Asymmetric strip shape forecasting method for twenty-high roll mill based on non-arc theory

Abstract

The invention provides a twenty-high roll mill asymmetric strip shape forecasting method based on a non-arc theory, and belongs to the technical field of metallurgical rolling. The method mainly comprises the following steps executed by a computer: collecting equipment parameters of a twenty-high rolling mill, characteristic parameters of typical rolled strips and corresponding rolling process parameters; dividing units; forecasting the transverse distribution value of the pre-tensile stress of the strip during rolling; and strip outlet plate shape transverse distribution during rolling is forecasted. According to the method, the rolling force is calculated based on the non-arc theory, the program crash phenomenon is avoided, the accuracy of the calculation result is guaranteed, and strip shape prediction under the asymmetric rolling condition can be achieved.

Description

Technical Field

[0001] The present invention relates to the technical field of metallurgical rolling, and more particularly, to an asymmetric shape prediction method for a twenty-high rolling mill based on non-circular arc theory. Background Art

[0002] Twenty-high rolling mill [1] When rolling thin stainless steel strips, the arc length of the contact deformation zone is much longer than the strip thickness [2] , and the profile of the work roll becomes a non-circular arc profile. The elastic flattening of the work roll has a great influence on the rolling pressure distribution, and the traditional rolling force calculation model will collapse during calculation. Since the shape prediction model is the basis of various shape control technologies [3-5] . Therefore, in order to obtain accurate rolling force during the asymmetric shape prediction process, the present invention calculates the rolling force based on non-circular arc theory [6] , which not only avoids the occurrence of program collapse, but also ensures the accuracy of the calculation results. On this basis, an asymmetric shape prediction method for a twenty-high rolling mill based on non-circular arc theory is invented, which can predict the shape of cold-rolled thin stainless steel strips under asymmetric rolling conditions.

[0003] References:

[0004] [1] Cao Wenchang, Chen Qingsong, Luo Xiaopeng. Twenty-high rolling mill: China, CN201220614749.1 [P]. 2012-11-19.

[0005] [2] Zhou Guanyu, He Anrui, Liu Chao, et al. Research on the deformation behavior of wide-width industrial pure titanium strip rolled by a 20-high rolling mill [J]. Rare Metal Materials and Engineering, 2020, 49(7): 2333-2339;

[0006] [3] Sun Jianliang, Yan Mingze, Li Mingyuan, et al. Analysis of the deformation of the backup roll group and shape control of a twenty-high rolling mill [J]. Iron and Steel, 2021, 56(12): 85-95.

[0007] [4] Zhang Qingdong, Dai Chang, Wen Jie, et al. Simulation study on the shape control performance of a twenty-high Sendzimir rolling mill [J]. Steel Rolling, 2013, 30(3): 1-6.

[0008] [5] Wang Hui, Qin Xiaofeng, Xu Kun. Optimization method for rolling process parameters of the roll system of a Sendzimir twenty-high rolling mill based on orthogonal test: China, CN202111566864.6 [P]. 2021-12-20.

[0009] [6] Yuan Zhengwen, Ren Zhongkai, Xiao Hong, et al. Shape control of extremely thin strips rolled by a twenty-high rolling mill [J]. Journal of Central South University, 2017, 48(4): 860-866. Summary of the Invention

[0010] According to the above technical problem that the twenty-high rolling mill has poor plate shape (straightness) during the production process, a method for predicting asymmetric plate shape of a twenty-high rolling mill based on non-circular arc theory is provided. The present invention calculates the rolling force based on the non-circular arc theory, which not only avoids the occurrence of program crashes, but also ensures the accuracy of the calculation results.

[0011] The technical means adopted by the present invention are as follows:

[0012] A method for predicting asymmetric plate shape of a twenty-high rolling mill based on non-circular arcs comprises the following steps:

[0013] Step 1: Obtain the basic equipment parameters of the twenty-high rolling mill and the rolling process parameters of typical specification products;

[0014] Step 2: Divide the roller and the strip into units, a total of t units; the coordinate of the center point of each unit width is y i , i=1,2,…,t, each unit width is Δy i , i=1,2,…,t;

[0015] Step 3: Calculate the strip plastic deformation by the strip element variation method in the three-dimensional plastic deformation model to solve the metal lateral flow and the front and rear tensile stress distribution of the strip;

[0016] Step 4: Calculate the rolling force based on the non-circular arc theory;

[0017] Step 5: The deformation coordination equations between the rollers, the force and moment balance equations, and the no-load roller gap equation are solved to solve the pressure distribution between the rollers;

[0018] Step 6: Determine whether the inequality max|q′-q|<0.01N / mm holds; if not, let q=q+0.1(q′-q) and proceed to step 5; if so, proceed to step 7;

[0019] Step 7: Calculate the transverse distribution h1 of the strip exit thickness;

[0020] Step 8: Determine whether the inequality max|h′1-H1|<0.001mm holds; if not, set h1=h1+0.001(h′1-h1) and proceed to step 3; if yes, proceed to step 9;

[0021] Step 9: Calculate the transverse distribution value σ of the strip pre-tension stress 1i , calculate the strip shape distribution F at the current moment i ;

[0022]

[0023] Compared with the prior art, the present invention has the following advantages:

[0024] The present invention calculates the rolling force based on the non-circular arc theory, which not only avoids the occurrence of program crashes but also ensures the accuracy of the calculation results. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0026] Figure 1 is the overall calculation flowchart of the present invention;

[0027] Figure 2 is the diagram of the distribution angle, numbering, and segmentation of the roll system of the twenty-high rolling mill of the present invention; wherein, (a) shows the numbering and angle of each roll; (b) shows the division of the strip and the roll system unit.

[0028] Figure 3 is the corresponding relationship diagram between the unit node line numbering and the unit numbering of the present invention;

[0029] Figure 4 is the transverse distribution diagram of the strip shape of the present invention. Among them, (a) is Embodiment 1; (b) is Embodiment 2. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0030] In order to enable those skilled in the art to better understand the solutions of the present invention, the following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0031] It should be noted that the terms "first", "second", etc. in the description, claims and the above-mentioned drawings of the present invention are used to distinguish similar objects, and do not necessarily describe a specific order or sequence. It should be understood that the data used in this way can be interchanged under appropriate circumstances, so that the embodiments of the present invention described herein can be implemented in an order other than those illustrated or described herein. In addition, the terms "comprising" and "having" and any variations thereof are intended to cover non-exclusive inclusion. For example, a process, method, system, product or device comprising a series of steps or units does not necessarily have to be limited to those steps or units clearly listed, but may include other steps or units not clearly listed or inherent to these processes, methods, products or devices.

[0032] As Figures 1-4 shown, the present invention provides a method for predicting the asymmetric shape of a twenty-high rolling mill based on the non-circular arc theory, comprising the following steps:

[0033] Step 1: The basic equipment parameters of the twenty-high rolling mill include: the roll body radius of rolls 0 to 5, denoted as R i , where i = 0 to 5, the elastic modulus of rolls 0 to 5, denoted as E i , where i = 0 to 5, the Poisson's ratio of rolls 0 to 5, denoted as v i , where i = 0 to 5, the distance between the two side reduction fulcrums L s , the roll body length L of roll 0 w , the roll body length L of roll 1 m1 , the roll body length L of rolls 2 and 3 m2 , the roll body length L of rolls 4 and 5 b , the angle between the line connecting the center points of the cross-sections of roll 0 and roll 1 and the horizontal direction is α, the angle between the line connecting the center points of the cross-sections of roll 1 and roll 3 and the vertical direction is δ, the angle between the line connecting the center points of the cross-sections of roll 1 and roll 2 and the horizontal direction is β, the angle between the line connecting the center points of the cross-sections of roll 3 and roll 4 and the horizontal direction is θ, the angle between the line connecting the center points of the cross-sections of roll 2 and roll 4 and the vertical direction is the angle between the line connecting the center points of the cross-sections of roll 2 and roll 5 and the horizontal direction is γ, as Figure 2 (a) shown. The roll crowns of roll 0 and roll 1 are ΔD 01i , the roll crowns of roll 1 and roll 2 are ΔD 12i , the roll crowns of roll 1 and roll 3 are ΔD 13i , the roll crowns of roll 2 and roll 4 are ΔD 24i , the roll crowns of roll 2 and roll 5 are ΔD 25i , the roll crowns of roll 3 and roll 4 are ΔD 34i , the superscript of the pressure between each roll of the lower roll system and the upper roll system is x, and by analogy, the others can be obtained and will not be elaborated here.

[0034] The rolling process parameters of the typical specification products include the average incoming thickness of the strip width B, the elastic modulus E of the strip s , the Poisson's ratio v of the strip s , the average post-tension stress of the strip the average pre-tension stress of the strip The allowable error ε1 of the roll pressure, the allowable error ε2 of the strip exit thickness, the relaxation factor χ1 of the roll pressure, and the relaxation factor χ2 of the strip exit thickness.

[0035] Step 2: Select the origin of coordinates at the midpoint of the strip. The whole of the roll and the strip is divided into t elements. The coordinates of the center point of the width of each element are y i (i = 1, 2, …, t), and the width of each element is Δy i (i = 1, 2, …, t). Among them, the starting element number of the contact part between the No. 4 roll and the No. 2 roll is t1, and the ending element number is t2; the starting element number of the contact part between the No. 2 roll and the No. 1 roll is t3, and the ending element number is t4; the starting element number of the contact part between the No. 0 roll and the strip is t5, and the ending element number is t6, as Figure 2 (b) shows. When calculating the plastic deformation of the strip, the transverse displacement at the exit of the strip element nodal line needs to be used as an unknown quantity. Therefore, the strip element nodal lines are re-numbered, as Figure 3 shown. The two nodal line numbers corresponding to element t5 are 0 and 1, the two nodal line numbers corresponding to element t6 are n - 1 and n, (n = t6 - t5 + 1), and the nodal line numbers of other elements can be obtained by analogy.

[0036] Step 3: Calculate the plastic deformation of the strip by the strip element variational method in the three-dimensional plastic deformation model, and solve the metal transverse flow and the distribution of the pre- and post-tension stresses of the strip;

[0037]

[0038] Among them, u0, u1, … u n respectively represent the transverse displacement at the exit of the strip element nodal line, which are unknown quantities; respectively represent those related to the element width, the elastic modulus of the strip, the Poisson's ratio of the strip, the shear deformation resistance of the strip, the neutral point thickness, the elastic flattening radius of the work roll, the friction coefficient, the average friction stress on the contact surface of the deformation zone, the thickness before rolling, the reduction, the length of the deformation zone, and the stress state coefficient;

[0039] Step 4: Based on Fleck's theory, the non-circular arc profile makes the deformation zone be divided into 5 parts: the entrance elastic deformation zone, the entrance plastic reduction zone, the neutral zone, the exit plastic reduction zone, and the exit elastic deformation zone.

[0040] The elastic flattening of the roll and the profile equation:

[0041]

[0042] Among them, h d0 is the thickness of the strip at the entrance side of the deformation zone; R0 is the radius of roll No. 0; x a is the distance from the entrance of the strip in the deformation zone to the z-axis; is the elastic flattening amount of the roll caused by the unit rolling force p d .

[0043] Entrance and exit elastic slip zones: The relationship between the frictional stress τ d and the unit rolling force p d adopts the Coulomb friction law. Then, the differential equation of the unit rolling force in the entrance and exit elastic slip zones is:

[0044]

[0045] Among them, h d represents the strip thickness distribution in the deformation zone; p d represents the unit rolling force distribution in the deformation zone; μ is the friction coefficient; σ represents the normal stress in the rolling direction in the deformation zone.

[0046] Entrance and exit plastic reduction zones: The Mises yield criterion is adopted, and the relationship between the frictional stress τ d and the unit rolling force p d adopts the Coulomb friction law. Then, the differential equation of the unit rolling force in the entrance and exit plastic reduction zones is:

[0047]

[0048] In the neutral zone, the differential equation of the unit rolling force in the entrance and exit plastic reduction zones is:

[0049]

[0050] By solving the differential equation, the distribution of the unit rolling force p d in the entire deformation zone can be obtained.

[0051] Step 5: Solve the system of equations to obtain the roll gap pressure distribution:

[0052] First, list the equations for 0 and 1, 0 x and 1 x , 1 and 2, 1 x and 2 x , 1 and 3, 1 x and 3 x , 2 and 4, 2 x and 4 x , 2 and 5, 2 x and 5 x , 3 and 4, 3x With roll No. 4 x the roll gap deformation coordination equation in the direction of the connecting line of the cross-section center points of the roll is as follows:

[0053]

[0054] where, f Xi represents the deflection of the i-th unit of roll No. X and the roll in contact with it in the direction of the connecting line of the cross-section center points, and f 4i is the deflection of any unit of roll No. 4 in the vertical direction, and ΔD XYi represents the original roll gap or convexity of roll No. X and roll No. Y at the i-th unit, and γ XYi represents the elastic flattening influence coefficient of roll No. X and roll No. Y at the i-th unit.

[0055] 0, 0 x 、1, 1 x The force and moment balance equations of roll No. 0, 0

[0056]

[0057] 2, 2 x 、3, 3 x The force and moment balance equations of roll No. 2, 2

[0058]

[0059] From the perspective of the elastic deformation of the roll system, the strip exit thickness distribution is expressed as:

[0060]

[0061] where, s0 is the no-load roll gap value; ΔD 0i 、ΔD 0i x are the roll profile distribution values of roll No. 0, 0 x respectively; δ 0i 、δ 0i x are the elastic flattening amounts between roll No. 0, 0 x and the rolled piece respectively.

[0062] When analyzing the shape problem of the strip, the no-load roll gap is usually not included in the input parameters, but the average strip exit thickness is directly given At this time, a new linear equation must be established. According to the condition that the average strip exit thickness is equal to this condition, the left and right sides of the following formula are discretely integrated. After integration, the left side of the equation is:

[0063]

[0064] After integrating the right side of the equation and substituting it, we get:

[0065]

[0066] Step 6: Determine whether the inequality max|q′ - q| < 0.01 N / mm holds; if not, let q = q + 0.1(q′ - q), and go to Step 5; if it holds, then go to Step 7.

