JP2002361309A - Method for forecasting plate crown in hot rolling and hot rolling method - Google Patents

Abstract

PROBLEM TO BE SOLVED: To forecast a plate crown with a high degree of accuracy and at a small calculation load even under rolling conditions wherein a non-contact area arises between a work roll and a backup roll. SOLUTION: Under a plurality of rolling conditions, the plate crown is calculated (S110), considering (S106, S109) contact area information using a splitting model and the plate crown (S110) is obtained by the plate crown forecasting formulas (A), (B) decided based on the calculation result; Crout /Hout =ζηCM/Hout +ηCrin/Hin ...(A) CM=αP.P+αB.FB+αCW.CRW+αCB.CRB+αCH.CRH...(B) Here, mechanical crown is indicated as CM, rolling load as P, bending force as FB, work roll initial crown as CRW, backup roll crown CRB, work roll thermal crown as CRH, and influence coefficient as αP, αB, αCW, αCB, αCH.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for predicting a sheet crown in hot rolling of a material to be rolled such as steel, aluminum, an aluminum alloy and the like, and a hot rolling method using the same.

[0002]

2. Description of the Related Art Generally, in hot rolling of a material to be rolled, such as steel, aluminum, or an aluminum alloy, in order to improve the quality of the sheet crown of the material to be rolled, a sheet crown after a rolling pass is predicted using a computer. Control of the rolling mill is performed based on the prediction result. FIG. 1 shows a configuration of a four-stage rolling mill as an example of the rolling mill. The rolling device, the work roll 1 is rolling acts directly on the rolled material 4, to reinforce it, backup roll 2 has a variable shape mechanism, and the acting on the work roll and the backup roll bending force F _B And a roll bending mechanism (not shown) for generating the pressure. When the material to be rolled 4 is passed (rolled) by such a rolling device, the work roll 1 receives a rolling load P of several hundred tons or more from the material to be rolled 4 and a contact load q from the backup roll, Work roll 1
The bow is formed on the rolled material 4 after the deflection. At this time, in order to obtain a preferable sheet crown from both the quality aspect and the operation aspect, the backup roll 2 by the variable shape mechanism is used based on the prediction result of the sheet crown after the pass.
Of and profile shapes, to control the bending force F _B by the roll bending mechanism.

[0003] A general control procedure of such a rolling mill is, for example, as shown in FIG. Hereinafter, S11, S1
2,, represent the number of the step (procedure).
First, the initial value of the profile shape of the bending force F _B and the backup roll, strip crown after paths to the target (target strip crown), the rolled material 4 having a thickness which then pass width, the load such as the following coils Rolling conditions such as information are input (S11 to S13). Further, a rolling history such as a temperature of the material 4 to be rolled and a cooling temperature of the work roll 1 is input (S14), and based on the rolling history, a predetermined thermal profile model 31 is used to perform axial expansion of the work roll 1 by thermal expansion. Is required (S1)
5). Then, based on the rolling conditions and the thermal profile, a predicted value of the sheet crown after passing is calculated using a predetermined sheet crown prediction model 30 (S21), and this value falls within a predetermined error range of the target sheet crown. If no (no side at S22) while performing the correction of the bending force F _B and profile shape of the backup roll (S23), the prediction calculation of the strip crown after path (S21) are repeated sequentially (S23 → S21 →
S22). Then, when the calculated value of the plate crown after the pass falls within the predetermined error range (Ye in S22).
profile shape of the bending force F _B and the backup s side) is set to the rolling device (S31).

Here, the thermal profile model 3
For example, Reference 1 (Kitahama et al .: Plasticity and Working (Journal of the Japan Society for Plastic Working)), Vol. 36, No. 417 (1995-10)
pp. 1163-1168) can be applied. The plate crown prediction model 30 for obtaining the plate crown after the pass is generally given by the following equation (1). In _{Cr out / H out = ζC M} / H out + ηCr in / H in ... (1) where, Cr _in and Cr _out each strip crown after path before and paths, H _in and H _{o ut} the material to be rolled 4 Before and after the pass, _CM is the mechanical crown of the work roll 1 (the crown of the work roll 1 when a uniform load acts on the material to be rolled in the width direction), and ζ and η are respectively the given a transfer rate of the mechanical crown C _M and the path before the sheet crown Cr _in.

