A New Rolling Schedule System for Plate Mill

Copyright © IFAC 12th Triennial World Congress. Sydney. Australia. 1993

A NEW ROLLING SCHEDULE SYSTEM FOR PLATE MILL K. Higashi*, K. Hirata*, S. Shimada*, Y. Ohbanya**, K. Nose*** and M . Nomura*** *Department of Plant Control Technology. Kakogawa Works. Ko/Je S teel Led .. I . Kanazawa-cho. Kakogawa. Hyogo. 675·01. Japan **No 1 Rolling Department. Kakogawa Works . Ko/Je Steel Ltd ***Electronics Research La/Joratory. Ko/Je Steel Ltd .. 5-5. I- chome. Takat.llIkadai. Nishi-ku. Ko/J e. Hyogo. 651 -22. Japan

Abstract. A new rolling schedule system has been developed for the purpose of improving productivity in the plate mill. It was thought that productivity could be improved by optimizing the processing time for each plate in each mill by considering rolling conditions and the combination of the rolled plates . This system has been compared with the conventional one by numerical simulation, which indicated that productivity can be improved by more than 10%. This system has just been put into use at the plate mill at Kakogawa Works. Key Words.

Steel industry; plate mill; integrated plant control ; pass schedule; simulation

1. INTRODUCTION

combination of plates with different processing times for each mill , FM or RM becomes idle because the processing time, which is determined by using fixed RM and FM pass schedules for each plate, cannot differ.

Efforts have been made to improve the productivity of plate rolling. Recently, a new process, the TMCP (thermo-mechanical control process), has been developed . This process is capable of giving a higher toughness and strength to the plate through temperature control during rolling. And its advantage is improvements in weldability due to a decrease in alloying elements. However, as the plate temperature should be strictly controlled in this process, a decrease in productivity cannot be avoided. With the growth of the ratio of TMCP in relation to ordinary rolling, improvements in productivity are becoming more and more important.

In plate rolling, the processing t ime for each mill can differ to vary the transfer thickness (the plate thickness after rough-rolling), that is , the pass schedule is varied . Figure 2 shows the relationship between the transfer thickness and the required time for ordinary rolling . For the TMCP shown in Fig. 3, the time for rough-rolling varies in proportion to transfer thickness, but, on the contrary, the time for finish-rolling varies inversely to transfer thickness . The period of time for ordinary rolling is maintained at a constant no matter how the transfer thickness is varied . However, the time for TMCP increases in proportion to transfer thickness . This is because of the presence of the shower cooling ; the time for the shower cooling varies with transfer thickness .

A new rolling schedule called "KCIP" (Kobe Steel' s combined and integrated pass schedule) has been developed to meet these requirements . This paper introduces our concept of improving productivity and an outline of the "KCIP" system.

2. OUTLINE OF PLATE ROLLING

The idea of how to improve productivity is derived from the relationship shown above, that is, determining the transfer thickness by considering the combination of plates makes it possible to reduce the idle time for each mill and shower cooling apparatus .

Figure 1 shows the layout of the plate mill at Kakogawa Works. The slabs, reheated in the furnace, are delivered to the roughing mill (RM ; reversible type) where they are rolled to obtain a targeted plate width . After rolling at the roughing mill, the plate is conveyed to the finishing mill (FM ' ; reversible type) where it is reduced to the final thickness. That is called ordinary rolling . For TMCP, the plate is water-cooled to the targeted temperature by using a shower cooling apparatus (SC) installed between the roughing mill and the finishing mill.

The time when the last plate of N completes its finish-rolling is used for the object to indicate the productivity of the line, as shown in Eq . (1) .

