Simulation of ring rolling using a rigid-plastic finite element model

This paper describes details of a finite element model for analysing three-dimensional flow in the roll gap during radial ring rolling between plain cylindrical rolls. The model considers such factors as curvature of the workpiece, unequal roll diameters and the fact that the inner roll or mandrel is unpowered. The results of the analysis compare favourably with experimental observations. Fishtailing is predicted satisfactorily, also the form of the pressure distribution in the roll gap, which shows twin peaks under some rolling conditions. The method has the merits of easy handling and short calculation time. It should be a useful aid to the design of ring rolling and other asymmetric rolling processes.     

A 3-D finite element method analysis of cold rolling of thin strip with friction variation

In this paper, a three-dimensional rigid-plastic finite element method (FEM) model to simulate the cold rolling of thin strip with different friction models is described. The effects of rolling parameters, such as work roll diameters and reductions, are analysed in this study. The simulation and experimental values of rolling pressure and spread (the difference of strip width before and after rolling) show a good agreement when friction variation in the roll bite is considered. The roll separating force, spread and forward slip for constant friction and friction variation models are also compared. The friction variation in the roll bite has a significant effect on the simulation results.     

Simulation of plane-strain rolling by the rigid-plastic finite element method

The rigid-plastic finite element method for a slightly compressible material is applied to steady and non-steady state strip rolling. Solutions for some technical problems using a finite element analysis for rolling process are given. Stress and strain distributions in steady state plane-strain strip rolling under the condition of a constant coefficient of friction are calculated for work-hardening and non-hardening materials. The calculated distribution of roll pressure exhibits a peak at the entry which does not appear in the analysis by the slab method. Non-steady state deformation of the front and tail ends is also analysed. The calculated end shapes are in good agreement with the experimental ones for aluminium strip.     

An explicit time integration elastic-plastic finite element algorithm for analysis of high speed rolling

A finite element formulation effective in simulating high speed rolling is presented. This formulation accounts for inertia force and requires modest computer primary memory during solution. Unlike static finite element formulations, this algorithm does not require the assemblage, and inversion, of a global stiffness matrix. After spatial discretization and mass lumping, the governing equations are uncoupled. They can be solved node by node with explicit time integration. Sample plane strain simulations of high speed rolling are presented. The results demonstrate the effect of roll speed and material work-hardening on deformation mechanics. The simulation succeeded in quantifying front and rear end deformation of a billet, and the algorithm can be applied to reduce crop loss. The formulation also seems suitable for the analysis of other high speed metalforming processes.     

Investigation of interfacial behaviors between the strip and roll in hot strip rolling by finite element method

A finite element (FE)-based approach is presented for the precision analysis of the interfacial thermo-mechanical behavior of the roll and strip in the entire tandem mill during hot strip rolling. The validity of the proposed model is examined through the comparison with measurements. Then, the effect of various process parameters on the detailed aspects of interfacial thermo-mechanical behavior of the roll and strip is investigated via a series of process simulations.     

Synthetic lubricants in cold strip rolling

The embedded-pin technique is used to monitor the variation of the interfacial forces during cold rolling of aluminium slabs. The results confirm earlier conclusions, indicating that the frictional coefficient is a strong function of the process and material parameters. Coefficient of friction values deduced from forward slip measurements are close to the present data, confirming that in spite of several drawbacks of the experimental technique, it can yield very useful results. Lubricants are shown to reduce the loads on the rolling mills in a significant manner.     

Ribbed strip rolling by three-dimensional finite element method combining extremely thin array of elements

In this paper, a three-dimensional finite element modelling of the ribbed strip rolling is carried out, coupling the use of an extremely thin array of elements that is equivalent to the calculation of the additional shear deformation work rate occurred by the velocity discontinuity in the roll bite. The formulation of the finite element modelling by adding a rib inclined contact surface boundary condition is derived, and the performance of the proposed method is conducted. The simulated rib height, forward slip, and the pulling down of rib height have been compared with the measured values and are in good agreement. The equivalent strain rate of the rib was obtained in the simulation. The effect of the rib inclined angle on pulling down of rib height has also been discussed, which is helpful in optimizing the design of the rib inclined angle.     

