cilindros_laminacion2.pdf

7/29/2019 cilindros_laminacion2.pdf

1/6

Journal of Materials Processing Technology 162163 (2005) 585590

Adaptive calculation of deformation resistance model of onlineprocess control in tandem cold mill

J.S. Wang a, , Z.Y. Jiang a, A.K. Tieu a, X.H. Liu b, G.D. Wang ba Faculty of Engineering, University of Wollongong, NSW 2522, Australia

b The State Key Laboratory of Rolling and Automation, NortheasternUniversity, Shenyang 110004, PR China

Abstract

The strip deformation resistance is an important factor for tandem cold mill control. The experiment data of strip yield stress measured in

the laboratory cannot satisfy the requirement of accuracy for tandem cold mill online control. In this paper, an adaptive calculation method forimproving accuracy of strip deformation resistance model is built up. Using measured rolling force of online control, the inverse calculation

method of deformation resistance is conducted for tandem cold mill control. The adaptive learning coefficients of deformation resistance

model can be determined with exponential smoothing. The deformation resistance model and Bland-Ford-Hill rolling force formula are used

for the calculation. The influences of plastic deformation zone, entry and exit elastic deformation zones in the roll bite on metal deformation

resistance are considered in the models. The practical application verifies that the accuracy and stability of calculated results can satisfy well

the need of online process control of tandem cold mill.

2005 Elsevier B.V. All rights reserved.

Keywords: Deformation resistance model; Adaptive learning; Tandem cold mill; Inverse calculation; Rolling force

1. Introduction

Tandem cold rolling is that a coil is rolled continuously be-

low the recrystallization temperature of metal strip on several

stands mill [1,2]. Deformation resistance is the important ma-

terial and control parameters for tandem cold strip rolling. It

is also a basic factor for rolling force calculation. Rolled strip

thickness accuracy is affected by strip deformation resistance

calculationbecause of the influence of deformation resistance

on the calculation model accuracy of rolling force [39]. The

steel strip deformation resistance is expressed by yield stress

which can be measured through compression-testing in labo-

ratory. Theflow stressmodelfor metal is obtained by themea-sured data. But, themetalflow stressmodelcannot be used for

online control of tandem cold mill directly because thedata of

flow stress is obtained in the condition of simple stress. How-

ever, three-dimensional plastic deformation of metal hap-

pens in the condition of complicated stresses for practical

Corresponding author. Tel.: 61 2 42214809; fax: +61 2 42213101.E-mail address: [email protected] (J.S. Wang).

cold rolling. Therefore, the model of deformation resistance,

which can represent metal feature of three-dimensional plas-

tic deformation correctly, should be used for online control

in order to improve the accuracy of rolling force.

Many factors affect metal deformation resistance, such as

friction, lubrication and so on [1012]. However, the correct

description of the model for material properties is difficult

because the control model by itself cannot include all these

factors. In this paper, adaptive learning calculation is adopted

for improving the model calculation accuracy of strip de-

formation resistance using online measured rolling force for

practical tandem cold mill.

2. Mathematical models of process control

2.1. Configuration for deformation zone

There are plastic deformation zone, elastic compression

zone at the entry of deformation zone and elastic recovery

zone at the exit of deformation zone in the roll bite, as showed

in Fig. 1.

0924-0136/$ see front matter 2005 Elsevier B.V. All rights reserved.

doi:10.1016/j.jmatprotec.2005.02.126


2/6

586 J.S. Wang et al. / Journal of Materials Processing Technology 162163 (2005) 585590

Fig. 1. Deformation zones of cold rolled strip.

where Feinis the deformation rolling force at the elastic

entry zone, Fp is the rolling force of the plastic deformation

zone, Feout is the rolling force at elastic exit zone, hin is the

entry strip thickness, hPin is the entry strip thickness in plastic

deformation zone, hout is the exit strip thickness, hPout is the

exitstrip thickness at plastic deformation zone, kin is the entry

strip deformation resistance, km is the average deformation

resistance, kout is the exit strip deformation resistance, inis the back tension, out is the front tension, Sin is the entry

elastic deformation zone, Sp is the plastic deformation zone,

Sout is the exit elastic deformation zone.

