scholarly journals On the Existence of Self-Excited Vibration in Thin Spur Gears: A Theoretical Model for the Estimation of Damping by the Energy Method

Symmetry ◽  
2018 ◽  
Vol 10 (12) ◽  
pp. 664 ◽  
Author(s):  
Yanrong Wang ◽  
Hang Ye ◽  
Long Yang ◽  
Aimei Tian
Keyword(s):  
Axial Force ◽  
Traveling Wave ◽  
The Self ◽  
Spur Gears ◽  
Contact Ratio ◽  
Symmetric Structure ◽  
Modal Damping ◽  
Excited Vibration ◽  
Cyclic Symmetric ◽  
The Stability

The gear is a cyclic symmetric structure, and each tooth is subjected to a periodic mesh force. These mesh forces have the same phase difference tooth by tooth, which can excite gear vibrations. The mechanism of additional axial force caused by gear bending is shown and examined, which can significantly affect the stability of a self-excited thin spur gears vibration. A mechanical model based on energy balance is then developed to predict the contribution of additional axial force, leading to the proposed numerical integration method for vibration stability analysis. By analyzing the change in the system energy, the occurrence of the self-excited vibration is validated. A numerical simulation is carried out to verify the theoretical analysis. The impacts of modal damping, contact ratio, and the number of nodal diameters on the stability boundaries of the self-excited vibration are revealed. The results prove that the backward traveling wave of the driven gear as well as the forward traveling wave of the driving gear encounter self-excited vibration in the absence of sufficient damping. The model can be used to predict the stability of the gear self-excited vibration.

Self-Excited Vibration of a Plate Supported by Air Pressure in a Floating Conveying Machine

2017 ◽  
Author(s):  
Masakazu Takeda ◽  
Masahiro Watanabe
Keyword(s):  
Air Pressure ◽  
The Self ◽  
Plate Motion ◽  
Bottom Surface ◽  
Fluid Force ◽  
Gap Flow ◽  
Excited Vibration ◽  
Unsteady Fluid ◽  
The Stability ◽  
Work Done

This paper presents experiments and an analysis on self-excited vibration of a plate supported by air pressure in a floating conveying machine. In this study, the instability conditions are examined by theoretical analysis in consideration of the effect of compressibility of air in a chamber. The system’s characteristic equation is derived from the plate motion coupled with equations of the gap flow between the plate and the chamber surface. The vibration characteristics and the instability conditions of the self-excited vibration are examined through experiments. The stability of the plate is affected by an air flow rate, a mass of the plate, a spring stiffness of the plate. We clarified those influences on the instability conditions of the self-excited vibration. The unsteady fluid force acting on the plate (bottom surface) is investigated by measuring the unsteady pressure. The local work done by the unsteady fluid force is also clarified. Lastly, the instability mechanism and important parameters of the self-excited vibration are discussed based on the theoretical model and experimental results.

The Influence of Oil-Film Journal Bearings on the Stability of Rotating Machines

1946 ◽  
Vol 13 (3) ◽  
pp. A211-A220
Author(s):  
A. C. Hagg
Keyword(s):  
Rotational Frequency ◽  
Journal Bearings ◽  
The Self ◽  
Stability Criteria ◽  
Oil Film ◽  
Oil Whip ◽  
Upper Limit ◽  
Excited Vibration ◽  
Tilting Pad ◽  
The Stability

Abstract The self-excited vibration caused by the lubricating films of journal bearings and commonly called oil-film whirl or oil whip is discussed. The upper limit of whirling frequency has been found to be one-half rotational frequency in the general case; actually the phenomenon will manifest itself at a frequency which is invariably below this limit. Stability criteria have been developed for certain common systems in terms of bearing and rotor parameters. The tilting-pad bearing of Michell has been established as a so-called “stable” or “nonwhirling” bearing. This bearing and related types are probably the only oil-film journal bearings which are incapable of exciting oil whip, regardless of the system to which they are applied. Qualitatively the results of the paper appear to be in agreement with observations. In certain cases, results have been substantiated experimentally.

scholarly journals The Modeling and Analysis for the Self-Excited Vibration of the Maglev Vehicle-Bridge Interaction System

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Jinhui Li ◽  
Jie Li ◽  
Danfeng Zhou ◽  
Lianchun Wang
Keyword(s):  
Ride Comfort ◽  
Interaction Model ◽  
Control Unit ◽  
The Self ◽  
Modeling And Analysis ◽  
Maglev Vehicle ◽  
Interaction System ◽  
Excited Vibration ◽  
Vibration Problems ◽  
The Stability

This paper addresses the self-excited vibration problems of maglev vehicle-bridge interaction system which greatly degrades the stability of the levitation control, decreases the ride comfort, and restricts the cost of the whole system. Firstly, two levitation models with different complexity are developed, and the comparison of the energy curves associated with the two models is carried out. We conclude that the interaction model with a single levitation control unit is sufficient for the study of the self-excited vibration. Then, the principle underlying the self-excited vibration is explored from the standpoint of work acting on the bridge done by the levitation system. Furthermore, the influences of the parameters, including the modal frequency and modal damping of bridge, the gain of the controller, the sprung mass, and the unsprung mass, on the stability of the interaction system are carried out. The study provides a theoretical guidance for solving the self-excited vibration problems of the vehicle-bridge interaction systems.

