Straightening strip steel optimization method based on vertical edge projection curve and curvature integral

Abstract

The invention discloses a straightening strip steel optimization method based on a vertical edge projection curve and curvature integration. The straightening strip steel optimization method comprises the steps that 1, geometric dimension parameters and attribute parameters of straightening strip steel with wave defects in actual working conditions are collected; step 2, establishing a vertical edge end projection curve model in the straightening process of the withdrawal and straightening strip steel, and obtaining a general analytical formula of a vertical edge straightening angle corresponding to each bending roller group in the straightening process based on a corresponding boundary condition; 3, constructing a geometric model of contact between the bending roller group and the strip steel by using asymmetric curvature integration, and deducing an optimal rolling reduction analytical model formula of the corresponding bending roller group suitable for different initial wave conditions; and 4, constructing a geometric model of the straightening roll group in contact with the strip steel by utilizing symmetrical curvature integration, further compensating the reverse bending rate generated by the bending roll group, and further deducing an optimal rolling reduction analytical model formula of the corresponding straightening roll group suitable for different initial wave conditions.

Description

Technical Field

[0001] The present invention belongs to the technical field of straightening, and particularly relates to an optimization method for tension levelling strip steel based on the vertical edge projection curve and curvature integral. Background Art

[0002] The tension levelling process (also known as the stretch-bend straightening process) is completed by multiple sets of bending rolls, straightening rolls and tension rolls. The tension levelling process is a metal processing technology that causes the strip steel to undergo plastic elongation to achieve straightening of the strip steel, eliminate defects such as waves and warping, and improve the flatness and surface quality of the strip steel.

[0003] The purpose of straightening is to straighten the shape defect with waviness to obtain strip steel with good flatness. The reduction of each roll group in stretch-bend straightening directly determines the quality of the final shape of the strip steel. Currently, there is a lack of a general method for optimizing the reduction of each roll group in the straightening process under actual working conditions in steel mills to ensure the final straightening effect and strip steel quality. Moreover, the stretch-bend straightening process involves multiple sets of bending rolls and straightening rolls. Currently, most straightening research mainly focuses on finite element simulation, lacking research on different roll groups, and unable to accurately carry out straightening work under actual working conditions. The formed quality of the strip steel after straightening is not good, and there is a lack of strict derivation to adapt to different straightening strip steel situations. Summary of the Invention

[0004] To solve the above technical problems, the purpose of the present invention is to provide an optimization method for tension levelling strip steel based on the vertical edge projection curve and curvature integral. First, a method for constructing a cubic curve of the vertical edge end projection is established, and the changing angles under the vertical edge ends of each roll group in the corresponding tension levelling process are solved. Then, symmetric and asymmetric curvature integral models are constructed to study the corresponding angles of each bending roll and straightening roll, and further an analytical model formula for the optimal reduction of the corresponding bending roll group and straightening roll group applicable to different initial wave conditions is derived, so as to improve the forming quality of the tension levelling strip steel and achieve the best straightening effect.

[0005] The present invention provides an optimization method for tension levelling strip steel based on the vertical edge projection curve and curvature integral, including: Step 1: Collect the geometric dimension parameters and attribute parameters of the tension levelling strip steel with wave defects in the actual working condition; Step 2: Establish a vertical edge end projection curve model in the straightening process of the tension levelling strip steel, and obtain a general analytical formula for the vertical edge straightening angle corresponding to each bending roll group in the straightening process based on the corresponding boundary conditions; Step 3: Use the asymmetric curvature integral to construct a geometric model of the contact between the bending roll group and the strip steel, and derive an analytical model formula for the optimal reduction of the corresponding bending roll group applicable to different initial wave conditions; Step 4: Construct a geometric model of the straightening roll set in contact with the strip using symmetric curvature integration to compensate for the reverse curvature generated by the bending roll set, and then derive an analytical model formula for the optimal reduction of the straightening roll set corresponding to different initial wave conditions.

