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。     

带材轧制过程应力及变形的计算机仿真

用三次样条流线条元法分析带材的三维塑性变形,用分割模型影响系数法分析辊系的弹性变形,用BP神经网络方法对轧后带材板形进行模式识别,将三者联立,对900 mm HC轧机冷轧带材轧制过程进行了计算机仿真,得到了较为详细的应力及变形的仿真结果。仿真实例表明,提出的方法和模型符合实际,对三维轧制理论、板形理论及控制技术的发展有重要意义。     

STUDY ON STRIP AND ROLL DEFORMATION COUPLING OF COLD STRIP ROLLING ON 4-H MILL

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模拟板带轧制三维变形的流面条元法

提出模拟板带轧制过程三维变形的一种新的数值方法——流面条元法。沿着金属的流动轨迹,将变形区划分为若干流面(曲面)条元,为方便分析和计算,又将其映射为平面条元。横向位移和高向位移的纵向分布被分别构造为四次曲线和二次曲线,其横向分布均用三次样条插值函数表示,高向分布均用二次曲线拟合。根据塑性力学流动理论,分析推导了变形区三维变形和应力的数学模型。与曾经提出的流线条元法相比,考虑了应力与变形沿高向的不均匀分布,实现了精确的三维分析和计算。仿真实例表明,该方法和模型符合实际,为板带轧制过程的三维力学仿真提供了一个新的实用工程数值方法。     

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.     

带钢平整机轧制压力的计算模型

平整较厚带材时，变形区水平应力沿板厚不均匀分布对平整轧制压力的计算有着重要影响。在考虑带材入口和出口弹性变形区影响的冷轧轧制压力计算模型的基础上，通过修改弹性变形区入口和出口应力边界条件，提出平整轧制压力计算模型，并对弹性区入口和出口表面水平应力进行了计算。用该模型计算的平整轧制压力与原有计算模型和实测值进行对比，证明模型提高了精度。     

An airy function to rapidly predict stresses in wound metal strip having asymmetric thickness profile

With increased demand for thin gage flat metals, control of strip flatness or shape in cold rolling processes has become very important. To improve the flatness quality of cold rolled metal strip and sheet, this work provides a rapid method to predict the transient strains (or stresses) occurring during the rewinding of flat-rolled steels having problematic asymmetric strip thickness profile (or wedge). Flatness control systems, used to monitor and correct the distribution of stress across the width of rolled sheet, are unable to distinguish between stresses induced during rolling, and those caused when rewinding strip containing asymmetric thickness profile. The winding stresses, unless large enough to plastically deform the strip, vanish upon unwinding during subsequent operations such as stamping. Therefore, to help avoid strip flatness defects in thin strip containing wedge, a method is developed to separate the winding stress contribution from the overall stresses that are measured indirectly by flatness control systems. A fourth-order polynomial Airy function is developed to rapidly predict the in-plane stresses based on mandrel wrap number and spatial location on the strip. The Airy function is obtained by applying two-dimensional finite element analysis to study the transient in-plane stresses during rewinding at various numbers of mandrel wraps for a strip containing wedge profile. Three-dimensional finite element analysis is first employed, however, to show justification to a simplified two-dimensional problem described by the plane-stress Airy function. The two-dimensional finite element analysis provides insight as to how the in-plane stresses evolve, and allows determination of coefficients for the Airy function based upon model geometry and displacement boundary conditions. This approach differs from other methods that employ Fourier series to solve the biharmonic equations for an assumed two-dimensional problem. Finally, filtering of the winding stresses from flatness control system input signals is also discussed based on data taken from a rolling mill different to that used for model development.     

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。     

Coupled approach for flatness prediction in cold rolling of thin strip

The paper presents a predictive model of the flatness defects, which appear during rolling of thin plates, the origin of which is the roll stack thermo-elastic deformation. The combination of the elastic deflection, the thermal crown and the roll grinding crown results in a non-parallel bite, and if the deformed roll transverse profile is not an affinity of the incoming strip profile, differential elongation results and induces high stresses in the outgoing strip. The latter, combined with the imposed strip tension force, result in a net post-bite stress field which may be sufficiently compressive locally to promote buckling. A variety of non-developable shapes may result, generally occurring as waviness (centre waves, wavy edges, quarter-buckles, etc.). This problem is most of the time addressed in a decoupled way, i.e. as a post-processing of the residual stresses computed by a strip rolling model; the present paper on the contrary describes a fully coupled approach of in-bite plastic deformation and post-bite buckling. For this purpose, a simple buckling criterion has been introduced in a FEM model of strip and roll deformation, Lam3/Tec3; its implementation is documented in details. The capabilities and limits of the present approach are described and discussed. Characterised by its coupled approach, it is primarily devoted to cases where on-line (under tension) manifested defects occur. It is shown that the impact of the post-bite, post-buckled stress field on the in-bite stress and strain fields is quite small in the cases investigated; however, subtle changes appear in the velocity field at bite exit, and this is sufficient to transform completely the post-bite stress field, which is found in much better agreement with measurements if such a coupled treatment is used.     

