CN103394561B

CN103394561B - Method for determining bending angle of each pass of cold roll forming of plate and strip

Info

Publication number: CN103394561B
Application number: CN201310332927.0A
Authority: CN
Inventors: 李立新; 叶奔; 曾祥明; 朱少文; 周绪昌; 胡盛德; 李烨
Original assignee: Wuhan University of Science and Technology WHUST
Current assignee: Wuhan University of Science and Technology WHUST
Priority date: 2013-08-01
Filing date: 2013-08-01
Publication date: 2015-04-15
Anticipated expiration: 2033-08-01
Also published as: CN103394561A

Abstract

The invention relates to a method for determining the bending angle of each pass of cold bending forming of a plate and strip. The technical solution is: first set the number of cold roll forming passes , select the bending angle of each pass and the work roll diameter of the roll as the test factors, pre-select the level values of each test factor, and design a virtual test plan for each test factor and the corresponding level value; then calculate the plate and strip strain of each virtual test plan distribution, establish the mathematical model of the maximum value of the absolute value of the positive strain along the tangential direction of the outer edge of each pass plate strip; The upper and lower limits are constrained conditions, and the maximum value of the absolute value of the positive strain in each pass is the pursuit of the goal, optimize and determine the number of cold-rolled forming passes, the bending angle of the cold-formed sheet and strip in each pass, and the diameter of the work roll of the roll. The invention has the characteristics of giving full play to the equipment capacity of the cold bending unit, avoiding the warping of the plate and strip and being able to overcome the wave shape defect at the edge of the plate and strip.

Description

A Method for Determining the Bending Angle of Each Pass in the Cold Forming of Plate and Strip

技术领域technical field

本发明属于板带材冷弯成型技术领域，尤其涉及一种确定板带材冷弯成型各道次弯曲角度的方法。The invention belongs to the technical field of cold-bending forming of plates and strips, and in particular relates to a method for determining the bending angle of each pass of cold-bending forming of plates and strips.

背景技术Background technique

冷弯成型是通过顺序配置的多道次成型轧辊，将金属板带材不断地进行横向弯曲，以制成特定断面型材的工艺技术。冷弯成型是一种节材、节能、高效、先进和适用的金属成型工艺，是板带材深度加工的一个重要领域。Cold roll forming is a process technology that continuously bends metal sheet strips transversely through sequentially configured multi-pass forming rolls to make specific cross-section profiles. Cold roll forming is a material-saving, energy-saving, high-efficiency, advanced and applicable metal forming process, and it is an important field of deep processing of plates and strips.

板带材的冷弯变形过程具有明显的几何非线性、物理非线性和边界非线性等特性。因此，迄今为止，冷弯技术仍主要基于工程技术人员的经验知识，依赖试错法获取工艺规律，冷弯成型工艺仍被普遍认为是一种“未掌握的艺术”。The cold-bending deformation process of plate and strip has obvious geometric nonlinearity, physical nonlinearity and boundary nonlinearity. Therefore, so far, cold-bending technology is still mainly based on the experience and knowledge of engineers and technicians, relying on trial and error to obtain process rules, and cold-bending forming technology is still generally regarded as an "unmastered art".

确定冷弯成型各道次的弯曲角度是冷弯成型工艺设计的重要内容。一般来说，冷弯成型的前段和后段采用较小的弯曲变形，而中间段采用较大的变形，并假设当板带材立边端部水平面投影轨迹用三次曲线表示时，板带材的弯曲角度分配是最佳的（小奈弘，刘继英.冷弯成型技术[M].北京：化学工业出版社2008年1月第一版），据此可推导出在总成型道次数给定条件下确定不同成型方式对应各道次弯曲角度分配的关系式。Determining the bending angle of each pass of cold roll forming is an important content of cold roll forming process design. Generally speaking, the front and rear sections of cold roll forming adopt a small bending deformation, while the middle section adopts a large deformation, and it is assumed that when the horizontal plane projection trajectory of the end of the vertical edge of the plate and strip is represented by a cubic curve, the plate and strip The distribution of the bending angle is the best (Xiao Naihong, Liu Jiying. Cold bending forming technology [M]. Beijing: Chemical Industry Press, January 2008, the first edition), it can be deduced that in the given number of total forming passes Under the conditions, the relational expression of different forming methods corresponding to the distribution of bending angles in each pass is determined.

然而，当机架间距不相等时，运用上述方法并不能直接导出各道次弯曲角度的分配关系；再者，该法未能考虑轧辊直径、板带材材质、轧件/轧辊接触状态等设备及工艺参数对板带材变形的影响；另外，总成型道次数的确定仍依赖于实际经验，若该值取得较大，则机组能力不能充分发挥，若取值较小，则会产生板带材翘曲和边部浪形的缺陷。However, when the stand spacing is not equal, the above method cannot directly derive the distribution relationship of the bending angle of each pass; moreover, this method fails to consider the equipment such as roll diameter, plate and strip material, rolling piece/roll contact state, etc. and the influence of process parameters on the deformation of the strip; in addition, the determination of the total number of passes still depends on actual experience. If the value is large, the capacity of the unit cannot be fully utilized; if the value is small, strips will be produced. Defects of material warpage and edge wave shape.

发明内容Contents of the invention

本发明旨在克服现有技术缺陷，目的是提供一种适于机架间距不相等、能充分发挥冷弯机组设备能力、能避免板带材翘曲和能克服板带材边部浪形缺陷的确定板带材冷弯成型各道次弯曲角度的方法。The purpose of the present invention is to overcome the defects of the prior art, and the purpose is to provide a machine that is suitable for unequal frame spacing, can fully utilize the equipment capacity of the cold bending unit, can avoid the warpage of the plate and strip, and can overcome the wave shape defect of the edge of the plate and strip. A method for determining the bending angle of each pass of cold-formed sheet and strip.

为实现上述目的，本发明采用技术方案的具体步骤是：To achieve the above object, the concrete steps that the present invention adopts technical solution are:

第一步、虚拟试验方案的设计The first step, the design of the virtual test plan

先根据形状因子函数或生产经验，设定冷弯成型的道次数n，进行辊花图设计，再选取板带材冷弯成型各道次的第一弯曲角度、第二弯曲角度和轧辊工作辊径作为试验因素；然后预选各试验因素的水平值，设计各试验因素和对应水平值的虚拟试验方案。Firstly, according to the shape factor function or production experience, set the number of passes n of cold bending forming, design the roll pattern, and then select the first bending angle, second bending angle and roll working roll of each pass of cold bending forming of the plate and strip. Then, the level value of each test factor is preselected, and the virtual test plan of each test factor and corresponding level value is designed.

第二步、有限元模拟计算The second step, finite element simulation calculation

先根据第一步设计的各道次的虚拟试验方案建立各自的有限元几何模型，选取单元，采用有限元软件进行网络划分，然后确定板带材与轧辊之间的摩擦模型：First, according to the virtual test plan of each pass designed in the first step, establish their own finite element geometric models, select units, use finite element software to divide the network, and then determine the friction model between the strip and the roll:

μ＝μ_d+(μ_s-μ_d)e^-cv （1）μ＝μ _d +(μ _s -μ _d )e ^-cv (1)

式（1）中：v—板带材与轧辊之间的相对滑动速度，m/s；In the formula (1): v—the relative sliding speed between the strip and the roll, m/s;

u_s—静摩擦系数，u_s＝0.2；u _s —coefficient of static friction, u _s =0.2;

u_d—动摩擦系数，u_d＝0.1；u _d —coefficient of dynamic friction, u _d =0.1;

c—衰减指数，c＝0.02～0.08。c—attenuation index, c=0.02～0.08.

最后对每个虚拟试验方案分别进行有限元模拟计算，得到各道次的每个虚拟试验方案的板带材应变分布。Finally, the finite element simulation calculation is carried out for each virtual test scheme separately, and the plate and strip strain distribution of each virtual test scheme for each pass is obtained.

第三步、模型建立The third step, model building

根据第二步各道次的每个虚拟试验方案的板带材应变分布，确定各道次的每个虚拟试验方案板带材外边缘沿其切线方向正应变值，得到各道次板带材外边缘沿其切线方向正应变绝对值的最大值：According to the plate and strip strain distribution of each virtual test scheme of each pass in the second step, determine the positive strain value of the outer edge of each virtual test scheme of each pass along the tangential direction of the plate and strip, and obtain the plate and strip of each pass The maximum value of the absolute value of the positive strain of the outer edge along its tangent direction:

${ϵ ϵ}_{i i} = = {a a}_{i i 11} + + {a a}_{i i 22} {β β}_{i i} + + {a a}_{i i 33} {γ γ}_{i i} + + {a a}_{i i 44} {D D.}_{i i} + + {a a}_{i i 55} {β β}_{i i}^{22} + + {a a}_{i i 66} {β β}_{i i} {γ γ}_{i i} + + {a a}_{i i 77} {β β}_{i i} {D D.}_{i i} + + {a a}_{i i 88} {γ γ}_{i i}^{22} + + {a a}_{i i 99} {γ γ}_{i i} {D D.}_{i i} + + {a a}_{i i 1010} {D D.}_{i i}^{22}$

$+ + {a a}_{i i 1111} {β β}_{i i}^{33} + + {a a}_{i i 1212} {β β}_{i i}^{22} {γ γ}_{i i} + + {a a}_{i i 1313} {β β}_{i i}^{22} {D D.}_{i i} + + {a a}_{i i 1414} {γ γ}_{i i}^{22} {β β}_{i i} + + {a a}_{i i 1515} {γ γ}_{i i}^{33} + + {a a}_{i i 1616} {γ γ}_{i i}^{22} {D D.}_{i i} + + {a a}_{i i 1717} {D D.}_{i i}^{22} {β β}_{i i} + + {a a}_{i i 1818} {D D.}_{i i}^{22} {γ γ}_{i i} - - - - - - ((22))$

$+ + {a a}_{i i 1919} {D D.}_{i i}^{33} + + {a a}_{i i 2020} {β β}_{i i}^{44} + + {a a}_{i i 21 twenty one} {β β}_{i i}^{22} {γ γ}_{i i}^{22} + + {a a}_{i i 22 twenty two} {β β}_{i i}^{22} {D D.}_{i i}^{22} + + {a a}_{i i 23 twenty three} {γ γ}_{i i}^{22} {D D.}_{i i}^{22} + + {a a}_{i i 24 twenty four} {D D.}_{i i}^{22} {β β}_{i i}^{22} + + {a a}_{i i 2525} {D D.}_{i i}^{44}$

式（2）中：a_i1，a_i2，…，a_i25为i道次的回归系数；In formula (2): a _i1 , a _i2 , ..., a _i25 are the regression coefficients of pass i;

β_i为i道次板带材第一弯曲角度；β _i is the first bending angle of the i-pass strip;

γ_i为i道次板带材第二弯曲角度；γ _i is the second bending angle of the i-pass plate and strip;

β_i和γ_i中至少有一个弯曲角度是试验因素；At least one bending angle among β _i and γ _i is a test factor;

D_i为i道次轧辊工作辊径；D _i is the working roll diameter of the i pass roll;

i为1,2,…,n。i is 1,2,...,n.

