Four-high Mill Research Articles

An innovative development of a four-high foil rolling mill

During foil or ultrathin strip rolling, elastic deflection variation of the work rolls at the contact surface with the strip causes non-uniform thickness distribution of the product in the width direction, which possibly causes a central wrinkling or an edge fracture on the product. This study developed a four-high prototype rolling mill, comprising two work rolls fabricated from an ultrastrength alloy. This prototype rolling mill was composed of a housing frame set, a roll set, a roll gap adjusting mechanism, and a power transmission system. The finite element analysis was used for determining the frame dimensions and work roll diameters. Several experimental rolling passes of stainless steel strips were conducted using this self-developed prototype rolling mill to achieve a 0.05-mm-thick foil product.

Using rollers with increased barrel length in four-high mills

Increase in barrel length of the working rollers from 3100 to 3400 mm is proposed in the 3000 mill, without change in barrel length of the supporting rollers (2980 mm) or in the structure of the cell. Calculations of the pressure between the rollers and the transverse thickness variation of the rolled metal when the barrel length of the working rollers is 3100 and 3400 mm shows that the maximum pressure between the rollers is increased by 6–8% for 3400-mm working rollers with rolled sheet of maximum width 3200 mm; the rolled material is concave. To obtain a convex cross section, the depth of the bevel of the edges of the supportingroller barrel is doubled. Increasing the length of the working rollers in the 3000 mill at PAO Mariupol’skii Metkombinat im. Il’icha permits the production of commercial sheet with a width up to 3000 mm.

Development of Statically Determinate Plate Rolling Mills That Maintain the Rolls Parallel

The design theory of a statically determinate rolling mill, including the redesign of the statically indeterminate characteristic and hyperstatic characteristic, is proposed in this paper. The statically indeterminate characteristic leading to the nonparallel running state of rolls is revealed based on analysis of three rolling mills, including a 2200 mm aluminum foil four-high mill, a 1580 mm PC four-high mill, and a 650 mm bar two-high rolling mill, etc. The hyperstatic characteristic leading to uneven load performance of four-row roller bearing is caused by redundant constraints in the roll system based on analysis of 17 two- and four-high rolling mills. In contemporary four- or six-high plate rolling mills, regular dynamic cross between the rolls is very common during the whole rolling process. Dynamic cross results in excessive axial forces causing frequent burning losses of the end-thrust bearings and leads to serious deviations in the rolling load on both ends of the backup roll. Hence, rolling mills designed for heavy loads and high speeds have yet to operate at their design load and speed in a safe and stable way. According to the analysis of the degrees of freedom of a spatial mechanism, the cause of dynamic cross lies in the statically indeterminate characteristic of the roll system caused by the small clearance in the system. In this paper, the theoretical analysis and experiments invalidate the accepted method of the offsetting of the mill. Furthermore, it is shown that offsetting causes an asymmetrical cross between the rolls. Therefore, it is proposed that offsetting should be eliminated, and additional jack devices should be introduced to maintain the rolls parallel. In addition, bending deflections of the roll induce hyperstatic characteristics of the roll system due to the existence of redundant constraints in the system. The hyperstatic characteristic of the roll system results in uneven load performance of the radial roller bearings and shortens bearing life. In the newly proposed statically determinate four- or six-high plate rolling mill, which can be operated in a safe and stable way under heavy load and high speed working conditions, this problem can also be solved.

Spatial Vibration Characteristics of Four-High Rolling Mills

The contemporary four-high mills are unstable and four-high rolling mill vibrations take place in six DOF leading to spatial behaviors involving vertical, horizontal, axial, reverse, cross and swinging vibration modes resulting in complex relative motions between the rolls. In this paper, a spatial vibration characteristic analysis of two four-high rolling mills with different stability will be presented based on the transfer matrix method (TMM) and Finite Element Method (FEM). The natural frequency and mode shape of four-high rolling mill are obtained. Vibration experimental results will be presented to prove the validity of the spatial vibration of rolling mill.

