基于共形映射的壁板型材挤压模具型腔建模  

Modeling for Shape Extrusion of Aluminum Alloy Flat-plate Based on Conformal Mapping

作　　者：胡龙飞[1] 刘全坤[1] 冯秋红 

机构地区：[1]合肥工业大学材料科学与工程学院,合肥230009 [2]中国联合工程公司,杭州310022

出　　处：《机械工程学报》2008年第8期180-184,共5页Journal of Mechanical Engineering

基　　金：安徽省自然科学基金(070414146);高等学校博士学科专项科研基金(2003 0359002)资助项目

摘　　要：针对复杂铝合金壁板导流模挤压过程中出现的挤压力大、变形不均等缺陷,采用流函数理论建立扁挤压筒型腔到型材出口之间过渡曲面的边界条件。根据复变函数共形映射理论,讨论Schwarz-Christoffel积分变换的正反求解过程;应用Taylor级数凸凹分级展开技术,处理映射精度问题。最终,构造壁板外形单连通域到单位圆周的映射函数,并以此建立壁板挤压模型腔曲面数学方程,利用三维造型软件完成了复杂型材挤压'流线型'过渡曲面的三维建模。Considering the excessive extrusion force and non-uniform deformation in the forming process of aluminum alloy flat-plate with flow-guide die, the boundary condition of transitional surface between flat extrusion container cavity and the inlet of shape metal is established based on the stream function method. According to conformal mapping theory of complex function, forward and reverse solution procedure of Schwarz-Christoffel transformation is analyzed. For handling the problem of mapping accuracy, the convex-concave expansion technology for Taylor series expansion is adopted. Further, the mapping function from the simply connected region of flat-plate to the unit circle is acquired, and based on this, the mathematical representation of transitional surface is established. Finally, the streamlined 3D model of transitional surface is obtained by using CAD software.

关 键 词：共形映射 壁板型材 Schwarz-Christoffel变换 流线型 过渡曲面 

分 类 号：TG376.2[金属学及工艺—金属压力加工]