CN103203371B

CN103203371B - Double closed-loop control method for roll gap position pressure of cold rolling mill

Info

Publication number: CN103203371B
Application number: CN201210011459.2A
Authority: CN
Inventors: 刘宝权; 张岩; 王军生; 姜梦春; 王革新; 宋蕾; 侯永刚; 秦大伟; 宋君; 王勇
Original assignee: Angang Steel Co Ltd
Current assignee: Angang Steel Co Ltd
Priority date: 2012-01-13
Filing date: 2012-01-13
Publication date: 2016-09-07
Anticipated expiration: 2032-01-13
Also published as: CN103203371A

Abstract

The invention relates to a double-closed-loop control method for the position and pressure of the roll gap of a cold rolling mill in the field of cold strip steel rolling, and is suitable for the main pressure of the cold rolling mill as a rolling force control mode. The content of this method is: calculation of asymmetrical rolling force on both sides after additional tilting of the rolling mill; derivation of the elastic bending influence function in the form of simply supported beams of backup rolls and work rolls suitable for asymmetrical rolling calculations according to Karl's energy theorem; Effective integration of roll system deformation theory and metal lateral flow theory; effective improvement of the deformation coordination equation in the traditional roll system deformation theory; taking into account the theoretical calculation error, real-time online adaptive correction of the theoretical calculation model. The application of this technology can effectively suppress the occurrence of broken belt accidents caused by excessive tilt adjustment, and has a significant effect on the control of unilateral waves.

Description

Double closed-loop control method of roll gap position and pressure in cold rolling mill

技术领域technical field

本发明涉及冷轧带钢轧制领域，适用于冷轧机主压上为轧制力控制模式。本技术的应用能够有效抑制因倾斜调整过量而导致的断带事故的发生，同时对单边浪的控制具有显著的效果。The invention relates to the field of cold-rolled steel strip rolling, and is suitable for a rolling force control mode on the main pressure of a cold-rolling mill. The application of this technology can effectively suppress the occurrence of broken belt accidents caused by excessive tilt adjustment, and has a significant effect on the control of unilateral waves.

背景技术Background technique

板厚精度和板形是决定板带材几何尺寸精度的两大质量指标。板厚精度的控制，经过多年的发展已日趋完善。而板形控制由于影响因素复杂多变，在基础理论、检测技术和控制技术等方面还有许多问题没有得到根本解决，时至今日，有关板形控制理论和控制技术的研究仍然在不断完善和更新。Plate thickness accuracy and plate shape are two major quality indicators that determine the geometrical dimension accuracy of plate and strip. The control of plate thickness accuracy has become more and more perfect after years of development. However, due to the complex and changeable influencing factors, there are still many problems in the basic theory, detection technology and control technology that have not been fundamentally resolved. Up to now, the research on the shape control theory and control technology is still being continuously improved and developed. renew.

冷轧带钢板形控制包括：目标板形的设定、板形的测量、实测数据的处理及板形控制执行机构的调整。对采集到的板形实际测量数据，通常采用一个多项式进行回归和正交分解，分解成一次、二次、三次、四次和高次板形分量，以各分量的实测值和目标值的偏差为调整量，利用弯辊、轧辊横移、分段冷却和轧辊倾斜来消除各种板形缺陷。调整弯辊力可以改变辊缝的凸度，消除板形偏差中的二次和四次分量。轧辊横移可以改变辊系的接触状态，消除工作辊有害弯矩的影响，提高弯辊效率及减小带钢的边部减薄。无法通过轧辊倾斜和弯辊控制消除的高次分量板形缺陷，可用分段冷却进行控制。Cold-rolled strip shape control includes: target shape setting, shape measurement, measured data processing and shape control actuator adjustment. For the actual measurement data of the collected plate shape, a polynomial is usually used for regression and orthogonal decomposition, decomposed into primary, secondary, tertiary, quaternary and high-order plate shape components, and the deviation between the actual measured value and the target value of each component In order to adjust the amount, various plate shape defects are eliminated by using roll bending, roll traverse, segmental cooling and roll tilting. Adjusting the bending force can change the convexity of the roll gap and eliminate the secondary and quaternary components in the shape deviation. The roll traversing can change the contact state of the roll system, eliminate the influence of the harmful bending moment of the work roll, improve the bending efficiency and reduce the edge thinning of the strip. High-order component shape defects that cannot be eliminated by roll tilt and roll bending control can be controlled by segmental cooling.

轧辊倾斜是通过调整传动侧和操作侧支撑辊液压缸的位置实现的，属于位置控制。轧辊倾斜后，构成楔形辊缝，用于消除板形偏差分量中的一次和三次非对称板形缺陷。冷轧机的倾斜控制系统嵌入在压上控制系统中，压上系统的控制方式有两种：位置控制和轧制力控制。若压上系统采用位置控制方式，倾斜控制嵌入其中后，设定值均属于位置量纲，其控制系统的稳定性是毋庸置疑的。如图1所示，若压上系统采用轧制力控制方式，倾斜控制嵌入其中，就构成了位置和压力双闭环控制系统。受液压系统油源压力和压上缸尺寸限制，轧制力设定值无需限幅控制，而倾斜设定值给定一个2.0mm的定值限幅。倾斜控制的设定值由人工干预量、轧机标定倾斜量、带钢张力偏差调整量和板形倾斜调整量叠加构成。The tilting of the roll is realized by adjusting the positions of the hydraulic cylinders of the transmission side and the operation side of the support roll, which belongs to position control. After the rolls are tilted, a wedge-shaped roll gap is formed to eliminate the primary and tertiary asymmetric plate shape defects in the plate shape deviation component. The tilt control system of the cold rolling mill is embedded in the pressing control system, and there are two control modes of the pressing system: position control and rolling force control. If the pressing system adopts the position control method, after the tilt control is embedded in it, the set values all belong to the position dimension, and the stability of the control system is beyond doubt. As shown in Figure 1, if the pressing system adopts the rolling force control method, and the tilt control is embedded in it, a double closed-loop control system of position and pressure is formed. Limited by the oil source pressure of the hydraulic system and the size of the upper cylinder, the setting value of the rolling force does not need limit control, and the setting value of the inclination is given a fixed value limit of 2.0mm. The setting value of inclination control is composed of manual intervention, rolling mill calibration inclination, strip tension deviation adjustment and flatness inclination adjustment.

不同厚度、不同宽度、不同来料楔形和不同材质的冷轧带钢，同时受边部厚度、边部质量和板形测量系统精度的影响，倾斜设定值的2.0mm固定值限幅显然过大，倾斜设定值稍有调节不当，就会导致带钢断带。图2为实际轧制断带过程中的倾斜、两侧轧制力和轧制力差值的PDA曲线，当倾斜设定值恒定时，传动侧和操作侧的轧制力差值基本保持恒定，随着倾斜实际值的增大，轧制力差值本应继续增大，但却保持定值，至后来急剧减小，说明带钢已出现边部裂纹，断带过程开始。分析原因：一是倾斜设定值调节过大；二是带钢的边部质量存在缺陷。判断轧制过程中是否断带的PDA曲线如图3所示，断带停车信号由轧机主传动系统发出，判断依据为：轧制速度不为0且张力为0。Cold-rolled steel strips of different thicknesses, widths, incoming wedges and materials are affected by edge thickness, edge quality, and the accuracy of the shape measurement system. The 2.0mm fixed value limit of the inclination setting value is obviously too much. If the inclination setting value is slightly improperly adjusted, the strip will be broken. Figure 2 is the PDA curve of inclination, rolling force on both sides and rolling force difference in the actual rolling process of broken strip. When the inclination setting value is constant, the rolling force difference between the driving side and the operating side remains basically constant , as the actual value of the inclination increases, the rolling force difference should continue to increase, but it remains constant, and then decreases sharply, indicating that edge cracks have appeared in the strip, and the strip breaking process has begun. Reasons for analysis: First, the adjustment of the tilt setting value is too large; second, there are defects in the edge quality of the strip. The PDA curve for judging whether the strip is broken during the rolling process is shown in Figure 3. The stop signal for broken strip is sent by the main drive system of the rolling mill. The judgment basis is that the rolling speed is not 0 and the tension is 0.

在带钢发生断带前，已开始出现明显的断带征兆：轧辊的倾斜已发生较大的变化，但操作侧与传动侧的轧制力差值仍然保持不变。由于倾斜的限幅值为±1.0mm，断带前20s内，倾斜已达到限幅值，而轧制力的差值未随着倾斜的变化而变化。这时若能限制倾斜值的继续增大或及时停车，则能避免断带事故的发生。Before the strip breakage occurs, obvious signs of strip breakage have begun to appear: the inclination of the roll has changed greatly, but the rolling force difference between the operating side and the driving side remains unchanged. Because the limit value of inclination is ±1.0mm, within 20s before the strip breaks, the inclination has reached the limit value, but the difference of rolling force does not change with the change of inclination. At this time, if the continued increase of the inclination value can be limited or the car can be stopped in time, the occurrence of a broken belt accident can be avoided.

发明内容Contents of the invention

本发明的目的是提供一种冷轧机辊缝位置压力双闭环控制方法，该方法的应用能够有效抑制因倾斜调整过量而导致的断带事故的发生，同时对单边浪的控制具有显著的效果。The purpose of the present invention is to provide a double-closed-loop control method for the pressure of the roll gap position of a cold rolling mill. The application of this method can effectively suppress the occurrence of broken belt accidents caused by excessive inclination adjustment, and at the same time, it has a significant effect on the control of unilateral waves. Effect.

