Simulation of the state of stress in a strip in a deformation zone with two neutral sections during cold rolling

It is found that a deformation zone with two neutral sections can exist in a strip during cold rolling in certain working stands in continuous rolling mills. A second neutral section appears in the region of elastic recovery of part of the strip thickness at the end of the rolls. A reliable procedure has been developed to identify the type of deformation zone; it can determine the number of neutral sections in the deformation zone of each working stand in a rolling mill. A method for the calculation of the contact stresses, forward-creep coefficient, and rolling force in the deformation zone with two neutral sections is described. The application of this method decreases the error of force calculation for rolling mills.     

Effect of sliding and rolling friction on the energy-force parameters during hot rolling in four-high stands

A procedure for the calculation of the main-drive power for a hot-rolling wide-strip mill is developed. It takes into account that 85–99% of the lengths of the deformation zones in the working stands of such mills are occupied by stick zones, in which a strip undergoes static friction stresses (which do useful work only in the backward slip zone). This procedure also takes into account the rolling friction energy losses, which account for 83–93% of the power consumed for the rotation of idle backup rolls or 29–68% of the total energy consumed by the main mill drive. The average power calculation error for this procedure is 5%, and the maximum error is 10%, which is three to five times smaller than the errors of well-known calculation procedures. Our procedure has a high potential for revealing the reserves of decreasing the contact stresses in rolls and the saving of electric power via the redistribution of the reductions and tensions between stands and an increase in the temperature of the semi-finished rolled products.     

State of stress in the deformation zone during rolling of high-strength plate steel

A new mathematical model is developed for the state of stress in the deformation zone for plate rolling, including rolling under controlled conditions at a low temperature in the last passes. The stick zone during plate rolling is shown to account for 88–99% of the deformation zone, and the fraction of elastic regions in the deformation zone in the last passes at low temperatures can reach 12%. When the stick zone and elastic regions of the deformation zone are taken into account, the roll-force calculation error is less than 5–6.5%. The model developed can be used to optimize plate-rolling conditions, including the conditions of integrated deformation-thermal production.     

Procedure and algorithms for the energy-force calculation of cold rolling allowing for the number of neutral sections in the deformation zone

A procedure and algorithms are described for the calculation of the rolling power and the main-drive engine power and torque of a working stand in a cold-rolling mill with regard for the number of neutral sections in the deformation zone, including the case of two neutral sections in the deformation zone. This work is a continuation of our earlier work, where we were the first to consider a deformation zone with two neutral sections and proposed a procedure for the calculation of the contact stresses and rolling forces in it. Taking into account the second neutral section is shown to decrease the engine power calculation error by a factor of 4.5–6.5 (on average from 25 to 4%), which allows one not to use too high safety factors when choosing the power rating of the main drive in a cold-rolling mill.     

超高强钢冷轧过程轧制力计算的改进模型

 为了解决采用圆弧模型计算超高强钢冷轧过程轧制变形区轧辊压扁曲线误差较大的问题,充分考虑到超高强钢的轧制特点,通过分析不同压扁半径下轧辊压扁曲线的变化规律,构造出新型轧辊压扁曲线函数模型,给出了该函数中轧制变形区接触弧长特性参数与轧辊压扁曲线特性参数的求解方法。基于此,根据弹塑性理论中的变形与应力关系,推导了入口弹性变形区、塑性压下变形区以及出口弹性变形区单位轧制压力分布计算过程,建立了超高强钢冷轧过程总轧制力计算模型。并将其推广应用到某钢厂2030冷连轧机组,验证了该模型的计算准确度。结果表明,超高强钢冷轧过程轧辊压扁曲线用二次函数表示,更能准确反映轧辊压扁状态,其计算结果与实际值具有较高的吻合度。同时,为冷连轧机组生产超高强钢产品极限轧制能力的评估与轧制规程的制定提供了理论依据。     

Improvement of the technique of calculating the energy–force parameters of pinch-pass mills for increasing the efficiency of producing cold-rolled strips

New propositions are introduced into the technique of energy-force calculation of pinch-pass mills in order to determine the energy–force and technological parameters of skin rolling of cold-rolled steel strips at the minimum errors. The application of these propositions decreases the errors of calculating the forces and torques in a working stand by a factor of 3–5 as compared to the calculation according to the well-known technique, saves the electric power in the existing mills, and demonstrates the possibility of decreasing the dimensions of working stands and the power of the rolling mill engine.     

