A method and system for optimizing a pass of a multi-stand strip three-roll mill

Abstract

This invention relates to the field of metal rolling systems, specifically to a method and system for optimizing the pass profile of a multi-stand three-high strip mill. The method includes: establishing graded differentiated compression ratio allocation rules for each stand according to the characteristics of the target strip and the mill stand configuration, based on the rolling deformation process; constructing a three-segment pass profile basic framework that matches the single-pass plastic deformation based on the graded compression ratio allocation rules, configuring pass profile opening parameters dynamically adapted to the rolling speed, and generating a three-dimensional closed pass profile tangentially connected to the pass profile basic framework; verifying the plastic deformation matching degree of the pass profile through thermo-mechanical coupling simulation based on the three-dimensional pass profile, combined with the material characteristics of the target strip and the influencing factors of the entire rolling process; and conducting rolling tests based on the corrected core parameters of the pass profile, using the single-pass plastic deformation control requirements as the core verification indicator. This solution can achieve precise design of the pass profile in a multi-stand three-high strip mill.

Description

Technical Field

[0001] This invention relates to the field of metal rolling systems, and more specifically to a method and system for optimizing the pass profile of a multi-stand three-roll strip mill. Background Technology

[0002] Bar rolling is a core production process in the steel industry. Three-roll mills, with their compact structure and uniform rolling deformation, have become key equipment for the production of high-end special steel bars. Multi-stand three-roll mills achieve plastic deformation of metal through multiple continuous rolling passes. The pass design, as a crucial mold for metal deformation, directly determines the quality of the rolled product, production efficiency, and equipment lifespan. As high-end manufacturing demands increasingly higher dimensional accuracy and rolling stability for special steel bars, the traditional pass design of multi-stand three-roll mills is no longer adequate for modern production needs.

[0003] Currently, numerous studies and improvements have been conducted on the design of pass profiles and optimization of rolling processes in three-roll mills, resulting in a variety of technical solutions. Regarding the fundamental calculations for pass profile design, related technologies optimize the calculation method for the cross-sectional area of ​​the rolled piece by determining the contour shape of the workpiece in the pass gap region, avoiding the drawbacks of selecting the pass profile filling coefficient, and improving the calculation accuracy of the workpiece cross-section.

[0004] Although existing technologies have made some progress in the design of pass profiles and optimization of rolling processes in three-roll mills, there are still many technical problems to be solved in the practical application of multi-stand three-roll strip mills, making it difficult to meet the production requirements of high-precision special steel strips. Firstly, the compression ratio allocation lacks a systematic design basis, and the insufficient matching of compression ratios between stands easily leads to uneven deformation of the rolled piece, stress concentration, and even problems such as cracking and dimensional deviations. Existing technologies have only optimized the calculation method of the cross-sectional area of ​​the rolled piece, without forming a complete compression ratio allocation system. Secondly, the basic architecture design of the pass profile lacks a standardized and parameterized system, relying heavily on the subjective settings of engineers based on experience. When different design schemes are adapted to the same specification of special steel strips, the product qualification rate varies greatly. Thirdly, the dynamic matching between the pass profile opening parameters and process conditions such as rolling speed is insufficient. Unreasonable settings of parameters such as roll gap and opening width can easily lead to workpiece deviation and difficulty in biting, affecting rolling stability.

[0005] In summary, there is an urgent need for an optimization method for the pass design of multi-stand three-roll strip mills to solve the core problem that existing pass designs are difficult to design accurately. Summary of the Invention

[0006] To address the technical problem that existing multi-stand three-roll strip mill pass designs cannot accurately adapt to the rolling deformation process and actual working conditions, making precise design difficult, this invention provides a method and system for optimizing the pass design of multi-stand three-roll strip mills.

[0007] To achieve the above objectives, this invention provides a method for optimizing the pass profile of a multi-stand three-roll strip mill, comprising the following steps: Based on the characteristics of the target strip and the mill stand configuration, a graded differentiated compression ratio allocation rule is formulated for each stand according to the rolling deformation process, and the single-pass plastic deformation control requirements are determined; based on the graded compression ratio allocation rule, a three-segment pass profile basic structure matching the single-pass plastic deformation is constructed, and pass opening parameters dynamically adapted to the rolling speed are configured to generate a three-dimensional closed pass profile tangentially connected to the pass profile basic structure; based on the three-dimensional pass profile, the plastic deformation matching degree of the pass profile is verified through thermo-mechanical coupling simulation, and the core parameters of the pass profile are dynamically adapted and corrected in conjunction with the material characteristics of the target strip and the influencing factors of the entire rolling process, wherein the core parameters of the pass profile include the pass opening parameters; rolling tests are conducted based on the corrected core parameters of the pass profile, with the single-pass plastic deformation control requirements as the core verification indicator.

[0008] Preferably, the step of formulating graded differentiated compression ratio allocation rules for each stand according to the rolling deformation process includes: determining the appropriate range of total rolling compression ratio based on the plastic deformation characteristics of the target strip; differentiating the single-pass compression ratio of each stand according to the rule of first increasing and then decreasing along the rolling feed direction; and matching the total number of stands of the rolling mill to complete the full-process compression ratio allocation.

[0009] Furthermore, the three-section hole-type basic structure includes a central working circle, a gradually extending section symmetrically arranged on both sides of the central working circle, and an edge transition section.

[0010] Preferably, the pass opening parameters refer to the geometric parameters of the pass opening area used to ensure the stability of the workpiece bite, including the pass opening width and the pass roll gap; wherein the pass opening width is positively correlated with the reference height of the pass base structure, and the pass roll gap is dynamically adapted to the rolling speed.

[0011] Furthermore, the core parameters of the aperture shape refer to the set of key parameters of the aperture shape geometry in all dimensions, including the aperture reference height, the expansion angle of the gradient extension, the transition fillet radius of the edge transition, the aperture opening width, and the aperture roll gap.

[0012] Preferably, the three-dimensional closed hole profile is constructed using a smooth parametric curve to form an extended trajectory surface, which is tangent to the central working circle of the hole profile basic structure.

