Method for analyzing the effect of bending roll of smartcrown rolling mill on plate shape based on digital twinning

Abstract

The method for analyzing the influence of roll bending of a SmartCrown rolling mill on strip shape based on digital twinning analysis of the application comprises the following steps: Step 1: collecting strip parameters, rolling process parameters and SmartCrown rolling mill parameters; Step 2: establishing a three-dimensional elastic-plastic finite element model of the SmartCrown rolling mill and the strip according to the parameters collected in Step 1; Step 3: performing simulation experiments on the strip rolling process by using the three-dimensional elastic-plastic finite element model; Step 4: extracting the transverse thickness distribution data of the rolled strip in the stable rolling stage of each simulation experiment in Step 3, calculating the strip crown, edge thinning and strip crown weight according to the transverse thickness distribution data, and then establishing a digital twin; and Step 5: analyzing the influence of the work roll bending force and the intermediate roll bending force on the plate shape of the rolled strip according to the digital twin obtained in Step 4.

Description

Technical Field

[0001] This invention belongs to the field of cold-rolled sheet shape control technology, and relates to a method for analyzing the influence of SmartCrown mill bending rolls on sheet shape based on digital twin analysis. Background Technology

[0002] The steel industry is a fundamental industry of the nation, and cold-rolled steel strip, with its aesthetically pleasing surface and good processing performance, is the most widely used steel product. In cold rolling production, shape control is a key focus, which can be achieved from both process and equipment perspectives. While process control can be implemented through adjusting the rolling rhythm and arranging the rolling schedule, these methods are insufficient for high-precision shape control. Therefore, many effective shape control technologies have emerged.

[0003] Strip shape control essentially involves controlling the shape of the roll gap during the rolling process. SmartCrown technology is an emerging strip shape control technology. This technology uses a rolling mill with an original roll shape, where the work roll or intermediate roll is ground into an S-shaped bottle structure. The upper and lower rolls have the same roll shape curve equation and are arranged in opposite directions (180°) on the mill. The roll gap shape is adjusted by lateral movement of the rolls. In SmartCrown mills, lateral movement of the intermediate roll is a commonly used strip shape actuator, which can effectively control the strip shape. However, its control effect is limited, and the strip shape problem urgently needs further solutions. It is necessary to introduce bending of the work roll and intermediate roll for further control to obtain a good strip shape. At the same time, digital twins fully utilize data such as physical models to integrate the simulation process and complete the mapping in virtual space, thereby reflecting the entire life cycle process of the corresponding physical equipment. This method can also be applied to the field of cold-rolled strip shape research.

[0004] To address the strip shape control problem in cold rolling production, domestic researchers have conducted numerous studies. Chinese invention patent application CN201810164342.5, entitled "A Method and Device for Controlling Strip Shape," discloses a method and device for controlling strip shape. This method, based on the crown equation, sets the exit crown variation of the strip to 0, obtains the relationship between the bending roll force variation and the lateral stiffness of the bending roll force, and compensates for the bending roll force based on the lateral stiffness of the intermediate roll and work roll. This improves the accuracy of rolling force setting and enhances strip shape. Chinese invention patent application CN202110238966.9, entitled "Calculation Method and Electronic Equipment for Equivalent Roll Shape Adjustment Range of Continuously Variable Crown Work Roll," discloses a method and electronic equipment for calculating the equivalent roll shape adjustment range of continuously variable crown work rolls. This method can quantitatively calculate the optimized equivalent roll shape adjustment range of continuously variable crown work rolls without relying on experience, improving the effectiveness of continuously variable crown work rolls and further controlling strip shape. The Chinese doctoral dissertation "Numerical Simulation and Theoretical Model Study of Strip Rolling Process and Shape Control" (Northeastern University, 2019) uses kinematic methods to derive the analytical mathematical model of strip shape considering the influence of width expansion deformation, and studies the mechanism of strip shape defect generation. Based on the elastoplastic finite element method, a three-dimensional high-precision numerical simulation model of different types of strip mills is established for research and analysis. A data-driven method is used to establish a multiple regression model between strip shape and process parameters to obtain the strip shape control effect. The Chinese journal article "Influence of Bending Roll and Interval Roll on Strip Shape" (Journal of Wuhan University of Technology, 2020, 42(03)) establishes a finite element model based on the finite element software ANSYS. By modifying the parameters in the program, the influence of parameters such as bending roll force, intermediate roll overlap, and strip width on strip shape and roll gap is calculated and analyzed.

