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CN111842508A - A method for expressing the shape of a cold-rolled strip after rolling - Google Patents

A method for expressing the shape of a cold-rolled strip after rolling Download PDF

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CN111842508A
CN111842508A CN202010678718.1A CN202010678718A CN111842508A CN 111842508 A CN111842508 A CN 111842508A CN 202010678718 A CN202010678718 A CN 202010678718A CN 111842508 A CN111842508 A CN 111842508A
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strip
length
formula
shape
chord length
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王鹏飞
李旭
张智杰
张殿华
么玉林
梁锦堂
李文田
宋章峰
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Yanshan University
Tangshan Iron and Steel Group Co Ltd
Northeastern University China
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Tangshan Iron and Steel Group Co Ltd
Northeastern University China
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B21—MECHANICAL METAL-WORKING WITHOUT ESSENTIALLY REMOVING MATERIAL; PUNCHING METAL
    • B21B—ROLLING OF METAL
    • B21B37/00—Control devices or methods specially adapted for metal-rolling mills or the work produced thereby
    • B21B37/28—Control of flatness or profile during rolling of strip, sheets or plates
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Abstract

本发明提供一种冷轧带材的轧后板形表示方法。首先基于最短距离表示的弦长，确定出每段带材的翘曲度、以及n段带材的平均长度，然后确定每段带材的弦长、弧长、其次计算出每段带材的弧长和弦长的相对长度差，最后给出每段带材的波形值；本发明基于波形表示法重新建立了板形与翘曲度之间的关系，在人工测量允许的误差范围内，求解的板形值等价于实测板形值，在离线状态下，此表征方法可以用于评估轧机的板形控制能力和板形控制系统的控制效率，也有助于建立和完善板形自动控制的数学模型。

Figure 202010678718

The invention provides a method for expressing the shape of a cold-rolled strip after rolling. First, based on the chord length represented by the shortest distance, determine the warpage of each strip and the average length of n strips, then determine the chord and arc length of each strip, and then calculate the length of each strip. The relative length difference between the arc length and the chord length, and finally the waveform value of each strip is given; the invention re-establishes the relationship between the plate shape and the warpage based on the waveform representation method, and solves the problem within the allowable error range of manual measurement. The shape value is equivalent to the measured shape value. In the off-line state, this characterization method can be used to evaluate the shape control ability of the rolling mill and the control efficiency of the shape control system, and it is also helpful to establish and improve the automatic control of the shape. mathematical model.

Figure 202010678718

Description

一种冷轧带材的轧后板形表示方法A method for expressing the shape of a cold-rolled strip after rolling

技术领域technical field

本发明涉及冶金轧制技术领域，尤其涉及一种冷轧带材的轧后板形表示方法。The invention relates to the technical field of metallurgical rolling, in particular to a method for expressing the shape of a cold-rolled strip after rolling.

背景技术Background technique

由于来料及轧制工艺设备自身特点的影响，轧制过程中的带材会沿宽度方向发生不均匀的纵向延伸变形，导致成品带材出现瓢曲、浪形等板形缺陷问题。科学定量的表示板形，既是生产中衡量板形质量的需要，也是研究板形问题和实现高精度板形自动控制的前提条件。随着下游用户对带材板形质量要求的不断提高，完善和发展现有的板形质量评价方法对成品带材板形控制效果的提高具有重要意义。Due to the influence of the incoming materials and the characteristics of the rolling process equipment, the strip during the rolling process will undergo uneven longitudinal extension deformation along the width direction, resulting in flat defects such as buckling and waves in the finished strip. The scientific and quantitative representation of the shape is not only the need to measure the quality of the shape in production, but also the precondition to study the shape of the shape and realize the high-precision automatic control of the shape. With the continuous improvement of downstream users' requirements for strip shape quality, it is of great significance to improve and develop the existing shape quality evaluation methods to improve the control effect of finished strip shape.

