JP2001347308A - Method and device for setting pass schedule of rolling mill - Google Patents

Abstract

PROBLEM TO BE SOLVED: To solve the problem that expensive equipment for controlling a shape such as a roll bender is required to prevent defects in shape because there is a possibility of the generation of the defects in shape on a material to be rolled when performing temperature control in the midst of rolling in order to satisfy the target thickness and the target material quality about the material to be rolled which is rolled by plural passes. SOLUTION: In the case that the error of the predicted material quality which is predicted based on the actual value after starting the rolling to the target material quality exceeds the allowable range, by on-line calculating such the proper values of the amount of correction of draft and time between passes as the target thickness and target flatness are maintained and correcting the pass schedule at any time based on the proper values, products which satisfies desired thickness, flatness and material quality are obtained by setting the pass schedule.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method and an apparatus for setting a pass schedule of a rolling mill, and more particularly to a rolling mill for setting a pass schedule so as to obtain a target thickness and a target material for a material to be rolled in a plurality of passes. The present invention relates to a path schedule setting method and apparatus.

[0002]

2. Description of the Related Art For example, JP-A-5-237507 and JP-A-5-69020 disclose a method of starting rolling in order to obtain a predetermined material (metal structure) for a material to be rolled in a plurality of passes. In advance, the rolling temperature of each pass is predicted in advance, a pass schedule for obtaining a desired thickness in consideration of the predicted rolling temperature of each pass is determined, the rolling temperature is measured during rolling, and the rolling temperature is measured based on the measured rolling temperature. It describes a method of controlling the rolling temperature by correcting the inter-pass time.

[0003]

However, as described in the above-mentioned publication, if the temperature is controlled during rolling in order to obtain a predetermined material, the rolling load changes. In addition, the roll shape changes due to the wear and thermal expansion of the roll during rolling. If the rolling load or roll shape changes, the plate shape (flatness) during rolling may change and shape defects may occur, so the conventional technology satisfies the target thickness, target material, and target flatness simultaneously. To do so, expensive equipment such as a roll bender and a pair cross roll for controlling the plate shape was indispensable. In order to solve the problems in the prior art, the present invention has improved a pass schedule setting method and apparatus of a rolling mill so that an error of a predicted material with respect to a target material, which is predicted based on actual values after starting rolling, is allowed. If the range is exceeded, the appropriate values of the reduction rate and the amount of time between passes are calculated online so as to maintain the target thickness and target flatness, and the pass schedule is revised as needed based on this. It is an object of the present invention to provide a method and an apparatus for setting a pass schedule of a rolling mill which can obtain a product satisfying a desired plate thickness, flatness and material by setting a pass schedule without introducing expensive shape equipment. It is assumed that.

[0004]

Means for Solving the Problems One of the inventions for achieving the above-mentioned object is to provide a reduction ratio, a pass rate and a pass rate so that a target thickness, a target flatness, and a target material can be obtained for a material to be rolled in a plurality of passes. Rolling is started by setting a pass schedule that defines the inter-time and material temperature, and while acquiring the actual draft, actual inter-pass time, and actual material temperature of each pass, the acquired actual draft, actual inter-pass time, Calculating a predicted material of the material to be rolled based on the actual material temperature and the pass schedule, and determining whether an error of the calculated predicted material of the material to be rolled with respect to the target material is within an allowable range for each pass; If it is determined that the error of the calculated predicted material of the material to be rolled with respect to the target material is not within an allowable range,
Under the equation constraint that the sum of the correction amounts for the rolling reduction of the pass schedule becomes 0, the correction amount for the rolling reduction and the correction amount for the inter-pass time are linearized from the target material. An appropriate value of the correction amount for the rolling reduction that minimizes an error is determined, and a crown change rate linearized for the correction amount for the rolling reduction and the correction amount for the inter-pass time in the pass schedule is determined by a shape dead zone. In order to satisfy the inequality constraint condition of being within the limit value, a proper value of the correction amount for the inter-pass time is determined using a proper value of the correction amount for the determined rolling reduction. It is configured as a pass schedule setting method for a rolling mill, wherein the pass schedule is corrected based on an appropriate value of the correction amount for the inter-pass time. There. In the pass schedule setting method for the rolling mill, first, a pass schedule in which a reduction ratio, an inter-pass time, and a material temperature are determined so that a target thickness, a target flatness, and a target material are obtained for a material to be rolled in multiple passes. The rolling is set and started. Next, while obtaining the actual rolling reduction, actual inter-pass time, and actual material temperature for each pass,
The predicted material of the material to be rolled is calculated based on the obtained actual rolling reduction, the actual inter-pass time, the actual material temperature, and the pass schedule, and the predicted material of the calculated material to be rolled is calculated for each pass. It is determined whether an error with respect to the target material is within an allowable range. An equation constraint condition that when it is determined that an error of the calculated predicted material of the material to be rolled with respect to the target material is not within an allowable range, the sum of correction amounts for the rolling reduction of the pass schedule becomes 0. Below, a suitable value of the correction amount for the rolling reduction that minimizes an error from the target material, which is linearized for the correction amount for the rolling reduction and the correction amount for the inter-pass time, is determined. Next, a linearized crown change rate of the correction amount for the rolling reduction and the correction amount for the inter-pass time of the pass schedule is set so as to satisfy an inequality constraint condition that the linearized crown change rate falls within a limit value defined by a shape dead zone. An appropriate value of the inter-pass time correction amount is determined using the determined appropriate value of the correction amount for the rolling reduction. Then, the path schedule is corrected based on at least an appropriate value of the correction amount for the determined inter-pass time. According to such a pass schedule setting method for a rolling mill, an appropriate value of a pass schedule correction amount that satisfies a target thickness, a target flatness, and a target material is calculated online (in an extremely short time) and calculated. Since the pass schedule is corrected based on the appropriate value of the correction amount, there is no need to introduce expensive shape equipment such as a roll bender or a pair cross roll, and the desired sheet thickness, flatness,
A product satisfying the material can be obtained.

