JP3406430B2 - Plate rolling method - Google Patents

Description

Description: BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method of rolling a thick plate by determining a pass schedule and setting a roll gap for each pass according to the pass schedule. . 2. Description of the Related Art Conventionally, in thick plate rolling, a method of determining a pass schedule in consideration of a change in a delivery crown and a crown ratio of each rolling pass has been used (for example, see Japanese Unexamined Patent Publication No. No. 55-81008) and further,
According to the pass schedule, a roll gap is set for each pass and rolling is performed. However, the model formulas used in the above-described conventional pass schedule determination and roll gap setting for each pass, namely, the sheet crown prediction formula for determining the pass schedule and the gauge meter model formula for setting the roll gap. Are modeled by statistical processing of actual rolling data or large-scale numerical analysis results. [0004] In such statistical model formulas, when rolling conditions such as rolling size (thickness and width) and rolling roll diameter change greatly, a new model formula is created or the coefficients of the model formula are revised each time. I had to take such measures. Further, because of the statistical model formula, the interaction between the influencing factors cannot be reflected, so that a large error has occurred under certain rolling conditions. [0005] Recently, as a plate crown prediction formula, the load distribution in the width direction has been made uniform by theoretically treating the deformation state of the roll in the case where the load distribution in the width direction between the rolled material and the work roll is uniform. A model equation configured as a linear combination of the output side crown obtained by multiplying the output side crown by a sheet crown correction coefficient and the input side sheet crown multiplied by a sheet crown genetic coefficient is disclosed. (See, for example, Japanese Patent Publication No. 6-2288). [0006] In the model formulas described in the above-mentioned publications, the sheet crown correction coefficient and the sheet crown genetic coefficient are also modeled by statistical processing of actual rolling data or large-scale numerical analysis results. When the rolling conditions change as described above, it is unavoidable that the labor required for reviewing the model formula and the occurrence of prediction errors occur. As described above, the conventional strip crown prediction formula has been modeled by a statistical method because of the uneven widthwise rolling load distribution generated between the rolled material and the work roll, and the resulting rolled material and roll. This is because it was not possible to theoretically handle the deformation state of. [0007] Therefore, in consideration of uneven rolling distribution in the width direction generated between the rolled material and the work roll, the deformation state of the rolled material and the deformation state of the rolling roll are adjusted accordingly, and a statistical method is used. An online crown prediction formula that does not depend on the system was developed, and an attempt was made to set a pass schedule using the prediction model (“Materials and Processes”, Vol. 6 (1993) No. 5, September 2, 1993).
Published by the Iron and Steel Institute of Japan). [0008] By the way, once the exit sheet thickness is set by the pass schedule, the roll gap of each pass must be set according to the sheet thickness. In setting the roll gap, the screw position is set using a gauge meter model formula or the like so that the roll gap at which the exit side plate thickness given in the pass schedule is realized. However, even if the pass schedule is set by the online crown prediction formula that does not use the developed statistical method, the model formula for calculating the roll gap uses a conventional statistically processed model formula. Then
In some cases, the target values of the sheet crown and the sheet thickness may not be satisfied, or an ear wave or a medium wave may occur as a rolled shape. That is, there is a demand for the development of a model formula that does not rely on a statistical method when setting the roll gap. In view of the above, the present invention considers an uneven width direction rolling load distribution generated between a rolled material and a work roll in order to satisfy a target sheet thickness and a sheet crown and secure a good rolling shape. Determine the pass schedule and set the roll gap for each pass using the online crown prediction formula and the gauge meter model formula that does not rely on statistical methods by adapting the deformation state of the rolled material and the deformation state of the rolling roll. To provide a method for rolling. In order to achieve the above object, the present invention has taken the following measures. That is, a feature of the present invention is that, in rolling a thick plate, a pass schedule is determined, and a roll gap is set for each pass in accordance with the pass schedule to perform rolling. And the load distribution in the width direction between the work roll and the backup roll are represented by polynomials of the fourth order or higher, and the entrance and the exit of the rolled material are displayed.
The sheet thickness distribution in the sheet width direction on the outlet side is expressed by a fourth-order polynomial, and the deformation state on the rolled material side and the deformation state on the rolling roll side are adapted to show the relationship between the outlet side sheet crown and the inlet side sheet crown.