Further, the mechanical crown _CM is:
Conventionally, it is given by the following equation (2). _{C M = α P · P +} α B · F B + α CW (C RW + C RH) + α CB · C RB ... (2) where, P is the rolling load, F _B is the bending force, C _RW is the work roll 1 initial crown,
C _RH is a thermal crown of the work roll 1, and C _RB is an initial crown of the backup roll 2. Also,
α _P , α _B , α _CW , and α _CB are influence coefficients on the mechanical crown C _M , respectively. As shown in the following equation (3), for example, the width W of the material 4 to be rolled, the work roll 1 as a function of the diameter of the backup roll 2. α _P = F ₁ α _P (W, D _w , D _B ) α _B = F ₁ α _B (W, D _w , D _B ) (3) α _CW = F ₁ α _CW (W, D _w , D _B ) Here, each function expressed by the equation (3) is obtained by virtually dividing the work roll 1 and the backup roll 2 in the axial direction by several tens of minutes, and applying a given plurality of rolling conditions to each divided area. Of the mechanical crown C _M obtained by a so-called divisional model in which the force balance and the conditions for adapting the surface displacement between the work roll 1 and the backup roll 2 are determined, and the deflection and flat deformation of each roll are strictly solved. , said each rolling conditions (sample data), the parameters W, D _w, is determined by multiple regression with factors such as D _B (conventional method). The division model is described in, for example, Reference 2 (Shohet, K.
N. & Townsend, NA: J. Iron and Steel Inst. 206
-11 (1968), p. 1088) is well known.

Here, for example, when the material 4 to be rolled is steel or the like, since the rolling load P is very large, for example, about 1000 t, the peripheral surfaces of the work roll 1 and the backup roll 2 are in the width direction. For areas that overlap, normally all areas touch. Therefore, in the conventional method, the sample data is obtained under the condition that the entire area is in contact with the sample data as shown in the document 1.

[0007]

However, the material to be rolled 4
However, for example, in the case of aluminum or an aluminum alloy, the rolling load P is relatively small, for example, about 200 t, and a gap originally formed between the work roll 1 and the backup roll is provided in the entire area. The flattening of each roll does not increase as far as the rolls disappear, and a non-contact area is formed between the two rolls. FIG. 2 shows a state in which the non-contact areas 21 are formed at both ends of the work roll 1. In such a case, the conventional method on the premise that the entire area comes into contact has a problem that the error of the calculation result of the sheet crown after the pass increases. In order to solve such a problem, a method of calculating a contact area between both rolls is disclosed in Japanese Patent No. 2978061. However, in this method, convergence calculation is required to obtain the contact area. If this is performed in S21 of FIG. 3, the convergence calculation will be performed in the convergence calculation, and the calculation load will increase, and depending on the computer's ability to perform the calculation, there will be a problem that online control cannot be performed in time. Obtained. Therefore, the present invention has been made in view of the above circumstances, and aims at high accuracy even under rolling conditions in which a non-contact area occurs between a work roll and a backup roll. Another object of the present invention is to provide a strip crown prediction method capable of predicting a strip crown after a pass with a small calculation load and a rolling method using the same.

[0008]

SUMMARY OF THE INVENTION In order to achieve the above object, the present invention provides a work roll, a backup roll having a roll shape variable mechanism, and a plate in hot rolling of a material to be rolled by a rolling apparatus having a roll bending mechanism. In the crown prediction method, a sheet crown Cr _out after the pass in the hot rolling is determined based on a plurality of sheet crown calculation results calculated based on predetermined parameters including contact area information between the work roll and the backup roll. This is a sheet crown prediction method in hot rolling, which is obtained by a sheet crown prediction equation.

