CN100385446C

CN100385446C - A Design Method of Roll Profile Curve in Temper Rolling Process of Thin and Narrow Material

Info

Publication number: CN100385446C
Application number: CNB2006100126005A
Authority: CN
Inventors: 白振华
Original assignee: Yanshan University
Current assignee: Yanshan University
Priority date: 2006-04-18
Filing date: 2006-04-18
Publication date: 2008-04-30
Anticipated expiration: 2026-04-18
Also published as: CN1828616A

Abstract

The present invention provides a method for designing the profile curves of work rolls and back-up rolls for ordinary four-roll temper mills when rolling thin and narrow materials. The method includes the following steps: (a) collecting equipment and process parameters of the temper mill; (b) Collect the variety and specification range of the strip; (c) Set the curve equation of the work roll and the backup roll; (d) Optimize and calculate the roll profile curve parameters; (e) Substitute the roll profile curve parameters into the roll profile of the work roll The curve equation and the roll profile curve equation of the back-up roll are optimized to obtain the roll profile curve equation of the work roll and the roll profile curve equation of the backup roll. The roll profile curves of the working rolls and backup rolls designed by the invention not only ensure the mechanical performance index of the finished product, but also meet the user's plate shape quality requirements. It should be noted that although the present invention is mainly used for the design of roll profile curves when flattening thin and narrow materials, at the same time, the present invention can also be used for the design of roll profile curves when wide and thick materials are flattened without pressure problems.

Description

A Design Method of Roll Profile Curve in Temper Rolling Process of Thin and Narrow Material

技术领域 technical field

本发明涉及一种平整设计技术，特别涉及一种针对普通四辊平整机在轧制薄窄料时的工作辊与支承辊辊型曲线优化设计方法。The invention relates to a skin pass design technology, in particular to a method for optimizing the profile curves of work rolls and back-up rolls when a common four-roll skin pass mill rolls thin and narrow materials.

背景技术 Background technique

生产实践中发现，普通四辊平整机在轧制薄窄料时，工作辊在板宽以外会出现相互接触压扁的所谓压靠现象，使得设定轧制压力仅仅一部分用于金属变形，而其它部分则消耗在工作辊的辊端压扁上，从而造成实际延伸率偏小，产品的机械性能达不到用户的要求。并且，在压靠发生之后，随着轧制压力的增大，其消耗在工作辊辊端压扁上的比例也随之增大。当轧制压力增大到一定程度之后，再增加的轧制压力几乎都消耗在压靠上了，而延伸率也不会出现明显的增加。与此同时，由于普通四辊平整机在平整过程中其工作辊与支承辊沿辊身是全长接触的，这样在板宽以外就形成了一个有害的接触区，使得平整机的横向刚度降低，从而影响平整成品的板形指标，也使得弯辊对板形的调节能力大大降低(见图1)。这样，如何同时保证普通四辊平整机在轧制薄窄料时产品的延伸率(机械性能)与板形指标，就成为现场技术攻关的重点与难点。In production practice, it is found that when the ordinary four-roll skin pass mill rolls thin and narrow materials, the work rolls will contact and flatten the so-called pressing phenomenon outside the width of the plate, so that only a part of the set rolling pressure is used for metal deformation. Other parts are consumed in the flattening of the roll ends of the work rolls, resulting in a relatively small actual elongation, and the mechanical properties of the product cannot meet the user's requirements. Moreover, after the pressing occurs, as the rolling pressure increases, the proportion of its consumption in the roll end flattening of the work rolls also increases. When the rolling pressure increases to a certain extent, the additional rolling pressure is almost consumed on the pressing, and the elongation will not increase significantly. At the same time, since the work roll and the back-up roll of the ordinary four-roll tempering machine are in contact with the entire length of the roll body during the leveling process, a harmful contact area is formed outside the width of the plate, making the transverse direction of the tempering machine Rigidity decreases, thereby affecting the plate shape index of the flattened product, and also greatly reducing the ability of the bending roller to adjust the plate shape (see Figure 1). In this way, how to simultaneously ensure the elongation (mechanical properties) and shape indicators of the product when the ordinary four-roll skin pass mill is rolling thin and narrow materials has become the focus and difficulty of on-site technical research.

