A method for designing segmented work roll contour for cold strip edge drop control

Abstract

The application provides a segmented work roll contour design method for cold-rolled strip edge drop control, and relates to the technical field of roll contour design. The method firstly determines the position of the roll contour modification area, then constructs a segmented edge drop control roll contour curve containing a flat roll segment, a conical segment and an edge protection segment by using a segmented function, then obtains the edge drop influence law corresponding to different cone heights and cone lengths by using a finite element model simulation, constructs a target function for comprehensive edge drop control and good overall cross section of the strip, and performs roll contour parameter optimization, finally, obtains the optimized best cone height and cone length combination, and completes the final SEDC roll contour design. Compared with the traditional flat roll or edge drop control roll contour, the SEDC roll contour designed by parameter optimization can greatly improve the reduction compensation capacity of the edge region without affecting the overall cross section quality of the strip, avoid the generation of high-order plate shape defects, and realize optimal control of the edge drop, thereby providing an effective solution for realizing high-precision production of high-value-added cold-rolled strip products.

Description

Technical Field

[0001] This invention relates to the field of roll shape design technology, and in particular to a method for designing the shape of segmented work rolls for edge drop control of cold-rolled strip. Background Technology

[0002] With the rapid development of modern energy equipment and high-end manufacturing industries, high-value-added cold-rolled sheet and strip products, represented by silicon steel and medium-high carbon steel, have become important basic materials in this field and occupy an irreplaceable position. Good edge drop control in cold rolling helps improve the transverse thickness uniformity of the sheet and strip, thereby meeting the stringent requirements of high-end applications for material cross-sectional quality. However, due to the limited edge drop control methods of traditional cold rolling mills, it is difficult to accurately control the transverse deformation behavior of the rolled piece. The prominent edge drop control problem has become a key bottleneck restricting the improvement of transverse thickness variation quality in high-value-added cold-rolled sheet and strip products.

[0003] Roll shape optimization technology, through precise design of the roll profile, can actively change the shape of the bearing roll gap, optimize the lateral pressure distribution during the rolling process, and significantly improve the edge drop control capability of cold rolling mills. Patent application 1 (CN 104874607.A, A work roll for edge drop control in cold rolling and its roll shape design method) designs an edge drop control roll shape including a quadratic curve segment and a slanted straight line segment, and optimizes the roll shape parameters based on the improved edge drop amount from industrial tests to complete the roll shape design. Patent application 2 (CN 104607468.A, Work roll shape technology that considers grinding accuracy and edge drop control in cold-rolled electrical steel) utilizes an exponential curve segment and a slanted straight line segment for edge drop control of silicon steel, and improves the grinding accuracy of the work roll through a sudden drop segment on the roll surface. Reference 1 (UCM cold continuous rolling mill silicon steel edge drop control technology) proposes a U-EDC roll shape, including an edge drop control segment based on a hexagonal curve and a taper compensation segment for compensating for edge drop of different specifications of silicon steel, and performs roll shape optimization design based on finite element simulation results. In the aforementioned studies, existing roll shape design methods mostly employ trial and error to determine roll shape parameters, making it difficult to achieve optimal performance in edge drop control. Furthermore, the optimization of roll shape parameters only considers edge drop control, neglecting the impact on the overall cross-section, which may lead to higher-order strip shape problems. Moreover, the design of a pure conical section at the edge of the work roll is prone to causing excessive tensile stress when the strip deviates, increasing the risk of strip breakage during cold rolling.

[0004] To address the aforementioned problems, this invention proposes a segmented work roll shape design method for edge drop control in cold-rolled strip. This method first constructs an SEDC roll shape curve comprising a flat roll section, a conical section, and an edge protection section. Then, it uses a finite element model to simulate and analyze the specific impact of roll shape parameters on strip edge drop. Next, with edge drop control and a good overall cross-section as optimization objectives, the cone height and cone length are globally optimized using GPR-PSO to obtain the optimal parameter combination and complete the final roll shape design. The newly developed SEDC roll shape, by combining a finite element model and intelligent algorithms to determine the optimal roll shape parameters, not only achieves optimal edge drop control but also effectively avoids high-order strip shape defects during rolling. Furthermore, the edge protection section design allows the roll shape to constrain strip deviation, preventing continuous increase in edge tensile stress that could lead to strip breakage. Therefore, the SEDC roll shape design method provided by this invention offers effective technical support for the stable production of high-value-added cold-rolled strip. Summary of the Invention

[0005] To address the aforementioned technical problems in existing technologies, this invention provides a segmented work roll shape design method for edge drop control in cold-rolled strip. Combining finite element simulation and intelligent algorithms, the method iteratively searches for the optimal combination of cone height and cone length parameters. This achieves optimal edge drop control while avoiding high-order strip shape defects, thus meeting the dual requirements of edge drop and strip shape quality in high-precision cold-rolled strip production. The technical solution is as follows:

