1　Introduction

The advantages of the twin-roll strip continuous casting and rolling process include low energy consumption,environmental protection,use of simple equipment,and low overall investment.Furthermore,the fast cooling rate of strip casting generates casting steel strips with a very fine microstructure and excellent ductility,such that this process represents the trend in modern iron and steel manufacturing.In recent decades,technology for the direct casting of steel strips has made significant progress.In particular,twin-roll strip casting technology has been developed globally to an industrial level[1-3].

In the twin-roll strip casting process,the hot casting steel strip is lowered from the nip between a pair of counter-rotating horizontal casting rolls to be rolled in a hot rolling mill.During the casting opera-tion,a casting strip guiding device changes the orientation of the hot casting steel strip with respect to the rolling direction from perpendicular to par-allel.To avoid breaking or tearing the hot casting steel strip after the onset of rolling,the usual method is for a certain length of hot steel strip to be hung freely between the nip point of the two casting rolls and the rolling mill to deal with the speed difference between the casting roll and rolling mill.In this paper,the hot steel strip hanging freely between the nip point of the casting rolls and rolling mill is referred to as the “free loop”.

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Accurately measuring and controlling the height of the free loop is the key factor in ensuring a stable casting operation.The height of the free loop is directly related to the length of the casting strip that forms the free loop;therefore,accurately calculating the length of the free loop of the casting strip is the basis for controlling the height of the free loop.The control system adjusts the speed difference between the twin-roll caster and rolling mill to directly control the height of the free loop.Compared with the disadvantages of the existing method for mea-suring the loop height of the steel strip,this paper presents a method for accurately measuring and controlling the loop height of hot steel strips.When combined with the practical casting loop quantity change curve,the proposed control method meets the requirements of casting strip operations.

2　Profile equation for free loop of a hot steel strip

The profile of the free loop of a hot steel strip is constrained by the relative position of the two support points that form the free loop and limit its height.When designing a twin-roll strip caster,an ideal free loop profile is calculated according to the process requirements,and then the structure of the equipment that forms the free loop is designed.In the casting operation,the height of free loop must be precisely detected and controlled to within a stable range by adjusting the speed difference between the casting roll speed and the rolling speed.In this way,we can avoid the generation of cracks and other defects in the strip surface at the lowest point of the free loop[4-5].

Once the head of the hot steel strip has passed the pinch roll following the guide roll table,the upper pinch roll is screwed down to pinch the strip,as shown in Fig.4.The strip is then sent to the hot rolling mill and strip tension is established between the pinch roll and the hot rolling mill.Next,loop control is established in which the height of the free loop is kept within a stable range by controlling the difference between the casting roll speed and the rolling speed.Speed deviation is controlled by propor-tional-integral-derivative (PID) control whose input value is the length deviation calculated using Equa-tions (3) and (4).

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Measurement error is inevitable when using a single infrared scanner to detect the height of free loops.If the detection range of a free loop is large,this measurement error will seriously affect the ability to control the accuracy of the free loop height.This is why the method for measuring the height of free loop with a single infrared scanner must be modified.

In Fig.1,the two support points of the free loop are points B (nip of casting roll) and C (guide roll).When the free loop hangs freely between the two support points by the influence of gravity while elasticity and deformation are ignored,the resulting profile is a catenary curve with support points of dif-ferent height.Assuming the coordinate points B and C,respectively,are(x1,y1) and (x2,y2),then by trans-lating the coordinate axis until the x coordinate of the lowest point of the catenary is 0,the simplified formula for the catenary is as follows:

(1)

As the vertex of the catenary,point A (0,a) is the intersection of the catenary and vertical axis y,as shown in Fig.1,and the loop height of the strip casting is defined as f,as expressed in Equation (2) below:

f=y1-a

(2)

Then,h,l,s are expressed as shown in Equations (3) and (4)[6]:

In the above equations:

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22例不合格标本中，1～12岁组8例（13.8%）；13～60岁组4例（3.0%）；60岁以上者10例（10.3%）。1～12岁组与13～60岁组人群比较，卡方=8.070 0，P=0.004 5，差异有显著性；60岁以上组与13～60岁组人群比较，卡方=5.301 8，P=0.021 3，差异有显著性。结果见表2。

h:the vertical distance between the two support points of the catenary,h=y2-y1.

l:the horizontal distance between the support points of the catenary,l=x2-x1.