[0005] The above research has two main shortcomings: (1) Although some control methods for the shape of steel plates can achieve certain effects, their control means are not diversified enough and the accuracy of plate shape control is limited; (2) Many plate shape control methods have limited control capabilities for higher-order plate shapes; (3) The use of the finite element method can simplify complex engineering problems, but the accuracy fluctuates greatly. Summary of the Invention

[0006] To address the aforementioned technical problems, the purpose of this invention is to provide a method for analyzing the influence of SmartCrown mill bending rolls on strip shape based on digital twin analysis. This method involves establishing a three-dimensional elastoplastic finite element model of the SmartCrown mill and strip steel. Based on the rolling process parameters at the site, after determining the lateral displacement of the intermediate roll, different bending forces are applied to the model for the work rolls and intermediate rolls. A reasonable comparison plan is then developed, and the influence of hydraulic bending rolls on strip shape is further analyzed. This guides the adoption of reasonable and effective combinations of strip shape actuators in on-site production, thereby improving strip shape and product quality.

[0007] The present invention provides a method for analyzing the influence of SmartCrown mill bending rolls on sheet shape based on digital twin analysis, comprising:

[0008] Step 1: Collect strip steel parameters, rolling process parameters, and SmartCrown mill parameters;

[0009] Step 2: Establish a three-dimensional elastoplastic finite element model of the SmartCrown rolling mill and strip steel based on the parameters collected in Step 1;

[0010] Step 3: Simulate the strip rolling process using a three-dimensional elastoplastic finite element model;

[0011] Step 4: Extract the transverse thickness distribution data of the strip after rolling in each simulated stable rolling stage in Step 3, calculate the strip crown, edge thinning, and strip crown weight based on the transverse thickness distribution data, and then establish a digital twin.

[0012] Step 5: Analyze the influence of the bending force of the work roll and the bending force of the intermediate roll on the shape of the rolled strip based on the digital twin obtained in Step 4.

[0013] Furthermore, step 1 specifically includes:

[0014] Step 1.1: Obtain all strip parameters, all rolling process parameters, and SmartCrown mill parameters from the primary and secondary systems on the cold rolling production line;

[0015] Step 1.2: The strip parameters include: strip width, strip thickness, strip density, strip elastic modulus, strip yield strength, strip Poisson's ratio, and strip tangential modulus;

[0016] The rolling process parameters include: reduction rate, friction coefficient, strip front and rear tension, work roll bending force, intermediate roll bending force, and intermediate roll lateral displacement.

[0017] The SmartCrown mill parameters include: work roll diameter, work roll body length, work roll density, work roll elastic modulus, work roll Poisson's ratio, intermediate roll diameter, intermediate roll body length, intermediate roll profile curve equation, intermediate roll density, intermediate roll elastic modulus, intermediate roll Poisson's ratio, support roll diameter, support roll body length, support roll density, support roll elastic modulus, and support roll Poisson's ratio.

[0018] Furthermore, the intermediate roll of the SmartCrown mill has a SmartCrown roll shape, and the equation of the intermediate roll shape curve is a superposition of a sine function and a linear function, specifically:

[0019]

[0020]

[0021] In the formula, R U (x) is the upper roll shape function of the intermediate roll, R L (x) is the shape function of the lower roll of the intermediate roll, where x is the transverse coordinate of the roll; R0 is the nominal radius of the roll, in mm; L is the shape angle, measured in degrees. REF 'c' represents the design length of the roll, in mm; 'c' represents the roll profile offset, in mm; 'A' and 'B' are undetermined roll profile parameters.

[0022] Furthermore, step 2 specifically includes:

[0023] Step 2.1: Assumptions and simplifications in the process of finite element modeling of SmartCrown rolling mill and strip;

[0024] Step 2.2: Use the ANSYS / LS-DYNA platform to create a three-dimensional elastoplastic finite element model of the SmartCrown rolling mill and strip steel;

[0025] Step 2.3: Apply a mass damping coefficient to the three-dimensional elastoplastic finite element model to improve its stability and verify its accuracy.

[0026] Furthermore, the assumptions and simplifications in step 2.1 are as follows:

[0027] (1) The mill stand is regarded as the limiting body of the intermediate roll and the support roll. It is set as a rigid material. The supporting roll limiting body plays the role of limiting the pressing, rolling and axial displacement, while the intermediate roll limiting body only limits the rolling and axial displacement.

[0028] (2) Set the rolls of the SmartCrown mill as isotropic linear elastic materials, calculate and limit the stress within the linear elastic range, the stress does not exceed the yield limit, and the stress-strain relationship of the material obeys the generalized Hooke's law;

[0029] (3) Treat the strip steel as an isotropic hardening material. In the modeling process, it is set as an isotropic bilinear hardening material. The stress-strain relationship during elastic deformation also follows the generalized Hooke's law. During the plastic deformation stage, it follows the von Mises yield criterion and the Prandtl-Reuss stress-strain relationship.

[0030] Furthermore, step 2.2 specifically includes:

[0031] Step 2.2.1: Select 3D SOLID164 eight-node hexahedral elements for modeling, define material properties, and obtain the material model parameters for simulation calculation based on the strip steel parameters, rolling process parameters, and SmartCrown mill parameters collected in Step 1.

