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]

Numerical Modeling of Mixed Lubrication and Flash Temperature in EHL Elliptical Contacts

2007 ◽  
Vol 130 (1) ◽  
Author(s):  
Neelesh Deolalikar ◽  
Farshid Sadeghi ◽  
Sean Marble
Keyword(s):  
Surface Deformation ◽  
Elastohydrodynamic Lubrication ◽  
Mixed Lubrication ◽  
Asperity Contact ◽  
Lubrication Regime ◽  
Predicting Performance ◽  
Pure Rolling ◽  
Rolling Element ◽  
Contact Pressures ◽  
Film Lubrication

Highly loaded ball and rolling element bearings are often required to operate in the mixed elastohydrodynamic lubrication regime in which surface asperity contact occurs simultaneously during the lubrication process. Predicting performance (i.e., pressure, temperature) of components operating in this regime is important as the high asperity contact pressures can significantly reduce the fatigue life of the interacting components. In this study, a deterministic mixed lubrication model was developed to determine the pressure and temperature of mixed lubricated circular and elliptic contacts for measured and simulated surfaces operating under pure rolling and rolling/sliding condition. In this model, we simultaneously solve for lubricant and asperity contact pressures. The model allows investigation of the condition and transition from boundary to full-film lubrication. The variation of contact area and load ratios is examined for various velocities and slide-to-roll ratios. The mixed lubricated model is also used to predict the transient flash temperatures occurring in contacts due to asperity contact interactions and friction. In order to significantly reduce the computational efforts associated with surface deformation and temperature calculation, the fast Fourier transform algorithm is implemented.

Elastohydrodynamic Lubrication of Soft-Layered Solids at Elliptical Contacts: Part 1: Elasticity Analysis

1994 ◽  
Vol 208 (1) ◽  
pp. 31-41 ◽  
Author(s):  
J Q Yao ◽  
D Dowson
Keyword(s):  
Aspect Ratio ◽  
Surface Deformation ◽  
Applied Pressure ◽  
Numerical Procedure ◽  
Elastohydrodynamic Lubrication ◽  
Thin Layers ◽  
Elasticity Analysis ◽  
Synovial Joint ◽  
Wide Range ◽  
Non Linear System

In this two-part paper we consider the elastohydrodynamic lubrication (EHL) of soft-layered solids representing elliptical contacts. The problem has not previously attracted much attention, partly due to the lack of an effective numerical procedure to solve the coupled non-linear system of equations, but it is essential to the proper design of bearings with soft elastomeric liners and the full understanding of synovial joint lubrication. In Part 1, the elasticity analysis for the surface deformation of a low elastic modulus layer on a hard-backing half-space under various forms of normal loadings is considered, by means of both the rigorous Hankel transform method and various simplifications. For layers of compressible materials (v ≤ 0.4), a generalized foundation model described by a second-order differential equation is proposed to represent the relationship between the surface deformation and the applied pressure. The empirical equation developed in this study is valid for a very wide range of the aspect ratio of the contact and provides an alternative way of modelling the elastic deformation without recourse to the often tedious integration in the numerical analysis of the EHL problem. The simplest form (constrained column model) of the equation, where the surface deformation is directly proportional to the local applied pressure, was found to be reasonably accurate for compressible thin layers (the aspect ratio 2b/ht ≥ 5 and Poisson's ratio v ≤ 0.4).

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.

Effects of Differential Scheme and Mesh Density on EHL Film Thickness in Point Contacts

2006 ◽  
Vol 128 (3) ◽  
pp. 641-653 ◽  
Author(s):  
Yuchuan Liu ◽  
Q. Jane Wang ◽  
Wenzhong Wang ◽  
Yuanzhong Hu ◽  
Dong Zhu
Keyword(s):  
Film Thickness ◽  
Numerical Solution ◽  
System Approach ◽  
Elastohydrodynamic Lubrication ◽  
Mesh Size ◽  
Point Contacts ◽  
Wide Range ◽  
Mesh Density ◽  
Differential Scheme

This paper investigates the effects of differential scheme and mesh density on elastohydrodynamic lubrication (EHL) film thickness based on a full numerical solution with a semi-system approach. The solution variation with different schemes and mesh sizes is revealed based on a set of numerical cases in a wide range of central film thickness from several hundred nanometers down to a few nanometers. It is observed that when the film is thick, the effects of differential schemes and mesh density are not significant. However, if the film becomes ultra-thin, e.g., below 10–20 nanometers, the influence of mesh density and differential schemes becomes more significant, and a proper dense mesh and differential scheme may be highly desirable. The present study also indicates that the solutions from the 1st-order backward scheme give the largest film thickness among all the solutions from different schemes at the same mesh size.

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.

