葉 雙

唐山學院信息工程系，河北唐山 063000

1．Introduction

As the most advanced technology for continuous casting and rolling of thin slabs，semi-endless rolling could avoid unsteadiness of both strip ends in the finishing process，thus it will greatly improve the rolling stability and productivity．In addition，since it could reduce the temperature fluctuation across a whole strip coil，the remarkable enhancement of quality for hot-rolled slabs could be obtained．Most importantly，by adopting this technology，extremely thin hot-rolled slabs(less than 1．2 mm)could be produced，with relative low production cost and higher gross profits．In order to produce such ultra-thin slabs by using this technology，F(xiàn)GC has to be adopted．However，currently the study of FGC was just focused on the cold rolling，and there were fewer research papers and literatures on the application in strip hot rolling．Although FGC has been successfully applied in endless continuous cold rolling，it was not yet applied in endless and semi-endless hot rolling until the end of the 20th century．As a key technology required by hot rolling process，F(xiàn)GC has rarely been studied．

2．Flying gauge change

During the production process of thin strips by using semi-endless rolling，flying gauge change(FGC)was commonly adopted to enable a stable rolling process．Since FGC involved the change of rolling schedule for the following strip coil without stopping the rolling of the previous one，the different thickness and width of two successive coils were allowed．Because the rolling speed and roll gap would be adjusted frequently and the rolling force and other parameters on different rolling racks would also be changed，the thickness fluctuation at each rack outlet will inevitably exist．There exists a wedged thickness zone，or transition zone，which shows a transition from the former schedule to the latter one with the gauge change．The length of such zone depends on the time required by the rolling mill to complete the designated roll-gap deviation and speed deviation，i．e．，dynamic response time required by the pressing action and host speed，and certainly it is related to strategy of gauge change．Therefore，the enhancement of steadiness and the length reduction of transition zone become very important things during the designing process of an FGC strategy．So far，F(xiàn)GC has been successfully applied in cold rolling，while it is still not mature for the process of hot rolling．For continuous cold rolling，there is a relatively big tension difference in rolling strips with different sizes due to the great tension force．Therefore，it is inappropriate to set the values of change for roll gap and rolling speed according to the principle of constant tension，when the tension of the former schedule is directly applied to that of the latter one．It is more reasonable to set FGC for cold continuous rolling according to the principle of variable tension．And for continuous hot rolling，the strips are rolled by constant micro-tension due to the existence of looper．The roll gap and rolling speed in FGC could be set according to the principle of constant tension(i．e．，constant looper height)and constant speed．

3．FGC control method

In order to obtain the successful process of FGC，some corresponding control method and model will used to calculate the adjustment values of roll gap and rolling speed in various transitional stages．Such values could be adjusted at the rolling direction or the opposite direction．For the latter scenario，more steady tension could be obtained in FGC．

Gauge change begins when the strips are steadily rolled by following the first schedule．When gauge change point enters the rack 1，roll gap and rolling speed will be re-set according to the given curve;meanwhile，tension force between the first two racks are kept constant to maintain the steady rolling of the previous coil in downstream rack．If the values are adjusted in a reverse direction，when the gauge change point enters the rack 2，the value of tension will be changed based on the values of the inlet speed of rack 2 and front tension of rack 1．Then，rolling speed and roll gap of rack 1 have to be adjusted at the second time．When gauge change point enters rack 3，the values will be changed based on the inlet speed of rack 3 and front tension of rack 2，and the rolling speed and roll gap of rack 2 have to be adjusted at the second time．Due to this adjustment，the inlet speed of rack w will be changed accordingly．In order to maintain the constant tension between rack 1 and 2 as well as the constant looper height，the rolling speed and roll gap of rack 1 must be adjusted at the third time．

Accordingly，when gauge change point enters rack i，the rolling speed and roll gap of rack i-1will be adjusted for the second time，and those of rack i-2 for the third time，until those of rack 1 is adjusted for the i time．Thus，when gauge change finishes，the rolling speed and roll gap of rack 1 will be changed i times，those of rack 2 i-1 times，those of rack 3 i-2 times，those of rack i-1 2 times，those of rack i-1 2 times，those of rack i 1 times．If take the five-rack continuous rolling as example，F(xiàn)GC control method is shown in Figure 1．