[0013] Furthermore, the dynamic adaptation and correction of the core parameters of the roll pass includes: simulating the metal flow state, roll pass stress distribution, and workpiece temperature field changes during the rolling process through thermo-mechanical coupling simulation; iteratively optimizing the core parameters of the roll pass with metal flow uniformity, roll pass stress bearing capacity, and workpiece temperature uniformity as core objectives; and dynamically correcting the core parameters of the roll pass by combining the target strip material composition with the actual rolling conditions.

[0014] Preferably, the rolling test based on the modified core parameters of the pass shape, with the single-pass plastic deformation control requirement as the core verification index, includes: conducting a small-sample rolling test based on the modified core parameters of the pass shape, detecting and obtaining the measured performance data of the rolled piece, including plastic deformation index, dimensional accuracy, form and position accuracy, and internal structure uniformity; if the measured performance data meets the single-pass plastic deformation control requirement, then the pass shape parameters are determined; if the measured performance data does not meet the single-pass plastic deformation control requirement, then the core parameters of the pass shape are iteratively adjusted until the measured performance data meets the single-pass plastic deformation control requirement.

[0015] Secondly, the present invention also provides a multi-stand bar three-roll mill pass optimization system, which is based on the above-mentioned multi-stand bar three-roll mill pass optimization method, including: a graded compression ratio determination module connected in sequence, used to determine the graded differentiated compression ratio allocation rules of each stand according to the characteristics of the target bar and the mill stand configuration, and to determine the single-pass plastic deformation control requirements; The parameterized pass construction module is used to construct a three-segment pass basic structure that matches the single-pass plastic deformation based on the graded compression ratio allocation rule, configure pass opening parameters that are dynamically adapted to the rolling speed, and generate a three-dimensional closed pass profile that is tangentially connected to the pass basic structure. The multi-dimensional optimization and correction module is used to verify the plastic deformation matching degree of the hole shape based on the three-dimensional hole shape profile through thermo-mechanical coupling simulation, and dynamically adapt and correct the core parameters of the hole shape by combining the material characteristics of the target strip and the influencing factors of the entire rolling process. The closed-loop verification iteration module is used to conduct rolling tests based on the corrected core parameters of the roll pass and detect the measured performance data of the rolled piece. If the measured performance data meets the preset single-pass plastic deformation control requirements, the roll pass parameters are finalized, forming a closed-loop process. If the measured performance data does not meet the preset single-pass plastic deformation control requirements, the core parameters of the roll pass are adjusted iteratively in reverse until the measured performance data meets the single-pass plastic deformation control requirements.

[0016] Furthermore, it also includes an online correction module, which is communicatively connected to the closed-loop verification iteration module. This module is used to adjust the pass opening parameters in the core parameters of the pass online based on the deviation between the actual rolling conditions and the design conditions, so as to match the changes in the actual rolling conditions.

[0017] The beneficial effects of this invention are as follows: By formulating graded and differentiated compression ratio allocation rules according to the rolling deformation process, constructing a three-segment pass profile and configuring pass opening parameters dynamically adapted to the rolling speed, a tangentially connected three-dimensional closed pass profile is generated. Combined with thermo-mechanical coupled simulation optimization and dynamic adaptation correction of the target strip material characteristics and influencing factors throughout the rolling process, as well as a closed-loop verification iteration design, parameterized and precise design of pass profiles for multi-stand strip three-roll mills is achieved. This effectively solves the problems of traditional pass profile design relying on experience, weak parameter correlation, and limited adaptability to specific scenarios. It is compatible with multiple specifications of strips and various types of three-roll mills such as positive Y-type and inverted Y-type, precisely controlling metal flow and microstructure evolution during the rolling process. This significantly improves the dimensional accuracy, shape and position accuracy, and internal microstructure uniformity of the rolled product, ensuring stable mass production of high-precision special steel strips. It also optimizes pass profile stress distribution and wear state, extends pass profile service life, reduces the number of trial rolling iterations, shortens the R&D cycle, and lowers production costs, achieving a synergistic improvement in rolling quality, production efficiency, and pass profile life.

[0018] Other advantages, objectives, and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination, or may be learned from practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description

[0019] To make the objectives, technical solutions, and advantages of the present invention clearer, the preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings, wherein: Figure 1 This is a flowchart of the multi-stand three-roll mill pass optimization method of the present invention; Figure 2 This is a structural diagram of the pass profile of the multi-stand three-roll strip mill of the present invention; Figure 3 This is a schematic diagram of a five-frame three-roller bore profile according to one embodiment of the present invention; Figure 4 This is a schematic diagram of a four-frame three-roller bore pattern according to another embodiment of the present invention; Figure 5 This is a schematic diagram of a three-frame, three-roller bore pattern according to another embodiment of the present invention; Figure 6 This is a flowchart illustrating the optimized design of the pass profile for a multi-stand three-roll strip mill according to the present invention. Figure 7 This is the first result of finite element analysis of the cross-sectional area of ​​each pass in the multi-stand three-roll strip mill of the present invention; Figure 8 The second result of finite element analysis of the cross-sectional area of ​​each pass in the multi-stand three-roll strip mill of this invention; Figure 9The third result is the finite element analysis of the cross-sectional area of ​​each pass in the multi-stand three-roll strip mill of this invention. Detailed Implementation

[0020] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. Unless otherwise specified, the following embodiments and features can be combined with each other.

[0021] The accompanying drawings are for illustrative purposes only and are schematic diagrams, not actual pictures. They should not be construed as limiting the invention. To better illustrate the embodiments of the invention, some parts in the drawings may be omitted, enlarged, or reduced, and do not represent the actual product dimensions. It is understandable to those skilled in the art that some well-known structures and their descriptions may be omitted in the drawings.

[0022] In the accompanying drawings of the embodiments of the present invention, the same or similar reference numerals correspond to the same or similar components. In the description of the present invention, it should be understood that if terms such as "upper," "lower," "left," "right," "front," and "rear" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, they are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, the terms used to describe positional relationships in the drawings are only for illustrative purposes and should not be construed as limiting the present invention. For those skilled in the art, the specific meaning of the above terms can be understood according to the specific circumstances.

[0023] like Figure 1 As shown, the method for optimizing the pass profile of a multi-stand three-roll strip mill provided by the present invention includes the following steps: Based on the characteristics of the target strip and the configuration of the rolling mill stands, a graded differentiated compression ratio allocation rule is formulated for each stand according to the rolling deformation process, and the single-pass plastic deformation control requirements are determined.

