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Vertical rolling is an important technique used to control the width of continuous casting slabs in the hot-rolling field. Accurate prediction of vertical rolling force is a core point maintaining rolling-mill equipment. Owing to the limitation of the algorithm in use, the prediction accuracy of most vertical rolling force models based on the energy method can only reach more than 10%. Therefore, it is challenging to optimize the rolling-force model to improve prediction accuracy. An innovative approach for optimizing the calculation of vertical rolling force with a unified yield criterion is presented in this paper. First, the maximal width of a dog-bone region is determined by the slip-line method, and the dog-bone shape is described using a sine-function model. Second, the velocity and corresponding strain-rate fields satisfying kinematically admissible conditions are proposed to calculate the total power of the vertical rolling process. Finally, the analytical solution of the rolling force and the dog-bone-shape model is obtained by repeatedly optimizing the weighted coefficient b of intermediate principal shear stress on the yield criterion. Moreover, the effectiveness of the proposed mechanical model is verified by measured data in the strip hot-rolling field and other models' results. Results show that the prediction accuracy of the vertical rolling force model can be improved by optimizing the value of b. Then, the impacts of reduction rate, initial thickness, and friction factor on dog-bone shape size and vertical rolling force are discussed. [ABSTRACT FROM AUTHOR]

To study the transverse temperature uniformity with transverse flux induction heating (TFIH) during endless strip production (ESP) rolling, a coupled electromagnetic-thermal finite element model of transverse flux induction heating is established. The initial temperature distribution at the TFIH inlet is taken into consideration, which is the basis of subsequent numerical studies. Magnetic screens are designed to weaken the influence of edge overheating, and the influence of magnetic shielding amounts on temperature uniformity is discussed. Moreover, an evaluation criterion is provided to determine the temperature uniformity. Furthermore, the effect of different shielding amounts on the edge temperature is studied. An ideal temperature distribution at the TFIH outlet is obtained based on a model combining various shielding amounts, and the temperature standard deviation of this method is 2.01% lower than the traditional arrangement of magnetic shielding amounts. Actual data are collected to verify the results of the proposed model. The temperature deviation between the middle and edge is approximately 12°C, and the temperature uniformity is enhanced with the optimized combination of magnetic shielding amounts. [ABSTRACT FROM AUTHOR]

A parabolic velocity field is proposed to get the minimum required rolling force in hot rolling process, the equal area yield criterion is used to calculate the plastic deformation power, the collinear vector inner product method is used to get friction power, the analytical equation of strip rolling power functional is obtained, and the required rolling force was calculated by minimizing the power functional. Meanwhile, the location of neutral point, shape factor, and stress state coefficient are discussed. The accuracy of the proposed theoretical model is examined through comparing with the experimental measured ones and online measured ones, it shows good agreement, the relative error of rolling force is less than 9.1%, and the proposed model is considered to be effective in hot tandem rolling process. [ABSTRACT FROM AUTHOR]

The flatness control system of cold-rolled strip is characterized by nonlinearity, strong coupling, and multivariable features. Theoretical models of flatness derived from physical mechanisms of the rolling process are intricate. This complexity makes it challenging to establish an accurate control model. Reinforcement learning (RL) is a machine learning method that uses an intelligent agent to learn from data interacting with its environment. In this study, considering the large quantity of historical data generated by the strip steel control system, we used the RL method to analyze the data offline in order to train a data-driven controller. We combined it with ensemble learning to propose a novel method for flatness control based on ensemble deep reinforcement learning (EDRL). Initially, we constructed a state space model for the cold-rolled flatness utilizing historical production data. This model served as the environment for offline RL training. We present an EDRL-based flatness control method that incorporates the principles of ensemble learning. Ensemble learning amalgamates multiple individual models to achieve superior performances. In the online simulation of rolling production, the EDRL-controlled flatness value was less than 5 (I-Unit) IU from the target flatness value, exceeding the performance of the proportional–integral (PI) controller. The proposed method surpassed the conventional approach in terms of both robustness and its capability to regulate flatness. • An EDRL control strategy is proposed for the cold rolling flatness control problem. • The integration strategy effectively improves the convergence speed of flatness. • The proposed control strategy outperforms state-of-the-art PI controllers. • The proposed integrated strategy exhibits robust stability in industrial scenarios. [ABSTRACT FROM AUTHOR]

• Adjustments of flatness actuators can be determined through overall modeling. • The improved interior penalty function method is efficient for global optimization. • Optimal allocation of actuator adjustments can be achieved between sub-systems. • Double-layer optimization based control strategy can achieve optimal flatness control. The flatness control system consists of two subsystems. One is the feedback control subsystem which is used to implement the closed-loop flatness control. Another is usually referred to as feedforward control subsystem in the field of strip flatness control. To realize the cooperative control of roll bending between two subsystems, a feedforward-–feedback coordination control strategy based on double-layer optimization is proposed to obtain the optimal adjustments of actuators. Firstly, a global optimization model of actuator adjustment is established by the overall modeling, and an improved interior penalty function method is developed and utilized to solve this model subsequently. On this basis, an optimal allocation model is proposed to achieve a global optimal allocation of actuator adjustments between feedforward control and feedback control. Numerical experiments and applications show that this new control strategy and the corresponding models are effective in the flatness control process of cold rolling mill. [ABSTRACT FROM AUTHOR]

Mill chatter is a major restriction in the high-speed rolling of high-strength and thin strips. To maintain mill stability, the friction coefficient must be kept within a certain range. Unfortunately, there is no model to calculate the lower limit of the friction. In this paper, a new model is developed to capture the minimum friction coefficient. This model is proposed based on mixed lubrication theory and monotonicity analysis in the friction curve. The verification results showed that the established model could accurately predict the minimum friction and the friction balance in tandem rolling mills. The model was utilized to design the optimal rolling conditions to expand the stability range of the friction and improve mill vibration stability. [Display omitted] • A mathematical model is proposed to predict the lower limit friction coefficient. • The model is proposed by monotonicity analysis based on mixed lubrication theory. • The model is validated to be accurate by previous literature and actual rolling test. • The optimization of the rolling condition is designed to increase mill vibration rolling stability. [ABSTRACT FROM AUTHOR]

The friction characteristics of rolling interface play a considerable role in rolling stability. In this work, vertical vibration speed is introduced into the Kármán equation. An unsteady lubrication model considering entraining and squeezing effect is proposed. Additionally, a dynamic chatter model is developed by coupling the improved rolling force and unsteady lubrication model. The verification results at the micro- and macro-scales indicate that this chatter model has high accuracy. The effects of main process parameters, such as reduction, back tension and viscosity, on the mill stability were analyzed. Moreover, the changes in parameters and tribological characteristics due to unstable rolling process were investigated. The work concludes that the rapid change of lubrication state and friction stress result in vibration intensification. Image 1 • Developed rolling force model considering vertical vibration speed is proposed. • Friction model that reflects lubrication state during unsteady rolling is obtained. • Natural frequency of the system slightly decreases with rolling speed increasing. • Lubrication state changes tremendously with time during unsteady rolling. • The decrease of average friction power leads to vibration more easily. [ABSTRACT FROM AUTHOR]