Self-excited Vibration Control of the Flexible Planar Parallel 3-RRR Robot

2018 ◽  
Vol 25 (2) ◽  
pp. 351-361
Author(s):  
Zhi-cheng Qiu ◽  
Jie Yang ◽  
Xian-min Zhang
Keyword(s):  
High Speed ◽  
Parallel Robot ◽  
The Self ◽  
Flexible Robot ◽  
Nonlinear Controller ◽  
Control Approach ◽  
Excited Vibration ◽  
Improve Accuracy ◽  
The Stability ◽  
Fuzzy Control Algorithm

A self-excited vibration active control approach for a 3-RRR flexible planar parallel robot is developed to improve accuracy and stability. The 3-RRR parallel flexible robot experimental setup is constructed. From the motion experiments, it is demonstrated that the residual vibration can be converted to self-excited vibration at a high-speed motion, which will affect the stability and positioning precision of the platform. To suppress the self-excited vibration owing to flexibility, friction, backlash, coupling, and other nonlinear factors, a nonlinear controller and a fuzzy control algorithm are designed to attenuate the self-excited vibration. Experiments are conducted in different positions of the 3-RRR flexible parallel robot. The experimental results demonstrate that the investigated control methods can suppress the self-excited vibration effectively.

Self-Excited Vibration of a Rotating Hollow Shaft Partially Filled with Liquid

1980 ◽  
Vol 102 (1) ◽  
pp. 185-192 ◽  
Author(s):  
S. Saito ◽  
T. Someya
Keyword(s):  
Viscous Liquid ◽  
Rotor System ◽  
The Self ◽  
Hollow Shaft ◽  
Excited Vibration ◽  
Negative Damping ◽  
The Stability

The self-excited vibration of a rotating hollow shaft partially filled with viscous liquid is investigated. The motion of liquid and the liquid force is analyzed. The stability of the rotor system is calculated and the influences of factors on the stability are studied. Moreover, the mechanism causing the negative damping which is the reason for the instability is discussed.

Impact of Tooth Friction and Its Bending Effect on Gear Dynamics

2007 ◽  
Author(s):  
Gang Liu ◽  
Robert G. Parker
Keyword(s):  
Dynamic Response ◽  
Gear Tooth ◽  
Approximate Solutions ◽  
Contact Ratio ◽  
Rotational Model ◽  
Bending Effect ◽  
Modal Damping ◽  
Parametric Instabilities ◽  
Iterative Integration ◽  
The Stability

This work studies the influences of tooth friction on parametric instabilities and dynamic response of a single-mesh gear pair. A mechanism whereby tooth friction causes gear tooth bending is shown to significantly impact the dynamic response. A dynamic translational-rotational model is developed to consider this mechanism together with the other contributions of tooth friction and mesh stiffness fluctuation. An iterative integration method to analyze parametric instabilities is proposed and compared with an established numerical method. Perturbation analysis is conducted to find approximate solutions that predict and explain the numerical parametric instabilities. The effects of time-varying friction moments about the gear centers and friction-induced tooth bending are critical to parametric instabilities and dynamic response. The impacts of friction coefficient, bending effect, contact ratio, and modal damping on the stability boundaries are revealed. Finally, the friction bending effect on the nonlinear dynamic response is examined and validated by finite element results.

Stability and Natural Characteristics of a Supported Beam

2011 ◽  
Vol 338 ◽  
pp. 467-472 ◽  
Author(s):  
Ji Duo Jin ◽  
Xiao Dong Yang ◽  
Yu Fei Zhang
Keyword(s):  
Eigenvalue Problem ◽  
Boundary Conditions ◽  
Axial Force ◽  
Critical Values ◽  
Rotational Spring ◽  
Analytical Expression ◽  
The Stability ◽  
Spring Constants ◽  
Critical Axial Force ◽  
Natural Characteristics

The stability, natural characteristics and critical axial force of a supported beam are analyzed. The both ends of the beam are held by the pinned supports with rotational spring constraints. The eigenvalue problem of the beam with these boundary conditions is investigated firstly, and then, the stability of the beam is analyzed using the derived eigenfuntions. According to the analytical expression obtained, the effect of the spring constants on the critical values of the axial force is discussed.

The Investigation of the Influence of Structure Parameters on the Friction-Induced Self-Excited Vibration

2011 ◽  
Vol 66-68 ◽  
pp. 933-936
Author(s):  
Xian Jie Meng
Keyword(s):  
Nonlinear Dynamics ◽  
Numerical Method ◽  
Calculation Result ◽  
Dry Friction ◽  
Vibration Amplitude ◽  
The Self ◽  
Structure Parameters ◽  
Dynamics Model ◽  
Excited Vibration ◽  
Nonlinear Dynamics Model

A one degree of freedom nonlinear dynamics model of self-excited vibration induced by dry-friction was built firstly, the numerical method was taken to study the impacts of structure parameters on self-excited vibration. The calculation result shows that the variation of stiffness can change the vibration amplitude and frequency of the self-excited vibration, but can not eliminate it, Along with the increase of system damping the self-excite vibration has the weakened trend and there a ritical damping, when damping is greater than it the self-excite vibration will be disappeared.

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