2.2. Deformation resistance model

Considering elastic deformation of the entry and exit of

roll, the strip entry deformation resistance Eq. (1), exit defor-

mation resistance Eq. (2) and average deformation resistance

Eq. (3) are obtained according to the different deformation

zones between the roll and strip [13]. Two adaptive learning

coefficients Ck0 and Cn are employed for the modification

of the influence of material properties and reduction on av-

erage deformation resistance. The adaptive learning includes

additive term and exponential term modifications according

to Ck0 and Cn, respectively.

kin =2

3Ck0 k0

2

3ln

100

100 rtin+ 0

cnn(1)

where rtin =h0 hin

h0 100

kout =2

3Ck0 k0

2

3ln

100

100 rtout+ 0

cnn(2)

where rtout = h0houth0 100

km =2

3Ck0 k0

2

3ln

100

100 rtm+ 0

cnn(3)

where rtm =

h0 hmh0

100, hm =

(1

)hin +

hout

.

In the above models, kin is the entry strip deformation resis-

tance, kout the exit strip deformation resistance, km the strip

average deformation resistance, h0 the original strip thick-

ness, hm the average thickness in deformation zone, hin the

entry strip thickness, hout the exit strip thickness, rtin the en-

try zone strip reduction, rtout the exit strip reduction, rtm the

average total reduction, the thickness influence coefficient,

k0, 0, n, are model coefficients.

2.3. Rolling force and roll flatten models

Bland-Ford-Hill model equation (4) is used to calculatethe rolling force in tandem cold rolling [14]. The total rolling

force includes rolling forces of plastic deformation zone, en-

try and exitelastic deformation zones.Total rolling force [14]:

F = Fp + Fe (4)Rolling force in plastic deformation zone:

Fp = QF(km )b

R(hin hout) (5)

where = in + out

QF = 1.08 1.02r + 1.79r1 r

Rhout

(6)

Rolling force in elastic deformation zone:

Fe = Fein + Feout

= 23

1 2

Ekm

hout

hin hout(km )b

R (hin hout)

(7)

where Fp is the rolling force of plastic deformation zone,

Fein the rolling force of elastic entry deformation zone, Feout

rolling force of elastic recovery deformation zone, b the strip

width, in the back tension, out the front tension, the fric-

tion coefficient between the roll and strip, R the flatten rollradius, QF the influence coefficient of friction, r the reduc-

tion at each pass, the Poisson ratio, Ethe Youngs module,

the influence coefficient of back tension, the influence

coefficient of front tension.

Strip deformation resistance will increase significantly

due to work-hardening in cold rolling. So, the roll flatten

radius becomes larger and the contact arc between the roll

and strip increases, which affects the rolling force signifi-

cantly. Therefore, Hitchcock model Eq. (8) is used to calcu-

late roll flatten radius [15]. The coupling calculation between


3/6

J.S. Wang et al. / Journal of Materials Processing Technology 162163 (2 005) 58559 0 587

the rolling force and roll flatten radius can be carried out by

iterative or explicit computation [16].

Roll flatten radius model [15]:

R = R

1 + CRFheq

(8)

where CR =16(1 2)

E

equivalent reduction:

heq = (

heout +

hp +

hein)2

(9)

heout =

1 2

Ehout(kout out)

hp+hein = hin hout + 1

2

E hout(kout tout)where R is the roll flatten radius, R the original roll radius,and Fthe rolling force.

3. Adaptive learning of deformation resistance model

3.1. Computation method

The function of adaptive learning of strip deformation

resistance model can improve the model calculation accu-

racy through learning coefficient, which describes the dif-

ference between the calculated results and measured values.

The learning coefficient of preceding coil rolling is adopted

for model setup calculation of next same specification coil

rolling as shown in Fig. 2. The feature of adaptive learning

is completed by level-1 basic automatic control and level-2

process control together.

