外文翻译--冷轧薄带时轧制参数对轧辊边缘接触的影响

附录 1 冷轧薄带时，轧制参数对轧辊边缘接触的影响 在一些冷轧制造薄带的过程中，我们已经发现了工作辊边部接触并且使薄带变形的问题。在工作辊边缘接触的问题上，形成了一个新的在滚动中变形的特性，这一特性已得到分析。在本文中，作者重点研究轧制参数对特定的力如轧制力，中间力，边缘接触力和薄带钢冷轧工作辊边缘接触时的影响。目前已研究出一个影响函数法来模拟此特殊轧制过程。基于数值模拟，得到了轧制参数对力学和变形影响的冷轧薄带。数字模拟试验，验证了这个已较为成熟的方法的有效性。 冷轧薄带被广泛的应用在电子和仪器行业当中。随 着科学和技术的迅速发展，薄带钢已经越来越广泛的应用于工业当中。一般来说 ,这种薄带是由一个冷连轧机组的一个非圆形的工作辊所制成。 Sutcliffe 等人为薄带的轧制研究了一种新的方法进行负载和带钢轧机断面轧薄的测量。在薄带钢轧制中，一个比较估计轧辊转矩和一个修正横向扩散的方法也已经被研究出来。 Jiang等人计算薄带的弹性变形，和在冷轧薄带中的薄带的形状、轮廓和平整度。轧辊的弹性变形导致轮廓、外形和平整度的问题。钢铁制造商一直关心如何改进它的形状，平整度和尺寸精度这一问题。研究员已经从新的制造工厂中发现对这些问 题的解决办法通过引入轧辊连续变型 (CVC)和轧辊交叉 (PC)的轧机。有了这些轧制程序，能够使相对较厚的薄带被轧制的时候，工作辊彼此不接触。 在一些冷轧过程中，例如当薄带被轧制的时候，工作辊的端部接触而且变形(见图 1)。在冷轧薄带的分析中，我们不得不考虑工作辊端部接触时可能导致毁灭性结构的问题。这种情况，模拟变形模型的技巧不同于传统的薄带冷轧程序。当工作辊接触边缘地带之外时，不仅改变了压力分布，而且对变形模型的工作辊、摩擦界面都将带来磨损。工作辊接触边缘地带研究如何确定轧制力、中间力量、边缘接触力和剖面的地带 ，以改善其质量。作者这篇文章的重点在于冷轧过程中旋转参数对特定的力量和轧件的描绘效果的研究。 当轧件超出轧辊接触边缘时， Edwards和 Spooner根据一个分析方法也简短地描述了冷轧薄带毁坏兼容性的关系。但是到目前为止详细的结果还没有被报告出来。基于数字的模拟、旋转参数和改变，冷轧过程中边缘的损坏的效果得以演示。数字的模拟测试已经证明此研究的可行性。 图 1 冷轧薄带工作辊的边缘接触 变形轧辊在工作辊和支撑辊之间，工作辊和轧件之间，是以工作辊之间的换置兼容性关系为基础的。由于左边和右边的对称，铸坯在 轧辊的中心线快速前进，一半轧辊当做一个研究目的被分离出来。分开区域在图 2被显示出来。工作辊和支撑辊之间的轧制力在该区域是统一的，轧辊和轧件的毁坏在图 2 也被表示出来。 图 2死滚轧机的力学模型 在工作辊和支撑辊之间，由于弯矩、剪切力和泊松比的影响，工作辊之间的干扰，通过计算轧辊歪斜得到不成形的工作卷物描绘，以上内容在下面的段 落中会详细介绍。 采用辊挠度的计算理论对弯曲和剪切组件得到了广泛的应用，一个典型的轧辊歪斜模型如图 3所示。 图 3 由于加载点的中性轴的偏转 轧辊歪斜在弯曲力的效果之下在某一位 置 x能被描述为： 式中， E是弹性模量， I是横截面积。 通过 Oconnor和 Weinstein，轧辊变形可以调整为 : 式中， A是横截面积， J是剪切模量。 如果有弯曲，中间的歪斜轴能在图 4被显示出来而且表示成： 式中， M是弯曲力矩， xR 是在 x位置的轧辊的半径。 卷物中轴的歪斜由于在表面运动的泊松比是 式中， R是工作辊半径。 基于假定长的接触的柔性气缸，适当大小的压力， -轧辊压力 q(x)能通过下面的公式能够被表达出来。 xywb 是在工作辊和支撑辊之间干扰的影响；写在底下的数字 W和 B分别地提及工作辊和支撑辊。Bw CC 和被下列的方程式决定： 式中，表示泊松比。 基于轧辊的等高线 ,工作辊和支撑辊之间的影响得计算： 式中， oywb是轧辊干扰的中心地带， xby是全体的支撑辊的挠度， xB 是完全的支撑辊隆起包括平面隆起，热的隆起和轧辊磨耗。 xyW是全体工作辊的挠度，而且 xCW是完全的工作辊隆起包括平面加冠，热的隆起和轧辊磨耗。 轧辊在工作轧辊的接触面积变平和薄带能被描述为 B是薄带宽度，而且 xyH 由： 图 5超越边缘地带的工作辊之间的影响 式中， xp 是旋转的压力，而且 1b 和 2b 是由实 验决定的常数。因为软钢(0.1-0.25%C)， 1b 和 2b 分别地被估计当做 32.92 和 0.86mm2 /kN。当轧制洋铁的时候，薄带可能是非常薄的，而且工作轧辊的挠度能充分造成工作轧辊接触超过薄带的边缘。现在的弯辊力系统使用单独的工作辊触摸彼此之外的边缘地带。工作轧辊之间的影响， xyWW能依照下列各项被计算： 式中， L 是工作辊的宽度， oh是出口薄带在薄带中心的厚度。 由图 5 可知，左边和右手边超过那被卷的薄带的边缘叫做轧辊边缘接触区域。 xp 和 p 分别是 x 接触压力在工作轧辊在左边和右手接触区域。 下面是被用在模拟冷轧方面的重要参数的价值： 工作辊的直径： 400mm； 支撑辊的直径： 1200mm； 工作辊的长度： 1600mm； 支撑辊的长度： 1600mm； 工作辊的初次隆起： 0mm； 支撑辊的初次隆起： 0mm； 中心距在螺旋之间： 2700mm； 中心距在弯曲气缸之间： 2700mm； 工作的杨氏模数卷： 220000N/mm； 支撑辊的杨氏模数： 22000N/mm； 工作辊的浦松氏比： 0.3； 支撑辊的浦松氏比： 0.3； 板层厚度： 2.02mm； 进入薄带的厚度： 0.45、 0.40、 0.35或 0.32mm； 薄带的出口厚度： 0.3mm； 薄带的宽度： 1000mm； 特定的前 面拉力： 165N/mm； 特定的背部之里面拉力： 160N/mm； 旋转的速度： 1000m/min； 磨擦系数： 0.017； 在进入的薄带的初次隆起： 0mm； 定义来自边缘的薄带隆起的点： 25mm； 工作轧辊弯曲力： 0、 50、 100或 150kN/chock. 轧制力由福特 -希尔公式计算 B是轧制前的薄带的宽度， k 拉力因数，pk被描述的变形阻力，由下列方程得 : 是一个常数， 污染率，写在底下的 s 指示静止的和 sk是静止的变形阻力0k一个常数，在这一公式0k=740MPa， m 和 n 是常数，m=0.01和 n=0.23，m是平均的整体还原被描述为 1H 是板层厚度 是一个常数。 (0.75)半径是一将工作辊的半径变平卷能被 Hitchcock 模型推论： b是轧制、 H薄带的宽度， h薄带的出口厚度，操作轧辊半径， CHHitchcock系数和 F轧制力。 PD 能被描述为 02.179.108.1 HRPD (17) 磨擦系数。 工作辊和支撑辊的挠度使用 简单梁理论计算弯曲和剪切。 基于影响力功能方法，模拟程序表在个人计算机上发展起来。 ,获得为不同的轧制薄带入口的厚度，弯曲力和工作的状态或没有边缘接触力；旋转的力、中间的力，边缘接触力和薄带的轮廓。 板层厚度是 2.02 毫米，薄带的出口厚度是 0.30毫米和弯曲力是零。进入厚度的效果在特定的力上的薄带在图 6被显示。它能被见到，旋转的力增加当进入薄带的厚度增加。因为还原增加当做薄带的进入厚度增加，它也被见到那中间的力增加当进入厚度薄带增加，而且它在边有一个逐渐增加的趋势由于边缘接触工作轧辊快速前进。当进入厚度是 0.32 毫米，边缘接触力是零，这方法没有边缘接触。边缘接触力用薄带 (还原 )的进入厚度的增大，那边缘工作轧辊的接触变得更重要当薄带增大的进入厚度，有一重要的在中间的力方面的影响力。 图 7表演薄带的出口厚度的分布对于不同进入厚度的薄带。当进入厚度薄带增大它能被见到那出口薄带的隆起增加 (也见表 1)因此，即使工作轧辊连络超过薄带的边当弯曲力是零，被卷的薄带的轮廓变成具有进入厚度的增加。 