第四步、正应变绝对值的最大值中的最小值The fourth step, the minimum value of the maximum value of the absolute value of positive strain

以各道次板带材外边缘沿其切线方向正应变绝对值的最大值ε_i最小为优化目标，以各道次板带材外边缘沿其切线方向正应变绝对值的最大值ε_i≤1%和各试验因素水平值的上下限为约束条件，确定各道次板带材的第一弯曲角度的优化值β_i0、第二弯曲角度的优化值γ_i0和轧辊工作辊径的优化值D_i0。Taking the maximum value of the absolute value of positive strain ε _i of the outer edge of each pass along the tangential direction as the optimization goal, and the maximum value of the absolute value of the positive strain of the outer edge of each pass along the tangential direction of the plate and strip ε _i ≤ 1% and the upper and lower limits of each test factor level value are constrained conditions, and the optimal value of the first bending angle β _i0 , the second bending angle γ _i0 and the optimal value of the work roll diameter of each pass plate and strip are determined D _i0 .

将各道次板带材的第一弯曲角度的优化值β_i0、第二弯曲角度的优化值γ_i0和轧辊工作辊径的优化值D_i0代替式(2)中对应的第一弯曲角度β_i、第二弯曲角度γ_i和轧辊工作辊径D_i,得到各道次板带材外边缘沿其切线方向正应变绝对值的最大值中的最小值：The optimized value of the first bending angle β _i0 , the optimized value of the second bending angle γ _i0 and the optimized value D _i0 of the work roll diameter of each pass plate and strip are substituted for the corresponding first bending angle β in formula (2) _i , the second bending angle γ _i and the work roll diameter D _i of the roll, the minimum value of the maximum value of the absolute value of the positive strain along the tangential direction of the outer edge of the plate and strip in each pass is obtained:

${ϵ ϵ}_{i i 00} = = {a a}_{i i 11} + + {a a}_{i i 22} {β β}_{i i 00} + + {a a}_{i i 33} {γ γ}_{i i 00} + + {a a}_{i i 44} {D D.}_{i i 00} + + {a a}_{i i 55} {β β}_{i i 00}^{22} + + {a a}_{i i 66} {β β}_{i i 00} {γ γ}_{i i 00} + + {a a}_{i i 77} {β β}_{i i 00} {D D.}_{i i 00} + + {a a}_{i i 88} {γ γ}_{i i 00}^{22} + + {a a}_{i i 99} {γ γ}_{i i 00} {D D.}_{i i 00} + + {a a}_{i i 1010} {D D.}_{i i 00}^{22}$

$+ + {a a}_{i i 1111} {β β}_{i i 00}^{33} + + {a a}_{i i 1212} {β β}_{i i 00}^{22} {γ γ}_{i i 00} + + {a a}_{i i 1313} {β β}_{i i 00}^{22} {D D.}_{i i 00} + + {a a}_{i i 1414} {γ γ}_{i i 00}^{22} {β β}_{i i 00} + + {a a}_{i i 1515} {γ γ}_{i i 00}^{33} + + {a a}_{i i 1616} {γ γ}_{i i 00}^{22} {D D.}_{i i 00} + + {a a}_{i i 1717} {D D.}_{i i 00}^{22} {β β}_{i i 00} + + {a a}_{i i 1818} {D D.}_{i i 00}^{22} {γ γ}_{i i 00} - - - - - - ((33))$

$+ + {a a}_{i i 1919} {D D.}_{i i 00}^{33} + + {a a}_{i i 2020} {β β}_{i i 00}^{44} + + {a a}_{i i 21 twenty one} {β β}_{i i 00}^{22} {γ γ}_{i i 00}^{22} + + {a a}_{i i 22 twenty two} {β β}_{i i 00}^{22} {D D.}_{i i 00}^{22} + + {a a}_{i i 23 twenty three} {γ γ}_{i i 00}^{22} {D D.}_{i i 00}^{22} + + {a a}_{i i 24 twenty four} {D D.}_{i i 00}^{22} {β β}_{i i 00}^{22} + + {a a}_{i i 2525} {D D.}_{i i 00}^{44}$

式（3）中：a_i1，a_i2，…，a_i25为i道次的回归系数；In formula (3): a _i1 , a _i2 , ..., a _i25 are the regression coefficients of pass i;

β_i0为i道次板带材第一弯曲角度的优化值；β _i0 is the optimized value of the first bending angle of the plate and strip for the i pass;

γ_i0为i道次板带材第二弯曲角度的优化值；γ _i0 is the optimized value of the second bending angle of the plate and strip for the i pass;

β_i0和γ_i0中至少有一个弯曲角度的优化值是试验因素；The optimal value of at least one bending angle among β _i0 and γ _i0 is a test factor;

D_i0为i道次轧辊工作辊径的优化值；D _i0 is the optimized value of the working roll diameter of the i-pass roll;

i为1,2,…,n。i is 1,2,...,n.

第五步、冷弯道次数的确定The fifth step, the determination of the number of cold bends

第一分步、如果式(3)所确定的各道次板带材外边缘沿其切线方向正应变绝对值的最大值中的最小值ε_i0均在0.8～1.0%范围内，则第一步设定的道次数n得以确定；The first sub-step, if the minimum value ε _i0 of the maximum value of the absolute value of positive strain along the tangential direction of the outer edge of each pass plate strip determined by formula (3) is within the range of 0.8 to 1.0%, then the first The number of passes n set by the step is determined;

第二分步、如果式(3)所确定的各道次中的某道次板带材外边缘沿其切线方向正应变绝对值的最大值中的最小值ε_i0小于0.8%，则将第一步设定的道次数n减1，然后重复第一步至第四步，直至符合第五步第一分步；In the second sub-step, if the minimum value ε _i0 of the maximum value of the absolute value of positive strain along the tangential direction of the outer edge of a certain pass in each pass determined by formula (3) is less than 0.8%, then the pass Subtract 1 from the number of passes n set in one step, and then repeat the first step to the fourth step until it meets the fifth step and the first sub-step;

第三分步、如果式(3)所确定的各道次中的某道次板带材外边缘沿其切线方向正应变绝对值的最大值中的最小值ε_i0不存在，则将第一步设定的道次数n加1，然后重复第一步至第四步，直至符合第五步第一分步；The third sub-step, if the minimum value ε _i0 of the maximum value of the absolute value of the positive strain of the outer edge of the strip along the tangential direction of each pass in each pass determined by formula (3) does not exist, then the first Add 1 to the number of passes n set in the first step, and then repeat the first step to the fourth step until it meets the fifth step and the first sub-step;

第六步、弯曲角度和轧辊工作辊径的确定The sixth step, the determination of the bending angle and the working roll diameter of the roll

第一分步、若各道次板带材外边缘沿其切线方向正应变绝对值的最大值中的最小值ε_i0的级差与各道次板带材外边缘沿其切线方向正应变绝对值的最大值中的最小值ε_i0的平均值之比小于或等于10%，则板带材冷弯成型各道次第一弯曲角度的优化值β_i0、第二弯曲角度的优化值γ_i0和轧辊工作辊径的优化值D_i0得以确定。The first sub-step, if the difference between the minimum value ε _i0 of the maximum value of the absolute value of positive strain along the tangential direction of the outer edge of the plate and strip of each pass and the absolute value of the positive strain of the outer edge of each pass of the plate and strip along its tangential direction The ratio of the average value of the minimum value ε _i0 in the maximum value of is less than or equal to 10%, then the optimal value β _i0 of the first bending angle, the optimal value γ _i0 of the second bending angle and The optimal value D _i0 of the work roll diameter of the roll is determined.

第二分步、若各道次板带材外边缘沿其切线方向正应变绝对值的最大值中的最小值ε_i0的级差与各道次板带材外边缘沿其切线方向正应变绝对值的最大值中的最小值的平均值之比大于10%，则对第五步所确定的各道次板带材外边缘沿其切线方向正应变绝对值的最大值中的最小值ε_i0按其大小进行排序，再对排序中最大值和排序中最小值所对应道次试验因素的水平值进行调整，重复进行第一步至第五步，直至符合第六步第一分步。The second sub-step, if the minimum value ε _i0 of the maximum value of the absolute value of the positive strain of the outer edge of each pass along the tangential direction of the strip is different from the absolute value of the positive strain of the outer edge of each pass along the tangential direction The ratio of the average value of the minimum value in the maximum value of the maximum value is greater than 10%, then the minimum value ε _i0 of the maximum value of the absolute value of the positive strain of the outer edge of each pass along the tangential direction determined in the fifth step is Sort their sizes, and then adjust the horizontal values of the test factors corresponding to the maximum and minimum values in the sorting, and repeat the first to fifth steps until the first sub-step of the sixth step is met.

所述单元为壳单元、或为六面体单元、或为四面体单元。The unit is a shell unit, or a hexahedron unit, or a tetrahedron unit.

由于采用上述技术方案，本发明与现有技术相比具有如下积极效果：Owing to adopting above-mentioned technical scheme, the present invention has following positive effect compared with prior art:

本发明涉及的确定各道次板带材弯曲角度的方法考虑了轧辊工作辊径、板带材材质、轧件/轧辊接触状态等因素对冷弯各道次板带材弯曲角度确定的影响，适合机架间距不相等时的情况。The method for determining the bending angle of each pass of the plate and strip involved in the present invention takes into account the influence of factors such as the diameter of the work roll of the roll, the material of the plate and strip, and the contact state of the rolled piece/roller on the determination of the bending angle of the plate and strip of each pass of cold bending, Suitable for situations where the spacing between racks is not equal.

本发明以各道次板带材外边缘沿其切线方向正应变绝对值的最大值最小为优化目标，以板带材外边缘沿其切线方向正应变绝对值的最大值小于或等于1%为约束条件，因此板带材成型时不会产生翘曲及边浪缺陷，并能充分发挥机组设备的生产潜力。In the present invention, the minimum maximum value of the absolute value of the positive strain along the tangential direction of the outer edge of the plate and strip in each pass is the optimization goal, and the maximum value of the absolute value of the positive strain along the tangential direction of the plate and strip is less than or equal to 1%. Therefore, there will be no warping and edge wave defects during the forming of the plate and strip, and the production potential of the unit equipment can be fully utilized.

因此，本发明具有适于机架间距不相等、能充分发挥冷弯机组设备能力、能避免板带材翘曲和能克服板带材边部浪形缺陷的特点。Therefore, the present invention has the characteristics of being suitable for unequal frame spacing, fully exerting the equipment capacity of the cold bending unit, avoiding the warping of the plate and strip, and overcoming the wave-shaped defect at the edge of the plate and strip.

