WO1994011129A1

WO1994011129A1 - Reverse rolling control system of pair cross rolling mill

Info

Publication number: WO1994011129A1
Application number: PCT/JP1993/001644
Authority: WO
Inventors: Yuji Hori; Tetsuya Ogawa
Original assignee: Nippon Steel Corporation
Priority date: 1992-11-10
Filing date: 1993-11-10
Publication date: 1994-05-26
Also published as: KR940703722A; KR0148612B1; SE505470C2; SE9402305L; GB9412120D0; GB2278464A; GB2278464B; SE9402305D0

Abstract

In a pair cross rolling mill, a true rolling load free from influences of a thrust load occurring during rolling and an actual difference in load between roll ends are calculated, and sheet thickness control and wedge control are carried out through learning on the basis of detection values and calculated values. To accomplish a predetermined sheet crown, an actual sheet crown is estimated and calculated on a real time basis and is used for feedback control so that an actual roll bending quantity of a previous pass is reflected on a cross angle set value of next and subsequent passes at the time of completion of a given pass, and the cross angle set value is updated through learning. Further, the range of a mechanical crown for satisfying the roll shape in each pass and setup capacity is calculated, and a pass schedule is decided so as to attain the smallest number of passes.

Description

'' Description Reverse rolling control method for pair-cross rolling mill

The present invention relates to a reverse rolling control method for a pair cross rolling mill having a function of crossing upper and lower rolls in pairs, and more particularly to a method for controlling the thickness, shape and pass schedule of a steel sheet. Conventional technology

Conventionally, in a pair cross rolling mill that reversely rolls a pair of rolls each having a backup port and a work port in a plane parallel to a rolled material, the rolling occurs during rolling. In order to cause imbalance in the load applied to the left and right rolling load detection load cells due to the effect of the thrust force, a method of controlling the thickness independently from left to right using a thrust load meter to eliminate the effect (particularly No. 63-23851) has been proposed. In addition, there is a method of reducing the effect of mill hysteresis and controlling the plate thickness by installing load cells above and below (Japanese Patent Publication No. 63-112128). In addition, a method has been proposed in which the unbalance of the load is canceled by the upper, lower, left and right load cells to calculate and control the true rolling load (left-right difference, left-right sum). In addition, the thrust load generated in the roll axis direction is detected by a single load cell, and rolling is performed while using it to check the withstand load on equipment.

In the conventional technology of canceling the load imbalance by the above-mentioned upper, lower, left, and right load cells, the power can be controlled on the assumption that the upper and lower mill stiffness is equal. Due to the detected load deviation due to the condition of the contact surface of the rack, the condition of the bearing maintenance, etc. There is a problem that the unbalance of the detected load cannot be separated strictly from an eccentric load due to thrust or an eccentric load due to the deformation behavior of the material to be rolled.

Also, when there is a difference between the upper and lower mill springs, the actual difference in the left and right mill elongation changes because the load imbalance effect by the thrust toe-mount is not uniform, and therefore, especially in reverse rolling. However, the tendency was reversed during forward rotation and reverse rotation, which made it difficult to control the edge of the material to be rolled.

On the other hand, in order to realize automatic crown shape control in a pair cloth rolling mill, the cross angle schedule was preset and controlled for each slab.

In this conventional technology, the preset control is performed before rolling one slab.If recalculation is not performed along with the progress of the pass while actually rolling the sheet material, even if the deviation from the predicted value occurs due to the rolling disturbance, etc. There is a problem that cannot be corrected.

As a method for determining a pass schedule in a conventional rolling mill, a change in a sheet crown for each pass is controlled for the purpose of flattening a rolling shape disclosed in Japanese Patent Application Laid-Open No. 62-259605. Therefore, there is a method to determine the rolling schedule under the condition that the rolling load is less than the maximum allowable capacity of equipment.

In addition, in order to perform rolling at high efficiency, there is a method of rolling at full load in the upstream pass where the shape influence is small, and determining the pass schedule by suppressing the load only in the downstream pass where the change of the sheet crown is sensitive to the shape. -Disclosed in Bulletin 123.

On the other hand, when the number of passes is fixed based on the number of stands as in continuous hot rolling, the schedule of the roll crossing angle is determined so as to satisfy the shape after the thickness schedule of all passes is determined in advance. The method was changed to the 120th Conference of the Iron and Steel Institute of Japan, CAMP- ISIJ Vol 3 (1990)-pl 383. It has been proposed in.

By the way, in the conventional rolling method, in order to flatten the shape of the rolled material, it is necessary to suppress the change of the sheet crown for each pass within a certain range, so that the rolling load, which is a controlling element of the mechanical crown, is limited. As a result, rolling had to be performed with a load much smaller than the capacity of the equipment, resulting in a problem that the number of passes was large and the rolling efficiency was reduced. Disclosure of the invention

The present invention has been achieved in view of the above problems. That is, the first object of the present invention is to control the thickness and the edge with high precision by automatically separating and canceling the load imbalance described above in the case of automatically controlling the thickness. It is to be.

A second object of the present invention is to accurately control the sheet material while grasping the condition of the above-mentioned material to be rolled in the middle of the pass when automatically controlling the sheet crown and shape, and correcting and calculating each pass. The purpose is to make it possible to control the shape of the object by predicting its shape.

The third objective is to make the most of the original capacity of the rolling equipment throughout all passes, assuming that the cross angle is changed in each pass, and to perform high-efficiency rolling that minimizes the number of passes. The purpose is to achieve a pass schedule that optimizes the rolling shape.

The gist of the present invention is as follows.

(1) In a rolling mill that reversely rolls a pair of rolls each having an upper and lower backup port and a single crawl in a plane parallel to a rolled material, the upper, lower, left and right rolling Using the load cell for load detection and the detection value of the open cell for detecting the thrust load generated in the roll axis direction, the difference between the true rolling actual load excluding the effect of the thrust load and the right and left load is calculated. These detection values and calculation An automatic thickness control method for reverse rolling of a pair-cross rolling mill, wherein the thickness and the edge are automatically controlled based on the values.

(2) Roll sets each having a pair of upper and lower backup rolls and work rolls intersect each other in a plane parallel to the rolled material, and each port control device at both ends of the port is used. In the rolling by the reverse rolling mill,

実績 To achieve the predetermined plate crown for flattening the final shape of the material, the actual plate crown is calculated in real time according to the rolling load fluctuation in the plate, and roll bending control is performed. At the end of the pass, the calculation amount of the sheet crown is corrected from the actual roll bending amount of the previous pass, and reflected on the cross angle set value after the next pass to control the shape of the sheet. Shape control method in reverse rolling of a rolling mill.

