中文摘要：

针对三维型材拉弯,提出一种基于变形控制有限元模拟的轨迹设计方法。首先提取模具长度方向特征线并将其离散成诸多线段单元,这样毛料逐步包覆模具的过程就变成毛料包覆这些线段单元的过程。给定毛料依次包覆线段单元发生的变形,根据切线接触条件（拉弯成形过程中毛料离开模具的位置处两者相切）计算出每步毛料末端位移。将这些位移作为边界条件输入有限元模型中计算毛料应力、应变和回弹。根据成形极限图和规定最大回弹超差量来调整变形模式,找到优化的变形模式和拉弯轨迹。以中空矩形截面型材三维拉弯为例,给出了轨迹设计的详细流程。

英文摘要：

A trajectory design method using deformation controlled finite element （FE） simulation is presented for the three-dimensional （3D） profile stretch bending process. First, a curve is extracted from the CAD model of the stretch bending die to represent the lengthwise feature of the die and it is discretized into many line segments. Thus the process of the blank wrapping the die becomes a process of the blank wrapping these line segments. Then the deformation of the blank as it wraps around each segment is given; thus blank end displacements are calculated according to this deformation mode and its tangent contact condition since in stretch bending the blank is tangent to the die surface where it leaves the die. The calculated end displacements are input into the FE model as boundary conditions to compute the stress, strain and springback of the workpiece. Deformation mode is adjusted according to forming limit diagram （FI.D） and maximum springback error, so the optimized one can be found, which in turn optimizes the stretch bending trajectory. Finally, the detailed design process of a trajectory for 3D stretch bending of a rectangular hollow profile is given as an example.