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类产品。随着技术设备的不断小型化，对通常冷轧的带材的形状公差提出了更高的要求。这些带材的最高精度等级的标准化厚度公差为±15 µm（DIN 10140）。在第一个供资期内减少了一半。这是通过将用于辊缝调节的辅助压电叠层致动器（PSA）添加到用于高频和高精度操作的辊架中来实现的。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，并在此基础上设计了一种双自由度控制器。此外，模型预测控制器已被开发。它使用输入的带材轮廓来生成PSA的最佳轨迹。在模拟方面已显示出进一步的改进，并将在本报告所述期间结束前通过实验加以验证。与带材厚度公差相比，带材宽度公差要大得多。这是由于制造过程中，窄带是从一个较宽的一块切割。在许多应用中，不仅带材厚度的精度很重要，而且带材宽度的精度也很重要。因此，拟议项目的目标是研究一种同时减少宽度和厚度公差的方法。标准化宽度公差±65 µm（钢，DIN 10140）和±100 µm（铜，DIN 13599）应减少到±10 µm。在轧制过程中，材料不仅沿着轧制方向流动，而且还沿轧制方向流动。因此，可以使用两个连续的轧辊道次来设定带材厚度和宽度。所使用的系统的能力足以实现材料在宽度方向上的延伸并同时控制其厚度。因此，该工艺将扩展到第二个轧机机架。通过选择两个特定的厚度压下量，将控制带材的宽度和厚度。开始时，两个专用厚度控制器将被命令从基于模型的查找表中生成单独的厚度压下量。两个厚度减小可以允许导致相同形状的模糊解决方案。因此，在稍后的阶段，材料模型将被集成到模型预测控制器的成本函数中，该模型预测控制器优化厚度减少以实现最小的致动器位移。为了实现该目标，底层的轧制模型将通过用无限小的杆代替来自平衡方法的板坯来扩展，该杆还允许考虑材料在宽度方向上的流动。力的方程然后导致一个偏微分方程，可以数值求解。在考虑流动规律的情况下，可以预测材料在宽度方向上的铺展。

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.