Deriving a round prediction model, the plate crown prediction model
To determine the exit plate crown,
The point to set . DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS First, the derivation of a model equation showing the relationship between the exit side plate crown and the entrance side plate crown necessary for determining a pass schedule will be described. In the following description, the load distributions in the width direction between the rolled material and the work roll and between the backup roll and the work roll are all fourth-order polynomials (the quadratic equation is used in the second-order equation). This is because the accuracy is not good, and the polynomial of the sixth order or higher is complicated, and the symmetry of right and left cannot be secured in the odd order.) Even when the distribution is represented by a polynomial expression exceeding the fourth order, it is possible to derive a model expression based on the same concept. Further, a coordinate system and a symbol for derivation,
The meanings of the symbols are as shown in FIG. 1, and the preconditions for derivation are as follows. The width direction load distribution q _WP between the work roll 2 and the plate material and the width direction load distribution q _WB between the work roll 2 and the backup roll 1 are represented by the following fourth-order polynomials. That is, the load in the width direction is not uniform, but is treated as non-uniform. Q _WP (x) = A ₁ X ⁴ + A ₂ X ² + A ₃ (0 ≦ X ≦ L _W / 2) (1) q _WB (x) = B ₁ X ⁴ + B _{2 ^{X 2 + B 3 (0 ≦}} X ≦ L B / 2) ...... (2) _{where, a i, B i (i} = 1,2,3): unknown constants L _W: body length of the work roll 2 L _B: Body length X of backup roll 1: position in width direction (X = 0 center) Roll flat deformation a _WB (x) between work roll 2 and backup roll 1 and roll flat deformation δ (between work roll 2 and plate) x) is the formula of Tsu-Tao-Loo, respectively.
Apply the modified Tozawa formula by Nakajima et al. Where a _WB (x) = a ₁ (x) + a ₂ (x) where a _{1 is the} amount of flat deformation of the backup roll 1 a _{2 is the} amount of flat deformation of the work roll 2 The thickness distributions H and h are represented by the following equations. [0016] [number 2] H (X) = H (0 ) -C H (X / Xe) 4 ...... (3) h (X) = h (0) -C h (X / Xe) 4 ...... (4) Xe = (B / 2) -β However, C _H: entrance side crown amount C _h: delivery side crown amount B: plate width Xe: defining the position of the plate end portion of the strip crown beta: distance from the plate edge The internal stress distribution resulting from the difference in elongation strain in the sheet width direction during rolling is represented by the following equation in consideration of the influence of the sheet width direction strain. Σ _f (x) = ξE _P (h (X) / h (0) −H (X) / H (0)) + σ ₀ (5) where ξ is a shape change coefficient E _P : Young's modulus of the sheet material σ ₀ : Constant determined by the balance condition of the internal stress The sheet material is in a plane strain state where there is no plastic flow in the sheet width direction.
_It is assumed that _P (X) holds and the following equation holds. Q _WP (x) = (k _f −σ _f (x)) · Q _P (x) · ld (x) (6) where k _{f is} the deformation resistance Q _{P of the} plate material. : Rolling force function ld: Contact arc length or more is a precondition. The equation (6) is transformed using the equations (3) and (4).
Can be approximated as follows. ## EQU5 ## q _WP (x) = (k _f −σ _f (x)) · Q _AP (x) (7) where Q _AP (x) = ld (0) Q _P (0 ) + (Z _{1 Ch} + Z ₂ C
_H ) (X / Xe) ⁴ Z ₁ , Z ₂ : constants Further, when a coefficient is compared between the equation obtained by substituting equation (5) into equation (7) and equation (1), the following equation is obtained. The undetermined constants A ₁ , A ₂ , and A _{3 in} 1) are specifically determined as in the following equation (8). [0021] [6] _{A 1 = (ξE P ld (} 0) / h (0) + PZ 1 / (ld (0) B)) C h ...... (8) + (ξE P ld (0) / H _{(0) + PZ 2 / (} ld (0) B)) C H A 2 = 0 A 3 = 2P / B 2 (ξE P ld (0) / h (0) + PZ 1 / (ld (0) B)) _{C h '+ 2 / B (} ξE P ld (0) / H (0) + PZ 2 / (ld (0) B)) C H' _{However, C h '= C h B} 5 / (80Xe 4) C H' = C _H B ⁵ / (80Xe ⁴ ) P: rolling load, ie, load distribution q in the width direction between the work roll 2 and the sheet material
_{The WP} is _expressed by a fourth-order polynomial (non-uniform load distribution in the width direction) of the equation (1), whereby the non-uniform load distribution q in the width direction is obtained.