[0032] Step 2.2.2: Use a high-order B-spline curve to draw the roll shape curve of the intermediate roll. Set the units of the roll, drive shaft and limit body to reduced integral mode. Use viscous hourglass control and set the strip unit to full integral mode.

[0033] Step 2.2.3: The strip steel is a rectangular piece. When dividing the grid, the unit lengths in the strip steel rolling direction, width direction, and thickness direction are set to 0.5mm, 10mm, and 0.3mm, respectively.

[0034] Step 2.2.4: After the mesh is generated, create a PART, define the contact modes between rolls and between rolls and strip, and create components to apply constraints and initial conditions. Submit the generated k-file to the solver for solving.

[0035] Furthermore, step 2.3 specifically includes:

[0036] Step 2.3.1: Apply a mass damping coefficient to the three-dimensional elastoplastic finite element model to reduce rolling force fluctuations and enable the strip rolling process to quickly enter the stable rolling stage;

[0037] Step 2.3.2: Using the established three-dimensional elastoplastic finite element model, input strip steel of different specifications to conduct a simulation experiment of the strip steel rolling process. Extract the average rolling force during the stable rolling stage of the strip steel in the simulation experiment, and compare the average rolling force with the theoretical rolling force calculated by the Bland-Ford-Hill formula to verify the accuracy of the model.

[0038] Furthermore, step 3 specifically involves:

[0039] Step 3.1: Determine the intermediate roller lateral displacement based on the on-site process parameters;

[0040] Step 3.2: Change the values ​​of the bending force of the work roll and the bending force of the intermediate roll in the three-dimensional elastoplastic finite element model, and conduct a simulation experiment.

[0041] Furthermore, step 4 specifically involves:

[0042] Step 4.1: Extract the transverse thickness distribution data of the strip after rolling in each simulated stable rolling stage in Step 3;

[0043] Step 4.2: Calculate the convexity index C based on the lateral thickness distribution data. 40 C 150 and the edge thinning index E of strip steel 40 :

[0044]

[0045]

[0046]

[0047] Among them, h c h is the thickness of the strip at the center point of the strip. i h′ is the strip thickness at a distance of 40mm from the operating side of the strip. i It is the strip thickness at 40mm from the drive side of the strip, h j h′ is the strip thickness at a distance of 150mm from the operating side of the strip. j It is the strip thickness at 150mm from the drive side of the strip, h e h′ is the strip thickness located 5-10 mm from the operating side of the strip. e It refers to the strip thickness located 5-10mm from the drive side of the strip.

[0048] Step 4.3: Based on the transverse thickness distribution of the strip, the influence of the change in hydraulic bending rolls in the SmartCrown mill on the strip crown weight is analyzed by fitting the transverse thickness distribution of the strip using the Legendre orthogonal polynomial:

[0049] h(η) = h0 + C w1 P1(η)+C w2 P2(η)+C w4 P3(η)+C w6 P4(η)

[0050]

[0051] Where h(η) is the transverse thickness distribution curve of the strip, h0 is the reference thickness of the strip; η is the normalized coordinate relative to the center position of the strip; C w1 C w2 C w4 C w6 η represents the fitting coefficients for each component, and their absolute values ​​represent the weight of the convexity component in the transverse thickness distribution curve. The positive and negative signs indicate the bending direction of the curve. P1(η), P2(η), P3(η), and P4(η) are the first, second, fourth, and sixth order Legendre orthogonal polynomials, respectively.

[0052] Furthermore, the influence of the bending force of the work roll and the bending force of the intermediate roll on the shape of the rolled strip in step 5 is as follows:

[0053] (1) The transverse thickness distribution curve of the strip after rolling has the characteristics of a quadratic parabola. The thickness drops sharply within 40 mm of the edge of the strip, which is called the edge thinning zone.

[0054] (2) As the bending force of the working roll increases, the thickness of the strip at the exit increases. The rate of increase in the thickness at the edge of the strip is much greater than that in the middle region. The cross-sectional shape of the strip changes significantly. The transverse thickness distribution curve of the strip tends to be flat. The plate crown and edge thinning gradually decrease. The secondary crown component changes significantly, while the other components do not change significantly.

[0055] (3) As the bending force of the intermediate roll increases, the thickness of the strip at the exit increases. The rate of increase in the thickness of the strip at the edge is slightly greater than that in the middle region. The cross-sectional shape of the strip does not change significantly. The plate convexity and edge thinning gradually decrease. The secondary convexity component changes significantly, while the other components do not change significantly.

