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An accurate description of the metal flow behavior during wedge zone deformation is key to the stability of the endless strip production rolling process. To predict the flatness distribution based on the law of volume invariance, a flatness calculation model of the wedge zone during the flying gauge change (FGC) process was established by considering the metal transverse flow. Furthermore, the effect of different rolling parameters on the flow of metal in the wedge zone was investigated using a combination of this model with a 3D finite element model. In addition, the influences of the reduction rate, roll crown, and friction coefficient on the flatness and metal lateral flow were analyzed and discussed. Finally, the numerical results provided by the finite element model were compared with the computed results of the flatness distribution to illustrate the effectiveness and stability of the proposed model. [ABSTRACT FROM AUTHOR]

The strips with good flatness after finish rolling will have flatness defects such as edge wave after run-out table cooling. These defects are caused by the residual stress due to inhomogeneous thermal and microstructural behaviors during the cooling stage. The traditional residual stress control methods rely too much on experience, resulting in poor control effect and poor universality. Therefore, this study proposed two residual stress control methods based on model calculation: water flow central crown and center wave compensation control. The former is mainly based on controlling the uniformity of strip transverse temperature and microstructure. The latter is mainly controlled by mutual compensation of internal stresses. In this paper, the mathematical models of water flow central crown cooling and critical center wave compensation stress were established, respectively. Meanwhile, a post-buckling model of hot-rolled strip was established to calculate the aim flatness value at exit of finishing mill under critical compensation stress. Furthermore, a fully coupled finite element model based on temperature, phase transitions, and stress was developed and it was verified using experimental data. Finally, the above two residual stress control methods were realized in the finite element model. The results showed that the two methods can reduce the residual stress and improve the flatness, and the application of center wave compensation control is more effective. [ABSTRACT FROM AUTHOR]

The accuracy of flatness actuator efficiency (FAE) is a prerequisite to achieve high precision automatic flatness control. This study proposes an accurate acquisition approach of FAE based on the combination of simulation modeling and data‐driven modeling for flatness control of cold‐rolled strip. First, a 3D rolling feature space model is constructed according to the change interval of rolling process parameters based on rolling conditions. A 3D finite element simulation model is subsequently established to determine the prior value of actuator efficiency at each node in the feature space model. Then, to improve the accuracy of prior value, an online optimization model is developed by means of data‐driven mechanism. The sorting algorithm and the central limit theorem are introduced to filter the measured process data and calculate the variable weighting. The processed data are imported into the model to improve the fitting model. Finally, a linear output prediction model based on the trend extrapolation method is proposed to realize the accurate acquisition of FAE under any rolling conditions. The data analysis of the production process shows that the model is adaptive and accurate, which can realize high precision flatness control. [ABSTRACT FROM AUTHOR]

Mill chatter in tandem cold rolling mill is a major rejection to the quality and production of the strips. In most mill vibration models, either the roll mass is usually limited to vibrate in vertical direction and vertical-horizontal directions, or the multiple rolls system is simplified to a single mass system. However, the torsional chatter is also a typical type of mill chatter, and the presence of intermediate roll and backup roll will affect the overall vibration of the mill structure system. In this paper, a newly cold rolling mill vibration model coupled with the dynamic rolling processing model and nonlinear vibration model is proposed with the consideration of dynamic coupling and nonlinear characteristics of the rolling process, multiroll equilibrium, and roll movement in both vertical-horizontal-torsional directions. By using Hopf bifurcation theorem and Routh–Hurwitz determinant, the existence of the Hopf bifurcation point of the mill vibration system and bifurcation characteristics are analyzed. At last, the influence of different rolling conditions on the stability of the coupled mill system is investigated, and these results can also be used to design an optimum rolling schedule and determine the appearance of mill chatter under certain rolling conditions. [ABSTRACT FROM AUTHOR]

• The symplectic approach is applied to solve the strip cross section temperature. • The mechanism of residual stress formation in hot strip rolling is studied by fiber rods model. • An analytical model for the coupling of temperature, crown and residual stress is established. • The strip critical exit crown ratio is obtained by using the residual stress analytical model. • Eliminating manifested and latent flatness defects by critical exit crown ratio of strip. Residual stress is introduced during hot-rolled strip production due to various factors, such as temperature distribution, crown change, and metal transverse flow. Excessive residual stress can cause flatness defects in the strip, while insufficient residual stress may result in deformation during subsequent cutting. To explore the mechanism of residual stress formation in hot-rolled strip and how to control it, an analytical model for the coupling of temperature, crown and residual stress is established. Firstly, based on the symplectic space Hamiltonian system, an analytical solution for the strip cross section temperature field in each inter-stand zone is obtained. Then the residual stress analytical model is derived based on the fiber rod model combined with the law of volume invariance, lateral metal flow function and high temperature stress relaxation phenomenon. Meanwhile, to verify the accuracy of the analytical model, a multi field coupled finite element model based on the measured data validation is established. The calculation results of the analytical model are in good agreement with the finite element model. Furthermore, the buckling model of strip in symplectic space Hamiltonian system is derived, and the critical buckling stress of different strip flatness defects is directly calculated. Finally, the residual stress analytical model is combined with critical buckling stress to calculate the critical exit crown ratio to keep the strip flat. [ABSTRACT FROM AUTHOR]

