Asymmetrical rolling analysis of bonded two-layer sheets and evaluation of outgoing curvature

A theoretical model based on slab method is proposed to analyze asymmetrical rolling of bonded two-layer sheets where the ingoing sheet is forced to horizontally enter the roll gap. Separate equilibrium equations as well as yield relations are derived for each layer by considering different stress fields for the two layers of any slab within the roll gap. A large angle of bite is considered in the governing equations as the experimental data used for verifying the results belong to the rolling conditions where small bite angle assumption is not reasonable. The curvature of the sheet at exit from the roll gap is estimated by studying variations of the normal and the shear strains within the whole roll gap. A very good agreement is shown to exist between the rolling force as well as the outgoing curvature predicted by the present model and the available analytical and experimental results reported by other investigators. By studying the outgoing curvature at different conditions, some practical suggestions to minimize the strip curvature at exit from the roll gap are proposed.     

Analysis of asymmetrical clad sheet rolling by stream function method

A mathematical model for asymmetrical clad sheet rolling is proposed by using the stream function method and the upper bound theorem to investigate the plastic deformation behaviour of sheets at the roll-gap. The curvature and thickness ratio of the rolled product and rolling power, effected by various rolling conditions such as roll speed ratio, roll radius ratio, initial thickness ratio and flow stress ratio of sheets, total thickness reduction, etc., are systematically discussed. Furthermore, experiments on asymmetrical clad sheet rolling are also conducted by employing aluminum, copper, and mild steel as layers of clad sheets. It is found that the theoretical predictions of the thickness ratio of the rolled products, rolling force, and rolling power are in good agreement with the experimental measurements. Through the study, it becomes clear that the proposed analytical method is applicable to simulate the asymmetrical clad sheet rolling processes and is able to offer useful knowledge in manufacturing clad sheets.     

Analytical and experimental study on asymmetrical sheet rolling

An analytical model assuming constant shear friction between the rolls and sheet is proposed to explore the characteristics of asymmetrical cold and hot sheet rolling. In the hot sheet rolling process, the surface friction stress is assumed to be equal to the yield shear strength (i.e. τ = k). As the friction factor m is less than 1, the simulation for the cold rolling process can be conducted. To verify the validity of the proposed analytical model, a series of experiments on asymmetrical cold sheet rolling of aluminium are carried out. The total rolling force and the forward slip are measured. The proposed model is also used to estimate friction factor (m) with the measured forward slip. With the estimated friction factors, the analytical rolling forces are calculated to compare with experimental data. Reasonable agreement is found. By this proposed analytical model, it is noted that a large amount of calculation time and computer expense are saved, and the characteristics of asymmetrical cold and hot sheet rolling are obtained easily and rapidly.     

Three dimensional thermal mechanical coupled simulation during hot rolling of aluminium alloy 3003

Rolling passes of a pass schedule supplied by an aluminium company and containing reliable measured data of roll load and torque is considered. Percentage reductions range from 6% to 20% and are analysed by a commercial thermo-mechanical coupled FEM program FORGE3 V5.3. An inverse analysis method is adopted to match the calculated rolling force and torque with the measured rolling force and torque by treating the friction law and the friction coefficient as free parameters. Three widely accepted friction laws are investigated; Tresca friction, Coulomb friction and viscoplastic friction. The use of viscoplastic friction is shown to yield both more reliable and more accurate results than other models. Significantly the friction coefficient can be traced to remain constant throughout the pass schedule of the breakdown rolling. The contact pressure distribution is then studied with different thickness reductions and compared with published experimental results. The predicted and experimental agreement is such that the load calculation can be regarded as satisfactory. Acceptable agreement is also obtained with the measured torque values. The distribution of equivalent strain, temperature and the stress in the roll gap and the lateral profile are discussed.     

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.     

An upper bound method for analysis of three-dimensional deformation in the flat rolling of bars

A new upper bound method for the analysis of three-dimensional deformation in the flat rolling of bars is proposed. In the conventional upper bound method, stress distribution is not calculated. Hence, a new method of calculating stress distribution is proposed in which the hydrostatic stress in each element and the contact stress on the contact surface between material and roll in each element are calculated. In the conventional upper bound method, the structure of the computer program also depends highly on the kinematically admissible velocity fields assumed. Hence, a new method of analysis in which the structure of the computer program depends minimally on the kinematically admissible velocity fields assumed is proposed. In the analysis of strip rolling, the calculated roll force and roll torque agree with the roll force and roll torque calculated from Sims’ slab method. In the analysis of the flat rolling of bars, the calculated width spread agrees with the width spread obtained by experiments reported in the literature. The effects of a reduction in thickness, roll radius, material width-to-height ratio, front tension, back tension, and front and back tensions on the width spread, forward slip, roll force and roll torque are demonstrated. Hence, the validity of the new upper bound method is confirmed.     