附图说明Description of drawings

图1为本发明的一种不对称Z型钢辊花设计示意图；Fig. 1 is a kind of asymmetrical Z-shaped steel roller flower design schematic diagram of the present invention;

图2为图1所示板带材的第7道次第7#实验方案的计算结果云图。Fig. 2 is a cloud diagram of the calculation results of the 7th pass No. 7# experimental scheme of the plate and strip shown in Fig. 1 .

具体实施方法Specific implementation method

以下结合附图和具体实施方式对本发明作进一步的描述，并非对其保护范围的限制。The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments, which are not intended to limit the scope of protection thereof.

实施例1Example 1

一种确定板带材冷弯成型各道次弯曲角度的方法。该方法的具体步骤是：A method for determining the bending angle of each pass of cold-bending forming of a plate and strip. The concrete steps of this method are:

根据形状因子函数，设定不对称Z型钢的冷弯成型道次数n为11，完成如图1所示的辊花图设计。本步骤以第7道次为例，选取第7道次第一弯曲角度β₇、第二弯曲角度γ₇和轧辊工作辊径D₇作为试验因素；每个试验因素各取三个水平值，即第一弯曲角度β₇值分别为16°、23°和30°，第二弯曲角度γ₇值分别为6°、12°和18°，轧辊工作辊径D₇值分别为320mm、400mm和480mm；按正交表L₉(3⁴)确定如表1所示的各试验因素及对应水平值的虚拟试验方案。According to the shape factor function, the number n of cold bending passes of the asymmetric Z-shaped steel is set to 11, and the design of the roller pattern shown in Figure 1 is completed. In this step, taking the seventh pass as an example, the first bending angle β ₇ , the second bending angle γ ₇ and the working roll diameter D ₇ of the seventh pass are selected as test factors; each test factor takes three levels, That is, the values of the first bending angle β ₇ are 16°, 23° and 30° respectively, the values of the second bending angle γ ₇ are 6°, 12° and 18° respectively, and the values of the working roll diameter D ₇ of the roll are 320mm, 400mm and 480mm; According to the orthogonal table L ₉ (3 ⁴ ), determine the virtual test plan for each test factor and the corresponding level value shown in Table 1.

表1.第7道次的虚拟试验方案Table 1. The virtual test plan of the 7th pass

试验号Test No. 第一弯曲角度β₇（°）First bending angle β ₇ (°) 第二弯曲角度γ₇（°）Second bending angle γ ₇ (°) 辊径D₇（mm）Roll diameter D ₇ (mm) 11 16.016.0 6.06.0 320320 22 16.016.0 12.012.0 400400 33 16.016.0 18.018.0 480480 44 23.023.0 6.06.0 400400 55 23.023.0 12.012.0 480480 66 23.023.0 18.018.0 320320 77 30.030.0 6.06.0 480480 88 30.030.0 12.012.0 320320 99 30.030.0 18.018.0 400400

先根据第一步设计的各道次的虚拟试验方案建立各自的有限元几何模型，由于板带材的厚度较其长度和宽度小很多，选取六面体单元，采用有限元软件进行网络划分，然后确定板带材与轧辊之间的摩擦模型：First, according to the virtual test plan of each pass designed in the first step, the respective finite element geometric models are established. Since the thickness of the plate and strip is much smaller than its length and width, the hexahedral element is selected, and the finite element software is used to divide the network, and then determine Friction model between strip and roll:

μ＝μ_d+(μ_s-μ_d)e^-cv （1）μ＝μ _d +(μ _s -μ _d )e ^-cv (1)

c—衰减指数，本实施例中，c＝0.02～0.06。c—attenuation index, in this embodiment, c=0.02-0.06.

最后对每个虚拟试验方案分别进行有限元模拟计算，得到各道次的每个虚拟试验方案的板带材应变分布。如：以第一步表1设计的第7道次的虚拟试验方案建立有限元几何模型，得到第7道次的9个虚拟实验方案的板带材的应变分布，图2为第7道次的第7#虚拟实验方案的应变分布云图。Finally, the finite element simulation calculation is carried out for each virtual test scheme separately, and the plate and strip strain distribution of each virtual test scheme for each pass is obtained. For example: the finite element geometric model is established based on the virtual test plan of the 7th pass designed in Table 1 of the first step, and the strain distribution of the plate and strip of the 9 virtual test plans of the 7th pass is obtained. Figure 2 shows the 7th pass The strain distribution cloud map of the 7# virtual experiment scheme.

第三步、模型建立The third step, model building

根据第二步各道次的每个虚拟试验方案所对应的板带材的应变分布，确定各道次的每个虚拟试验方案板带材外边缘沿其切线方向正应变值，得到各道次板带材外边缘沿其切线方向正应变绝对值的最大值：According to the strain distribution of the plate and strip corresponding to each virtual test scheme of each pass in the second step, the positive strain value of the outer edge of the plate and strip along the tangential direction of each virtual test scheme of each pass is determined, and each pass is obtained The maximum value of the absolute value of the positive strain at the outer edge of the strip along its tangential direction:

式(2)中：a_i1，a_i2，…，a_i25为i道次的回归系数；In formula (2): a _i1 , a _i2 , ..., a _i25 are the regression coefficients of pass i;

i为1,2,…,n。i is 1,2,...,n.

以i等于7为例，根据第二步第7道次的每个虚拟试验方案的板带材应变分布，确定第7道次的每个虚拟试验方案板带材外边缘沿其切线方向正应变值，得到第7道次板带材外边缘沿其切线方向正应变绝对值的最大值：Taking i equal to 7 as an example, according to the plate and strip strain distribution of each virtual test scheme of the seventh pass in the second step, determine the positive strain along the tangential direction of the outer edge of the plate and strip for each virtual test scheme of the seventh pass value, the maximum value of the absolute value of the positive strain along the tangential direction of the outer edge of the 7th pass plate and strip is obtained:

${ϵ ϵ}_{77} = = {a a}_{7171} + + {a a}_{7272} {β β}_{77} + + {a a}_{7373} {γ γ}_{77} + + {a a}_{7474} {D D.}_{77} + + {a a}_{7575} {β β}_{77}^{22} + + {a a}_{7676} {β β}_{77} {γ γ}_{77} + + {a a}_{7777} {β β}_{77} {D D.}_{77} + + {a a}_{7878} {γ γ}_{77}^{22} + + {a a}_{7979} {γ γ}_{77} {D D.}_{77} + + {a a}_{710710} {D D.}_{77}^{22}$

$+ + {a a}_{711711} {β β}_{77}^{33} + + {a a}_{712712} {β β}_{77}^{22} {γ γ}_{77} + + {a a}_{713713} {β β}_{77}^{22} {D D.}_{77} + + {a a}_{714714} {γ γ}_{77}^{22} {β β}_{77} + + {a a}_{715715} {γ γ}_{77}^{33} + + {a a}_{716716} {γ γ}_{77}^{22} {D D.}_{77} + + {a a}_{717717} {D D.}_{77}^{22} {β β}_{77} + + {a a}_{718718} {D D.}_{77}^{22} {γ γ}_{77} - - - - - - ((22 - - 11))$

$+ + {a a}_{719719} {D D.}_{77}^{33} + + {a a}_{720720} {β β}_{77}^{44} + + {a a}_{721721} {β β}_{77}^{22} {γ γ}_{77}^{22} + + {a a}_{722722} {β β}_{77}^{22} {D D.}_{77}^{22} + + {a a}_{723723} {γ γ}_{77}^{22} {D D.}_{77}^{22} + + {a a}_{724724} {D D.}_{77}^{22} {β β}_{77}^{22} + + {a a}_{725725} {D D.}_{77}^{44}$

式（2-1）中：a₇₁，a₇₂，…，a₇₂₅为7道次的回归系数；In formula (2-1): a ₇₁ , a ₇₂ , ..., a ₇₂₅ are the regression coefficients of 7 passes;

β₇为7道次板带材的第一弯曲角度；β ₇ is the first bending angle of the 7-pass strip;

γ₇为7道次板带材的第二弯曲角度；γ ₇ is the second bending angle of the 7-pass strip;

D₇为7道次轧辊工作辊径。D ₇ is the working roll diameter of the 7-pass roll.

将各道次板带材的第一弯曲角度的优化值β_i0、第二弯曲角度的优化值γ_i0和轧辊工作辊径的优化值D_i0代替式(2)中对应的第一弯曲角度β_i、第二弯曲角度γ_i和轧辊工作辊径D_i，得到各道次板带材外边缘沿其切线方向正应变绝对值的最大值中的最小值:The optimized value of the first bending angle β _i0 , the optimized value of the second bending angle γ _i0 and the optimized value D _i0 of the work roll diameter of each pass plate and strip are substituted for the corresponding first bending angle β in formula (2) _i , the second bending angle γ _i and the work roll diameter D _i of the roll, the minimum value of the maximum value of the absolute value of the positive strain along the tangential direction of the outer edge of the plate and strip in each pass is obtained:

i为1,2,…,n。i is 1,2,...,n.

以i等于7为例，即以第7道次板带材外边缘沿其切线方向正应变绝对值的最大值ε₇最小为优化目标，以第7道次板带材外边缘沿其切线方向正应变绝对值的最大值ε₇≤1%和各试验因素水平值的上下限为约束条件，确定第7道次板带材的第一弯曲角度的优化值β₇₀为25.98°、第二弯曲角度的优化值γ₇₀为17.93°和轧辊工作辊径的优化值D₇₀为348.27mm。Taking i equal to 7 as an example, that is, the maximum value of the absolute value of the positive strain ε ₇ of the outer edge of the seventh-pass plate and strip along its tangential direction is the optimization goal, and the outer edge of the seventh-pass plate and strip along its tangential direction The maximum value of the absolute value of positive strain ε ₇ ≤ 1% and the upper and lower limits of the level values of each test factor are constrained conditions, and the optimal value β ₇₀ of the first bending angle of the seventh pass plate and strip is determined to be 25.98°, and the second bending angle The optimal value of the angle γ ₇₀ is 17.93° and the optimal value D ₇₀ of the work roll diameter is 348.27 mm.

