EP1600221A1 - Method for the calculation of the geometrical form of rolled material - Google Patents

Abstract

Variation in geometrical form of the rolled material is calculated for each individual pass, introducing the geometry of the roller gap into the calculation for one or more passes. To determine this geometry, a mathematical model is employed. Thickness profile in the preceding pass is taken into account in each current pass under observation. The results are used to improve the geometric form of the rolled material, using a control process to approach the desired form. The sequential quadratic programming (SQP) method is employed. Results of calculation are used as control magnitudes for the process.

Description

The invention relates to a method for calculating the geometric shape of Rolling stock, in particular of sheet metal, using mathematical equations.

The invention is particularly suitable for unfinished metal sheets, which are located on a heavy plate mill, Rolling broadband line or Steckel-Mill.

The change of the geometric shape arises from material shifts in Longitudinal direction (towards the head and towards the foot of the sheet) and in the lateral direction Direction. For example, arise from rectangular slabs (materials) mostly Sheets with a deviation from the rectangular shape. With the geometric shape of the Rolled material is in this invention, the shape, ie the contour of the rolling stock (sheet) meant when looking in the direction of the surface normal of the rolling stock on the rolling stock looks (about the rolling stock viewed from above or below).

From the article Development of a New Plan View Control Pattern System in Plate Rolling ", by Tadaaki Yanazawa, Takahiro lkeya, Jun Miyoshi, Hiroyuki Kikugawa, Kazuya Tsubota, Kazushi Baba; Kawasaki Steel Technical Report No. 1 September 1980 (first published at the AISE 1979 Annual Convention in Cleveland, Ohio) known to predict the geometric shape of a sheet after rolling, by using statistical evaluations empirical formulas for the geometric Form of the relative reduction (reduction r, page 37, Formula (1)) and the length of the arc of contact, page 37, formula (1)) depend on the individual stitches. To correct the geometric shape is then rolled about a wedge-shaped contour.

An object of the present invention is now to provide a more accurate method for Calculation of the geometric shape of rolling stock to provide, with which a more accurate method for improving the geometric shape of rolling stock can be created.

This object is achieved by a method according to claim 1.

New to this invention is that the geometry of the roll gap (also called Roll gap contour or nip profile called) is taken into account, usually with the help calculated from mathematical models, see for example the European Patent Application No. EP-A 1240955 of the Applicant, which is hereby incorporated into the subject Revelation is included. Material shifts occur during rolling namely among other things by the differences between the incoming rolling stock profile and the nip profile. Because of this, it is corresponding to elongations and / or Breitungen, so that the rolling form undesirable forms and of the most deviates rectangular nominal shape. This results in loss of output caused by the Invention can be reduced.

By calculating the geometric shape of the rolling stock after each pass, can much more targeted unwanted changes in the geometric shape of the rolling stock detected and measures are taken against it.

The material shifts are described by mathematical equations, in the rolling parameters (e.g., entrance thickness, entrance width, entrance length, exit thickness, Exit width, exit length, length of the contact arc, rolling force, temperature, Material strength), the geometric shape before the stitch and possibly the Enter parameters of a stuffer.

Preferably, the geometry of the roll gap goes in the previous stitches and in the considered stitch. The geometry of the roll gap results from the deformation of the set of rollers due to the forces occurring (see European patent application no. EP-A 1240955 of the applicant) taking into account the thermal crowning and the Wear of the rollers. For the thermal crowning and the roll wear are the skilled person known models, so that the modeling of these processes does not need to be discussed further.

When heavy plate rolling, the material is rotated between some stitches, mostly to 90 °. These rotations are taken into account. When rotated by 90 °, the Material edges on the head and foot to side edges, the side edges to head and Foot edges.

Preferably, the course of the exit thickness over the length (in the rolling direction) is also in the considered stitch and the previous stitches. For example, between The stitches turn 90 °, the differences in thickness, which now transverse to Rolling lie, for material displacements in the longitudinal direction. Did not turn, The thickness differences in the rolling direction can be different Material shifts in latitude and also lead longitudinally.

• Aufwalzen einer Dickenkontur in bestimmten Stichen
• Verwendung eines Vertikal-Stauchgerüstes
• gezieltes Schleifen der Walzen
• Verändern des Brammenformates (bzw. allgemein des Vormaterialformates)
• gezieltes Verändern des Stichplanes
• gezieltes Drehen des Materials um bestimmte Winkel (Schrägwalzen)

entgegengewirkt werden.The deviation from the desired shape (eg rectangle) can be achieved by measures such as

• Rolling a thick contour in certain stitches
• Use of a vertical upsetting frame
• targeted grinding of the rolls
• Modification of the slab format (or in general of the pre-material format)
• purposefully changing the stitch plan
• targeted turning of the material by certain angles (oblique rollers)

be counteracted.