[0024] The strip material in this embodiment is a continuous long strip metal profile formed by multi-stand three-roll continuous rolling. The cross-section includes regular geometric shapes such as circles, squares, flats and irregular shapes. The cross-sectional dimensions are relatively narrow and thin, with a moderate length-to-diameter ratio. It has both good plastic deformation continuity and controllable dimensional accuracy. It is suitable for precision rolling scenarios such as high-precision structural parts and mechanical basic parts. It can achieve graded compression deformation and precise die adaptation during multi-stand continuous rolling, ensuring uniform metal flow, stable dimensional accuracy and uniform internal structure of the rolled part.

[0025] Based on the graded compression ratio allocation rule, a three-segment pass profile is constructed to match the single-pass plastic deformation. Pass opening parameters are configured to dynamically adapt to the rolling speed, and a three-dimensional closed pass profile is generated that is tangentially connected to the pass profile profile.

[0026] Based on the three-dimensional die profile, the plastic deformation matching degree of the die is verified by thermo-mechanical coupling simulation. Combining the material characteristics of the target strip and the influencing factors of the entire rolling process, the core parameters of the die are dynamically adapted and corrected, including the die opening parameters.

[0027] Rolling tests were conducted based on the modified core parameters of the pass shape, with the single-pass plastic deformation control requirements as the core verification indicator.

[0028] For example, this embodiment can be used to optimize the pass design for special steel bars with nominal diameters of 12mm to 150mm, adapting to various types of 3-5 stand three-roll mills such as positive Y-shaped, inverted Y-shaped, positive triangular, and inverted triangular. The specific implementation process is as follows: First, based on the material characteristics, finished product specifications, and mill stand configuration of the target bar, a graded differentiated compression ratio allocation rule is formulated for each stand according to the rolling deformation process, determining the single-pass plastic deformation control requirements for each pass. Then, based on the graded compression ratio allocation rule, a three-section pass basic framework is constructed that perfectly matches the single-pass plastic deformation requirements. Simultaneously, pass opening parameters dynamically adapted to the rolling speed are configured, generating a three-dimensional closed pass profile tangentially connected to the pass basic framework. Subsequently, based on the generated three-dimensional pass profile, the matching degree between the pass and the plastic deformation requirements is verified through thermo-mechanical coupling simulation. Combining the material characteristics of the target strip and the influencing factors of the entire rolling process, the core parameters of the pass are dynamically adapted and corrected. Finally, rolling tests are carried out based on the corrected core parameters of the pass, and the preset single-pass plastic deformation control requirements are used as the core verification index to complete the closed-loop optimization of the pass design.

[0029] Understandably, by establishing graded and differentiated compression ratio allocation rules according to the rolling deformation process, constructing a three-segment pass architecture and configuring pass opening parameters dynamically adapted to the rolling speed, a tangentially connected three-dimensional closed pass profile is generated. Combined with thermo-mechanical coupled simulation optimization and dynamic adaptation correction of the target strip material characteristics and influencing factors throughout the rolling process, as well as a closed-loop verification and iterative full-process design, parameterized and precise design of pass profiles for multi-stand strip three-roll mills is achieved. This effectively solves the problems of traditional pass profile design relying on experience, weak parameter correlation, and limited adaptability to specific scenarios. It is compatible with multiple specifications of strips and various types of three-roll mills, such as positive Y-type and inverted Y-type, precisely controlling metal flow and microstructure evolution during the rolling process. This significantly improves the dimensional accuracy, shape and position accuracy, and internal microstructure uniformity of the rolled product, ensuring stable mass production of high-precision special steel strips. It also optimizes pass profile stress distribution and wear state, extends pass profile service life, reduces the number of trial rolling iterations, shortens the R&D cycle, and lowers production costs, achieving a synergistic improvement in rolling quality, production efficiency, and pass profile life.

[0030] In one possible implementation, a graded differentiated compression ratio allocation rule is established for each stand according to the rolling deformation process. This includes: firstly, determining the suitable range of the total rolling compression ratio as 1.35~2.3 based on the plastic deformation characteristics of the target strip, the specifications of the inlet billet, and the specifications of the finished product. Then, along the rolling feed direction, the single-pass compression ratio of each stand is differentiated according to a pattern of first increasing and then decreasing. Specifically, the compression ratio of the first stand is controlled at 1.05~1.20, the compression ratio of the second and third stands is controlled at 1.08~1.28, the compression ratio of the fourth stand is controlled at 1.10~1.30, and the compression ratio of the fifth stand is controlled at 1.04~1.10. Finally, the total number of stands in the rolling mill is matched to complete the full-process compression ratio allocation for 3-stand, 4-stand, or 5-stand rolling lines. For example, when rolling φ30mm strip with 5 stands, the single-pass compression ratio is set to 1.12, 1.17, 1.17, 1.16, and 1.06 in sequence; when rolling φ50mm strip with 4 stands, the single-pass compression ratio is set to 1.06, 1.15, 1.11, and 1.06 in sequence; and when rolling φ103mm strip with 3 stands, the single-pass compression ratio is set to 1.06, 1.13, and 1.10 in sequence.

[0031] In one possible implementation, such as Figure 2As shown, the basic structure of the die-cutting pattern consists of three parts: a central working circle, symmetrically arranged gradient extension sections on both sides of the central working circle, and edge transition sections. The diameter of the central working circle is defined as the die-cutting reference height H, and the radius of the central working circle is R. H is calculated using the formula H = D × (1.015~1.025), where D is the nominal diameter of the target strip for the corresponding pass. The roundness error of the central working circle is controlled within 0.01 mm. The extension angle α of the gradient extension section is set according to the deformation frame classification. For the 1st and 2nd frames, α ≤ 30°; for the 3rd, 4th, and 5th frames, α is controlled between 40° and 84°. The transition fillet radius r of the edge transition section is controlled between 1.5 and 7 mm, and R and H satisfy the proportional relationship of R = H × (0.06 ~ 0.08). For example, when rolling φ30 mm strip, the transition fillet radius is set to 2 mm; when rolling φ50 mm strip, the transition fillet radius is set to 3.5 ~ 4 mm; and when rolling φ103 mm strip, the transition fillet radius is set to 6.5 ~ 7 mm.

