应变矢量内积法求解带鼓形的矩形坯锻压(英文)

Solution of rectangular bar forging with bulging of sides by strain rate vector inner-product

提出一种新的线性化积分方法用于求解平锤头压缩带外端的矩形件。在锻压过程中,锤头没有覆盖整个工件,并且工件的侧面通过变形产生鼓形。应用该方法得到了平均锻压力,同时在求解的过程中进行了下列假设:工件与工具间的摩擦力为常数,工件是刚-塑性材料,锻压是在低速度下进行的。然后,通过纯铅的锻压实验,将由黄金分割法得到的优化结果与试验机的实测值进行比较,结果表明优化值比实测值高2.60%-10.14%,这在工程上都是允许的。

Abstract：ools. The effective strain rate for for determining the total pressure developed during forging of a rectangular bar forging with bulging was expressed in terms of four-dimensional strain rate vector. The inner-product of the vector was termwise integrated and summed. The integral mean value theorem was applied to determining the ratio of the strain rate components and the values of direction cosine of the vector and then an analytical solution of stress effective factor was obtained. The compression experiments of pure lead bar were performed to test the accuracy of the solution. The optimized results of total pressure by golden section search were compared with those of the indicator readings of the testing machine. It indicates that the optimized total pressures are 2.60%-10.14% higher than those measured. The solution is available and still an upper-bound solution.