Analysis of plate rolling using the dual-stream function method and cylindrical coordinates

A mathematical model for plate rolling using the dual-stream function method and cylindrical coordinates has been proposed in this work to examine the plastic-deformation behavior of the plate at the roll gap. The velocity fields derived from this newly developed dual-stream function can automatically satisfy the volume constancy and the velocity boundary conditions within the roll gap. In the formulation, an inclined rigid-plastic boundary plane at the entrance of the roll gap is considered. Although this effect can be easily included in a finite element method, the demanding amount of memory and the computer time by an FEM approach makes it impractical as a personal computer routine. By this model, effects of various forming parameters such as the roll diameter, thickness of the plate, the friction factor, the aspect ratio of the plate, etc., upon the width spread of the product and the rolling power were discussed systematically. Furthermore, experiments on plate rolling using aluminum sheets were carried out. From the comparison between the analytical and experimental results, it is clear that this model can offer useful knowledge in designing the pass-schedule of plate rolling process.     

Asymmetrical sheet rolling analysis and evaluation of developed curvature

A theoretical method based on slab method of analysis is presented to give an account to the developed curvature in asymmetrical sheet rolling where the work rolls radii, their speeds, and the interfacial frictions may be different. In this model the ingoing sheet is considered to be guided to enter the roll gap horizontally and the work rolls may have different pressure distributions. The nonuniformity of normal and shear stresses acting along the vertical sides of each slab are taken into account, and the equilibrium equations together with the yield relations are considered as the governing equations. The strip curvature at exit is calculated based on the differences in shear as well as normal strains within the upper and lower portions of the slab. Results are compared with analytical and experimental findings of previous investigators and are shown to be in good agreement.     

SENSITIVITY ANALYSIS FOR ROLLING PROCESS BASED ON SUPPORT VECTOR MACHINE

A method for the calculation of the sensitivity factors of the rolling process has been obtained by differentiating the roll force model based on support vector machine. It can eliminate the algebraic loop of the analytical model of the rolling process. The simulations in the first stand of five stand cold tandem rolling mill indicate that the calculation for sensitivities by this proposed method can obtain a good accuracy, and an appropriate adjustment on the control variables determined directly by the sensitivity has an excellent compensation accuracy. Moreover, the roll gap has larger effect on the exit thickness than both front tension and back tension, and it is more efficient to select the roll gap as the control variable of the thickness control system in the first stand.     

液压缸非线性约束下的轧机辊系振动行为

以四辊板带轧机为例,分析液压压下缸及弯辊缸在轧机辊系振动时表现出的分段弹性力和摩擦力两种非线性约束,建立液压缸非线性约束作用下的轧机辊系振动模型,并采用平均法求得振动系统的幅频响应。通过比较两种非线性作用下辊系振动速度和振动幅值的仿真曲线,研究辊系受分段弹性力和摩擦力影响时的行为特性。取不同分段弹性力和摩擦力,仿真分析两种非线性因素分别对轧机辊系幅频特性的影响规律。结果表明,轧机辊系振动速度受分段弹性力大小影响,系统不稳定频率区域随分段弹性力增大而变宽;摩擦力较小时,对辊系振动行为影响表现为阻尼特性,较大时,摩擦力的非线性成为影响辊系振动行为的主要特性。该结论为轧机辊系振动控制提供了理论参考。     

An analytical model to investigate skidding in rolling element bearings during acceleration

Skidding, which occurs in rolling element bearings during shaft rotational acceleration, causes wear and incipient failure. This paper presents an analytical model to investigate skidding during rolling element bearing acceleration, taking account of the contact force and friction force between the rolling elements and the races and the cage, gravity, and the centrifugal force of the rolling elements. The Hertzian contact theory is applied to calculate the non-linear contact force. The Coulomb friction law is used to calculate the friction force. All forces above are included in force equilibrium equations to derive the non-linear governing equations of the bearing during acceleration, and are solved using a fourth-order Runge-Kutta algorithm with fixed time step. The proposed model is verified by comparison to other published results and with experimental results. The proposed model can be used to investigate skidding in rolling element bearings during acceleration and the transient motion behavior of rolling elements, and it will lay the theoretical foundations for eliminating skidding in rolling element bearings.     

基于CFD方法的冷轧过程乳化液特性研究

应用CFD工具FLUENT建立冷轧过程乳化液内部压强及轧板所受压力求解分析模型,计算分析冷轧过程乳化液进口速度对乳化液内部压强及轧板所受压力的影响。模拟结果表明,乳化液内部压强随着乳化液进口速度的加大而增加,轧板所受压力也随之增加。通过对比生产现场的轧制力数据,得到乳化液的最优进口速度。通过分析不同油水混合比例乳化液的离水展着性,得到最优的油水混合比例,使得冷轧润滑效果最好,进而实现最优的板面质量。     

