A method for controlling the roll gap crown of a hot finishing mill stand

Abstract

This invention relates to a method for controlling the crown of the load-bearing roll gap in a hot-rolling finishing mill, belonging to the technical field of hot rolling methods in the metallurgical industry. The technical solution of this invention is as follows: The finite element method is used to analyze the crown of the load-bearing roll gap under different rolling forces, bending roll forces, workpiece widths, and roll parameters, analyzing the influence relationship of each factor on the roll gap crown; the model coefficients of the load-bearing roll gap crown model are regressed; the calculation results are compared with those of the finite element method and the existing TMEIC mill load-bearing roll gap model to determine the accurate values ​​for bending rolls and shifting rolls; the influence function method is used to study the magnitude and direction of the frictional force between the roll systems, identifying the wear law of the support rolls and its influence on the crown of the load-bearing roll gap. The beneficial effects of this invention are: it not only effectively reduces the frequency of premature roll replacement due to mill tailing and improves the mill's operating rate, but also significantly reduces roll consumption, does not affect the thickness tolerance of thin-gauge strip products, simplifies operation, and requires no manual intervention.

Description

Technical Field

[0001] This invention relates to a method for controlling the crown of the bearing roll gap in a hot-rolled finishing mill, belonging to the technical field of hot rolling methods in the metallurgical industry. Background Technology

[0002] The load-bearing roll gap crown model, as a core sub-model of the TMEIC shape model, directly affects the accuracy of plate crown and shape control, thus impacting product quality. While many hot rolling production lines in China use the TMEIC shape model, few can independently calculate the load-bearing roll gap crown and identify calculation errors. The hot rolling secondary model requires continuous adaptation and optimization, and research and development units are working to use different methods to calculate the load-bearing roll gap crown in order to improve the accuracy of shape control.

[0003] Problems with strip shape control accuracy typically emerge gradually during product development. This manifests as difficulty in achieving the desired crown and shape after changing steel grades or specifications. Strip shape indicators such as crown hit rate and strip symmetry and straightness hit rate show a gradual decreasing trend as product and specification development progresses. Process control issues include unstable roll crown compensation values ​​within the same rolling stroke and the inability to properly implement long-term roll crown self-learning. Furthermore, during the TMEIC strip shape model correction process, significant setting deviations were found in the load-average roll gap crown model. For high-strength steel and thin-gauge strips, large correction values ​​are often required to achieve the desired crown and straightness. Therefore, a comprehensive analysis of the TMEIC load-average roll gap crown model (UFD) is necessary to support subsequent strip shape correction work. Summary of the Invention

[0004] The purpose of this invention is to provide a method for controlling the crown of the support roll gap in a hot-rolled finishing mill. By using the influence function method and modifying the automated first-level control program, the impact of support roll wear on strip shape control was verified using actual production data. A strip shape compensation model for support roll wear was established. After setting the preset values ​​for various parameters, the program operation is accurate and simplified, without increasing any equipment investment. It is environmentally friendly and can be widely applied to hot continuous rolling production lines. It not only effectively reduces the frequency of premature roll replacement due to mill tailing and improves the mill's operating rate, but also significantly reduces roll consumption without affecting the thickness tolerance of thin-gauge strip products. After being integrated into the mill's first-level operation program, the operation is simplified, and the timing and degree of roll gap lifting are accurately controlled without manual intervention, effectively solving the aforementioned problems in the background technology.

[0005] The technical solution of this invention is: a method for controlling the crown of the bearing roll gap in a hot-rolled finishing mill, comprising the following steps:

[0006] (1) The finite element method was used to analyze the bearing roll gap crown under different rolling forces, bending roll forces, workpiece widths and roll parameters, and to analyze the influence relationship of each factor on the roll gap crown.

[0007] (2) Use the obtained roll gap crown data to regress the model coefficients of the uniform load roll gap crown model;

[0008] (3) Compare the calculation results with those of the finite element method and the calculation results of the existing TMEIC mill load-average roll gap model to determine the accurate values ​​of the bent roll and the shifting roll.

[0009] (4) Use the influence function method to study the magnitude and direction of friction between the roller system, find out the wear law of the support roller and the influence law on the convexity of the bearing roller gap.

[0010] In step (1), the calculation accuracy is improved by using a mesh densification method at the contact points between rolls and between rolls and strip; as the rolling force increases, the bearing roll gap convexity increases; as the width of the rolled piece increases, the bearing roll gap convexity decreases.

[0011] In step (2), the regression model for the TMEIC uniform roll gap crown is as follows:

[0012] (21) Introducing the concept of unloaded roll gap crown, the unloaded roll gap crown between the work rolls is shown in the following formula:

[0013]

[0014] In the formula, C ws The unloaded roll gap crown between the work rolls, in mm; S e1 and S e2 The roll gap at the end of the work roll body, in mm; S c The roll gap at the rolling centerline, in mm;

[0015] (22) Assuming the shape of the unloaded roll gap changes according to a quadratic curve, the convexity of the unloaded roll gap between the work rolls is calculated using the following formula:

[0016]

[0017] In the formula, C ws C represents the unloaded roll gap crown between the work rolls, in mm. W0 The original grinding crown of the work roll can be obtained by interpolation based on the lateral displacement position of the work roll for CVC mills, in mm; C eqv Equivalent crown of the work roll, mm. and The wear amounts of the upper and lower work rolls at the rolling centerline are respectively, in mm; and The figures represent the average wear of the upper and lower work rolls at the edge of the strip, in mm. and These are the thermal expansion amounts of the upper and lower work rolls at the rolling centerline, respectively, in mm; and These represent the average thermal expansion of the upper and lower work rolls at the edge of the strip, in mm; W represents the strip width, in mm. wr The width of the work roll surface;

[0018] (23) The concept of unloaded roll gap convexity between the work roll and the support roll is introduced, and its calculation method is shown in the following formula:

[0019]

[0020] In the formula, C wb C represents the unloaded roll gap crown between the work roll and the support roll, in mm. W0 and C b0 These are the original grinding crowns of the work roll and support roll, respectively, in mm; L br Support roller surface width, mm; L wr Width of the work roll surface, in mm; The average wear at the midpoint of the upper and lower support rollers, in mm; Average wear of the upper and lower support rollers around their sides, in mm; The average thermal expansion at the midpoint of the upper and lower support roller bodies, in mm; Average thermal expansion of the upper and lower support rollers around their sides, in mm; and These represent the wear amounts of the upper and lower work rolls at the rolling centerline, respectively. and These are the average wear amounts (in mm) of the upper and lower work rolls corresponding to the positions on the sides of the support roll. and These are the thermal expansion amounts of the upper and lower work rolls at the rolling centerline, respectively, in mm; and These are the average thermal expansion amounts (in mm) of the upper and lower work rolls corresponding to the positions on the sides of the support roll.

