椭圆异型挤压塑性成形映射理论及模腔优化解析

MAPPING ANALYSIS OF METAL FORMING AND OPTIMIZATION OF DIE CAVITY IN ELLIPSE-SHAPED EXTRUSION

针对金属椭圆异型挤压塑性成形及模腔优化的理论课题,应用复变共形映射数学研究成果,利用奇偶点相互迭代的三角插值法和法线收敛法,将三维金属异型挤压塑性成形问题转化为二维轴对称成形问题,求解异型挤压模腔曲面函数,建立映射函数解析方法,推导椭圆异型材挤压金属塑性成形连续流动场和应变速度场的数学解析式,并应用金属塑性成形能量极值原理,进行异型材挤压模腔参数的优化,同时为精密快速地实现挤压模腔的CAD/CAM一体化目标提供技术支持。

On the basis of conformal mapping, a three-dimensional metal forming problem during irregular extrusion is transformed into a two-dimensional axisymmetric problem. The normal convergence approach and the trigonometric iterative interpolation between odd and even grid points are employed in the transform. An analytical expression of the curved surface of extruding die cavity is obtained. The plastic flow during metal forming and the strain rate are given explicitly. With the help of energy principle for metal forming, the parameters for optimization of die cavity are determined. It is believed that the present work offers useful information for quick and accurate CAD/CAM integration.