为实现上述目的，本发明通过以下技术方案实现：To achieve the above object, the present invention is achieved through the following technical solutions:

冷轧机辊缝位置压力双闭环控制方法，轧机附加倾斜后双侧非对称轧制力计算；根据卡氏能量定理推导了适于非对称轧制计算的支撑辊、工作辊简支梁形式的弹性弯曲影响函数；辊系变形理论和金属横向流动理论的有效整合；对传统辊系变形理论中的变形协调方程进行了有效的改进；考虑到理论计算的误差，对理论计算模型进行实时在线自适应修正；Double-closed-loop control method of roll gap position and pressure in cold rolling mill, calculation of asymmetric rolling force on both sides after additional inclination of the rolling mill; according to Karl’s energy theorem, the simply supported beam form of backup roll and work roll suitable for asymmetric rolling calculation is deduced Elastic bending influence function; Effective integration of roll deformation theory and metal lateral flow theory; Effective improvement of deformation coordination equation in traditional roll deformation theory; Considering the theoretical calculation error, real-time online self-automation of the theoretical calculation model adaptation correction;

轧机支撑辊附加倾斜后轧制变形区已不再是传统意义上的以轧制中心线为中心左右对称，而是非对称的，进行非对称计算时，左右两侧的轧制力是未知数；进行计算时单元划分为沿辊全身自左向右排列，推导支撑辊弯曲影响函数为：After additional inclination of the support rolls of the rolling mill, the rolling deformation zone is no longer symmetrical with the rolling center line as the center in the traditional sense, but asymmetrical. When performing asymmetrical calculations, the rolling forces on the left and right sides are unknown; When calculating, the units are divided into arranged from left to right along the whole body of the roller, and the bending influence function of the support roller is deduced as:

${g g}_{b b} ((i i,, j j)) = = \frac{11}{{33 E E.}_{b b} {I I}_{b b 11}} \frac{{l l}_{b b} - - {x x}_{i i}}{{l l}_{b b}} \frac{{l l}_{b b} - - {x x}_{j j}}{{l l}_{b b}} {l l}_{O o}^{33} + + \frac{11}{{33 E E.}_{b b} {I I}_{b b 22}} \frac{{l l}_{b b} - - {x x}_{i i}}{{l l}_{b b}} \frac{{l l}_{b b} - - {x x}_{j j}}{{l l}_{b b}} (({x x}_{j j}^{33} - - {l l}_{O o}^{33}))$

$+ + \frac{11}{{E E.}_{b b} {I I}_{b b 22}} \frac{{l l}_{b b} - - {x x}_{i i}}{{l l}_{b b}} {{- - \frac{{x x}_{j j}}{{l l}_{b b}} \frac{11}{33} [[{x x}_{i i}^{33} - - {x x}_{j j}^{33}]] + + \frac{11}{22} {x x}_{j j} [[{x x}_{i i}^{22} - - {x x}_{j j}^{22}]]}}$

$+ + \frac{11}{{E E.}_{b b} {I I}_{b b 22}} {{\frac{{x x}_{i i} {x x}_{j j}}{{l l}_{b b}^{22}} \frac{11}{33} [[{l l}_{D D.}^{33} - - {x x}_{i i}^{33}]] - - \frac{{x x}_{i i} {x x}_{j j}}{{l l}_{b b}} [[{l l}_{D D.}^{22} - - {x x}_{i i}^{22}]] + + {x x}_{i i} {x x}_{j j} [[{l l}_{D D.} - - {x x}_{i i}]]}}$

$\begin{matrix} + + \frac{11}{{E E.}_{b b} {I I}_{b b 11}} {{\frac{{x x}_{i i} {x x}_{j j}}{{l l}_{b b}^{22}} \frac{11}{33} [[{l l}_{b b}^{33} - - {l l}_{D D.}^{33}]] - - \frac{{x x}_{i i} {x x}_{j j}}{{l l}_{b b}} [[{l l}_{b b}^{22} - - {l l}_{D D.}^{22}]] + + {x x}_{i i} {x x}_{j j} [[{l l}_{b b} - - {l l}_{D D.}]]}} & (({x x}_{i i} {> > x x}_{j j})) \end{matrix}$

$+ + \frac{Φ Φ}{{GA GA}_{b b 11}} \frac{{l l}_{b b} - - {x x}_{j j}}{{l l}_{b b}} \frac{{l l}_{b b} - - {x x}_{i i}}{{l l}_{b b}} {l l}_{O o} + + \frac{Φ Φ}{{GA GA}_{b b 22}} \frac{{l l}_{b b} - - {x x}_{j j}}{{l l}_{b b}} \frac{{l l}_{b b} - - {x x}_{i i}}{{l l}_{b b}} (({x x}_{j j} - - {l l}_{O o}))$

$+ + \frac{Φ Φ}{{GA GA}_{b b 22}} ((- - \frac{{x x}_{j j}}{{l l}_{b b}})) \frac{{l l}_{b b} - - {x x}_{i i}}{{l l}_{b b}} (({x x}_{i i} - - {x x}_{j j})) + + \frac{Φ Φ}{{GA GA}_{b b 22}} ((- - \frac{{x x}_{j j}}{{l l}_{b b}})) \frac{{l l}_{b b} - - {x x}_{i i}}{{l l}_{b b}} (({l l}_{D D.} - - {x x}_{i i}))$

$+ + \frac{Φ Φ}{{GA GA}_{b b 11}} ((\frac{{x x}_{j j} {x x}_{i i}}{{l l}_{b b}^{22}})) (({l l}_{b b} - - {l l}_{D D.}))$

${g g}_{b b} ((i i,, j j)) = = \frac{11}{{33 E E.}_{b b} {I I}_{b b 11}} \frac{{l l}_{b b} - - {x x}_{i i}}{{l l}_{b b}} \frac{{l l}_{b b} - - {x x}_{j j}}{{l l}_{b b}} {l l}_{O o}^{33} + + \frac{11}{{33 E E.}_{b b} {I I}_{b b 22}} \frac{{l l}_{b b} - - {x x}_{i i}}{{l l}_{b b}} \frac{{l l}_{b b} - - {x x}_{j j}}{{l l}_{b b}} (({x x}_{i i}^{33} - - {l l}_{O o}^{33}))$

$+ + \frac{11}{{E E.}_{b b} {I I}_{b b 22}} \frac{{l l}_{b b} - - {x x}_{j j}}{{l l}_{b b}} [[\frac{{x x}_{i i}}{22} (({x x}_{j j}^{22} - - {x x}_{i i}^{22})) - - \frac{{x x}_{i i}}{{33 l l}_{b b}} (({x x}_{j j}^{33} - - {x x}_{i i}^{33}))]]$

$+ + \frac{11}{{E E.}_{b b} {I I}_{b b 22}} [[\frac{{x x}_{i i} {x x}_{j j}}{{l l}_{b b}^{22}} \frac{11}{33} (({l l}_{D D.}^{33} - - {x x}_{j j}^{33})) - - \frac{{x x}_{i i} {x x}_{j j}}{{l l}_{b b}} (({l l}_{D D.}^{22} - - {x x}_{j j}^{22})) + + {x x}_{i i} {x x}_{j j} (({l l}_{D D.} - - {x x}_{j j}))]]$

$\begin{matrix} + + \frac{11}{{E E.}_{b b} {I I}_{b b 11}} [[\frac{{x x}_{i i} {x x}_{j j}}{{l l}_{b b}^{22}} \frac{11}{33} (({l l}_{b b}^{33} - - {l l}_{D D.}^{33})) - - \frac{{x x}_{i i} {x x}_{j j}}{{l l}_{b b}} (({l l}_{b b}^{22} - - {l l}_{D D.}^{22})) + + {x x}_{i i} {x x}_{j j} (({l l}_{b b} - - {l l}_{D D.}))]] & (({x x}_{i i} {< < x x}_{j j})) \end{matrix}$

$+ + \frac{Φ Φ}{{GA GA}_{b b 11}} \frac{{l l}_{b b} - - {x x}_{j j}}{{l l}_{b b}} \frac{{l l}_{b b} - - {x x}_{i i}}{{l l}_{b b}} {l l}_{O o} + + \frac{Φ Φ}{{GA GA}_{b b 22}} \frac{{l l}_{b b} - - {x x}_{j j}}{{l l}_{b b}} \frac{{l l}_{b b} - - {x x}_{i i}}{{l l}_{b b}} (({x x}_{i i} - - {l l}_{O o}))$

$+ + \frac{Φ Φ}{{GA GA}_{b b 22}} \frac{{l l}_{b b} - - {x x}_{j j}}{{l l}_{b b}} ((- - \frac{{x x}_{i i}}{{l l}_{b b}})) (({x x}_{j j} - - {x x}_{i i})) + + \frac{Φ Φ}{{GA GA}_{b b 22}} ((\frac{{x x}_{j j} {x x}_{i i}}{{l l}_{b b}^{22}})) (({l l}_{D D.} - - {x x}_{j j}))$

工作辊弯曲影响函数为：The work roll bending influence function is:

${g g}_{w w} ((i i,, j j)) = = \frac{11}{{33 E E.}_{w w} {I I}_{w w 11}} \frac{{l l}_{w w} - - {x x}_{i i}}{{l l}_{w w}} \frac{{l l}_{w w} - - {x x}_{j j}}{{l l}_{w w}} {l l}_{OW ow}^{33} + + \frac{11}{{33 E E.}_{w w} {I I}_{w w 22}} \frac{{l l}_{w w} - - {x x}_{i i}}{{l l}_{w w}} \frac{{l l}_{w w} - - {x x}_{j j}}{{l l}_{w w}} (({x x}_{j j}^{33} - - {l l}_{OW ow}^{33}))$

$+ + \frac{11}{{E E.}_{w w} {I I}_{w w 22}} \frac{{l l}_{w w} - - {x x}_{i i}}{{l l}_{w w}} {{- - \frac{{x x}_{j j}}{{l l}_{w w}} \frac{11}{33} [[{x x}_{i i}^{33} - - {x x}_{j j}^{33}]] + + \frac{11}{22} {x x}_{j j} [[{x x}_{i i}^{22} - - {x x}_{j j}^{22}]]}}$

$+ + \frac{11}{{E E.}_{w w} {I I}_{w w 22}} {{\frac{{x x}_{i i} {x x}_{j j}}{{l l}_{w w}^{22}} \frac{11}{33} [[{l l}_{DW DW}^{33} - - {x x}_{i i}^{33}]] - - \frac{{x x}_{i i} {x x}_{j j}}{{l l}_{w w}} [[{l l}_{DW DW}^{22} - - {x x}_{i i}^{22}]] + + {x x}_{i i} {x x}_{j j} [[{l l}_{DW DW} - - {x x}_{i i}]]}}$

$\begin{matrix} + + \frac{11}{{E E.}_{w w} {I I}_{w w 11}} {{\frac{{x x}_{i i} {x x}_{j j}}{{l l}_{w w}^{22}} \frac{11}{33} [[{l l}_{w w}^{33} - - {l l}_{DW DW}^{33}]] - - \frac{{x x}_{i i} {x x}_{j j}}{{l l}_{w w}} [[{l l}_{w w}^{22} - - {l l}_{DW DW}^{22}]] + + {x x}_{i i} {x x}_{j j} [[{l l}_{w w} - - {l l}_{DW DW}]]}} & (({x x}_{i i} {> > x x}_{j j})) \end{matrix}$