(3) A roll set having upper and lower backup rolls and work rolls, each intersecting relatively in a plane parallel to the rolled material, and having a roll bending control device at each end of the roll. —In rolling by a rolling mill,

When the roll bending amount is corrected according to the exit side shape of each pass, the predicted shape value of the pass is corrected based on the actual roll bending amount of the pass, and the plate crown is predicted. In the reverse rolling of a pair cross rolling mill, the value is corrected, the target mechanical crown amount is recalculated after the next pass, and the shape of the plate is controlled by reflecting the value in the cross angle setting value. Shape control method.

(4) The upper roll set and the lower roll set, each paired with the upper and lower backup rolls and work rolls, are used to reverse the sheet material by a reverse rolling mill having a control device that relatively intersects in a plane parallel to the rolled material. In determining the pass schedule for rolling, Calculate the area that satisfies both the mechanical crown allowable range judged from the shape and the mechanical crown allowable range judged from the equipment capacity, and sequentially pile up from the bottom so that the maximum allowable rolling load is obtained. A method for determining a reverse rolling schedule of a pair-aque mill, comprising determining a sheet thickness schedule, and simultaneously determining a rolling and crossing angle schedule of the shortest number of passes satisfying a shape. BRIEF DESCRIPTION OF THE FIGURES

FIG. 1 is a front view showing an outline of a rolling mill to which the present invention is applied.

FIG. 2 is a block diagram showing a rolling control system of the rolling mill shown in FIG.

FIG. 3 is a flowchart showing the contents of the path schedule determination method of the present invention.

FIG. 4 is a graph showing a chamber generated in the conventional thick plate rolling and a chamber generated in the embodiment of the present invention.

FIG. 5 is a block diagram showing components of a rolling mill and a controller according to one embodiment of the present invention.

Fig. 6 is a side view showing the outline of the mechanism of the reverse rolling mill shown in Fig. 5.

FIG. 7 is a flowchart showing the contents of the previous path actual calculation and learning calculation processing of the adaptive control calculation processing section 11B shown in FIG.

FIG. 8 is a flowchart showing the next path setting calculation processing of the adaptive control calculation processing section 11B shown in FIG.

FIG. 9 is a block diagram showing the contents of the dynamic shape control processing of the plant controller 13 shown in FIG.

Fig. 10 shows the dynamics of the plant controller 13 shown in Fig. 5. FIG. 4 is a block diagram showing a configuration of a lock shape control function.

FIG. 11 is a time chart showing the timing of various arithmetic processes included in the shape control of the present invention.

FIG. 12 is a graph showing (a) the actual crown ratio value and (b) the cross angle setting value according to the present invention and the conventional shape control.

FIG. 13 is a graph showing the frequency of occurrence of the crown ratio change amount of the final pass by (a) the present invention and (b) the conventional shape control.

FIG. 14 is a graph showing the number of passes, (a) rolling load, (b) cross angle, and (c) crown ratio of the present invention and the conventional method. BEST MODE FOR CARRYING OUT THE INVENTION

In order to achieve the above object, the first invention of the present invention is based on the detection results of the vertical load detection opening cell and the thrust load detection load cell, and the actual rolling actual load excluding the influence of the thrust load and the left and right The load difference is calculated, and the sheet thickness and the camber are controlled based on the detected value and the calculated value.

Hereinafter, the details of the first invention will be described. First, the contents of the calculation of the true actual load and the difference between the left and right loads will be described. Fig. 1 shows the front view of the pair cross rolling mill and the load acting on the rolling mill and rolls during material rolling. First, in this rolling mill, when rolling the material, the rolling load in the vertical direction from the material: P and

Thrust load in the roll axis direction: F

Occurs.

The loads P and F generated from these materials are detected by the load cells 1 and 6 via a single crawl 5 to a knock-up roll 2 or a work roll 5 to a work roll chick 4, respectively.

Here, during the actual rolling, the material 7 to be rolled moves in the roll axis direction. P is not always distributed equally to the left and right because the center position deviates by a or the material has a left-right plastic resistance deviation. In this case, the basic formulas (1) to (8) are established from the load balance formula and the rotational moment formula centered on the point A between the left and right load cells.

(Rolling load)

Oh Inlay de time on _{_{PT WS + PT DS = P +}} PF T (1)

Lower PB _WS + PB _DS = P-PFT …… (2) When offloading Upper PT _WS + PT _DS = P — PF _T …… (3)

Under _{_{PB WS + PB DS = P +}} PF T ...... (4)

(Thrust load)

Upper F = FT _WR + FT _{B UE} + FTHG ... (5) Lower F = FBWR + FBBUR + FBHG (6)

(Rotation moment agreement)

Upper F [d + (DB 2) + DW] -FTWR C d + (DB / 2) + (DW / 2) 3-FTBUR d-PTDS (L / 2) + PTws (L / 2) — Pa = 0

…… (7) Lower F [e + (DBZ 2) + DW] One FB _WR (e + (DB / 2) + (DW 2)]-FBBUR e-PBDS (L / 2)-PBws (L / 2 ) + P a = 0

…… (8)

The symbols in the equations (1) to (8) are as shown in FIG. The method of detecting the true load P received from the material 7 from the load cell load (detected values of load cells 1 and 6) that can be actually observed using these load imbalance equations is described below.

In the thrust load formulas (5) and (6), the component forces applied to the work roll 5 and the backup roll 2 are represented by the distribution coefficients,; FTw _R = a F (9)

FTBUH = B F (10)

FT _HG = (I-a-β F …… (11) Substituting these equations (9), (10) and (11) into equation (7) and rearranging

F [d + (DB / 2) + DW]-a F C d + (DB / 2) + (DW / 2))

—; SF · d— (LZ 2) (PT _DS -PTws)-P a = 0

PT _DS -PTws = F-(1 / L) (2 d (I-a-β) + DB (1 —)

+ DW (2-a)) + (2 P a / L) (7 ').

