JPH0474084B2 - - Google Patents

Description

[Detailed description of the invention]

(Industrial Field of Application) The present invention relates to a method of setting and controlling a rolling device used in plate rolling to ensure the accuracy of the thickness of a rolled material. (Prior art) In order to set and control the rolling device in a rolling mill for plate rolling, the elastic deformation of the rolling mill due to rolling load and roll bending force is understood as an increment in the gap between the upper and lower work rolls, that is, a mill stretch. , this needs to be predicted online. A method for theoretically determining the mill stiffness, which is defined as the reciprocal of the influence coefficient of the rolling load on mill stretch, for a four-high rolling mill offline has been proposed by Ataka et al. (Matsuo Ataka, Hiroshi Suzuki: Plasticity and Processing, 13−143 (1972), 960.). However, this method is limited to the deformation of the roll and requires the release of numerical calculations, so it is difficult to apply it to actual operations online. Therefore, at present, the mill stiffness formula used for rolling mill settings and control is a simplified formula developed for each rolling mill based on experimental results or numerical analysis results. (For example, Kazuo Omata, Yasuyuki Nanami, Akihiro Tanaka, Hideo Tsukamoto: Tetsu to Hagane, 67
-4 (1981), 341.). In recent years, precision requirements for the widthwise thickness distribution of rolled plates have become increasingly strict. A roll bending device is a typical rolling mill hardware that meets this requirement, but if this device is used for the purpose of controlling the plate crown and shape for each rolled material, it will have a considerable effect on the mill stretch, so roll bending Conventional techniques that do not theoretically take into account the influence of force on mill stretching cannot deal with this problem. In particular, in the case of hot rolling, from the viewpoint of energy conservation, bulk rolling, which was performed for each strip width and thickness, has been abolished, and schedule-free rolling is now being promoted. If this type of operation is adopted, the strip width and rolling load will vary greatly from strip to strip.
If mill stretch or mill rigidity remains as it is with conventional technology, plate thickness accuracy will inevitably deteriorate. (Objective of the Invention) The present invention solves the problems of the prior art as described above, and aims to provide a rolling mill reduction setting method and control method that can roll a plate material with high plate thickness accuracy. It is something. (Structure and operation of the invention) The gist of the invention is as follows. 1 In the rolling reduction setting method of a plate rolling mill, the increment of the gap between the upper and lower work rolls due to rolling load and roll bending force, that is, the mill stretch, is separated into the contribution of roll deformation and the contribution of deformation other than the rolls, and the contribution of roll deformation is Regarding the elastic deformation of each roll constituting the rolling mill, the predicted value of rolling load, predicted value of roll bending force, plate width, entrance plate thickness,
Calculation is done taking into account the target value of the exit plate thickness, and for the contribution of deformation other than the rolls, a tightening experiment is performed in advance with upper and lower work rolls in contact in the absence of rolled material, and the rolling reduction setting obtained from this is calculated. Calculated from the predicted value of the load cell load for each rolling operation, using the deformation characteristics of parts other than the roll, which are obtained by subtracting the contribution of roll deformation during the tightening experiment from the relationship between the load cell load measurement value and the load cell load measurement value. However, the mill stretch given as the sum of the contribution of the roll deformation and the contribution of deformation other than the roll determined in this way is used to determine the rolling reduction setting value for obtaining the desired plate thickness. How to set the rolling reduction of a plate rolling machine. 2. In the rolling reduction setting method for a multi-high plate rolling mill with four or more stages, the contribution of roll deformation to mill stretch is determined by a straight line that uniquely determines the distribution of the contact load between rolls in the plate width direction from the equilibrium conditions of the force and moment of each roll. The roll flattening deformation is obtained by assuming the distribution, and the effect of the axial deflection of the work roll and the reinforcing roll is superimposed on this using the axial approximate straight line in the contact area with each adjacent roll as a reference. A rolling reduction setting method for a plate rolling mill according to item 1 above. 3 In a rolling control method for a plate rolling mill, the increment in the gap between the upper and lower work rolls due to rolling load and roll bending force, that is, the mill stretch, is separated into the contribution of roll deformation and the contribution of deformation other than the rolls, and the contribution of roll deformation is Regarding the elastic deformation of each roll constituting the rolling mill, the predicted value of rolling load, predicted value of roll bending force, plate width, entrance plate thickness,
Calculation is done taking into account the target value of the exit plate thickness, and for the contribution of deformation other than the rolls, a tightening experiment is performed in advance with upper and lower work rolls in contact in the absence of rolled material, and the rolling reduction setting obtained from this is calculated. Calculated from the predicted value of the load cell load for each rolling operation using the deformation characteristics of parts other than the roll, which are obtained by subtracting the contribution of roll deformation from the tightening experiment etc. from the relationship between the value and the load cell load measurement value. However, using a calculation method in which the mill stretch is determined as the sum of the contribution of the roll deformation and the contribution of deformation other than the roll determined in this way, the influence coefficient of the rolling load on the mill stretch or the roll bending force can be calculated as the mill stretch. 1. A rolling control method for a plate rolling mill, characterized in that one or both of influence coefficients are determined, and based on this, a rolling operation amount for adjusting the thickness of a plate to a desired value during rolling is determined. 