国内外学者围绕板形质量评价方法做了大量的研究工作，例如：通过对冷轧带材板形分段接触式检测过程进行力学建模与仿真，引入欧式距离法表征板形检测误差；采用函数逼近法来表征带材的板形分布及控制偏差，实现对冷轧板形控制系统性能的定量评价；或将带材的板形分布或控制偏差进行模式识别，进而求解用于消除或优化改善这些板形缺陷的执行机构调节量。这些方法主要是通过数学方法将实测带材板形准确转换为板形控制系统的输入信号，可以保证板形自动控制过程中板形输入信号的精度，但在离线状态下，对下线带材的板形表征并没有较好的评价方法。带材板形质量评价方法仍然是基于相对长度差法或波形表示法来表征板形，无法跟实测板形建立对应关系。Scholars at home and abroad have done a lot of research work on the flatness quality evaluation method, for example: through the mechanical modeling and simulation of the cold-rolled strip flatness contact detection process, the Euclidean distance method is introduced to characterize the flatness detection error; The function approximation method is used to characterize the shape distribution and control deviation of the strip, so as to realize the quantitative evaluation of the performance of the cold-rolled shape control system; The amount of actuator adjustment to improve these plate defects. These methods are mainly to accurately convert the measured strip shape into the input signal of the shape control system through mathematical methods, which can ensure the accuracy of the shape input signal in the process of automatic shape control. There is no good evaluation method for the plate shape characterization. The strip shape quality evaluation method is still based on the relative length difference method or the waveform representation method to characterize the shape, which cannot establish a corresponding relationship with the measured shape.

发明内容SUMMARY OF THE INVENTION

针对现有技术的不足，本发明提出一种冷轧带材的轧后板形表示方法，基于波形表示法提出一种新的求解模型，重新建立翘曲度与板形之间的关系，包括如下步骤：In view of the deficiencies of the prior art, the present invention proposes a method for expressing the shape of a cold-rolled strip after rolling, and proposes a new solution model based on the waveform representation method to re-establish the relationship between the warpage and the shape, including: Follow the steps below:

步骤1：将长度为L的轧后带材沿带材宽度方向等分为n段，将每段带材沿带材宽度方向的波形曲线视为一条正弦波形曲线，测量出第i段带材的正弦波形曲线中相邻两个波峰或相邻两个波谷之间的距离，记为L′i，i＝1,2,…,n，定义{L′1,L′2,…,L′n}中的最短距离为Lmin；Step 1: Divide the rolled strip of length L into n equal sections along the width direction of the strip, regard the wave curve of each section of the strip along the strip width direction as a sinusoidal wave curve, and measure the i-th strip. The distance between two adjacent peaks or two adjacent valleys in the sinusoidal waveform of , denoted as L′ i , i=1,2,…,n, defined as {L′ 1 ,L′ 2 ,…,L The shortest distance in ′ n } is L min ;

步骤2：利用公式(1)计算出每段带材相对于最短距离Lmin的翘曲度；Step 2: Use formula (1) to calculate the warpage of each strip relative to the shortest distance L min ;

Figure BDA0002585085050000011
Figure BDA0002585085050000011

式中，λi表示第i段带材相对于最短距离Lmin的翘曲度，Ri表示第i段带材相对于最短距离Lmin的波幅；In the formula, λ i represents the warpage of the i-th strip relative to the shortest distance L min , and R i represents the wave amplitude of the i-th strip relative to the shortest distance L min ;

步骤3：利用公式(2)计算第i段带材相对于最短距离Lmin的曲线长度Li；Step 3: use formula (2) to calculate the curve length Li of the i -th strip relative to the shortest distance L min ;

Figure BDA0002585085050000021
Figure BDA0002585085050000021

步骤4：利用公式(3)计算n段带材正弦波形曲线总长度的平均值

Figure BDA0002585085050000022
Step 4: Use formula (3) to calculate the average value of the total length of the sinusoidal waveform of the n-segment strip
Figure BDA0002585085050000022

Figure BDA0002585085050000023
Figure BDA0002585085050000023

步骤5：确定第i段带材正弦波形的弧长和弦长，如果

Figure BDA0002585085050000024
则将Li作为第i段带材正弦波形的弧长，将
Figure BDA0002585085050000025
作为第i段带材正弦波形的弦长；如果
Figure BDA0002585085050000026
则将
Figure BDA0002585085050000027
作为第i段带材正弦波形的弧长，将Li作为第i段带材正弦波形的弦长；Step 5: Determine the arc length and chord length of the sine waveform of the i-th strip, if
Figure BDA0002585085050000024
Then take Li as the arc length of the sine waveform of the i -th strip, and set
Figure BDA0002585085050000025
as the chord length of the sine waveform of the i-th strip; if
Figure BDA0002585085050000026
will
Figure BDA0002585085050000027
As the arc length of the sine waveform of the i-th strip, let L i be the chord length of the sine-wave of the i-th strip;

步骤6：计算第i段带材正弦波形的弧长和弦长的相对长度差；Step 6: Calculate the relative length difference between the arc length and the chord length of the sinusoidal waveform of the i-th strip;