It is conceivable that the contact area information is determined based on the profile shape of each of the work roll and the backup roll. In addition, the above-described plate crown prediction formula is calculated by using each plate crown Cr before and after the pass.
and _in and Cr _out, the given by the respective plate thickness H _in and H _out after the path before and path of the rolled material, the following expression representing the relation between the mechanical crown C _M of the work rolls (A), Cr _out / H _out = ζC _M / H _out + ηCr _in / H _in
... (A) The mechanical crown _CM is
Rolling load P, bending force F _B , work roll initial crown C _RW , backup roll crown C _RB ,
And the relationship with the work roll thermal crown C _RH is given by the following equation (B). _{C M = α P · P +} α B · F B + α CW · C RW + α CB · C RB + α CH · C RH ... (B) , however, in the formula (A), the ζ and eta, the mechanical each given previously a transfer ratio and the transfer rate of the crown Cr _in the path front plate of the crown C _M, in the formula _{(B), α P, α B, α} CW, α CB, α CH , each said mechanical crown C _M a influence coefficient of the width W of the material to be rolled, the rolling load P, the work roll diameter D _w, the backup roll diameter D _B, the material to be rolled in the following path and the previous path And the dimensionless parameter τ representing the profile shape of the backup roll determined by the roll shape variable mechanism.
Is a function of at least one parameter.

Further, the influence coefficients α _P , α _B , α _CW ,
alpha _CB, the alpha _CH, the parameter _{W, P, D w, D} B, Δ
The following functions of W and τ may be used. _{α P = Fα P (W,} P, D w, τ) α B = Fα B (W, P, D B, τ) α CW = Fα CW (W, P) α CB = Fα CB (W, P) α _CH = Fα _CH (W, P, ΔW)

The above functions Fα _P , Fα _B , Fα _CW ,
Under a plurality of rolling conditions, Fα _CB and Fα _CH are assumed to be the contact area information, and based on the assumption, a division model is used to calculate an axial contact load distribution between the work roll and the backup roll, If the contact load distribution has a negative contact load, the assumption of the contact area information is corrected and the calculation of the contact load distribution is sequentially repeated, and the contact load distribution has a negative value of the contact load. If no more, the sample value of the sheet crown after the pass is calculated based on the calculation result of the contact load distribution, and is determined based on the multiple regression analysis of the sample values obtained under the plurality of rolling conditions. It is possible.

A hot rolling method using the above-described sheet crown prediction method in hot rolling may be considered. That is, the bending force by the bending mechanism and the profile shape of the backup roll by the roll shape variable mechanism are assumed, and based on the assumption,
The plate crown Cr _out after the pass is calculated by the plate crown prediction formula determined by the plate crown prediction method, and the difference between the plate crown Cr _out after the pass and a preset target plate crown is within a predetermined error range. If not, the assumption of at least one of the bending force and the profile shape of the backup roll is corrected, and the calculation of the sheet crown after the pass by the sheet crown prediction method is sequentially repeated, so that the difference is within the error range. A hot rolling method in which the bending force and the backup roll profile shape at that time are set in the rolling device.

[0013]

Embodiments of the present invention will be described below with reference to the accompanying drawings to provide an understanding of the present invention. It should be noted that the following embodiments are examples embodying the present invention, and do not limit the technical scope of the present invention. Here, FIG. 1 is a diagram showing a configuration example of a rolling device used for general hot rolling, and FIG. 2 is a diagram showing a case where a non-contact region occurs at both ends of a roll of a rolling device used for general hot rolling. FIG. 3 is a block diagram showing a procedure of a general rolling method. FIG. 4 is a flowchart showing a procedure for obtaining a sheet crown prediction formula used in the sheet crown prediction method according to the embodiment of the present invention. Is a graph for explaining a dimensionless parameter representing a profile shape of a backup roll used in the strip crown prediction method according to the embodiment of the present invention, and FIG. 6 is calculated using the strip crown prediction method according to the embodiment of the present invention. It is a figure which compares the calculated crown value of a sheet and the calculated crown value of a sheet calculated by a conventional method.

The strip crown prediction method according to the embodiment of the present invention is applied to the strip crown prediction model 30 of S21 in the above-described general rolling method shown in FIG. 3, and calculates the strip crown Cr _out after passing. the included in the strip crown prediction equation for (the equation (1)) are those characterized by the formula mechanical crown C _M. Therefore,
The calculation method of the range other than the calculation formula of the mechanical crown C _M is well-known, in addition to the method described in the above-mentioned reference 1, and the description is omitted here.

