A thermal analysis of strip-rolling in mixed-film lubrication with O/W emulsions

Increase of both roll and strip surface temperatures can significantly affect a rolling process, roll conditions and strip mechanical properties. A comprehensive thermal analysis in cold rolling, especially in a mixed film regime, is needed to understand how thermal fields develop in roll and strip during rolling. It requires a simultaneous solution of the mixed film model for friction in the roll bite and the thermal model for roll and strip thermal fields. This paper presents a numerical procedure to analyse strip rolling process using lubrication with oil-in-water (O/W) emulsions. The thermal model includes the effect of heat generation due to the strip deformation and frictional shear stress at the asperity contacts. The numerical analysis employs a coupled thermal model and a mixed film lubrication model for calculating the friction and the asperity deformation in the bite. The thermal model considers the initial temperatures of the roll and strip, temperature rise due to the strip plastic deformation and friction. While the O/W mixed-film lubrication model takes into account the effect of surface roughness and oil concentration (%vol) of the emulsion. The thermal effect is analysed in terms of strip surface temperature and roll temperature, which are influenced by rolling parameters such as reduction, rolling speed, oil concentration in the emulsion. The results of the parametric study indicate that the effect of oil concentration on the thermal field is relatively small compared to that of reduction ratio and rolling speed. The reduction ratio increases the maximum interface temperature in the roll bite. In the mixed film regime, rolling speed also increases the maximum interface temperature and alters the temperature field of the strip. The numerical procedure was validated against known experimental data and can readily be extended to hot rolling or used to analyse roll strip temperature subjected to different cooling system.     

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.     

Roll-pressure distribution and coefficient of friction in hot rolling by caustics

The optical method of reflected caustics was employed to investigate the variation of the coefficient of friction in the roll gap during strip rolling. Experiments have been carried out on an experimental rolling mill, using lead at room temperature, to obtain quantitative information about pressure distribution and friction, relevant to hot rolling, i.e. when frictional effects are pronounced. The rolls were made of Plexiglas. The normal and tangential pressure distribution and thence the coefficient of friction along the arc of contact at the outer edge of the strip were calculated from the caustic curves formed due to elastic deformation of the rolls, although the rolled strip was deformed plastically.An almost linear decrease of the friction coefficient from a maximum value, at the entry plane to the roll gap. to zero at the neutral plane and then a parabolic, tending to linear, increase of it, towards the exit plane, were predicted, in contradiction to what is up-to-now accepted in the praxis, that the friction coefficient remains constant during hot rolling.     

Friction variation in the cold-rolling process

Friction variation along the rolling contact interface was measured by a ‘sensor roll’ embedded with sensors on an experimental rolling mill. The measured results show that the friction coefficient is not constant along the contact length. Empirical formulae describing the friction variation for certain rolling condition were obtained. Experiments were also carried out to study the surface roughness of the strip. It was found that the roll and strip surface roughness can be transferred to each other along the rolling direction. Only slight change of roughness in the transverse direction was observed.     

模拟带材轧制过程的条元法

本文介绍了模拟带材轧制过程三维应力与变形的一个新的工程实用方法——条元法。本方法对于四辊轧机冷轧带材单位轧制压力、两向单位摩擦力在变形区内的分布以及前、后张力横向分布的计算结果与实验结果吻合较好,证明用本方法模拟带轧材轧制过程是可行的。与三维差分法、三维有限元法及三维边界元法相比,本方法具有计算简便、经济和实用的特点。     

Study on the oxidation of stainless steels 304 and 304L in humid air and the friction during hot rolling

In rolling process, the contact friction is of crucial importance for accurate modeling, optimum design and control of industrial rolling processes. It is important to characterize the features of the oxide scale of stainless steel in hot strip rolling because the scale on the strip surface affects friction coefficient and thermal conductivity coefficient. To some extent, the rolling force and friction condition depend on the thickness and the microstructure of the oxide scale. Oxidation tests of stainless steels 304 and 304L were carried out in a high temperature electric resistance furnace. The humid air in which the water vapour content can be controlled was generated and remained to flow into the chamber of the furnace in 2.5 × 10⁻⁴ m³/s to study the effect of humidity on the oxidation of stainless steels. The microstructure and thickness of oxide scale layer of stainless steels were obtained and two or three oxide layers can be found. The humid air has a significant effect on the growth of oxide scale. Hot rolling tests were carried out on Hille 100 rolling mill. The friction condition at the roll–strip interface during hot rolling of stainless steel was determined and the transfer of surface roughness was discussed.     

