Strip Width Direction Research Articles

Design and Simulation of Torque Control for Hot Rolling Steel Mill

Lateral movement of a strip in the hot rolling process is an important unsolved technical problem. To minimize the strip thickness variations, the state space model formulation is usually used. It results in reducing productivity and, in the extreme case, strip tearing during tailing out at the finishing mill. This movement is caused by various asymmetric factors such as mechanical asymmetry of the mill and different temperatures along the strip width direction. Furthermore, the difference in the temperature and the thickness of steel strip resulting in deformation of the steel, which affects the bending torque of the steel strip. This study aims to understand the influences of these various factors on lateral movement. In order to reduce the lateral movement and the disturbance terms, that act on uncertain inter-connected systems, a new control approach, based on a combination of Integral Sliding Mode Control (ISMC) and Linear Matrix Inequalities (LMI) technique, is proposed. Simulation results of hot rolling system with three interconnected systems are presented to validate the new controller performance.

Novel three-dimensional multi-objective numerical modeling for hot strip tandem rolling

During the hot strip tandem rolling (HSTR) process, the strip is compressed and elongated continuously, causing significant elastic deformation of rolls. At the same time, the strip temperature undergoes rapid increase and decrease, and distributes unevenly along the strip width direction. Elastic deformation of rolls and strip temperature variations have a significant effect on strip deformation, resulting in various strip shape. In this study, a novel three-dimensional (3D) coupled thermal-mechanical elastic-plastic finite element (FE) model for the HSTR is proposed based on the segmentation modeling strategy, where the finish mill is divided into several sub-models. The data transfer technology is developed to integrate the sub-models into a whole model via transferring the strip crown and temperature among the sub-models. Furthermore, the active and deactive element method, rigid pushing technology, and element remesh are also used to improve the calculation efficiency and accuracy of the model. Multi-objective parameters, such as strip temperature, strip crown, elastic deformation of roll stacks, and rolling force during the HSTR process are studied systematically using the developed FE model. The results show that the calculated strip temperature and strip crown after F7 agree well with the measured values, and the relative error between calculated and measured rolling force at each stand is less than 10%. This work offers a fresh perspective on the HSTR simulation.

Sensitivity Analysis of Design Parameters in Transverse Flux Induction Heating Device

In this paper, the Morris method of qualitative global sensitivity analysis (GSA) is used to rank the sensitivity values among four design parameters and three objectives of transverse flux induction heating (TFIH) device. The design parameters include effective value and frequency of the exciting current, the moving speed of the strip and the length of the coil along the width direction of the strip. The objective functions include relative non-uniformity of strip surface temperature distribution along strip width direction at heater outlet, average temperature of strip surface perpendicular to strip movement direction at heater outlet and heating efficiency of TFIH device. Each objective function is calculated by three dimensional (3D) finite element method (FEM). The sensitivity values ranking provides an optimal priority for the optimization or change of the design parameters of TFIH device.

Effect of Internal Stress of Incoming Strip on Hot Rolling Deformation Based on Finite Element and Infinite Element Coupling Method

Limited by the deficiency of the finite element method (FEM) to deal with infinite domain problems, the traditional FEM rolling model is not suitable enough to study the effect of the complex internal stress of the incoming strip on hot rolling deformation. To solve this problem, the finite element and infinite element (FE-IE) coupling method is adopted, where the finite element is for the rolling area of the strip and the infinite element is for the elastic constraint of the strip end. Based on the improved rolls-strip coupling model, several internal stresses with typical distribution forms are applied to the strip by a programmed user subroutine, and the effect of the internal stress of the incoming strip on hot rolling deformation is evaluated. The results show that under the same average stress, the various distribution forms of internal stress have little effect on the total roll force, mainly because of the average effect. The uniform internal stress decreases the central thickness and quadratic crown of the strip. Under the symmetric stress and asymmetric stress, the thickness of each fiber along the strip width direction is closely related to the magnitude and distribution of the stress deviation (subtract the average stress from the longitudinal stress). Under the quadratic wave stress, the central thickness and quadratic crown vary almost linearly with the amplitude of the stress deviation. The efficiency coefficients obtained can be treated as a theoretical basis for the further development of an accurate prediction model of hot rolling.

Closure behavior of spherical void in slab during hot rolling process

The mechanical properties of steels are heavily deteriorated by voids. The influence of voids on the product quality should be eliminated through rolling processes. The study on the void closure during hot rolling processes is necessary. In present work, the closure behavior of voids at the center of a slab at 800 °C during hot rolling processes has been simulated with a 3D finite element model. The shape of the void and the plastic strain distribution of the slab are obtained by this model. The void decreases along the slab thickness direction and spreads along the rolling direction but hardly changes along the strip width direction. The relationship between closure behavior of voids and the plastic strain at the center of the slab is analyzed. The effects of rolling reduction, slab thickness and roller diameter on the closure behavior of voids are discussed. The larger reduction, thinner slab and larger roller diameter all improve the closure of voids during hot rolling processes. Experimental results of the closure behavior of a void in the slab during hot rolling process mostly agree with the simulation results..