图 6 入口厚度在特定地带的影响 图 7 入口厚度在轮廓地带的影响 板层厚度是 2.02 毫米，进入厚度 0.40 毫米，出口厚度 0.30 毫米，弯曲力是零。特定的力作用下的效果边缘接触如图 8所示。它能反应当边缘接触的时候，在薄带的边附近的旋转的力减少。因为边缘接触工作轧辊，边缘接触力增大和那中间的力超过薄带的边也增加。因此，旋转的力减少。边缘接触的效果在薄带的轮廓上在图 9显示出来。很轻易能发现那出口薄带的隆起的减少。工作轧辊接触彼此的边缘 (见表 2)，因此工作轧辊的边缘接触能改良轮廓。如果没有在薄带中被应用的卷板机系统。 图 8特定力量对边缘的影响 板层厚度是 2.02 毫米，进入厚度 0.40 毫米，出口厚度 0.30 毫米。弯曲特性方面的力的效果力在 如图 10 所示。它能反应当弯曲力增大的时候在轧辊边缘的力的减小。然而，当宽度里面的中间的力使薄带减少，然后在边缘附近增的力和那当弯曲应力增加的时候，就能操作轧辊。因为边缘接触的效果，接近的中间力工作的边缘卷桶稍微增加。当弯曲力增加，中间增大力时，使工作的边缘卷桶变得更重要。我们能看到边缘接触力减少，弯曲力增加的时候，表示那边缘接触力可能是可以忽略的。这时弯曲应力 150kN/chock。当弯曲力增大时，薄带的轮廓变成比较的弯曲。 (见到图 11)因此，减少边缘接触力而有效的改良边缘变形的方法就是增大弯曲应力。 图 9 边缘接触对薄带边缘的影响 图 10弯曲力的影响 图 11边缘地带弯曲力的影响 这是一个研究轧辊在轧制过程中通过模拟边缘力和弯曲应力而改善轧辊作用下薄带边缘变形的模型。结果表示那些特定的力，像是旋转的力，中间的力而且对于薄带轧制这种特殊的生产过程所造成的特别的影响。当薄带的厚度增加的时候，那边缘接触力增大，工作的边缘接触轧辊变得非常重要，在中间施加作用力所产生的中还要得效果就是使，出口薄带的形变成很小的。如果没有弯曲应力的作用，薄带在出口处的隆起将会减小，工作辊边缘的变形也随之减小。因为边缘接 触能改良薄带的轮廓，因此各个生产厂家已经引入了边缘检出应力分析的装置来提升薄带生产的产品质量。在这些装置的作用下，薄带的变形变的微乎其微。因此，增加弯曲和应力能够在成产过程中很大程度上减小薄带边缘在工作辊作用下的变形。 致谢 这项工作受到一个澳大利亚研究理事会的支持。 附录 2 Effect of rolling parameters on cold rolling of thin strip during work rolls edge contact In some cold rolling mills, a problem has been found that the sides of work rolls touch and deform when thin strip is rolled. The problem of work roll contact at the edges, which forms a new deformation feature in rolling, is analyzed. In this paper, the authors focus on the research of the effects of rolling parameters on specific force such as rolling force, intermediate force, edge contact force and the profile of thin strip in cold rolling when the work roll edges contact. An influence function method is developed to simulate this special rolling process. Based on numerical simulation, the effects of the rolling parameters on the mechanics and deformation of the cold rolled thin strip are obtained. Numerical simulation tests have verified the validity of this developed method. A cold rolled thin strip is widely used in the electronic and instrument industries. With the rapid development of science and technology, thin strip has been finding more and more applications in industry. In general, this kind of strip is produced by a tandem cold rolling mill where the work rolls are flattened to a non-circular deformed shape. At et al. developed a robust model for rolling of thin strip and foil and carried out the experimental measurements of load and strip profile during thin strip rolling. In thin strip rolling, a comparison of methods to estimate the roll torque and a modified method for lateral spread has also been conducted. et al. calculated the elastic deformation of strip, and the shape, profile and flatness of strip in cold rolling of thin strip. Elastic deformation of the rolls brings about problems of profile, shape and flatness. The problem on how to improve its shape and flatness, and the dimensional accuracy has always been of major interest to the steel manufacturers. Researchers have found solutions to these problems by introducing new types of mills, such as continuous variable crown (CVC) and pair cross (PC) mills equipped with roll shifting roll crossing and work roll bending. These are rolling processes where the work rolls do not contact each other when relatively thick strip is rolled. In some cold rolling mills, for example, it has often been found that the edges of work rolls touch and deform (see Fig. 1) when the thin