Structure optimal design of four-high rolling mill stand based on improved collaborative optimization algorithm

Structure optimal design of four-high rolling mill stand based on improved collaborative optimization algorithm

SIMULAÇÃO NUMÉRICA DO PRIMEIRO PASSE DE LAMINAÇÃO A FRIO DE UMA TIRA DE AÇO C-Mn

This work presents the modeling by the finite element method of the first cold rolling pass of a four-high mill at the CSN steel plant. For this purpose, a two dimensional model is proposed considering the work-roll as a rigid surface together with the assumptions of plane-strain state for the strip and material isotropy with nonlinear isotropic workhardening. A C-Mn steel strip with initial thickness of 3.5 mm was first characterized by means of uniaxial tensile tests in specimens cut along the rolling direction to evaluate the work-hardening parameters. In the finite element model, the contact is defined by means of the Coulomb’s law to describe the friction between the work-roll and the strip surfaces. Moreover, the industrial back and forward tensions are also taken into account as prescribed conditions in the finite element model. The numerical predictions of the rolling load show a good agreement with the measured data and the forecasted value is determined with the slab-method.

Study on Predictive Model of Plate Camber

The plate camber is one of the thorny problems in the plate rolling process. The characteristic variables of plate camber at the delivery and at the entry sides of the mill were illustrated based on the primary concepts of camber. The relationship between the plate characteristic variable and velocity distribution in the deformation area of the plate was also determined. This paper focuses on the features of asymmetry in the transverse direction during rolling, an elastic deformation mathematical model of four-high mill has been developed to optimize the predictive model of plate camber, which ensures the theory of influence factors of plate camber to be applied in plate rolling.

Displacement of Multiple, Coupled Timoshenko Beams in Discontinuous Nonlinear Elastic Contact, With Application to Rolling Mills

Introduced is an efficient numerical method to calculate the displacements of structures involving multiple, shear-deformable beams in lengthwise nonlinear elastic contact. Applicability of the method is general, and includes structures such as stacked beams, pipes, or machine components. A particularly relevant application, which is discussed and demonstrated in this paper, is the prediction of deflections and contact conditions between the rolls and strip in rolling mills used to process flat metals. The presented nonlinear displacement calculation method involves iteration using an efficient, simplified mixed finite element formulation. Nonlinearities in the general coupled beam problem can arise either from changing contact conditions between the lengthwise-coupled shear-deformable beams (opening/closing of gaps) or from nonlinear elastic coupling-stiffness between the beams. Unlike the conventional problem of end-connected beams resting on elastic foundations, this work presents an element stiffness matrix formulation and sample nonlinear solution techniques for the problem involving multiple beams that are mutually coupled along their lengths by intervening, nonlinear elastic foundations. Important practical examples of the method are given, based on production cold rolling mill data for type 301 stainless steel on a four-high mill. The examples demonstrate efficiency and value of the nonlinear coupled beam formulation in identifying appropriate machined roll profiles to produce desired strip flatness quality. The cold rolling applications presented are characterized by nonlinear Hertz foundations with stiffness-hardening, and by discontinuous contact conditions arising from nonuniform, machined roll diameter profiles. Solution efficiencies for the new formulation are compared using modified Newton–Raphson, average stiffness, and direct substitution techniques. While the average stiffness method is relatively slower, its characteristics may make it beneficial for transfer function development in flatness control systems. Application of the method to cold rolling mills illustrates the importance of including discontinuous contact nonlinearities, and enables reduced trial and error to determine suitable roll profiles. Presented is a new efficient variational formulation for computing displacements in structures involving multiple beams laterally coupled with nonlinear elastic foundations and changing contact conditions. Practical value of the method is demonstrated for identification of machined roll profiles in cold rolling mills in order to achieve desirable flatness of rolled products.

Dynamical Reliability of Four-high Rolling Mill under Stochastic Strip Characteristics Excitation

It has great significance to research the dynamical reliability probability of rolling mill rolls system for improving its stochastic dynamical reliability and products quality rolled. The fifth-octave vertical vibration stochastic dynamical model of rolls system was established, and the pseudo-excitation method was used to obtain the power spectral density and the variance variation characteristics with the rolling speed and time under stationary rolling force stochastic excitation, and the stochastic dynamical reliability of rolls system was analyzed by using the first-passage failure criterion. The results show that rolls system reliability has strong relationship with stochastic excitation intensity and thickness tolerance of rolled strip and damping of the roll gap, among them, the stochastic excitation intensity and thickness tolerance of rolled strip have greater influence on the dynamical reliability of rolls system than other parameters, and rolls system stochastic dynamical reliability can be improved by mainly controlling the rolled plate/strip accuracy and roll gap damping, thus improving the quality of rolled strip in rolling operation.

