板材多步逆成形中的滑移约束曲面优化构造方法

针对板材成形多步逆成形法中,滑移约束曲面构造的方法不能处理复杂形状零件的问题,提出一种基于优化的伪最小面积算法。该算法从优化的角度以滑移约束曲面的面积属性为研究对象,从而降低对零件形状的依赖度。该算法假定冲压时刻板材上的各物质点不发生流动,以冲压某一时刻凸、凹模的离散网格信息为已知量,此时刻凸、凹模各网格节点的z向坐标为约束,以所求滑移约束曲面的面积平方最小为目标函数,计算各三角形网格单元的面积,按与力学有限元中整体刚度矩阵相同的组装方式形成曲面的整体面积方矩阵,将空间曲面构造问题转化为一个标准二次规划问题,采用基于信赖域的方法求解该二次规划问题。弹簧支座和中柱算例的迭代次数和中间滑移约束曲面形状表明,该算法可以针对形状不规则的零件快速、有效的生成空间滑移约束曲面。

Research on Intermediate Configurations of Multi-step Inverse Approach in Sheet Metal Forming

Constructing the sliding constraint surface which is introduced to guide the movement of nodes on intermediate configurations is one process of the multi-step inverse approach in sheet metal forming.Because of the poor handling complicated parts of traditional methods in constructing the sliding surface,the pseudo minima area approach based on the optimization is developed by the authors’ group.The algorithm assumes that the sliding surface has minima area of all possible curved surfaces under the constrains of the current positions of die and punch,and the optimization is solved by the trust-region methods.By numerical simulation on spring bracket and center pillar,the effectiveness of the pseudo minima area approach is verified.