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In practical applications,because the two support points of the free loop are known,the height of the free loop can be calculated using the catenary Equations (1)-(4) with different loop lengths.Fig.2 shows profiles of free loops with different heights and lengths.

a:a constant.

s:the length of the hot steel strip between the support points of the catenary.

3　Method for measuring height of steel strip loop

Several types of detection systems are commonly used in detecting the height of a cold strip loop,including a loop scanner with a single photo cell,a loop scanner with a multipoint photoelectric switch,and a loop scanner with a linear CCD[7].These detection methods require additional light sources as feedback signals in the detection systems.In the strip casting process,the temperature of the hot steel strips is so high that it interferes with the imaging of the feedback light on the detection element,which degrades the measurement accuracy.Therefore,in-frared scanners are typically used as the detection instrument for measuring the height of the free loop in the strip casting process.

The basic principle involves detecting the infrared ray emitted from the hot steel strip by a photo-electric cell connected to a rotating mirror drum that reflects the infrared ray to the photoelectric cell.The optical signal is then converted to a measure-ment pulse signal for comparison with a reference pulse signal,and the phase signal difference is determined by the measurement system.This phase signal difference is proportional to the scanning angle α of the infrared scanner in the detection scope.Lastly,based on the scanning angle α and the distance between the bottom of the hot steel strip and the infrared scanner,the measurement system calculates the height of the free loop.

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Fig.3 shows a diagram of the free loop height mea-surement process with an infrared scanner.

3.1　Method for measuring the free loop height of hot steel strip with single infrared scanner

Because the installed position and structure size of the detected objects differ,the infrared scanner must be calibrated according to a preset center line x=Cn′ before it measures the height of the free loop.It is assumed that the lowest points of free loop having different heights will fall on this preset center line.However,this method is only feasible for free loop whose corresponding two support points are on the same heights.

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In the strip casting process,since the two support points of free loop are on different heights,with one located at the nip point of the twin casting rolls and the other at the guide roll in front of the pin-ch roll,the abscissa value x at the lowest point of the free loop changes with the height of the free loop.

During actual operation,the mearsurement error appears as shown in Fig.4,such that when the lowest point’s horizontal ordinate of the free loop changes from Cn′ to Cn,the real height of the free loop is fn,although the measurement height in the infrared scanner is fn′ at the same scanner angle as that of fn.Equation (5) is used to obtain the measurement error of the free loop height of the casting strip by a single infrared scanner:

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Δf=y-y′

(5)

Fig.4　Diagram of measurement error for the free loop height with single infrared scanner

Fig.1 shows a profile diagram of a free loop.

3.2　Method for measuring the loop height of hot steel strip with double infrared scanners

To improve the measurement accuracy of free loops of casting steel strips,this paper proposes a method that uses opposed dual infrared scanners to measure the height of the free loop.Fig.5 shows a diagram of the process for measuring the free loop height using opposed dual infrared scanners.Two infrared scanners are installed on the outer sides of the two support points of the free loop,respec-tively,and these infrared scanners are also on the same horizontal level as their adjoining scanning centers.After the formation of a free loop,the two infrared scanners simultaneously detect the free loop of hot steel strip and the measurement system cal-culates the free loop height corresponding to the scanning angle.

Here,we take free loop No.1 shown in Fig.5 as an example to illustrate the method used to calculate the free loop height.In the range of the free loop height,there is a certain stiffness in the hot strip steel forming the free loop,so there is little change in the contact position with the guide roll.As such,it is assumed that the hot strip steel forming the free loop is in contact with the guide roll at the same position.The horizontal distance between two infrared scanners can be represented as follows:

L=y1/tanα1+y1/tanα2

(6)

The ordinate value at the lowest point A of free loop No.1 can be calculated using Equation (6),as shown in Equation (7):

(7)

The height of the free loop is as follows:

f1=H-y1

(8)

In Equations (6)-(8):

H:the vertical distance between the lowest support point of the free loop and the scanning center of the two infrared scanners(the scanning angle is zero in the scanning center).

L:the horizontal distance between the two in-frared scanners.

In the same way,the values of the vertical coor-dinates at the bottom of loop No.2 and the height of the loop can be obtained using Equations (7) and (8).

f1:the height of free loop No.1.

y1:the ordinate at the lowest point of free loop No.1.