Here, assuming that the thrust load is the force FT _HG 0 received by the housing itself, on the other hand, in the case of DB ^ 2 DW,

PT _DS -PTws = F (DW / L) (4-3 a) + (2 Pa / L)

…… (12) For example, when the thrust load on work roll 5 (WR) is observable,

PT _DS -PTWS = FTWR (DW / LK 4-3 α) / α + (2 Pa / L)

…… (13)

Similarly, if you arrange the lower side,

PB _DS + PBws =-F (1 / L) [2 e (1-a-β + DB (1 —)

+ DW (2-a)) + 2 Pa / L …… From (8 ') PB _DS — PB _WS = — F-DW (4-3 a) / L + (2 P a / L)

…… From (14) PB _DS — PB _WS = — FB _WR (DW / L) (4-2> a / a)

+ (2 Pa / L) ·································································· (12) and (14), the first term on the right-hand side (thrust load Impact term) can be offset,

_{(PT D s- PTws) + (} PBDS - PBWS) = a (4 P a / L) ...... (16). From equation (16), the true rolling load difference due to off-center can be calculated.

In addition, the second term on the right side (off-center effect term) can be canceled by the difference between Eqs. (12) and (14).

(PTDS-PTWS)-(PBDS + PBWS) = 2F · [DW (4-3) ZL]

…… (17), and the imbalance force due to the thrust force can be extracted.

For example, if the thrust load F _WR on work roll 5 (WR) can be detected or calculated,

((PT _D s-PTws)-(PB _DS -PBws)) / 2

= F WR · (DW / L) (4-3 a / a) …… (18) and the α value can be estimated '.

Substituting the work port diameter DW = 985 and the distance between the left and right bearings L = 5918, and expressing it as ΔPm on the left,

α = 4 / C (LD Pm) (F WRDW + 3)

4 / ί (6 Δ Pm) / (F WR + 3)) …… (19) For example,

F WR = 200 ^τ Δ P m = 150 ^τ = 0.533

Becomes In addition, from Eqs. (19) and (9), the true thrust load F received from the material is expressed as

F = (3 Δ P m / 2) + (3 F WR / 4) (20) becomes, for example, the F ^ 375ton when the.

The thrust load on backup roll 2 (BUR) is

F BUR = (3 ΔPm / 2) one (IF _WR Z 4) …… (21), and the true rolling load sum excluding the effect of mill hysteresis Can be easily recognized by the synthesis of the equations (1) to (4).

To summarize the above relationship,

True rolling load sum excluding the effect of mill rolling friction (hysteresis)

P = (PTDS + PTWS + PB D S + PBWS) / 2 ...... (22) the true right rolling load difference undergoing slide be sampled load effects from the materials excluded

P REF = (PT _D s-PTws + PB _D s-PBws) / 2 (23) True thrust load received from material 7

F = (3 Δ Ρ Π1 Ζ 2) + (3 F WR 4) …… (24) Thrust load received by the backup roll 2

F BUR = (3 Δ Pm / 2)-(IF _WR / 4) …… (25) Thrust load distribution rate that crawl 5 receives

α = 4 / [6 (A Pm ZFwR) +3] (26) can be obtained by such an operation. In the present invention, a vertical load and a lateral load are detected by using a rolling load detecting opening / closing cell 1 arranged on the upper, lower, left and right sides and a thrust load detecting load cell 6 acting on the work roll 2. The true load P received from the material 7 and the left-right load difference P _REF are calculated according to the above equations (22) to (26), and the thrust load F and the like are calculated.

Next, the effect of the load imbalance on the difference between the left and right mill elongation is shown below. Top, the spring constant of the lower backup roll support portion, Wa -.. Xi-de (WS) Z drive Sai de (DS) respectively KT _{_D} KTw KB _D, when the KBW, as elongation rolling load detecting single load cell load Will be reflected in the quantity.

DS growth

S p = (PTDS / KTD) + (PB _D s / KB _D )

WS growth

S w = (PTws / KTw) + (PBws / KBw) DS—WS elongation difference

S-REF ⁼ SD ― S

SRE F. = [(PTD S / KT _D )-(PTws / KTw)]

+ [(PBD S / KBD) one (PBws / KBw)] = [1 (PT _D s-PTws) / KT _D ]

+ [1 (PB _D s- PT _D s) / KB _D ]

+ PTws [(1 ZKT _D ) — (1 / KTw)] + PBws [(1 KB KB _D ) — (1 / KBw)] (27) For example, if the left and right mill stiffnesses are temporarily equal ,

ΛΤ―

Equation (27) is

SEEF = [1 (PTD S-PTWS) no KT] + [1 (PB _D s-PT _D s) / KB]

S R E F = C P R E F (1 ZKT) + (1 / KB)] + [Δ Pm (1 KT) one (1 / KB)] …… (28) where Δ P m is

Δ Pm = [(2/3) — α] F …… (29) and (1 ZKT) + (1 / KB) = 1 ZK,

S RE P = [PR E F / K) + [F (2/3) —] C (1 ZKT)

― (1 / KB)) …… (30) If the spring constant is known, if the true differential load P _KEF and the thrust load F can be estimated, the deviation S _{EEF of} the left and right mill stretch amounts is estimated. it can.

The reflection (feedback: FB) of the calculated load, etc. on the sheet thickness and edge control is shown below.

The FB for control can be broadly divided into two from control timing.

(1) Reflection on preset control between paths

(2) Reflection on dynamic control during roll byte The following describes how the above (1) is applied to the preset control between passes. Fig. 2 shows the system configuration that performs this preset control. The process computer 11, which receives the information required for rolling by the business computer 12, first determines the rolling schedule for all passes in advance (pass schedule calculation unit).

Next, in the timing of actually rolling the plate, the “adaptive control calculation unit” calculates preset information for controlling the rolling mill for each pass, and transmits the information to the sequencer 10. The sequencer 10 receives the set value for each pass from the process computer 11 and converts it into a signal for performing the actual rolling position control, drives the hydraulic equipment and the electric motor of the rolling mill, Set to pressure. The above is the outline of the preset control. When performing the calculation, the process computer 11 stores the rolling results and sensor detection values of the immediately preceding pass or the pass including the previous pass, and the learning calculation unit and the roll to reflect the results in the setting calculation of this pass. It has a roll profile calculator for estimating changes over time due to wear and thermal expansion.

Next, the reflection of the above (1) on the pre-cut control in the setting calculation of the process computer 11 will be described in detail.

The process computer 11 that has received the detection information of the load cells 1 and 6 in the previous pass calculates the true load from the material in the previous pass from the equations (22) to (26) shown above. I do.