Starting from a stitch plan, or in connection with the creation and optimization of a stitch plan, the geometric shape of the rolling stock can during and at the end of the rolling stock Rolling process can be predicted.

In a mathematical procedure, such as an iterative process or a Method of mathematical optimization, the possible influencing variables (such as e.g. Thick contour, width or width in one stitch, stitch number, Stichabnahmen) changed so that the deviation from the desired shape (am End and during the rolling process) becomes minimal. The actuators are doing this also considered their functional limits.

The inventive method can be used on the one hand, that the Calculation off-line for calculating pass-through schedules for subsequent ones Rolling processes is performed. The calculated pass plans can be used, for example, for Design of equipment, selection of pre-material formats or selection of a Roll grinding be used.

On the other hand, the inventive method can also be used for that the calculation on-line immediately before and / or during the rolling process performed and the results of the calculation to control the rolling process be used. In this case, immediately before the rolling process using actual measured values of the rolling train the calculation of setting values for the control of the Rolling process done as well as the rolling process itself by a during rolling performed calculation.

The shape of the blank sheet during rolling and after rolling can be done by hand or by means of automatic measuring devices, e.g. Camera, to be measured. The measured values can be used to adapt the parameters of the calculation. For the Parameterization could also be used neural networks.

The invention is based on the calculation of the sheet shape on the foot after a stitch a heavy plate mill are exemplified:

bezeichnet.The shape of the sheet at the head after the stitch n can be represented by a function k _n (x), which is defined over the interval [-w _n / 2, w _n / 2]. x represents the running variable along the width direction of the tape. Now, if the next stitch without material rotation in the opposite direction, the shape of the sheet on the foot after the stitch n + 1 by a function f _{n + 1} (x) can be described. The function f _{n + 1} (x) is dependent on the entrance thickness h _n , entrance width w _n , entrance length In, exit thickness h _{n + 1} , exit width w _{n + 1} , exit length I _{n + 1} , length of the contact arc Id _{n + 1} , Rolling force F _{n + 1} , temperature T _{n + 1} , material strength s _{n + 1} according to the equation f n + 1 (x) = (h n /H n + 1 ) (K n * P (h n , w n , I n , H n + 1 , w n + 1 , I n + 1 , Id n + 1 , F n + 1 , T n + 1 , s n + 1 )) (X) + Q (h n , w n , I n , H n + 1 , w n + 1 , I n + 1 , Id n + 1 , F n + 1 , T n + 1 , s n + 1 , x) + R (x) where P and Q are the material equations which also contain empirically determined parameters, and (f * g) the mathematical convolution according to

designated.

An example of a function is P P (h n , w n , I n , H n + 1 , w n + 1 , I n + 1 , Id n + 1 , F n + 1 , T n + 1 , s n + 1 ) (x) = min (0, max (p 1 , p 2 + (p 3 H n + p 4 w n + p 5 I n + p 6 H n + 1 + p 7 w n + 1 + p 8th I n + 1 + p 9 id n + 1 + p 10 F n + 1 + p 11 T n + 1 + p 12 s n + 1 + p 13 ) | x | p 14 )), an example of a function Q is Q (h n , W n , I n , H n + 1 , w n + 1 , I n + 1 , Id n + 1 , F n + 1 , T n + 1 , s n + 1 , x) = (q 2 + q 3 H n + q 4 w n + q 5 I n + q 6 H n + 1 + q 7 w n + 1 + q 8th I n + 1 + q 9 id n + 1 + q 10 Fn + 1 + q 11 T n + 1 + q 12 s n + 1 ) (1 + q 1 | x / w n | q 13 ).

The parameters p ₁ to p ₁₄ and q ₁ to q ₁₃ represent empirically determined parameters.

