The Phan-Thien and Tanner Model Applied to the Lubrication of Knee Prostheses

2019 ◽  
Vol 141 (8) ◽  
Author(s):  
Brenda A. Weiss ◽  
Benyebka Bou-Saïd ◽  
Sebastián Ubal ◽  
José Di Paolo
Keyword(s):  
Elastic Deformation ◽  
Polyethylene Wear ◽  
Quantitative Information ◽  
Knee Prostheses ◽  
Governing Equations ◽  
Cross Model ◽  
Articular Surfaces ◽  
Geometrical Features ◽  
Film Lubrication ◽  
Fluid Film Lubrication

This work aims to provide a contribution to determine a proper model for the study of fluid film lubrication for the reduction of knee prostheses failure due to polyethylene wear. The Phan-Thien and Tanner (PTT) rheological law and the elastic deformation of the articular surfaces were considered in this modeling. The governing equations were solved numerically for different geometries and different Weissenberg numbers. The lubrication approximation applied to the PTT rheological law leads to an expression for the apparent viscosity similar to the Cross model. The results attest the importance of considering the non-Newtonian behavior of the synovial fluid, the elastic deformation, and the geometrical features of the prostheses to obtain quantitative information.

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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