Analysis of Startup Process and Its Optimization for a Two ...

Research ArticleAnalysis of Startup Process and Its Optimization for aTwo-Stand Reversible Cold Rolling Mill

Guangming Liu1 Yugui Li1 Qingxue Huang1 Xia Yang1 and Aimin Liu2

1Heavy Machinery Engineering Research Center of the Ministry of Education Taiyuan University of Science and TechnologyTaiyuan 030024 China2Cold Rolling Plant Jinan Iron and Steel Group Co Ltd Jinan 250101 China

Correspondence should be addressed to Guangming Liu brightliu2008126com

Received 20 May 2017 Accepted 28 August 2017 Published 10 October 2017

Academic Editor Marco Rossi

Copyright copy 2017 Guangming Liu et alThis is an open access article distributed under the Creative CommonsAttribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Dynamic characteristic analysis of a two-stand reversible cold rollingmill in the startup process was carried outThedelay algorithmof the interstand thickness was proposed A new method combined with the accelerated secant and the tangent methods wasestablished to solve the simultaneous equations The thickness and interstand tension transition processes with different statictension establishing processes were analyzed Both mills were operated under constant rolling force control mode in the aboveprocess The results show that the strip thickness in the rolling gap reduces in the static mill screwdown process The entry standruns inversely to establish the static interstand tension This area becomes an abnormal thickness reduction area of the incomingstrip It results in several abnormal interstand tension increases in the subsequent startup process The tension increase leads to animpact force on the strip that is themain reason of the strip breakage in the startup process So the static tension establishing processwas optimized and the interstand tension fluctuation and the strip breakage accidents both reduced significantly The results arebeneficial to the startup process of the two-stand reversible cold rolling mill

1 Introduction

Two-stand reversible cold rolling mills a typical layout ofwhich is shown in Figure 1 are also called compact coldmill (CCM) It was specially developed for moderate scalecold rolling plant Strip breakage occurs frequently duringthe initial commission phase of some CCM which hasnot been solved effectively This phenomenon is the mostsevere when starting rolling or the strip running about aninterstand distance which is called the startup process Inour mill about 30 strip breakage accidents occurred in thisstep in the most serious month After taking some improvingmeasures the accidents caused by startup process still takeup about one-fifth except the reasons of electric technologyand incoming material It is very difficult to investigate thecauses in the actual rolling mill while simulation is a feasiblemethod to analyze the composite control system and is alsoan indispensable tool to establish new control systems oroperation schemes

The thickness control and tension establishing process ofa five-stand tandem cold rolling mill (TCM) were analyzedusing a linearization physical model based on dynamictension differential equations and the thickness delaymethodby PHILLIPS [1] It is the origin of computer simulationof continuous rolling processes This method was usuallyused to analyze the automatic gauge control (AGC) systemsof TCM [2] The steady-state dynamic behavior [3 4] anddisturbance rejection characteristics [5] of AGC systemswereinvestigated It was also used for transient property simu-lation of continuous rolling mills such as transient rollingcharacteristics [6] and control system performance [7] Andthe interactions between interstand tension and thicknesscontrol [8] steady-state characteristic [9] and process sensi-tivity [10 11] of the transient processes were obtained as well

The above simulation processes were all carried out usingthe linearization algorithmThis linear approximation repre-sents very well the system in simulation for small variationsof process variables around the operation points However a

HindawiAdvances in Materials Science and EngineeringVolume 2017 Article ID 8715340 10 pageshttpsdoiorg10115520178715340

2 Advances in Materials Science and Engineering

2 recoiler 1 recoiler Pay-o reel

1 stand

Rolling direction

Laser speed ickness gauge

2 stand

Hydraulic screwdown

Tension meter

Figure 1 Typical two-stand reversible cold rolling mill

big error would occur if the parameters variations are largein other words the linearization algorithm is not proper forsimulating large disturbances Then the nonlinear algorithmwhich was proposed in around 1970s with the developmentof computer should be a good choice The transient charac-teristics of threading acceleration deceleration and tail-outprocesses with and without AGC [12] were analyzed usingthe nonlinear method And this method was also extendedto strip crown control and rolling force analysis with a two-dimensional dynamic metal model [13]

For the thickness deviation is large at the stand positionin the steady tension establishing process of some CCMIn the present study at first the dynamic characteristicanalysis program was developed using nonlinear algorithmsin which the formulas of the rolling theory are numericallycalculated directly without any approximation Second thetransient process in the startup process was analyzed andthe influence factors on the rolling stability were examinedin detail Finally the optimization of the running status ofthe CCM startup process was presented and carried out inthe production line The running status of the new startupstrategy was discussed

2 Physical Equations and Calculation Methods

The mathematical model used for dynamic characteristicanalysis includes the intrastand equations such as springequation rolling force equation forward slip equation andinterstand equations such as tension continuity thicknesscontinuity and tension differential equations connectingthe adjacent stands [4] The calculation methods used inthe dynamic characteristic analysis include the thicknessdelay algorithm of each stand the roll gap and thicknesscalculation method under constant rolling force mode andthe special solving method of dynamic continuous rollingstatus The connections jointing the adjacent stands involvesimulation of time delayed transport of thickness from onestand to the next and the calculation of interstand tension

21 Spring Equation As the rolling mill is not perfectly rigidthe exit thickness can be expressed by the elastic equation of

the rolling mill

ℎ = 119878 + 119875119870119898

(1)

22 Rolling Force Equation The Hillrsquos simplified form ofBland-Ford equation is selected as the rolling force equationin this study

119875 = 119861119896 [1198771015840 (119867 minus ℎ)]12

119876119901119899119905 (2)

with 119896 = 1198861(120576 + 1198862)1198863 120576 = 04120576119867 + 06120576ℎ 120576119867 = 1 minus 1198671198670 120576ℎ =1minusℎ11986701198771015840 = 119877[1+1198620119875(119861(119867minusℎ))]119876119901 = 108+179120576119891(1198771015840119867)12minus102120576 and 120576 = (119867minusℎ)119867 119899119905 = 1minus[(1minus120583119905)119905119891+120583119905119905119887]119896

23 Forward Slip Equation The width spread is small in thecold rolling process and can be ignored The neutral angle issmall as the deformation zone is narrow The ratio of workroll diameter (119863 119863 = 2 lowast 119877) to strip exit thickness (ℎ) is farmore than 1 So the D Dresden [8] forward slip equation isused

119904ℎ =1198771015840

ℎsdot 1205742 (3)

with 120574 = (ℎ1198771015840)12 tan((ℎ1198771015840)12 sdot 1198671198992) 119867119899 = 1198671198872 minus 1(2119891) ln(119867ℎ sdot (1 minus 119905119891119896ℎ)(1 minus 119905119887119896119867)) 120572 = (Δℎ1198771015840)12119867119887 =2 sdot (1198771015840ℎ)12 arctan((1198771015840ℎ)12 sdot 120572)

24 Interstand Tension Equation The interstand strip thick-ness is uneven due to the interstand tension establishingprocess So the interstand tension is solved by integrating thetension differential equation for a variable section [14] Thedifferential equation is related to the difference between theexit speed of the strip from one stand and entry speed to thesubsequent stand Thus the forward tension is obtained by

Advances in Materials Science and Engineering 3

the stress strain relationship and the back tension is obtainedby the equalization principle of the interstand tension

d119905119891119894 =119864

[ℎ119894 (sum119899119895=1 119897119895ℎ119895)] int (V119867119894+1 minus Vℎ119894) d119905