$+ + \frac{Φ Φ}{{GA GA}_{w w 11}} \frac{{l l}_{w w} - - {x x}_{j j}}{{l l}_{w w}} \frac{{l l}_{w w} - - {x x}_{i i}}{{l l}_{w w}} {l l}_{OW ow} + + \frac{Φ Φ}{{GA GA}_{w w 22}} \frac{{l l}_{w w} - - {x x}_{j j}}{{l l}_{w w}} \frac{{l l}_{w w} - - {x x}_{i i}}{{l l}_{w w}} (({x x}_{j j} - - {l l}_{OW ow}))$

$+ + \frac{Φ Φ}{{GA GA}_{w w 22}} ((- - \frac{{x x}_{j j}}{{l l}_{w w}})) \frac{{l l}_{w w} - - {x x}_{i i}}{{l l}_{w w}} (({x x}_{i i} - - {x x}_{j j})) + + \frac{Φ Φ}{{GA GA}_{w w 22}} ((- - \frac{{x x}_{j j}}{{l l}_{w w}})) \frac{{l l}_{w w} - - {x x}_{i i}}{{l l}_{w w}} (({l l}_{DW DW} - - {x x}_{i i}))$

$+ + \frac{Φ Φ}{{GA GA}_{w w 11}} ((\frac{{x x}_{j j} {x x}_{i i}}{{l l}_{w w}^{22}})) (({l l}_{w w} - - {l l}_{DW DW}))$

$\begin{matrix} + + \frac{11}{{E E.}_{w w} {I I}_{w w 11}} {{\frac{{x x}_{i i} {x x}_{j j}}{{l l}_{w w}^{22}} \frac{11}{33} [[{l l}_{w w}^{33} - - {l l}_{DW DW}^{33}]] - - \frac{{x x}_{i i} {x x}_{j j}}{{l l}_{w w}} [[{l l}_{w w}^{22} - - {l l}_{DW DW}^{22}]] + + {x x}_{i i} {x x}_{j j} [[{l l}_{w w} - - {l l}_{DW DW}]]}} & (({x x}_{i i} {< < x x}_{j j})) \end{matrix}$

工作辊和支撑辊间的变形协调方程为：The deformation coordination equation between the work roll and the backup roll is:

式中In the formula

$\overset{r}{T} = {[\begin{matrix} t (1) & t (2) & L & t (NB) \end{matrix}]}^{T}$ 为支撑辊的倾斜向量； $\overset{r}{T} = {[\begin{matrix} t (1) & t (2) & L & t (NB) \end{matrix}]}^{T}$ is the inclination vector of the support roller;

${\overset{r}{Y}}_{wb} = {[\begin{matrix} y_{wb} (1) & y_{wb} (2) & L & y_{wb} (n) \end{matrix}]}^{T}$ 为辊间压扁向量， ${\overset{r}{Y}}_{wb} = {[\begin{matrix} {the y}_{wb} (1) & {the y}_{wb} (2) & L & {the y}_{wb} (no) \end{matrix}]}^{T}$ is the flattening vector between the rolls,

${\overset{r}{Y}}_{wb 0} = {[\begin{matrix} y_{wb 0} (0) & y_{wb 0} (0) & L & y_{wb 0} (0) \end{matrix}]}^{T}$ 是常向量，即辊面中心处的压扁量； ${\overset{r}{Y}}_{wb 0} = {[\begin{matrix} {the y}_{wb 0} (0) & {the y}_{wb 0} (0) & L & {the y}_{wb 0} (0) \end{matrix}]}^{T}$ is a constant vector, that is, the amount of flattening at the center of the roll surface;

${\overset{r}{M}}_{b} = {[\begin{matrix} m_{b} (1) & m_{b} (2) & L & m_{b} (n) \end{matrix}]}^{T}$ 是支撑辊凸度向量； ${\overset{r}{m}}_{b} = {[\begin{matrix} m_{b} (1) & m_{b} (2) & L & m_{b} (no) \end{matrix}]}^{T}$ is the crown vector of the backup roll;

${\overset{r}{M}}_{w} = {[\begin{matrix} m_{w} (1) & m_{w} (2) & L & m_{w} (n) \end{matrix}]}^{T}$ 是工作辊凸度向量。 ${\overset{r}{m}}_{w} = {[\begin{matrix} m_{w} (1) & m_{w} (2) & L & m_{w} (no) \end{matrix}]}^{T}$ is the work roll crown vector.

附加倾斜后通过辊系变形和变形区金属横向流动计算，最终可获得两侧轧制力及差值为：After the additional inclination is calculated through the deformation of the roll system and the lateral flow of metal in the deformation zone, the rolling force on both sides and the difference can be obtained finally:

传动侧轧制力： $F_{D} = \frac{1}{l_{b}} Σ_{i = 1}^{NB} q (i) X (i)$ Drive side rolling force: $f_{D.} = \frac{1}{l_{b}} Σ_{i = 1}^{NB} q (i) x (i)$

操作侧轧制力为： $F_{O} = Σ_{i = 1}^{NB} q (i) - F_{D}$ The rolling force on the operating side is: $f_{o} = Σ_{i = 1}^{NB} q (i) - f_{D.}$

两侧轧制力差为：ΔF＝F_D-F_O The rolling force difference on both sides is: ΔF＝F _D -F _O

以轧制力差值为自变量，以倾斜为因变量，用多项式拟合出轧制力差值和倾斜的函数关系为Taking the rolling force difference as the independent variable and the inclination as the dependent variable, the functional relationship between the rolling force difference and the inclination is obtained by polynomial fitting:

$tilt tilt = = {Σ Σ}_{i i = = 00}^{n no} {a a}_{00} ((i i)) {((ΔF ΔF))}^{i i}$

式中：a₀为拟合系数。In the formula: a ₀ is the fitting coefficient.

为消除理论计算模型的误差，可根据检测的实际轧制力差和实际倾斜数据对[ΔF_act(k)，tilt_act(k)](k＝1，2，3，…)，用最小二乘法，依据误差平方和最小原理动态修正倾斜-轧制力差多项式中的各项系数，修正后轧制力差值和倾斜的函数关系为In order to eliminate the error of the theoretical calculation model, [ΔF _act (k), tilt _act (k)] (k = 1, 2, 3, ...), the least squares can be used according to the actual rolling force difference detected and the actual tilt data Multiplication, based on the error square sum minimum principle to dynamically correct the coefficients in the inclination-rolling force difference polynomial, the functional relationship between the corrected rolling force difference and inclination is

$tilt tilt = = {Σ Σ}_{i i = = 00}^{n no} {a a}_{11} ((i i)) {((ΔF ΔF))}^{i i} . .$

式中：a₁为修正后多项式系数。In the formula: a ₁ is the modified polynomial coefficient.

本发明的有益效果是：该方法的应用能够有效抑制因倾斜调整过量而导致的断带事故的发生，同时对单边浪的控制具有显著的效果。The beneficial effects of the present invention are: the application of the method can effectively suppress the occurrence of broken belt accidents caused by excessive inclination adjustment, and at the same time, it has a remarkable effect on the control of unilateral waves.

附图说明Description of drawings

图1冷轧机位置和压力双闭环控制系统图2轧机工作辊对称弯辊液压原理图；Fig. 1 Cold rolling mill position and pressure double closed-loop control system Fig. 2 Rolling mill working roll symmetrical roll bending hydraulic schematic diagram;

图2实际断带过程的轧制力和倾斜PDA曲线；The rolling force and inclined PDA curve of the actual strip breaking process in Fig. 2;

图3实际轧制过程中断带信号PDA曲线；Fig. 3 PDA curve of interrupted band signal in actual rolling process;

图4两侧轧制力差值计算流程；Figure 4 Calculation process of rolling force difference on both sides;

图5轧辊轧件离散编码；Fig. 5 Discrete coding of rolling pieces;

图6支撑辊受力图(xi＞xj)；Fig. 6 force diagram of support roller (xi>xj);

图7支撑辊受力图(xi＜xj)；Fig. 7 force diagram of supporting roller (xi<xj);

图8工作辊受力图(xi＞xj)；Figure 8 Work roll force diagram (xi>xj);

图9工作辊受力图(xi＜xj)；Figure 9 Work roll stress diagram (xi<xj);

图10悬臂梁式工作辊受力图；Fig. 10 Force diagram of cantilever beam type work roll;

图11横向分布张力计算中带钢单元划分；Figure 11 Division of strip steel units in the calculation of lateral tension distribution;

图12支撑辊受力分析；Figure 12 Force analysis of support rollers;

图13计算结果；Figure 13 calculation results;

图14改进后的位置轧制力双闭环控制系统。Figure 14 Improved position rolling force double closed-loop control system.

具体实施方式detailed description

一种冷轧机辊缝位置压力双闭环控制方法，通过影响函数法计算附加倾斜后辊系变形，同时用三次样条函数拟合轧制入、出口厚度分布进行张力修正，最后得出不同厚度、不同宽度和不同材质坯料在附加倾斜后双侧轧制力差值和倾斜之间的关系，用轧制力差值动态修正倾斜设定值的限幅。A double-closed-loop control method for roll gap position and pressure in a cold rolling mill. The deformation of the roll system after additional inclination is calculated by the influence function method. At the same time, the cubic spline function is used to fit the thickness distribution of the rolling entrance and exit for tension correction, and finally different thicknesses are obtained. 1. The relationship between the difference between the rolling force on both sides and the inclination of billets of different widths and different materials after additional inclination, and the limit of the inclination setting value is dynamically corrected by the difference in rolling force.

板带材的轧制过程是一个极其复杂的金属压力加工过程，轧后板带材的板凸度和板形决定于轧件在辊缝中的三维变形。金属三维塑性变形模型为辊系变形模型提供轧制压力及其横向分布，辊系变形模型为金属三维塑性变形模型提供轧后带材厚度横向分布。因此依据金属的三维变形模型和辊系变形模型，可以计算出倾斜与两侧轧制力差间的关系，具体计算流程见图4。The rolling process of plate and strip is an extremely complex metal pressure processing process. The plate crown and plate shape of the rolled plate and strip are determined by the three-dimensional deformation of the rolled piece in the roll gap. The three-dimensional plastic deformation model of metal provides rolling pressure and its lateral distribution for the deformation model of the roll system, and the deformation model of the roll system provides the lateral distribution of strip thickness after rolling for the three-dimensional plastic deformation model of the metal. Therefore, based on the three-dimensional deformation model of the metal and the deformation model of the roll system, the relationship between the inclination and the rolling force difference on both sides can be calculated. The specific calculation process is shown in Figure 4.