Edge stresses in wide strip hot rolling

In the rolling of wide strip, longitudinal tensile stresses develop along the edges which enhance edge cracking. Theoretical assessment of these stresses and the factors affecting their magnitude and spread are not emphasized in existing solutions, since most of the solutions are based on the assumption of plane strain along the entire width. In the present work a flowline field solution is developed to analyze the flow and stresses in steady state wide strip hot rolling based on the concept of a plane-strain middle zone and two lateral flow edge zones from which edge stresses and edge zones width have been determined. The results obtained show that the maximum value of the longitudinal edge stresses is 1/√3 the flow stress and occurs at the neutral point where the width of edge zone is maximum. The influence of the coefficient of friction at roll-strip interface, roll diameter and thickness reduction ratio on the magnitude and spread of edge stresses is not appreciable.     

Stream surface strip element method for simulation of the three-dimensional deformations of plate and strip rolling

A new method—the stream surface strip element method (SSSEM)—for simulating the three-dimensional deformations of plate and strip rolling process is proposed. The rolling deformation zone is divided into a number of stream surface (curved surface) strip elements along metal flow traces, and the stream surface strip elements are mapped into the corresponding plane strip elements for analysis and computation. The longitudinal distributions of the lateral displacement and the altitudinal displacement of metal are constructed respectively to be a quartic curve and a quadratic curve, the transverse distributions of them are expressed as the third-power spline function, and the altitudinal distributions of them are fitted to be a quadratic curve. Based on the flow theory of plastic mechanics, the three-dimensional deformations and stresses of the deformation zone are analyzed and formulated. Compared with the streamline strip element method, the SSSEM considers the uneven distributions of stresses and deformations along altitudinal direction, and realizes an accurate three-dimensional analysis and computation. The simulation examples indicate that the method and the model of this paper are in accord with facts, and provide a new reliable engineering-computation method for the three-dimensional mechanics simulation of plate and strip rolling process.     

基于影响函数法的轧制压力横向分布规律分析

轧制压力横向分布直接影响轧辊的弹性变形和轧件的出口厚度分布。文中基于影响函数矩阵法,对轧机辊系受力和弹性变形进行计算分析,研究轧制过程中弯辊力和压下率对轧制力横向分布的影响,揭示轧制压力横向分布系数与弯辊力呈近似线性增长、与压下率呈近似线性减小的规律。分析表明,通过调节弯辊力或在轧制规程中改变压下率设定,可改变轧制压力的分布。为轧制压力横向分布函数的在线快速计算和板凸度控制模型的建立提供基础。     

Buckling phenomena related to rolling and levelling of sheet metal

The paper deals with analytical and numerical considerations of buckling phenomena in thin plates or strips under in-plane loads which typically appear during rolling and levelling, i.e. straightening by stretching, of sheet metal. Buckling due to self-equilibrating residual stresses, caused by the rolling process, in eventual conjunction with global tensile stresses (denoted as “rolling buckling”) as well as buckling during the levelling process (denoted as “stretching buckling” or “towel buckling”) are considered. Analytical estimates are derived and compared against results of numerical simulations and field observations. Mode jumping by varying the global strip tension is explained on the basis of the derived analytical solutions. It is shown how from the waves, i.e. height and length, observed on the strip sliding over or lying on a rigid plane one can provide information about the distribution of the differences in the plastic strains over the width of the strip which lead to the buckled configuration. And, vice versa, knowledge of the plastic strain distribution can be used for estimating the expected wave heights representing a measure for the geometrical quality of the rolled product. The influence of the dead weight of the strip on the post-buckling pattern is also discussed on the basis of non-linear analyses.     

The decay of stresses induced by flat rolling of metal strip

Current simulation models for the prediction of residual stresses in flat metal rolling utilize heuristic assumptions about the roll-gap entrance and exit velocity distributions. The nature of the velocity distributions which occur in the strip adjoining the roll-gap is investigated. The problem is formulated in terms of velocity perturbations and the resulting nonlinear equations are approximated by a linear set of equations. The method of solution uses either the stress function or its integral to allow mixed boundary conditions of velocities and/or stresses at the elastic boundaries. The resulting semi-infinite problem is solved using a Laplace transform technique. Two examples are provided to illustrate the velocity and stress distribution behaviour in a moving elastic strip.     