119905119887119894+1 =ℎ119894119867119894+1

sdot 119905119891119894

(4)

25 Delay Algorithm of InterstandThickness For steady-stateanalysis we have ℎ119894 = 119867119894+1 but in the dynamic characteristicanalysis process the exit thickness of the 119894th stand ℎ119894 equalsthe entry thickness of the 119894+1th stand only when the positionwith thickness ℎ119894 reaches the 119894 + 1th stand The point leavesthe 119894th stand at time 120591119899 with strip thickness ℎ119899119894 and exit speedV119899ℎ119894 The running distance will be 119871119899119905119894 = V119899ℎ119894d120591 at the time120591119899+1 = 120591119899 + d120591 when it moves with this speed for d120591 Thenthe exit thickness and exit speed will change to ℎ119899+1119894 and V119899+1ℎ119894 respectively due to the change of tension or other factorsat time 120591119899+1 Thus the distance from the 119894th stand of thispoint is 119871119899+1119905119894 = 119871119899119905119894 + V119899+1ℎ119894 d120591 after d120591 and at time 119898 thedistance is 119871119898119905119894 = sum119898119895=119899 V

119895

ℎ119894d120591 If 119871119898119905119894 is equal to or larger than the

interstand distance 119871 119894 it is considered that the point reachesthe 119894+1th standTherefore the interstand delay thickness canbe obtained in the converse way while ℎ119894 and Vℎ119894 are put intothe delay table [15] In order to acquire the entry thickness ofthe 119894 + 1th stand119867119894+1 at time119898 we only need to find out thetime that the point leaves the 119894th stand and obtain ℎ119894

26 Solution of Simultaneous Equations In the simulationprocess the known variables are entry thickness and rollingforce and the unknown variables are exit thickness ℎ119894 androll gap 119878119894 respectively since the mill is under constant forcecontrol mode

The entry thickness is inquired from the delay tableand the rolling force is the preset value The exit thicknessis obtained through solving the rolling force equation bythe accelerated secant method or tangent method and then

the roll gap is obtained by the spring equation Howeverthe tangent method is stringent conditional convergenceand highly sensitive to the initial solution In opposite thesecant method requires two better initial solutions and itsconvergence speed is slower than that of the tangent methodSo a method combined by the accelerated secant and thetangent methods is proposed as is shown in Figure 2

First a better initial solution for the tangent method isobtained by the accelerated secant method then the tangentmethod is executed based on the above initial solution toachieve a better approximate solution The rolling forces1198751119894 and 1198752119894 are calculated corresponding to two given stripthicknesses ℎ1119894 and ℎ

2119894 respectively and a secant of the plastic

curve is obtained by joining point (ℎ1119894 1198751119894 ) and point (ℎ

2119894 1198752119894 )

respectively which meets the constant rolling force curve atpoint (ℎ3119894 119875119894) Then the rolling force 1198753119894 with thickness ℎ3119894 canbe obtained and the point (ℎ3119894 119875

3119894 ) is the solution of the first

stepReplacing point (ℎ1119894 119875

1119894 ) with point (ℎ3119894 119875

3119894 ) a new solu-

tion can be obtainedThe calculation iterates until |119875119899119894 minus119875119894| lt1205761 where 1205761 is the convergence limit of the secant methodThe point (ℎ119899119894 119875

119899119894 ) is the required approximate solution

The secantrsquos slope is

119870119899minus1119892119894 =(119875119899minus1119894 minus 119875119899minus2119894 )(ℎ119899minus1119894 minus ℎ119899minus2119894 )

(5)

The new solution for the strip thickness is

ℎ119899119894 =(119875119894 minus 119875119899minus1119894 )

119870119899minus1119892119894+ ℎ119899minus1119894 (6)

Since the above approximate solution is obtained takingpoint (ℎ119899119894 119875

119899119894 ) as the initial solution of the tangentmethod and

the equation solution with tangentmethod is carried outThetangentrsquos slope is obtained by the partial differential of (2) therolling force model

119870119899119902119894 =120597119875119894120597ℎ119894

=minus (119875119867) minus (061198863 (120576 + 1198862)) (1198671198670) (1119899119905) minus (12120576) (1198771198771015840) minus (1791198912119876119901)radic1198771015840119867 (1 + 1198771198771015840) + 102119876119901

1 minus ((1198771015840 minus 119877) 2119877) (1 + (179120576119891119899119905)radic1198771015840119867)

(7)

The new solution for the strip thickness by the tangentmethod is

ℎ119899+1119894 =(119875119894 minus 119875119899119894 )119870119899119902119894

+ ℎ119899119894 (8)

Replacing point (ℎ119899119894 119875119899119894 ) by point (ℎ119899+1119894 119875119899+1119894 ) a new

solution can be obtained The calculation iterates until |119875119898119894 minus119875119894| lt 1205762 where 1205762 is the convergence limit of the tangent

method and the point (ℎ119898119894 119875119898119894 ) is approximate to the real

solutionSubstituting (8) into (1) the rolling gap is

119878119894119898 =

(119875119894 minus 119875119898minus1119894 )119870119898minus1119902119894

+ ℎ119898minus1119894 minus119875119898119894119870119898119894

(9)

27 Solving Step Among the above mathematic equationsand calculation methods the solution of the simultaneous


Plastic curve of strip Spring curve of mill

ickness h (mm)

Rolli

ng fo

rce P

(N)

ℎ1

iℎ2

iℎ4

iℎ5

i

ℎn

iℎ3

i

Pi

Hi

P1

i

P3

i

P2

i

P4

i

P5

i

Sn

i

Figure 2 Schematic of simultaneous solution of the elastic-plasticity curve

equations is essentially steady In fact the rolling forceequation forward and backward slip equations frictioncoefficient and spring equations are all steady However inthe dynamic state the steady equations and algorithms ofeach stand are correlative for the connection of the thicknessdelay equation and tension differential equation between theadjacent stands So the rolling process simulation needs tosolve huge combination equations including many algebraicequations of each stand the interstand tension differentialequation and the thickness delay equationThen the parame-ters of each stand can be obtained by solving the combinationequations at time 1205911 Taking the above parameters as constantthe parameters at new time 1205912 = 1205911 + d120591 are obtainedby resolving the combination equations Then the variationlaws of each parameter namely the simulation results areobtained with this method

However it is very difficult to solve the combination equa-tions So here a special calculation method which includestwo steps is adopted [15] First step the parameters of eachstand including 119875(1)119894 119867(1)119894 V(1)119894 119905

(1)119891119894 and 119905(1)

119887119894are constant at

time 1205911 then the parameters including 119878(1)119894 ℎ(1)119894 119904(1)ℎ119894 119904(1)119867119894 119891

(1)119894

V(1)ℎ119894 and V(1)119867119894 are obtained by the calculation of steady

equations Second step assume the above parameters to beconstant in a small time interval then the tension incrementat time 1205912 = 1205911 + d120591 can be obtained from the tensiondifferential equation the interstand tension can be obtainedby 119905(2)119891119894

= 119905(1)119891119894+ d119905(1)119891119894

A new calculation process starts at time 1205912 = 1205911 + d120591The entry thickness of each stand changes from 119867(1)119894 to119867(2)119894 for the thickness delay effect and the interstand tensionchanges as well Then the parameters of each stand such as119878(2)119894 ℎ

(2)119894 119904(2)ℎ119894 119904(2)119867119894 119891

(2)119894 V(2)ℎ119894 and V(2)119867119894 are recalculated The

parameters variation process of each stand can be obtainedwith this process being executed successively This is theimplementation method of dynamic characteristic analysisfor the continuous rolling process

