥角等于一定值;在凹模圆角区,将圆角部分的弧段分成若干个微锥段,每一微锥段都可分别作为一个小的等锥角的锥环处理。采用该方法,不仅可以计算锥形件的拉深成形问题,而且可以计算曲面形状已知的一般轴对称曲面零件的成形问题。用直接积分法替代迭代法求解非线性方程,使求解过程大大简化。选取厚0.87mm的ST16板材进行了拉深成形实验,以板坯内层为测量面,测量了凸缘区、凹模圆角区和锥壁区的应变分布,理论计算结果与实验结果一致。

Under the conditions of plane stress and proportional loading, differential equations of strain and stress in deformation zone of conical part in deep drawing were obtained by the method of parametric equation. After solving the differential equations under the corresponding boundary condi- tions in the regions of flange, die corner and conical wall of the conical part the stresses and strains might be obtained respectively in every regions by the direct integral method. The applications of the direct integral method were extended from solving the in-plane axisymmetic sheet metal forming prob- lems to analyze conical part deep drawing process. The conical angles were equal to zero and a certain value in flange region and conical wall respectively. The die arc regions might be divided into several small segments and each of them could be taken as a conical part with constant conical angle. This method was applied to solve conical part deep drawing problems and to analyze the forming problem of axisymmetric curved parts with given profile shape. As the substitute of iteration method, the direct integral method was applied to solve nonlinear equations and the solving process could be simplified greatly. The experiments of conical part deep drawing were carried out by using 0.87 mm-thick ST16 sheet and the strain distributions in flange, die arc and conical wall regions were measured. It shows that the analytical solutions by the direct integral method are accordant with experimental results.