影响函数方法是一种离散化的方法。它的基本思想是，将轧辊离散成若干单元，将轧辊所承受的载荷及轧辊弹性变形也按相同单元离散化，应用数学物理中关于影响函数的概念先确定对各单元施加单位力时在各点引起的变形，然后将全部载荷作用时在各单元引起的变形叠加，就得出各单元的变形量，从而可以计算出口处的厚度分布，结合金属在辊缝中的横向流动可计算出出口带钢张力分布。The influence function method is a discretization method. Its basic idea is to discretize the roll into several units, discretize the load borne by the roll and the elastic deformation of the roll according to the same unit, and apply the concept of influence function in mathematical physics to first determine when a unit force is applied to each unit. The deformation caused by the point, and then superimpose the deformation caused by each unit when all the loads act, and the deformation of each unit can be obtained, so that the thickness distribution at the exit can be calculated, and the exit can be calculated by combining the lateral flow of metal in the roll gap. Strip tension distribution.

本文以四辊轧制为例计算附加倾斜与两侧轧制力差值的关系，该方法也可以推广到六辊轧机。This paper takes four-high rolling as an example to calculate the relationship between additional inclination and rolling force difference on both sides. This method can also be extended to six-high rolling mill.

1离散化1 discretization

轧件和轧辊离散化过程有两种编号方法，第1中方法是沿辊全身自左向右排列，第2种方法是由轧辊中心向左右两端排列。考虑轧制的对称性，目前国内外的参考文献均采用第2中离散编号方法。由于本技术应用的特殊性，附加倾斜后轧制变形区已不再是以轧制线为中心左右对称，因此工作辊和支撑辊的单元离散编码方法采用第1种编码方法，见图5。There are two numbering methods for the discretization process of rolled pieces and rolls. The first method is to arrange from left to right along the whole body of the roll, and the second method is to arrange from the center of the roll to the left and right ends. Considering the symmetry of rolling, the references at home and abroad all adopt the second discrete numbering method. Due to the particularity of the application of this technology, the rolling deformation zone after additional inclination is no longer symmetrical with the rolling line as the center, so the unit discrete coding method of the work roll and backup roll adopts the first coding method, as shown in Figure 5.

2支撑辊弹性弯曲影响函数g_b 2 Support roll elastic bending influence function g _b

2.1支撑辊弹性弯曲影响函数g_b(xi＞xj)2.1 Support roll elastic bending influence function g _b (xi>xj)

支撑辊的受力可简化为如图6所示的简支梁形式，影响函数可用卡氏定理求出。在距离左支撑点距离为xj点作用单位力1，在距离左支撑点距离为xi点作用虚力且xi＞xj，则在xi点的变形量，即xj点对xi点的影响函数为：The force of the support roller can be simplified as a simply supported beam as shown in Figure 6, and the influence function can be obtained by Karl's theorem. The unit force 1 acts on the point xj from the left support point, and the virtual force acts on the point xi from the left support point. And xi>xj, then the amount of deformation at point xi, that is, the influence function of point xj on point xi is:

$+ + \frac{11}{{E E.}_{b b} {I I}_{b b 11}} {{\frac{{x x}_{i i} {x x}_{j j}}{{l l}_{b b}^{22}} \frac{11}{33} [[{l l}_{b b}^{33} - - {l l}_{D D.}^{33}]] - - \frac{{x x}_{i i} {x x}_{j j}}{{l l}_{b b}} [[{l l}_{b b}^{22} - - {l l}_{D D.}^{22}]] + + {x x}_{i i} {x x}_{j j} [[{l l}_{b b} - - {l l}_{D D.}]]}}$

式中，E_b为支撑辊弹性模量；I_b1、I_b2为支撑辊轴径和辊身的抗弯截面系数；Φ为剪切变形能系数，Φ＝10//9；G为剪切弹性模量；A_b1为轴径处的横截面积；A_b2为辊身的横截面积。In the formula, E _b is the elastic modulus of the support roll; I _b1 and I _b2 are the shaft diameter of the support roll and the bending section coefficient of the roll body; Φ is the shear deformation energy coefficient, Φ=10//9; G is the shear Elastic modulus; A _b1 is the cross-sectional area at the shaft diameter; A _b2 is the cross-sectional area of the roll body.

2.2支撑辊弹性弯曲影响函数g_b(xi＜xj)2.2 Support roll elastic bending influence function g _b (xi<xj)

如图7所示，当xi＜xj时，在距离左支撑点距离为xj点作用单位力1，在距离左支撑点距离为xi点作用虚力xj点对xi点的影响函数可用卡氏定理求出。As shown in Figure 7, when xi<xj, the unit force 1 acts on the point xj from the left support point, and the virtual force acts on the point xi from the left support point The influence function of point xj on point xi can be obtained by Karl's theorem.

$+ + \frac{11}{{E E.}_{b b} {I I}_{b b 11}} [[\frac{{x x}_{i i} {x x}_{j j}}{{l l}_{b b}^{22}} \frac{11}{33} (({l l}_{b b}^{33} - - {l l}_{D D.}^{33})) - - \frac{{x x}_{i i} {x x}_{j j}}{{l l}_{b b}} (({l l}_{b b}^{22} - - {l l}_{D D.}^{22})) + + {x x}_{i i} {x x}_{j j} (({l l}_{b b} - - {l l}_{D D.}))]]$

$+ + \frac{Φ Φ}{{GA GA}_{b b 22}} \frac{{l l}_{b b} - - {x x}_{j j}}{{l l}_{b b}} ((- - \frac{{x x}_{i i}}{{l l}_{b b}})) (({x x}_{j j} - - {x x}_{i i})) + + \frac{Φ Φ}{{GA GA}_{b b 22}} ((- - \frac{{x x}_{j j} {x x}_{i i}}{{l l}_{b b}^{22}})) (({l l}_{D D.} - - {x x}_{j j}))$

支撑辊弯曲影响函数写成矩阵形式为The support roll bending influence function is written in matrix form as

3工作辊弹性弯曲影响函数g_w 3 Work roll elastic bending influence function g _w

3.1工作辊弹性弯曲影响函数g_w(xi＞xj)3.1 Work roll elastic bending influence function g _w (xi＞xj)

如图8所示，当xi＞xj时，在距离左支撑点距离为xj点作用单位力1，在距离左支撑点距离为xi点作用虚力xj点对xi点的影响函数可用卡氏定理求出。As shown in Figure 8, when xi>xj, the unit force 1 acts at the point xj from the left support point, and the virtual force acts on the point xi at the distance from the left support point The influence function of point xj on point xi can be obtained by Karl's theorem.

$+ + \frac{11}{{E E.}_{w w} {I I}_{w w 11}} {{\frac{{x x}_{i i} {x x}_{j j}}{{l l}_{w w}^{22}} \frac{11}{33} [[{l l}_{w w}^{33} - - {l l}_{DW DW}^{33}]] - - \frac{{x x}_{i i} {x x}_{j j}}{{l l}_{w w}} [[{l l}_{w w}^{22} - - {l l}_{DW DW}^{22}]] + + {x x}_{i i} {x x}_{j j} [[{l l}_{w w} - - {l l}_{DW DW}]]}}$

式中，E_w为工作辊弹性模量；I_w1、I_w2为工作辊轴径和辊身的抗弯截面系数；Φ为剪切变形能系数，Φ＝10//9；G为剪切弹性模量；A_w1为工作辊轴径处的横截面积；A_w2为工作辊辊身的横截面积。In the formula, E _w is the elastic modulus of the work roll; I _w1 and I _w2 are the shaft diameter of the work roll and the bending section coefficient of the roll body; Φ is the shear deformation energy coefficient, Φ=10//9; G is the shear deformation coefficient Elastic modulus; A _w1 is the cross-sectional area at the shaft diameter of the work roll; A _w2 is the cross-sectional area of the work roll body.

3.2工作辊弹性弯曲影响函数g_w(xi＜xj)3.2 Work roll elastic bending influence function g _w (xi<xj)

如图9所示，当xi＜xj时，在距离左支撑点距离为xj点作用单位力1，在距离左支撑点距离为xi点作用虚力xj点对xi点的影响函数可用卡氏定理求出。As shown in Figure 9, when xi<xj, the unit force 1 acts on the point xj from the left support point, and the virtual force acts on the point xi from the left support point The influence function of point xj on point xi can be obtained by Karl's theorem.

工作辊弹性弯曲影响函数写成矩阵形式为The work roll elastic bending influence function is written in matrix form as

4轧件和工作辊弹性压扁影响函数g_ws 4 Influence function g _ws of elastic flattening of rolled piece and work roll

轧件和工作辊间由轧制压力引起的工作辊弹性压扁采用户泽推导的工作辊弹性压扁影响函数公式，按照中岛修正理论进行修正后，工作辊弹性压扁影响函数为The elastic flattening of the work roll caused by the rolling pressure between the rolled piece and the work roll is based on the formula of the influence function of the elastic flattening of the work roll derived by the user. After being corrected according to the Nakajima correction theory, the influence function of the elastic flattening of the work roll is

${g g}_{ws ws} ((i i,, j j)) = = \frac{11 - - {v v}_{w w}^{22}}{{πE πE}_{w w} Δx Δx} {{ln ln \frac{\sqrt{{l l}_{d d}^{22} + + {(({X x}_{i i} + + \frac{Δx Δx}{22}))}^{22}} + + {X x}_{i i} + + \frac{Δx Δx}{22}}{\sqrt{{l l}_{d d}^{22} + + {(({X x}_{i i} - - \frac{Δx Δx}{22}))}^{22}} + + {X x}_{i i} - - \frac{Δx Δx}{22}}$

$+ + \frac{(({X x}_{i i} + + \frac{Δx Δx}{22}))}{{l l}_{d d}} ln ln \frac{\sqrt{{l l}_{d d}^{22} + + {(({X x}_{i i} + + \frac{Δx Δx}{22}))}^{22}} + + {l l}_{d d}}{| | {X x}_{i i} + + \frac{Δx Δx}{22} | |} - - \frac{(({X x}_{i i} - - \frac{Δx Δx}{22}))}{{l l}_{d d}} ln ln \frac{\sqrt{{l l}_{d d}^{22} + + {(({X x}_{i i} - - \frac{Δx Δx}{22}))}^{22}} + + {l l}_{d d}}{| | {X x}_{i i} - - \frac{Δx Δx}{22} | |}}}$

$- - \frac{11}{22 ((11 - - {v v}_{w w}))} \times \times [[\frac{{X x}_{i i} + + \frac{Δx Δx}{22}}{\sqrt{{(({X x}_{i i} + + \frac{Δx Δx}{22}))}^{22} + + {R R}_{w w}^{22}}} - - \frac{{X x}_{i i} - - \frac{Δx Δx}{22}}{\sqrt{{(({X x}_{i i} - - \frac{Δx Δx}{22}))}^{22} + + {R R}_{w w}^{22}}}]]$

$- - ln ln \frac{\sqrt{{(({X x}_{i i} - - \frac{Δx Δx}{22}))}^{22} + + {R R}_{w w}^{22}} - - (({X x}_{i i} - - \frac{Δx Δx}{22}))}{\sqrt{{(({X x}_{i i} + + \frac{Δx Δx}{22}))}^{22} + + {R R}_{w w}^{22}} - - (({X x}_{i i} + + \frac{Δx Δx}{22}))}}}$

式中E_w为工作辊的弹性模量；v_w为工作辊的泊松比；Δx为各单元宽度；l_d为第j单元轧件和工作辊接触弧长度，可由希契柯克公式确定，l_d沿板宽方向是一个变量，随各单元轧制压力不同而不同；X_i为第j单元中心点至第i单元中心点的距离；R_w为工作辊半径。In the formula, _{Ew is the modulus of elasticity of the work roll; vw} _is the Poisson’s ratio of the work roll; Δx is the width of each unit; l _d is the length of the contact arc between the rolling piece and the work roll of the jth unit, which can be determined by the Hitchcock formula , l _d is a variable along the plate width direction, which varies with the rolling pressure of each unit; X _i is the distance from the j-th unit center point to the i-th unit center point; R _w is the radius of the work roll.

