AT500764A1 - METHOD FOR CALCULATING THE GEOMETRIC FORM OF ROLLING MATERIAL - Google Patents

Description

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Method for calculating the geometric shape of rolling stock

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

The invention is particularly suitable for unfinished sheets, which are rolled on a plate mill, 5 broadband line or Steckel Mill.

The change of the geometric shape results from material displacements in the longitudinal direction (in the direction of the head and in the direction of the foot of the sheet) and in the lateral direction. For example, cuboid slabs (primary materials) usually produce sheets with a deviation from the rectangular shape. In the case of this invention, the geometric shape of the rolling stock means the shape, that is to say the contour of the rolling stock (sheet), when looking at the rolling stock in the direction of the surface normal of the rolling stock (for example the rolling stock viewed from above or below).

From the article "Development of a New Plan View Pattern Control System in Plate Rolling," by Tadaaki Yanazawa, Takahiro Ikeya, Jun Miyoshi, Hiroyuki Kikugawa, 15 Kazuya Tsubota, Kazushi Baba; Kawasaki Steel Technical Report No. September 1, 1980 (first published at the AISE 1979 Annual Convention in Cleveland, Ohio), it is known to predict the geometric shape of a sheet after rolling by establishing empirical formulas for the geometric shape based on statistical evaluations derived from relative sampling ( reduction r, page 37, 20 formula (1)) and the length of the contact arc (length of arc of contact, page 37, formula (1)) depend on the individual stitches. To correct the geometric shape, a wedge-shaped contour is then rolled on.

It is therefore an object of the present invention to provide a more accurate method of calculating the geometric shape of rolling stock with which a more accurate method of improving the geometric shape of rolling stock can be provided.

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

A novelty of this invention is that the geometry of the roll gap (also referred to as roll gap contour or nip profile) is taken into account, which is usually calculated by means of mathematical models 30, see for example the applicant's European Patent Application No. EP-A 1240955, which is hereby incorporated into the subject disclosure. Material displacements during rolling arise, inter alia, from the differences between the incoming rolling stock profile. REPAYMENT j A401080.AT ······ «· · · · ···························································································. ··· ····················································································································································································· Because of this, there are corresponding to elongations and / or widths, so that the rolling mold forms undesirable and deviates from the usually rectangular desired shape. This results in output losses that can be reduced by the invention. 5 The fact that the geometric shape of the rolling stock is calculated after each stitch, much targeted undesirable changes in the geometric shape of the rolling stock can be detected and measures against it.

The material displacements are described by mathematical equations, in which the rolling parameters (eg entrance thickness, entrance width, entry length, exit thickness, exit width, exit length, contact arc length, rolling force, temperature, material strength), the geometric shape before the pass and, if applicable, the parameters of a swage received.

Preferably, the geometry of the roll gap is in the previous stitches and in the considered stitch. The geometry of the roll gap results from the deformation 15 of the roll set by 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 rolls. For the thermal crowning and the roller wear suitable models are known in the art, so that the modeling of these processes need not be discussed further. 20 When heavy plate rolling, the material is rotated between some stitches, mostly by 90 °. These rotations are taken into account. When rotated by 90 °, the edges of the material on the head and foot become side edges, the side edges to the top and bottom edges.

Preferably, the course of the exit thickness over the length (in the rolling direction) 25 in the considered stitch and the previous stitches. If, for example, a rotation of 90 ° occurred between the stitches, the differences in thickness, which are now transverse to the rolling direction, lead to material displacements in the longitudinal direction. If no rotation occurs, the thickness differences in the rolling direction can lead to different material displacements in the width and also in the longitudinal direction. 30 The deviation from the desired shape (for example rectangle) can be achieved by measures such as

SUBSEQUENT

Rolling of a thickness contour in specific stitches Use of a vertical swaging stand Targeted grinding of the rolls A401080.AT ································································································· ··· · · · · · · ····

Modifying the slab format (or in general the Vormaterialformates) targeted changing the stitch plan targeted rotation of the material by certain angles (oblique rollers) are counteracted. 5 Based on a pass schedule, or in conjunction with the creation and optimization of a pass schedule, the geometric shape of the rolling stock can be predicted during and at the end of the rolling process.

In a mathematical procedure, such as an iterative method or a method of mathematical optimization, the possible influencing variables (such as eg thickness contours, width or width profile in an upsetting stitch, number of stitches, stitch decreases) are changed so that the deviation from the desired shape (at the end and during the rolling process) becomes minimal. The actuators also take their functional limits into account.

On the one hand, the method according to the invention can be used so that the calculation is off-line for the calculation of pass-through schedules for chronologically subsequent ones

Rolling processes is performed. The calculated pass charts can be used, for example, to design equipment, to select pre-material formats or to select a roll grinding.

On the other hand, the method according to the invention can also be used to carry out the calculation on-line immediately before and / or during the rolling process and to use the results of the calculation to control the rolling process. In this case, immediately before the rolling process using actual measured values of the rolling train, the calculation of setting values for controlling the rolling process can take place and the rolling process itself can be controlled by a calculation carried out during rolling 25.