F

=

X (N)

+ A (N) + TR (N) + B + TS (N) + C + TF

(N) (1 )

3. THE METHOD TO IMPROVE PRODUCTIVITY 3.1 A Basic Idea for Improving Productivity Recently, in order to improve productivity, the conveyance of plates is controlled so that they do not collide with each other. However, in case of a 589

The following three constraints for the Kth plate are to be considered so as to prevent the plates from colliding with each other ; equations (2), (3) and (4) are for the entrance of RM, the exit of RM and the entrance of FM .

x (K-l)

+A

(K-l)

+ TR

(K-l)

~

X (K)

+A

(K)

(2)

X (K-1) + A (K-1) + TR (K-1) 2:: X (K) + A (K) + TR (K)

+ B + TS (K-1)

it has been adopted to actual control. (3)

x

(K-1) + A (K - 1) + TR (K-1) + B + TS (K - 1) + C + TF (K - 1) 2:: X (K) + A (K) + TR (K) + B + TS (K)

(~

And the following two constraints are considered ; equations (5) and (6) are for the plate length when the plate has completed its rough -rolling and for the temperature of the TMCP plate after finishrolling. LMIN 2:: L (K) 2:: LMAX

(5)

= 8AIM

(6)

8 f (K)

where X (K) : extraction time from the reheating furnace A (K) : time to transfer a plate from reheating furnace to RM TR (K) : time for rough-rolling TF (K) : time for finish-rolling TS (K) : time for shower-cooling B : time to convey a plate from RM to shower C : time to convey a plate from shower to FM 8 f (K) : plate temperature after finish-rolling 8 AIM : target temperature after finish-rolling L (K) : plate length after rough-rolling LMIN : minimum plate length after rough-rolling LMAX : maximum plate length after rough-rolling The quantities TR (K), TF (K), TS (K) and 8 f (K) are considered to be a function of the transfer thickness which is determined by the pass number of rough-rolling . Therefore , constraints of Eqs . (2) to (6) and the objective function of Eq . (1) are formulated as a mixed integer programming problem (Nomura et al., 1992), and in several cases, this problem is solved ; a numerical simulation is done. Figure 4 shows the numerical simulation results of ordinary rolling. For TMCP , as shown in Fig. 5, the productivity is improved compared with the conventional method. In the proposed method, the transfer thickness is varied in order to reduce the idle time for each mill and shower cooling apparatus. Especially in TMCP, the transfer thickness is thinner.

3.3 A Method for Improving Productivity of TMCP Although reducing the transfer thickness as much as possible is more effective for improving productivity in TMCP, it is a matter of concern that the mechanical properties of plate are affected by decreasing the reduction at the FM. The relationship between the mechanical properties and the transfer thickness is shown in Fig . 7 . The transfer thickness can be varied in a wide range, but there is a limitation that does not affect the mechanical properties of plates. In applying actual control to TMCP, the thinner transfer thickness is selected within those limitations. Figure 8 shows the effectiveness when the transfer thickness is reduced within the limitation. Productivity is improved about 18%.

4. OUTLINE OF THE "KelP" SYSTEM Figure 9 shows a comparison of " KCIP" and conventional control. The required time model which is needed for predicting the processing time accurately in order to decide the transfer thickness has been newly developed and applied . It is necessary to estimate the time for finish-rolling in advance . Therefore, the RM and FM pass schedules are sequentially executed once before the rough-rolling is started . An outline of these functions is shown as follows: (1) RM and FM pass schedule The pass schedule determines how much the thickness of the plate should be reduced at each pass so that the total pass number may be minimized . The thickness at each pass i s calculated as shown in Eq . (7) by using maximum rolling load, power and reduction which are imposed to express the limits of the capabilities of the mill , or to assure the quality of rolled plate within a permissible range. These pass schedules have been developed (Tanaka et al., 1980) as in the past and have been applied to actual control. HO = MAX (HL, HP, HR)

The above numerical simulation results make it clear that varying the transfer thickness is very effective for the improvement of productivity. Our ideas for improving the productivity of ordinary rolling and TMCP are as follows : (1) For ordinary rolling, the transfer thickness, which is determined by the pass schedule, has to be optimized in order to reduce the time lag from the preceding and following plates.

where HO : thickness at each pass HL : thickness from maximum rolling load HP : thickness from maximum rolling power HR : thickness from maximum reduction (2) Temperature prediction model The model based on a thermal conduction equation has been newly developed (Yasuda et al., 1992) and applied, and can estimate the temperature from the surface to the center along the thickness direction. A (x, t) = A O

(2) For TMCP, a thinner transfer thickness has to be selected within the allowable range in order to reduce the rolling time .

