Rolling Pressure Distribution Research Articles

Modelling of axial thrust force considering 3D rolling deformation

The axial thrust force in the rolling deformation zone is influenced by interconnected factors, such as the metal transverse flow velocity, rolling pressure distribution, and strip shear deformation, often resulting in roll wear and a lower strip surface quality. Despite its significance in the design and manufacturing of strip mills, the available literature primarily focuses on the single-variable complete difference method as a means of evaluating this force. In this study, a novel approach is proposed for calculating the axial thrust force in the rolling deformation zone, incorporating the coupling variables of the 3D rolling space. The accuracy of the results is confirmed using data obtained from an industrial test rig, indicating that the axial thrust force in the rolling deformation zone can be precisely calculated through the integration of the energy method and the 3D difference method. The results indicate that the axial thrust force decreases with the transverse flow of the metal and the transverse shear deformation of the strip. It increases with a non-uniform distribution of rolling pressure and grows as the crossover angle increases. Conversely, the axial thrust force decreases with an increasing reduction rate of the strip. In general, a non-uniform distribution of rolling pressure enhances the axial thrust force, albeit with a minor effect when the crossover angle exceeds 0.8°. Conversely, metal transverse flow significantly reduces the axial thrust force when the crossover angle is small (φ < 0.4°), but only marginally so when the crossover angle falls within the range of 0.4° to 1.0°.

A Theoretical Study of Reverse Roll Coating for a Non-Isothermal Third-Grade Fluid under Lubrication Approximation Theory

The flow of non-Newtonian fluids is extremely important in a variety of industrial applications and processes, including painting, printing, and coating. The goal of this paper is to develop a mathematical model for an incompressible, non-isothermal third-grade fluid as it travels through a minor gap between two heated rolls that are revolving in the opposite direction. Using appropriate dimensionless parameters, the dimensionless version of the governing equations is constructed. To simplify the nondimensional form of the governing equations, the LAT (lubrication approximation theory) is applied. It is mentioned that the perturbation approach should be used. It is a very important tool in modern mathematical physics and practical fluid mechanics, and it is used a lot. Through perturbation techniques, exact solutions for velocity distribution, flow rate, temperature distribution, and pressure gradient are offered. To observe the flow pattern, streamlines are also drawn. Numerical outcomes of some substantial engineering quantities like flow rate, roll separation force, power input, and pressure distribution are found. Some outcomes are displayed graphically although others are presented in tabular form. We have observed that the third-grade parameters give a way to control velocity, pressure gradients, flow rate, and coating thickness. Further, increasing the velocities ratio values lowers the coating thickness on the web. Furthermore, the Brickman number has a significant influence on the temperature profile and has increased with the increase in the Brickman number. Both the model and the numerical calculations are in agreement with the viscous fluid model that is already present in the literature.

Simulation study on steel pipe deformation behavior in retained mandrel pipe mill

Continuous rolling technology of seamless steel pipe is the leading technology in the production of steel pipes in recent years. However, due to the complicated pipe rolling process, the rolling parameters must be adjusted according to the rolling conditions after many trials of rolling. This paper focuses on a Φ180mm retained mandrel pipe mill, and the continuous rolling process finite element analysis model of seamless steel pipe is established by using ABAQUS software. The finite element model is validated by the measured wall thickness and pipe diameter data of industrial production, and the model is designed to reveal the evolution of rolling pressure distribution, metal flow, strain, wall thickness and pipe diameter during the continuous rolling process. The simulation results support key structural design of the rolling mill, the determination of rolling process parameters and the optimization of process parameters in engineering commissioning.

Effects of varying friction coefficient on rolling pressure distribution

Accurate characteristics of roll pressure distribution is essential in the estimation of the energy and power requirements for parts undergoing plastic deformation. The nature of the pressure distribution is very sensitive to the friction coefficient between the roller and the deformed part. The physics of the deformation process points to a variable friction coefficient, however, current research and practices result in the use of a constant friction coefficient. This work explored the development of a technique to determine a quantitative relationship between the variable friction coefficient and the process parameters. The pressure distribution was then developed within the contact region using the variable friction coefficient model. Results show that current approach used by industry (‘the rule of thumb’) overestimates the pressure distribution, compared to the current research, thus wasting power needed for the rolling operation by about 18%. Keywords: Rolling; varying friction coefficient; pressure distribution; power

Analysis of rate dependency on roll force calculation during hot strip rolling based on Karman equation

Due to the development of thin slab hot rolling technology, hot rolling thin strip at a higher speed is inevitable. As a result of high-speed rolling, thin slab is deformed at a wide range of strain rate inside the rolling zone. Because the flow stress of steel is strongly dependent on strain rate at elevated temperature, it is imperative to consider its variation when calculating roll force and roll pressure. By substituting time with speed and length, strain rate variation is obtained. A strain rate–dependent flow stress curve for non-oriented silicon steel is implemented into Karman equation to calculate rolling pressure distribution. It is revealed that the rolling force can be effectively reduced by decreasing the radius of work roll. It is further revealed that the appearance of strip/roll surface sticking is more likely at the exit of rolling zone than the neutral point, because strain rate reaches zero and the flow stress drops at the exit. Combined with Influence Function Method for elastic deformation of roll surface, the proposed model can predict roll force with a good accuracy compared with industrial data.

Analysis of mechanical parameters for asymmetrical strip rolling by slab method

An analytical model is proposed to analyze the asymmetrical cold strip rolling by the slab method, and used to easily determine the rolling pressure distribution, roll force, and torque. The effects of asymmetrical rolling conditions including roll speed, roll radius and friction coefficient on rolling pressure, roll force and torque are analyzed separately. The influences of different asymmetrical conditions on rolling pressure distribution are different and unrelated, but will superimpose each other when multiple asymmetrical conditions coexist. An appropriate combination of asymmetrical conditions can improve the non-uniform distribution of roll torques due to the unequal roll speed. The analysis results are in good agreement with experimental measurements and other studies, which verify the accuracy of the proposed model.

Mathematical model of lever arm coefficient in cold rolling process

The prediction precision of mechanics parameters such as rolling force and torque affects the yield, quality, cost, and benefit of products during the cold strip rolling. The lever arm coefficient is the core linking rolling force and torque, but there is no mathematical model of this in cold rolling. The distribution of rolling pressure and the change rule of lever arm coefficient under different reduction, forward and backward tension stress, deformation resistance, and friction coefficient in cold rolling are illustrated based on 3D (three-dimensional) elastic-plastic FEM (finite element model) simulation. The mathematical model of lever arm coefficient is built according to online measured data processed by BP (back propagation) neural network in the tandem cold rolling plant. The predicted rolling forces calculated on the basis of this model and upper bound method are consistent with online measured values. The proposed model provides valuable guidelines to determine the reduction and check the strength of the equipment such as rolls and stands.

Analysis of symmetrical flatness actuator efficiencies for UCM cold rolling mill by 3D elastic–plastic FEM

As the basis for a flatness control system, flatness actuator efficiency describes an actuator’s control ability, but it is difficult to obtain an actuator efficiency factor accurately through rolling tests because of the complicated subsidiary facilities of the mill. This paper proposes a novel simulation approach that is applied to obtain the actuator efficiency factors in terms of work roll bending, intermediate roll bending, and intermediate roll shifting for a six-high Universal Crown Control mill (UCM mill). A three-dimensional (3D) finite element model of the mill was developed to simulate the dynamic strip rolling process. The validation of rolling experiments shows that this model has enough precision, where the relative error of strip thickness between simulated values and actual values is less than 1.0%. The effects of the actuators on strip thickness profile, crown, edge drop, and elongation difference of longitudinal fibers were investigated. In the case of different actuator parameters, the curves of actuator efficiency factors were obtained and quantitatively descripted by truncated Legendre orthogonal polynomials. The mechanism of flatness control was studied based on an analysis of the actuator’s influence rule on the elastic deflection of rolls and 3D distribution of rolling pressure. The results indicate that the curves of actuator efficiency factors have a symmetrical upside-down v-shaped distribution and contain the quadratic and quartic flatness components. The actuator efficiency factors of intermediate roll shifting have a nonignorable variation with the change of actuator parameters. This study is the first attempt to obtain actuator efficiency factors for UCM mill using an elastic–plastic finite element method.