In the method for setting a pass schedule of the rolling mill,
The correction amount for the rolling reduction is, for example, the following equation (A
To use Lagrange's undetermined multiplier method for 1)
The appropriate value of the correction amount of the inter-pass time is determined by the following equation
It is determined using (A2). φ = μΣδr_n+ (F_tk・ Δt_k+ ΣF_rn・ Δr_n+ F
₀)^Two (A1) │G_tk・ Δt_k+ Σ_1mG_rn・ Δr_n+ G₀│
 <ΔCr ^Limit _rm・ Δr_m+ ΔCr^Limit
₀ (A2) where Σ represents the first pass to the last pass N
The sum at_1mIs the first to m-th passes (1 <m <N)
Is the Lagrange multiplier, δr_nIs npa
Correction amount for the rolling reduction of the grid (1 ≦ n ≦ N), δt_kIs
the amount of correction for the time between passes at the k-th pass (m <k <N),
ΔCr^{Li mit} _rmIs the m-th pass determined by the shape dead zone
Limit value for F_tk, F_rn, G_tk, G_rn, F₀, G₀,
ΔCr^Limit ₀Is a predetermined coefficient or constant.
Further, in the method for setting the pass schedule of the rolling mill,
The correction of the pass schedule is performed, for example, by the calculation described above.
Error of the predicted material of the rolled material with respect to the target material
If it is the first time that it is not within the allowable range,
The appropriate value of the correction amount for the rolling reduction and the time between passes
This is performed based on the appropriate value of the correction amount, and the calculated pressure
The tolerance of the predicted material of the rolled material to the target material is within the allowable range.
If it is not the first time that the
The correction is performed based on an appropriate value of the correction amount for the inter-scan time.

Another invention for attaining the above object is to provide a target material having a target thickness, a target flatness, and a reduction ratio, an inter-pass time, and a material temperature so that a target material can be obtained. Schedule setting means for setting a pass schedule that defines the actual rolling reduction, the actual inter-pass time, and the actual material temperature of each path while obtaining the actual rolling reduction, the actual inter-pass time, the actual material temperature, and A predicted material calculating means for calculating a predicted material of the material to be rolled based on the pass schedule set by the path schedule setting means; and a predicted material of the material to be rolled calculated for each pass by the predicted material calculating means. A material discriminating means for discriminating whether or not an error with respect to the target material is within an allowable range, and the target material of a predicted material of the material to be rolled by the material discriminating means. If the error for the rolling reduction is determined to be not within the allowable range, the correction amount for the rolling reduction and the distance between the passes under the equation constraint that the sum of the correction amounts for the rolling reduction in the pass schedule becomes zero. An appropriate value of the correction amount for the rolling reduction that minimizes the error from the target material linearized with respect to the correction amount for time is determined, and the correction amount for the rolling reduction of the pass schedule and the correction amount for the inter-pass time are determined. Using an appropriate value of the correction amount for the determined rolling reduction, so as to satisfy the inequality constraint condition that the crown change rate linearized with respect to and falls within the limit value determined by the shape dead zone,
Correction amount appropriate value determining means for determining an appropriate value of the inter-pass time correction amount, and correcting the path schedule based on at least the correction amount appropriate value for the inter-pass time determined by the correction amount appropriate value determining means. This is configured as a pass schedule setting device for a rolling mill, which comprises pass schedule correcting means for performing the above. The pass schedule setting device for the rolling mill is a device suitable for implementing the pass schedule setting method for the rolling mill. If the pass schedule setting device of the rolling mill is used, the target thickness, the target flatness,
An appropriate value of the correction amount of the pass schedule that satisfies the target material is calculated online (in an extremely short time), and the pass schedule is corrected based on the calculated appropriate value of the correction amount. It is not necessary to introduce expensive shape equipment such as pair cross rolls.
A product satisfying the flatness and the material can be obtained.

