scholarly journals Vibration Characteristics of Rolling Mill System under Constraints of the Nonlinear Spring Force and Friction Force from Hydraulic Cylinder

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Zhaolun Liu ◽  
Guixiang Pan ◽  
Jiahao Jiang ◽  
Bin Liu
Keyword(s):  
Friction Force ◽  
Rolling Mill ◽  
Period Doubling ◽  
Time History ◽  
Hydraulic Cylinder ◽  
Excitation Amplitude ◽  
System Stability ◽  
External Excitation ◽  
Nonlinear Spring ◽  
Spring Force

Considering the two kinds of nonlinear constraints of rolling mill hydraulic cylinder, spring force and friction force, the vibration model of rolling mill system is established. The amplitude frequency response equations are obtained by using the average method. Comparing the time history curves of vertical vibration displacement of rolling mill system under the nonlinear spring force and friction force, the amplitude frequency characteristic curves are simulated. The external excitation amplitude is viewed as the bifurcation parameter, and the system bifurcation response changing with the external excitation amplitude is analyzed. The influence of the external excitation amplitude on the system stability is studied. The results indicate that the increase of the nonlinear spring force makes the rolling mill system’s unstable area to become wider, and the influence on the rolling mill system of nonlinear friction force behaves as the damping characteristics; the vibration of rolling mill system is alternating between the periodic, period-doubling, and the chaotic motion. The research results provide a theoretical support for restraining the vibration of the rolling mill system in the actual production process.

scholarly journals Coupled Vibration Behavior of Hot Rolling Mill Rolls under Multinonlinear Effects

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Rongrong Peng ◽  
Xingzhong Zhang ◽  
Peiming Shi
Keyword(s):  
Hot Rolling ◽  
Rolling Mill ◽  
Hydraulic Cylinder ◽  
Excitation Amplitude ◽  
Coupled Vibration ◽  
External Excitation ◽  
Strip Surface ◽  
Coupling Vibration ◽  
Spring Force ◽  
Hot Rolling Mill

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.

Nonlinear dynamics characteristics and influence factors analysis of servo hydraulic cylinder

2017 ◽  
Vol 232 (20) ◽  
pp. 3629-3638
Author(s):  
Jun Li ◽  
Huanliang Li ◽  
Hongxin Cui ◽  
Yawei Zhu
Keyword(s):  
Friction Force ◽  
Nonlinear Dynamic ◽  
Coupling Effect ◽  
Influence Factors ◽  
Hydraulic Cylinder ◽  
Theoretical Derivation ◽  
Precise Control ◽  
Spring Force ◽  
Vibration Impact ◽  
Dynamic Simulation Model

Aiming at problems of vibration, impact, and noise, the nonlinear dynamic characteristics of servo hydraulic cylinder are studied by using combination of theoretical derivation and simulation experiment methods. The nonlinear effect rules of spring force and friction force are analyzed based on nonlinear dynamic theory; it can be derived that the coupling effect rules of nonlinear spring force and friction force can be described by Duffing–Van Der Pol equation. The dynamic simulation model of servo hydraulic cylinder is established by using SimHydraulics software. The numerical simulation and experiment results showed that nonlinear vibration of servo hydraulic cylinder is mainly caused by exciting force, spring force, and friction force; the system has different motion states when the parameters take different values, which lays a good foundation for the optimal designs and precise control of hydraulic cylinder.

scholarly journals Vertical–Horizontal Coupling Vibration of Hot Rolling Mill Rolls under Multi-Piecewise Nonlinear Constraints

Metals ◽  
2021 ◽  
Vol 11 (1) ◽  
pp. 170
Author(s):  
Rongrong Peng ◽  
Xingzhong Zhang ◽  
Peiming Shi
Keyword(s):  
Hot Rolling ◽  
Rolling Mill ◽  
Hydraulic Cylinder ◽  
Nonlinear Constraints ◽  
Nonlinear Friction ◽  
Vibration System ◽  
Coupled Vibration ◽  
Coupling Vibration ◽  
Spring Force ◽  
Hot Rolling Mill

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.

scholarly journals Analysis of the Dynamic Stiffness, Hysteresis Resonances and Complex Responses for Nonlinear Spring Systems in Power-Form Order

2021 ◽  
Vol 11 (16) ◽  
pp. 7722
Author(s):  
Qingtao Wang ◽  
Zhiyong Zhang ◽  
Yongheng Ying ◽  
Zhaojun Pang
Keyword(s):  
Normal Load ◽  
Dynamic Stiffness ◽  
Mechanical Systems ◽  
Contact Fatigue ◽  
Period Doubling ◽  
Excitation Amplitude ◽  
Hertzian Contact ◽  
Restoring Force ◽  
Nonlinear Spring ◽  
Stiffness Characteristics