3 Running Status Analyses

In order to find out the causes that result in strip breakagethe running status should be analyzed Then the causes willbe evaluated with the established simulation program andthe improvingmeasurewill be proposedThe forward tensionof the exit stand and the back tension of the entry standare tracking controlled by speed of the uncoiler and recoilerrespectively So the influences of these two tension variationsare not considered in this simulation process

31 Startup Process Analyses The original designed startupprocess of this CCM is as follows threading completed rarr alower rolling force reachedrarr a static tension reachedrarr thepreset rolling force reachedrarr the preset tension reachedrarrrolling startup The screwdown control mode the interstandtension rolling force and mill speed variation processes ofthe startup process from Process Data Acquisition (PDA)system are shown in Figure 3(a) The rolling gap is set to 6to 12mm which is larger than the original strip thickness inthe threading stage that is to say the rolling mills do notwork and there is no thickness reduction in this stage Whenthe strip has passed the rolling mills and the recoiler haswinded 3 to 4 circles a small tension between the uncoilerand recoiler has been established and the threading processcompleted Then the stands under force control mode screwdown to a lower rolling force which is about 4000 kN and thestrip was forced by the work roll to contact with the tensionmeter resulting in a small static tension Next the rollingstands both continue screwing down to the preset rollingforce before millrsquos startup Afterward the entry stand movesinversely with a low speed in order to establish the interstandtension In this process the entry stand hasmade a short-timeinverse rolling process whichmakes the strip become thinneron the entry side of the entry stand as is shown in Figure 3(b)[15]

After the above preparing process the mills start rollingThe interstand tension is controlled by the speed of the entrystand in the subsequent startup process On the entry sideof both stands the strip thickness is the same as the originalthickness at this moment except the thickness reduction areaof the entry stand as is shown in Figure 3(b)Whenmills startto run the reduction area firstly enters the entry stand whichis still under force control mode It is to say that the entrystand will screw down to reach the preset rolling force whichmakes the thickness reduction area even thinner as is shownin Figure 4(b) Meanwhile the mass flow rate of the entrystand reduces which will cause the first interstand tensionincrease as is shown in Figure 4(b) The tension increase willcause an impact force on the strip If the strip is thin or thereare some defects strip breakagewill occur It is consistent withthe strip breakage accident occurring at the moment of millsstartup

The time interval between the adjacent sample pointsis 003 s The entry stand changed from force control modeto position control mode after running for about 15 s as isshown in Figure 4(a) while the exit stand is still under forcecontrol mode because the exit thickness has not reached thetarget thickness So the exit stand will screw down to reach


Entry standExit stand


Operation sideDrive side

Preset rolling force reached

Entry stand running inversely

Inter-stand tension reached

HG

C co

ntro

l mod

eH

GC

cont

rol m

ode

01

Exit

stan

d

(1) Force control(0) Position control


Tens

ion

Spee

dRo

lling

forc

e

500 1000 1500 2000 2500 3000 35000Sample points

000612

(102

kN)

500 1000 1500 2000 2500 3000 35000Sample points

01

Entr

y st

and

minus505

(10minus2

ms

)

500 1000 1500 2000 2500 3000 35000Sample points

500 1000 1500 2000 2500 3000 35000Sample points

500 1000 1500 2000 2500 3000 35000Sample points

048

1216

(103

kN)

(a)

Rolling direction

ickness reduction area

Tension establishmentMill screwdown

(b)

Figure 3 Schematic diagram and PDA of interstand tension establishing process (a) schematic of interstand tension establishing process(b) tension establishing process by entry stand

the preset rolling force when the further reduced thicknessreduction area reaches the exit standAs a result the thicknessreduction area still exists on the exit thickness curve asis shown in Figure 4(b) The mass flow rate relationshipbetween the exit stand and the recoiler is destroyed whenthe thickness reduction area passes the exit stand There isa speed increase of the exit stand in order to retain thisrelationship and it causes the second tension increase asis shown in Figure 4(b) [15] It is consistent with the stripbreakage accident occurring with the strip running about aninterstand distance The mass flow rate relationship betweenthe entry stand and the exit stand is also destroyed at the same

time and then the entry stand accelerates in order to meetthe mass flow rate of the exit stand while the speed of the exitstand is the reference speed of the whole system Afterwardthe exit stand changes from force control mode to positioncontrol mode about 20 s after the target thickness is detectedby the exit gauge meter as is shown in Figure 4(a)

It can be seen from Figure 4(b) that there is one transitionof the interstand thickness while there are two transitionsof the exit thickness The first one is generated by thepreset rolling force in the tension establishing process Andthe second one is generated when the thickness transitionposition of the entry stand reaches the exit stand Due to

6 Advances in Materials Science and EngineeringH

GC

cont

rol m

ode

HG

C co

ntro

l mod

e

(1) Force control

Exit standEntry stand

0

3

6Li

ne sp

eed

(ms

)

0

1

Exit

stand

1000 2000 3000 4000 5000 6000 70000Sample points

0

1

Entr

y st

and

1000 2000 3000 4000 5000 6000 70000Sample points

1000 2000 3000 4000 5000 6000 70000Sample points

(0) Position control


(a)

Exit thicknessInterstand thickness Interstand tensile stress


Tensile stress increase



20

40

60

80

100

120

Tens

ile st

ress

(MPa

)

1000 2000 3000 4000 5000 6000 70000Sampling points

00

05

10

15

20

25

30

Exit

thic

knes

s (m

m)

(b)

Figure 4 HGC control mode thickness and tensile stress variations in the startup process (a) HGC control mode and line speed variation(b) tensile stress and thickness variation

the special interstand tension establishing mode there aretwo abnormal thickness reduction areas at the thicknesstransition position of the interstand and the exit thicknessrespectively Therefore two sharp tension increases appearwhen the thickness transition area enters the entry and exitstands respectively and the second tension increase is largerthan the first oneThese tension increases will result in impactforce to the strip The strip at stand position is relativelythinner and becomes a weak section where the strip breakagemay easily happen

32 Influence of Thickness Transition Area on Rolling StatusIt is necessary to analyze the influence of the thicknesstransition area on the rolling status in the startup processAnd the variation of strip thickness and interstand tension inthe startup stage were simulated using the model establishedabove A typical rolling schedule of the CCM to be usedfor simulation is listed in Table 1 The work roll diameter is450mm its Youngrsquos modulus is 210GPa and Poisson ratiois 03 The longitudinal stiffness of mill is 5280 kNmm Thetwo stands are identical The distance between the standsis 4500mm The strip width is 1000mm The abnormalentry thickness variation form was considered as a half cyclesinusoidal type the peak value of which is about 02mm

321 Simulation of the Original Startup Process The thick-ness and interstand tension variation process in the startupstage with the interstand tension established by the speedof the entry stand are shown in Figure 5 There are threeobvious thickness reduction areas on the interstand thicknesscurve while there are four on the exit thickness curve asis shown in Figure 5(a) The first one on the interstandthickness curve was formed in the static interstand tensionestablishing process And it was rolled by the entry standin the following startup process that caused the first tensionincrease as is shown in Figure 5(b) This interstand tensionincrease results in a rolling force decrease which makes theexit thickness of both stands reduce This is the reason ofthe first thickness reduction on the exit thickness curveWhen the first thickness reduction area on the interstandthickness curve reaches the exit stand which is still underforce control mode it will screw down to reach the presetrolling force The second thickness reduction area on theexit thickness curve formed as is shown in Figure 5(a) andit leads to the second interstand tension increase as is shownin Figure 5(b) This interstand tension increase again resultsin rolling forces decrease which makes the exit thickness ofboth stands reduceThis is the reason of the second thicknessreduction on the interstand thickness curve


