对柔性三维拉弯成形工艺进行了研究，给出了三维弯曲成形件的数学表达式．通过分析柔性三维拉弯成形过程中型材的水平和垂直方向的变形，给出了控制成形件水平方向和垂直方向形状的单元体调形方法与夹钳的拉弯轨迹计算方法．根据柔性三维拉弯工艺中单元体调形多点控制的特点，定义了多点模具的调形参数，给出了单元体与成形件接触的几何关系，并给出了描述单元体上多点模具包络形状的三次 B 样条插值方法．基于上述的几何关系和多点模具的调形参数，使用圆弧对夹钳的拉弯轨迹进行计算．对 L形截面铝型材的三维拉弯成形实验结果表明，成形件轮廓误差小于0.7%，验证了上述方法的实用性．

In this paper,the flexible 3D stretch- bending (FSB) process is investigated,and the mathematicalexpressions of the formed parts are put forward.Then,a method to adjust the flexible fundamental units (FFU)and a calculation algorithm of clamp stretch- bending trajectories are proposed by analyzing the deformation processin the horizontal and vertical directions.By considering the multipoint control of the FFU envelop shape,theadjustment parameters of multi- points dies (MPD) are defined,and the geometric relationship between the FFUand the workpiece is established.Moreover,an interpolation method based on cubic B- spline is presented todescribe the envelop shape of MPD.Based on the above- mentioned geometric relationship and MPD adjustmentparameters,the arc stretch- bending trajectories of the clamp are calculated.Finally,3D stretch- bending experi-ments of the L- section aluminum profile are conducted.The results show that the formed part is of a measured con-tour error of less than 0.7%,which indicates that the proposed methods are practical.