Process: Iron and Steel
Rolling Mill

Modeling and control of a four-high heavy plate rolling mill / ACIN - Automation and Control Institute / Research / CDS / Four-high heavy plate rolling mill

Burgess COMMENTARY
My first job after graduating from Cambridge was at Davy United in Sheffield, UK. Davy was one of the world's largest manufacturer of heavy equipment for the iron and steel industry including rolling mills. We were a leader in the development of automatic gauge control ... but this was in the early 1960s before large computers and mathematical simulation was being applied to the control of industrial processes. Nevertheless, the ideas described in this paper are very similar to the issues we were addressing in a much more clumsy way more than 50 years ago.
Peter Burgess

/ ACIN - Automation and Control Institute / Research / CDS / Four-high heavy plate rolling mill Home News Institute Research CDS IAT V4R Publications Teaching FESTO System Laboratory CD-Laboratory Prof. Kugi CD-Laboratory Prof. Schitter Modeling and control of a four-high heavy plate rolling mill Status: finished Project focus Modeling, identification and analysis of mechanical and hydraulic components of a finishing mill Control of heavy plate mills (feedforward thickness control) Online-Adaptation of model parameters for model based control

Description

In heavy plate rolling, the heated plates are plastically deformed by rolling mills. For this task, reversing four-high mill stands consisting of two work-rolls and two backup-rolls are often used. The deformation of the plate takes place between the two work-rolls. The high rolling forces during the deformation cause the rolls to bend which in turn yields a nonuniform thickness profile of the final product. The two backup-rolls reduce the bending deflection of the work-rolls. Additionally the mills are equipped with devices for bending compensation like hydraulic bending systems and/or specifically shaped rolls (CVC-rolls). These measures shall ensure a plain roll gap and thus a uniform lateral thickness profile of the final product.


Fig. Four-high mill stand. ... Fig. 1 Four-high rolling mill, Copyright: Dillinger Hüttenwerke AG.

During the rolling process, forces up to 90 MN act on the mill, which causes deformations of the mill of up to 13 mm. This compliance mainly consists of the elastic deformation of the mill and the bending deflection and the compression of the rolls. As thickness tolerances of 0.1 mm have to be met, it is necessary to compensate the compliance. Furthermore, the mill has to be set up in such a way that the roll gap between the two work-rolls is as flat as possible to ensure a uniform exit thickness of the plate in lateral direction. However, the exit thickness of the plate cannot be reliably measured close to the roll gap due to the hostile environment (heat, steam). The thickness measurement, which is located some meters away from the mill stand, is not useful for real-time thickness control due to the time lag. Thus, the exit thickness has to be calculated with a mathematical model. The model has to include the compliance of the hydraulic and the mechanical components of the mill stand and - especially for the calculation of the thickness profile in lateral direction - the bending and the compression of the rolls. The model results may then be used for real-time control.

For the calculation of the exit thickness, the hydraulic and the mechanical components of the mill stand have to be considered. For the calculation of the thickness profile in lateral direction, the bending and compression of the rolls have to be taken into account.


Finishing Mill - scematic. ... Fig. 2 Setup of a four-high finishing mill - front view.

Due to the dimensions of the rolls, a deflection model based on the Timoshenko beam theory is used. To fully describe the problem, the loads of the rolls and the boundary conditions have to be determined.

The rolling force is the force between the two work-rolls required for the plastic deformation of the plate. This force depends on the material of the plate, the rolling velocity, the temperature distribution as well as the entry and exit thickness profile of the plate. As the exit thickness depends on the bending of the two work-rolls, a nonlinear coupling of the differential equations of the work-rolls is obtained.

Similar considerations may be made about the contact of the work- and backup-rolls. Generally, there is a nonlinear relation between the contact force, which can be calculated using Hertz's formula -among others-, and the bending of the work- and backup-rolls.

To determine the boundary conditions, the distance between the backup-roll journals has to be identified. Apart from a calibration of the model, this requires the calculation of the deflection of the mill stand which depends on the rolling force. Moreover, friction forces acting between the roll chocks and the columns have to be taken into account. Furthermore, the position of the backup-roll journals in the hydrodynamic bearings, which depends nonlinearly on the rolling force and the rolling velocity, has to be determined.

A 2-point boundary value problem consisting of 16 coupled nonlinear differential equations has to be solved. As the model is to be used for real-time control, its calculation time must not exceed the sampling periode of the system.

The developed solution has been successfully verified with measurement data from an industrial finishing mill.


Finishing Mill - scematic side view. ... Fig. 3 Setup of a four-high finishing mill - side view.

If such a model is used in a conventional feedback controller, it is not possible to compensate for fast disturbances in the entry thickness and the yield strength of the plate due to the limited response characteristic of the positioning system and the closed loop control. Thus, strategies to estimate the entry thickness and yield strength profile during a pass where developed. By applying these profiles in the sense of a feedforward control to the next pass, it is possible to partially compensate the thickness deviations in the entry profiles.

The developed solutions were tested in computer simulations before they were applied to an industrial finishing mill stand where they are further developed successfully.

Selected publications

T. König: 'Entwicklung, Parametrierung und Online-Adaption eines mathematischen Modells eines Walzgerüstes beim Warmwalzen'; in series: 'Modellierung und Regelung komplexer dynamischer Systeme', editors: A. Kugi, K. Schlacher; Shaker Verlag, Aachen, 2014. [BibTeX]

T. König, A. Steinböck and A. Kugi: 'Online Calibration of a Mathematical Model for the Deflection of a Rolling Mill'; in: 'Proceedings of Rolling 2013', Venezia, Italy, 10.06.-12.06.2013, pp. 1-12. [BibTeX]

T. König, A. Steinböck, A. Kugi, R. Heeg and T. Kiefer: 'Deflection and bending model of a four-high mill stand for heavy plate rolling'; in: 'Proceedings of the 4th International Conference on Modelling and Simulation of Metallurgical Processes in Steelmaking, STEELSIM, METEC InSteelCon 2011', Düsseldorf, Germany, 27.06.-01.07.2011. [BibTeX]

R. Heeg: 'Modellierung und Dickenregelung beim Warmwalzen'; in series: 'Modellierung und Regelung komplexer dynamischer Systeme', editors: A. Kugi, K. Schlacher; Shaker Verlag, Aachen, 2009. [BibTeX]

T. König: 'Mathematische Modelle zur Berechnung der Auffederung eines Fertiggerüstes'; Master thesis, Vienna University of Technology, 2008. [BibTeX]

R. Heeg, T. Kiefer, A. Kugi, O. Fichet and L. Irastorza: 'Feedforward Control of Plate Thickness in Reversing Plate Mills'; IEEE Transactions on Industry Applications, 43 (2007), 2, pp. 386-394. [BibTeX]

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