Numerical simulation of roll forming for channel section with outer edge

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HC轧机辊间接触与辊系变形的Taylor级数多极边界元数学规划解析

分析HC轧机辊间接触分布和辊系弹性变形对于改善辊间压力分布状态,减少轧故褂檬倜案纳瓢逍畏浅Ｖ匾?醯捎诩扑懔亢艽?使用传统数值方法(有限元法或边界元法)分析辊间接触和辊系变形是非常困难的.本文描述了一种基于点-面接触模型的三维弹性接触Taylor级数多极边界元法,给出了数学规划解析方法,适合大规模弹性接触问题的求解....     

Parametric study of macrosegregation in the horizontal strip casting process for different cooling rates and different casting speeds

The objective of this paper is to investigate sensitivity of the macrosegregation profiles in steel strips produced by the horizontal strip casting process to the major technological parameters controlling this process, such as the cooling rate and the casting speed. To perform this investigation, a mathematical model which accounts for fluid flow as well as for heat and solute transport is suggested. Extensive numerical simulations of the horizontal strip casting process for different cooling rates and different casting speeds are carried out. Received on 17 September 1998     

应变硬化薄板夹持型滚弯成形过程分析

现存文献对薄板的连续滚弯成形过程的数学模拟多限于讨论三辊轮解锥型弯板过程,且基于较多的假定和板的小变形情况。而开发有更多的功能和更高的生产效率的四辊轮连续弯板机需研究夹持型滚弯成形过程。本文将「１」的工作,理想塑性材料平面应变薄板的夹持型连续滚弯成形过程的弹塑性大变形弯曲的力学分析,推广至一般应变硬化材料的情形。得出了控制微分方程的解析解。采用固支边界条件模拟刚度很大的平持系统对板的夹持。通过对线     

矩形倾斜腔体中的两种对流斑图和分区

为了研究矩形倾斜腔体中普朗特数Pr=0.72的流体对流斑图和分区,本文基于流体力学方程组进行了数值模拟。在相对瑞利数r=6.0的情况下,观察了倾角θ=10°和θ=60°时对流斑图随着时间的发展,发现系统存在单圈型对流和多圈型对流两种斑图。流线随着倾角的变化说明:随着倾角增加,对流圈数逐渐减少,对流波长逐渐增加,对流波数减小;然后,随着对流圈数显著地减少,系统由多圈型对流过渡到单圈型对流。根据模拟计算结果,给出了多圈型对流过渡到单圈型对流的临界倾角θc随着相对瑞利数r变化的关系曲线。对流在θ-r平面上分为两个区域:θ<θc时系统是单圈型对流,θ>θc时系统是多圈型对流。对流最大振幅A和努塞尔数Nu随着倾角θ的变化曲线被临界倾角θc分成两段,它们有不同的变化规律。因此,临界倾角也可以由对流最大振幅A或努塞尔数Nu的变化曲线来确定。     

四辊轧机辊系变形分析的有限元方法

采用有限元方法求解四辊轧机辊系变形问题,由于在工作辊及支承辊之间存在着未知接触压力和位移因而该问题无法用简单方法求解;根据辊系变形与受力的特殊性对方程进行变换可解出辊系各点位移,从而实现对辊系变形及辊缝形状进行较为准确的预报及控制。     

A numerical and experimental investigation into residual stress in thermally sprayed coatings

This paper is concerned with an investigation into the thermal spray process and is particularly concerned with the residual stresses that arise when a steel-alloy coating is sprayed onto a copper-alloy substrate. This material combination was used recently to enhance the thermal and mechanical efficiency of the pressure die casting process. A difficulty with the spraying of steel on copper is the attainment of appreciable thickness of the coating due to debonding during the thermal spraying process. Prominent among possible causes of debonding is residual stress, which is the focus of the research presented in the paper. An investigation into the thermal spray process is performed using experimentation, simplified numerical modelling and finite element modelling. The development of residual stress for a range of process parameters, i.e. deposited layer thickness, interval of layer deposition and the number of layers in a coating (i.e. block deposition versus multilayer deposition for a desired coating thickness) is recorded. The results from the three investigation methods agreeably indicate a progressive change in average interfacial residual stress from compressive towards tensile with increase in thickness of deposited layer; and a tensile interfacial stress in a two-layer coating, which increases with increase in interval of deposition between the two layers. On the whole, the observations from the results suggest an increase in potential for coating debonding with increase in both deposited layer thickness and layer deposition interval. The results further suggest higher potential for coating debonding with block deposition compared to multilayer deposition for a desired coating thickness.     

Observation of the transient behaviour of Taylor vortex flow between rotating concentric cylinders after sudden start

Transient behaviour of Taylor vortex flow between rotating concentric cylinders after sudden start has been observed by measuring axial velocity distributions V _z (z) for Reynolds number between 70–1,300. We found that a somewhat noisy roll structure is established at an early time after the start. Azimuthal partial rolls can exist and fusions of rolls occur. These phenomena dissipate, and while definite sizes and locations of the rolls are adjusted, the system approaches the ordered structure steady state. The time needed for this transient process is in the order of (or shorter than) the diffusion time.     