Figure 1．FGCcontrol method

4．Looper height control system

Looper support on racks of a finishing rolling unit is used to adjust tension between different racks to keep constant micro-tension and prevent bigger looper height between racks and narrower strip width，maintain the required looper value and raise steadiness of rolling process．Looper control for strip hot rolling includes the adjustment of looper angle，tension，and strip flow．Looper angle is controlled by adjusting velocity of the main motor，tension is controlled by adjusting current flowing through the looper motor，and strip flow is controlled by maintaining a relatively constant looper height，which could be realized by adjusting the main speed of the upstream rack．Looper control is realized by two control systems:one is a tension control system，with voltage regulation and current regulation functions realized by an inner loop;the other is a looper height automatic control system，which is a closed loop and controlled by rack main drive．The latter control system can convert the looper arm rotation angleθinto looper height l，and it could use a particular set value of looper height as a benchmark value to compare．In case of looper height deviation，main drive velocity of upper stream rack could be automatically adjusted to maintain a constant looper height．Since the main drive velocity is used to control looper height，the looper becomes a detector of unequal metal flow(per second)between different racks．

4．1．Correlation between looper height and looper arm swing angle

In the looper height automatic control system，to maintain an appropriate speed of metal flow per second，looper height of strips should be adjusted because the deviation growth of looper height is directly proportional to the deviation of main drive velocity．However，in actual operation，what need to be maintained and detected is the looper arm swing angle，which has no linear relationship with looper height and speed．To accurately set the looper height，the correlation between looper height and the looper must be determined．The correlation between looper height and looper working angle is shown in Figure 2．In this figure，l is the rack distance，R is arm length of looper，lais distance between looper rotatition axis and working roll center of the previous rack，r is radius of looper arm，αandβare the angles between strips and rolling line，respectively，θis the looper angle．Therefore，the relationship between looper height and looper angle could be obtained as follows．

Since Δl is only a function ofθ，thusΔl=f(θ)．The correlation between Δl and θat working section is mainly in line with a quadratic curve equation

Figure 2．Correlation between different looper perimeters

4．2．Mechanism of looper height control system

Strip thickness is controlled by an AGC system during steady rolling when the system does not work during FGC．Begin from the basic principles of continuous hot rolling，schedule and appropriate method for FGC are studied to provide the theoretical basis and guidance for the design of the best FGC scheme．Since roll gap and rolling speed have to be adjusted frequently within a very short period of time during FGC，it is not possible to conduct feedback control but feedforward control based on a model set value．As seen from Figure 3，vi=Vi+1．Strip thickness will follow the change of FGC．Suppose strip thickness rolled according to the latter schedule is less than that according to the former one．When the gauge change point arrives at rack 1，in accordance with the principle of balanced flow per second，vi＞Vi+1．Calculate from the looper height equation，length of strip rolled out from rack i within unit time is vidt;that from rack i+1 within unit time is Vi+1dt．Thus looper height change isΔl= ∫(Vi+1-vi)d t．When Vi+1is not equal to vi，as time passes，looper height will increase indefinitely and if it is not controlled timely，three layers of strips will be rolled into rack i+1 to cause severe accident．Therefore，to maintain looper height unchanged，speed at outlet rack and inlet rack must be maintained unchanged when gauge change point arrives at a rack，i．e．vi=Vi+1．Rolling speed of rack i must be slow down to the set value before gauge change point arrives．It is a control system that features feedforward by speed inner loop and feedback by looper outer loop．

Figure 3．FGC rolling

The mechanism of looper height control system is shown in Figure 4．When the looper works，the heightθis detected before it is converted through G into actual looper height lf．Input signal Δl can be obtained by comparing lfwith set height lR．When Δl=0，actual value of looper height is equal to its set value，which means the equal metal flow is obtained between the racks．In case of imbalanced metal flow caused by the fluctuation of production process or equipment parameters，actual value of looper height becomes unequal to its set value，i．e．Δl≠0．WhenΔl is adjusted by height adjustment HT and speed adjustment ST，velocity of main drive will be changed．At this time，by adjusting the front and rear deviationΔv，looper heigh deviationΔl could be eliminated or reduced to the allowed value range．When gauge change begins and the change point arrives at rack 1，main drive new valueΔn will be calculated in advance beforeΔl=0 is ensured by the looper heigh control system．