The sheet crown prediction formula used in the sheet crown prediction method according to the present embodiment includes the sheet crowns Cr _in and Cr _out before and after the pass, and the sheet crowns before and after the pass of the material to be rolled. and the plate thickness H _in and H _out, given by the following expression representing the relation between the mechanical crown C _M of the work roll (a). This is the same as equation (1) in the conventional method. Cr _out / H _out = ζC _M / H _out + η Cr _in / H _in (A) Here, ζ and η are the transfer rate of the mechanical crown C _M and the crown C of the pass front plate respectively given in advance.
which I am a transfer rate of r _in. The specific contents of ζ and η are well-known in, for example, Reference 3 (Awazu et al., Proceedings of the 33rd Joint Lecture on Plastic Working (1982), p. 143) and the like, and therefore description thereof is omitted here.

Further, the mechanical crown C_MIs
Rolling load P, bending force F_B, Work roll initiator
Dial Crown C_RW, Backup roll initial class
Un C _RB, And work roll thermal crown C_RHWith
The relation is given by the following equation (B). C_M= Α_P・ P + α_B・ F_B+ Α_CW・ C_RW+ Α_CB・ C_RB + Α_CH・ C_RH ... (B) where α_P, Α_B, Α_CW, Α_CB, Α_CHIs the mechanism
Nikal Crown C_MIs the influence coefficient. Equation (B) is
The difference from equation (2) in the conventional method is that
Crawling initial crown C_RW, And the worklaw
Le Thermal Crown C_RHThe influence coefficient α of_CW, Α_CHEach
It is a point provided individually. This generally gives the shape
The work roll initial class having a substantially parabolic shape;
Un C_RW, And the work roll thermistor having a substantially trapezoidal shape
Le Crown C_RHIs the mechanical crown C_MAffect
Regarding the effect, the difference in the effect caused by the difference in the shape
Can be reflected.

The influence coefficients α _P , α _B , α _CW ,
α _CB and α _CH are given by functions shown in the following equations (C1) to (C5). _{α P = Fα P (W,} P, D w, τ) ... (C1) α B = Fα B (W, P, D B, τ) ... (C2) α CW = Fα CW (W, P) ... ( C3) α _CB = Fα _CB (W, P) (C4) α _CH = Fα _CH (W, P, ΔW) (C5) where W is the width of the material to be rolled, P is the rolling load, and D _w is a diameter of the work roll, the backup D _B is a diameter of the backup roll, [Delta] w is the difference between the width of the rolled material in the following path and the previous path, which τ is determined by the roll variable shape mechanism It is a dimensionless parameter representing the profile shape of the roll.

Here, the dimensionless parameter τ representing the profile shape of the backup roll will be described with reference to FIG. In the graph of FIG. 5, the X axis is the distance from the axial center of the backup roll, and the Y axis (left side) is the amount of displacement of the surface in the radial direction when the backup roll 2 is deformed by the variable shape mechanism. And the relative displacement amount where the position when no deformation is given is 0 (zero). The backup roll 2 shown in FIG.
Has a variable mechanism that can change its profile shape in 11 steps, including a flat state without deformation. The dimensionless parameter τ is defined as 0 (zero) for a flat state in which the backup roll 2 is not deformed, 1 for a deformation state having the largest deformation amount (displacement amount of the surface), and nine stages of deformation states in the meantime. It is a parameter obtained by rendering the profile shape of the backup roll non-dimensional by expressing it in 0.1 steps from 0.1 to 0.9 (the right side of the Y axis in FIG. 5). Thus, as an element a change in profile shape of the backup roll gives influence on the mechanical crown C _M, the influence coefficient alpha _P, the function of alpha _B F
Since they are included in α _P and Fα _B, it is not necessary to individually calculate the influence coefficients α _P and α _B for each profile shape of the backup roll 2.