4. In a rolling reduction control method for a multi-high plate rolling mill with four or more stages, the contribution of roll deformation to mill stretch is determined by a straight line that uniquely determines the distribution of the contact load between rolls in the plate width direction from the equilibrium conditions of the force and moment of each roll. The roll flattening deformation is obtained by assuming the distribution, and the effect of the axial deflection of the work roll and the reinforcing roll is superimposed on this using the axial approximate straight line in the contact area with each adjacent roll as a reference. The rolling reduction control method for a plate rolling mill according to item 3 above. FIG. 1 shows the relationship between rolling load and roll gap increment, and the roll gap increment due to rolling load is called mill stretch. In addition, in the present invention, roll bending force other than the rolling load is also considered as the rolling load, and the roll gap increment due to the roll bending force is also included in the mill stretch. Additionally, the rolling load increment required to change the roll gap by a unit amount is called mill rigidity. Mill stretching is necessary to set the reduction before rolling because it is necessary to estimate the absolute amount of roll gap change due to rolling load. In addition, mill rigidity is required for reduction control during rolling because it is necessary to estimate the amount of relative change in the roll gap corresponding to fluctuations in rolling load. Since the mill stiffness is determined as the slope of the mill stretch curve as shown in FIG. 1, the object of the present invention will be achieved if the mill stretch can be estimated with high accuracy. As shown in FIG. 2, the mill stretch of a rolling mill can be considered separately into the contribution of roll deformation and the contribution other than roll deformation. Although it is difficult to derive a practical simple formula for the contribution of roll deformation, as will be explained later, it is possible to understand the roll geometry very precisely, so a high It is possible to predict it theoretically with accuracy. On the other hand, the deformation of parts other than the roll includes elastic contact deformation of the pressure-receiving surface of the liner and chock, the screw part of the rolling screw, and the threaded part of the screw nut, whose geometric shapes are difficult to grasp precisely. However, there are aspects that cannot be completely explained theoretically, such as the fact that these characteristics greatly depend on the delicate shape of the contact surface, especially in the low-load region, and that the characteristics change each time the reinforcing roll chock is replaced. In order to solve this problem, in the present invention, we conduct a tightening experiment by making the upper and lower work rolls kiss in advance, and remove the contribution of roll deformation from the relationship between the rolling reduction setting value and the load cell load obtained as a result.
Extract the deformation characteristics of the housing, rolling system, etc., store this data, and when the estimated value of the load cell load is obtained for each rolling, refer to this data to determine the deformation of parts other than the roll. We have invented a method of estimating mill stretch by calculating the contribution and adding to it the contribution of roll deformation calculated for each rolling. FIG. 3 schematically shows a kiss roll tightening test carried out before the start of a series of rolling operations, and a procedure for separating the deformation characteristics of the housing, rolling system, etc. other than the rolls from the experimental data. The deformation of parts other than the rolls is uniquely determined only by the total load transmitted through the reinforcing roll chock during rolling or kiss rolling. All you have to do is go around. If this is done immediately after replacing the reinforcing roll or liner, the effect of changes in these parts on the mill stretch can also be accurately taken into account. FIG. 4 shows a calculation procedure for the mill stretch performed immediately before each rolling operation for each material during a series of rolling operations. Figure 4 shows the procedure after obtaining the predicted value of rolling load, roll bending force, and other setting values in normal setting calculations. This operation needs to be performed for each rolling operation, since the rolling operation of each material may change significantly due to the influence of shifts and the like. If such a highly accurate mill stretch equation is obtained, it is also possible to determine the mill rigidity, which is defined as the reciprocal of the coefficient of influence of rolling load on mill stretch, with high precision. When the mill stiffness estimation becomes more accurate, the accuracy of calculation of the amount of rolling operation to adjust the plate thickness to the desired value during rolling improves, and automatic plate thickness control becomes possible with higher precision than before. Furthermore, there is a technology to control the crown and shape by operating a roll bender during rolling, but at this time the applicant
Patent application for "Rolling control method" (Japanese Patent Application Laid-open No. 177818/1989) filed on April 24, 2017 (hereinafter referred to as application A)
High plate thickness accuracy cannot be ensured unless non-interferential control as disclosed in 2007 is also implemented. The coefficient of influence of roll bending on mill stretching, which is necessary when implementing this non-interference control, can also be determined with high precision using this mill stretching formula. Next, a method for determining the contribution of roll deformation in a multi-high rolling mill with four or more stages will be explained. The biggest problem when calculating the roll deflection of a rolling mill with four or more stages is that the contact load distribution between the rolls, which is the boundary condition when calculating the roll deflection, depends on the roll deflection itself, which is the solution. This is where the problem lies. This problem can be almost completely solved by a so-called split model, in which the roll body is divided into several elements in the axial direction and numerical calculations are performed (for example, Shohet,
KN & Townsend, NA: J.of lron and
Steel Institute, 206-11 (1968), 1088. (hereinafter referred to as Document A). In addition, the present applicant
``Rolling control method'' (Japanese Patent Application Laid-Open No. 1983-1999)
-130614 (hereinafter referred to as Application B), discloses a method to solve such an indefinite problem and calculate roll deflection using a simple formula. It is possible to calculate the deformation. However, when determining mill stretch, it is necessary to determine the amount of roll flatness at the center of the rolled material, but it is not enough to determine only the roll deflection. The amount of flattening must be determined.