步骤7：根据计算得到的第i段带材正弦波形的弧长和弦长的相对长度差，得到以I单位表示板形的具体形式：Step 7: According to the calculated relative length difference between the arc length and the chord length of the sinusoidal waveform of the i-th strip, the specific form of the plate shape expressed in I unit is obtained:

当第i段带材正弦波形的弧长为Li、弦长为

Figure BDA0002585085050000028
时，第i段带材的板形表示为：When the arc length of the sinusoidal waveform of the i -th strip is Li and the chord length is
Figure BDA0002585085050000028
When , the plate shape of the i-th strip is expressed as:

Figure BDA0002585085050000029
Figure BDA0002585085050000029

当第i段带材正弦波形的弧长为

Figure BDA00025850850500000210
弦长为Li时，第i段带材的板形表示为：When the arc length of the sine wave of the i-th strip is
Figure BDA00025850850500000210
When the chord length is Li, the plate shape of the i -th strip is expressed as:

Figure BDA00025850850500000211
Figure BDA00025850850500000211

所述的步骤6具体表述为：The step 6 is specifically expressed as:

1)计算弧长为Li、弦长为

Figure BDA00025850850500000212
带材的弧长、弦长相对长度差：1) Calculate the arc length as Li and the chord length as
Figure BDA00025850850500000212
The difference between the arc length and the chord length of the strip relative to the length:

1.1)利用公式(6)计算第i段带材相对于弦长

Figure BDA00025850850500000213
的翘曲度λ′i，则第i段带材的弧长Li、弦长
Figure BDA00025850850500000214
与翘曲度λ′i之间的关系如公式(7)所示，1.1) Use formula (6) to calculate the i-th strip relative to the chord length
Figure BDA00025850850500000213
The warpage λ′ i , then the arc length Li and chord length of the i -th strip
Figure BDA00025850850500000214
The relationship between warpage degree λ′ i is shown in formula (7),

Figure BDA00025850850500000215
Figure BDA00025850850500000215

式中，R′i表示第i段带材相对于弦长

Figure BDA00025850850500000216
的波幅；In the formula, R′ i represents the length of the i-th strip relative to the chord
Figure BDA00025850850500000216
the volatility;

Figure BDA0002585085050000031
Figure BDA0002585085050000031

1.2)联立公式(2)与公式(7)，结合公式(3)消去变量

Figure BDA0002585085050000032
Lmin，得到λ′i与λi的转换关系，如公式(8)所示，1.2) Simultaneous formula (2) and formula (7), combined with formula (3) to eliminate variables
Figure BDA0002585085050000032
L min , the conversion relationship between λ′ i and λ i is obtained, as shown in formula (8),

Figure BDA0002585085050000033
Figure BDA0002585085050000033

1.3)利用公式(9)计算出弧长为Li、弦长为

Figure BDA0002585085050000034
带材的弧长、弦长相对长度差，1.3) Using formula (9), calculate the arc length as Li and the chord length as
Figure BDA0002585085050000034
The difference between the arc length and the chord length of the strip relative to the length,

Figure BDA0002585085050000035
Figure BDA0002585085050000035

2)计算弧长为

Figure BDA0002585085050000036
弦长为Li带材的弧长、弦长相对长度差：2) Calculate the arc length as
Figure BDA0002585085050000036
The chord length is the difference between the arc length and the relative length of the chord length of the strip:

2.1)利用公式(10)计算第i段带材相对于弦长Li的翘曲度λ″i，则第i段带材的弧长

Figure BDA0002585085050000037
弦长Li与翘曲度λ″i之间的关系如公式(11)所示，2.1) Use formula (10) to calculate the warpage λ″ i of the i -th strip relative to the chord length Li, then the arc length of the i-th strip
Figure BDA0002585085050000037
The relationship between the chord length Li and the warpage λ″ i is shown in formula (11),

Figure BDA0002585085050000038
Figure BDA0002585085050000038

式中，R″i表示第i段带材相对于弦长Li的波幅；In the formula, R″ i represents the amplitude of the i -th strip relative to the chord length Li;

Figure BDA0002585085050000039
Figure BDA0002585085050000039

2.2)联立公式(3)与公式(11)，结合公式(2)消去变量Li、Lmin，得到λ″i与λi的转换关系，如公式(12)所示，2.2) Simultaneous formula (3) and formula (11), combined with formula (2) to eliminate variables L i and L min , to obtain the conversion relationship between λ″ i and λ i , as shown in formula (12),

Figure BDA00025850850500000310
Figure BDA00025850850500000310

2.3)利用公式(13)计算弧长为

Figure BDA00025850850500000311
弦长为Li带材的弧长、弦长相对长度差，2.3) Using formula (13) to calculate the arc length as
Figure BDA00025850850500000311
The chord length is the difference between the arc length of the strip and the relative length of the chord length,

Figure BDA0002585085050000041
Figure BDA0002585085050000041

本发明的有益效果是：The beneficial effects of the present invention are:

本发明提出了一种冷轧带材的轧后板形表示方法，重新建立了板形与翘曲度之间的关系，在人工测量误差的允许范围内，可用本方法得出的板形值代替实测板形值；离线状态下，通过本方法得出的板形值，可以进一步评估轧机的板形控制能力和板形控制系统的控制效率；基于本发明提出的表示方法，有助于建立和完善板形自动控制的数学模型。The invention proposes a method for expressing the shape of a cold-rolled strip after rolling, which re-establishes the relationship between the shape and the warpage. Within the allowable range of manual measurement error, the shape value obtained by the method can be used. Instead of measuring the shape value; in the offline state, the shape value obtained by this method can further evaluate the shape control ability of the rolling mill and the control efficiency of the shape control system; And improve the mathematical model of automatic control of plate shape.

附图说明Description of drawings

图1为一种冷轧带材的轧后板形表示方法流程图。Fig. 1 is a flow chart of a method for expressing the shape of a cold-rolled strip after rolling.

图2为基于现有波形表示法的带材波幅-波长正弦曲线图。Figure 2 is a graph of strip amplitude-wavelength sinusoids based on existing waveform representations.

图3为基于本发明给出的轧后板形表示方法的带材波幅-波长正弦曲线图，其中图(a)表示

Figure BDA0002585085050000042
时，带材波幅-波长正弦曲线图，其中图(b)表示
Figure BDA0002585085050000043
时，带材波幅-波长正弦曲线图。Fig. 3 is a strip amplitude-wavelength sinusoidal graph based on the method for expressing the shape of a rolled sheet based on the present invention, wherein Fig. (a) shows
Figure BDA0002585085050000042
When , the strip amplitude-wavelength sinusoidal graph, in which figure (b) shows
Figure BDA0002585085050000043
, the strip amplitude-wavelength sinusoidal graph.

图4为带材实测板形值的3D网格分布图。Figure 4 is a 3D grid distribution diagram of the measured strip shape value.

图5为本发明得出的板形值与实测板形值对比图。FIG. 5 is a comparison diagram of the shape value obtained by the present invention and the measured shape value.

具体实施方式Detailed ways

下面结合附图和具体实施实例对发明做进一步说明。本实施例基于现有技术中的一组1450mm五机架冷连轧机组，对本发明提出的一种冷轧带材的轧后板形表示方法进行详细说明，所述轧机组中的板形调节机构有轧辊倾斜、工作辊正/负弯辊、中间辊正弯辊和中间辊横移，主要控制参数及轧制参数如表1所示。The invention will be further described below with reference to the accompanying drawings and specific implementation examples. Based on a group of 1450mm five-stand tandem cold rolling mills in the prior art, this embodiment describes in detail a method for expressing the shape of a cold-rolled strip after rolling proposed by the present invention. The mechanisms include roll inclination, positive/negative bending of work rolls, positive bending of intermediate rolls and lateral movement of intermediate rolls. The main control parameters and rolling parameters are shown in Table 1.

表1轧制过程主要参数Table 1 Main parameters of rolling process

Figure BDA0002585085050000044
Figure BDA0002585085050000044

Figure BDA0002585085050000051
Figure BDA0002585085050000051

基于波形表示法，本发明提出了一种冷轧带材的轧后板形表示方法，其流程图如图1所示，包括如下步骤：Based on the waveform representation method, the present invention proposes a method for representing the shape of a cold-rolled strip after rolling, the flow chart of which is shown in Figure 1, and includes the following steps:

步骤1：将长度为L＝5m的轧后带材置于带材检测平台上，沿带材宽度方向等分为n＝20段，将每段带材沿带材宽度方向的波形曲线视为一条正弦波形曲线，测量出第i段带材的正弦波形曲线中相邻两个波峰或相邻两个波谷之间的距离，记为L′i，i＝1,2,…,n，定义{L′1,L′2,…,L′n}中的最短距离为Lmin；测量得到的20段带材的平直度参数如表2所示；Step 1: Place the rolled strip with a length of L=5m on the strip detection platform, and divide it into n=20 sections along the strip width direction. The wave curve of each strip strip along the strip width direction is regarded as A sine wave curve, measure the distance between two adjacent peaks or two adjacent wave troughs in the sine wave curve of the i-th strip, denoted as L′ i , i=1,2,…,n, the definition The shortest distance in {L′ 1 , L′ 2 ,…,L′ n } is L min ; the straightness parameters of the 20 strips obtained by measurement are shown in Table 2;

表2平直度参数表Table 2 Flatness parameter table

Figure BDA0002585085050000052
Figure BDA0002585085050000052

步骤2：利用公式(1)计算出每段带材相对于最短距离Lmin的翘曲度；Step 2: Use formula (1) to calculate the warpage of each strip relative to the shortest distance L min ;

Figure BDA0002585085050000053
Figure BDA0002585085050000053

式中，λi表示第i段带材相对于最短距离Lmin的翘曲度，Ri表示第i段带材相对于最短距离Lmin的波幅；In the formula, λ i represents the warpage of the i-th strip relative to the shortest distance L min , and R i represents the wave amplitude of the i-th strip relative to the shortest distance L min ;

步骤3：利用公式(2)计算第i段带材相对于最短距离Lmin的曲线长度Li，Step 3: Use formula (2) to calculate the curve length Li of the i -th strip relative to the shortest distance L min ,

Figure BDA0002585085050000054
Figure BDA0002585085050000054

计算得到的20段带材的翘曲度与曲线长度Li的具体数值如表3-1、表3-2所示，其中表3-2为表3-1的续表，其中20段带材中的最短距离Lmin＝450mm；The specific values of the warpage and the curve length Li of the 20-segment strips calculated are shown in Table 3-1 and Table 3-2, of which Table 3-2 is the continuation of Table 3-1, in which the 20-segment strips are shown in Table 3-1 and Table 3-2. The shortest distance in the material L min =450mm;

表3-1翘曲度λi与曲线长度Li的数值表Table 3-1 Numerical table of warpage degree λ i and curve length Li

Figure BDA0002585085050000061
Figure BDA0002585085050000061

表3-2翘曲度λi与曲线长度Li的数值表(续表)Table 3-2 Numerical table of warpage degree λ i and curve length Li (continued)

Figure BDA0002585085050000062
Figure BDA0002585085050000062

步骤4：利用公式(3)计算n段带材正弦波形曲线总长度的平均值

Figure BDA0002585085050000063
Step 4: Use formula (3) to calculate the average value of the total length of the sinusoidal waveform of the n-segment strip
Figure BDA0002585085050000063

Figure BDA0002585085050000064
Figure BDA0002585085050000064

步骤5：确定第i段带材正弦波形的弧长和弦长，如果

Figure BDA0002585085050000065
则将Li作为第i段带材正弦波形的弧长，将
Figure BDA0002585085050000066
作为第i段带材正弦波形的弦长；如果
Figure BDA0002585085050000067
则将
Figure BDA0002585085050000068
作为第i段带材正弦波形的弧长，将Li作为第i段带材正弦波形的弦长；例如第8段带材的曲线长度Li＝450.111mm，而
Figure BDA0002585085050000069
则第8段带材的弧长为450.111mm，弦长为450.067mm；例如第16段带材的曲线长度Li＝450.060mm，而
Figure BDA00025850850500000610
则第16段带材的弧长为450.067mm，弦长为450.060mm。Step 5: Determine the arc length and chord length of the sine waveform of the i-th strip, if
Figure BDA0002585085050000065
Then take Li as the arc length of the sine waveform of the i -th strip, and set
Figure BDA0002585085050000066
as the chord length of the sine waveform of the i-th strip; if
Figure BDA0002585085050000067
will
Figure BDA0002585085050000068
As the arc length of the sine waveform of the ith strip, let Li be the chord length of the sine waveform of the ith strip; for example, the curve length of the 8th strip is Li = 450.111mm ,
Figure BDA0002585085050000069
Then the arc length of the 8th strip is 450.111mm, and the chord length is 450.067mm; for example, the curve length Li = 450.060mm of the 16th strip, and
Figure BDA00025850850500000610
Then the arc length of the 16th strip is 450.067mm, and the chord length is 450.060mm.