The influence coefficient α_P, Α_B, Α_CW,
α_CB, Α_CHThe function Fα_P, Fα_B, Fα_CW, F
α_CB, Fα_CHAre given by the following equations (D1) to (D5), respectively.
It is. α_P= Fα_P(W, P, D_w, Τ) = Σ (a1_n・ Wⁿ) ・ Σ (b1_n・ P^m) ・ Σ (c1_l・ D_W ^l) ・ Σ (t1_k・ Τ^k)… (D1) α_B= Fα_B(W, P, D_B, Τ) = Σ (a2_n・ Wⁿ) ・ Σ (b2_n・ P^m) ・ Σ (c2_l・ D_B ^l) ・ Σ (t2_k・ Τ^k)… (D2) α_CW= Fα_CW(W, P) = Σ (a3_n・ Wⁿ) ・ Σ (b3_n・ P^m)… (D3) α_CB= Fα_CB(W, P) = Σ (a4_n・ Wⁿ) ・ Σ (b4_n・ P^m)… (D4) α_CH= Fα_CH(W, P, ΔW) = Σ (a5_n・ Wⁿ) ・ Σ (b5_n・ P^m) ・ Σ (d5_l.DELTA.W) (D5) where a1 to a5, b1 to b5, c1, c2, d5
t1 to t2 are unknown coefficients, and k, l, m, and n are
The predetermined expansion order of the unknown coefficient. These unknown coefficients are
The influence coefficient α_P, Α_B, Α_CW,
α_CB, Α _CHIs obtained, and as a result, the above equation (B) is obtained.
Further, the above equation (A), that is, the sheet crown prediction equation is obtained.
You.

Next, referring to FIG._P,
α_B, Α_CW, Α_CB, Α_CHExplain the procedure for requesting
You. Here, before the procedure of FIG.
Given a plurality of (1 to N) rolling conditions
I do. First, the first (i =
Select the rolling conditions of 1) (S101 → S102)
You. Here, the rolling conditions are defined as the sheet crown Cr before the pass.
_in, Temperature T before pass of rolled material 4_iAnd plate shape, rolled
Thickness H before and after pass of material 4_inAnd H_out, Pressure
The plate width W of the rolled material 4 and the bendin of the work roll 1
Power F_B, The work roll 1 and the backup roll
7 is an initial shape of each rule.

Next, based on the selected rolling conditions, the work roll initial crown C _RW and the backup roll crown C _RB at the start of rolling are calculated (S103). Next, based on the rolling conditions, a heat balance calculation is performed to calculate a rising temperature of the material to be rolled 4 after the pass in the rolling, and the rising temperature is compared with the initial crowns C _RW and C _RB obtained in S103. Based on the above, each thermal crown of the backup roll 1 and the work roll 2 is calculated using the thermal profile model 31 (S104). Next, based on the respective thermal crowns determined in S104, the work roll 1 and the backup roll
Is calculated (S105). S10
The specific contents of 2 to S105 are described in the above-mentioned document 2 and are well known, and thus the description thereof is omitted here.

Next, contact area information between the work roll 1 and the backup roll 2 is assumed based on the respective deformation profiles obtained in S105 (S10).
6) Yes. As the initial state of the assumption, for example, a method of assuming that all areas where the work roll 1 and the backup roll 2 overlap may come into contact with each other can be considered. Next, assuming that the rolling load P acts only on the area assumed to be in contact with the contact area information,
The deformation of the work roll 1 and the backup roll 2 and the contact load distribution q (x) in the axial direction between the work roll 1 and the backup roll 2 are calculated using the divided model shown in the document 2 or the like. (S107). (X represents a position in the axial direction.) Next, in the calculated contact load distribution q (x), a load at any position x in the axial direction is a negative value (S10).
8 (Yes side), after changing the contact area information assumed in S106 (S109), calculates the contact load distribution q (x) again (S107). Here, the contact area information may be changed, for example, based on the contact load distribution q (x), assuming that only the position x whose load value is equal to or greater than a predetermined value is changed. Can be

Thus, the contact load distribution q
In (x), until there is no negative load at any position x in the axial direction, the contact area information is changed and the contact load distribution q (x) is calculated (S109 → S10).
Repeat step 7). Then, when the load of the negative value no longer exists at any position x in the axial direction (No in S108)
Side), the sheet crown at predetermined evaluation points (for example, the center and both ends in the sheet width direction) of the material to be rolled is calculated based on the contact load distribution q (x) at that time (S110).
I do. Next, another rolling condition is sequentially selected (the i-th rolling condition is selected, i = 2, 3,...) (S112 → S
102), the above-described procedures of S103 to S110 are repeated, and the calculated values of the sheet crown are obtained for all the given rolling conditions (S102 to S111 → S1).
12). Then, the calculated values of the plurality of plate crowns obtained in this manner are subjected to multiple regression processing using the equations (D1) to (D5), whereby the unknown coefficients a1 to
a5, b1 to b5, c1, c2, d5, t1 to t2 are obtained, and the influence coefficients α _P , α _B , α _CW , α _CB , α
_CH is obtained (S113). At this time, the expansion order k,
l, m, and n are, for example, quadratic.

