楔横轧轧齐曲线的微分方程解法

Differential equations for solving shaping curve of inside right-angle steps in cross wedge rolling

为了解决当前轧齐理论应用于复杂台阶轧齐曲线求解时存在精确性不足的问题,同时为了进一步探究轧齐成形的本质,通过改进以往解法中的几何模型,分析并给出各影响因素之间的关系函数,将轧齐曲线求解问题描述为微分方程初值问题;以内直角台阶作为实例,通过数学软件编程对微分方程进行求解,得到轧齐曲线离散函数;利用结果建立三维模型并设计轧辊,进行有限元成形模拟和轧制实验。通过对比台阶面的平面性以及展宽槽宽度,证明该解法不仅成立,同时能够成形质量更优的内直角台阶。

In order to solve the weaker precision problem when using existing method to calculate some complicated sha- ping curve, the study was conducted. The shaping curve solution was described as initial value problems of differential equation by improving the previous geometric model and analyzing the relationships between various factors of shaping. Using mathematical programming software, the shaping curve of inside right-angle step was presented. According to the results, the three-dimensional models were established. The shaping process was simulated by the method o{ FEM. The rolling experiments with same parameters were conducted too. According to comparison between results of simulations and experiments, the step-face plainness and the step-slot width obtained by the new methods are better than the older, which prove this method is not only tenable, but also can get better inside right-angle step.