A method for calculating the loaded roll gap of a four-high rolling mill for rolling a round disc-shaped sheet

Abstract

The present application relates to a kind of four-roller rolling mill rolling pie-shaped plate load roll gap calculation method, based on considering the characteristics of pie-shaped plate, with roll parameter, pie-shaped plate parameter, rolling piece entrance width, initial roll gap and so on adjusting parameter as input variable, establish single pass rolling full process five stages: just bite in stage, bite in quarter stage, center stage, throw out three quarter stage, throw out stage.Using segmentation model influence function method, roll system stress balance module, rolling pressure calculation module, roll system elastic deformation module are operated in turn.3D model of pie-shaped plate rolling full process load roll gap is established, the load roll gap transverse distribution of rolling piece under different entrance width is collected, the dynamic elastic deformation process of roll system is analyzed, and the shape of rolled pie-shaped plate is drawn, so that the thickness distribution of pie-shaped plate in transverse direction in rolling full process is obtained.

Description

Technical Field

[0001] This invention relates to the field of plate shape control technology in medium and heavy plate rolling, and in particular to a method for calculating the loaded roll gap in a four-roll mill for rolling disc-shaped plates. Background Technology

[0002] With advancements and developments in rolling technology, rolling is no longer limited to the steel industry; the shapes of rolled products are becoming increasingly diverse, and their applications are becoming more widespread. Besides conventional plates, strips, bars, wires, and cylinder sections, round disc rolls are used in the semiconductor materials industry for producing high-purity metal sputtering targets.

[0003] When rolling disc-shaped plates, the constantly changing entry width of the workpiece leads to an initial increase followed by a decrease in the area of ​​the rolling deformation zone. The transient changes in rolling force cause continuous variations in the elastic deformation of the roll system—namely, the deflection and flattening of the rolls. The plastic deformation of the workpiece and the elastic deformation of the rolls differ at different locations, resulting in a disc-shaped workpiece with an elliptical circumference that is thinner at the edges and thicker in the center. Without considering the elastic deformation recovery of the workpiece, the lateral distribution of the exit thickness is directly determined by the exit thickness of the loaded roll gap. Therefore, accurately calculating the lateral distribution of the exit thickness of the roll gap during the rolling process is crucial and an indispensable part of the elastic deformation model of the roll system in shape control technology.

[0004] Currently, methods for studying the elastic deformation of roll systems can be divided into three categories: analytical methods, influence function methods, and finite element numerical calculation methods. Analytical methods involve complex calculation models and operations, often requiring significant simplification, and are rarely used in practical engineering. The finite element method involves excessive computation; obtaining accurate results requires extensive meshing, leading to low computational efficiency and limiting its suitability to offline analysis rather than real-time online feedback. The influence function method is highly effective in handling the elastic deformation of rolls in practical engineering problems. Its basic idea is to discretize the roll into several elements, and simultaneously discretize the load and elastic deformation of the roll into the same elements. Applying the concept of influence functions from mathematical physics, it first determines the deformation at each point on the roll body when a unit force is applied to each element. Then, it superimposes the deformations caused by all loads on each element to obtain the deformation value of each element, thus determining the thickness and tension distribution at the exit. Clearly, due to the discretization method, the distribution of rolling force, inter-roll pressure, and roll crown does not require distribution function assumptions, allowing for flexible handling of various complex practical problems with high computational accuracy. However, the traditional influence function method does not take into account the change in the width of the workpiece entrance during the rolling process, and cannot be directly applied to round cake rolling, thus having certain limitations. Summary of the Invention

[0005] The purpose of this invention is to provide a method for calculating the loaded roll gap of a four-roll mill rolling a disc-shaped plate, which is used to calculate the transverse thickness distribution of the disc-shaped plate throughout a single rolling process.

[0006] The technical solution adopted in this invention is as follows:

[0007] The present invention proposes a method for calculating the loaded roll gap in a four-roll mill for rolling disc-shaped plates, comprising the following steps:

[0008] S1: Collect and input the parameters of the four-high mill rolls, the parameters of the disc-shaped plate, the rolling adjustment parameters, and the initial roll gap;

[0009] S2: The discretization and calculation stage for parameters of the four-roll mill and the disc-shaped plate;

[0010] S3: The initial biting stage of the disc-shaped sheet material: including the roll system force balance module, the rolling pressure calculation module, and the roll system elastic deformation module;

[0011] S4: Quarter-end biting stage of disc-shaped sheet material: includes roll system force balance module, rolling pressure calculation module, and roll system elastic deformation module; module content is consistent with S3;

[0012] S5: Central stage of disc-shaped plate: includes roll system force balance module, rolling pressure calculation module and roll system elastic deformation module; the module content is the same as S3;

[0013] S6: Three-quarters of the disc-shaped sheet material is thrown out: including the roll system force balance module, the rolling pressure calculation module, and the roll system elastic deformation module; the module content is the same as S3;

[0014] S7: Round disc-shaped plate ejection stage: includes roller system force balance module, rolling pressure calculation module and roller system elastic deformation module; the module content is the same as S3;

[0015] S8: Establish a three-dimensional model of the loaded roll gap for the entire rolling process of disc-shaped plates, collect the transverse distribution of the loaded roll gap under different entry widths of the rolled piece, analyze the dynamic elastic deformation process of the roll system, draw the shape of the disc-shaped plate after rolling, and obtain the transverse thickness distribution of the disc-shaped plate shape throughout the rolling process.