Next, referring to FIG. 6, the crown crown calculation value A calculated using the plate crown prediction equations (Equations (1) and (2)) obtained by the above-mentioned conventional method and FIG. 4 are shown. Prediction formula ((A) formula, (B)) of plate crown obtained according to the procedure
Is compared with the plate crown calculation value B calculated using the formula (1). Here, since it is difficult to collect the measured values of the sheet crown under a number of rolling conditions, the exact solution of the sheet crown after the pass calculated strictly by the above-mentioned division model is substituted for the measured value. The correlation between the calculated value of the plate crown and the exact solution was evaluated.

The graph shown in FIG.
The influence coefficient α of the equation (3) obtained by_P, Α_B,
α_CWIs calculated using the above equations (1) and (2).
The result A of the plate crown after the calculated pass is set to the Y axis
FIG. 8 is a scatter diagram in which the exact solution of the later plate crown is taken on the X axis.
You. Further, the graph shown in FIG.
, The expansion orders k, l, of the equations (D1) to (D5)
By taking m and n up to the second order, the influence coefficient α_P, Α_B, Α _CW,
α_CB, Α_CHIs calculated, and based on this, the equation (B) and
(A) Calculation result of sheet crown after pass calculated using equation
Result B on the Y axis and the exact solution of the strip crown after the pass on the X axis
It is a scatter diagram taken. Compare FIGS. 6 (a) and 6 (b)
As is apparent, the calculated value B of the plate crown according to the present invention is
Is better than the calculated value A of the sheet crown by the conventional method.
It is also found that the exact solution is approximated over a wide range.
Call FIG. 6C shows each of FIGS. 6A and 6B.
For the exact solution, the calculated value of the crown of the plate
It is a bar graph which showed each error of A and B. According to the invention
The error (25.9 μm) of the calculated value B of the sheet crown is
The error of the calculated value A of the plate crown by the conventional method (67.1)
μm) of 40% or less.
It turns out that the fruit is big. In addition, the prediction accuracy
Fig. 3 shows the prediction formula (prediction model) for the high strip crown.
Perform rolling control by applying to sheet crown prediction model 30
It is clear that the quality of the strip crown is improved.

[0026]

As described above, according to the present invention,
Even under rolling conditions where a non-contact area is created between the work roll and the backup roll, the strip crown can be predicted with high accuracy and with a small calculation load, and as a result, the strip crown quality can be improved. Can be.

[Brief description of the drawings]

FIG. 1 is a diagram showing a configuration example of a rolling apparatus used for general hot rolling.

FIG. 2 is a diagram showing a case where a non-contact area occurs at both ends of a roll of a rolling device used for general hot rolling.

FIG. 3 is a block diagram showing a procedure of a general rolling method.

FIG. 4 is a flowchart showing a procedure for obtaining a sheet crown prediction equation used in the sheet crown prediction method according to the embodiment of the present invention.

FIG. 5 is a graph for explaining a dimensionless parameter representing a profile shape of a backup roll used in the strip crown prediction method according to the embodiment of the present invention.

FIG. 6 is a diagram comparing a calculated crown value calculated using the strip crown prediction method according to the embodiment of the present invention with a calculated crown value calculated using a conventional method.

