Modified slab analysis of asymmetrical plate rolling

In this paper the general case of asymmetrical plane strain rolling due to unequal roll diameter, unequal surface speed of the rolls and different contact friction is considered. An analytical model based on the slab method of analysis was used and further developed to obtain the characteristics of asymmetrical sheet rolling and to predict strip curvature. This method describes an enhancement to the rolling theory where friction becomes an integral part of deformation mechanics in the roll gap. To verify the validity of the proposed analytical model, the analytical rolling force, torque and curvature were compared with experimental and analytical results of other investigators. Very good agreements are found. Capability as well as the simplicity of the proposed model in predicting more accurate theoretical results for the rolling force, torque and curvature makes it suitable for the online control application.     

A 3-D finite element method analysis of cold rolling of thin strip with friction variation

In this paper, a three-dimensional rigid-plastic finite element method (FEM) model to simulate the cold rolling of thin strip with different friction models is described. The effects of rolling parameters, such as work roll diameters and reductions, are analysed in this study. The simulation and experimental values of rolling pressure and spread (the difference of strip width before and after rolling) show a good agreement when friction variation in the roll bite is considered. The roll separating force, spread and forward slip for constant friction and friction variation models are also compared. The friction variation in the roll bite has a significant effect on the simulation results.     

Asymmetrical sheet rolling analysis and evaluation of developed curvature

A theoretical method based on slab method of analysis is presented to give an account to the developed curvature in asymmetrical sheet rolling where the work rolls radii, their speeds, and the interfacial frictions may be different. In this model the ingoing sheet is considered to be guided to enter the roll gap horizontally and the work rolls may have different pressure distributions. The nonuniformity of normal and shear stresses acting along the vertical sides of each slab are taken into account, and the equilibrium equations together with the yield relations are considered as the governing equations. The strip curvature at exit is calculated based on the differences in shear as well as normal strains within the upper and lower portions of the slab. Results are compared with analytical and experimental findings of previous investigators and are shown to be in good agreement.     

Round-to-square section drawing through flat idle rolls

Cold drawn metal bars of regular polygonal section are industrially produced by direct drawing from round stock using either a round-to-polygonal section converging die or a drawing head comprising an adjustable set of symmetrically arranged flat idle rolls. In the present work a solution is obtained to determine the roll load and drawing force for steady state direct cold drawing of square section from round stock through flat idle rolls. The results obtained have shown that the drawing force in a case of fair lubrication condition amounts to about 40% of that required for drawing through converging dies, which allows using a drawbench of lower load capacity. The drawing stress is highly influenced by the friction conditions at the roll surface and to a lesser extent by the area reduction ratio and roll diameter, indicating the need for good quality finish and adequate lubrication for the rolls contact surface. The ratio of the drawing stress to the roll mean pressure is independent of friction and increases almost linearly with the increase of area reduction ratio.     

弯辊系统在四辊轧机辊缝控制中的应用研究

以四辊轧机的弯辊系统为研究对象,利用有限元分析软件ANSYS研究弯辊力和辊间接触应力引起工作辊形状的变化,计算工作辊弯曲的最大变形量,并用最小二乘法对辊缝曲线进行拟合,为进一步计算有载辊缝形状提供可靠的理论依据。     

Cold drawing of regular polygonal tubular sections from round tubes

An analytical solution is obtained for the problem of cold drawing through flat idle rolls of regular polygonal metal tubular sections from round tube. The solution is based on obtaining a compatible velocity field that satisfies kinematic conditions to yield the strain-rate components. The stresses are obtained by combining the material constitutive law with Levy–Mises flow rule and integrating the equations of equilibrium. The solution is applied to the case of a low-carbon steel standard round pipe to investigate the effects of drawn section shape, friction at the roll interface, roll radius and wall thickness on the roll load and drawing force. The results obtained have shown that for different section shapes the roll load and drawing force decrease with the increase of the number of sides and increase with the decrease of corners radius. Surface friction has no appreciable effect on the loads which allows dry drawing. An increase in the roll radius increases the roll load but the drawing force remains unchanged. Increasing the wall thickness does not proportionally increase the roll load and drawing force; the tube wall behaves as a thin shell subjected to biaxial combined membrane and bending stresses.     