[0016] Furthermore, in step S1, the roll parameters of the four-high mill include: support roll radius R1, work roll radius R2, and support roll elastic modulus E. B The elastic modulus E of the work roll W Poisson's ratio v of the support roller B Poisson's ratio v of the working roll W The parameters for the disc-shaped sheet include: post-rolling tensile stress σ0, pre-rolling tensile stress σ1, B is the sheet width, entry thickness h0, and deformation resistance K; rolling adjustment parameters include: support roll bending force F.b Work roll bending force F w The initial design thickness of the export plate is h1.

[0017] Furthermore, step S2 specifically includes:

[0018] 2a1) Collect and input the parameters of the four-high mill rolls and the round plate. Using the element segmentation model method, discretize the four-high mill rolls and the rolled piece. Divide the roll body into m elements along the roll body direction, where m is an odd number. The x-coordinate of the midpoint of the element is Δy. i The distance of each unit from the midpoint of the roller body is y. i (i = 1, 2, ..., m), the workpiece and the roll are corresponding discrete units and divided into n parts. The first unit of the workpiece is the d-th unit of the roll, d = (mn) / 2. Except for the two edge units, the coordinates and widths of the remaining units are the same as those of the roll body.

[0019] 2a2) Following the method described in 2a1), the characteristic parameters of the work roll, support roll, and workpiece are discretized into multiple equally divided units, and the rolling force of the work roll is discretized as follows: The contact pressure between the support roll and the work roll is discrete as follows: The thickness of the rolled product at the exit plate is discrete. And accordingly, the lateral distribution of the flattening between the rolls, the lateral distribution of each deflection, the roll system deformation parameters, and the force parameters are discretized along the roll axis;

[0020] Furthermore, in step S3:

[0021] The roller system force balancing module includes:

[0022] 3a1) Establish the tension distribution model before the work roll and the tension distribution model after the work roll:

[0023]

[0024]

[0025] Calculate the deflection angle of the work roll rolling force:

[0026]

[0027] 3a2) Substitute the parameters and model obtained in 3a1) into the output equations for the force and torque balance between the support roller and the working roller;

[0028] Establish the force balance equation for the support roller in the vertical direction:

[0029]

[0030] Establish the torque balance equation in the vertical direction of the support roller:

[0031]

[0032] Establish the force balance equation for the work roll in the vertical direction:

[0033]

[0034] Establish the torque balance equation in the vertical direction of the work roll:

[0035]

[0036] Where σ1 is the pre-tension stress of the rolled plate, σ0 is the tension before the rolling unit, and σ0 is the tensile stress after the rolling unit. θ is the tension after the rolling unit, B is the width of the rolling plate, and θ is the tension after the rolling unit. i It is the rolling force offset angle, F zl It is the vertical pressing reaction force at the left end of the support roller, F. zr It is the vertical pressing reaction force at the right end of the support roller, F. b It is the bending force of the support roller, F w It is the bending force of the work roll, L Z L is the distance between the left and right support reaction forces of the support rollers. b It is the length of the roller body, L w It is the distance between the left and right bending forces of the work roll body, L bf L is the distance between the left and right bending forces of the support roller. wf C is the distance between the left and right bending forces of the work roll and C is the distance between the point of action of the support roll reaction force and the edge of the roll.

[0037] The rolling pressure calculation module includes:

[0038] 3b1) Collect and input the parameters of the rolled sheet, and calculate the reduction amount and reduction rate of the work roll;

[0039]

[0040]

[0041] Calculate the neutral angle of the work roll during rolling:

[0042]

[0043] Calculate the rolling force per unit length in the deformation zone of the work roll:

[0044]

[0045] Calculate the length of the deformation zone during work roll rolling:

[0046]

[0047] Substitute the parameters obtained above and output the transverse rolling force of the work roll:

[0048] Calculate the transverse rolling force of the work roll:

[0049]

[0050] Where h0 is the inlet plate thickness, h1 is the initial outlet plate thickness, R2 is the roll radius, K is the deformation resistance, and Δh i It is the amount of roller reduction, ε i It is the reduction rate of the roller system. It is the neutral angle of the work roll rolling process. L is the rolling force per unit length in the deformation zone of the work roll. i It is the length of the deformation zone during work roll rolling, p i It is the rolling force per unit length of the work roll;

