The extreme operating environment of the 20-high rolling mill subjects its roll system to multi-frequency external disturbances, inducing complex nonlinear vibrations. By incorporating a dynamic rolling force model under mixed lubrication conditions, a nonlinear dynamic model of the roll system under multi-frequency excitation was established. System parameters were identified by model-data integration. The results demonstrate that the steady-state rolling force calculated by this model exhibits an error of only 0.05 %-0.2 %, with a rolling force fluctuation range of +/- 0.5 kN, which is highly consistent with the experimental results. Furthermore, the rolling force fluctuation intensifies with prolonged operation. Nonlinear dynamic analysis reveals that under singlefrequency excitation, the system transitions from periodic to quasi-periodic motion via a Hopf bifurcation. Crucially, when amplitude differences are significant or frequency ratios approach rational numbers under multifrequency excitation, the system exhibits high-order frequency locking and evolves into a chaotic state via the Ruelle-Takens-Newhouse route. This study provides novel insights into the complex vibration mechanisms of the 20-high rolling mill and establishes a theoretical foundation for vibration monitoring and control technologies.

The development of parsimonious and accurate models is highly dependent on the quality of training data. To extract the underlying physical laws from noisy data, we introduce a noisecorrected data-driven approach. It begins by formulating a nonlinear sparse least-squares problem in the frequency domain, where noise correction terms and physical parameters are treated as unknowns. To solve this problem, we present a novel nested Levenberg-Marquardt (LM)Sequential Thresholded Least-Squares (STLS) approach, which inherits the strengths of LM algorithm for solving nonlinear optimization problems and the sparsity-promoting capabilities of the STLS. This approach also offers a simple and intuitive way to incorporate prior physical knowledge into the sparsification process, preventing small coefficient terms from being pruned due to excessively large thresholds. Finally, the effectiveness of the proposed approach is validated by both numerical simulations and experimental tests. The results indicate its effectiveness in extracting underlying dynamic structures from measured data, which might be corrupted not only by white noise but also by distorted streaming.

The effect of vibration on rolling equipment is an internationally recognized issue in the steel rolling industry. In this study, a negative-stiffness vibration absorber (NSVA) is applied to vibration control of roll and the influence of the NSVA parameters on the nonlinear vibration characteristics from the perspective of dynamics and vibration transmission characteristics from the perspective of the energy mechanism are investigated. Considering the nonlinearity of the rolling interface, a nonlinear two-degree-of-freedom vertical vibration model is established. The vibration displacement and velocity are obtained using the incremental harmonic balance method. The amplitude-frequency characteristic equations of the main and secondary resonances are solved using the multi-scale method. We analyze how equivalent stiffness, equivalent damping, external excitation, upper roll damping on the frame, and rolling interface stiffness/damping affect amplitude-frequency curves under different resonance conditions. Using solutions at various excitation frequencies, we study how NSVA stiffness and damping impact power flow. Results show directional power flow transfer in the roll-NSVA system can effectively control the energy loss shares in the mill via NSVA parameter adjustment. In addition, the effect of NSVA vibration suppression under different reduction rates is studied experimentally. The experimental and simulation results verify the reliability of the established model and validity of the theoretical analysis.

An explicit critical criterion for Flip-Hopf-Hopf bifurcation of discrete systems is proposed for detecting the existence of the codimension-three bifurcation. The explicit critical criteria including eigenvalue assignment, transversality condition and non-resonance condition are established based on the properties of the coefficients of characteristic polynomial equation, which is not involved with the computation of eigenvalues of the linearization matrix. The equivalence between the proposed criterion and the corresponding classical criterion is proved. The map is reduced to a five-dimensional map by the central manifold method. The expressions for the coefficients of the normal form are derived in detail to obtain the normal for corresponding to the reduced five-dimensional map. A three-degree-of-freedom vibro-impact system is taken as an example to show the effectiveness of the proposed explicit criterion and the local dynamical behaviors near bifurcation point.

