On the energy equation for fluid-film lubrication

1952 ◽  
Vol 214 (1116) ◽  
pp. 133-136 ◽  
Keyword(s):  
Energy Equation ◽  
Fluid Film ◽  
Qualitative Estimate ◽  
Energy Equations ◽  
Film Lubrication ◽  
Fluid Film Lubrication

The energy equation for fluid-film lubrication is developed in such a way as to resolve the discrepancy that now exists in the literature because of the fact that two obviously different energy equations have been used. A qualitative estimate of the error introduced by the use of the incorrect equation is given.

scholarly journals About the Accuracy and the Grid Convergence of the Numerical Solution of the Energy Equation in Fluid Film Lubrication

2018 ◽  
Author(s):  
Silun Zhang ◽  
Mohamed-Amine Hassini ◽  
Mihai Arghir
Keyword(s):  
Numerical Solution ◽  
Reynolds Equation ◽  
Energy Equation ◽  
Computation Time ◽  
Fluid Film ◽  
Hydrodynamic Analysis ◽  
One Dimensional ◽  
Grid Convergence ◽  
Film Lubrication ◽  
Fluid Film Lubrication

The present work is focused on the numerical solution of the complete energy equation used in fluid film lubrication. The work was motivated by the fact the complete energy equation has no analytic solution that could be used for validations. Its accuracy and computation time are related to the employed numerical method and to the grid resolution. The natural discretization method (NDM) applied on different grids is systematically compared with the spectral method (the Lobatto Point Colocation Method or LPCM) with different polynomial degrees. A one dimensional inclined slider is used for the numerical tests and the energy equation is artificially decoupled from Reynolds. This approach enables to focus all the attention on the numerical solution of the energy equation. The results show that the LPCM is one or two orders of magnitudes more efficient than the NDM in terms of computation time. The energy equation is then coupled with Reynolds equation in a thermo-hydrodynamic analysis of the same 1D slider; the numerical results confirm again the efficiency of the LPCM. A thermo-hydrodynamic analysis of a two-lobe journal bearing is then presented as a practical application.

Nonuniform Temperature in Non-Newtonian Compressible Fluid Film Lubrication of Rollers

1988 ◽  
Vol 110 (4) ◽  
pp. 653-658 ◽  
Author(s):  
Dhaneshwar Prasad ◽  
Punyatma Singh ◽  
Prawal Sinha
Keyword(s):  
Power Law ◽  
Compressible Fluid ◽  
Fluid Film ◽  
Power Law Model ◽  
Pressure Peak ◽  
Energy Equations ◽  
Cylindrical Roller ◽  
Adiabatic Case ◽  
Film Lubrication ◽  
Fluid Film Lubrication

A theoretical analysis of heavily loaded rigid cylindrical roller bearings lubricated by a thin compressible fluid film, considering cavitation, is presented. The lubricating fluid is assumed to follow the non-Newtonian power law model and the consistency as well as density varies exponentially with pressure and temperature. The modified Reynolds and energy equations (adiabatic case) for a compressible power law fluid are obtained and are solved simultaneously. It is observed that the compressible fluid film pressure is comparatively higher than the incompressible one whereas this trend is reversed in case of temperature. Moreover, consistency and density variations, especially in the pressure peak region, are quite significant.

scholarly journals Accuracy and Grid Convergence of the Numerical Solution of the Energy Equation in Fluid Film Lubrication: Application to the 1D Slider

Lubricants ◽  
2018 ◽  
Vol 6 (4) ◽  
pp. 95
Author(s):  
Silun Zhang ◽  
Mohamed-Amine Hassini ◽  
Mihai Arghir
Keyword(s):  
Numerical Solution ◽  
Reynolds Equation ◽  
Energy Equation ◽  
Computation Time ◽  
Fluid Film ◽  
Hydrodynamic Analysis ◽  
One Dimensional ◽  
Grid Convergence ◽  
Film Lubrication ◽  
Fluid Film Lubrication

The present work is focused on the numerical solution of the complete energy equation used in fluid film lubrication. The work was motivated by the fact that the complete energy equation has no analytical solution that can be used for validations. Its accuracy and computation time are related to the employed numerical method and to the grid resolution. The natural discretization method (NDM) applied on different grids is systematically compared with the spectral method (the Lobatto Point Colocation Method or LPCM) with different polynomial degrees. A one dimensional inclined slider is used for the numerical tests, and the energy equation is artificially decoupled from the Reynolds equation. This approach enables us to focus all the attention on the numerical solution of the energy equation. The results show that the LPCM is one or two orders of magnitude more efficient than the NDM in terms of computation time. The energy equation is then coupled with the Reynolds equation in a thermo-hydrodynamic analysis of the same 1D slider; the numerical results confirm again the efficiency of the LPCM. A thermo-hydrodynamic analysis of a two-lobe journal bearing is then presented as a practical application.