Interstand thicknessExit thickness


135

140

145

150

Exit

thic

knes

s (m

m)

200

205

210

215In

ter-

stan

d th

ickn

ess (

mm

)

0 2 4 6 8 10 12 14 16 18minus2Time (s)

(a)

Fourth increase

ird increase

First increase

Second increase

100

120

140

160

180

200

Tens

ile st

ress

(MPa

)

2 4 6 8 10 12 14 16 180Time (s)

(b)

Figure 5Thickness and tension variation in the startup process with tension established by the entry stand (a) thickness variation (b) tensilestress variation

Table 1 Typical rolling schedule for simulation calculation

Stand Entry thickness119867mm Exit thickness ℎmm Forward tension 119905119891MPa Back tension 119905119887MPa Rolling speed Vmsdotminminus1

Entry stand 3000 2120 126 29 mdashExit stand 2120 1417 84 126 574

The other thickness reductions are caused by the sequen-tial effect of the previous abnormal thickness deviations Asa result four obvious sharp tension increases appear in thestartup process due to the thickness transition area as shownin Figure 5(b) [15] The first and second tension increasescorresponding to the thickness transition area reached theentry and exit stands The third tension increase is dueto the thickness deviation caused by the second tensionincrease reaching the exit stand The fourth tension increaseis due to the thickness deviation caused by the third tensionincrease reaching the exit stand Therefore the first and thesecond tension increases are relatively larger The sequentialthickness and tension deviations are relatively smaller theinfluences of which on the strip are not that severe

The simulation result is similar to the phenomenonwhichoccurred in the rolling process confirming the validity ofthe simulation method These tension increases will resultin an impact force to the strip The strip at stand positionis relatively thinner but cold worked and becomes a weaksection at these moments Strip breakage accident may easilyoccur due to these tension increases This is just the reasonthat results in the strip breakage at themoment of startup andwhen strip runs an interstand distance In order to reduce thestrip breakage accident the impact force should be decreasedor eliminated

322 Simulation of the Startup Process with Static InterstandTension Established by Exit Stand In order to avoid the

abnormal thickness reduction area formed in the static inter-stand tension establishing process due to the inverse rollingof the entry stand a new static interstand tension establishingmethod is introduced The difference from the originalmethod is that once the preset rolling force is reached theexit stand runs forward to build the interstand tension So thethickness reduction area on the entry side of the entry standis eliminated The thickness and interstand tension variationprocess in the startup stage are shown in Figure 6 The millsare still under force control mode in the subsequent startupprocess Since the abnormal thickness reduction area on theentry side of the entry stand is eliminated the first thicknessand tension fluctuations disappear as shown in Figures 6(a)and 6(b) There are two obvious thickness reduction areason both the interstand and exit thickness curve and twotension increases Although the fluctuations of thickness andtension do not disappear the numbers decrease There is stilla thickness transition area for the incoming thickness of theexit stand The interstand thickness is equal to the originalthickness before the rolling process startsOnce rolling beginsthe interstand thickness gradually becomes the exit thicknessof the entry stand so there is an incoming thickness transitionarea of the exit stand When this transition area reaches theexit stand the first tension increase occurs and it makes therolling forces of both stands reduce The exit thicknessesof both stands reduce at the same time The subsequentthickness and tension fluctuation mode and mechanisms aresimilar to the original startup process as shown in Figure 6




135

140

145

150

Exit

thic

knes

s (m

m)

200

205

210

215In

ters

tand

thic

knes

s (m

m)

2 4 6 8 10 12 14 16 180Time (s)

(a)

Second increase

First increase

100

120

140

160

180

200

Tens

ile st

ress

(MPa

)

2 4 6 8 10 12 14 16 180Time (s)

(b)

Figure 6 Thickness and tensile stress variations in the startup process with tension established by the exit stand (a) thickness variation (b)tensile stress variation

4 Application and Discussions of NewStartup Strategy

It can be obtained from the above analyses that the thicknesstransition area is the main reason that causes the sharpinterstand tension increases and the sharp interstand tensionincreases result in the strip breakage in the startup stage Theabnormal thickness reduction area at the thickness transi-tion area is eliminated by changing the interstand tensionestablishing mode So the thickness and tension fluctuationquantity decrease obviouslyThis illustrates that the abnormalthickness reduction area can make the thickness and inter-stand tension fluctuations much more severe Furthermorethe abnormal thickness reduction area is thinner than anyother position on the strip and it is the weak section

In the actual rolling process the first two tensionincreases are severe and they are both caused by the thicknesstransition area of the entry stand due to the special interstandtension establishing mode In order to avoid strip breakagein the startup process the abnormal thickness reductionarea should be decreased or eliminated In other words thestartup mode should be modified or changed It is difficultto change the startup process entirely as the practical rollingmill requires a complicated control program modificationwhich might affect the productivity So taking some measureto decrease the thickness reduction amount could be afeasible way The mill is still under force control mode Thenreducing the preset rolling force in the tension establishingstage becomes a proper choice without changing the controlsystem

For the startupmode is not allowed to change entirely thestartup process ismodified as shown in Figure 7(a) threadingcompleted rarr a minimize rolling force reached rarr statictension reached rarr some preset rolling force reached rarr thepreset tension reached rarr the preset rolling force reachedrarr rolling startup In the field application process the preset

rolling force for interstand tension establishing is half of thepreset rolling force As shown in Figure 7(b) the thicknessreduction is very small and even disappears for using thedeveloped new startup process The second tension increasestill exists while the first tension increase disappears but thetension increased amount decreases dramatically [15] Thistension increase is due to the strip rolled in the entry standthat enters the exit stand It is an inevitable problem of theCCM with a static tension establishing process The stripbreakage accidents in the startup process are almost elimi-nated after the optimization of interstand tension establishingprocess

In addition the preset rolling force of the strip head islarger and the hydraulic gauge control (HGC) mode of theentry stand changes from force control to position controlresulting in a thickness reductionWhen this thickness reduc-tion area reaches the exit stand it also causes a sharp tensionincrease which may cause strip breakage Therefore in orderto reduce the thickness reduction which can result in a sharptension increase the preset rolling force value of the striphead should also be decreasedThen the thickness fluctuationis reduced the stability of interstand tension is improvedand the probability of strip breakage caused by unreasonableprocess parameters is reduced Furthermore the thicknessand interstand tension fluctuation caused by deformationresistant fluctuation resulting fromuneven cooling or frictionvariation can also result in strip breakage in this stage Sothe homogeneity of strip temperature in the cooling processof hot strip and good lubrication condition are also veryimportant to the rolling stability

5 Conclusions

(1) The dynamic characteristic analysis of the CCM wasdeveloped using physical equations based on dynamic con-tinuous rolling theory In order to solve the rolling force


Drive sideOperation side

HG

C co

ntro

l mod

eH

GC

cont

rol m

ode

Tens

ion

Spee

dRo

lling

forc

e


Some preset rolling force


05

10(103

kN)

05

10

(10minus2

ms

)

000612

(102

kN)