Ribbed strip rolling by three-dimensional finite element method combining extremely thin array of elements

In this paper, a three-dimensional finite element modelling of the ribbed strip rolling is carried out, coupling the use of an extremely thin array of elements that is equivalent to the calculation of the additional shear deformation work rate occurred by the velocity discontinuity in the roll bite. The formulation of the finite element modelling by adding a rib inclined contact surface boundary condition is derived, and the performance of the proposed method is conducted. The simulated rib height, forward slip, and the pulling down of rib height have been compared with the measured values and are in good agreement. The equivalent strain rate of the rib was obtained in the simulation. The effect of the rib inclined angle on pulling down of rib height has also been discussed, which is helpful in optimizing the design of the rib inclined angle.     

Elastic-plastic finite-element modelling of cold rolling of strip

The rolling of copper strip has been simulated using an elastic-plastic finite-element method (EPFEM) for plane-strain deformation. The use of this program, which includes both material and geometric non-linearities, permits the identification of elastic and plastic deformation in rolling, and also the effects of unloading. The rolling model is based on the physically realistic concept that the strip is drawn into the roll gap by the action of interface friction.The results clearly show the maximum pressure associated with the neutral point and are in good quantitative agreement with earlier work. In addition, the stresses and deformation outside the nominal contact are presented.     

圆柱滚子轴承内圈冷辗扩过程有限元分析的方法

以圆柱滚子轴承内圈为研究对象,利用Abaqus／Explicit通用有限元程序来模拟冷辗扩过程。而进行有限元分析前处理的工作是运用冷辗扩理论来设计环件的毛坯尺寸及确定其工艺参数,建立符合实际加工有限元模型。     

Measurement of the forward slip in cold strip rolling using a high speed digital camera

The forward slip in strip rolling was defined as the relative difference between the roll surface speed and strip exit speed. It was always an important parameter because of its significant influence on friction and tension control. In this study a Phantom V3.0 digital high speed image acquisition and motion analysis system was used to record the movement of the roll and the workpiece during rolling. The pictures captured were analyzed to obtain the speeds of the roll and the workpiece along the roll bite, which then yielded the forward slip. The measurement accuracy has been validated by the mass conservation. The maximum relative error of the forward slip was only 1.6 %. The results have shown that the forward slip increased as the reduction increased for both dry and lubricated rolling. The roll speed did not change the forward slip in the case of dry rolling, but the forward slip was significantly reduced with roll speed when lubricated.     

高精度冷轧窄带钢轧机的技术发展

针对我国目前高精度冷轧窄带钢轧机研制和产品供求关系现状以及对冷轧窄带钢质量,品种新的需求,着重介绍了国内外冷轧带钢轧机设计选型,关键机械零件制造,板形控制等方面的新技术发展特点和设计要求,阐明了对新技术的应用原则和建议。     

Simulation of T-section profile ring rolling by the 3-D rigid-plastic finite element method

The three-dimensional rigid-plastic finite element method is used to simulate the open pass profile ring rolling of a T-shaped section from an initially rectangular cross-section. Because the ring rolling process is incremental and the deforming region is restricted to the vicinity of the roll gap, only a ring segment spanning the roll gap is analysed in order to save computation time. As the thickness of the ring is reduced, the mesh system is progressively modified to treat profile development more effectively. Roll separating force, strain distribution, strain rate distribution and cross-sectional configuration of the deformed ring are calculated. Comparisons between computation and experiment show good agreement in roll separating force and cross-sectional configuration of the deformed ring.     

Mathematical model for cold rolling and temper rolling process of thin steel strip

A mathematical model for cold rolling and temper rolling process of thin steel strip has been developed using the influence function method. By solving the equations describing roll gap phenomena in a unique procedure and considering more influence factors, the model offers significant improvements in accuracy, robustness and generality of the solution for the thin strip cold and temper rolling conditions. The relationship between the shape of the roll profile and the roll force is also discussed. Calculation results show that any change increasing the roll force may result in or enlarge the central flat region in the deformation zone. Applied to the temper rolling process, the model can well predict not only the rolling load but also the large forward slip. Therefore, the measured forward slip, together with the measured roll force, was used to calibrate the model. The model was installed in the setup computer of a temper rolling mill to make parallel setup calculations. The calculation results show good agreement with the measured data and the validity and precision of the model are proven.     