[0067] Step 7: Solve the transverse distribution h1 of the strip exit thickness;

[0068] Step 8: Determine whether the inequality max|h′1 - h1| < 0.001 mm holds; if not, let h1 = h1 + 0.001(h′1 - h1), and go to Step 3; if it holds, then go to Step 9;

[0069] Step 9: Calculate the transverse distribution value σ of the strip front tension 1i , and calculate the shape distribution F of the strip at the current moment i ;

[0070]

[0071] Example 1

[0072] Taking a twenty-high rolling mill of a certain factory as an example, according to Figure 1 the total calculation flow chart of the non-iterative shape prediction method for the twenty-high rolling mill shown, first, collect the basic equipment parameters of the twenty-high rolling mill in Step 1: the roll body radius R0 of roll 0 = 31.75 mm, the roll body radius R1 of roll 1 = 51 mm, the roll body radius R2 of roll 2 = 86.5 mm, the roll body radius R3 of roll 3 = 86.5 mm, the roll body radius R4 of roll 4 = 150 mm, the roll body radius R5 of roll 5 = 150 mm, the elastic modulus E0 of roll 0 = 540 GPa, the elastic modulus E1 of roll 1 = 210 GPa, the elastic modulus E2 of roll 2 = 210 GPa, the elastic modulus E3 of roll 3 = 210 GPa, the elastic modulus E4 of roll 4 = 210 GPa, the elastic modulus E5 of roll 5 = 210 GPa, the Poisson's ratio υ0 of roll 0 = 0.3, the Poisson's ratio υ1 of roll 1 = 0.3, the Poisson's ratio υ2 of roll 2 = 0.3, the Poisson's ratio v3 of roll 3 = 0.3, the Poisson's ratio v4 of roll 4 = 0.3, the Poisson's ratio υ5 of roll 5 = 0.3, the left and right screwdown fulcrum distance L s = 1800 mm, the roll body length L of roll 0 w = 1444 mm, the roll body length L of roll 1 m1 = 1580 mm, the roll body lengths L of rolls 2 and 3 m2 = 1444 mm, the roll body lengths L of rolls 4 and 5 b= 1312 mm, the angle α between the line connecting the central points of the cross-sections of roll 0 and roll 1 and the horizontal direction is 49.84°, the angle δ between the line connecting the central points of the cross-sections of roll 1 and roll 3 and the vertical direction is 22.84°, the angle β between the line connecting the central points of the cross-sections of roll 1 and roll 2 and the horizontal direction is 29.6°, the angle θ between the line connecting the central points of the cross-sections of roll 3 and roll 4 and the horizontal direction is 48.53°, and the angle between the line connecting the central points of the cross-sections of roll 2 and roll 4 and the vertical direction The angle γ between the line connecting the central points of the cross-sections of roll 2 and roll 5 and the horizontal direction is 13.11°, as Figure 2 (a) shows. The roll crown ΔD of roll 0 and roll 1 01i , the roll crown ΔD of roll 1 and roll 2 12i , the roll crown ΔD of roll 1 and roll 3 13i , the roll crown ΔD of roll 2 and roll 4 24i , the roll crown ΔD of roll 2 and roll 5 25i , the roll crown ΔD of roll 3 and roll 4 34i , the superscript of the pressure between each roll of the lower roll system and the upper roll system is x, and it can be analogously obtained, so it will not be elaborated.

[0073] Meanwhile, in step 1, the rolling process parameters of typical specification products are collected, mainly including the average incoming thickness of the strip width B = 1039 mm, the elastic modulus E of the strip s = 194 GPa, the Poisson's ratio v of the strip s = 0.3, the average post-tension stress of the strip the average pre-tension stress of the strip The allowable error of the inter-roll pressure ε1 = 0.01 N / mm, the allowable error of the strip exit thickness ε2 = 0.001 mm, the relaxation factor χ1 of the inter-roll pressure = 0.1, and the relaxation factor χ2 of the strip exit thickness = 0.001.

[0074] Subsequently, in step 2, element division is carried out. The element division of the strip and the roll system is as Figure 2 (b) shows. The coordinate origin is selected at the midpoint of the strip. The whole of the roll and the strip is divided into elements, with a total of 181 elements. The coordinate of the center point of the width of each element is y i (i = 1, 2,..., 181), and the width of each element is Δy i (i = 1, 2,..., 181). Among them, the starting element number of the contact part between roll 4 and roll 2 is 14, and the ending element number is 168; the starting element number of the contact part between roll 2 and roll 1 is 1, and the ending element number is 181; the starting element number of the contact part between roll 0 and the strip is 26, and the ending element number is 156. When calculating the plastic deformation of the strip, the transverse displacement at the exit of the strip element nodal line needs to be used as an unknown quantity. Therefore, the strip element nodal line is re-numbered, as Figure 3As shown. The two node lines corresponding to unit 26 are numbered 0 and 1, the two node lines corresponding to unit 156 are numbered 130 and 131, and the node line numbers of other units can be deduced by analogy;

[0075] Then, in step 2,

[0076]

[0077] Then, in step 4, based on Fleck theory, the non-circular arc contour divides the deformation zone into five parts: an inlet elastic deformation zone, an inlet plastic depression zone, a neutral zone, an outlet plastic depression zone, and an outlet elastic deformation zone.

[0078] Elastic flattening and profile equation of the roller:

[0079]

[0080] Inlet and outlet elastic sliding zone: friction stress τ d With unit rolling force p d The relationship between and adopts Coulomb friction law, then the differential equation of unit rolling force in the elastic sliding zone between the inlet and outlet is:

[0081]

[0082] Inlet and outlet plastic reduction zones: Mises yield criterion is used, and the friction stress τ d With unit rolling force p d The relationship between and adopts Coulomb's friction law, then the differential equation of unit rolling force in the inlet and outlet plastic reduction zones is:

[0083]

[0084] In the neutral zone, the differential equation of unit rolling force in the inlet and outlet plastic reduction zones is:

[0085]

[0086] Solving the differential equation, we can get the unit rolling force p in the entire deformation zone: d distribution.