附加轴向力对离心风机自由端滚动轴承温升的影响

摩擦力矩的大小决定了轴承的功率消耗和发热量的大小,发热量的大小直接影响轴承的温升,严重时直接导致轴承的失效。结合算例对SKF推出的滚动轴承摩擦力矩的计算模型及其影响因素进行了分析,重点探讨了附加轴向力对离心风机自由端轴承摩擦力矩的影响。在离心风机自由端滚动轴承设计选型中,通常不考虑轴向力的影响,但结果表明,附加轴向力对自由端轴承摩擦力矩影响显著。本文为离心风机自由端滚动轴承设计选型提供工程实用价值。     

Analysis of the roll hunting force due to hardness in a hot rolling process

A hot rolling operation is performed to alter the thickness of a metal by passing the material through a pair of rollers, forming a gap that is somewhat narrower than the thickness of the material. Therefore, the quality of the product is a function of the pressure applied by the rollers. However, in this process, a roll hunting force occurs in which the rolling force is irregularly changed during the rotation of the rollers due to various complex mechanisms, which include roll surface hardness, difference in rotational speed between rolls, heat treatment conditions, and roll wear. In this study, roll wear tests were conducted to analyze the roll hunting force caused by variation in the hardness of the work roll. The friction coefficient of the work roll was then examined based on hardness. Then, a two-dimensional finite element model was constructed to investigate the roll hunting force as a function of the change in friction coefficient of the work roll. This finite element model was verified in relation to the theoretical rolling expression. Finite element model analysis was performed for three friction coefficients, and the effect of the roll hunting force was determined based on the reduction ratio and temperature. In addition, the wear depth of the work roll by the hardness was predicted. The influence of the abrasion of the work roll on the hunting force was analyzed.

     

Elastic-plastic analysis of the stress and strain distributions in asymmetric rolling

Asymmetric plane strain plate rolling is analysed numerically by using an elastic-viscoplastic finite-element method. The asymmetric conditions are here due to different interface friction conditions of the two rolls. Two sets of different interface friction conditions are used. The influence of the degree of reduction on the curvature of the rolled plate and the corresponding distributions of the stress and strain are examined. For the rolling parameters considered, the curvature of the plate is found to be towards the roll with highest friction. The largest curvature is obtained for the biggest difference in interface friction conditions. The curvature shows a change from increasing to decreasing curvature with increasing reduction followed by a change in the distribution of the strain.     

Simplified theories of flat rolling—II. Comparison of calculated and experimental results

A simplified inhomogeneous solution for the roll pressure has been used as the basis for computing consistent precise estimates of roll force and roll torque from the theory of cold flat rolling. The accuracy of the new method is established in this paper by re-analysing previous data for the rolling of prestrained copper, data for the rolling of annealed mild steel and results for the rolling of low carbon steel with lubrication. Both Swift's stress-strain law and a polynomial function are used to represent the experimental yield data for the rolled materials.     

Multi-factor coupling system characteristic of the dynamic roll gap in the high-speed rolling mill during the unsteady lubrication process

In the present work, a multi-factor coupling dynamic model of a rolling mill system for a dynamic roll gap during an unsteady lubrication process was developed on the basis of the rolling theory, lubrication and the friction theory, and the mechanical vibration theory. The multi-factor coupling model of interfacial film binding was coupled with the rolling force model, dynamic roll gap interface friction model and work roll movement model. The corresponding distributions of friction and pressure at varying surface roughness and times were systematically analyzed during the unsteady mixed lubrication process. The effects of the main processing parameters on the critical speed and amplitude for self-excited vertical vibration were investigated.     

Simulation of Mannesmann piercing process by the three-dimensional rigid-plastic finite-element method

Simulation of the Mannesmann piercing process is performed for the first time by the three-dimensional rigid-plastic finite-element method. Firstly, a method of analysis is proposed for the steady-state formulation in the case that the sides of the finite elements cannot be made to coincide with the streamline of the material flow. Secondly, the simulation of the Mannesmann piercing process is performed under the variation of rolling conditions such as the feed angle, the minimum roll gap, the maximum plug diameter, the plug advance and the guide shoe diameter, and the effects of the rolling conditions on various rolling properties such as the outer diameter, the inner diameter, the roll force, the mandrel force, the equivalent strain distribution and the equivalent strain rate distribution are demonstrated. Finally, the results of the analysis are compared with the results of an experiment using Plasticine. The dimension in the rolling condition of the experiment is scaled to one-third of the dimension in the rolling condition in an actual Mannesmann piercing process. The analytical results agree with the experimental results and the validity of the method of analysis is confirmed.     

Flow and stresses in round–oval–round roll pass sequence

Analysis of flow and stresses in isothermal steady-state round–oval–round pass sequence for the production of round bars has been obtained from a flowline field solution. The velocity, strain-rate and stress components are derived from kinematic and static considerations together with the material constitutive law and friction boundary conditions. The results obtained show that the roll pressure and friction shear traction at the roll interface are fairly uniform and the normalized average roll pressure and friction shear factor have lower values than those for flat bar rolling at the same rolling conditions. Small variations in the rolls clearance gap have no appreciable effect on the roll load and torque. Increasing friction causes a significant increase in the roll load and torque. The analysis predicts pass grooves’ dimensions, roll load and torque for different values of height reductions.