The Isothermal Elastohydrodynamic Lubrication of Spheres

1981 ◽  
Vol 103 (4) ◽  
pp. 547-557 ◽  
Author(s):  
H. P. Evans ◽  
R. W. Snidle
Keyword(s):  
Iterative Method ◽  
Reynolds Equation ◽  
Point Contact ◽  
Numerical Procedure ◽  
Elastohydrodynamic Lubrication ◽  
Hydrodynamic Pressure ◽  
Operating Conditions ◽  
Analysis Of Results ◽  
Approximate Formulas ◽  
Pressure Analysis

The paper describes a numerical procedure for solving the point-contact elastohydrodynamic lubrication problem under isothermal conditions at moderate loads. Results are presented showing the shape of the film and variation of hydrodynamic pressure. Analysis of results for a range of operating conditions gives the following approximate formulas for minimum and central film thickness, repsectively: Hm = 1.9 M−0.17 L0.34 and Ho = 1.7 M−0.026 L0.40 where H, M, and L are the Moes and Bosma nondimensional groups. In common with earlier solutions based upon the forward-iterative method the solution breaks down under moderately heavily loaded conditions. Ways of extending the solution to heavier loads using the authors’ inverse solution of Reynolds’ equation under point-contact elastohydrodynamic conditions are discussed.

Inverse Solution of Reynolds’ Equation of Lubrication Under Point-Contact Elastohydrodynamic Conditions

1981 ◽  
Vol 103 (4) ◽  
pp. 539-546 ◽  
Author(s):  
H. P. Evans ◽  
R. W. Snidle
Keyword(s):  
Film Thickness ◽  
Pressure Distribution ◽  
Reynolds Equation ◽  
Point Contact ◽  
Elastohydrodynamic Lubrication ◽  
Hydrodynamic Pressure ◽  
Inverse Solution ◽  
Heavy Loads

The paper describes a technique for solving the inverse lubrication problem under point contact elastohydrodynamic conditions, i.e. the calculation of a film thickness and shape corresponding to a given hydrodynamic pressure distribution by an inverse solution of Reynolds’ equation. The effect of compressibility and influence of pressure upon viscosity are included in the analysis. The technique will be of use in solving the point contact elastohydrodynamic lubrication problem at heavy loads.

On the Behavior of Friction in Lubricated Point Contact With Provision for Surface Roughness

2009 ◽  
Vol 132 (1) ◽  
Author(s):  
H. Sojoudi ◽  
M. M. Khonsari
Keyword(s):  
Surface Roughness ◽  
Friction Coefficient ◽  
Numerical Solutions ◽  
Point Contact ◽  
Elastohydrodynamic Lubrication ◽  
Hydrodynamic Pressure ◽  
Operating Conditions ◽  
Asperity Contact ◽  
Type Curve ◽  
Lift Off

This paper presents a simple approach to predict the behavior of friction coefficient in the sliding lubricated point contact. Based on the load-sharing concept, the total applied load is supported by the combination of hydrodynamic film and asperity contact. The asperity contact load is determined in terms of maximum Hertzian pressure in the point contact while the fluid hydrodynamic pressure is calculated through adapting the available numerical solutions of elastohydrodynamic lubrication (EHL) film thickness formula for smooth surfaces. The simulations presented cover the entire lubrication regime including full-film EHL, mixed-lubrication, and boundary-lubrication. The results of friction, when plotted as a function of the sum velocity, result in the familiar Stribeck-type curve. The simulations are verified by comparing the results with published experimental data. A parametric study is conducted to investigate the influence of operating condition on the behavior of friction coefficient. A series of simulations is performed under various operating conditions to explore the behavior of lift-off speed. An equation is proposed to predict the lift-off speed in sliding lubricated point contact, which takes into account the surface roughness.

scholarly journals Nano-lubricant film formation due to combined elastohydrodynamic and surface force action under isothermal conditions

2001 ◽  
Vol 215 (9) ◽  
pp. 1019-1029 ◽  
Author(s):  
M. F. Abd-AlSamieh ◽  
H Rahnejat
Keyword(s):  
Film Formation ◽  
Point Contact ◽  
Elastohydrodynamic Lubrication ◽  
Hydrodynamic Pressure ◽  
Surface Force ◽  
Lubricant Film ◽  
Operating Conditions ◽  
Numerical Work ◽  
Isothermal Conditions ◽  
Numerical Predictions

This paper presents the results of numerical prediction of the lubricant film thickness and pressure distribution in concentrated counterformal point contact under isothermal conditions. The operating conditions, which include load and speed of entraining motion, promote the formation of ultra-thin films; these are formed under the combined action of elastohydrodynamic lubrication (EHL), the surface contact force of solvation and molecular interactions due to the presence of Van der Waals forces. A numerical solution has been carried out, using the low-relaxation Newton-Raphson iteration technique, applied to the convergence of the hydrodynamic pressure. The paper shows that the effect of surface forces become significant as the elastic film (i.e. the gap) is reduced to a few nanometres. The numerical predictions have been shown to conform well to the numerical work and experimental findings of other research workers.