Occurrence of surface defects on strips during hot rolling process by FEM

During a hot rolling process, surface defects on strips can severely affect the quality of the rolled product, particularly for two conditions: (1) there are initial defects on continuous casting slabs that propagate and/or are inherited from those on the surface of rolled steels from upstream rolling processes; and (2) there are no initial defects on continuous casting slabs, and they consequently appear on the surface of rolled steels due to improper rolling technologies. In this paper, the authors present a new 3D finite element model coupled with constrained node failure to understand better the initiation and growth of surface defects on strips during the hot rolling process for case 2. The strip deformation processes were simulated for various rolling reduction ratios and friction coefficients between the roll and the strip. The occurrence of surface defects on strips was modeled under some rolling conditions. The plastic strain distribution in strips and the rolling forces were obtained. The risk of occurrence of surface defects on strips increases as the friction between the roll and strip increases for the same reduction ratio.     

A multi-scale model for friction in cold rolling of aluminium alloy

A simple and robust friction model is proposed for cold metal rolling in the mixed lubrication regime, based on physical phenomena across two length scales. At the primary roughness scale, the evolution of asperity contact area is associated with the asperity flattening process and hydrodynamic entrainment between the roll and strip surfaces. The friction coefficient on the asperity contacts is related to a theoretical oil film thickness and secondary-scale roll surface roughness. The boundary friction coefficient at the “true” asperity contacts is associated with tribo-chemical reactions between fresh metal, metal oxide, boundary additives, the tool and any transfer layer on the tool. The asperity friction model is verified by strip drawing simulations under thin film lubrication conditions with a polished tool, taking the fitting parameter of the boundary lubrication friction factor on the true contact areas equal to 0.1. Predicted values of average friction coefficient, using a boundary friction factor in the range 0.07–0.1, are in good agreement with measurements from laboratory and industrial rolling mill trials.     

Simulation of plane-strain rolling by the rigid-plastic finite element method

The rigid-plastic finite element method for a slightly compressible material is applied to steady and non-steady state strip rolling. Solutions for some technical problems using a finite element analysis for rolling process are given. Stress and strain distributions in steady state plane-strain strip rolling under the condition of a constant coefficient of friction are calculated for work-hardening and non-hardening materials. The calculated distribution of roll pressure exhibits a peak at the entry which does not appear in the analysis by the slab method. Non-steady state deformation of the front and tail ends is also analysed. The calculated end shapes are in good agreement with the experimental ones for aluminium strip.     

水雾化铁粉轧制试验研究

对自制的设备进行控制系统的改装,使得轧制参数便于调整.进行水雾化铁粉轧制试验,确定了随机轧制时带材相对密度和粉末松装相对密度及厚度的关系,分析了初始辊缝大小和摩擦系数对带材性能的影响.试验表明,对于150mm轧辊,当初始辊缝为0.475mm时,可轧制出最厚为1.22mm带材.     

Effect of speed in cold strip rolling with Coulomb friction

The Bland and Ford theory of cold strip rolling, with Coulomb friction, is extended to cover the effect of speed of rolling. A good agreement between theoretical and experimental results is shown.     

Analysis of friction and surface roughness effects on edge crack evolution of thin strip during cold rolling

Experimental investigation and mechanical analysis have been carried out to study the edge crack formation during cold strip rolling using Atomic Force Microscopy (AFM) and Scanning Electron Microscopy (SEM). The effects of friction and surface roughness on edge crack initiation and growth rate have been discussed. Friction leads to an increase in fracture loads and decreasing the friction coefficient is effective in preventing the microcracks. Surface roughness variation along the strip width contributes to stress distribution and inhibits crack nucleation. The findings reveal that the behaviour of crack evolution is influenced by fracture surface roughness as well as rolling friction.     