为了控制压靠影响同时消除辊间有害接触区，以往人们对于平整机的辊型设计一般仅仅考虑到板形、辊耗等问题，例如：白振华、顾廷权和吴安民等发表的宝钢18003#CGL热镀锌平整机辊型技术的研究，《中国机械工程》2006，17(1)；33-35；白振华，连家创，刘峰和王建强发表的宝钢2050热轧厂平整机辊型优化技术的研究《钢铁》2002，37(9)；35-38；这些公开的技术研究对象主要是轧制普通带材，而尚未发现有以薄窄料群为研究对象，同时保证产品机械性能与板形指标的辊型设计方法见于文献。In order to control the impact of pressure and eliminate the harmful contact area between the rolls, in the past, people generally only considered the plate shape and roll consumption in the roll profile design of the skin pass mill. For example, Baosteel 18003#CGL published by Bai Zhenhua, Gu Tingquan, and Wu Anmin Research on roll profile technology of hot-dip galvanizing skin pass mill, "China Mechanical Engineering" 2006, 17(1); 33-35; Bai Zhenhua, Lian Jiachuang, Liu Feng and Wang Jianqiang published roll profile of Baosteel 2050 hot rolling mill Research on optimization technology "Steel" 2002, 37(9); 35-38; the research objects of these disclosed technologies are mainly rolling ordinary strips, but no thin and narrow material group has been found as the research object, while ensuring the mechanical properties of the product The roll shape design method with shape index can be found in literature.

发明内容 Contents of the invention

本发明的目的在于提供一种薄窄料平整轧制过程的辊型曲线设计方法，使得该类型的平整机在轧制薄窄料时能够同时控制压靠的影响与消除辊间有害接触区，不但保证了成品的延伸率指标，而且满足用户对板形质量的要求。The purpose of the present invention is to provide a method for designing roll curves in the temper rolling process of thin and narrow materials, so that this type of temper mill can simultaneously control the influence of pressure and eliminate the harmful contact area between rolls when rolling thin and narrow materials , not only ensures the elongation index of the finished product, but also meets the user's requirements for the shape quality.

本发明解决其技术问题所采用的技术方案是：这种薄窄料平整轧制过程的辊型曲线设计方法，包括以下由计算机系统执行的步骤：The technical solution adopted by the present invention to solve the technical problem is: the roll profile curve design method of the thin and narrow material smooth rolling process, including the following steps performed by the computer system:

a、收集平整机的设备及工艺参数包括：工作辊辊身长度L_W、工作辊直径D_W、支承辊辊身长度L_b、支承辊直径D_b、支承辊传动侧与工作侧压下螺丝中心距l₁、工作辊正负弯辊、传动侧与工作侧弯辊液压缸中心距l₂、最大弯辊力S、最大轧制压力P和最大轧制速度V；a. The equipment and process parameters of the collecting skin pass machine include: work roll body length L _W , work roll diameter D _W , back-up roll body length L _b , back-up roll diameter D _b , back-up roll driving side and working side pressing down Screw center distance l ₁ , working roll positive and negative bending, drive side and working side bending hydraulic cylinder center distance l ₂ , maximum bending force S, maximum rolling pressure P and maximum rolling speed V;

b、收集带钢的品种规格范围包括：带钢宽度b、厚度h、抗拉强度σ_b和允许最小延伸率ε_min；b. The variety and specification range of collected strip steel includes: strip steel width b, thickness h, tensile strength σ _b and allowable minimum elongation ε _min ;

c、以a，b，c，k₁，δ，l_z，g为辊型曲线参数和优化变量，分别设定工作辊与支撑辊的曲线方程。其中，设定工作辊的辊型曲线方程为：c. Using a, b, c, k ₁ , δ, l _z , g as roll shape curve parameters and optimization variables, set the curve equations of the work roll and backup roll respectively. Among them, the roll shape curve equation of the set work roll is:

${D D.}_{w w} ((x x)) = = {D D.}_{w w} - - a a ((11 - - cos cos ((b b \frac{22 x x}{{L L}_{w w}})))) - - c c {((\frac{22 x x}{{L L}_{w w}}))}^{{k k}_{11}}$

设定支承辊的辊型曲线方程为：The roll shape curve equation of the backup roll is set as:

${D D.}_{b b} ((x x)) = = \{\begin{matrix} {D D.}_{b b} & | | x x | | \leq \leq (({L L}_{b b} / / 22 - - {l l}_{z z})) \\ {D D.}_{b b} - - 22 δ δ {((\frac{| | x x | | - - (({L L}_{b b} / / 22 - - {l l}_{z z}))}{{l l}_{z z}}))}^{k k} & | | x x | | > > (({L L}_{b b} / / 22 - - {l l}_{z z})) \end{matrix}$

上述两式中：In the above two formulas:

D_w-工作辊原始直径(mm)；D _w - the original diameter of the work roll (mm);

L_w-工作辊辊身长度(mm)；L _w - work roll body length (mm);

D_b-支承辊原始直径(mm)；D _b - the original diameter of the backup roll (mm);

L_b-支承辊辊身长度(mm)；L _b - length of back-up roll body (mm);

a-工作辊凸度值；a-work roll crown value;

b-余弦相位系数；b- cosine phase coefficient;

c-工作辊高次曲线分项系数；c- sub-item coefficient of high degree curve of work roll;

k₁-工作辊高次曲线分项指数；k ₁ - sub-index of high degree curve of work roll;

l_z-支承辊辊型曲线削肩长度(mm)；l _z - the shoulder length of the back-up roll curve (mm);

δ-支承辊辊型曲线削肩深度(mm)；δ-back-up roll curve shoulder depth (mm);

g-支撑辊辊型曲线指数；g-backup roll profile curve index;

d、优化计算出辊型曲线参数，包括以下步骤：d. Optimize and calculate the parameters of the roll shape curve, including the following steps:

d1)、给定初始曲线参数X₀＝[a，b，c，k₁，δ，l_z，g]；d1), given initial curve parameter X ₀ =[a, b, c, k ₁ , δ, l _z , g];

d2)、计算出典型规格产品j的最佳弯辊力Sa_j及相应的延伸率ε_aj；d2), calculate the optimum roll bending force Sa _j and the corresponding elongation ε _aj of the typical specification product j;

d3)、判断 $ϵ_{a_{j}} &GreaterEqual; ϵ_{\min}$ 是否成立，若不成立，调整辊型曲线参数，重复步骤d2)；d3), judgment $ϵ_{a_{j}} &Greater Equal; ϵ_{\min}$ Whether it is established, if not established, adjust the roll shape curve parameters, repeat step d2);

d4)、计算出辊型优化设计的目标函数G(X)；d4), calculate the objective function G (X) of roll profile optimal design;

d5)、判断Powell条件是否成立，若不成立，重复上述步骤d2)、d3)、和d4)，直至Powell条件成立，结束计算，得出最优辊型曲线参数；d5), determine whether the Powell condition is established, if not established, repeat the above steps d2), d3), and d4), until the Powell condition is established, end the calculation, and obtain the optimal roll shape curve parameters;

e、将上述最优辊型曲线参数代入工作辊的辊型曲线方程和支承辊的辊型曲线方程得到最优工作辊的辊型曲线方程和最优支承辊的辊型曲线方程；E, substituting the above-mentioned optimal roll curve parameters into the roll curve equation of the work roll and the roll curve equation of the backup roll to obtain the roll curve equation of the optimal work roll and the roll curve equation of the optimal backup roll;

步骤(d)中所述最佳弯辊力Sa的求解包括以下由计算机系统执行的步骤(见图3)：The solution of optimum roll bending force Sa described in the step (d) comprises the following steps (see Fig. 3) carried out by the computer system:

d21)给定弯辊力的计算步长ΔS，标记函数biaoji＝100，板形目标函数初始值F₀＝10¹¹，并取计算次数k＝1；d21) Given the calculation step ΔS of the bending force, the marking function biaoji=100, the initial value of the flatness objective function F ₀ =10 ¹¹ , and the number of calculations k=1;

d22)给定弯辊力S＝S_+(k-1)ΔS(S_-最大负弯辊力，如果平整机没有负弯辊，则S_＝0)；d22) given bending force S=S_+(k-1)ΔS (S_-maximum negative bending force, if the skin pass machine does not have negative bending, then S_=0);

d23)计算对应的延伸率ε；d23) calculate the corresponding elongation ε;

d24)判断S≥S₊与biaoji＞0是否同时成立，若成立，则令S_a＝S₊、ε_a＝ε，转入步骤d210)；d24) Judging whether S≥S ₊ and biaoji>0 are established at the same time, if established, set S _a =S ₊ , ε _a =ε, and turn to step d210);

d25)判断ε≥ε_min是否成立，若不成立，令：k＝k+1，转入步骤d22)；d25) judging whether _ε≥εmin is established, if not established, order: k=k+1, proceed to step d22);

d26)计算出相应的带材前张力横向分布值σ_1i；d26) Calculate the corresponding strip front tension transverse distribution value σ _1i ;

d27)计算出板形目标函数F(X)的值，并令biaoji＝-100；d27) Calculate the value of the plate shape objective function F(X), and make biaoji=-100;

d28)判断F(X)≤F₀是否成立，若成立则令：F₀＝F(X)、S_a＝S、ε_a＝εd28) Judging whether F(X)≤F ₀ is established, if established: F ₀ =F(X), S _a =S, ε _a =ε

d29)判断S_a≤S₊是否成立，若成立则令：k＝k+1，转入步骤d22)；否则转入步骤d210)；d29) judging whether S _a ≤ S ₊ is established, if established then order: k=k+1, proceed to step d22); otherwise proceed to step d210);

d210)输出最佳弯辊力Sa及相应的延伸率ε_a。d210) Output the optimum roll bending force Sa and the corresponding elongation ε _a .

步骤d27)中所述板形目标函数F(X)可以用下式表示：The plate shape objective function F (X) described in the step d27) can be represented by the following formula:

F(X)＝((max(σ_1i)-min(σ_1i))/T₁)F(X)＝((max(σ _1i )-min(σ _1i ))/T ₁ )

式中：T₁-前张力的平均值；In the formula: T ₁ - the average value of the front tension;

步骤(d)中所述辊型优化设计的目标函数G(X)可以定义为：The objective function G (X) of roll shape optimization design described in the step (d) can be defined as:

$G G ((X x)) = = {Σ Σ}_{i i = = 11}^{m m} {[[{S S}_{ai ai} - - {S S}_{jitai jitai}]]}^{22}$

式中：S_ai-在特定辊型下，第i个规格产品满足目标函数F(X)最小的最佳弯辊力；In the formula: S _ai - under the specific roll type, the i-th specification product satisfies the minimum optimal roll bending force of the objective function F(X);

S_jitai-基态弯辊力。S _jitai - ground state roll bending force.

本发明的有益效果是：该发明是在充分考虑到普通四辊平整机轧制薄窄料时生产工艺特点的基础上，兼顾控制压靠影响与消除辊间有害接触区的要求，将带材的出口前张力与横向分布均匀作为优化目标函数、而把保证最小延伸率作为约束条件来完成工作辊与支承辊辊型曲线的优化设计。根据本发明所设计出的工作辊与支承辊辊型曲线不仅保证了成品的机械性能指标，而且满足了用户的板形质量要求。同时，本发明也可以用于不发生压靠问题的宽厚料平整时的辊型曲线设计。The beneficial effects of the present invention are: the present invention fully considers the characteristics of the production process when the ordinary four-roller pass mill rolls thin and narrow materials, and takes into account the requirements of controlling the impact of pressure and eliminating the harmful contact area between the rolls. The tension and transverse distribution before the exit of the material are uniform as the optimization objective function, and the minimum elongation is taken as the constraint condition to complete the optimal design of the roll profile curve of the work roll and the back-up roll. The roll profile curves of the working rolls and backup rolls designed according to the invention not only ensure the mechanical performance index of the finished product, but also meet the user's plate shape quality requirements. At the same time, the present invention can also be used in the design of the roll curve when the wide and thick material is flat without the problem of pressing.

附图说明 Description of drawings

图1是普通四辊平整机在轧制薄窄料时的辊系示意图；Figure 1 is a schematic diagram of the roll system of a common four-roller skin pass mill when rolling thin and narrow materials;

图2是实施例1的普通四辊平整机轧制薄窄料时的工作辊与支撑辊辊型曲线参数求解计算流程图；Fig. 2 is the calculation flow chart of calculating the profile curve parameters of the work roll and the back-up roll when the common four-roll skin pass mill of embodiment 1 rolls thin and narrow materials;

图3是实施例2的普通四辊平整机轧制典型规格薄窄料时的最佳弯辊力求解计算流程图；Fig. 3 is the optimal roll bending force solution calculation flowchart when the common four-roller skin pass mill of embodiment 2 rolls typical specification thin narrow material;

图4是辊型曲线方程设计的工作辊辊型曲线示意图；Fig. 4 is a schematic diagram of the work roll profile curve designed by the profile curve equation;

图5是辊型曲线方程设计的支承辊辊型曲线示意图。Fig. 5 is a schematic diagram of the backup roll profile curve designed by the roll profile curve equation.

具体实施方式 Detailed ways

以下借助附图描述本发明的较佳实施例Describe preferred embodiment of the present invention below with the aid of accompanying drawing

实施例1Example 1

以下给出了采用本发明的方法优化设计某普通四辊平整机轧制薄窄料时的工作辊与支撑辊辊型曲线参数求解过程，如图2所示。The process of solving the profile curve parameters of the work roll and backup roll when the method of the present invention is used to optimize the design of a common four-roll skin pass mill for rolling thin and narrow materials is given below, as shown in FIG. 2 .

