scholarly journals The Solution of the Elrod Algorithm for a Dynamically Loaded Journal Bearing Using Multigrid Techniques

1989 ◽  
Vol 111 (2) ◽  
pp. 302-308 ◽  
Author(s):  
C. M. Woods ◽  
D. E. Brewe
Keyword(s):  
Reynolds Equation ◽  
Journal Bearing ◽  
Control Volume ◽  
Computational Time ◽  
Iterative Technique ◽  
Solution Approach ◽  
Present Solution ◽  
Dynamically Loaded ◽  
Control Volume Approach ◽  
Mixed Nature

Numerical solution to a theoretical model of vapor cavitation in a dynamically loaded journal bearing is developed, utilizing a multigrid iterative technique. The method is compared with a noniterative approach in terms of computational time and accuracy. The computational model is based on the Elrod algorithm, a control volume approach to the Reynolds equation which mimics the Jakobsson-Floberg and Olsson cavitation theory. Besides accounting for a moving cavitation boundary and conservation of mass at the boundary, it also conserves mass within the cavitated region via a smeared mass or striated flow extending to both surfaces in the film gap. The mixed nature of the equations (parabolic in the full film zone and hyperbolic in the cavitated zone) coupled with the dynamic aspects of the problem create interesting difficulties for the present solution approach. Emphasis is placed on the methods found to eliminate solution instabilities. Excellent results are obtained for both accuracy and reduction of computational time.

A Hybrid Mobility Solution Approach for Dynamically Loaded Misaligned Journal Bearings

2012 ◽  
Vol 135 (2) ◽  
Author(s):  
S. Boedo
Keyword(s):  
Finite Element ◽  
Reynolds Equation ◽  
Solution Method ◽  
Journal Bearings ◽  
Finite Element Solution ◽  
Computational Time ◽  
Element Solution ◽  
Solution Approach ◽  
Dynamically Loaded ◽  
Mobility Solution

This paper presents a hybrid mobility solution approach to the analysis of dynamically loaded misaligned journal bearings. Mobility data obtained for misaligned bearings (calculated from a finite element representation of the Reynolds equation) are compared with existing curve-fitted mobility maps representative of a perfectly aligned bearing. A relative error analysis of mobility magnitude and direction provides a set of misaligned journal bearing configurations (midplane eccentricity ratio and normalized misalignment angle), where existing curve-fitted mobility map components based on aligned bearings can be used to calculate the resulting journal motion. For bearing configurations where these mobility maps are not applicable, the numerical simulation process proceeds using a complete finite element solution of the Reynolds equation. A numerical example representing a misaligned main bearing in a four-stroke automotive engine illustrates the hybrid solution method. Substantial savings in computational time are obtained using the hybrid approach over the complete finite element solution method without loss of computational accuracy.

A Hybrid Mobility Solution Method for Dynamically Loaded Misaligned Journal Bearings

2012 ◽  
Author(s):  
S. Boedo
Keyword(s):  
Finite Element ◽  
Reynolds Equation ◽  
Solution Method ◽  
Hybrid Approach ◽  
Journal Bearings ◽  
Finite Element Solution ◽  
Computational Time ◽  
Element Solution ◽  
Dynamically Loaded ◽  
Mobility Solution

This paper presents a hybrid mobility solution approach to the analysis of dynamically loaded misaligned journal bearings. Mobility data obtained for misaligned bearings (calculated from a finite element representation of the Reynolds equation) are compared with existing curve-fitted mobility maps representative of a perfectly aligned bearing. A relative error analysis of mobility magnitude and direction provides a set of misaligned journal bearing configurations (midplane eccentricity ratio and normalized misalignment angle) where existing curve-fitted mobility map components based on aligned bearings can be used to calculate the resulting journal motion. For bearing configurations where these mobility maps are not applicable, the numerical simulation process proceeds using a complete finite element solution of the Reynolds equation. A set of numerical examples representing misaligned main and connecting rod bearings in a four-stroke automotive engine illustrate the hybrid solution method. Substantial savings in computational time are obtained using the hybrid approach over the complete finite element solution method without loss of computational accuracy.

