Full-length model with multi-point settings for finishing rolling

Research Institute,Baoshan Iron & Steel Co.,Ltd.,Shanghai 201999,China

Abstract: Thickness,width,temperature,and profile are considered as control targets in process control of hot strip finishing rolling.The pre-calculated settings of the model information include rolling force,cooling water flow between stands,bending force,and roll shifting position.Without changing the load distribution,the interaction among thread speed,rolling force,rolling power,and cooling water flow between stands is comprehensively considered based on the quantifiable relationship among speed,force,and temperature.This paper proposes a full-length multi-point-setting model that uses the settings of strip head to combine the rolling speed diagram with the target finishing mill delivery temperature(FDT) to achieve the calculation of the control parameters along full length of strip.Traditional models cannot effectively predict rolling force of strip body or the maximum and minimum temperatures of FDT.It is also difficult for traditional models to suppress fluctuations in shape accuracy of full-length strip or improve the shape accuracy of the product.Calculation results show that the proposed full-length multi-point-setting model can provide the control parameters for temperature and rolling-force over full length of strip,predict the risk of rolling exceeding the equipment capability,and improve the shape accuracy and rolling stability of hot-rolled products.

Key words: hot continuous rolling; finishing rolling; full-length multi-point setting

1 Introduction

In hot strip rolling lines,dimensions and temperature control are important factors in finishing rolling.Existing control models for finishing area provide control parameters for strip head before threading,including rolling force,roll gap,speed,cooling water between stands,and roll bending force.The dimen-sions and temperature of strip body are dynamically feedback-controlled by the automatic gauge control (AGC) and finishing mill delivery temperature (FDT) control model during the rolling process[1].Affected by material properties and rolling speeds,rolling force and rolling temperatures over the entire length of the strip vary with different amplitudes.When temperature fluctuations are large,the feed-back control cannot adjust cooling water flow be-tween stands in time to achieve accurate tempera-ture control.In addition,these temperature fluctuations cause sudden changes in rolling force[2],and the AGC cannot manage roll-gap deviations caused by these sudden changes in rolling force.

2 Multi-point-setting model for finishing full length

To improve accuracy in the control of strip thick-ness and temperature,a full-length multi-point setting calculation strategy is adopted.Existing setup model performs calculations only for strip head and then outputs rolling force,power,temperature,speed,roll gap,and cooling water flow between stands.According to rolling speed diagram and roll gap of each stand,speed of each stand is calculated for the full-length rolling process of strip.Based on the principle that the speed diagram does not change,the cooling water flowing between stands is adjusted to con-trol the FDT.Rolling force and power of each stand are then calculated at different rolling speeds and temperatures[3].Because rolling force is used in the temperature calculation,the rolling force and tem-perature need to be calculated iteratively until the interaction between the rolling force and tempera-ture becomes small enough to achieve the multi-point setting calculation of the entire length of strip[4].

2.1 Strip length position mapping calculation

Multi-point setting refers to the calculation of control parameters for different positions on strip in length direction.Strip width remains unchanged during rolling,and exit thickness is pre-calculated for each stand.According to the slab volume,the actual exit length of each multi-point-setting position in each stand can be calculated.

LRi=S/Si

(1)

where,iis the hot-rolling stand number;LRiis the ratio of rolling length of standito slab length;Sis the slab cross-sectional area;andSiis the cross-sectional area of exit strip of standi.

2.2 Positions of multi-point settings along slab length

Based on the length of slab,multiple multi-point-setting positions are established in the length direc-tion.Multi-point-setting positions on head and tail are spaced densely by small distances,and positions in the middle of slab are spaced more sparsely.

lz=lz-1+Δlz

(2)

where,zis the sequence number of multi-point-setting position;lzis the distance from multi-point-setting sequencezto slab head;and Δlzis the distance from multi-point-setting sequencezto previous set point.

Slab multi-point-setting positions can be mapped from rolling lenght at each stand as follows:

Liz=LRi·lz

(3)

where,Lizis the actual length to the exit of standiat multi-point-setting positionz.

2.3 Mapping calculation of strip speed diagram and position

According to thread speed,primary acceleration,and secondary acceleration,the mapping diagram of the full-length position and speed of strip during rolling process at each stand is calculated as shown in Fig.1.

Using the following equation,elapsed rolling time from the start of primary acceleration to the start of secondary acceleration (t1) can be calculated:

(4)

where,v0is the thread speed;a1is primary acceleration;andLa1is the distance from strip head as it leaves the finishing mill exit to the beginning of secondary acceleration.