If the mill stretch is honestly determined using such a method, it is thought that even if the simple method disclosed in the above application is used, the equation will still be complicated. Therefore, in the present invention, the following method was devised. First, the roll flattening deformation is calculated assuming that the roll does not bend at all. This is equivalent to making the contact load distribution between the rolls a linear distribution. The effect of roll deflection can be added to this as follows. No matter how much the rolls are deflected, as long as the rolling load does not change, it is thought that the average amount of flattening over the entire contact area between the rolls will not change, so the axial center deflection curve of each roll is approximated by a straight line across the contact area between the rolls, The displacement due to the axial center deflection may be extracted and superimposed using this approximate straight line as a reference. Note that the method for calculating this approximate straight line may be an integral average of the deflection curve, least squares approximation, or the like. Considering this, it can be seen that the deflection of the intermediate roll of a multi-high rolling mill does not directly affect the mill stretch since the deflection does not cause a change in diameter. Roll crown can also be considered in the same way as roll deflection. According to the method described above, the effect of roll deformation on mill stretch can be determined by simply determining the deflection of the work roll and reinforcing roll using the method disclosed in Application B. (Example) 4 having the following work roll bending device
The present invention will be specifically explained by taking as examples a high rolling mill (4Hi mill) and a 6-high rolling mill (6Hi mill) having an intermediate roll shift function. Figure 5 schematically shows the roll deformation state of the 4Hi mill. FIG. 5a shows the no-load state, and FIG. 5b shows the loaded state during actual rolling. Reinforcement roll 1 (referred to as BUR) and work roll 2 under load
To calculate the deflection of (WR),
The BUR-WR load distribution 3 must be given as a boundary condition, but this load distribution depends on the roll deflection, which is the solution, and cannot be given accurately in advance. This is the difficulty of the roll deflection analysis mentioned above, but according to the decomposition model method disclosed in Document A, by dividing the roll into several elements in the axial direction and performing numerical calculations,
It is possible to find solutions to such problems.
However, since this method involves numerical calculations, it is practically inconvenient in that it takes a long calculation time, and it is difficult to provide a clear explanation of the Mill Stretch formula. An example of calculating roll deflection will be explained in detail. In this method, before considering the actual rolling condition, a hypothetical deformation condition is considered in which the load distribution between the rolls is assumed to be a linear distribution. Roll deflection in this state can be easily calculated using material mechanics, and herein this state will be referred to as a simple deflection state. However, the fifth
As shown in Figure c, in this state, the compatibility condition at the contact surface between BUR and WR is ignored. If symmetrical rolling without roll shift is performed, the distribution will be uniform, but if not, the distribution will be a straight line with a slope determined by the moment equilibrium condition. Next, we will consider a method of mapping the simple deflection state to the actual rolling state. This means considering the influence of the nonlinear component of the load distribution between rolls on roll deflection, and is made possible by introducing the concept of nonlinear load distribution correction coefficient, which will be described in detail below. The definition of the nonlinear load distribution correction coefficient is as follows. “The absolute value of the influence coefficient that the axial distribution of the gap that exists between the roll in the simple deflection state and the other roll in contact with it has on the change in deflection of the roll from the simple deflection state to the actual rolling state is It is defined as the nonlinear load distribution correction coefficient for the gap between the rolls of the roll." Therefore, if the nonlinear load distribution correction coefficient for all the rolls and gaps between the rolls that make up the rolling mill have been found, the rest is By simply finding the roll deflection in a simple deflection state, you can also find the roll deflection in an actual rolling state. (1) Derivation of nonlinear load distribution correction coefficient (a) Nonlinear load distribution correction coefficient during rolling () For 4Hi mill During rolling, the upper and lower WRs do not contact at the body except in special cases, so the upper and lower WR The roll system can be considered separately. BUR
