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 by 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.

Study on increasing calculation precision and convergence speed of streamline strip element method

The calculation precision and convergence speed of streamline strip element method are increased by (using) the method whose initial value of the exit lateral displacement is determined with strip element variation method, and the accurate tension lateral distribution model is adopted based on the original third power spline function streamline strip element method. The basic theory of the strip element method is developed. The calculated results by the improved streamline strip element method and the original streamline strip element method are compared with the measured results, showing that the calculated results of the improved method are in good agreement with the measured results.

Finite Element Analysis of the Influence of Artificial Cementation on the Strength Parameters and Bearing Capacity of Sandy Soil under a Strip Footing

Artificial cementation is a method commonly used to enhance and improve soil properties. This paper investigates the effect of using different amounts of cement on soil strength parameters and soil bearing capacity, using the finite element method. Experimental tests are conducted on soil samples with different amounts of Portland cement. A 2-D numerical model is created and validated using the numerical modelling software, COMSOL Multiphysics 5.6 software. The study finds that the cohesion, and the angle of the internal friction of the soil samples increase significantly as a result of adding 1%, 2%, and 4% of Portland cement. The results demonstrate that the stresses and strain under the strip footing proposed decrease by 3.24% and 7.42%. Moreover, the maximum displacement also decreases by 1.47% and 2.97%, as a result of adding cements of 2% and 4%. The bearing capacity values obtained are therefore excellent, especially when using the 2% and 4% cement. The increase identified is due to the increased values of the bearing capacity factors. It is concluded that from an economic viewpoint, using 2% cement is the best option.

Complete Mill Simulation of the Rolling Process of 1660 mm Hot Strip Continuous Mills

The three-dimensional plastic deformations of strip are analyzed using the stream surface strip element method, the elastic deformations of rolls are analyzed using the influence coefficient method, the analyzing and computing model of shape and crown of 4-high mill was established by combining them, and the rolling process of 1660 mm hot strip continuous mills was simulated. The simulated results tally well with the experimental results. The modei and the method for simulation of shape analysis and control of hot strip mills were provided.

表面变质层非等双轴残余应力的X射线/剥层测试与有限元矩阵修正

采用有限元模拟了剥层后渗碳+热处理+喷丸强化处理后18CrNiMo7-6合金钢表面变质层的残余应力,经试验验证后对其进行了有限元矩阵修正,研究了喷丸强化前后x和y方向残余应力分布,最后进行了有限元矩阵修正法的试验应用。结果表明:局部剥层后残余应力模拟值和测试值相对误差小于10%,证明模型准确;根据残余应力方向选择适用的修正矩阵后,平面非等双轴残余应力有限元矩阵修正值与初始值之间较接近;试验可得未喷丸试样表面变质层内存在近似等双轴残余应力,残余应力修正值与测试值相差不大,喷丸试样x和y方向残余应力间相差显著,表面变质层内存在非等双轴残余应力,残余应力修正值均小于测试值。

Re-reddening on Strip Surface After Water Cooling

After water cooling, there is a big temperature difference between the center and the surface of strip, which leads to the heat transfer from the center to the surface, and the surface temperature can rise in a short time. The finite element method was used to simulate the phenomena of re-reddening on the surface of strip and to analyze the temperature field of hot roiled strip during laminar cooling, and the periodical variation curve of the cooling rate was obtained during water cooling and subsequent re-reddening. The results show that the critical line of the cooling rate is at 1/3 of the half-thickness from the strip surface. The regression model of the relation of rereddening temperature, time, and distance from the surface was obtained in the re-reddening region. Re-reddening regularity on the surface of strip under the condition of different thickness and cooling rate was also studied.

Numerical Simulation of Temperature Field and Thermal Stress Field of Work Roll During Hot Strip Rolling

Based on the thermal conduction equations, the three-dimensional （3D） temperature field of a work roll was investigated using finite element method （FEM）. The variations in the surface temperature of the work roll during hot strip rolling were described, and the thermal stress field of the work roll was also analyzed. The results showed that the highest roll surface temperature is 593 ℃, and the difference between the minimum and maximum values of thermal stress of the work roll surface is 145.7 MPa. Furthermore, the results of this analysis indicate that temperature and thermal stress are useful parameters for the investigation of roll thermal fatigue and also for improving the quality of strip during rolling.