Rolling speed at the start of secondary acceleration(v1) can be calculated as follows:

v1=v0+a1·t1

(5)

Rolling time from the start of secondary acceleration to the maximum rolling speed (t2) can be calculated as follows:

(6)

where,vmaxis the maximum rolling speed of the finishing rolling;anda2is secondary acceleration.

Using the following equation,rolling length at the maximum rolling speed (Lacc) can be calculated:

(7)

Using the following equation,the ratio of strip length at standito the finishing-rolling length(LEi) can be calculated:

(8)

Using the following equation,the rolling length of slab at standiwhen strip passes successfully(LHi) can be calculated:

(9)

where,Lfmis the distance between two adjacent stands in the finishing area.

Speed at each position of each stand can be calculated with following procedure:

(1) If the position is located before the secondary-acceleration start position:

(10)

where,vizis the rolling speed of standiat multi-point-setting positionz.

(2) If the position is within the range of secondary acceleration:

(11)

(3) If the secondary acceleration range has been exceeded:

viz=vmax

(12)

2.4 Initialization of cooling water flow

Cooling water flow between stands at all locations can be initialized using the pre-calculated cooling water flow for strip:

ISCiz=PISCi

(13)

where,ISCizis the cooling water flow of standiat multi-point-setting position z;and PISCiis the pre-calculated cooling water flow for head of standi.

2.5 Initialize the rolling force

Rolling force of each stand at all locations can be initialized using the pre-calculated rolling force for strip:

Fiz=PFi

(14)

where,Fizis the rolling force of standiat multi-point-setting positionz;and PFiis the rolling force pre-set for head of standi.

2.6 Calculate the effect of changes in temperature and speed on the rolling force during rolling

Using the following equation,rolling force(F) can be calculated:

F=km·lw·ld·Qp·KF

(15)

where,kmis the material deformation resistance;lwis the slab width;ldis the flattened contact arc length;Qpis the external friction influence coefficient; andKFis the rolling-force learning coefficient.

The influence coefficient of temperature change onkm(TIC) can be calculated:

(16)

where,BK0is the temperature coefficient in the calculation of deformation resistance;Tnew1is the temperature of strip after cooling and rolling deformation;andTold1is the temperature pre-set for head of strip.

The influence coefficient of speed change onkm(VIC) can be calculated:

(17)

where,BK4is the temperature coefficient in the calculation of deformation resistance;vnewis the speed of strip after rolling acceleration;andvoldis the speed pre-set for head of strip.

2.7 Adjust the rolling force of the strip affected by speed

Using the following equation,the rolling force of strip affected by speed(F′iz) can be adjusted:

F′iz=Fiz·VICiz

(18)

where,VICizis the influence coefficient affected by speed of standiat multi-point-setting positionz.

2.8 Calculate the FDT

Air-cooling temperature,deformation temperature,and water-cooling temperature of the continuous-rolling zone F1-F7 can be calculated based on the known inlet strip temperature[5].

Using the following equation,the temperature after air cooling(Tnew2) can be calculated:

Tnew2=Fair(Told2,Tair,tair)

(19)

where,Fairis the air-cooling temperature calculation model;Told2is the temperature before air cooling;Tairis the air temperature;andtairis the air-cooling time.

The temperature after rolling deformation(Tnew3) can be calculated as follows:

Tnew3=Told3+ΔTdeform-ΔTcon

(20)

where,Told3is the temperature before rolling defor-mation;ΔTdeformis the temperature increase brought by rolling deformation;and ΔTconis heat conduction tem-perature loss between rolling strip and roll.

The temperature after water cooling(Tnew4) can be calculated as follows:

Tnew4=Fisc(Told4,Twater,ISC,tisc)

(21)

where,Fiscis the water-cooling temperature calculation model;Told4is the temperature before water cooling;Twateris the cooling water temperature;ISC is the cooling water flow;andtiscis the water-cooling time.

Outlet temperature of next stand can be calculated based on the outlet temperature of previous stand,water cooling,air cooling,and deformation.Com-bining the calculation equations for air cooling,deformation,and water cooling,the following equation for outlet temperature calculation can be established.The outlet temperature of each stand can be calculated using Equation (22):

TEi=Fexport(TP,Fi,Tair,tair,Twater,ISC,tisc)

(22)

where,TEiis the exit temperature of standi;Fexportis the exit temperature calculation model;TPis the exit temperature of front stand;andFiis the rolling force of standi.

