板材最优路径成形理论与方法

按最优路径成形板材将获得理想的成形效果，这种最优成形路径可通过多点成形技术来实现。本文基于理想路径（最小塑性功路径）成形理论，提出了板材最优路径成形的概念。最优成形路径可由初始构形、目标构形以及一系列中间构形描述出来，根据理想路径成形的变形及本构关系，文中建立了计算初始构形的有限元方法；建立了确定中间构形的泛函，给出了求解中间构形的数值方法。根据给出的方法设计了近似最优路径成形──多道次多点成形实验，实验结果表明，采用近似最优路径成形，球面目标形状的最大变形曲率提高了１１％～４０％；马鞍面目标形状的最大变形曲率提高了１５％－５０％。

Theory and Method of Optimum Path Forming for Sheet Metal

Ideal forming results will be achieved if the sheet metal is formed along an optimum forming path. Such a path can be realized by multi-point forming technique. On the basis of the theory of the ideal formig path (or minimum plastic work path), the concept of an optimum forming path is proposed in this paper. The forming path can be described by the initial configuration, objective configuration and a series of intermediate configurations. According to the deformation theory and constitutive equation in ideal path forming, a finite element method to calculate the initial configuration is set up. The functional to determinate intermediate con- figurations is introduced and the numerical method to solve the configuration is presented. Based on the method presented in the paper, multi-step multi-point forming tests for sheet metal are designed. The test results dem- onstrate that when the sheet is deformed along an approximate optimum forming path, the maximum deforma- tion curvature for the sphere objective shape and saddle objective shape are 11%-40% and 15%-50% greater than those of a sheet deformed along a common path respectively.