strip is rolled. The problem of work roll contact at the edges should be considered in an analysis of the cold rolling of thin strip, which forms a new deformation feature. In this case, the models of deformation and mechanics are different from the traditional cold rolling processes of strip. Not only the distribution of the roll pressure will change when the work rolls contact beyond the edges of the strip, but also the deformation model of work rolls, friction at the interface of the rolls and the strip and work roll wear. How to determine the rolling force, intermediate force, edge contact force and profile of the strip, to improve its quality when the work rolls contact beyond the edges of the strip is the main feature of this study. The authors focus on the research of the effect of rolling parameters on specific force and profile of thin strip in cold rolling, which is a highlight of this paper. Edwards and Spooner also described briefly deformation compatibility relationship for the cold rolling of the thin strip when the work rolls contact beyond the edges of strip by an analysis method. But up to now detailed results have not been reported. In this study, an influence function method has been developed to simulate this special rolling process. Based on the numerical simulation, the effect of the rolling parameters on the mechanics and deformation of the cold rolling of thin strip are obtained. Numerical simulation tests have verified the validity of this developed method. The calculation of the deformed rolls is based on the displacement compatibility relationships between the work roll and backup roll, work roll and thin strip, and the work rolls. Due to symmetry of the left and right sides of the rolls at the central line of the roll barrels, one-half of the roll barrels is selected as a research objective, and the equal divided zone is shown in Fig. 2. The rolling pressure and the pressure between the work roll and backup roll are uniform in zone. The deformations of the rolls and the strip are described in Fig. 2. The deformed work roll profile is obtained by calculating the roll deflections due to bending, shear and effect of Poisson s ratio, bending moment, interference between the work roll and the backup roll, and work roll flattening, which are described in the following paragraphs. Beam theory for the bending and shear components has been widely employed to calculate the roll deflections. A typical roll deflection model under the effect of point load is shown in Fig. 3. The roll deflection of the beam under the effect of bending at a position x can be described as follows: Where E is the Young s modulus, I the second moment of area zp and zq the point loads According to O Connor , the deflection of the neutral axis for short stubby beams due to shear is given by Where A is the cross-sectional area and G the shear modulus of the beam? If there is a bending moment, the deflection of the neutral axis can be illustrated in Fig. 4 and expressed as follows: Where v is the Poisson s ratio, M the bending moment, and R(x) the radius of the roll at x position. The deflection of the roll neutral axis due to the effect of Poissons ratio on the movement of the surfaces is Given by Where R is the work roll radius? Based on the assumption of two infinitely long elastic cylinders