[0006] A method for designing segmented work roll profiles for edge drop control of cold-rolled strip, the method comprising: S1. Determine the location of the roll shaping area based on the width of the rolled strip; S2. Construct a segmented edge drop control SEDC roll profile curve that includes a flat roll section, a conical roll section, and an edge protection section using a segmented function; S3. Using the finite element model of coupled deformation calculation of roll system and rolled piece, the side drop influence law corresponding to different cone heights and cone lengths is obtained through simulation. S4. Based on the results in S3, construct an objective function for comprehensive edge drop control and good overall strip cross-section, and use Gaussian process regression and particle swarm algorithm to optimize the roll shape parameters. S5. Obtain the optimized combination of cone height and cone length to complete the final SEDC roll shape design.

[0007] The roll shaping area in S1 is symmetrically designed. The roll shape is divided into a flat roll section, a conical section, and an edge protection section along the length of the roll body, with the midpoint of the roll body as the origin. The positions of each section are calculated as follows:

[0008] In the formula, L 1 indicates the end point of the flat roller section; L and L 2 represents the length of the tapered segment and the end point of the tapered segment, respectively. Since the end point of the tapered segment offers the strongest edge reduction control, to improve the control effect of thinning at the strip edge, the end point of the tapered segment needs to coincide with the strip edge. Therefore... L 2= B / 2; B The width of the strip; L 3 indicates the end point of the edge protection section, which is also the outermost edge of the roll. L 3= L R / 2; L R This refers to the length of the roller body.

[0009] The formula for the SEDC roller profile curve on the drive side in S2 is as follows:

[0010] In the formula, the roll shape value of the flat roll section is 0, indicating that no shaping is performed; The roll shape value of the conical section f ( x The value increases with increasing coordinates, and the roll shape at the end of the conical section is [value missing]. H This indicates the maximum height of the tapered segment; H This indicates the maximum height of the tapered section; the roll shape value of the edge protection section remains constant. H This indicates that the edge correction amount will not be increased further to prevent accidents such as strip breakage caused by continuous thickening of the edges when the strip deviates. Specifically, the optimal tapered segment length L and tapered segment height H are obtained through GPR-PSO iterative search.

[0011] The roller profile of the conical section consists of a quadratic curve section, a sloping straight line section, and a quadratic margin section. To ensure a smooth roller profile, all sections are tangent at their joints. The specific calculations are as follows:

[0012] In the formula, a This is the adjustment coefficient for the cone height, used to change the slope of the cone segment, thereby adjusting the size of the cone height while keeping the cone length constant. The quadratic curve segment connects the flat roller segment and the sloping straight line segment. L a This indicates the length of the quadratic curve segment, used to achieve a rapid and smooth transition in the roller shape. L a =0.2 L ; Lb This represents the sum of the lengths of the quadratic curve segment and the oblique straight line segment, where the oblique straight line segment is used to quickly increase the cone height to enhance edge descent control. L b =0.8 L ; The secondary margin section is for edge drop control during the rolling of multi-specification strips. It ensures the edge drop control capability of narrow-specification strips while preventing the edge drop control effect of wide-specification strips from being too strong.

[0013] The secondary margin section is connected to the edge protection section, when the cone height is H At that time, the control coefficient a The calculation is as follows: .

[0014] The specific process in S3 is as follows: S31. Use Abaqus software to establish a finite element model for calculating the coupled deformation of the roll system and the rolled piece: S32. Adjust the cone height and cone length, and limit the maximum and minimum values ​​of the cone height and cone length based on experience to complete the SEDC roll shape design under different combinations of roll shape parameters; S33. Using the finite element model established in S31, the relative thickness reduction of the cross-section under different roll shape parameters is obtained through simulation. The edge drop, plate shape, and maximum edge thickness increase indices corresponding to changes in cone height and cone length are extracted respectively, as follows: Calculate the edge drop value of the current section using the edge drop calculation formula. ED :

[0015] In the formula, h e1 Indicates the distance from the edge of the strip as e The thickness of the marker point 1, h e2 Indicates the distance from the edge of the strip as e The thickness of the marker point 2, e 1 = 15mm e 2 = 100mm; The maximum edge thickening value is the maximum relative thinning value corresponding to the current cross-sectional roll transition position. The plate shape results are obtained by fitting the relative thinning amount of the current section using Chebyshev polynomials to obtain its second-order convexity and fourth-order convexity. The plate shape results are as follows:

[0016] In the formula, C w1 , C w2 ,C w4 , C w6 These represent the coefficients of the first, second, fourth, and sixth degree terms of the polynomial, respectively, corresponding to the components of the current cross section. x 0 represents a constant term; generally, the relative thickness reduction of the cross-sectional profile under the current roll shape parameters can be obtained through simulation. The above formula is used to fit the relative thickness reduction of the entire cross-section to obtain the above coefficients. The second-order convexity reflects the symmetrical plate shape characteristics of the current cross section, while the fourth-order convexity represents the higher-order plate shape characteristics at the 1 / 4 position of the current cross section.