[0006] An optimized method for tension leveling of strip steel based on vertical edge projection curve and curvature integration according to the present invention first constructs a cubic curve model of the vertical edge end projection, solves the changing angles under the vertical edges of each roll set during the tension leveling process, and then establishes symmetric and asymmetric curvature integration models, strictly deriving analytical model formulas for the optimal reduction of the bending roll set and the straightening roll set applicable to different initial wave defects, so as to more accurately optimize the reduction distribution of each roll set, significantly improve the flatness and shape quality of the strip steel. Through this method, the optimal reduction of different roll sets can be calculated by an analytical formula, meeting the tension leveling requirements under various initial shape defects, ensuring the forming quality of the straightened strip steel, simplifying the calculation process, improving the straightening efficiency, and providing efficient and reliable technical support for the optimization of the strip steel straightening process in steel mills. Brief Description of the Drawings

[0007] Figure 1 It is a flow chart of an optimized method for tension leveling of strip steel based on vertical edge projection curve and curvature integration according to the present invention; Figure 2 It is a schematic diagram of the vertical edge end projection curve model during the straightening process of the tension leveled strip steel provided by an embodiment of the present invention; Figure 3 It is a geometric model diagram of the bending roll set in contact with the strip steel provided by an embodiment of the present invention; Figure 4 It is a geometric model diagram of the straightening roll set in contact with the strip steel provided by an embodiment of the present invention; Figure 5 It is a diagram of the internal residual stress results in the edge wave region of the strip steel after straightening provided by an embodiment of the present invention. Detailed Description of the Embodiments

[0008] The following combines the drawings and embodiments to further describe in detail the specific embodiments of the present invention. The following embodiments are used to illustrate the present invention, but are not used to limit the scope of the present invention.

[0009] At present, regarding the optimization problem of the reduction amounts of multiple sets of bending rolls and straightening rolls involved in the tension leveling process, there is a lack of a general calculation method for actual working conditions. Most existing research relies on finite element simulation, lacking a systematic study of the effects of different roll sets. It is difficult to ensure the forming quality of the strip after straightening, and it cannot effectively meet the diverse strip straightening requirements in steel mills. To address the above problems, the present invention proposes an optimization method for tension leveled strip based on the vertical edge projection curve and curvature integral. First, a cubic curve for the projection of the vertical edge end is constructed to solve the changing angles under the vertical edge ends of each roll set during the tension leveling process. Then, symmetric and asymmetric curvature integral models are constructed to study the corresponding angles of each bending roll and straightening roll, and further an analytical model formula for the optimal reduction amounts of the corresponding bending roll set and straightening roll set applicable to different initial wavy conditions is derived, so as to improve the forming quality of the tension leveled strip and achieve the best straightening effect.

[0010] As Figure 1 shown, an optimization method for tension leveled strip based on the vertical edge projection curve and curvature integral of the present invention includes the following steps: Step 1: Collect the geometric dimension parameters and property parameters of the tension leveled strip with wavy defects in the actual working condition. The geometric dimension parameters include: the length, width, and thickness of the tension leveled strip. The property parameters include: the density, Young's modulus, Poisson's ratio, and yield strength of the tension leveled strip.

[0011] In this example, high-strength steel that is more likely to generate shape defects during the stretch bending straightening process is selected for research. Combining the actual steel mill processing situation, the geometric dimension parameters of the straightened strip are as follows: the length of the straightened strip is 5000 mm, the width is 1083 mm, and the thickness is 1.5 mm. The property parameters of the straightened strip are as follows: the density is 7850 kg / m 3 ³, the Young's modulus is 2.1×10 5 (MPa), the Poisson's ratio is 0.3, the yield strength is 420 MPa, and the tensile strength is 780 MPa; Step 2: As Figure 2 shown, establish a vertical edge end projection curve model during the straightening process of the tension leveled strip, and obtain a general analytical formula for the vertical edge straightening angles of each bending roll set during the straightening process based on the corresponding boundary conditions, specifically: Step 2.1: According to the initial waveform of the straightened strip, construct a cubic projection curve formula for the vertical edge end: (1) where A , B , C , D are parameters to be determined; x is the vertical direction coordinate of the vertical edge end projection curve; y is the horizontal direction coordinate of the vertical edge end projection curve.