Research on the Behavior and Effects of Flatness Control in Strip Temper Rolling Process

A new indicator is proposed that can describe flatness control effect—ultimate longitudinal plastic extension strain difference and the plastic deformation of strip in the rolling process is divided into two states according to the behavior of flatness control, active state and saturation of shape control. The temper rolling process is modeled by the nonlinear elastic-plastic finite element software called ABAQUS. The influence law of the yield strength of strip on the behavior and effect of flatness control is revealed. The difficulty in flatness control of high strength / ultra-high strength strip in temper rolling is interpreted. The relationship between the value of ultimate longitudinal plastic extension strain difference and yield strength of strip is directly proportional. When the reduction distribution in the width direction of strip is within a certain range, the plastic deformation of the strip is in active state of shape control. When the reduction distribution in the width direction of strip is over a certain range, the plastic deformation of the strip is in saturation of shape control. When the plastic deformation of the strip is in active state of shape control, reduction in the middle of strip and its front and backward tension all have little effect on the distribution of longitudinal plastic extension strain difference. When the plastic deformation of the strip is in saturation of shape control, reduction in the middle of strip and its front and backward tension all have effect on the distribution of longitudinal plastic extension strain difference.

Thermal, Microstructural and Mechanical Coupling Analysis Model for Flatness Change Prediction During Run-Out Table Cooling in Hot Strip Rolling

Non-uniformity of temperature distribution across strip width direction is the ultimate reason why the flatness defect occurs on the strip after cooling process although the strip is flat at the exit of finishing mill. One thermal, microstructural and mechanical coupling analysis model for predicting flatness change of steel strip during the run-out table cooling process was established using ABAQUS finite element software. K Esaka phase transformation kinetics model was employed to calculate the phase transformation, and coupled with temperature calculation using the user subroutine program HETVAL. Elasto-plasticity constitutive equations of steel material, in which conventional elastic and plastic strains, thermal strain, phase transformation strain and transformation induced plastic strain were considered, were derived and programmed in the user subroutine program UMAT. The conclusion that flatness of steel strip will develop to edge wave defect under the functions of the differential thermal and microstructural behaviors across strip width during the run-out table cooling procedure was acquired through the analysis results of this model. Calculation results of this analysis model agree well with the actual measurements and observation.

FEM analysis for residual stress prediction in hot rolled steel strip during the run-out table cooling

With the increasing demand of higher quality hot rolled strips, flatness defects occurred on the strips during the cooling process on the run-out table have received significant attention and should be considered in the online shape control model. Non-uniform temperature distribution and cooling across the strip width are the main reasons why the strip becomes unflatten after cooling process although the strip is rolled flat at the finishing mill. A thermal, microstructural and mechanical coupling analysis model for predicting flatness change of steel strip during the run-out table cooling process was established using ABAQUS Finite Element Software. In this model, Esaka phase transformation kinetics model was employed to calculate the phase transformation, and coupled with temperature calculation by means of the user subroutine program HETVAL. An elasto-plasticity constitutive model of the material, in which conventional elastic and plastic strains, thermal strain, phase transformation strain and transformation induced plastic strain were taken into account, was derived and realized using the user subroutine program UMAT. The conclusion that the flatness of the steel strip will develop to edge wave defect under the functions of the different thermal and microstructural behaviors across strip width direction during the run-out table cooling procedure was acquired through the analysis results of this model. The calculation results of this analysis model agree with the actual measurements and observation, therefore this model has a high accuracy. To better control the flatness quality of hot rolled steel strip, the shape compensation control strategy of slight center wave rolling is proposed based on the analysis result. This control strategy has been verified by actual measurements, and applied in actual production.

PID sliding mode control for steering of lateral moving strip in hot strip rolling

Lateral movement of a strip in the hot rolling process is an important unsolved technical problem. It results in reduced productivity and, in the extreme case, in strip tearing during tailing out at the finishing mill. Lateral movement of a strip is caused by various asymmetric factors such as mechanical asymmetry of the mill, and different temperatures along the strip width direction. This study aims to understand the influences of these various factors on lateral movement, and to develop a controller that is useful for reducing lateral movement. Mathematical models which consider initial off-center value, leveling error of the mill, and strip tension for lateral movement of the strip are proposed. A Proportional-Integral-Derivative(PID) based sliding mode controller using an observer is also proposed to prevent lateral movement of strips. In addition, a control algorithm is designed to solve the chattering problem of a sliding mode control. The effectiveness of the proposed method is evaluated by numerical simulation of hot rolling by a pinch roll.

