Thermohydrodynamic Lubrication in Laminar and Turbulent Regimes

1974 ◽  
Vol 96 (1) ◽  
pp. 48-56 ◽  
Author(s):  
Z. Safar ◽  
A. Z. Szeri
Keyword(s):  
Boundary Condition ◽  
Effective Viscosity ◽  
Radial Direction ◽  
Energy Equation ◽  
Homogeneous Boundary Condition ◽  
Journal Bearings ◽  
Kantorovich Method ◽  
Local Shear ◽  
Energy Equations ◽  
Laminar And Turbulent Regimes

The distribution of “effective viscosity”—assumed dependent on local shear and temperature—is obtained via iteration between the “long bearing” momentum and energy equations. In this treatment the shaft is isothermal and the bearing conducts heat only in the radial direction. This last assumption leads to essential simplifications: the bearing is replaced by an equivalent homogeneous boundary condition of the energy equation, which thus becomes amenable to solution by the Galerkin-Kantorovich method. The resulting effective viscosity is used to calculate the performance of finite journal bearings.

Thermohydrodynamic Analysis of Journal Bearings Considering Cavitation and Reverse Flow

1988 ◽  
Vol 110 (3) ◽  
pp. 439-447 ◽  
Author(s):  
H. H. Ott ◽  
G. Paradissiadis
Keyword(s):  
Boundary Condition ◽  
Theoretical Model ◽  
Energy Equation ◽  
Journal Bearing ◽  
Reverse Flow ◽  
Iterative Solution ◽  
Journal Bearings ◽  
Flow Area ◽  
Hydrodynamic Journal Bearing ◽  
Energy Equations

The flow field of a hydrodynamic journal bearing is calculated by the iterative solution of the system of Reynolds and energy equations. In the case of reverse flow at the film inlet, the temperature profile there can not be prescribed as a boundary condition but has to be determined from the flow in the film. This is achieved by a separate integration of the energy equation in the reverse flow area. The flow in the cavitation regions is approximated by a theoretical model leading to a form of the energy equation similar to that for pressure regions, thus enabling the integration of the energy equation over the whole film.

Thermohydrodynamic Analysis for Laminar Flow Journal Bearing

1978 ◽  
Vol 100 (4) ◽  
pp. 510-512 ◽  
Author(s):  
Z. S. Safar
Keyword(s):  
Heat Flow ◽  
Radial Direction ◽  
Energy Equation ◽  
Journal Bearing ◽  
Separation Of Variables ◽  
Isoperimetric Problem ◽  
Momentum Equation ◽  
Journal Bearings ◽  
The Third ◽  
Semianalytical Method

This paper describes a semianalytical method for solving the thermohydrodynamic problem in journal bearings. It is assumed that the shaft is isothermal and the bearing heat flow is in the radial direction. The momentum equation is reduced to ordinary differential equations by separation of variables. Two of the resulting equations are integrated directly, while the third equation is interpreted and solved as an isoperimetric problem. The energy equation with its boundary conditions is solved by the Galerkin Kantarovich method.

Research on Energy Equation of Lubrication Model on Large-Scale Journal Bearing System

2010 ◽  
Vol 145 ◽  
pp. 139-144
Author(s):  
Jian Mei Wang ◽  
Qing Xue Huang ◽  
Jian Feng Kang ◽  
Yang Fan
Keyword(s):  
Service Life ◽  
Large Scale ◽  
Energy Equation ◽  
Journal Bearing ◽  
Hydrodynamic Lubrication ◽  
Journal Bearings ◽  
Calculation Results ◽  
Major Factors ◽  
Energy Equations ◽  
Bearing System

To prolong the service life of large-scale journal bearings, the major factors that have influences on bearing performances should be taken into account. By consideration of the variations of viscosity and density with pressure and temperature, a more thorough thermo-hydrodynamic lubrication model was established. With designation of variables with nondimensional parameters, a series of equations were nondimensionied, and the corresponding energy equations at different oil-film layers and boundaries were obtained respectively according to proper difference formats, and then solved by the integration of Finite Difference Method (FDM) with Boundary Element Method (BEM). Calculation results have proved that such complete mathematical model could provide great theoretical guide meaning to improve the lubrication performances and to prolong the service life of contact components of heavy journal bearings.

A Finite Volume Analysis of the Thermohydrodynamic Performance of Finite Journal Bearings

1990 ◽  
Vol 112 (3) ◽  
pp. 557-565 ◽  
Author(s):  
T. Han ◽  
R. S. Paranjpe
Keyword(s):  
Finite Volume ◽  
Numerical Scheme ◽  
Reverse Flow ◽  
Journal Bearings ◽  
Simultaneous Solution ◽  
Volume Analysis ◽  
Recirculating Flow ◽  
Supply Pressure ◽  
Good Sample ◽  
Energy Equations

A rigorous thermohydrodynamic (THD) analysis of finite journal bearings has been developed. THD analysis not only allows a more accurate prediction of the bearing performance characteristics, but it also provides the temperature distribution in the bearing. It involves the simultaneous solution of the Reynolds and energy equations and can handle a wide variety of flow situations, including reverse flow, recirculating flow, and cavitation. The overall numerical scheme is based on a fully conservative finite-volume formulation. The calculated results are compared with the published literature. The qualitative agreement is good. Sample calculations for a typical automotive bearing show that the oil supply pressure and supply configuration significantly affect the bearing performance.

