求解冷轧带材金属横向流动和前张应力横向分布的一种新型条元变分法

将变形区划分为许多纵向条元,根据最小能量原理,通过对单个条元的变分,由欧拉微分方程求得条元上的出口横向位移函数模式,再通过对整个变形区的变分,由一组线性方程直接求得条元节线上的出口横向位移值,进而确定前张应力的横向分布。冷轧窄带和宽带的前张应力横向分布的计算结果与实验结果吻合较好,证明了该理论模型的正确性。     

B3 Spline Function Method Used in Simulating Flatness and Profile of Cold Rolled Strip

Flatness and profile are important quality indexes of strip. Combining the influence function method to solve the elastic deformation of roll system with the variational method to solve the lateral flow of metal, the flatness and profile of the strip during cold eontinuous rolling were simulated. The B3 spline funetion was used to analogize the lateral distribution of strip thickness. The transverse distributions of the exit thiekness and the front tension stress for eaeh pass were obtained. Compared with the measured results, it is proved that using the spline funetion to analogize the lateral distribution of strip thickness ean improve the ealculation accuraey of flatness and profile largely.     

冷轧带钢局部高点卷取过程起筋控制的建模与仿真

为了研究带钢局部高点卷取起筋的控制方法,利用三维弹塑性变形基本理论,并引入带钢塑性流动因子,建立了弹塑性卷取应力和起筋量模型.基于应力函数假设、S.Timoshenko最小功原理和伽辽金虚位移法建立了起筋带钢的应力场分布和可用于在线计算的起筋临界卷取张力设定模型.仿真结果表明:局部高点在径向累积叠加所引起的带钢张力不均匀分布和轴向压应力是导致带钢起筋的主要原因;起筋量随局部高点高度、卷径和卷取张力增加而增大,薄带钢比厚带钢起筋量增幅明显;临界卷取张力随卷径、带钢厚度和局部高点高度增大而减小.      

热轧带钢局部高点对冷轧带钢板形的影响

热轧带钢局部高点对冷轧带钢板厚和内应力分布具有重要影响。采用B3样条函数拟合带材厚度横向分布，定量研究热轧来料局部高点对冷轧带钢板厚和内应力分布的影响。研究结果表明：轧后带钢局部高点高度及附加张应力的大小与来料高点高度成正比，随总轧制压下率的增大而减小。     

研究冷轧带材金属横向流动和张力横向分布的线性条元法

本文提出了分析冷轧带材金属横向流动和前、后张力横向分布的线性条元法,并用简明的矩阵形式来表示。由于本方法使横向位移在整个变形区处处连续,保证了条元间的横向位移协调,进一步发展了条元法的理论。前、后张力横向分布的计算结果与实验结果吻合较好。     

Flexural Forces of the Working Rollers and the Broadening of Thin Steel Strip in Hot Rolling

On the basis of the Jourdain variational principle for a rigid–plastic body and the kinematically permissible velocity field, a model of the free expansion in the hot rolling of thin sheet is developed. The functional used in the variational equation is the total power of the internal resistances, the slipping-friction forces, the shear forces, and the front and rear tension. The Ritz method is used in solving the Jourdain variational equation for rolling with tension. The Jourdain variational equation is converted to a system of uniform equations, with a derivative of a variable parameter on the left side of each. The variable parameters are the exponent of the kinematic condition; the total broadening in the plastic-deformation region; and the expansion in its neutral cross section. The mathematical model developed for the broadening of hot-rolled strip may be used to investigate the distribution of broadening along the plastic-deformation region as a function of the parameters of the rolling process and the strip. To verify the model of free expansion, experiments are conducted on a two-roller laboratory cold-rolling mill. Lead samples are rolled. Their measured broadening matches the theoretical values to within 10%. The cold rolling of lead samples simulates hot rolling. Theoretical analysis of the influence of tension on the free expansion is consistent with practical results in the literature. The nonuniform tensile stress seen in the input and output cross sections of the deformation region when tension is applied gives rise to additional powers in the balance equation, with consequent decrease in the broadening. The resulting nonuniformity of the tensile stress may be used to regulate the broadening in thin-sheet rolling. In turn, the nonuniformity of the tensile stress over the strip width may be increased or decreased by means of the flexural forces of the working rollers in the mill. A method of regulating the broadening of the strip in hot rolling by means of the flexural forces of the working rollers is outlined in the present work.     