[0017] The specific process in S31 is as follows: S311. Obtain the actual roll size parameters and rolled strip specifications from the cold rolling production line, and complete the creation of instances of each component of the model; S312. Add material properties to the model, where the material property of the roll is an elastic body and the material property of the rolled piece is an elasto-plastic body. Obtain the stress-strain curve of the strip and add it to the material property of the rolled piece. S313. Set the contact type between components according to the different contact objects, namely roll-to-roll contact and roll-to-strip contact, and set the corresponding friction coefficients respectively (generally, the friction coefficients of roll-to-roll contact and roll-to-strip contact are 0.3 and 0.05 respectively). S314. Set the analysis steps of the model. By reasonably decomposing the rolling action, the analysis steps are set sequentially as initialization, small reduction contact, large reduction contact, applying tension, applying bending roll force, and applying rotation. S315. Apply the corresponding loads in different analysis steps and set boundary condition constraints. Specifically, during the pressing action, a fixed constraint is applied to the end of the strip to prevent the strip position from changing, and the constraint is removed when the work roll starts to rotate; to prevent the strip from lateral displacement, an axial constraint is applied to the center plane of the strip; to ensure the level of the rolling center line, a vertical displacement constraint is added to the neutral plane of the strip's deformation-free zone. S316. The mesh is refined locally in the contact area between the roll and the strip, the area between the roll and the strip, and the edge of the strip. The encrypted area of ​​the strip component adopts the C3D8R grid type, with a width of 200mm in the middle encrypted area and a length of 150mm in the edge encrypted area; The angles of the denser areas of the support roller, intermediate roller, and work roller are set to 30°, 60°, and 80°, respectively, and the grid types are C3D8R and C3D6. After mesh generation is completed, the finite element model is constructed.

[0018] The specific process in S4 is as follows: S41. Obtain the maximum values ​​of edge drop, secondary crown, quaternary crown, and edge thickness corresponding to different combinations of roller shape parameters obtained in S3 simulation, and perform normalization processing to prevent bias problems caused by differences in magnitude between different indicators:

[0019] In the formula, This represents the normalized data. , , These are the original data, the maximum data, and the minimum data, respectively. S42. Considering the requirements for edge drop control and strip shape control in cold-rolled strip production, the objective function needs to include edge drop control and strip shape control terms. The edge drop control effect is taken as the primary objective, while second-order and fourth-order convexity are secondary objectives. Weighting coefficients are introduced to adjust the importance of each indicator, thereby optimizing the multi-objective problem. The objective function for comprehensive edge drop control and good overall strip cross-section is constructed as follows:

[0020] In the formula, ED , C w2 , C w4 These represent the results of edge drop, secondary crown, and quaternary crown under the current combination of roller shape parameters, respectively. β , a 1. b 1 represents the weighting factor, used to adjust the degree of attention the objective function pays to the different indicators mentioned above; In the constraints, T E This indicates the maximum edge thickness under the current roll shape. To prevent excessive edge thickening from causing rib formation, T E It needs to be less than the thickness at the center of the strip, i.e. T E <0; h max , h min This represents the maximum and minimum values ​​of the cone height. l max , l min These represent the maximum and minimum values ​​of the cone length; S43. Initialize GPR and PSO, including the kernel function of GPR, the population size of PSO, the maximum number of iterations, and the inertia weight. ωt Individual learning factor c 1 and group learning factors c 2. And randomly generate the initial position of the particles. x 0 and initial velocity v 0; S44. Train the GPR surrogate model to describe the nonlinear mapping relationship between roll shape parameters and output performance; S45. Calculate the fitness value of the particles, perform a constraint check on edge thickening, and update the fitness value. A penalty term is introduced for the maximum edge thickness. When the maximum edge thickness is less than 0, the penalty term is 0; when the maximum edge thickness is greater than 0, the penalty term is positive and penalizes the objective function, thus worsening the fitness. The updated fitness function is:

[0021] In the formula, J ( x ij ) represents the original fitness function. λ This is a penalty factor used to adjust the severity of the penalty applied to the fitness function; S46. Based on the updated fitness, compare and update the optimal position of the individual and the optimal position of the population, and update the velocity and position of each particle as follows:

[0022] In the formula, and They represent the first i Individual particles t Velocity and position updated at time +1; , This represents a random number with a value between [0, 1]. , The first i Individual particles t The optimal position of the individual and the optimal position of the group at any given time; ω t The inertia weight is usually taken as 0.6 based on experience; and The first i Individual particles t Speed ​​and position at any given moment; c 1 and c2 represents the individual learning factor and the group learning factor, which are set based on experience, typically 1.5 and 2.5 respectively; S47. Determine if the iteration condition is met (i.e., the maximum number of iterations is used as the iteration termination condition). If not, return to S45 and repeat the above search process to continuously approach the global optimal solution. If it is met, stop the iteration and output the current result, which is the optimal parameter.