[Explanation of symbols]

1 ... work roll 2 ... backup roll 4 ... the material to be rolled 21 ... non-contact area 30 ... plate crown prediction model 31 ... thermal profile model F _B ... bending force P ... rolling load q ... contact load S11, S12 ,,, ... Step (Step) number

──────────────────────────────────────────────────の Continued on the front page (51) Int.Cl. ⁷ Identification symbol FI Theme coat ゛ (Reference) B21B 37/00 117B (72) Inventor Hiroshi Kunii 15 Kinuigaoka, Moka City, Tochigi Prefecture Kobe Steel Ltd. F-term in Moka Works (reference) 4E024 AA03 BB01 CC02 DD01 DD02

Claims (6)

[Claims] In a method for predicting a sheet crown in hot rolling of a material to be rolled by a rolling device having a work roll and a backup roll having a variable roll shape mechanism and a roll bending mechanism, the sheet crown after a pass in the hot rolling is provided. Cr _out is obtained by a sheet crown prediction equation determined based on a plurality of sheet crown calculation results calculated based on predetermined parameters including contact area information between the work roll and the backup roll. A method for predicting sheet crown in hot rolling. 2. The method according to claim 1, wherein the contact area information is determined based on a profile shape of each of the work roll and the backup roll. The method according to claim 3, wherein the plate crown prediction formula, and each strip crown Cr _in and Cr _out after the path before and path, and the plate thickness H _in and H _out after the path before and path of the material to be rolled, the following expression representing the relation between the mechanical crown C _M of the work roll given by _{(a), Cr out / H} out = ζC M / H out + ηCr in / H in ... the (a) the mechanical crown C _M, the rolling load P , bending force F _B, work roll initial crown C _RW, backup roll crown C _RB, and work following expression representing the relationship between the roll thermal crown C _RH (B) consisting given by claim 1 or 2 between heat according Method for predicting sheet crown in rolling. _{C M = α P · P +} α B · F B + α CW · C RW + α CB · C RB + α CH · C RH ... (B) , however, in the formula (A), the ζ and eta, the mechanical each given previously a transfer ratio and the transfer rate of the crown Cr _in the path front plate of the crown C _M, in the formula _{(B), α P, α B, α} CW, α CB, α CH , each said mechanical crown C _M a influence coefficient of the width W of the material to be rolled, the rolling load P, the work roll diameter D _w, the backup roll diameter D _B, the material to be rolled in the following path and the previous path And the dimensionless parameter τ representing the profile shape of the backup roll determined by the roll shape variable mechanism.
Is a function of at least one parameter. 4. Each of the influence coefficients α _P , α _B , α _CW , α _CB ,
alpha _CH is, the parameter _{W, P, D w, D} B, ΔW, strip crown prediction method in hot rolling according to claim 3 which is the function of the following tau. _{α P = Fα P (W,} P, D w, τ) α B = Fα B (W, P, D B, τ) α CW = Fα CW (W, P) α CB = Fα CB (W, P) α _CH = Fα _CH (W, P, ΔW) 5. The function Fα _P (W, P, D _w , τ),
Fα _B (W, P, D _B , τ), Fα _CW (W, P), Fα _CB
(W, P) and Fα _CH (W, P, ΔW) assume the contact area information under a plurality of rolling conditions, and, based on the assumption, determine the distance between the work roll and the backup roll by a division model. The contact load distribution in the axial direction is calculated, and if a negative contact load exists in the contact load distribution, the assumption of the contact area information is corrected, and the calculation of the contact load distribution is sequentially repeated. When the contact load having a negative value in the distribution no longer exists, a sample value of the sheet crown after the pass is calculated based on the calculation result of the contact load distribution, and the sample value obtained under the plurality of rolling conditions is calculated. The method according to claim 4, wherein the method is based on multiple regression analysis of sample values. 6. A method of hot rolling a material to be rolled by a backup roll having a work roll and a roll shape variable mechanism and a rolling device having a roll bending mechanism, wherein the bending force by the bending mechanism and the roll force by the roll shape variable mechanism. Assuming the profile shape of the backup roll, a plate crown prediction formula determined based on a plurality of plate crown calculation results obtained based on parameters including contact area information between the work roll and the backup roll based on the assumption. the calculated strip crown Cr _out after the path, the difference between the preset target strip crown and the strip crown Cr _out after the path is not within a predetermined error range, the bending force and the backup roll Modify at least one of the profile shape assumptions The calculation of the sheet crown after the pass by the sheet crown prediction method is sequentially repeated, and when the difference falls within the error range, the bending force and the backup roll profile shape at that time are set in the rolling device. A hot rolling method characterized by comprising: