An optimization method for tension-leveling strip steel based on vertical edge projection curve and curvature integral

Abstract

The present invention provides an optimization method for straightening strip steel based on vertical edge projection curve and curvature integral, comprising: step 1: collecting geometric dimension parameters and property parameters of straightening strip steel with wave defects in actual working conditions; step 2: establishing a vertical edge end projection curve model during the straightening process of the straightening strip steel, and obtaining 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: using asymmetric curvature integral to construct a geometric model of contact between the bending roller group and the strip steel, and deriving an analytical model formula for the optimal reduction amount of the bending roller group corresponding to different initial wave conditions; step 4: using symmetric curvature integral to construct a geometric model of contact between the straightening roller group and the strip steel, thereby compensating for the reverse curvature generated by the bending roller group, and further deriving an analytical model formula for the optimal reduction amount of the straightening roller group corresponding to different initial wave conditions.

Description

Technical Field

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

[0002] The stretch leveling process (also known as stretch bending straightening) is accomplished using multiple sets of bending, straightening, and tensioning rollers. This process is a metalworking process that causes the strip to plastically stretch and straighten, eliminating defects such as ripples and warping, while improving the strip's flatness and surface quality.

[0003] The purpose of straightening is to straighten out the wavy strip defects to obtain a strip with good flatness and shape. The reduction of each roller group in the tensile bending straightening process directly determines the quality of the final strip shape. Currently, there is a lack of a universal method to optimize the reduction of each roller group during the straightening process under actual working conditions in steel mills to ensure the final straightening effect and strip quality. In addition, the tensile bending straightening process involves multiple sets of bending rollers and straightening rollers. Most current straightening research focuses on finite element simulation and lacks research on different roller groups. As a result, it is impossible to accurately perform straightening work under actual working conditions. The strip forming quality after straightening is poor, and there is a lack of rigorous derivation to adapt to different straightening strip conditions. Summary of the Invention

[0004] To solve the above technical problems, the purpose of the present invention is to provide a method for optimizing the straightening strip based on vertical edge projection curves and curvature integrals. First, a method for projecting a cubic curve of the vertical edge end is constructed to solve the changing angle of each roll group under the vertical edge end during the straightening process. Then, symmetric and asymmetric curvature integral models are constructed to study the angles corresponding to each bending roll and straightening roll. Then, an analytical model formula for the optimal reduction of the bending roll group and straightening roll group corresponding to different initial wave conditions is derived, thereby improving the forming quality of the straightening strip and achieving the best straightening effect.

[0005] The present invention provides a method for optimizing the tension and straightening of strip steel based on a vertical edge projection curve and a curvature integral, comprising:

[0006] Step 1: Collect the geometric size parameters and property parameters of the straightening strip with wave defects in actual working conditions;

[0007] Step 2: Establish a projection curve model of the vertical edge end during the straightening process of the tension 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;

[0008] Step 3: Use the asymmetric curvature integral to construct a geometric model of the contact between the bending roll group and the strip, and derive the analytical model formula for the optimal reduction amount of the bending roll group corresponding to different initial wave conditions;

[0009] Step 4: Use the symmetrical curvature integral to construct a 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.

[0010] The present invention provides a strip straightening optimization method based on vertical edge projection curve and curvature integral. First, a vertical edge end projection cubic curve model is constructed to solve the changing angle of each roller group under the vertical edge end during the straightening process. Then, symmetric and asymmetric curvature integral models are established to strictly derive the analytical model formula of the optimal reduction amount of the bending roller group and the straightening roller group suitable for different initial wave defects, thereby more accurately optimizing the reduction amount distribution of each roller group and significantly improving the flatness and plate shape quality of the strip. Through this method, the optimal reduction amount of different roller groups can be calculated through analytical formulas to adapt to the straightening requirements under various initial plate shape defects, ensure the forming quality of the strip after straightening, simplify the calculation process, improve the straightening efficiency, and provide efficient and reliable technical support for the optimization of the strip straightening process in steel mills. BRIEF DESCRIPTION OF THE DRAWINGS

[0011] Figure 1 This is a flow chart of a method for optimizing a straightening strip steel based on a vertical edge projection curve and curvature integral according to the present invention;

[0012] Figure 2 A schematic diagram of a projection curve model of a vertical edge end portion during the straightening process of a tensile strip provided by an embodiment of the present invention;

[0013] Figure 3 A geometric model diagram of the contact between the bending roller group and the strip provided in an embodiment of the present invention;

[0014] Figure 4 A geometric model diagram of the contact between the straightening roller set and the strip provided in an embodiment of the present invention;

[0015] Figure 5 This is a diagram showing the residual stress results in the edge wave area of the strip after straightening provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0016] The following embodiments of the present invention are described in further detail with reference to the accompanying drawings and examples. The following examples are used to illustrate the present invention but are not intended to limit the scope of the present invention.