[0051] The roller system elastic deformation module includes:

[0052] 3c1) Collect and input the influence functions of roll elastic deflection and flattening, the initial pressure between the support roll and the work roll, and the transverse rolling force of the work roll obtained from the rolling pressure calculation module;

[0053] 3c2) Establish the three-dimensional deflection displacement calculation equations for the support roller axis, the work roller axis, and the flattening displacement equation between the support roller and the work roller:

[0054] Establish the equation for calculating the vertical deflection displacement of the support roller axis:

[0055]

[0056] Establish the equation for calculating the deflection displacement in the vertical direction of the work roll axis:

[0057]

[0058] Establish the equation for the flattening displacement between the support roll and the work roll:

[0059]

[0060]

[0061]

[0062] Among them, E B It is the elastic modulus of the support roller, E W It is the elastic modulus of the work roll, v B It is the Poisson's ratio of the support roller, v W It is the Poisson's ratio of the working roll. It is half the width of the roll flattening system. It is the deflection displacement in the vertical direction of the support roller axis. It is the deflection displacement in the vertical direction of the working roller axis. It is the elastic flattening displacement of the roller system;

[0063] 3c3) By combining the equations obtained in 3c2), we can establish the calculation equations for the deformation coordination between the support roll and the work roll:

[0064] Establish the calculation equations for the deformation coordination between the support roll and the work roll:

[0065]

[0066] 3c4) Calculate the pressure between the support roller and the work roller using the deformation coordination calculation equation between the support roller and the work roller.

[0067] 3c5) Using the Jacobi iteration method, determine whether the difference between the pressure between the support roller and the working roller and the initial pressure between the support roller and the working roller input in 3c1) is less than the iteration accuracy of 0.000001. If yes, directly execute 3c6); otherwise, continue to execute 3c4) until the difference between the pressure between the support roller and the working roller obtained in 3c4) and the pressure between the support roller and the working roller obtained in the previous iteration in 3c4) meets the iteration accuracy and execute 3c6).

[0068] 3c6) Output the pressure between the support roller and the work roller calculated in the last step 3c4) and substitute it into the three-dimensional flexural displacement of the work roller in step 3c2).

[0069] Furthermore, in step 3c1), the influence function of roll elastic deflection and flattening is: the influence coefficient of support roll bending. Work roll bending influence coefficient The influence coefficient of the support roller on the bending roller force The influence coefficient of bending force on the work roll Roller flattening influence coefficient λ i η, the influence coefficient of contact flattening between the work roll and the workpiece ij , where i = 1, ..., m and j = 1, ..., m.

[0070] Furthermore, step S8 specifically includes:

[0071] 8a1) Establish the calculation equations for the rigid displacement of the rolls and the elastic flattening displacement between the work rolls and the workpiece, and combine them with the three-dimensional flexural displacement of the work rolls obtained in 3c5) to form a three-dimensional model of the loaded roll gap of a four-roll mill.

[0072] 8b1) The rigid displacement of the roll is related to the axial displacement of the support roll at the roll end. Substitute the pressure between the support roll and the work roll output in 3c6) into the force and moment balance equation of the support roll output in 3a3), calculate the support reaction force of the support roll, and establish the calculation equation for the rigid displacement of the support roll:

[0073] 8b2) Establish the equation for calculating the rigid displacement in the vertical direction of the support roller axis:

[0074]

[0075] 8b3) The contact flattening displacement between the work roll and the workpiece is calculated by the roll y j The pressure on a small area at a point affects y i The flattening amount caused by the contact point is used to establish calculation equations for the contact flattening displacement between the upper work roll and the workpiece, and for the contact flattening displacement between the lower work roll and the workpiece.

[0076] 8b4) Establish the equation for calculating the contact flattening displacement between the work roll and the workpiece:

[0077]

[0078] K g S is the stiffness of the load-bearing components of the single-chip microcomputer base other than the roller system. r It is the amount of the right-end tilting roller, S l It is the amount of the right-end tilting roller. It is the rigid displacement of the support roller axis in the vertical direction. It is the contact flattening displacement between the work roll and the workpiece;

[0079] Substituting the equations obtained from 8b1) and 8b3) into 8b2) and 8b4), a calculation model for the exit plate thickness is established to represent the loaded roll gap model:

[0080]

[0081] It's the thickness of the exported plate;

[0082] 8a2) Output the lateral distribution of the load roll gap under the current entry width of the workpiece, and increase the current entry width of the workpiece by B. i Determine the entry width B of the workpiece. i Is it smaller than the workpiece diameter B? If not, execute 8a3). If yes, then adjust the workpiece inlet width B. i Substitute back into S3-S7 and repeat the cycle until the workpiece entry width B is reached. i If the diameter of the rolled piece is equal to B, then 8a3) is executed.