• Based on the fiber rods model, the formation mechanism of residual stress caused by temperature and phase transformation is studied. • An analytical model is established to calculate the residual stresses at different run-out table cooling stages. • Based on symplectic space Hamiltonian system, the mathematical relationship between residual stress and flatness is solved directly. • The edge wave defects in strip run-out table cooling process are calculated directly by using the analytical model. The residual stress formed in the run-out table cooling stage of hot-rolled strip has a great influence on flatness and subsequent cutting. Based on the fiber rods model, the formation mechanism of residual stress induced by incompatible deformation caused by temperature and phase transformation is studied in this paper. Meanwhile, the present study makes a first attempt to establishing the analytical model for calculating residual stresses at different run-out table cooling stages. Moreover, in order to further investigate the relationship between residual stress and flatness defects, a strip buckling model is introduced. The traditional buckling equilibrium equation of Lagrange system is introduced into the Hamiltonian system of symplectic space, and the mathematical relationship between residual stress and strip flatness is obtained directly without assuming stress and deflection function. Then the strip flatness is calculated by using this mathematical relationship and residual stress analytical model. Furthermore, to verify the accuracy of the analytical model, a multi-field coupled finite element model based on the validation of the measured data is established. Finally, the distribution of residual stress calculated by the analytical model and the finite element model is basically consistent. The analytical model calculated that the strip would have edge wave defects during run-out table cooling, which is highly consistent with the results of finite element model. [ABSTRACT FROM AUTHOR]

• A symplectic analytical approach is proposed to study the thermal-metallurgical coupling problems. • The symplectic analytical solution of three-dimensional temperature field is derived directly. • An alternating algorithm is designed to realize the nonlinear thermal-metallurgical coupling calculation. • The symplectic approach considers both quantization mechanism and computational efficiency. • The temperature and microstructure evolution during the coil cooling process are precisely calculated. The cooling process of hot-rolled coil directly affects the mechanical and metallurgical properties of the final product. The non-uniform behavior of temperature and microstructure can easily result in sufficient residual stress to induce subsequent cutting deformation. Therefore, the focus of this study is to analyze the thermal-metallurgical coupling problem during the cooling process of hot-rolled coil. Unlike before, a symplectic analytical approach is proposed to calculate the temperature and microstructure evolution of hot-rolled coil. Firstly, the hot-rolled coil is discretized to convert the three-dimensional heat transfer problem in cylindrical coordinate system to cartesian coordinate system. Then, the traditional heat transfer model is introduced into the symplectic Hamiltonian system and the symplectic superposition method is employed to handle complex cooling boundary conditions. The symplectic analytical solution of the three-dimensional temperature field is obtained through rigorous derivation without any assumptions or predetermined solution forms. Meanwhile, an alternating algorithm is designed between the heat transfer model and the phase transformation dynamics model to realize the coupling process. Moreover, a high-precision finite element model verified by the measured data is established. The symplectic analytical solution of coil temperature and microstructure during the cooling process is in good agreement with the finite element solution. Finally, the symplectic approach has been proven to enable quantitative mathematical analysis of the coupling mechanism of thermal-metallurgical processes. [ABSTRACT FROM AUTHOR]

• A mathematical model of flatness defects accounting for lateral metal flow is proposed. • A 3D finite element model for the strip and work roll with variable roll contour was developed. • Rolling experiments in a hot rolling mill confirmed the accuracy of the simulation. • Influences of reduction rate and entry thickness of strip on flatness were investigated. • Coupling effect between crown ratio, lateral metal flow, and flatness was studied. Geometric dissimilarity between the thickness profile of the entry strip and the deformed roll gap is the main cause of flatness defects. However, the combination of the crown ratio and the lateral metal flow complicates the flatness defect mode, making it difficult to predict. A variety of rolled flatness defects may result, generally occurring as center waviness, edge waviness, M-mode waviness, and W-mode waviness. The effect of lateral metal flow on the flatness has rarely been considered or quantified in the traditional flatness model. To address this deficiency, an original mathematical model is proposed for computing the rolled flatness defects while accounting for lateral metal flow during the rolling process. The proposed analytical model was employed to compute the flatness deviations with and without lateral metal flow, and the flatness calculated results were compared with the numerical solutions provided by a three-dimensional finite element model. The influence of the lateral metal flow on the strip flatness distribution was clearly identified and explained. Finally, the effects of the reduction rate, entry thickness, and exit crown ratio on the flatness deviation and lateral metal flow are described and discussed. [ABSTRACT FROM AUTHOR]

• An analytical model of two-dimensional temperature field of strip in symplectic space Hamiltonian system is established. • Symplectic superposition method is used to deal with complex cooling boundary conditions. • Based on the basic equation, the analytical solution of two-dimensional unsteady temperature field is obtained by mathematical method. • Neglecting the latent heat of phase transformation in strip can lead to significant errors in temperature prediction. The cooling process of hot-rolled strip has an important influence on the mechanical and metallurgical properties of the final product. In particular, the uneven temperature of the hot-rolled strip in the run-out table cooling after rolling will lead to the formation of residual stress and eventually cause the flatness defects. Therefore, this study focused on the temperature distribution prediction of steel strips during run-out table cooling. For this purpose, an analytical model for calculating temperature distribution of strip width and thickness is presented. It is different from the traditional analytical models, this study introduces the two-dimensional heat conduction equation with an internal heat source under the traditional Lagrange system into the symplectic space Hamiltonian system to obtain the symplectic dual equations. Meanwhile, symplectic superposition method is used to deal with complex cooling boundary conditions. The symplectic analytical solution of the two-dimensional temperature field is calculated by strict derivation without any assumptions or predetermination of the solution forms. In order to verify the accuracy of the symplectic analytical solution, a temperature−phase transformation coupled finite element model for run-out table cooling of hot strip was established. Then the accuracy of the finite element model is verified by the measured data. Finally, it has been determined that the symplectic analytical solution exhibits a high degree of consistency with the computed results obtained from the finite element model. [ABSTRACT FROM AUTHOR]