轧制压力引起的工作辊弹性压扁影响函数写成矩阵形式为The influence function of elastic flattening of work rolls caused by rolling pressure is written in matrix form as

5工作辊弯辊力影响函数Gf5 Work roll bending force influence function Gf

如图10所示，在轧制中心xj处的工作辊轴端支撑处作用单位载荷，由其引起的工作辊弹性变形，即工作辊弯辊力影响函数，可由卡氏定理求出。As shown in Figure 10, the elastic deformation of the work roll caused by the unit load acting on the shaft end support of the work roll at the rolling center xj, that is, the influence function of the work roll bending force, can be obtained by Karnofsky's theorem.

${g g}_{f f} ((i i)) = = \frac{11}{{22 E E.}_{w w} {I I}_{w w 11}} [[{x x}_{i i}^{22} {x x}_{j j} - - \frac{11}{33} {x x}_{i i}^{33}]] = = \frac{11}{{66 E E.}_{w w} {I I}_{w w 11}} [[{x x}_{i i}^{22} ((\frac{{33 l l}_{B B}}{22} - - {x x}_{i i})) + + \frac{55}{66} ((11 + + &upsi; &upsi;)) {D D.}_{w w}^{22} {x x}_{i i}]]$

式中，E_w为工作辊弹性模量；I_w1为工作辊辊身的抗弯截面系数；D_w为工作辊直径。In the formula, E _w is the elastic modulus of the work roll; I _w1 is the bending section coefficient of the work roll body; D _w is the diameter of the work roll.

工作辊弯辊力影响函数的矩阵形式为The matrix form of work roll bending force influence function is

${\overset{r r}{G G}}_{f f} = = {[\begin{matrix} {g g}_{f f} ((11)) & {g g}_{f f} ((22)) & L L & {g g}_{f f} ((NW NW)) \end{matrix}]}^{T T}$

6辊间压扁影响函数g_wb 6 Roll flattening influence function g _wb

辊间压扁影响函数为：The impact function of flattening between rolls is:

${g g}_{wb wb}^{b b} ((i i,, j j)) = = \frac{11 - - {v v}_{b b}^{22}}{{πE πE}_{b b}} . . \frac{33}{44 bΔx bΔx} \times \times {{22 b b ln ln \frac{\sqrt{{b b}^{22} + + {(({X x}_{i i} + + \frac{Δx Δx}{22}))}^{22}} + + {X x}_{i i} + + \frac{Δx Δx}{22}}{\sqrt{{b b}^{22} + + {(({X x}_{i i} - - \frac{Δx Δx}{22}))}^{22}} + + {X x}_{i i} - - \frac{Δx Δx}{22}}$

$+ + 22 (({X x}_{i i} + + \frac{Δx Δx}{22})) ln ln \frac{\sqrt{{b b}^{22} + + {(({X x}_{i i} + + \frac{Δx Δx}{22}))}^{22}} + + b b}{| | {X x}_{i i} + + \frac{Δx Δx}{22} | |} - - 22 (({X x}_{i i} - - \frac{Δx Δx}{22})) ln ln \frac{\sqrt{{b b}^{22} + + {(({X x}_{i i} - - \frac{Δx Δx}{22}))}^{22}} + + b b}{| | {X x}_{i i} - - \frac{Δx Δx}{22} | |}$

$- - \frac{11}{{b b}^{22}} [[- - \frac{b b}{33} (({X x}_{i i} - - \frac{Δx Δx}{22})) \sqrt{{b b}^{22} + + {(({X x}_{i i} - - \frac{Δx Δx}{22}))}^{22}} + + \frac{b b}{33} (({X x}_{i i} + + \frac{Δx Δx}{22})) \sqrt{{b b}^{22} + + {(({X x}_{i i} + + \frac{Δx Δx}{22}))}^{22}}$

$+ + \frac{22}{33} {b b}^{33} ln ln \frac{\sqrt{{b b}^{22} + + {(({X x}_{i i} - - \frac{Δx Δx}{22}))}^{22}} - - (({X x}_{i i} - - \frac{Δx Δx}{22}))}{\sqrt{{b b}^{22} + + {(({X x}_{i i} + + \frac{Δx Δx}{22}))}^{22}} - - (({X x}_{i i} + + \frac{Δx Δx}{22}))} + + \frac{11}{66} {(({X x}_{i i} - - \frac{Δx Δx}{22}))}^{33} ln ln \frac{\sqrt{{b b}^{22} + + {(({X x}_{i i} - - \frac{Δx Δx}{22}))}^{22}} + + b b}{\sqrt{{b b}^{22} + + {(({X x}_{i i} - - \frac{Δx Δx}{22}))}^{22}} - - b b}$

$- - \frac{11}{66} {(({X x}_{i i} + + \frac{Δx Δx}{22}))}^{33} ln ln \frac{\sqrt{{b b}^{22} + + {(({X x}_{i i} + + \frac{Δx Δx}{22}))}^{22}} + + b b}{\sqrt{{b b}^{22} + + {(({X x}_{i i} + + \frac{Δx Δx}{22}))}^{22}} - - b b}]]}}$

$- - \frac{11 - - {v v}_{b b}^{22}}{{πE πE}_{b b} Δx Δx} {{\frac{11}{22 ((11 - - {v v}_{b b}))} [[\frac{{X x}_{i i} + + \frac{Δx Δx}{22}}{\sqrt{{(({X x}_{i i} + + \frac{Δx Δx}{22}))}^{22} + + {R R}_{b b}^{22}}} - - \frac{{X x}_{i i} - - \frac{Δx Δx}{22}}{\sqrt{{(({X x}_{i i} - - \frac{Δx Δx}{22}))}^{22} + + {R R}_{b b}^{22}}}]]$

$+ + ln ln \frac{\sqrt{{(({X x}_{i i} - - \frac{Δx Δx}{22}))}^{22} + + {R R}_{b b}^{22}} - - (({X x}_{i i} - - \frac{Δx Δx}{22}))}{\sqrt{{(({X x}_{i i} + + \frac{Δx Δx}{22}))}^{22} + + {R R}_{b b}^{22}} - - (({X x}_{i i} + + \frac{Δx Δx}{22}))}}}$

式中，v_b为支撑辊的泊松比；E_b为支承辊的弹性模量；b为j单元辊间接触区宽度的一半，由Herz公式计算；X_i为第j单元中点至第i单元中点的距离；Δx为各单元的宽度；R_b为支撑辊的半径。In the formula, v _b is the Poisson's ratio of the support roll; E _b is the elastic modulus of the support roll; b is half the width of the contact area between the j unit rolls, calculated by the Herz formula; X _i is the midpoint of the jth unit to the first The distance between the midpoint of unit i; Δx is the width of each unit; R _b is the radius of the support roller.

工作辊的压扁影响函数为The flattening influence function of the work roll is

${g g}_{wb wb}^{w w} ((i i,, j j)) = = \frac{11 - - {v v}_{w w}^{22}}{{πE πE}_{w w}} . . \frac{33}{44 bΔx bΔx} \times \times {{22 b b ln ln \frac{\sqrt{{b b}^{22} + + {(({X x}_{i i} + + \frac{Δx Δx}{22}))}^{22}} + + {X x}_{i i} + + \frac{Δx Δx}{22}}{\sqrt{{b b}^{22} + + {(({X x}_{i i} - - \frac{Δx Δx}{22}))}^{22}} + + {X x}_{i i} - - \frac{Δx Δx}{22}}$

$- - \frac{11 - - {v v}_{w w}^{22}}{{πE πE}_{w w} Δx Δx} {{\frac{11}{22 ((11 - - {v v}_{b b}))} [[\frac{{X x}_{i i} + + \frac{Δx Δx}{22}}{\sqrt{{(({X x}_{i i} + + \frac{Δx Δx}{22}))}^{22} + + {R R}_{w w}^{22}}} - - \frac{{X x}_{i i} - - \frac{Δx Δx}{22}}{\sqrt{{(({X x}_{i i} - - \frac{Δx Δx}{22}))}^{22} + + {R R}_{w w}^{22}}}]]$

$+ + ln ln \frac{\sqrt{{(({X x}_{i i} - - \frac{Δx Δx}{22}))}^{22} + + {R R}_{w w}^{22}} - - (({X x}_{i i} - - \frac{Δx Δx}{22}))}{\sqrt{{(({X x}_{i i} + + \frac{Δx Δx}{22}))}^{22} + + {R R}_{w w}^{22}} - - (({X x}_{i i} + + \frac{Δx Δx}{22}))}}}$

式中，v_w为工作辊的泊松比；E_w为工作辊的弹性模量；b为j单元辊间接触区宽度的一半，由Herz公式计算；X_i为第j单元中点至第i单元中点的距离；Δx为各单元的宽度；R_w为工作辊的半径。In the formula, v _w is the Poisson's ratio of the work roll; E _w is the elastic modulus of the work roll; b is half of the width of the contact area between the j unit rolls, calculated by the Herz formula; X _i is the midpoint of the jth unit to the first The distance between the midpoint of unit i; Δx is the width of each unit; R _w is the radius of the work roll.

