Enhancement of width and thickness tolerances of metallic strips by using a piezo-electric control system for roll gap adjustment of a tandem mill

金属薄带是工业上广泛加工的一组产品。随着技术设备的不断小型化，对通常为冷轧带材的形状公差提出了更高的要求。最高精度级别的标准化厚度公差为±15微米。它在第一个资助期减半。这是通过在辊架中添加用于调整辊缝的辅助压电叠层致动器(PSA)来实现的，以实现高频和高精度操作。在此基础上，利用平衡法建立了基于轧制理论的精确辊缝模型，设计了两自由度控制器。同时，设计了一种模型预测控制器。它使用输入的带钢轮廓来生成PSA的最优轨迹。它在模拟方面显示出了进一步的改进，并将得到实验验证，直到本周期结束。与带钢厚度公差相比，带钢宽度公差要大得多。这是因为在制造过程中，从较宽的部分切割出较窄的条带。在许多应用中，不仅关系到带钢厚度的精度，而且关系到带钢宽度的精度。因此，拟议项目的目标是研究一种同时减小宽度和厚度公差的方法。±65微米(钢，DIN10140)和±100微米(铜，DIN13599)的标准宽度公差应降至±10微米。在轧制过程中，材料不仅沿轧制方向流动，而且横向流动。因此，可以使用两个连续的辊型来设置带钢厚度和宽度。所用系统的能力足以实现材料在宽度方向上的延伸，同时控制其厚度。因此，该工艺将扩展到第二个辊架。通过选择两个特定的厚度减量，将控制带材的宽度和厚度。在开始时，将命令两个专用的厚度控制器根据基于模型的查找表生成单独的厚度减量。这两个厚度减小可能允许产生产生相同形状的不明确解。因此，在以后的阶段，材料模型将被集成到模型预测控制器的成本泛函中，该模型预测控制器优化减薄以最小化执行器的位移。为了实现这一目标，基本的轧制模型将被扩展，将平衡法中的板坯替换为无限小的棒材，这也允许考虑材料在宽度方向上的流动。力方程导出一个可以用数值方法求解的偏微分方程式。在考虑流动规律的情况下，可以预测材料在宽度方向上的扩散。

Thin and narrow metallic strips belong to a group of products which is widely processed in industry. The ongoing miniaturization of technical devices comes with a demand for enhanced shape tolerances of those strips which are usually cold rolled.The standardized thickness tolerance of the highest precision class is ±15 µm for those strips (DIN10140). It was halved in the first funding period. This was done by adding supplementary piezoelectric stack actuators (PSA) for roll gap adjustment into a roll stand for high frequency and high precision operation. Furthermore a two-degree-of-freedom controller was developed on the basis of a precise roll gap model based on the rolling theory using the equilibrium method. Also, a model predictive controller has been developed. It uses the incoming strip profile to generate an optimal trajectory for the PSA. It has shown further improvement in simulation and will be experimentally validated until the end of the current period. Compared to strip thickness tolerances, the tolerances for strip width are a lot larger. This is due to the manufacturing process in which narrow strips are cut from a broader piece. In many applications, not only the precision of the strip thickness, but also the precision of its width matters. Hence, the goal of the proposed project is the investigation of a method for reduction of width and thickness tolerances at once. The standardized width tolerances of ±65 µm (steel, DIN10140) and ±100 µm (copper, DIN13599) shall be reduced to ±10 µm. In the rolling process, material does not only flow along the rolling direction, but also flows crosswise. Therefore, two consecutive roll passes can be used to both set the strip thickness and its width. The capabilities of the used system are sufficient to achieve a material extension in width direction and simultaneously control its thickness. Hence, the process will be extended to a second roll stand. By choosing two specific thickness reductions the strips width and thickness will be controlled.In the beginning, two dedicated thickness controllers will be commanded an individual thickness reduction which is generated from a model-based lookup table. The two thickness reductions may allow for ambiguous solutions which result in the same shape. Thus, in a later stage, the material model will be integrated in the cost functional of the model predictive controller which optimizes the thickness reductions for minimal actuator displacements.To achieve that goal, the underlying rolling model will be extended by replacing the slabs from the equilibrium method with infinitely small rods which also allows the consideration of material flow in width direction. The equation of forces then leads to a partial differential equation which can be solved numerically. Under consideration of the flow law the material spread in width direction can be predicted.