Effect of phase difference on dynamic characteristics for a synchronous vibrating system with double eccentric rotors

Phase difference is an important factor affecting the performances of the synchronous vibrating system driven by the two excited motors. The nonlinear dynamic models of the synchronous vibrating system under the action of the nonlinear elastic force are established. The periodic solutions for the synchronous vibrating system are theoretically derived using the nonlinear dynamic models. The stabilities of periodic solution for the synchronous vibrating system are theoretically analyzed using Jacobi matrix of the amplitude-frequency-characteristic equation. Using Matlab, the amplitude-frequency characteristics are analyzed through the selected parameters. The relations between the phase difference and the amplitude in the synchronous vibrating system are also investigated. Various nonlinear phenomena, such as the jump phenomenon and the multiple-valued periodic solutions, are reproduced using relation between the phase difference and the amplitude. The stable periodic solutions can be obtained by the different initial conditions, using Runge–Kutta method. The effects of the phase difference on the amplitude are presented for the changes of system parameters (including the stiffness of the soil and the damping of the soil, the mass of the eccentric block). The effects of the dynamic characteristics on the phase difference are analyzed through the difference rates of the two excited motors and the initial conditions of the system. It has been shown that the research results can provide a theoretical basis for the research of the synchronous vibrating system.

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

Journal of Low Frequency Noise Vibration and Active Control ◽

10.1177/1461348419867515 ◽

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.

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Dynamic Modeling, Response, and Chaos Analysis of 2-DOF Hybrid Mechanism with Revolute Clearances

Shock and Vibration ◽

10.1155/2020/9172853 ◽

2020 ◽

Vol 2020 ◽

pp. 1-20

Author(s):

Xiulong Chen ◽

Yuefei Tang

Keyword(s):

Dynamic Modeling ◽

Dynamic Characteristics ◽

Nonlinear Dynamic ◽

High Speed ◽

Degrees Of Freedom ◽

Dynamic Models ◽

Modeling And Analysis ◽

Hybrid Mechanism ◽

Nonlinear Dynamic Models ◽

Collision Force

Due to the errors arising from machining or assembly, the deformation during movement, and the wear of movement pairs, the clearance will be generated at the kinematic pair of the mechanism, and the service life or working accuracy of the mechanism is reduced. At present, most of the researches are in a simple mechanism with a single clearance, and there are few papers on the complex mechanism, such as the high-speed mechanism which contains multiple clearances. In order to give a computational methodology for the dynamic modeling and analysis of the planar multilink mechanism with multiple degrees of freedom and multiple clearances and master the dynamic characteristics of the planar multilink mechanism, the nonlinear dynamic models of the multiclearance hybrid seven-bar mechanism under different clearance numbers, different clearance values, different clearance positions, and different driving velocities are established and analyzed. The dynamic output response comparison diagram of the mechanism and the collision force diagrams and center trajectory diagrams of the mechanism at the clearance are given. Then, nonlinear dynamics of the mechanism is studied by different clearance values and driving speeds. The corresponding trajectory phase diagrams, Poincare maps, and bifurcation diagrams are given. The above research results provide an effective theoretical basis for the study about the nonlinear dynamic characteristics of the planar link mechanism with clearance and how to compensate or control the clearances.

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Robust and Dynamically Consistent Model Order Reduction for Nonlinear Dynamic Systems

Journal of Dynamic Systems Measurement and Control ◽

10.1115/1.4028470 ◽

2014 ◽

Vol 137 (2) ◽

Cited By ~ 3

Author(s):

David B. Segala ◽

David Chelidze

Keyword(s):

Nonlinear Dynamic ◽

Dynamic Models ◽

Initial Conditions ◽

Order Reduction ◽

Orthogonal Decomposition ◽

System Parameters ◽

New Concepts ◽

Consistent Model ◽

Dynamical Consistency ◽

Nonlinear Dynamic Models

There is a great importance for faithful reduced order models (ROMs) that are valid over a range of system parameters and initial conditions. In this paper, we demonstrate through two nonlinear dynamic models (pinned–pinned beam and thin plate) that are both randomly and periodically forced that smooth orthogonal decomposition (SOD)-based ROMs are valid over a wide operating range of system parameters and initial conditions when compared to proper orthogonal decomposition (POD)-based ROMs. Two new concepts of subspace robustness—the ROM is valid over a range of initial conditions, forcing functions, and system parameters—and dynamical consistency—the ROM embeds the nonlinear manifold—are used to show that SOD, as opposed to POD, can capture the low order dynamics of a particular system even if the system parameters or initial conditions are perturbed from the design case.

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