Investigation of Single Pass Shape Rolling Using an Upper Bound Method

This paper presents a generalized analytical upper bound method for the study of external shape, pressure, and torque in the single pass rolling of shaped sections. Generalized kinematically admissible velocity fields have been calculated from an assumed deforming geometry, in turn mathematically developed from a new parameterization of curves for the stream line flow of the material. An upper bound on rolling power was established based on the calculated velocity fields. Unknown variables in the velocity field were determined by minimizing rolling power with respect to unknown velocity field variables, yielding an upper limit to the actual power required as well as rolling pressure and torque. As an applied example, the single oval-to-round and rectangle-to-diamond roll passes have been chosen and analyzed. Velocity fields and power relations were obtained for each pass and computer analysis was carried out to analyze and simulate the process of shape rolling. External shape, average roll torque, and rolling pressure data from the analysis were compared with other worker’s analytical solutions, numerical analyses, and experimental data. The results were found to be in good agreement with previous research and the method was shown to be quicker and easier to use.     

Roll force,torque, lever arm coefficient,and strain distribution in edge rolling

Due to the growing importance of width control in strip and plate mills, edge rolling is currently an im-portant process in hot rolling mills. Research in edge rolling has been carried out, and in the present ar-ticle, models for roll force, torque, and lever arm coefficient are derived using the upper bound method. A simple, kinematically admissible deformation zone and velocity field, independent of friction in the roll gap, is proposed, and the energy dissipation rate is derived. The formula for energy dissipation rate has, in practice, no limitation because all edge rolling geometries are safely in the area where the formula is valid. Roll force and torque are derived by means of two independent integrals. Thus, the lever arm coef-ficient is evaluated from the expressions for roll force and torque using conventional rolling theory. Roll-ing trials report good agreement with theory. Measured roll forces are similar to calculated forces. Furthermore, the shape of the dogbone that arises during edge rolling is in fairly good agreement with the calculated dogbone shape. Deviations are due to the deviation from ideally plastic material in the ex-periments. Also, the strain distribution over the dogbone is similar to the proposed deformation zone. Thus, a new formula has been developed to a stage that it can be implemented in width control systems for edge rolling stands in hot strip and plate mills.     

半固态金属触变塑性成形上限法

在高固相率时,半固态金属的力学模型可简化为连续多孔体力学模型。针对半固态金属触变塑性成形的特点,本文发展了上限法理论在半固态金属触变塑性成形分析中的应用。提出速度间断值不仅要包括切向分量,还要包括法向分量。速度间断的法向分量是由金属通过速度不连续面时,材料固相率的变化而引起的。由此建立了半固态金属触变塑性成形的上限分析模型和理论方法,导出了上限功率的计算公式。为在实际触变塑性成形工艺分析中的进一步应用奠定了理论基础。     

An upper bound solution for twist extrusion process

Twist extrusion, a promising severe plastic deformation technique for grain refinement down to ultrafine/nanocrystalline microstructures, was introduced as an attempt to provide large plastic deformation conditions similar to those in high pressure torsion while allowing large workpiece dimensions for industrial applications. As a relatively new severe plastic deformation technique, twist extrusion requires in-depth investigation of its plastic deformation characteristics. In this study, the twist extrusion process with a square shape die cavity has been analyzed using an upper bound solution to estimate the required power, deformation pattern, and optimum process condition. The analysis has been performed based on two kinematically admissible velocity fields while the effects of friction condition, die geometry, and mean equivalent strain have been considered. The results indicate that the die geometry and process parameters can dramatically change the deformation pattern and extrusion power.     

环件开式辗扩力和力矩计算

用上限法分析了环件开式辗扩变形，导出了辗扩力和力矩计算公式，阐述了辗扩力和力矩与辗扩进给速度的关系。根据环件辗扩实验结果，对文中的辗扩力和力矩计算公式进行了验证。     

An analytical approach to asymmetrical cold strip rolling using the slab method

An analytical model for general asymmetrical cold rolling is proposed to investigate the behavior of sheet during asymmetrical rolling using the slab analysis. Neutral points between the upper and lower rolls and the strip, rolling pressure distribution along the contact interface of the roll and strip, and rolling forces, as well as rolling torque, can be calculated easily using this model. Rolling pressure distribution, rolling force, and rolling torque, which are affected by various rolling conditions such as roll speed ratio, thick-ness reduction, front and back tension, etc., are analyzed. Additionally, the limiting rolling conditions be-tween reduction and roll speed ratio, or front and back tension, under which the rolling process can be accomplished successfully, are discussed. By comparing analytical results and experimental measure-ments of rolling force, it is apparent that the proposed model can successfully provide useful knowledge for designing the pass schedule of the asymmetrical cold strip rolling process.     