[0021] (24) Based on the offline calculation results of the finite element method, regression analysis was performed on the uniform load roll gap crown under different roll widths, and the resulting model structure is shown below:

[0022]

[0023]

[0024] In the formula, The uniform load roll gap crown is measured in mm. The rolling force per unit width is kN / mm; The bending force is kN. The unloaded roll gap crown between the working rolls, in mm; The unloaded roll gap convexity between the work roll and the support roll, in mm; and Diameters of the work roll and support roll, respectively, in mm; and Diameters of the work roll and support roll, respectively, in mm; The elastic modulus of the work roll; These are the model regression coefficients. Table 3.1 shows the model regression coefficients for different rolled piece widths;

[0025] (25) Obtaining the model regression coefficients b under different rolled piece widths i Then, the regression coefficient b of the model is... i The cubic polynomial expressed as the width of the rolled piece is shown below:

[0026] b i =c i,0 +c i,1 ·W+c i,2 ·W 2 +c i,3 ·W 3 i = 1 to 18

[0027] In the formula, W is the width of the rolled piece, mm, c i,j These are the polynomial coefficients.

[0028] In step (4), a calculation model for the bearing roll gap crown is established based on the influence function method, and the bearing roll gap crown under uniform load is calculated using the finishing mill stand of the hot rolling line.

[0029] The relationship between rolling force and roll gap crown: As the rolling force increases, the roll gap crown increases, and the roll gap crown of wide specifications is generally smaller than that of narrow specifications;

[0030] The relationship between bending force and roll gap crown: as the bending force increases, the roll gap crown decreases, and the reduction in roll gap crown for wide specifications is greater than that for narrow specifications.

[0031] The relationship between work roll crown and roll gap crown: as roll crown increases, roll gap crown decreases, and the reduction in roll gap crown for wide specifications is greater than that for narrow specifications.

[0032] The relationship between support roll crown and roll gap crown: as roll crown increases, roll gap crown decreases, and the reduction in roll gap crown for wide specifications is greater than that for narrow specifications.

[0033] The relationship between work roll diameter and roll gap crown: For narrow specifications, the roll gap crown decreases as the roll diameter increases; for wide specifications, the work roll diameter has little effect on the roll gap crown.

[0034] The relationship between the support roll diameter and the roll gap crown is as follows: as the roll diameter increases, the roll gap crown decreases.

[0035] The relationship between the elastic modulus of a roll and the roll gap crown: The elastic modulus of a roll has a relatively small effect on the roll gap crown.

[0036] In step (4), the amount of wear on the support roller is related to factors such as the material of the roller, surface hardness and smoothness, lateral distribution of pressure between rollers, relative sliding amount and rolling distance.

[0037] (41) Friction on the contact arc and wear model of the work roll:

[0038]

[0039] Where: w - wear amount, mm; α - wear rate; β - roll diameter correction coefficient; P - rolling force per unit width, N·mm-1; N - number of revolutions during roll rolling; L - total roll rolling length, m; L0 - roll surface hardening rate parameter;

[0040] (42) Calculation of friction between roller systems and wear of support rollers:

[0041] Speed ​​difference formula:

[0042] k V (i)=V WR (i)-V BUR (i)

[0043] In the formula, i is the i-th node of the inter-roller contact area along the length of the roll body; V BUR (i), V WR (i) - are the linear velocities of the support roller and the work roller at the i-th node, respectively;

[0044] The influence function method is used to calculate the inter-roll contact pressure, and the actual rolling parameters are adopted. The formula for calculating the inter-roll friction balance is as follows:

[0045]

[0046] In the formula, f(i) is the frictional force at the i-th node; q(i) is the inter-roller pressure at the i-th node; u is the constant term in the friction coefficient; R BUR (i) and R WR (i) are the radii of the support roller and the working roller at the i-th node, respectively; w BUR and w WR These are the angular velocities of the support roller and the work roller, respectively.

[0047] (43) The effect of support roll wear on roll gap crown: The influence function method is used to calculate the effect of new support roll and worn support roll on the exit crown of the stand. The rolling parameters are the same as above. The plate crown corresponding to the worn support roll is larger, which corresponds to the phenomenon that double-sided waves are more likely to occur in the downstream stand of the finishing mill in the later stage of support roll use.

[0048] (44) Shape Compensation Model for Support Roller Wear: In a hot rolling production line, the influence of support roll wear on the shape model is not considered under initial conditions. Before and after the replacement of the worn support roll, the roll crown self-learning of the finishing mill stand in the shape model shows obvious reverse learning, indicating that the shape control conditions change significantly before and after the support roll replacement. Before the roll replacement, the shape model learns in the direction of eliminating double-sided waves, and after the roll replacement, it learns in the direction of eliminating central waves. This phenomenon is significantly improved after adding compensation for support roll wear on the shape model.

[0049] The beneficial effects of this invention are as follows: By using the influence function method, the automated first-level control program was modified, and the impact of support roll wear on strip shape control was verified using actual production data. A strip shape compensation model for support roll wear was established. After setting the preset values ​​for various parameters, the program operation is accurate and simplified, without increasing any equipment investment. It is green and environmentally friendly and can be widely applied to hot strip production lines. It not only effectively reduces the frequency of early roll replacement due to mill tailing and improves the mill's operating rate, but also significantly reduces the consumption of rolls. It does not affect the thickness tolerance of thin-gauge strip products. After being integrated into the mill's first-level operation program, the operation is simplified, and the timing and degree of roll gap lifting are accurately controlled without manual intervention. Attached Figure Description

[0050] Figure 1 This is the strain contour plot calculated by the finite element method of this invention;

[0051] Figure 2 This is a diagram showing the shape of the empty roller gap between the working rollers of the present invention;

[0052] Figure 3 This is a schematic diagram illustrating the calculation principle of the influence function method of this invention. Detailed Implementation

[0053] To make the purpose, technical solutions, and advantages of the invention's embodiments clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the embodiments described are only a small part of the embodiments of the present invention, not all of them. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the protection scope of the present invention.

[0054] A method for controlling the crown of the bearing roll gap in a hot-rolled finishing mill includes the following steps:

[0055] (1) The finite element method was used to analyze the bearing roll gap crown under different rolling forces, bending roll forces, workpiece widths and roll parameters, and to analyze the influence relationship of each factor on the roll gap crown.

