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

将变形区划分为许多同条元，根据最小能量原理，通过对单个条件的变分，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量结果与实验结果吻合较好，证明了该理论的正确性。     

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。     

板带轧制变形区金属出口横向位移函数的能量法修正

通过引入修正系数ｍ，修正变分法求解辊缝中金属横向流动得出的出口横向位移函数式中的Ｋ和Ｎ值，以使变形区金属出口横向位移分布接近实际，从而能较准确计算前，后张力的横向分布。ｍ用最不能量原理确定。修正后，前，后张力横向分布的计算值与实测结果基本吻合。     

四辊轧机轧制带材前后张力横向分布的研究

设变形区横向位移为出口(x=l)横向位移。在前张力足以拉平轧后带材的条件下,出口速度沿横向不变。根据秒流量相等原理,可确定变形区内的流动速度和应变速度。前张力横向分布模型σ_1(y)=     

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。     

20辊轧机辊系弹性变形横向分布的计算

以实测张力分布值为依据，求得２０辊轧机轧制压力沿板宽方向的分布。根据弹性理论，采用迭代算法，求得辊系弹性变形横向分布，并且以出口辊缝为度量，求得板厚横向分布。     

钛带在带钢连续退火炉内张应力横向分布仿真

为了探讨利用现有带钢连续退火线生产冷轧钛带产品,基于ABAQUS仿真平台,针对国内某带钢连续退火炉设备条件,建立钛带在退火炉内弹塑性变形的有限元仿真模型,并开展数值模拟研究。结果表明,炉辊辊形、钛带初始板形缺陷及钛带工艺张力大小是钛带张应力横向分布的主要影响因素;钛带的张应力横向分布不均度在凸度辊、单锥度辊和双锥度辊上依次趋于严重;钛带的初始板形缺陷使其张应力横向分布更不均匀,初始有边浪和中浪的钛带都会出现张应力分布不均匀现象;工艺张力对于钛带张应力横向分布均匀性影响不大。针对钛带张应力横向分布的影响因素及其影响规律的研究结果,对于设计炉辊辊形和确定对来料钛带实际板形的要求都具有参考价值。     

热轧宽带钢厚度及轧制力横向分布的研究

 板形是板带几何尺寸的一个重要指标,忽略横向变形的二维轧制理论已不能满足板形精度要求,掌握金属三维变形规律,建立各因素与出口带钢厚度分布之间的关系,可准确地进行板形设定。基于理论基础,应用影响函数法实现辊系变形计算,三维差分法求解轧件塑性变形,辊系变形向轧件变形提供出口厚度分布,轧件变形向辊系变形提供轧制力横向分布,两者相互迭代求得厚度分布结果。结合现场实际,验证了模型的准确性,为在线计算出口辊缝提供了思路和依据。     

CVC轧机冷轧宽带材板形控制特性的数值模拟

以六次偶函数拟合宽带材出口横向厚度分布，计算了ＣＶＣ轧机冷轧宽带材前张应力横向分布，首次以张应力横向分布的形式，模拟了ＣＶＣ轧机冷轧宽带材板形控制特性，模拟结果证明：ＣＶＣ轧机冷轧宽带材时具有很强的板形控制能力。     

模拟热轧板带三维变形的条层法及仿真实例

提出一种模拟板带轧制过程三维变形的新的数值方法———条层法。首先沿高向将变形区均匀地划分为若干层 ,然后再沿着金属的流动轨迹将变形区内的每层带材划分为若干流线条元 ,为了方便分析和计算 ,又将流线条元映射为矩形条元。横向位移的纵向分布被构造为四次曲线 ,横向分布用三次样条插值函数表示 ,高向分布用二次曲线拟合。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。与本文作者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。关于热带钢连轧和厚板轧制的仿真实例表明 ,提出的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。     

Elastoplastic 3D Deformation and Stress Analysis of Strip Rolling

Ｉｎｃｏｌｄｓｔｒｉｐｒｏｌｉｎｇ，ｔｈｅｔｒａｎｓｖｅｒｓｅｄｉｓｔｒｉｂｕｔｉｏｎｏｆｔｅｎｓｉｏｎｓｔｒｅｓｓｉｓａｄｅｃｉｓｉｖｅｆａｃｔｏｒｏｆｓｔｒｉｐｓｈａｐｅ．Ｌａｒｇｅｎｏｎ－ｕｎｉｆｏｒｍｔｅｎｓｉｏｎｓｔｒｅｓｓｄｉｓｔｒｉｂｕ...     

A Model Coupling Method for Shape Prediction

 The shape of strip is calculated by iterative method which combines strip plastic deformation model with rolls elastic deformation model through their calculation results, which can be called results coupling method. Because the shape and rolling force distribution are very sensitive to strip thickness transverse distribution′s variation, the iterative course is rather unstable and sometimes convergence cannot be achieved. In addition, the calculating speed of results coupling method is low, which restricts its usable range. To solve the problem, a new model coupling method is developed, which takes the force distribution between rolls, rolling force distribution and strip′s exit transverse displacement distribution as basic unknowns, and integrates strip plastic deformation model and rolls elastic deformation model as a unified linear equations through their internal relation, so the iterative calculation between the strip plastic deformation model and rolls elastic deformation model can be avoided. To prove the effectiveness of the model coupling method, two examples are calculated by results coupling method and model coupling method respectively. The results of front tension stress, back tension stress, strip′s exit gauge, the force between rolls and rolling force distribution calculated by model coupling method coincide very well with results coupling method. However the calculation course of model coupling method is more steady than results coupling method, and its calculating speed is about ten times as much as the maximal speed of results coupling method, which validates its practicability and reliability.     

PC带钢热连轧机力能参数研究之一——轧制力的计算

考虑了轧辊交叉对轧制力的影响，建立了ＰＣ热连轧机轧制力计算模型，利用能量变分法和秒流量相等原则计算出前后张力分布，并以其作为边界条件，将变形区离散后，用差分法计算出轧制力的纵横向分布，进而得出总轧制力值。计算结果与实测值吻合。     

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.     

Stream Surface Strip Element Method and Simulation of Three-Dimensional Deformation of Continuous Hot Rolled Strip

A new method, the stream surface strip element method, for simulating the three-dimensional deformation of plate and strip rolling process was proposed. The rolling deformation zone was divided into a number of stream surface (curved surface) strip elements along metal flow traces, and the stream surface strip elements were mapped into the corresponding plane strip elements for analysis and computation. The longitudinal distributions of the lateral displacement and the altitudinal displacement of metal were respectively constructed to be a quartic curve and a quadratic curve, of which the lateral distributions were expressed as the third-power spline function, and the altitudinal distributions were fitted in the quadratic curve. From the flow theory of plastic mechanics, the mathematical models of the three-dimensional deformations and stresses of the deformation zone were constructed. Compared with the streamline strip element method proposed hy the first author of this paper, the stream surface strip element method takes into account the uneven distributions of stresses and deformations along altitudinal direction, and realizes the precise three-dimensional analysis and computation. The simulation example of continuous hot rolled strip indicates that the method and the model accord with facts and provide a new reliable engineering-computation method for the three-dimensional mechanics simulation of plate and strip rolling process.     

Three-Dimensional Model for Strip Hot Rolling

Steel stripis widely usedin many fields such asautomobile ,building,transportation and householdappliance ,etc·. Withthei mprovement in productiv-ity and automation of strip processing,the require-ments for crown and flatness of strip have been in-creasingly severe ,and“crown free”steel strips arerequired for some special applications such as for au-tomobile parts andtinplate cans .In order toi mprovethe strip quality , an effective three-di mensionalmodel is needful to further study on the…