带钢局部高点 卷取过程起筋控制的建模与仿真研究.docx

1、带钢局部高点 卷取过程起筋控制的建模与仿真研究带钢局部高点卷取过程起筋控制的建模与仿真研究管健龙1) 何安瑞1) 孙文权1) 郭睿2)1)北京科技大学高效轧制国家工程研究中心, 北京 100083 2) 首都航天机械公司, 北京 100076通信作者, E-mail: wqsun18摘 要 为了研究带钢局部高点卷取起筋的控制方法，借鉴三维弹塑性变形思想，并引入带钢塑性流动因数，建立了弹塑性卷取应力和起筋量模型，并基于应力函数假设、S. Timoshenko最小功原理和伽辽金虚位移法建立了起筋带钢的应力场分布和可用于在线计算的起筋临界卷取张力设定模型。对钢卷起筋量、应力场分布和临界卷取张力的各影

2、响参数进行仿真研究，仿真结果表明：局部高点在径向累积叠加所引起的带钢张力不均匀分布和轴向压应力是导致带钢起筋的主要原因；起筋量随局部高点高度、卷径和卷取张力增加而增大，薄带钢比厚带钢起筋量增幅明显，起筋多发生在带钢中部和距中部100mm附近；临界卷取张力随卷径、带钢厚度、局部高点高度增大而减小。通过与实际生产控制方法和ANSYS有限元分析结果对比，验证了本模型的计算精度和可行性。关键词 局部高点; 弹塑性变形; 塑性流动因数; 起筋; 临界卷取张力; ANSYS有限元法分类号 TG335.5Research and simulation of the ridge-buckle control

3、model in the coiling process of strip steel with local high pointGUAN Jian-long1), HE An-rui1), SUN Wen-quan1) , GUO Rui2)1) University of Science & Technology, National Engineering Research Center for Advanced Rolling Technology, Beijing 100083, China2) Capital Aerospace Machinery Co. Ltd., Beijing

4、 100076, China)Corresponding author, E-mail: wqsun18ABSTRACT In order to research the ridge-buckle control method in coiling process of strip steel with local high point, by using the theory of three dimensional elastic-plastic deformation, introducing plastic flow factor, to establish the model of

5、elastic-plastic stress and ridge-buckle, getting the stress field distribution of ridge-buckle base on the hypothesis about stress function and the S. Timoshenko least work principle, establish the buckling critical coiling tension setting model can be calculated online using the theory of Galerkin

6、virtual displacement. Through the simulation of stress field distribution, the amount of ridge-buckle and factors on critical coiling tension, shows that uneven distribution of strip steel tension caused by radial accumulation of local high points is the main cause of strip ridge-buckle; the ridge-b

7、uckle quantity increases with local high point, diameter and coiling tension, the ridge-buckle of thin strip is more obvious than the thick ones, ridge-buckle occurs frequently in the middle or from the middle of 100mm of strip steel; critical coiling tension decreases with the increase of the thick

8、ness of strip, height of local high points and coiling radius. Thecomputational accuracy and feasibility of this model is confirmed by the comparison of actual production control method and ANSYS finite element method results.KEY WORDS local high point; elastic-plastic deformation; plastic flow fact

9、or; ridge-buckle; critical coiling stress; ANSYS FEM.前言“起筋”缺陷是指带材在卷取过程中由于局部高点沿径向逐层累加而在钢卷表面形成的一种“鼓包”现象，如图1所示。当起筋量较大时，开卷后在起筋部位表现为附加浪形，严重影响产品性能，造成产品降级或报废1。由于“起筋”现象机理复杂，多年来对其成因一直未能得到理性的、正确的解释，成为严重困扰生产、亟待解决的技术难题2。目前关于起筋问题的研究，卷取应力和起筋量计算方法都是基于弹性理论3，而在实际卷取过程中，起筋达到一定高度时，带钢产生局部塑性变形和金属局部塑性流动。因此，弹性理论不再适用于起筋带钢的卷

10、取应力和起筋量计算。本文借鉴三维弹塑性变形的一些处理思想，并引入带钢塑性流动因数，建立了可用于在线计算的卷取应力和起筋量模型。在此基础上，基于应力函数假设和S. Timoshenko最小功原理获得了起筋带钢的应力场分布，并采用伽辽金虚位移法建立了可用于在线计算的起筋临界卷取张力设定模型，为起筋在线控制提供了理论依据。Ridge-buckle defect is a kind of bump on the surface of the steel rolls caused by the accumulation of local high points in vertical, as shown

11、 in figure 1. When the amount of ridge-bucket is large, appear additional waves on the area where has ridge-bucket after uncoiling, has serious effect on the properties of product, cause degradation and discard1. The ridge-bucket is a serious problem that affects production and needs to be solved ur