The distribution of the gap υ between ~WR in the roll axis direction is approximated by a quadratic equation as shown below. υ=f _g・x ² (1) where x is the coordinate in the roll axis direction with the mill center as the origin and the working side (WS) in the positive direction. The distribution factor of υ may be a roll crown as shown in FIG. 6, or may be a deflection in a simple deflection state. The present inventors are concerned only with the ratio of change in roll deflection when transitioning from the simple deflection state to the actual rolling state with respect to the gap between BUR and WR that existed in the simple deflection state. can be thought of as idealized to some extent. Therefore, not only the gap distribution between rolls but also the distribution of roll deflection changes due to this gap distribution are
Assume the following curve distribution. That is, when the BUR deflection and WR deflection due to υ are y _B and y _W, respectively, it is assumed that y _B = f _B x ² (2) y _W = f _W x ² (3). However, as shown in Fig. 6, y _B and y _W are positive in the direction away from the rolled material. With this arrangement, if f _B and f _W can be found for a given f _g , then
A nonlinear load distribution correction coefficient can be obtained as the ratio of f _B and f _W to f _g . From equations (1) to (3), the linear load distribution p _BW generated by υ is expressed by the following equation based on the concept of the inter-roll spring model shown in Reference A. p _BW = k _BW (f _g + f _B − f _W ) (l _BW ² /12−x ² ) (4) where l _BW is the length of the contact area between BUR and WR, and is usually equal to the roll body length. . formula
Since (4) extracts the nonlinear component of the load distribution, this alone satisfies the force equilibrium condition. Further, k _BW is a spring constant per unit body length of the contact flatness of BUR to WR, and is obtained as the reciprocal of the equation regarding the amount of axial center approach of two cylinders differentiated with respect to the line load. For example, the axial center approach amount δ ^BW _i according to the solution of Nakajima et al. (Hiroe Nakajima, Hiromi Matsumoto: 1973, 25.) is δ ^BW _i = c・p _BW [ln{2(D _B + D _W )/(c・p _BW )}−1] (5) c=2(1−ν ² )/(π・E) (6) Therefore, the spring constant k _BW is given by the following formula. . 1/k _BW = c[l _o {2(D _B +D _W )/(c・p _BW )}-2] (7) where D is the roll diameter, E is Young's modulus,
ν is Poisson's ratio, and subscripts B and W are respectively
BUR means WR. In this specification, in order to simplify the notation, the elastic constants of all the rolls of the rolling mill are assumed to be common, and the amount of axial center approach, that is, the amount of roll flattening, is calculated using equations (5) and (6). When analyzing a rolling mill that combines rolls with significantly different elastic constants, Loo's equation (Loo, TT: J.of Applied Mechanics,
25-1 (1958), 122.). From equation (7), it can be seen that k _BW is strictly a function of p _BW , but since the change in k _BW due to p _BW is generally very small, here we use the average value of p _BW in the trunk length direction to calculate k _BW Calculate the formula
In (4), we will treat it as a constant. The roll deflection caused by the load distribution in equation (4) is expressed as y=0, d _y /d _x =0 at x=0.
Under the boundary conditions, the following equation is obtained by considering bending deformation and shear deformation using beam theory. y _B =k _BW /12(f _g +f _B −f _W ) [−1/EI _B {x ⁶ /30 −(l _BW /2) ² x ⁴ /6+(l _BW /2) ⁴ x ² /2 +4/3GS _B {x ⁴ −2(l _BW /2) ² x ² }] (8) y _W =k _BW /12(f _g +f _B −f _W ) [−1/EI _W {x ⁶ /30 −(l _BW /2) ² x ⁴ /6+(l _BW /2) ⁴ x ² /2
} −4/3GS _W {x ⁴ −2(l _BW /2) ² x ² }] (9) where is the second moment of area of the roll, S is the cross-sectional area of the roll, and G is the transverse modulus of the roll. . While there are 4th and 6th order terms of x on the right side of equations (8) and (9), as in equations (2) and (3),
y _B and y _W were approximated by quadratic equations. Therefore, strictly speaking, f _B and f _W must be functions of the plate width, but in this case, equations (2), (3) and
A method was adopted in which the right-hand sides of (8) and (9) were integrated over the entire contact area between the rolls and equated to determine f _B and f _W . the result,
Nonlinear load distribution correction coefficient α _B regarding the gap between BUR and WR of BUR is α _B = −f _B / f _g = A _BW / (1 + A _BW + A _WB ) (10) Nonlinear load distribution correction regarding the gap between BUR and WR of WR The coefficient α _W is determined as α _W =f _W /f _g =A _WB /(1+A _BW +A _WB ) (11). However, A _BW = K _BW / π (l _BW / D _B ) ² {29/210 1/E (l _BW / D _B )
² +7/45 1/G} (12) A _WB = K _BW /π(l _BW /D _W ) ² {29/210 1/E(l _BW /D _W )
² +7/45 1/G} (13) and the signs in equations (10) and (11) are assigned so that the nonlinear load distribution correction coefficient becomes a positive value. () For 6Hi mills For 6Hi mills, the gap between the rolls is between BUR and intermediate roll (IMR),
It is necessary to consider two factors between IMR and WR, and their distributions are expressed using quadratic equations according to equation (1). Also, if the deformation of the three rolls is expressed according to equation (2) or (3), the load distribution between each roll is expressed similarly to equation (4), so the load distribution on all rolls is is determined, and the deformation of each roll can be calculated in the same way as Equations (8) and (9). these
As in the case of the 4Hi mill, the initially assumed 2
If we assume that the following equation deformation and integral average are equal, then the magnitude of each roll deformation f _B , f _l , f _W
The original simultaneous equations are obtained and the influence coefficient α of each roll gap is determined by solving them.