The study of rolling mill vibration theory has always been a scientific frontier in the field of rolling forming, which is very important to the quality of sheet metal and the stable operation of equipment. A magnetorheological fluid damper absorber is designed to control the nonlinear vertical vibration of rolling mill. Considering the fractional order and delay factors in the control effect of magnetorheological fluid, the fractional order delay nonlinear vertical vibration equation with magnetorheological damping damper is established. The amplitude-frequency characteristic equations of the main resonance and sub-resonance of the system are solved by multi-scale method. The effects of stiffness coefficient, damping coefficient, time delay, fractional order, and exciting force on the vibration characteristics of roller system are analyzed by comparing the amplitude-frequency curve, time-domain curve and phase diagram. The transition set of the steady-state response of the system and the corresponding bifurcation topology structure are analyzed by using the singularity theory. A magnetorheological fluid damper absorber platform of rolling mill is built based on modern test technology, and the influence laws of the control threshold, control current, type of magnetorheological fluid and reduction rate are analyzed. The correctness and feasibility of the design of the magnetorheological fluid damper absorber are verified, which provided theoretical guidance and technical support for the nonlinear dynamic analysis and stability control of the rolling mill.

The vibrating flip-flow screen (VFFS) is an effective solution for screening sticky and fine materials. To improve screening efficiency, the flip-flow screen panel (FFSP) must periodically tension and relax, generating high vibration intensity (quantified by the g value). However, an excessively high g value will increase the risk of structural damage (related to its stress value). To address the conflicting of maximizing g value and minimizing stress value, this study proposes a nonlinear modeling and multi-objective optimization framework. The effectiveness of nonlinear model and their superiority over linear model have been verified through experiments. Then, a bi-objective particle swarm optimization (PSO) algorithm is employed to simultaneously optimize the structural and excitation parameters of FFSP, which yields a Pareto front. The Pareto front represents the optimal tradeoff between maximizing g value and minimizing stress value with different weights. The results are validated through numerical simulations. This work offers a practical tool for the design of FFSP, with potential applications in dry deep screening technologies.

This study proposes a parallel multi-stable nonlinear energy sink (NES) integrating triboelectric generator capabilities to simultaneously address vibration suppression and power generation. Based on a novel nonlinear restoring-force-customized structure, we developed a multi-stable oscillator with the grid structure to achieve triboelectric energy harvesting. A dynamic model of three parallel oscillators with piecewise nonlinear dry friction damping is established to investigate the vibration suppression and energy harvesting performance of the NES. Results demonstrate that the proposed NES achieves a significant vibration suppression rate of 22.40% while simultaneously attaining an energy harvesting efficiency of up to 18.4%. Crucially, the multi-stable oscillators enable high-frequency resonance capture, and demonstrate superior energy absorption rates, dissipation efficiency, and harvesting performance, compared to single-stable systems. The parallel connection of mono-stable, bi-stable, and tri-stable oscillators exhibits a unique complementary resonance capture mechanism, enabling 1:1, 1:2, 1:3, 2:3, and 2:4 resonances. In addition, the multi-stable oscillators generate high-frequency alternating current (AC). Experimental validation on a manufactured prototype confirms a 20.61% vibration suppression rate and an output voltage with a peak-to-peak value of 2.4 V. This work represents the firstinte-gration of triboelectric energy harvesting within multi-stable NES, offering a compact dual-functional solution for vibration suppression and energy harvesting.

Precision ultra-thin strips with high precision, corrosion resistance, excellent surface finish and other properties are widely used in micro-manufacturing, microelectronics, and other high-tech fields. The vibration characteristics of twenty-high rolling mills significantly affect the surface quality of extremely thin strips. In this study, a coupled nonlinear dynamic model of a twenty-high rolling mill with linear damping and nonlinear stiffness between the roll and strip was established. The amplitude-frequency equations of the main, super-harmonic and sub-harmonic resonances, and internal resonances were obtained using the multi-scale method. The influence of different parameters on the amplitude-frequency curves was analyzed. According to Lyapunov's first approximation stability criterion, the stability of the roll system was analyzed using a moving phase plane phase trajectory diagram. A tuned mass damper was designed to control the nonlinear vibration characteristics of the twenty-high rolling mill, and a coupling dynamics model between the tuned mass damper and the roll system was established. The influences of the mass, stiffness, and damping ratios on the dynamic magnification coefficient of the roll were analyzed. To minimize the peak value of the dynamic amplification coefficient, an adaptive genetic algorithm was used to optimize the parameters of the tuned mass damper, and the optimal mass, stiffness, and damping ratios were determined. Finally, the feasibility and effectiveness of the tuned-mass damper were verified using time-domain, phase, and Poincare section diagrams, which provide an important reference values and theoretical basis for the design and analysis of the roll system for the twenty-high rolling mill.