An analytical approach of heat transfer modelling with thermal stresses in circular plate by means of Gaussian heat source and stress function

2021 ◽  
Author(s):  
Sangita Pimpare ◽  
Chandrashekhar Shalik Sutar ◽  
Kamini Chaudhari
Keyword(s):  
Boundary Condition ◽  
Heat Source ◽  
Circular Plate ◽  
Thermal Stresses ◽  
Research Work ◽  
Homogeneous Boundary Condition ◽  
Flux Boundary Condition ◽  
Differential Transform ◽  
The Mathematical Model

Abstract In the proposed research work we have used the Gaussian circular heat source. This heat source is applied with the heat flux boundary condition along the thickness of a circular plate with a nite radius. The research work also deals with the formulation of unsteady-state heat conduction problems along with homogeneous initial and non-homogeneous boundary condition around the temperature distribution in the circular plate. The mathematical model of thermoelasticity with the determination of thermal stresses and displacement has been studied in the present work. The new analytical method, Reduced Differential Transform has been used to obtain the solution. The numerical results are shown graphically with the help of mathematical software SCILAB and results are carried out for the material copper.

scholarly journals Theoretical and Experimental Investigations on Transient Run-Up Procedures of Journal Bearings Including Mixed Friction Conditions

Lubricants ◽  
2018 ◽  
Vol 6 (4) ◽  
pp. 105 ◽  
Author(s):  
Maximilian Prölß ◽  
Hubert Schwarze ◽  
Thomas Hagemann ◽  
Philipp Zemella ◽  
Philipp Winking
Keyword(s):  
Experimental Data ◽  
Energy Equation ◽  
Hydrodynamic Lubrication ◽  
Frictional Coefficient ◽  
Journal Bearings ◽  
Numerical Code ◽  
Experimental Investigations ◽  
Lubrication Regime ◽  
Mixed Friction ◽  
Run Up

This paper focuses on the operating behavior of journal bearings for industrial machinery application during run-ups. For this purpose, a numerical simulation code that is based on a two-dimensional extended and generalized Reynolds equation and a full three-dimensional energy equation, was advanced by a theoretical model considering the effects of mixed friction and warming of journal components during start-up. The mixed friction routine contained the elastic half-spaces model proposed by Boussinesq, which considers the influence of rough surfaces by implementing flow factors and calculates additional stiffness and dissipation in areas with solid interactions. Furthermore, a transient term was added in the energy equation to consider the thermal inertia of journal, and bearing to ensure a realistic heating during run-ups. Results of the prediction were compared to experimental data taken from a special test rig built up for validation procedures. Besides the conventional sensors for temperature, oil flow, and relative motion between shaft and stator, a contact voltage measurement was installed to determine the intensity of mixed friction. The evaluation of experimental data by Stribeck curves, based on a shaft torsion measurement, indicated a significant influence of run-up time on frictional moment. The friction coefficient of the rotor bearing system was strongly influenced by the run-up time. A short run-up time reduced the frictional coefficient in the mixed lubrication regime while the opposite behavior was observed in the hydrodynamic lubrication regime. The numerical code predicted these tendencies in good agreement with experimental data, however, only if the transient energy model was applied.

Paper 6: A Thermohydrodynamic Analysis of Journal Bearings

1966 ◽  
Vol 181 (15) ◽  
pp. 117-126 ◽  
Author(s):  
D. Dowson ◽  
C. N. March
Keyword(s):  
Heat Conduction ◽  
Journal Bearing ◽  
Journal Bearings ◽  
General Nature ◽  
Two Dimensional ◽  
Approximate Representation ◽  
Full Account ◽  
Design Procedures ◽  
Experimental Findings ◽  
Energy Equations

A thermohydrodynamic analysis is discussed which takes account of the general nature of the experimental observations in work which forms part of a programme of research designed to develop an improved understanding of better design procedures for journal bearings. The analysis considers compatible solutions of the Reynolds, energy, and heat conduction equations for two-dimensional conditions. It is shown that the solutions are in reasonable agreement with experimental findings. The two-dimensional solutions of the Reynolds and energy equations take full account of the variation of lubricant properties along and across the film. A very simple and approximate representation is used to estimate the temperature distribution in the bush, but the solutions present a reasonable estimate of bush and shaft temperatures. The ‘thermohydrodynamic’ or ‘heat conduction’ solution to journal bearing problems will provide intermediate, and it is hoped more realistic, results between the extreme ‘isothermal’ and ‘adiabatic’ conditions.

On the Continuous Spectra of Singular Boundary Value Problems

1954 ◽  
Vol 6 ◽  
pp. 420-426 ◽  
Author(s):  
C. R. Putnam
Keyword(s):  
Differential Equation ◽  
Boundary Condition ◽  
Boundary Value ◽  
Homogeneous Boundary Condition ◽  
Continuous Functions ◽  
Singular Boundary ◽  
Singular Boundary Value Problems ◽  
Image Position ◽  
Type 3 ◽  
Point Type

Suppose that p(t) > 0, that both p(t) and f(t) are continuous functions on the half-line 0 ≤ t < ∞, and that λ denotes a real parameter. Only real-valued functions will be considered in this paper. Let the differential equation,be of the limit-point type (3, p. 238), so that (1) and a linear homogeneous boundary condition, 0 ≤ α < π,determine a boundary value problem on 0 ≤ t < ∞ for every fixed α.

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