Finite Element System Approach to EHL of Elliptical Contacts: Part I—Isothermal Circular Non-Newtonian Formulation

1998 ◽  
Vol 120 (4) ◽  
pp. 695-704 ◽  
Author(s):  
Hsing-Sen S. Hsiao ◽  
Bernard J. Hamrock ◽  
John H. Tripp
Keyword(s):  
Finite Element ◽  
System Approach ◽  
Reynolds Equation ◽  
Solution Method ◽  
Fluid Model ◽  
Elastohydrodynamic Lubrication ◽  
Weak Form ◽  
Weighting Method ◽  
Element System ◽  
User Friendly

The column continuity equation is used in formulating a modified Reynolds equation for elastohydrodynamic lubrication of elliptical contacts. A finite element method (FEM), here the Galerkin weighting method with isoparametric Q9 elements, is used to discretize the weak form of the Reynolds equation. In addition to the nodal pressures and the offset film thickness, the locations of the two-dimensional irregular free boundary are explicitly solved for by simultaneously forcing the essential and the natural Reynolds boundary conditions. Newton-Raphson’s iterations with a user-friendly yet efficient meshless scheme (i.e., automatic meshing-remeshing) are finally applied to solve these equations. A decoupled circular non-Newtonian fluid model is adapted in a way to illustrate the implementation of this new solution method. Extensive results will be given in Part II.

Finite Element System Approach to EHL of Elliptical Contacts: Part II—Isothermal Results and Performance Formulas

1999 ◽  
Vol 121 (4) ◽  
pp. 711-720 ◽  
Author(s):  
Hsing-Sen S. Hsiao ◽  
Juan L Bordon ◽  
Bernard J. Hamrock ◽  
John H. Tripp
Keyword(s):  
Finite Element ◽  
System Approach ◽  
Elastohydrodynamic Lubrication ◽  
Pure Rolling ◽  
Element System ◽  
And Performance ◽  
Good Agreement

Extensive isothermal solutions for elastohydrodynamic lubrication (EHL) of elliptical contacts under pure rolling are obtained by using the newly developed finite element system approach. The Hamrock-Dowson type of performance formula is revisited with these close-to-Newtonian results. Additional solutions are also compared with those obtained by a multigrid technique. The current solutions show good agreement with their existing counterparts.

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.

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.

Finite Element Analysis of Grooved Gas Thrust Bearings and Grooved Gas Face Seals

1993 ◽  
Vol 115 (3) ◽  
pp. 348-354 ◽  
Author(s):  
D. Bonneau ◽  
J. Huitric ◽  
B. Tournerie
Keyword(s):  
Finite Element ◽  
Reynolds Equation ◽  
Weak Form ◽  
Oscillating Solution ◽  
Element Analysis ◽  
Finite Element Program ◽  
Thrust Bearings ◽  
Face Seals ◽  
Element Program ◽  
Gas Seals

A finite element method enabling the Reynolds equation solution for any face geometry of gas thrust bearing or of gas seal is presented. Difficulties due to thickness discontinuities are reduced by integration by parts of the terms involving derivatives. The weak form of the finite element Reynolds equation is then solved and the nonlinearity of the equation leads to the use of Newton-Raphson procedure. The process is fast convergent. The problem of oscillating solution is solved by the use of an upwind procedure. Some numerical examples show the accuracy and efficiency of the procedures. It is shown that the developed finite element program provides a numerical tool, more efficient than the method used until now, for the grooved gas seals design.

EHL of Coated Surfaces: Part II—Non-Newtonian Results

1994 ◽  
Vol 116 (4) ◽  
pp. 786-793 ◽  
Author(s):  
A. A. Elsharkawy ◽  
B. J. Hamrock
Keyword(s):  
Newtonian Fluid ◽  
Reynolds Equation ◽  
Fluid Model ◽  
Elastohydrodynamic Lubrication ◽  
Elastic Half Space ◽  
Hard Coatings ◽  
Surface Shear Stress ◽  
Coating Materials ◽  
Surface Shear ◽  
Pressure Profiles

A complete non-Newtonian elastohydrodynamic lubrication solution for multilayered elastic solids is introduced in this paper. A modified form for the Reynolds equation was derived by incorporating the circular non-Newtonian fluid model associated with a limiting shear strength directly into the momentum equations that govern the instantaneous equilibrium of a fluid element inside the lubricated conjunction. The modified Reynolds equation, the elasticity equations of multilayered elastic half-space, the lubricant pressure-viscosity equation, the lubricant pressure-density equation, and the load equilibrium equation were solved simultaneously by using the system approach. The effects of the surface coating on pressure profiles, film shapes, and surface shear stress profiles are shown. Furthermore, the effects of coating thickness on the minimum film thickness and on the coefficient of friction are presented for different coating materials. The results show that for hard coatings non-Newtonian fluid effects on the pressure profiles and film shapes are significant because of the increase in the contact pressure.