步骤6：计算第i段带材正弦波形的弧长和弦长的相对长度差，具体表述为：Step 6: Calculate the relative length difference between the arc length and the chord length of the sinusoidal waveform of the i-th strip, which is specifically expressed as:

1)计算弧长为Li、弦长为

Figure BDA00025850850500000611
带材的弧长、弦长相对长度差：1) Calculate the arc length as Li and the chord length as
Figure BDA00025850850500000611
The difference between the arc length and the chord length of the strip relative to the length:

1.1)利用公式(6)计算第i段带材相对于弦长

Figure BDA00025850850500000612
的翘曲度λ′i，则第i段带材的弧长Li、弦长
Figure BDA00025850850500000613
与翘曲度λ′i之间的关系如公式(7)所示，1.1) Use formula (6) to calculate the i-th strip relative to the chord length
Figure BDA00025850850500000612
The warpage λ′ i , then the arc length Li and chord length of the i -th strip
Figure BDA00025850850500000613
The relationship between warpage degree λ′ i is shown in formula (7),

Figure BDA00025850850500000614
Figure BDA00025850850500000614

式中，R′i表示第i段带材相对于弦长

Figure BDA00025850850500000615
的波幅；In the formula, R′ i represents the length of the i-th strip relative to the chord
Figure BDA00025850850500000615
the volatility;

Figure BDA00025850850500000616
Figure BDA00025850850500000616

1.2)联立公式(2)与公式(7)，结合公式(3)消去变量

Figure BDA00025850850500000617
Lmin，得到λ′i与λi的转换关系，如公式(8)所示，1.2) Simultaneous formula (2) and formula (7), combined with formula (3) to eliminate variables
Figure BDA00025850850500000617
L min , the conversion relationship between λ′ i and λ i is obtained, as shown in formula (8),

Figure BDA0002585085050000071
Figure BDA0002585085050000071

1.3)利用公式(9)计算出弧长为Li、弦长为

Figure BDA0002585085050000072
带材的弧长、弦长相对长度差，1.3) Using formula (9), calculate the arc length as Li and the chord length as
Figure BDA0002585085050000072
The difference between the arc length and the chord length of the strip relative to the length,

Figure BDA0002585085050000073
Figure BDA0002585085050000073

2)计算弧长为

Figure BDA0002585085050000074
弦长为Li带材的弧长、弦长相对长度差：2) Calculate the arc length as
Figure BDA0002585085050000074
The chord length is the difference between the arc length and the relative length of the chord length of the strip:

2.1)利用公式(10)计算第i段带材相对于弦长Li的翘曲度λ″i，则第i段带材的弧长

Figure BDA0002585085050000075
弦长Li与翘曲度λ″i之间的关系如公式(11)所示，2.1) Use formula (10) to calculate the warpage λ″ i of the i -th strip relative to the chord length Li, then the arc length of the i-th strip
Figure BDA0002585085050000075
The relationship between the chord length Li and the warpage λ″ i is shown in formula (11),

Figure BDA0002585085050000076
Figure BDA0002585085050000076

式中，R′i表示第i段带材相对于弦长

Figure BDA0002585085050000077
的波幅；In the formula, R′ i represents the length of the i-th strip relative to the chord
Figure BDA0002585085050000077
the volatility;

Figure BDA0002585085050000078
Figure BDA0002585085050000078

2.2)联立公式(3)与公式(11)，结合公式(2)消去变量Li、Lmin，得到λ″i与λi的转换关系，如公式(12)所示，2.2) Simultaneous formula (3) and formula (11), combined with formula (2) to eliminate variables L i and L min , to obtain the conversion relationship between λ″ i and λ i , as shown in formula (12),

Figure BDA0002585085050000079
Figure BDA0002585085050000079

2.3)利用公式(13)计算弧长为

Figure BDA00025850850500000710
弦长为Li带材的弧长、弦长相对长度差，2.3) Using formula (13) to calculate the arc length as
Figure BDA00025850850500000710
The chord length is the difference between the arc length of the strip and the relative length of the chord length,

Figure BDA00025850850500000711
Figure BDA00025850850500000711

步骤7：根据计算得到的第i段带材正弦波形的弧长和弦长的相对长度差，得到以I单位表示板形的具体形式，即每段带材的波形值，其中一个I单位相当于相对长度差为10- 5mm；Step 7: According to the relative length difference between the arc length and the chord length of the sinusoidal waveform of the i-th strip, the specific form of the plate shape expressed in I unit is obtained, that is, the waveform value of each strip, where one I unit is equivalent to The relative length difference is 10 - 5 mm;