A comparative study of slabe, upper bound and finite element methods for predicting force and torque in cold rolling

Rolling force and torque are often measured during the rolling process and their magnitudes used in the process control algorithms. Slab, upper bound and rigid-plastic finite element methods have been applied for predicting force and torque in rolling. This paper compares the results of these methods and that of DEFEL (an elastic-plastic finite element code) with experimental data. It is concluded that slab and upper bound results are very approximate. The rigid-plastic finite element method is fairly accurate for low (roll radius by sheet half thickness) ratios. However, for large ratios (> 100) the elastic response of the roller has to be considered. Elastic-plastic finite element results, on the other hand, are found to have reasonable agreement with experimental data for all ratios.     

双锥辊轴向轧机轧制原理及轧制力能参数计算

阐明了轴向轧制原理,介绍了双锥辊轴向轧机的特点;导出了双锥辊轴向轧机轧制环、盘件回转体接触面投影面积的计算公式;提出了能量法计算轧制扭矩、功率的移位体积理论;给出了扭矩和功率的计算公式;实例计算了热轧600mm钢法兰件的轧制力、扭矩和主电机功率;设计了WGSH80型双锥辊轴向轧机的力能参数,并把实测的主电机功率与计算值进行了比较。     

螺旋孔型斜轧球类件的上限分析

本文根据螺旋孔型斜轧球类零件的变形特点，采用流函数方法提出一种连续上限速度场，利用该速度场计算了轧制功率及轧制力矩，编制了计算程序，并给出了一种典型球类件轧制的计算实例并与实测进行了对比。     

楔横轧工艺成形阶梯轴类件时轧件表面缺陷形成条件分析

依据文献 [4]的模拟实验结果 ,拟定了楔横轧工艺成形阶梯轴类件时轧件表面出现表面缺陷 (蛇皮状或鱼鳞状缺陷 )时的金属流动速度场。以此为基础 ,并借助于上限原理和最小能量原理 ,获得了楔横轧成形阶梯轴时轧件表面缺陷形成的必要条件。同时 ,研究了表面缺陷产生与变形程度、摩擦因数及模具整形段相对长度的关系。从而为估测楔横轧成形阶梯轴类件时轧件表面是否会产生缺陷提供理论指导。     

Analysis of Bonding Behavior and Critical Reduction of Two-Layer Strips in Clad Cold Rolling Process

In recent years, two-layer metallic sheets have been increasingly used in various industries to create combined functions. Among cladding methods, the cold rolling is most widely used in producing bimetallic sheets. In this research, to thoroughly provide guidelines for cold rolling of bimetal strip, an attempt has been made to develop an analytical model based on upper bound method. Also, the bonding strength and critical reduction were calculated using upper bound theorem and the finite element simulation was used for Al/St bimetallic strip. Finally, an experimental study was run for our model to be verified analytically and numerically. Results show that the bonding strength of strips increases with increasing the total thickness reduction of bimetal strips and because of subsequent occurrence of strips bonding in roll gap, increasing the yield strength of base layer gives rise to critical reduction. Through the study, it becomes clear that the proposed analytical model is applicable for simulating the cold rolling process of the two-layer strips and is capable to broaden our knowledge in manufacturing and production of bimetal strips and sheets.     

Spread Model for TC4 Alloy Rod during the Three-Roll Tandem Rolling Process

为了保证三辊连轧过程中棒材的成型精度,研究了TC4钛合金棒材的宽展。采用正交试验优化设计方法设计数值模拟方案,在Marc有限元平台上,研究轧制工艺参数(轧制温度、轧制速度、孔型内切圆直径、轧辊直径、摩擦系数)对宽展的影响,并分析了各参数的影响显著性顺序。在此基础上,建立了三辊轧制TC4棒材的宽展模型。试验在自行研制的8机架Y型连轧机上进行,孔型系统为平三角-圆。宽展测量结果和模型计算结果吻合较好。     

FEM analysis for V–H rolling process by updating geometric method

Three passes of slab rolling during vertical–horizontal rolling process were simulated with explicit dynamic FEM by updating geometric method. Simulation model of the next pass was built when the rolling geometry model was updated after previous pass was finished, changing roll gap, material attribution and boundary conditions. The calculated results of the slab shape are in good agreement with the experimental ones. It is shown that the explicit dynamic FEM and updating geometric method can be used effectively to analyze the multi-passes of V–H rolling process.     

