Numerical Assessment of Interstand Tensions in Continuous Hot Rolling Processes of Flat and Long Products

The paper deals with the calculation of interstand tensions in continuous rolling mills for flat and long products. In the rolling mill industry, the digitization has reached a state in which a continuous measurement and data collection of roll forces, roll torques, temperatures and roll velocities is possible. However, the important process parameter of interstand tensions is not directly measurable and no direct calculation of the interstand tensions in the form of mechanical stresses is possible. A fast calculation method for the interstand tensions from measurable process quantities is a critical point to enable the construction of digital twins for the rolling process of continuous rolling mills.
It is straightforward to calculate the effects of the tensions on roll forces, torques and the strip or bar velocity. However, the inverse problem of calculating the acting interstand tensions including their effects from the process parameters is of much greater interest but also of a higher complexity, because the interactions between all of the stands in the continuous rolling mill must be taken into account.
The present paper aims at filling this research gap by presenting a mathematical model to solve the inverse problem by subsequent linearization of the tensions influences in the rolling mill. Extra nonlinearities are taken into account by modeling the tension-dependent spread by an empirical model. The overall model is solved by an iteration method to yield a fully compatible solution for the constant volume flux as well as the force and torque equilibria in the roll gaps. Results are shown for the tension distributions in strip and rod mills. The results indicate that the present friction conditions and the spreading behaviour of the rolled material have a high impact on the tension distributions.

本文针对扁平材与长材用连续轧机的机架间张力（interstand tensions）计算展开研究。当前轧钢行业已实现数字化转型，可对轧辊力、轧辊扭矩、轧制温度及轧辊速度开展连续测量与数据采集。然而，作为关键工艺参数的机架间张力无法直接测得，也无法通过机械应力形式直接计算。从可测工艺量快速计算机架间张力的方法，是构建连续轧机轧制过程数字孪生（digital twins）的核心前提。

通过张力对轧辊力、扭矩及带材/棒材轧制速度的影响进行正向计算较为简单。但从工艺参数反推实际作用的机架间张力及其影响的逆问题，虽更具研究价值，复杂度也更高——因为必须考虑连续轧机各机架间的相互作用。

本文旨在填补这一研究空白，提出一种通过对轧机中张力影响进行后续线性化来求解该逆问题的数学模型。通过经验模型对张力相关的轧制延展行为进行建模，可进一步纳入额外非线性因素。整体模型采用迭代法求解，能够同时满足体积流量恒定、轧辊间隙内力与力矩平衡的全相容条件。文末给出了带材轧机与棒材轧机的张力分布计算结果，结果表明，当前摩擦条件及轧制材料的延展行为对张力分布具有显著影响。