[0017] At present, there is a lack of general calculation methods for actual working conditions in order to optimize the reduction of multiple sets of bending rollers and straightening rollers involved in the straightening process. Most existing studies rely on finite element simulation and lack systematic research on the effects of different roller groups. The forming quality of the strip after straightening is difficult to guarantee, and it cannot effectively adapt to the diverse strip straightening needs in steel mills. In response to the above problems, the present invention proposes a straightening strip optimization method based on the vertical edge projection curve and curvature integral. First, a vertical edge end projection cubic curve is constructed to solve the changing angle under the vertical edge end of each roller group in the straightening process. Then, a symmetrical and asymmetrical curvature integral model is constructed to study the angles corresponding to each bending roller and straightening roller, and then the analytical model formula for the optimal reduction of the bending roller group and straightening roller group corresponding to different initial wave conditions is derived, thereby improving the forming quality of the straightening strip and achieving the best straightening effect.

[0018] like Figure 1 As shown, the present invention provides a strip straightening optimization method based on vertical edge projection curve and curvature integral, comprising the following steps:

[0019] Step 1: Collect the geometric dimensions and property parameters of the straightened steel strip with wave defects in actual working conditions. The geometric dimensions include the length, width, and thickness of the straightened steel strip. The property parameters include the density, Young's modulus, Poisson's ratio, and yield strength of the straightened steel strip.

[0020] In this example, we selected high-strength steel, which is more prone to plate defects during the stretch bending straightening process, for research. Based on the actual processing conditions of the steel plant, the geometric dimensions of the straightening strip are as follows: the length of the straightening strip is 5000mm, the width is 1083mm, and the thickness is 1.5mm. The attribute parameters of the straightening strip are as follows: the density is 7850kg / m 3 , Young's modulus is 2.1×10 5 (MPa), Poisson's ratio is 0.3, yield strength is 420MPa, and tensile strength is 780MPa;

[0021] Step 2: If Figure 2 As shown in the figure, a projection curve model of the vertical edge end in the straightening process of the tensile strip is established, and based on the corresponding boundary conditions, a general analytical formula for the vertical edge straightening angle corresponding to each bending roller group in the straightening process is obtained, specifically:

[0022] Step 2.1: Based on the initial waveform of the straightened strip, construct the formula for the triple projection curve of the vertical edge end:

[0023] (1)

[0024] in, A 、 B 、 C 、 Dis the parameter to be sought; x is 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.

[0025] When implementing it specifically, Figure 2 in y The arc curve above the axis represents the i The local plate shape corresponding to the bending roller group is projected onto the right end point of the arc curve. y The cubic projection curve of the vertical edge end is obtained below the axis.

[0026] According to the actual wave condition of the straightening strip and the final ideal state, the following boundary conditions are met:

[0027] (2)

[0028] In this example, the “two bends and one straightening” straightening process is selected for research. N = n +1 ，n is the number of bending roller groups n= 2, 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, unit: mm.

[0029] 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 side end to obtain:

[0030] (3)

[0031] The straightening process i The projection curve of the vertical side end corresponding to the bending roller group is:

[0032] (4)

[0033] in, x i For the i The vertical coordinate of the projection curve of the vertical side end corresponding to the bending roller group; y i For the i The horizontal coordinates of the projection curve of the vertical side end corresponding to the bending roller group.

[0034] Step 2.3: Based on the arc law and the relationship between angle and curvature radius, combine formula 4 and use Mathmatica to derive the first iGeneral formula for the vertical edge straightening angle corresponding to the bending roller group:

[0035] (5)

[0036] 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, i =1,2,..., n .

[0037] The arc law is: ; The relationship between angle and curvature radius is: .

[0038] in, ρ i For the i The curvature radius of the projection curve of the vertical side end corresponding to the bending roller set.

[0039] Step 3: Use the asymmetric curvature integral to construct the geometric model of the contact between the bending roll group and the strip, and derive the analytical model formula for the optimal reduction amount of the bending roll group corresponding to different initial wave conditions, specifically:

[0040] Step 3.1: If Figure 3 As shown in the figure, the geometric model of the contact between the bending roller set and the strip is constructed using the asymmetric curvature integral. The distance between the actual contact points and the roller pitch satisfy the geometric relationship:

[0041] (6)

[0042] in, L i1 is the distance between the contact point between the strip and the bending upper roll and the contact point between the strip and the bending lower roll, r is the radius of the bending roller set, r= 80 mm ; 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 vertical line of the contact point between the upper bending roller and the strip and the vertical direction, P It is the roller distance between the bending upper roller and the bending lower roller.

[0043] Step 3.2: Construct the physical equations of the curvature integral model:

[0044] (7)

[0045] Combining Formula 6 and Formula 7, the analytical formula for the reduction of each bending roller group is derived using Mathmatica:

[0046] (8)

[0047] in, δ i1 For the i The pressing amount of the bending roller group; k is the curvature distribution of the bending roller group.