[0056] The present invention provides a method for analyzing the influence of SmartCrown mill bending rolls on plate shape based on digital twin analysis, which has the following beneficial effects:

[0057] The method of this invention constructs a digital twin by establishing a three-dimensional elastoplastic finite element model of the SmartCrown rolling mill and strip steel. Based on the digital twin, the effects of the bending force of the work roll and the bending force of the intermediate roll on the strip shape during the rolling process can be analyzed. It has wide applicability and can also combine different shape-controlling mechanisms in actual production to better control the strip shape, which can help improve the strip shape quality, further improve product quality, and enhance enterprise efficiency. Attached Figure Description

[0058] Figure 1 This is a flowchart of the method for analyzing the influence of SmartCrown mill bending rolls on plate shape based on digital twin analysis according to the present invention;

[0059] Figure 2 It is the SmartCrown roller profile curve;

[0060] Figure 3 This is a comparison chart of the effects of the bending of the work roll on the transverse thickness distribution curve of the strip.

[0061] Figure 4 This is a comparison chart showing the influence of intermediate roll bending on the transverse thickness distribution curve of strip steel.

[0062] Figure 5 It is the work roll bending roll pair C 40 C 150 and E 40 Impact comparison chart;

[0063] Figure 6 It is the intermediate roll bending roll pair C 40 C 150 and E 40 Impact comparison chart;

[0064] Figure 7 This is a comparison chart showing the influence of the bending of the work roll on the weight of the strip crown.

[0065] Figure 8 This is a comparison chart showing the influence of intermediate roll bending on the weight of strip crown. Detailed Implementation

[0066] In this embodiment, a 1740mm SmartCrown six-roll cold continuous rolling mill of a certain factory is used as an example to conduct numerical simulation research and analysis. The working rolls of the mill are flat rolls, and the intermediate rolls are SmartCrown rolls.

[0067] like Figure 1 As shown, the method of the present invention for analyzing the influence of SmartCrown mill bending rolls on sheet shape based on digital twin analysis includes:

[0068] Step 1: Collect strip steel parameters, rolling process parameters, and SmartCrown mill parameters. Specifically, Step 1 involves:

[0069] Step 1.1: Obtain all strip parameters, all rolling process parameters, and SmartCrown mill parameters from the primary and secondary systems on the cold rolling production line;

[0070] Step 1.2: The strip parameters include: strip width, strip thickness, strip density, strip elastic modulus, strip yield strength, strip Poisson's ratio, and strip tangential modulus;

[0071] The rolling process parameters include: reduction rate, friction coefficient, strip front and rear tension, work roll bending force, intermediate roll bending force, and intermediate roll lateral displacement.

[0072] The SmartCrown mill parameters include: work roll diameter, work roll body length, work roll density, work roll elastic modulus, work roll Poisson's ratio, intermediate roll diameter, intermediate roll body length, intermediate roll profile equation, intermediate roll density, intermediate roll elastic modulus, intermediate roll Poisson's ratio, support roll diameter, support roll body length, support roll density, support roll elastic modulus, and support roll Poisson's ratio. In this example, the strip steel parameters are shown in Table 1. The obtained rolling process parameters are shown in Table 2. The obtained SmartCrown mill parameters are shown in Table 3.

[0073] Table 1 Strip Steel Parameters

[0074] strip steel parameters Parameter values strip steel grades SpCC strip width 1400mm strip thickness 3.6mm strip density <![CDATA[7850kg / m 3 ]]> elastic modulus 207 GPa Yield strength 245MPa Poisson's ratio 0.362 Tangent modulus 670MPa

[0075] Table 2 Rolling process parameters

[0076] Rolling process parameters Parameter values reduction rate 32％ coefficient of friction 0.06 Pretension 330kN Post-tension 200kN Work roll bending range 0~490kN Intermediate roll bending range 0~539kN Intermediate roller lateral movement range -120~120mm

[0077] Table 3 SmartCrown Mill Parameters

[0078] project numerical values Parameters of rolls, drive shafts, and limiters numerical values Work roll diameter / roll body length 450 / 1740mm density <![CDATA[7850kg / m 3 ]]> Intermediate roll diameter / roll body length 550 / 1990mm elastic modulus 210GPa Support roller diameter / roller body length 1400 / 1750mm Poisson's ratio 0.3

[0079] In this embodiment, the intermediate roll of the SmartCrown mill is a SmartCrown roll shape, and the curve equation of the intermediate roll shape is a superposition of a sine function and a linear function.

[0080] like Figure 2 As shown, the upper and lower rollers of the intermediate roll are placed in a Cartesian coordinate system, and their roll profile curve functions are as follows:

[0081]

[0082]

[0083] In the formula, R U (x), R L (x) represents the shape functions of the upper and lower rolls of the intermediate roll, respectively, where x is the transverse coordinate of the roll; R0 is the nominal radius of the roll, in mm; L is the shape angle, measured in degrees. REF 'c' represents the roll design length in mm; 'c' represents the roll profile offset in mm; 'A' and 'B' represent the roll profile coefficients. The parameters of the intermediate roll profile curve in this example are shown in Table 4.