[0032] In one possible implementation, the pass opening parameters are geometric parameters of the pass opening area used to ensure the stability of the rolled piece bite, specifically including the pass opening width W and the pass roll gap s. The pass opening width W is positively correlated with the reference height H of the pass base structure and is calculated using the formula W=H×(1.03~1.06). The pass roll gap s is dynamically adapted to the rolling speed; when the rolling speed v≤15m / s, s=H×0.08~0.10. And s≥1.2mm. When the rolling speed v>15m / s, s=H×0.10~0.13 and s≥1.2mm. For example, when rolling φ30mm strip in 5 stands, the opening width of each pass is set to 37.25mm, 30.93mm, 30.02mm, 28.82mm, and 27.34mm respectively, and the roll gap is set to 3.35mm, 2.78mm, 2.70mm, 2.59mm, and 2.46mm respectively.

[0033] In one possible implementation, the core parameters of the pass profile are a set of key parameters across all dimensions of the pass profile geometry. Specifically, these include five core parameters: the pass profile reference height H, the extension angle α of the gradient extension section, the transition fillet radius r of the edge transition section, the pass profile opening width W, and the pass profile roll gap s. These parameters are designed in a coordinated and matched manner: the pass profile reference height H is determined according to the nominal diameter D of the target strip and serves as the basic core parameter for pass profile design; the extension angle α is adjusted in stages according to the deformation process of each rolling pass to adapt to the plastic deformation requirements of different passes; the transition fillet radius r is adapted to the change of the reference height H in a fixed proportion to avoid stress concentration and surface scratches; the opening width W is positively correlated with the change of the reference height H to ensure smooth bite of the rolled piece; and the roll gap s is dynamically adapted to the change of rolling speed to match the production stability under different rolling rhythms. These five parameters together form a complete pass profile parameter system that adapts to the single-pass plastic deformation control requirements.

[0034] In one possible implementation, such as Figure 6 As shown, a three-dimensional coordinate system is established with the center of the working circle of the pass as the origin. The X-axis is parallel to the rolling direction. An extension starting point is set 1-2 mm outside the working circle along the XY plane of the coordinate system. A smooth, parameterized quadratic Bézier curve is used to construct the extension trajectory surface. The angle between the line connecting the curve control point and the center of the working circle and the rolling direction is controlled at 40°-50°. The X coordinate of the control point is H×0.3-0.4, the Y coordinate is H×0.4-0.5, and the Z coordinate is adapted to the pass thickness. The constructed extension trajectory surface is tangentially connected to the working circle. The intersection of the endpoint of the surface with the edge of the pass opening and the roll gap line is closed, finally forming a complete three-dimensional closed pass profile, realizing uniform flow control of metal in three-dimensional space.

[0035] The specific implementation method of dynamic adaptation and correction of core parameters of the roll pass in this embodiment is as follows: First, the entire rolling process is simulated through thermo-mechanical coupling simulation. The simulation uses finite element analysis software, with mesh generation accuracy controlled within 0.1mm~0.3mm. The simulation boundary conditions are set as follows: rolling speed v=0.5m / s~45m / s, rolling temperature T=750℃~1150℃, and friction coefficient μ between the roll and the workpiece μ=0.25~0.45. The simulation obtains the metal flow state, roll pass stress distribution, and workpiece temperature field during the rolling process. The changes are then analyzed; with metal flow uniformity, die stress bearing capacity, and workpiece temperature uniformity as the core optimization objectives, quantitative indicators are set as follows: metal flow rate uniformity error ≤ 4%, maximum stress of the die ≤ 75% of the material yield strength, and core-surface temperature difference of the workpiece ≤ 25℃. If the targets are not met, the core parameters of the die are iteratively optimized by adjusting α by a step size of 0.5°, R by a step size of 0.25mm, and W by a step size of 0.05H. Finally, the carbon content ωC, chromium content ωCr, and other material components of the target strip, as well as the rolling temperature T and predicted rolling force F are considered. 预测 Based on actual rolling conditions such as rolling speed v, a correction model is established to dynamically correct the pass reference height H and opening width W. The correction formula is as follows: H 修正 =H×[1+K1×(ω C -0.45)+K2×(ω Cr -0.25)-K3×(T-1000) / 100] W 修正 =W×[1+K4×(F 预测 -1450kN) / 1000kN+K5×(v-10) / 5] Where: K1=-0.02~-0.01, K2=-0.01~0, K3=0.008~0.012, K4=0.005~0.01, K5=0.003~0.006;

[0036] K : Working condition correction coefficient, with a value of 1.05~1.15 (adjusted according to the rolling speed v: when v≤5m / s, K=1.02~1.04; when 5<v≤15m / s, K=1.04~1.08; when v>15m / s, K=1.08~1.17). σs The yield strength (MPa) of the target strip at rolling temperature T is obtained through a correlation model between material composition and temperature. σ s = σ s0 [1 α ( T 1000), where σ s0 The yield strength at 1000℃; A Contact area between the rolled piece and the die (mm²), A=π H 平均 L, H 平均 =k(H0+H) / 2 (H0 is the entry thickness of the rolled piece, H is the exit thickness of the rolled piece, i.e., the reference height of the pass, H, k is the contact area correction coefficient, k=0.35~0.75), L is the contact arc length (mm), L=R 工作 (H0 H) (R) 工作 R is the working radius of the roll. 工作 =D - Exit area of ​​rolled piece / width of material / 3, where D is the diameter of the roll); ln(H / H0): Logarithm of the degree of deformation, reflecting the amount of plastic deformation of the rolled piece; μ: The coefficient of friction between the roll and the workpiece, which is related to the rolling temperature and ranges from 0.25 to 0.45; H 平均 Average thickness of rolled product (mm).

[0037] For example, in the pass design of a 5-stand three-roll mill for rolling φ30mm, refer to Figure 3 , Figure 6 According to Table 1, the production process sequence of the present invention includes sequentially setting the compression ratio, constructing the basic structure of the hole type, designing the hole type opening parameters, generating the extended trajectory surface, multi-field coupling simulation optimization, multi-factor dynamic correction, and hole type verification and iteration.