Comparison of methods for vibration analysis of electrostatic precipitators

The paper presents two methods for the formulation of free vibration analysis of collecting electrodes of precipitators.The first,called the hybrid finite element method, combines the finit element method used for calculations of spring deformations with the rigid finite element method used to reflect mass and geometrical features,which is called the hybrid finite element method.As a result,a model with a diagonal mass matrix is obtained.Due to a specific geometry of the electrodes,which are long plates of complicated shapes,the second method proposed is the strip method which is a semi-analytical method.The strip method allows us to formulate the equations of motion with a considerably smaller number of generalized coordinates.Results of numerical calculations obtained by both methods are compared with those obtained using commercial software like ANSYS and ABAQUS.Good compatibility of results is achieved.

Effect of roller shapes on strip buckling in a continuous annealing furnace

The effect of roller shapes on strip buckling in a continuous annealing furnace was focused on. The tensile stress distribution, the transverse compressive stress, and the critical buckling stress of the strip were studied by the finite element method （FEM） when the flat roller, crown roller, single taper roller, and double taper roller were used, respectively. Simulation results show that strip buckling is most likely to occur with the crown roller, then the double taper roller, and finally the single taper roller. Also, strip buckling can not occur when the flat roller is used. Considering strip snaking, the single taper roller and double taper roller are suggested in the continuous annealing fur-nace. The double taper roller with a better strip snaking-prevention ability should be applied in the sections with high strip temperature, and the single taper roller with a better buckling-prevention ability should be used in the sections with low strip temperature.

THREE DIMENSIONAL ELASTO-PLASTIC CONTACT BOUNDARY ELEMENT ANALYSIS FOR ROLLING WITH CONSIDERATION OF FRICTION

The boundary element method in framework is given to evaluate three dimensional frictional contact problems. Elasto plastic material behavior is taken into account by mean of an initial stress formulation and Von Mises yield criterion. The amount of tangential traction at contact surface is limited by Coulomb's friction law and constant shear rule. From some numerical results of a plate rolling problem, it is demonstrated here that the BEM can be used to efficiently and accurately analyze this class of forming problems.

Three-Di mensional Model for Strip Hot Rolling

A three-dimensional model for strip hot rolling was developed, in which the plastic deformation of strip, the thermal crown of rolls, roll deflection and flattening were calculated by rigid-plastic finite element method, finite difference method, influential function method and elastic finite element method respectively. The roll wear was taken into consideration. The model can provide detailed information such as rolling pressure distribution, contact pressure distribution between backup rolls and work rolls, deflection and flattening of work rolls, lateral distribution of strip thickness, and lateral distribution of front and back tensions. The finish rolling on a 1 450 mm hot strip mill was simulated.

板带热轧中间坯厚度分布规律研究

在热连轧生产过程中,受测量环境和测量手段的限制,尚未实现对中间坯厚度的实时在线精确测量,对产品最终的厚度精度和精轧区穿带过程稳定性造成影响。为解决此问题,采用轧制特性法分析中间坯厚度产生偏差的原因;为进一步研究各因素对厚度偏差影响的规律,通过影响系数法计算中间坯长度方向上温度和厚度分布,建立热力耦合有限元模型,并将有限元结果与计算结果进行比较。研究结果表明:随着轧制过程的进行,在轧制方向上,中间坯温度逐渐降低,头、尾温度的平均偏差约为22℃,头、尾最大温度偏差达到32℃;由于温度偏差导致中间坯厚度呈变大趋势,中间坯头尾厚度偏差为0.20 mm,长度方向最大厚度偏差达0.53 mm;本文得到的中间坯厚度和温度的分布能够为后续精轧过程提供前提条件,为高精度控制成品轧件的厚度以及维持穿带稳定性提供依据。

