**Abstract: **The shape control of hot-rolled strip is multifaceted. Influencing factors mainly include rolling force, roll bending force, stringing roll position, roll thermal expansion, roll profile, and roll wear. These factors interact and restrict each other, and jointly control the shape of the strip. Among many factors, the roll wear factor is the most uncontrollable. The surface of the back-up roll is often uneven and wears for a long time, and the back-up roll belongs to the basic bearing rolling force, so the calculation of the wear model of the back-up roll is very necessary. The compensation control method is added to the existing shape control model, and the quality of the product has also been greatly improved.

In the production process of hot rolling, the shape of the strip directly affects the economic value of a coil, so high-tech technology and mathematical models are most widely used in the production of hot rolling. Roll quality and use technology are getting more and more attention from people in the industry. The strip steel is leveled by a tempering machine, and a small deformation of 0.5%~3% is applied to the strip steel to eliminate the yield platform, improve the mechanical properties, and also improve the shape of the strip. After the steel strip is flattened, it is cut into finished steel plates or strip steel coils, and then sent to users after sorting and packaging.

**This paper analyzes the roll wear calculation and compensation control of a 1780 mm hot continuous rolling finishing mill in a steel plant.**

The shape control of strip steel in hot rolling production is mainly controlled by the shape model, which mainly consists of two parts: the shape setting model and the shape self-adaptive model. The strip shape definition is mainly composed of flatness and cross-sectional shape, and the cross-sectional shape includes roll gap shape, strip crown and work roll wear shape. These four factors interact and restrict each other, and jointly control the shape of the strip.

**Shape setting model**

During the hot rolling process, the shape of the product is mainly controlled in the finish rolling area. When the intermediate slab with rolling information passes through the 7 rolling mills in the finish rolling area, it will become a strip with target thickness, crown and flatness, and the control of the crown and flatness of the strip is controlled by Shape setting model is controlled.

After the intermediate slab with a certain degree of convexity passes through hot rolling, finish rolling and hot continuous rolling for 7 stands, it will become a strip steel with the target convexity. The cross section of the intermediate slab with convexity is shown in Figure 1.

According to the definition, the convexity C_{0 }of the intermediate billet is:

The convexity C_{1} of the F7 export strip is:

The cross-section of the F7 strip outlet is shown in Figure 2.

The relationship between convexity and thickness is the convexity ratio. The schematic diagram of the side of the strip is shown in Figure 3. According to the principle of constant strip volume:

According to the above formula, the relationship of the convex ratio is:

However, the state in production will have many objective factors, and the relationship of the convex ratio cannot achieve the ideal state:

When the convex ratio is within the range of the above formula, the strip shape is good, when the convex ratio is greater than

When the strip produces side waves. The schematic diagram of the wave shape is shown in Figure 4.

When

The strip produces intermediate waves

When

The strip produces edge waves.

**2. Rolling mill Roll wear model**

Roll wear is divided into work wheel wear and support roll wear. In the rolling process, the wear of the roll is an inevitable loss of material, and with the increase of the number of rolling, the amount of wear of the roll will increase accordingly. As the requirements for hot-rolled products are getting higher and higher, the expansion to thinner gauges is also gradually increasing, so the number of kilometers of rolled rolls is on the rise. The number of kilometers rolled has an inevitable relationship with the wear of the backup rolls, which will lead to an increase in the daily wear of the backup rolls. The influence of wear of back-up rolls in finishing rolling on the shape of products is becoming more and more prominent.

**2.1 Work roll wear model**

In the process of establishing the work roll model, the work roll is divided into several areas in the longitudinal direction for calculation, and each area is represented by a point. See Figure 5.

Work roll wear calculation formula:

**formula:**

W is the wear of the work roll in the diameter direction.

α is the offline adaptive compensation coefficient.

K_{w }is the work roll wear coefficient.

F is rolling force.

M is the non-uniform pressure correction coefficient.

w is the strip width.

l_{c} is the length of the strip contact surface.

out is the strip rolling length.

D is the working wheel diameter.