[0048] 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. Then, derive the analytical model formula for the optimal reduction amount of the straightening roll group corresponding to different initial wave conditions. Specifically,

[0049] Step 4.1: If Figure 4 As shown in the figure, the geometric model of the contact between the straightening roll group and the strip is constructed using the symmetrical curvature integral, and then the reverse curvature produced by the bending roll group is compensated to study the reduction of the straightening roll group. The strip produces symmetrical bending deformation, and according to the geometric relationship, it is deduced that:

[0050] (9)

[0051] in, R 1=200mm is the radius of the straightening upper roller; R 2=80mm is the radius of the straightening lower 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 straightening upper rollers, δ i2 For the i The reduction of the straightening roller group.

[0052] Step 4.2: Establish the following physical equation between the straightening roll set and the strip:

[0053] (10)

[0054] Combining Formula 9 and Formula 10, and using Mathmatica to deduce the analytical formula for the reduction of the straightening roller group:

[0055] (11)

[0056] in, E is the elastic modulus of the strip steel, ρ is the radius of curvature, his the strip thickness, σ s is the yield stress of the strip steel, and the specific value can be used to calculate δ i2 .

[0057] This embodiment establishes a finite element simulation model of the entire process of high-strength steel stretching, bending and straightening, and further verifies the analytical numerical results obtained by the general analytical model formula for straightening.

[0058] In this example, the finite element simulation of the entire stretch bending and straightening process was performed using Abaqus software. The geometrical parameters and property parameters of the straightening strip, as well as the analytical results of the reduction of each bending roller group and straightening roller group in the "two bends and one straightening" stretch bending and straightening process obtained using the general analytical formula from steps 2 to 4, were used as input parameters of the finite element model. High-strength steel was selected for the straightening strip for the study. The strip had a length of 5000 mm, a width of 1083 mm, a thickness of 1.5 mm, and a density of 7850 kg / m 3 , Young's modulus is 2.1×10 5 (MPa), Poisson's ratio is 0.3, yield strength is 420MPa, and tensile strength is 780MPa;

[0059] Figure 5 The straightening results of the strip in this embodiment are shown. Data from the middle path of the edge wave area are selected for study, and it is found that the maximum internal residual stress after straightening is 10.9 MPa, which is much smaller than the initial internal residual stress of the strip of 108.2 MPa and the critical buckling stress of 69.799 MPa. This indicates that the internal residual stress of the strip is reduced after straightening, the initial plate shape defects are eliminated, and the plate shape quality is improved, which illustrates the reliability of the research method of the present invention.

[0060] In this embodiment, an optimization method for straightening strip steel based on the vertical edge projection curve and curvature integral is established. Based on the vertical edge end projection curve and curvature integral model, the analytical model formula of the optimal reduction amount of the bending roller group and the straightening roller group suitable for different initial wave defects is strictly derived to ensure the forming quality of the strip steel after straightening, simplify the calculation process, improve the straightening efficiency, and provide efficient and reliable technical support for the optimization of the strip steel straightening process in steel mills.

[0061] The foregoing description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Those skilled in the art will readily appreciate that various modifications and variations of the present invention are possible. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention shall be included within the scope of protection 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 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 the asymmetric curvature integral to construct a geometric model of the contact between the bending roll group and the strip, and derive the analytical model formula for the optimal reduction amount of the bending roll group corresponding to different initial wave conditions; Step 4: Use the symmetrical curvature integral to construct a 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. Then, derive the analytical model formula for the optimal reduction 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 bending upper roll and the contact point between the strip and the bending lower 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 vertical 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, the analytical formula for the reduction of each bending roller group is derived using Mathmatica: (8) in, δ i1 For the i The pressing amount of the bending roller group; k is the curvature distribution of the bending roller group; 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, and then compensate for the reverse curvature produced by the bending roll group to study the reduction of the straightening roll group. The strip produces symmetrical bending deformation. 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 straightening lower 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 straightening upper rollers, δ i2 For the i The 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 strip straightening optimization method based on vertical edge projection curve and curvature integral according to claim 1 is characterized in that: The geometric dimension parameters include: length, width and thickness of the tension and straightening strip; the property parameters include: density, Young's modulus, Poisson's ratio and yield strength of the tension and straightening strip.

3. The strip straightening optimization method based on vertical edge projection curve and curvature integral according to claim 1 is characterized in that: The step 2 is specifically as follows: Step 2.1: Based on the initial waveform of the straightened strip, construct the formula for the triple projection curve of the vertical edge end: (1) in, A 、 B 、 C 、 D is the parameter to be sought; x is 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 groups, 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, unit: 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 side end to obtain: (3) The straightening process i The projection curve of the vertical side end corresponding to the bending roller group is: (4) in, x i For the i The vertical coordinate of the projection curve of the vertical side end corresponding to the bending roller group; y i For the i Horizontal coordinates of the projection curve of the vertical side end corresponding to the bending roller group; Step 2.3: Based on the arc law and the relationship between angle and curvature radius, combine formula 4 and use Mathmatica to derive the first 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 strip straightening optimization method based on vertical edge projection curve and curvature integral according to claim 3 is characterized in that: The arc law is: ;in, ρ i For the i The curvature radius of the projection curve of the vertical side end corresponding to the bending roller set.

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

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