Theoretical Study of the Dynamic Effects Based on Work-Roll Model in Metal Sheet Rolling Process

A new analytical model for the configuration of a four-high rolling mill stand is proposed in this article. Using the model, the dominant sources of stiffness in the fifth octave and the third octave models are identified. The assumptions made for the derivation of the model are that the work rolls are isotropic linear elastic, that there is no gap or separation between the work roll and the backup roll at all times. In addition, only the vertical interactions of the work roll and the roll-bite are considered. The nonlinear characteristics of this dynamic system are contributed from the contact area of the work roll and the backup roll. Analyses show that the natural frequency of the nonlinear analytical model matches the fifth octave rolling chatter, and the dominant parameters of the dynamic instability are characterized. The effects of inter-stand tensions, rolling speeds, friction between the work roll and the metal sheet roll-bite, and the thickness of the metal sheet on rolling chatter are discussed in the analysis of the dynamics of the rolling model.

Building the Mathmatical Model of Elastic Deformation for Rolls System by Four-High Mill Strip Rolling with a Composite Back-Up Roll

For buliding the mathmatical model of elastic deformation for rolls system with a composite back-up roll assemblled by the shrinkage fit, the roll sleeve and roll mandrel was studied individually, the bending force was acted on the working roll and the load acted on the contact zone was discreted segment by segment, then the deflection model of the working roll and the roll sleeve and roll mandrel was put forward based on the influence function method. According to the force equilibrim function and the deformation compatibility function between the roll sleeve, the roll mandrel and working roll, the solution matrix was listed and the solving programe was compiled to solve the deflection of working roll and composite back-up roll, the pressure between the working roll and the roll sleeve and the cross-section thickness of rolled strip. Therefore, it is an important theoretical foundation to improve the manufacturing technology and practical application of the composite back-up roll.

Improved model to solve influence coefficients of work roll deflection

According to the concept of virtual bending force, a rational explanation for SHOHET’s model was presented. Considering the deformation characters of the work rolls in four-high mill, the deformation model of the work roll was regarded as a cantilever beam and new influence coefficients were deduced. The effect of the bending force was taken into account independently. Therefore, the contribution to work roll deflection caused by rolling load, rolling pressure between rolls and bending force can be got from the new formulas. To validate the accuracy of the formulas, the results obtained from the new formulas were compared with those from SHOHET’s formulas. It is found that they highly coincide, which illustrates that the formulas are reliable.

Four-High Cold Rolling Mill for Control of Edge-Drop and Thrust Force

In the paper, control principle and working characters of T－WRS&C（Taper Work Roll Shifting and Crossing）cold rolling mill are analyzed. The working schedule and control parameters are worked out. The mill working modes are determined according to different working conditions. The taper work roll shifting is used for edge drop control and the work roll crossing is used for thrust force control when work rolls shifting. The actual application verifies that the edge drop and thrust force can be controlled effectively during cold strip rolling.

Four-High Mill with Statically Determinate Characteristics of Micro Displacement of the Components

The theory of micro dimensional behavior on rolling mill is used for a typical 450 mm hot plate four-high mill. A statically determinate device is adopted on the back-up roll system to adapt to the micro-dimensional deflection. We replace the traditional single base with the force divided base for the rolling load. To make the rolls parallel, a worm-screw device is set in the chock, with a clearance between the chock and the stand window to allow convenient roll replacement and retain a thermal expansion space. In the new mill, the center line of the roll body is constant when the rolling is stopped or running. It can be predicted that the mill will be strengthened two times and the roller bearing life will be prolonged ten times.

Development of Strip Flatness and Crown Control Model for Hot Strip Mills

The strip flatness and crown control model is the foundation of automatic strip shape control. Considering the metal transverse flows and the inter stand second deformation, the trip flatness and crown control model has been developed, which can be applied to CVC mills and PC mills as well as normal four-high mills. The strip flatness and crown control model has high precision, and has been successfully applied to the automatic strip shape control system reconstruction of Tangshan Ganglu 1 250 mm hot strip plant.

Indeterminacy of the Offset Mechanism and Microscale Static Determinacy of Roll System in Four-high Mill

