A kinematic analytical approach to predict roll force,rolling torque and forward slip in thin hot strip continuous rolling

Abstract

A kinematic analytical approach has been developed to predict the roll force, rolling torque and forward slip in thin hot strip continuous rolling under various rolling conditions. The approach is based on formulating a velocity field in the roll bite zone that expresses the effect of interfacial friction on the distribution of axial velocity and longitudinal stresses across the strip thickness. The results obtained from the proposed approach are in fair agreement with finite element simulation results, whereas available analytical methods, which are usually valid for billets and thick plates, have given considerable error in the results. The proposed approach is applied to study the effect of thickness reduction ratio, coefficient of friction, work roll diameter and front and back tensions on the roll force, rolling torque and forward slip in thin hot strip rolling. The main merit of the proposed analytical approach, as compared to finite element simulation, lies in the drastic reduction in the computational time required in finite element simulation, which favours its use in online control of rolling thin strips.     

Evaluation on some important force models for cold strip rolling

To improve the accuracy of rolling force prediction, some important force models were evaluated through applied computation for cold rolling of low carbon steel and aluminum alloy according to measured data on lab mill. The effects of model structure and three important variables ‐ flow stress, contact length and friction coefficient ‐ on the precision of computed force were quantitatively studied. Flow stress was measured with plane‐strain compression test, contact length was based on elastic flattening of work‐roll by Hitchcock, and friction‐coefficient was determined by rolling strain and numerical iteration. In steel rolling Bland & Ford integration model and Bryant & Osborn algebraic equation are better in accuracy than Ekelund and Parkins. In aluminum rolling all the models produce large deviations ΔF_R = 10–20% if flow stress, contact length and friction coefficient are determined with the same method as steel rolling. The elastic deformation of aluminum strip is now taken into account for its low elastic modulus. An effective method to determine plastic and elastic contact has been developed in this investigation. The accuracy of force computation is obviously improved for aluminum rolling.     

A novel approach to improve the computing accuracy of rolling force and forward slip

In cold strip rolling control system, rolling force and forward slip are the prerequisites for the model setting calculation, and the deformation resistance and friction coefficient are the main parameters that affect their predictions. A new method based on objective function is first proposed in this paper to improve the calculation accuracy of rolling force and forward slip, and the deformation resistance and friction coefficient are taken as optimisation variables. Using the multi-population co-evolutionary algorithm to solve the objective function, the required rolling force and forward slip are obtained. The pre-set values of rolling force and roller line speed are compared with the actual measured ones in a 1450?mm five-stand tandem cold mill and other researcher’s method. Results show that the calculated values are in fair agreements with the on-line measured ones, and the thickness and flatness accuracy of the final product are improved.     

基于极限静摩擦力矩的轧机打滑预测模型

冷连轧轧制过程中,当轧制转矩大于轧辊与轧件间的极限静摩擦力矩时,轧辊与轧件之间将出现相对滑动,从而导致打滑的发生.为减少因打滑导致的冷轧带钢带钢表面缺陷,以板带轧制塑性变形基本公式为基础,将前滑区与后滑区的单位轧制力分布做线性简化,继而推导出极限静摩擦力矩模型.并以实测数据验证该模型的准确性,且从轧制转矩与极限静摩擦力...     

Determination of Forward Slip Coefficient During Heavy Rail Rolling Using Universal Mill

The forward slip coefficient is one of the most important parameters for heavy rail rolling using universal mill.For simplifying the theoretical model,the vertical roll with box pass was simplified as an equivalent flat roll first.Second,the neutral angle of horizontal roll and vertical roll was represented.Then,the equation of neutral line on the flank of horizontal roll was determined and the forward slip coefficient of the web was derived according to different positions of neutral line.Finally,the forward slip coefficient of the top and base of heavy rail was obtained.The theoretical results were basically in agreement with the experimental data.     