[0083] 8a3) Collect rolled pieces at different inlet widths B i The transverse distribution of the roll gap under load is analyzed, the dynamic elastic deformation process of the roll system is analyzed, the shape of the disc-shaped plate after rolling is drawn, and the transverse thickness distribution of the disc-shaped plate in the whole rolling process is obtained.

[0084] Compared with the prior art, the present invention has the following advantages:

[0085] 1. Compared with the traditional method for calculating the loaded roll gap of rolling mills, this invention establishes a calculation model for the loaded roll gap of four-high rolling mills for rolling disc-shaped plates;

[0086] 2. Compared with the traditional method for calculating the loaded roll gap, this invention considers the dynamic changes of the loaded roll gap under the change of the rolling inlet width, and establishes a loaded roll gap model for single-pass full-process rolling of disc-shaped plates, providing a theoretical basis for variable width rolling.

[0087] 3. The loaded roll gap calculation method proposed in this invention can continuously adjust the module parameters and perform repeated iterative calculations based on the change in the thickness of the exit plate. The iteration accuracy is satisfied by comparing the difference between two adjacent iterations. The method is simple and easy to operate. Attached Figure Description

[0088] Figure 1 This is a front view of the roll system of a four-high rolling mill under stress.

[0089] Figure 2 A schematic diagram of the five-stage roller system flexural deformation of a disc-shaped sheet material;

[0090] Figure 3 This is a schematic diagram of the force balance module calculation for the roller system;

[0091] Figure 4 This is a schematic diagram of the rolling pressure calculation module;

[0092] Figure 5 This is a schematic diagram of the calculation for the roller deformation module;

[0093] Figure 6 A schematic diagram for calculating the loaded roll gap of a four-high rolling mill;

[0094] Figure 7 This is a schematic diagram of the thickness distribution of a disc-shaped sheet material.

[0095] Figure 8 This is a schematic diagram showing the distribution of plate thickness and misalignment along the roller body unit calculated according to an embodiment of the present invention. Detailed Implementation

[0096] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0097] The present invention proposes a method for calculating the loaded roll gap in a four-roll mill for rolling disc-shaped plates, such as... Figures 1 to 7 As shown, taking the rolling of a disc-shaped plate using a four-roll mill as an example, the specific implementation process is as follows:

[0098] S1: Collect and input the parameters of the four-high mill rolls, the parameters of the disc-shaped plate, the rolling adjustment parameters, and the initial roll gap;

[0099] In this embodiment, the roll parameters of the four-high mill include: support roll radius R1, work roll radius R2, and support roll elastic modulus E. B The elastic modulus E of the work roll W Poisson's ratio v of the support roller B Poisson's ratio v of the working roll W The parameters for the disc-shaped sheet include: post-rolling tensile stress σ0, pre-rolling tensile stress σ1, B is the sheet width, entry thickness h0, and deformation resistance K; rolling adjustment parameters include: support roll bending force F. b Work roll bending force F w Initially set the export plate thickness as h1;

[0100] Table 1 Input Parameters

[0101]

[0102]

[0103] S2: The discretization and calculation stage for parameters of the four-roll mill and the disc-shaped plate; specifically including:

[0104] 2a1) Collect and input the parameters of the four-high mill rolls and the round plate. Using the element segmentation model method, discretize the four-high mill rolls and the rolled piece. Divide the roll body into m elements along the roll body direction, where m is an odd number. The x-coordinate of the midpoint of the element is Δy. i The distance of each unit from the midpoint of the roller body is y. i (i = 1, 2, ..., m), the workpiece and the roll are corresponding discrete units and divided into n parts. The first unit of the workpiece is the d-th unit of the roll, d = (mn) / 2. Except for the two edge units, the coordinates and widths of the remaining units are the same as those of the roll body.

[0105] 2a2) Following the method described in 2a1), the characteristic parameters of the work roll, support roll, and workpiece are discretized into multiple equally divided units, and the rolling force of the work roll is discretized as follows: The contact pressure between the support roll and the work roll is discrete as follows: The thickness of the rolled product at the exit plate is discrete. And accordingly, the lateral distribution of the flattening between the rolls, the lateral distribution of each deflection, the roll system deformation parameters, and the force parameters are discretized along the roll axis;

[0106] S3: The initial biting stage of the disc-shaped sheet material: including the roll system force balance module, the rolling pressure calculation module, and the roll system elastic deformation module; among which...