Effect of roll compactor sealing system designs: A finite element analysis

In the pharmaceutical industry, the roll compaction is part of the dry granulation process, densifying fine powders into ribbons that will be later milled to produce granules with good flowability for subsequent die compaction process. Roll compactors are constructed with a sealing system, limiting the loss of powder from the sides. However, the sealing system may result in unwanted non-uniformity of the ribbon's properties. In this work, a 3D Finite Elements Method (FEM) modeling is used to analyze the roll compaction process and the effect of sealing system designs on the compacted ribbon's density distribution. A density dependent Drucker–Prager Cap (DPC) constitutive model for microcrystalline cellulose (Avicel PH-101) was calibrated and implemented in Abaqus/Explicit. Two different FEM models were investigated, one with a fixed side sealing called cheek plates and another where the side sealing is integrated with the bottom roll called rimmed-roll. Both numerical and experimental results clearly show the non-uniform roll pressure and density distribution for the cheek plates assembly, whereas the rimmed-roll shows an overall more uniformly distributed resultant pressure and density distribution. These results demonstrate the capability of FEM modeling to provide insight and help achieving a better understanding of the roll compaction process.

Strip layer method for analysis of the three-dimensional stresses and spread of large cylindrical shell rolling

As the traditional forging process has many problems such as low efficiency, high consumption of material and energy, large cylindrical shell rolling is introduced. Large cylindrical shell rolling is a typical rotary forming technology, and the upper and lower rolls have different radii and speeds. To quickly predict the three-dimensional stresses and eliminate fishtail defect, an improved strip layer method is developed, in which the asymmetry of the upper and lower rolls, non-uniform deformation and stress, as well as the asymmetrical spread on the end surface are considered. The deformation zone is divided into a certain number of layers and strips along the thickness and width, respectively. The transverse displacement model is constructed by polynomial function, in order to increase the computation speed greatly. From the metal plastic mechanics principle, the three-dimensional stress models are established. The genetic algorithm is used for optimization calculation in an industrial experiment example. The results show that the rolling pressure, the normal stresses, the upper and lower friction stress distributions are not similar with those of a general plate rolling. There are two relative maximum values in rolling pressure distribution. The upper and lower longitudinal friction stresses change direction nearby the upper and lower neutral points, respectively. The fishtail profile of spread on the end surface is predicted satisfactorily. The reduction could be helpful to eliminate fishtail defect. The large cylindrical shell rolling example illustrates the calculation results acquired rapidly are good agreements with the finite element simulation and experimental values of previous study. A highly effective and reliable three-dimensional simulation method is proposed for large cylindrical shell rolling and other asymmetrical rolling.

Calculation of rolling pressure distribution and force based on improved Karman equation for hot strip mill

An improved Karman equation for hot-rolled strip was deduced to generate a new rolling pressure formula, based on comprehensive consideration of the slipping and sticking friction on the contact arc between hot-rolled strip and work rolls. The Runge–Kutta method was applied to solve the improved differential equation, and then the distribution of rolling pressure on the contact arc was obtained. The roll force in the roll-bite can be calculated by integrating the vertical component of positive pressure and friction shear stress of every slice. This paper also analyzed the influence of friction condition, flow stress, roller distortion and other factors on the results of rolling pressure and force per unit width. Using 7 stands of hot strip mills as an example, this paper conducted actual industrial application verification. The computational results demonstrate that the proposed new model improves the setting precision of roll force and can be applied to online control of hot rolled strip.