基于CF-PSO-SVM的冷连轧非稳态工作辊弯辊模型优化

 板形质量是冷轧带钢重要的技术质量指标,同时工作辊弯辊是改善冷轧带钢板形质量的最有效的控制手段之一。冷连轧机组在高速稳定的轧制过程中板形控制精度能够达到较高的水平,但在升降速非稳态的轧制过程中板形控制效果非常不理想,这也成为制约冷轧带钢产品质量的不利因素。为了提高冷连轧机在升降速非稳态轧制过程中带钢板形的控制精度,在深入研究了冷连轧弯辊力设定原理的基础上,利用智能算法和包括出入口带钢厚度、机架间口张力、轧制速度、中间辊窜辊、带钢宽度、轧辊倾斜以及轧制力等现场实际轧制大数据样本,提出了一种基于粒子群算法优化支持向量机的工作辊弯辊力预测模型。同时阐明了粒子群优化算法和支持向量机的基本原理,引入压缩因子的概念,提升了粒子群算法参数寻优的效率,选取冷连轧机组五机架为研究对象,利用拉依达准则对轧制数据样本进行处理,通过平均绝对误差、均方差误差和平均绝对误差百分比等评价指标对比预测模型的性能。结果表明,改进的预测模型具有良好的模型预测性能和泛化能力,同时根据实际生产数据样本,回归出基于轧制速度和辊间弹性系数的弯辊力缝补偿模型,并验证了模型的有效性,模型的投入降低了板形控制系统的负荷,改善了非稳态轧制过程中的板形控制精度,产品头尾部的质量合格率提高了5.1%。     

Optimization technology of original surface roughness of cold tandem rolling mill

In order to improve the efficiency and product quality, the one- to- one relationship was established between the forward slip value, slipping factor, product roughness and work roll surface, by the analysis to the rolling instability in the rolling process of cold rolling mill. Then, combining with the equipment and technology feature of cold rolling mill, a set of original surface roughness of work roll optimization technology was set up for cold rolling mill, which can meet the product roughness requirements and achieve forward slip control, slipping prevention. Finally, this optimization model was applied to production practice of 1420 cold rolling mill in a factory, which improved the unit speed and strip surface quality; therefore the technology has brought great economic effect.     

一种新型的基于最小二乘回归St14钢变形抗力模型的方法

冷连轧的主要工艺参数为轧制力和前滑,而轧制力和前滑设定计算的精度取决于轧件的变形抗力和摩擦因数的精度,变形程度是影响变形抗力的一个重要因素,将所选变形抗力回归模型经过取对数等变换成线性函数,以鞍钢生产的St14钢为例,利用现场实际数据通过最小二乘来逐次拟合变形抗力回归模型中的系数。在同一轧制条件下,摩擦因数用3种不同的获得方法,其中前2种是由实测前滑值反算得到的,以使所得模型能够很好地与实际生产的数据相吻合。用回归出的3种不同变形抗力模型,分别带入轧制力迭代公式进行计算,所得轧制力基本与实测轧制力相符,其中由斯通公式拟合出的变形抗力回归模型计算出的轧制力平均误差很小,由此可以选出最优的变形抗力模型来应用于实际生产中轧制力和前滑的预设定。     

不锈钢冷连轧轧制力显函数模型的开发与应用

针对不锈钢冷连轧生产工艺,提出动态变形抗力概念,利用四辊可逆冷轧机和Inston高速拉伸实验机进行轧制-拉伸实验,在MMS-200热模拟实验机上测定不锈钢的应力-应变曲线,建立不锈钢动态变形抗力模型。在Hill方程的基础上建立了轧制力显函数模型,并通过变形抗力和摩擦因数的逆向回归计算实现模型的在线自学习。提出了适合轧制力模型的可信度评估方法,引入Theil不等式系数法,依据TIC值定性分析了模型的适用性。最终确立了适合于冷连轧生产的精确的轧制力显函数模型,并将其应用到生产实践中。统计结果表明：冷连轧过程中轧制力的模型计算值与实测值的相对误差小于3.67%,该模型具有良好的计算精度和较好的泛化能力,适合于工业生产实践。     