当第i段带材正弦波形的弧长为Li、弦长为

Figure BDA0002585085050000081
时，第i段带材的板形表示为：When the arc length of the sinusoidal waveform of the i -th strip is Li and the chord length is
Figure BDA0002585085050000081
When , the plate shape of the i-th strip is expressed as:

Figure BDA0002585085050000082
Figure BDA0002585085050000082

当第i段带材正弦波形的弧长为

Figure BDA0002585085050000083
弦长为Li时，第i段带材的板形表示为：When the arc length of the sine wave of the i-th strip is
Figure BDA0002585085050000083
When the chord length is Li, the plate shape of the i -th strip is expressed as:

Figure BDA0002585085050000084
Figure BDA0002585085050000084

基于本发明给出的轧后板形表示方法进行现场板形测量，并且与板形仪测量的实测板形值进行对比。The on-site shape measurement is carried out based on the method for expressing the shape after rolling provided by the present invention, and is compared with the measured shape value measured by the shape meter.

现有技术中的波形表示法，虽然可以定量的描述板形，但是与带材实际测量值没有建立对应关系，选取的最短距离Lmin与正弦波形的弧长相对长度差得到的板形值始终是一个正值，但是实际带材测量值有正有负，不符合实际板形情况，其中波幅-波长正弦曲线图如图2所示。而本发明给出的方法，建立了n段带材正弦波形曲线总长度的平均值与正弦波形的弧长相对长度差关系，符合实际板形情况，其中带材波幅-波长正弦曲线图如图3所示。 Although the waveform representation method in the prior art can quantitatively describe the shape of the strip, it does not establish a corresponding relationship with the actual measurement value of the strip. is a positive value, but the actual measurement value of the strip is positive or negative, which does not conform to the actual shape of the strip. The amplitude-wavelength sinusoidal graph is shown in Figure 2. The method provided by the present invention establishes the relationship between the average value of the total length of the sinusoidal waveform curve of n sections of the strip and the relative length difference of the arc length of the sinusoidal waveform, which conforms to the actual shape of the strip. The strip amplitude-wavelength sinusoidal curve is shown in the figure 3 shown.

图4所示为带材实测板形值的3D网格分布图，从图4中可以看出，此卷带材板形良好，基本控制在5I左右。图5所示为同一卷带材实测板形值与本发明得到的板形值的对比图，图5中横坐标表示的20个测量点即为划分的20段带材，从图5中可以看出，由本发明得到的板形值并不等于实测板形值，原因是由于人工测量误差所导致，但本发明得到的板形值其趋势与实测板形值一致，所以本发明给出的方法可以用于评估轧机的板形控制能力和板形控制系统的控制效率，也有助于建立和完善板形自动控制的数学模型；如果在误差范围内，通过本发明得到的板形值与板形仪等测量设备测得结果近似相等的话，可以用本发明得到的板形值验证板形控制系统的稳定及正确性。Figure 4 shows the 3D grid distribution diagram of the measured strip shape value. It can be seen from Figure 4 that the coil strip has a good shape and is basically controlled at around 5I. Figure 5 shows the comparison between the measured flatness value of the same coil and the flatness value obtained by the present invention. The 20 measurement points represented by the abscissa in Figure 5 are the divided 20 strips. From Figure 5, it can be seen that It can be seen that the shape value obtained by the present invention is not equal to the measured shape value, the reason is due to the artificial measurement error, but the trend of the shape value obtained by the present invention is consistent with the measured shape value, so the present invention provides The method can be used to evaluate the flatness control ability of the rolling mill and the control efficiency of the flatness control system, and also helps to establish and perfect the mathematical model of the flatness automatic control; If the results obtained by measuring equipment such as a shape meter are approximately equal, the stability and correctness of the shape control system can be verified by the shape value obtained by the present invention.

最后应说明的是：以上所述的实施例仅用于说明本发明的技术方案，而非对其限制；尽管参照前述实施例对本发明进行了详细的说明，本领域的普通技术人员应当理解：其依然可以对前述实施例所记载的技术方案进行修改，或者对其中部分或全部技术特征进行等同替换；而这些修改或替换，并不使相应技术方案的本质脱离本发明各实施例技术方案的范围。Finally, it should be noted that the above-described embodiments are only used to illustrate the technical solutions of the present invention, but not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that: It is still possible to modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements on some or all of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the technical solutions of the embodiments of the present invention. scope.