[0023] Due to the limited grinding precision of the grinding machines in the cold rolling production line, in order to reduce the difficulty of roller grinding and improve the actual grinding roller shape, the optimized cone height and cone length are rounded to the nearest integer in S5. Based on the rounded cone height and cone length, the final SEDC roller shape design is completed.

[0024] The beneficial effects of the technical solutions provided in the embodiments of the present invention include at least the following: The above-mentioned scheme, through the SEDC roll shape designed by parameter optimization, can significantly improve the compression compensation capability of the edge area without affecting the overall cross-sectional quality of the strip, avoid the generation of high-order strip shape defects and achieve optimal control of edge drop, providing an effective solution for achieving high-precision production of high-value-added cold-rolled strip products. Attached Figure Description

[0025] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0026] Figure 1 This is a schematic diagram of a segmented work roll shape for edge drop control of cold-rolled strip provided in an embodiment of the present invention; Figure 2 This is a flowchart of a segmented work roll shape design method for controlling edge drop of cold-rolled steel strip, provided by an embodiment of the present invention. Figure 3 This is a finite element model for calculating the coupled deformation of the roll system and the rolled piece in this embodiment of the invention, wherein (a) is the overall model, (b) is a side view of the model, and (c) is a schematic diagram of the local mesh refinement in (b). Figure 4 These are different SEDC roller profile curves in the embodiments of the present invention, wherein (a) is a change in cone height and (b) is a change in cone length; Figure 5 These are the changes in side drop corresponding to different roller shape parameters in the embodiments of the present invention, where (a) represents different cone heights and (b) represents different cone lengths; Figure 6These are the secondary crown variations corresponding to different roller shape parameters in the embodiments of the present invention, where (a) represents different cone heights and (b) represents different cone lengths; Figure 7 These are four crown variations corresponding to different roller shape parameters in the embodiments of the present invention, where (a) represents different cone heights and (b) represents different cone lengths; Figure 8 The maximum value of the edge thickness corresponding to different roller shape parameters in the embodiments of the present invention is shown, where (a) represents different cone heights and (b) represents different cone lengths; Figure 9 This is the iterative convergence curve for parameter optimization in the embodiments of the present invention; Figure 10 This is the optimized SEDC roll profile curve in this embodiment of the invention; Figure 11 These are the results of industrial experiments in the embodiments of this invention. Detailed Implementation

[0027] The technical solution of the present invention will now be described with reference to the accompanying drawings.

[0028] In embodiments of the present invention, words such as "exemplarily," "for example," etc., are used to indicate that something is an example, illustration, or description. Any embodiment or design described as "exemplary" in the present invention should not be construed as being more preferred or advantageous than other embodiments or designs. Specifically, the use of the word "exemplary" is intended to present the concept in a concrete manner. Furthermore, in embodiments of the present invention, the meaning expressed by "and / or" can be both, or either one.

[0029] In this embodiment of the invention, sometimes a subscript such as W1 may be written in a non-subscript form such as W1. When the difference is not emphasized, the meaning they express is the same.

[0030] To make the technical problems, technical solutions and advantages of the present invention clearer, a detailed description will be given below in conjunction with the accompanying drawings and specific embodiments.

[0031] This invention provides a segmented work roll shape design method for edge drop control of cold-rolled strip. For example... Figure 2 The flowchart shown is a method for designing the segmented work roll profile for edge drop control of cold-rolled strip. This method may include the following steps:

[0032] S1. Determine the location of the roll shaping area based on the width of the rolled strip; S2. Construct a segmented edge drop control SEDC roll profile curve that includes a flat roll section, a conical roll section, and an edge protection section using a segmented function; S3. Using the finite element model of coupled deformation calculation of roll system and rolled piece, the side drop influence law corresponding to different cone heights and cone lengths is obtained through simulation. S4. Based on the results in S3, construct an objective function for comprehensive edge drop control and good overall strip cross-section, and use Gaussian process regression and particle swarm algorithm to optimize the roll shape parameters. S5. Obtain the optimized combination of cone height and cone length to complete the final SEDC roll shape design.

[0033] Taking a cold rolling mill production line in a domestic steel plant as a specific example, the segmented work roll shape design method for edge drop control of cold-rolled strip described in this invention is explained. The specific implementation steps are as follows:

[0034] S1: Determine the location of the roll trimming zone based on the width of the rolled strip: like Figure 1 The SEDC roll shape adopts a symmetrical design, with the midpoint of the roll body as the origin of the coordinate system. The roll body is divided into a flat roll section, a tapered section, and an edge protection section along its length. The positions of each section are calculated as follows:

[0035] In the formula, L 1 indicates the end point of the flat roller section; L and L 2 represents the length of the conical segment and the endpoint of the conical segment, respectively; B The width of the strip; L 3 indicates the end point of the edge protection section; L R This refers to the length of the roller body.