α1,α2:the scanning angle of the lowest point G of free loop No.1,as detected by infrared scanners No.1 and 2,respectively.

In Equations (6)-(8),values H,L are known values and α1,α2 are the measured values of the free loop detected by infrared scanners No.1 and 2,

式中:xk为状态向量;zk为测量向量；wk，vk分别为过程噪声和零均值高斯序列的测量噪声,相应的协方差矩阵分别为Qk和Rk.

respectively.Even if the height of the free loop changes from f1 to f2,the loop height can be calculated using Equations(7) and(8),which are not affected by changes in the lowest point of the free loop.As such,the measurement error associated with the measurement of the height of a free loop by a single infrared scanner is eliminated.

4　Method for controlling free loop height of hot steel strip

A stable free loop height also decreases the swinging frequency and amplitude of the hot steel strip,thereby facilitating the formation of the free loop without quality defects in the nip point of the two casting rolls.

This scheme mainly utilizes the relationship bet-ween the height of the free loop and the length of the casting steel strip which forms the free loop (Fig.2).Thus,the length of the casting steel strip is used to control the free loop height.Fig.6 shows the free loop control logic diagram.

In typical PID control systems,significant error cannot be eliminated quickly when the control system starts,stops,or has step change input.Due to the integral control,the system generates a large overshoot and oscillation,and a proportional and integral separation algorithm is used to decrease this overshoot and improve the control quality of the system (Equation (9)).This means that integral control can be switched on only if the error is small.

(9)

In this formula,N is a logical coefficient,with the following values:

(10)

In the Equation (10),M is a predetermined threshold.

Integral control can be switched off if ΔL is greater than M.

Integral control can be switched on if ΔL is no more than M.

Using this method to control the height of the free loop of hot steel strip,the free loop can be estab-lished quickly and stably,as shown in Fig.5.Fig.7 shows that the time spent in the formation of a free loop is less than 40 s and the control precision is ±2.5%.

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5　Conclusions

By analyzing the profile characteristics and formation method of free loops in the twin-roll strip casting process,the relation equation for the length and height of the free loop was derived.

曲堤排闸孔深20m。闸基高程5.1～5.7m为第②层壤土，构成地基直接持力层，具中等压缩性，微透水性。高程5.1～3.7m为第②3层粉砂，中密，具中等透水性，渗透稳定性较差，具液化潜势。高程3.7m以下为第②、③壤土和④1层黏土层，各具中等压缩性，微透水性。其中，第③层壤土粉黏粒分布不均，含腐殖质和贝壳碎屑等，局部软塑，工程地质性质相对较差。

This paper compared the basic principles of the existing measurement methods for loop height of strip and chose the infrared scanner for measuring the free loop height of hot steel strip in strip casting process.

By studying the principles used in measurements of the free loop height using the single infrared scanner,the measurement strategy was identified.Then,a measurement method was developed to accurately measure the free loop height of hot steel strip using double infrared scanners.

在文献存储与共享学习空间都需要不断拓展空间的当下，本着合作共享、协同发展之目的，图书馆可以利用有限的馆舍，以较少的投入实现空间最大限度的合理利用，使馆藏低利用率文献得以长期保存和再利用。这其中联合存储书库有其建设的合理价值，应当予以考虑。

In the proposed measurement method for the freeloop height of hot steel strip,the length of the hot steel strip is controlled using a PID control method.The application results show that,using the pro-posed method,the free loop of hot steel strip is established quickly and stably and the control precision of the free loop height meets operational casting requirements.

References

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[2]　KILLMORE C R,CREELY H,PHILIPS A,et al.Deve-lopment of ultra-thin cast strip products by the CASTRIP process[C]∥AISTech (Iron & Steel Technology Con-ference).Indianapolis:Association for Iron & Steel Technology,2007:465- 480.

[3]　ZHANG X Z,LIAO P and WANG M L.Investigation on development of twin roll cast strip[J].Iron and Steel,2010,45(3):13-17.

[4]　YE C H,FANG Y,GU L F,et al.Study on design of strip casting loops[J].Heavy Machinery,2009(4):23-26.

[5]　SAN Z H.Mechanics of Materials[M].Beijing:Higher Education Press,1999:142.

[6]　XING F C.Method of calculation for the difference between ordinates of support points and vertex of catenary[J].Mathematics in Practice and Theory,2004,34(11):98-101.

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