in contact, the interference under inter-roll pressure can be described as follows Where is the interference between the work roll and backup roll； subscripts W and B refer to the work roll and backup roll, respectively. And are determined By the following equation: Where v is the Poisson s ratio? Based on the contours of the rolls, the interference between the work roll and backup roll can be calculated as follows Where oywb is the total roll interference at the strip , xyb the total backup roll-axis deflection, and CB(x) the total backup roll crown including ground crown, thermal crown and roll wear. xyw The total work roll-axis deflection, and CW(x) the total work roll crown including ground crown, thermal crown and roll wear. Work roll flattening at the contact area of work roll and strip can be described as follows Where B is the strip width, and xyH is given by Where p(x) is the rolling pressure, and b1 and b2 are constants determined by experiments. For mild steel (0.1 0.25% C), b1 and b2 are estimated as 32.92 and 0.86 mm2 /kN , respectively. When rolling tinplate, the strip can be very thin and the deflection of work rolls can be sufficient to result in work roll contact beyond the edges of the strip. Nowadays the roll bending systems are employed to separate work rolls from touching each other beyond the edges of the strip. The interference between work rolls xyww can then be calculated as follows: Where L is the width of work roll barrel, oh the exit strip thickness at the strip ? Given in Fig. 5, the left and right hand sides beyond the edges of the strip being rolled are named roll edge contact region. p_(x) and p_(x) are contact pressures between the work rolls at the left and right hand contact regions, respectively. Given below are values of the important parameters used in the simulation for cold rolling: Diameter of the work roll: 400 mm； Diameter of the backup roll: 1200 mm； Length of the work roll barrel: 1600 mm； Length of the backup roll barrel: 1600 mm； Initial crown of the work roll: 0.0 mm； Initial crown of the backup roll: 0.0 mm； Center distance between housing screw: 2700 mm； Center distance between bending cylinder: 2700 mm； Young s modulus of the work roll: 220 000 N/mm2； Young s modulus of the backup roll: 22 000 N/mm2； Poisson s ratio of the work roll: 0.3； Poisson s ratio of the backup roll: 0.3； Slab thickness: 2.02 mm； Entry thickness of strip: 0.45, 0.40, 0.35 or 0.32 mm； Exit thickness of strip: 0.3 mm； Width of strip: 1000 mm； Specific front tension: 165 N/mm2； Specific back tension: 160 N/mm2； Rolling speed: 1000 m/min； Friction coefficient: 0.017； Initial crown of strip at entry: 0.0 mm； Defining point of strip crown from edge: 25 mm； Work roll bending force: 0, 50, 100 or 150 kN /chock. Rolling force is calculated by using Bland Ford Hill model where B is the width of strip before rolling, the tension factor, kp the deformation resistance which can be described by the following equation: where is a constant, the stain rate, subscript s indicates static and where sk is the static deformation resistance, which is determined under a constant stain rate 103 s1, k0 a constant, in this simulation k0 = 740MPa, m and n are constants, m = 0.01 and n = 0.23, m is average integral reduction which can be described as Where H1 is slab thickness and where is