Where: true rolling load sum: Pm _aet (= P)

True rolling load difference: A Pm _{ac t} (= P _DS -P ws) Thrust load from material: F _{ac t} (= F) On the other hand, from the actual rolling reduction information, temperature, etc. of the previous pass, The load at the path is estimated and calculated, and the difference between the estimated load and the load calculated based on the detected values of the load cells 1 and 6 is calculated. Correct the predicted load value of the next pass based on the value. In other words, the load prediction is learned and updated.

In other words, if the calculated values of the previous pass (the values calculated by estimating the load) are P m cal, Δ Ρ cal, and F cal,

Load sum error E _P = Pm ac ./Pm cal

Load difference error Ε _{Δ Ρ} = Δ Ρ ₃ — AP cal

Thrust load error E _F = F ac / F cal

Is calculated, and for the predicted values P EST, ΔP EST, F EST of the next path,

P EST ⁼ PEST xs E p

PEST '= ΔP EST + sE △ P

P EST ~ F E S T X S E F

Make a correction with the formula Here, S means the value of the error after smoothing. For example, when the error is 1.10, if 50% learning is reflected, it means to reduce to 1.05.

The above is the content to learn and correct the setting calculation for the next material from the pass information (rolling actual value & detected value) of the previous pass. As a result, the load that the material actually applies to the rolling mill (particularly, the difference between the left and right loads) is fed back to the thickness control, and the reliability of the set values for the thickness control after the next pass increases. As a result, the accuracy of the rolled sheet thickness increases.

On the other hand, since the difference between the left and right mill elongations in the previous pass is calculated from the load cell detection signal by Eq. (27), the following equation is obtained from the left and right mill elongation differences and the actually measured sheet thickness ゥ edge amount or camber amount. Learn and correct the vertical and horizontal mill stiffness (panel constant) in the formula. Next, when calculating the roll gap setting for the next pass, it is predicted in the next pass

P REP: true rolling load difference

F: Thrust load

And calculate the difference in mill elongation due to the load imbalance using Equation (30). Calculate and set in advance the left and right roll gaps so that the mill elongation deviation is canceled by a preset. This significantly reduces the number of members.

Next, the second and third aspects of the present invention will be described below.

The second and third inventions of the present invention achieve a predetermined plate crown for flattening the final shape of the plate material in recalculating the roll gap setting value when rolling the material. In order to perform rolling, the actual plate crown is calculated in real time in accordance with the rolling load fluctuations in the plate, and a single-pending control is performed.At the end of the pass, the plate crown is calculated from the actual roll banding amount of the previous pass. This is to control the shape of the plate by correcting the calculation amount of the pattern and reflecting it on the set value of the cross angle after the next pass.

Also, when the operator corrects the roll bending amount according to the exit shape of each pass, the shape prediction value of the path is corrected based on the actual roll bending amount of the pass, and In addition, the plate shape is controlled by correcting the plate crown prediction value, recalculating the target mechanical crown amount after the next pass, and reflecting it in the cross angle setting value.

In other words, according to the second and third aspects of the present invention, the crown estimation error caused by the preset control of the cross angle based on the predicted load is measured by real-time measurement of the actually measured load while controlling the inside of the bar by roll bending. It is possible to perform absorption and capture, and it is possible to perform accurate crank control.

Also, using the actual roll bending amount in the previous pass, the deviation amount between the predicted value and the actual crown value can be grasped, and the error can be reflected in the cross angle preset control after the next pass. As a result, feedback control with high tracking capability becomes possible. In addition, in order to realize the flattening of the plate shape, when the operator intervenes in order to flatten the plate shape on the outgoing side during the roll byte, based on the actual correction amount, By adding correction learning to shape and crown predictions, It is possible to control the feed feed to the next pass, and it is possible to more accurately flatten the shape of the plate.

Next, the fourth invention will be described below.

According to the fourth invention of the present invention, when determining the pass schedule for rolling a sheet by a reverse rolling mill having a function of crossing the upper and lower rolls in pairs, a conventional “load-constraining path for shape adjustment” + The concept of separating the "pass rolling at full load" or the concept of adjusting the load distribution for shape adjustment by setting the number of passes in advance is eliminated. The shape, crown and load (reduction) schedule of the rolled material are calculated and determined at the same time for each pass. Determine the pass schedule that can be rolled at the maximum value. Since the number of passes is automatically adjusted in accordance with the shape control ability, the ability to vary the number of passes in the reverse rolling mill can be sufficiently exhibited.

Hereinafter, the contents of the fourth invention of the present invention will be described with reference to FIG. In the method for determining a pass schedule according to the fourth invention of the present invention, first, a target final exit sheet thickness and a sheet crown amount are set (S21). Then, the finish temperature and finish direction of the final pass are simply assumed.

(S22, S23), and the rolling schedule and the angle of intersection are determined for each pass simultaneously from the downstream pass to the upstream pass by the following calculation. That is, first, the temperature on the entrance side (entrance side) of the pass and the expected rolling speed are assumed (S25, S26).

Here, the upper and lower limits of the permissible steepness of the pass and the target values (represented as l _max , λ _min , and λ _aim ) are given from the strip width and the exit thickness of the rolled material. The values of I _a and _m are basically 0, and the values of I _ma , and λ _min are parameters representing the allowable range of the shape for each rolled material size, and are determined according to the operating conditions or the required flatness of the steel sheet. Determined empirically. Using this ί value,

Ε ε = (π / 2 ² · λ ² ……………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………… (31)

C _in / H _in = C. _ul / H ou,-Αε / ξ + a Yes (S27).

However, C, „entrance side plate crown,

H _in entry side thickness,

C _out exit plate crown,

H ou, Outboard thickness,

Δ ε elongation strain difference,

値 Value indicating shape sensitivity (shape change coefficient)

a Shape change correction coefficient

M

Here, from the max, min, and aim of (C _in / H _in ), the allowable range of the mechanical crown restricted by the shape in this path and the target value are calculated by the following equation (S28).

MCK = [1 Z (1 —)]

X [C. _ut -7?-H ou, (C, „/ H,„)] (33)

MCK: Mechanical crown from shape

77: Crown genetic coefficient.

Meanwhile, main Kanikarukurau emissions from rolling load and equipment-bearing capacity is rolling load P, the beauty if mouth Lumpur base Ndi ring load F _B and mouth one Le cross angle by roll Prof I Lumpur can estimate calculated by the following equation.