将第一弯曲角度的优化值β₇₀、第二弯曲角度的优化值γ₇₀和轧辊工作辊径的优化值D₇₀代替式(2)中对应的第一弯曲角度β₇、第二弯曲角度γ₇和轧辊工作辊径D₇，得到第7道次板带材外边缘沿其切线方向正应变绝对值的最大值中的最小值： _{Replace the corresponding first bending angle β 7} _and _second _bending angle γ ₇ and the work roll diameter D ₇ of the roll, the minimum value of the maximum value of the absolute value of the positive strain along the tangential direction of the outer edge of the plate and strip in the 7th pass is obtained:

${ϵ ϵ}_{7070} = = {a a}_{7171} + + {a a}_{7272} {β β}_{7070} + + {a a}_{7373} {γ γ}_{7070} + + {a a}_{7474} {D D.}_{7070} + + {a a}_{7575} {β β}_{7070}^{22} + + {a a}_{7676} {β β}_{7070} {γ γ}_{7070} + + {a a}_{7777} {β β}_{7070} {D D.}_{7070} + + {a a}_{7878} {γ γ}_{7070}^{22} + + {a a}_{7979} {γ γ}_{7070} {D D.}_{7070} + + {a a}_{710710} {D D.}_{7070}^{22}$

$+ + {a a}_{711711} {β β}_{7070}^{33} + + {a a}_{712712} {β β}_{7070}^{22} {γ γ}_{7070} + + {a a}_{713713} {β β}_{7070}^{22} {D D.}_{7070} + + {a a}_{714714} {γ γ}_{7070}^{22} {β β}_{7070} + + {a a}_{715715} {γ γ}_{7070}^{33} + + {a a}_{716716} {γ γ}_{7070}^{22} {D D.}_{7070} + + {a a}_{717717} {D D.}_{7070}^{22} {β β}_{7070} + + {a a}_{718718} {D D.}_{7070}^{22} {γ γ}_{7070} - - - - - - ((33 - - 11))$

$+ + {a a}_{719719} {D D.}_{7070}^{33} + + {a a}_{720720} {β β}_{7070}^{44} + + {a a}_{721721} {β β}_{7070}^{22} {γ γ}_{7070}^{22} + + {a a}_{722722} {β β}_{7070}^{22} {D D.}_{7070}^{22} + + {a a}_{723723} {γ γ}_{7070}^{22} {D D.}_{7070}^{22} + + {a a}_{724724} {D D.}_{7070}^{22} {β β}_{7070}^{22} + + {a a}_{725725} {D D.}_{7070}^{44}$

式（3-1）中：a₇₁，a₇₂，…，a₇₂₅为7道次的回归系数；In formula (3-1): a ₇₁ , a ₇₂ , ..., a ₇₂₅ are regression coefficients for 7 passes;

β₇₀为7道次板带材第一弯曲角度的优化值；β ₇₀ is the optimal value of the first bending angle of the 7-pass plate and strip;

γ₇₀为7道次板带材第二弯曲角度的优化值；γ ₇₀ is the optimal value of the second bending angle of the 7-pass sheet and strip;

D₇₀为7道次轧辊工作辊径的优化值。D ₇₀ is the optimized value of the working roll diameter of the 7-pass roll.

将归整后的优化结果中的第一弯曲角度的优化值β₇₀＝26°、第二弯曲角度的优化值γ₇₀＝18°和轧辊工作辊径的优化值D₇₀＝348mm代入式（3-1）中，得ε₇₀＝0.89%。Substituting the optimized value of the first bending angle β ₇₀ = 26°, the optimized value of the second bending angle γ ₇₀ = 18° and the optimized value of the work roll diameter D ₇₀ = 348mm in the optimized results after normalization into the formula (3 -1), get ε ₇₀ =0.89%.

同理，由式(3)可得：ε₁₀＝0.82%，ε₂₀＝0.83%，ε₃₀＝0.87%，ε₄₀＝0.95%，ε₅₀＝0.92%，ε₆₀＝0.85%，ε₈₀＝0.90%，ε₇₀＝0.89%，ε₉₀＝0.92%，ε₁₀₀＝0.96%，ε₁₁₀＝0.89%。Similarly, from formula (3), we can get: ε ₁₀ = 0.82%, ε ₂₀ = 0.83%, ε ₃₀ = 0.87%, ε ₄₀ = 0.95%, ε ₅₀ = 0.92%, ε ₆₀ = 0.85%, ε ₈₀ = 0.90%, ε ₇₀ =0.89%, ε ₉₀ =0.92%, ε ₁₀₀ =0.96%, ε ₁₁₀ =0.89%.

由于式(3)所确定的各道次板带材外边缘沿其切线方向正应变绝对值的最大值中的最小值ε_i0均在0.8～1.0%范围内，则第一步设定的道次数11得以确定。Since the minimum value ε _i0 of the maximum value of the absolute value of the positive strain along the tangential direction of the outer edge of each pass determined by formula (3) is within the range of 0.8 to 1.0%, the pass set in the first step The number 11 was determined.

由于各道次板带材外边缘沿其切线方向正应变绝对值的最大值中的最小值ε_i0的级差与各道次板带材外边缘沿其切线方向正应变绝对值的最大值中的最小值的平均值之比大于10%，则对第五步所确定的各道次板带材外边缘沿其切线方向正应变绝对值的最大值中的最小值ε_i0按其大小进行排序，详见表2。Since the difference between the minimum value ε _i0 of the maximum value of the absolute value of the positive strain along the tangential direction of the outer edge of each pass plate strip and the maximum value of the maximum value of the positive strain absolute value of the outer edge of each pass plate strip along the tangential direction If the ratio of the average value of the minimum value is greater than 10%, the minimum value ε _i0 of the maximum value of the absolute value of the positive strain along the tangential direction of the outer edge of each pass determined in the fifth step is sorted according to its size, See Table 2 for details.

表2 ε_i0（%）值的大小排序Table 2 Ranking of ε _i0 (%) values

大小排序Sort by size 11 22 33 44 55 66 77 88 99 1010 1111 道次数Number of passes 1010 44 55 99 88 77 1111 33 66 22 11 ε_i0（%）ε _i0 (%) 0.960.96 0.950.95 0.920.92 0.920.92 0.900.90 0.890.89 0.890.89 0.870.87 0.850.85 0.830.83 0.820.82

由表2知，应分别对第10道次和第1道次的每个试验因素对应的三个水平值进行调整，重复进行第一步至第五步。得到表3所示的各道次板带材外边缘沿其切线方向正应变绝对值的最大值中的最小值ε_i0。From Table 2, it is known that the three levels corresponding to each test factor in the 10th pass and the 1st pass should be adjusted respectively, and the first step to the fifth step should be repeated. The minimum value ε _i0 among the maximum values of the absolute value of the positive strain along the tangential direction of the outer edge of each pass plate strip shown in Table 3 is obtained.

表3 调整后的ε_i0（%）值Table 3 Adjusted ε _i0 (%) value

道次数Number of passes 第1No. 1 第22nd 第3No. 3 第4No. 4 第5number 5 第6number 6 第7No. 7 第8No. 8 第9No. 9 第10the 10th 第11number 11 ε_i0（%）ε _i0 (%) 0.860.86 0.880.88 0.890.89 0.960.96 0.880.88 0.880.88 0.900.90 0.920.92 0.920.92 0.890.89 0.890.89

可以看出：各道次板带材外边缘沿其切线方向正应变绝对值的最大值中的最小值ε_i0的级差与各道次板带材外边缘沿其切线方向正应变绝对值的最大值中的最小值ε_i0的平均值之比小于10%，则再次优化后的板带材冷弯成型各道次第一弯曲角度的优化值β_i0、第二弯曲角度的优化值γ_i0和轧辊工作辊径的优化值D_i0得以确定。如再次优化后的第7道次的第一弯曲角度的优化值β₇₀为26.04°、第二弯曲角度的优化值γ₇₀为18.03°和轧辊工作辊径的优化值D₇₀为347.87mm。It can be seen that the difference between the minimum value ε _i0 of the maximum value of the absolute value of the positive strain along the tangential direction of the outer edge of the plate and strip of each pass and the maximum absolute value of the positive strain of the outer edge of each pass along the tangential direction The ratio of the average value of the minimum value ε _i0 among the values is less than 10%, then the optimized value β _i0 of the first bending angle, the optimized value of the second bending angle γ _i0 and The optimal value D _i0 of the work roll diameter of the roll is determined. For example, the optimized value β ₇₀ of the first bending angle of the 7th pass after re-optimization is 26.04°, the optimized value γ ₇₀ of the second bending angle is 18.03° and the optimized value D ₇₀ of the working roll diameter of the roll is 347.87mm.

实施例2Example 2

一种确定板带材冷弯成型各道次弯曲角度的方法。该方法的具体步骤是：第一步、虚拟试验方案的设计A method for determining the bending angle of each pass of cold-bending forming of a plate and strip. The specific steps of the method are: the first step, the design of the virtual test program

根据生产经验，初步确定不对称Z型钢的冷弯成型道次数n为12，据此完成辊花图设计。本步骤以第6道次为例，选取第6道次第一弯曲角度β₆、第二弯曲角度γ₆和轧辊工作辊径D₆作为试验因素；每个试验因素各取三个水平值，即第一弯曲角度β₆值分别为16°、21°和26°，第二弯曲角度γ₆分别为6°、11°和16°，轧辊工作辊径D₆分别为320mm、380mm和440mm；按正交表L₉(3⁴)确定如表1所示的各试验因素及对应水平值的虚拟试验方案。According to the production experience, it is preliminarily determined that the number n of cold bending passes of the asymmetric Z-shaped steel is 12, and the design of the roll pattern is completed accordingly. In this step, taking the sixth pass as an example, the first bending angle β ₆ , the second bending angle γ ₆ and the working roll diameter D ₆ of the sixth pass are selected as test factors; each test factor takes three levels, That is, the values of the first bending angle _β6 are 16°, 21° and 26° respectively, the second bending angles _γ6 are 6°, 11° and 16° respectively, and the working roll diameters _D6 of the rolls are 320mm, 380mm and 440mm respectively; According to the orthogonal table L ₉ (3 ⁴ ), determine the virtual test plan for each test factor and the corresponding level value shown in Table 1.

表1.第6道次的虚拟试验方案Table 1. Virtual test plan for the sixth pass

试验号Test No. 第一弯曲角度β₆(°)First bending angle β ₆ (°) 第二弯曲角度γ₆(°)Second bending angle γ ₆ (°) 辊径D₆(mm)Roll diameter D ₆ (mm) 11 16.016.0 6.06.0 320320 22 16.016.0 12.012.0 380380 33 16.016.0 18.018.0 440440 44 21.021.0 6.06.0 380380 55 21.021.0 12.012.0 440440 66 21.021.0 18.018.0 320320 77 26.026.0 6.06.0 440440 88 26.026.0 12.012.0 320320 99 26.026.0 18.018.0 380380

先根据第一步设计的各道次的虚拟试验方案建立各自的有限元几何模型，由于板带材的厚度较其长度和宽度小很多，选取四面体单元，采用有限元软件进行网络划分，然后确定板带材与轧辊之间的摩擦模型：First, establish the respective finite element geometric models according to the virtual test plan of each pass designed in the first step. Since the thickness of the plate and strip is much smaller than its length and width, the tetrahedron element is selected, and the network is divided by finite element software, and then Determine the friction model between the strip and roll:

μ＝μ_d+(μ_s-μ_d)e^-cv （1）μ＝μ _d +(μ _s -μ _d )e ^-cv (1)

c—衰减指数，本实施例中，c＝0.03～0.07。c—attenuation index, in this embodiment, c=0.03-0.07.

第三步、模型建立The third step, model building

i为1,2,…,n。i is 1,2,...,n.

以i等于6为例，根据第二步第6道次的每个虚拟试验方案的板带材应变分布，确定第6道次的每个虚拟试验方案板带材外边缘沿其切线方向正应变值，得到第6道次板带材外边缘沿其切线方向正应变绝对值的最大值：Taking i equal to 6 as an example, according to the plate and strip strain distribution of each virtual test scheme in the sixth pass of the second step, determine the positive strain along the tangential direction of the outer edge of the plate and strip for each virtual test scheme in the sixth pass value, the maximum value of the absolute value of the positive strain along the tangential direction of the outer edge of the plate and strip in the sixth pass is obtained:

${ϵ ϵ}_{66} = = {a a}_{6161} + + {a a}_{6262} {β β}_{66} + + {a a}_{6363} {γ γ}_{66} + + {a a}_{6464} {D D.}_{66} + + {a a}_{6565} {β β}_{66}^{22} + + {a a}_{6666} {β β}_{66} {γ γ}_{66} + + {a a}_{6767} {β β}_{66} {D D.}_{66} + + {a a}_{6868} {γ γ}_{66}^{22} + + {a a}_{6969} {γ γ}_{66} {D D.}_{66} + + {a a}_{610610} {D D.}_{66}^{22}$

$+ + {a a}_{611611} {β β}_{66}^{33} + + {a a}_{612612} {β β}_{66}^{22} {γ γ}_{66} + + {a a}_{613613} {β β}_{66}^{22} {D D.}_{66} + + {a a}_{614614} {γ γ}_{66}^{22} {β β}_{66} + + {a a}_{615615} {γ γ}_{66}^{33} + + {a a}_{616616} {γ γ}_{66}^{22} {D D.}_{66} + + {a a}_{616616} {D D.}_{66}^{22} {β β}_{66} + + {a a}_{618618} {D D.}_{66}^{22} {γ γ}_{66} - - - - - - ((22 - - 11))$

$+ + {a a}_{619619} {D D.}_{66}^{33} + + {a a}_{620620} {β β}_{66}^{44} + + {a a}_{621621} {β β}_{66}^{22} {γ γ}_{66}^{22} + + {a a}_{622622} {β β}_{66}^{22} {D D.}_{66}^{22} + + {a a}_{623623} {γ γ}_{66}^{22} {D D.}_{66}^{22} + + {a a}_{624624} {D D.}_{66}^{22} {β β}_{66}^{22} + + {a a}_{625625} {D D.}_{66}^{44}$

式（2-1）中：a₆₁，a₆₂，…，a₆₂₅为6道次的回归系数；In formula (2-1): a ₆₁ , a ₆₂ , ..., a ₆₂₅ are regression coefficients for 6 passes;

β₆为6道次板带材的第一弯曲角度；β ₆ is the first bending angle of the 6-pass strip;

γ₆为6道次板带材的第二弯曲角度；γ ₆ is the second bending angle of the 6-pass strip;

D₆为6道次轧辊工作辊径。D ₆ is the working roll diameter of the 6-pass roll.

i为1,2,…,n。i is 1,2,...,n.

以i等于6为例，即以第6道次板带材外边缘沿其切线方向正应变绝对值的最大值ε₆最小为优化目标，以第6道次板带材外边缘沿其切线方向正应变绝对值的最大值ε₆≤1%和各试验因素水平值的上下限为约束条件，确定第6道次板带材的第一弯曲角度的优化值β₆₀为18.87°、第二弯曲角度的优化值γ₆₀为13.14°和轧辊工作辊径的优化值D₆₀为327.25mm；Taking i equal to 6 as an example, that is, the maximum value of the absolute value of the positive strain ε ₆ of the outer edge of the sixth pass along its tangential direction is the optimization goal, and the outer edge of the sixth pass along its tangential direction is The maximum value of the absolute value of positive strain ε ₆ ≤ 1% and the upper and lower limits of the level values of each test factor are constrained conditions, and the optimal value β ₆₀ of the first bending angle of the sixth pass plate and strip is determined to be 18.87°, and the second bending angle The optimal value of the angle γ ₆₀ is 13.14° and the optimal value D ₆₀ of the work roll diameter is 327.25mm;

将第一弯曲角度的优化值β₆₀、第二弯曲角度的优化值γ₆₀和轧辊工作辊径的优化值D₆₀代替式(2)中对应的第一弯曲角度β₆、第二弯曲角度γ₆和轧辊工作辊D₆,得到第6道次板带材外边缘沿其切线方向正应变绝对值的最大值中的最小值: _Replace _{the corresponding first bending angle β 6} _and _second bending angle γ ₆ and roll work roll D ₆ to obtain the minimum value of the maximum value of the absolute value of the positive strain along the tangential direction of the outer edge of the plate and strip in the 6th pass:

${ϵ ϵ}_{6060} = = {a a}_{6161} + + {a a}_{6262} {β β}_{6060} + + {a a}_{6363} {γ γ}_{6060} + + {a a}_{6464} {D D.}_{6060} + + {a a}_{6565} {β β}_{6060}^{22} + + {a a}_{6666} {β β}_{6060} {γ γ}_{6060} + + {a a}_{6767} {β β}_{6060} {D D.}_{6060} + + {a a}_{6868} {γ γ}_{6060}^{22} + + {a a}_{6969} {γ γ}_{6060} {D D.}_{6060} + + {a a}_{610610} {D D.}_{6060}^{22}$

$+ + {a a}_{611611} {β β}_{6060}^{33} + + {a a}_{612612} {β β}_{6060}^{22} {γ γ}_{6060} + + {a a}_{613613} {β β}_{6060}^{22} {D D.}_{6060} + + {a a}_{614614} {γ γ}_{6060}^{22} {β β}_{6060} + + {a a}_{615615} {γ γ}_{6060}^{33} + + {a a}_{616616} {γ γ}_{6060}^{22} {D D.}_{6060} + + {a a}_{617617} {D D.}_{6060}^{22} {β β}_{6060} + + {a a}_{618618} {D D.}_{6060}^{22} {γ γ}_{6060} - - - - - - ((33 - - 11))$

$+ + {a a}_{619619} {D D.}_{6060}^{33} + + {a a}_{620620} {β β}_{6060}^{44} + + {a a}_{621621} {β β}_{6060}^{22} {γ γ}_{6060}^{22} + + {a a}_{622622} {β β}_{6060}^{22} {D D.}_{6060}^{22} + + {a a}_{623623} {γ γ}_{6060}^{22} {D D.}_{6060}^{22} + + {a a}_{624624} {D D.}_{6060}^{22} {β β}_{6060}^{22} + + {a a}_{625625} {D D.}_{6060}^{44}$

式（3-1）中：a₆₁，a₆₂，…，a₆₂₅为6道次的回归系数；In formula (3-1): a ₆₁ , a ₆₂ , ..., a ₆₂₅ are regression coefficients for 6 passes;

β₆₀为6道次板带材第一弯曲角度的优化值；β ₆₀ is the optimal value of the first bending angle of the 6-pass plate and strip;

γ₆₀为6道次板带材第二弯曲角度的优化值；γ ₆₀ is the optimal value of the second bending angle of the 6-pass sheet and strip;

D₆₀为6道次轧辊工作辊径的优化值。D ₆₀ is the optimized value of the working roll diameter of the 6-pass roll.

将归整后的优化结果中的第一弯曲角度的优化值β₆₀＝19°，第二弯曲角度的优化值γ₆₀＝13°，轧辊工作辊径的优化值D₆₀＝327mm代入式（3-1）中，得ε₆₀＝0.86%Substituting the optimized value of the first bending angle β ₆₀ = 19°, the optimized value of the second bending angle γ ₆₀ = 13°, and the optimized value of the work roll diameter D ₆₀ = 327mm into the formula (3 -1), get ε ₆₀ ＝0.86%

同理，由式(3)可得：ε₁₀＝0.76%，ε₂₀＝0.80%，ε₃₀＝0.86%，ε₄₀＝0.90%，ε₅₀＝0.84%，ε₇₀＝0.89%，ε₈₀＝0.90%，ε₉₀＝0.88%，ε₁₀₀＝0.84%，ε₁₁₀＝0.83%，ε₁₂₀＝0.81%。Similarly, from formula (3), we can get: ε ₁₀ = 0.76%, ε ₂₀ = 0.80%, ε ₃₀ = 0.86%, ε ₄₀ = 0.90%, ε ₅₀ = 0.84%, ε ₇₀ = 0.89%, ε ₈₀ = 0.90%, ε ₉₀ =0.88%, ε ₁₀₀ =0.84%, ε ₁₁₀ =0.83%, ε ₁₂₀ =0.81%.

由于式(3)所确定的各道次中的某道次板带材外边缘沿其切线方向正应变绝对值的最大值中的最小值ε_i0小于0.8%，则将第一步设定的道次数12减1，即第二次设定的道次数为11。Since the minimum value ε _i0 of the maximum value of the absolute value of the positive strain along the tangential direction of the outer edge of a certain pass in each pass determined by formula (3) is less than 0.8%, the value set in the first step The number of passes is 12 minus 1, that is, the number of passes set for the second time is 11.

然后重复第一步至第四步，得到各道次板带材外边缘沿其切线方向正应变绝对值的最大值中的最小值：ε₁₀ ^′＝0.82%，ε₂₀ ^′＝0.85%，ε₃₀ ^′＝0.86%，ε₄₀ ^′＝0.91%，ε₅₀ ^′＝0.87%，ε₆₀ ^′＝0.85%，ε₇₀ ^′＝0.88%，ε₈₀ ^′＝0.92%，ε₉₀ ^′＝0.94%，ε₁₀₀ ^′＝0.89%和ε₁₁₀ ^′＝0.88%。Then repeat the first step to the fourth step to obtain the minimum value of the maximum value of the absolute value of the positive strain along the tangential direction of the outer edge of each pass plate strip: ε ₁₀ ^′ = 0.82%, ε ₂₀ ^′ = 0.85%, ε ₃₀ ^′ = 0.86%, ε ₄₀ ^′ = 0.91%, ε ₅₀ ^′ = 0.87%, ε ₆₀ ^′ = 0.85%, ε ₇₀ ^′ = 0.88%, ε ₈₀ ^′ = 0.92%, ε ₉₀ ^′ = 0.94%, ε ₁₀₀ ^′ = 0.89% and ε ₁₁₀ ^′ = 0.88%.

可以看出：再次确定的各道次板带材外边缘沿其切线方向正应变绝对值的最大值中的最小值均在0.8～1.0%范围内，则再次设定的道次数11得以确定。It can be seen that the minimum value of the maximum value of the absolute value of the positive strain along the tangential direction of the outer edge of the plate and strip determined again for each pass is within the range of 0.8-1.0%, and the re-set number of passes 11 is determined.

由于各道次板带材外边缘沿其切线方向正应变绝对值的最大值中的最小值ε_i0的级差与各道次板带材外边缘沿其切线方向正应变绝对值的最大值中的最小值ε_i0的平均值之比大于10%，则对第五步所确定的各道次板带材外边缘沿其切线方向正应变绝对值的最大值中的最小值ε_i0按其大小进行排序，详见表2。Since the difference between the minimum value ε _i0 of the maximum value of the absolute value of the positive strain along the tangential direction of the outer edge of each pass plate strip and the maximum value of the maximum value of the positive strain absolute value of the outer edge of each pass plate strip along the tangential direction If the ratio of the average value of the minimum value ε _i0 is greater than 10%, the minimum value ε _i0 of the maximum value of the absolute value of the positive strain along the tangential direction of the outer edge of each pass determined in the fifth step shall be determined according to its size. For sorting, see Table 2 for details.