[0087] Then, in step 5, the system of equations is solved for the pressure distribution between the rollers:

[0088] First list 0 and 1, 0 x with 1 x , 1 and 2, 1 x with 2 x , 1 and 3, 1 x with 3 x ,2 and 4,2 x With 4 x , 2 and 5, 2x With 5 x , 3 and 4, 3 x and 4 x The roll - gap deformation coordination equation of the rolls numbered 0, 0

[0089]

[0090] in the direction of the connecting line of the cross - section center points is as follows: x , 1, 1 x The force and moment balance equations of the rolls numbered 0, 0

[0091]

[0092] 2, 2 x , 3, 3 x The force and moment balance equations of the rolls numbered 2, 2

[0093]

[0094] From the perspective of the elastic deformation of the roll system, the strip exit thickness distribution is expressed as:

[0095]

[0096] When analyzing the shape problem, the no - load roll gap is usually not included in the input parameters, but the average strip exit thickness is directly given At this time, a new linear equation must be established. According to the condition that the average strip exit thickness is equal to this condition, discrete integration is performed on both sides of the following formula. After integration of the left - hand side of the equation, it is:

[0097]

[0098] After integration of the right - hand side of the equation and substitution, we get:

[0099]

[0100] Subsequently, in step 6, it is judged whether the inequality max|q′ - q| < 0.01 holds. Obviously, the inequality 1324.962 < 0.01 does not hold. Let q = q + 0.1(q′ - q), and then go back to step 5. Loop until the inequality 0.007 < 0.01 holds, then go to step 7.

[0101] Subsequently, in step 7, solve the transverse distribution h1 of the strip exit thickness;

[0102] Subsequently, in step 8, it is judged whether the inequality max|h′1 - h1| < 0.001mm holds. Obviously, the inequality 0.1 < 0.001 does not hold. Let h1 = h1 + 0.001(h′1 - h1), and then go to step 3. Loop until the inequality 0.0009 < 0.001 holds, and then go to step 9;

[0103] Finally, in step 9, calculate the transverse distribution value σ of the front tension of the strip 1i , and calculate the shape distribution F of the strip at the current moment i , as shown in Figure 4 (a).

[0104]

[0105] Example 2

[0106] Taking a twenty-high rolling mill of a certain factory as an example, according to the overall calculation flow chart of the non-iterative shape prediction method for the twenty-high rolling mill shown Figure 1 , first, in step 1, collect the basic equipment parameters of the twenty-high rolling mill: the roll body radius R0 of roll 0 = 31.75mm, the roll body radius R1 of roll 1 = 51mm, the roll body radius R2 of roll 2 = 86.5mm, the roll body radius R3 of roll 3 = 86.5mm, the roll body radius R4 of roll 4 = 150mm, the roll body radius R5 of roll 5 = 150mm, the elastic modulus E0 of roll 0 = 540GPa, the elastic modulus E1 of roll 1 = 210GPa, the elastic modulus E2 of roll 2 = 210GPa, the elastic modulus E3 of roll 3 = 210GPa, the elastic modulus E4 of roll 4 = 210GPa, the elastic modulus E5 of roll 5 = 210GPa, the Poisson's ratio υ0 of roll 0 = 0.3, the Poisson's ratio υ1 of roll 1 = 0.3, the Poisson's ratio v2 of roll 2 = 0.3, the Poisson's ratio v3 of roll 3 = 0.3, the Poisson's ratio υ4 of roll 4 = 0.3, the Poisson's ratio υ5 of roll 5 = 0.3, the distance L between the left and right screw-down fulcrums s = 1800mm, the roll body length L of roll 0 w = 1444mm, the roll body length L of roll 1 m1 = 1580mm, the roll body lengths L of rolls 2 and 3 m2 = 1444mm, the roll body lengths L of rolls 4 and 5 b = 1312mm, the angle α between the connecting line of the center points of the cross-sections of roll 0 and roll 1 and the horizontal direction = 49.84°, the angle δ between the connecting line of the center points of the cross-sections of roll 1 and roll 3 and the vertical direction = 22.84°, the angle β between the connecting line of the center points of the cross-sections of roll 1 and roll 2 and the horizontal direction = 29.6°, the angle θ between the connecting line of the center points of the cross-sections of roll 3 and roll 4 and the horizontal direction = 48.53°, the angle between the connecting line of the center points of the cross-sections of roll 2 and roll 4 and the vertical direction The included angle γ between the connection line of the central points of the cross-sections of Roll 2 and Roll 5 and the horizontal direction is 13.11°, as shown in Figure 2 (a). The roll crown ΔD of Roll 0 and Roll 1 01i , the roll crown ΔD of Roll 1 and Roll 2 12i , the roll crown ΔD of Roll 1 and Roll 3 13i , the roll crown ΔD of Roll 2 and Roll 4 24i , the roll crown ΔD of Roll 2 and Roll 5 25i , the roll crown ΔD of Roll 3 and Roll 4 34i . The superscript of the pressure between each roll of the lower roll system and the upper roll system is x, and it can be analogously obtained, so it will not be elaborated here.