Dynamic Loading of Micropolar Fluid Lubricated Short Journal Bearings

1981 ◽  
Vol 23 (1) ◽  
pp. 37-44
Author(s):  
C. Singh ◽  
P. Sinha
Keyword(s):  
Micropolar Fluid ◽  
Effective Viscosity ◽  
Reynolds Equation ◽  
Dynamic Behaviour ◽  
Journal Bearing ◽  
Constant Load ◽  
Journal Bearings ◽  
Detailed Consideration ◽  
Dynamically Loaded ◽  
Sinusoidal Load

Dynamically loaded bearings in which the load alternates or rotates are studied in this paper. The Reynolds equation for the general case of a dynamically loaded infinitely short bearing is derived, where the lubricant is assumed to be micropolar. Detailed consideration is given to the dynamic behaviour of squeeze films in a short journal bearing under a sinusoidal load with no journal rotation. Various bearing characteristics are calculated, assuming a full film to exist. The micropolarity of the fluid results in more resistance to journal motion, thereby allowing smaller eccentricities for a constant load. The overall conclusion of this study is an increase in the effective viscosity due to the micropolarity of the lubricant. This theory may find application in lubrication when additives are used.

scholarly journals A Simplified Mass Conserving Algorithm for Journal Bearing under Large Dynamic Loads

2001 ◽  
Vol 7 (1) ◽  
pp. 41-51 ◽  
Author(s):  
H. Hirani ◽  
K. Athre ◽  
S. Biswas
Keyword(s):  
Reynolds Equation ◽  
Journal Bearing ◽  
Computational Method ◽  
Maximum Pressure ◽  
Entry And Exit ◽  
Main Bearing ◽  
Solution Approach ◽  
Analytical Technique ◽  
Oil Flow ◽  
Force Components

A simplified mass conserving solution approach, consisting of analytical and numerical methods, for performance evaluation of dynamically loaded journal bearings is presented. The analytical technique is used to determine position and velocity of journal center for given force components. Subsequently a finite difference formulation of universal Reynolds equation is used to calculate realistic oil flow. The proposed formulation is applied for analysis of an engine main bearing. The entry and exit flow and maximum pressure in the bearing are determined over complete cycle and matched with published results obtained by numerical scheme. The suggested hybrid computational method typically takes 55 s on ICL DRS 6000, and 29 s on 150 MHz Pentium-Pro computer.

scholarly journals Theoretical Modeling of the Vapor Cavitation in Dynamically Loaded Journal Bearings

1986 ◽  
Vol 108 (4) ◽  
pp. 628-637 ◽  
Author(s):  
D. E. Brewe
Keyword(s):  
High Speed ◽  
Reynolds Equation ◽  
Control Volume ◽  
Circular Path ◽  
High Speed Photography ◽  
Computational Domain ◽  
Alternating Direction Implicit ◽  
Alternating Direction ◽  
Dynamically Loaded ◽  
Volume Method

A theoretical investigation is made of the evolution of a vapor bubble for a submerged journal bearing under dynamically loaded conditions. The solution to the Reynolds equation is determined numerically using a control volume method (Elrod algorithm). This method conserves mass throughout the computational domain including the liquid-vapor interface which may or may not be in motion relative to the minimum film line. An ADI (Alternating Direction Implicit) method is used to effect the time march. Excellent agreement was found with the experimental work of Jakobsson and Floberg for stationary cavitation. Predictions of bubble life for nonstationary cavitation compare reasonably well with that measured by Jacobson and Hamrock using high-speed photography. A comparison study was performed to determine some of the consequences of applying a nonconservative theory to a dynamic problem. A complete dynamic cycle of a journal whirling in a circular path was chosen for the basis of comparison. Significant differences were observed in the load components near the end of the cycle. In each case, onset of cavitation was observed followed by bubble growth and subsequent collapse. More complete details of this phenomena are illustrated with the use of perspective graphic plots depicting the associated pressure distribution and region of cavitation with position and motion of the journal within the housing.

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.

A Control-Volume Model of the Compressible Euler Equations with a Vertical Lagrangian Coordinate

2013 ◽  
Vol 141 (7) ◽  
pp. 2526-2544 ◽  
Author(s):  
Xi Chen ◽  
Natalia Andronova ◽  
Bram Van Leer ◽  
Joyce E. Penner ◽  
John P. Boyd ◽  
...  
Keyword(s):  
Euler Equations ◽  
Control Volume ◽  
Test Cases ◽  
Riemann Solver ◽  
New Approach ◽  
Vertical Coordinate ◽  
Low Mach Number ◽  
Atmospheric Flows ◽  
Lagrangian Coordinate ◽  
Control Volume Approach

Abstract Accurate and stable numerical discretization of the equations for the nonhydrostatic atmosphere is required, for example, to resolve interactions between clouds and aerosols in the atmosphere. Here the authors present a modification of the hydrostatic control-volume approach for solving the nonhydrostatic Euler equations with a Lagrangian vertical coordinate. A scheme with low numerical diffusion is achieved by introducing a low Mach number approximate Riemann solver (LMARS) for atmospheric flows. LMARS is a flexible way to ensure stability for finite-volume numerical schemes in both Eulerian and vertical Lagrangian configurations. This new approach is validated on test cases using a 2D (x–z) configuration.

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