[0038] Step 1: Allocate compression ratio. The multi-stand strip three-roll mill adopts a 5-stand mode with an inlet diameter of 42mm. The total compression ratio of the 5 passes is 1.90. The compression ratio of the first stand is 1.12, the second stand is 1.17, the third stand is 1.17, the fourth stand is 1.16, and the fifth stand is 1.06.

[0039] Step 2: Construct the basic structure of the pass profile. The pass profile consists of a central working circle, symmetrically arranged gradient extension sections on both sides of the central working circle, and edge transition sections. The diameter of the central working circle is defined as the reference height H of the pass profile, H = D × (1.015~1.025), where D is the nominal diameter of the target strip after each pass rolling. The extension angle α of the gradient extension section is set according to the deformation stand grade: α = 20° for the first deformation stand, α = 20° for the second deformation stand, α = 20° for the third deformation stand, α = 50° for the fourth deformation stand, and α = 78° for the fifth deformation stand. The transition fillet radius of the edge transition section is r = 2mm for the first deformation stand, r = 2mm for the second deformation stand, r = 2mm for the third deformation stand, r = 2mm for the fourth deformation stand, and r = 2mm for the fifth deformation stand.

[0040] Step 3: Design the pass opening parameters. Pass opening width W: W=37.25mm for the first deformation stand, W=30.93mm for the second deformation stand, W=30.02mm for the third deformation stand, W=28.82mm for the fourth deformation stand, and W=27.34mm for the fifth deformation stand. Pass roll gap s: Rolling speed is less than 15m / s. s=3.5mm for the first deformation stand, s=2.5mm for the second deformation stand, s=2.5mm for the third deformation stand, s=2.8mm for the fourth deformation stand, and s=2.5mm for the fifth deformation stand.

[0041] Step 4: Generate the extended trajectory surface. Establish a three-dimensional coordinate system with the center of the central working circle as the origin. Set the extension starting point along the XY plane of the coordinate system. The extended trajectory surface is constructed using a quadratic Bézier curve. The angle between the line connecting the curve control point and the center of the central working circle and the rolling direction is 40°~50°. The surface is tangent to the central working circle. The intersection of the endpoint of the surface with the opening edge and the roll gap edge forms a closed die profile.

[0042] Step 5: Multi-field coupled simulation optimization. The rolling process is simulated through thermo-mechanical coupled simulation. The distribution of metal flow rate, stress field of the roll pass and temperature field of the rolled piece are analyzed. The optimization objectives are set as follows: metal flow rate uniformity error ≤ 4%, maximum stress of the roll pass ≤ 75% of the material yield strength, and core-surface temperature difference of the rolled piece ≤ 25℃. If the objectives are not met, iterative optimization is performed by adjusting the step size of α by 0.5°, R by 0.25mm, and W by 0.05H.

[0043] Step 6: Multi-factor dynamic correction, based on the material composition of the target strip (carbon content ω) C Chromium content ω Cr ), rolling temperature T and predicted rolling force F 预测 Establish a correction model to correct the hole reference height H and opening width W. The correction formula is as follows: H 修正 =H×[1+K1×(ω C -0.45)+K2×(ω Cr -0.25)-K3×(T-1000) / 100] W 修正 =W×[1+K4×(F 预测 -1450kN) / 1000kN+K5×(v-10) / 5] Where: K1=-0.02~-0.01, K2=-0.01~0, K3=0.008~0.012, K4=0.005~0.01, K5=0.003~0.006;

[0044] K: Working condition correction coefficient, with a value of 1.05~1.15 (adjusted according to the rolling speed v: K=1.02~1.04 when v≤5m / s; K=1.04~1.08 when 5<v≤15m / s; K=1.08~1.17 when v>15m / s).

[0045] σs: Yield strength (MPa) of the target strip at rolling temperature T, obtained through a correlation model between material composition and temperature: σ s =σ s0 [1 α (T 1000), where σ s0 The yield strength is the yield strength at 1000℃, where the basic strength is 145MPa.

[0046] A: Contact area between the rolled piece and the die (mm²), A=π H 平均 L, H 平均 =k(H0+H) / 2 (H0 is the entry thickness of the workpiece, H is the exit thickness of the workpiece, i.e., the reference height of the pass, H, and k is the contact area adjustment coefficient. k=0.35~0.75), L is the contact arc length (mm), L=R 工作 (H0 H) (R) 工作 R is the working radius of the roll.工作 =D - Exit area of ​​rolled piece / width of material / 3, where D is the diameter of the roll).

[0047] ln(H / H0): Logarithm of the degree of deformation, reflecting the amount of plastic deformation of the rolled piece.

[0048] μ: The coefficient of friction between the roll and the workpiece, which is related to the rolling temperature and ranges from 0.25 to 0.45.

[0049] H 平均 Average thickness of rolled product (mm).

[0050] Step 7: Reference Figure 7-9 The die shape verification and iteration involves processing die shape test blocks for small-scale rolling tests to detect the dimensional accuracy, ellipticity, and internal structure uniformity of the rolled piece. If the standards are not met, the process returns to step 4 to adjust the parameters of the extended trajectory surface until all indicators meet the preset requirements. The final die shape parameters are shown in Table 1.

[0051] Table 1. Rolling pass structure and rolling parameters for φ30mm specification in 5 passes.

[0052] For example, the pass design of a 4-stand three-roll mill for rolling φ50mm is referenced. Figure 4 , Figure 6 According to Table 2, the production process sequence of the present invention includes sequentially setting the compression ratio, constructing the basic structure of the hole type, designing the hole type opening parameters, generating the extended trajectory surface, multi-field coupling simulation optimization, multi-factor dynamic correction, and hole type verification and iteration.

[0053] Step 1: Allocate compression ratio. The multi-stand strip three-roll mill adopts a 4-stand mode with an inlet diameter of 61mm. The total compression ratio of the 4 passes is 1.44, the compression ratio of the first stand is 1.06, the compression ratio of the second stand is 1.15, the compression ratio of the third stand is 1.11, and the compression ratio of the fourth stand is 1.16.