Rheological Models for Thin Film EHL Contacts

1995 ◽  
Vol 117 (1) ◽  
pp. 22-28 ◽  
Author(s):  
Siyoul Jang ◽  
John Tichy
Keyword(s):  
Reynolds Equation ◽  
Fluid Model ◽  
Elastohydrodynamic Lubrication ◽  
Classical Case ◽  
Solid Surfaces ◽  
Nanometer Scale ◽  
Rheological Models ◽  
Flat Surfaces ◽  
Porous Layers ◽  
Viscous Fluid Model

Rheological behavior in concentrated contacts has been studied extensively. In certain conditions such as a rough concentrated contact or sliding of nominally flat surfaces, films may be of molecular (nanometer) scale. The question arises as to whether the application of any viscous fluid model is appropriate. In this study, elastohydrodynamic lubrication analysis is performed on three candidate rheological models: (1) the classical case of viscosity variation with pressure, (2) an isoviscous model which idealizes porous layers on the solid surfaces representing the molecular microstructure, and (3) an isoviscous model which includes van der Waals and solvation surface forces. The latter two models predict behavior similar to classical behavior. The study is not sufficiently sensitive to determine which model best predicts experimental results, but some credence must be given to the latter two because experimental evidence suggests that Reynolds’ equation is not valid for molecularly thin films.

A Circular Non-Newtonian Fluid Model: Part I—Used in Elastohydrodynamic Lubrication

1990 ◽  
Vol 112 (3) ◽  
pp. 486-495 ◽  
Author(s):  
Rong-Tsong Lee ◽  
B. J. Hamrock
Keyword(s):  
Shear Strength ◽  
Newtonian Fluid ◽  
Reynolds Equation ◽  
Fluid Model ◽  
Elastohydrodynamic Lubrication ◽  
Pressure Profile ◽  
Load Parameter ◽  
Viscosity Term ◽  
Pure Rolling ◽  
The Coefficient Of Friction

A circular non-Newtonian fluid model associated with the limiting shear strength was considered. Using this model a modified Reynolds equation was developed which is almost the same as the classical Reynolds equation except for the viscosity term. Results show that the calculation of the central and minimum film thicknesses from the classical Reynolds equation is still valid for pure rolling conditions. The effects on performance of dimensionless load parameter, dimensionless speed parameter, slide/roll ratio, different oils, the limiting shear strength proportionality constant were studied. Such parameters as the pressure profile, the film shape, the coefficient of friction, the dimensionless shear stress at surface a, and the velocitiy contour in the conjunction were considered.

Non-Newtonian Thermal Elastohydrodynamic Lubrication

1991 ◽  
Vol 113 (2) ◽  
pp. 390-396 ◽  
Author(s):  
P. C. Sui ◽  
F. Sadeghi
Keyword(s):  
Film Thickness ◽  
Numerical Solution ◽  
Reynolds Equation ◽  
Fluid Model ◽  
Traction Force ◽  
Elastohydrodynamic Lubrication ◽  
Simultaneous System ◽  
Energy Equations ◽  
Rheology Model ◽  
Generalized Reynolds Equation

A numerical solution to the problem of thermal and non-Newtonian fluid model in elastohydrodynamic lubrication is presented. The generalized Reynolds equation was modified by the Eyring rheology model to incorporate the non-Newtonian effects of the fluid. The simultaneous system of modified Reynolds, elasticity and energy equations were numerically solved for the pressure, temperature and film thickness. Results have been presented for loads ranging from W = 7 × 10−5 to W = 2.3 × 10−4 and the speeds ranging from U* = 2 × 10−11 to U* = 6 × 10−11 at various slip conditions. Comparison between the isothermal and thermal non-Newtonian traction force has also been presented.

A Full-System Approach of the Elastohydrodynamic Line/Point Contact Problem

2008 ◽  
Vol 130 (2) ◽  
Author(s):  
W. Habchi ◽  
D. Eyheramendy ◽  
P. Vergne ◽  
G. Morales-Espejel
Keyword(s):  
Finite Element ◽  
Nonlinear System ◽  
System Approach ◽  
Jacobian Matrix ◽  
Point Contact ◽  
System Of Equations ◽  
Nonlinear System Of Equations ◽  
Full System ◽  
Element Discretization ◽  
Fully Coupled

The solution of the elastohydrodynamic lubrication (EHL) problem involves the simultaneous resolution of the hydrodynamic (Reynolds equation) and elastic problems (elastic deformation of the contacting surfaces). Up to now, most of the numerical works dealing with the modeling of the isothermal EHL problem were based on a weak coupling resolution of the Reynolds and elasticity equations (semi-system approach). The latter were solved separately using iterative schemes and a finite difference discretization. Very few authors attempted to solve the problem in a fully coupled way, thus solving both equations simultaneously (full-system approach). These attempts suffered from a major drawback which is the almost full Jacobian matrix of the nonlinear system of equations. This work presents a new approach for solving the fully coupled isothermal elastohydrodynamic problem using a finite element discretization of the corresponding equations. The use of the finite element method allows the use of variable unstructured meshing and different types of elements within the same model which leads to a reduced size of the problem. The nonlinear system of equations is solved using a Newton procedure which provides faster convergence rates. Suitable stabilization techniques are used to extend the solution to the case of highly loaded contacts. The complexity is the same as for classical algorithms, but an improved convergence rate, a reduced size of the problem and a sparse Jacobian matrix are obtained. Thus, the computational effort, time and memory usage are considerably reduced.

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