[0107] The roller system force balancing module includes:

[0108] 3a1) Establish the tension distribution model before the work roll and the tension distribution model after the work roll:

[0109]

[0110]

[0111] Calculate the deflection angle of the work roll rolling force:

[0112]

[0113] 3a2) Substitute the parameters and model obtained in 3a1) into the output equations for the force and torque balance between the support roller and the working roller;

[0114] Establish the force balance equation for the support roller in the vertical direction:

[0115]

[0116] Establish the torque balance equation in the vertical direction of the support roller:

[0117]

[0118] Establish the force balance equation for the work roll in the vertical direction:

[0119]

[0120] Establish the torque balance equation in the vertical direction of the work roll:

[0121]

[0122] Where σ1 is the pre-tension stress of the rolled plate, σ0 is the tension before the rolling unit, and σ0 is the tensile stress after the rolling unit. θ is the tension after the rolling unit, B is the width of the rolling plate, and θ is the tension after the rolling unit. i It is the rolling force offset angle, F zl It is the vertical pressing reaction force at the left end of the support roller, F. zr It is the vertical pressing reaction force at the right end of the support roller, F. b It is the bending force of the support roller, F w It is the bending force of the work roll, L Z L is the distance between the left and right support reaction forces of the support rollers. b It is the length of the roller body, L w It is the distance between the left and right bending forces of the work roll body, L bf L is the distance between the left and right bending forces of the support roller. wf C is the distance between the left and right bending forces of the work roll and C is the distance between the point of application of the support roll reaction force and the edge of the roll.

[0123] The rolling pressure calculation module includes:

[0124] 3b1) Collect and input the parameters of the rolled sheet, and calculate the reduction amount and reduction rate of the work roll;

[0125]

[0126]

[0127] Calculate the neutral angle of the work roll during rolling:

[0128]

[0129] Calculate the rolling force per unit length in the deformation zone of the work roll:

[0130]

[0131] Calculate the length of the deformation zone during work roll rolling:

[0132]

[0133] Substitute the parameters obtained above and output the transverse rolling force of the work roll:

[0134] Calculate the transverse rolling force of the work roll:

[0135]

[0136] Where h0 is the inlet plate thickness, h1 is the initial outlet plate thickness, R2 is the roll radius, K is the deformation resistance, and Δh i It is the amount of roller reduction, ε i It is the reduction rate of the roller system. It is the neutral angle of the work roll rolling process. L is the rolling force per unit length in the deformation zone of the work roll. i It is the length of the deformation zone during work roll rolling, p i It is the rolling force per unit length of the work roll;

[0137] The roller system elastic deformation module includes:

[0138] 3c1) Collect and input the influence functions of roll elastic deflection and flattening, the initial pressure between the support roll and the work roll, and the transverse rolling force of the work roll obtained from the rolling pressure calculation module;

[0139] 3c2) Establish the three-dimensional deflection displacement calculation equations for the support roller axis, the work roller axis, and the flattening displacement equation between the support roller and the work roller:

[0140] Establish the equation for calculating the vertical deflection displacement of the support roller axis:

[0141]

[0142] Establish the equation for calculating the deflection displacement in the vertical direction of the work roll axis:

[0143]

[0144] Establish the equation for the flattening displacement between the support roll and the work roll:

[0145]

[0146]

[0147]

[0148]

[0149] Among them, E B It is the elastic modulus of the support roller, E W It is the elastic modulus of the work roll, v B It is the Poisson's ratio of the support roller, v W It is the Poisson's ratio of the working roll. It is half the width of the roll flattening system. It is the deflection displacement in the vertical direction of the support roller axis. It is the deflection displacement in the vertical direction of the working roller axis. It is the elastic flattening displacement of the roller system;

[0150] 3c3) By combining the equations obtained in 3c2), we can establish the calculation equations for the deformation coordination between the support roll and the work roll:

[0151] Establish the calculation equations for the deformation coordination between the support roll and the work roll:

[0152]

[0153] 3c4) Calculate the pressure between the support roller and the work roller using the deformation coordination calculation equation between the support roller and the work roller.

[0154] 3c5) Using the Jacobi iteration method, determine whether the difference between the pressure between the support roller and the working roller and the initial pressure between the support roller and the working roller input in 3c1) is less than the iteration accuracy of 0.000001. If yes, directly execute 3c6); otherwise, continue to execute 3c4) until the difference between the pressure between the support roller and the working roller obtained in 3c4) and the pressure between the support roller and the working roller obtained in the previous iteration in 3c4) meets the iteration accuracy and execute 3c6).

[0155] 3c6) Output the pressure between the support roller and the work roller calculated in the last step 3c4) and substitute it into the three-dimensional flexural displacement of the work roller in step 3c2).

[0156] Furthermore, in step 3c1), the influence function of roll elastic deflection and flattening is: the influence coefficient of support roll bending. Work roll bending influence coefficient The influence coefficient of the support roller on the bending roller force The influence coefficient of bending force on the work roll Roller flattening influence coefficient λ i η, the influence coefficient of contact flattening between the work roll and the workpiece ij , where i = 1, ..., m and j = 1, ..., m.