Using measured rolling force the deformation resistance

of cold rolled strip can be calculated through rolling force

model because it is impossible to measure the strip defor-

mation resistance online by sensors. The method that the

Fig. 2. The types of data sampling and adaptive learning.

deformation resistance is calculated by rolling force model

employing measured values indirectly is called inverse cal-

culation. Though the deformation resistance is not measured,

the inverse calculated value is considered as true value.

3.2. Deformation resistance inverse calculation

The measured rolling force and other parameters are used

for rolling force model Eq. (4) and set X =

kmiback, Eq.

(10) can be obtained:

2

3bmea

Rmdlhimea

1 2

E

hmeai

hmeaiX3

+ bmea

Rimdl

hmeai QFiX2 2

3{imeai imeai1 }

bmeaRmdli h

meai

1 2

E

hmeai

himea X

+{iimea imeai1 }bmea

Rimdl

hmeai QFiFmeai = 0(10)

where

QFi = 1.08 1.02rmeai + 1.79rmeai

1 rmeai mdli

Rmdlihmeai

(11)

where hmeai = hmeai1 hmeai , rmeai =hmeai1hmeai

hmeai1. Here kbackmi

is the inverse calculation value of deformation resistance,

Fmeai the measured rolling force, h

meai the measured strip

thickness, meai the measured tension, bmea the measured strip

width, mdli the friction modelcalculation value, Rmdli theroll

flatten model calculation value, i the stand number of tandem

cold mill.

Fmeai ,hmeai ,

meai and b

meacanbe measured by differentsen-

sors. mdli and Rmdli are obtained by calculation of friction

model and roll flatten model using actual parameters in the

models. Eq. (10) is a higher ordered equation with inverse

calculation value of deformation resistance as independent

variable and it can be solved by Newton-Raphson iterative

calculation.

3.3. Adaptive learning of deformation resistance model

The calculated deformation resistance values are consid-

ered as actual values and used for average deformation

resistance model Eq. (3) after inverse calculation. Eq. (12)

can be obtained after logarithmic transformation for Eq. (3).

ln(kbackmi ) = ln

23

Ck0 k0

+Cnn ln

23

ln100

100 rtmi+ 0

(12)


4/6


Eq. (12) can be written as a linear equation

Yi = a0 + a1Xi (13)

where Xi = ln

23

ln 100100rtmi + 0

is a known value and

the unknown variable is Yi=

ln(kbackmi ) which includes the

two adaptive learning coefficients of a1 = Cnn and a0 =ln( 2

3Ck0 k0).

Eq. (13) is a linear equation, and the deformation resis-

tance is as an independent variable. The coefficients a0 and

a1 can be calculated by linear regression method using each

stand measured (X1,Y1) (X3,Y3) for five stands tandem coldmill, and the adaptive learning coefficients Ck0 =

3 ea02k0

and

Cn = a1n can be obtained from a0 and a1.

3.4. Update of adaptive learning coefficient

The new adaptive learning coefficients are obtained by ex-ponential smoothing calculation using the calculated coeffi-

cientsof thecurrent rolledsteelcoil andpreceding rolledsteel

coil as shown in Eqs. (14) and (15). The criteria check will be

carried out for the calculation coefficients, as shown in Eqs.

(16) and (17). The new adaptive learning coefficients will be

used for online setup calculation of the next coil rolling.

Cnextk0 = (1 Ck0 )Coldk0

+ Ck0 Ccal

k0(14)

Cnextn = (1 Cn )Coldn + Cn Ccaln (15)

Clow

k0 Cnext

k0 Cupper

k0 (16)

Clown Cnextn Cuppern (17)

where Cnextk0 , Cnextn are the learning coefficients for next coil

model setup calculation, Coldk0

,Coldn the learning coefficients

for preceding coil model setup calculation,Ccalk0

, Ccaln the

learning coefficients for current coil model setup calcula-

tion, Clowk0

, Clown the low limit for learning coefficients,Cupperk0

,

Cuppern the upper limit for learning coefficients and Ck0 ,

Cn the smoothing factors.