Multigrid method for the solution of EHL point contact with bio-based oil as lubricants for smooth and rough asperity

2018 ◽  
Vol 70 (4) ◽  
pp. 599-611 ◽  
Author(s):  
Vishwanath B. Awati ◽  
Shankar Naik ◽  
Mahesh Kumar N.
Keyword(s):  
Design Methodology ◽  
Reynolds Equation ◽  
Multigrid Method ◽  
Approximation Scheme ◽  
Point Contact ◽  
Elastohydrodynamic Lubrication ◽  
Alternative Source ◽  
Content Type ◽  
Longitudinal Roughness ◽  
Isothermal Case

Purpose The purpose of this paper is to study the elastohydrodynamic lubrication point contact problem with bio-based oil as lubricants for an isothermal case. The simulation of the problem is analyzed on smooth and rough asperity. Design/methodology/approach The modified Reynolds equation is discretized using finite difference and multigrid method with full approximation scheme (FAS), applied for its solution with varying load and speed. Findings This paper traces out the comparison of minimum and central film thickness with the standard formulation of Hamrock and Dowson. The effect of longitudinal roughness on surfaces is investigated by means of numerical simulations. Originality/value The results obtained are comparable with the standard results, and are shown by graphs and tables. Bio-based products bring out an alternative source of lubricant to reduce energy crises.

Effect of changing geometrical characteristics for different shapes of a single ridge passing through elastohydrodynamic of point contacts

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Mohamed Abd Alsamieh
Keyword(s):  
Film Thickness ◽  
Pressure Distribution ◽  
Reynolds Equation ◽  
Point Contact ◽  
Elastohydrodynamic Lubrication ◽  
Point Contacts ◽  
Time Step ◽  
Content Type ◽  
Geometrical Characteristics ◽  
Different Shapes

Purpose The purpose of this paper is to study the behavior of a single ridge passing through elastohydrodynamic lubrication of point contacts problem for different ridge shapes and sizes, including flat-top, triangular and cosine wave pattern to get an optimal ridge profile. Design/methodology/approach The time-dependent Reynolds’ equation is solved using Newton–Raphson technique. Several shapes of surface feature are simulated and the film thickness and pressure distribution are obtained at every time step by simultaneous solution of the Reynolds’ equation and film thickness equation, including elastic deformation. Film thickness and pressure distribution are chosen to be the criteria in the comparisons. Findings The geometrical characteristics of the ridge play an important role in the formation of lubricant film thickness profile and the pressure distribution through the contact zone. To minimize wear, friction and fatigue life, an optimal ridge profile should have smooth shape with small ridge size. Obtained results are compared with other published numerical results and show a good agreement. Originality/value The study evaluates the performance of different surface features of a single ridge with different shapes and sizes passing through elastohydrodynamic of point contact problem in relation to film thickness and pressure profile.

Flow Continuity of Isothermal Elastohydrodynamic Point-Contact Lubrication under Different Numerical Iteration Configurations

2021 ◽  
pp. 1-26
Author(s):  
Liangwei Qiu ◽  
Shuangbiao Liu ◽  
Zhijian Wang ◽  
Xiaoyang Chen
Keyword(s):  
Error Control ◽  
Multigrid Method ◽  
Point Contact ◽  
Elastohydrodynamic Lubrication ◽  
Operating Conditions ◽  
Point Contacts ◽  
Numerical Iteration ◽  
Mesh Method ◽  
Iteration Methods ◽  
Relaxation Factors

Abstract Elastohydrodynamic Lubrication (EHL) in point contacts can be numerically solved with various iteration methods, but so far the flow continuity of such solutions has not been explicitly verified. A series of closed regions with the same inlet side boundary is defined and two treatments to total all flows related to the other boundaries of the closed regions are defined to enable flow continuity verifications. The multigrid method and the traditional single mesh method with different relaxation configurations are utilized to solve different cases to evaluate computation efficiencies. For the multigrid method, the combination of a pointwise solver together with hybrid relaxation factors is identified to perform better than other combinations. The single mesh method has inferior degrees of flow continuity than the multigrid method and needs much smaller error control values of pressure to achieve a decent level of flow continuity. Because flow continuity has a physical meaning, its verifications should be routinely included in any self-validation process for any EHL results. Effects of control errors of pressure, mesh sizes, differential schemes and operating conditions on flow continuities are studied. Then, trends of film thickness with respect to speed are briefly discussed with meshes up to 4097 by 4097.

scholarly journals Multiphysics Investigations on the Dynamics of Differential Hypoid Gears

2014 ◽  
Vol 136 (4) ◽  
Author(s):  
M. Mohammadpour ◽  
S. Theodossiades ◽  
H. Rahnejat
Keyword(s):  
Multiscale Analysis ◽  
Point Contact ◽  
Elastohydrodynamic Lubrication ◽  
Transmission Efficiency ◽  
Operating Conditions ◽  
Hypoid Gear ◽  
Tooth Contact Analysis ◽  
Hypoid Gears ◽  
Gear Teeth ◽  
Noise Vibration