[0107] Meanwhile, in Step 1, the rolling process parameters of typical specification products are collected, mainly including the average incoming thickness of the strip width B = 1035 mm, the elastic modulus E of the strip s = 194 GPa, the Poisson's ratio υ of the strip s = 0.3, the average back tension of the strip the average front tension of the strip The allowable error of the roll pressure ε1 = 0.01 N / mm, the allowable error of the strip exit thickness ε2 = 0.001 mm, the relaxation factor of the roll pressure χ1 = 0.1, and the relaxation factor of the strip exit thickness χ2 = 0.001.

[0108] Subsequently, in Step 2, element division is carried out. The element division of the strip and the roll system is shown in Figure 2 (b). The coordinate origin is selected at the midpoint of the strip. The whole of the roll and the strip is divided into elements, with a total of 181 elements. The coordinate of the center point of the width of each element is y i (i = 1, 2,..., 181), and the width of each element is Δy i (i = 1, 2,..., 181). Among them, the starting element number of the contact part between Roll 4 and Roll 2 is 14, and the ending element number is 168; the starting element number of the contact part between Roll 2 and Roll 1 is 1, and the ending element number is 181; the starting element number of the contact part between Roll 0 and the strip is 26, and the ending element number is 156. When calculating the plastic deformation of the strip, the transverse displacement at the exit of the strip element nodal line needs to be taken as an unknown quantity. Therefore, the nodal lines of the strip elements are re-numbered, as shown in Figure 3 . The two nodal line numbers corresponding to Element 26 are 0 and 1, the two nodal line numbers corresponding to Element 156 are 130 and 131, and the nodal line numbers of other elements can be analogously obtained;

[0109] Subsequently, in Step 2,

[0110]

[0111] Then, in step 4, based on Fleck theory, the non-circular arc contour divides the deformation zone into five parts: an inlet elastic deformation zone, an inlet plastic depression zone, a neutral zone, an outlet plastic depression zone, and an outlet elastic deformation zone.

[0112] Elastic flattening and profile equation of the roller:

[0113]

[0114] Inlet and outlet elastic sliding zone: friction stress τ d With unit rolling force p d The relationship between and adopts Coulomb friction law, then the differential equation of unit rolling force in the elastic sliding zone between the inlet and outlet is:

[0115]

[0116] Inlet and outlet plastic reduction zones: Mises yield criterion is used, and the friction stress τ d With unit rolling force p d The relationship between and adopts Coulomb's friction law, then the differential equation of unit rolling force in the inlet and outlet plastic reduction zones is:

[0117]

[0118] In the neutral zone, the differential equation of unit rolling force in the inlet and outlet plastic reduction zones is:

[0119]

[0120] Solving the differential equation, we can get the unit rolling force p in the entire deformation zone: d distribution.

[0121] Then, in step 5, the system of equations is solved for the pressure distribution between the rollers:

[0122] First list 0 and 1, 0 x with 1 x , 1 and 2, 1 x with 2 x , 1 and 3, 1 x with 3 x ,2 and 4,2 x With 4 x , 2 and 5, 2 x with 5 x ,3 and 4,3 x With 4 x The deformation coordination equation between the rollers in the direction of the line connecting the center points of the cross section is:

[0123]

[0124] 0, 0x 1, 1, 1 x The roll force and moment balance equations for roll No. 1 are as follows:

[0125]

[0126] 2, 2 x 3, 3 x The roll force and moment balance equations for roll No. 3 are as follows:

[0127]

[0128] From the perspective of the elastic deformation of the roll system, the strip exit thickness distribution is expressed as:

[0129]

[0130] When analyzing the strip shape problem, the no-load roll gap is usually not included in the input parameters, but the average strip exit thickness is directly given. At this time, a new linear equation must be established. According to the condition that the average strip exit thickness is equal to For this condition, discrete integration is performed on both sides of the following formula. After integration on the left side of the equation, it is:

[0131]

[0132] After integration on the right side of the equation and substitution, we get:

[0133]

[0134] Subsequently, in step 6, it is judged whether the inequality max|q′ - q| < 0.01 holds. Obviously, the inequality 1065.32 < 0.01 does not hold. Let q = q + 0.1(q′ - q), and then go to step 5. Loop until the inequality 0.008 < 0.01 holds, and then go to step 7.

[0135] Subsequently, in step 7, the transverse distribution h1 of the strip exit thickness is solved;

[0136] Subsequently, in step 8, it is judged whether the inequality max|h′1 - h1| < 0.001 mm holds. Obviously, the inequality 0.08 < 0.001 does not hold. Let h1 = h1 + 0.001(h′1 - h1), and then go to step 3. Loop until the inequality 0.0007 < 0.001 holds, and then go to step 9;

[0137] Finally, in step 9, the transverse distribution value σ of the strip's front tension stress is calculated 1i , and the strip shape distribution F at the current moment is calculated i , as shown in Figure 4 (b).

