Fixed Geometry Bearing Analysis Using 2 Dimensional Pad Data

2015 ◽  
Author(s):  
Wei Li ◽  
Manish Thorat
Keyword(s):  
Reynolds Equation ◽  
Dimensional Space ◽  
Journal Bearings ◽  
Analysis Method ◽  
Benchmark Study ◽  
Assembly Method ◽  
Turbulent Flow Regime ◽  
Load Vector ◽  
Vector Orientation ◽  
Rotor Dynamic

A fast and efficient method for evaluating bearing coefficients of the fixed geometry bearings is presented. In a typical industrial application, where the accuracy of the solution is desired, this paper presents a method whose accuracy is verified to be good by the benchmark study. Reynolds equation is solved to obtain non-dimensionalised static and rotor-dynamic characteristics for a pre-defined bearing pad geometry. The solution in the form of non-dimensional functions is obtained for a 2 dimensional space representing all possible journal loci for any load vector orientation. Laminar flow is considered in the analysis, although the method of analysis can be extended to Turbulent flow regime. The analysis method is most efficient for isoviscous boundary condition. A pad assembly method for the fixed pad journal bearings is presented. Any fixed pad bearing geometry including multi-pad bearings, preload with any load vector orientation can be evaluated using this method. In this paper, demonstrating cases for a four-pad bearing are presented.

Analysis of Noncircular Gas Journal Bearings

1975 ◽  
Vol 97 (4) ◽  
pp. 616-623 ◽  
Author(s):  
O. Pinkus
Keyword(s):  
Reynolds Equation ◽  
Load Capacity ◽  
Full Range ◽  
Maximum Load ◽  
Journal Bearings ◽  
Operating Conditions ◽  
Significant Advance ◽  
Arbitrary Direction ◽  
Isothermal Conditions ◽  
Load Vector

The compressible Reynolds Equation under isothermal conditions was solved for finite elliptical and 3-lobe bearings with the load vector acting in any arbitrary direction over the full range of 360 deg. Envelopes of minimum and maximum eccentricity for a given set of operating conditions are provided, the first to yield maximum load capacity, and the second to assist stability by a choice of the highest possible ε. Some values of the spring and damping forces are also given and it is shown that in comparison with conventional bearings, the non-circular designs offer a significant advance in stiffness, particularly for low ε, when instability is most often encountered.

Dynamics of a motorized spindle supported on water-lubricated bearings

2016 ◽  
Vol 231 (3) ◽  
pp. 459-472 ◽  
Author(s):  
Huihui Feng ◽  
Shuyun Jiang
Keyword(s):  
Reynolds Equation ◽  
Dynamic Stiffness ◽  
Journal Bearings ◽  
Motorized Spindle ◽  
Dynamic Coefficients ◽  
Numerical Predictions ◽  
Tilting Angle ◽  
Dynamic Performances ◽  
Experimental Values ◽  
Rotor Dynamic

The purpose of this paper is to investigate the dynamic performances of a motorized spindle supported on water-lubricated bearings. A modified transfer matrix method considering both of the translational and tilting dynamic coefficients of the bearings is established. The turbulent Reynolds equation is adopted and numerically solved by the perturbation method and the finite difference method, and the dynamic characteristics of the water-lubricated journal bearings are obtained; the effects of the eccentricity ratio, tilting angle, and the rotational speed on the dynamic coefficients of the water-lubricated journal bearings are analyzed. The critical speed, the dynamic stiffness of spindle nose, and unbalance response of the motorized spindle are investigated. Finally, a comparative study of rotor dynamic behaviors between the 32- and the eight-coefficient bearing models is conducted. The numerical predictions obtained by the 32-coefficient bearing models correlate well with the experimental values available in the literature.

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.

