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.

Non-linear dynamic analysis of a flexible rotor supported by self-acting gas journal bearings

2004 ◽  
Vol 218 (12) ◽  
pp. 1527-1538 ◽  
Author(s):  
C-C Wang ◽  
M-J Jang ◽  
C-K Chen
Keyword(s):  
Reynolds Equation ◽  
Dynamic Behaviour ◽  
Rotational Velocity ◽  
Power Spectra ◽  
Journal Bearings ◽  
Operating Conditions ◽  
Flexible Rotor ◽  
Non Linear ◽  
Subharmonic Response ◽  
Rotor Mass

This paper studies the bifurcation of a flexible rotor supported by gas film bearings. A time dependent mathematical model for gas journal bearings is presented. The finite difference method, with the successive overrelation method (SOR), is employed to solve the Reynolds equation. The system state trajectory, Poincare maps, power spectra and bifurcation diagrams are used to analyse the dynamic behaviour of the rotor and journal centre in the horizontal and vertical directions under different operating conditions. The analysis reveals a complex dynamic behaviour comprising periodic and subharmonic response of the rotor and journal centre. This paper shows how the dynamic behaviour 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 non-linear dynamics of gas film rotor-bearing systems.

Nonlinear Dynamic Analysis of a Flexible Rotor Supported by Externally Pressurized Porous Gas Journal Bearings

2002 ◽  
Vol 124 (3) ◽  
pp. 553-561 ◽  
Author(s):  
Cheng-Chi Wang ◽  
Cheng-Ying Lo ◽  
Cha’o-Kuang Chen
Keyword(s):  
Dynamic Analysis ◽  
Dynamic Behavior ◽  
Nonlinear Dynamic ◽  
Nonlinear Dynamic Analysis ◽  
Power Spectra ◽  
Journal Bearings ◽  
Operating Conditions ◽  
Flexible Rotor ◽  
Bearing Number ◽  
Rotor Mass

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

Bifurcation analysis of externally pressurized porous gas journal bearings

2003 ◽  
Vol 217 (12) ◽  
pp. 1325-1338 ◽  
Author(s):  
C-C Wang ◽  
C-K Chen
Keyword(s):  
Reynolds Equation ◽  
Dynamic Behaviour ◽  
Power Spectra ◽  
Journal Bearings ◽  
Operating Conditions ◽  
Complex Dynamic ◽  
Bearing Number ◽  
Squeeze Number ◽  
Rotor Mass ◽  
Gas Journal Bearing

This paper studies the bifurcation of a rigid rotor supported by an externally pressurized porous gas journal bearing. A time-dependent mathematical model for porous gas journal bearings is presented. The modified Reynolds equation is solved using the finite difference method and the SOR (successive over relation) method. The system state trajectory, Poincaré maps, power spectra and bifurcation diagrams are used to analyse the dynamic behaviour of the rotor centre in the horizontal and vertical directions under different operating conditions. The analysis reveals a complex dynamic behaviour comprising periodic and quasi-periodic responses of the rotor centre. This paper shows how the dynamic behaviour of systems of this type varies with changes in rotor mass, squeeze number and bearing number. The results of this study contribute to a further understanding of the non-linear dynamics of gas-lubricated, externally pressurized, porous rotor-bearing systems.

Analysis of an aerodynamic grooved journal bearing with plain sleeve

2006 ◽  
Vol 220 (1) ◽  
pp. 51-60 ◽  
Author(s):  
C-C Wang
Keyword(s):  
Reynolds Equation ◽  
Dynamic Behaviour ◽  
Journal Bearing ◽  
Power Spectra ◽  
Operating Conditions ◽  
Complex Dynamic ◽  
Non Linear ◽  
Linear Behaviour ◽  
Bearing Number ◽  
Rotor Mass

This article studies the non-linear behaviour of a herringbone-grooved rigid rotor supported by a gas film bearing. A numerical method is employed to a time-dependent mathematical model for herringbone-grooved gas journal bearings. The finite difference method with successive over-relation method is employed to solve the Reynolds equation. The system state trajectory, Poincaré maps, power spectra, and bifurcation diagrams are used to analyse the dynamic behaviour of the rotor centre in the horizontal and vertical directions under different operating conditions. The analysis reveals a complex dynamic behaviour comprising periodic and quasi-periodic responses of the rotor centre. This article shows how the dynamic behaviour of this type of system varies with changes in rotor mass and bearing number. The results of this study contribute to a further understanding of the non-linear dynamics of aerodynamic-grooved journal bearing systems.

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.

Cyclic Squeeze Films in Micropolar Fluid Lubricated Journal Bearings

1976 ◽  
Vol 98 (3) ◽  
pp. 412-417 ◽  
Author(s):  
J. Prakash ◽  
P. Sinha
Keyword(s):  
Dynamic Behavior ◽  
Dynamic Loading ◽  
Micropolar Fluid ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Journal Bearings ◽  
Detailed Consideration ◽  
Sinusoidal Load ◽  
Fluid Theory ◽  
Curve Form

The Reynolds equation for the general case of dynamic loading is derived for fluid suspensions, using the micropolar fluid theory. Detailed consideration is given to the dynamic behavior of squeeze films in journal bearings under a fluctuating load with no journal rotation. The characteristics of an infinitely long journal bearing under a cyclic sinusoidal load are shown in curve form, so as to elaborate the micropolar effects.