[0157] S4: Quarter-end biting stage of disc-shaped sheet material: includes roll system force balance module, rolling pressure calculation module, and roll system elastic deformation module; the module content is the same as S3;

[0158] S5: Central stage of disc-shaped plate: includes roll system force balance module, rolling pressure calculation module and roll system elastic deformation module; module content is the same as S3;

[0159] S6: Three-quarters of the disc-shaped sheet material is thrown out: including the roll system force balance module, the rolling pressure calculation module, and the roll system elastic deformation module; the module content is the same as S3;

[0160] S7: Round disc plate ejection stage: includes roller system force balance module, rolling pressure calculation module and roller system elastic deformation module; the module content is the same as S3;

[0161] S8: Establish a three-dimensional model of the loaded roll gap for the entire rolling process of disc-shaped plates, collect the transverse distribution of the loaded roll gap under different entry widths, analyze the dynamic elastic deformation process of the roll system, draw the shape of the disc-shaped plate after rolling, and obtain the transverse thickness distribution of the disc-shaped plate throughout the entire rolling process, specifically including:

[0162] 8a1) Establish the calculation equations for the rigid displacement of the rolls and the elastic flattening displacement between the work rolls and the workpiece, and combine them with the three-dimensional flexural displacement of the work rolls obtained in 3c5) to form a three-dimensional model of the loaded roll gap of a four-roll mill.

[0163] 8b1) The rigid displacement of the roll is related to the axial displacement of the support roll at the roll end. Substitute the pressure between the support roll and the work roll output in 3c6) into the force and moment balance equation of the support roll output in 3a3), calculate the support reaction force of the support roll, and establish the calculation equation for the rigid displacement of the support roll:

[0164] 8b2) Establish the equation for calculating the rigid displacement in the vertical direction of the support roller axis:

[0165]

[0166] 8b3) The contact flattening displacement between the work roll and the workpiece is calculated by the roll y jThe pressure on a small area at a point affects y i The flattening amount caused by the contact point is used to establish calculation equations for the contact flattening displacement between the upper work roll and the workpiece, and for the contact flattening displacement between the lower work roll and the workpiece.

[0167] 8b4) Establish the equation for calculating the contact flattening displacement between the work roll and the workpiece:

[0168]

[0169] K g S is the stiffness of the load-bearing components of the single-chip microcomputer base other than the roller system. r It is the amount of the right-end tilting roller, S l It is the amount of the right-end tilting roller. It is the rigid displacement of the support roller axis in the vertical direction. It is the contact flattening displacement between the work roll and the workpiece;

[0170] Substituting the equations obtained from 8b1) and 8b3) into 8b2) and 8b4), a calculation model for the exit plate thickness is established to represent the loaded roll gap model:

[0171]

[0172] It's the thickness of the exported plate;

[0173] 8a2) Output the lateral distribution of the load roll gap under the current entry width of the workpiece, and increase the current entry width of the workpiece by B. i Determine the entry width B of the workpiece. i Is it smaller than the workpiece diameter B? If not, execute 8a3). If yes, then adjust the workpiece inlet width B. i Substitute back into S3-S7 and repeat the cycle until the workpiece entry width B is reached. i If the diameter of the rolled piece is equal to B, then 8a3) is executed.

[0174] 8a3) Collect rolled pieces at different inlet widths B i The transverse distribution of the roll gap under load is analyzed, the dynamic elastic deformation process of the roll system is analyzed, the shape of the disc-shaped plate after rolling is drawn, and the transverse thickness distribution of the disc-shaped plate in the whole rolling process is obtained.

[0175] like Figure 8 The figure shown is a schematic diagram of the three-dimensional thickness distribution calculated in this embodiment.

[0176] All matters not covered in this invention are common knowledge.