首先，在步骤21中，收集平整机的设备及工艺参数：工作辊辊身长度L_w＝1300mm，工作辊直径D_w＝φ440/480mm，支承辊辊身长度L_b＝1300mm，支承辊直径D_b＝φ1100/1200mm，支承辊传动侧与工作侧压下螺丝中心距l₁＝2.32m，工作辊正负弯辊，传动侧与工作侧弯辊液压缸中心距l₂＝2.32m。最大弯辊力±60t，最大轧制压力700t，最大轧制速度1000m/min。First, in step 21, the equipment and process parameters of the tempering machine are collected: work roll body length L _w = 1300 mm, work roll diameter D _w = φ440/480 mm, back-up roll body length L _b = 1300 mm, back-up roll diameter D _b = φ1100/1200mm, center distance between drive side and working side press screw l ₁ = 2.32m, work roll positive and negative bending, drive side and working side bending roll hydraulic cylinder center distance l ₂ = 2.32m. The maximum bending force is ±60t, the maximum rolling pressure is 700t, and the maximum rolling speed is 1000m/min.

随后，在步骤22中，收集带钢的品种规格范围：带钢宽度800～1000mm，厚度0.15～0.50mm，屈服强度σ_s：280～620Mpa，最小延伸率0.5％，同时按照产品厚度、宽度、强度等级组合选取8种典型规格产品，具体数据如表1所示。Subsequently, in step 22, the variety specification range of strip steel is collected: strip steel width 800-1000mm, thickness 0.15-0.50mm, yield strength σ _s : 280-620Mpa, minimum elongation 0.5%. The combination of strength grades selects 8 products with typical specifications, and the specific data are shown in Table 1.

表1典型规格产品Table 1 Typical Specifications Products

序号serial number 厚度(mm)Thickness (mm) 宽度(mm)Width (mm) 屈服强度(MPa)Yield strength (MPa) 1 1 0.150.15 800800 300300 2 2 0.180.18 820820 300300 33 0.200.20 900900 300300 44 0.280.28 880880 300300 55 0.150.15 800800 600600 66 0.180.18 850850 600600 77 0.200.20 880880 600600 8 8 0.280.28 900900 600600

随后，在步骤23、24中，以a，b，c，k₁，δ，l_z，g为辊型曲线参数和优化变量，分别设定工作辊与支撑辊的曲线方程，并取X₀＝[a，b，c，k₁，δ，l_z，g]＝[0.01，1，0.1，8.0，0.8，120，3.0]。Subsequently, in steps 23 and 24, set a, b, c, k ₁ , δ, l _z , g as roll shape curve parameters and optimization variables, set the curve equations of the work roll and backup roll respectively, and take X ₀ = [a, b, c, k ₁ , δ, l _z , g] = [0.01, 1, 0.1, 8.0, 0.8, 120, 3.0].

随后，在步骤25中，调用图3所述相关程序计算出各个典型规格产品最佳弯辊力及相应的延伸率，分别为 $S_{a_{j}} = {20,15,26,43,37,42,45,20},$ $ϵ_{a_{j}} = {0.6 %, 0.72 %, 0.83 %, 0.56 %, 0.77 %, 1.0 %, 0.73 %, 1.3 %};$ Subsequently, in step 25, call the relevant program described in Figure 3 to calculate the best roll bending force and corresponding elongation of each typical specification product, respectively $S_{a_{j}} = {20,15,26,43,37,42,45,20},$ $ϵ_{a_{j}} = {0.6 %, 0.72 %, 0.83 %, 0.56 %, 0.77 %, 1.0 %, 0.73 %, 1.3 %};$

随后，在步骤26中，判断 $ϵ_{a_{j}} &GreaterEqual; ϵ_{\min}$ 是否成立，若不成立，调整辊型曲线参数X₀，重复步骤25；Then, in step 26, it is judged that $ϵ_{a_{j}} &Greater Equal; ϵ_{\min}$ Whether it is true, if not, adjust the roll shape curve parameter X ₀ , and repeat step 25;

随后，在步骤27中，计算出辊型优化设计的目标函数G(X)＝8708Subsequently, in step 27, calculate the objective function G(X)=8708 of roll shape optimal design

随后，在步骤28中，判断Powell条件是否成立，若不成立，调整辊型曲线参数X₀，重复步骤25、26、27，直至Powell条件成立，结束计算，得出最优辊型曲线参数。Subsequently, in step 28, it is judged whether the Powell condition is satisfied, if not, the roll profile curve parameter X ₀ is adjusted, and steps 25, 26, and 27 are repeated until the Powell condition is satisfied, and the calculation is ended to obtain the optimal roll profile curve parameter.

