超薄快速铸轧过程轧制压力分布的数学模型与实验研究(Ⅰ)——铸造区轧制压力分布的数学模型

Modelling and Simulating Investigation of Rolling Pressure Distribution at Ultra-thin High-speed Roll Casting(Ⅰ)-Model of Rolling Pressure Distribution in Casting Zone

超薄快速铸轧速度可达常规铸轧速度的十几倍 ,甚至二十几倍 ,在快速铸轧条件下铸造区长度将增加 ,其轧制压力分布对总轧制力的影响就不可忽略。因此建立该区的轧制压力分布模型是必须的。本文利用切块法推导出超薄快速铸轧过程铸造区 (结晶区 )内微元体静力平衡微分方程 ,并利用龙格 库塔法对该微分方程进行数值求解 ,即可求出铸造区轧制压力分布。该模型同样适用于常规铸轧条件。

The speed of ultra thin high speed roll casting is ten times,even more than twenty times as high as that of the conventional roll casting.The length of the casting zone will increase under high speed roll casting condition;thus the influence of roll pressure distribution in the casting zone on the total rolling force can not be ignored.Therefore,it is necessary to establish a model of rolling pressure distribution in the casting zone.Static equilibrium differential equation of the micro body in the casting zone during ultra thin high speed roll casting process is deduced by using slab method in this paper.The differential equation is solved by using Runge Kutta method;consequently,the rolling pressure distribution in the casting zone is obtained.This model can also applied to the conventional roll casting condition.