4. Practical application

4.1. Working condition

The adatptive learning of deformation resistance model is

applied for online process control of five stands tandem cold

mill,asshownin Fig.3. The sensors arearrangedin therolling

line. Rolling force, tension, strip speed and strip thickness

can be measured by load cell, tension meter, velocity meter

and gauge meter, respectively. The technical parameters of

experiments are shown in Table 1.

Fig. 3. 5 Stands tandem cold mill and sensors.

Table 1

Experiment technical parameters of tandem cold mill

Name Parameter

Work roll diameter (mm) 550

Work roll length (mm) 1220

Backup roll diameter (mm) 1320

Backup roll length (mm) 1092

Steel grade of rolled strip SPHC, Stw23

Strip width (mm) 550900

Strip thickness (mm) 1.53.5Reduction (%) 2040

Maximum motor power (kW) 3800

4.2. Data processing

There are two kind adaptive learning modes for strip de-

formation resistance calculation. One is low speed adaptive

learning, the other is high speed adaptive learning. Each type

learning is related to the necessary rolling speed. A speed

of 400 m/min is defined as the speed border of high speed

adaptive learning and low speed adaptive learning, as shown

in Fig. 4.A point indicates the beginning time for data sampling of

low speed. The sampling starts when the head of the delivery

strip passes the shear on rolling line. B1 is the beginning time

for data sampling of high speed. The sampling begins when

the acceleration completes in 5 s. During rolling, sampling

data of the higher speed has the priority for adaptive learning

calculation. It can be seen that the rolling speed of B2 point is

higher than that at B1 point. In this case, the adaptive learning

coefficient calculated by the sampling data of B2 point will

replace the coefficient at B1 point.

The sampling interval is 0.5 s and sampling number is

10 for each sampling both low speed and high speed datacollection.

Fig. 4. Speed schedule of tandem cold mill.


5/6

J.S. Wang et al. / Journal of Materials Processing Technology 162163 (2005) 585590 589

Fig. 5. Processes of model adaptive learning.

The sampling data must be checked before it is used for

modeladaptive learning. The stability of measured values,forexample rolling force, tension, roll speed and strip thickness,

will be identified. The rules to identify the data are shown

in Eqs. (18)(20). For strip thickness, the reference value

of gauge meter measurement should be same as the setup

thickness for stand rolling. The data will be ignored if the

stability of data cannot meet the requirement.

Fimax FiminFisetup

< KiF-limit (18)

Timax TiminT

i

setup

< KiT-limit (19)

VRimax VRimax VRiminVRisetup

< Kiv-limit (20)

whereFimax, Ti

max, VR are the maximum values of 10 sam-

pled data for rolling force, total tension and rolling speed,

respectively. Fimin, Ti

min, VR are the minimum values of 10

sampled data for rolling force, total tension and rolling speed,

respectively. Fisetup,Ti

setup, VR are model setup target values

for rolling force, total tension and rolling speed, respectively.

i is the stand number 15.

The last step for data processing is the average calculation

for the 10 sampled data. The average of all measured values

will be used for model adaptive learning calculation. The

process of model adaptive learning is shown in Fig. 5.

4.3. Results analysis

Comparisons of calculated rolling force with measured

values are shown in Figs. 6 and 7 for without and with appli-

cation of adaptive learning of deformation resistance model.

The diagonal lines in Figs. 6 and 7 indicate that the calculated

rolling force is same as the measured values. According to

the analysis of relative error x and mean square deviation

Fig. 6. Comparison of calculated and measured rolling forces without adap-

tive learning of deformation resistance.

Fig. 7. Comparison of calculated and measured rolling forces with adaptive

learning of deformation resistance.

of 250 coils cold rolled strip. It can be seen that the calcula-tion accuracy of rolling force is improved by introducing the

adaptive learning of the deformation resistance model.