[0056] (2) Use the obtained roll gap crown data to regress the model coefficients of the uniform load roll gap crown model;

[0057] (3) Compare the calculation results with those of the finite element method and the calculation results of the existing TMEIC mill load-average roll gap model to determine the accurate values ​​of the bent roll and the shifting roll.

[0058] (4) Use the influence function method to study the magnitude and direction of friction between the roller system, find out the wear law of the support roller and the influence law on the convexity of the bearing roller gap.

[0059] In step (1), the calculation accuracy is improved by using a mesh densification method at the contact points between rolls and between rolls and strip; as the rolling force increases, the bearing roll gap convexity increases; as the width of the rolled piece increases, the bearing roll gap convexity decreases.

[0060] In step (2), the regression model for the TMEIC uniform roll gap crown is as follows:

[0061] (21) Introducing the concept of unloaded roll gap crown, the unloaded roll gap crown between the work rolls is shown in the following formula:

[0062]

[0063] In the formula, C ws The unloaded roll gap crown between the work rolls, in mm; S e1 and S e2 The roll gap at the end of the work roll body, in mm; S c The roll gap at the rolling centerline, in mm;

[0064] (22) Assuming the shape of the unloaded roll gap changes according to a quadratic curve, the convexity of the unloaded roll gap between the work rolls is calculated using the following formula:

[0065]

[0066] In the formula, C ws C represents the unloaded roll gap crown between the work rolls, in mm. W0 The original grinding crown of the work roll can be obtained by interpolation based on the lateral displacement position of the work roll for CVC mills, in mm; C eqv Equivalent crown of the work roll, mm. and The wear amounts of the upper and lower work rolls at the rolling centerline are respectively, in mm; and The figures represent the average wear of the upper and lower work rolls at the edge of the strip, in mm. and These are the thermal expansion amounts of the upper and lower work rolls at the rolling centerline, respectively, in mm; and These represent the average thermal expansion of the upper and lower work rolls at the edge of the strip, in mm; W represents the strip width, in mm. wr The width of the work roll surface;

[0067] (23) The concept of unloaded roll gap convexity between the work roll and the support roll is introduced, and its calculation method is shown in the following formula:

[0068]

[0069] In the formula, C wb C represents the unloaded roll gap crown between the work roll and the support roll, in mm. W0 and C b0 These are the original grinding crowns of the work roll and support roll, respectively, in mm; L br Support roller surface width, mm; L wr Width of the work roll surface, in mm; The average wear at the midpoint of the upper and lower support rollers, in mm; Average wear of the upper and lower support rollers around their sides, in mm; The average thermal expansion at the midpoint of the upper and lower support roller bodies, in mm; Average thermal expansion of the upper and lower support rollers around their sides, in mm; and These represent the wear amounts of the upper and lower work rolls at the rolling centerline, respectively. and These are the average wear amounts (in mm) of the upper and lower work rolls corresponding to the positions on the sides of the support roll. and These are the thermal expansion amounts of the upper and lower work rolls at the rolling centerline, respectively, in mm; and These are the average thermal expansion amounts (in mm) of the upper and lower work rolls corresponding to the positions on the sides of the support roll.

[0070] (24) Based on the offline calculation results of the finite element method, regression analysis was performed on the uniform load roll gap crown under different roll widths, and the resulting model structure is shown below:

[0071]

[0072] In the formula, The uniform load roll gap crown is measured in mm. The rolling force per unit width is kN / mm; The bending force is kN. The unloaded roll gap crown between the working rolls, in mm; The unloaded roll gap convexity between the work roll and the support roll, in mm; and Diameters of the work roll and support roll, respectively, in mm; and Diameters of the work roll and support roll, respectively, in mm; The elastic modulus of the work roll; These are the model regression coefficients. Table 3.1 shows the model regression coefficients for different rolled piece widths;

[0073] (25) Obtaining the model regression coefficients b under different rolled piece widths i Then, the regression coefficient b of the model is... i The cubic polynomial expressed as the width of the rolled piece is shown below:

[0074] b i =c i,0 +c i,1 ·W+c i,2 ·W 2 +c i,3 ·W 3 i = 1 to 18

[0075] In the formula, W is the width of the rolled piece, mm, c i,j These are the polynomial coefficients.

[0076] In step (4), a calculation model for the bearing roll gap crown is established based on the influence function method, and the bearing roll gap crown under uniform load is calculated using the finishing mill stand of the hot rolling line.

[0077] The relationship between rolling force and roll gap crown: As the rolling force increases, the roll gap crown increases, and the roll gap crown of wide specifications is generally smaller than that of narrow specifications;

[0078] The relationship between bending force and roll gap crown: as the bending force increases, the roll gap crown decreases, and the reduction in roll gap crown for wide specifications is greater than that for narrow specifications.

[0079] The relationship between work roll crown and roll gap crown: as roll crown increases, roll gap crown decreases, and the reduction in roll gap crown for wide specifications is greater than that for narrow specifications.

[0080] The relationship between support roll crown and roll gap crown: as roll crown increases, roll gap crown decreases, and the reduction in roll gap crown for wide specifications is greater than that for narrow specifications.

[0081] The relationship between work roll diameter and roll gap crown: For narrow specifications, the roll gap crown decreases as the roll diameter increases; for wide specifications, the work roll diameter has little effect on the roll gap crown.

[0082] The relationship between the support roll diameter and the roll gap crown is as follows: as the roll diameter increases, the roll gap crown decreases.

[0083] The relationship between the elastic modulus of a roll and the roll gap crown: The elastic modulus of a roll has a relatively small effect on the roll gap crown.

[0084] In step (4), the amount of wear on the support roller is related to factors such as the material of the roller, surface hardness and smoothness, lateral distribution of pressure between rollers, relative sliding amount and rolling distance.

[0085] (41) Friction on the contact arc and wear model of the work roll:

[0086]

[0087] Where: w - wear amount, mm; α - wear rate; β - roll diameter correction coefficient; P - rolling force per unit width, N·mm-1; N - number of revolutions during roll rolling; L - total roll rolling length, m; L0 - roll surface hardening rate parameter;

[0088] (42) Calculation of friction between roller systems and wear of support rollers:

[0089] Speed ​​difference formula:

[0090] k V (i)=V WR (i)-V BUR (i)

[0091] In the formula, i is the i-th node of the inter-roller contact area along the length of the roll body; V BUR (i), V WR (i) - are the linear velocities of the support roller and the work roller at the i-th node, respectively;

[0092] The influence function method is used to calculate the inter-roll contact pressure, and the actual rolling parameters are adopted. The formula for calculating the inter-roll friction balance is as follows:

[0093]

[0094] In the formula, f(i) is the frictional force at the i-th node; q(i) is the inter-roller pressure at the i-th node; u is the constant term in the friction coefficient; R BUR (i) and R WR (i) are the radii of the support roller and the working roller at the i-th node, respectively; w BUR and w WR These are the angular velocities of the support roller and the work roller, respectively.