Ch = c l-P + c 2-F B + E + C 3 (34) where

MCh: Mechanical crown from equipment load, P: Rolling load

F B: Roll bending load,

E: amount of mechanical crown formed by roll crossing angle, c1: mechanic crown influence coefficient by rolling load,

c 2: mechanical crown influence coefficient by bending load, c 3: mechanical crown amount formed by roll profile,

If there is no roll bending control device, the second term in the above equation is omitted, and if there is no roll crossing device, the third term in the above equation is omitted. Can be calculated.

(34) Maximum rolling load P _{ma x,} minimum cross angle 2 6 _min Noto-out MCh is maximized in formula, conversely, the minimum rolling load P _min, the MCh at the maximum cross angle 2 theta _{ma x} to the smallest The allowable range of mechanical crown from the equipment load can be determined (S29). Here, in determining the mechanical crown amount formed by the roll crossing angle: E, a constraint condition is added at the last pass to minimize the crossing angle at the last pass. From the rolling load constraint range, the mechanical crown constraint range can be determined.

The range that satisfies both the mechanical crown restriction range from the shape according to Eq. (33) and the mechanical crown allowable range from the equipment load according to Eq. (34) is the true mechanical crown allowable range for this path. Is determined. Furthermore, the MCK _aim is corrected so as to be within this range, and the true mechanical crown aim value MC _aim is determined (S30).

Subsequently, assume that to achieve MC _aim, determined reduction rate r, roll cross angle 2 0, and the optimal combination of Bendi ring load F _B at the same time. That is,

P = fp (r)

E = fe (2 ^)

Then, from equation (34),

_{MC aim = c 1 · fp (} r) + c 2 - F B + fe (2 ^) because a + c 3,

And to be represented, MC _a, _ra - in certain conditions, reduction ratio r is 2 theta pent '' can be searched determined by I ing load F _B.

In Eq. (35), in general, the bending efficiency FB is determined to be 20 so that the rolling reduction _r is maximized in order to favor high-efficiency rolling in operation. It is also possible to reflect the other operating conditions using an evaluation function or the like, and to find the optimal combination by a linear programming method or the like.

After determining the pass draft r (S31), calculate the thickness of the inlet side plate, estimate the temperature drop amount on the outlet side of the pass including the temperature change in the portal byte (S32), and calculate Recalculate the plate temperature at the time. Then, using that temperature, a more accurate rolling load (S33) and rolling torque (S34) are calculated, and after checking the load (S35), the temperature, load, and crown in the next upstream pass are determined. Repeat the calculation of

The above-mentioned calculations for each pass are piled up from the downstream pass to the upstream pass, and the pass schedule is determined in sequence, and finally the pass where the pass entry side thickness exceeds the expected thickness at the start of rolling. To end the calculation.

If the scheduled thickness at the start of rolling cannot be changed during the preparation of this pass schedule, load distribution correction calculation is performed as necessary, the thickness schedule is corrected, the calculation is completed, and all pass schedules are changed. decide. According to the pass schedule determination method according to the present invention, the shape of the rolled material, the crown, and the load (reduction) schedule are simultaneously calculated and determined for each pass in accordance with the shape control capability that is assumed to minimize the cross angle in the final stage. In addition, by performing the stacking calculation with the optimum value, it is possible to determine the pass schedule that can satisfy the shape consistently for all passes and can roll at the maximum value of the rolling equipment capacity. In addition, since the number of passes is automatically adjusted according to the above-described shape control ability, the ability to vary the number of passes in a reversible rolling mill can be sufficiently exhibited.

Hereinafter, the present invention will be described in more detail based on examples. Example

Example 1

The actual detected load of the previous pass is

2222ton 2101ton 2105ton 2231ton 182ton

In the case of, from (22), the true rolling load

P = 4330ton

From equation (23), the true rolling load difference

P REF =-5 ton

From equation (24), the true thrust load received from the material

ΔP m = 124ton

F = 323ton

Further, the thrust load received by the work roll is α = 0.563.

For the true load group received from the above materials, the setting calculation of the next pass was learned and corrected based on the actual reduction amount of the previous pass. That is, P eal = 4250ton

Δ P cal = 0

F cal = 350ton

SE p B = 0.99 from E P = 0.981

From Ε _Δ p = 5 s E 3

SE = 0.95 from E = 0.923

The learning value was determined as follows.

Next, learning correction was performed for the predicted value of the next pass.

P = 4110ton is 4069ton (corrected value)

Δ P = 0 is 3 ton (corrected value)

E = 315ton is 299ton (correction value)

On the other hand, regarding the difference in mill elongation due to the load imbalance in the previous pass, KT = KT _B = KT _w = 1509ton / mm

KB = KB _D = KT _w = 2708ton / mm

K = 969

And the path before S _KEF = (2222—2101) / 1509 + (SlOS—SfOZSTOS

S = 0.034mm

Next, in the next pass, from Eq. (30)

S = (3/969) + [299 X {(2/3) — 0.563)

{(1 1509)-(1-/ 2708)}] X (-1)

S — 0.029mm

In the above equation, the negative of the second term is a characteristic of reverse rolling.

Table 1 shows the load and roll gap performance for each pass when rolling was actually carried out in the above manner. Table 1

As shown in Table 1, the actual rolling load is such that the differential load of DS-WS is reversed between upper and lower sides during forward rotation and reverse rotation,

Mill elongation deviation occurs alternately in the forward and reverse directions as S R E F.

For this reason, the camber is generated in the direction in which the front part of the plate is bent toward the WS side during the normal rotation of the mill, and repeatedly bent toward the DS side during the reverse rotation. As the rolling pass progresses, this bending diverges in the direction of the maximum, and in the conventional rolling, the camber becomes larger as shown by the solid line in FIG.

On the other hand, the S _REF shown in Table 1 is predicted for each pass immediately before each pass as in this embodiment, and the amount is determined in advance as a roll gap unbalance value, so that the camber can be reduced. As shown by the dotted line in FIG.

Example 2

Hereinafter, second and third embodiments of the present invention will be described with reference to the drawings. FIG. 5 is a block diagram showing a configuration of a control system for realizing the shape control of the present invention. First, the configuration in FIG. 5 will be described. Process computer 11 is a business computer 12 Before the start of rolling, the schedule of thickness, temperature, etc. for each pass is calculated in advance to determine the processing content of the entire finish rolling pass, and information on the actual results between passes is next calculated. Finishing path schedule calculation unit 11 A for performing learning calculation to feed-forward to the pass, and a plate is actually rolled for each pass according to the schedule obtained by the pass schedule calculation unit 11 A. However, it comprises a finish adaptive control calculation unit 11B that controls work roll bending in real time according to the detected value during rolling and the operator input value.