Slab Analysis of Large Cylindrical Shell Rolling

Considering the characteristics of large cylindrical shell rolling, such as double driving rolls, asymmetrical rolling and huge workpiece, a slab method was developed to establish the rolling force model. In this model, the non-uniform normal and shear stresses and the upper and lower surface temperatures of the workpiece were taken into account. Moreover, the flow stress model, considering the dynamic recovery and dynamic recrystallization behaviors of the material, was established. The rolling pressure distribution, the rolling force, the rolling torque and the neutral points could be calculated quickly and easily by the rolling force model. The predicted results were shown to be in good agreement with the measured values, which indicated that the model can satisfy the requirement of industrial application.

Development of Three-Dimensional Strip Profile Model for Thin-Foil Cold Rolling

Accurately predicting the strip profile after thin-foil cold rolling is very difficult because of the thinness of the strip. In this study, a three-dimensional (3D) strip profile model was developed to improve the accuracy of a rolled thin-foil profile. The distribution of the contact pressure between rolls (i.e., the work, intermediate, and backup rolls) and the rolling pressure between the strip and work roll were calculated by using the geometric structure of a 6-high mill and boundary conditions imposed in the width direction by a numerical method. The rolling pressure distribution in the rolling direction was determined by Fleck's model of thin-foil rolling. The 3D rolled-strip profile was predicted by using the pressures in the width and rolling directions. In order to investigate the effect of the rolling speed and rise in strip temperature on the lubrication, the friction coefficient was estimated through an analytical method and experiments to test the viscosity and friction. The resulting 3D strip profile was verified by a thin-foil cold rolling test and was compared with the profile obtained using the proposed 3D model and finite element simulation.

Study of edge-cracking characteristics during thin-foil rolling of Cu-Fe-P strip

A three-dimensional (3D) strip profile model is proposed to improve the accuracy of predicting the profile of the as-rolled thin-foil strip. The contact and rolling pressure distributions at a 6-high mill are calculated numerically using the geometric structure and boundary conditions in the width direction. The rolling pressure distribution in the rolling direction is determined by Fleck’s model, and the as-rolled 3D strip profile is predicted using the pressures in the width and rolling directions. The rolling force in the width direction causes elastic deformation of the rolls, which induces uneven deformation at the strip edges. Strip failure frequently occurs in the cold rolling process because of increasing edge-cracking. The onset of edge-cracking is introduced using the ductile fracture criterion in continuous thin-foil rolling. The states of stresses in the deformation zone are calculated using the finite element (FE) method. Thin-foil rolling experiments are carried out, and the results are compared with those of the proposed 3D model and FE simulations to verify the precision of the 3D strip profile model.

Strip layer method for simulation of the three-dimensional deformations of large cylindrical shell rolling

Abstract A strip layer method is presented for analyzing the three-dimensional deformations and stresses of large cylindrical shell rolling process. In this approach, the different radii and velocities of upper and lower rolls, the uneven distributions of deformations and stresses at the roll gap, are taken into account. The rolling deformation zone is divided into a number of strip and layer elements along the width and thickness directions, respectively. In order to reduce the optimization parameters and improve the computation efficiency, the exit lateral displacement distribution is expressed as polynomial function. Based on the fundamental principles of plasticity, the three-dimensional deformations and stresses of the deformation zone are formulated. The simulation results can be obtained quickly and easily. The fishtail spread is predicted satisfactorily on the free side, and the rolling pressure distribution is quite different from that of a conventional strip rolling. The predicted rolling force and average spread of the proposed method are in agreement with the experimental and FEM results.

Slab Analysis of Asymmetrical Rolling of Bonded Two-layer Sheets

In this paper, asymmetrical rolling of bonded two-layer clad sheets is studied using the slab method of analysis. It is assumed that the ingoing sheet is guided to horizontally enter the roll gap and that the work rolls may have different pressure distributions. Unlike the existing slab models, the slabs are not divided into two parts with different materials, and the whole slab is subjected to one stress field containing non-uniform normal and shear stresses acting on the vertical sides. By combining the sticking and coulomb friction models, a mixed friction model is proposed, and the work roll pressure distributions as well as the rolling force and torque are studied at different conditions. The predicted rolling force and torque of the proposed model are shown to be in a very good agreement with the analytical and experimental results of previous investigators.