表2 ε_i0（%）值的大小排序Table 2 Ranking of ε _i0 (%) values

大小排序Sort by size 11 22 33 44 55 66 77 88 99 1010 1111 道次数Number of passes 99 88 44 1010 1111 77 55 66 33 22 11 ε_i0（%）ε _i0 (%) 0.940.94 0.920.92 0.910.91 0.890.89 0.880.88 0.880.88 0.870.87 0.870.87 0.860.86 0.850.85 0.820.82

由表2知，应分别对第9道次和第1道次的每个试验因素对应的三个水平值进行调整，重复进行第一步至第五步。得到表3所示的各道次板带材外边缘沿其切线方向正应变绝对值的最大值中的最小值ε_i0。From Table 2, we should adjust the three level values corresponding to each test factor in the 9th pass and the 1st pass respectively, and repeat the first step to the fifth step. The minimum value ε _i0 among the maximum values of the absolute value of the positive strain along the tangential direction of the outer edge of each pass plate strip shown in Table 3 is obtained.

表3 调整后的ε_i0（%）值Table 3 Adjusted ε _i0 (%) value

道次数Number of passes 第1No. 1 第22nd 第3No. 3 第4No. 4 第5number 5 第6number 6 第7No. 7 第8No. 8 第9No. 9 第10the 10th 第11number 11 ε_i0（%）ε _i0 (%) 0.850.85 0.870.87 0.890.89 0.920.92 0.870.87 0.860.86 0.920.92 0.900.90 0.920.92 0.870.87 0.880.88

可以看出：各道次板带材外边缘沿其切线方向正应变绝对值的最大值中的最小值ε_i0的级差与各道次板带材外边缘沿其切线方向正应变绝对值的最大值中的最小值ε_i0的平均值之比小于10%，则再次优化后的板带材冷弯成型各道次第一弯曲角度的优化值β_i0、第二弯曲角度的优化值γ_i0和轧辊工作辊径的优化值D_i0得以确定。如再次优化后的第6道次的第一弯曲角度的优化值β₆₀为19.24°、第二弯曲角度的优化值γ₆₀为13.32°和轧辊工作辊径的优化值D₆₀为326.87mm。It can be seen that the difference between the minimum value ε _i0 of the maximum value of the absolute value of the positive strain along the tangential direction of the outer edge of the plate and strip of each pass and the maximum absolute value of the positive strain of the outer edge of each pass along the tangential direction The ratio of the average value of the minimum value ε _i0 among the values is less than 10%, then the optimized value β _i0 of the first bending angle, the optimized value of the second bending angle γ _i0 and The optimal value D _i0 of the work roll diameter of the roll is determined. For example, the optimized value β ₆₀ of the first bending angle in the sixth pass after re-optimization is 19.24°, the optimized value γ ₆₀ of the second bending angle is 13.32° and the optimized value D ₆₀ of the working roll diameter of the roll is 326.87mm.

实施例3Example 3

根据形状因子函数，设定不对称Z型钢的冷弯成型道次数n为10，据此完成辊花图设计。选取各道次板带材的弯曲角度和轧辊工作辊径作为试验因素，预选各试验因素的水平值，本步骤以第3道次为例，选取第一弯曲角度β₃和轧辊工作辊径D₃为试验因素；每个试验因素各取三个水平值，即第一弯曲角度β₃分别为16°、22°和28°，轧辊工作辊径D₃分别为400mm、450mm和500mm；按正交表L₉(3⁴)确定如表1所示的各试验因素及对应水平值的虚拟试验方案。According to the shape factor function, the number n of cold bending passes of the asymmetric Z-shaped steel is set to 10, and the design of the roll pattern is completed accordingly. Select the bending angle of each pass plate strip and the diameter of the work roll of the roll as the test factors, and pre-select the level value of each test factor. This step takes the 3rd pass as an example, and selects the first bending angle β ₃ and the work roll diameter of the roll D ₃ is the test factor; each test factor takes three horizontal values, that is, the first bending angle _β3 is 16°, 22° and 28° respectively, and the work roll diameter _D3 of the roll is 400mm, 450mm and 500mm respectively; Submit form L ₉ (3 ⁴ ) to determine the virtual test plan for each test factor and corresponding level value shown in Table 1.

表1.第3道次的虚拟试验方案Table 1. Virtual test plan for the third pass

试验号Test No. 第一弯曲角度β₃（°）First bending angle β ₃ (°) 辊径D₃（mm）Roll diameter D ₃ (mm) 11 16.016.0 400400 22 16.016.0 450450 33 16.016.0 500500 44 22.022.0 400400 55 22.022.0 450450 66 22.022.0 500500 77 28.028.0 400400 88 28.028.0 450450 99 28.028.0 500500

先根据第一步设计的各道次的虚拟试验方案建立各自的有限元几何模型，由于板带材的厚度较其长度和宽度小很多，选取壳单元，采用有限元软件进行网络划分，然后确定板带材与轧辊之间的摩擦模型：First, establish the respective finite element geometric models according to the virtual test plan of each pass designed in the first step. Since the thickness of the plate and strip is much smaller than its length and width, the shell element is selected, and the finite element software is used to divide the network, and then determine Friction model between strip and roll:

μ＝μ_d+(μ_s-μ_d)e^-cv （1）μ＝μ _d +(μ _s -μ _d )e ^-cv (1)

c—衰减指数，本实施例中，c＝0.04～0.08。c—attenuation index, in this embodiment, c=0.04～0.08.

第三步、模型建立The third step, model building

根据第二步各道次的每个虚拟试验方案所的板带材应变分布，确定各道次的每个虚拟试验方案板带材外边缘沿其切线方向正应变值，得到各道次板带材外边缘沿其切线方向正应变绝对值的最大值：According to the strain distribution of the plate and strip in each virtual test scheme of each pass in the second step, the positive strain value of the outer edge of the plate and strip along the tangential direction of each virtual test scheme of each pass is determined, and the plate and strip of each pass are obtained The maximum value of the absolute value of the positive strain along the tangential direction of the outer edge of the material:

$\begin{matrix} {ϵ ϵ}_{i i} = = {a a}_{i i 11} + + {a a}_{i i 22} {β β}_{i i} + + {a a}_{i i 33} {D D.}_{i i} + + {a a}_{i i 44} {β β}_{i i}^{22} + + {a a}_{i i 55} {β β}_{i i} {D D.}_{i i} + + {a a}_{i i 66} {D D.}_{i i}^{22} + + {a a}_{i i 77} {β β}_{i i}^{33} + + {a a}_{i i 88} {β β}_{i i}^{22} {D D.}_{i i} \\ + + {a a}_{i i 99} {D D.}_{i i}^{22} {β β}_{i i} + + {a a}_{i i 1010} {D D.}_{i i}^{33} + + {a a}_{i i 1111} {β β}_{i i}^{44} + + {a a}_{i i 1212} {β β}_{i i}^{22} {D D.}_{i i}^{22} + + {a a}_{i i 1313} {D D.}_{i i}^{22} {β β}_{i i}^{22} + + {a a}_{i i 1414} {D D.}_{i i}^{44} \end{matrix} - - - - - - ((22))$

式（2）中：a_i1，a_i2，…，a_i14为i道次的回归系数In formula (2): a _i1 , a _i2 ,..., a _i14 are the regression coefficients of pass i

i为1,2,…,n。i is 1,2,...,n.

以i等于3为例，根据第二步第3道次的每个虚拟试验方案的板带材应变分布，确定第3道次的每个虚拟试验方案板带材外边缘沿其切线方向正应变值，得到第3道次板带材外边缘沿其切线方向正应变绝对值的最大值：Taking i equal to 3 as an example, according to the plate and strip strain distribution of each virtual test scheme in the third pass of the second step, determine the positive strain along the tangential direction of the outer edge of the plate and strip for each virtual test scheme in the third pass value, the maximum value of the absolute value of the positive strain along the tangential direction of the outer edge of the plate and strip in the third pass is obtained:

$\begin{matrix} {ϵ ϵ}_{33} = = {a a}_{3131} + + {a a}_{3232} {β β}_{33} + + {a a}_{3333} {D D.}_{33} + + {a a}_{3434} {β β}_{33}^{22} + + {a a}_{3535} {β β}_{33} {D D.}_{33} + + {a a}_{3636} {D D.}_{33}^{22} + + {a a}_{3737} {β β}_{33}^{33} + + {a a}_{3838} {β β}_{33}^{22} {D D.}_{33} \\ + + {a a}_{3939} {D D.}_{33}^{22} {β β}_{33} + + {a a}_{310310} {D D.}_{33}^{33} + + {a a}_{311311} {β β}_{33}^{44} + + {a a}_{312312} {β β}_{33}^{22} {D D.}_{33}^{22} + + {a a}_{313313} {D D.}_{33}^{22} {β β}_{33}^{22} + + {a a}_{314314} {D D.}_{33}^{44} \end{matrix} - - - - - - ((22 - - 11))$

式（2-1）中：a₃₁，a₃₂，…，a₃₁₄为3道次的回归系数；In formula (2-1): a ₃₁ , a ₃₂ , ..., a ₃₁₄ are the regression coefficients of 3 passes;

β₃为3道次板带材第一弯曲角度；β ₃ is the first bending angle of the 3-pass plate strip;

D₃为3道次轧辊工作辊径。D ₃ is the working roll diameter of the 3-pass roll.

以各道次板带材外边缘沿其切线方向正应变绝对值的最大值ε_i最小为优化目标，以各道次板带材外边缘沿其切线方向正应变绝对值的最大值ε_i≤1%和各试验因素水平值的上下限为约束条件，确定各道次板带材的第一弯曲角度的优化值β_i0和轧辊工作辊径的优化值D_i0。Taking the maximum value of the absolute value of positive strain ε _i of the outer edge of each pass along the tangential direction as the optimization goal, and the maximum value of the absolute value of the positive strain of the outer edge of each pass along the tangential direction of the plate and strip ε _i ≤ 1% and the upper and lower limits of each test factor level value are constrained conditions, and the optimal value β _i0 of the first bending angle of each pass plate and strip and the optimized value D _i0 of the work roll diameter of the roll are determined.