[0095] (43) The effect of support roll wear on roll gap crown: The influence function method is used to calculate the effect of new support roll and worn support roll on the exit crown of the stand. The rolling parameters are the same as above. The plate crown corresponding to the worn support roll is larger, which corresponds to the phenomenon that double-sided waves are more likely to occur in the downstream stand of the finishing mill in the later stage of support roll use.

[0096] (44) Shape Compensation Model for Support Roller Wear: In a hot rolling production line, the influence of support roll wear on the shape model is not considered under initial conditions. Before and after the replacement of the worn support roll, the roll crown self-learning of the finishing mill stand in the shape model shows obvious reverse learning, indicating that the shape control conditions change significantly before and after the support roll replacement. Before the roll replacement, the shape model learns in the direction of eliminating double-sided waves, and after the roll replacement, it learns in the direction of eliminating central waves. This phenomenon is significantly improved after adding compensation for support roll wear on the shape model.

[0097] In practical applications, this invention includes the following steps:

[0098] 1. Finite element analysis of rolling mill roll gap crown

[0099] To reduce analysis costs, the finite element model in this patent uses a 1 / 4 scale model. In the contact analysis, either the first-order hexahedral non-conforming element C3D8I or the first-order hexahedral reduced integral element C3D8R is selected. However, if the model focuses on calculating the strain at the element nodes, C3D8R is used; therefore, this paper adopts C3D8R. Furthermore, the model employs a mesh refinement method at the contact areas between rolls and between rolls and strip to improve calculation accuracy. The total number of mesh elements is 84,136 (which can be adjusted appropriately according to the roll size). The calculated strain contour plot is shown below. Figure 1 .

[0100] The shape and values ​​of the bearing roll gap crown under different working conditions were analyzed and compiled. Data analysis shows that the bearing roll gap crown increases with increasing rolling force and decreases with increasing workpiece width. The finite element calculation results for rolling force, workpiece width, bending force, roll diameter, and roll crown were used for the bearing roll gap crown model regression in the next subsection.

[0101] 2. Regression Model of TMEIC Roll Gap Crown

[0102] Primetals establishes an integrated rapid calculation model for rolls and rolled products that combines a three-dimensional deformation model of strip steel with a roll system deformation model. Taking the calculation of the cross-sectional profile shape of strip steel as the core, it iteratively calculates and finally outputs the inter-roll contact pressure and the cross-sectional profile of strip steel.

[0103] The TMEIC load-equalizing roll gap crown is the shape of the load-equalizing roll gap when the reduction coefficient is the same along the width of the rolled piece. It reflects the inherent shape control capability of the rolling mill. The load-equalizing roll gap crown is related to factors such as the rolling force per unit width, strip width, bending force, material and diameter of the work roll and support roll, and the shape of the unloaded roll gap. Factors affecting the shape of the unloaded roll gap include the lateral position of the work roll, the original crown of the work roll and support roll, wear of the work roll and support roll, and thermal expansion.

[0104] To quantitatively describe the shape of the unloaded roll gap, the concept of unloaded roll gap crown is introduced. The relative positions of the upper and lower work rolls under no-load conditions are shown in [reference needed]. Figure 2 The crown of the unloaded roll gap between the working rolls is shown in the following formula:

[0105]

[0106] In the formula, C ws The unloaded roll gap crown between the work rolls, in mm; S e1 and S e2 The roll gap at the end of the work roll body, in mm; S c The roll gap at the center line of the rolling mill is measured in mm.

[0107] Assuming the shape of the unloaded roll gap changes according to a quadratic curve, the convexity of the unloaded roll gap between the work rolls can be calculated using the following formula:

[0108]

[0109]

[0110] In the formula, C ws C represents the unloaded roll gap crown between the work rolls, in mm. W0 The original grinding crown of the work roll can be obtained by interpolation based on the lateral displacement position of the work roll for CVC mills, in mm; C eqv Equivalent crown of the work roll, mm. and The wear amounts of the upper and lower work rolls at the rolling centerline are respectively, in mm; and The figures represent the average wear of the upper and lower work rolls at the edge of the strip, in mm. and These are the thermal expansion amounts of the upper and lower work rolls at the rolling centerline, respectively, in mm; and These represent the average thermal expansion of the upper and lower work rolls at the edge of the strip, in mm; W represents the strip width, in mm. wr This refers to the width of the work roll surface.

[0111] Under no-load conditions, the work roll and the support roll are in partial contact, with a certain gap between them. To describe the shape of the no-load gap between the work roll and the support roll, similar to the previous method, the concept of the no-load gap convexity between the work roll and the support roll is introduced, and its calculation method is shown in the following formula:

[0112]

[0113] In the formula, C wb C represents the unloaded roll gap crown between the work roll and the support roll, in mm. W0 and C b0These are the original grinding crowns of the work roll and support roll, respectively, in mm; L br Support roller surface width, mm; L wr Width of the work roll surface, in mm; The average wear at the midpoint of the upper and lower support rollers, in mm; Average wear of the upper and lower support rollers around their sides, in mm; The average thermal expansion at the midpoint of the upper and lower support roller bodies, in mm; Average thermal expansion of the upper and lower support rollers around their sides, in mm; and These represent the wear amounts of the upper and lower work rolls at the rolling centerline, respectively. and These are the average wear amounts (in mm) of the upper and lower work rolls corresponding to the positions on the sides of the support roll. and These are the thermal expansion amounts of the upper and lower work rolls at the rolling centerline, respectively, in mm; and These represent the average thermal expansion of the upper and lower work rolls at the positions on the sides of the support roller, in mm.

[0114] The advantage of introducing unloaded roll gap crown is that it integrates multiple factors affecting the shape of the unloaded roll gap into two factors, greatly reducing the complexity of the uniformly loaded roll gap crown regression model. Furthermore, the uniformly loaded roll gap crown regression model is applicable to three types of mills: conventional mills, PC mills, and CVC mills.