_WP is the entry side and delivery side crown C _h, is determined as a function of the C _H. Next, the undetermined constants B ₁ , B ₂ , B
₍₃ ) The rolling load is calculated using the axial displacement V _W (x) of the work roll 2 and the axial displacement V _B (x) of the backup roll 1 obtained by beam deformation analysis taking into account bending and shear deformation. And the least-squares solution of the simultaneous system of linear equations consisting of the following equations (9) and the appropriate conditions for the roll surface displacement at each body length direction position shown in the following equation (9). [0023] [number 7] F (B / 4) = F (X e) = F ((B + L B) / 4) = F (L B / 2) = 0 ...... (9) However, F (X ) = V _B (x) −V _W (x) −a _WB (x) + a
_{WB (0) + (C B} (0) + C w (0) -C B (x) -C w (x))
/ 2 a _WB: the sum of the flat deformation amount of the work rolls 2 (a ₂₎ a flat deformation amount of the backup roll _{1 (a 1) (a WB} = a 1 +
a ₂ ) C _w : Crown amount of work roll 2 C _B : Crown amount of backup roll 1 That is, when the load distribution acting on the roll is determined, V _B , V _W , and a _WB are determined under the load distribution. . When the load distribution is given by the above equations (1) and (2),
Since A ₁ , A ₂ , and A ₃ are functions of _Ch and C _H , a simple calculation (expansion of the equation) is given by: V _B = g ₁₁ × B ₁ + g ₁₂ × B ₂ + g ₁₃ × B ₃ + g ₁₄ V _W = g ₂₁ × B ₁ + g ₂₂ × B ₂ + g ₂₃ × B ₃ + g ₂₄ a _WB = g ₃₁ × B ₁ + g ₃₂ × B ₂ + g ₃₃ × B ₃ + g ₃₄ , G _ij = g _ij ( _Ch , C _H ). When these are used, the equation (9) becomes as follows: F (x) = f ₁ × B ₁ + f ₂ × B ₂ + f ₃ × B ₃ + f ₄ (a) f _i = _{f i (x, C h,} C H) x = B / 4, X e, the _{(B + L B) / 4} , L B / 2. Also, the load balancing equation ∫q _WP (x) dx =
P / 2 from (L _B / 2 from the integration range 0), [0028] Equation 10] ^{_{(L B / 2) 5 ×}} B 1/5 + (L B / 2) 3 × B 2/3 + (L B / 2) ² × B ₃ / 2−P / 2 = 0 (b). Here, assuming that B ₁ , B ₂ , and B ₃ are unknowns, the simultaneous equations composed of the above equations (a) and (b) have five equations for three unknowns. And B ₁ , B ₂ , and B ₃ can be easily solved by performing least-squares approximation for each of them, and B ₁ = b ₁₁ × _Ch + b ₁₂ × C _H + B ₁₃ B ₂ = b ₂₁ × _Ch + b ₂₂ × C _H + b ₂₃ (c) B ₃ = b ₃₁ × _Ch + b ₃₂ × C _H + b ₃₃ As a result, the axial center deformation amount V of the work roll 2
_W, and, the [delta] flat deformation amount of the work roll 2 at the time of contact with the plate material, and out the side plate crown amount C _h, C respectively as a function of _{H V W (x, C h} , C H), δ (x, C _h , C _H ), and the linear relational expression shown below is obtained. [0031] Equation 12] _{C h / 2 = S W (} 0, C h, C H) -S W (X e, C h, C H) + (C w (0) -C W (X e) ) / 2 (10) where _SW (x, _Ch , _CH ) is the surface displacement in the roll body length direction x (displacement of the roll axis + flat deformation of the roll surface). ] [formula 13] _{S W (x, C h,} C H) = V W (x, C h, C H) -δ (x, C h, C H) plate out by solving the equation (10) Crown C _H
A model formula which gives the relationship entry side crown C _h (strip crown prediction formula) is determined by the following equation (11). [0033] Equation 14] _{C h = {(0.5b 1 +} b 2 / B) P + b 1 F} / (0.5b 3 / h (0) + b 4 P) -1 / (0.5b ₃ / h (0) + b ₄ P) × C _WE + (− b ₃ / H (0) + b ₅ P) / (0.5−b ₃ / h (0) + b ₄ P) × C _H …… (11) where C _WE = C _w (0) −C _W (X _e ): effective work roll crown amount F: roll balance force b _{1 to} b ₅ : known constant. it is a model expression representing the relationship between delivery side crown C _h and at entrance side crown C _H derived when adapted to deformation of the deformation and the rolling roll 1 side of the side. What is important here is that the distribution of the load acting on the roll is approximated by the fourth order, the load distribution is determined from the deformation state of the sheet material at the time of rolling, and then the deformation of the roll under the load distribution is determined dynamically. That is, a sheet crown prediction model was derived by obtaining it in a typical manner. Next, the derivation of a model formula showing the relationship between the amount of roll deformation required for setting the roll gap according to the exit side plate thickness of each pass and the rolling conditions will be described. Generally, a gauge meter model equation shown below is used for setting the roll gap. [0036] Equation 15] _{h (X e) = S 0} + Y H + 2Y RR (X e) -2C W (0) -C B (0) ...... (12) where, h: exit side thickness S _0: screw position Y _H: amount of deformation than the housing or roll Y _RR: roll deformation amount C _W: crown value of the work rolls 2 C _B: in crown value above formula of the backup roll 1 (12), the amount of deformation of the other housing or roll the model equation for calculating the Y _H with high accuracy, because one of the present inventors have already disclosed (see JP-a-6-254613), in the present invention, the roll deformation amount Y _RR
