A Method for Solving Stiffness of Finite Length Self-Acting Gas-Lubricated Journal Bearing

2012 ◽  
Vol 562-564 ◽  
pp. 643-649
Author(s):  
Jian Lu Wang ◽  
Yan Jun Lu ◽  
Hui Ma ◽  
Yong Fang Zhang ◽  
Yong Hui Chen
Keyword(s):  
Finite Length ◽  
Efficient Method ◽  
Partial Derivative ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Transformation Method ◽  
The Self ◽  
Time Dependent ◽  
Dynamic Design ◽  
Derivative Method

Based on the differential transformation method, an efficient method is proposed to calculate stiffness of finite length self-acting gas-lubricated journal bearing. Time dependent Reynolds equation in gas lubrication of the self-acting journal bearing is solved, gas film pressure distribution and stiffness of the bearing are obtained. In comparison with the partial derivative method, the proposed method for solving stiffness of self-acting gas-lubricated journal bearing is verified. The proposed method can provide the theoretical reference to the dynamic design of self-acting gas-lubricated journal bearing-rotor system.

Numerical Analysis Method and Bifurcation of Gas-Lubricated Journal Bearing-Rotor System with Gyroscopic Effect

2011 ◽  
Vol 230-232 ◽  
pp. 197-201
Author(s):  
Yong Fang Zhang ◽  
Xiao Lei Shi ◽  
Yan Jun Lu ◽  
Lie Yu
Keyword(s):  
Reynolds Equation ◽  
Journal Bearing ◽  
Transformation Method ◽  
Rotor System ◽  
Time Dependent ◽  
Analysis Method ◽  
Gyroscopic Effect ◽  
Dynamic Motion ◽  
Nonlinear Behaviors ◽  
Gas Journal Bearing

Based on the nonlinear theory, the unbalanced responses of the gas-lubricated journal bearing-rotor system are investigated. A time-dependent mathematical model is established to describe the pressure distribution of gas-lubricated journal bearing with nonlinearity. The rigid rotor with gyroscopic effect supported by self-acting gas journal bearing with three axial grooves is modeled. The differential transformation method is employed to solve the time-dependent gas-lubricated Reynolds equation, and the dynamic motion equation is solved by Newmark-β method. The unbalanced responses of the rotor system supported by finite gas-lubricated journal bearings are analyzed by bifurcation diagram, orbit diagram, Poincaré map. The numerical results reveal periodic, period-4 motion of nonlinear behaviors of the system.

On the Performance of Journal Bearings Under Conditions of Film Rupture, Part II

1975 ◽  
Vol 97 (4) ◽  
pp. 591-598
Author(s):  
W. A. Crosby ◽  
E. M. Badawy
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Finite Length ◽  
Infinite Number ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Journal Bearings ◽  
Operating Characteristics ◽  
Film Rupture ◽  
Rupture Part

An analytical analysis of journal bearing performance under conditions of film rupture by separation and by cavitation is performed. The ruptured region is considered to have an infinite number of cavities. The boundary condition of Reynolds’ equation at the trailing edge is influenced by the bearing’s operating characteristics and the method of oil admission. A variational solution is given in order to extend the applicability of the boundary conditions to bearings of finite length.

Nonlinear Dynamic Behaviors and Bifurcation of Symmetrical Rotor System Supported by Self-Acting Gas Jounal Bearings

2010 ◽  
Vol 97-101 ◽  
pp. 2634-2638 ◽  
Author(s):  
Wei Min Wang ◽  
Yan Jun Lu ◽  
Zhi Jun Cao ◽  
Yong Fang Zhang ◽  
Lie Yu
Keyword(s):  
Reynolds Equation ◽  
Journal Bearing ◽  
Period Doubling ◽  
Journal Bearings ◽  
Time Dependent ◽  
Jeffcott Rotor ◽  
Successive Over Relaxation ◽  
Rotor Dynamic ◽  
Gas Journal Bearing ◽  
Bifurcation Behavior

The unbalanced response and corresponding bifurcation behavior of the rotor dynamic system supported by gas journal bearings are investigated. A time-dependent mathematical model is used to describe the pressure distribution of gas journal bearing with nonlinearity. The rigid Jeffcott rotor with self-acting gas journal bearing supports is modeled. The finite difference method and the Successive Over Relaxation (S.O.R.) method are employed to solve the time-dependent Reynolds equation of gas journal bearings. The bifurcation of unbalanced responses of the rotor is analyzed by a Poincaré map. The numerical results reveal periodic, period-doubling, quasi-periodic, and chaotic motion of rich and complex non-linear behaviors of the system.

The Rayleigh Step Bearing Applied to a Gas-Lubricated Journal of Finite Length

1967 ◽  
Vol 89 (1) ◽  
pp. 38-46 ◽  
Author(s):  
F. R. Archibald ◽  
B. J. Hamrock
Keyword(s):  
Friction Force ◽  
Finite Length ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Convergent Series ◽  
Linearization Method ◽  
Friction Torque ◽  
Diameter Ratio ◽  
Eccentricity Ratio ◽  
Bearing Load

A linearization method is employed on the Reynolds equation to obtain the load and friction torque of a Rayleigh step-film scheme applied to a journal bearing of finite length. The analysis is broken into two parts; i.e., the stepped and ridge regions. The film thickness is considered constant in each region thereby simplifying the linearized Reynolds equation. In addition to the usual plain-bearing parameters (the compressibility number, eccentricity ratio, and length-to-diameter ratio), the load and friction force of a stepped bearing depend on the ratio of the stepped clearance to ridge clearance, the ratio of the width of ridge to the width of the pad, and the number of pads. The solution for the load and friction force for a single pad is obtained in the form of a highly convergent series. A number of equal pads are disposed around a journal and the total bearing load is computed for various eccentricities. Computation from the infinite series is lengthy and a digital computer was used in order to carry out the calculational work. This enabled optima to be selected for each system composed of different numbers of pads. The friction torque and hence the bearing power loss were computed for every case.