Power-form nonlinear contact force models are widely adopted in relatively moving parts of macro (e.g., rolling bearings considering Hertzian contact restoring force between rolling elements and bearing raceways) or micro (e.g., the micro cantilever probe system of atomic force microscopy) scale mechanical systems, and contact resonance could cause serious problems of wear, contact fatigue, vibration, and noise, which has attracted widespread attention. In the present paper, the softening/hardening stiffness characteristics of continuous and one-sided contact power-form nonlinear spring models are addressed, respectively, by the analysis of the monotone features of resonant frequency-response skeleton lines. Herein, the period-n solution branch and its stability characteristics are obtained by the harmonic balance and alternating frequency/time domain (HB–AFT) method and Floquet theory. Compared with previous studies, this paper will furtherly clarify the influences of externally normal load, the power form exponent term, and excitation amplitude on the softening/hardening stiffness characteristics of general power-form spring systems. In addition, for a power-form system with a one-sided contact, the phenomena of primary and super/sub-harmonic hysteretic resonances inducing period-doubling, folding bifurcation, the coexistence of multiple solutions are demonstrated. Besides, it gives the evolution mechanism of two types of intermittency chaos in a one-sided contact system. The overall results may have certain basic theoretical significance and engineering values for the control of vibration and noise in contact mechanical systems.

scholarly journals Complex response analysis of a non-smooth oscillator under harmonic and random excitations

2021 ◽  
Vol 42 (5) ◽  
pp. 641-648
Author(s):  
Shichao Ma ◽  
Xin Ning ◽  
Liang Wang ◽  
Wantao Jia ◽  
Wei Xu
Keyword(s):  
Excitation Frequency ◽  
System Stability ◽  
Response Analysis ◽  
External Excitation ◽  
Stochastic Response ◽  
Impact Oscillator ◽  
Nonlinear Parameters ◽  
Bifurcation Phenomena ◽  
Mc Simulation ◽  
Smooth System

AbstractIt is well-known that practical vibro-impact systems are often influenced by random perturbations and external excitation forces, making it challenging to carry out the research of this category of complex systems with non-smooth characteristics. To address this problem, by adequately utilizing the stochastic response analysis approach and performing the stochastic response for the considered non-smooth system with the external excitation force and white noise excitation, a modified conducting process has proposed. Taking the multiple nonlinear parameters, the non-smooth parameters, and the external excitation frequency into consideration, the steady-state stochastic P-bifurcation phenomena of an elastic impact oscillator are discussed. It can be found that the system parameters can make the system stability topology change. The effectiveness of the proposed method is verified and demonstrated by the Monte Carlo (MC) simulation. Consequently, the conclusions show that the process can be applied to stochastic non-autonomous and non-smooth systems.

Two Groups of Chaotic Vibrations in a Single-Degree-of-Freedom Maglev System

1997 ◽  
Author(s):  
Zhixiang Xu ◽  
Hideyuki Tamura
Keyword(s):  
Magnetic Levitation ◽  
Excitation Frequency ◽  
Power Spectra ◽  
Period Doubling ◽  
Excitation Amplitude ◽  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Moving Base ◽  
Period Doubling Bifurcations

Abstract In this paper, a single-degree-of-freedom magnetic levitation dynamic system, whose spring is composed of a magnetic repulsive force, is numerically analyzed. The numerical results indicate that a body levitated by magnetic force shows many kinds of vibrations upon adjusting the system parameters (viz., damping, excitation amplitude and excitation frequency) when the system is excited by the harmonically moving base. For a suitable combination of parameters, an aperiodic vibration occurs after a sequence of period-doubling bifurcations. Typical aperiodic vibrations that occurred after period-doubling bifurcations from several initial states are identified as chaotic vibration and classified into two groups by examining their power spectra, Poincare maps, fractal dimension analyses, etc.

scholarly journals Nonlinear Dynamics of the Rigid Drum for Vibratory Roller on Elastic Subgrades

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Lun Liu ◽  
Fenghui Wang ◽  
Shupeng Sun ◽  
Weiming Feng ◽  
Chao Guo
Keyword(s):  
Nonlinear Dynamics ◽  
Phase Diagram ◽  
Dynamic Characteristics ◽  
Nonlinear Dynamic ◽  
Period Doubling ◽  
Time History ◽  
Nonlinear Dynamic Model ◽  
Compaction Process ◽  
Adjustment Strategy ◽  
Vibratory Compaction