[0115] Based on the offline calculation results of the finite element method, regression analysis was performed on the uniform load roll gap crown under different workpiece widths, and the resulting model structure is shown below:

[0116]

[0117] In the formula, The uniform load roll gap crown is measured in mm. The rolling force per unit width is kN / mm; The bending force is kN. The unloaded roll gap crown between the working rolls, in mm; The unloaded roll gap convexity between the work roll and the support roll, in mm; and Diameters of the work roll and support roll, respectively, in mm; and Diameters of the work roll and support roll, respectively, in mm; The elastic modulus of the work roll; These are the model regression coefficients. Table 3.1 shows the model regression coefficients for different rolled piece widths.

[0118] Table 3.1 Model Regression Coefficients

[0119] Width, mm 1000 1250 1500 1800 b1 6.5E-02 1.0E-01 1.3E-01 1.3E-01 b2 1.4E-03 2.1E-03 2.5E-03 1.9E-03 b3 -2.1E-01 -3.4E-01 -4.8E-01 -6.6E-01 b4 -1.0E-03 -1.3E-03 -1.6E-03 -2.0E-03 b5 1.3E-04 1.6E-04 1.9E-04 2.3E-04 b6 -1.8E-04 -3.1E-04 -4.7E-04 -7.2E-04 b7 1.3E-07 2.1E-07 3.1E-07 4.5E-07 b8 -1.4E-09 -2.3E-09 -3.5E-09 -5.3E-09 b9 -2.6E-02 -4.3E-02 -6.0E-02 -8.1E-02 b10 -6.1E-05 -9.0E-05 -1.1E-04 -9.3E-05 b11 1.7E-07 2.8E-07 4.3E-07 6.5E-07 b12 -6.7E-06 -1.3E-05 -2.1E-05 -3.3E-05 b13 -6.9E-09 -1.0E-08 -1.1E-08 -7.2E-09 b14 1.4E-10 2.4E-10 3.9E-10 6.9E-10 b15 1.2E-04 1.9E-04 2.7E-04 3.7E-04 b16 5.6E-08 7.5E-08 7.0E-08 5.8E-09 b17 1.6E-08 3.4E-08 6.5E-08 1.3E-07 b18 -5.4E-11 -1.1E-10 -2.1E-10 -4.2E-10

[0120] To facilitate online application, the model regression coefficients b for different rolled piece widths were obtained. i Then, the regression coefficient b of the model is... i The cubic polynomial expressed as the width of the rolled piece is shown below:

[0121] b i =c i,0 +c i,1 ·W+c i,2 ·W 2 +c i,3 ·W 3 i = 1 to 18

[0122] In the formula, W is the width of the rolled piece, in mm. These are polynomial coefficients, which can be obtained using regression analysis based on the data in the table above. Polynomial Regression Coefficients As shown in Table 3.2.

[0123] Table 3.2 Polynomial Regression Coefficients

[0124] j 0 1 2 3 C1,j 1.37E-01 -4.35E-04 5.18E-07 -1.55E-10 C2,j 3.60E-03 -1.18E-05 1.40E-08 -4.47E-12 C3,j -4.54E-02 1.94E-04 -4.40E-07 7.89E-11 C4,j 5.24E-04 -2.09E-06 6.89E-10 -1.70E-13 C5,j -8.00E-05 3.11E-07 -1.34E-10 3.18E-14 C6,j 3.93E-05 -1.13E-07 -3.45E-11 -7.63E-14 C7,j 7.37E-08 -2.14E-10 3.09E-13 -4.13E-17 C8,j -8.49E-10 2.19E-12 -2.83E-15 1.33E-19 C9,j -1.26E-02 5.20E-05 -8.54E-08 1.96E-11 C10,j -1.40E-04 4.42E-07 -5.28E-10 1.65E-13 C11,j -1.45E-08 3.00E-11 1.20E-13 3.77E-17 C12,j -9.58E-06 2.97E-08 -3.07E-11 3.92E-15 C13,j -1.77E-08 5.84E-11 -7.06E-14 2.30E-17 C14,j -1.43E-10 4.75E-13 -4.30E-16 2.35E-19 C15,j 2.91E-05 -1.23E-07 2.72E-10 -5.55E-14 C16,j 1.21E-07 -4.32E-10 5.70E-13 -2.03E-16 C17,j -1.68E-08 7.30E-11 -9.46E-14 5.48E-17 C18,j 5.13E-11 -2.30E-13 3.01E-16 -1.76E-19

[0125] Taking 2.75*1850mm cold-rolled SPHC-S as an example, the roll shifting position was calculated using the UFD coefficients of the finishing mill stand obtained through regression, and compared with the original calculation results from TMEIC. The calculation results are shown in Tables 3.3 and 3.4, respectively. A comparison of the two tables reveals that the roll shifting position calculated using the new UFD coefficients tends towards negative shifting, which is consistent with our direction of correcting the TMEIC calculation results, indicating to some extent that the new UFD coefficients are more reasonable. These new UFD coefficients are currently used for offline calculations.

[0126] Table 3.3 Roll shifting position calculated using TMEIC UFD coefficient

[0127] project unit F1 F2 F3 F4 F5 F6 F7 Deformation temperature ℃ 1101.81 1072.61 899.77 894.63 889.61 884.65 879.79 reduction ratio r ％ 49.15 46.14 32.10 30.09 26.08 19.06 13.04 Inlet thickness mm 40.65 20.67 11.13 7.56 5.29 3.91 3.16 Export thickness mm 20.67 11.13 7.56 5.29 3.91 3.16 2.75 Rolling force kN 32273 32327 32268 27947 20151 13361 10413 Bending roller force kN 1000 1000 1000 1000 1000 1000 1000 Roller shifting mm 4 24 34 37 65 41 32

[0128] Table 3.4 Roll shifting position calculated with the new UFD coefficient

[0129] project unit F1 F2 F3 F4 F5 F6 F7 Deformation temperature ℃ 1101.81 1072.61 899.77 894.63 889.61 884.65 879.79 reduction ratio r ％ 49.15 46.14 32.10 30.09 26.08 19.06 13.04 Inlet thickness mm 40.65 20.67 11.13 7.56 5.29 3.91 3.16 Export thickness mm 20.67 11.13 7.56 5.29 3.91 3.16 2.75 Rolling force kN 32273 32327 32268 27947 20151 13361 10413 Bending roller force kN 1000 1000 1000 1000 1000 1000 1000 Roller shifting mm -10 11 23 29 65 41 32

[0130] 3. Analysis of the Influence Function Method on Roll Gap Crown of Rolling Mill

[0131] A calculation model for the bearing roll gap crown is established based on the influence function method. The bearing roll gap crown under uniform load is calculated using the finishing mill stand of a hot rolling line. The calculation principle is described in [link to calculation]. Figure 3 .