Deformation behavior of inclusions in stainless steel strips during multi-pass cold rolling

The strip quality is affected by the shape and the distribution of inclusions. The investigation of inclusion deformation in rolling process is significant for understanding the deformation mechanism of inclusion and guiding production. In present work, the behavior of spherical non-metallic inclusions in type 304 stainless steel strips during multi-pass cold rolling has been simulated by 3D finite element method and updating geometric method. The shape of inclusions is obtained under a variety of the inclusion sizes and positions. The inclusions elongate along rolling direction and compress along strip thickness direction, but slightly change along strip width direction. When the inclusion diameter is less than 10 μm, the inclusion scarcely deforms. As the inclusion sizes increase, the inclusion deformation gradually increases. The inclusion deformation also increases with the inclusion approaching the strip surface. As the rolling pass increases, the differences of inclusion shapes increase under various inclusion sizes and positions. The inclusion profile after cold rolling calculated by simulation is consistent with that by experiments. Finally, the relationship between the inclusion deformation and the crack generation is discussed.

Inconsistencies in Plane‐strain Elasto‐plastic Rolling Simulations

AbstractPlane strain conditions are frequently used as model assumptions for the approximate calculation of flat rolling processes for sufficiently wide strips. This means that during the entire forming process, the strain rate in strip width direction (z‐direction) remains zero. In the case of elasto‐plastic material, the transitions from elastic to plastic states and vice versa are of particular interest. If we accept the flow rule of Levy‐Mises, the normal stress σzz equals the average value of the normal stresses σxx and σyy inside plastic domains. Using Hooke's law we obtain a different relation for σzz in elastic domains. At transition points from elastic to plastic domains and vice versa, above relations for σzz have to be fulfilled simultaneously. Generally, this yields a discontinuous behaviour of σzz at the transition points and consequently to discontinuities of the stress σyy as well as the strains εzz and εyy, provided a continuous behaviour of σxx in rolling direction is postulated. The resulting discontinuity of εzz indicates therefore an inconsistency of such a plane strain model. Some key aspects of the underlying theory and consequences of such model assumptions will be pointed out. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Analysis of rolling load generated by pair crossed rolling mill

Although a pair crossed rolling mill has a very high control capability of strip crown, a frictional force always occurs in the strip width direction between the strip and the work rolls. An analysis of rolling load was carried out, considering the shear deformation of strip cross-section caused by the frictional force. From the examination of the calculated results for a large-scale mill for production, the following conclusions were obtained: (a) the cross angle hardly influences the rolling force and torque, (b) the thrust force on the roll induced by the frictional force decreases as a result of shear deformation, (c) the thrust factor, i.e. the thrust force divided by the rolling force, is little influenced by the strip deformation resistance and the friction coefficient between the work rolls and the strip during hot rolling, (d) the thrust force applied to the rolls during hot rolling is 3–6% of the rolling force for the cross angle of 1° and this is not an obstacle related to the design of rolling mills.

A model for deformation, temperature and phase transformation behavior of steels on run-out table in hot strip mill

A numerical model was developed to simulate the deformation, temperature and phase transformation behavior in both thickness and width direction of strip on a run-out table (ROT) in hot strip mill. The heat capacity of each phase and the heat evolution due to phase transformation were obtained from the thermodynamic analysis of the Fe–C–Mn system. The phase transformation kinetics of the steels on ROT was derived from the continuous cooling experiments. A thermal model is developed using a finite element method based on the heat transfer coefficients of strips determined from the actual mill data. In order to calculate the deformation behavior of steels on the ROT of the hot strip mill, the elastic strain, the volumetric strain due to thermal contraction and phase transformation, the plastic strain, and the transformation induced superplastic strain were taken into account. A constitutive equation for the transformation induced superplastic deformation of steels, which is based on the concept of MIgration of Transformation Interface induced Plasticity (MITIP), was adopted in a finite element method coupled with the thermal, thermodynamic and kinetics models. Using the model, the temperature-phase-deformation behavior of the steel on the ROT was calculated.

Lubricant Behaviors in the Compression-Friction Test of Strip Metals

The lubrication mechanisms were investigated in a modified plane strain compression test where the friction is also measured by simultaneous sliding of one of the dies in the strip-width direction. Though the average film-thickness of lubricant trapped between tool and workpiece agreed well with the theoretical calculation based on the squeeze effect, the subsequent behaviors of lubricant seemed to change with the viscosity under the pressure given and the shear rate. Lubricants trapped in small pits on the deforming surface function predominantly hydrostatically when relatively low viscosity mineral oils or vegetable oils are used under relatively low pressures, but develop hydrodynamically considerable shearing stresses on the workpiece and thus even alter the surface micro structures when higher viscosity mineral oils are used under high pressures.