In this paper, a coupling nonlinear dynamic model of the drum and subgrade is established for the vibratory roller. The dynamic characteristics of the rigid drum of the vibratory roller in the process of vibratory compaction are comprehensively investigated by time history, phase diagram, frequency spectrum, Poincare map, and bifurcation diagram. During the compaction process, the stiffness of the subgrade increases and the motion of the rigid drum of the vibratory roller changes from a single period to multiple periods and finally enters chaos by the way of period doubling. Moreover, the roller parameters also significantly affect the dynamic characteristics of the rigid drum and the compaction effect of the subgrade. Based on detailed numerical results, a parameter adjustment strategy about the roller frequency and nominal amplitude is proposed, which can avoid the “bouncing” of the drum during compaction and improve the compaction efficiency.

scholarly journals Dynamics of a Duopoly Game with Two Different Delay Structures

2017 ◽  
Vol 2017 ◽  
pp. 1-12 ◽  
Author(s):  
Shumin Jiang ◽  
Fei Xu ◽  
Zhanwen Ding ◽  
Chen Yang ◽  
Huanhuan Liu
Keyword(s):  
Time Delay ◽  
Market Price ◽  
Period Doubling ◽  
System Stability ◽  
Delayed Feedback Control ◽  
System Control ◽  
Heterogeneous Players ◽  
Cournot Game ◽  
The Stability ◽  
Time Delayed Feedback

Two different time delay structures for the dynamical Cournot game with two heterogeneous players are considered in this paper, in which a player is assumed to make decision via his marginal profit with time delay and another is assumed to adjust strategy according to the delayed price. The dynamics of both players output adjustments are analyzed and simulated. The time delay for the marginal profit has more influence on the dynamical behaviors of the system while the market price delay has less effect, and an intermediate level of the delay weight for the marginal profit can expand the stability region and thus promote the system stability. It is also shown that the system may lose stability due to either a period-doubling bifurcation or a Neimark-Sacker bifurcation. Numerical simulations show that the chaotic behaviors can be stabilized by the time-delayed feedback control, and the two different delays play different roles on the system controllability: the delay of the marginal profit has more influence on the system control than the delay of the market price.

Hydraulic Model and Simulation Analysis for Monorail Brake System

2013 ◽  
Vol 278-280 ◽  
pp. 350-353 ◽  
Author(s):  
Feng Gao ◽  
Lin Jing Xiao ◽  
Shuai Guo ◽  
Hong Gang Ma
Keyword(s):  
Hydraulic System ◽  
Simulation Analysis ◽  
Hydraulic Cylinder ◽  
Mine Safety ◽  
Brake System ◽  
Flow Area ◽  
Throttle Valve ◽  
Model And Simulation ◽  
Spring Force ◽  
Unloading Time

This paper mainly analyzes the hydraulic system principle during the monorail braking, and come to a conclusion that the spring stiffness and the throttle valve flow area are main factors affect the brake system. Then we use the MSC.EASY5 to modeling the hydraulic system, and simulate the unloading time of hydraulic cylinder under the spring force, the result shows that, the response time of a braking system can meet the requirement of the coal mine safety regulation, and change the flow area of throttle valve will affect the brake system.

scholarly journals Stability and control of planar compass gait walking with series-elastic ankle actuation

2016 ◽  
Vol 39 (3) ◽  
pp. 312-323 ◽  
Author(s):  
Deniz Kerimoğlu ◽  
Ömer Morgül ◽  
Uluç Saranli
Keyword(s):  
Equations Of Motion ◽  
Period Doubling ◽  
Basic Structure ◽  
System Stability ◽  
Gravitational Potential Energy ◽  
Extended Model ◽  
Stability And Control ◽  
Inclined Surfaces ◽  
And Control ◽  
Series Elastic

Passive dynamic walking models are capable of capturing basic properties of walking behaviours and can generate stable human-like walking without any actuation on inclined surfaces. The passive compass gait model is among the simplest of such models, consisting of a planar point mass and two stick legs. A number of different actuation methods have been proposed both for this model and its more complex extensions to eliminate the need for a sloped ground, balancing collision losses using gravitational potential energy. In this study, we introduce and investigate an extended model with series-elastic actuation at the ankle towards a similar goal, realizing stable walking on level ground. Our model seeks to capture the basic structure of how humans utilize toe push-off prior to leg liftoff, and is intended to eventually be used for controlling the ankle joint in a lower-body robotic orthosis. We derive hybrid equations of motion for this model, and show numerically through Poincaré analysis that it can achieve asymptotically stable walking on level ground for certain choices of system parameters. We then study the bifurcation regimes of period doubling with this model, leading up to chaotic walking patterns. Finally, we show that feedback control on the initial extension of the series ankle spring can be used to improve and extend system stability.

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