[0007]

Embodiments of the present invention will be described below with reference to the accompanying drawings to provide an understanding of the present invention.
The following embodiment is a specific example of the present invention and does not limit the technical scope of the present invention. Here, FIG. 1 is a flowchart for explaining a pass schedule setting method for a rolling mill according to the present embodiment,
FIG. 2 is a functional block diagram showing a schematic configuration of a pass schedule setting device for a rolling mill according to the embodiment of the present invention.
As shown in FIG. 1, a pass schedule setting method for a rolling mill according to the present embodiment includes, for example, a target plate thickness (corresponding to a target thickness) and a target flatness for a thick plate (corresponding to a material to be rolled) which is rolled in a plurality of passes. , Rolling reduction to obtain the target material,
Rolling is started by setting a pass schedule that defines the inter-pass time and the material temperature (S2), and while acquiring the actual rolling reduction, the actual inter-pass time, and the actual material temperature of each pass (S3), the acquired actual rolling reduction is obtained. The predicted material of the thick plate is calculated based on the ratio, the actual inter-pass time, the actual material temperature, and the pass schedule (S4), and the error of the calculated predicted material of the thick plate with respect to the target material for each pass is calculated. Is determined to be within the allowable range (S5). If it is determined that the error of the calculated predicted material of the thick plate with respect to the target material is within the allowable range, the pass schedule is corrected. The rolling is continued without performing (S6), and when it is determined that the error of the calculated predicted material of the thick plate with respect to the target material is not within the allowable range, the correction of the rolling reduction of the pass schedule is performed. Under the equality constraint condition that the sum of the values becomes zero, the correction amount for the reduction ratio and the correction amount for the inter-pass time, which are linearized with respect to the correction amount for the reduction ratio, are minimized. An inequality constraint that determines an appropriate value of the amount, and that the crown change rate linearized for the correction amount for the rolling reduction and the correction amount for the inter-pass time of the pass schedule falls within the limit value defined by the shape dead zone. So that
An appropriate value of the correction amount of the inter-pass time is determined using the determined appropriate value of the correction amount for the rolling reduction (S7), and based on at least the appropriate value of the correction amount for the determined inter-pass time. After the pass schedule is corrected (S8), the rolling is continued.

Further, as shown in FIG. 2, the pass schedule setting apparatus for a rolling mill according to the present embodiment obtains a target thickness, a target flatness, and a target material for a thick plate rolled by a rolling mill 1 in a plurality of passes. Reduction rate, time between passes,
It includes a pass schedule calculating means 21 for calculating a pass schedule defining a material temperature, a pass schedule setting means 2 for setting a pass schedule to the rolling mill 1, and an actual rolling reduction, an actual inter-pass time, and an actual material temperature of each pass. The actual value acquiring means 3 for acquiring the actual rolling reduction, the actual inter-pass time, the actual material temperature acquired by the actual value acquiring means 3, and the path schedule set by the path schedule setting means 2. A predicted material calculating means for calculating a predicted material of the material to be rolled, and an error between the target material and the predicted material of the material to be rolled calculated by the predicted material calculating means for each pass is within an allowable range. The material discriminating means 5 for discriminating whether or not the predicted material of the material to be rolled has an allowable error with respect to the target material by the material discriminating means 5. When it is determined that they are not within the range, the correction amount for the rolling reduction and the correction amount for the inter-pass time are set under the equation constraint that the sum of the correction amounts for the rolling reduction in the pass schedule becomes 0. An appropriate value of the correction amount for the rolling reduction at which the error from the target material linearized with respect to the minimum is determined, and the correction amount for the rolling reduction of the pass schedule and the correction amount for the inter-pass time are linearized. In order to satisfy the inequality constraint that the crown change rate falls within the limit value defined by the shape dead zone, the appropriate amount of correction for the rolling reduction is used to adjust the amount of correction for the inter-pass time. A correction amount appropriate value determining means for determining a value, and at least a correction amount appropriate value for the inter-pass time determined by the correction amount appropriate value determining means. It is intended to and a pass schedule correction means 7 for correcting the serial path schedule. The pass schedule setting device of the rolling mill is implemented by a computer by executing a program corresponding to the procedure of the pass schedule setting method of the rolling mill, for example, and is implemented by a computer.
1, pass schedule setting means 2, predicted material calculating means 4, material discriminating means 5, correction amount appropriate value determining means 6, and pass schedule correcting means 7, and the actual value embodied by measuring equipment such as a temperature measuring instrument. This is a combination with the acquisition means 4.