[0132] Using the above calculation results, the coefficients for calculating the bearing roll gap crown were regressed. The regression coefficients are shown in Table 3.5. The regression accuracy of the coefficients is controlled within 95% of ±0.005mm, which is a high level of accuracy.

[0133] Table 3.5 UFD Regression Coefficients of a Certain 1580 Line from F1 to F4

[0134] j 0 1 2 3 C1,j 2.8E-02 3.7E-02 4.2E-02 4.1E-02 C2,j 5.5E-04 4.6E-04 4.8E-04 1.2E-03 C3,j -1.8E-01 -2.5E-01 -3.3E-01 -6.0E-01 C4,j -5.3E-04 -3.0E-03 -6.8E-03 -1.8E-03 C5,j 6.8E-05 4.4E-04 9.7E-04 2.3E-04 C6,j -1.1E-04 -1.6E-04 -2.1E-04 -3.7E-04 C7,j -3.8E-07 -8.8E-07 -1.2E-06 -9.0E-08 C8,j 1.2E-08 2.7E-08 3.6E-08 6.4E-09 C9,j -6.8E-02 -8.6E-02 -9.6E-02 -1.6E-01 C10,j -2.3E-05 -2.8E-05 -3.0E-05 -3.0E-05 C11,j 9.4E-08 1.3E-07 1.5E-07 3.2E-07 C12,j -7.1E-07 -1.0E-06 -2.6E-06 -5.8E-06 C13,j -5.1E-09 -6.3E-09 -6.7E-09 -6.6E-09 C14,j 1.1E-10 1.4E-10 2.4E-10 2.8E-10 C15,j 8.2E-05 9.5E-05 9.1E-05 3.1E-04 C16,j 2.4E-08 3.4E-08 1.1E-07 1.5E-07 C17,j 1.3E-08 2.1E-09 6.0E-09 -4.9E-09 C18,j -1.0E-10 -1.0E-10 -1.2E-10 -2.7E-11

[0135] (1) Effect of rolling force on roll gap crown

[0136] The relationship between rolling force and roll gap crown: As the rolling force increases, the roll gap crown increases, and the roll gap crown of wide specifications is generally smaller than that of narrow specifications.

[0137] (2) Influence of bending force on roll gap crown

[0138] The relationship between bending force and roll gap crown is as follows: as bending force increases, roll gap crown decreases, and the reduction in roll gap crown for wide specifications is greater than that for narrow specifications.

[0139] (3) The influence of work roll crown on roll gap crown

[0140] The relationship between work roll crown and roll gap crown: as roll crown increases, roll gap crown decreases, and the reduction in roll gap crown for wide specifications is greater than that for narrow specifications.

[0141] (4) The effect of support roll crown on roll gap crown

[0142] The relationship between support roll crown and roll gap crown: as roll crown increases, roll gap crown decreases, and the reduction in roll gap crown for wide specifications is greater than that for narrow specifications.

[0143] (5) The effect of work roll diameter on roll gap crown

[0144] The relationship between work roll diameter and roll gap crown: For narrow specifications, the roll gap crown decreases as the roll diameter increases; for wide specifications, the work roll diameter has little effect on the roll gap crown.

[0145] (6) Influence of support roller diameter on roll gap crown

[0146] The relationship between the support roll diameter and the roll gap crown is as follows: as the roll diameter increases, the roll gap crown decreases.

[0147] (7) The effect of the elastic modulus of the roll on the roll gap crown

[0148] The relationship between the elastic modulus of a roll and the roll gap crown: The elastic modulus of a roll has a relatively small effect on the roll gap crown.

[0149] 4. The effect of support roll wear on hot-rolled strip shape

[0150] To a large extent, the crown and shape control of hot-rolled strip depends on finishing milling; therefore, the shape model must accurately predict roll system deformation, including the elastic deformation, thermal expansion, and wear of the work rolls and support rolls. Typically, mill model settings only consider wear at the centerline of the support rolls, primarily for thickness control. However, studies of actual shape data show that support roll wear significantly affects strip straightness. Ignoring support roll wear will negatively impact shape model calculations, making it impossible to achieve the expected straightness and crown. For example, support rolls on downstream stands are more prone to double-sided waviness in later stages of use. Simultaneously, support roll wear significantly affects strip crown, especially for wide strips.

[0151] Wear of the support roll is mainly caused by relative sliding and rolling with the work roll. During contact friction, metal particles on the support roll surface are ground off, causing wear. The amount of wear is related to factors such as the roll material, surface hardness and finish, lateral pressure distribution between rolls, relative sliding amount, and rolling distance. Based on the analysis of wear causes, domestic scholars have developed a new support roll wear model.

[0152] (1) Friction on the contact arc and wear model of the work roll

[0153] The wear model for work rolls is relatively mature and can be described as follows:

[0154]

[0155] Where: w - wear amount, mm; α - wear rate; β - roll diameter correction coefficient; P - rolling force per unit width, N·mm-1; N - number of revolutions during roll rolling; L - total roll rolling length, m; L0 - roll surface hardening rate parameter.

[0156] The above model predicts the wear caused by relative sliding between the rolls and the strip surface. According to rolling theory, the roll speed is constant in the deformation zone, while the strip's horizontal speed increases rapidly, approaching the roll speed at the boundary between the forward and backward sliding zones, and increasing slowly above the roll's horizontal speed in the forward sliding zone. Tserikoff's calculations of the frictional force on the contact arc show that the frictional force is relatively stable in the backward sliding zone, while the rolling force reaches its peak at the boundary between the forward and backward sliding zones and then decreases; the frictional force is significantly lower in the forward sliding zone. The adhesive friction zone is distributed near the center angle, dividing the deformation zone into forward and backward sliding zones. Compared to the sliding friction zone, the roll wear in the adhesive friction zone is negligible.

[0157] (2) Calculation of friction between roller systems and wear of support rollers

[0158] The interaction between the work roll and the support roll is completely different. The work roll drives the support roll to rotate through frictional contact. When rotating, the rotational angular velocity of each point on the work roll or support roll is the same. However, due to the existence of the initial crown, wear crown, and thermal crown of the roll, the rotation radius of each point on the roll is different, and the contact pressure between the rolls is also different. This results in different relative linear velocities and sliding friction forces at each point on the contact line between the work roll and the support roll.