辊间压扁影响函数为The influence function of flattening between rolls is

${g g}_{wb wb} ((i i,, j j)) = = {g g}_{wb wb}^{b b} ((i i,, j j)) + + {g g}_{wb wb}^{w w} ((i i,, j j))$

辊间压扁影响函数的矩阵形式为The matrix form of the impact function of flattening between rolls is

${\overset{ρ ρ}{G G}}_{wb wb} = = [\begin{matrix} {g g}_{wb wb} ((1,1 1,1)) & Λ Λ & {g g}_{wb wb} ((11,, n no)) \\ M m & M m \\ {g g}_{wb wb} ((n no,, 11)) & Λ Λ & {g g}_{wb wb} ((n no,, n no)) \end{matrix}]$

式中n＝min{NW，NB}。In the formula, n=min{NW, NB}.

7静力平衡方程7 Static Balance Equations

工作辊静力平衡方程为The static balance equation of the work roll is

式中，为轧制压力；F_WD为工作辊传动侧的弯辊力；F_WO为工作辊操作侧的弯辊力；为辊间压力； $\overset{r}{P} = {[\begin{matrix} p (1) & p (2) & L & p (NS) \end{matrix}]}^{T},$ $\overset{r}{Q} = {[\begin{matrix} q (1) & q (2) & L & q (n) \end{matrix}]}^{T} .$ In the formula, is the rolling pressure; F _WD is the bending force of the driving side of the work roll; F _WO is the bending force of the operating side of the work roll; is the pressure between the rollers; $\overset{r}{P} = {[\begin{matrix} p (1) & p (2) & L & p (NS) \end{matrix}]}^{T},$ $\overset{r}{Q} = {[\begin{matrix} q (1) & q (2) & L & q (no) \end{matrix}]}^{T} .$

支撑辊的静力平衡方程为The static balance equation of the support roller is

式中FR_WD为支撑辊传动侧轧制力；FR_WO为支撑辊操作侧轧制力。In the formula, FR _WD is the rolling force of the driving side of the backup roll; FR _WO is the rolling force of the operating side of the backup roll.

8变形协调关系方程8 Deformation coordination relation equation

8.1工作辊和支撑辊间的变形协调关系8.1 Deformation coordination relationship between work rolls and backup rolls

式中In the formula

$\overset{r}{T} = {[\begin{matrix} t (1) & t (2) & L & t (NB) \end{matrix}]}^{T}$ 为支撑辊的倾斜向量。 $\overset{r}{T} = {[\begin{matrix} t (1) & t (2) & L & t (NB) \end{matrix}]}^{T}$ is the tilt vector of the support roller.

${\overset{r}{Y}}_{wb 0} = {[\begin{matrix} y_{wb 0} (0) & y_{wb 0} (0) & L & y_{wb 0} (0) \end{matrix}]}^{T}$ 是常向量，即辊面中心处的压扁量。 ${\overset{r}{Y}}_{wb 0} = {[\begin{matrix} {the y}_{wb 0} (0) & {the y}_{wb 0} (0) & L & {the y}_{wb 0} (0) \end{matrix}]}^{T}$ is a constant vector, that is, the amount of flattening at the center of the roll surface.

${\overset{r}{M}}_{b} = {[\begin{matrix} m_{b} (1) & m_{b} (2) & L & m_{b} (n) \end{matrix}]}^{T}$ 是支撑辊凸度向量。 ${\overset{r}{m}}_{b} = {[\begin{matrix} m_{b} (1) & m_{b} (2) & L & m_{b} (no) \end{matrix}]}^{T}$ is the backup roll crown vector.

8.2工作辊和带钢之间的变形协调关系8.2 Deformation coordination relationship between work roll and strip steel

式中In the formula

式中是轧件轧后厚度向量；In the formula is the thickness vector of the rolled piece after rolling;

是常向量，即板中心处轧后厚度； is a constant vector, that is, the rolled thickness at the center of the plate;

是常向量，即板中心处的压扁量； is a constant vector, the amount of flattening at the center of the plate;

${\overset{r}{Y}}_{ws} = {[\begin{matrix} y_{ws} (1) & y_{ws} (2) & L & y_{ws} (NS) \end{matrix}]}^{T},$ 由轧制压力引起的工作辊弹性压扁向量， ${\overset{r}{Y}}_{ws} = {[\begin{matrix} {the y}_{ws} (1) & {the y}_{ws} (2) & L & {the y}_{ws} (NS) \end{matrix}]}^{T},$ The elastic flattening vector of the work rolls caused by the rolling pressure,

${\overset{r}{Y}}_{w} = {[\begin{matrix} y_{w} (1) & w_{w} (2) & L & y_{w} (NW) \end{matrix}]}^{T},$ 为工作辊挠度向量； ${\overset{r}{Y}}_{w} = {[\begin{matrix} {the y}_{w} (1) & w_{w} (2) & L & {the y}_{w} (NW) \end{matrix}]}^{T},$ is the work roll deflection vector;

9张应力分布计算9 stress distribution calculations

冷轧生产过程采用大张力轧制，张力分布影响轧制力分布，从而影响辊缝形状和出口带钢厚度分布。因此冷轧机出口厚度的分布必须考虑张力的影响。冷轧带钢张力分布计算方法有变分法、条元法、边界元法和实验方法。本专利中张应力的计算采用变分能量法，考虑到轧制的非对称性，带钢的出、入口厚度采用三次样条函数拟合，并没有采用基于对称性的高次多项式拟合，最终可求得出口带钢横向张应力分布。The cold rolling production process adopts high-tension rolling, and the tension distribution affects the distribution of rolling force, thereby affecting the shape of the roll gap and the thickness distribution of the exit strip. Therefore, the distribution of the exit thickness of the cold rolling mill must take into account the influence of tension. Calculation methods for tension distribution of cold-rolled strip include variational method, strip element method, boundary element method and experimental method. The calculation of the tensile stress in this patent adopts the variational energy method. Considering the asymmetry of rolling, the exit and entrance thickness of the strip is fitted by a cubic spline function instead of a high-order polynomial fitting based on symmetry. Finally, the transverse tensile stress distribution of the outlet strip can be obtained.

${σ σ}_{11} ((y the y)) = = \overset{&OverBar; &OverBar;}{{σ σ}_{11}} + + \frac{E E.}{11 - - {&upsi; &upsi;}^{22}} [[11 + + \frac{h h ((y the y))}{\overset{&OverBar; &OverBar;}{h h}} - - \frac{H h ((y the y))}{\overset{&OverBar; &OverBar;}{H h}} - - \frac{L L ((y the y))}{\overset{&OverBar; &OverBar;}{L L}} + + {u u}^{' '} ((y the y)) - - \frac{Δb Δb}{B B}]]$

式中，H(y)、h(y)——入、出口板厚横向分布函数，mm；In the formula, H(y), h(y)—transverse distribution function of inlet and outlet plate thickness, mm;

E、υ——带材弹性模量和泊松比；E, υ——strip elastic modulus and Poisson's ratio;

——带材的平均前张应力，MPa； ——the average pretension stress of the strip, MPa;

L(y)——来料长度横向分布函数，mm；L(y)——transverse distribution function of incoming material length, mm;

H，h，L——H(y)，h(y)，L(y)的平均值，mm；H, h, L—the average value of H(y), h(y), L(y), mm;

u(y)——带材出口横向位移函数，mm；u(y)——transverse displacement function of strip outlet, mm;

Δb——带材宽展量，mm；Δb——strip width, mm;

如图11所示，带钢横向张应力计算过程中将带钢分成NS个单元，每个单元的宽度为Δx。各单元带钢的出入口厚度和入口带钢长度用三次样条函数拟合为As shown in Figure 11, the strip is divided into NS units during the calculation of the transverse tensile stress of the strip, and the width of each unit is Δx. The entrance and exit thickness and entrance strip length of each unit strip are fitted by the cubic spline function as

H(y)＝A_jy³+B_jy²+C_jy+D_j H(y)＝A _j y ³ +B _j y ² +C _j y+D _j

h(y)＝F_jy³+G_jy²+M_jy+N_j h(y)＝F _j y ³ +G _j y ² +M _j y+N _j

L(y)＝P_jy³+Q_jy²+R_jy+T_j L(y)＝P _j y ³ +Q _j y ² +R _j y+T _j

根据轧制过程中变性能最小原理，通过变分求解欧拉方程的方法，可求得第j个单元内金属的横向位移函数为According to the minimum principle of variable performance in the rolling process, the lateral displacement function of the metal in the jth unit can be obtained by solving the Euler equation by variation:

u(j)＝C₁ch(Ky)+C₂sh(Ky)+d_jy²+e_jy+f_j u(j)＝C ₁ ch(Ky)+C ₂ sh(Ky)+d _j y ² +e _j y+f _j

式中， $C_{1} = - \frac{ξ_{1} + ξ_{3} + ξ_{5}}{ξ_{2} + ξ_{4} + ξ_{6}}$ In the formula, $C_{1} = - \frac{ξ_{1} + ξ_{3} + ξ_{5}}{ξ_{2} + ξ_{4} + ξ_{6}}$

${ξ ξ}_{11} = = \frac{{kh kh}_{c c}}{Δh Δh} {Σ Σ}_{j j = = 11}^{NS NS} \{\begin{matrix} [[(({44 d d}_{j j} {y the y}_{j j} + + {22 e e}_{j j})) ch ch (({Ky Ky}_{j j})) - - (({44 d d}_{j j} {y the y}_{j j - - 11} + + {22 e e}_{j j})) ch ch (({Ky Ky}_{j j - - 11}))]] \\ - - \frac{44}{K K} {d d}_{j j} [[sh sh (({Ky Ky}_{j j})) - - sh sh (({Ky Ky}_{j j - - 11}))]] \end{matrix}\}$