Vehicular differential hypoid gears play an important role on the noise, vibration, and harshness (NVH) signature of the drivetrain system. Additionally, the generated friction between their mating teeth flanks under varying load-speed conditions is a source of power loss in a drivetrain while absorbing some of the vibration energy. This paper deals with the coupling between system dynamics and analytical tribology in multiphysics, multiscale analysis. Elastohydrodynamic lubrication (EHL) of elliptical point contact of partially conforming hypoid gear teeth pairs with non-Newtonian thermal shear of a thin lubricant film is considered, including boundary friction as the result of asperity interactions on the contiguous surfaces. Tooth contact analysis (TCA) has been used to obtain the input data required for such an analysis. The dynamic behavior and frictional losses of a differential hypoid gear pair under realistic operating conditions are therefore determined. The detailed analysis shows a strong link between NVH refinement and transmission efficiency, a finding not hitherto reported in literature.

scholarly journals Numerical Modeling of Wear in a Thrust Roller Bearing under Mixed Elastohydrodynamic Lubrication

Lubricants ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 58 ◽  
Author(s):  
Andreas Winkler ◽  
Max Marian ◽  
Stephan Tremmel ◽  
Sandro Wartzack
Keyword(s):  
Numerical Modeling ◽  
Wear Behavior ◽  
Roller Bearing ◽  
Numerical Procedure ◽  
Elastohydrodynamic Lubrication ◽  
Numerical Approach ◽  
Operating Conditions ◽  
Oil Viscosity ◽  
Low Viscosity ◽  
Machine Elements

Increasing efforts to reduce frictional losses and the associated use of low-viscosity lubricants lead to machine elements being operated under mixed lubrication. Consequently, wear effects are also gaining relevance. Appropriate numerical modeling and predicting wear in a reliable manner offers new possibilities for identifying harmful operating conditions or for designing running-in procedures. However, most previous investigations focused on simplified model contacts and the wear behavior of application-oriented contacts is relatively underexplored. Therefore, the contribution of this paper was to provide a numerical procedure for studying the wear evolution in the mixed elastohydrodynamically lubricated (EHL) roller/raceway contact by coupling a finite element method (FEM)-based 3D EHL model with surface topography changes following a local Archard-type wear model, a Greenwood–Williamson-based load-sharing approach and the Sugimura surface adaption model. This study applied the operating conditions of an 81212 thrust roller bearing, considering realistic geometry and locally varying velocities. The calculated wear profiles in the raceway featured asymmetries, which were in good agreement with the experimental results reported in the literature and could be correlated with the velocity and slip distribution. In addition, the effects of speed, load and oil viscosity were investigated by means of four load cases and two lubricants, demonstrating the broad range of applying the numerical approach.

A Full Numerical Solution to the Mixed Lubrication in Point Contacts

1999 ◽  
Vol 122 (1) ◽  
pp. 1-9 ◽  
Author(s):  
Yuan-Zhong Hu ◽  
Dong Zhu
Keyword(s):  
Numerical Solution ◽  
Reynolds Equation ◽  
Surface Deformation ◽  
Full Range ◽  
Computing Time ◽  
Numerical Procedure ◽  
Elastohydrodynamic Lubrication ◽  
Asperity Contact ◽  
Point Contacts ◽  
Severe Condition

A full numerical solution for the mixed elastohydrodynamic lubrication (EHL) in point contacts is presented in this paper, using a new numerical approach that is simple and robust, capable of handling three-dimensional measured engineering rough surfaces moving at different rolling and sliding velocities. The equation system and the numerical procedure are unified for a full coverage of all the lubrication regions including the full film, mixed and boundary lubrication. In the hydrodynamically lubricated areas the Reynolds equation is used. In the asperity contact areas, where the film thickness is zero, the Reynolds equation is reduced to an expression equivalent to the mathematical description of dry contact problem. In order to save computing time, a multi-level integration method is used to calculate surface deformation. Sample cases under severe condition show that this approach is capable of analyzing different cases in a full range of λ ratio, from infinitely large down to nearly zero (less than 0.03). [S0742-4787(00)00101-6]

Elastohydrodynamic lubrication of a circular point contact for a compliant layered surface bonded to a rigid substrate Part 1: Theoretical formulation and numerical method

2000 ◽  
Vol 214 (3) ◽  
pp. 267-279 ◽  
Author(s):  
Z. M. Jin
Keyword(s):  
Numerical Method ◽  
Reynolds Equation ◽  
Point Contact ◽  
Elastohydrodynamic Lubrication ◽  
Contact Radius ◽  
Rigid Substrate ◽  
Theoretical Formulation ◽  
Circular Point ◽  
Present Solution ◽  
Raphson Method

A full numerical analysis of the elastohydrodynamic lubrication problem of a circular point contact involving a compliant layered surface firmly bonded to a rigid substrate is reported in the present study. The Reynolds equation has been solved simultaneously with the full elasticity equation for the layered bearing surface under entraining motion, using the Newton-Raphson method. The theoretical formulation and the numerical method are presented in the present paper (Part 1), together with the comparison of the predicted minimum and central film thickness between the present solution when the contact radius is much smaller than the layer thickness and the results for a semi-infinite solid reported in the literature.

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