Analysis of the roll hunting force due to hardness in a hot rolling process

A hot rolling operation is performed to alter the thickness of a metal by passing the material through a pair of rollers, forming a gap that is somewhat narrower than the thickness of the material. Therefore, the quality of the product is a function of the pressure applied by the rollers. However, in this process, a roll hunting force occurs in which the rolling force is irregularly changed during the rotation of the rollers due to various complex mechanisms, which include roll surface hardness, difference in rotational speed between rolls, heat treatment conditions, and roll wear. In this study, roll wear tests were conducted to analyze the roll hunting force caused by variation in the hardness of the work roll. The friction coefficient of the work roll was then examined based on hardness. Then, a two-dimensional finite element model was constructed to investigate the roll hunting force as a function of the change in friction coefficient of the work roll. This finite element model was verified in relation to the theoretical rolling expression. Finite element model analysis was performed for three friction coefficients, and the effect of the roll hunting force was determined based on the reduction ratio and temperature. In addition, the wear depth of the work roll by the hardness was predicted. The influence of the abrasion of the work roll on the hunting force was analyzed.

     

Elastic-plastic analysis of the stress and strain distributions in asymmetric rolling

Asymmetric plane strain plate rolling is analysed numerically by using an elastic-viscoplastic finite-element method. The asymmetric conditions are here due to different interface friction conditions of the two rolls. Two sets of different interface friction conditions are used. The influence of the degree of reduction on the curvature of the rolled plate and the corresponding distributions of the stress and strain are examined. For the rolling parameters considered, the curvature of the plate is found to be towards the roll with highest friction. The largest curvature is obtained for the biggest difference in interface friction conditions. The curvature shows a change from increasing to decreasing curvature with increasing reduction followed by a change in the distribution of the strain.     

Roll shape design for foil rolling of a four-high mill

In this paper, a mathematical model for a four-high mill is proposed to analyze the elastic deformation of the backup and work rolls, including their respective axial deflection and surface flatness. The contact pressure between the backup and work rolls and that between the work roll and foil are functions of the roll’s position in the axial direction. In this analytical model, the rolls and foil are divided into many small regions and finite difference or matrix methods are used to derive the deflections of the work and backup rolls as a function of the force density in the foil width direction. A camber shape at the surfaces of the backup and work rolls is designed to counteract the rolls’ elastic deformation and to make the rolled foil as flat as possible. The effects of the selected roll materials upon the rolled thickness distribution are also discussed. A thickness variation within 1 μm can be obtained for a foil of 50-μm thick and 40-mm wide under reduction of 32 % using a WC work roll with a camber radius of 150 m.     

Viscoplastic analysis of plane-strain rolling using different friction models

Plane-strain rolling is analyzed numerically. The nonlinearities arising from the large plastic deformations, the strain-rate dependence of the stress and the influence of the roll velocity are described by using a finite-strain elastic-viscoplastic material model. The stress-strain variation with temperature is included by approximating the isothermal behaviour at a given temperature and strain rate. The combined contact and frictional problem at the interface between the rolls and the plate is modelled by using elastic springs with high stiffnesses and by assuming two different friction models. The influence of different rolling and material parameters on the variation of the frictional stress and the normal stress along the contact length is shown for one of the friction models. Furthermore, the difference between the results obtained by the two different friction models is emphasized.     

Coupled dynamic modeling of rolls model and metal model for four high mill based on strip crown control

The crown is a key quality index of strip and plate,the rolling mill system is a complex nonlinear system,the strip qualities are directly affected by the dynamic characteristics of the rolling mil.At present,the studies about the dynamic modeling of the rolling mill system mainly focus on the dynamic simulation for the strip thickness control system,the dynamic characteristics of the strip along the width direction and that of the rolls along axial direction are not considered.In order to study the dynamic changes of strip crown in the rolling process,the dynamic simulation model based on strip crown control is established.The work roll and backup roll are considered as elastic continuous bodies and the work roll and backup roll are joined by a Winkler elastic layer.The rolls are considered as double freely supported beams.The change rate of roll gap is taken into consideration in the metal deformation,based on the principle of dynamic conservation of material flow,the two dimensional dynamic model of metal is established.The model of metal deformation provides exciting force for the rolls dynamic model,and the rolls dynamic model and metal deformation model couple together.Then,based on the two models,the dynamic model of rolling mill system based on strip crown control is established.The Newmark-β method is used to solve the problem,and the dynamic changes of these parameters are obtained as follows:(1) The bending of work roll and backup roll changes with time;(2) The strip crown changes with time;(3) The distribution of rolling force changes with time.Take some cold tandem rolling mill as subject investigated,simulation results and the comparisons with experimental results show that the dynamic model built is rational and correct.The proposed research provides effective theory for optimization of device and technological parameters and development of new technology,plays an important role to improve the strip control precision and strip shape quality.     