Applicability of the laws of elasticity for the determination of the elastic-region length in the deformation zone during cold rolling

The errors of calculating the energy-force parameters of cold rolling are analyzed. They appear because of the assumption of the classic rolling theory about the applicability of the Hertz formula, which is known in the theory of elasticity, to the calculation of the elastic-region length in the deformation zone. The Hertz formula, which is used to calculate the half-width of the contact area between a fixed cylinder and a plane that bounds an elastic half-space, is shown not to take into account the following factors that are characteristic and important for the roll-strip contact: the cold working of the strip, the strip thickness, the rotation of rolls accompanied by sliding friction, and the wear that decreases the initial roll roughness (i.e., changes in the friction coefficient). A method is proposed for taking into account these factors in the calculation of the energy-force parameters of cold rolling; it is based on the statistical processing of the parameters that are measured in operating mills and are present in the databases of their process control systems. The application of this method decreases the errors of calculating the rolling forces by 35–40% and refines some laws of the state of stress in a rolled strip.     

Simulation of rolling friction in the working stands of wide-strip mills

The energy consumed for rolling friction in the interroll contact area in the working stands of cold-rolling and pinch-pass mils intended for the production of wide steel strips has been analyzed. The coefficients and power of rolling friction are obtained for the first time using the databases of the process control systems of operating mills and simulating these quantities. A statistically reliable regression relation is obtained between the coefficient of rolling friction and the significant parameters of rolling and skin rolling (i.e., the interroll force, the roll speed, and the roll body roughness). The power fraction consumed for rolling friction is found to reach 60–80% of the total power of the main drive of working stands for skin rolling and 30–50% for cold rolling. Therefore, it is necessary to take into account these power losses in designing mills and developing technological cold-rolling conditions.     

Experimental and theoretical analysis of roll flattening in the deformation zone for ultra-thin strip rolling

For ultra-thin strip rolling, the conventional rolling force models are no longer applicable. To obtain accurate rolling force in the shape and gauge control process, Fleck proposed a new roll flattening model. In this study, experimental analysis, finite element simulation, and theoretical analysis were conducted to evaluate the Fleck model. The experiments and simulations show a clear neutral zone in the deformation zone with decreasing strip thickness. The finite element simulation results show that the proportion of the elastic unloading zone is small, when an elastic unloading phenomenon appears in the neutral zone. Thus, to simplify the rolling force model, the effect of an elastic zone could be ignored. Based on this finding, we develop a rolling force model with quick calculation speed, high precision, and convenient online application. Finally, the accuracy of the simplified model is verified by the measured rolling force.     

极薄带轧制变形区轧辊压扁试验与有限元模拟

 极薄带在轧制及平整过程中,工作辊的弹性压扁对轧制压力的分布有很大影响,传统的轧制力模型已经不再适用。为了在极薄带板形板厚控制过程中得到准确的轧制力,Fleck提出了新的轧辊压扁模型。针对Fleck模型进行试验研究,同时进行有限元模拟分析。试验过程中使用合金工具钢轧辊,轧制不同厚度的轧件,通过显微镜测量变形区各部位的厚度,得到变形区轧辊的近似轮廓形状。试验与有限元模拟结果表明,随着轧件厚度的减小,变形区出现了明显的中性区,但是很难出现Fleck模型中提到的弹性卸载区,因此计算极薄带轧制力时可以忽略中性区内的弹性卸载区以简化轧制力模型。     