Study on the improved accuracy of strip profile using numerical formula model in continuous cold rolling with 6-high mill

The quality requirements for thickness accuracy in cold rolling continue to become more stringent. In cold rolling mill, it is very important that the rolling force calculation considers rolling conditions. The rolled strip thickness was predicted using calculated rolling force. However, the prediction of strip thickness in cold rolling is very difficult; in particular, for 6-high mill with shifted intermediate roll (IMR), the accuracy of thickness is not good. In this study, to improve the accuracy of rolled strip thickness, the roll gap flattening can be given based on Hertz contact theory, with contact between rolls and the smooth cylindrical rolls for the rolling elastic deformation. Also, the distribution of the roll gap flattening may be calculated using the contact force of unit transverse length. The strip profile at the continuous cold rolling is calculated by using the numerical analysis model considering the initial strip profile before cold rolling. Hence, we propose that the numerical model can predict the rolled strip profile more quickly and accurately and be applicable to the field. The results of the proposed numerical model were verified by FE-simulation and cold rolling experiments of 6-high mill with five stands.     

Strip Layer Method for Analysis of the Three-Dimensional Stresses and Spread of Large Cylindrical Shell Rolling

As the traditional forging process has many problems such as low efficiency, high consumption of material and energy, large cylindrical shell rolling is introduced. Large cylindrical shell rolling is a...     

板形标准曲线的理论计算方法

联立板形预报模型和板形判别模型,提出板带轧机板形标准曲线的理论计算方法。该理论计算方法的思路和原则是最大限度地消除板凸度并同时兼顾板形良好,最终使板形趋于最好,这种计算方法的目标是实现板形和板凸度的综合最优控制。以1 220 mm五机架带钢冷连轧机和900 mm单机架带钢冷轧机5道次轧制为例,分别对轧制中凸板和中凹板的情况进行计算,计算结果证实了理论分析计算的正确性。这种板形标准曲线的理论计算方法为进一步从理论上定量研究板形标准曲线模型奠定了良好的理论基础。     

双金属复合板冷轧变形行为的Avitzur上限模式分析

应用Avitzur上限理论建立双金属冷轧塑性变形模式的数学模型。应用此模型计算变形区域的速度场、能量消耗及轧制力的上限解等变形行为,给出相关参数的相应计算公式。应用这些理论公式对铝-钢复合板进行分析,计算与试验结果得到较好的吻合。分析模型能够很好地应用于模拟双金属冷轧过程,并能为双金属复合板的生产提供一些有益的理论依据。     

Experimental and numerical study of O/W emulsion lubricated strip rolling in mixed film regime

An experimental and numerical study of cold rolling lubricated by O/W emulsion has been carried out. The strip rolling experiment was carried out on a Hille experimental rolling mill with a view to study the performance of emulsion lubrication in terms of practical rolling parameters. Accordingly, rolling parameters such as rolling force and torque were measured. The experimental measurements compare favourably with the computed results from a numerical scheme developed by the authors. The scheme, based on a two-phase lubricant model, is capable of calculating the oil concentration at any point within the inlet zone and work zone, rolling pressure, film thickness, and fractional contact area ratio associated with strip rolling under mixed film lubrication at different rolling speeds. Using this scheme, the intertwined effects of an emulsion’s parameters such as: oil concentration, mean oil droplet size, and rolling speed on strip rolling were investigated. The numerical study encompassed the mixed film regime for speed, S ranges from 10⁻⁴ to 10⁻², supply oil concentration level λ_ds from 1 to 10%, and oil droplet size D _S from 5 to 10. Experimentally, the differences between water, oil and emulsion-lubricated rolling are not discernible except for film thickness. At a low speed of 10 RPM, force and torque of water-lubricated rolling are marginally higher than oil- or emulsion-lubricated ones. However, the difference between emulsion and neat oil is not apparent. The numerical results show the occurrence of a moderate oil concentration increase in the inlet zone followed by a sharp one at the beginning of the work zone. The effect of the concentration process is predominantly seen in the film thickness and the lubricant pressure whilst its effect on the total pressure is less pronounced. The analysis of the results suggests that it is possible to lower the emulsion oil concentration without any adverse effect on the rolling process. This principle can be used to control the outlet lubricant film thickness and hence the surface quality of the rolled strip.     

窄带钢轧后冷却速度研究及其温度场模拟

通过热模拟机Gleeble-1500对Q215热轧窄带钢在不同的轧后冷却速度下进行了模拟,研究了冷却速度对热轧窄带钢组织性能的影响.根据现场条件,得到了合理的冷速范围.同时,采用MARC对其冷却过程进行有限元数值模拟,分析了冷却速度对钢带温度场分布的影响.对提高产品的强度及韧性,使其适应以后的冷轧工艺提供了帮助.