Complex nonlinear factors exist in the rolling interface of the mill, resulting in a rich nonlinear dynamic behavior of the roll system. Accurate dynamic model and parameters are the prerequisite for correctly analyzing the vibration characteristics of the roll system. In this paper, the influence of roll vibration on the friction state of rolling deformation zone is considered, and the dynamic rolling force model under the influence of variable friction factors is established. The vertical-horizontal coupling nonlinear dynamic model of the roll system under the action of dynamic rolling force is further established for the electric press-down mill, in which the tilting of the press-down stud caused by vibration is taken into account. The roll vibration acceleration signals are collected through experiments, and the equivalent stiffness, equivalent damping, dynamic change of rolling force and external disturbance force in the model are identified by extended Kalman filtering algorithm. The identification results are verified by the experimental data of dynamic rolling force. Based on the identification results, the 6th order sinusoidal approximation functions of the external disturbance forces are established. The effects of parameters on the amplitude-frequency characteristics of 2nd super-harmonic resonance, 1/2 sub- harmonic resonance, and the combined resonance of the roll under multi-frequency excitation are analyzed. The findings of this study can provide theoretical guidance for mill parameters design and rolling process selection to improve the stability of the mill.

This study discusses the resonance, bifurcation, and chaotic motion of a class of fractional order high power damped dissipative systems. By combining multi-scale methods with averaging methods, the amplitude frequency relationship expressions of the steady-state response of the system under linear viscous damping, square damping, cubic damping, and fourth power damping were derived. The existence and stability of fixed points in the mean equation, which correspond to non-trivial periodic solutions of the original system, are studied. For the studied system, only additive combination parameter resonance is possible. The Melnikov theory for high power damping systems of the n -th power has been extended to decouple complex systems, and the conditions for the existence of homoclinic/heteroclinic bifurcations have been obtained through approximating the time variable and Fourier transform. We have studied the period doubling bifurcation caused by external excitation amplitude changes to understand the chaotic high-power system potential behavior exhibited by the extended Duffing oscillator under parameter excitation. In addition, the safety basin exhibiting fractal patterns was analyzed by us, and the chaotic behavior of the system was verified through the analysis.

This article establishes a two degree of freedom asymmetric Duffing system model with fractional damping through the study of the Jeffcott rotor system with horizontal support, and analyzes the dynamic behavior of its resonance and attraction domain structures. The second-order approximate solution of the system equation is obtained using a multiscale method, and the slow flow modulation equations of both the amplitudes and phases are extracted. The comparison between approximate and numerical solutions has shown their high consistency and the Routh Hurwitz criterion is utilized to study the stability of the system. Finally, we explore the effect of fractional damping on the vibration behavior of the system using amplitude frequency curves, attractive watersheds, and time trajectory plots, including both negative and positive values of the nonlinear stiffness coefficient. The analysis shows that if the coefficient and order of the fractional damping term are reasonably selected, the horizontal and vertical displacements of the system vibration can be effectively controlled. The importance of this work lies in its application in rotor vibration, which has significant implications for the study of the system under investigation.

The acoustic field calculation model of ultrasonic vibration-mixed cement slurry is established to investigate the preparation and optimization process of the slurry as well as to study the dispersion mechanism of cement particles under the action of ultrasound. The acoustic field distribution of freshly mixed cement slurry in various mixer structures at 20 kHz is calculated by using Finite Element Method (FEM) in conjunction with multi-physical field simulation. The sound field is radially spread and produces a standing wave field with sound pressure amplitude amplified close to the wall. Average sound pressure and ultrasonic effect distance at the mid-axis likewise increase as the outer diameter of the mixer bottom plate increases, and so are the positive and negative sound pressure limits in the cement slurry. The movement of cavitation bubbles can be intensified by ultrasound with a larger acoustic pressure amplitude, hence promoting the ultrasonic cavitation effect. This can be accomplished by solving the Rayleigh–Plesset equation to determine the change rule of cavitation bubbles under the effect of different acoustic pressures. The results show that the narrow space adjacent to the wall and the bottom center of the mixer arch region are the locations of the cavitation effect's core zone when the cavitation numerical simulation is utilized in conjunction with the acoustic field calculation, and the center section is lower in vertical height than the core zone along the wall. Lastly, the simulation results were verified using laser vibrometer combined with acoustic-structural coupling relations.

