This study establishes a vertical–horizontal coupling vibration model of hot rolling mill rolls under multi-piecewise nonlinear constraints considering the piecewise nonlinear spring force and piecewise nonlinear friction force constraints of the hydraulic cylinder in the vertical direction of the rolls, the piecewise stiffness constraints in the horizontal direction, and the influence of the nonlinear dynamic rolling force in the rolling process. Using the average method to solve the amplitude–frequency response equation of the coupled vibration system and taking the actual parameters of a 1780 mm hot rolling mill (Chengde Steel Co., Ltd., Chengde, China) as an example, we study the amplitude–frequency characteristics of the mill rolls under different parameter settings. The results show that the amplitude and resonance region can be reduced by appropriately reducing the external disturbance force and the nonlinear spring force of the hydraulic cylinder, appropriately increasing the nonlinear friction force, and eliminating the gap between the bearing seat and the mill housing, to avoid the amplitude jump phenomenon due to piecewise variation. Furthermore, using the singularity theory to study the static bifurcation characteristics of the coupled vibration system, we establish a relationship between the vibration parameters and the topological bifurcation solution of the coupled system. The transition sets and their corresponding bifurcation topological structure in three cases are given, and the steady and unsteady process parameter regions of the rolls are obtained. The dynamic behavior of the coupled vibration system can be controlled by varying the bifurcation parameter. This study provides a theoretical basis for restraining the vibration of hot rolling mill rolls and optimizing the process parameters.

Based on the analysis of the influence of roll vibration on the elastoplastic deformation state of a workpiece in a rolling process, a dynamic rolling force model with the hysteresis effect is established. Taking the rolling parameters of a 1780 mm hot rolling mill as an example, we analyzed the hysteresis between the dynamic rolling force and the roll vibration displacement by varying the rolling speed, roll radius, entry thickness, front tension, back tension, and strip width. Under the effect of the dynamic rolling force and considering the nonlinear effect between the backup and work rolls as well as the structural constraints on the rolling mill, a hysteretic nonlinear vertical vibration model of a four-high hot rolling mill was established. The amplitude-frequency equations corresponding to 1/2 subharmonic resonance and 1:1 internal resonance of the rolling mill rolls were obtained using a multi-scale approximation method. The amplitude-frequency characteristics of the rolling mill vibration system with different parameters were studied through a numerical simulation. The parametric stiffness and nonlinear stiffness corresponding to the dynamic rolling force were found to have a significant influence on the amplitude of the subharmonic resonance system, the bending degree of the vibration curve, and the size of the resonance region. Moreover, with the change in the parametric stiffness, the internal resonance exhibited an evident jump phenomenon. Finally, the chaotic characteristics of the rolling mill vibration system were studied, and the dynamic behavior of the vibration system was analyzed and verified using a bifurcation diagram, maximum Lyapunov exponent, phase trajectory, and Poincare section. Our research provides a theoretical reference for eliminating and suppressing the chatter in rolling mills subjected to an elastoplastic hysteresis deformation.

Given the complexity of the operating conditions of rolling bearings in the actual rolling process of a hot mill and the difficulty in collecting data pertinent to fault bearings comprehensively, this paper proposes an approach that diagnoses the faults of a rolling mill bearing by employing the improved sparrow search algorithm deep belief network (ISAA-DBN) with limited data samples. First, the fast spectral kurtosis approach is adopted to convert the non-stationary original vibration signals collected by the acceleration sensors installed at the axial and radial ends of the rolling mill bearings into two-dimensional (2D) spectral kurtosis time–frequency images with higher feature recognition, and the principal component analysis (PCA) technique is used to decrease the dimension of the data in order to achieve a high diagnosis rate with a limited number of samples. Subsequently, the sparrow search algorithm (SSA) is used to realize the intelligent optimized self-adaptive function of a deep belief network (DBN). Furthermore, the firefly disturbance algorithm is employed to improve the spatial search capability and robustness of SSA-DBN in order to achieve better performance of the ISSA-DBN method. Finally, the proposed approach is experimentally compared to other approaches used for diagnosis. The results show that the proposed approach not only retains the useful features of the data through dimension reduction but also improves the efficiency of the diagnosis and achieves the highest diagnosis accuracy with limited data samples. In addition, the optimal position of the sensor for diagnosing rolling mill roll faults is identified.

The multi-process manufacturing of steel rolling products requires the cooperation of complicated and variable rolling conditions. Such conditions pose challenges to the fault diagnosis of the key equipment of the rolling mill. The development of transfer learning has alleviated the problem of fault diagnosis under variable working conditions to a certain extent. However, existing diagnosis methods based on transfer learning only consider the distribution alignment from a single representation, which may only transfer part of the state knowledge and generate fuzzy decision boundaries. Therefore, this paper proposes a multi-representation domain adaptation network with duplex adversarial learning for hot rolling mill fault diagnosis. First, a multi-representation network structure is designed to extract rolling mill equipment status information from multiple perspectives. Then, the domain adversarial strategy is adopted to match the source and target domains of each pair of representations for learning domain-invariant features from multiple representation networks. In addition, the maximum classifier discrepancy adversarial algorithm is adopted to generate target features that are close to the source support, thereby forming a robust decision boundary. Finally, the average value of the predicted probabilities of the two classifiers is used as the final diagnostic result. Extensive experiments are conducted on an experimental platform of a four-high hot rolling mill to collect the fault state data of the reduction gearbox and roll bearing. The experimental results reveal that the method can effectively realize the fault diagnosis of rolling mill equipment under variable working conditions and can achieve average diagnostic rates of up to 99.15% and 99.40% on the data sets of the rolling mill gearbox and bearing, which are respectively 2.19% and 1.93% higher than the rates achieved by the most competitive method.

A coupled vibration model of hot rolling mill rolls under multiple nonlinear effects is established by considering the nonlinear spring force produced by the hydraulic cylinder, the nonlinear friction between the work rolls, the dynamic variation of rolling force, and the effect of external excitation as well as according to the structural constraints of a four-high hot rolling mill in the vertical and horizontal directions. The amplitude-frequency response equation of rolling mill rolls is determined by using a multiple-scale approximation method. Furthermore, use of actual data for simulation indicates that the internal resonance is the main cause of coupling vibration of the rolling mill rolls. In addition, changes in the movement displacement of the hydraulic cylinder and the coupling parameters strongly affect the coupling system of the rolling mill rolls. Finally, the study of the dynamic bifurcation characteristics of the rolling mill rolls indicates that, with varying external excitation amplitude, the vibration of rolls alternates between periodic motion, period-doubling motion, and chaotic motion in both vertical and horizontal directions. This is one of the reasons for the appearance of periodic light and dark stripes on the strip surface. Furthermore, the range of the external excitation amplitude (F₀) at which the rolling mill roll system vibrates violently, that is, 5.68e5 N < F₀ < 5.84e5 N and F₀ > 6.12e5 N, must be avoided. The research results can provide a theoretical reference for further exploration of the coupling vibration mechanism of hot rolling mills.