[0177] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made by those skilled in the art to the technical solutions of the present invention without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A method for calculating the loaded roll gap in a four-roll mill for rolling disc-shaped plates, characterized in that: Includes the following steps: S1: Collect and input the parameters of the four-high mill rolls, the parameters of the disc-shaped plate, the rolling adjustment parameters, and the initial roll gap; S2: The discretization and calculation stage for parameters of the four-roll mill and the disc-shaped plate; S3: The initial biting stage of the disc-shaped sheet material: including the roll system force balance module, the rolling pressure calculation module, and the roll system elastic deformation module; S4: Quarter-end biting stage of disc-shaped sheet material: includes roll system force balance module, rolling pressure calculation module, and roll system elastic deformation module; module content is consistent with S3; S5: Central stage of disc-shaped plate: includes roll system force balance module, rolling pressure calculation module and roll system elastic deformation module; the module content is the same as S3; S6: Three-quarters of the disc-shaped sheet material is thrown out: including the roll system force balance module, the rolling pressure calculation module, and the roll system elastic deformation module; the module content is the same as S3; S7: Round disc-shaped plate ejection stage: includes roller system force balance module, rolling pressure calculation module and roller system elastic deformation module; the module content is the same as S3; S8: Establish a three-dimensional model of the loaded roll gap for the entire rolling process of disc-shaped plates, collect the transverse distribution of the loaded roll gap under different entry widths, analyze the dynamic elastic deformation process of the roll system, draw the shape of the disc-shaped plate after rolling, and obtain the transverse thickness distribution of the disc-shaped plate shape throughout the rolling process. In step S3: The roller system force balancing module includes: 3a1) Establish the tension distribution model in front of the work roll and the tension distribution model behind the work roll; 3a2) Substitute the parameters and model obtained in 3a1) into the output equations for the force and torque balance between the support roller and the working roller; The rolling pressure calculation module includes: 3b1) Collect and input the parameters of the rolled sheet, and calculate the reduction amount and reduction rate of the work roll; The roller system elastic deformation module includes: 3c1) Collect and input the influence functions of roll elastic deflection and flattening, the initial pressure between the support roll and the work roll, and the transverse rolling force of the work roll obtained from the rolling pressure calculation module; 3c2) Establish the three-dimensional flexural displacement calculation equations for the support roller axis, the three-dimensional flexural displacement calculation equations for the work roller axis, and the flattening displacement equations between the support roller and the work roller; 3c3) By combining the equations obtained in 3c2), we can establish the calculation equations for the deformation coordination between the support roller and the work roller; 3c4) Calculate the pressure between the support roller and the work roller using the deformation coordination calculation equation between the support roller and the work roller; 3c5) Using the Jacobi iteration method, determine whether the difference between the pressure between the support roller and the working roller and the initial pressure between the support roller and the working roller input in 3c1) is less than the iteration accuracy of 0.000001. If yes, directly execute 3c6); otherwise, continue to execute 3c4) until the difference between the pressure between the support roller and the working roller obtained in 3c4) and the pressure between the support roller and the working roller obtained in the previous iteration in 3c4) meets the iteration accuracy and execute 3c6). 3c6) Output the pressure between the support roller and the work roller calculated in the last step 3c4) and substitute it into the three-dimensional flexural displacement of the work roller in step 3c2).

2. The method for calculating the loaded roll gap in a four-roll mill for rolling disc-shaped plates according to claim 1, characterized in that: In step S1, the roll parameters of the four-high mill include: support roll radius. Work roll radius support roller elastic modulus elastic modulus of the work roll Poisson's ratio of the support roller Poisson's ratio of the working roll The parameters for disc-shaped sheet metal include: post-rolling tensile stress. Pre-tension stress of rolled steel plate Rolled plate width, entry plate thickness Deformation resistance Rolling adjustment parameters include: support roll bending force. Work roll bending force Initial design export plate thickness .

3. The method for calculating the loaded roll gap in a four-roll mill for rolling disc-shaped plates according to claim 2, characterized in that, Step S2 specifically includes: 2a1) Collect and input the parameters of the four-high mill rolls and the disc-shaped sheet metal. Using a unit partitioning model, discretize the four-high mill rolls and the rolled sheet. Divide the roll body into m units along the roll body direction, where m is an odd number. The x-coordinate of the midpoint of each unit is... The distance of each unit from the midpoint of the roller body is... (i = 1, 2, ..., m), the workpiece and the roll are corresponding discrete units and divided into n parts. The first unit of the workpiece is the d-th unit of the roll, d = (mn) / 2. Except for the two edge units, the coordinates and widths of the remaining units are the same as those of the roll body. 2a2) Following the method described in 2a1), the characteristic parameters of the work roll, support roll, and workpiece are discretized into multiple equally divided units, and the work roll rolling force is discretized as follows: , ..., , ..., The contact pressure between the support roll and the work roll is discretized as follows: , ..., , ..., The thickness of the rolled product at the exit plate is discrete. , ..., , ..., The lateral distribution of the flattening between the rolls, the lateral distribution of each deflection, the roll system deformation parameters, and the force parameters are discretized along the roll axis.