Paper 3: Recent Developments in Fluid Film Lubrication Theory

1967 ◽  
Vol 182 (1) ◽  
pp. 36-50 ◽  
Author(s):  
T. Lloyd ◽  
H. McCallion
Keyword(s):  
Finite Difference ◽  
High Speed ◽  
Lubrication Theory ◽  
Fluid Film ◽  
Special Topic ◽  
Finite Difference Schemes ◽  
Great Activity ◽  
Wide Range ◽  
Film Lubrication ◽  
Fluid Film Lubrication

Developments in high-speed electronic computers have greatly influenced the progress in fluid film lubrication over the past ten years. Static and dynamic oil film parameters have been computed for a wide range of finite geometries, for hydrostatic and hydrodynamic bearings lubricated by compressible and incompressible lubricants. These are either sufficient in themselves or else act as a yardstick against which approximate formulas may be tested. Much use has been made of iterative finite difference schemes, which are particularly well suited to digital computers, and these methods are now more fully understood. Other methods of solution include direct inversion of finite difference matrices and solution by expression of the pressure by some infinite series, a finite number of terms of which give adequate representation. Besides the increase in design data available, there has been substantial progress through a re-examination of the effects of modifying some of the assumptions inherent in most of the available solutions of the Reynolds equation. These include the assumption of constant lubricant viscosity, of rigid surfaces and of laminar flow. Major progress has been witnessed in two fields. The interaction of the lubricant film with elastic boundaries has been shown to be of prime importance in highly loaded contacts such as gears. This has led to the development of the special topic of elastohydrodynamic lubrication theory. The applicability of gas bearings in such growing industries as computers, space vehicles and nuclear reactors has resulted in great activity and progress in this field.

The breakdown of fluid film lubrication in elastic-isoviscous point contacts

Wear ◽  
1980 ◽  
Vol 63 (1) ◽  
pp. 25-40 ◽  
Author(s):  
J.B. Medley ◽  
A.B. Strong ◽  
R.M. Pilliar ◽  
E.W. Wong
Keyword(s):  
Fluid Film ◽  
Point Contacts ◽  
Film Lubrication ◽  
Fluid Film Lubrication

scholarly journals Mixed and Fluid Film Lubrication Characteristics of Worn Journal Bearings

2012 ◽  
Vol 2012 ◽  
pp. 1-7 ◽  
Author(s):  
Toshiharu Kazama ◽  
Yukihito Narita
Keyword(s):  
Frictional Coefficient ◽  
Journal Bearings ◽  
Mixed Lubrication ◽  
Operating Conditions ◽  
Fluid Film ◽  
Asperity Contact ◽  
Lubrication Regimes ◽  
Lubrication Characteristics ◽  
Film Lubrication ◽  
Fluid Film Lubrication

The mixed and fluid film lubrication characteristics of plain journal bearings with shape changed by wear are numerically examined. A mixed lubrication model that employs both of the asperity-contact mechanism proposed by Greenwood and Williamson and the average flow model proposed by Patir and Cheng includes the effects of adsorbed film and elastic deformation is applied. Considering roughness interaction, the effects of the dent depth and operating conditions on the loci of the journal center, the asperity-contact and hydrodynamic fluid pressures, friction, and leakage are discussed. The following conclusions are drawn. In the mixed lubrication regime, the dent of the bearing noticeably influences the contact and fluid pressures. For smaller dents, the contact pressure and frictional coefficient reduce. In mixed and fluid film lubrication regimes, the pressure and coefficient increase for larger dents. Furthermore, as the dent increases and the Sommerfeld number decreases, the flow rate continuously increases.

Optimum Design of Hydrostatic Spherical Bearings in Fluid Film Lubrication

2000 ◽  
Vol 122 (4) ◽  
pp. 866-869 ◽  
Author(s):  
Toshiharu Kazama
Keyword(s):  
Optimum Design ◽  
Analytical Solutions ◽  
Power Loss ◽  
Fluid Film ◽  
Optimal Size ◽  
Minimum Power ◽  
Maximum Stiffness ◽  
The Difference ◽  
Film Lubrication ◽  
Fluid Film Lubrication

The optimum design of hydrostatic spherical bearings in fluid film lubrication is examined theoretically. The analytical solutions are derived for both fitted and clearance types of bearings with capillary and orifice restrictors. The optimal size based on the minimum power loss and the maximum stiffness is presented, and the difference between two types of bearings is discussed. [S0742-4787(00)02204-9]

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