冷轧机工作辊非对称弯辊的板形调控理论研究与应用

为减少冷轧带钢的非对称板形缺陷的产生,设计了工作辊非对称弯辊控制系统.应用影响函数法计算辊系变形,同时考虑辊缝中金属横向流动对带钢出口横向张力分布的影响,通过迭代法计算出工作辊两端施加不同弯辊力后的辊间压力分布、出口厚度横向分布以及出口横向张应力分布.理论分析结果表明,工作辊非对称弯辊可以在一定程度上改善辊间压力分布不均,减轻轧辊磨损和减少轧辊掉皮事故的发生,降低带钢边部的非对称板形缺陷.实际应用结果证明,当倾斜调整量小于10%时,应用工作辊非对称弯辊替代倾斜调整,可以获得更好的板形精度.      

Boundary Shear Stress in Spatially Varied Flow with Increasing Discharge

The distribution of the wall shear stress on the bed and sidewalls of an open channel receiving lateral inflow was obtained from experimental measurements of the distribution of the velocity in the viscous sublayer using a laser doppler velocimeter. The experiments were conducted in a 0.4 m wide by 7.5 m long flume. Lateral inflow was provided into the channel from above via sets of nozzles positioned toward the downstream end of the flume. Lateral inflow was provided over a length of 1.9 m. The results indicate that the local boundary shear stresses are significantly influenced by lateral inflow. The significant variation occurs near and around the region where the lateral inflow enters the channel. At various measurement positions along the lateral inflow zone, mean boundary, mean wall, and mean bed shear stresses were obtained and compared. The results indicate that the mean boundary shear stresses increase from the upstream to the downstream ends of the lateral inflow zone. The results also indicate that the mean bed shear stress is always greater than the mean wall shear stress, which are approximately 30–60% of the mean bed shear stress. The friction factor in the Darcy–Weisbach equation was obtained from both the mean boundary shear stress and from the equation describing the water surface elevation in an open channel receiving lateral inflow (equation for spatially varied flow with increasing discharge). The results indicate that the estimated friction factors from the latter approach are significantly larger. Also, the estimated friction factors from both approaches are higher than the values predicted from the Blasius equation which describes the friction factor for wide uniform open channel flows. They were also higher than values predicted from the Keulegan equation, which is an empirically derived equation for flow in roof drainage gutters. The study highlights the deficiencies in the existing equations used to predict friction factors for spatially varied flow and that further research is required to explore the distribution of boundary shear stress in an open channel receiving lateral inflow.     

基于非协调F?ppl-von Kármán方程组的冷轧带材后屈曲分析

为了揭示冷轧带材前屈曲面内残余应力与后屈曲挠度、后屈曲残余应力的关系,引入非协调F?ppl-von Kármán方程组,建立了两边自由无限长带条后屈曲的非线性偏微分方程组边值问题模型。根据冷轧带材后屈曲挠度具有轧制方向单波长周期性变化的特点,将非线性偏微分方程组边值问题分离变量而形成非线性常微分方程组边值问题。将边值问题中涉及的各物理量无量纲化,并分析这些物理量的数量级,进而确定出带有待定系数的无量纲挠度函数的形式。然后将总势能写成只与无量纲挠度函数有关的形式,并利用Ritz法确定各待定系数。最后采用其他文献中的计算结果与本文提出方法的计算结果进行对比,发现较为吻合,并解释了产生误差的原因。同时针对某冷轧厂产品计算出后屈曲释放后的残余应力,并计算了使带钢保持平直的最小张应力,为板形仪的合理应用提供了参考。     