Figure 4．Functioning of looper height automatic control system

5．Model and simulation of looper height control system

After the text edit has been completed，the content is ready for the template．Duplicate the template file by using the Save As command，and use the naming convention prescribed by the conference for the name of file．In this newly created file，highlight all of the contents and import the prepared text file．It is now ready to style the file．

To analyze quantitatively and determine dynamic quality and stability of the system，transfer functions at different stages and system dynamics diagram must be obtained．

1)Transfer function of adjuster

PI adjuster is adopted as looper adjuster whose transfer function is:

2)Transfer function of speed system

Speed system of rack main drive could be simplified to an equivalent inertia factor whose transfer function can be written as as:

3)Transfer function of looper

Looper height is an integral factor whose transfer function is

4)Transfer function of looper height detection and conversion is

Dynamic structure of the looper control system is shown in Figure 5．Looper ring could be then designed according to Type II system，thus the proportional magnification factor Kpand integral time factor τof PI adjuster could be determined by adopting“optimal engineering symmetry”(h=4)or Mpminprinciple．

Figure 5．Dynamic structure of looper ring

Choose an appropriate proportion factor to make sure that Kpl=0．1，τl=1．12 s，Tl=0．053 s，Kn=0．026 7，Tn=0．26 s，Kl=1，and Tfl=0．15 s．When gauge change begins，vi，speed of rack i gets increased to result in a speed difference Δv，from Vi+1，speed of rack i+1．Since the increase of looper height will cause vibration，the system becomes unstable，as shown in Figure 6．By adjusting the parameters of PI，the oscillation will not be obviously eliminated．Feedforward Δn is calculated at the time of gauge change，and then rear looper height could be added to stabilize the system．

Figure 6．Looper height simulation

6．Conclusion

Based on the simulation results and analysis，the looper height control system for FGC in continu-ous rolling is comprehensively studied in this paper．The simulation results showed that as strip thickness changes when gauge change begins，the speed at outlet will be different from that at inlet and it will result in a change of looper height．When gauge change begins，rolling speed will be slowed to a level that has been calculated in advance，so that strip moving speed at outlet of the former rack will be slowed to match that at inlet of the latter rack．Thus，looper height could be maintained as a constant or vibrated within a certain range．

［1］ Wang JS，Jiao ZJ，Zhao QL，et al．Load Distribution and correction calculation for on-lionprocess control of the tandem cold mill［J］．Journal of Northeastern University:NaturalScience，2001，22(4):427-431．

［2］ Sims R B．The Calculation of Roll Force and Torque in Hot Rolling Mills［J］．Inst Mech Engr，1954，168(6):231-236．

［3］ Orowan E．Graphical Calculation of the Roll Pressure with the Assumption ofHomogeneous Compression and Slipping Friction［J］．Proc I Mech E，1943，150:141．

［4］ Sun Yikang．Model and Control of Strip Continuous Hot Rolling［M］．Beijing:Metallurgical Industry Press，2002．

［5］ Kamata M．Continuous Rolling of Slabs and Strips［M］．Translated by Li Futao．Beijing:Metallurgical Industry Press，2002．

［6］ Li Hongcui．Analysis of and Strategy for FGC in Semiendless Continuous Hot Rolling．Master’s distertation［M］．Beijing:Jinan Iron＆ Steel Group，2006．

［7］ Peng Kaixiang，Dong Jie，Tong Chaonan．Overall Looper Control for Strip Continuous Hot Rolling Mill［J］．Journal of Metallurgical Equipment，2005，4(2):11-14．

［8］ Hua Jianxin，Wang Zhenxiang．Working Process of Continuous Cold Rolling Mill［M］．Beijing:Metallurgical Industry Press，2002．

［9］ Ge Ping．FGC for Strip Continuous Cold Rolling Mill［D］．Beijing:Beijing University of Science＆ Technology，2001．