This requires some calculations, but since it is similar to the case of the 4Hi mill, only the results are shown. Nonlinear load distribution correction coefficient α _BI.B regarding the gap between BUR and intermediate roll (IMR) of BUR is α _BI.B = A _BI (1 + A _WI + A _IW )/B (14) Nonlinear load regarding the gap between IMR and WR of BUR The distribution correction coefficient α _IW.B is α _IW.B = A _BI・A _IW /B (15) The nonlinear load distribution correction coefficient _{α BI.W regarding the gap between BUR and IMR of WR is α BI.W =} A _WI・A _IB /B (16) The nonlinear load distribution correction coefficient α _IW.W regarding the gap between IMR and WR of WR is given by α _IW.W = A _WI (1 + A _BI + A _IB )/B (17). However, B = (1 + A _BI + A _IB ) (1 + A _WI + A _IW ) - A _IB A _IW (18) A _BI = k _BI /π (l _BI /D _B ) ² {29/210 1/E (l _BI /D _B )
² +7/45 1/G}(19) A _IB =k _BI /π(l _BI /D _I ) ² {29/210 1/E(l _BI /D _I )
² +7/45 1/G}(20) A _IW =k _IW /π(l _IW /D _I ) ² {29/210 1/E(l _IW /D _I )
² +7/45 1/G} (21) A _WI =k _IW /π(l _IW /D _W ) ² {29/210 1/E(l _IW /D _W )
² +7/45 1/G} (22) The subscript I means IMR, and the right side BI, IW
are the contact part of BUR~IMR, and IMR~
This means the WR contact area. Note that the IMR nonlinear load distribution correction coefficient is also calculated at the same time, but it is omitted because it is not necessary for later analysis. (b) Nonlinear load distribution correction coefficient during kiss roll Since the nonlinear load distribution correction coefficient during kiss roll will be needed later when separating the deformation characteristics of the housing and rolling system from the kiss roll tightening data, it will be derived here. () In case of 4Hi mill When the upper and lower WRs are kissed, the upper and lower rolls cannot be considered separately, but must be considered as a contact problem between the four rolls. If we extend the problem of two rolls related to a 4Hi mill during rolling to a problem of four rolls, the deflection coefficients of each roll f ^T _B , f ^T _W ,
f ^B _W , f ^B _B (coefficient of deflection equation assumed as quadratic equation)
Obtain the following four-dimensional simultaneous linear equations for .

[Table] However, in the superscript, T represents the upper roll system, B represents the lower roll system, and the definition of A is expressed by formula (19) ~
Expanded according to (22). In the case of A _WW , as can be seen from equations (20) and (21), the upper WR
The formula differs depending on whether or not is the previous subscript, so the order is shown using superscripts. If the nonlinear load distribution is obtained by solving equation (23) as it is, the equation will be quite complicated, so we will simplify it here as follows. That is, since the problems dealt with by the present inventors can often be considered to be vertically symmetrical, it is assumed that the roll diameter, roll body length, and roll crown are all vertically symmetrical. At this time, Equation (23) becomes a simple two-dimensional simultaneous linear equation, and by solving this, the BRU nonlinear load distribution correction coefficient during kiss roll is given as follows. α ^o _BW.B regarding the gap between BUR and WR is α ^o _BW.B = A _BW (1 + 2A _WW ) / {1 + A _BW + A _WB + 2A _WW (1 + A _BW )} (24) α ^o _{WW regarding the gap between upper and lower WR. B} is α ^o _WW.B = A _BW・A _WW / {1 + A _BW + A _WB + 2A _WW (1 + A _BW )} (25) Here, in order to distinguish the nonlinear load distribution correction coefficient during kiss rolling from that during rolling, , superscript O was added. However, A _BW is the formula
(12), A _WB is determined by formula (13), and A _WW is determined by the following formula. A _WW =k _WW /π(l _WW /D _W ) ² {29/210 1/E(l _WW /D _W )
² +7/45 1/G} (26) Note that the WR nonlinear load distribution correction coefficient is not needed here, so it will be omitted. () In the case of a 6Hi mill If the problem is handled as a problem of six rolls of a 6Hi mill, a six-element simultaneous linear equation corresponding to equation (23) can be obtained. Therefore, by simplifying the assumption of vertical symmetry, the BUR nonlinear load distribution correction coefficient during kiss roll is given as follows. α ^o _BI.B regarding the gap between BUR and IMR is α ^O _BI.B = A _BI {(1+A _IW )(1+2A _WW )+A _WI }/B′
(27) α ^O _IW.B regarding the gap between IMR and WR is α ^O _IW.B = A _BI A _IW (1+2A _WW )/B′ (28) α ^O _WW.B regarding the gap between upper and lower WR is α ^O _{WW. B} = A _BI A _IW A _WW /B' (29) However, B' = (1+A _BI ) {(1+A _IW ) (1+2A _WW
)+A _WI }+A _IB (1+A _WI +2A _WW ) (30) A _BI ′A _IB ′A _IW ′A _WI is determined by equations (19) to (22), and A _WW is determined by equation (26). (2) Mill stretch calculation model for 6Hi mill Here, the upper half of the model is shown in Figure 7.
