Stability and synchronous characteristics of a two exciters vibration system considering material motion

2021 ◽  
pp. 146441932110561
Author(s):  
Yongjun Hou ◽  
Guang Xiong ◽  
Pan Fang ◽  
Mingjun Du ◽  
Yuwen Wang
Keyword(s):  
Phase Difference ◽  
Abrupt Change ◽  
Vibration System ◽  
Mass Ratio ◽  
Chaotic State ◽  
Lagrange Principle ◽  
Frequency Responses ◽  
Stable Periodic ◽  
Numerical Simulation Methods ◽  
The Stability

Nowadays, two exciters vibration system played an indispensable role in a majority of machinery and devices, such as vibratory feeder, vibrating screen, vibration conveyer, vibrating crusher, and so on. The stability of the system and the synchronous characteristics of two exciters are affected by material motion. However, those effects of material on two exciters vibration system were studied very little. Based on the special background, a mechanical model that two exciters vibration system considering material motion is proposed. Firstly, the system's dynamic equations are solved by using Lagrange principle and Newton's second law. Then, the motion stability of the system when material with different mass move on the vibrating body is analyzed by [Formula: see text] mapping and numerical simulation methods, and the motion forms of the material are also studied. Meanwhile, the frequency responses of the vibrating body are analyzed. Finally, the influence of material on the phase difference of the two exciters is revealed. It can be concluded that with the mass ratio of the material to the vibrating body increasing, the system's motion evolves from stable periodic motion to chaotic state, the synchronization ability of two exciters decline, and the unpredictability of abrupt change about the phase difference increases. Further, the uncertainties of both the abrupt change of phase difference and the collision location affect each other and eventually lead to the instability of the system.

scholarly journals Analysis of harmonic vibration synchronization for a nonlinear vibrating system with hysteresis force

2019 ◽  
Vol 39 (4) ◽  
pp. 1087-1101
Author(s):  
Nan Zhang ◽  
Shiling Wu
Keyword(s):  
Nonlinear Vibration ◽  
Phase Difference ◽  
Nonlinear Dynamic ◽  
Dynamic Models ◽  
Harmonic Vibration ◽  
Vibration System ◽  
The Difference ◽  
Nonlinear Dynamic Models ◽  
The Stability ◽  
Nonlinear Vibration System

Harmonic vibration synchronization of the two excited motors is an important factor affecting the performance of the nonlinear vibration system driven by the two excited motors. From the point of view of the hysteresis force, the nonlinear dynamic models of the nonlinear vibration system driven by the two excited motors are presented for the analysis of the hysteresis force with the asymmetry. An approximate periodic solution for the nonlinear vibration system with the hysteresis force is investigated using the nonlinear models. The condition of harmonic vibration synchronization is theoretically analyzed using the rotor–rotation equations of the two excited motors in the nonlinear dynamic models and the stability condition of harmonic vibration synchronization also is theoretically analyzed using Jacobi matrix of the phase difference equation of two excited motors. Using Matlab/Simlink, harmonic vibration synchronization of the two excited motors and the stability of harmonic vibration synchronization for the nonlinear vibration system with the hysteresis force are analyzed through the selected parameters. Various synchronous processes of the nonlinear vibration system with the hysteresis force are obtained through the difference rates of the two excited motors (including the initial phase difference, the initial rotational speed difference, the difference of the motors parameters). It has been shown that the research results can provide theoretical basis for the design and research of the vibration system driven by the two-excited motors.

Research on the Theories of Self-Synchronization of Dual Mass for Vibrating System with Two-Motor Drives

2013 ◽  
Vol 300-301 ◽  
pp. 928-931
Author(s):  
Duo Yang ◽  
Ye Li ◽  
He Li ◽  
Bang Chun Wen
Keyword(s):  
Average Method ◽  
Motor Drives ◽  
The Self ◽  
Vibration System ◽  
Mass Ratio ◽  
Vibration Model ◽  
Coupling Equations ◽  
Synchronous Operation ◽  
The Stability ◽  
Synchronization Theory

A vibration model is proposed and analyzed dynamically to study the self-synchronization theory of dual-mass vibration system. The differential equations of systematic motion are derived by applying Lagrange’s equations. Two uncertain parameters are introduced to derive the coupling equations of angular velocity of the two exciters. The conditions of synchronous implementation and stability are derived by utilizing the modified small parameter average method treated as non-dimension to the parameters. The swing of the vibration model plays a major role in the self-synchronization of two motors. The mass ratio of two eccentric blocks has an effect on the stability of synchronous operation.