STUDY OF THE 3-DIMENSIONAL STRESSES OF COLD STRIP ROLLING UNDER CENTRE WAVE

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Plane strain hot rolling of slab and strip

A numerical solution of the steady-state plane strain hot rolling problem with maximum friction is found in the range from the thick slab to the thin strip rolling geometries. The problem is kinematically determinate, and it is solved on the physical and hodograph planes using the finite-difference approximation of hyperbolic differential equations of the plane strain rigid–plastic flow theory. A sequence of the boundary value problems defined by the slipline field mode is treated as a non-linear vector equation which is solved by Broyden’s secant method. Six versions of the FORTRAN PC programs are written for a wide range of the slab/strip rolling geometries. The solution for the thin strip rolling with large roll radius and small strip thickness reduction is approached to Prandtl’s thin plastic layer with homogeneous velocity field.     

Elastic-plastic finite-element modelling of cold rolling of strip

The rolling of copper strip has been simulated using an elastic-plastic finite-element method (EPFEM) for plane-strain deformation. The use of this program, which includes both material and geometric non-linearities, permits the identification of elastic and plastic deformation in rolling, and also the effects of unloading. The rolling model is based on the physically realistic concept that the strip is drawn into the roll gap by the action of interface friction.The results clearly show the maximum pressure associated with the neutral point and are in good quantitative agreement with earlier work. In addition, the stresses and deformation outside the nominal contact are presented.     

轧制过程中板形控制的计算机模拟

采用三维弹塑性有限元法同时考虑材料、几何双重非线性对板带轧制过程中影响板形的几大关键因素（诸如接触摩擦、辊缝形状、板凸度和前后张力）进行了广泛研究,建立了与之相应的力学模型并编写了大型程序EPFEP3。采用基于UL法的Lagrange描述,从非稳态咬入到稳态轧制在VAX11/780计算机上实现了对板形控制参数设定量值化的研究。以图形跟踪形式给出了大量金属流动信息和应力分布信息,为板形控制过程模拟、预报以及缺陷形成机理提供一种准确而有效的分析方法。     

冷连轧机轧制力的影响因素

通过将轧制变形区划分为微单元,对变形区内轧制力影响因素的变化规律进行研究。根据微单元塑性变形方程式,建立单位轧制压力的计算模型。针对变形抗力、摩擦因数等非线性因素,建立基于神经网络校正系数和工作参考点方法的数学模型,分析其在变形区内的变化规律。针对轧辊压扁和轧制力计算的耦合现象,采用计算机迭代计算的模型完成轧制力的解耦计算。工业轧机实际数据验证了采用微单元方式计算轧制力预报精度高,可用于生产实践。     

Mixture Lubrication with Emulsions in Cold Rolling

A mixture model of lubrication in cold rolling with two adsorbed layers on the solid surfaces and an emulsion layer between them has been developed. The elastic deformation of the strip and the rolls is considered. A series of simulations using this model is carried out, and this model predicted that the value of the inlet film thickness is in good qualitative agreement with the experimental results. There exists a range of roll speeds that provides sufficient friction to perform the rolling process without front tension under the merged conditions and lower roll speeds. At high roll speed, the two adsorbed layers are separated by the emulsion layer, and the pressure hill disappears due to the smaller surface shear stress acting on the strip, so that rolling is no longer possible unless accompanied by a front tension.     

薄带平整轧制时轧制压力模型的研究

考虑到轧辊的弹性变形以及轧件的弹性变形,建立了一套新的薄带平整轧制时的轧制压力模型。在模型中,对于一般薄带,考虑到停滞区的不对称性,采用混合摩擦理论分析了变形停滞区的摩擦力分布;而对于极薄带材,根据平整时塑性区相对弹性区缩小,摩擦力模型中的停滞区的范围并不止于塑性区,有可能扩大到弹性变形区这一特性,对相应的单位轧制压力分布情况进行了详细推导。同时,为了验证相关模型的准确性,采用该模型对宝钢1550CAL平整机相关典型规格产品轧制压力进行了理论计算,并在线实测出相应的轧制压力,其计算结果与实测值很好吻合,完全达到了工程上所需要的预报精度要求。因而该模型具有重要的理论意义和实用价值,可作进一步的推广与应用。     

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.