FDT can be calculated using the following calculation procedure:

(23)

where,T0is the inlet temperature of the finishing zone;andTfmis the temperature at the finishing-zone temperature measurement point.

2.9 FDT feedback control

FDT can be calculated by feedback control.Under the condition of keeping the preset control parameters of strip head unchanged,cooling water flow between stands is adjusted according to the measured FDT to control the subsequent strip temperature consistent with target value[6],as shown in Fig.2.

During the adjustment,rolling speed remains unchanged from the original speed diagram,and only cooling water flow between the stands is adjusted.The new temperature is recalculated after the change of ISC in Equation (21),and TICiz(the influence coefficient affected by temperature of the standiat the multi-point-setting positionz) value is recalculated using Equation (16).Therefore,rolling force is corrected by the temperature influence factor(F″iz):

F″iz=Fiz·TICiz

(24)

Changes in rolling force cause changes in temperature,which can be calculated using Equation (20).In reverse,temperature also affects rolling force,which is described in Equation (15).Iterative calculation of rolling temperature and rolling force is performed until a convergence threshold is met.The FDT adjustment is made after convergence.

2.10 Summary of full-length multi-point settings

Based on the feedback control of FDT[5],the cooling water flow between stands is adjusted to achieve target FDT,the temperature of strip between stands is recalculated,and the rolling force is corrected in combination with the change in rolling speed.Finally,the multi-point setting of strip length direction is achieved.The input of multi-point-setting model includes temperature diagram at the entrance of finishing mill,multi-point-setting distance configuration of slab,the equipment capability and layout of finishing area,pre-calculated setting information,speed strategy,and finishing rolling goal.The output information is a set of multi-point settings for entire length of strip,including rolling force curve,speed curve,and cooling-water change curve.

3 Application effect

Using the proposed model,the multi-point settings for entire length of strip are calculated before rolling.The results of the model are displayed in the form of a curve describing the change of rolling force,tempera-ture,speed,and the cooling water between stands in the entire length direction.On the multi-point-setting curve,the extreme values of the rolling load are clearly visible,which is helpful for indicating whether the equipment capability limits are reached.The cooling-water load curve between stands facilitates pre-rolling analysis for the FDT control model[7],which is more helpful for optimizing FDT control strategy[8].

We use this model to calculate the actual perfor-mance data of production line,the samples of which are provided below.

3.1 Configuration of length-direction multi-point distribution

Calculation of the division in the length direction is provided by the multi-point-setting model,length of slab head and tail is defined,and different calculation intervals are configured for the head,body,and tail,respectively,as shown in Table 1.

3.2 Configuration of equipment layout and equip-ment capacity

The equipment layout mainly involves the distance between stands.The spacing between finishing stands is the same.The equipment capacity mainly describes the upper limit of cooling water flow between stands,as shown in Table 2.

Table 1 Multi-point distribution configuration in the length directionm

Table 2 Equipment capacity configuration when finishing stand spacing is 7 mm3/h

3.3 Speed control

Speed control includes the threading speed of finishing rolling,primary acceleration,secondary acceleration,and the maximum rolling speed,as shown in Table 3.

3.4 Head pre-set model output

Head pre-set data are used as input to provide a starting point for the calculation of the multi-point settings.The subsequent position setting value is calculated on this basis,which will greatly reduce the time complexity of the multi-point-setting calculation model,as shown in Table 4.

3.5 Data for temperature curve at finishing mill inlet

The multi-point settings for the entire length is based on the inlet temperature for the finishing rolling,and the temperature change is calculated step by step until reaching the outlet for the finishing rolling.The feedback calculation of the FDT is based on the matching between the outlet temperature for the finishing rolling and the target temperature,as shown in Fig.3.

Table 4 Head pre-set model output

3.6 Multi-point calculation output

The output values of multi-point setting calculation include speed curve (Fig.4),the change curve of cooling water flow (Fig.5),the change curve of rolling force (Fig.6),and the change curve of FDT (Fig.7).

4 Conclusions

(1) In this paper,calculation of rolling force load for each stand in rolling cycle of strip steel is provided using full-length and multi-point settings,and the maximum and minimum rolling forces are clearly described,which can serve as a data basis for load adjustment.

(2) The multi-point-setting model takes the finishing mill inlet temperature as benchmark,and then adjusts cooling water between stands,and controls FDT in a feedforward manner.The output cooling-water-flow curve of the model can clearly describe whether the equipment capability meets the requirements of FDT control,which provides a data basis for the adjustment of FDT control strategy.