A mill stretch calculation model for a 6Hi mill capable of IMR shift and WR shift is derived. Note that mill stretch is evaluated centering on the rolled material, and is defined on the assumption that the load between the WR and the rolled material is uniformly distributed in the width direction. Based on the above-mentioned concept of how to superimpose roll deformation in a multi-high rolling mill, the contribution term δ _R of deformation of either the upper or lower roll system to mill stretch is considered separately for each factor as shown in the following equation. δ _R = δ _i + δ _B + δ _W + δ _C (31) However, δ _i is roll flatness, δ _B is BUR deflection, and δ _W is
The WR deflection, δ _C , is a term that indicates the direct influence of the roll crown. In this explanation, for the sake of simplicity, the roll crown is assumed to be a smooth parabolic shape, and BUR,
Roll crown for radius of IMR and WR
C _RB ′C _RI ′C _RW ′ are respectively C _RB = f _RB・(l _B /2) ² (32) C _RI = f _RI・(l _I /2) ² (33) C _RW = f _RW・( l _W /2) ² (34). l _B , l _I , and l _W are the respective roll body lengths. The sign is positive for a convex crown. (a) The contribution term δ _i δ _i of roll flattening is the flattening amount δ ^BI _i between BUR~IMR, IMR~
The amount of flattening between WRs can be separated into δ ^IW _i and WR flattening δ ^W _i due to contact with the rolled material, and is given by the following equation. δ _i = δ ^BI _i + δ ^IW _i + δ ^W _i (35) Since the contact load distribution when considering roll flatness can be assumed to be a linear distribution according to the concept of the present invention, the equilibrium condition equation for the force and moment of each roll can be From this, the contact load distribution between rolls is determined, and from this the contact load between rolls P _BI (between BUR and IMR) and P _IW (IMR
~WR) and calculate the amount of roll flatness using equation (5), the following equation is obtained. δ ^BI _i =c・p _BI [ln{2(D _B +DI)/(
c・p _BW )}−1] (36) p _BI = (l _BI ² +12x _BI ² ) (P+2F)/b _BI ³ (37) δ ^IW _i =c・p _IW [ln{2(D _I +D _W )/(
c・p _IW )}-1] (38) p _IW = (l _IW ² +12x _IW ² ) (P + 2F) / lY _IW ³ (39) Here, P is rolling load, F is roll bending per chock The increase side is positive and the decrease side is negative. Also, x _BI and x _IW are BUR~IMR, respectively
This is the x-coordinate of the midpoint of the contact area between IMR and WR. Regarding roll flattening due to contact between WR and materials, for example, Nakajima et al.
(1973), 29.) is given by the following equation. δ ^W _i = (c/2)・P _W [ln{32D _W /(H
-h+8cp _W )}-3] (40) p _W =P/b (41) However, b is the plate width, H is the inlet side plate thickness, and h is the outlet side plate thickness. (b) BUR deflection contribution term δ _B δ _B is derived by calculating the deflection amount in a simple deflection state and then correcting it using a nonlinear load distribution correction coefficient. The results are as follows. δ _B = Δy _BM + Δy _BS + ( _B ^* − _B ) (2a _B l _BI −
l _BI ² −4x _BI ² ) /l _BI ² − _B ^* {1−12(
x _BI / l _BI ) ² } / 3 (42) In equation (42), Δy _BM and +Δy _BS are the deflections due to the bending moment and shear force, respectively, at the center position of the rolled material in a simple deflection state, and according to beam theory, Δy _BM =P+2F/2K _oM +P+2F/EI _B [x _BI ^6/10
l _BI ³ −5x _BI ⁴ /24l _BI +x _BI ³ /6−l _BI x _BI ² /32+1/24 −(1/2a _B +x _BI ) ² (a _B −4x
_BI ) −l _BI ² a _B /96+l _BI ³ /384+a _B ³ /32〕(43) Δy _BS =P+2F/2K _oS +4(P+2F)/3GS _B [a
_B /4−l _BI /8+x _BI ² /l _BI +x _BI ⁴ /l _BI ³ ] (44). K _oM , K _oS of equations (43) and (44)
is the spring constant when the increment of deformation caused by the narrowing of the roll neck as shown in Figure 7 is replaced by a spring, and is the spring constant of a conical beam whose diameter is linearly deformed in the longitudinal direction. The following equation is obtained by comparing the deflections of the cylindrical beams. 1/K _oM = {8(a _B +l _B ) ³ /(3πE
)}{1/D _C ³ D _o )−1/D _B ⁴ }(45) 1/K _oS = {8(a _B +l _B )/(3πG
)} {1/D _C D _o )−1/D _B ² } (46) _B in equation (42) is the deflection of the simple deflection state defined in the contact area between BUR and IMR, and is given by the following equation. _B = (l _BI /2) ² [1/8EI _B (a _B
−7/12l _BI )+2/3GS _B l _BI ](P+2F) (47) _B ^* is the deflection in the actual rolling state and is given by the following formula. _B ^* + _B + α _BI.B {(f _RB +f _RI ) (l _BI /2
) ² − _B } +α _IW.B {(f _RI +f _RW ) (l _BI /2
) ² + _W (l _BI / l _IW ) ² } (48) Equation (48) is the calculation result using the nonlinear load distribution correction coefficient, and the second term on the right side, α _BI.B , is calculated in the simple deflection state. BUR that existed
This is the influence term of the IMR gap, and the third
The term _αIW.B is the influence term of the gap between IMR and WR that existed in the simple deflection state. _W is the deflection of WR in a simple deflection state defined in the contact area between IMR and WR, and is given by the following equation. _W = [1/384EI _W {3l _IW ³ +4l _IW (b ² +12x _IW ² ) + b ³ +
24b.x _IW ² +16x _IW ⁴ /b}+1/6GS _W {l _IW −b−4x _IW ² /b}
]P-[1/192EI _W (12a _W -7l _IW )l _IW ² +l _IW /3GS _W ]