+

i "

3.2 A Method for Improving Productivity of Ordinary Rolling To apply those concepts to actual operation , a simplified method is considered in which the transfer thickness is determined in relation to the preceding plate. Figure 6 shows a comparison of the proposed method and the conventional method . Productivity has been improved about 7% . The effectiveness of this proposed method has been confirmed and

590

(7)

(Uk (t) (1-x / qk (t))

+ Rk

(t)) (8)

where 8 (x, t) : plate temperature (-) 0 : the center temperature of the initial condition Uk (t), qk (t) : the function of time, express the temperature distribution in the thickness direction Rk (t) : the function of time, express the change of center temperature x : axis of the thickness direction t : time m : the number of boundary conditions which have changed n : constant, expresses the temperature distribution in the thickness direction

(3) Required time prediction model The time required for rolling at each pass and for conveying th e plate from point to point is accurately calculated, even if the velocity is changing. Equation (9) shows the formulation of time for rolling at one-pass .

t

= (V ' + La

)/ (a V)

(9)

where t : time for rolling at one-pass V : maximum rolling velocity L : plate length a : the ratio of velocity change An outline of actual control of " KCIP" at each stage is as follows : (a) When the slab reaches just in front of the RM, the rolling schedule is determined by an integrated prediction of the RM and FM pass schedule so that the idle time of the RM , the shower cooling apparatus and the FM should be minimal. The shower cooling time is also determined (see Fig .

10) . (b) During rough-rolling, the predicted time for rolling is corrected by actual data and the transfer thickness determined above is adapted . Reheating Furnaces

D

Roughing Mill (RM)

--

Finishing Mill (FM)

(c) After rough -rolling , the temp erature of the plate is calculated by using actual rolling data, and the cooling time for the shower cooling is recalculated.

5. CONCLUSION " KCIP" ,that is, the new rolling schedule system for the plate mill, has been developed for the purpose of improving the productivity of ordinary rolling, in addition to the TMCP. This system has just been started at the plate mill at Kakogawa Works . This system should be continually improved and expanded and combined with the automatic combustion control system to promote further integrated control, that is, mill pacing.

6. REFERENCES Nomura , M ., K . Nose, K. Higashi and S . Shimada (1992) . Optimal Pacing of Plate Rolling Mill Using Mixed Integer Programming , Proc. of the Pacific Conference on Manufacturing, pp . 839-846. Tanaka, E., T . Ohnishi, M. Fukui and K. Amagata (1980). Computer control for plate mill , Kobe Steel Engineering Reports, 30 (4), 33-37 Yasuda, K ., K . Ohe, A . Mizuta and K. Higashi (1992) . Temperature prediction model of steel plate during plate rolling , CA MP-ISIJ, 5, 1568

~~~~t ~ . ~3 ~

-:-

RMin

~

Sho w or RM o ut

f;

Scale Vertical Breaker Edger

Shower Cooling apparatus

.

Furnaco O 100

5

S how~r

ii! 150 ]200[ J

:~

.i £

RMifl

100

50

~:7::-~~'.:-:~:=-~:--:'70 0 ,Time

~

150

Transfer thickness

SeQuenliill plat e numbe r

(s oc )

200 (mm)

FMout

~~

FM in

~ 150

Show~r

200

~ 100

RMout

400r-~~-.-------r------.--.

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Time

SCQuenli,ll plille numb~r

(se c )

(a) Proposed mothod

FMout

Cl)

.'E"

200

4 5

FMin Shower

RMout

..

j

:a

.~

....... j

RMin

~~~~~-h-t~00~0~ 1 20·0

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Time

(so c )

.