Hereinafter, a method and an apparatus for setting a pass schedule of a rolling mill according to the present embodiment will be described in detail.
In the pass schedule setting method for a rolling mill according to the present invention,
First, a pass schedule is calculated before rolling is started (S1), and the pass schedule is set for the rolling mill 1. In calculating the pass schedule, the entrance temperature T ₀ of the rolling mill (finish rolling mill) 1 is measured in advance. This entry side temperature T ₀ is the average temperature (material temperature) within the plate thickness.
Thus, even if the surface temperature of the material to be rolled is actually measured, it can be predicted from the surface temperature even if the temperature is not directly measured by the temperature measuring device. Next, the rolling time interval (inter-pass time) of each pass is set. What is set is a predetermined fixed value for the inter-pass time.
Next, the rolling reduction of each pass is calculated. The calculation of the rolling reduction of each pass is described in JP-A-7-178424 or JP-A-9-1984.
-57316 and JP-A-11-169929. According to the techniques described in these publications, based on the outlet plate crown and outlet plate thickness of a certain pass, the outlet plate crown of the previous pass (the inlet plate crown of the certain pass) and the outlet plate thickness (the certain pass) The process of inversely calculating with the crown model is repeated starting from the final pass with the target plate crown and target plate thickness as the initial values, and in the direction of the start pass. If it does not fall within the limits defined by the above, or if the predicted rolling load or torque does not satisfy those constraints, the inlet-side sheet crown and the inlet-side sheet thickness are readjusted to satisfy each of the constraints, and the thickness is adjusted. When the transfer thickness when the plate is transferred to the finishing mill is satisfied by the above-mentioned inlet plate thickness and various restrictions are satisfied in all the passes, the rolling reduction is determined for each pass. Once the inter-pass time and the rolling reduction of each pass are determined, the material temperature T _Cn of each pass from the first pass to the final pass N (n = 1, 2,...) Based on the entrance temperature T ₀ of the finishing mill. , N) can be predicted according to the following equation (1). _{T Cn = T 0 -ΣΔT RCn -ΣdT} n · t n -ΣΔT nd (1) where, [Delta] T _RCn is the temperature drop during the roll bite of the n th pass, reduction ratio r _n, the function of the rolling speed v _n Is given as, for example, the following equation (2). _{ΔT RCn = a · r n /} v n + b (2) Further, dT _n is the temperature drop per unit time by the cooling of n th pass, t _n is the path between the time n pass, [Delta] T _nd is predetermined This is the amount of temperature decrease due to de-scaling (water cooling).

[0010] The material temperature T _Cn of each pass is used for predicting the deformation resistance and consequently the rolling load in the process of determining the rolling reduction of each pass. The predicted rolling load is compared with the rolling load constraint and used to calculate the roll elastic deflection. The change in crown ratio is determined from the amount of roll elastic deflection. In the process of determining the rolling reduction of each pass, these rolling loads and crown ratio changes are required. To determine the material temperature of each pass, the rolling reduction of each pass is required. Assuming that the draft of each pass is determined, the material temperature of each pass is determined according to the above equation. If various constraints are not satisfied in all the passes, the process of determining the draft of each pass is repeated. When the various constraints are satisfied by the path may acquire a rolling reduction r _n and the material temperature T _n of each path. Further, if the material temperature T _Cn of each pass is appropriately regulated in the process of obtaining the rolling reduction of each pass, the material of the product after the completion of rolling can be controlled. In this way, a pass schedule in which the draft, the inter-pass time, and the material temperature are determined so as to obtain the target plate thickness, the target flatness (corresponding to the target plate crown), and the target material can be calculated. Incidentally, the measured inlet side temperature T _0, on the basis of the inter-set path time t _n, the read reduction rate r _n of each path, a program for calculating the pass schedule defining the material temperature T _n from the recording device such as a hard disk An arithmetic processing unit of a computer that executes the program is a specific example of the path schedule calculation unit 21 in the present embodiment. Further, in addition to the program corresponding to the path schedule calculating means 21, the path schedule calculated by the path schedule calculating means 21 is stored in the storage device 22 of the computer, and the storage device 22 stores the path schedule in the input / output device 23 of the computer. A specific example of the pass schedule setting means 2 in the present invention is a computer processing device that supplies a pass schedule and executes a program for performing a process of setting the pass schedule for the rolling mill 1. When the pass schedule is set in the rolling mill 1 (controller thereof) by the pass schedule setting means 2, rolling is started (S2).

When rolling is started, the actual reduction of each pass
Rate, actual time between passes, and actual material temperature
(S3), acquired actual rolling reduction, actual inter-pass time, actual
Based on the material temperature and the pass schedule,
The predicted material is calculated (S4). Actual reduction rate of each pass
And actual value acquisition to acquire the actual inter-pass time and actual material temperature.
A specific example of the obtaining means 3 is a thick plate provided on the entry side of the rolling mill 1.
Load on a temperature measuring device that measures the surface temperature of the
Measurement device that measures the time when
You. Focus on reduction, time between passes, and material temperature
By these, for example, the tensile strength TS (Tensile
 Evaluation of materials such as Strength) and YP (Yield Point)
This is because an index can be represented. Evaluation finger of the material
The mark (hereinafter simply referred to as material) X is the rolling reduction of the n-th pass,
The time between passes and the material temperature are r_n, T_n, T_nso
When expressed, generally given by the following equation (3)
it can. X = F (r₁, T₁, T₁, ..., r_n, T_n, T_n,…, R_N, T_N, T_N(3) The actual draft, the actual time between passes, and the actual material temperature are acquired.
From the first pass to the corresponding pass (mth pass)
Therefore, the material is calculated according to the above equation (3).
In order to calculate the
The draft, time between passes, and material temperature are required. m pass
Material temperature of each subsequent pass (pass (m + 1) to final pass N)
Degree T_CnIs the actual material temperature T acquired at the m-th pass_mFor
And calculated according to the following equation (4) similar to the above equation (1)
be able to. T_Cn= T_m−Σ_mNΔT_RCn −Σ_mNδT_n・ (T_n+ Δt_n) -Σ_mNΔT_nd (4) where_mNFrom the (m + 1) th pass to the final pass N
Represents the sum. Also, δt _nIs the n-th pass already defined
((M + 1) <n <N)
But the correction amount for the inter-pass time has been determined by then.
If not, it becomes 0. At this time, one pass at the start of rolling
Actual rolling reduction r for each pass from the first pass to the m-th pass^ob _n,Performance
Time between passes t^ob _n, Actual material temperature T^ob _nConsidering thick plate
Material X_mCan be expressed as in the following equation (5). X_m= X₀+ Σ_1mK_n・ R^ob _n+ Σ_mNK_n・ R '_n + Σ_1mJ_n・ T^ob _n+ Σ_mNJ_n・ T '_n + Σ_1mL_n・ T^ob _n+ Σ_mNL_n・ T_Cn (5) where K_n, J_n, L_nIs a predetermined constant.
r ’_n= R_n+ Δr_n, T '_n= T_n+ Δt_nIt is.
Also, δr_nIs the reduction rate of the n-th pass already determined
Represents the amount of correction to the reduction ratio by the m-th pass.
If the correction amount is not determined, it becomes 0 and the pass schedule
Reduction r in the n-th pass determined by the rule calculation_nAnd supplement
Post-rolling reduction ratio r '_nAre equal. Note that the actual value
The actual value supplied from the obtaining means 3 and the pass schedule
Path read from the storage device 22 of the file setting means 2
Reduction rate, time between passes, material temperature and
Based on the above formula, a calculation that predicts the material according to the above equation
The computing device of the computer that executed the program
4 is a specific example of the predicted material calculation means 4 in the present embodiment.