12、gently, due to the complex principle without rational and correct explanation for years. The calculation method of rolling stress and the amount of ridge-bucket in current thinking are all based on elastic-plastic theory, but in the real process of rolling, there are Local plastic deformation and me

13、tal plastic flow when ridge-bucket reaches certain height. As a result, plastic theory in no longer suitable for the calculation of rolling stress and the amount of ridge-bucket of strip steel. This paper used the theory of three dimensional elastic-plastic deformation, introducing the plastic flow

14、factor, established the buckling critical coiling tension setting model can be calculated online. Besides , getting the stress field distribution of ridge-buckle base on the hypothesis about stress function and the S. Timoshenko least work principle, establish the buckling critical coiling tension s

15、etting model can be calculated online using the theory of Galerkin virtual displacement.图1 起筋现象Fig.1 The phenomenon of ridge-buckle defect 1 卷取应力与起筋量解析模型 analytical model of coiling stress and the amount of ridge-bucket1 1.1 钢卷几何方程与平衡微分方程 geometric equation and equilibrium differential equation of c

16、oil带钢卷取的几何方程可以表示为4：geometric equation of strip steel coiling (1)式中：u为径向位移；w为轴向位移。in the equation: u for radial displacement; w for axial displacement钢卷可以看成是轴对称的各向异性体，即带钢的应变、应力分布与极角无关。因此，柱坐标下的平衡微分方程为5： the steel coil can be seen as the anisotropic bodies of axisymmetry, that means the strain and stre

17、ss distribution of strip steel have no relation with polar angle. As a result, the equilibrium differential equation under cylindrical coordinate system is: (2)式中：，分别为钢卷径向、周向、轴向和剪应力分布。in the equation:， for the distribution of radical, circumferential , axial and cut force.钢卷径向、周向、轴向和剪应力分布。1.2 钢卷物理方程

18、 physical equation of coil钢卷弹塑性本构关系的张量形式可以表示为：elastic-plastic constitutive equation of coil in tensor form: (3)式中：ii为应变球张量；m为应力球张量；ij为单位球张量；eij为应变偏张量,Sij为应力偏张量；为应变偏量与应力偏量间的比例系数。对于弹性变形，=1/2G；对于弹塑性变形，比例系数与位置及载荷水平有关，=3i /2i。i、i分别为应变强度和应力强度。 in the equation: ii for sphericaltensorofstrain; m for spheric

19、altensorofstress; eij for deviatorictensorofstrain; Sij for deviatori tensor of stress; for the ration between eij andSij .For elasticdeformation, =1/2G；for elastic-plastic deformation, =3i /2i. i、i for strain intensity and stress intensity.带钢的弹塑性判定采用Mise屈服条件：the elastic-plastic judgement of strip s

20、teel adopt Mise yield condition: (4)式中：为带钢的屈服强度。in the equation, for yield strength of strip steel钢卷在卷取过程中，卷取张力为，由于外层带钢压力使内层带钢产生周向压缩变形，引起的带钢张力消失可表示为6：in the process of coiling, for the coiling tension, for the compressive deformation of interior strip steel caused by the pressure of exterior strip s

21、teel, the disappearance of steel tension is: (5)式中：为带钢卷取张力轴向分布；为卷取n 圈时第i圈带钢的实际张力分布。in the equation, for the axial distribution of coiling tension; for the distribution of actual distribution of tension on no.i lap when coil n laps in total.1.3 带钢塑性流动因数的引入 the introduction of plastic flow factor of s

22、trip steel带钢卷取过程中，除局部高点外的大部分区域，带钢的塑性流动是极其有限的。但是，在局部高点附近，由于局部高点累积叠加，引起径向和轴向应力不均匀分布，并形成金属塑性流动。因此，带钢起筋中部与边部横向流动差异较大。为了对带钢塑性流动状态进行描述，本文引入塑性流动因数的表述，定义带钢塑性流动因数为：in the process of coiling, for most of the area in addition to local high points, the plastic flow of strip steel is extremely limited. But near

23、the local high points, because of the accumulation local points, cause uneven distribution of stress in both radial and axial directions, and produce metal plastic flow. As a result, the difference of lateral flow between the middle and edge is considerable. To describe the status of plastic flow, t

24、his paper introduced the expression of plastic flow factor, define it as follow: (6)式中：ez为轴向应变偏张量；e为周向应变偏张量。in the equation, ez for deviatorictensorofstrain in axial direction; e for deviatorictensorofstrain in circumferencial idrection.根据体积不变原理，有：according to phase volume invarient theorem: (7)应变偏张