A derivation method will be described for the model equation of FIG. The coordinate system and prerequisites for the derivation are the same as those in the above-described plate crown prediction formula. As described above, the rolled material and the work roll 2
Width direction load distribution q _WP during and between the backup roll 1 and the work rolls 2 of, q _WB is the inlet and outlet of the strip crown C _h, C
Backup roll 1 because it is obtained as a function of _H
Torso central axis deformation amount V _B, the flat deformation amount δ of the flat deformation amount a _WB and torso center of the rolled material and work rolls 2 of the body center between the work rolls 2 and the backup rolls 1, respectively V _B (L _{B / 2 + L CH, C} h, C H), a WB (0, C h, C H), δ
(0, _Ch , _CH ). Therefore, considering the mechanical deformation of the roll at the time of rolling load and the change in the roll gap between the upper and lower work rolls caused by the change in the profile of the roll surface as the rolling progresses, the model formula of the roll deformation amount Y _RR ( The roll deformation prediction formula) is obtained by the following formula. [0039] [Expression 16] _{Y RR (X e) = V} B (L B / 2 + L CH, C h, C H) + a WB (0, C h, C H) + δ (0, C h, C _{H) -C h / 2 ...... (} 13) where, L _CH: length of chock portion of the backup roll 1 Note (one side), and the work roll 2 included in plate crown prediction formula and the gauge meter model formula according to the invention Backup roll
The crown amounts C _W and C _B of 1 gradually change due to wear and thermal expansion due to rolling, and these can be treated as known by estimation using a model formula or by direct measurement. Next, according to the present invention, when rolling a thick plate, the pass schedule is determined and the roll gap is set for each pass to perform rolling. Therefore, the pass schedule is determined using the above model formula. The method and the roll gap setting method for each pass will be described below. The pass schedule, that is, the rolling load and the exit side plate thickness of each pass are determined by the following procedures (1) to (4). A given target plate thickness (outside plate thickness of the last pass) and a target plate crown (outside plate crown of the last pass)
, The exit side crown ratio of the final pass is determined, and the rolling load of the final pass is set. Rolling load prediction formula (P = B × Q _p
× ld × k _f ), the thickness H on the incoming side of the final pass, that is, the thickness h on the outgoing side of the path immediately before the final pass (hereinafter, this pass is referred to as the “pass”) is obtained. According to the plate crown prediction formula expressed by the above equation (11), the entrance side plate crown C _H of the final pass, that is,
Determine the side plate crown C _h out of "the path". From these values, the entrance side plate crown ratio of the final pass, that is, the exit side plate crown ratio of the "pass" is obtained. The change in the sheet crown ratio determined as the difference between the exit sheet crown ratios of the “final pass” and “the pass” is such that the rolling load and the exit sheet thickness of the “pass” are adjusted so as to satisfy a predetermined set value of the shape dead zone. decide. The above operations are sequentially repeated to sequentially determine the rolling load and the exit side plate thickness of the immediately preceding pass. (The path that determines the rolling load and the exit side plate thickness in this manner is referred to as a “shape adjustment pass”.) When the rolling load of the shape adjustment pass exceeds the maximum rolling load of the rolling mill, the above operations are stopped. By replacing the rolling load in the shape adjustment pass with the maximum rolling load (with the exit side plate thickness unchanged), the exit side plate thickness and the rolling load are determined. (The path determined in this way is called a "joint path."