0

1

Exit

stan

d

0

1

Entr

y st

and

1000 2000 3000 4000 50000Sample points

1000 2000 3000 4000 50000Sample points

1000 2000 3000 4000 50000Sample points

1000 2000 3000 4000 50000Sample points

1000 2000 3000 4000 50000Sample points



(a)

Exit thicknessInterstand thicknessInterstand tensile stress


00

05

10

15

20

25

30

35

40

Exit

thic

knes

s (m

m)

30

45

60

75

90

105

Tens

ile st

ress

(MPa

)

1000 2000 3000 40000Sampling points

(b)

Figure 7New tension establishing process thickness and tensile stress variations ofmodified startup process (a) schematic of new interstandtension establishing process (b) tensile stress and thickness variation

equation a new method combined with the acceleratedsecant and the tangent methods is proposed The interstandtension was calculated by integrating the tension differentialequation of variation section

(2) Sharp tension increases are caused by the thick-ness transition area and abnormal thickness reduction areaformed in the static tension establishing process The tensionincrease results in an impact force on the strip which is themain reason for strip breakage in the startup stage

(3)Themill startup process is modified in order to reduceor eliminate the sharp tension increase and the abnormalthickness reduction area The strip breakage accidents inthe startup process are almost eliminated by using the

new developed startup mode The interstand tension andthickness fluctuations cannot be eliminated completely forthe special static interstand tension establishing process

Symbols

119886119894 Deformation resistance parameters119894 = 1 2 3

119861 Strip width1198620 Constant 1198620 = 21208 times 10minus3MPaminus1119864 Elastic modulus of strip119891 Friction coefficient1198670 Thickness of incoming hot rolled strip


119867 Strip entrance thicknessℎ Strip exit thicknessΔℎ Reduction of strip Δℎ = 119867 minus ℎ119870119892119894 Plastic coefficient of strip by secant

method where 119894 = 1 2 denotes the standnumber

119870119898 Longitudinal stiffness of mill119870119902119894 Plastic coefficient of strip by tangent


119896 Average deformation resistance119896119867 Deformation resistance of the strip entry

section119896ℎ Deformation resistance of the strip exit

section119871 Interstand distance where sum119899119895=1 119897119895 = 119871

119895 = 1 119899 is number of the interstandthickness segments

119897119895 Length with the exit thickness ℎ119895 where119895 = 1 119899 is number of the interstandthickness segments

119899119905 Tension factor119875 Rolling force119876119901 Stress state coefficient119877 Work roll radius1198771015840 Flattening work roll radius119878 Roll gap119905119891 Forward tension stress119905119887 Back tension stressV119867 Strip entrance speedVℎ Strip exit speed120572 Bite angle120574 Neutral angle120576 Average reduction ratio120576 Reduction ratio120583119905 Tension weighting coefficient 120583119905 = 07

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

The authors would like to thank the National Key BasicResearch Program of China (no 2012CB722801) NationalNatural Science Foundation of China (nos 51404159 and51504157) and Natural Science Foundation of Shanxi (nos2013021019-1 and 2015081011) for their financial support ofthe research The authors would also like to thank ProfessorJIANG Zheng-yi (University of Wollongong) for the sugges-tions for improving the paper

References

[1] R A Phillips ldquoAnalysis of tandem cold reduction mill withautomatic gauge controlrdquo American Institute of Electrical Engi-neers vol 1 pp 355ndash363 1957

[2] H W Smith ldquoDynamic control of a two-stand cold millrdquo Auto-matica vol 5 no 2 pp 183ndash190 1969

[3] T Arimura M Kamata and M Saito ldquoAn analysis of thedynamic behavior of tandem cold millsrdquo Automatica vol 6 no4 pp 601ndash607 1970

[4] R-M Guo ldquoAnalysis of dynamic behaviors of tandem coldmills using generalized dynamic and control equationsrdquo IEEETransactions on Industry Applications vol 36 no 3 pp 842ndash853 2000

[5] S S Kim J S Kim S Y Yang et al ldquoHinfin Control system fortandem cold mills with roll eccentricityrdquo KSME InternationalJournal vol 18 no 1 pp 45ndash54 2004

[6] WH Lee and S R Lee ldquoComputer simulation of dynamic char-acteristics of tandem cold rolling processrdquo KSME InternationalJournal vol 13 no 8 pp 616ndash624 1999

[7] S K Yildiz J F Forbes B Huang et al ldquoDynamic modellingand simulation of a hot strip finishing millrdquo Applied Mathemat-ical Modelling vol 33 no 7 pp 3208ndash3225 2009

[8] K Asano and M Morari ldquoInteraction measure of tension-thickness control in tandem cold rollingrdquo Control EngineeringPractice vol 6 no 8 pp 1021ndash1027 1998

[9] G-M Liu H-S Di C-L Zhou H-C Li and J Liu ldquoTensionand thickness control strategy analysis of two stands reversiblecold rolling millrdquo Journal of Iron and Steel Research Interna-tional vol 19 no 10 pp 20ndash25 2012

[10] P G Alves L P Moreira and J A Castro ldquoDynamic simulatorfor control of tandem cold metal rollingrdquo in In Proceedings ofCobem rsquo11 pp 287ndash297 Natal Brazil 2011

[11] L E Zarate and F R Bittencout ldquoRepresentation and control ofthe cold rolling process through artificial neural networks viasensitivity factorsrdquo Journal of Materials Processing Technologyvol 197 no 1-3 pp 344ndash362 2008

[12] M Tanuma ldquoSimulation of dynamic behavior of whole rollingprocessrdquo Journal of the Japan Society of Technology of Plasticityvol 14 no 149 pp 429ndash438 1973

[13] J Sun Y Peng and H Liu ldquoCoupled dynamic modeling of rollsmodel and metal model for four high mill based on strip crowncontrolrdquo Chinese Journal of Mechanical Engineering (EnglishEdition) vol 26 no 1 pp 144ndash150 2013

[14] S T Zhang and Y R Liu ldquoDifferential equation of tensionfor varying strip section and mathematical model for dynamicdigital simulation of cold tandem rollingrdquo Acta MetallurgicaSinica vol 17 no 2 pp 206ndash212 1981

[15] G M Liu Study on rolling characteristic and flatness controlcharacteristic of 4-high two-stand reversible cold rolling millDoctoral dissertation [Doctoral thesis] NortheasternUniversityShenyang Liaoning China 2010

Submit your manuscripts athttpswwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of



CeramicsJournal of


CompositesJournal of

NanoparticlesJournal of



International Journal of

Biomaterials


NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research



MetallurgyJournal of


BioMed Research International

MaterialsJournal of



2 recoiler 1 recoiler Pay-o reel

1 stand

Rolling direction

Laser speed ickness gauge

2 stand

Hydraulic screwdown

Tension meter

Figure 1 Typical two-stand reversible cold rolling mill

big error would occur if the parameters variations are largein other words the linearization algorithm is not proper forsimulating large disturbances Then the nonlinear algorithmwhich was proposed in around 1970s with the developmentof computer should be a good choice The transient charac-teristics of threading acceleration deceleration and tail-outprocesses with and without AGC [12] were analyzed usingthe nonlinear method And this method was also extendedto strip crown control and rolling force analysis with a two-dimensional dynamic metal model [13]

For the thickness deviation is large at the stand positionin the steady tension establishing process of some CCMIn the present study at first the dynamic characteristicanalysis program was developed using nonlinear algorithmsin which the formulas of the rolling theory are numericallycalculated directly without any approximation Second thetransient process in the startup process was analyzed andthe influence factors on the rolling stability were examinedin detail Finally the optimization of the running status ofthe CCM startup process was presented and carried out inthe production line The running status of the new startupstrategy was discussed