[0054] Step 2: Construct the basic structure of the pass profile. The pass profile consists of a central working circle, symmetrically arranged gradient extension sections on both sides of the central working circle, and edge transition sections. The diameter of the central working circle is defined as the reference height H of the pass profile, H = D × (1.015~1.025), where D is the nominal diameter of the target strip after each pass rolling. The extension angle α of the gradient extension section is set according to the deformation stand grade: α = 20° for the first deformation stand, α = 20° for the second deformation stand, α = 50° for the third deformation stand, and α = 70° for the fourth deformation stand. The transition fillet radius of the edge transition section is r = 4mm for the first deformation stand, r = 4mm for the second deformation stand, r = 3.5mm for the third deformation stand, and r = 3.5mm for the fourth deformation stand.

[0055] Step 3: Design the pass opening parameters. Pass opening width W: W=46.03mm for the first deformation stand, W=46.10mm for the second deformation stand, W=41.86mm for the third deformation stand, and W=45.46mm for the fourth deformation stand. Pass roll gap s: The rolling speed is less than 15m / s. s=4.2mm for the first deformation stand, s=4.2mm for the second deformation stand, s=3.8mm for the third deformation stand, and s=4.0mm for the fourth deformation stand.

[0056] Step 4: Generate the extended trajectory surface. Establish a three-dimensional coordinate system with the center of the central working circle as the origin. Set the extension starting point along the XY plane of the coordinate system. The extended trajectory surface is constructed using a quadratic Bézier curve. The angle between the line connecting the curve control point and the center of the central working circle and the rolling direction is 40°~50°. The surface is tangent to the central working circle. The intersection of the endpoint of the surface with the opening edge and the roll gap edge forms a closed die profile.

[0057] Step 5: Multi-field coupled simulation optimization. The rolling process is simulated through thermo-mechanical coupled simulation. The distribution of metal flow rate, stress field of the roll pass and temperature field of the rolled piece are analyzed. The optimization objectives are set as follows: metal flow rate uniformity error ≤ 4%, maximum stress of the roll pass ≤ 75% of the material yield strength, and core-surface temperature difference of the rolled piece ≤ 25℃. If the objectives are not met, iterative optimization is performed by adjusting the step size of α by 0.5°, R by 0.25mm, and W by 0.05H.

[0058] Step 6: Multi-factor dynamic correction, based on the material composition of the target strip (carbon content ω) C Chromium content ω Cr ), rolling temperature T and predicted rolling force F 预测 Establish a correction model to correct the hole reference height H and opening width W. The correction formula is as follows: H 修正 =H×[1+K1×(ω C -0.45)+K2×(ω Cr -0.25)-K3×(T-1000) / 100] W 修正 =W×[1+K4×(F 预测 -1450kN) / 1000kN+K5×(v-10) / 5] Where: K1=-0.02~-0.01, K2=-0.01~0, K3=0.008~0.012, K4=0.005~0.01, K5=0.003~0.006;

[0059] K: Working condition correction coefficient, with a value of 1.05~1.15 (adjusted according to the rolling speed v: K=1.02~1.04 when v≤5m / s; K=1.04~1.08 when 5<v≤15m / s; K=1.08~1.17 when v>15m / s).

[0060] σs: Yield strength (MPa) of the target strip at rolling temperature T, obtained through a correlation model between material composition and temperature: σ s =σ s0 [1 α (T 1000), where σ s0 The yield strength is the yield strength at 1000℃, where the basic strength is 145MPa.

[0061] A: Contact area between the rolled piece and the die (mm²), A=π H 平均 L, H 平均 =k(H0+H) / 2 (H0 is the entry thickness of the rolled piece, H is the exit thickness of the rolled piece, i.e., the reference height of the pass, H, k is the contact area correction coefficient, k=0.35~0.75), L is the contact arc length (mm), L=R 工作 (H0 H) (R) 工作 R is the working radius of the roll. 工作 =D - Exit area of ​​rolled piece / width of material / 3, where D is the diameter of the roll).

[0062] ln(H / H0): Logarithm of the degree of deformation, reflecting the amount of plastic deformation of the rolled piece.

[0063] μ: The coefficient of friction between the roll and the workpiece, which is related to the rolling temperature and ranges from 0.25 to 0.45.

[0064] H 平均 Average thickness of rolled product (mm).

[0065] Step 7: Refer to Figure 7-9 The die shape verification and iteration involves processing die shape test blocks for small-scale rolling tests to detect the dimensional accuracy, ellipticity, and internal structure uniformity of the rolled piece. If the standards are not met, the process returns to step 4 to adjust the extended trajectory surface parameters until all indicators meet the preset requirements. The final die shape parameters are shown in Table 2.

[0066] Table 2 shows the roll pass structure and rolling parameters for φ50mm specification in four passes.

[0067] For example, in the design of the pass profile for a three-stand three-roll mill rolling mill with a diameter of φ103mm, refer to Figure 5-6 According to Table 3, the production process sequence of the present invention includes sequentially setting the compression ratio, constructing the basic structure of the hole type, designing the hole type opening parameters, generating the extended trajectory surface, multi-field coupling simulation optimization, multi-factor dynamic correction, and hole type verification and iteration.

[0068] Step 1: Allocate compression ratio. The multi-stand strip three-roll mill adopts a 3-stand mode with an inlet diameter of 120mm. The total compression ratio of the 3 passes is 1.32, the compression ratio of the first stand is 1.06, the compression ratio of the second stand is 1.13, and the compression ratio of the third stand is 1.10.

[0069] Step 2: Construct the basic structure of the pass profile. The pass profile consists of a central working circle, symmetrically arranged gradient extension sections on both sides of the central working circle, and edge transition sections. The diameter of the central working circle is defined as the reference height H of the pass profile, H = D × (1.015~1.025), where D is the nominal diameter of the target strip after each pass rolling. The extension angle α of the gradient extension section is set according to the deformation stand grade: α = 30° for the first deformation stand, α = 30° for the second deformation stand, and α = 50° for the third deformation stand. The transition fillet radius of the edge transition section is r = 7mm for the first deformation stand, r = 7mm for the second deformation stand, and r = 6.5mm for the third deformation stand.

[0070] Step 3: Design the pass opening parameters. Pass opening width W: W=93.44mm for the first deformation stand, W=93.11mm for the second deformation stand, and W=85.04mm for the third deformation stand; Pass roll gap s: Rolling speed is less than 15m / s for the first deformation stand, s=11.2mm for the second deformation stand, and s=10.0mm for the third deformation stand.