Speed vs. comfort: Testing the efficacy of a single question for predicting transit users’ route choices

2019 ◽  
Author(s):  
Joseph John Pyne Simons ◽  
Ilya Farber
Keyword(s):  
Data Collection ◽  
Efficient Method ◽  
Choice Task ◽  
The Self ◽  
Self Report ◽  
Model Parameters ◽  
Single Item ◽  
Alternative Approach ◽  
Single Question ◽  
Insight Into

Not all transit users have the same preferences when making route decisions. Understanding the factors driving this heterogeneity enables better tailoring of policies, interventions, and messaging. However, existing methods for assessing these factors require extensive data collection. Here we present an alternative approach - an easily-administered single item measure of overall preference for speed versus comfort. Scores on the self-report item predict decisions in a choice task and account for a proportion of the differences in model parameters between people (n=298). This single item can easily be included on existing travel surveys, and provides an efficient method to both anticipate the choices of users and gain more general insight into their preferences.

A General Solution of Reynolds’ Equation for a Full Finite Journal Bearing

1967 ◽  
Vol 89 (2) ◽  
pp. 203-210 ◽  
Author(s):  
R. R. Donaldson
Keyword(s):  
Fourier Series ◽  
Series Solution ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Load Capacity ◽  
Separation Of Variables ◽  
Hill Equation ◽  
Eigenvalues And Eigenvectors ◽  
General Series ◽  
Bearing Load

Reynolds’ equation for a full finite journal bearing lubricated by an incompressible fluid is solved by separation of variables to yield a general series solution. A resulting Hill equation is solved by Fourier series methods, and accurate eigenvalues and eigenvectors are calculated with a digital computer. The finite Sommerfeld problem is solved as an example, and precise values for the bearing load capacity are presented. Comparisons are made with the methods and numerical results of other authors.

Theoretical Condition for the Cxy=Cyx Relation in Fluid Film Journal Bearings

1989 ◽  
Vol 111 (3) ◽  
pp. 426-429 ◽  
Author(s):  
T. Kato ◽  
Y. Hori
Keyword(s):  
Reynolds Equation ◽  
Journal Bearing ◽  
Journal Bearings ◽  
Fluid Film ◽  
Finite Width ◽  
Damping Coefficients ◽  
Dynamic Coefficients ◽  
Cross Terms ◽  
Linear Damping ◽  
Theoretical Condition

A computer program for calculating dynamic coefficients of journal bearings is necessary in designing fluid film journal bearings and an accuracy of the program is sometimes checked by the relation that the cross terms of linear damping coefficients of journal bearings are equal to each other, namely “Cxy = Cyx”. However, the condition for this relation has not been clear. This paper shows that the relation “Cxy = Cyx” holds in any type of finite width journal bearing when these are calculated under the following condition: (I) The governing Reynolds equation is linear in pressure or regarded as linear in numerical calculations; (II) Film thickness is given by h = c (1 + κcosθ); and (III) Boundary condition is homogeneous such as p=0 or dp/dn=0, where n denotes a normal to the boundary.

The Effect of Lubricant Inertia in Journal-Bearing Lubrication

1957 ◽  
Vol 24 (4) ◽  
pp. 494-496
Author(s):  
J. F. Osterle ◽  
Y. T. Chou ◽  
E. A. Saibel
Keyword(s):  
Reynolds Number ◽  
Steady State ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Journal Bearings ◽  
Hydrodynamic Theory ◽  
Simple Relationship ◽  
Inertia Effect ◽  
Laminar Regime ◽  
Steady State Operation

Abstract The Reynolds equation of hydrodynamic theory, modified to take lubricant inertia into approximate account, is applied to the steady-state operation of journal bearings to determine the effect of lubricant inertia on the pressure developed in the lubricant. A simple relationship results, relating this “inertial” pressure to the Reynolds number of the flow. It is found that the inertia effect can be significant in the laminar regime.

Numerical and Experimental Investigations on Preload Effects in Air Foil Journal Bearings

2017 ◽  
Author(s):  
Marcel Mahner ◽  
Pu Li ◽  
Andreas Lehn ◽  
Bernhard Schweizer
Keyword(s):  
Reynolds Equation ◽  
Journal Bearing ◽  
Journal Bearings ◽  
Compressible Fluids ◽  
Experimental Investigations ◽  
Hysteresis Curves ◽  
Numerical Predictions ◽  
Bearing Stiffness ◽  
Gasdynamic Model ◽  
Good Agreement

A detailed elasto-gasdynamic model of a preloaded three-pad air foil journal bearing is presented. Bump and top foil deflections are herein calculated with a nonlinear beamshell theory according to Reissner. The 2D pressure distribution in each bearing pad is described by the Reynolds equation for compressible fluids. With this model, the influence of the assembly preload on the static bearing hysteresis as well as on the aerodynamic bearing performance is investigated. For the purpose of model validation, the predicted hysteresis curves are compared with measured curves. The numerically predicted and the measured hysteresis curves show a good agreement. The numerical predictions exhibit that the assembly preload increases the bearing stiffness (in particular for moderate shaft displacements) and the bearing damping.

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