[0036] Taking the cold-rolled silicon steel produced on this production line as an example, after pickling and edge trimming, the strip entry width is 1250mm, therefore L 2 = 625mm; the length of the working roller on frame S1 of this production line is 1720mm, therefore L 3 = 860mm.

[0037] S2: Construct a segmented edge drop control (SEDC) roll profile curve that includes a flat roll section, a tapered roll section, and an edge protection section using a piecewise function. The specific steps are as follows: (1) Taking the drive side as an example, the SEDC roller profile curve is designed using a piecewise function:

[0038] In the formula, the roll shape value of the flat roll section is 0, indicating that no shaping is performed; The roll shape value of the conical section f ( x ); H This indicates the maximum height of the tapered section; the roll shape value of the edge protection section remains constant. H This indicates that the edge correction amount will no longer be increased.

[0039] (2) The roller shape value of the conical section is composed of a quadratic curve section, a sloping straight line section, and a quadratic margin section. The connection points of each section are tangent. The specific calculation is as follows:

[0040] In the formula, a The control coefficient for cone height; L a This indicates the length of the quadratic curve segment, used to achieve a rapid and smooth transition in the roller shape. L a =0.2 L ; L b This represents the sum of the lengths of the conic section and the oblique line section. L b =0.8 L ; The secondary margin section is connected to the edge protection section, when the cone height is H At that time, the control coefficient a The calculation is as follows: .

[0041] S3: Using a finite element model for coupled deformation calculation of the roll system and the rolled piece, the influence of edge drop on different cone heights and lengths is obtained through simulation. The specific steps are as follows: (1) A finite element model for coupled deformation calculation of the roll system and the rolled piece was established using Abaqus software, specifically including: First, the actual roll size parameters and rolled strip specifications were obtained from the cold rolling production line to create instances of each component. The roll data for the S1 stand of this production line is shown in Table 1. The rolled strip is 50W800 grade silicon steel with dimensions of 2.75mm × 1250mm. Second, material properties were added to the above model. The roll material property is an elastomer, and the rolled piece material property is an elasto-plastic body. The stress-strain curve of this grade of silicon steel was obtained and added to the rolled piece material properties. The specific data is shown in Table 2. Then, the contact types between components were set to roll-to-roll contact and roll-to-strip contact according to the different contact objects, and the friction coefficients were set to 0.3 and 0.05 respectively.

[0042] Table 1. Dimensional parameters of the S1 stand rolls

[0043] Table 250W800 grade silicon steel stress-strain parameters

[0044] In the analysis step settings, the rolling action is reasonably decomposed, and the analysis steps are set sequentially as initialization, small reduction contact, large reduction contact, applying tension, applying bending roll force, and applying rotation. Corresponding loads are applied in different analysis steps, and boundary condition constraints are set. Specifically, during the reduction action, a fixed constraint needs to be applied to the end of the strip to prevent changes in strip position, and this constraint is removed when the work roll begins to rotate. To prevent lateral displacement of the strip, an axial constraint needs to be applied to the center plane of the strip. Simultaneously, to ensure the horizontality of the rolling centerline, a vertical displacement constraint needs to be added to the neutral plane of the strip's deformation-free zone to restrict its vertical movement.

[0045] To balance computational accuracy and efficiency, a local mesh refinement method was employed to refine the mesh in the contact areas between the rolls and the strip, as well as at the edges of the strip. The refined areas for the strip components used the C3D8R mesh type, with a width of 200 mm in the central refined area and a length of 150 mm in the edge refined area. The refined areas for the support roll, intermediate roll, and work roll were set at angles of 30°, 60°, and 80°, respectively, using C3D8R and C3D6 mesh types. After mesh generation, the finite element model was completed, as shown below. Figure 3 As shown.

[0046] (2) Adjust the cone height and cone length, and limit their maximum and minimum values ​​based on experience. Taking all factors into consideration, set the cone heights to 30μm, 40μm, 50μm and 60μm, and the cone lengths to 80mm, 100mm, 120mm and 140mm, respectively, to complete the SEDC roll shape design under different combinations of roll shape parameters, such as Figure 4 As shown.