FIG. 6 shows a side view of the rolling mill shown in FIG. Referring to FIGS. 5 and 6, the radiation thermometer 15 T (FIG. 5) detects the surface temperature of the material 7 to be rolled during rolling, and the a-line thickness gauge 15 H measures the thickness crown. The table roll 16 is located on the front and rear surfaces of the rolling mill and transports the material 7 to be rolled in synchronization with the rolling mill speed. The peripheral surface of the work roll 5 is supported by a backup roll 2, and the backup roll 2 is supported by a bearing 3. The work roll bending device (hereinafter referred to as WRB) 9 A adjusts the distance between the work roll bearing 4 and the bearing 3 to bend the work roll. The setting device 9B is a controller of the device 9A for setting the bending amount. Hydraulic screw-down device (hereinafter referred to as AG C) 8 A

(Fig. 5) defines the distance between the upper and lower backup roll bearings 3, that is, the mouth-to-roll gap (gap between the upper and lower work rolls). The screw down setting device 8B determines the screw down position. That is, the setting device 8B is a control device of the device 8A. The load cell 1 detects the rolling load while the material to be rolled 7 is rolled into a rolling mill. 18 is the bearing support frame of the cross device that sets the crossing angle (twice the cross angle) of the upper and lower sets of rotating shafts by setting the backup roll and the work roll as a set on the upper and lower sides, respectively. It is. The support frame 18 is connected to the screw 8 and is driven in the horizontal direction (left and right in FIG. 6) by its rotation. Pull back cylinder 19 is attached to support frame 18 It always applies a force in the evacuation direction, and suppresses displacement due to backlash when the support frame 18 is driven by the screw 8. By driving the upper and lower support frames 18 in opposite directions, the upper and lower rolls cross as shown in FIG. The cross angle setting device 17 (Fig. 5) is a controller that biases this cross angle adjustment mechanism.

Fig. 7 shows the contents of the previous path actual calculation and the learning calculation based on it, which are the premise of the next path setting calculation using the shape control of the present invention, and Fig. 8 shows the contents of the next path setting calculation .

First, with reference to FIG. 7, the contents of the actual calculation and the learning calculation of the previous pass will be described. Before starting the calculation of the previous pass results, the sheet thickness schedule for all passes is roughly determined in advance, and the draft (sheet thickness) schedule set here generally includes the rolling load and sheet thickness. It is determined to satisfy the shape and is determined after appropriate load distribution. S in FIG. 7 means a step.

First, in response to the one-pass metal-off signal, the finishing path schedule calculation processing unit 11A of the process computer 11 stores the sensor detection value of the path (hereinafter referred to as the previous path) held by the adaptive control calculation unit 11B. The actual values (rolling conditions and rolling results) are extracted (S1). The schedule calculation processing unit 11A then uses a gauge meter formula based on the actual roll gap S _act and the measured load cell load P _act

― P ac,

Hga e ™ act + + H ₀ ί s

M

Then, the sheet thickness H _sage on the exit side of the previous pass is calculated (S 2). Where H. _fs is the thickness correction term by learning.

Next, the calculated thickness obtained in S 2 and the H of the observed value. _Recognize the error by comparing _ut and H up to the previous pass. Is modified (S3). Similarly, for the crown, the actual calculation value is calculated and the learning value is updated. (S4, S5). That is, in S 4, the amount of mechanical crown Cm formed in the roll byte

Cm = px P ac + fx F ac, + rx R ac, + E + Cm. _fs , taking into account the genetic effects of the incoming crown,

C _gag = 77 C, n + (1 — 7?) Cm

As a result, the actual calculation crown amount is calculated. Next, in S5, the error between the measured crown C _ac , and C _sage was calculated, and this error was used as the mechanical crown Cm. (Convert to _s error and perform crown learning.

In addition, after the correction learning calculation for the temperature in S6 and S7, the actual calculation load and the load learning coefficient are calculated in S8 and S9.

Finally, shape learning, which is a feature of the present invention, is performed in S10 and S11. In other words, the shape of the material to be rolled is evaluated by wave height / wave pitch, and when expressed as steepness, the shape is generally sinusoidal,

= {2 / π) νΤ {[(C _in ZH _in ) — (C cut ZH ou, + a] ξ}

+ _f s

ξ: Expressed as the coefficient of influence of the crown ratio on the shape (hereinafter referred to as the shape change coefficient).

Here, by calculation up to S 9,

C _{ι η} : Incoming crown,

H,: Inlet thickness,

H i t · H g a g e ヽ

C: t ♦ then β a g 6,

Is known and the actual shape of the previous pass is calculated; _Igage is calculated ( _S10 ) 0 Here, if the output shape of the actual result is flat,

Actual steepness λ a c t = 0

, It is recognized in the calculation; there will be a difference from lge o Naturally, it is desirable to evaluate the above-mentioned shape recognition error using the actual shape sensor.However, during actual rolling, the WRB is designed so that the operator can visually judge the shape and flatten the shape. (ヮ -Crawl bending) The load is corrected in the bar. In other words, the driver acts as a sensor and feeds the result back to the WRB operating end as feedback (FB), and as a result, corrective intervention is performed so that s _a , → 0 Therefore, the error Δ λ ^ λ

; i. _fs ' = a A λ + (1-a) , ₅ (a: learning smoothing term) enables control FB (S11).

Next, the contents of the next path setting calculation will be described with reference to FIG. 8, which shows a calculation processing flow in which the learning result determined in FIG. 7 is actually reflected in the next path setting calculation. Here, first, the target thickness and crown shape are set according to the schedule calculation set in advance (S12). At the same time, the initial value of the next pass WRB load is set to a neutral point, and the shape and crown are set. The crown control should be reflected in the cross angle setting with a large control ability. Next, the temperature of the next pass is estimated from the predicted time to the next pass (S13), and the load learning value P up to the previous pass is estimated based on the temperature. Estimate the predicted load _Pesl of the next pass using _fs ' ( _S14 ).