Film Thickness and Asperity Load Formulas for Line-Contact Elastohydrodynamic Lubrication With Provision for Surface Roughness

2012 ◽  
Vol 134 (1) ◽  
Author(s):  
M. Masjedi ◽  
M. M. Khonsari
Keyword(s):  
Surface Roughness ◽  
Film Thickness ◽  
Reynolds Equation ◽  
Surface Deformation ◽  
Elastohydrodynamic Lubrication ◽  
Load Ratio ◽  
Material Surface ◽  
Line Contact ◽  
Wide Range ◽  
Minimum Film Thickness

Three formulas are derived for predicting the central and the minimum film thickness as well as the asperity load ratio in line-contact EHL with provision for surface roughness. These expressions are based on the simultaneous solution to the modified Reynolds equation and surface deformation with consideration of elastic, plastic and elasto-plastic deformation of the surface asperities. The formulas cover a wide range of input and they are of the form f(W, U, G, σ¯, V), where the parameters represented are dimensionless load, speed, material, surface roughness and hardness, respectively.

A Computer Thermal Model of Mixed Lubrication in Point Contacts

2004 ◽  
Vol 126 (1) ◽  
pp. 162-170 ◽  
Author(s):  
Wen-Zhong Wang ◽  
Yu-Chuan Liu ◽  
Hui Wang ◽  
Yuan-Zhong Hu
Keyword(s):  
Surface Temperature ◽  
Thermal Model ◽  
Reynolds Equation ◽  
Equation System ◽  
Mixed Lubrication ◽  
Successful Implementation ◽  
Asperity Contact ◽  
Point Contacts ◽  
Wide Range ◽  
Lubrication Conditions

This paper presents a transient thermal model for mixed lubrication problems in point contacts. The model deterministically calculates pressure and surface temperature by simultaneously solving a system of equations that govern the lubrication, contact and thermal behaviors of a point contact interface. The pressure distribution on the entire computation domain is obtained through solving a unified Reynolds equation system without identifying hydrodynamic or asperity contact regions. The point heat source integration method is applied to determine the temperature distributions on contact surfaces. The interactions between pressure and temperature are considered through incorporating viscosity-temperature and density-temperature relations in the Reynolds equation, then solving the equation system iteratively. With the successful implementation of an FFT-based algorithm (DC-FFT) for calculation of surface deformation and temperature rise, the numerical analysis of lubricated contact problems, which used to involve a great deal of computation, can be performed in acceptable time. The model enables us to simulate various lubrication conditions, from full film elastohydrodynamic lubrication (EHL) to boundary lubrication, for a better understanding of the effect of surface roughness. Numerical examples are analyzed and the results show that the present model can be used to predict pressure and surface temperature over a wide range of lubrication conditions, and that the solution methods are computationally efficient and robust.

Isothermal Elastohydrodynamic Lubrication of Point Contacts: Part 1—Theoretical Formulation

1976 ◽  
Vol 98 (2) ◽  
pp. 223-228 ◽  
Author(s):  
B. J. Hamrock ◽  
D. Dowson
Keyword(s):  
Numerical Analysis ◽  
Entire Range ◽  
Reynolds Equation ◽  
Point Contact ◽  
Elastohydrodynamic Lubrication ◽  
Uniform Pressure ◽  
Point Contacts ◽  
Elasticity Analysis ◽  
Simultaneous Solution ◽  
Theoretical Formulation

The analysis of an isothermal elastohydrodynamic lubrication (EHL) point contact was evaluated numerically. This required the simultaneous solution of the elasticity and Reynolds equations. In the elasticity analysis the contact zone is divided into equal rectangular areas and it is assumed that a uniform pressure is applied over each element. In the numerical analysis of the Reynolds’ equation a phi analysis where phi is equal to the pressure times the film thickness to the 3/2 power is used to help the relaxation process. The EHL point contact analysis is applicable for the entire range of elliptical parameters and is valid for any combination of rolling and sliding within the contact.

Rolling of an Elastic Ellipsoid Upon an Elastic-Plastic Flat

2007 ◽  
Vol 129 (4) ◽  
pp. 791-800 ◽  
Author(s):  
Daniel Nélias ◽  
Eduard Antaluca ◽  
Vincent Boucly
Keyword(s):  
Surface Deformation ◽  
Normal Load ◽  
Permanent Deformation ◽  
Computing Time ◽  
Equivalent Plastic Strain ◽  
Numerical Procedure ◽  
Theoretical Background ◽  
Rolling Contact ◽  
Von Mises Stress ◽  
Elastic Plastic

The paper presents a numerical analysis of the rolling contact between an elastic ellipsoid and an elastic-plastic flat. Numerical simulations have been performed with the help of a contact solver called Plast-Kid®, with an algorithm based on an integral formulation or semi-analytical method. The application of both the conjugate gradient method and the discrete convolution and fast Fourier transform technique allows keeping the computing time reasonable when performing transient 3D simulations while solving the contact problem and calculating the subsurface stress and strain states. The effects of the ellipticity ratio k—ranging from 1 to 16—and of the normal load—from 4.2 GPa to 8 GPa—are investigated. The reference simulation corresponds to the rolling of a ceramic ball on a steel plate made of an AISI 52100 bearing steel under a load of 5.7 GPa. The results that are presented are, first, the permanent deformation of the surface and, second, the contact pressure distribution, the von Mises stress field, the hydrostatic pressure, and the equivalent plastic strain state within the elastic-plastic body. A comparison with an experimental surface deformation profile is also given to validate the theoretical background and the numerical procedure.

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