The function R (x) describes the material flow, which arises in the longitudinal direction beyond that the relative nip profile in the stitch n + 1 Gr _{n + 1} (x) from the material profile after the stitch n pr _n (x) (which in turn is known from the roll gap profiles Gr ₁ , ..., Gr _n accordingly pr k + 1 (x) = X (h k , w k , I k , H k + 1 , w k + 1 , I k + 1 , Id k + 1 , F k + 1 , T k + 1 , s k + 1 ) (Gr k + 1 (x) - Pr k (x)) + Pr k (X) depends) according to the equation R (x) = Y (h n , w n , I n , H n + 1 , w n + 1 , I n + 1 , Id n + 1 , F n + 1 , T n + 1 , P n + 1 ) (Gr n + 1 (x) - Pr n (X)). An example of a function X is X (h k , w k , I k , H k + 1 , w k + 1 , I k + 1 , Id k + 1 , F k + 1 , T k + 1 , s k + 1 ) = min (0, max (1, x 1 + x 2 (H k + 1 / w k + 1 - x 3 ) x 4 )), an example of a function is Y. Y (h n , w n , I n , H n + 1 , w n + 1 , I n + 1 , Id n + 1 , F n + 1 , T n + 1 , s n + 1 ) = min (0, max (1, y 1 + y 2 (H n + 1 / w n + 1 - y 3 ) y 4 )), where the parameters x ₁ , x ₂ , x ₃ , x ₄ , y ₁ , y ₂ , y ₃ , y ₄ of h _n , w _n , I _n , h _{n + 1} , w _{n + 1} , I _{n + 1} , Id _{n + 1} , F _{n + 1} , T _{n + 1} , s _{n + 1} .

If the sheet has been rotated by 90 ° between stitches n and n + 1, then the flow of the exit thickness rolled in stitch n over the length Lr _n in stitch n replaces Pr _n .

For the realization on a computer system all mentioned functions have to be done by Standard methods of numerical mathematics are discretized. (such as. described in Schwarz, Hans R .: Numerische Mathematik. Teubner, 1997.)

The method just explained for calculating the geometric shape of the rolling stock is now used to determine manipulated variables by means of which the deviation from the desired shape (at the end and during the rolling process) is minimized. This will be explained below by way of example for the case that the stitch plan (the sequence of stitch heights) is already determined that a rectangle as long as possible with a given nominal width should be included in the sheet shape, and that in the stitches i ₁ ,. .., i _j , rolling longitudinal contour represents the manipulated variable.

The target size for the sheet shape on the head and foot after the last stitch m is the sum of the minima of the sheet metal form descriptive functions over the target width

gegeben.The manipulated variables in this case are the curves of the outlet thicknesses, which, as described above with Lr _{i l} ( x ), ..., Lr _{i j} ( x ) are designated. Restrictions are mostly due to the mechanics and hydraulics of the rolling mill in the mold

given.

For optimization can now be a standard mathematical method, such as a SQP method (Sequential Quadratic Programming, for example described in Schittkowski Klaus: "On the Convergence of a Sequential Quadratic Programming Method with Augmented Lagrangian Line Search Function ", Math. Operations Research and Statistics, Ser. Optimization, Vol. 14 (1983) No.2, pages 197-216).

The erfindungegemäße method can be both for homogeneous cuboid Materials (slabs), as well as non-cuboid materials (ingots), as also used for materials which are composed of several layers become.

Claims (8)

Method for calculating the geometric shape of rolling stock, in particular sheets, using mathematical equations, characterized in that the change in the geometric shape of the rolling stock is calculated in each individual stitch, wherein for at least one stitch, the geometry of the roll gap is included in the calculation. A method according to claim 1, characterized in that a mathematical model of the roll gap is used for the determination of the geometry of the roll gap. A method according to claim 1 or 2, characterized in that for each stitch the geometry of the roll gap in the previous stitches and in the considered stitch enter into the calculation. Method according to one of claims 1 to 3, characterized in that for each stitch, the thickness profile in the previous stitches and in the considered stitch enter into the calculation. Method according to one of claims 1 to 5, characterized in that the mathematical function which describes the shape of the rolling stock after a stitch, the folding of the mathematical function of the shape of the rolling stock before the stitch contains the material equation for the rolling stock. Method for improving the geometric shape of rolling stock, are calculated in the possible manipulated variables for the rolling process, characterized in that in the calculation of the geometric shape of rolling stock according to one of claims 1 to 5 possible manipulated variables that have an influence on the geometric shape of the rolling stock be changed so that the deviation from a desired geometric shape is minimal. A method according to claim 6, characterized in that for this purpose a mathematical method, such as a SQP method (Sequential Quadratic Programming), is used. A method according to claim 6 or 7, characterized in that results of the calculation are used as manipulated variables for the rolling process.