[0012] During specific implementation, Figure 2 in y the arc curve above the axis represents the local strip shape corresponding to the i bending roll group. Project the right endpoint of the arc curve onto the y axis below to obtain the cubic projection curve of the vertical edge end.

[0013] According to the actual wave condition of the tension leveling strip steel and the condition of finally tending to the ideal state, the following boundary conditions are satisfied: (2) In this example, the tension leveling process of "two bends and one straightening" is selected for research. Among them N = n +1 ，n is the number of bending roll groups n= 2, L is the length of the strip steel after straightening under local strip shape defects, in mm, L 1 is the length of the strip steel before straightening under local strip shape defects, in mm.

[0014] Step 2.2: Solve to obtain the parameters A , B , C , D , and substitute them into the formula of the cubic projection curve of the vertical edge end to obtain: (3) Then the projection curve of the vertical edge end corresponding to the i bending roll group in the tension leveling process is: (4) Among them, x i is the vertical coordinate of the projection curve of the vertical edge end corresponding to the i bending roll group; y i is the horizontal coordinate of the projection curve of the vertical edge end corresponding to the i bending roll group.

[0015] Step 2.3: According to the arc law and the relationship between the angle and the radius of curvature, combine formula 4 and use Mathmatica to deduce the general formula for the vertical edge straightening angle corresponding to the i bending roll group: (5) Among them, θ i is the vertical edge straightening angle corresponding to the i bending roll group, that is XThe included angle between the axis and x = i the tangent of the curve at the position, i = 1, 2, ..., n .

[0016] The so-called arc law is: ; The relationship between the angle and the radius of curvature is: .

[0017] Among them, ρ i is the radius of curvature of the projection curve of the vertical edge end corresponding to the i nth bending roll group.

[0018] Step 3: Use the asymmetric curvature integral to construct the geometric model of the contact between the bending roll group and the strip steel, and derive the analytical model formula for the optimal reduction of the corresponding bending roll group under different initial wave conditions, specifically: Step 3.1: As Figure 3 shown, use the asymmetric curvature integral to construct the geometric model of the contact between the bending roll group and the strip steel. The distance between the actual contact points and the roll pitch satisfy the geometric relationship: (6) Among them, L i1 is the distance between the contact point of the strip steel and the upper bending roll and the contact point with the lower bending roll, r is the radius of the bending roll group, r= 80 mm ; θ i1 is the angle between the perpendicular line of the contact point of the i nth lower bending roll and the strip steel and the vertical direction, θ i1+1 is the angle between the perpendicular line of the contact point of the upper bending roll and the strip steel and the vertical direction, P is the roll pitch between the upper bending roll and the lower bending roll.

[0019] Step 3.2: Construct the physical equation of the curvature integral model: (7) Combining Formula 6 and Formula 7, use Mathmatica to derive the analytical general formula for the reduction of each bending roll group: (8) Among them, δ i1 is the reduction of the i nth bending roll group; k is the curvature distribution of the bending roll group.

[0020] Step 4: Use symmetric curvature integration to construct a geometric model of the straightening roll set in contact with the strip steel, compensate for the reverse curvature generated by the bending roll set, and then derive an analytical model formula for the optimal reduction of the straightening roll set corresponding to different initial waviness conditions, specifically: Step 4.1: As Figure 4 shown, use symmetric curvature integration to construct a geometric model of the straightening roll set in contact with the strip steel, and then compensate for the reverse curvature generated by the bending roll set to study the reduction of the straightening roll set. The strip steel undergoes symmetric bending deformation, and according to geometric relationships, it is deduced that: (9) where, R 1 = 200 mm is the radius of the upper straightening roll; R 2 = 80 mm is the radius of the lower straightening roll; θ i2 is the angle between the perpendicular line at the contact point of the i th straightening roll set and the strip steel and the vertical direction, M is the roll pitch between two upper straightening rolls, δ i2 is the reduction of the i th straightening roll set.