On Journal Bearings of Finite Length With Variable Viscosity

1959 ◽  
Vol 26 (2) ◽  
pp. 179-183
Author(s):  
L. N. Tao
Keyword(s):  
Exact Solution ◽  
Analytical Solution ◽  
Finite Length ◽  
Reynolds Equation ◽  
Variable Viscosity ◽  
Load Capacity ◽  
Journal Bearings ◽  
Heun Functions ◽  
Load Vector ◽  
Constant Viscosity

Abstract An exact solution of the Reynolds equation for journal bearings of finite length with viscosity as a function of pressure is found. The analytical solution is expressed in terms of Heun functions. The load capacity and the attitude angle are derived. It is found that the load vector, in general, is not perpendicular to the line of journal and bearing centers as shown in the constant-viscosity case.

Analysis method ofrecruitment needs for the regional economy: Occupational section

2017 ◽  
pp. 142-149 ◽  
Author(s):  
E. Pitukhin ◽  
S. Shabaeva ◽  
I. Stepus ◽  
D. Moroz
Keyword(s):  
Cluster Analysis ◽  
Labor Market ◽  
Comparative Analysis ◽  
Regional Economy ◽  
Dimensional Space ◽  
Analysis Method ◽  
Scalar Form ◽  
Regional Labor Market ◽  
Regional Labor ◽  
Regional Specificity

The paper deals with comparative analysis of occupations in the regional labor market. Occupation is treated as a multi-dimensional space of characte- ristics, whereas a scalar form of a characteristic makes it possible to carry out a comparative analysis of occupations. Using cluster analysis of a pilot region indicators five meaningfully interpretable clusters of occupations were identified, reflecting their regional specificity.

Bifurcation Analysis of Self-Acting Gas Journal Bearings

2001 ◽  
Vol 123 (4) ◽  
pp. 755-767 ◽  
Author(s):  
Cheng-Chi Wang ◽  
Cha’o-Ku`ang Chen
Keyword(s):  
Dynamic Behavior ◽  
Reynolds Equation ◽  
Rotational Velocity ◽  
Power Spectra ◽  
Journal Bearings ◽  
Operating Conditions ◽  
Finite Differences Method ◽  
Subharmonic Response ◽  
Rotor Center ◽  
Rotor Mass

This paper studies the bifurcation of a rigid rotor supported by a gas film bearing. A time-dependent mathematical model for gas journal bearings is presented. The finite differences method and the Successive Over Relation (S.O.R) method are employed to solve the Reynolds’ equation. The system state trajectory, Poincare´ maps, power spectra, and bifurcation diagrams are used to analyze the dynamic behavior of the rotor center in the horizontal and vertical directions under different operating conditions. The analysis shows how the existence of a complex dynamic behavior comprising periodic and subharmonic response of the rotor center. This paper shows how the dynamic behavior of this type of system varies with changes in rotor mass and rotational velocity. The results of this study contribute to a further understanding of the nonlinear dynamics of gas film rotor-bearing systems.

The Effect of Journal Bearing Misalignment on Load and Cavitation for Non-Newtonian Lubricants

1986 ◽  
Vol 108 (4) ◽  
pp. 645-654 ◽  
Author(s):  
R. H. Buckholz ◽  
J. F. Lin
Keyword(s):  
Reynolds Equation ◽  
Numerical Solutions ◽  
Journal Bearings ◽  
Surface Boundary ◽  
Film Rupture ◽  
Aspect Ratios ◽  
Free Surface Boundary Condition ◽  
Load Carrying ◽  
Boundary Location ◽  
Surface Boundary Condition

An analysis for hydrodynamic, non-Newtonian lubrication of misaligned journal bearings is given. The hydrodynamic load-carrying capacity for partial arc journal bearings lubricated by power-law, non-Newtonian fluids is calculated for small valves of the bearing aspect ratios. These results are compared with: numerical solutions to the non-Newtonian modified Reynolds equation, with Ocvirk’s experimental results for misaligned bearings, and with other numerical simulations. The cavitation (i.e., film rupture) boundary location is calculated using the Reynolds’ free-surface, boundary condition.

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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