Analysis of the bending of the rolling material in asymmetrical sheet rolling

In asymmetric rolling the workpiece is often bent to an unexpected shape. Its curvature may be caused by a speed difference, by a lubrication mismatch or a radius difference of the work rolls, and depends on various rolling parameters, such as the ratio of the peripheral velocities of the upper roll and the lower roll, reduction ratio, average radius of the work rolls, initial plate thickness and friction between the rolls and the workpiece. A finite element simulation, which shows the influence of different diameters of the working rolls and of the degree of reduction on the bending of the workpiece, has been performed.     

Fuzzy algorithm for calculating roll speed variation based on roll separating force in hot rolling

Thickness control of hot-rolled strips has become an important issue in recent years because of the need for improving the quality of the hot-rolled strip. For this purpose, various thickness control systems such as finishing mill set-up (FSU), automatic gauge control (AGC), and looper control system, have been developed at steel works. Although these systems have greatly improved the quality of the strip thickness, there still exists a small amount of thickness deviation. It is difficult to adequately control by applying conventional thickness control techniques since hot rolling process is a highly nonlinear system in which many process parameters are coupled. In this study, a fuzzy algorithm to calculate the roll speed variations was developed in order to improve the thickness uniformity of hot-rolled strips. Since the strip thickness is mostly affected by the magnitude of roll separating force depending on the roll speed, the strip thickness deviation between the desired and actual thicknesses can be reduced by controlling roll speed. In order to carry out this investigation, slab analysis was carried out to determine the relation between roll separating force and roll speed for various process parameters such as roll speed, reduction ratio, strip entry thickness, and front and back tensions. From the production data, the effective stress-strain rate relations of the materials used in slab analyses were acquired. Based on the analytical results, the relation between roll separating force and roll speed was approximated by a log function. A fuzzy algorithm was developed to determine variations in roll speed according to variations of roll separating force, depending on various ranges of rolling temperature, reduction ratio, front and back tensions, and strip thickness. In addition, simulations to predict roll speed variations for a small amount of thickness deviation were carried out at continuous finishing mills consisting of seven stands and the calculated roll speed variations were found to be reasonable. Thus, the developed fuzzy algorithm might be useful in reducing the thickness deviation in the actual hot rolling mills.     

A study on the fault diagnosis of the 3-d roll shape in cold rolling

The metal processing system usually consists of various components such as motors, work rolls, backup rolls, idle rolls, sensors, etc. Even a simple fault in a single component in the system may cause a serious damage on the final product. It is, therefore, necessary to diagnose the faults of the components to detect and prevent a system failure. Especially, the defects in a work roll are critical to the quality of strip. In this study, a new 3-D diagnosis method was developed for roll shape defects in rolling processes. The new method was induced from analyzing the rolling mechanism by using a rolling force model, a tension model, the Hitchcock’ s equation, and measurement of the strip thickness, etc. Computer simulation shows that the proposed method is very useful in the diagnosis of the 3-D roll shape.     

小型四辊轧机工作辊水平位移对板形的影响

小型四辊轧机由于工作辊长径比较大且辊径较小而造成工作辊沿轧制方向很容易出现水平位移现象,常规四辊轧机板形计算模型不能满足出口板形的准确计算与预测,为此,充分结合小型四辊轧机的设备与工艺特点,建立了四辊轧机考虑工作辊水平位移时的板形模型;通过板形对比说明了该模型计算结果的准确性。在此基础上,具体分析了工作辊水平位移产生的规律以及在考虑工作辊水平位移时弯辊力对板形控制的影响,并将该模型应用到某钢厂650可逆四辊轧机机组,开发了650可逆四辊轧机工作辊水平位移对板形影响分析软件,有效地解决了以往板形计算误差大的问题,实现了对出口板形的准确计算与预测,大大提高了板形控制精度。     

A theoretical analysis of the sandwich rolling process

The rolling of high-strength metal sheets to thin gauges causes excessively high-roll forces which result from the flattening of the rolls. One effective way of reducing the rolling load is to roll the sheet sandwiched between layers of softer metal. The situation is similar to that of the production of clad metal. This paper aims to show how to predict the load to which a mill is likely to be subjected and the effect on the load of the various process parameters. A theory is developed which predicts the roll separating force to the same level of accuracy as that normally obtained from cold rolling theories; it takes account of the thickness of the sheets, the relative yield stresses and the interfacial friction. The results of the analysis are verified by comparison with experimental measurements.     