将各道次板带材的第一弯曲角度的优化值β_i0和轧辊工作辊径的优化值D_i0代替式(2)中对应的第一弯曲角度β_i和轧辊工作辊径D_i，得到各道次板带材外边缘沿其切线方向正应变绝对值的最大值中的最小值:The optimized value of the first bending angle β _i0 and the optimized value of the _{working roll diameter D i0 of the plate and strip in each pass are substituted for the corresponding first bending angle β i} _and the working roll diameter D _i in formula (2), to obtain The minimum value of the maximum value of the absolute value of positive strain along the tangential direction of the outer edge of each pass plate strip:

$\begin{matrix} {ϵ ϵ}_{i i 00} = = {a a}_{i i 11} + + {a a}_{i i 22} {β β}_{i i 00} + + {a a}_{i i 33} {D D.}_{i i 00} + + {a a}_{i i 44} {β β}_{i i 00}^{22} + + {a a}_{i i 55} {β β}_{i i 00} {D D.}_{i i 00} + + {a a}_{i i 66} {D D.}_{i i 00}^{22} + + {a a}_{i i 77} {β β}_{i i 00}^{33} + + {a a}_{i i 88} {β β}_{i i 00}^{22} {D D.}_{i i 00} \\ + + {a a}_{i i 99} {D D.}_{i i 00}^{22} {β β}_{i i 00} + + {a a}_{i i 1010} {D D.}_{i i 00}^{33} + + {a a}_{i i 1111} {β β}_{i i 00}^{44} + + {a a}_{i i 1212} {β β}_{i i 00}^{22} {D D.}_{i i 00}^{22} + + {a a}_{i i 1313} {D D.}_{i i 00}^{22} {β β}_{i i 00}^{22} + + {a a}_{i i 1414} {D D.}_{i i 00}^{44} \end{matrix} - - - - - - ((33))$

式（3）中：a_i1，a_i2，…，a_i14为i道次的回归系数；In formula (3): a _i1 , a _i2 , ..., a _i14 are the regression coefficients of pass i;

i为1,2,…,n。i is 1,2,...,n.

以i等于3为例，即以第3道次板带材外边缘沿其切线方向正应变绝对值的最大值ε₃最小为优化目标，以第3道次板带材外边缘沿其切线方向正应变绝对值的最大值ε₃≤1%和各试验因素水平值的上下限为约束条件，确定第3道次板带材的第一弯曲角度的优化值β₃₀为21.87°和轧辊工作辊径的优化值D₃₀为324.15mm。Taking i equal to 3 as an example, that is, the maximum value of the absolute value of the positive strain ε ₃ of the outer edge of the third-pass plate and strip along its tangential direction is the optimization goal, and the outer edge of the third-pass plate and strip along its tangential direction The maximum value of the absolute value of the positive strain ε ₃ ≤ 1% and the upper and lower limits of the level values of each test factor are constrained conditions, and the optimal value β ₃₀ of the first bending angle of the third pass plate and strip is determined to be 21.87° and the roll work roll The optimal value D ₃₀ of diameter is 324.15mm.

将第一弯曲角度的优化值β₃₀和轧辊工作辊径的优化值D₃₀代替式(2)中对应的第一弯曲角度β₃和轧辊工作辊D₃，得到本道次板带材外边缘沿其切线方向正应变绝对值的最大值中的最小值：The optimized value of the first bending angle β ₃₀ and the optimized value of the work roll diameter D ₃₀ of the roll are substituted for the corresponding first bending angle β ₃ and the work roll D ₃ in the formula (2), and the outer edge edge of the strip in this pass is obtained The minimum value of the maximum value of the absolute value of the positive strain in the tangential direction:

$\begin{matrix} {ϵ ϵ}_{3030} = = {a a}_{3131} + + {a a}_{3232} {β β}_{3030} + + {a a}_{3333} {D D.}_{3030} + + {a a}_{3434} {β β}_{3030}^{22} + + {a a}_{3535} {β β}_{3030} {D D.}_{3030} + + {a a}_{3636} {D D.}_{3030}^{22} + + {a a}_{3737} {β β}_{3030}^{33} + + {a a}_{3838} {β β}_{3030}^{22} {D D.}_{3030} \\ + + {a a}_{3939} {D D.}_{3030}^{22} {β β}_{3030} + + {a a}_{310310} {D D.}_{3030}^{33} + + {a a}_{311311} {β β}_{3030}^{44} + + {a a}_{312312} {β β}_{3030}^{22} {D D.}_{3030}^{22} + + {a a}_{313313} {D D.}_{3030}^{22} {β β}_{3030}^{22} + + {a a}_{314314} {D D.}_{3030}^{44} \end{matrix} - - - - - - ((33 - - 11))$

式（3-1）中：a₃₁，a₃₂，…，a₃₁₄为3道次的回归系数；In formula (3-1): a ₃₁ , a ₃₂ , ..., a ₃₁₄ are the regression coefficients of 3 passes;

β₃₀为3道次板带材第一弯曲角度的优化值；β ₃₀ is the optimized value of the first bending angle of the 3-pass plate strip;

D₃₀为3道次轧辊工作辊径的优化值；D ₃₀ is the optimized value of the work roll diameter of the 3-pass roll;

将归整后的优化结果中的第一弯曲角度的优化值β₃₀＝22°和轧辊工作辊径的优化值D₃₀＝324mm代入式（3-1）中，得ε₃₀＝0.94%。Substituting the optimized value of the first bending angle β ₃₀ =22° and the optimized value of the work roll diameter D ₃₀ =324mm in the optimized results after normalization into the formula (3-1), ε ₃₀ =0.94%.

同理，由式(3)可得：ε₁₀＝0.89%，ε₂₀＝0.92%，ε₄₀＝0.93%，ε₅₀＝0.89%，ε₆₀＝0.96%，ε₇₀＞1%。Similarly, from formula (3), we can get: ε ₁₀ =0.89%, ε ₂₀ =0.92%, ε ₄₀ =0.93%, ε ₅₀ =0.89%, ε ₆₀ =0.96%, ε ₇₀ >1%.

ε₇₀＞1%说明由式(3)所确定的第7道次道次板带材外边缘沿其切线方向正应变绝对值的最大值中的最小值在约束范围内不存在，则将第一步设定的道次数10加1，即第二次设定的道次数为11。ε ₇₀ >1% means that the minimum value of the maximum value of the absolute value of positive strain along the tangential direction of the outer edge of the 7th pass plate strip determined by formula (3) does not exist within the constraint range, then the 7th pass The number of passes set in one step is 10 plus 1, that is, the number of passes set for the second time is 11.

然后重复第一步至第四步，得到再次优化后的各道次板带材外边缘沿其切线方向正应变绝对值的最大值中的最小值：ε₁₀ ^′＝0.83%，ε₂₀ ^′＝0.86%，ε₃₀ ^′＝0.87%，ε₄₀ ^′＝0.92%，ε₅₀ ^′＝0.89%，ε₆₀ ^′＝0.86%，ε₇₀ ^′＝0.87%，ε₈₀ ^′＝0.95%，ε₉₀ ^′＝0.89%，ε₁₀₀ ^′＝0.87%和ε₁₁₀ ^′＝0.84%。Then repeat the first step to the fourth step to obtain the minimum value of the maximum value of the absolute value of the positive strain along the tangential direction of the outer edge of each pass after optimization: ε ₁₀ ^′ = 0.83%, ε ₂₀ ^′ = 0.86%, ε ₃₀ ^′ = 0.87%, ε ₄₀ ^′ = 0.92%, ε ₅₀ ^′ = 0.89%, ε ₆₀ ^′ = 0.86%, ε ₇₀ ^′ = 0.87%, ε ₈₀ ^′ = 0.95%, ε ₉₀ ^′ = 0.89 %, ε ₁₀₀ ^′ = 0.87% and ε ₁₁₀ ^′ = 0.84%.

表2 ε_i0（%）值的大小排序Table 2 Ranking of ε _i0 (%) values

大小排序Sort by size 11 22 33 44 55 66 77 88 99 1010 1111 道次数Number of passes 88 44 55 99 1010 33 77 66 22 1111 11 ε_i0（%）ε _i0 (%) 0.950.95 0.920.92 0.890.89 0.890.89 0.870.87 0.870.87 0.870.87 0.860.86 0.860.86 0.840.84 0.830.83

由表2知，应分别对第8道次和第1道次的每个试验因素对应的三个水平值进行调整，重复进行第一步至第五步。得到表3所示的各道次板带材外边缘沿其切线方向正应变绝对值的最大值中的最小值ε_i0。From Table 2, we should adjust the three level values corresponding to each test factor in the 8th pass and the 1st pass respectively, and repeat the first step to the fifth step. The minimum value ε _i0 among the maximum values of the absolute value of the positive strain along the tangential direction of the outer edge of each pass plate strip shown in Table 3 is obtained.

表3 调整后的ε_i0（%）值Table 3 Adjusted ε _i0 (%) value

道次数Number of passes 第1No. 1 第22nd 第3No. 3 第4No. 4 第5number 5 第6number 6 第7No. 7 第8No. 8 第9No. 9 第10the 10th 第11number 11 ε_i0（%）ε _i0 (%) 0.860.86 0.860.86 0.870.87 0.910.91 0.900.90 0.870.87 0.880.88 0.920.92 0.890.89 0.860.86 0.890.89

可以看出：各道次板带材外边缘沿其切线方向正应变绝对值的最大值中的最小值ε_i0的级差与各道次板带材外边缘沿其切线方向正应变绝对值的最大值中的最小值ε_i0的平均值之比小于10%，则再次优化后的板带材冷弯成型各道次第一弯曲角度的优化值β_i0和轧辊工作辊径的优化值D_i0得以确定。如再次优化后的第3道次的第一弯曲角度的优化值β₆₀为21.75°和轧辊工作辊径的优化值D₆₀为324.38mm。It can be seen that the difference between the minimum value ε _i0 of the maximum value of the absolute value of the positive strain along the tangential direction of the outer edge of the plate and strip of each pass and the maximum absolute value of the positive strain of the outer edge of each pass along the tangential direction The ratio of the average value of the minimum value ε _i0 in the values is less than 10%, then the optimized value β _i0 of the first bending angle of each pass of cold bending forming of the plate and strip and the optimized value D _i0 of the work roll diameter of the roll can be obtained Sure. For example, the optimized value β ₆₀ of the first bending angle of the third pass after re-optimization is 21.75° and the optimized value D ₆₀ of the working roll diameter of the roll is 324.38mm.

本具体实施方式与现有技术相比具有如下积极效果：Compared with the prior art, this specific embodiment has the following positive effects:

本具体实施方式涉及的各道次板带材弯曲角度的分配方法考虑了轧辊工作辊径、板带材材质、轧件/轧辊接触状态等因素对冷弯各道次板带材弯曲角度确定的影响，适合机架间距不相等时的情况，且方法科学，不必过分依赖实际经验。The distribution method of the bending angle of each pass of the plate and strip involved in this specific embodiment takes into account factors such as the diameter of the work roll of the roll, the material of the plate and strip, and the contact state of the rolled piece/roller to determine the bending angle of the plate and strip of each pass of cold bending It is suitable for the situation when the rack spacing is not equal, and the method is scientific, and it is not necessary to rely too much on actual experience.