Effect of speed in cold strip rolling with Coulomb friction

The Bland and Ford theory of cold strip rolling, with Coulomb friction, is extended to cover the effect of speed of rolling. A good agreement between theoretical and experimental results is shown.     

A strip holding system for finite element simulation of Almen strip testing

We propose a strip holding system that can provide a clear boundary condition for a specimen (strip) during finite element simulation of Almen strip testing. The proposed strip holding system does not need a mounting block and bolts to grasp the strip before and during the test. Both ends of the strip are grabbed by two plane clamps to set a clear boundary condition for the strip during finite element simulation. We performed a series of Almen strip tests with a current strip holding system and the proposed strip holding system at different impingement velocities and exposure times. The lengthwise deflection shapes of the peened strip and saturation curves were measured and compared. The results revealed that the saturation curves obtained with the proposed strip holding system were about 6.2–19.6% larger on average than those obtained with the current strip holding system, but there was an error tendency between the two saturation curves. It denotes that the conventional strip holding system currently in use can be replaced with the proposed strip holding system if we capitalize on the error tendency.     

Stream surface strip element method for simulation of the three-dimensional deformations of plate and strip rolling

A new method—the stream surface strip element method (SSSEM)—for simulating the three-dimensional deformations of plate and strip rolling process is proposed. The rolling deformation zone is divided into a number of stream surface (curved surface) strip elements along metal flow traces, and the stream surface strip elements are mapped into the corresponding plane strip elements for analysis and computation. The longitudinal distributions of the lateral displacement and the altitudinal displacement of metal are constructed respectively to be a quartic curve and a quadratic curve, the transverse distributions of them are expressed as the third-power spline function, and the altitudinal distributions of them are fitted to be a quadratic curve. Based on the flow theory of plastic mechanics, the three-dimensional deformations and stresses of the deformation zone are analyzed and formulated. Compared with the streamline strip element method, the SSSEM considers the uneven distributions of stresses and deformations along altitudinal direction, and realizes an accurate three-dimensional analysis and computation. The simulation examples indicate that the method and the model of this paper are in accord with facts, and provide a new reliable engineering-computation method for the three-dimensional mechanics simulation of plate and strip rolling process.     

A practical method for finite element ring rolling simulation using the ALE flow formulation

Finite element ring rolling simulation by conventional Lagrangian codes carries an excessive computational cost. The main reason for this is the large number of incremental stages typically required to complete a full simulation. The nature of ring rolling however means that the amount of deformation taking place in a given increment is relatively small compared with typical metal forming processes. This paper describes measures that make the analysis of ring rolling a practicable proposition. The resulting model is based on a threefold approach, comprising the finite element flow formulation, an arbitrary Lagrangian Eulerian update strategy, and a novel iterative solution scheme called the successive preconditioned conjugate gradient method. The approach exploits the slowly evolving nature of the problem with the effect of reducing the time penalty for each deformation increment. In addition, a number of issues specific to ring rolling have been addressed including the problem of how the mandrel interface is dealt with for arbitrarily shaped rollers. The importance of addressing this particular issue is also illustrated. The method is validated by comparison with earlier experimental work and previously developed models for both pure radial, and radial–axial ring rolling.     

Mechanics of roll edge contact in cold rolling of thin strip

Simulation of cold rolling of thin strip due to roll edge contact with oil lubrication was performed successfully using a developed influence function method. Roll edge contact and related surface roughness was discussed in this paper. The calculated rolling force, intermediate force and work roll edge contact force increase significantly when the reduction increases. The strip profile becomes poor with a higher reduction, and the calculated rolling forces are consistent with the measured values. A modified edge shape of work roll determined from the roll edge contact length and roll edge flattening value is helpful to reduce the work roll edge wear and to extend the work roll life. Surface roughness and asperity of the rolled strip are characterized by surface profilometer and atomic force microscope. The research shows that the surface roughness reduces with a higher reduction or rolling speed. The effect of the strip width on surface roughness is not significant.