[0071] Step 4: Generate the extended trajectory surface. Establish a three-dimensional coordinate system with the center of the central working circle as the origin. Set the extension starting point along the XY plane of the coordinate system. The extended trajectory surface is constructed using a quadratic Bézier curve. The angle between the line connecting the curve control point and the center of the central working circle and the rolling direction is 40°~50°. The surface is tangent to the central working circle. The intersection of the endpoint of the surface with the opening edge and the roll gap edge forms a closed die profile.

[0072] Step 5: Multi-field coupled simulation optimization. The rolling process is simulated through thermo-mechanical coupled simulation. The distribution of metal flow rate, stress field of the roll pass and temperature field of the rolled piece are analyzed. The optimization objectives are set as follows: metal flow rate uniformity error ≤ 4%, maximum stress of the roll pass ≤ 75% of the material yield strength, and core-surface temperature difference of the rolled piece ≤ 25℃. If the objectives are not met, iterative optimization is performed by adjusting the step size of α by 0.5°, R by 0.25mm, and W by 0.05H.

[0073] Step 6: Multi-factor dynamic correction, based on the material composition of the target strip (carbon content ω) C Chromium content ω Cr ), rolling temperature T and predicted rolling force F 预测 Establish a correction model to correct the hole reference height H and opening width W. The correction formula is as follows: H 修正 =H×[1+K1×(ω C -0.45)+K2×(ω Cr -0.25)-K3×(T-1000) / 100] W 修正 =W×[1+K4×(F 预测 -1450kN) / 1000kN+K5×(v-10) / 5] Where: K1=-0.02~-0.01, K2=-0.01~0, K3=0.008~0.012, K4=0.005~0.01, K5=0.003~0.006;

[0074] K: Working condition correction coefficient, with a value of 1.05~1.15 (adjusted according to the rolling speed v: K=1.02~1.04 when v≤5m / s; K=1.04~1.08 when 5<v≤15m / s; K=1.08~1.17 when v>15m / s).

[0075] σs: Yield strength (MPa) of the target strip at rolling temperature T, obtained through a correlation model between material composition and temperature: σ s =σ s0 [1 α (T 1000), where σ s0 The yield strength is the yield strength at 1000℃, where the basic strength is 145MPa.

[0076] A: Contact area between the rolled piece and the die (mm²), A=π H 平均 L, H 平均 =k(H0+H) / 2 (H0 is the entry thickness of the rolled piece, H is the exit thickness of the rolled piece, i.e., the reference height of the pass, H, k is the contact area correction coefficient, k=0.35~0.75), L is the contact arc length (mm), L=R 工作 (H0 H) (R) 工作 R is the working radius of the roll.工作 =D - Exit area of ​​rolled piece / width of material / 3, where D is the diameter of the roll).

[0077] ln(H / H0): Logarithm of the degree of deformation, reflecting the amount of plastic deformation of the rolled piece.

[0078] μ: The coefficient of friction between the roll and the workpiece, which is related to the rolling temperature and ranges from 0.25 to 0.45.

[0079] H 平均 Average thickness of rolled product (mm).

[0080] Step 7: Refer to Figure 7-9 The die shape verification and iteration involves processing die shape test blocks for small-scale rolling tests to detect the dimensional accuracy, ellipticity, and internal structure uniformity of the rolled piece. If the standards are not met, the process returns to step 4 to adjust the extended trajectory surface parameters until all indicators meet the preset requirements. The final die shape parameters are shown in Table 3.

[0081] Table 3 shows the roll pass structure and rolling parameters for φ103mm specification in three passes.

[0082] In one possible implementation, a die test block is fabricated based on the modified die core parameters, and a small-scale rolling test is conducted. After rolling, the measured performance data of the rolled piece is obtained, including single-pass plastic deformation index, dimensional accuracy, ellipticity and other dimensional and positional accuracy, as well as internal microstructure uniformity. Dimensional accuracy and ellipticity are assessed according to strip specifications, with acceptance standards set as follows: for D≤50mm, dimensional accuracy ≤±0.05mm and ellipticity ≤0.1mm; for 50mm<D≤80mm, dimensional accuracy ≤±0.08mm and ellipticity ≤0.16mm; and for 80mm<D≤150mm, dimensional accuracy ≤±0.20mm and ellipticity ≤0.4mm. Simultaneously, the internal microstructure grain size deviation is required to be ≤1.5 grade. If the measured performance data meets the preset single-pass plastic deformation control requirements and acceptance standards, the die parameters are finalized. If the measured performance data does not meet the requirements, the die core parameters are iteratively adjusted, and simulation optimization and rolling tests are repeated until all indicators meet the preset requirements, forming a closed-loop design.

[0083] Secondly, this invention also provides a pass optimization system for a multi-stand three-roll strip mill. This system is used to execute the entire process of the aforementioned pass optimization method. It includes four functional modules connected in sequence. First, a graded compression ratio setting module receives input target strip characteristics and mill stand configuration parameters, automatically calculates and sets graded differentiated compression ratio allocation rules for each stand according to the rolling deformation process, and determines the single-pass plastic deformation control requirements. Second, a parameterized pass construction module automatically constructs a three-segment pass basic structure matching the single-pass plastic deformation based on the compression ratio allocation rules output by the graded compression ratio setting module, and synchronously configures pass opening parameters dynamically adapted to the rolling speed. The system consists of three main components: a three-dimensional closed-loop profile that is tangentially connected to the basic profile of the pass; a multi-dimensional optimization and correction module that can verify the plastic deformation matching degree of the pass based on the three-dimensional profile generated by the parametric pass construction module through a built-in thermo-mechanical coupling simulation model, and automatically complete the dynamic adaptation and correction of the core parameters of the pass by combining the input target strip material characteristics and the influencing factors of the entire rolling process; and a closed-loop verification and iteration module that can output rolling test schemes based on the core parameters of the pass output by the multi-dimensional optimization and correction module, simultaneously collect the measured performance data of the rolling test, complete the index verification and pass parameter finalization, or iteratively adjust the core parameters of the pass to achieve fully automated closed-loop design.