Next, the target crown value of the next pass is corrected in consideration of the shape tolerance from the crown ratio of the previous pass (S15). That is,

C i „π

C. _ul = H. _ut [{(-) ² (λ _aim — λ.,) ² } — α]

Η _{ι η} 2

And

Generally a I _{a im} = 0, λ _aim soil; rt (limit steepness), if sooner initial schedule C _{ai ra} = C. _{If ut} is good and if exceeds, correct C _aim by the above formula. Next, the amount of mechanical crown required in the next pass

C HI… = (C a irn-77 C in) / (1 — 77)

To find the cross angle required to achieve Cm a i n

(S16).

RSET = (Cm- p XPES T- fx FSET - E -. Cm) / R where, P _EST is estimated load at S 14, F _SET is WRB load the neutral point, Cm. _fs ' is the learned mechanical crown correction. According to the above equation, both 1) reflection of the crown learning result up to the previous pass and 2) reflection of the WRB operator correction up to the previous pass are absorbed by the large cross angle of the control ability.

Finally, the S 17 is a gagemeter type

e s t

O set ⁼ H _a im + + H o ί s

M

Then, the next path setting roll gap value is calculated, and the next path setting calculation ends.

FIG. 9 shows an outline of a calculation process of the dynamic shape control process of the plant controller 13 shown in FIG. 5, and FIG. 10 shows a functional configuration for performing the calculation process. Next, referring to FIG. 9 and FIG. 10, the following actual values are grasped in real time during the _c- roll byte, which describes a method for dynamically controlling the plate shape during the roll byte of the WRB.

(1) Actual instantaneous rolling load: P

(2) Actual instantaneous WRB load: F _WB

(3) WRB correction value by operator: ΔF0

On the other hand, in the process computer 11 immediately before the rolling of the pass, the finishing pass schedule calculation processing unit 11A sends the information to the adaptive control calculation unit 11B. The following data is transmitted.

(1) Next pass target crown: C a, _m

(2) Crown effect coefficient of load: d c d p

(3) WRB crown influence coefficient: d c 5 F WB

(4) Other crown term offset e

(5) Preset WRB Load: F0

Where, as shown earlier,

Cm = p X P + f x F wB + E

C = C i n? + (I-77) Cm

The power that is

d c

C d p) P + () F WB + e

3 F W B

Can be expressed as Therefore, by transmitting 3 c / dp, 5 c / 5 F WB, e as the crown control constant from the pass schedule calculation processing unit 11 A to the adaptive control calculation unit 11 B, the adaptive The control calculation unit 11B estimates (calculates) the actual crown amount in real time.

5 ru 0

Adaptive control calculation unit 11 B calculates the actual calculation click la c down amount C real in Rorubai up by internal calculation in real time, sequentially recognizes the error Deruta_〇 between the target value C _{ai ra.} Tuning gain is applied to the AC (error), converted to WRB feedback correction amount ΔF _WB , and interference with AGC (Automatic Gauge Control) is removed to set WRB Automatically make corrections to In other words, the calculation of the actual crown amount C real—the calculation of the error AC—the correction amount of the WRB ΔF _WB— the correction of the set value of the WRB is repeated over a feedback buckle.

In addition, the correction amount by the operator can be reflected outside the above-mentioned feedback loop, and the shape correction machine by the operator can be used. Function (“WRB correction amount” in Fig. 10).

FIG. 11 shows execution timings of the above-mentioned various operations of the process computer 11. As described above, in the present invention, in addition to the closed loop of the automatic control of the WRB, the correction correction of the operator can be reflected without disturbance, and the result of the inter-pass preset after the roll byte is obtained. is characterized in that so as to reflect the cross angle control follows path _£ in FIG. 12, a cross angle set value and click La c down ratio actual value according to this embodiment, in comparison with the conventional method. The conventional method is an example in which the automatic control function of the WRB is provided, but the feedback of the actual value including the operator's correction is not reflected in the cross angle setting.

In the conventional method, the change in the crown ratio for each pass is unstable, and especially in the final pass, the crown ratio changes significantly, resulting in rolling waves. Rolling with a constant crown ratio is possible, and the flatness shape is improved.

Fig. 13 shows the results of a comparison between the conventional method and the method of the present invention with respect to the frequency distribution of the crown ratio change in the last pass that most sensitively affects the rolling shape. By applying the present invention to control, it is possible to dramatically improve crown control accuracy.

Example 3

An embodiment relating to the schedule determination method according to the fourth invention of the present invention will be described below.

The pass schedule of the rolled material was calculated under the following preconditions.

Final target thickness: 6.0mm

Final pass exit side crown amount: 0.02 mm

Board width: 3500mm

Finishing temperature of the final pass: 750 ° C (finish in the rear direction)

Descaling execution pass: 1st pass & 3rd pass from initial pass Maximum cross angle: 0.585 °

Final corner angle constraint: 0.000.

The above prerequisites are, in actual online calculations by the process computer, transmitted as rolling material information from a higher-level business computer or as information patterned in accordance with operating conditions. Given.

By the following calculation, the rolling schedule and the roll crossing angle schedule were determined simultaneously for each angular pass from the downstream pass toward the upstream pass. Here, the calculation process for the last one pass (calculation start pass) is shown by numerical examples.

[Assumption of inlet (inlet) temperature]

Assuming that the temperature drop is 30 ° C, the assumed inlet-side temperature is 780 ° C. [Assumed rolling speed]

Set the standard mill speed to lOOrpm based on the width of the rolled material and the thickness at the exit side.

[Upper and lower limits of allowable steepness and target value]

λ _max = 0.4%, λ _ra , n = _-0.4 %,; i _aim = 0. It is a parameter that indicates the allowable range of the shape according to each rolled material size, and is empirically determined according to the operating conditions using table values. ,

[Calculate allowable elongation strain difference and target elongation strain difference]

According to Eq. (31) Δ ε = (ττ / 2) ² -λ ²

Δ ε _max = 0.004%

Ε _min =-0.004%

Δ £ _a im = 0

(Calculate the allowable range and target value of the inlet-side plate crown ratio)

C _in / H _in = C according to equation (32). _ul H _ou ,-L ε / ξ + a

= 0.15 = 0.61

C. _u,. _ut = 0.33%

m _i n = 0.48%

a i n, = 0.48%

[Calculate the allowable range and target value of mechanical crown restricted by the shape]

From equation (33),

MCK = 1 / (1-7?)

