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.     

Modified slab analysis of asymmetrical plate rolling

In this paper the general case of asymmetrical plane strain rolling due to unequal roll diameter, unequal surface speed of the rolls and different contact friction is considered. An analytical model based on the slab method of analysis was used and further developed to obtain the characteristics of asymmetrical sheet rolling and to predict strip curvature. This method describes an enhancement to the rolling theory where friction becomes an integral part of deformation mechanics in the roll gap. To verify the validity of the proposed analytical model, the analytical rolling force, torque and curvature were compared with experimental and analytical results of other investigators. Very good agreements are found. Capability as well as the simplicity of the proposed model in predicting more accurate theoretical results for the rolling force, torque and curvature makes it suitable for the online control application.     

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.     

Analysis of cross and vertical buckling in sheet metal rolling

In sheet metal rolling, shape defects called “cross buckling” or “vertical buckling” sometimes appear, which are wrinkles like washboards. The direction of the crest line of the cross buckling inclines at a certain degree against the rolling direction, while that of the vertical buckling is parallel to the rolling direction. In this study, analysis of the cross and vertical buckling is performed using the elementary theory of buckling. First, we calculate the stress distribution in three-dimensional sheet metal rolling near the exit cross section inside the roll gap. Next, we calculate the residual stress distribution near the exit cross section outside the roll gap. Furthermore, sheet metal buckling is analysed using the residual stress distribution. Type of buckling, distance between neighboring wrinkles, inclination of the crest line of the wrinkles against the width direction and the region where the wrinkles appear are obtained. We compare analytical results with published experimental results, and find that the former agree well with the latter. Hence, we conclude that this method of analysis is valid, and that the cause of the cross and vertical buckling is the residual stress distribution near the exit cross section outside the roll gap.     

Continuous-forming method for three-dimensional surface parts combining rolling process with multipoint-forming technology

Flexible rolling is a novel forming process for three-dimensional surface parts, which combines the rolling process with multipoint-forming technology. This process employs a pair of forming rolls as a forming tool. By controlling the gap between the upper and lower forming rolls, residual stress caused by the longitudinal non-uniform elongation of sheet metal makes the sheet metal generate three-dimensional deformation. In this paper, the improvement of the process is introduced that the middle curve radius of the roll gap is much larger than the transverse curvature radius of the forming surface in the forming process. The forming roll rotates around its own axis easily because of the small bending deformation which is suitable for producing three-dimensional surface parts including the wide sheet metal with a relatively small transversal curvature radius. The forming principle is set forth, and corresponding formulations are presented. Finite element analysis model is established, and spherical and saddle surface are simulated. The forming precision and the causes of the shape errors are analyzed through simulated results. The experimental equipment is designed and their experimental results are obtained. Simulation results are in well agreement with the experimental results, which verifies the feasibility of using simulation to guide the experiment. The results of both numerical simulations and experiments show that the proposed process is a feasible and effective way of forming three-dimensional surface parts.     

A theoretical study on the application of asymmetric rolling for the estimation of friction

In this work, a method for the estimation of friction coefficient is proposed based on the asymmetric rolling operation. Asymmetry is produced by operating the lower and upper rolls at different speeds. A slab method based computer code is developed for estimating the curvature of the rolled sheet under asymmetric rolling conditions. Strain-hardening behavior of the material has been incorporated and Wanheim and Bay's friction model is employed. The developed code is used for solving the inverse problem of estimating the coefficient of friction by measuring the curvature of the rolled sheet under known operating conditions. The simulations show a good potential of the method.     

Analytical model for predicting the surface profile of a work piece in round-to-2-R and square-to-2-R oval groove rolling

This paper presents an analytical model that predicts the surface profile of a workpiece in a round-to-2-R oval groove and a square section-to-2-R oval groove rolling sequence. “2-R oval” indicates a profile of the roll groove that has two different radii of curvature. Using low carbon steel (S10C) and stainless steel (STS304), we conduct a hot groove rolling experiment to verify the robustness of the proposed model. Results show that the predicted surface profile and exit cross-sectional area are in good agreement with experimental results. The second radius of curvature of the 2-R oval groove is important in reducing the exit cross-sectional area of the workpiece and partly squeezing the workpiece outward (i.e., in the roll gap direction) when in contact with the workpiece. Therefore, the surface profile of the workpiece in the 2-R oval groove is smaller than that of the 1-R oval groove.     