Modeling and Analysis of Interstand Tension Control in 6-high Tandem Cold Rolling Mill

The interstand tension control is one of the most important ways to meet tight tolerances for strip product quality during tandem cold rolling process. Using coordinate analysis and parabolic approximation for the mass flow balance principle, the strip velocities eliminating the use of forward slips and backward slips were calculated. In order to reduce the effect of roll eccentricity on the tension measurement, a filter based on bilinear transformation was de- signed. Applying a first-order Taylor series approximation, the transfer function matrix model of interstand tension stress was derived. The actual measurements on-site and the final calculation results showed that the established model had high calculation accuracy and was beneficial for interstand tension control of random cold rolling process.     

Determination of Boundary Shear Stress and Reynolds Shear Stress in Smooth Rectangular Channel Flows

A method for computing three-dimensional Reynolds shear stresses and boundary shear stress distribution in smooth rectangular channels is developed by applying an order of magnitude analysis to integrate the Reynolds equations. A simplified relationship between the lateral and vertical terms is hypothesized for which the Reynolds equations become solvable. This relationship has the form of a power law with an exponent of n = 1, 2, or infinity. The semiempirical equations for the boundary shear distribution and the distribution of Reynolds shear stresses are compared with measured data in open channels. The power-law exponent of 2 gave the best overall results while n=infinity gave good results near the boundary.     

四辊冷轧带材中张应力横向分布的求解

以六次偶函数拟合铝带入、出口横向厚度分布，将求解辊系弹性变形的影响函数法与求解金属横向流动的变分法相结合；成功地计算了四辊冷轧机前、后张应力横向分布。计算过程具有较好的收敛性，运算效率高。实验结果与理论计算结果相一致。     

Plasticity of continuous fiber-reinforced metals

Continuous parallel alumina fiber-reinforced metals produced by pressure infiltration are tested in tension/compression along the fiber axis with a goal of measuring the influence exerted by long fibers on the flow stress of their matrix. In this configuration, the equistrain rule of mixtures, modified to take into account stresses due to differential lateral contraction, can be used to back-calculate the matrix flow stress from that of the composite. This method provides the least physically ambiguous measurement of matrix flow stress in the composite; however, experimental uncertainty can be high. This uncertainty is evaluated in detail for the present experiments, in which matrix in situ stress-strain curves are measured for cast 3M NEXTEL 610 and DUPONT FIBER FP reinforced pure and alloyed aluminum- and copper-based matrices of varying propensity for recovery and cross-slip. Within experimental uncertainty, data show no enhanced matrix work-hardening rates such as those those that have been measured with tungsten fiber-reinforced copper. It is found that the fibers alter the matrix plastic flow behavior by increasing the flow-stress amplitude of the matrix, and by rendering initial yield in compression more progressive than in initial tension. Essentially, all observed features of matrix/fiber interaction can be rationalized as attributable to dislocation emission in the matrix caused by thermal mismatch strains within the material during composite cooldown from processing temperatures.     

张力对冷轧板带变形的影响

在大型商业有限元软件平台上,开发了板带轧制三维模拟系统,讨论了改变前,后张力时,轧件的三维变形特点。模拟结果显示,增加张力限制金属横向流动,加大厚向变形,使断面厚度更加均匀,其中同时改变前后张力对变形的影响效果最大。     

Bubble and liquid flow characteristics during horizontal cold gas injection into a water bath

In refining processes such as the AOD process cold gas is blown horizontally into the molten metal bath of the processes. The spatial distribution of bubbles in the bath is one of the important factors influencing the efficiency of the processes. In this study, a water model study was carried out to understand the characteristics of bubbles and liquid flow generated by horizontal gas injection. The bubble and liquid flow characteristics were measured using an electro‐resistivity probe and a laser Doppler velocimeter, respectively. In the flow field near the nozzle the bubble characteristics for the horizontal cold gas injection can be predicted by empirical equations derived for isothermal gas injection systems. The liquid flow characteristics could not be measured in this region. On the other hand, in the region far from the nozzle the two characteristics for the cold gas injection became different from those for the isothermal gas injection because of enhanced buoyancy force acting on expanding cold bubbles due to heat transfer.     