F(49) The third term including ( _B ^* − _B ) in Equation (42) is a correction term for converting the effect of deflection in the simple deflection state evaluated by Δy _BM and Δy _BS to the actual rolling state. Yes, the correction amount of depth ( _B ^* − _B ) in the contact area between BUR and IMR is
It is assumed that the correction shape has a parabolic distribution within the contact area between the rolls, and a linear distribution outside the contact area, and is converted into a correction amount of the deflection depth from the position between the supports. In addition, the fourth term including _B ^* is calculated by calculating the difference at the center of the plate between the deflection distribution in the actual rolling state in the contact area between BUR and IMR and the integral average straight line in the same area, assuming that the correction shape is parabolic. This is what I calculated. (c) Contribution term of WR deflection δ _W The difference between the deflection at the center position of the rolled material and the integral average straight line in the simple deflection state is Δy _PM + Δy _PS
When +Δy _FM +Δy _FS , δ _W is given by the following formula. δ _W = (1−α _IW.W ) (Δy _PM +Δy _PS +Δy _FM
+Δy _FS )−α _IW.W (f _RI +f _RW ) (l _IW /2) ² {1-12(x _IW /l _IW )
² }/3−α _BI.W {(f _RB +f _RI ) (l _BI /2) ² − _B }{(1−12(x
_BI / l _BI ) ² } / 3 (50) Δy _PM , +Δy _PS are terms due to bending moment and shear force due to rolling load, Δy _FM , +Δy _FS are terms due to bending moment and shear force due to roll bending force, respectively. It is given by Eq. EI _W Δy _PM /P=W(5)・m/120+W(4)・n/24−(l _IW
/2+x _IW ) ³ (l _IW /2-3x _IW )/(24l _IW )-b ² (l _IW /2+x _IW ) (l _IW /2-x _IW )/(48l _IW )+b ³
(5-b/l _IW )/1920(51) GS _W Δy _PS /P=-W(3)・2m/9-W(2)・2n/
3 +2 (l _IW /2+x _IW ) (l _IW /2−x
_IW )/(3l _IW )-b(3-b/l _IW )/18(52) EI _W Δy _FM /F=W(5)・m/60+W(4)・n/12-W(3)
/6-(a _W /2+x _IW -l _IW /2)・W(2)/2(53) GS _W Δy _FS /F =-W(3)・4m/9-W(2)・4n/3 (54) However, m and n are IMR~WR contact load distribution p _IW using the Z coordinate shown in Fig. 7 as p _IW −
It is a coefficient when expressed as (m・Z+n)(P+2F) and is given by an equation of order. m=-12x _IW /l _IW ³ (55) n=(l _IW +6x _IW )/l _IW ² (56) In addition, W(j) means the following formula. W(j)=l _IW ^j /(j+1)−l ^(j-1) _IW・x _IW
−(l _IW /2−x _IW ) ^j (57) In Equation (50), the first term on the right side, that is, the item containing (1−α _IW.W ), expresses the effect of WR deflection in a simple deflection state on a nonlinear load distribution. It is converted to the actual rolling state using the correction coefficient, and the second term on the right side, that is, the term including α _IW.W , is
This is the influence term of the gap distribution between IMR and WR in the simple deflection state due to the roll crown of WR and IMR, and the third term on the right side, i.e. α _BI.W
The term containing is an influence term of the gap distribution between BUR and IMR in a simple deflection state due to the roll crown of IMR and BUR and deflection of BUR. (d) Direct contribution term of roll crown δ _C The influence of roll crown through roll deflection is already included in δ _B and δ _W , and in δ _C , the WR profile and the zero adjustment position at the time of kill roll are used as a reference. Consider the deviation at the center of the plate from the integral average straight line, and the effect of changes in the contact area due to roll shift on the integral average diameter of the rolls. The latter is due to the superposition method in which the roll profile is directly approximated by integral averaging in the area of contact between the rolls, and then the influence of the roll profile is taken into account. Therefore, δ _C can be given as follows by simple calculation. δ _C = −f _RW {l _W ² /12−x _W ² }+f _RW (x _W ² −x _IW ²
) + f _RI (2x _I − ² x _IW ² −x _BI ² ) − f _RB x _BI ² (58) However, x _W and x _I are the x-coordinates of the center of the torso of WR and IMR, respectively, and the sign of the roll shift amount is given. (e) Extracting the deformation of the housing and reduction system Here, if the correspondence relationship between the reduction setting value g and the load cell output P _t due to kiss roll tightening is given as g - g (P _t ) (59), this data A method for extracting the deformation characteristics of the housing and the rolling system will be explained in detail. When separating the data in equation (59) into roll deformation and other deformations, only roll flattening and BUR deflection need be considered as roll deformation. Since the deflection of WR and IMR does not change the diameter of the roll, it is thought that it will not have a direct effect on the data obtained using the load cell as the detection end. The roll flattening amount Δ _i ′, which is the sum of the upper and lower rolls when the kiss roll is tightened, can be given by the following formula since it is sufficient to consider the flattening amount between the upper and lower WR in addition to the upper and lower rolls in equations (36) and (38). Δ _i ′=2 (δ ^BI _i + δ ^IW _i ) + δ ^WW _i (60) δ ^WW _i =c・p _WW [ln(4D _W /c・p _WW )−1]
(61) p _WW =P/l _W (62) Here, P is the load acting on the trunk between the upper and lower WRs, and is obtained by back calculation from P _t . Care must be taken as the relationship between P _t and P varies depending on the type of rolling mill. It is also assumed that the upper and lower rolls are perfectly symmetrical in size and shape, and the data in equation (59) is obtained by tightening without roll shift. The contribution term Δ _B ′ of the vertical BUR deflection during a kiss roll can be obtained by multiplying δ _B ′, where x _BI =0 in equation (42), by the vertical roll. However, formula (42)