Non-steady-state elastic–plastic behavior of metal forming (rolling) with a generalized friction law

An analytical and generalized friction law is formulated and a three-dimensional large-strain non-steady-state elastic–plastic finite element analysis has been performed for rolling process. The contact/friction problem at the interface between the workpiece and the rolls is treated rigorously by using this new friction law. The numerical results, including the evolutions of roll torque and roll forces, and the interfacial normal and shear stresses, are presented and discussed.     

激光毛化轧辊技术的特色与进展

轧辊激光毛化技术的用途是什么? 什么样的轧辊需要毛化处理? 激光毛化轧辊技术 的优势是什么? 还存在什么不足? 激光毛化处理为什么能够延长轧辊的寿命? 激光毛化轧辊 改善了所轧钢板的哪些性能? 其机制是什么? 针对轧辊激光毛化技术的这几个基本问题 进行了讨论和释疑, 并指出了下一步的改进方向.     

Hydraulic analysis of free-surface flows with solidification

Summary The paper is concerned with a one-dimensional analysis of plane open-channel flow with continuous solidification. The process is of relevance for recent developments in the casting of steel and other metals. The bottom of the channel consists of a rotating casting roll and a horizontal cooling table, where the solidified material is withdrawn with given velocity. The study is restricted to the region downstream of the top of the casting roll. Surface tension is neglected. In the main part of the analysis inviscid fluid flow is considered since the Reynolds number is very large in the applications. It is found that the steady-state solutions are nonunique in a certain parameter range. In addition to a continuous solution, there are two solutions including hydraulic jumps, with one hydraulic jump being located on the casting roll, the other one on the cooling table. Regarding the stability of the non unique solutions, the evolution of disturbances is investigated numerically as an initial-value problem. It is concluded that the hydraulic jump on the cooling table is unstable, while the other discontinuous solution as well as the continuous solution are stable for sufficiently small disturbances. Which stable solution is attained in the steady state, depends on the history of the process. Friction at the liquid/solid interface is taken into account in the last part of the analysis. A constant friction coefficient is assumed. It is found that the history of the process determines the steady-state solution if, and only if, the friction coefficient is sufficiently small. For larger values of the friction coefficient, the steady-state solution is unique and independent of the history of the transient process. Furthermore, for sufficiently large friction coefficients, stable hydraulic jumps are found, in contrast to the inviscid case, also on the cooling table. Received 19 March 1999; accepted for publication 3 May 1999     

Stress intensity factors for cracks in grooved rolls used for hot-rolling

A procedure is described for the calculation of stress intensity factors for surface cracks in a section roll. Results are given in terms of the load acting on the roll and the average pressure acting on the roll/workpiece interface. It is noted that the load acting on the roll can be determined for individual cases by experimentally measuring the deformation of the roll stands: this obviates the necessity of relying on theoretical estimates of the roll/workpiece pressure. The stresses in the uncracked roll are determined using an axisymmetric finite element model. However, for the subsequent calculation of stress intensity factors the analysis is reduced to a plane strain model. It is shown that it may not be necessary to carry out finite element stress analyses on cracked rolls to determine stress intensity factors.     

Spray and jet cooling in steel rolling

Prediction and control of roll and strip cooling are necessary in modern steel mills because they not only affect the process efficiency but also strongly influence the quality of rolled products. In this article, relationships among metallurgy, heat transfer, and control of the cooling system in steel rolling are first discussed. Heat transfer characteristics associated with the water spray and jet cooling used in rolling processes are then studied. The effects of important convective heat transfer parameters on cooling perormance for both stationary and moving surfaces are examined. Results indicate that local heat fluxes up to 20 × 10⁶ W/m² are observed in the nucleate boiling regime. The present results are compared with typical boiling heat transfer studies in terms of heat fluxes, heat transfer coefficients, spray rate, and cooling efficiency. The effect of surface motion is found to increase the cooling efficiency of roll and strip cooling. Finally, implementation of the present finding in roll and strip cooling to thermomechanical processing in steel rolling is proposed.     

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在重轨万能轧制过程中,首先建立了简化的三维理论模型. 然后分别给出了轨腰、轨头及轨 底的运动学许可速度场以及相应的应变速度场和剪应变速度强度,并求出了相应变形区的塑 性变形功率、速度间断面上消耗的功率以及由于摩擦产生的摩擦功率. 最后根据上限原理分 别求解了水平辊和两个立辊的轧制力上限解. 通过比较可知,二辊轧制理论公式误差很大因 此不能用于万能轧制过程,而上限法求得的轧制力近似解大于轧制现场数据但最大误差不超 过13\%, 因此根据上限原理进行轧制工艺参数设定及优化是比较可靠的.     