[0021] Step 4.2: Establish the following physical equation between the straightening roll set and the strip steel: (10) Combining Formula 9 and Formula 10 and using Mathmatica for derivation, the general analytical formula for the reduction of the straightening roll set is obtained: (11) where, E is the elastic modulus of the strip steel, ρ is the radius of curvature, h is the thickness of the strip steel, σ s is the yield stress of the strip steel. Substituting specific values can calculate δ i2 .

[0022] In this embodiment, a finite element simulation model of the entire process of tension leveling of high-strength steel is established to verify the analytical numerical results obtained from the general leveling analytical model formula.

[0023] In this embodiment, the finite element simulation of the whole process of stretch-bending straightening is carried out by Abaqus software, and the geometric dimension parameters and property parameters of the straightened strip steel, as well as the analytical results of the reduction amounts of each bending roll group and straightening roll group in the stretch-bending straightening process of "two bends and one straightening" obtained by using the general analytical formulas in Steps 2 - 4 are used as the input parameters of the finite element model. High-strength steel is selected for the study of the straightened strip steel. The strip steel has a length of 5000 mm, a width of 1083 mm, a thickness of 1.5 mm, and a density of 7850 kg / m 3 , a Young's modulus of 2.1×10 5 (MPa), a Poisson's ratio of 0.3, a yield strength of 420 MPa, and a tensile strength of 780 MPa; Figure 5 The straightening result of the strip steel in this embodiment is shown. The data of the middle path in the edge wave region is selected for the study, and it is found that the maximum value of the internal residual stress after straightening is 10.9 MPa, which is much smaller than the initial internal residual stress of the strip steel of 108.2 MPa and the critical buckling stress of 69.799 MPa. This shows that the internal residual stress of the strip steel after straightening is reduced, the initial shape defects are eliminated, and the shape quality is improved, indicating the reliability of the research method of the present invention.

[0024] An optimization method for stretch-bending straightened strip steel based on the vertical edge projection curve and curvature integral established in this embodiment, based on the vertical edge end projection curve and curvature integral model, strictly derives the analytical model formula for the optimal reduction amounts of the bending roll group and straightening roll group applicable to different initial wave defects, ensures the forming quality of the strip steel after straightening, simplifies the calculation process, improves the straightening efficiency, and provides efficient and reliable technical support for the optimization of the strip steel straightening process in steel mills.