The deflection _B ^* during actual rolling used in Equation (48)
Instead, it must be calculated using the following formula using the nonlinear load distribution correction coefficient during kiss roll. _B ^* = (1−α ^o _BI

Claims (1)

[Claims] 1. In a method for setting the rolling reduction of a plate rolling mill, the increment of the gap between the upper and lower work rolls due to the rolling load and the roll bending force, that is, the mill stretch, is
The contribution of roll deformation and the contribution of deformation other than rolls are separated, and for the contribution of roll deformation, the elastic deformation of each roll constituting the rolling mill is calculated by calculating the predicted value of the rolling load for each rolling operation, Calculation takes into account the predicted value of roll bending force, target values of sheet width, entrance side sheet thickness, and exit side sheet thickness, and for the contribution of deformation other than rolls, the upper and lower work rolls are calculated in advance in the absence of rolled material. We conducted a tightening experiment with the rollers in contact, and used the deformation characteristics of parts other than the roll, which was obtained by subtracting the contribution of roll deformation during the tightening experiment from the relationship between the rolling reduction setting value obtained from this and the load cell load measurement value. Then, for each rolling operation, the mill stretch is calculated from the predicted value of the load cell load, and the mill stretch given as the sum of the contribution of roll deformation and the contribution of deformation other than the roll, is used to form the desired plate. A rolling reduction setting method for a plate rolling mill, characterized by determining a rolling reduction setting value for obtaining thickness. 2. In the rolling reduction setting method for a multi-high plate rolling mill with four or more stages, the contribution of roll deformation to mill stretch is determined by a straight line that uniquely determines the distribution of the contact load between rolls in the plate width direction from the equilibrium conditions of the force and moment of each roll. The roll flattening deformation is obtained by assuming the distribution, and the effect of the axial deflection of the work roll and the reinforcing roll is superimposed on this using the axial approximate straight line in the contact area with each adjacent roll as a reference. A rolling reduction setting method for a plate rolling mill according to claim 1. 3 In a rolling control method for a plate rolling mill, the increment in the gap between the upper and lower work rolls due to rolling load and roll bending force, that is, the mill stretch, is separated into the contribution of roll deformation and the contribution of deformation other than the rolls, and the contribution of roll deformation is For each rolling operation, calculate the elastic deformation of each roll that makes up the rolling mill, the predicted value of rolling load, the predicted value of roll bending force, and the target values of plate width, entry side plate thickness, and exit side plate thickness. In order to account for the contribution of deformation other than the rolls, we conducted a tightening experiment in which the upper and lower work rolls were brought into contact in the absence of rolled material, and calculated the reduction setting value obtained from this and the load cell load measurement value. Using the deformation characteristics of the parts other than the roll, which are obtained by subtracting the contribution of the roll deformation during the tightening experiment from the relationship, it is calculated from the predicted value of the load cell load for each rolling operation. Using a calculation method that calculates the mill stretch as the sum of the contribution of roll deformation and the contribution of deformation other than the roll, it is possible to calculate either the influence coefficient of rolling load on mill stretch or the influence coefficient of roll bending force on mill stretch. 1. A rolling reduction control method for a plate rolling mill, characterized in that one or both of them are determined, and based on this, a rolling operation amount for adjusting the thickness of the plate during rolling to a desired value is determined. 4. In a rolling reduction control method for a multi-high plate rolling mill with four or more stages, the contribution of roll deformation to mill stretch is determined by a straight line that uniquely determines the distribution of the contact load between rolls in the plate width direction from the equilibrium conditions of the force and moment of each roll. The roll flattening deformation is obtained by assuming the distribution, and the effect of the axial deflection of the work roll and the reinforcing roll is superimposed on this using the axial approximate straight line in the contact area with each adjacent roll as a reference. A rolling control method for a plate rolling mill according to claim 3.