[0047] (3) The relative thickness reduction of the cross section under different roll shape parameters was obtained by simulation using the established finite element model, and the edge drop, plate shape and maximum edge thickness index corresponding to the changes in cone height and cone length were extracted respectively, including: Calculate the edge drop value of the current section using the edge drop calculation formula:

[0048] In the formula, h e1 Indicates the distance from the edge of the strip as e The thickness of the marker point 1, h e2 Indicates the distance from the edge of the strip as e The thickness of the marker point 2, e 1 = 15mm e 2 = 100mm; The maximum edge thickening value is the maximum relative thinning value corresponding to the current cross-sectional roll transition position. The plate shape results are obtained by fitting the relative thinning amount of the current section using Chebyshev polynomials to obtain its second-order convexity and fourth-order convexity. The plate shape results are as follows:

[0049] In the formula, C w1 , C w2 , C w4 , C w6 These represent the coefficients of the first, second, fourth, and sixth degree terms of the polynomial, respectively, corresponding to the components of the current cross section. x 0 is a constant term; The second-order convexity reflects the symmetrical plate shape characteristics of the current cross section, while the fourth-order convexity represents the higher-order plate shape characteristics at the 1 / 4 position of the current cross section. Figure 5 , Figure 6 , Figure 7 and Figure 8 The specific effects of changes in cone height and cone length on the edge drop, secondary convexity, quaternary convexity, and maximum edge thickening of the strip are shown respectively.

[0050] S4: Based on the above results, an objective function for comprehensive edge drop control and good overall strip cross-section is constructed, and Gaussian process regression and particle swarm optimization (GPR-PSO) are used to optimize the roll shape parameters. The specific steps are as follows: (1) Obtain the maximum values ​​of edge drop, secondary crown, quaternary crown, and edge thickness corresponding to different combinations of roller shape parameters obtained from the simulation in S3, and normalize them to prevent bias problems caused by differences in magnitude between different indicators:

[0051] In the formula, This represents the normalized data. , , These are the original data, the maximum data, and the minimum data, respectively. (2) Considering the requirements of edge drop control and plate shape control in cold-rolled strip production, the objective function needs to include edge drop control term and plate shape control term. The edge drop control effect is taken as the main objective, while the second-order convexity and fourth-order convexity are taken as secondary objectives. The importance of each indicator is adjusted by introducing weight coefficients, thereby achieving the optimization of the multi-objective problem.

[0052]

[0053] In the formula, ED , C w2 , Cw4 These represent the results of edge drop, secondary crown, and quaternary crown under the current combination of roller shape parameters, respectively. β , a 1. b 1 represents a weighting factor, used to adjust the degree of attention the objective function pays to the different indicators mentioned above. To achieve the primary objective of edge reduction control while also considering the secondary objective of a good overall cross-section, the following will be implemented: β Setting it to 0.7 indicates giving greater attention to edge drop; in the shape control items, fourth-order convexity represents a higher-order shape, and to emphasize the focus on higher-order shapes, a 1. b 1 is set to 0.4 and 0.6 respectively;

[0054] In the constraints, T E This indicates the maximum edge thickness under the current roll shape; h max , h min This represents the maximum and minimum values ​​of the cone height. h max =60μm h min =30μm, l max , l min These represent the maximum and minimum values ​​of the cone length. l max =140mm l min =80mm; (3) Initialize GPR and PSO, where the kernel function of GPR is the radial basis function, the population size of PSO is 15, the maximum number of iterations is 120, and the inertia weight is... ω t The individual learning factor is 0.6. c 1 and group learning factors c 2 is set to 1.5 and 2.5 respectively, and the initial positions of the particles are randomly generated. x 0 and initial velocity v 0; (4) Train the GPR surrogate model to describe the nonlinear mapping relationship between the roll shape parameters and the output performance; (5) Calculate the fitness value of the particles and perform a constraint check on edge thickening, then update the fitness value. Introduce a penalty term for the maximum edge thickness. When the thickness is less than 0, the corresponding penalty term is 0; when it is greater than 0, the penalty term is positive and penalizes the objective function, causing the fitness to deteriorate. The updated fitness function is:

[0055]

[0056] In the formula, J ( x ij ) represents the original fitness function. λ This is a penalty factor used to adjust the severity of the penalty applied to the fitness function; (6) Based on the updated fitness, compare and update the individual optimal position and the population optimal position, and update the velocity and position of each particle as follows:

[0057] In the formula, and They represent the first i Individual particles t Velocity and position updated at time +1; , This represents a random number with a value between [0, 1]. , The first i Individual particles t The optimal position of the individual and the optimal position of the group at any given time; ω t Inertial weight; and The first i Individual particles t Speed ​​and position at any given moment; c 1 and c 2 represents individual learning factors and group learning factors, respectively; (7) Use the maximum number of iterations as the iteration termination condition and determine whether it is satisfied. If not, return to step (5) and repeat the above search process to continuously approach the global optimum; if satisfied, stop the iteration and output the current result. The iterative convergence curve of GPR-PSO is as follows: Figure 9 As shown, the optimal combination of roller profile parameters is the cone height. H =47.93μm, cone length L =112.14mm.

[0058] S5: Obtain the optimized combination of cone height and cone length to complete the final SEDC roll shape design. The specific steps are as follows: (1) Due to the limited grinding accuracy of the grinding machines in the cold rolling production line, in order to reduce the difficulty of roller grinding and improve the actual grinding roller shape, it is necessary to appropriately round the optimized cone height and cone length. The rounded cone height H=48μm, cone length L =110mm.