[0084] Table 4 SmartCrown Intermediate Roll Profile Parameters

[0085]

[0086] Step 2: Based on the parameters collected in Step 1, establish a three-dimensional elastoplastic finite element model of the SmartCrown rolling mill and strip steel. Specifically, Step 2 involves:

[0087] Step 2.1: Assumptions and simplifications in the SmartCrown rolling mill and strip finite element modeling process. The assumptions and simplifications in Step 2.1 are as follows:

[0088] (1) The mill stand is regarded as the limiting body of the intermediate roll and the support roll. It is set as a rigid material. The supporting roll limiting body plays the role of limiting the pressing, rolling and axial displacement, while the intermediate roll limiting body only limits the rolling and axial displacement.

[0089] (2) Set the rolls of the SmartCrown mill as isotropic linear elastic materials, calculate and limit the stress within the linear elastic range, the stress does not exceed the yield limit, and the stress-strain relationship of the material obeys the generalized Hooke's law;

[0090] (3) Treat the strip steel as an isotropic hardening material. In the modeling process, it is set as an isotropic bilinear hardening material. The stress-strain relationship during elastic deformation also follows the generalized Hooke's law. During the plastic deformation stage, it follows the von Mises yield criterion and the Prandtl-Reuss stress-strain relationship.

[0091] Step 2.2: Model the three-dimensional elastoplastic finite element model of the SmartCrown mill and strip steel using the ANSYS / LS-DYNA platform. Write the finite element simulation program for the SmartCrown mill and strip steel using the APDL language in ANSYS, and then convert it into a macro file. By integrating the scripting language for finite element modeling and analysis into macro commands, rapid parametric modeling of this process is achieved. Specifically, Step 2.2 involves:

[0092] Step 2.2.1: Select 3D SOLID164 eight-node hexahedral elements for modeling, define material properties, and obtain the material model parameters for simulation calculation based on the strip steel parameters, rolling process parameters, and SmartCrown mill parameters collected in Step 1.

[0093] Step 2.2.2: In the modeling, high-order B-spline curves are used to accurately draw the roll shape curve of the intermediate roll. The elements of the roll, drive shaft and limit body are all set to reduced integral mode. Viscous hourglass control is used to improve the calculation efficiency and enhance the robustness of the model. Since the strip steel will undergo large-scale irreversible plastic deformation during rolling, the strip steel element is set to full integral mode.

[0094] Step 2.2.3: The strip is a rectangular piece with a length, thickness, and width of 500mm, 3.6mm, and 1400mm, respectively. When meshing, the element lengths in the rolling direction, width direction, and thickness direction of the strip are set to 0.5mm, 10mm, and 0.3mm, respectively. In addition, a mesh refinement strategy is adopted in areas with large stress gradients during deformation, which can effectively improve the model accuracy, reduce calculation errors, and prevent initial contact penetration.

[0095] Step 2.2.4: After meshing, create a PART, define the contact modes between rolls and between rolls and strip, and create components to apply constraints and initial conditions. Adopting a mass scaling strategy to control the minimum time step can effectively improve computational efficiency and shorten computation time. In this process, the overall mass scaling factor is set to 10, and the critical time step for mass scaling is set to 7.8 × 10⁻⁶. -7 The virtual mass of the model increased by mass scaling shall not exceed 0.5% of the overall model mass. The generated k-file is then submitted to the solver for solving. In this embodiment, the material model parameters for simulation calculation are shown in Table 5.

[0096] Table 5 Material Models for Simulation Calculation

[0097]

[0098] Step 2.3: Apply a mass damping coefficient to the three-dimensional elastoplastic finite element model to improve its stability and verify its accuracy. Specifically, step 2.3 involves:

[0099] Step 2.3.1: Apply a mass damping coefficient to the three-dimensional elastoplastic finite element model to reduce rolling force fluctuations and enable the strip rolling process to quickly enter the stable rolling stage;

[0100] Step 2.3.2: Using the established three-dimensional elastoplastic finite element model, input strip steel of different specifications to conduct a simulation experiment of the strip steel rolling process. Extract the average rolling force during the stable rolling stage of the strip steel in the simulation experiment, and compare the average rolling force with the theoretical rolling force calculated by the Bland-Ford-Hill formula to verify the accuracy of the model.

[0101] In this process, based on the rolling process conditions, multiple sets of strip steel of different specifications were input for simulation verification tests, as shown in Table 6. The steel grade was SPCC steel, and the length was 500mm. Different values ​​were set for the incoming material thickness and strip width. The rolling force verification results are shown in the table. Analysis shows that the absolute value of the relative error between the finite element value and the theoretical value of the rolling force is less than 5%, and the error between the finite element value and the theoretical value of the rolling force is very small. Therefore, it can be concluded that using the three-dimensional elastoplastic finite element model of the SmartCrown rolling mill and strip steel to analyze the influence of hydraulic bending rolls on the strip shape is reliable.