The predicted material X_mIs calculated,
Material X_mError ΔX for the target material is within the allowable range
It is determined whether or not there is (S5). Target material, allowable range
Is given in advance by the product specification,
The material discriminating means 5 embodied by the arithmetic unit of
Predicted material X_mThe difference between the target material and the target material (error ΔX).
And calculate the difference between the difference and the predetermined tolerance.
If the difference is smaller than the allowable range,
The value of the stored variable is set to a value indicating that the error ΔX is within the allowable range.
If the difference is larger than the allowable range,
Is a value indicating that the error ΔX is not within the allowable range.
Perform the process of setting the value of the storage variable. The material discriminating means 5
It is determined that the error ΔX is within the allowable range.
The input / output device of the path schedule 2
The value of the storage variable is supplied to the storage 23, and based on it,
The input / output device 23 is stored in the storage device 22.
Keep the pass schedule settings. Sand
That is, rolling was continued without changing the pass schedule.
(S6). On the other hand, the material discrimination means 5 causes the error.
If it is determined that the difference ΔX is not within the allowable range,
To satisfy the target material, pass schedule
Correction is performed. Reduction rate r of n-th pass_n, Time between passes t
_n, Material temperature T_nΔr _n, Δt_n, Δ
T_nThe error ΔX is expressed by the following equation (6).
Can be expressed as ΔX = F (δr₁, Δt₁, ΔT₁, ..., δr_n, Δt_n, ΔT_n(6) The above equation (6) is Taylor-expanded, and the second-order and higher partial differential terms are
If ignored (linearized), the error ΔX is given by the following equation (7)
It is represented as follows. ΔX = ΣF_r・ Δr_n+ ΣF_t・ Δt_n+ ΣF_T・ ΔT_n+ F₀ (7) where F_rn= (∂F / ∂r_n), F_tn= (∂F / ∂t
_n), F_T= (∂F / ∂T_n), F₀Is determined by the actual value
This is a constant term. And the material temperature T_nAbout real
Only the correction based on the performance value is performed, and the time between passes
t_nIs assumed to be the k-th pass only.
Then, from the above equation (7), the error ΔX is given by the following equation (8).
Become. ΔX = F_tk・ Δt_k+ ΣF_rn・ Δr_n+ F₀ (8) A correction amount δt that minimizes the error X_k, Δr_nTo
If required, set a pass schedule that satisfies the target material
It is possible to do. However, the error X is minimized.
Some products do not satisfy the target plate thickness and target flatness
There is. Simultaneously set the target thickness, target flatness and target material
In order to obtain a satisfactory correction amount, regarding the correction amount,
One evaluation function and one inequality constraint are used. The comment
The valence function φ is related to the target thickness and the target material.
Σδr_nLagrangian with equality constraint
Using the undetermined multiplier method (optimization method with equality constraint),
Provided based on (9). φ = μΣδr_n+ (F_tk・ Δt_k+ ΣF_rn・ Δr_n+ F₀)^Two (9) Here, μ is a Lagrange multiplier. 2nd right side of the above formula
The term function is the function to be optimized,
This means that the difference ΔX is minimized, and the first term on the right side of the above equation
The function is that the sum of the reduction amounts is zero, ie
That is, it means that the target thickness is satisfied. In the above equation,
The correction amount δr_nSatisfies the following equation (10) when
You. (∂φ / ∂δr_n) = 0, (∂φ / ∂μ) = 0 (10) By using these equations (9) and (10), the correction amount
μ, δr_nWe can obtain a system of linear equations for
The correction amount δr_nCan get a good candidate immediately
You.