In the following passes, the rolling load prediction formula and the rolling torque prediction formula given separately are used to satisfy the stricter restrictions on the maximum rolling load or the maximum rolling torque of the rolling mill, so that the rolling load and the delivery side plate are satisfied. Determine the thickness. (The path determined in this way is referred to as the “maximum milling capacity path”) where the sheet crown ratio = the sheet crown / the sheet thickness crown ratio change at the center position of the sheet width = the exit side sheet crown ratio. -Incoming side plate crown ratio shape dead zone: A region where no wave is generated even if the plate crown ratio changes. Next, a method of setting a roll gap for each pass will be described. The roll gap for each pass is set by the following procedures. For the path, a rolling load calculated from a rolling load prediction formula (P = B × Q _p × ld × k _f ) separately given;
Based on the delivery side crown C _h obtained from strip crown prediction expression represented by the formula (11), with a gauge meter model equation of the roll deformation equation of the equation (13) (12), pass schedule The screw position S ₀ is set so that the roll gap at which the delivery side plate thickness h given by the above is realized. Based on the measured rolling load of the pass, the exit crown C _h , the roll deformation equation (1)
3) and the gauge thickness of the outlet side are determined from the gauge meter model formula (12), and these are set as the inlet side crown _CH and the inlet side thickness H of the next pass, and the roll gap of the next pass, that is, the screw position S, is determined by the above procedure. Set ₀ . Repeat the above until the final pass. [0046] Here, for the first pass, and out the side plate thickness H, h is thick, since the impact of the entry side crown C _H on the delivery side crown C _h almost negligible, the entry side crown C _H = 0 be able to. FIG. 2 shows a comparison between the path schedule determined by the method of the present invention and that obtained by the conventional method. In the conventional method, a sheet crown prediction equation modeled by statistical processing of actual rolling data was used. As is clear from the figure, in the method of the present invention, a pass schedule that satisfies the target plate crown and can secure a good rolling shape is used. However, the conventional method (described in the above-mentioned Japanese Patent Publication No. 6-2288). ), It can be seen that the pass schedule is such that neither the target sheet crown nor the rolling shape is satisfied due to an error in the sheet crown prediction formula. FIG. 3 shows a comparison between the accuracy of the gauge meter method used in the method of the present invention and the accuracy of the gauge method used in the conventional method. It can be seen that the accuracy in the method of the present invention is extremely high. From this, it is understood that the roll gap setting of each pass can be performed with high accuracy by using the gauge meter type (12) of the present invention. The gauge meter formula (for example, Y _H + 2Y _RR (X _e ) = M / P where M: constant) of the conventional method is a statistical model formula like the plate crown prediction formula. From the above, it is apparent that the thick plate rolling method according to the present invention makes it possible to satisfy the target plate thickness and the target plate crown and to secure a good rolled shape. According to the present invention, the roll gap of each pass can be adjusted with high precision in order to satisfy the target plate thickness and plate crown and secure a good rolled shape for each rolled material. It becomes possible to set, and a significant improvement in sheet thickness, sheet crown, and rolled shape can be realized.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is an explanatory diagram showing a roll coordinate system for deriving a model expression. FIG. 2 is a diagram comparing a path schedule determined by the method of the present invention with that of the conventional method. FIG. 3 is an accuracy comparison diagram of a gauge meter type used in the method of the present invention and a conventional method. [Explanation of symbols] 1 backup roll 2 work roll

──────────────────────────────────────────────────の Continuing on the front page (72) Inventor Shintaro Shimada 1 Kanazawacho, Kakogawa City, Hyogo Prefecture Kobe Steel, Ltd. Inside the Kakogawa Works (72) Inventor Keima Anraku 1 Kanazawacho, Kakogawa City, Hyogo Prefecture Kobe Steel, Ltd. Inside the Kakogawa Works (56) References JP-A-6-254613 (JP, A) (58) Fields investigated (Int. Cl. ⁷ , DB name) B21B 37/00-37/78

Claims (1)

(57) [Claims 1] In a plate rolling method for rolling a thick plate, a pass schedule is determined, and a roll gap is set for each pass according to the pass schedule to perform rolling. The load distribution in the width direction between the work rolls and between the work rolls and the backup rolls is represented by a polynomial of the fourth order or higher, and the entrance side and the exit side of the rolled material.
The thickness distribution in the sheet width direction is expressed by a 4th-order polynomial, and the deformation state on the rolled material side and the deformation state on the rolling roll side are matched to output.
Plate crown showing the relationship between side plate crown and entrance plate crown
Deriving a prediction model, and calculating the exit-side sheet crown using the sheet crown prediction model
And setting the pass schedule by using the method.