Dynamic Analysis of a Flexible Rotor Supported on Two Turbulent Model Journal Bearings with Micropolar Fluid Lubrication

2014 ◽  
Vol 592-594 ◽  
pp. 1386-1390
Author(s):  
Sushant Bhatia ◽  
Jaideep Gupta
Keyword(s):  
Dynamic Analysis ◽  
Micropolar Fluid ◽  
Reynolds Equation ◽  
Journal Bearings ◽  
Flexible Rotor ◽  
Wide Range ◽  
Dimensional Parameters ◽  
Rotor Center ◽  
Nonsynchronous Vibrations ◽  
Tangential Directions

This paper presents the complex dynamic analysis of a flexible rotor–bearing system supported by two turbulent micropolar fluid film journal bearings under nonlinear suspension. The Modified Reynolds equation based on the assumptions of turbulent flow and the micropolar parameters has been considered. The system considers Short bearing approximation to simplify the numerical computations. The pressure distribution thus obtained is used to find out the resulting forces about the journal center in the radial and tangential directions. The Non-dimensional dynamic equations are derived considering appropriate non dimensional parameters and solved using MATLAB for a wide range of non-dimensional speed ratios. Plots of the journal center trajectories and rotor center trajectories are obtained. The results show that the system undergoes undesirable nonsynchronous vibrations due to bearing center displacement. Micropolar fluid is found to stabilize the system even when the flow of the system becomes turbulent. The study presented enhances the understanding of the nonlinear dynamics of turbulent journal bearings with respect to dimensionless parameters.

Dynamic Stiffness and Damping Coefficients of Aerostatic, Porous, Journal Bearings

1978 ◽  
Vol 20 (5) ◽  
pp. 291-296 ◽  
Author(s):  
N. S. Rao ◽  
B. C. Majumdar
Keyword(s):  
Continuity Equation ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Dynamic Pressure ◽  
Dynamic Stiffness ◽  
Journal Bearings ◽  
Operating Conditions ◽  
Damping Coefficients ◽  
Design Charts ◽  
Stiffness And Damping

A periodic (displacement) disturbance is imposed on an aerostatic, porous, journal bearing of finite length under steady-state conditions. The dynamic pressure distribution is obtained by a pressure perturbation analysis of Reynolds equation and a modified flow continuity equation in a porous medium. Dynamic stiffness and damping coefficients for different operating conditions are calculated numerically, using a digital computer, and presented in the form of design charts.

Thermoelastohydrodynamic behavior of misaligned plain journal bearings

2013 ◽  
Vol 227 (11) ◽  
pp. 2582-2599 ◽  
Author(s):  
ZS Zhang ◽  
XD Dai ◽  
YB Xie
Keyword(s):  
Thermal Effects ◽  
Reynolds Equation ◽  
Energy Equation ◽  
Three Dimensional ◽  
Journal Bearings ◽  
Operating Conditions ◽  
Misalignment Angle ◽  
Synthetic Solution ◽  
Simulation Results ◽  
Generalized Reynolds Equation

Under severe operating conditions, the thermal effects and various deformations play an important role in determining the performance of misaligned plain journal bearings. However, the thermal effects and various deformations are rarely considered simultaneously in most studies on the misaligned plain journal bearings. In this article, a comprehensive thermoelastohydrodynamic model of the misaligned plain journal bearings is developed that involves the synthetic solution of the generalized Reynolds equation, three-dimensional energy equation, and heat conduction equations of the solids. Based on this model, series of simulation results are provided to examine the influence of the thermal effects and deformations on the behavior of the misaligned plain journal bearings. In addition, the comparisons between the thermohydrodynamic and complete thermoelastohydrodynamic model are also presented for different misalignment angle and magnitude. Results show that the thermal effects and various deformations should not be ignored because of their significant influence on the film thickness, film pressure as well as other bearings characteristics.

Dynamic Behavior of Unbalanced Rigid Shaft Supported on Turbulent Journal Bearings—Theory and Experiment

1990 ◽  
Vol 112 (2) ◽  
pp. 404-408 ◽  
Author(s):  
H. Hashimoto ◽  
S. Wada
Keyword(s):  
Dynamic Behavior ◽  
Equations Of Motion ◽  
Journal Bearings ◽  
Operating Conditions ◽  
Experimental Results ◽  
Fluid Film ◽  
Force Components ◽  
The Stability ◽  
Nonlinear Equations Of Motion ◽  
Analytical Expressions

In this paper, the combined effects of turbulence and fluid film inertia on the dynamic behavior of an unbalanced rigid shaft supported horizontally on two identical aligned short journal bearings are investigated theoretically and experimentally. Utilizing analytical expressions for the dynamic fluid film force components considering the effects of turbulence and fluid film inertia, the nonlinear equations of motion for the rotor-bearing systems are solved by the improved Euler’s forward integration method. The journal center trajectories with unbalance eccentricity ratio of εμ = 0, 0.1 and 0.2 are examined theoretically for Reynolds number of Re = 2750, 4580, and 5500, and the theoretical results are compared with experimental results. From the theoretical and experimental results, it was found that the fluid film inertia improves the stability of unbalanced rigid shaft under certain operating conditions.

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