On the Stability of the Linearly Related Modes of Certain Nonlinear Two-Degree-of-Freedom Systems

1961 ◽  
Vol 28 (1) ◽  
pp. 71-77 ◽  
Author(s):  
C. P. Atkinson
Keyword(s):  
Nonlinear Differential Equations ◽  
Mass Ratio ◽  
Positive Mass ◽  
Fourth Degree ◽  
Real Roots ◽  
General Stability ◽  
The Stability ◽  
The Masses ◽  
Spring Constants ◽  
Two Degree Of Freedom

This paper presents a method for analyzing a pair of coupled nonlinear differential equations of the Duffing type in order to determine whether linearly related modal oscillations of the system are possible. The system has two masses, a coupling spring and two anchor springs. For the systems studied, the anchor springs are symmetric but the masses are not. The method requires the solution of a polynomial of fourth degree which reduces to a quadratic because of the symmetric springs. The roots are a function of the spring constants. When a particular set of spring constants is chosen, roots can be found which are then used to set the necessary mass ratio for linear modal oscillations. Limits on the ranges of spring-constant ratios for real roots and positive-mass ratios are given. A general stability analysis is presented with expressions for the stability in terms of the spring constants and masses. Two specific examples are given.

Study on Self-Excited Vibration Mechanism of Wheel-Rail Lateral Contact System

2013 ◽  
Vol 427-429 ◽  
pp. 257-261
Author(s):  
Li Xia Sun ◽  
Jian Wei Yao ◽  
Fu Guo Hou ◽  
Xin Zhao
Keyword(s):  
Feedback Mechanism ◽  
Point Of View ◽  
Contact System ◽  
Vibration System ◽  
Lateral Contact ◽  
System A ◽  
Vibration Model ◽  
Excited Vibration ◽  
Vibration Mechanism ◽  
The Stability

In order to investigate self-excited vibration mechanism of wheel-rail lateral contact system, a two DOF elasticity position wheelset lateral vibration model is established which considers the dry friction; the mechanism of the wheelset lateral self-excited vibration is investigated from the energy point of view. It shows that: the bifurcation diagram of this wheel-rail lateral contact system has a supercritical Hopf bifurcation. The energy of self-excited vibration derives from a part of traction energy; the creep rate in the wheel-rail system act as a feedback mechanism in the wheelset lateral self-excited vibration system. The stability of the wheelset self-excited vibration system depends mainly on the total energy removed from and imported into the system.

Hopf Bifurcation Induced by Delay Effect in a Diffusive Tumor-Immune System

2018 ◽  
Vol 28 (11) ◽  
pp. 1850136 ◽  
Author(s):  
Ben Niu ◽  
Yuxiao Guo ◽  
Yanfei Du
Keyword(s):  
Immune System ◽  
Hopf Bifurcation ◽  
Periodic Solutions ◽  
Center Manifold ◽  
Immune Cell ◽  
Tumor Treatment ◽  
Delay Effect ◽  
Stable Periodic ◽  
The Stability ◽  
Bifurcation And Stability

Tumor-immune interaction plays an important role in the tumor treatment. We analyze the stability of steady states in a diffusive tumor-immune model with response and proliferation delay [Formula: see text] of immune system where the immune cell has a probability [Formula: see text] in killing tumor cells. We find increasing time delay [Formula: see text] destabilizes the positive steady state and induces Hopf bifurcations. The criticality of Hopf bifurcation is investigated by deriving normal forms on the center manifold, then the direction of bifurcation and stability of bifurcating periodic solutions are determined. Using a group of parameters to simulate the system, stable periodic solutions are found near the Hopf bifurcation. The effect of killing probability [Formula: see text] on Hopf bifurcation values is also discussed.

Synchronization Analysis of the Double Exciting Motors in Nonlinear Vibration System Based on Reaching Law

2011 ◽  
Vol 295-297 ◽  
pp. 2197-2200
Author(s):  
Xiao Hao Li ◽  
Jie Liu
Keyword(s):  
State Space ◽  
Nonlinear Vibration ◽  
Dynamic Model ◽  
Phase Difference ◽  
Sliding Mode ◽  
Design Feature ◽  
Vibration System ◽  
Reaching Law ◽  
Speed Difference ◽  
Nonlinear Vibration System

Based on the dynamic model of the nonlinear vibration system which driven by double exciting motors, the rotate speed difference and phase difference state space equations have been deduced. According to the design feature of the nonlinear vibration system and the vibration synchronization requirement of double exciting motors, the approach control synchronization strategy has been deduced with sliding mode reaching law. The practical examples and tests shows that the reaching law synchronization controller can effectively control the double exciting motors to realize the synchronization movement, and the synchronization controller has stronger robustness. The analysis result can provide the theoretical and test basis for the further exploitation of synchronization vibrating machine.

scholarly journals Research on Periodic Motion Stability of Rotor-Bearing System with Dual-Unbalances

