楔横轧窄台阶轧齐曲线的微分方程解法

Differential equation solution of shaping curves for narrow steps in cross wedge rolling

为了解决目前轧齐理论应用于窄台阶轧齐曲线求解时精确性不足的问题,同时为了进一步了解轧齐成形本质,通过改进几何模型,分析并给出各影响因素之间关系函数,将轧齐曲线求解问题描述成为微分方程初值问题.通过软件编程应用数值方法进行求解,得到窄台阶轧齐曲线函数的离散值.使用有限元模拟计算及轧制试验的方法,将计算结果与文献作对比.通过对比分析模拟和实验结果中台阶面的尺寸,证明该解法不但是成立的,而且有利于成形更加精确的内侧较窄直角台阶.

Existing methods are not accurate enough to apply in the solution of shaping curves for narrow steps in cross wedge rolling.In order to solve this problem and explore the shaping essence,the curve solution was described as the initial value problem of a differential equation by improving the previous geometric model and analyzing the relationships among various factors in shaping processes.A numerical method by mathematical programming software was used to solve the discrete results of the shaping curves.Through simulation and practice experiments,the calculated results were compared with data in literatures.The comparison of step size obviously shows that this method is not only able to be established,but also better than previous methods on the shaping accuracy of narrow steps.