Claims (2)

1. A representation method of a rolled strip shape of a cold-rolled strip is characterized by comprising the following steps:
step 1: equally dividing the rolled strip with the length of L into n sections along the width direction of the strip, regarding the wave curve of each section of the strip along the width direction of the strip as a sine wave curve, measuring the distance between two adjacent wave crests or two adjacent wave troughs in the sine wave curve of the ith section of the strip, and marking the distance as L'iI ═ 1,2, …, n, and defines { L'1,L′2,…,L′nThe shortest distance in (L) } ismin；
Step 2: calculating the shortest distance L of each section of the strip by using the formula (1)minThe degree of warp of (a);
Figure FDA0002585085040000011
in the formula, λiIndicating the i-th section of the strip relative to the shortest distance LminWarp of (2), RiIndicating the i-th section of the strip relative to the shortest distance LminThe amplitude of (a);
and step 3: calculating the i-th section of the strip relative to the shortest distance L by using the formula (2)minLength L of curvei；
Figure FDA0002585085040000012
And 4, step 4: calculating the average value of the total length of the sine wave curve of the n sections of the strip by using the formula (3)
Figure FDA00025850850400000111
Figure FDA0002585085040000013
And 5: determining the arc length and chord length of the sine wave of the ith section of the strip if
Figure FDA0002585085040000014
Then L will beiAs the arc length of the sine wave of the ith section of the strip material, will
Figure FDA0002585085040000015
The chord length is taken as the sine waveform of the ith section of the strip material; if it is not
Figure FDA0002585085040000016
Then will be
Figure FDA0002585085040000017
As the arc length of the sine wave of the ith section of the strip, LiThe chord length is taken as the sine waveform of the ith section of the strip material;
Step 6: calculating the relative length difference between the arc length and the chord length of the sine waveform of the ith section of the strip;
and 7: and according to the calculated relative length difference between the arc length and the chord length of the sine waveform of the ith section of the strip, obtaining a specific form of expressing the shape of the strip by an I unit:
when the arc length of the sine wave of the ith section of the strip is LiA chord length of
Figure FDA0002585085040000018
The shape of the ith strip is expressed as:
Figure FDA0002585085040000019
when the arc length of the sine wave of the ith section of the strip is equal to
Figure FDA00025850850400000110
A chord length of LiThe shape of the ith strip is expressed as:
Figure FDA0002585085040000021
2. the method for representing a rolled strip shape of a cold-rolled strip according to claim 1, wherein the step 6 is specifically expressed as:
1) calculating arc length as LiA chord length of
Figure FDA0002585085040000022
Relative length difference of arc length and chord length of the strip:
1.1) calculating the chord length of the i-th section of the strip material relative to the chord length by using the formula (6)
Figure FDA0002585085040000023
Of warp λ'iThe arc length L of the ith section of stripiChord length
Figure FDA0002585085040000024
And warp λ'iThe relationship therebetween is as shown in the formula (7),
Figure FDA0002585085040000025
in the formula (II), R'iShowing the relative chord length of the i-th section of the strip
Figure FDA0002585085040000026
The amplitude of (a);
Figure FDA0002585085040000027
1.2) simultaneous equations (2) and (7), in combination with equation (3), to eliminate the variables
Figure FDA0002585085040000028
LminTo give λ'iAnd λiThe conversion relationship of (2) is shown in the formula (8),
Figure FDA0002585085040000029
1.3) calculating the arc length L by using the formula (9)iA chord length of
Figure FDA00025850850400000210
The relative length difference of the arc length and the chord length of the strip material,
Figure FDA00025850850400000211
2) Calculating the arc length of
Figure FDA00025850850400000212
A chord length of LiRelative length difference of arc length and chord length of the strip:
2.1) calculating the chord length L of the i-th section of the strip material relative to the formula (10)iOf angularity λ ″)iThe arc length of the ith strip
Figure FDA00025850850400000213
Chord length LiAnd angularity lambdaiThe relationship therebetween is shown in formula (11),
Figure FDA00025850850400000214
in the formula, R ″)iShowing the i-th section of the strip with respect to the chord length LiThe amplitude of (a);
Figure FDA0002585085040000031
2.2) simultaneous expression (3) and expression (11), elimination of variable L in combination with expression (2)i、LminTo obtain lambda ″)iAnd λiThe conversion relationship of (2) as shown in the formula (12),
Figure FDA0002585085040000032
2.3) calculating the arc length using equation (13) to
Figure FDA0002585085040000033
A chord length of LiThe relative length difference of the arc length and the chord length of the strip material,
Figure FDA0002585085040000034
CN202010678718.1A 2020-07-15 2020-07-15 A method for expressing the shape of a cold-rolled strip after rolling Pending CN111842508A (en)

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