Stability of an Equilibrium Position

2010 ◽  
pp. 53-62
Keyword(s):  
Equilibrium Position

A new dynamic mesh algorithm for studying the 3D transient flow field of tilting pad journal bearings

2016 ◽  
Vol 230 (12) ◽  
pp. 1470-1482 ◽  
Author(s):  
Mengxuan Li ◽  
Chaohua Gu ◽  
Xiaohong Pan ◽  
Shuiying Zheng ◽  
Qiang Li
Keyword(s):  
Flow Field ◽  
Equilibrium Position ◽  
Transient Flow ◽  
Journal Bearings ◽  
Dynamic Mesh ◽  
Static Equilibrium ◽  
Time Step ◽  
Tilting Pad ◽  
Grid Nodes ◽  
Tilting Pad Journal Bearings

A new dynamic mesh algorithm is developed in this paper to realize the three-dimensional (3D) computational fluid dynamics (CFD) method for studying the small clearance transient flow field of tilting pad journal bearings (TPJBs). It is based on a structured grid, ensuring that the total number and the topology relationship of the grid nodes remain unchanged during the dynamic mesh updating process. The displacements of the grid nodes can be precisely recalculated at every time step. The updated mesh maintains high quality and is suitable for transient calculation of large journal displacement in FLUENT. The calculation results, such as the static equilibrium position and the dynamic characteristic coefficients, are consistent with the two-dimensional (2D) solution of the Reynolds equation. Furthermore, in the process of transient analysis, under conditions in which the journal is away from the static equilibrium position, evident differences appear between linearized and transient oil film forces, indicating that the nonlinear transient calculation is more suitable for studying the rotor-bearing system.

An I.R. Spectroscopic Study of the Conformational Equilibrium in 2-Acetylfuran

1976 ◽  
Vol 31 (10) ◽  
pp. 1217-1219 ◽  
Author(s):  
Giulio Paliani ◽  
Rosario Cataliotti ◽  
Antonio Poletti
Keyword(s):  
Dielectric Constant ◽  
Spectroscopic Study ◽  
Equilibrium Position ◽  
Conformational Equilibrium ◽  
Energy Difference ◽  
Temperature Changes

Abstract The conformational cis/trans equilibrium of 2-Acetylfuran has been studied by i.r. spectroscopy, in various physical states. This equilibrium is strongly influenced by the dielectric constant of the medium. The isomeric energy difference is very small as revealed by the insensitivity of the equilibrium position to temperature changes.

Dynamics of a DC Motor-Driving Arm with a Circular Periodic Potential and DC/AC Voltage Input

2021 ◽  
Vol 31 (12) ◽  
pp. 2150178
Author(s):  
R. F. Kouam Tagne ◽  
R. Tsapla Fotsa ◽  
P. Woafo
Keyword(s):  
Equilibrium Position ◽  
Periodic Potential ◽  
Permanent Magnets ◽  
Critical Value ◽  
Dc Motor ◽  
Chaotic Regime ◽  
Dc Voltage ◽  
Large Amplitude Motions ◽  
Sinusoidal Oscillations ◽  
Angular Oscillations

In this paper, we investigate the dynamics of an electromechanical system consisting of a DC motor-driving arm within a circular periodic potential created by three permanent magnets. Two configurations of the circular potential appear when one varies the positions of the magnets and the length of the DC motor, respectively. Two different forms of input signal are used: DC and AC voltage sources. For each case, conditions under which the mechanical arm can perform a complete rotation are obtained. Under the DC voltage excitation, the arm oscillates and then is stabilized at an equilibrium position for a DC voltage lower than a critical value [Formula: see text]. When the DC voltage is higher than the critical value [Formula: see text], the arm performs large amplitude motions (complete rotation). Submitted to an AC voltage with amplitude lower than a critical value, the mechanical arm exhibits sinusoidal oscillations around the equilibrium position [Formula: see text] with amplitudes less than one turn. Angular oscillations with amplitudes greater than one turn are observed when the voltage amplitude is higher than the critical value. Bifurcation diagrams show that the simple system can enter chaotic regime with the amplitudes of angular oscillations varying erratically from small to high values.

scholarly journals Journal Bearing: An Integrated CFD-Analytical Approach for the Estimation of the Trajectory and Equilibrium Position

2020 ◽  
Vol 10 (23) ◽  
pp. 8573
Author(s):  
Franco Concli
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Pressure Distribution ◽  
Equilibrium Position ◽  
Analytical Approach ◽  
Journal Bearing ◽  
Cfd Model ◽  
Cavitation Model ◽  
Computational Fluid Dynamics Cfd ◽  
The Mathematical Model

For decades, journal bearings have been designed based on the half-Sommerfeld equations. The semi-analytical solution of the conservation equations for mass and momentum leads to the pressure distribution along the journal. However, this approach admits negative values for the pressure, phenomenon without experimental evidence. To overcome this, negative values of the pressure are artificially substituted with the vaporization pressure. This hypothesis leads to reasonable results, even if for a deeper understanding of the physics behind the lubrication and the supporting effects, cavitation should be considered and included in the mathematical model. In a previous paper, the author has already shown the capability of computational fluid dynamics to accurately reproduce the experimental evidences including the Kunz cavitation model in the calculations. The computational fluid dynamics (CFD) results were compared in terms of pressure distribution with experimental data coming from different configurations. The CFD model was coupled with an analytical approach in order to calculate the equilibrium position and the trajectory of the journal. Specifically, the approach was used to study a bearing that was designed to operate within tight tolerances and speeds up to almost 30,000 rpm for operation in a gearbox.