[0159] Therefore, a speed difference is introduced, as shown in the following formula:

[0160] k V (i)=V WR (i)-V BUR (i)

[0161] In the formula, i is the i-th node of the inter-roller contact area along the length of the roll body; V BUR (i), V WR (i) - are the linear velocities of the support roller and the work roller at the i-th node, respectively.

[0162] When the support roll rotates at a constant speed, the inter-roller frictional torque on the support roll is balanced with the frictional torque of the support roll bearing. Ignoring the rotational friction of the support roll oil film bearing, the inter-roller frictional force on the support roll is balanced. That is, similar to the rolling zone, there exists a slip zone and a neutral line between the work roll and the support roll.

[0163] This paper uses the influence function method to calculate the inter-roll contact pressure, adopts actual rolling parameters, and the calculation formula for the inter-roll friction balance is shown below.

[0164]

[0165] In the formula, f(i) is the frictional force at the i-th node; q(i) is the inter-roller pressure at the i-th node; u is the constant term in the friction coefficient; R BUR (i), R WR (i) are the radii of the support roller and the working roller at the i-th node, respectively; w BUR w WR These are the angular velocities of the support roller and the work roller, respectively.

[0166] The inter-roll pressure and friction distribution of the new work roll and the new support roll, as well as the inter-roll pressure and friction distribution of the new work roll and the worn support roll, were calculated using formulas. Due to the chamfer at the end of the support roll, the inter-roll pressure and friction in this area are zero. The calculation results show that for the middle region of the support roll, as the work roll reciprocates, the absolute value of the inter-roll friction corresponding to the new support roll is relatively uniformly distributed, indicating relatively uniform wear in this area. However, towards the end of the support roll's service life, the absolute value of the inter-roll friction in the middle region of the support roll will no longer be uniformly distributed. The absolute value of the inter-roll friction during negative lateral movement will be significantly greater than that during positive lateral movement, meaning that the worn support roll tends to amplify the uneven distribution of inter-roll friction, thus leading to uneven wear. When using a CVC roll type work roll and its matching CVC roll type support roll, at any lateral movement position, the inter-roll pressure on both sides of the roll body is basically symmetrical, but the inter-roll friction is significantly asymmetrical. This also explains, to some extent, the asymmetrical wear of the support roll.

[0167] Taking the intermediate stand of a hot rolling line as an example, the wear of the rolls over one service cycle is calculated using the above friction calculation method. The wear is proportional to the friction and the rolling length, as shown in Formula 3-9 below.

[0168]

[0169] In the formula, w(i) is the wear amount of the i-th node; L(i) is the relative sliding distance of the i-th node; α is the wear coefficient; and t is the rolling time.

[0170] The distribution of shifting roll positions used in the calculation is the same as the actual distribution, conforming to a normal distribution, and the mean and standard deviation of the actual shifting rolls are used. To simplify the calculation, conventional steel grades and average specifications are used. The distribution trend of wear along the roll body shows good agreement between the calculated and actual values.

[0171] (3) The effect of support roller wear on roll gap crown

[0172] The influence function method was used to calculate the impact of new and worn support rolls on the exit crown of the mill stand, with the same rolling parameters as above. The results show that the plate crown corresponding to the worn support roll is larger, which corresponds to the phenomenon that double-sided waves are more likely to occur in the downstream stand of the finishing mill in the later stages of support roll use.

[0173] (4) Plate shape compensation model for support roller wear

[0174] In a hot rolling production line, under initial conditions where the impact of support roll wear on the shape model is not considered, the roll crown self-learning of the finishing mill stand in the shape model shows a significant reverse learning pattern before and after the replacement of the worn support rolls. This indicates that the shape control conditions change significantly before and after the support roll replacement. Furthermore, before the replacement, the shape model learns towards eliminating bilateral waviness, while after the replacement, it learns towards eliminating central waviness. This phenomenon is significantly improved after adding compensation for support roll wear on the shape model.

[0175] The beneficial effects of the present invention using the above technical solution are as follows:

[0176] 1. The method of the present invention, by modifying the automated first-level control program and setting the preset values ​​of various parameters, makes the program operation accurate and simplified, without increasing any equipment investment, and is green and environmentally friendly. It can be widely applied to hot rolling production lines.

[0177] 2. This invention can prevent strip throwing and tailing, and reduce the damage to the rolls caused by tailing. Applying this method not only effectively reduces the frequency of premature roll replacement due to strip throwing and improves the mill's operating rate, but also significantly reduces roll consumption.

[0178] 3. This control method does not affect the thickness tolerance of thin-gauge strip products. For example, for the 1500×2.0mm specification, after F4 polishing and before F5 polishing, the roll gap value of the F5 stand increases by 0.68mm from the original value, and the maximum deviation of the strip thickness increase is 0.15~0.17, which matches the actual thickness. For the 1500×1.8mm specification, after F4 polishing and before F5 polishing, the roll gap value of the F5 stand increases by 0.63mm from the original value, and the maximum deviation of the strip thickness increase is 0.12~0.14, which matches the actual thickness.

[0179] 4. Once this method is integrated into the rolling mill's primary operating procedure, operation is simplified, and the timing and degree of roll gap lifting are accurately controlled without manual intervention. Operators do not require special professional training or experience; they only need to carefully read the operating procedures and diligently follow the regulations.

Claims

1. A method for controlling the crown of the bearing roll gap in a hot-rolled finishing mill, characterized in that... Includes the following steps: (1) The finite element method was used to analyze the bearing roll crown under different rolling forces, bending roll forces, workpiece widths and roll parameters, and to analyze the influence relationship of each factor on the roll crown. (2) Use the obtained roll gap crown data to regress the model coefficients of the uniform load roll gap crown model; (3) Compare the calculation results with those of the finite element method and the calculation results of the existing TMEIC mill load-sharing roll gap model to determine the accurate values ​​of the bent roll and the shifting roll. (4) Use the influence function method to study the magnitude and direction of friction between the rollers, and find out the wear law of the support roller and the influence law on the convexity of the bearing roller gap.

2. The method for controlling the crown of the bearing roll gap in a hot-rolled finishing mill according to claim 1, characterized in that: In step (1), the calculation accuracy is improved by using a mesh densification method at the contact points between rolls and between rolls and strip; as the rolling force increases, the bearing roll gap convexity increases; as the width of the rolled piece increases, the bearing roll gap convexity decreases.

