有鼓形圆坯锻造应变速率矢量内积的积分

SOLUTION FOR DISK FORGING WITH BULGE BY STRAIN RATE VECTOR INNER-PRODUCT INTEGRATION

提出了一种新的线性化积分方法。首先将有鼓形圆盘锻造等效应变速率表示成二维应变速率矢量,对该矢量的内积进行了逐项积分;其次,将逐项积分结果求和并证明了求和结果与传统直接积分法的塑性功率表达式相同;最后由速度场推导出圆盘锻造应力影响因子的解析解与相应的鼓形参数b的计算公式。此外,进行了实际的压缩试验并按上述公式计算了应力状态系数;并将计算结果与Avitzur公式的计算结果及实验机的压力读数进行了比较,结果表明,计算的总压力与Avitzur公式的计算结果基本一致,但高于实测压力值,该解仍属于上界解。

A new linear integration is proposed in this paper. First, effective strain rate for disk forging with bulge is expressed in terms of two-dimensional strain rate vector and its inner-product term by term integrated. Then, sum of the termwise integrated results is proved to be equal to that obtained from traditional immediate integration for plastic deformation power. Finally, an analytical solution of stress effective factor and corresponding calculation formula of bulge parameter b are deduced from velocity field for the disk forging. Furthermore, the actual press tests were performed and the stress factors calculated from above formula. The calculated results were compared with those obtained from Avitzur formula and total indicator reading of the machine. It turns out that the total pressures calculated are basically in agreement with those obtained from Avitzur＇s, and higher than the measured values. It still belongs to an upper bound solution.