本具体实施方式以各道次板带材外边缘沿其切线方向正应变绝对值的最大值最小为优化目标，以板带材外边缘沿其切线方向正应变绝对值的最大值小于或等于1%为约束条件，因此板带材成型时不会产生翘曲及边浪缺陷，并能充分发挥机组设备的生产潜力。In this specific embodiment, the maximum value of the absolute value of the absolute value of the positive strain along the tangential direction of the outer edge of the plate and strip in each pass is the minimum as the optimization goal, and the maximum value of the absolute value of the positive strain along the tangential direction of the outer edge of the plate and strip is less than or equal to 1 % is the constraint condition, so there will be no warping and edge wave defects when the plate and strip are formed, and the production potential of the unit equipment can be fully utilized.

因此，本具体实施方式具有适于机架间距不相等、能充分发挥冷弯机组设备能力、能避免板带材翘曲和能克服板带材边部浪形缺陷的特点。Therefore, this specific embodiment has the characteristics of being suitable for unequal frame spacing, fully exerting the equipment capacity of the cold bending unit, avoiding warping of the plate and strip, and being able to overcome the wave-shaped defect of the edge of the plate and strip.

Claims

1. A method for determining the bending angles of each pass of plate and strip cold-formed forming, characterized in that the specific steps of the method are:

The first step, the design of the virtual test plan

First, according to the shape factor function or production experience, set the number of passes n of cold-bending forming, design the roll pattern, and then select the two bending angles of each pass of cold-bending forming of the plate and strip and the diameter of the work roll of the roll as the experimental factors. Or select any one of the two bending angles and the work roll diameter of the plate and strip cold-formed each pass as the test factor; then pre-select the level value of each test factor, design the test factor and the corresponding level value Virtual trial protocol;

The second step, finite element simulation calculation

First, establish the respective finite element geometric models according to the virtual test plan of each pass designed in the first step, then select the unit, use the finite element software to divide the network, and then determine the friction model between the strip and the roll:

μ＝μ _d +(μ _s -μ _d )e ^-cv (1)

In the formula (1): v—the relative sliding speed between the strip and the roll, m/s;

u _s —coefficient of static friction, u _s =0.2;

u _d —coefficient of dynamic friction, u _d =0.1;

c—attenuation index, c=0.02～0.08;

Finally, the finite element simulation calculation is carried out for each virtual test plan separately, and the plate and strip strain distribution of each virtual test plan for each pass is obtained;

The third step, model building

According to the plate and strip strain distribution of each virtual test scheme of each pass in the second step, determine the positive strain value of the outer edge of each virtual test scheme of each pass along the tangential direction of the plate and strip, and obtain the plate and strip of each pass The maximum value of the absolute value of the positive strain of the outer edge along its tangent direction:

{ϵ ϵ}_{i i} = = {a a}_{i i 11} + + {a a}_{i i 22} {β β}_{i i} + + {a a}_{i i 33} {γ γ}_{i i} + + {a a}_{i i 44} {D D.}_{i i} + + {a a}_{i i 55} {β β}_{i i}^{22} + + {a a}_{i i 66} {β β}_{i i} {γ γ}_{i i} + + {a a}_{i i 77} {β β}_{i i} {D D.}_{i i} + + {a a}_{i i 88} {γ γ}_{i i}^{22} + + {a a}_{i i 99} {γ γ}_{i i} {D D.}_{i i} + + {a a}_{i i 1010} {D D.}_{i i}^{22}

+ + {a a}_{i i 1111} {β β}_{i i}^{33} + + {a a}_{i i 1212} {β β}_{i i}^{22} {γ γ}_{i i} + + {a a}_{i i 1313} {β β}_{i i}^{22} {D D.}_{i i} + + {a a}_{i i 1414} {γ γ}_{i i}^{22} {β β}_{i i} + + {a a}_{i i 1515} {γ γ}_{i i}^{33} + + {a a}_{i i 1616} {γ γ}_{i i}^{22} {D D.}_{i i} + + {a a}_{i i 1717} {D D.}_{i i}^{22} {β β}_{i i} + + {a a}_{i i 1818} {D D.}_{i i}^{22} {γ γ}_{i i} - - - - - - ((22))

+ + {a a}_{i i 1919} {D D.}_{i i}^{33} + + {a a}_{i i 2020} {β β}_{i i}^{44} + + {a a}_{i i 21 twenty one} {β β}_{i i}^{22} {γ γ}_{i i}^{22} + + {a a}_{i i 22 twenty two} {β β}_{i i}^{22} {D D.}_{i i}^{22} + + {a a}_{i i 23 twenty three} {γ γ}_{i i}^{22} {D D.}_{i i}^{22} + + {a a}_{i i 24 twenty four} {D D.}_{i i}^{22} {β β}_{i i}^{22} + + {a a}_{i i 2525} {D D.}_{i i}^{44}

In formula (2): a _i1 , a _i2 , ..., a _i25 are the regression coefficients of pass i;

β _i is the first bending angle of the i-pass strip;

γ _i is the second bending angle of the i-pass plate and strip;

At least one bending angle among β _i and γ _i is a test factor;

D _i is the working roll diameter of the i pass roll;

i is 1,2,...,n;

The fourth step, the minimum value of the maximum value of the absolute value of positive strain

Taking the maximum value of the absolute value of positive strain ε _i of the outer edge of each pass along the tangential direction as the optimization goal, and the maximum value of the absolute value of the positive strain of the outer edge of each pass along the tangential direction of the plate and strip ε _i ≤ 1% and the upper and lower limits of each test factor level value are constrained conditions, and the optimal value of the first bending angle β _i0 , the second bending angle γ _i0 and the optimal value of the work roll diameter of each pass plate and strip are determined D _i0 ;

The optimized value of the first bending angle β _i0 , the optimized value of the second bending angle γ _i0 and the optimized value D _i0 of the work roll diameter of each pass plate and strip are substituted for the corresponding first bending angle β in formula (2) _i , the second bending angle γ _i and the work roll diameter D _i of the roll, the minimum value of the maximum value of the absolute value of the positive strain along the tangential direction of the outer edge of the plate and strip in each pass is obtained:

{ϵ ϵ}_{i i 00} = = {a a}_{i i 11} + + {a a}_{i i 22} {β β}_{i i 00} + + {a a}_{i i 33} {γ γ}_{i i 00} + + {a a}_{i i 44} {D D.}_{i i 00} + + {a a}_{i i 55} {β β}_{i i 00}^{22} + + {a a}_{i i 66} {β β}_{i i 00} {γ γ}_{i i 00} + + {a a}_{i i 77} {β β}_{i i 00} {D D.}_{i i 00} + + {a a}_{i i 88} {γ γ}_{i i 00}^{22} + + {a a}_{i i 99} {γ γ}_{i i 00} {D D.}_{i i 00} + + {a a}_{i i 1010} {D D.}_{i i 00}^{22}

+ + {a a}_{i i 1111} {β β}_{i i 00}^{33} + + {a a}_{i i 1212} {β β}_{i i 00}^{22} {γ γ}_{i i 00} + + {a a}_{i i 1313} {β β}_{i i 00}^{22} {D D.}_{i i 00} + + {a a}_{i i 1414} {γ γ}_{i i 00}^{22} {β β}_{i i 00} + + {a a}_{i i 1515} {γ γ}_{i i 00}^{33} + + {a a}_{i i 1616} {γ γ}_{i i 00}^{22} {D D.}_{i i 00} + + {a a}_{i i 1717} {D D.}_{i i 00}^{22} {β β}_{i i 00} + + {a a}_{i i 1818} {D D.}_{i i 00}^{22} {γ γ}_{i i 00} - - - - - - ((33))

+ + {a a}_{i i 1919} {D D.}_{i i 00}^{33} + + {a a}_{i i 2020} {β β}_{i i 00}^{44} + + {a a}_{i i 21 twenty one} {β β}_{i i 00}^{22} {γ γ}_{i i 00}^{22} + + {a a}_{i i 22 twenty two} {β β}_{i i 00}^{22} {D D.}_{i i 00}^{22} + + {a a}_{i i 23 twenty three} {γ γ}_{i i 00}^{22} {D D.}_{i i 00}^{22} + + {a a}_{i i 24 twenty four} {D D.}_{i i 00}^{22} {β β}_{i i 00}^{22} + + {a a}_{i i 2525} {D D.}_{i i 00}^{44}

In formula (3): a _i1 , a _i2 , ..., a _i25 are the regression coefficients of pass i;

β _i0 is the optimized value of the first bending angle of the plate and strip for the i pass;

γ _i0 is the optimized value of the second bending angle of the plate and strip for the i pass;

The optimal value of at least one bending angle among β _i0 and γ _i0 is a test factor;

D _i0 is the optimized value of the working roll diameter of the i-pass roll;

i is 1,2,...,n;

The fifth step, the determination of the number of cold bends

The first sub-step, if the minimum value ε _i0 of the maximum value of the absolute value of positive strain along the tangential direction of the outer edge of each pass plate strip determined by formula (3) is within the range of 0.8 to 1.0%, then the first The number of passes n set by the step is determined;

In the second sub-step, if the minimum value ε _i0 of the maximum value of the absolute value of positive strain along the tangential direction of the outer edge of a certain pass in each pass determined by formula (3) is less than 0.8%, then the pass Subtract 1 from the number of passes n set in one step, and then repeat the first step to the fourth step until it meets the fifth step and the first sub-step;

The third sub-step, if the minimum value ε _i0 of the maximum value of the absolute value of the positive strain of the outer edge of the strip along the tangential direction of each pass in each pass determined by formula (3) does not exist, then the first Add 1 to the number of passes n set in the first step, and then repeat the first step to the fourth step until it meets the fifth step and the first sub-step;

The sixth step, the determination of the bending angle and the working roll diameter of the roll

The first sub-step, if the difference between the minimum value ε _i0 of the maximum value of the absolute value of positive strain along the tangential direction of the outer edge of the plate and strip of each pass and the absolute value of the positive strain of the outer edge of each pass of the plate and strip along its tangential direction The ratio of the average value of the minimum value ε _i0 in the maximum value of is less than or equal to 10%, then the optimal value β _i0 of the first bending angle, the optimal value γ _i0 of the second bending angle and The optimal value D _i0 of the work roll diameter of the roll is determined;

The second sub-step, if the minimum value ε _i0 of the maximum value of the absolute value of the positive strain of the outer edge of each pass along the tangential direction of the strip is different from the absolute value of the positive strain of the outer edge of each pass along the tangential direction The ratio of the average value of the minimum value in the maximum value of the maximum value is greater than 10%, then the minimum value ε _i0 of the maximum value of the absolute value of the positive strain of the outer edge of each pass along the tangential direction determined in the fifth step is Sort their sizes, and then adjust the horizontal values of the test factors corresponding to the maximum and minimum values in the sorting, and repeat the first to fifth steps until the first sub-step of the sixth step is met.

2. The method for determining the bending angles of each pass of the cold-formed sheet and strip according to claim 1, wherein the unit is a shell unit, or a hexahedron unit, or a tetrahedron unit.