薄带材轧制的最小可轧厚度理论及数值模拟

 智能制造、电子通信等行业向微型化、集成化方向发展要求不断提升精密轧制带材产品质量,提高厚度精度控制是其中关键组成部分,因此,精密带材轧制过程接触变形区理论研究有着极其重要的意义。以Stone轧制力模型为代表的传统薄带材冷轧理论假设轧辊在接触变形区内保持圆弧状轮廓,利用Hitchcock公式求解接触弧长进而求得平均单位压力,并在此基础上建立了Stone最小可轧厚度理论。在试验及实际生产中很多学者发现有时Stone轧制力计算值与实际值相差甚远,这是由于某些轧制工况下接触变形区内存在中性区,轧辊圆弧状假设不再适用。中性区的存在使轧制力剧烈增大而带材金属延伸变形增加甚微,即轧制难度增大、轧制效率降低。通过对不同厚度薄带材轧制过程进行有限元分析,得到了不同道次压下率下接触变形区轮廓与接触压力分布的变化规律,带材初始厚度越小或道次压下率越大,接触变形区内中性区所占比例越大,接触压力分布趋于椭圆形分布;基于Stone轧制力公式建立了考虑轧制效率的薄带材最小可轧厚度模型,对于一定初始厚度与Stone最小可轧厚度比值,根据轧制工艺参数可计算接触变形区内恰好不存在中性区时的临界道次压下率,以此临界道次压下率为依据可确定高效轧制厚度范围及Stone轧制力模型的适用条件,为精密薄带材轧制生产过程提供理论指导。     

极薄箔带轧制的适轧厚度理论及数值模拟

 微制造、微电子行业的小型化、轻量化和移动化的发展方向需要厚度更薄、尺寸精度更高的极薄和超薄金属箔材，极薄和超薄金属箔材制造技术越来越重要。极薄带轧制试验及生产实际中,Stone最小可轧厚度公式有较多不合理之处。通过有限元模拟得到不同厚度极薄箔带在不同压下率时的接触轮廓与轧制压力变化规律，为Stone最小可轧厚度赋予新含义，即表示在极小压下变形量条件下是否存在中性区的临界厚度值；建立了极薄箔带适轧厚度解析计算模型，即根据轧制力条件和箔带厚度可计算出其单道次能够获得的最大压下量，为已有轧机确定产品规格范围并制定轧制规程及为设计轧机时确定轧辊直径和力学参数提供理论指导。     

六辊CVC冷轧机凸度控制能力分析及应用

 基于三维有限元建立了六辊CVC辊系模型,该模型耦合了CVC辊形曲线、辊间轧制力分布以及带钢的弹塑性变形和辊系弹性变形,通过迭代计算辊间轧制力及轧辊与轧件的弹塑性变形。通过实际轧制规程数据对比验证了模型的有效性,其模拟计算结果与实际数据的绝对误差在10 μm内,相对误差小于1%。采用该模型研究了板形控制机构如中间辊弯辊、中间辊窜辊和工作辊弯辊对带钢2次凸度和4次凸度的控制规律,并成功消除了生产现场宽薄带钢的边中复合浪缺陷。     

Measurements of multiple normal pressure peaks in flat rolling

During normal pressure measurements in flat rolling, conducted in the roll gap of laboratory mills, unexpected multiple pressure peaks appeared. These multiple pressure peaks, such as a double peak, have not only been measured during rolling of billets, but also when rolling slabs or strips. Not explained by the established rolling theory stating just a single maximum point. In order to investigate its physical mechanisms a number of rolling experiments are presented. A model duo mill, load transducers, powder lubrication or by vaseline and wax as model material were used. The normal pressure, the shear stress and its angular movement were measured simultaneously. By first measuring a double normal pressure peak during rolling of a wax specimen and then by consciously making changes in draft, specimen thickness, rolling velocity, specimen width or the friction conditions, respectively, the double peak phenomena were investigated by means of the responding normal pressure distribution. A number of direct measurements in the roll gap by other researchers using different techniques, have also been investigated. The conclusion from the wax rolling experiments and the rewiew of measurements by others is that the peak at entry of contact is caused by the presence of compressive stresses from rigid zones outside the deformation zone, raising the hydrostatic pressure and the normal pressure. The effect is observed by inhomogeneous deformation. The peak value at the entry of contact can then be very high, by analogy to plane indentation with elastic regions present. The resistance of the wax material to the height deformation of the specimen was seen to increase at small reductions or by a specimen with a greater nominal thickness, supporting the “rigid end” theory. The result of this study is also that the exit peak in the double peak is caused by frictional surface stresses at the roll/specimen interface. The effect was seen by changes in frictional influencing factors, such as the reduction or the surface friction condition. Lateral spread of the material rolled was at the same time seen to make the double peak more distinct, decreasing the normal pressure in the “valley” between the two peaks and at exit of contact.     