a constant (0.75). R_ is a flatten radius of work roll which can be deduced by Hitchcock model: Where b is the width of strip after rolling, H, h the entry and exit thickness of strip, respectively, R the radius of the work roll, CH the Hitchcock coefficient 9, and F the rolling force. DP can be described as 02.179.108.1 HRPD (17) where is the reduction and the friction coefficient. Deflections of the work roll and backup roll are calculated by using simple beam theory for bending and shear. Based on the influence function method, a simulation program was developed and performed on a PC. For different entry thickness of strip before rolling, bending force and the status of the work roll with or without edge contact, the rolling force, intermediate force, edge contact force and strip profile are obtained. The slab thickness is 2.02mm, exit thickness of strip is 0.30mm and bending force is zero. The effect of entry thickness of strip Hen on specific force is shown in Fig. 6. It can be seen that the rolling force increases when the entry thickness of strip increases. Because the reduction increases as the entry thickness of strip increases. It is also seen that the intermediate force increases when the entry thickness of strip increases, and it has an increasing trend at the side of work roll barrel due to the edge contact. When the entry thickness is 0.32 mm, the edge contact force is zero； this means that there is no edge contact. The edge contact force increases with the entry thickness of strip (reduction). The edge contact of work rolls becomes more significant when the entry thickness of strip increases, which has a significant influence on the intermediate force. Fig. 7 shows the distribution of the exit thickness of strip for different entry thickness of strip Hen. It can be seen that the crown of exit strip increases when the entry thickness of strip increases (also see Table 1). Therefore, when the bending force is zero, the profile of the rolled strip becomes poor with the increasing of entry thickness even if the work rolls contact beyond the side of strip. Because of the edge contact of the work rolls, the edge contact force increases and the intermediate force beyond the side of strip also increases. Therefore, the rolling force reduces. The effect of edge contact on the profile of strip is shown in Fig. 9. It is found that the crown of exit strip reduces significantly when the edges of work rolls contact each other (see Table 2). So the edge contact of work rolls can improve the profile of strip if there is no bending roll systems applied in a strip rolling mill . The slab thickness is 2.02 mm, entry thickness 0.40 mm, exit thickness 0.30mm and bending force is zero. The effect of edge contact on specific force is shown in Fig. 8. It can be seen that the rolling force near the side of strip reduces when the edge contact. The slab thickness is 2.02 mm, entry thickness 0.40 mm, exit thickness 0.30 mm. The effect of bending force on specific force is shown in Fig. 10. It can be seen that the rolling force near the side of strip reduces when the bending force increases. However, the intermediate force within the width of strip decreases and then increases near the side of the work roll barrel when the bending force increases. Because of the effect of edge contact, the interme