[0013] The following is required from the candidate of the optimum value of the correction amount [delta] r _n obtaining in this way, thereby satisfying the target flatness, that is, within limits defined by the shape deadband crown ratio change That is, what is contained is extracted as an appropriate value. The change in crown ratio can be obtained from the rolling load _Pn . rolling load n pass, the rolling reduction r _n, the pass time t _n, the following equation using a material temperature T _n (1
1). P _n = P (r ₁ , t ₁ , T ₁ ,..., R _n , t _n , T _n ) (11) From the rolling load P _n , first, the roll profile Cr _Rn ,
According to the following equation (12) using the genetic coefficient ξ and the transcription rate ，,
The crown ratio Cr _n is determined. Cr _n = ξ · Cr _n-1 + ζ · (Cr _Rn + α · P _Cn ) (12) The change in crown rate ΔCr _n is determined from the crown rate Cr _{n as in the} following equation (13). ΔCr _n = Cr _n −Cr _n−1 = (ξ−1) · Cr _n−1 + ζ · (ΔCr _Rn + α · P _Cn ) (13) That is, the crown rate change ΔCr _n is also _equal to the rolling load P _n . Similarly, using the rolling reduction r _n , the inter-pass time t _n , and the material temperature T _n , the following expression (14) can be used. ΔCr _n = G (r ₁ , t ₁ , T ₁ ,..., R _n , t _n , T _n ) (14) For the crown ratio Cr _n expressed as the above equation (14), the correction amount δr _{When n} , δt _n , and δT _n are added, a change ΔCr _n of the crown ratio Cr _n accompanying the addition is represented by the following equation (15). _{ΔCr n = G (δr 1,} δt 1, δT 1, ..., δr n, δt n, δT n) (15) above equation (15) by Taylor expansion, and ignoring secondary or more partial differential term ( When linearized), change in crown ratio ΔCr
_n is represented by the following equation (16). _{ΔCr n = ΣG rn · δr n} + ΣG tn · δt n + ΣG Tn · δT n + G 0 (16) _{where, G rn = (∂G / ∂r} n), G tn = (∂G / ∂t
_n ), G _Tn = (∂G / ∂T _n ), G ₀ is a constant determined by the actual value. It is assumed that only the correction based on the actual value is performed for the material temperature T _n , and the inter-pass time t
Assuming that the path to be corrected for _n is only the k-th path, the crown ratio change ΔCr _n from the above equation (16) is as follows. _{ΔCr n = G tk · δt k} + ΣG rn · δr n + G 0 (17) In this way the crown index change [Delta] CR _n given by the,
It is necessary to fall within a shape dead zone given as a change in crown ratio using a shape change coefficient depending on the plate thickness h. That is, the limitation of the change of the crown ratio due to the shape dead zone is ΔCr
Expressed by ^Limit , the crown rate change ΔCr _n needs to satisfy the inequality represented by the following equation (18). ^{_{│ΔCr n │ <ΔCr Limit (18}} ) , where the limits [Delta] CR ^Limit is the plate thickness h, i.e. is a function of the reduction ratio r _n, can be given by the following equation (19). ΔCr ^Limit = ΔCr ^Limit (r _n ) (19) If the above equation is Taylor-expanded and the second-order or higher partial differential terms are ignored (linearized), the limit ΔCr ^Limit is given by the following equation (20). expressed. _{^{ΔCr Limit = ΔCr Limit rn · δr}} n + ΔCr Limit 0 (20) ^{_{here, ΔCr Limit rn = (∂ΔCr Limit}} (r n) /
∂r _n), ΔCr ^{Limi t} ₀ is a constant term. Assuming that the path determined to need correction is the m-th path (m <N), the above inequality (18) can be rewritten as the following equation (21). _{│G tk · δt k + Σ 1m} G rn · δr n + G 0 │ <ΔCr Limit rm · δr m + ΔCr Limit 0 (21) where, sigma _{1 m} represents the sum from the first pass to m pass.