3. The method for controlling the crown of the bearing roll gap in a hot-rolled finishing mill according to claim 1, characterized in that: In step (2), the regression model for the TMEIC uniform load roll gap crown is as follows: (21) Introducing the concept of unloaded roll gap crown, the unloaded roll gap crown between the work rolls is shown in the following formula: ； In the formula, The unloaded roll gap crown between the working rolls, in mm; and The roll gap at the end of the work roll body, in mm; The roll gap at the rolling centerline, in mm; (22) Assuming the shape of the unloaded roll gap changes according to a quadratic curve, the convexity of the unloaded roll gap between the working rolls is calculated using the following formula: ； ； In the formula, The unloaded roll gap crown between the working rolls, in mm; The original grinding crown of the work roll can be obtained by interpolation based on the lateral displacement position of the work roll for CVC mills, in mm; Equivalent crown of the work roll, mm. and The wear amounts of the upper and lower work rolls at the rolling centerline are respectively, in mm; and The figures represent the average wear of the upper and lower work rolls at the edge of the strip, in mm. and These are the thermal expansion amounts of the upper and lower work rolls at the rolling centerline, respectively, in mm; and These represent the average thermal expansion of the upper and lower work rolls at the edge of the strip, in mm; W is the strip width. The width of the work roll surface; (23) The concept of unloaded roll gap convexity between the work roll and the support roll is introduced, and its calculation method is shown in the following formula: ； ； ； In the formula, The unloaded roll gap convexity between the work roll and the support roll, in mm; and The original grinding crown of the work roll and support roll are respectively, in mm; The width of the support roller surface is in mm; Width of the work roll surface, in mm; The average wear at the midpoint of the upper and lower support rollers, in mm; Average wear of the upper and lower support rollers around their sides, in mm; The average thermal expansion at the midpoint of the upper and lower support roller bodies, in mm; Average thermal expansion of the upper and lower support rollers around their sides, in mm; and These represent the wear amounts of the upper and lower work rolls at the rolling centerline, respectively. and These are the average wear amounts (in mm) of the upper and lower work rolls corresponding to the positions on the sides of the support roll. and These are the thermal expansion amounts of the upper and lower work rolls at the rolling centerline, respectively, in mm; and These are the average thermal expansion amounts (in mm) of the upper and lower work rolls corresponding to the positions on the sides of the support roll. (24) Based on the offline calculation results of the finite element method, regression analysis was performed on the uniform load roll gap crown under different roll widths, and the resulting model structure is shown below: ； ； ； ； In the formula, The uniform load roll gap crown is measured in mm. The rolling force per unit width is kN / mm; The bending force is kN. The unloaded roll gap crown between the working rolls, in mm; The unloaded roll gap convexity between the work roll and the support roll, in mm; and Diameters of the work roll and support roll, respectively, in mm; and Diameters of the work roll and support roll, respectively, in mm; The elastic modulus of the work roll; Table 3.1 shows the model regression coefficients for different rolled piece widths. (25) Obtaining the model regression coefficients for different rolled piece widths Then, the regression coefficients of the model were... The cubic polynomial expressed as the width of the rolled piece is shown below: ； In the formula, W is the width of the rolled piece, in mm. These are the polynomial coefficients.

4. The method for controlling the crown of the bearing roll gap in a hot-rolled finishing mill according to claim 1, characterized in that: In step (4), a calculation model for the bearing roll gap crown is established based on the influence function method, and the bearing roll gap crown under uniform load is calculated using the finishing mill stand of the hot rolling line. The relationship between rolling force and roll gap crown: As the rolling force increases, the roll gap crown increases, and the roll gap crown of wide specifications is generally smaller than that of narrow specifications; The relationship between bending force and roll gap crown: as the bending force increases, the roll gap crown decreases, and the reduction in roll gap crown for wide specifications is greater than that for narrow specifications. The relationship between work roll crown and roll gap crown: as roll crown increases, roll gap crown decreases, and the reduction in roll gap crown for wide specifications is greater than that for narrow specifications. The relationship between support roll crown and roll gap crown: as roll crown increases, roll gap crown decreases, and the reduction in roll gap crown for wide specifications is greater than that for narrow specifications. The relationship between work roll diameter and roll gap crown: For narrow specifications, the roll gap crown decreases as the roll diameter increases; for wide specifications, the work roll diameter has little effect on the roll gap crown. The relationship between the support roll diameter and the roll gap crown is as follows: as the roll diameter increases, the roll gap crown decreases. The relationship between the elastic modulus of a roll and the roll gap crown: The elastic modulus of a roll has a relatively small effect on the roll gap crown.

5. The method for controlling the crown of the bearing roll gap in a hot-rolled finishing mill according to claim 1, characterized in that: In step (4), the amount of wear on the support roller is related to factors such as the material of the roller, surface hardness and smoothness, lateral distribution of pressure between rollers, relative sliding amount and rolling distance. (41) Friction on the contact arc and wear model of the work roll: ； In the formula: - represents wear amount, in mm; - Wear rate; - Roll diameter correction factor; P - Rolling force per unit width, N·mm⁻¹; N - Number of revolutions during rolling; L - Total length of rolling mill, m; - Roll surface hardening rate parameter; (42) Calculation of friction between roller systems and wear of support rollers: Speed ​​difference formula: ； In the formula, i is the i-th node of the inter-roller contact area along the length of the roll body; , - These are the linear velocities of the support roller and the work roller at the i-th node, respectively; The influence function method is used to calculate the inter-roll contact pressure, and the actual rolling parameters are adopted. The formula for calculating the inter-roll friction balance is as follows: ; In the formula, - The frictional force at the i-th node; - The pressure between the rollers at the i-th node; - The constant term in the coefficient of friction; and These are the radii of the support roller and the working roller at the i-th node, respectively; and These are the angular velocities of the support roller and the work roller, respectively. (43) The effect of support roll wear on roll gap crown: The influence function method is used to calculate the effect of new support roll and worn support roll on the exit crown of the mill stand. The rolling parameters are the same as above. The plate crown corresponding to the worn support roll is larger, which corresponds to the phenomenon that double-sided waves are more likely to occur in the downstream mill stand of finishing rolling in the later stage of support roll use. (44) Plate shape compensation model for support roll wear: In the hot rolling production line, the influence of support roll wear on the plate shape model is not considered under the initial conditions. Before and after the replacement of the worn support roll, the roll system convexity self-learning of the finishing mill stand in the plate shape model shows obvious reverse learning. This indicates that the plate shape control conditions have changed significantly before and after the support roll replacement. Before the roll replacement, the plate shape model learns in the direction of eliminating double-sided waves, and after the roll replacement, it learns in the direction of eliminating middle waves. After increasing the compensation of support roll wear on the plate shape model, this phenomenon is significantly improved.

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