5. Conclusion

A method for improving calculation accuracy of deforma-

tion resistance model is presented. The inverse calculation of

thedeformation resistance and the adaptive learning model of

tandem cold strip rolling are built based on calculated rolling

force using the measured rolling force. The difference be-

tween the calculated and actual strip deformation resistancecan be compensated by the model adaptive learning coeffi-

cients. The accuracy of rolling force calculation can be im-

proved through corrected strip deformation resistance model.

Practical application of online process control of five stands

tandem cold mill verifies the effectiveness of this method.

Acknowledgement

This work was supported by the Australian Research

Council (ARC).


6/6


References

[1] T.S. Bilkhu, Dynamic control of tension, thickness and flatness for

a Tandem Cold Mill, AISE Steel Technol. 78 (10) (2001) 49

54.

[2] D.D. Wang, A.K. Tieu, F.G. De Boer, B. Ma, W.Y.D. Yuen, Toward

a heuristic optimum design of rolling schedules for tandem cold

rolling mills, Eng. Appl. Artif. Int. 13 (4) (2000) 397406.[3] Yoshikazu, Modernization of gauge control system at Sumitomo

Wakayama 5-stand cold mill, Iron Steel Eng. 8 (1999) 4650.

[4] K. Tomohiro, Technologies for high speed rolling and gauge con-

trol in cold tandem mill for ultra-thin gauge strip, Kawasaki Steel

Technical Report 37 (10) (1997) 2532.

[5] J. Larkiola, P. Myllykoski, J. Nylander, Prediction of rolling force

in cold rolling by using physical models and neural computing, J.

Mater. Process. Technol. 60 (6) (1996) 381386.

[6] S.Q. Yu, Y.Q. He, Z. Gu, Harmonious distribution method of multi-

load, Iron Steel 31 (7) (1996) 4851.

[7] R.N. Venkata, G. Suryanarayana, A set-up model for tandem cold

rolling mills, J. Mater. Process. Technol. 116 (10) (2001) 269

277.

[8] S. Cho, M. Jang, S. Yoon, A hybrid neural-network/mathematical

prediction model for tandem cold mill, Comp. Ind. Eng. 33 (12)(1997) 453456.

[9] C. Ozsoy, et al., Optimum scheduling of a hot rolling process by

nonlinear programming, Can. Metall. Quart. 31 (3) (1992) 217224.

[10] Z.Y. Jiang, H.T. Zhu, A.K. Tieu, Effect of rolling parameters on cold

rolling of thin strip during work roll edge contact, J. Mater. Process.

Technol. 140 (2003) 535541.

[11] Z.Y. Jiang, A.K. Tieu, A 3-D finite element method analysis of cold

rolling of thin strip with friction variation, Tribol. Int. 37 (2) (2004)

185191.

[12] H. Pawelski, Friction inhomogeneities in cold rolling, J. Mater. Pro-

cess. Technol. 125 (9) (2002) 392397.

[13] J.S. Wang, Principle and Application of Flying Gauge Change for T-

WRS&C Tandem Cold Mill, Ph.D. Thesis, Northeastern University,

Shenyang, 2002.

[14] C.C.Y. Lin, M. Atkinson, C.J. Cinkowski, New rolling force modifi-

cation equation for the bland and ford cold rolling model, in: Interna-

tional Symposium on Information Storage and Processing Systems,

American Society of Mechanical Engineers/Manufacturing Engineer-

ing Division, New York, USA, 1996, pp. 355363.

[15] J. Yang, Rolling Mathmetical Models, Metallurgy Industry Press,

Beijing, 1993.

[16] J.S. Wang, Z.J. Jiao, C. Lu, X.H. Liu, G.D. Wang, Explicit express

of rolling force taking elastic deformation into account of strip, in:

Proceedings of the Fourth International ESAFORM Conference OnMaterial Forming, Liege, Belgium, 2001.

Documents

cilindros_laminacion2.pdf