The correction amount δr_nUsing the candidates for the appropriate value of
An appropriate value δr of the correction amount satisfying the inequality_m, Δt_kTo
You only need to extract it. Simultaneously perform the evaluation function and the inequality constraint
The correction amount Δt that satisfies_k, ∂r_mSearch for an appropriate value for
First, the correction amount δt_kAssuming an initial value for
The correction amount δr at which the differentiation of the evaluation function becomes zero_mSeeking
Then, due to the inequality constraint, the correction amount δt_kUp and down
Limit. The upper and lower limits are calculated by the bisection method.
Correction amount δt_kAnd the evaluation function and the inequality system
The correction amount δt that satisfies approximately_k, Δr_mExtract
You. Note that F included in the evaluation function and the inequality constraint
_tk, F_rn, G_tk, G_rmCoefficients such as
Is referred to as the influence coefficient, since it represents the magnitude of the effect of each term
It can be easily obtained numerically. For pass schedule
The calculated unit variable for a variable z is Δ
z, the function value determined by the variable z is Z, the variable z
When the function value when the value fluctuates slightly is represented by Z ′,
The influence coefficient (∂Z / ∂z) is expressed as the following equation (22).
It is. (∂Z / ∂z) = (Z′−Z) / Δz (22) Note that such an appropriate value δt of the correction amount_k, Δr_mTo
A computer that executes a program that performs the required arithmetic processing
The arithmetic unit of the data is a correction amount appropriate value determining means 6 according to the present invention.
Is a specific example. The correction amount δt as described above_k, Δr
_nThe pass schedule corrected by
It satisfies the target flatness and target shape.
Quantity δt_k, Δr_mIn the calculation of suitable candidates for, the linear system
It is only necessary to solve the equation, and there is no need for repeated operations.
Can reduce the load on the device and reduce the time required for computation.
Yes, especially when doing calculations online.
Then, the correction amount is determined by the appropriate correction amount determining means 6.
Suitable value δt of the correction amount _k, Δr_mBased on the
Joule is corrected (S8). Computer computing equipment
Path schedule correcting means embodied by
7 is the input / output device of the path schedule setting means 2.
The correction value is supplied from the correction amount appropriate value determination means 6 by controlling the
The appropriate value δt of the correction amount_k, Δr_mBy said memory
The path schedule stored in the device 22 is corrected.
You. Is such a pass schedule correction made?
Then, the rolling is continued (S6), and the actual values as described above are collected.
The process from acquisition to correction of the pass schedule is repeated for each pass.
Will be returned. However, the error ΔX is not within the allowable range.
If it is determined multiple times, the second and subsequent times
Is the target plate thickness and target flatness only by the higher-order correction of temperature.
And pass schedule to satisfy the target shape.
I can correct it. That is, the error ΔX is not within the allowable range.
If it is determined multiple times, the second and subsequent times
Means that the reduction rate is not corrected and the correction amount δt_kOnly by
To correct the pass schedule. To do this
For this purpose, the material discriminating means 5 determines that the error ΔX is within an allowable range.
Count the number of times it is determined that the
When the numerical value becomes 2 or more, the correction amount appropriate value
Step 6 determines the correction amount δt._kOnly by changing
In order to satisfy the function and the inequality constraint, the correction amount δt
_kMay be determined.

FIGS. 3 to 3 show examples of the rolling results when rolling is performed using the conventional temperature control and when rolling is performed according to the pass schedule set by the pass schedule setting method of the rolling mill according to the present invention. 6 is shown. here,
FIG. 3 is a diagram showing the relationship between the rolling time and the rolling load, FIG. 4 is a diagram showing the relationship between the rolling time and the thickness of the exit side of each pass, FIG. 5 is a diagram showing the tensile strength as an example of the material, and FIG. It is a figure showing the relation between rolling time and crown rate change. Each figure (a) shows the result of the conventional rolling, and each figure (b) shows the result of the rolling according to the pass schedule setting according to the present invention. In each figure, the solid line shows the setting of the pass schedule calculated before the start of rolling, and the dotted line shows the actual rolling result. As shown in FIGS. 3 and 4, in the pass schedule setting method of the rolling mill according to the present invention, the inter-pass time and rolling reduction during rolling are corrected, but in the final pass, the target sheet thickness is determined according to the pass schedule. Are satisfied. The vertical axis in each drawing of FIG. 5 indicates the magnitude of the tensile strength of the thick plate, and two straight lines are drawn at right angles corresponding to the strength limit value (corresponding to the allowable range). In the pass schedule setting method for the rolling mill according to the present invention, the actual tensile strength falls within the above-mentioned strength limit, although there is a difference from the tensile strength set at the time of the pass schedule calculation. Further, as shown in FIG. 6, in the method for setting a pass schedule of a rolling mill according to the present invention, the crown ratio change is limited to a limit value (limit value) ΔCr.
^It is within the range of ^Limit , and shape defects are suppressed. As described above, according to the method and apparatus for setting the pass schedule of the rolling mill according to the present embodiment, the appropriate values of the pass schedule correction amount satisfying the target thickness, the target flatness, and the target material can be set online (very short). Calculated in time)
Since the pass schedule is corrected based on the appropriate value of the calculated correction amount, the desired sheet thickness, flatness, and material can be satisfied without the need to introduce expensive shape equipment such as a roll bender or a pair cross roll. Products can be obtained.
In the present embodiment, the pass schedule setting device of the rolling mill is embodied by combining a computer that executes a program corresponding to the procedure of the pass schedule setting method of the rolling mill with a measuring device. The present invention is not limited to this, and may be configured using dedicated hardware corresponding to the procedure of the pass schedule setting method of the rolling mill.

[0016]

As described above, in the method and the apparatus for setting the pass schedule of the rolling mill according to the present invention, the appropriate values of the pass schedule correction values satisfying the target thickness, the target flatness, and the target material are set online ( Calculated in a very short time)
Since the pass schedule is corrected based on the appropriate value of the calculated correction amount, the desired sheet thickness, flatness, and material can be satisfied without the need to introduce expensive shape equipment such as a roll bender or a pair cross roll. Products can be obtained.

[Brief description of the drawings]

FIG. 1 is a flowchart illustrating a pass schedule setting method for a rolling mill according to an embodiment of the present invention.

FIG. 2 is a functional block diagram showing a schematic configuration of a pass schedule setting device for a rolling mill according to the embodiment of the present invention.

FIG. 3 is a diagram showing an example of a relationship between a rolling time and a rolling load.

FIG. 4 is a diagram illustrating an example of a relationship between a rolling time and a thickness of an exit side of each pass.

