用流函数分析平面轧制问题

Analysis of Plate Rolling Process Using Flow Function

给出了一种用流函数求解理想刚塑性材料的平面应变轧制的方法。速度场被分解为基础速度场和附加速度场。基础速度场满足边界上给定的速度条件,附加速度场满足齐次边界条件。与这两部分速度场相对应,有基础流函数和附加流函数。基础流函数可以确定地写出,附加流函数则借助于Weierstrass定理写成完备空间的向量族,即多项式。通过使全功率极小化,可以将多项式系数确定。用这一方法求得了速度场、应力场、塑性区前后边界,接触弧上中性点的位置和轧制单位压力,并与工程方法的计算结果作了比较。

The velocity field is devided into the basic and additional fields. The basic velocity field should satisfy given conditions on boundary, but the additional velocity field should only satisfy the uniform boundary conditions. Corresponding to those two parts of velocity field there are basic flow function and additional flow function. The basic flow function can be written definitly, while the additional flow function, according to the Weierstrass theorem, has been written as a family of vectors in complete space, i.e. a polynomial. With the aid of minimization of the total power the coefficients of the polynomial hare been defined. By using this method, the following results are obtained: velocity field, field of strain-rate, stress field, the back and front boundaries of plastic zone, the position of neuture point on the contact arc, and the rolling pressure acting on the contact surface of the strip.