2 Physical Equations and Calculation Methods

The mathematical model used for dynamic characteristicanalysis includes the intrastand equations such as springequation rolling force equation forward slip equation andinterstand equations such as tension continuity thicknesscontinuity and tension differential equations connectingthe adjacent stands [4] The calculation methods used inthe dynamic characteristic analysis include the thicknessdelay algorithm of each stand the roll gap and thicknesscalculation method under constant rolling force mode andthe special solving method of dynamic continuous rollingstatus The connections jointing the adjacent stands involvesimulation of time delayed transport of thickness from onestand to the next and the calculation of interstand tension

21 Spring Equation As the rolling mill is not perfectly rigidthe exit thickness can be expressed by the elastic equation of

the rolling mill

ℎ = 119878 + 119875119870119898

(1)

22 Rolling Force Equation The Hillrsquos simplified form ofBland-Ford equation is selected as the rolling force equationin this study

119875 = 119861119896 [1198771015840 (119867 minus ℎ)]12

119876119901119899119905 (2)

with 119896 = 1198861(120576 + 1198862)1198863 120576 = 04120576119867 + 06120576ℎ 120576119867 = 1 minus 1198671198670 120576ℎ =1minusℎ11986701198771015840 = 119877[1+1198620119875(119861(119867minusℎ))]119876119901 = 108+179120576119891(1198771015840119867)12minus102120576 and 120576 = (119867minusℎ)119867 119899119905 = 1minus[(1minus120583119905)119905119891+120583119905119905119887]119896

23 Forward Slip Equation The width spread is small in thecold rolling process and can be ignored The neutral angle issmall as the deformation zone is narrow The ratio of workroll diameter (119863 119863 = 2 lowast 119877) to strip exit thickness (ℎ) is farmore than 1 So the D Dresden [8] forward slip equation isused

119904ℎ =1198771015840

ℎsdot 1205742 (3)

with 120574 = (ℎ1198771015840)12 tan((ℎ1198771015840)12 sdot 1198671198992) 119867119899 = 1198671198872 minus 1(2119891) ln(119867ℎ sdot (1 minus 119905119891119896ℎ)(1 minus 119905119887119896119867)) 120572 = (Δℎ1198771015840)12119867119887 =2 sdot (1198771015840ℎ)12 arctan((1198771015840ℎ)12 sdot 120572)

24 Interstand Tension Equation The interstand strip thick-ness is uneven due to the interstand tension establishingprocess So the interstand tension is solved by integrating thetension differential equation for a variable section [14] Thedifferential equation is related to the difference between theexit speed of the strip from one stand and entry speed to thesubsequent stand Thus the forward tension is obtained by



d119905119891119894 =119864


119905119887119894+1 =ℎ119894119867119894+1

sdot 119905119891119894

(4)


119895









2119894 1198752119894 )




1119894 ) with point (ℎ3119894 119875

3119894 ) a new solu-





(5)


ℎ119899119894 =(119875119894 minus 119875119899minus1119894 )

119870119899minus1119892119894+ ℎ119899minus1119894 (6)




119870119899119902119894 =120597119875119894120597ℎ119894



(7)


ℎ119899+1119894 =(119875119894 minus 119875119899119894 )119870119899119902119894

+ ℎ119899119894 (8)





119878119894119898 =


+ ℎ119898minus1119894 minus119875119898119894119870119898119894

(9)




ickness h (mm)

Rolli

ng fo

rce P

(N)

ℎ1

iℎ2

iℎ4

iℎ5

i

ℎn

iℎ3

i

Pi

Hi

P1

i

P3

i

P2

i

P4

i

P5

i

Sn

i




(1)119891119894 and 119905(1)



(1)119894



= 119905(1)119891119894+ d119905(1)119891119894


(2)119894 119904(2)ℎ119894 119904(2)119867119894 119891















HG

C co

ntro

l mod

eH

GC

cont

rol m

ode

01

Exit

stan

d



Tens

ion

Spee

dRo

lling

forc

e

500 1000 1500 2000 2500 3000 35000Sample points

000612

(102

kN)

500 1000 1500 2000 2500 3000 35000Sample points

01

Entr

y st

and

minus505

(10minus2

ms

)

500 1000 1500 2000 2500 3000 35000Sample points

500 1000 1500 2000 2500 3000 35000Sample points

500 1000 1500 2000 2500 3000 35000Sample points

048

1216

(103

kN)

(a)

Rolling direction



(b)






GC

cont

rol m

ode

HG

C co

ntro

l mod

e

(1) Force control


0

3

6Li

ne sp

eed

(ms

)

0

1

Exit

stand

1000 2000 3000 4000 5000 6000 70000Sample points

0

1

Entr

y st

and

1000 2000 3000 4000 5000 6000 70000Sample points

1000 2000 3000 4000 5000 6000 70000Sample points



(a)






20

40

60

80

100

120

Tens

ile st

ress

(MPa

)

1000 2000 3000 4000 5000 6000 70000Sampling points

00

05

10

15

20

25

30

Exit

thic

knes

s (m

m)

(b)








135

140

145

150

Exit

thic

knes

s (m

m)

200

205

210

215In

ter-

stan

d th

ickn

ess (

mm

)

0 2 4 6 8 10 12 14 16 18minus2Time (s)

(a)

Fourth increase

ird increase

First increase

Second increase

100

120

140

160

180

200

Tens

ile st

ress

(MPa

)

2 4 6 8 10 12 14 16 180Time (s)

(b)












135

140

145

150

Exit

thic

knes

s (m

m)

200

205

210

215In

ters

tand

thic

knes

s (m

m)

2 4 6 8 10 12 14 16 180Time (s)

(a)

Second increase

First increase

100

120

140

160

180

200

Tens

ile st

ress

(MPa

)

2 4 6 8 10 12 14 16 180Time (s)

(b)








5 Conclusions




HG

C co

ntro

l mod

eH

GC

cont

rol m

ode

Tens

ion

Spee

dRo

lling

forc

e




05

10(103

kN)

05

10

(10minus2

ms

)

000612

(102

kN)

0

1

Exit

stan

d

0

1

Entr

y st

and

1000 2000 3000 4000 50000Sample points

1000 2000 3000 4000 50000Sample points

1000 2000 3000 4000 50000Sample points

1000 2000 3000 4000 50000Sample points

1000 2000 3000 4000 50000Sample points



(a)



00

05

10

15

20

25

30

35

40

Exit

thic

knes

s (m

m)

30

45

60

75

90

105

Tens

ile st

ress

(MPa

)


(b)






Symbols
















Acknowledgments


References























CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of




d119905119891119894 =119864


119905119887119894+1 =ℎ119894119867119894+1

sdot 119905119891119894

(4)


119895









2119894 1198752119894 )




1119894 ) with point (ℎ3119894 119875

3119894 ) a new solu-





(5)


ℎ119899119894 =(119875119894 minus 119875119899minus1119894 )

119870119899minus1119892119894+ ℎ119899minus1119894 (6)




119870119899119902119894 =120597119875119894120597ℎ119894



(7)


ℎ119899+1119894 =(119875119894 minus 119875119899119894 )119870119899119902119894

+ ℎ119899119894 (8)





119878119894119898 =


+ ℎ119898minus1119894 minus119875119898119894119870119898119894

(9)




ickness h (mm)

Rolli

ng fo

rce P

(N)