The paper presents a topology optimization methodology for 2D elastodynamic problems using the boundary element method (BEM). The topological derivative is derived based on the variation method and the adjoint variable method. The level set method is employed for the representation of the material domain and voids within a specified design domain. Thus, the boundaries can easily be generated, following the zero isocontour of the level set function. Numerical implementation is carried out to demonstrate the effectiveness of the proposed topology optimization methodology in wave isolation and waveguide problems.

The various forms of coupled and nonlinear vibrations generated by the rolling mill during the plate or strip rolling process restrict the high-speed, efficient, and continuous rolling production, which is an urgent problem to be solved in the field of plate or strip rolling. This paper designs a spring-damping dynamic vibration absorber for suppressing rolling mill vibration based on the work roll structure and working characteristics of the rolling mill. A four-degree-of-freedom horizontal and vertical coupled vibration model with piecewise function form is established through considering the gap between the bearing seat of work roller and mill housing. The parameters of the absorber are optimized by using adaptive genetic algorithm, and the effect of the absorber on system vibration under the optimal parameters is analyzed. The amplitude frequency characteristic equations of the primary resonance and internal resonance of the system are obtained by using the average method and multi-scale method respectively. The influence of the parameters of the dynamic vibration absorber on vibration is analyzed. A horizontal and vertical vibration control experiment is conducted on the work roll of the rolling mill. The results show that the dynamic vibration absorber can effectively suppress the horizontal and vertical vibration of the roll, and the difference in amplitude reduction between experimental and theoretical analysis is within 5 %, which verifies the effectiveness of the designed dynamic vibration absorber. These results provide some guidance for the research on vibration suppression of rolling mills.

The research of rolling mill vibration theory has always been a scientific problem in the field of rolling forming, which is very important to the quality of sheet metal and the stable operation of equipment. The essence of rolling mill vibration is the transfer of energy, which is generated from inside and outside. Based on particle damping technology, a dynamic vibration absorber (DVA) is proposed to control the vertical vibration of roll in the rolling process from the point of energy transfer and dissipation. A nonlinear vibration equation for the DVA-roller system is solved by the incremental harmonic balance method. Based on the obtained solutions, the effects of the basic parameters of the DVA on the properties of vibration transmission are investigated by using the power flow method, which provides theoretical guidance for the selection of the basic parameters of the DVA. Furthermore, the influence of the parameters of the particles on the overall dissipation of energy of the particle group is analyzed in a more systematic way, which provides a reference for the selection of the material and diameter and other parameters of the particles in the practical application of the DVA. The effect of particle parameters on roll amplitude inhibition is studied by experiments. The experimental results agree with the theoretical analysis, which proves the correctness of the theoretical analysis and the feasibility of the particle damping absorber. This research proposes a particle damping absorber to absorb and dissipate the energy transfer in rolling process, which provides a new idea for nonlinear dynamic analysis and stability control of rolling mills, and has important guiding significance for practical production.

In this paper, we mainly study the bifurcation and resonance of under-damped Duffing systems with fractional order delay and fractional order under-damped Duffing systems with linear delay. Based on the separation method of fast and slow variables, the high-frequency excitation components in the system are eliminated, and the equivalent system of slow variables is obtained. For the under-damped Duffing system with fractional delay term, the harmonic balance method is used to solve the amplitude and phase analytic solution of the slow variable system, and for the under-damped fractional Duffing system with linear delay term, the average method is used to solve the amplitude and phase analytic solution of the slow variable system. Then the resonance and bifurcation of bistable and monostable systems with different parameters are analyzed. In the last section of this paper, numerical simulation is carried out to study the influence of fractional order, control parameters, delay quantity and other factors on the two systems, and the correctness of the analytical analysis is verified by comparing the numerical simulation results.