满足最优化成立条件后得到最优辊型参数：After satisfying the optimization establishment condition, the optimal roll shape parameters are obtained:

X＝[a，b，c，k₁，δ，l_z，g]＝[3.0e-5，2.0，1.6e-4，9.0，0.215e-3，180，3.4]X = [a, b, c, k ₁ , δ, l _z , g] = [3.0e-5, 2.0, 1.6e-4, 9.0, 0.215e-3, 180, 3.4]

即优化后的工作辊辊型曲线方程为：That is, the optimized work roll profile curve equation is:

${D D.}_{w w} ((x x)) = = {D D.}_{w w} - - 3.0 3.0 \times \times 1010^{- - 55} \times \times ((11 - - cos cos ((\frac{44 x x}{{L L}_{w w}})))) - - 1.60 1.60 \times \times 1010^{- - 44} \times \times {((\frac{22 x x}{{L L}_{w w}}))}^{99}$

支撑辊辊型曲线方程为：The roll shape curve equation of the backup roll is:

${D D.}_{b b} ((x x)) = = \{\begin{matrix} {D D.}_{b b} & | | x x | | \leq \leq (({L L}_{b b} / / 22 - - 180180)) \\ {D D.}_{b b} - - 22 \times \times 0.215 0.215 \times \times {((\frac{| | x x | | - - (({L L}_{b b} / / 22 - - 180180))}{180180}))}^{3.4 3.4} & | | x x | | > > (({L L}_{b b} / / 22 - - 180180)) \end{matrix}$

相关辊型曲线示意图如图4、图5所示。The schematic diagrams of the relevant roll profile curves are shown in Figure 4 and Figure 5.

实施例2Example 2

以下给出了采用本发明的方法求解某普通四辊平整机轧制典型规格薄窄料时的最佳弯辊力的计算过程，如图3所示。The following provides the calculation process of using the method of the present invention to solve the optimal roll bending force when a common four-roll skin pass mill rolls typical specifications of thin and narrow materials, as shown in Figure 3.

相关平整机的设备及工艺参数为：工作辊辊身长度L_w＝1300mm，工作辊直径D_w＝φ440/480mm，支承辊辊身长度L_b＝1300mm，支承辊直径D_b＝φ1100/1200mm，支承辊传动侧与工作侧压下螺丝中心距l₁＝2.32m，工作辊正负弯辊，传动侧与工作侧弯辊液压缸中心距l₂＝2.32m。最大弯辊力±60t，最大轧制压力700t，最大轧制速度1000m/min。The relevant equipment and process parameters of the tempering machine are: work roll body length L _w = 1300mm, work roll diameter D _w = φ440/480mm, back-up roll body length L _b = 1300mm, back-up roll diameter D _b = φ1100/1200mm , The center distance between the driving side of the back-up roll and the working side of the pressing screw l ₁ =2.32m, the positive and negative bending of the working roll, the center distance of the hydraulic cylinder of the driving side and the working side of the bending roll l ₂ =2.32m. The maximum bending force is ±60t, the maximum rolling pressure is 700t, and the maximum rolling speed is 1000m/min.

典型规格的薄窄料宽度800mm，厚度0.15mm，屈服强度σ_s：300Mpa，最小延伸率0.5％。Typical specifications of thin and narrow material width 800mm, thickness 0.15mm, yield strength σ _s : 300Mpa, minimum elongation 0.5%.

相关辊型曲线为： $D_{w} (x) = D_{w} - 3.0 \times 10^{- 5} \times (1 - \cos (\frac{4 x}{L_{w}})) - 1.60 \times 10^{- 4} \times {(\frac{2 x}{L_{w}})}^{9}$ (工作辊)； $D_{b} (x) = \{\begin{matrix} D_{b} & | x | \leq (L_{b} / 2 - 180) \\ D_{b} - 2 \times 0.215 \times {(\frac{| x | - (L_{b} / 2 - 180)}{180})}^{3.4} & | x | > (L_{b} / 2 - 180) \end{matrix}$ (支承辊)The relevant profile curves are: ${D.}_{w} (x) = {D.}_{w} - 3.0 \times 10^{- 5} \times (1 - \cos (\frac{4 x}{L_{w}})) - 1.60 \times 10^{- 4} \times {(\frac{2 x}{L_{w}})}^{9}$ (work roll); ${D.}_{b} (x) = \{\begin{matrix} {D.}_{b} & | x | \leq (L_{b} / 2 - 180) \\ {D.}_{b} - 2 \times 0.215 \times {(\frac{| x | - (L_{b} / 2 - 180)}{180})}^{3.4} & | x | > (L_{b} / 2 - 180) \end{matrix}$ (backup roll)