• [C _out -7? · H ou, · (C _in / H _in )]? 7 = 0.702 (hereditary coefficient)

MCK _ma x = 0.00mm

m i n = 0.00mm

a i m = 0.00mm

[Mechanical crown allowable range from rolling load and equipment allowable capacity]

P _m ax = 6500ton

P _min = 2200ton

a x = 0.000 °

Θ _min = 0.000 °

That is, the final pass has a constraint of cross angle = 0 degree,

Assuming that F B = 130ton, from Eq. (34),

MCh = c 1P + c 2-F B + E + c 3

MCh max = 0.72mm

MCh _min = + 0.01mm

Here, the roll penting load was fixed at a preset value. [True main Kanikarukurau down tolerance target value MC _a, determination of _ra]

MC _ma X = 0.01mm

MC _m , π = 0.01mm

MC _aim = 0.01mm

In [reduction ratio r, the search determination of the roll cross angle 2 theta pent 'I ing load F _B] (35) _{r = fr (MC aim 2 Θ} , FB), directed to a high efficiency rolling, the maximum rolling reduction When we search for, under the fixed condition of F,

θ = Θ… = 0.000. When is the maximum,

r = 0.1328 (= r seek) is obtained.

[Calculate the entry side thickness]

From H, n / H ou, / (1 — r), H in = 6.84 mm

[Estimation calculation of the temperature drop amount on the exit side of the pass]

Temperature drop = 15 ° C

Plate temperature at loading = 765 ° C

[Calculate rolling load and rolling torque]

P = 3120ton

torqe = 98tonm

All are within the facility capacity range.

[Estimation calculation of the amount of temperature drop on the path entrance side]

Temperature drop = 21 ° C

Plate temperature at exit of previous pass = 786 ° C

This completes the calculation of temperature, load, and crown for one pass.

By calculating the above calculation for each pass by stacking from the downstream pass to the upstream pass, the pass schedule is determined sequentially, and finally the pass entry side thickness exceeds the expected thickness at the start of rolling. End the calculation repeatedly with the pass. In this example, the scheduled thickness at the start of rolling was set to 45 dragons, and the pass schedule for all passes was calculated. Table 2 compares the results with the conventional method. And Figure 14.

Table 2

In both cases, the shape adjustment ability by the roll cross function is the same, but the conventional pass schedule does not allow the rolling load on the upstream side to reach the maximum equipment capacity, resulting in an increase in the number of passes. On the other hand, in the present invention, the schedule calculation is performed by searching for the allowable maximum rolling load under the cross constraint condition, so that the shape is maintained even when the cross angle at the final stage is minimized. The shortest number of passes can be achieved. Example 4

Final target thickness: 20.0mm

Final pass exit side plate crown amount: 0.00 mm

Board width: 3500mm Finishing temperature of the final pass: 850 ° C (finish in the rear direction) Descaling execution pass: The first pass from the initial pass Maximum cross angle: 0.600 °

The final stage Pasuku loss angle constraints: 0.200 ⁰

Maximum rolling load: 6000 t on

Planned thickness at the start of rolling: 93mm

The path schedules for all the paths in this embodiment were calculated. Table 3 shows the results.

Table 3

Example 5

Final target thickness: 45.0 mm

Final pass exit side plate crown amount: 0.20mm

Board width ： 1500mm

Finishing temperature of the final pass: 850 ° C (finish in the rear direction) Descaling execution pass 1st, 3rd & 5th pass from initial pass

Maximum cross angle: 0.500 ⁰

The final stage path cross-angle constraints: 0.000 ⁰

Maximum rolling load: 4200 t on

Maximum torque: 420 ton

Planned thickness at the start of rolling: 1 57mm

The path schedules for all the paths in this embodiment were calculated. Table 4 shows the results.

Table 4

Industrial applicability

As is clear from the above embodiment, according to the present invention, the load actually applied to the rolling mill by the material is fed back to the plate thickness and the edge control, and the rolled plate thickness accuracy is improved. The members are greatly suppressed. Furthermore, the present invention enables rolling with a constant crown ratio over all passes, and improves the flatness shape. Further, according to the present invention, the shape of the rolled material, the crown and the load (reduction) schedule are determined simultaneously for each pass, and the shape is satisfied consistently for all passes. It is possible to determine the pass schedule that allows rolling at the maximum capacity.

Claims

The scope of the claims

1. In a rolling mill that reversely rolls a roll set with the upper and lower backup rolls and work rolls as bases in a plane parallel to the rolled material, the upper, lower, left and right rolling load detection rolls are used. The actual difference between the true rolling load excluding the influence of the thrust load and the left and right load is calculated using the detected value of the thrust load generated in the roll cell and the thrust load generated in the roll axis direction. An automatic thickness control method for reverse rolling of a pair cross rolling mill, which automatically controls the thickness and the edge based on the detected value and the calculated value. .

2. A set of rolls in which the upper and lower backup rolls and work rolls are respectively crossed relative to each other in a plane parallel to the rolled material, and have a roll bending control device at each end of the roll. In order to achieve a predetermined strip crown for flattening the final shape of the strip in rolling by a rolling mill, the actual strip crown is calculated in real time according to the rolling load fluctuation in the strip. Roll bending control is performed, and at the end of the pass, the plate crown calculation amount is corrected from the actual roll bend amount of the previous pass, and the plate shape is controlled by reflecting it on the cross angle setting value for the next and subsequent passes. A shape control method in reverse rolling of a pair cross rolling mill.

3. A set of rolls, each of which has a backup roll and a work roll above and below, intersects relatively in a plane parallel to the rolled material, and has a lip-pending control device at each end of the roll. In rolling by a rolling mill, when the amount of mouth bending is corrected according to the exit shape of each pass, the predicted shape of the pass is corrected based on the actual amount of roll bending of that pass, and Correct the predicted crown value and re-establish the target mechanical crown amount after the next pass. A shape control method in reverse rolling of a pair cross rolling mill, wherein the shape of the plate is controlled by calculating the value and reflecting the calculated value on a cross angle setting value.

4. Rolling the sheet material using a reverse rolling mill with a control device that relatively intersects the upper roll set and the lower roll set, each paired with the upper and lower backup rolls and work rolls, in a plane parallel to the rolled material In determining the pass schedule for each pass, calculate the area that satisfies both the mechanical crown allowable range determined from the shape of each pass and the mechanical crown allowable range determined from the equipment capacity, and within that, the allowable maximum rolling load A method for determining a reverse rolling schedule for a pair cross rolling mill, which is characterized in that a sheet thickness schedule is determined by sequentially stacking from the bottom so as to satisfy the following conditions, and the rolling and crossing angle schedule of the shortest number of passes satisfying the shape are simultaneously determined.