In the four-high mill used for rolling plate,an offset is generally set to keep the rolls parallel and prevent the cross between the rolls,and which becomes the parallel positioning mechanism of roll system in four-high mill entered into the textbook of rolling mills.In all contemporary four-high mills,there is an offset between the rolls.But the offset cannot ensure the certainty of its mechanism,and the dynamic cross between the rolls happens frequently,which induces ultra-large axial force to damage the thrust rolling bearing or generate support reaction deviation in rolling to break the stability of plate shape control.Online inspection test of the axial force of a high-speed four-high mill for rolling aluminum foil and with a 3 mm offset distance is carried out,which reveals the occurrence of regular dynamic cross between work roll and backup roll during the rolling process.The dynamic cross behavior between the rolls is corresponding to the size of small clearance between bearing seat and housing window column,limited only in the range of β≤0.05° cross angle of rolling mill,and far lower than β=1°～1.5° cross angle of PC mill.But the derivative axial force of the dynamic cross exceeds three times of the rated value The static acyclic test of the offset distance of four-high mill roll system proves that with constant original installation position between the rolls there is no horizontal displacement of rolls.The dynamic cross phenomenon and zero static horizontal displacement reveal the indeterminacy of the mechanism of setting offset distance,so it cannot be used for parallel positioning and stability design of four-high mill.

Forced transverse vibration of rolls for four-high rolling mill

In order to investigate the forced transverse vibration of rolls under distributed draught pressure and moment of bending roll force, the forced transverse vibration model of rolls for four-high rolling mill was established. The work roll and backup roll were considered as elastic continuous bodies that were joined by a Winkler elastic layer. According to Euler-Bernoulli beam theory, the forced transverse vibration of rolls was analyzed based on modal superposition method. The forced vibration equations were established when the draught pressure and moment of bending roll force were imposed on the rolls respectively. Numerical modeling was made on 2 030mm cold tandem rolling mill of Baoshan Iron and Steel Company. Simulation results show that when the work roll is only subjected to different forms of draught pressures, the vibration curves of work roll and backup roll are quadratic curves with amplitudes of 0.3mm and 45μm, respectively. When only the moments of bending roll force are imposed on the work roll and backup roll, the vibration curves of work roll and backup roll are quadratic curves, and the amplitudes are 5.0 and 1.6μm, respectively. The influence of moment of bending roll force on the vibration of work roll is related with the bending roll force.

Statically determinate characteristics of microdisplacement in a four-high mill

Contemporary high-speed four-high mills are statically indeterminate structures because of microdisplacement of their components. This displacement involves movement of the chock in the stand window. In this paper, regular micro-scale dynamic cross between the work roll and the back-up roll is discussed. This dynamic cross results in excessive axial force and causes frequent burning loss of the end-thrust bearing of the work roll. A gyroscopic effect and a propelling mechanism due to friction force are proposed as the causes of the dynamic cross. Experiments confirmed the existence of micro-scale dynamic cross throughout the whole rolling process. To prevent dynamic cross between the rolls, a roll system that is a statically determinate structure has been designed. This markedly decreases burning loss of the end-thrust bearing.

Dynamic model building of thickness control system for four-high rolling mill and HCO∞ robust controller design

In this paper, the integral dynamic model of four-high mill is built which includes the rolling process model, the dynamic model of mill stand-rolls and the dynamic model of hydraulic servo system. The three models are coupled and linearised, the MIMO transfer function of four-high mill system is obtained. Considering the quality of the product, the MIMO model is simplified and the thickness control system based on thickness gauge is derived. The H∞ robust controller is designed for the thickness control system based on the mixed sensitivity robust control theory. The weighting functions are selected based on genetic algorithm. Simulation results and comparison with the effect of PI controller show that the robust controller designed has better disturbance attenuation performance for parameter uncertainty and external disturbance. The dynamics performances and stability of the thickness control system based on thickness gauge are improved significantly.

Numerical and experimental analysis of the dynamic effects in compact cluster mills for cold rolling

Prevention of dynamic instability caused by chatter phenomenon may be difficult in case of the so-called “cluster mill” because of the number of back-up rolls used to avoid bending of the work roll. A numerical simulation of the dynamics of the cluster mill may help to prevent the strip defects and to predict the life of bearings and rolls. Analytical models proposed in the literature for the two- and four-high mills are unfortunately inapplicable. This paper investigates whether the multi-body dynamics approach can be effective in analysing the so-called “Z-Mill”. Service monitoring detected in a real case some clear and dark bands on the strip surface, which disappeared after a calibration of rolls position. A numerical model was built by assuming that the mill stand and the strip could be analysed separately. Validation allowed concluding that modelling is effective, if relevant parameters are tuned on the experimental evidences. In particular damping and friction coefficients look the most critical to predict the actual value of rolling force. Mechanical nonlinearities introduced by the contact among rolls and by bearings increase the computational effort, but their role is somewhere overestimated in the literature. In practice, the multi-body dynamics approach still shows some limits, but they should be overcome, if a deeper experimental validation will be performed on a dedicated test rig, suitably designed to be largely instrumented.