首先，在步骤31中，给定弯辊力的计算步长ΔS＝2.0，标记函数biaoji＝100，板形目标函数初始值F₀＝1.0·10¹¹，并取计算次数k＝1；Firstly, in step 31, the calculation step size of bending force is given as ΔS=2.0, the marking function biaoji=100, the initial value of flatness objective function F ₀ =1.0·10 ¹¹ , and the number of times of calculation k=1;

随后，在步骤32中，给定弯辊力S＝S_-+(k-1)ΔS＝-60Subsequently, in step 32, given roll bending force S=S _- +(k-1)ΔS=-60

随后，在步骤33中计算对应的延伸率ε＝0.7％；Subsequently, the corresponding elongation ε=0.7% is calculated in step 33;

随后，在步骤34中，判断S≥S₊与biaoji＞0是否同时成立，若成立，则令S_a＝S₊、ε_a＝ε，转入步骤41)Subsequently, in step 34, it is judged whether S≥S ₊ and biaoji>0 are established at the same time, if established, S _a =S ₊ , ε _a =ε, and turn to step 41)

随后，在步骤35中，判断ε≥ε_min是否成立，若不成立，令：k＝k+1，转入步骤32)；Subsequently, in step 35, it is judged whether ε≥ε _min is established, if not established, order: k=k+1, proceed to step 32);

随后，在步骤36中，计算出相应的带材前张力横向分布值σ_1i；Subsequently, in step 36, the corresponding strip front tension transverse distribution value σ _1i is calculated;

随后，在步骤37中，计算出板形目标函数F(X)＝12500的值，并令biaoji＝-100；Subsequently, in step 37, calculate the value of plate shape objective function F (X)=12500, and make biaoji=-100;

随后，在步骤38中，判断F(X)≤F₀是否成立，若成立则进入步骤39)，令：F₀＝F(X)＝12500、S_a＝S＝-60、ε_a＝ε＝0.7％；Subsequently, in step 38, it is judged whether F(X)≤F ₀ is established, and if it is established, then enter step 39), order: F ₀ =F(X)=12500, S _a =S=-60, ε _a =ε = 0.7%;

随后，在步骤40中，判断S_a≤S₊是否成立，若成立则令：k＝k+1，转入步骤32)。否则转入步骤41)；Subsequently, in step 40, it is judged whether S _a ≤ S ₊ is true, if true, set: k=k+1, and go to step 32). Otherwise, go to step 41);

最后，在步骤41中，输出最佳弯辊力Sa及相应的延伸率ε_a。Finally, in step 41, the optimal roll bending force Sa and the corresponding elongation ε _a are output.

最终，经过以上计算，得出最佳弯辊力为S_a＝2.5t，而对应的延伸率ε_a＝0.7％。Finally, through the above calculations, it is obtained that the optimum roll bending force is S _a =2.5t, and the corresponding elongation ε _a =0.7%.

Claims

1. a roll profile curve design method of thin and narrow material smooth rolling process, it is characterized in that: comprise the following steps:

a. Collect the equipment and process parameters of the tempering machine;

b. Collect the range of varieties and specifications of strip steel;

c. Using a, b, c, k ₁ , δ, l _z , g as roll shape curve parameters and optimization variables, respectively set the curve equations of the work roll and backup roll, where:

a-work roll crown value;

b- cosine phase coefficient;

c- sub-item coefficient of high degree curve of work roll;

k ₁ - sub-index of high degree curve of work roll;

l _z - the shoulder length of the back-up roll curve;

δ-back-up roll profile curve shoulder depth;

g-backup roll profile curve index;

d. Optimize and calculate the parameters of the roll shape curve, and complete the optimization of the roll shape curve parameters according to the following steps:

d1), given initial curve parameter X ₀ =[a, b, c, k ₁ , δ, l _z , g];

d2), calculate the optimum roll bending force Sa _j and the corresponding elongation ε _aj of product j of typical specifications, which can be completed according to the following steps:

d21), given the calculation step size ΔS of the bending force, the marking function biaoji=100, the initial value of the plate shape objective function F ₀ =10 ¹¹ , and the calculation times k=1;