[0025] The above are only the preferred embodiments of the present invention and are not used to limit the present invention. For those skilled in the art, the present invention can have various changes and modifications. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A strip straightening optimization method based on vertical edge projection curve and curvature integral, characterized in that: include: Step 1: Collect the geometric size parameters and property parameters of the straightening strip with wave defects in actual working conditions; Step 2: Establish a projection curve model of the vertical edge end during the straightening process of the tension and straightening strip, and obtain a general analytical formula for the vertical edge straightening angle corresponding to each bending roller group in the straightening process based on the corresponding boundary conditions; Step 3: Use asymmetric curvature integral to construct a geometric model of contact between the bending roll set and the strip, and derive the analytical model formula for the optimal reduction amount of the bending roll set corresponding to different initial wave conditions; Step 4: Use the symmetrical curvature integral to construct the geometric model of the contact between the straightening roll group and the strip to compensate for the reverse curvature produced by the bending roll group, and then derive the analytical model formula for the optimal reduction amount of the straightening roll group corresponding to different initial wave conditions; The step 3 is specifically as follows: Step 3.1: Use the asymmetric curvature integral to construct the geometric model of the contact between the bending roller set and the strip. The distance between the actual contact points and the roller pitch satisfy the geometric relationship: (6) in, L i1 is the distance between the contact point between the strip and the upper bending roll and the contact point between the strip and the lower bending roll, r is the radius of the bending roller set, θ i1 For the i The angle between the perpendicular line of the contact point between the bending lower roller and the strip and the vertical direction, θ i1+1 is the angle between the perpendicular line of the contact point between the upper bending roller and the strip and the vertical direction, P is the roller distance between the bending upper roller and the bending lower roller; Step 3.2: Construct the physical equations of the curvature integral model: (7) Combining Formula 6 and Formula 7, Mathmatica is used to derive the analytical formula for the reduction of each bending roller group: (8) in, δ i1 For the i The pressing amount of the bending roller group; k is the curvature distribution of the bending roller set; The step 4 is specifically as follows: Step 4.1: Use the symmetrical curvature integral to construct the geometric model of the contact between the straightening roll group and the strip steel, and then compensate for the reverse curvature produced by the bending roll group to study the reduction of the straightening roll group. The strip steel produces symmetrical bending deformation, and according to the geometric relationship, it is deduced that: (9) in, R 1 is the radius of the straightening upper roller; R 2 is the radius of the lower straightening roller, θ i2 For the i The angle between the perpendicular line of the contact point between the straightening roller group and the strip and the vertical direction, M is the roller distance between the two upper straightening rollers, δ i2 For the i The amount of pressure reduction of the straightening roller group; Step 4.2: Establish the following physical equation between the straightening roll set and the strip: （10） Combining Formula 9 and Formula 10, and using Mathmatica to deduce the analytical formula for the reduction of the straightening roller group: （11） in, E is the elastic modulus of the strip steel, ρ is the radius of curvature, h is the strip thickness, σ s is the yield stress of the strip steel, and the specific value can be used to calculate δ i2 .

2. The method for optimizing the straightening strip based on the vertical edge projection curve and the curvature integral according to claim 1 is characterized in that: The geometric dimension parameters include: length, width and thickness of the straightening steel strip; the property parameters include: density, Young's modulus, Poisson's ratio and yield strength of the straightening steel strip.

3. The method for optimizing the straightening strip based on the vertical edge projection curve and the curvature integral according to claim 1 is characterized in that: The step 2 is specifically as follows: Step 2.1: According to the initial waveform of the straightened strip, construct the formula of the three-dimensional projection curve of the vertical edge end: (1) in, A , B , C , D is the parameter to be requested; x The vertical coordinate of the projection curve at the end of the vertical side; y is the horizontal coordinate of the projection curve of the vertical side end; According to the actual wave condition of the straightening strip and the final ideal state, the following boundary conditions are met: (2) in, N = n +1, n is the number of bending roller sets, L is the length of the strip after straightening under local flatness defects, in mm, L 1 is the strip length before straightening under local flatness defects, in mm; Step 2.2: Solve the boundary conditions to obtain the parameters A , B , C , D , and put it into the cubic projection curve formula of the vertical edge end to get: (3) The straightening process i The projection curve of the vertical edge end corresponding to the bending roller group is: (4) in, x i For the i The vertical coordinates of the projection curve of the vertical edge end corresponding to the bending roller group; y i For the i Horizontal coordinates of the projection curve of the vertical edge end corresponding to the bending roller group; Step 2.3: According to the arc law and the relationship between angle and curvature radius, combined with formula 4 and using Mathmatica, we can derive the i General formula for the vertical edge straightening angle corresponding to the bending roller group: (5) in, θ i For the i The vertical edge straightening angle corresponding to the bending roller group is X Axis and x = i The angle between the tangent lines of the curve.

4. The method for optimizing the straightening strip based on the vertical edge projection curve and the curvature integral according to claim 3 is characterized in that: The arc law is: ;in, ρ i For the i The radius of curvature of the projection curve of the vertical edge end corresponding to the bending roller set.

5. The method for optimizing the straightening strip based on the vertical edge projection curve and the curvature integral according to claim 4 is characterized in that: The relationship between angle and radius of curvature is: .

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