Powell's optimal identification of material constants of thin-walled box girders based on Fibonacci series search method

A dynamic Bayesian error function of material constants of the structure is developed for thin-walled curve box girders. Combined with the automatic search scheme with an optimal step length for the one-dimensional Fibonacci series, Powell＇s optimization theory is used to perform the stochastic identification of material constants of the thin-walled curve box. Then, the steps in the parameter identification are presented. Powell＇s identification procedure for material constants of the thin-walled curve box is compiled, in which the mechanical analysis of the thin-walled curve box is completed based on the finite curve strip element （FCSE） method. Some classical examples show that Powell＇s identification is numerically stable and convergent, indicating that the present method and the compiled procedure are correct and reliable. During the parameter iterative processes, Powell＇s theory is irrelevant with the calculation of the FCSE partial differentiation, which proves the high computation efficiency of the studied methods. The stochastic performances of the system parameters and responses axe simultaneously considered in the dynamic Bayesian error function. The one-dimensional optimization problem of the optimal step length is solved by adopting the Fibonacci series search method without the need of determining the region, in which the optimized step length lies.

Multi-scale Simulation on Bonding Mechanism of Solid-Liquid Cast-Rolling of Cu/Al Cladding Strip based on FEM and MD

To explore the complex thermal-mechanical-chemical behavior in the solid-liquid cast-roll bonding(SLCRB) of Cu/Al cladding strip, numerical simulations were conducted from both macro and micro scales. In macro-scale, with birth and death element method, a thermo-mechanical coupled finite element model(FEM) was set up to explore the temperature and contact pressure distribution at the Cu/Al bonding interface in the SLCRB process. Taking these macro-scale simulation results as boundary conditions, we simulated the atom diffusion law of the bonding interface by molecular dynamics(MD) in micro-scale. The results indicate that the temperature in Cu/Al bonding interface deceases from 700 to 320 ℃ from the entrance to the exit of caster, and the peak of contact pressure reaches up to 140 MPa. The interfacial diffusion thickness depends on temperature and rolling reduction, higher temperature results in larger thickness, and the rolling reduction below kiss point leads to significant elongation deformation of cladding strip which yields more newborn interface with fresh metal and make the diffusion layer thinner. The surface roughness of Cu strip was found to be benefit to atoms diffusion in the Cu/Al bonding interface. Meanwhile, combined with the SEM-EDS observation on the microstructure and composition in the bonding interface of the experimental samples acquired from the castrolling bite, it is revealed that the rolling reduction and severe elongation deformation in the solid-solid contact zone below kiss point guarantee the satisfactory metallurgical bonding with thin and smooth diffusion layer. The bonding mechanisms of reactive diffusion, mechanical interlocking and crack bonding are proved to coexist in the SLCRB process.

基于离散元法的柔性片烟建模及仿真参数标定

为确定片烟在离散元仿真模拟中的合理模型参数取值,更好地计算出片烟在松散润叶设备中的复杂运动,基于离散元软件(Rocky DEM),创建了与以往球形黏结刚性颗粒模型不同的柔性片烟壳体模型,并分析了柔性片烟壳体模型形变特点。以物理和仿真试验的堆积角为对比对象,选取“Hysteretic Linear Spring”法向接触模型、“Linear Spring Coulomb Limit”切向接触模型以及“Constant Adhesive Force”黏附力模型,对仿真接触参数进行标定。再通过对片烟本征参数测定、查阅文献及Rocky DEM说明手册,分析得到了片烟的离散元参数取值范围,设计Plackett-Burman、最陡爬坡以及Box-Behnken试验,确定了影响柔性片烟堆积角的显著性参数以及堆积角的拟合方程。以堆积角物理试验35.83°为目标值,得到显著性参数的最优解:片烟与片烟间静摩擦系数为0.67,片烟与片烟间滑动摩擦系数为0.31,片烟与片烟黏间黏附力系数为0.2,其余非显著性参数取平均值。仿真试验与物理试验相对误差为0.78%,从而验证了模型的准确性与真实性,可为工业生产进一步计算柔性片烟在松散润叶装置内的运动提供理论依据。