Analysis of the non-steady state vertical–horizontal rolling process in roughing trains by the three-dimensional finite element method

The vertical–horizontal rolling process is often used to accomplish width reduction so as to provide a synchronising operation between the continuous slab casting and hot rolling processes. Numerical simulation of the non-steady state deformation behaviour around the head and tail ends during this process is made by the full three-dimensional rigid–plastic finite element method. An explanation is provided in the theory for the ‘thin element technique’ at the inlet surface of velocity discontinuity. To deal with the interpolation of friction within a surface of an element contacting partly with the roll, a new term, so-called ‘pseudo shape function’, is presented and a related new equation formula is deduced. The calculated shape of the slab edge, the separating force and the rolling torque are consistent with those measured experimental ones for the model material lead.     

径向挤压直齿圆柱齿轮的上限分析

用上限法分析了径向冷挤直齿圆柱齿轮的成形过程，提出了一种动可容速度场，其对齿形渐开线部分未做简化。并运用这种速度场计算分析了摩擦，齿轮的齿数和模数对成形力的影响。     

板带轧制过程的三维耦合有限元分析

对板带轧制过程进行严密的三维分析是研究轧制参数对轧后板带尺寸、板形和机械性能的影响 ,从而实施有效控制的基础。本文简要回顾了板带轧制过程三维数值模拟的研究进展 ,提出了一个分析板带轧制过程的耦合有限元模型 ,其中 ,轧件塑性变形采用刚塑性有限元法计算 ,辊系弹性变形采用弹性有限元法计算。计算实践表明 ,该模型具有良好的精度和较高的效率。     

On constructing kinematically admissible velocity fields in cold sheet rolling

The main objective of the presented study is to introduce a rigorous, systematic method for constructing kinematically admissible velocity fields, which are necessary in the analysis of the plastic forming processes by the upper bound method. The mathematical structure of the method is discussed in full detail. To demonstrate the application of the presented method, three different deformation models for the symmetric strip rolling are obtained. And also, to prove the superb accuracy of the deformation models obtained by the presented method, an upper bound solution for the deformation model subjected to the elliptic flow lines family is given. The results obtained in this analysis are compared with the results of modelling in [B. Avitzur, Metal Forming: Processes and Analysis, McGraw-Hill, New York, 1968], and the advantages provided by the presented method, and some new research directions are pointed out.     

基于负荷均衡的高速线材轧机孔型优化设计

采用大型非线性有限元软件MSC.Marc,通过三维热力耦合弹塑性有限元方法对高速线材中轧区五机架热连轧过程进行了模拟,以各轧机相对等负荷为目标函数,运用Visual FORTRAN语言对MSC.Marc进行二次开发,准确计算了现场及孔型优化后的各道次轧制力和轧制力矩,相对负荷由现场的3.46%～133.91%减小到2.62%～19.3%,使生产工艺更加合理,对实际生产具有重要的指导意义.     

The effects of rolling method changes on productivity in thick plate rolling process

We present a draft schedule scheme to estimate the productivity in thick plate rolling process. Dependency of design force, design torque and maximum bite angle of a rolling mill on the reduction ratio models were fully considered in the draft schedule scheme. Roll force and torque equations used in the reduction ratio models were verified by comparing the measurements with the predictions. Using the draft schedule scheme, we examined the influence of rolling method changes on the productivity (i) material position after the broadside passes, (ii) material position after the longitudinal passes and (iii) the number of turn, i.e., number of times that slab (material) is rotated by 90 degree, before the broadside and/or longitudinal passes begin. Results reveal that the number of turn gives the major influence on productivity. Rolling time can be minimized if material positions after the broadside and longitudinal passes are not fixed in advance.     

连铸板坯切分轧制力矩的上界解析

利用上界定理计算连铸板坯在切分轧制成品孔型中的轧制力矩。在计算过程中 ,将楔形辊面看作平辊组合 ,通过积分方法用平辊速度场计算轧制过程中的各项功率 ,得出与实测值近似的计算值 ,为现场生产提供了理论依据。