The wear model of the work roll can be established according to the above formula, in which the work roll wear coefficient, offline self-adaptive compensation coefficient and other parameters need to be configured in the configuration file to facilitate optimization and modification. The wear parameter table is shown in Figure 6.

The width of the roll needs to be wider than the strip to roll a quality product. Therefore, when the work rolls move with a fixed step according to the placement position and roll until the end of the roll change, the wear of the work rolls will be very serious, and the closer to the middle, the more serious the wear. Since the rolling site is free rolling, pits corresponding to the width of the strip will appear if the product width is different.

Take the strip steel of the above block specification as an example. The roll width is 1780 mm, the strip width is 1028 mm, and the moving step of F7 is 100 mm, so the maximum contact edge between the working side and the driving side is 180 mm to 1680 mm, which will produce stepped wear, as shown in Figure 7. See Figure 8 for a schematic diagram of the positions of the string spokes with equal step lengths.

In order to solve this problem, it is necessary to add a step-changing module on the basis of the original model, and reduce the wear of the rolls by changing the equal-step rolling, so as to roll out products with better shape. Changing the step size into a regular array, the purpose is to distribute the wear evenly on the roll and avoid roll pits. The schematic diagram of the step size is shown in Figure 9.

**2.2 Support roller wear model**

The wear of the back-up rolls is the most serious in the F6F7 of the finishing mill. In the shape control, the influence of the last two stands on the shape is relatively high, so the calculation deviation of the wear of the back-up rolls will lead to a decrease in the quality of the shape of the product, and the wear of the rolls will continue to increase as the rolling progresses , and its influence on the shape control characteristics of the rolling mill is also constantly changing [+-5]. Therefore, the support roll model is particularly important in the control of the strip shape.

When the working wheel with dimples is in contact with the backup roll and rolled, the dimples of the working wheel change the deformation of the contact and the shape of the bite mark when the load is applied, and more bending force is required to compensate This abnormal deviation from the rolling force.

Statistical field data analysis shows that after a certain number of kilometers of rolling, the back-up roll will be rubbed by the work roll with pits to form a special wear shape. The wear of the back-up roll is in an arched distribution, which is the same as the pressure distribution between the rolls . A second-order equation can be used to approximate the wear of work rolls and backup rolls during work roll rolling, as shown in Figure 10.

A simulated second-order equation is:

Therefore, the roll system deformation of the support roll is calculated by the finite element in the support roll model:

**formula:**

C_{m} is the crown of the loaded roll gap.

F_{r }is the rolling force per unit width of the working wheel.

B is the resultant force of the bending force.

C_{p-w} is the wheel train crown of the contact surface between the strip and the work roll, that is, the original roll shape of the work wheel under no load.

C_{w-b} is the convexity of the work roll to the backup roll contact surface.

**3 Adaptive model of backup roll compensation**

The feedback compensation adaptive system is very important in industrial production. The existence of the compensation control system makes up for the defects of the original control system to a large extent and ensures the stability and accuracy of the system control. The two main functions of the compensation system are: compare the actual data with the model calculation data, feed back the difference between the two to the compensation system and organize and store the data, directly reflecting the accuracy of the calculation model and making a contribution to the subsequent adaptive learning. Preparation: Modify the model subsystem to account for uncertainties and improve the accuracy of the set model.

The adaptive control model of the roll is mainly composed of three subsystem modules:

1) Data feedback comparison module. The model calculation data Ymeam and the field real data Yalc are used as input at the same time, and the result △Y obtained by comparison and calculation is used as the output of the comparison module;

2) Tuning parameter module. AY is the input of this module, analyze the parameters related to the calculation deviation of the original set model, and optimize the parameters;

3) Model setting module. The optimized parameters are brought into the model setting module to calculate the setting data, and finally output.

The adaptive model control logic diagram is shown in Figure 11.

The specific implementation method of the compensation adaptive model is as follows.

**3.1 Calculation of self-adaptive coefficient of strip steel**

3.1.1 Calculation of convexity adaptive parameters

**formula:**

△Crown is the difference between the target convexity and the actual convexity average.