[0102] Table 6 Comparison of Rolling Force Verification for Different Strip Steels

[0103]

[0104] Step 3: Conduct simulation experiments on the strip rolling process using a three-dimensional elastoplastic finite element model. Specifically, Step 3 involves:

[0105] Step 3.1: Determine the intermediate roller lateral displacement based on the on-site process parameters;

[0106] According to the on-site process parameters, the range of the lateral displacement of the intermediate roll of the SmartCrown mill is -120mm to 120mm. A comparative experiment was conducted using a three-dimensional elastic-plastic finite element model. Based on the simulation results, it was found that a lateral displacement of -60mm is more suitable for subsequent comparative experiments on hydraulic bending roll force, namely the bending roll force of the work roll and the bending roll force of the intermediate roll.

[0107] Step 3.2: Change the values ​​of the bending force of the work roll and the bending force of the intermediate roll in the three-dimensional elastoplastic finite element model, and conduct a simulation experiment.

[0108] In practice, according to step 3.1, the intermediate roller lateral displacement is set to -60mm in the subsequent control experiment. At the same time, based on the on-site process parameters, a simulation experiment plan is formulated as shown in Tables 7 and 8 (intermediate roller lateral displacement is -60mm).

[0109] Table 7. Work Roll Bending Roll Comparison Experiment Plan

[0110]

[0111] Table 8. Experimental Plan for Intermediate Roll Bending Roll

[0112]

[0113] Step 4: Extract the transverse thickness distribution data of the strip after rolling in each simulated stable rolling stage in Step 3. Calculate the strip crown, edge thinning, and strip crown weight based on the transverse thickness distribution data, and then establish a digital twin. Specifically, Step 4 involves:

[0114] Step 4.1: Extract the transverse thickness distribution data of the strip after rolling in each simulated stable rolling stage in Step 3;

[0115] Step 4.2: Calculate the convexity index C based on the lateral thickness distribution data. 40 C 150 and the edge thinning index E of strip steel 40 .

[0116] The transverse thickness distribution of strip steel, i.e., its cross-sectional shape, mainly reflects the thickness distribution characteristics of the strip steel in the width direction. Key indicators include crown and edge thinning. In actual production, C is typically used. 40 C 150 The crown deviation of strip steel is evaluated using E. 40 The formula for calculating the edge thinning of the strip is as follows:

[0117]

[0118]

[0119]

[0120] Among them, h c h is the thickness of the strip at the center point of the strip. i h′ is the strip thickness at a distance of 40mm from the operating side of the strip. i It is the strip thickness at 40mm from the drive side of the strip, h j h′ is the strip thickness at a distance of 150mm from the operating side of the strip. j It is the strip thickness at 150mm from the drive side of the strip, h e h′ is the strip thickness located 5-10 mm from the operating side of the strip. e It refers to the strip thickness located 5-10mm from the drive side of the strip.

[0121] Step 4.3: Based on the transverse thickness distribution of the strip, the influence of the change in hydraulic bending rolls in the SmartCrown mill on the strip crown weight is analyzed by fitting the transverse thickness distribution of the strip using the Legendre orthogonal polynomial:

[0122] h(η) = h0 + C W1 P1(η)+C w2 P2(η)+C w4 P3(η)+C w6 P4(η)

[0123]

[0124] Where is the transverse thickness distribution curve of the strip, h0 is the reference thickness of the strip; η is the normalized coordinate relative to the center position of the strip; C w1 C w2 C w4 C w6η represents the fitting coefficients for each component, and their absolute values ​​represent the weight of that convexity component in the transverse thickness distribution curve. The positive or negative sign indicates the direction of curvature of the curve. P1(η), P2(η), P3(η), and P4(η) are the first, second, fourth, and sixth degree Legendre orthogonal polynomials, respectively.

[0125] Data is extracted using the above formulas, a digital twin is created, and the graph is drawn. Figure 3-8 . Figure 3 This is a comparison chart of the effects of the bending of the work roll on the transverse thickness distribution curve of the strip. Figure 4 This is a comparison chart showing the influence of intermediate roll bending on the transverse thickness distribution curve of strip steel. Figure 5 This is a comparison chart of the effects of work roll bending on C40, C150, and E40. Figure 6 This is a comparison chart of the effects of intermediate roll bending on C40, C150 and E40. Figure 7 This is a comparison chart showing the influence of the bending of the work roll on the weight of the strip crown. Figure 8 This is a comparison chart showing the influence of intermediate roll bending on the weight of strip crown.