${ξ ξ}_{22} = = \frac{{h h}_{c c}}{Δh Δh} kK k [[sh sh ((KB KB)) - - KB KB]]$

${ξ ξ}_{33} = = \{\begin{matrix} \frac{88 t t}{Δhl Δhl} \frac{11}{{K K}^{22}} {Σ Σ}_{j j = = 11}^{NS NS} [[(({22 d d}_{j j} {y the y}_{j j - - 11} + + {e e}_{j j})) ch ch (({Ky Ky}_{j j - - 11})) - - (({22 d d}_{j j} {y the y}_{j j} + + {e e}_{j j})) ch ch (({Ky Ky}_{j j}))]] \\ + + \frac{88 t t}{Δhl Δhl} \frac{11}{{K K}^{33}} {Σ Σ}_{j j = = 11}^{NS NS} [[{22 d d}_{j j} + + {f f}_{j j} {K K}^{22} + + {e e}_{j j} {K K}^{22} {y the y}_{j j} + + {d d}_{j j} {K K}^{22} {y the y}_{j j}^{22}]] sh sh (({Ky Ky}_{j j})) \\ - - \frac{88 t t}{Δhl Δhl} \frac{11}{{K K}^{33}} {Σ Σ}_{j j = = 11}^{NS NS} [[{22 d d}_{j j} + + {f f}_{j j} {K K}^{22} + + {e e}_{j j} {K K}^{22} {y the y}_{j j - - 11} + + {d d}_{j j} {K K}^{22} {y the y}_{j j - - 11}^{22}]] sh sh (({Ky Ky}_{j j - - 11})) \end{matrix}\}$

${ξ ξ}_{44} = = \frac{44 t t}{ΔhlK ΔhlK} [[sh sh ((KB KB)) + + KB KB]]$

${ξ ξ}_{66} = = \frac{E E.}{11 - - {&upsi; &upsi;}^{22}} \frac{K K}{22} [[sh sh ((KB KB)) - - KB KB]]$

${C C}_{22} = = - - \frac{{ζ ζ}_{22} + + {ζ ζ}_{33} + + {ζ ζ}_{55} + + {ζ ζ}_{77} + + {ζ ζ}_{88} + + {ζ ζ}_{99} + + {ζ ζ}_{1010} + + {ζ ζ}_{1111} + + {ζ ζ}_{1212}}{{ζ ζ}_{11} + + {ζ ζ}_{44} + + {ζ ζ}_{66}}$

${ζ ζ}_{11} = = \frac{{kh kh}_{c c} K K}{Δh Δh} [[sh sh ((KB KB)) + + KB KB]]$

${ζ ζ}_{22} = = - - 22 ksh ksh ((\frac{KB KB}{22}))$

${ζ ζ}_{33} = = \frac{{22 kh kh}_{c c}}{Δh Δh} {Σ Σ}_{j j = = 11}^{NS NS} {{[[(({e e}_{j j} + + {22 d d}_{j j} {y the y}_{j j})) sh sh (({Ky Ky}_{j j})) - - (({e e}_{j j} + + {22 d d}_{j j} {y the y}_{j j - - 11})) sh sh (({Ky Ky}_{j j - - 11}))]] - - \frac{{22 d d}_{j j} [[ch ch (({Ky Ky}_{j j})) - - ch ch (({Ky Ky}_{j j - - 11}))]]}{K K}}}$

${ζ ζ}_{44} = = \frac{44 t t}{Δhlk Δhlk} [[sh sh ((KB KB)) - - KB KB]]$

${ζ ζ}_{55} = = \{\begin{matrix} \frac{88 t t}{Δhl Δhl} \frac{11}{{K K}^{33}} {Σ Σ}_{j j = = 11}^{NS NS} [[{22 d d}_{j j} + + {f f}_{j j} {K K}^{22} + + {e e}_{j j} {K K}^{22} {y the y}_{j j} + + {d d}_{j j} {K K}^{22} {y the y}_{j j}^{22}]] ch ch (({Ky Ky}_{j j})) \\ - - \frac{88 t t}{Δhl Δhl} \frac{11}{{K K}^{33}} {Σ Σ}_{j j = = 11}^{NS NS} [[{22 d d}_{j j} + + {f f}_{j j} {K K}^{22} + + {e e}_{j j} {K K}^{22} {y the y}_{j j - - 11} + + {d d}_{j j} {K K}^{22} {y the y}_{j j - - 11}^{22}]] ch ch (({Ky Ky}_{j j - - 11})) \\ + + \frac{88 t t}{Δhl Δhl} \frac{11}{{K K}^{22}} {Σ Σ}_{j j = = 11}^{NS NS} {{[[(({e e}_{j j} + + {22 d d}_{j j} {y the y}_{j j - - 11})) sh sh (({Ky Ky}_{j j - - 11})) - - (({e e}_{j j} + + {22 d d}_{j j} {y the y}_{j j})) sh sh (({Ky Ky}_{j j}))]]}} \end{matrix}\}$

${ζ ζ}_{66} = = \frac{E E.}{22 B B ((11 - - {&upsi; &upsi;}^{22}))} [[{B B}^{22} {K K}^{22} + + BKsh BYZGR ((KB KB)) - - {88 sh sh}^{22} ((\frac{KB KB}{22}))]]$

${ζ ζ}_{77} = = - - \frac{E E.}{11 - - {&upsi; &upsi;}^{22}} \frac{11}{{K K}^{33}} {Σ Σ}_{j j = = 11}^{NS NS} [[{66 g g}_{j j} + + {l l}_{j j} {K K}^{22} + + {22 d d}_{j j} {K K}^{22} + + {22 h h}_{j j} {K K}^{22} {y the y}_{j j} + + {33 g g}_{j j} {K K}^{22} {y the y}_{j j}^{22}]] ch ch (({Ky Ky}_{j j}))$

${ζ ζ}_{88} = = \frac{E E.}{11 - - {&upsi; &upsi;}^{22}} \frac{11}{{K K}^{33}} {Σ Σ}_{j j = = 11}^{NS NS} [[{66 g g}_{j j} + + {l l}_{j j} {K K}^{22} + + {22 d d}_{j j} {K K}^{22} + + {22 h h}_{j j} {K K}^{22} {y the y}_{j j - - 11} + + {33 g g}_{j j} {K K}^{22} {y the y}_{j j - - 11}^{22}]] ch ch (({Ky Ky}_{j j - - 11}))$

${ζ ζ}_{99} = = - - \frac{E E.}{66 B B ((11 - - {&upsi; &upsi;}^{22}))} sh sh ((\frac{KB KB}{22})) {Σ Σ}_{j j = = 11}^{NS NS} [[{1212 m m}_{j j} {y the y}_{j j} + + {1212 e e}_{j j} {y the y}_{j j} + + {1212 d d}_{j j} {y the y}_{j j}^{22} + + {66 l l}_{j j} {y the y}_{j j}^{22} + + {44 h h}_{j j} {y the y}_{j j}^{33} + + {33 g g}_{j j} {y the y}_{j j}^{44}]]$

${ζ ζ}_{1010} = = \frac{E E.}{66 B B ((11 - - {&upsi; &upsi;}^{22}))} sh sh ((\frac{KB KB}{22})) {Σ Σ}_{j j = = 11}^{NS NS} [[{1212 m m}_{j j} {y the y}_{j j - - 11} + + {1212 e e}_{j j} {y the y}_{j j - - 11} + + {1212 d d}_{j j} {y the y}_{j j - - 11}^{22} + + {66 l l}_{j j} {y the y}_{j j - - 11}^{22} + + {44 h h}_{j j} {y the y}_{j j - - 11}^{33} + + {33 g g}_{j j} {y the y}_{j j - - 11}^{44}]]$

${ζ ζ}_{1111} = = \frac{E E.}{11 - - {&upsi; &upsi;}^{22}} \frac{11}{{K K}^{22}} {Σ Σ}_{j j = = 11}^{NS NS} [[{22 h h}_{j j} + + {m m}_{j j} K K + + {e e}_{j j} K K + + {66 g g}_{j j} {y the y}_{j j} + + {22 d d}_{j j} {K K}^{22} {y the y}_{j j} + + {l l}_{j j} {K K}^{22} {y the y}_{j j} + + {h h}_{j j} {K K}^{22} {y the y}_{j j}^{22} + + {g g}_{j j} {K K}^{22} {y the y}_{j j}^{33}]] sh sh (({Ky Ky}_{j j}))$

${ζ ζ}_{1212} = = - - \frac{E E.}{11 - - {&upsi; &upsi;}^{22}} \frac{11}{{K K}^{22}} {Σ Σ}_{j j = = 11}^{NS NS} [[{22 h h}_{j j} + + {m m}_{j j} K K + + {e e}_{j j} K K + + {66 g g}_{j j} {y the y}_{j j - - 11} + + {22 d d}_{j j} {K K}^{22} {y the y}_{j j - - 11} + + {l l}_{j j} {K K}^{22} {y the y}_{j j - - 11} + + {h h}_{j j} {K K}^{22} {y the y}_{j j - - 11}^{22} + + {g g}_{j j} {K K}^{22} {y the y}_{j j - - 11}^{33}]] sh sh (({Ky Ky}_{j j - - 11}))$

${d d}_{j j} = = - - \frac{{a a}_{j j}}{{K K}^{22}}$

${e e}_{j j} = = - - \frac{{b b}_{j j}}{{K K}^{22}}$

${f f}_{j j} = = - - \frac{{22 a a}_{j j}}{{K K}^{44}} - - \frac{{c c}_{j j}}{{K K}^{22}}$

${a a}_{j j} = = - - \frac{33}{ξ ξ} ((\frac{{F f}_{j j}}{h h} - - \frac{{A A}_{j j}}{H h} - - \frac{{P P}_{j j}}{L L}))$

${b b}_{j j} = = - - \frac{22}{ξ ξ} ((\frac{{G G}_{j j}}{h h} - - \frac{{B B}_{j j}}{H h} - - \frac{{Q Q}_{j j}}{L L}))$

${c c}_{j j} = = - - \frac{11}{ξ ξ} ((\frac{{M m}_{j j}}{h h} - - \frac{{C C}_{j j}}{H h} - - \frac{{R R}_{j j}}{L L}))$

各式中，k为剪切应变强度；h_c为变形区带钢平均厚度；Δh带钢出入口厚度平均值差；K是与h_c、k、Δh、E、υ等相关的过程计算变量；t为变形区表面平均摩擦力；l为轧辊压扁弧长；ξ是与υ、E、k、h_c、Δh等相关的过程计算变量。Among the various formulas, k is the shear strain intensity; h _c is the average thickness of the strip steel in the deformation zone; Δh is the difference between the average thickness of the strip steel entrance and exit; K is the process calculation variable related to h _c , k, Δh, E, υ, etc.; t is the average friction force on the surface of the deformation zone; l is the flattening arc length of the roll; ξ is the process calculation variable related to υ, E, k, h _c , Δh, etc.

