几何非可展异型盒形件拉深毛坯近似展开计算

Approximative unbending of drawing workpiece for free-form boxshaped part with non-unbendable features in differential geometry

提出了一种映射变换方法:在分析传统拉深件毛坯尺寸计算方法的基础上,建立异型盒形件的毛坯近似展开的计算模型。利用微分几何中的诱导映射理论求得非可展曲面到平面域内的变换关系。分析该变换关系的简化算法,以一换挡板拉深件为实例验证了该算法的有效性。结果表明,该算法与传统毛坯计算方法相结合,可以获得符合生产的毛坯尺寸和形状,对异型盒形件的毛坯展开计算具有普适意义。

A mapping transformation method was put forward to accurately determinate workpiece dimension of boxshaped drawing parts with non-unbendable features in differential geometry. The calculation model of the workpiece approximative unbending was set up on the basis of the analysis of the traditional unbending method of the drawing part. The abduction mapping method was introduced to deduce the transformation relation between the non-unbendable surface and the flat surface. A discrete algorithm was analyzed for simplifying this transformation. The validity of this algorithm was confirmed via a shift panel. The results show that this method combined with the traditional method can obtain the correct workpiece shape and dimension, and is suitable for the workpiece calculation of the free-form boxshaped drawing part.