[0126] Step 5: Analyze the influence of the work roll bending force and the intermediate roll bending force on the shape of the rolled strip based on the digital twin obtained in Step 4, such as... Figure 3-8 Analysis shows that the bending force of the work roll and the bending force of the intermediate roll have the following effects on the shape of the rolled strip:

[0127] (1) The transverse thickness distribution curve of the strip after rolling has the characteristics of a quadratic parabola, but the thickness drops sharply within 40mm of the edge of the strip, which is called the edge thinning zone.

[0128] (2) As the bending force of the working roll increases, the thickness of the strip at the exit increases. The rate of increase in the thickness at the edge of the strip is much greater than that in the middle region. The cross-sectional shape of the strip changes significantly. The transverse thickness distribution curve of the strip tends to be flat. The plate crown and edge thinning gradually decrease. The secondary crown component changes significantly, while the other components do not change significantly.

[0129] (3) As the bending force of the intermediate roll increases, the thickness of the strip at the exit also increases. The rate of increase in the thickness of the strip at the edge is slightly greater than that in the middle region. The cross-sectional shape of the strip does not change significantly. The plate convexity and edge thinning gradually decrease. The secondary convexity component changes significantly, while the other components do not change significantly.

[0130] This invention presents a method for analyzing the influence of bending rolls on strip shape in a SmartCrown rolling mill based on digital twin analysis. Utilizing measured parameters from a cold rolling production line, a three-dimensional elastoplastic finite element model of the SmartCrown rolling mill and strip is established using a finite element platform, constructing a digital twin. A scientifically sound verification plan is developed to ensure the stability and accuracy of the digital twin model. Based on on-site process parameters, after determining the lateral displacement of the intermediate roll, different bending forces on the work roll and intermediate roll are set for comparative experiments. The influence patterns are analyzed based on the obtained twin model, enhancing the persuasiveness of the comparative experiments.

[0131] The above description is only a preferred embodiment of the present invention and is not intended to limit the ideas of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for analyzing the influence of SmartCrown mill bending rolls on sheet shape based on digital twin analysis, characterized in that, include: Step 1: Collect strip steel parameters, rolling process parameters, and SmartCrown mill parameters; Step 2: Establish a three-dimensional elastoplastic finite element model of the SmartCrown rolling mill and strip steel based on the parameters collected in Step 1; Step 3: Simulate the strip rolling process using a three-dimensional elastoplastic finite element model; Step 4: Extract the transverse thickness distribution data of the strip after rolling in each simulation experiment stable rolling stage in Step 3, calculate the strip crown, edge thinning, and strip crown weight based on the transverse thickness distribution data, and then establish a digital twin. Step 5: Analyze the influence of the bending force of the work roll and the bending force of the intermediate roll on the shape of the rolled strip based on the digital twin obtained in Step 4. Step 1 specifically involves: Step 1.1: Obtain all strip parameters, all rolling process parameters, and SmartCrown mill parameters from the primary and secondary systems on the cold rolling production line; Step 1.2: The strip parameters include: strip width, strip thickness, strip density, strip elastic modulus, strip yield strength, strip Poisson's ratio, and strip tangential modulus; The rolling process parameters include: reduction rate, friction coefficient, strip front and rear tension, work roll bending force, intermediate roll bending force, and intermediate roll lateral displacement. The SmartCrown mill parameters include: work roll diameter, work roll body length, work roll density, work roll elastic modulus, work roll Poisson's ratio, intermediate roll diameter, intermediate roll body length, intermediate roll profile curve equation, intermediate roll density, intermediate roll elastic modulus, intermediate roll Poisson's ratio, support roll diameter, support roll body length, support roll density, support roll elastic modulus, and support roll Poisson's ratio. The intermediate roll of the SmartCrown mill has a SmartCrown roll shape, and the equation of the intermediate roll shape curve is a superposition of a sine function and a linear function, specifically: In the formula, Let be the upper roll shape function of the intermediate roll. Let x be the lower roll shape function of the intermediate roll, and x be the transverse coordinate of the roll; The nominal radius of the roll is in mm. Shape angle, unit: degree; 'c' represents the design length of the roll, in mm; 'c' represents the roll profile offset, in mm; 'A' and 'B' are undetermined roll profile parameters.

2. The method for analyzing the influence of SmartCrown mill bending rolls on sheet shape based on digital twin analysis as described in claim 1, characterized in that, Step 2 specifically involves: Step 2.1: Assumptions and simplifications in the process of finite element modeling of SmartCrown rolling mill and strip; Step 2.2: Use the ANSYS / LS-DYNA platform to create a three-dimensional elastoplastic finite element model of the SmartCrown rolling mill and strip steel; Step 2.3: Apply a mass damping coefficient to the three-dimensional elastoplastic finite element model to improve its stability and verify its accuracy.