轧制界面非稳态润滑过程系统动力学模型的建立及其数值模拟

运用轧机辊缝动力学的基本理论结合非稳态润滑理论，建立了基于非稳态工作界面的动力学模型。该模型考虑了界面上金属塑性流动过程、界面上部分流体润滑与干摩擦并存的混合摩擦学过程以及工作辊的运动等多重耦合作用。塑性流动过程分析中考虑了界面摩擦状态的动态变化，界面摩擦特性分析中考虑了工作辊运动的动态耦合，因此工作界面上的轧制力模型、界面摩擦模型、工作辊运动模型构成了界面的薄膜约束多重耦合模型。对某大型公司2800轧机垂直系统的自激振动进行了仿真，定量地分析了一些主要参数对轧机垂直自激振动临界速度的影响。     

Modi cation of Roll Flattening Analytical Model Based on the Plane Assumption

Roll flattening is an important component in the roll stack elastic deformation,which has important influence on controlling of the strip crown and flatness. Foppl formula and semi?infinite body model are the most popular analyti?cal models in the roll flattening calculation. However,the roll flattening calculated by traditional flattening models has a great deviation from actual situation,especially near the barrel edges. Therefore,in order to improve the accuracy of roll flattening,a new model is proposed based on the elastic half plane theory. The calculation formulas of roll flatten?ing are deduced respectively under the assumptions of plane strain and plane stress. Then,the two assumptions are combined through the method of introducing an transition coe cient,and the distribution rules of roll flattening for di erent rolling force,flattening width,roll length and roll diameter are analyzed by using the FEM analysis software Marc. Regarding the ratio of the length to roll end and the roll diameter as variable to fit the transition coe cient,the new model of roll flattening is established based on the elastic half plane theory. Finally,the transition coe cient is fitted to establish the model. Compared with the traditional models,the new model can e ectively improve the cal?culation deviation in the roll end,which has important significance for accurate simulation of plate shape,especially for the distribution of rolling force between rolls.     

Three dimensional thermal mechanical coupled simulation during hot rolling of aluminium alloy 3003

Rolling passes of a pass schedule supplied by an aluminium company and containing reliable measured data of roll load and torque is considered. Percentage reductions range from 6% to 20% and are analysed by a commercial thermo-mechanical coupled FEM program FORGE3 V5.3. An inverse analysis method is adopted to match the calculated rolling force and torque with the measured rolling force and torque by treating the friction law and the friction coefficient as free parameters. Three widely accepted friction laws are investigated; Tresca friction, Coulomb friction and viscoplastic friction. The use of viscoplastic friction is shown to yield both more reliable and more accurate results than other models. Significantly the friction coefficient can be traced to remain constant throughout the pass schedule of the breakdown rolling. The contact pressure distribution is then studied with different thickness reductions and compared with published experimental results. The predicted and experimental agreement is such that the load calculation can be regarded as satisfactory. Acceptable agreement is also obtained with the measured torque values. The distribution of equivalent strain, temperature and the stress in the roll gap and the lateral profile are discussed.     

Simulation of T-section profile ring rolling by the 3-D rigid-plastic finite element method

The three-dimensional rigid-plastic finite element method is used to simulate the open pass profile ring rolling of a T-shaped section from an initially rectangular cross-section. Because the ring rolling process is incremental and the deforming region is restricted to the vicinity of the roll gap, only a ring segment spanning the roll gap is analysed in order to save computation time. As the thickness of the ring is reduced, the mesh system is progressively modified to treat profile development more effectively. Roll separating force, strain distribution, strain rate distribution and cross-sectional configuration of the deformed ring are calculated. Comparisons between computation and experiment show good agreement in roll separating force and cross-sectional configuration of the deformed ring.