应变速率矢量内积解三维锻压

Solving forging of three-dimensional with strain rate vector inner-product

将三维锻压的等效应变速率表示成二维的应变速率矢量,然后利用积分中值定理确定应变速率比值函数及该矢量的方向余弦,再对其内积进行逐项积分。将逐项积分结果求和,并得出三维锻压力的计算公式与鼓形测量公式的解析解,经纯铅锻压试验将锻压力的计算结果与实测结果比较表明,由该解析解计算的结果高于实测结果,优化后的误差缩小到不大于11.2%,说明此解仍属于上界解。

First,effective strain rate for three-dimensional forging is expressed in terms of two-dimensional strain rate vector,then,strain rate ratio function and direction cosine of this vector are determined,and finally the inner-product of the vector is term by term integrated.Sum of the integrated results yields the analytical solution of forging force and bulging parameter.With the pure lead press and compared the pressure between the measured one and the calculate,the result turns out that the calculated results by the analytical solution are higher than measured.However,after optimization of the results,the relative error is reduced to no more than 11.2 %.It shows that the solution is still an upper-bound one.