2011 ◽  
Vol 2-3 ◽  
pp. 728-732
Author(s):  
Chao Feng Li ◽  
Guang Chao Liu ◽  
Qin Liang Li ◽  
Bang Chun Wen
Keyword(s):  
Stability Analysis ◽  
Phase Difference ◽  
Periodic Motion ◽  
Initial Phase ◽  
Shooting Method ◽  
Small Eccentricity ◽  
Rotor Bearing ◽  
Large Eccentricity ◽  
The Stability ◽  
Bearing System

Multiple freedom degrees model of rotor-bearing system taking many factors into account is established, the Newmark-β and shooting method are combined during the stability analysis of periodic motion in such system. The paper focused on the influence law of two eccentric phase difference on the instability speed of rotor-bearing system. The results have shown that the instability speed rises constantly with the eccentric phase difference angle increasing in small eccentricity system. When the two unbalance be in opposite direction, the system reached its maximum instability speed. However, the unstable bifurcation generates mutation phenomenon for large eccentricity system with the eccentric phase difference angle increasing. In summary, the larger initial phase angle can inhibit system instability partly. The conclusions have provided a theoretical reference for vibration control and stability design of the more complex rotor-bearing system.

scholarly journals Hopf Bifurcation and Chaos of a Delayed Finance System

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-18 ◽  
Author(s):  
Xuebing Zhang ◽  
Honglan Zhu
Keyword(s):  
Numerical Simulation ◽  
Hopf Bifurcation ◽  
Center Manifold ◽  
Chaotic State ◽  
Bifurcation And Chaos ◽  
Finance System ◽  
Center Manifold Theorem ◽  
Normal Form Method ◽  
Simulation Results ◽  
The Stability

In this paper, a finance system with delay is considered. By analyzing the corresponding characteristic equations, the local stability of equilibrium is established. The existence of Hopf bifurcations at the equilibrium is also discussed. Furthermore, formulas for determining the direction of Hopf bifurcation and the stability of the bifurcating periodic solutions are derived by applying the normal form method and center manifold theorem. Finally, numerical simulation results are presented to validate the theoretical analysis. Numerical simulation results show that delay can lead a stable system into a chaotic state.

Preparation and Research of Oil in Water Microemulsion

2020 ◽  
Vol 1001 ◽  
pp. 110-114
Author(s):  
Xiao Qi Chen ◽  
Meng Meng Zhou ◽  
Zheng Zheng Wang ◽  
Hai Jun Zhou ◽  
Shu Lan Yang ◽  
...  
Keyword(s):  
Particle Size ◽  
Constant Temperature ◽  
Polydispersity Index ◽  
Stable System ◽  
Mass Ratio ◽  
Drop Method ◽  
Mean Particle Size ◽  
Oil In Water ◽  
The Mean ◽  
The Stability

A series of oil in water (O/W) microemulsions were prepared through drop by drop method at constant temperature, taking Span80/Tween80 as a composite emulsifying system and Macol-52 as oil phase. Effects of the mass ratio of composite emulsifying system and oil/emulsifier ratio on the particle size were studied. Finally, the best technological conditions were selected and the stability of the microemulsion was also researched. Results showed that the most suitable Span80/Tween80 mass ratio was 1:1 and the oil/emulsifier ratio is 1:1. Under this condition, the mean particle size of the o/w microemulsion was 71.1 nm and the polydispersity index was 0.151. Moreover, the microemulsion maintain a bright and uniform stable system after 20minutes’ centrifugation at the speed of 4000r/min and the particle size increased slightly.

Determination of the Fluid-Elastic Stability Threshold in the Presence of Turbulence: A Theoretical Study

1989 ◽  
Vol 111 (4) ◽  
pp. 407-419 ◽  
Author(s):  
J. H. Lever ◽  
G. Rzentkowski
Keyword(s):  
Theoretical Study ◽  
Cross Flow ◽  
Elastic Stability ◽  
Mass Ratio ◽  
Response Curves ◽  
Stability Threshold ◽  
Pitch Ratio ◽  
The Stability ◽  
Experimental Findings

A model has been developed to examine the effect of the superposition of turbulent buffeting and fluid-elastic excitation on the response of a single flexible tube in an array exposed to cross-flow. The modeled response curves for a 1.375-pitch ratio parallel triangular array are compared with corresponding experimental data for the same array; reasonably good qualitative agreement is seen. Turbulence is shown to have a significant effect on the determination of the stability threshold for the array, with increasing turbulent buffeting causing a reduction in the apparent critical velocity. The dependence of turbulence response on mass ratio is also found to yield a slight independence between mass and damping parameters on stability threshold estimates, which may account for similar experimental findings. Different stability criteria are compared, and an attempt is made to provide some guidance in the interpretation of response curves from actual tests.

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