[0059] (2) Based on the rounded cone height and cone length, complete the final SEDC roll shape design. The roll shape curve is as follows: Figure 10 As shown, the specific formula is as follows:

[0060] The roller curve of the conical section is calculated as follows:

[0061] The above roll shape was applied to the S1 stand of the cold rolling production line, and 46 coils of 50W800 grade silicon steel were selected for roll shape testing. The results of the edge drop comparison between the experimental roll period and the adjacent flat roll period are as follows. Figure 11 As shown, compared to the original flat roll profile, the edge reduction of cold-rolled silicon steel is significantly reduced overall after rolling with the SEDC roll profile. The average edge reduction decreases from 4.04 μm during the flat roll period to 2.11 μm, a reduction of 47.7%, effectively controlling edge thinning. Furthermore, silicon steel coils produced using the new roll profile show no obvious rib defects and no strip breakage incidents, demonstrating good rolling stability. Therefore, the above experimental results indicate that the SEDC roll profile designed in this invention, by locally modifying the edges of the work rolls and reducing the reduction at the strip edges, significantly improves the edge reduction control capability of the cold rolling mill. This provides an important guarantee for promoting the overall improvement of the transverse thickness difference quality of cold-rolled strip.

[0062] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for designing the shape of segmented work rolls for edge drop control of cold-rolled strip, characterized in that, The method includes: S1. Determine the location of the roll shaping area based on the width of the rolled strip; S2. Construct a segmented edge drop control SEDC roll profile curve that includes a flat roll section, a conical roll section, and an edge protection section using a segmented function; S3. Using the finite element model of coupled deformation calculation of roll system and rolled piece, the side drop influence law corresponding to different cone heights and cone lengths is obtained through simulation. S4. Based on the results in S3, construct an objective function for comprehensive edge drop control and good overall strip cross-section, and use Gaussian process regression and particle swarm algorithm to optimize the roll shape parameters. S5. Obtain the optimized combination of cone height and cone length to complete the final SEDC roll shape design.

2. The segmented work roll shape design method for edge drop control of cold-rolled strip according to claim 1, characterized in that, The roll shaping area in S1 is symmetrically designed. The roll shape is divided into a flat roll section, a conical section, and an edge protection section along the length of the roll body, with the midpoint of the roll body as the origin. The positions of each section are calculated as follows: ； In the formula, L 1 indicates the end point of the flat roller section; L and L 2 represents the length of the conical segment and the endpoint of the conical segment, respectively; B The width of the strip; L 3 indicates the end point of the edge protection section; L R This refers to the length of the roller body.

3. The segmented work roll shape design method for edge drop control of cold-rolled strip according to claim 1, characterized in that, The formula for the SEDC roller profile curve on the drive side in S2 is as follows: ； In the formula, the roll shape value of the flat roll section is 0, indicating that no shaping is performed; The roll shape value of the conical section f ( x ), H Indicates the maximum height of the tapered segment; The roll shape value of the edge protection section remains constant. H This indicates that the edge correction amount will no longer be increased.

4. The segmented work roll shape design method for edge drop control of cold-rolled strip according to claim 3, characterized in that, The roller profile of the conical section is composed of a quadratic curve section, a sloping straight line section, and a quadratic margin section. The joints of each section are tangent. The specific calculation is as follows: ； In the formula, a The control coefficient for cone height; L a This indicates the length of the quadratic curve segment, used to achieve a rapid and smooth transition in the roller shape. L a =0.2 L ; L b This represents the sum of the lengths of the conic section and the oblique line section. L b =0.8 L ; The secondary margin section is connected to the edge protection section, when the cone height is H At that time, the control coefficient a The calculation is as follows: 。 5. The segmented work roll shape design method for edge drop control of cold-rolled strip according to claim 1, characterized in that, The specific process in S3 is as follows: S31. Use Abaqus software to establish a finite element model for calculating the coupled deformation of the roll system and the rolled piece: S32. Adjust the cone height and cone length, and limit the maximum and minimum values ​​of the cone height and cone length based on experience to complete the SEDC roll shape design under different combinations of roll shape parameters; S33. Using the finite element model established in S31, the relative thickness reduction of the cross-section under different roll shape parameters is obtained through simulation. The edge drop, plate shape, and maximum edge thickness increase indices corresponding to changes in cone height and cone length are extracted respectively, as follows: Calculate the edge drop value of the current section using the edge drop calculation formula. ED : ； In the formula, h e1 Indicates the distance from the edge of the strip as e The thickness of the marker point 1, h e2 Indicates the distance from the edge of the strip as e The thickness of the marker point 2, e 1 = 15mm e 2 = 100mm; The maximum edge thickening value is the maximum relative thinning value corresponding to the current cross-sectional roll transition position. The plate shape results are obtained by fitting the relative thinning amount of the current section using Chebyshev polynomials to obtain its second-order convexity and fourth-order convexity. The plate shape results are as follows: ； In the formula, C w1 , C w2 , C w4 , C w6 These represent the coefficients of the first, second, fourth, and sixth degree terms of the polynomial, respectively, corresponding to the components of the current cross section. x 0 is a constant term; The second-order convexity reflects the symmetrical plate shape characteristics of the current cross section, while the fourth-order convexity represents the higher-order plate shape characteristics at the 1 / 4 position of the current cross section.