The shape of the blank sheet during rolling and after rolling may be by hand or by means of automatic measuring instruments, e.g. Camera, to be measured. The measured values can be used to adapt the parameters of the calculation. However, neural networks could also be used for the parameterization. The invention will be explained by way of example with reference to the calculation of the sheet shape on the foot after a pass on a plate mill:

The shape of the sheet at the head after the stitch n can be represented by a function kn (x), which is defined over the interval [-Wn / 2, Wn / 2], x represents the running variable

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If the next stitch without material rotation in the opposite direction, the shape of the sheet at the foot after the stitch n + 1 by a function fn + i (x) can be described. The function fn + 1 (x) becomes hn depending on the entrance thickness, entrance width wn, entrance length ln, exit thickness hn + i, exit width wn + i, exit length ln + i, length of the contact sheet ldn + 1, rolling force Fn + i, temperature Tn + 1, material strength sn + i according to the equation fn + 1 (x) = (hn / hn + 1) (kn * P (h ", Wn Jn, hn + 1, Wn + i, ln + 1» ldn + 1> F * n + 1 iTn + 1, Sn + i)) (x) + Q (hn, Wn, ln, hn + 1, Wn + i, ln + 1> ldn + 1, Fn + 1 » Tn + 1> Sn + 1, X) + R (x), where P and Q are the material equations which also contain empirically determined 10 parameters, and (f * g) the mathematical convolution according to oo (/ * $ X *) = designated.

An example of a function P is P (hn, wn Jn, hn + 1, Wn + i, ln + 1, ldn + i, Fn + 1, Tn + i, Sn + l) (x) = min (0, max ^, p2 + (p3hn + p4wn + psln + p6hn + i + p7wn + i + p8ln + i + pgldn + i + PioFn + i + pn 15 Tn + i + Pi2sn + 1 + Pis) | x | Pl4)) An example of a function Q is Q (hn, Wn Jn, hn + i, Wn + i, ln + 1> ldn + 1, Fn + 1, Τη + 1, Sn + 1, x) = (q2 + dehn + q4wn + qsln + qhn + i + q7wn + i + q8ln + i + q8ldn + i + qioFn + i + qnTn + i + qi2sn + i) (1 + q1 | x / wn | q13). 20 Parameters pi to pi4 and up to qi3 represent empirically determined parameters.

The function R (x) describes the flow of material, which also arises in the longitudinal direction in that the relative nip profile in the n + 1 Grn + i (x) of the material profile after the stitch n Prn (x) (which in turn is known from the nip profiles Grn, .... Grn corresponding to 25 Prk + i (x) = X (hk, wk, lk, hk + i, wk + i, lk + i, ldk + i, Fk + i, Tk + i, sk + i) (Grk + i (x) - Prk (x)) + Prk (x)) according to the equation R (x) = Y (hn, Wn Jn, hn + 1, Wn + i, ln + 1 > ldn + 1, Fn + 1, Tn + 1> Sn + l) (Grn + i (x) - ηη (Χ)) ·

An example of a function X is X (hk, wkjk, hk + i, wk + i, lk + 1, ldk + i, Fk + i, Tk + i, sk + i) = 30 min (0, max (1 , Xi + x2 (hk + 1 / wk + i - Xa) * 4)), an example of a function Y is Y (hn, Wn Jn, hn + i »Wn + 1, ln + 1, ldn + 1 > Fn + 1, Τη + 1, Sn + i) = min (0, max (1, y, + y2 (hn + i / wn + i -y3) y4)), submitted later A401080.AT ··· ·· ···· ·· ··· ····· ··· < Where the parameters Xi, x2, X3, X4, yi, y2) are y3 , y4 of hn, w ", l", hn + i, wn + 1, ln + i, ldn + i, Fn + 1, Tn + i, Sn + 1.

If the sheet has been rotated by 90 ° between stitches n and n + 1, then the flow of the thickness of the cut, which has been nip-rolled, over the length Lrn in stitch n replaces Prn. 5 For realization on a computer, all the functions mentioned above must be discretized by standard methods of numerical mathematics (as described, for example, 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 of 10 of the desired shape (at the end and during the rolling process) is minimized. This will be explained below by way of example in the case that the stitch plan (the sequence of stitch heights) is already determined that as long a rectangle as possible with a given nominal width should be included in the bending mold, and that in the stitches H ... ..ij, the longitudinal contour to be rolled up represents the manipulated variable. 15 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 functions describing the sheet shape over the set width

Zy = min min -> max! -ws I2 <x <, ws 12 -ws I2 <x <ws 12

The manipulated variables in this case are the curves of the outlet thicknesses, which are as described above with Lr. (x), ..., Lr (x) are designated. Restrictions are usually by the mechanics '1' 1 20 and hydraulics of the rolling mill in the form \ Lrik (x) \ &lt; ck or lLn '(x) - dk for k = 1, ..., j.

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

The method according to the invention can be used both for homogeneous cuboidal materials (slabs) and for non-cuboidal materials (blocks), as well as for materials composed of several layers. I REPLACED l

Claims (8)

1. 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. 2. The 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. 3. The method of claim 1 or 2, characterized in that for each stitch, the geometry of the nip in the previous stitches and in the considered stitch enter into the calculation. 4. The method according to any one of claims 1 to 3, characterized in that received for each stitch of the thickness profile in the previous stitches and in the considered 15 stitch in the calculation. 5. The method according to any 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. 6. A 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 control variables that affect the geometric shape of the Walzguts have to be changed so that the deviation of a desired geometric shape is minimal. | filed later ············· • • • • · -7- A401080.AT 7. The method according to claim 6, characterized in that for this purpose a mathematical method, such as a SQP method (Sequential Quadratic Programming), is used. 8. The method according to claim 6 or 7, characterized in that results of the calculation are used as manipulated variables for the rolling process. SUBSEQUENT