改进有限条法在平壳条振动特性研究中的应用

针对平壳条结构的振动特性问题,通过分析有限单元法的特点和应用,将改进的傅里叶级数法与有限单元法结合实现了任意边界条件的模拟,解决了平壳条结构对其梁函数边界条件的依赖性,从而提出一种高效、准确的半解析半数值方法—改进有限条法。根据Hamilton能量变分原理,推导出有限条元的刚度矩阵和质量矩阵并进行了平壳条结构自振特性分析。通过上机编程完成数值计算,并与商业有限元软件计算得到的结果进行对比分析,验证了该方法的有效性和准确性。进一步分析了截断级数、边界弹簧刚度系数、尺寸参数对系统频率的影响规律。

条形基础加载下软弱夹层边坡应变特征及其与稳定性的关系研究

为明晰不同形式荷载作用下软弱夹层边坡稳定性与应变的关系,基于Midas GTS NX软件,建立了条形基础荷载作用下边坡变形及稳定性分析模型,获得了加载过程中边坡不同高程处的变形分布规律,探讨了基于应变的边坡稳定性评价方法,分析了荷载宽度和位置对边坡稳定性的影响.结果表明:土体拉应变出现在荷载下部一定深度处,且随荷载增加而增加并往上部移动;最大水平拉应变与荷载呈指数型增长,其出现位置随测线高程的降低逐渐向右移动,与边坡潜在滑面位置一致,而最大水平位移位于滑面之上.荷载宽度对边坡极限承载能力影响小,边坡稳定性系数与最大水平应变符合对数函数关系;当荷载离坡面越远,边坡承载能力越大,失稳前会发生更大程度的应变,稳定性系数与应变的关系更符合指数函数关系.研究结果可为多土层边坡的稳定性评价提供理论指导.

基于有限条法的薄壁构件畸变屈曲分析

为验证有限条方法编写的Channelsteeltypic(简称CSTFSM)在计算冷弯薄壁卷边槽钢柱弹性临界畸变屈曲应力时的可靠性,文章选取76个不同截面形式的槽钢,分别采用有限元法和CSTFSM对其进行分析,比较两种方法计算的临界畸变屈曲应力与临界畸变屈曲半波长度。对比结果表明:CSTFSM计算的临界畸变屈曲应力与有限元方法计算的屈曲应力比较吻合,能够准确快速的计算各种截面形式的临界畸变屈曲应力和临界畸变屈曲半波长度,可以应用于冷弯薄壁型钢构件的弹性畸变屈曲分析。

混合光滑有限元法在岩土体变形及稳定性分析中的应用

在节点光滑有限元法(NS-FEM)中,位移、应力和应变等变量均存储于单元节点,有助于该方法的数值精度提升和便利实施。然而,在岩土体变形分析中,NS-FEM可能会导致非物理的变形。本文针对该问题,对NS-FEM引起岩土体非物理变形的原因进行研究,发现非物理变形由NS-FEM组装刚度的不均匀引起。为了避免或减轻组装刚度的不均匀问题,采用有限元法(FEM)和NS-FEM的组合方法,即混合光滑有限元法(HS-FEM),对岩土体变形和稳定性进行分析。分别对平面应变条件下柔性条形基础(不考虑土体自重)、带有圆形孔洞的线弹性介质和双层土质边坡问题进行分析,结果表明:结合推荐的α值,HS-FEM(α)在岩土体变形和稳定性分析中具有较好的应用效果和适用性。

HC轧机板形板凸度控制策略的研究

采用开发的基于条元法冷轧带材板形分析与控制仿真软件 ,分析了 90 0 m m HC轧机板形控制特性 ,确定出该轧机的板形板凸度控制策略。经工业应用表明 ,该控制策略应用于 HC轧机板形控制过程中 ,提高了轧后带材板形精度 。