3. The method for analyzing the influence of SmartCrown mill bending rolls on sheet shape based on digital twin analysis as described in claim 2, characterized in that, The assumptions and simplifications in step 2.1 are as follows: (1) The mill stand is regarded as the limiting body of the intermediate roll and the support roll. It is set as a rigid material. The support roll limiting body plays the role of limiting the pressing, rolling and axial displacement, while the intermediate roll limiting body only limits the rolling and axial displacement. (2) Set the rolls of the SmartCrown mill as isotropic linear elastic materials, calculate and limit the stress within the linear elastic range, the stress does not exceed the yield limit, and the stress-strain relationship of the material obeys the generalized Hooke's law; (3) Treat the strip steel as an isotropic hardening material. In the modeling process, set it as an isotropic bilinear hardening material. The stress-strain relationship during elastic deformation also follows the generalized Hooke's law. During the plastic deformation stage, it follows the von Mises yield criterion and the Prandtl-Reuss stress-strain relationship.

4. The method for analyzing the influence of SmartCrown mill bending rolls on sheet shape based on digital twin analysis as described in claim 2, characterized in that, Step 2.2 specifically involves: Step 2.2.1: Select 3D SOLID164 eight-node hexahedral elements for modeling, define material properties, and obtain the material model parameters for simulation calculation based on the strip steel parameters, rolling process parameters, and SmartCrown mill parameters collected in Step 1. Step 2.2.2: Use a high-order B-spline curve to draw the roll shape curve of the intermediate roll. Set the units of the roll, drive shaft and limit body to reduced integral mode. Use viscous hourglass control and set the strip unit to full integral mode. Step 2.2.3: The strip steel is a rectangular piece. When dividing the grid, the unit lengths in the strip steel rolling direction, width direction, and thickness direction are set to 0.5mm, 10mm, and 0.3mm, respectively. Step 2.2.4: After the mesh is generated, create a PART, define the contact modes between rolls and between rolls and strip, and create components to apply constraints and initial conditions. Submit the generated k-file to the solver for solving.

5. The method for analyzing the influence of SmartCrown mill bending rolls on sheet shape based on digital twin analysis as described in claim 2, characterized in that, Step 2.3 specifically involves: Step 2.3.1: Apply a mass damping coefficient to the three-dimensional elastoplastic finite element model to reduce rolling force fluctuations and enable the strip rolling process to quickly enter the stable rolling stage; Step 2.3.2: Using the established three-dimensional elastoplastic finite element model, input strip steel of different specifications to conduct a simulation experiment of the strip steel rolling process. Extract the average rolling force during the stable rolling stage of the strip steel in the simulation experiment, and compare the average rolling force with the theoretical rolling force calculated by the Bland-Ford-Hill formula to verify the accuracy of the model.

6. The method for analyzing the influence of SmartCrown mill bending rolls on sheet shape based on digital twin analysis as described in claim 1, characterized in that, Step 3 specifically involves: Step 3.1: Determine the intermediate roller lateral displacement based on the on-site process parameters; Step 3.2: Change the values ​​of the bending force of the work roll and the bending force of the intermediate roll in the three-dimensional elastoplastic finite element model, and conduct a simulation experiment.

7. The method for analyzing the influence of SmartCrown mill bending rolls on sheet shape based on digital twin analysis as described in claim 1, characterized in that, Step 4 specifically involves: Step 4.1: Extract the transverse thickness distribution data of the strip after rolling in each simulated stable rolling stage in Step 3; Step 4.2: Calculate the convexity index C based on the lateral thickness distribution data. 40 C 150 and the edge thinning index E of strip steel 40 : Among them, h c h is the thickness of the strip at the center point of the strip. i It refers to the strip thickness at a point 40mm from the operating side of the strip. It is the strip thickness at 40mm from the drive side of the strip, h j It refers to the strip thickness at a point 150mm from the operating side of the strip. It is the strip thickness at 150mm from the drive side of the strip, h e It refers to the strip thickness located 5-10mm from the operating side of the strip. It refers to the strip thickness located 5-10mm from the drive side of the strip. Step 4.3: Based on the transverse thickness distribution of the strip, the influence of the change in hydraulic bending rolls in the SmartCrown mill on the strip crown weight is analyzed by fitting the transverse thickness distribution of the strip using the Legendre orthogonal polynomial: Where h(η) is the transverse thickness distribution curve of the strip, h0 is the reference thickness of the strip; η is the normalized coordinate relative to the center position of the strip; C w1 C w2 C w4 C w6 η represents the fitting coefficients for each component, and their absolute values ​​represent the weight of the convexity component in the transverse thickness distribution curve. The positive and negative signs indicate the bending direction of the curve. P1(η), P2(η), P3(η), and P4(η) are the first, second, fourth, and sixth order Legendre orthogonal polynomials, respectively.

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