变厚度轧制时质量守恒的表述方式

On the law of mass conservation for variable gauge rolling

在等厚度稳定轧制过程中,质量守恒定律通常被表述为秒流量相等原则.变厚度轧制时仍需满足质量守恒定律,但是否遵守秒流量相等原则,需要进行充分论证.本文从分析变厚度轧制的几何关系及微元体变形入手,研究了轧辊在垂直方向的刚性位移速度对微元体变形的影响.采用拉格朗日构形和欧拉构形两种方法论证了变厚度轧制时秒流量相等关系不再成立,秒流量差与轧辊垂直方向刚性位移速度有关.在轧辊旋转角速度ω给定的条件下,趋厚轧制时秒流量逐渐增大,趋薄轧制时秒流量逐渐减小.对变厚度轧制过程,质量守恒定律可以表述为变形区及各个微元体发生塑性变形时体积保持不变,但不能表述为秒流量相等.

The law of mass conservation, when applied to the normal rolling processes, can be expressed as the constant mass flow principle （CMFP）. Variable gauge rolling （VGR） processes must obey the law of mass conservation, but whether these processes also satisfy the CMFP requires verification. This paper reports the effect of roll rigid displacement speed in vertical direction in rolling on the element deforment of the work piece, by analyzing the geometric relationship, metal flow, and slab element movement during VGR progress. Using both Lagrange and Euler configurations, the CMFP is demonstrated to not be suitable for VGR processes. The flow difference is related to the vertical speed of the roll. When the roll rotational speed ω is constant, the flow amount of materials in the rolling direction increases during upward rolling but decreases during downward rolling. Rather than the CMFP being applied in VGR processes, the law of mass conservation can be expressed as material volume remains constant at any time for each element during plastic deformation.