Analysis of rolling load generated by pair crossed rolling mill

Abstract

Although a pair crossed rolling mill has a very high control capability of strip crown, a frictional force always occurs in the strip width direction between the strip and the work rolls. An analysis of rolling load was carried out, considering the shear deformation of strip cross-section caused by the frictional force. From the examination of the calculated results for a large-scale mill for production, the following conclusions were obtained: (a) the cross angle hardly influences the rolling force and torque, (b) the thrust force on the roll induced by the frictional force decreases as a result of shear deformation, (c) the thrust factor, i.e. the thrust force divided by the rolling force, is little influenced by the strip deformation resistance and the friction coefficient between the work rolls and the strip during hot rolling, (d) the thrust force applied to the rolls during hot rolling is 3–6% of the rolling force for the cross angle of 1° and this is not an obstacle related to the design of rolling mills.     

基于辊缝动态摩擦方程的铝板冷轧机垂振机理分析

针对高速铝板轧制过程中频繁出现的冷轧机垂直振动现象,结合轧制工艺润滑原理和机械振动理论,建立基于辊缝动态摩擦方程的轧机垂直振动模型.该模型由辊缝几何形状模型,轧辊-轧件工作界面的动态摩擦模型,变形区内的正向轧制应力、摩擦应力分布模型,以及单机架铝板冷轧机二自由度垂向系统结构模型组成.同时,为研究轧辊-轧件工作界面动态摩擦机制影响下的冷轧机垂振机理及系统稳定性,采用某厂单机架铝轧机设备及工艺参数,搭建Matlab/Simulink平台,分别模拟仿真轧制压力和正向轧制应力曲线,验证该模型的有效性;并讨论分析了变形区混合摩擦状态,轧辊-轧件表面粗糙度、轧件入口厚度与系统稳定性的关系.     

带钢冷连轧材料变形抗力模型研究

针对冷连轧轧制过程的特点,变形程度是影响变形抗力的一个重要因素。建立了变形抗力的机理模型,并将理论模型与实际数据相结合。采用某钢厂生产的低碳钢08AlA稳定轧制时的现场实测数据,利用最小二乘逐次回归变形抗力模型中的各个参变量,并选用不同的方法来获得摩擦系数,选出与实际生产数据相吻合的最佳模型。将回归出的不同变形抗力模型,分别代入轧制力迭代公式进行计算,通过比较与实测轧制力的误差,选出最优的形抗力模型应用于实际生产中轧制力和前滑的预设定。     

平整机控制系统优化

通过对某钢厂单机架4辊冷轧平整机工艺设置、控制系统组成、控制功能的研究,用激光测速仪代替编码器,成功的解决了由于入口张力辊、出口转向辊打滑造成延伸率控制精度无法满足生产的问题。同时提出增加板形辊,实现板形自动控制;增加张力计,用变张力、变轧制力控制方式解决恒张力变轧制力控制方式中薄带钢延伸率控制效果不理想的问题。     

Theoretical study of the effect of asymmetries on the cold rolling process

In cold rolling of strip, geometrical, kinematical, and tribological asymmetries in the roll gap can exert an influence on roll force and torque. For its calculation the elementary theory of rolling is modified. The statics on the strip element are described in polar coordinates. The effects of non-horizontal strip entry and of different diameters of the upper and lower work roll are investigated in detail.     

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The general cold rolling mill cannot dynamical display and quantitative control the section properties of strip due to lack of profile gaugemeter. To this problem, through a large number of field trials and theoretical studies, taking the general four-roll cold rolling unit as research object, comprehensive considered the equipment and process characteristics in tandem cold rolling process, based on the strip thickness distribution mechanism model of tandem cold rolling, a whole set of design method for the virtual profile gaugemeter and the feedback control technology for section properties was put forward. It make full use of incoming materia??s section configuration data which come from the profile gaugemeter of hot rolling unit, and the real-time rolling process parameters, such as rolling force, tension, roll bending force and roll tilt amount, which come from the level 1 of tandem cold rolling unit. It can not only dynamical display the section configuration of cold rolled product and dynamic forecast the wedge quantity and plate crown, but also feedback control the section properties of strip. The section quality of cold rolled steel strip product was greatly improved. This technology should be used widely.     

