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

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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.