6. The segmented work roll shape design method for edge drop control of cold-rolled strip according to claim 5, characterized in that, The specific process in S31 is as follows: S311. Obtain the actual roll size parameters and rolled strip specifications from the cold rolling production line, and complete the creation of instances of each component of the model; S312. Add material properties to the model, where the material property of the roll is an elastic body and the material property of the rolled piece is an elasto-plastic body. Obtain the stress-strain curve of the strip and add it to the material property of the rolled piece. S313. Set the contact type between components according to the different contact objects, namely roll-to-roll contact and roll-to-strip contact, and set the corresponding friction coefficient respectively; S314. Set the analysis steps of the model. By reasonably decomposing the rolling action, the analysis steps are set sequentially as initialization, small reduction contact, large reduction contact, applying tension, applying bending roll force, and applying rotation. S315. Apply the corresponding loads in different analysis steps and set boundary condition constraints. Specifically, during the pressing action, a fixed constraint is applied to the end of the strip to prevent the strip position from changing, and the constraint is removed when the work roll starts to rotate; to prevent the strip from lateral displacement, an axial constraint is applied to the center plane of the strip; to ensure the level of the rolling center line, a vertical displacement constraint is added to the neutral plane of the strip's deformation-free zone. S316. The mesh is refined locally in the contact area between the roll and the strip, the area between the roll and the strip, and the edge of the strip. The encrypted area of ​​the strip component adopts the C3D8R grid type, with a width of 200mm in the middle encrypted area and a length of 150mm in the edge encrypted area; The angles of the denser areas of the support roller, intermediate roller, and work roller are set to 30°, 60°, and 80°, respectively, and the grid types are C3D8R and C3D6. After mesh generation is completed, the finite element model is constructed.

7. The segmented work roll shape design method for edge drop control of cold-rolled strip according to claim 1, characterized in that, The specific process in S4 is as follows: S41. Obtain the maximum values ​​of edge drop, secondary crown, quaternary crown, and edge thickness corresponding to different combinations of roller shape parameters obtained in S3 simulation, and perform normalization processing: ； In the formula, This represents the normalized data. , , These are the original data, the maximum data, and the minimum data, respectively. S42. Construct an objective function for comprehensive edge drop control and good overall cross-section of the strip: ； In the formula, ED , C w2 , C w4 These represent the results of edge drop, secondary crown, and quaternary crown under the current combination of roller shape parameters, respectively. β , a 1. b 1 represents the weighting factor; In the constraints, T E This indicates the maximum edge thickness under the current roll shape; h max , h min This represents the maximum and minimum values ​​of the cone height. l max , l min These represent the maximum and minimum values ​​of the cone length; S43. Initialize GPR and PSO, and randomly generate the initial positions of the particles. x 0 and initial velocity v 0; S44. Train the GPR surrogate model to describe the nonlinear mapping relationship between roll shape parameters and output performance; S45. Calculate the fitness value of the particles, perform a constraint check on edge thickening, and update the fitness value. A penalty term is introduced for the maximum edge thickness. When the maximum edge thickness is less than 0, the penalty term is 0; when the maximum edge thickness is greater than 0, the penalty term is positive and penalizes the objective function, thus worsening the fitness. The updated fitness function is: ； In the formula, J ( x ij ) represents the original fitness function. λ This is a penalty factor used to adjust the severity of the penalty applied to the fitness function; S46. Based on the updated fitness, compare and update the optimal position of the individual and the optimal position of the population, and update the velocity and position of each particle as follows: ； In the formula, and They represent the first i Individual particles t Velocity and position updated at time +1; , This represents a random number with a value between [0, 1]. , The first i Individual particles t The optimal position of the individual and the optimal position of the group at any given time; ω t Inertial weight; and The first i Individual particles t Speed ​​and position at any given moment; c 1 and c 2 represents the individual learning factor and the group learning factor, respectively; S47. Determine if the iteration condition is met. If not, return to S45 and repeat the above search process to continuously approach the global optimal solution. If the condition is met, stop the iteration and output the current result, which is the optimal parameter.

8. The segmented work roll shape design method for edge drop control of cold-rolled strip according to claim 1, characterized in that, In step S5, the optimized cone height and cone length are rounded to the nearest integer, and the final SEDC roll shape design is completed based on the rounded cone height and cone length.

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