25、量与应力偏张量间的关系为：the relation between deviatorictensorofstrain and deviatori tensor of stress is: (8)将式6与式7代入式8，即可得出钢卷轴向、周向和径向应力偏张量间的关系：substitute equation 6 and 7 into equation 8, to get the relation of deviatori tensor of stress in axial direction, circumferencial direction and radial direction: (9)将式

26、9代入弹塑性物理方程中，从而将带钢塑性流动条件合理地引入差分计算。使用克莱姆(Cramer)法则求解线性方程组，即可得到钢卷各单元应力与应变的关系，其中M为线性方程组系数：substitute equation 9 into elastic-plastic physical equation, so that to introduce plastic flow conditions into calculusofdifferences. solvelinearequation sets with Cramer principle to get the relation of stress an

27、d strain in each strip steel unit : (10)1.4 带钢厚度与钢卷半径轴向分布模型 带钢在宽度方向存在局部高点或厚差，因此厚度分布可以通过带钢凸度和局部高点描述7： (11)带钢凸度和局部高点的轴向厚度分布函数分别为： (12) (13)式中：表示带钢中部厚度；为带钢半宽；、c、为带钢凸度轮廓系数；为起筋宽度系数；、为局部高点轮廓系数。钢卷半径轴向分布可以通过下式计算8： (14)式中：为钢卷层间间隙，为钢卷最外层带钢的层间间隙，为径向压缩系数，为层间径向压力。径向位移u和轴向位移w可以用变量为r和z的函数表示。设:u=f (r, z)，w= (r, z)，

28、则径向与轴向位移的各阶差分方程可以表示为f (r, z)与 (r, z)的形式。将式1、式2、式11、式14和位移差分方程代入式10中，这样，在钢卷内部就得到了用两个位移函数表示的差分方程，它包括了平衡条件、物理方程和几何方程： (15)式中：S、L为差分方程系数；f，分别为钢卷径向和轴向位移函数。2 卷取应力与起筋量解析模型的仿真研究1 2 3 2 2.1 卷取应力与起筋量模型的计算流程图2 模型计算流程Fig.2 Calculation process of coiling strip stress model首先对钢卷进行网格划分，设定径向和轴向节点数m、n，假定比例系数和塑性流动因数G

29、，形成整体方程系数矩阵。通过LU分解法求解线性方程组，得出径向位移u和轴向位移w，并代入卷取应力差分方程和物理方程，求出各节点的应力和应变，循环迭代修正各节点比例系数、塑性流动因数和卷径轴向分布。2.2 起筋钢卷的卷取应力分布针对表1所示的工况参数，对起筋钢卷的卷取应力分布进行仿真计算，结果如图3所示。表1 模型计算参数Table 1 The calculated parameters参数尺寸数值参数尺寸数值钢卷内外径/ mm300/900带钢宽度/ mm1000卷取张力/ MPa30带钢厚度/ mm0.5弹性模量/ GPa205局部高点/ m5泊松比/ -0.3高点位置/ -带钢中部 ( a

30、 ) 径向应力； ( b ) 周向应力； ( c ) 轴向应力； ( d ) 等效应力图3中部局部高点带钢的卷取应力分布Fig.3 Stress distribution of the coil with central local high point由图3可以看出，局部高点在钢卷径向累积叠加，引起径向和周向应力集中9，是导致等效应力骤增的主要原因。钢卷最外层带钢等效应力最大，因此，卷取过程中，起筋首先发生在钢卷外层。2.3 各模型参数与起筋量间的关系基于数学仿真软件Mathematica，针对表1所示的工况参数，分别对卷径为300 mm900 mm、带钢厚度0.5 mm1.0 mm、局部高

31、点高度为3 m10 m、卷取张力为20 MPa50 MPa的钢卷进行起筋量计算，计算结果如图4所示。从图中可以看出，起筋量随局部高点高度、卷径和卷取张力增加而增大，薄的带钢比厚带钢起筋量增幅更加明显。因此，解决起筋问题最根本的还是要控制带钢的局部高点。 图4各模型参数与起筋量间的关系Fig.4 The relationship between the model parameters andridge-buckle value3 起筋临界卷取张力解析模型卷取过程中，由于起筋首先发生在钢卷最外层，因此，对于起筋临界卷取张力的求解，可以简化为对钢卷最外层带钢屈曲临界张力的求解过程。3 3.1 起筋带钢挠度函数由于起筋挠度沿带钢宽度方向急剧变化,因此,在宽度方向引入Hermitean多项式作为衰减函数,根据现场实际起筋模态，带钢的起筋挠度函数可以表示为： (16)式中：An为带钢起筋挠度幅值；a为带钢半长；bw为起筋区域半宽；。带钢起区域的边界条件为： (17)3.2 起筋带钢受力分析图5钢卷起筋最外层带钢受力分析Fig.5 Forceanalysis of the outmost lay