[0138]

[0139] The serial numbers of the embodiments of the present invention above are only for description and do not represent the superiority or inferiority of the embodiments.

[0140] In the above embodiments of the present invention, the descriptions of the respective embodiments have their own emphases. For parts not detailed in a certain embodiment, reference may be made to the relevant descriptions of other embodiments.

[0141] In the several embodiments provided in the present application, it should be understood that the disclosed technical content can be implemented in other ways. Among them, the device embodiments described above are only illustrative. For example, the division of the units can be a logical function division. In actual implementation, there can be other division methods. For example, multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. Another point is that the displayed or discussed coupling or direct coupling or communication connection between each other can be through some interfaces. The indirect coupling or communication connection of units or modules can be in an electrical or other form.

[0142] The units described as separate components may or may not be physically separated. The components displayed as units may or may not be physical units, that is, they can be located in one place or distributed to multiple units. Some or all of the units can be selected according to actual needs to achieve the purpose of the solution of this embodiment.

[0143] In addition, the functional units in the various embodiments of the present invention can be integrated into one processing unit, or each unit can exist physically alone, or two or more units can be integrated into one unit. The above integrated units can be implemented in the form of hardware or in the form of software functional units.

[0144] If the above integrated unit is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on such an understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions for causing a computer device (which can be a personal computer, a server or a network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. And the foregoing storage medium includes: USB flash drives, read-only memories (ROMs), random access memories (RAMs), mobile hard disks, magnetic disks or optical discs and other various media that can store program codes.

[0145] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements on some or all of the technical features; and these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for predicting asymmetric plate shape of a twenty-high rolling mill based on non-circular arcs, characterized in that: The following steps are involved: Step 1: Obtain the basic equipment parameters of the twenty-high rolling mill and the rolling process parameters of typical specification products; Step 2: Divide the roller and the strip into units, a total of t units; the coordinate of the center point of each unit width is y i , i=1,2,…,t, each unit width is Δy i , i=1,2,…,t; Step 3: Calculate the strip plastic deformation by using the strip element variation method in the three-dimensional plastic deformation model to solve the metal lateral flow and the front and rear tensile stress distribution of the strip; Step 4: Calculate the rolling force based on the non-circular arc theory; Step 5: The deformation coordination equations between the rollers, the force and moment balance equations, and the no-load roller gap equation are solved to solve the pressure distribution between the rollers; Step 6: Determine whether the inequality max|q′-q|<0.01N / mm holds; if not, let q=q+0.1(q′-q) and proceed to step 5; if so, proceed to step 7; Step 7: Calculate the transverse distribution h1 of the strip exit thickness; Step 8: Determine whether the inequality max|h′1-h1|<0.001mm holds; if not, set h1=h1+0.001(h′1-h1) and proceed to step 3; if yes, proceed to step 9; Step 9: Calculate the transverse distribution value σ of the strip pre-tension stress 1i , calculate the strip shape distribution F at the current moment i ; 2. The method for predicting asymmetric flatness of a twenty-high mill based on non-circular arc theory according to claim 1, characterized in that: In step 1, the basic equipment parameters of the twenty-high rolling mill include: the radius of the roller body of rollers 0 to 5, denoted by R i , i = 0 ~ 5, 0 ~ 5 roller elastic modulus, denoted as E i , i = 0 ~ 5, 0 ~ 5 roller Poisson's ratio, denoted as v i , i = 0 ~ 5, the distance between the two sides of the support point is L s , No. 0 roller body length L w , No. 1 roller body length L m1 , Length of rollers No. 2 and No. 3 L m2 , 4th and 5th roller body length L b , the angle between the line connecting the center points of the cross sections of rollers 0 and 1 and the horizontal direction is α, the angle between the line connecting the center points of the cross sections of rollers 1 and 3 and the vertical direction is δ, the angle between the line connecting the center points of the cross sections of rollers 1 and 2 and the horizontal direction is β, the angle between the line connecting the center points of the cross sections of rollers 3 and 4 and the horizontal direction is θ, and the angle between the line connecting the center points of the cross sections of rollers 2 and 4 and the vertical direction is The angle between the line connecting the center points of the cross sections of roller No. 2 and roller No. 5 and the horizontal direction is γ.

3. The method for predicting asymmetric flatness of a twenty-high rolling mill based on non-circular arc theory according to claim 1, characterized in that: In step 1, the rolling process parameters of the typical specification products include: the average thickness of the incoming strip Width B, strip elastic modulus E s , Strip Poisson's ratio υ s , average post-tensioning stress of the strip Average pre-tension stress of strip The allowable error of the pressure between rollers ε1, the allowable error of the strip exit thickness ε2, the relaxation factor of the pressure between rollers χ1 and the relaxation factor of the strip exit thickness χ2.