The vibration of rolling mill in rolling process and its harm to rolling equipment have become an international problem in steel rolling industry. The essence of the vibration behavior of a mechanical structure is the transfer of energy in the system. In this work, for a proposed particle damped absorber (PDA) applied to roll vibration control, the influences of the PDA parameters on the vibration transmission characteristics of the system and the energy consumption characteristics of particle groups are studied from the standpoint of energy mechanism. Considering the nonlinearity of rolling interface and particle impact, a non-smooth four-degree-of-freedom vertical vibration model is established. The vibration displacement and velocity of the system are obtained by the incremental harmonic balance method (IHBM). The influence laws of the stiffness coefficients and damping coefficients in the PDA on the power flow are investigated according to the solutions of the system at different excitation frequencies. The effects of particle parameters on the energy consumption behavior of the particle groups are investigated to reveal the energy dissipation mechanism of PDA by using PFC3D software. The results show that the power flow transfer in Roll-PDA system has the targeting performance. This means that the energy loss share of each mechanism in the PDA can be effectively controlled by adjusting the parameters of the PDA. The energy consumption of the particle group increases in step form, which is more obvious in the case of low frequency vibration. In addition, the effects of particle material, particle size, filling rate and particle mixing on vibration suppression of PDA are investigated by experiments. The experimental results are compared with the simulation results to verify the reliability of the established model and the validity of the theoretical analysis. The findings of this study can provide insight into the selection of parameters for PDAs applied to different excitation frequencies.

The chaos and subharmonic bifurcation of a cantilever beam supported by oblique springs under bilateral asymmetric rigid constraints are investigated in this paper. It is difficult to investigate analytically the chaos and subharmonic bifurcation of the system because the stiffness term of the oblique spring support structure is a transcendental function. Firstly, the stiffness term of the system is fitted by the approximation method, and the homoclinic orbit and its internal orbits of the approximate system are compared with the orbits of the original system. Secondly, the threshold conditions for subharmonic bifurcation and homoclinic chaos are presented by applying the Melnikov method to the non-smooth impacting cantilever beam system. Moreover, the stability of impacting orbits is analyzed by combining characteristic multipliers of smooth manifolds with impact function, and the relationship between subharmonic bifurcation and chaos is investigated. Finally, the effects of damping, excitation frequency, excitation amplitude and impact coefficient of restitution on chaos and subharmonic bifurcation are investigated based on threshold conditions, which further verifies the theoretical analysis.

轧机振动理论的研究一直是轧制成形领域的前沿科学问题,对板材的质量和设备的稳定运行至关重要.随着轧制复合成形技术的快速发展,波纹辊轧机作为一种具有特殊辊型的设备,在复合板制备上具有细化晶粒、改善板形、提高结合强度等突出优点,逐渐成为当前的研究热点,但是复杂辊型曲线所诱发的轧制力动态变化对轧机的稳定性控制提出了新的挑战.为了对波纹辊轧机的非线性垂振进行合理的控制,建立了考虑波平辊系之间的非线性刚度、波纹界面非线性阻尼和轧制力动态波动的非线性垂振方程,通过分岔图、最大Lyapunov指数、相轨迹和Poincare截面分析了轧制力的动态变化对系统稳定性的影响,发现轧制力的动态变化诱发系统产生了复杂的动力学行为.设计了一种颗粒阻尼吸振器对波纹辊轧机非线性垂振进行控制,运用多尺度法求解得到了安装颗粒阻尼吸振器系统的幅频特性曲线方程,分析了钢珠颗粒群质量、吸振器刚度系数、阻尼系数以及质量比对幅频特性曲线的影响,通过数值仿真研究了颗粒阻尼吸振器对非线性垂振的控制效果.最后,通过试验验证了颗粒阻尼吸振器设计的正确性和可行性,缩短动态过程调整时间的同时也减小了系统的振幅,为波纹辊轧机非线性动力学分析及稳定性控制提供理论指导和技术支持.

A variable mass tuned particle absorber is designed for the nonlinear vertical vibration control of the corrugated rolling mill in the composite plate rolling process. Considering the nonlinear damping and nonlinear stiffness between the corrugated interface, a three-degree-of-freedom nonlinear vertical vibration mathematical model of corrugated rolling mill based on dynamic vibration absorber control is established. The multi-scale method is used to solve the amplitude–frequency characteristic curve equation of the installed dynamic vibration absorber (DVA) system. The effects of stiffness coefficient and damping coefficient on the amplitude–frequency characteristic curve are analyzed. The expressions of the dynamic developed factor of the corrugated roll are derived, and the influence laws of mass ratio, frequency ratio and damping ratio on the dynamic amplification factor are analyzed. The optimal parameters of the DVA are obtained by adaptive genetic algorithm. The control effect of the DVA on the nonlinear vertical vibration is studied by numerical simulation. The feasibility of the designed dynamic absorber is verified through experiments. The results show that the designed dynamic absorber can effectively suppress the vertical vibration of the corrugated roller.