On the Equilibrium Position of Bis[1,2,3] Triazolopyrimidines (A revision)

2010 ◽  
Vol 95 (8) ◽  
pp. 679-680 ◽  
Author(s):  
Gerrit L'Abbé ◽  
Françoise Godts ◽  
Suzanne Toppet
Keyword(s):  
Equilibrium Position

Dynamic Stability of Hovercraft in Heave

1970 ◽  
Vol 37 (4) ◽  
pp. 895-900 ◽  
Author(s):  
H. J. Davies ◽  
G. A. Poland
Keyword(s):  
Mathematical Model ◽  
Dynamic Behavior ◽  
Dynamic Stability ◽  
Equilibrium Position ◽  
Forced Oscillation ◽  
Dynamic Equilibrium ◽  
Forced Oscillations ◽  
Two Dimensional ◽  
Oscillation Characteristics ◽  
Nonlinear Nature

The regimes of flow governing the dynamic behavior of a two-dimensional mathematical model of an edge-jet Hovercraft in heaving motion are described and the equations associated with such regimes derived. Both the free and forced-oscillation characteristics are studied. The nonlinear nature of the system manifests itself, in the case of the forced oscillations, as a shift in the dynamic equilibrium position resulting in a loss of mean hoverheight.

Lateral Equilibrium Position Analysis Program With Applications to Electric Submersible Pumps

2017 ◽  
Author(s):  
Clay S. Norrbin ◽  
Dara W. Childs
Keyword(s):  
Equilibrium Position ◽  
Static Equilibrium ◽  
Analysis Program ◽  
Eccentricity Ratio ◽  
Vertical Orientation ◽  
Maximum Curvature ◽  
First Finding ◽  
Static Eccentricity ◽  
Lateral Equilibrium ◽  
Vertical Case

The long length of sub-sea Electric Submersible Pumps (ESPs) requires a large amount of annular seals. Loading caused by gravity and housing curvature changes the Static Equilibrium Position (SEP) of the rotor in these seals. This analysis predicts the SEP due to gravity and/or well curvature loading. The analysis also interfaces displays the rotordynamics around the SEP. A static and rotordynamic analysis is presented for a previously studied ESP model. This study differs by first finding the SEP and then performing a rotordynamic analysis about the SEP. Predictions are shown in a horizontal and a vertical orientation. In these two configurations, viscosities and clearances are varied through 4 cases: 1X 1cP, 3X 1cP, 1X 30cP, and 3X 30cP. In a horizontal, straight-housing position, the model includes gravity and buoyancy on the shaft. At 1cP-1X and 1cP-3X, the horizontal statics show a moderate eccentricity ratio for the shaft with respect to the housing. With 30cP-1X, the predicted static eccentricity ratio is low at 0.08. With 30cP-3X, the predicted eccentricity ratio increases to 0.33. Predictions for a vertical case of the same model are also presented. The curvature of the housing is varied in the Y-Z plane until rub or close-to-wall rub is expected. The curvature needed for a rub with a 1X 1cP fluid is 7.5 degrees of curvature. Curvature has little impact on stability. With both 1X 30cP and 3X 30cP, the maximum curvature for a static rub are over 25 degrees of curvature. Both 1X 30cP and 3X 30cP remain unstable with increasing curvature.

Micro Mechanism of BaTiO3 Ferroelectric Phase Transition Described by Electron Cloud Model

2012 ◽  
Vol 479-481 ◽  
pp. 619-622
Author(s):  
Chao Fang ◽  
Liang Yan Chen
Keyword(s):  
Phase Transition ◽  
Dielectric Constant ◽  
Equilibrium Position ◽  
Ferroelectric Phase Transition ◽  
Ferroelectric Phase ◽  
Cloud Model ◽  
Electron Cloud ◽  
Oxygen Ions ◽  
Expansion Effect ◽  
Coulomb Attraction

In this paper the micro mechanism of BaTiO3 ferroelectric phase transition is studied based on the thermodynamic model using electron cloud model, and further the Curie - Weiss law is explained. The results indicate that the contraction of the electron cloud, as the temperature decreased through Curie temperature, causes oxygen ions shift the equilibrium position, and the Coulomb attraction makes Ti ion shift the equilibrium position causing phase transition; With temperature rising, the ion displacement polarization decreases owing to the electron cloud expansion effect, and the variation of dielectric constant with temperature follows the Curie - Weiss law.

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