ℎ1

iℎ2

iℎ4

iℎ5

i

ℎn

iℎ3

i

Pi

Hi

P1

i

P3

i

P2

i

P4

i

P5

i

Sn

i




(1)119891119894 and 119905(1)



(1)119894



= 119905(1)119891119894+ d119905(1)119891119894


(2)119894 119904(2)ℎ119894 119904(2)119867119894 119891















HG

C co

ntro

l mod

eH

GC

cont

rol m

ode

01

Exit

stan

d



Tens

ion

Spee

dRo

lling

forc

e

500 1000 1500 2000 2500 3000 35000Sample points

000612

(102

kN)

500 1000 1500 2000 2500 3000 35000Sample points

01

Entr

y st

and

minus505

(10minus2

ms

)

500 1000 1500 2000 2500 3000 35000Sample points

500 1000 1500 2000 2500 3000 35000Sample points

500 1000 1500 2000 2500 3000 35000Sample points

048

1216

(103

kN)

(a)

Rolling direction



(b)






GC

cont

rol m

ode

HG

C co

ntro

l mod

e

(1) Force control


0

3

6Li

ne sp

eed

(ms

)

0

1

Exit

stand

1000 2000 3000 4000 5000 6000 70000Sample points

0

1

Entr

y st

and

1000 2000 3000 4000 5000 6000 70000Sample points

1000 2000 3000 4000 5000 6000 70000Sample points



(a)






20

40

60

80

100

120

Tens

ile st

ress

(MPa

)

1000 2000 3000 4000 5000 6000 70000Sampling points

00

05

10

15

20

25

30

Exit

thic

knes

s (m

m)

(b)








135

140

145

150

Exit

thic

knes

s (m

m)

200

205

210

215In

ter-

stan

d th

ickn

ess (

mm

)

0 2 4 6 8 10 12 14 16 18minus2Time (s)

(a)

Fourth increase

ird increase

First increase

Second increase

100

120

140

160

180

200

Tens

ile st

ress

(MPa

)

2 4 6 8 10 12 14 16 180Time (s)

(b)












135

140

145

150

Exit

thic

knes

s (m

m)

200

205

210

215In

ters

tand

thic

knes

s (m

m)

2 4 6 8 10 12 14 16 180Time (s)

(a)

Second increase

First increase

100

120

140

160

180

200

Tens

ile st

ress

(MPa

)

2 4 6 8 10 12 14 16 180Time (s)

(b)








5 Conclusions




HG

C co

ntro

l mod

eH

GC

cont

rol m

ode

Tens

ion

Spee

dRo

lling

forc

e




05

10(103

kN)

05

10

(10minus2

ms

)

000612

(102

kN)

0

1

Exit

stan

d

0

1

Entr

y st

and

1000 2000 3000 4000 50000Sample points

1000 2000 3000 4000 50000Sample points

1000 2000 3000 4000 50000Sample points

1000 2000 3000 4000 50000Sample points

1000 2000 3000 4000 50000Sample points



(a)



00

05

10

15

20

25

30

35

40

Exit

thic

knes

s (m

m)

30

45

60

75

90

105

Tens

ile st

ress

(MPa

)


(b)






Symbols
















Acknowledgments


References























CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of




ickness h (mm)

Rolli

ng fo

rce P

(N)

ℎ1

iℎ2

iℎ4

iℎ5

i

ℎn

iℎ3

i

Pi

Hi

P1

i

P3

i

P2

i

P4

i

P5

i

Sn

i




(1)119891119894 and 119905(1)



(1)119894



= 119905(1)119891119894+ d119905(1)119891119894


(2)119894 119904(2)ℎ119894 119904(2)119867119894 119891















HG

C co

ntro

l mod

eH

GC

cont

rol m

ode

01

Exit

stan

d



Tens

ion

Spee

dRo

lling

forc

e

500 1000 1500 2000 2500 3000 35000Sample points

000612

(102

kN)

500 1000 1500 2000 2500 3000 35000Sample points

01

Entr

y st

and

minus505

(10minus2

ms

)

500 1000 1500 2000 2500 3000 35000Sample points

500 1000 1500 2000 2500 3000 35000Sample points

500 1000 1500 2000 2500 3000 35000Sample points

048

1216

(103

kN)

(a)

Rolling direction



(b)






GC

cont

rol m

ode

HG

C co

ntro

l mod

e

(1) Force control


0

3

6Li

ne sp

eed

(ms

)

0

1

Exit

stand

1000 2000 3000 4000 5000 6000 70000Sample points

0

1

Entr

y st

and

1000 2000 3000 4000 5000 6000 70000Sample points

1000 2000 3000 4000 5000 6000 70000Sample points



(a)






20

40

60

80

100

120

Tens

ile st

ress

(MPa

)

1000 2000 3000 4000 5000 6000 70000Sampling points

00

05

10

15

20

25

30

Exit

thic

knes

s (m

m)

(b)








135

140

145

150

Exit

thic

knes

s (m

m)

200

205

210

215In

ter-

stan

d th

ickn

ess (

mm

)

0 2 4 6 8 10 12 14 16 18minus2Time (s)

(a)

Fourth increase

ird increase

First increase

Second increase

100

120

140

160

180

200

Tens

ile st

ress

(MPa

)

2 4 6 8 10 12 14 16 180Time (s)

(b)












135

140

145

150

Exit

thic

knes

s (m

m)

200

205

210

215In

ters

tand

thic

knes

s (m

m)

2 4 6 8 10 12 14 16 180Time (s)

(a)

Second increase

First increase

100

120

140

160

180

200

Tens

ile st

ress

(MPa

)

2 4 6 8 10 12 14 16 180Time (s)

(b)








5 Conclusions




HG

C co

ntro

l mod

eH

GC

cont

rol m

ode

Tens

ion

Spee

dRo

lling

forc

e




05

10(103

kN)

05

10

(10minus2

ms

)

000612

(102

kN)

0

1

Exit

stan

d

0

1

Entr

y st

and

1000 2000 3000 4000 50000Sample points

1000 2000 3000 4000 50000Sample points

1000 2000 3000 4000 50000Sample points

1000 2000 3000 4000 50000Sample points

1000 2000 3000 4000 50000Sample points



(a)



00

05

10

15

20

25

30

35

40

Exit

thic

knes

s (m

m)

30

45

60

75

90

105

Tens

ile st

ress

(MPa

)


(b)






Symbols
















Acknowledgments


References























CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of









HG

C co

ntro

l mod

eH

GC

cont

rol m

ode

01

Exit

stan

d



Tens

ion

Spee

dRo

lling

forc

e

500 1000 1500 2000 2500 3000 35000Sample points

000612

(102

kN)

500 1000 1500 2000 2500 3000 35000Sample points

01

Entr

y st

and

minus505

(10minus2

ms

)

500 1000 1500 2000 2500 3000 35000Sample points

500 1000 1500 2000 2500 3000 35000Sample points

500 1000 1500 2000 2500 3000 35000Sample points

048

1216

(103

kN)

(a)

Rolling direction



(b)






GC

cont

rol m

ode

HG

C co

ntro

l mod

e

(1) Force control


0

3

6Li

ne sp

eed

(ms

)

0

1

Exit

stand

1000 2000 3000 4000 5000 6000 70000Sample points

0

1

Entr

y st

and

1000 2000 3000 4000 5000 6000 70000Sample points

1000 2000 3000 4000 5000 6000 70000Sample points



(a)






20

40

60

80

100

120

Tens

ile st

ress

(MPa

)