Experimental study for roll gap adjustment due to roll wear in single-stand rolling and multi-stand rolling test

To investigate a correlation between the amount of wear and roll gap (pass height) adjustment, we performed a single-stand reversible pilot groove rolling test as well as rolling test in an actual rod mill. In case of the pilot rolling test, we designed wear contour (profile) and machined it on the original roll groove (i.e., roll groove with no wear) to make the roll groove worn down. For the actual rod mill test, we developed a measuring device which can detect the actual wear profile. To determine the amount of roll gap adjustment, we propose a model for equivalent roll gap decrement which reduces the increased exit cross sectional area due to wear. We applied the proposed model to multi-stand rolling (roughing train of POSCO No. 2 Rod Mill) as well as single-stand reversible rolling. The wear profile of rolls worn down at each stand in mill yard was measured at different roll tonnage. The pilot hot rolling test shows that variation of exit cross sectional area is almost linearly proportional to roll gap change while the roll gap decreases from reference roll gap (6.5mm) to 3.5mm. In an actual rod mill which has consecutive rolling system, relationship between tonnage (total amount of tons that the produced rod weighs) and roll gap change at a stand is dependent on the rolling type (oval-to-round or round-to-oval) together with the cross sectional shape of incoming workpiece.     

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.     

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.     

Unsteady state work-roll temperature distribution during continuous hot slab rolling

Predicting temperature distributions in the work-rolls during the hot slab rolling process is of great importance to mill designers. This is because the temperature distribution and the dimensional accuracy of the slab being rolled are both dependent on the work-roll temperature. In addition, the life of the roll is also a function of its own temperature distribution. In this paper, the unsteady state heat transfer equations with time dependent boundary conditions are coupled with a two-dimensional finite element method to predict the work-roll temperature distribution during the continuous hot slab rolling process. To achieve an accurate temperature field, the effects of various factors including the thermal relationships of the work-roll and the metal slab, the idling work-roll revolutions, the rolling speed, the slab/roll interfacial heat transfer coefficient, and the magnitude of the thickness reduction of the slab at each deformation pass are taken into account. Comparisons between the predicted and published experimental results are used to illustrate the validity of the mathematical model.     

Analysis of sandwich sheet rolling by stream function method

A mathematical model for symmetrical sandwich sheet rolling is proposed by using the stream function method and the upper bound theorem to investigate the plastic deformation behavior of sheets at the roll-gap. The velocity fields derived from the newly proposed stream functions can automatically satisfy the volume constancy and the velocity boundary conditions within the roll-gap. Effects of various rolling conditions such as the thickness ratio and flow stress ratio of sheets, total thickness reduction, friction factor between the sheet and roll, etc., upon the thickness ratio of the rolled product, the relative length of the plastic region in each layer, rolling force and rolling power are discussed systematically. Furthermore, experiments on sandwich sheet rolling are also conducted by employing aluminium, mild steel and stainless steel as layers of sandwich sheets. It is found that the theoretical predictions of the thickness ratio of the rolled products and rolling force are in good agreement with the experimental measurements. Through the study, it becomes clear that the proposed analytical method is applicable for simulating the sandwich sheet rolling processes and is able to offer useful knowledge in manufacturing sandwich sheets.     

Coupled approach for flatness prediction in cold rolling of thin strip

The paper presents a predictive model of the flatness defects, which appear during rolling of thin plates, the origin of which is the roll stack thermo-elastic deformation. The combination of the elastic deflection, the thermal crown and the roll grinding crown results in a non-parallel bite, and if the deformed roll transverse profile is not an affinity of the incoming strip profile, differential elongation results and induces high stresses in the outgoing strip. The latter, combined with the imposed strip tension force, result in a net post-bite stress field which may be sufficiently compressive locally to promote buckling. A variety of non-developable shapes may result, generally occurring as waviness (centre waves, wavy edges, quarter-buckles, etc.). This problem is most of the time addressed in a decoupled way, i.e. as a post-processing of the residual stresses computed by a strip rolling model; the present paper on the contrary describes a fully coupled approach of in-bite plastic deformation and post-bite buckling. For this purpose, a simple buckling criterion has been introduced in a FEM model of strip and roll deformation, Lam3/Tec3; its implementation is documented in details. The capabilities and limits of the present approach are described and discussed. Characterised by its coupled approach, it is primarily devoted to cases where on-line (under tension) manifested defects occur. It is shown that the impact of the post-bite, post-buckled stress field on the in-bite stress and strain fields is quite small in the cases investigated; however, subtle changes appear in the velocity field at bite exit, and this is sufficient to transform completely the post-bite stress field, which is found in much better agreement with measurements if such a coupled treatment is used.     