10操作侧轧制力和传动侧轧制力差值计算10 Calculation of the difference between the rolling force on the operating side and the rolling force on the driving side

支撑辊受力分析见图12，轧辊沿轴线分成NB个单元，每个单元的宽度为Δx，各单元作用集中载荷q(i)，操作侧支点的载荷为F_o，传动侧支撑点的载荷为F_D。根据力矩平衡条件，各力相对于操作侧支撑点的和力矩为零，即The force analysis of the support roll is shown in Fig. 12. The roll is divided into NB units along the axis, the width of each unit is Δx, and the concentrated load q(i) acts on each unit. The load of the fulcrum on the operating side is F _o , and the The load is F _D . According to the moment balance condition, the sum moment of each force relative to the support point on the operating side is zero, that is

${Σ Σ}_{i i = = 11}^{NB NB} q q ((i i)) X x ((i i)) - - {F f}_{D D.} {l l}_{b b} = = 00$

${F f}_{D D.} = = \frac{11}{{l l}_{b b}} {Σ Σ}_{i i = = 11}^{NB NB} q q ((i i)) X x ((i i))$

${F f}_{O o} = = {Σ Σ}_{i i = = 11}^{NB NB} q q ((i i)) - - {F f}_{D D.}$

两侧轧制力差值为The rolling force difference on both sides is

ΔF＝F_D-F_O ΔF＝F _D -F _O

带钢的屈服强度σ_s＝600MPa，带钢宽度为1380mm，入口厚度为6mm，压下率为0.32，入口设定张力为130MPa，出口带钢设定张力136MPa，支撑辊直径0.9906m，工作辊直径0.60007m，工作辊凸度为0.02mm，支撑辊凸度0.05mm，各划分单元宽度为20mm，弯辊力为30KN，计算结果如图13所示。The yield strength of the strip steel σ _s = 600MPa, the strip width is 1380mm, the entrance thickness is 6mm, the reduction rate is 0.32, the entrance tension is 130MPa, the exit strip tension is 136MPa, the support roll diameter is 0.9906m, the work roll The diameter is 0.60007m, the crown of the work roll is 0.02mm, the crown of the backup roll is 0.05mm, the width of each division unit is 20mm, and the bending force is 30KN. The calculation results are shown in Figure 13.

拟合多项式为The fitting polynomial is

tilt＝3.9×10^-10ΔF+2.4×10^-9 tilt=3.9×10 ^-10 ΔF+2.4×10 ^-9

11模型自适应修正11 Model Adaptive Correction

影响函数法计算辊系变形和能量变分法求解辊缝中金属横向流动问题，是实用的计算带钢出口横向厚度分布和张力分布的工程计算方法。但在求解辊系变形、张力公式的推导和求解欧拉微分方程的过程中做了许多近似和简化，使得出口横向厚度分布和张应力分布的计算结果存在一定的误差。实际应用时可根据实际带钢的入口厚度、出口厚度、压下量、变形抗力、带钢宽度、出口设定张力、入口设定张力、工作辊和支撑辊辊径、工作辊和支撑辊凸度、带钢跑偏值等预计算出倾斜与两侧轧制力差值间的关系，并用多项式进行拟合，在线使用时依据实测倾斜和两侧轧制力差值在线修正多项式模型中各项系数。根据两侧轧制力差值，计算出相应的倾斜值，以该倾斜值作为设定倾斜的限幅值，其原理如图14所示。The influence function method to calculate the deformation of the roll system and the energy variation method to solve the problem of metal lateral flow in the roll gap are practical engineering calculation methods for calculating the lateral thickness distribution and tension distribution of the strip outlet. However, many approximations and simplifications have been made in the process of solving the deformation of the roll system, the derivation of the tension formula and the solution of the Euler differential equation, so that there are certain errors in the calculation results of the outlet transverse thickness distribution and tensile stress distribution. In actual application, it can be based on the actual strip entrance thickness, exit thickness, reduction, deformation resistance, strip width, exit set tension, entrance set tension, work roll and backup roll diameter, work roll and support roll convexity Pre-calculate the relationship between the inclination and the rolling force difference on both sides, and use polynomials to fit it, and correct the items in the polynomial model online based on the measured inclination and the rolling force difference on both sides. coefficient. According to the rolling force difference on both sides, the corresponding inclination value is calculated, and this inclination value is used as the limiting value of the inclination setting. The principle is shown in Figure 14.

实施例：根据实际带钢的入口厚度、出口厚度、压下量、变形抗力、带钢宽度、出口设定张力、入口设定张力、工作辊和支撑辊辊径、工作辊和支撑辊凸度、带钢跑偏值等预计算出倾斜与两侧轧制力差值间的关系，以轧制力差值为自变量，以倾斜为因变量，用多项式拟合出轧制力差值和倾斜的函数关系 Example: According to the actual strip entrance thickness, exit thickness, reduction, deformation resistance, strip width, exit set tension, entrance set tension, work roll and back-up roll diameter, work roll and back-up roll crown Pre-calculate the relationship between the inclination and the rolling force difference on both sides, taking the rolling force difference as the independent variable and the inclination as the dependent variable, and use polynomial fitting to obtain the rolling force difference and inclination functional relationship

应用时根据实际检测的两侧轧制力差值ΔE_DO，通过上式计算出轧辊的倾斜值，并把它作为设定倾斜值的限幅。当带钢出现部裂纹、原料板形问题导致两侧张力差或板形系统检测元件精度下降，致使倾斜调整量不断增加，通过有效的限幅，可以限制倾斜调整量幅值，避免倾斜值过大而导致断带事故的发生，其原理见图13。In application, according to the actually detected rolling force difference ΔE _DO on both sides, the inclination value of the roll is calculated by the above formula, and it is used as the limit of the set inclination value. When cracks appear in the strip steel, the shape of the raw material leads to tension difference on both sides or the accuracy of the detection element of the plate shape system decreases, resulting in a continuous increase in the tilt adjustment. Through effective limiting, the amplitude of the tilt adjustment can be limited to avoid excessive tilt. Large and lead to the occurrence of broken belt accident, its principle is shown in Figure 13.

为消除理论计算模型的误差，可根据检测的实际轧制力差和实际倾斜数据对[ΔF_act(k)，tilt_act(k)](k＝1，2，3，…)，用最小二乘法，依据误差平方和最小原理动态修正倾斜-轧制力差多项式中的各项系数，修正后的多项式为下一次修正前的倾斜限幅值，可根据修正后的多项式计算。In order to eliminate the error of the theoretical calculation model, [ΔF _act (k), tilt _act (k)] (k = 1, 2, 3, ...), the least squares can be used according to the actual rolling force difference detected and the actual tilt data Multiplication, according to the error square sum minimum principle to dynamically correct the coefficients in the tilt-rolling force difference polynomial, the corrected polynomial is The slope limit value before the next correction can be calculated according to the corrected polynomial.

Claims

1. cold-rolling mill Roll-gap position pressure double-closed-loop control method, it is characterised in that after milling train additional tilt, bilateral is asymmetric rolls Power processed calculates；Derived according to Ka Shi energy theorem be suitable to that Asymmetric Rolling calculates support roller, working roll simply supported beam form Elastic bending influence function；Rolls' deformation theory effectively integrates with metal theory of cross-flow；To conventional roll system Deformation Theory In Coordinate deformation equation be effectively improved；The error calculated in view of theory, is carried out theoretical calculation model in real time Online adaptive correction；

After rolling mill additional tilt, contact in rolling is the most no longer traditional left and right centered by rolling centerline Symmetry, but asymmetrical, when carrying out asymmetric calculating, the roll-force of the left and right sides is unknown number；When calculating, unit is drawn Being divided into and arranging from left to right along roller whole body, support bending influence function of deriving is:

In formula, E_bFor supporting roller elastic modelling quantity；I_b1For supporting the bending resistant section coefficient in roll shaft footpath；I_b2For supporting the bending resistance of the roller body of roll Section factor；Φ is shearing deformation energy coefficient, Φ=10//9；G is the coefficient of rigidity；A_b1Transversal for support at roll shaft footpath Area；A_b2For supporting the cross-sectional area of the roller body of roll；l_bFor supporting roller two ends strong point spacing；l_OFor the axle head strong point to body of roll end The distance in face；x_iFor the virtual force application point distance away from the axle head strong point；x_jFor the unit point of force application distance away from the axle head strong point； l_DFor the axle head strong point distance away from opposite side end surface of roll；

Working roller bending influence function is:

In formula, E_wFor working roll elastic modelling quantity；I_w1Bending resistant section coefficient for the working roll diameter of axle；I_w2Bending resistance for the working roll body of roll Section factor；Φ is shearing deformation energy coefficient, Φ=10//9；G is the coefficient of rigidity；A_w1Transversal at the working roll diameter of axle Area；A_w2Cross-sectional area for the working roll body of roll；l_wFor working roll two ends support distances；x_iSupport away from axle head for virtual force application point The distance of point；x_jFor the unit point of force application distance away from the axle head strong point；l_OWThe fore side strong point is away from fore side end surface of roll Distance；l_DWFor the fore side strong point distance away from transmission side end surface of roll；

Coordinate deformation equation between working roll and support roller is:

In formula

For supporting the tilt vector of roller；

For flattening vector between roller,

Constant vector, i.e. the flattening amount of roll surface center；

It is to support roll crown vector；

It it is work roll crown vector；

NB is for supporting roller cutting unit quantity；For working roller bending amount of deflection vector.

Cold-rolling mill Roll-gap position pressure double-closed-loop control method the most according to claim 1, it is characterised in that additional tilt Calculated by rolls' deformation and deformed area metal lateral flow afterwards, finally can obtain both sides roll-force and difference is:

Transmission side roll-force:

Fore side roll-force is:

Both sides roll-force difference is: Δ F=F_D-F_O

L in formula_bFor supporting roller two ends strong point spacing；NB is for supporting roller cutting unit quantity；Q (i) is that i-th cutting unit is made Load；X (i) is the i-th cutting unit distance away from the fore side strong point；With roll-force difference as independent variable, to tilt Value is dependent variable, and the functional relation going out roll-force difference and tilting value with fitting of a polynomial is

In formula: tilt is tilting value；a₀I () is the coefficient of polynomial fitting i & lt item；N is the high reps of polynomial fitting.

Cold-rolling mill Roll-gap position pressure double-closed-loop control method the most according to claim 1, it is characterised in that for eliminating reason The error of opinion computation model, can be according to the actual roll-force of detection is poor and actual tilt data are to [Δ F_act(k), tilt_act(k)] K=1,2,3 ..., by least square method, according in error sum of squares minimum principle dynamic corrections inclination-roll-force difference multinomial Each term coefficient, after correction, the functional relation of roll-force difference and tilting value is

In formula: tilt is tilting value；a₁I () is the coefficient of revised polynomial fitting i & lt item；N be polynomial fitting High reps；Δ F is the difference of transmission side rolling and fore side roll-force.