FIG. 5 is a diagram showing an example of a tensile strength which is an example of a material of a thick plate.

FIG. 6 is a diagram showing an example of a relationship between a rolling time and a change in crown ratio.

[Explanation of symbols]

 2 ... Pass schedule setting means 3 ... Actual value acquisition means 4 ... Predicted material calculation means 5 ... Material determination means 6 ... Correction amount appropriate value determination means 7 ... Pass schedule correction means

Claims (4)

[Claims] 1. A reduction ratio, a target reduction ratio, and a target material of a rolled material to be rolled in a plurality of passes.
Rolling is started by setting a pass schedule that defines the inter-pass time and material temperature, and while acquiring the actual draft, actual pass time, and actual material temperature of each pass, the acquired actual draft, actual inter-pass time The predicted material of the material to be rolled is calculated based on the actual material temperature and the pass schedule, and whether an error of the calculated predicted material of the material to be rolled with respect to the target material is within an allowable range for each pass. If it is determined that the error of the calculated predicted material of the material to be rolled with respect to the target material is not within the allowable range,
Under the equation constraint that the sum of the correction amounts for the rolling reduction of the pass schedule becomes 0, the correction amount for the rolling reduction and the correction amount for the inter-pass time are linearized from the target material. An appropriate value of the correction amount for the rolling reduction that minimizes an error is determined, and a crown change rate linearized for the correction amount for the rolling reduction and the correction amount for the inter-pass time in the pass schedule is determined by a shape dead zone. In order to satisfy the inequality constraint condition of being within the limit value, a proper value of the correction amount for the inter-pass time is determined using a proper value of the correction amount for the determined rolling reduction. A pass schedule setting method for a rolling mill, wherein the pass schedule is corrected based on an appropriate value of a correction amount for a time between passes. 2. An appropriate value of a correction amount with respect to the rolling reduction is represented by Σ
δr_nAbout the following equation (A1) where = 0 is the equation constraint
Determined by using Lagrange's undetermined multiplier method,
The appropriate value of the correction amount of the inter-pass time is calculated using the following equation (A2).
The pass schedule of the rolling mill according to claim 1, which is determined.
Setting method. φ = μΣδr_n+ (F_tk・ Δt_k+ ΣF_rn・ Δr_n+ F
₀)^Two (A1) │G_tk・ Δt_k+ Σ_1mG_rn・ Δr_n+ G₀│
 <ΔCr ^Limit _rm・ Δr_m+ ΔCr^Limit
₀ (A2) where Σ represents the first pass to the last pass N
The sum at_1mIs the first to m-th passes (1 <m <N)
Is the Lagrange multiplier, δr_nIs npa
Correction amount for the rolling reduction of the grid (1 ≦ n ≦ N), δt_kIs
the amount of correction for the time between passes at the k-th pass (m <k <N),
ΔCr^{Li mit} _rmIs the m-th pass determined by the shape dead zone
Limit value for F_tk, F_rn, G_tk, G_rn, F₀, G₀,
ΔCr^Limit ₀Is a predetermined coefficient or constant. 3. When it is the first time that it is determined that the error of the calculated predicted material of the material to be rolled with respect to the target material is not within an allowable range, an appropriate value of the correction amount for the rolling reduction and the time between passes are determined. The pass schedule is corrected based on the appropriate value of the correction amount with respect to, and if it is not the first time that it is determined that the error of the calculated predicted material of the material to be rolled with respect to the target material is not within the allowable range, The pass schedule setting method for a rolling mill according to claim 1, wherein the pass schedule is corrected based on an appropriate value of a correction amount for an inter-pass time. 4. A reduction ratio, such that a target thickness, a target flatness, and a target material are obtained for a material to be rolled in a plurality of passes.
Path schedule setting means for setting a pass schedule that defines the inter-pass time and material temperature, and the obtained actual reduction rate and actual inter-pass time while acquiring the actual draft, actual pass time, and actual material temperature of each pass , Actual material temperature, and a predicted material calculation means for calculating a predicted material of the material to be rolled based on the pass schedule set by the pass schedule setting means, and a predicted material calculation means for each pass. A material discriminating means for discriminating whether or not an error of the predicted material of the material to be rolled with respect to the target material is within an allowable range, and an error of the predicted material of the material to be rolled with respect to the target material is allowed by the material discriminating means. If it is determined that they are not within the range, the total amount of correction for the rolling reduction of the pass schedule becomes zero under the equality constraint that An appropriate value of the correction amount for the reduction ratio that minimizes the error from the target material, which is linearized with respect to the correction amount for the reduction ratio and the correction amount for the inter-pass time, is determined, and the pass schedule is corrected for the reduction ratio. In order to satisfy the inequality constraint that the crown change rate linearized with respect to the amount and the correction amount for the inter-pass time falls within the limit value defined by the shape dead zone, the appropriate amount of the correction amount for the determined rolling reduction is determined. A correction amount appropriate value determining means for determining an appropriate value of the inter-pass time correction amount using a value, and at least a correction amount appropriate value for the inter-pass time determined by the correction amount appropriate value determining means. A pass schedule setting device for a rolling mill, comprising: a pass schedule correcting means for correcting the pass schedule.