' ~ 'Jr -,. . : •

l

200 150

1! 100 -

100

Transfer thickness

'

1 23 ~5

A Total

Ul

.. , .. '

RMifl

Cl)

~ .....

0 1 2 345

Fig.4 Effect of transfer thickness optimization on productivity of ordinary rolling

Fig.2 The relationship between transfer thickness and required time for ordinary rolling

()

~,

( b ) COflvoflti ofl DI mothod

100~ 100

.

RM out

200

050

Sequential plate number

FM out

Cl)

.~

'.' '.

0 1 2 345

I::

(soc)

FMifl

A Total o Finishing mill • Roughing mill

300

.,

50

( D) Proposod mothod

400r------.------.------.--.

'0 ~

20--0---·J.30~0-'-4~00-50~0-6~00-100 Tim o

Fig. 1 Layout of the rolling line at the plate mill

::[j

~ 100 ",

9·

50

~"-

01 23 45 Sequential plate number

(b) Conventional method

(mm)

Fig. 3 The relationship between transfer thickness and required time for TMCP

Fig, 5 Effect of transfer thickness optimization on productivity of TMCP 591

FMout~~·· · .· · 1

FMout~ .................................. · .. · .............. ·· 1

FM," Shower RM out

.. ....... ....... ... ... .... . .................... . ..... .... .... ........ .......... ..... ........ . . ...... .. ........ . ............. ........... .. ...... .

FM.n Shower RMout

................................................. .. .......... . ...... ............ .. ...................... .. ....................... .... .

RMin

.............................................. .

RMin

..................... ............................. .

Furnace O-"--'
Furnace 0

FMin FMout Sh ower RMout

· · ·F . . . ......

Furnaee

500

600

700

............................ . ............. ............ ......... .. .......... . ..................... ........... .. .. .............. ..

.. ............... .. ................. ... .... .

RMin

................................................. .

100

100

300

400

500

600

00-..... 50-0--'6oo'---7ool-l Furnaee OL-~I0c.,0---"1"-00-L.3,...00-L4.....

700

Time

(sec)

(b) Conventional method

Fig. 6 Comparison of simplified method and conventional method in regard to productivity of ordinary rolling

E 560

400

FM.n Shower RMout

Time ( sec) ( b ) Conven tional method

~ 540 ~ 520 ~ 500

300

.......................... .... ..................... .

"-~'--:c~....r..,--L-c'--L:---'---'-.J

o

100

FM~ut~~· · ·1

··· ······ ..... .. ............... ...... ....... ... . w················· ·.··1 ............. ......... .. ..................... .. ..... .

RMin

100

Time (sec) (a) Simplified method

Time ( sec ) ( a) Simplified method

Fig.8 Comparison of simplified method and conventional method in regard to productivity of TMCP

r----.----,-----r----.-----.--~

•

Jl

480 460 ~ __ ! ..i____ . ___ . ____ .. _.. __~~r_!:!.~tt~?__ !~__ ~ ~ 35f------1r---i---t---t---t---I ~

~

30

.~

25

d3

20

g'

• i..: _ _. _ . _ ~I ~'::! a.l? I ~ . !a~g.!'. _ . _

_ ~

•

I• •

i ~ __!~:~~!!~~ _.E.I . _____ .... .. .. __ ............... ~ .... __ ~

15~---L----L---~----~--~----~

1.5

2.0

2.5

3.0

3.5

4.0

4.5

Transfer thickness/Final thickness

Fig. 7 The allowable range of transfer thickness for TMCP Conventional Control

YES Calculation 9 R (n). HRF) Plate

H 9

FM

to

: : : :

HRF R F b. tC

: : : :

thickness Plate temperature t ime the time when the preceding plate may complete finish rolling transfer thickness roughing mill finishing mill time for water cooling at shower

Fig. 10 The flow of " KCIP"

Fig.9 A comparison of " KCIP" and conventional control 592