A New Analytic Approximation for the Hydrodynamic Forces in Finite-Length Journal Bearings

2009 ◽  
Vol 132 (1) ◽  
Author(s):  
Yaser Bastani ◽  
Marcio de Queiroz
Keyword(s):  
Finite Length ◽  
Reynolds Equation ◽  
Computational Study ◽  
Hydrodynamic Forces ◽  
Journal Bearings ◽  
Closed Form Expression ◽  
Impedance Method ◽  
Analytic Approximation ◽  
State Behavior ◽  
Order Polynomial

A new method for determining a closed-form expression for the hydrodynamic forces in finite-length plain journal bearings is introduced. The method is based on applying correction functions to the force models of the infinitely long (IL) or infinitely short (IS) bearing approximation. The correction functions are derived by modeling the ratio between the forces from the numerical integration of the two-dimensional Reynolds equation and the forces from either the IL or IS bearing approximation. Low-order polynomial models, dependent on the eccentricity ratio and aspect ratio, are used for the correction functions. A comparative computational study is presented for the steady-state behavior of the bearing system under static and unbalance loads. The results show the proposed models outperforming the standard limiting approximations as well as a model based on the finite-length impedance method.

An Alternative Hydrodynamic Force Model for Finite Bearings

2009 ◽  
Author(s):  
Yaser Bastani ◽  
Marcio de Queiroz
Keyword(s):  
Reynolds Equation ◽  
Hydrodynamic Force ◽  
Journal Bearings ◽  
Closed Form Expression ◽  
Force Model ◽  
Eccentricity Ratio ◽  
Form Expression ◽  
Order Polynomial ◽  
Polynomial Models ◽  
Bearing System

A method for determining a closed-form expression for the hydrodynamic forces in finite plain journal bearings is introduced. The method is based on applying correction functions to the force models of the infinitely-long (IL) or infinitely-short (IS) bearing approximation. The correction functions are derived by modeling the ratio between the forces from the numerical integration of the two-dimensional Reynolds equation and the forces from either the IL or IS bearing approximation. Low-order polynomial models, dependent on the eccentricity ratio and aspect ratio, are used for the correction functions. The models are shown to outperform the standard limiting approximations in the steady-state analysis of the bearing system under static loading.

Gas-Lubricated Cylindrical Journal Bearings of the Finite Length: Static Loading

1961 ◽  
Vol 28 (4) ◽  
pp. 535-543 ◽  
Author(s):  
B. Sternlicht
Keyword(s):  
Finite Length ◽  
Static Loading ◽  
Reynolds Equation ◽  
Numerical Solutions ◽  
Journal Bearings ◽  
First Order ◽  
Advantages And Disadvantages ◽  
Iterative Solutions ◽  
Constant Magnitude ◽  
First Order Perturbation

This paper presents numerical solutions of the Reynolds equation for finite length, gas-lubricated cylindrical journal bearings under static loading (this corresponds to a load of constant magnitude and direction with respect to the bearing). It is shown that the incompressible results are but only limiting cases to the more general compressible solutions. The results of the two solutions are dovetailed together through the use of two dimensionless parameters: the inverse of the Sommerfeld number and the compressibility number. Comparisons of the iterative solutions and the first-order perturbation and the “linearized ph” methods are made. The advantages and disadvantages of these methods of analysis are discussed.

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.

Influence of the Lubrication Model on the Dynamic Response of Mechanical Systems

2013 ◽  
Author(s):  
Paulo Flores
Keyword(s):  
Dynamic Response ◽  
Reynolds Equation ◽  
Hydrodynamic Force ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Hydrodynamic Forces ◽  
Journal Bearings ◽  
Dynamic Responses ◽  
Force Model ◽  
Revolute Joints

The main objective of this work is to present a study on the use of different hydrodynamic force models on the dynamic response of mechanical systems with lubricated revolute joints. For this purpose, the fundamental issues related to the classical theory of lubrication for dynamically loaded journal-bearings are revised, which is used to evaluate the Reynolds’ equation for dynamic regime. The hydrodynamic forces that develop at the lubricated revolute joints are determined and included into the dynamic equations of motion. In this study, three different approaches are considered to evaluate the hydrodynamic forces, namely the Pinkus and Sternlicht approach for long journal-bearings and the Frêne et al. models for both long and short journal-bearings. Results for a mechanical system with a lubricated revolute joint are presented and used to discuss the main assumptions and procedures adopted in this work. From the computational simulations performed, it can be observed that the hydrodynamic force model play a crucial role in predicting the dynamic behavior of mechanical systems and originate some uncertainties in their dynamic responses.

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.

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.

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