Mathematical model for cold rolling based on energy method

There is an increasing requirement for improved accuracy of the rolling models which are widely used in rolling plant in order to produce high-quality products, because this accuracy is important for rolling schedule setup and automatic control. A three-dimensional mathematical model for cold rolling using tangential velocity field and energy method is firstly proposed to investigate the deformation of the strip at the roll gap based on elastic and plastic mechanics. The field and geometrical approximation yield criterion are used to integrate the internal plastic deformation power. The friction power is analyzed using the co-line vector inner product method. Finally, the analytical expressions of roll separating force and roll torque are obtained quickly considering the effect of roll flattening on the roll separating force. The predicted roll separating forces are consistent with other researchers’ models, especially for on-line measured roll separating forces in a tandem cold rolling plant. The accurate predicted results provide valuable guidelines for optimization of rolling process.     

Interface crack problem in layered orthotropic materials under thermo-mechanical loading

In the present paper, the behavior of an interface crack for a homogeneous orthotropic strip sandwiched between two different functionally graded orthotropic materials subjected to thermal and mechanical loading is considered. It is assumed that interface crack is partly insulated, and the temperature drop across the crack surfaces is the result of the thermal resistance due to the heat conduction through the crack region. The elastic properties of the material are assumed to vary continuously along the thickness direction. The principal directions of orthotropy are parallel and perpendicular to the crack orientation. The complicated mixed boundary problems of equations of heat conduction and elasticity are converted analytically into singular integral equations, which are solved numerically. The main objective of the paper is to study the effects of material nonhomogeneity parameters and the dimensionless thermal resistance on the thermal stress intensity factors for the purpose of gaining better understanding of the thermal behavior of graded layer.     

Experimental investigation of helicoidal rolls in an advective flow over a hot horizontal surface

A digital tracer technique is applied to reconstruct the velocity fields in a convective flow developing in a rectangular cavity filled with a layer of fluid and having a bottom consisting of two heat exchangers kept at different temperatures. The upper boundary of the fluid is free. The structure of the secondary flows in the form of streamwise helicoidal rolls generated in the boundary layer over a hot plate is studied. It is shown that the centers of roll rotation coincide with temperature minima in the boundary layer, while the roll shape and dimensions vary with the distance from the temperature jump. With increase in the temperature difference the roll dimensions decrease but the velocity of their rotation increases.     

Rayleigh–Bénard convection driven by a long wavelength heating

Natural convection in a two-dimensional horizontal layer has been investigated. The layer is confined between two parallel horizontal plates. The upper plate is kept isothermal, while the lower plate has an externally imposed, long wavelength, spatially sinusoidal heating with the amplitude expressed in terms of the Rayleigh number Ra and the wavelength characterized by the wave number α. Only steady-state flow structures and their bifurcations have been considered. The detailed analysis has been carried out for two Prandtl numbers, i.e. Pr = 0.7 and Pr = 7, and only small differences in the bifurcation diagrams have been observed. When Ra < Ra _cr = 427, convection has a simple topology consisting of one pair of counter-rotating rolls per heating period. Secondary motion in the form of rolls aligned in the direction of the primary rolls and concentrated around the hot spots occurs for Ra > 427. When 427 < Ra < ～470 and α < ～0.14, the secondary motion is described by the supercritical pitchfork bifurcation. One of the branches of this bifurcation is associated with an odd number of secondary rolls per half wavelength, with rolls above the hot spots rotating in the direction opposite to the primary rolls. The other branch is associated with an even number of secondary rolls per half wavelength, with the rolls above the hot spots co-rotating with the primary rolls. The new rolls are pinched off in pairs when α decreases. When Ra > ～470 and α > ~0.14, bifurcation assumes the form of “bifurcation from infinity”. The main branch is associated with one pair of rolls per heating period for α > 0.25. Decrease in α along this branch results in the formation of secondary rolls, with the rolls at the hot spot co-rotating with the primary rolls. The lower part of the other branch is associated with one pair of rolls per heating period in the limit α → 0. Increase in α results in pinching off a single roll which counter-rotates with respect to the primary roll at the hot spot.     

应用三维光弹性分析轧辊的接触应力

对有限长，外载荷又集中作用的轧辊，当其母线接触压靠性，接触面上的应力分布是不均匀的。于是，根据弹性力学理论推导的无限长辊子相互压靠的接触应力“赫芝”解法无法得到充分应用。由于这个原因。该文提出了一个辊子接触应力非均匀分布模型假设，它是在横向满足半椭圆分布，而纵向为未可知的曲线分布，根据这个假设应用三维光弹性的应力切片法及有限元数值计算概念。导出了这类辊子接触应力的混合计算方法。作为一个应用实例，该文讨论了宝钢1420双平整轧机轧辊的接触问题，该轧机有六个辊子组成，上下三三对称，其中最外层为支承辊，中间是中间辊，下层是工作辊，工作辊与轧件接触，钢厂在板形控制研究中，十分需了解各辊子之间的接触应力，应用该文分析方法。可以得到接触面上理想的三向接触应力值。为厂方的板形控制工艺改进提供了极有用的参数。     

轧制过程的显式动力学有限元模拟

采用显式动力学弹塑性有限元方法对平板轧制问题进行了模拟计算,得出咬入,稳定轧制和抛钢阶段整个轧制过程的应力应变场。通过将板宽对称中心线轧制压力分布的计算结果与实验值进行对比,表明计算结果准确。