1 800 mm CSP轧机板形调控特性分析

 为掌握1 800 mm CSP轧机的板形调控特性,以某1 800 mm CSP轧机为研究对象,建立了不同机架的有限元模型。利用有限元模型分析了不同带钢宽度下的弯辊力与窜辊对带钢板廓的影响,计算出上、中、下游机架的板形调控特性,得出当前中游机架板形调控能力最强,上游次之,下游最弱,并且板形控制能力随着带钢宽度的减小而减小。根据弯辊与窜辊在当前板形控制中所占比例,得出CVC窜辊是当前凸度控制的主要手段。对现场实际窜辊数据进行分析,得出上游机架凸度控制能力不足,中游机架凸度控制能力偏大,同时,通过对不同宽度带钢窜辊数据的分析得出轧制窄带钢时更易出现凸度控制能力不足的情况。现场数据与有限元仿真结果相互验证,研究结论可以为现场的辊形改进提供较好的理论分析基础。     

Simulation of the energy-force parameters of pinch-pass mills

A procedure is proposed for the calculation of the energy-force parameters of pinch-pass mills; it does not use the hypothesis of constant instantaneous volumes, which is employed in the computation of most plastic-deformation processes. Elastic regions occupy the major portion of the deformation zone of a strip subjected to skin rolling; therefore, a static friction model is taken as a model for contact friction during skin rolling. The strip speed is assumed to be equal to the peripheral roll velocity. The reliability of the new procedure is supported by the comparison of the calculated and actual skin-rolling forces and powers performed on a working mill. The possibility of a significant decrease in the specific quantity of metal per work stand and in the pinch-pass-mill engine power is grounded.     

一个精确计算压扁接触弧长模型及其在冷连轧机上的应用

以弹性接触理论为基础,利用Hertz基本公式,同时考虑轧辊的弱性压扁变形和轧件的弹性回复变形,推导出一个精确计算压扁接触弧长的模型。与多个有代表性的模型之间进行了对比分析,模型与实际情况更加相符。利用本模型建立的轧制压力模型计算精度优于原轧制力模型。     

A 3-D Differential Method for Solving Rolling Force of PC Hot Strip Mill

 According to the character of the deformation zone on pair cross rolls, which is different from the regular 4-high mill, there are longitudinal and transverse two-way shear deformation in the deformation zone, the character of metal particles flowing velocity is more complicated than normal rolling. Comprehensive influences of normal stress and shear stress in rolling direction, width direction and thickness direction are considered. Establish the rolling force calculation model of PC hot strip mills. After the longitudinal and transverse discretization of deformation zone, the longitudinal and transverse distribution of rolling force is worked out by the differential method, then calculate total rolling force. Calculated results are verified by experimental data.     

Study of rolling friction in a four-high working stand using a full-scale roll-assembly model

The rolling-friction coefficient has been studied in the interroll contact of a four-high stand using a full-scale roll-assembly model. The ranges of the contact stresses, the ratio of the backup to the work-roll-body diameter, the rate of roll rotation, and the roll roughness correspond to those in real wide-strip cold-rolling and pinch-pass mills. The ranges of the reliable rolling-friction coefficients have been established. The results obtained support the importance of the energy consumed for rolling friction, which accounts for 50–80% of the total energy consumed for cold rolling and skin rolling, and the reliability of the rolling-friction coefficients determined for real mills.     

Nonlinear Finite Element Analysis of Thin Strip Temper Rolling Process

 To reveal the basic deformation mechanisms under the conditions of high friction, small reduction, and long contact length in thin strip temper rolling process, an elastoplastic finite element analysis of plane strain upsetting was made based on the FEM software Marc. The results indicated that a near flat ‘zero reduction’ region was present in the center of the contact arc. The simulation results about the effect of rolling parameters on the central flat region showed that any change of increasing the rolling force could result in or enlarge the central flat region in the deformation zone. Stress distribution results illustrated that the metal was in triaxial compression state. Although the maximum and minimum principal stresses were all much larger than the yield stress of the strip, the equivalent stress became lower than that, and no further plastic strain, even a small elastic spring back occurred in the central flat region. That was the problem of ‘hydrostatic pressure’ in thin strip temper rolling.