Friction Estimation and Roll Force Prediction during Hot Strip Rolling

A mathematical model of friction coefficient was proposed for the roll force calculation of hot-rolled strips. The online numerical solving method of the roll force calculation formula based on the proposed friction model was developed and illustrated by the practical calculation case.Then,the friction coefficient during hot strip rolling was estimated from the measured roll force by force model inversion.And then,the expression of friction model was pro-posed by analyzing the calculation process of stress state coefficient,and the model parameters were determined by the shared parameter multi-model nonlinear optimization method.Finally,the industrial experiments demonstrated the feasibility and effectiveness of the related models.The accuracy of the new roll force model based on the built friction model was much higher than that of the traditional Sims model,and it could be applied in the online hot roll-ing process control.     

Calculation and Analysis of Force in Roll System of 20-High Sendzimir Mill

The calculation of force for a roll system has significant effects on cold rolled thin strip gauge adjustment of a 20-high Sendzimir mill. According to the rolling parameters and rolling plans of a ZR-22BS-42 Sendzimir mill in a silicon steel factory, the contact force and the resultant force of each roll in the roll system were calculated both in the static state and in the rolling state through C++ programs. It was found that the contact force between the second intermediate driven roll and the back-up rolls B and C was much lower than that between the other rolls in static state. The results also demonstrated that the resultant force are 59. 5% — 62%, 37. 7% —10. 3%, 87. 1% — 88. 7% and 53. 9% — 56. 7% of the rolling force at the second intermediate driven roll, the second intermediate idler roll, the back-up rolls B and C and the back-up rolls A and D, respectively. It was also revealed that the minimum contact force generated between the first intermediate roll and the second intermediate idler roll is 206. 7 kN on the first rolling pass, and that on the second rolling pass, the minimum contact force generated between the second intermediate driven roll and the back-up roll C is 470. 7 kN.     

二十辊森吉米尔轧机板形控制方法

介绍了二十辊森吉米尔轧机板形控制方法和各道次板形控制要求。二十辊森吉米尔轧机虽然具有很强的板形控制能力,然而也同样具有可逆冷轧机的一些缺点,如起车轧制和甩尾作业板形变化剧烈,甚至轧制过程中均需要操作工手动控制,二十辊森吉米尔轧机板形调控手段虽多,但有时并不能轻易地消除复杂的不良板形。生产实践表明,预设好第 1 中间辊第 1 道次起车值、控制好带钢板形对称和带钢边部受力情况以及统一规范各道次的轧制板形控制均能有效避免断带,保证二十辊森吉米尔轧机顺稳轧制,提高硅钢产品板形的均一性。     

Simplified Weighted Velocity Field for Prediction of Hot Strip Rolling Force by Taking into Account Flattening of Rolls

The weighted velocity field was simplified for analysis of hot strip rolling. Using the field and GM （geometric midline） yield criterion, the deformation power, friction power and shear power were obtained respectively. Summing the partial power contributions, the total deformation power for strip rolling was presented. Then, by minimizing the power function, the rolling force was obtained; meanwhile, considering the effect of roll elastic flattening, iterative calculation of the roll radius was carried out until the radius was convergent. On line data were corn pared with the calculated results to verify the model accuracy. It was indicated that the calculated rolling forces were basically in agreement with the measured ones since the maximum error was less than 10.0%. Moreover, the effects of various rolling conditions such as thickness reduction, friction factor and shape factor, upon separating force, location of neutral angle, and stress state coefficient were discussed systematically.     

Prediction of roll force in skin pass rolling using numerical and artificial neural network methods

A combination of finite element method and neural network methods was used for rapid prediction of the roll force during skin pass rolling of 980DP and 1180CP high strength steels. The FE based commercial package DEFOEM-2D was used to develop a mathematical model of the skin pass rolling operation. Numerical experiments were designed with different process parameters to produce training data for a neural network algorithm. The friction coefficient was considered as an input parameter in the neural network but it was optimised using an iterative method employing an equation that relates the friction coefficient to the rolling force. The load prediction method described in this paper is sufficiently rapid that it can be used in real-time as an adjustment tool for skin pass rolling mills with error within 10% (based on plant data from POSCO).