General Solution to Bond Rolling of Unbounded Sandwich Sheet with Outer Soft and Inner Hard Layers Considering Coulomb Friction

This study derives the stress field of the bond rolling of unbounded sandwich sheet with outer soft and inner hard layers at the roll gap considering Coulomb friction between the roll and the sandwich, and Coulomb friction at the interface of the unbounded region. Due to the sandwich sheet unbounded before rolling, three-layer sheets are not bonded firmly. The neutral point between the roll and the sandwich sheet, the rolling pressure distribution along contact interface between the roll and sandwich sheet, the horizontal stress of whole sandwich sheet, the horizontal stresses in the component layers of sandwich, the shear stress at the interface of sandwich sheet, the rolling force, and rolling torque, etc. are effectively calculated via this model. Furthermore, it is of great important to obtain the bonding point at the interface and the thickness ratio of sandwich sheet at the exit from this study. Additionally, the bonding conditions of the unbounded sandwich sheet are found to avoid the failure in bond rolling. This study proposed is suitable for the on-line bond rolling; it offers useful knowledge to conduct the experimental bonding conditions.

Analyzing Rolling Pressure of Rolling Strip by Multi-Object Contact Multi-Pole Boundary Element Method

For guiding production effectively and revealing rolling mechanisms, the analysis of rolling-pressure distribution regulation is very important. Because rolling strip belongs to multi-object contact engineering problem which involves coupling deformation, obviously the accuracy of disaggregate mathematical method is low. Therefore, in this paper,it is developed that multi-object, elasto-plastic and frictional contact multipole Boundary Element Method (BEM) by Fortran program. It can simulate five object synchronous contact accurately without artificial assumption.The three dimensional rolling-pressure distribution regulation of rolling strip has been obtained through this program. Through testing and calculating the load properties of bearing, the result shows that it is accordant for test and calculation. Therefore, multi-pole BEM is one of the effective numerical analytic tools of rolling contact problem, and the obtained result of rolling-pressure distribution can provide for reference value for analyzing rolling strip.

Research on Roll Force for Variable Gauge Rolling

The production of materials saving products such as Longitude Profile plates (LP plate) and Tailor Rolled Blanks (TRB) needs to solve the problem of the calculation of variable gauge rolling (VGR) parameters. It has been proved that Karman differential equation of force equilibrium for simple rolling is a special case of VGR equations when vy＝0. Differential equations of force equilibrium for both upwards rolling and downwards rolling were solved and the rolling pressure distribution function for VGR was got in this paper. Finally, details of a set of experiments were presented and the theoretical model of rolling force was proved to be reasonable.

Vision-based camber measurement system in the endless hot rolling process

In the endless hot rolling process, camber is a significant defect where camber is flatness asymmetries produced by nonuniform distribution of rolling pressure. This kind of defect may not only cause clogging of the finishing mill, but also visible defects, such as bar edge folds, edge cracks, holes, and scrapes. It is important to measure the exact camber values of the overall shape and head/tail part of steel bars to reduce camber for hot-rolled steel bars. We introduce a vision-based camber measurement system based on two-area-scan charge-coupled device (CCD) cameras and proposes a camber-detection algorithm to achieve the optimal cutting-line, the overall bar shape, and camber values from the obtained image. The proposed algorithm consists of three parts: optimal cutting-line detection, image-stitching, and camber detection. The optimal cutting-line detection part determines the cutting line of the head/tail part of the bar for continuous joining between steel bars. The image-stitching part obtains the overall shape of a hot-rolled steel bar with continuous image sequence obtained by two-area-scan CCD cameras. The camber-detection part measures head camber, tail camber, and whole camber of the steel bar. Through the proposed camber-detection algorithm, the system not only satisfies a time constraint for detecting the camber of the steel bar but also obtains the optimal cutting line, the overall bar shape, and the camber values.