4. The method for calculating the loaded roll gap in a four-roll mill for rolling disc-shaped plates according to claim 3, characterized in that: The tension distribution models before and after the work roll are established as follows: 3a1) Calculate the deflection angle of the work roll rolling force: 3a2) The force and torque balance equations for the output support roller and the work roller are as follows: Establish the force balance equation for the support roller in the vertical direction: Establish the torque balance equation in the vertical direction of the support roller: Establish the force balance equation for the work roll in the vertical direction: Establish the torque balance equation in the vertical direction of the work roll: in, It is the pre-tension stress of the rolled plate. It is the tension before the rolling unit. It is the post-tension stress of the rolled plate. It is the tension after the rolling unit. Plate width, It is the rolling force offset angle. It is the vertical pressing reaction force at the left end of the support roller. It is the vertical pressing reaction force at the right end of the support roller. It is the bending force of the support roller. It is the bending force of the work roll. It is the distance between the left and right support reaction forces of the support roller. It is the length of the roller body. It is the distance between the left and right bending forces of the work roll body. It is the distance between the left and right bending forces of the support roller. C is the distance between the left and right bending forces of the work roll and C is the distance between the point of application of the support roll reaction force and the edge of the roll. 3b1) The process for calculating the reduction amount and reduction rate of the work roll is as follows: Calculate the neutral angle of the work roll during rolling: Calculate the rolling force per unit length in the deformation zone of the work roll: Calculate the length of the deformation zone during work roll rolling: Substitute the parameters obtained above and output the transverse rolling force of the work roll: Calculate the transverse rolling force of the work roll: in, It's the thickness of the inlet plate. The initial design thickness for the export plate is... It is the radius of the rolling mill. It is deformation resistance. It is the amount of pressure applied by the roller system. It is the reduction rate of the roller system. It is the neutral angle of the work roll rolling process. It is the rolling force per unit length in the deformation zone of the work roll. It is the length of the deformation zone during work roll rolling. It is the rolling force per unit length of the work roll; 3c2) The process of establishing the equation is as follows: Establish the equation for calculating the vertical deflection displacement of the support roller axis: Establish the equation for calculating the deflection displacement in the vertical direction of the work roll axis: Establish the equation for the flattening displacement between the support roll and the work roll: in, It is the elastic modulus of the support roller. It is the elastic modulus of the work roll. It is the Poisson's ratio of the support roller. It is the Poisson's ratio of the working roll. It is half the width of the roll flattening system. It is the deflection displacement in the vertical direction of the support roller axis. It is the deflection displacement in the vertical direction of the working roller axis. It is the elastic flattening displacement of the roller system; 3c3) Establish the calculation equation for the deformation coordination between the support roll and the work roll: 。 5. The method for calculating the loaded roll gap in a four-roll mill for rolling disc-shaped plates according to claim 4, characterized in that: In step 3c1), the influence function of roll elastic deflection and flattening is: support roll bending influence coefficient. ; Work roll bending influence coefficient The influence coefficient of the support roller on the bending force. The coefficient of influence of bending force on the work roll ; Roller flattening influence coefficient Contact flattening influence coefficient between work roll and workpiece ,in .

6. The method for calculating the loaded roll gap in a four-roll mill for rolling disc-shaped plates according to claim 5, characterized in that, Step S8 specifically includes: 8a1) Establish the calculation equations for the rigid displacement of the rolls and the elastic flattening displacement between the work rolls and the workpiece, and combine them with the three-dimensional flexural displacement of the work rolls obtained in 3c5) to form a three-dimensional model of the loaded roll gap of a four-roll mill. 8b1) The rigid displacement of the roll is related to the axial displacement of the support roll at the roll end. Substitute the pressure between the support roll and the work roll output in 3c6) into the force and moment balance equation of the support roll output in 3a3), calculate the support reaction force of the support roll, and establish the calculation equation for the rigid displacement of the support roll: 8b2) Establish the equation for calculating the rigid displacement in the vertical direction of the support roller axis: 8b3) The contact flattening displacement between the work roll and the workpiece is calculated by the roll. Pressure on a micro-area The flattening amount caused by the contact point is used to establish calculation equations for the contact flattening displacement between the upper work roll and the workpiece, and for the contact flattening displacement between the lower work roll and the workpiece. 8b4) Establish the equation for calculating the contact flattening displacement between the work roll and the workpiece: It refers to the rigidity of the load-bearing components of the single-chip microcomputer base other than the roller system. It is the amount of the right-end tilting roller. It is the amount of the right-end tilting roller. It is the rigid displacement of the support roller axis in the vertical direction. It is the contact flattening displacement between the work roll and the workpiece; Substituting the equations obtained from 8b1) and 8b3) into 8b2) and 8b4), a calculation model for the exit plate thickness is established to represent the loaded roll gap model: It's the thickness of the exported plate; 8a2) Output the lateral distribution of the load roll gap under the current entry width of the workpiece, and increase the current entry width of the workpiece by B. i Determine the entry width B of the workpiece. i Is it smaller than the workpiece diameter B? If not, execute 8a3). If yes, adjust the workpiece inlet width B. i Substitute back into S3-S7 and repeat the cycle until the workpiece entry width B is reached. i If the diameter of the rolled piece is equal to B, then 8a3) is executed. 8a3) Collect rolled pieces at different inlet widths B i The transverse distribution of the roll gap under load is analyzed, the dynamic elastic deformation process of the roll system is analyzed, the shape of the disc-shaped plate after rolling is drawn, and the transverse thickness distribution of the disc-shaped plate in the whole rolling process is obtained.

Images