Explicit models of thickness profile and tension stress distribution for process control applications

This contribution aims to present a compact and efficient model for the calculation of strip thickness profile and shape which refers to the tension stress distribution. The model is derived from appropriate combination and generalisation of analytical approaches well known in the published literature. The basis for the model is given from analytical solutions of the gaugemeter, roll force and tension stress differential equations linearised about the actual operating point. A novel profile and flatness prediction algorithm is developed which leads to more efficient solutions for cold and hot rolling mills. The resulting algorithm has substantial advantages over the traditional models in its efficient computation, and hence, provides an opportunity for real‐time implementation in advanced model based control systems.     

Finite Element Modelling of TRIP Steels

A constitutive model that describes the mechanical behaviour of steels exhibiting “Transformation Induced Plasticity” (TRIP) during martensitic transformation is presented. Multiphase TRIP steels are considered as composite materials with a ferritic matrix containing bainite and retained austenite, which gradually transforms into martensite. The effective properties and overall behaviour of TRIP steels are determined by using homogenization techniques for non‐linear composites. The developed constitutive model considers the different hardening behaviour of the individual phases and estimates the apportionment of plastic strain and stress between the individual phases of the composite. A methodology for the numerical integration of the resulting elastoplastic constitutive equations in the context of the finite element method is developed and the constitutive model is implemented in a general‐purpose finite element program. The prediction of the model in uniaxial tension agrees well with the experimental data. The problem of necking of a bar in uniaxial tension is studied in detail.     

考虑成卷-展平过程的冷弯残余应力分析

 从不考虑材料冷作硬化（理想弹塑性体）与考虑冷作硬化（双线性随动硬化）两个方面对带坯在成卷、开卷、展平、塑性弯曲及回弹过程中产生的应力进行了解析分析,获得了冷弯残余应力沿厚度方向上的分布,随后对比研究了考虑硬化与不考虑硬化对冷弯残余应力分布的影响,并将理论计算结果与实测残余应力进行了对比。结果表明,理想弹塑性模型和硬化模型预测的残余应力分布形式几乎一致;成卷上存在屈服时,纵向残余应力由内外表面向板厚中心方向呈非线性分布（成卷上无屈服时呈线性分布）,横向残余应力呈近似线性分布;在变形外区主要为残余拉应力（横向残余应力在外侧有极小部分受压区）,内区主要为残余压应力（横向残余应力在内侧有极小部分受拉区）;横、纵向残余应力最大值均在中性层位置;研究结果与试验测量结果基本一致。     

冷轧钢卷卷取过程内部应力三维分布的研究

冷轧钢卷卷取过程中,带材的板形与板凸度以及卷取张力的横向分布决定钢卷内部的应力分布。同时,带材与卷筒之间、带材与带材之间的摩 擦力对应力分布的影响不可忽略。此外,由于层间接触表面缝隙的存在,钢卷必须按各向性体处理。基于上述因素,提出了一套新的三维数学模型,以计算钢卷内部应力分布,并根据降低钢卷在罩式退火粘经率的要求,研究了钢卷的卷取张力制度。     

基于有限元法数值模拟的冷连轧弹性压扁模型的研究

在采用弹塑性有限元法模拟五机架四/六辊冷连轧轧制过程的基础上,采用拟合函数法得到轧辊弹性压扁后的辊形曲线函数,据此计算轧辊弹性压扁曲率半径。该模型与常用的Hitchcock公式相比,计算的压扁半径能使轧制力计算值更接近实测值,提高了轧制力的预设定精度。