d22), given roll bending force S=S _- + (k-1) ΔS, wherein: S _- - maximum negative roll bending force, if the skin pass machine has no negative roll bending force, then S _- = 0;

d23), calculate the corresponding elongation ε;

d24), judging whether S≥S ₊ and biaoji>0 are true at the same time, if true, set S _a = S ₊ , ε _a = ε, and turn to step d210), wherein: S ₊ - the largest positive bending roll of the skin pass mill Force; S _a - the best bending force under this step; ε _a - the elongation corresponding to the best bending force under this step;

d25), judging whether ε≥ε _min is established, if not established, order: k=k+1, and proceed to step d22), wherein: ε _min -minimum elongation;

d26), calculate the corresponding strip front tension lateral distribution value σ _1i ;

d27), calculate the value of the plate shape objective function F (X), and make biaoji=-100;

d28), judging whether F(X)≤F ₀ is established, if established, order: F ₀ =F(X), S _a =S, ε _a =ε; the plate shape objective function F(X) is represented by the following formula:

F(X)＝((max(σ _1i )-min(σ _1i ))/T ₁ )

In the formula:

F(X)-shape objective function;

T ₁ - mean value of front tension;

d29), judging whether S _a ≤ S ₊ is established, if established, order: k=k+1, proceed to step d22), otherwise proceed to step d210);

d210), order

S_{a_{j}} = S_{a};

ϵ_{a_{j}} = ϵ_{a},

Output the best roll bending force S _aj and the corresponding elongation ε _aj ;

d3), judgment

ϵ_{a_{j}} &Greater Equal; ϵ_{\min}

Whether it is established, if not established, adjust the roll shape curve parameters, repeat step d2);

d4), calculate the objective function G (X) of roll profile optimal design; Roll profile optimal design objective function G (X) represents with following formula:

G G ((X x)) = = {Σ Σ}_{i i = = 11}^{m m} {[[{S S}_{ai ai} - - {S S}_{jital jital}]]}^{22}

In the formula:

G(X)-Roll shape optimization design objective function;

S _ai - Under a specific roll type, the i-th specification product satisfies the minimum optimal roll bending force of the objective function F(X);

S _jital - roll bending force in the ground state;

d5), determine whether the Powell condition is established, if not established, repeat the above steps d2), d3), and d4), until the Powell condition is established, end the calculation, and obtain the optimal roll shape curve parameters;

e. Substituting the optimal roll profile curve parameters into the roll profile curve equation of the work roll and the roll profile curve equation of the backup roll to obtain the roll profile curve equation of the optimal work roll and the roll profile curve equation of the optimal backup roll.

2. The roll profile curve design method of the thin and narrow material temper rolling process as claimed in claim 1, characterized in that, the equipment parameters of the temper mill in the step a include: work roll body length L _w , Work roll diameter D _w , back-up roll body length L _b , back-up roll diameter D _b , back-up roll driving side and working side press-down screw center distance l ₁ , working roll positive and negative bending, driving side and working side bending roll hydraulic pressure Cylinder center distance l ₂ , maximum roll bending force S, maximum rolling pressure P, maximum rolling speed V.

3. the roll profile curve design method of thin and narrow material smooth rolling process as claimed in claim 1, it is characterized in that, the variety specification scope of the strip steel in the described step b comprises strip width b, thickness h, tensile strength Strength σ _b and allowable minimum elongation ε _min .

4. The roll profile curve design method of thin and narrow material tempering rolling process as claimed in claim 1, it is characterized in that, the curve equation of work roll and back-up roll in the described step c comprises: setting the roll profile of work roll The curve equation is:

{D D.}_{w w} ((x x)) = = {D D.}_{w w} - - a a ((11 - - cos cos ((b b \frac{22 x x}{{L L}_{w w}})))) - - c c {((\frac{22 x x}{{L L}_{w w}}))}^{{k k}_{11}}

The roll shape curve equation of the backup roll is set as:

{D D.}_{b b} ((x x)) = = \{\begin{matrix} {D D.}_{b b} & | | x x | | \leq \leq (({L L}_{b b} / / 22 - - {l l}_{z z})) \\ {D D.}_{b b} - - 22 δ δ {((\frac{| | x x | | - - (({L L}_{b b} / / 22 - - {l l}_{z z}))}{{l l}_{z z}}))}^{k k} & | | x x | | > > (({L L}_{b b} / / 22 - - {l l}_{z z})) \end{matrix}

In the above two formulas:

D _w - the original diameter of the work roll;

L _w - work roll body length;

D _b - the original diameter of the backup roll;

L _b - length of backup roll body.