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.     

A thermal analysis of strip-rolling in mixed-film lubrication with O/W emulsions

Increase of both roll and strip surface temperatures can significantly affect a rolling process, roll conditions and strip mechanical properties. A comprehensive thermal analysis in cold rolling, especially in a mixed film regime, is needed to understand how thermal fields develop in roll and strip during rolling. It requires a simultaneous solution of the mixed film model for friction in the roll bite and the thermal model for roll and strip thermal fields. This paper presents a numerical procedure to analyse strip rolling process using lubrication with oil-in-water (O/W) emulsions. The thermal model includes the effect of heat generation due to the strip deformation and frictional shear stress at the asperity contacts. The numerical analysis employs a coupled thermal model and a mixed film lubrication model for calculating the friction and the asperity deformation in the bite. The thermal model considers the initial temperatures of the roll and strip, temperature rise due to the strip plastic deformation and friction. While the O/W mixed-film lubrication model takes into account the effect of surface roughness and oil concentration (%vol) of the emulsion. The thermal effect is analysed in terms of strip surface temperature and roll temperature, which are influenced by rolling parameters such as reduction, rolling speed, oil concentration in the emulsion. The results of the parametric study indicate that the effect of oil concentration on the thermal field is relatively small compared to that of reduction ratio and rolling speed. The reduction ratio increases the maximum interface temperature in the roll bite. In the mixed film regime, rolling speed also increases the maximum interface temperature and alters the temperature field of the strip. The numerical procedure was validated against known experimental data and can readily be extended to hot rolling or used to analyse roll strip temperature subjected to different cooling system.     

STUDY ON STRIP AND ROLL DEFORMATION COUPLING OF COLD STRIP ROLLING ON 4-H MILL

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Effect of roll gap change of oval pass on interfacial slip of workpiece and roll pressure in round-oval-round pass rolling sequence

This paper presents a study of the effect of varying the roll gap of oval pass in round-oval-round pass sequence on the interfacial slip of workpiece, entrance and exit velocities, stresses and roll load that the workpiece experiences during rolling, by applying analytical method, finite element simulation and verification through hot bar rolling tests. The results have shown that the roll gap variation of oval pass affects the interfacial slip of workpiece along the groove contact and the specific roll pressure. The optimum conditions in terms of minimum interfacial slip and minimum specific roll pressure, which might influence the maximum groove life, is obtained when the subsequent round pass is completely filled.     

Chatter dynamics in sheet rolling

Two and four degree of freedom (DOF) systems describing chatter in sheet rolling are investigated. In the two DOF case, this includes studying the nonlinear behavior that arises due to the deformation at the work-backup roll interface. The force displacement relation between two cylindrical rolls being pressed together is inherently nonlinear due to the changing contact area. The investigation also includes the additional plastic deformation of the sheet in the roll-bite that is present during chatter. As the work rolls vibrate the gap widens and narrows inducing additional plastic deformation of the sheet.For the two DOF case, one mode of vibration is a motion of the work roll-sheet mass center. The other mode is a squeezing motion of the sheet in the bite by the work rolls. The natural frequencies seem to correspond with fifth octave chatter. The nonlinear theory predicts a small shift in the vibrational frequency. The role of inter-stand tension in triggering instability is also discussed.The four DOF system extends the research of Yarita et al. by providing analytic expressions for the natural frequencies. It appears that this system is capable of predicting third octave chatter, in addition to fifth octave chatter.     

Prediction model of the exit cross sectional shape of workpiece in round-oval-round pass rolling

A reliable analytic model that predicts the surface profile of the exit cross section of workpiece in round-oval (or oval-round) pass sequence is established. The presented model does not require any plasticity theory but needs the only geometric information on workpiece and roll groove. Formulation is based on the linear interpolation of the radius of curvature of an incoming workpiece and that of roll groove in the roll axis direction when the maximum spread of workpiece is known beforehand. The validity of the analytic model is examined by hot rod rolling experiment with the roll gap, specimen size, design parameter of oval groove and steel grade changed. Results revealed that the cross sectional shapes predicted by the model were in good agreement with those obtained experimentally. We found that the analytic model not only has simplicity and accuracy for practical usage but also saves a large amount of computational time in comparison with finite element method.     

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.