4. The method for predicting asymmetric flatness of a twenty-high rolling mill based on non-circular arc theory according to claim 1, characterized in that: In step 2, the origin of the coordinates is selected at the midpoint of the strip; the roller and the strip are divided into units, a total of t units; the coordinate of the center point of the width of each unit is y i (i=1,2,…,t), each unit width is Δy i (i=1,2,…,t); Among them, the starting unit number of the contact part between roller 4 and roller 2 is t1, and the ending unit number is t2; the starting unit number of the contact part between roller 2 and roller 1 is t3, and the ending unit number is t4; the starting unit number of the contact part between roller 0 and the strip is t5, and the ending unit number is t6; When calculating the plastic deformation of the strip, the outlet lateral displacement of the strip unit node line is taken as an unknown quantity. Therefore, the strip unit node lines are renumbered, and the two node lines corresponding to unit t5 are numbered 0 and 1, and the two node lines corresponding to unit t6 are numbered n-1 and n, (n=t6-t5+1). The node line numbers of other units can be obtained by analogy.

5. The method for predicting asymmetric flatness of a twenty-high rolling mill based on non-circular arc theory according to claim 1, characterized in that: In step 3, the strip plastic deformation is calculated by the strip element variation method in the three-dimensional plastic deformation model, and the expression for solving the metal lateral flow and the front and rear tensile stress distribution of the strip is: Among them, u0, u1, ...u n They represent the lateral displacement of the strip unit node line outlet, which is an unknown quantity; They are respectively related to unit width, strip elastic modulus, strip Poisson's ratio, strip shear deformation resistance, neutral point thickness, work roll elastic flattening radius, friction coefficient, average friction stress of contact surface in deformation zone, pre-rolling thickness, reduction, deformation zone length, and stress state coefficient; 6. The method for predicting asymmetric flatness of a twenty-high rolling mill based on non-circular arc theory according to claim 1, characterized in that: In step 4, based on Fleck theory, the non-circular arc profile makes the deformation zone divided into five parts: an inlet elastic deformation zone, an inlet plastic depression zone, a neutral zone, an outlet plastic depression zone, and an outlet elastic deformation zone; Elastic flattening and profile equation of the roller: Among them, h d0 Indicates the thickness of the strip at the entrance of the deformation zone; R0 indicates the radius of roller No. 0; x a Indicates the distance from the strip entrance to the z-axis in the deformation zone; Indicates the unit rolling force p d The amount of elastic flattening of the roll caused; Inlet and outlet elastic sliding zone: friction stress τ d With unit rolling force p d The relationship between and adopts Coulomb friction law, then the differential equation of unit rolling force in the elastic sliding zone between the inlet and outlet is: Among them, h d Indicates the strip thickness distribution in the deformation zone; p d represents the unit rolling force distribution in the deformation zone; μ represents the friction coefficient; σ represents the normal stress in the rolling direction in the deformation zone; Inlet and outlet plastic reduction zones: Mises yield criterion is used, and the friction stress τ d With unit rolling force p d The relationship between and adopts Coulomb's friction law, then the differential equation of unit rolling force in the inlet and outlet plastic reduction zones is: In the neutral zone, the differential equation of unit rolling force in the inlet and outlet plastic reduction zones is: Solving the differential equation, we can get the unit rolling force p in the entire deformation zone: d distribution.

7. The method for predicting asymmetric flatness of a twenty-high rolling mill based on non-circular arc theory according to claim 1, characterized in that: In step 5, the pressure distribution between the rollers is solved by solving the simultaneous equations: First list 0 and 1, 0 x with 1 x , 1 and 2, 1 x with 2 x , 1 and 3, 1 x with 3 x ,2 and 4,2 x With 4 x , 2 and 5, 2 x with 5 x ,3 and 4,3 x With 4 x The deformation coordination equation between the rollers in the direction of the line connecting the center points of the cross section is: Among them, f Xi represents the deflection of the i-unit in the direction of the line connecting the center points of the cross section between the X-roll and the contacting rolls, f 4i is the arbitrary unit deflection of roller 4 in the vertical direction, ΔD XYi It represents the original gap or crown of roller X and roller Y on unit i, γ XYi It represents the elastic flattening influence coefficient of roller X and roller Y on unit i; Then 0, 0 x , 1, 1 x The force and moment balance equation of roller No. is: 2.2 x ,3,3 x The force and moment balance equation of roller No. is: From the perspective of roll elastic deformation, the strip outlet thickness distribution is expressed as: Where s0 represents the no-load roll gap value; ΔD 0i , ΔD 0i x Respectively represent roller No. 0, x Roller type distribution value of roller number; δ 0i , δ 0i x Respectively represent roller No. 0, x The elastic flattening amount between the No. roller and the rolled piece; When analyzing the strip shape problem, the input parameters usually do not include the no-load roll gap, but directly give the average thickness of the strip outlet. At this time, a new linear equation must be established; according to the average thickness of the strip outlet is equal to Under this condition, the left and right sides of the following equation are discretely integrated, and the left side of the equation is integrated as follows: After integrating the right side of the equation, we get:

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