[0084] In one possible implementation, the pass optimization system is further equipped with an online correction module. The online correction module is communicatively connected to the closed-loop verification iteration module and can collect real-time actual operating data of the rolling production line, including actual rolling force, real-time rolling speed, and measured rolling temperature. It compares the deviation between the design conditions and the actual conditions. When the deviation between the actual rolling force and the predicted value exceeds 5%, the online correction program for the pass parameters is triggered in real time. Based on the preset correction model, the pass opening width and roll gap value in the core parameters of the pass are adjusted online.

[0085] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for optimizing the pass profile of a multi-stand three-roll strip mill, characterized in that, Includes the following steps: Based on the characteristics of the target strip and the configuration of the rolling mill stand, a graded differentiated compression ratio allocation rule for each stand is formulated according to the rolling deformation process, and the single-pass plastic deformation control requirements are determined. Based on the graded compression ratio allocation rule, a three-segment pass profile is constructed to match the single-pass plastic deformation, and pass opening parameters are configured to dynamically adapt to the rolling speed to generate a three-dimensional closed pass profile that is tangentially connected to the pass profile profile. Based on the three-dimensional die profile, the plastic deformation matching degree of the die is verified by thermo-mechanical coupling simulation. Combined with the material characteristics of the target strip and the influencing factors of the whole process of rolling, the core parameters of the die are dynamically adapted and corrected, including the die opening parameters. Rolling tests were conducted based on the modified core parameters of the pass shape, with the single-pass plastic deformation control requirements as the core verification indicator.

2. The method for optimizing the pass profile of a multi-stand three-roll strip mill according to claim 1, characterized in that, The rule for assigning graded, differentiated compression ratios to each stand based on the rolling deformation process includes: Determine the appropriate range of total rolling compression ratio based on the plastic deformation characteristics of the target strip; Along the rolling feed direction, the single-pass compression ratio of each stand is configured differently according to the rule of first rising and then falling; Match the total number of mill stands to complete the allocation of compression ratios throughout the entire process.

3. The method for optimizing the pass profile of a multi-stand three-roll strip mill according to claim 1, characterized in that, The three-section hole-type basic structure includes a central working circle, a gradually extending section symmetrically arranged on both sides of the central working circle, and an edge transition section.

4. The method for optimizing the pass profile of a multi-stand three-roll strip mill according to claim 1, characterized in that, The pass opening parameters refer to the geometric parameters of the pass opening area used to ensure the stability of the workpiece bite, including the pass opening width and the pass roll gap; wherein the pass opening width is positively correlated with the reference height of the pass base structure, and the pass roll gap is dynamically adapted to the rolling speed.

5. The method for optimizing the pass profile of a multi-stand three-roll strip mill according to claim 1, characterized in that, The core parameters of the aperture shape refer to the set of key parameters of the aperture shape geometry in all dimensions, including the aperture reference height, the expansion angle of the gradient extension, the transition fillet radius of the edge transition, the aperture opening width, and the aperture roll gap.

6. The method for optimizing the pass profile of a multi-stand three-roll strip mill according to claim 1, characterized in that, The three-dimensional closed hole profile is constructed using a smooth parametric curve to create an extended trajectory surface, which is tangent to the central working circle of the hole profile's basic structure.

7. The method for optimizing the pass profile of a multi-stand three-roll strip mill according to claim 1, characterized in that, The dynamic adaptation and correction of the core parameters of the hole shape includes: Thermo-mechanical coupling simulation was used to simulate the metal flow state, die stress distribution and temperature field changes of the rolled piece during the rolling process. With metal flow uniformity, die stress bearing capacity, and workpiece temperature uniformity as the core objectives, the core parameters of the die are iteratively optimized. The core parameters of the roll pass are dynamically adjusted based on the material composition of the target strip and the actual rolling conditions.

8. The method for optimizing the pass profile of a multi-stand three-roll strip mill according to claim 1, characterized in that, The rolling test based on the modified pass core parameters, with the single-pass plastic deformation control requirement as the core verification indicator, includes: Based on the modified core parameters of the die, a small-scale rolling test was conducted to obtain the measured performance data of the rolled piece. The measured performance data included plastic deformation index, dimensional accuracy, geometric accuracy and internal structure uniformity. If the measured performance data meets the requirements for single-pass plastic deformation control, then determine the hole profile parameters; If the measured performance data does not meet the single-pass plastic deformation control requirements, the core parameters of the hole shape are iteratively adjusted until the measured performance data meets the single-pass plastic deformation control requirements.

9. A pass optimization system for a multi-stand three-roll strip mill, characterized in that, The system is used to execute the multi-stand three-roll strip mill pass optimization method according to any one of claims 1 to 8, comprising sequentially connected communication links: The graded compression ratio setting module is used to formulate graded differentiated compression ratio allocation rules for each stand according to the characteristics of the target strip and the configuration of the rolling mill stand, and to determine the single-pass plastic deformation control requirements. The parameterized pass construction module is used to construct a three-segment pass basic structure that matches the single-pass plastic deformation based on the graded compression ratio allocation rule, configure pass opening parameters that are dynamically adapted to the rolling speed, and generate a three-dimensional closed pass profile that is tangentially connected to the pass basic structure. The multi-dimensional optimization and correction module is used to verify the plastic deformation matching degree of the hole shape based on the three-dimensional hole shape profile through thermo-mechanical coupling simulation, and dynamically adapt and correct the core parameters of the hole shape by combining the material characteristics of the target strip and the influencing factors of the entire rolling process. The closed-loop verification iteration module is used to conduct rolling tests based on the corrected core parameters of the roll pass and to detect the measured performance data of the rolled piece. If the measured performance data meets the preset single-pass plastic deformation control requirements, the final shape of the hole parameters is completed, forming a closed loop of the entire process. If the measured performance data does not meet the preset single-pass plastic deformation control requirements, the core parameters of the hole shape are adjusted in reverse iteration until the measured performance data meets the single-pass plastic deformation control requirements.

10. The multi-stand strip three-roll mill pass optimization system according to claim 9, characterized in that, It also includes an online correction module, which is communicatively connected to the closed-loop verification iteration module. This module is used to adjust the pass opening parameters in the core parameters of the pass online based on the deviation between the actual rolling conditions and the design conditions, so as to match the changes in the actual rolling conditions.

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