△B_{c }is the bending wheel force required to eliminate the strip crown difference.

h is the adaptive adjustment coefficient.

B_{setup} is the set bending force of the corresponding strip.

In order to ensure the accuracy of the system and the stability of rolling, the strip crown self-adaptation will only be applied in the first 4 stands of the finishing tandem rolling unit.

3.1.2 Calculation of flatness adaptive parameters

**formula:**

△Flatness is the difference between the target flatness and the actual flatness average.

△BF is the bending force required to eliminate the difference in strip flatness; k is the self-adaptive adjustment coefficient.

B_{SETUP} is the set bending force of the corresponding strip.

3.1.3 Operator Input Adaptive Parameter Calculation

The operator’s roll bending force corrections for all stands are used as correction parameters for the adaptive model control.

3.1.4 Adaptive coefficient of strip steel

The data information and setting calculation data of each strip during the rolling process will be recorded in the database. The self-adaptive parameters of the strip are also calculated on the basis of the self-adaptive parameters of the rolled strip of the same specification, so as to achieve timely correction. The adaptive coefficient formula is as follows:

**formula:**

g^{NEW }is the self-adaptive coefficient of the strip.

g^{OLD} is the self-adaptive coefficient of the upper strip of the same specification.

k_{v} is an adaptive adjustment coefficient.

K_{OP} is the operator adjustment coefficient.

**3.2 Compensation control model**

The rolling quality of the product can be improved by dynamically adjusting the wear amount of the back-up roll during the rolling process. The dynamic compensation adaptive control model is calculated as follows:

In the formula: α and B are adaptive adjustable constants; L is the rolling kilometers of the corresponding stand.

Taking the back-up roll wear of 1780 hot-rolled finish rolling F7 in the steel plant as an example, the back-up roll wear is calculated based on the measured strip head shape and adaptively optimized and corrected, so that the site can realize free rolling and reduce the impact of roll wear on the strip. The effect of steel plate shape. When the hot rolling model does not apply the compensation control model, the bending force setting will be inaccurate due to the inaccurate calculation of roll wear, and the strip will have a wavy shape, which will easily cause deviations in flatness. Fig. 12 is the flatness control diagram of the strip before the compensation control system is not put into use.

The head flatness deviation of the strip is –100I, the rolling force is 9000 k_{N}, the rolling kilometer is 1.1 km, the wheel bending force is 880 k_{N}, g^{OLD} is 1.003, ge, gr and gop are calculated respectively is 1.061, 1.033, 1.003, then g^{NEW}=1.003+0.5[( 1.06 – 1)+ ( 1.033 -1)]+0.85( 1.003 -1) =1.052

o, β usually take 0.1 and 0.5, then the wear amount of the F7 support wheel is: W =[0.1 + 0.5 ( 1 – 1.052 ) ] × 1.1 =0.081 4 cm

Using the adaptive control model can fully adapt to the influence of various working conditions on the wear amount of the backup roll in the actual rolling, and based on the original wear amount, it can effectively prevent the deviation of the wear amount calculation caused by the unexpected situation from being too large big. After the self-adaptive correction value of the wear of the support roll of the strip steel accurately predicts the wear amount, the bending force of the set roll will be increased in rolling again to compensate for the wave shape caused by the wear. While improving the shape quality of hot-rolled products, it can also extend the rolling service life of the backup rolls, achieving the effect of reducing costs and increasing efficiency.

The test results are very obvious. The service life of the back-up rollers has been increased from the original 80,000 tons to 200,000 tons. It can be seen from Figure 13 that after the compensation control system is adopted, the wear calculation of the back-up rollers is accurate and the bending The calculation of roll force setting is accurate, the situation of poor shape is reduced, and the control of strip flatness is improved.

**4 Conclusion**

The accuracy of roll wear calculation has a great influence on the setting of roll bending force and the strip shape. The compensation control system can improve the calculation accuracy of back-up roll wear, which is beneficial to improve the service life of the roll and the flatness control of the strip. But at present, the compensation control system is only used in the finishing stand F7, and the application of this system in all hot rolling stands still needs to be further perfected.