1000 2000 3000 4000 5000 6000 70000Sampling points

00

05

10

15

20

25

30

Exit

thic

knes

s (m

m)

(b)








135

140

145

150

Exit

thic

knes

s (m

m)

200

205

210

215In

ter-

stan

d th

ickn

ess (

mm

)

0 2 4 6 8 10 12 14 16 18minus2Time (s)

(a)

Fourth increase

ird increase

First increase

Second increase

100

120

140

160

180

200

Tens

ile st

ress

(MPa

)

2 4 6 8 10 12 14 16 180Time (s)

(b)












135

140

145

150

Exit

thic

knes

s (m

m)

200

205

210

215In

ters

tand

thic

knes

s (m

m)

2 4 6 8 10 12 14 16 180Time (s)

(a)

Second increase

First increase

100

120

140

160

180

200

Tens

ile st

ress

(MPa

)

2 4 6 8 10 12 14 16 180Time (s)

(b)








5 Conclusions




HG

C co

ntro

l mod

eH

GC

cont

rol m

ode

Tens

ion

Spee

dRo

lling

forc

e




05

10(103

kN)

05

10

(10minus2

ms

)

000612

(102

kN)

0

1

Exit

stan

d

0

1

Entr

y st

and

1000 2000 3000 4000 50000Sample points

1000 2000 3000 4000 50000Sample points

1000 2000 3000 4000 50000Sample points

1000 2000 3000 4000 50000Sample points

1000 2000 3000 4000 50000Sample points



(a)



00

05

10

15

20

25

30

35

40

Exit

thic

knes

s (m

m)

30

45

60

75

90

105

Tens

ile st

ress

(MPa

)


(b)






Symbols
















Acknowledgments


References























CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of



GC

cont

rol m

ode

HG

C co

ntro

l mod

e

(1) Force control


0

3

6Li

ne sp

eed

(ms

)

0

1

Exit

stand

1000 2000 3000 4000 5000 6000 70000Sample points

0

1

Entr

y st

and

1000 2000 3000 4000 5000 6000 70000Sample points

1000 2000 3000 4000 5000 6000 70000Sample points



(a)






20

40

60

80

100

120

Tens

ile st

ress

(MPa

)

1000 2000 3000 4000 5000 6000 70000Sampling points

00

05

10

15

20

25

30

Exit

thic

knes

s (m

m)

(b)








135

140

145

150

Exit

thic

knes

s (m

m)

200

205

210

215In

ter-

stan

d th

ickn

ess (

mm

)

0 2 4 6 8 10 12 14 16 18minus2Time (s)

(a)

Fourth increase

ird increase

First increase

Second increase

100

120

140

160

180

200

Tens

ile st

ress

(MPa

)

2 4 6 8 10 12 14 16 180Time (s)

(b)












135

140

145

150

Exit

thic

knes

s (m

m)

200

205

210

215In

ters

tand

thic

knes

s (m

m)

2 4 6 8 10 12 14 16 180Time (s)

(a)

Second increase

First increase

100

120

140

160

180

200

Tens

ile st

ress

(MPa

)

2 4 6 8 10 12 14 16 180Time (s)

(b)








5 Conclusions




HG

C co

ntro

l mod

eH

GC

cont

rol m

ode

Tens

ion

Spee

dRo

lling

forc

e




05

10(103

kN)

05

10

(10minus2

ms

)

000612

(102

kN)

0

1

Exit

stan

d

0

1

Entr

y st

and

1000 2000 3000 4000 50000Sample points

1000 2000 3000 4000 50000Sample points

1000 2000 3000 4000 50000Sample points

1000 2000 3000 4000 50000Sample points

1000 2000 3000 4000 50000Sample points



(a)



00

05

10

15

20

25

30

35

40

Exit

thic

knes

s (m

m)

30

45

60

75

90

105

Tens

ile st

ress

(MPa

)


(b)






Symbols
















Acknowledgments


References























CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of





135

140

145

150

Exit

thic

knes

s (m

m)

200

205

210

215In

ter-

stan

d th

ickn

ess (

mm

)

0 2 4 6 8 10 12 14 16 18minus2Time (s)

(a)

Fourth increase

ird increase

First increase

Second increase

100

120

140

160

180

200

Tens

ile st

ress

(MPa

)

2 4 6 8 10 12 14 16 180Time (s)

(b)












135

140

145

150

Exit

thic

knes

s (m

m)

200

205

210

215In

ters

tand

thic

knes

s (m

m)

2 4 6 8 10 12 14 16 180Time (s)

(a)

Second increase

First increase

100

120

140

160

180

200

Tens

ile st

ress

(MPa

)

2 4 6 8 10 12 14 16 180Time (s)

(b)








5 Conclusions




HG

C co

ntro

l mod

eH

GC

cont

rol m

ode

Tens

ion

Spee

dRo

lling

forc

e




05

10(103

kN)

05

10

(10minus2

ms

)

000612

(102

kN)

0

1

Exit

stan

d

0

1

Entr

y st

and

1000 2000 3000 4000 50000Sample points

1000 2000 3000 4000 50000Sample points

1000 2000 3000 4000 50000Sample points

1000 2000 3000 4000 50000Sample points

1000 2000 3000 4000 50000Sample points



(a)



00

05

10

15

20

25

30

35

40

Exit

thic

knes

s (m

m)

30

45

60

75

90

105

Tens

ile st

ress

(MPa

)


(b)






Symbols
















Acknowledgments


References























CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of





135

140

145

150

Exit

thic

knes

s (m

m)

200

205

210

215In

ters

tand

thic

knes

s (m

m)

2 4 6 8 10 12 14 16 180Time (s)

(a)

Second increase

First increase

100

120

140

160

180

200

Tens

ile st

ress

(MPa

)

2 4 6 8 10 12 14 16 180Time (s)

(b)








5 Conclusions




HG

C co

ntro

l mod

eH

GC

cont

rol m

ode

Tens

ion

Spee

dRo

lling

forc

e




05

10(103

kN)

05

10

(10minus2

ms

)

000612

(102

kN)

0

1

Exit

stan

d

0

1

Entr

y st

and

1000 2000 3000 4000 50000Sample points

1000 2000 3000 4000 50000Sample points

1000 2000 3000 4000 50000Sample points

1000 2000 3000 4000 50000Sample points

1000 2000 3000 4000 50000Sample points



(a)



00

05

10

15

20

25

30

35

40

Exit

thic

knes

s (m

m)

30

45

60

75

90

105

Tens

ile st

ress

(MPa

)


(b)






Symbols
















Acknowledgments


References























CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of




HG

C co

ntro

l mod

eH

GC

cont

rol m

ode

Tens

ion

Spee

dRo

lling

forc

e




05

10(103

kN)

05

10

(10minus2

ms

)

000612

(102

kN)

0

1

Exit

stan

d

0

1

Entr

y st

and

1000 2000 3000 4000 50000Sample points

1000 2000 3000 4000 50000Sample points

1000 2000 3000 4000 50000Sample points

1000 2000 3000 4000 50000Sample points

1000 2000 3000 4000 50000Sample points



(a)



00

05

10

15

20

25

30

35

40

Exit

thic

knes

s (m

m)

30

45

60

75

90

105

Tens

ile st

ress

(MPa

)


(b)






Symbols
















Acknowledgments


References























CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of















Acknowledgments


References























CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of









CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Analysis of Startup Process and Its Optimization for a Two ...

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Transcript of Analysis of Startup Process and Its Optimization for a Two ...