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.

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.

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.

The elastohydrodynamic lubrication of point contacts at heavy loads

1982 ◽  
Vol 382 (1782) ◽  
pp. 183-199 ◽  
Keyword(s):  
Present Method ◽  
Reynolds Equation ◽  
Pressure Coefficient ◽  
Point Contact ◽  
Elastohydrodynamic Lubrication ◽  
Engineering Practice ◽  
Point Contacts ◽  
Pressure Distributions ◽  
Heavy Loads ◽  
Coefficient Of Viscosity

A method of solving the elastohydrodynamic point contact problem at heavy loads is presented. Earlier solutions based upon straightforward iterative techniques have been restricted to relatively light loads. The present method makes use of the inverse solution of the two-dimensional Reynolds equation and is similar in principle to the well known line contact elastohydrodynamic solution of Dowson and Higginson. The method is applicable to the heavily loaded point contacts found in engineering practice. Material combinations of steel–glass and steel–steel have been considered and results have been obtained at maximum Hertzian pressures of 0.7 GPa and 1.4 GPa respectively. Solutions are presented showing the effect of speed and the influence of the pressure coefficient of viscosity of the lubricant on film thickness and pressure distributions at these heavy loads.

scholarly journals A thermal resistances-based approach for thermal-elastohydrodynamic calculations in point contacts

2017 ◽  
Vol 232 (11) ◽  
pp. 2088-2102 ◽  
Author(s):  
Eduardo de la Guerra Ochoa ◽  
Javier Echávarri Otero ◽  
Enrique Chacón Tanarro ◽  
Benito del Río López
Keyword(s):  
Friction Coefficient ◽  
Film Thickness ◽  
Thermal Effects ◽  
Good Accuracy ◽  
Computational Cost ◽  
Point Contact ◽  
Elastohydrodynamic Lubrication ◽  
Point Contacts ◽  
New Approach ◽  
Ball On Disc

This article presents a thermal resistances-based approach for solving the thermal-elastohydrodynamic lubrication problem in point contact, taking the lubricant rheology into account. The friction coefficient in the contact is estimated, along with the distribution of both film thickness and temperature. A commercial tribometer is used in order to measure the friction coefficient at a ball-on-disc point contact lubricated with a polyalphaolefin base. These data and other experimental results available in the bibliography are compared to those obtained by using the proposed methodology, and thermal effects are analysed. The new approach shows good accuracy for predicting the friction coefficient and requires less computational cost than full thermal-elastohydrodynamic simulations.

Theoretical and experimental studies of the oil film in lubricated point contact

1966 ◽  
Vol 291 (1427) ◽  
pp. 520-536 ◽  
Keyword(s):  
Surface Layer ◽  
Film Thickness ◽  
Strong Evidence ◽  
Experimental Studies ◽  
Point Contact ◽  
Elastohydrodynamic Lubrication ◽  
Experimental Results ◽  
Point Contacts ◽  
Previous Theory ◽  
Oil Film

A technique using Newton’s rings for mapping the oil film of lubricated point contacts is described. A theoretical value for the film thickness of such contacts in elastohydrodynamic lubrication is derived. The experimental results give the exit constriction predicted by previous theory but never shown in detail. The comparison of theoretical and experimental oil film thicknesses, which is satisfactorily accurate, gives strong evidence for a viscous surface layer some 1000Å thick. This film agrees with the known ‘lubricating power’ of the various oils tested.

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.

Solution of the Non-Newtonian Elastohydrodynamic Problem for Circular Contacts Based on a Flow Continuity Method

1996 ◽  
Vol 210 (4) ◽  
pp. 247-258 ◽  
Author(s):  
C A Holt ◽  
H P Evans ◽  
R W Snidle
Keyword(s):  
Film Thickness ◽  
Numerical Solution ◽  
Control Volume ◽  
Point Contact ◽  
Elastohydrodynamic Lubrication ◽  
Theoretical Formulation ◽  
New Approach ◽  
Limiting Shear Stress ◽  
Pure Rolling ◽  
Stress Behaviour

The paper describes a numerical solution method for the point contact elastohydrodynamic lubrication (EHL) problem under non-Newtonian, isothermal conditions. The theoretical formulation of the non-Newtonian effect is general and may be applied to both shear thinning and limiting shear stress behaviour. The particular rheological model investigated in this work is the Eyring ‘sinh law’ relation. The numerical solution of the lubrication equations is based upon a control volume approach rather than the more usual methods that utilize a modified Reynolds equation. This new approach ensures that flow continuity is satisfied at the discretization level. Results are presented to show the effect of non-Newtonian behaviour on film thickness and pressure distribution in circular EHL contacts operating over a range of slide-roll ratios from 0 (pure rolling) to 1.5. Under conditions of pure rolling or low sliding there is found to be little effect of non-Newtonian behaviour, but at the highest degree of sliding the film thickness over the central, flattened area of the contact is reduced by up to 10 per cent at the highest rolling speed of 0.75 m/s.

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.

Elastohydrodynamic Lubrication of Spherical Surfaces of Low Elastic Modulus

1976 ◽  
Vol 98 (4) ◽  
pp. 524-529 ◽  
Author(s):  
S. Biswas ◽  
R. W. Snidle
Keyword(s):  
Elastic Modulus ◽  
Point Contact ◽  
Elastohydrodynamic Lubrication ◽  
Point Contacts ◽  
High Elastic Modulus ◽  
Spherical Surfaces ◽  
Low Elastic Modulus ◽  
Alternative Approach ◽  
Low Modulus ◽  
Theoretical Results

The paper presents a numerical solution for the elastohydrodynamic lubrication of low modulus point contacts which is broadly equivalent to the theory of Grubin for materials of high elastic modulus. The theoretical results obtained for the variation of minimum film thickness using this approach are therefore expected to apply to conditions of high load and low speed. For less severe conditions in which elastic deformation is less significant an alternative approach has been developed. Results of this analysis show the transition from undeformed to heavily loaded conditions. The effect of lubricant starvation has been examined for heavily loaded conditions and the theoretical results are compared with those obtained previously for high elastic modulus point contact.

Uniform Equations in the Inlet and Exit Zones of Heavily Loaded Point and Line Elastohydrodynamically Lubricated Contacts Involved in Various Steady Motions

2015 ◽  
Vol 137 (2) ◽  
Author(s):  
Ilya I. Kudish
Keyword(s):  
Film Thickness ◽  
Point Contact ◽  
Elastohydrodynamic Lubrication ◽  
Point Contacts ◽  
Lubrication Film ◽  
Lubricated Contacts ◽  
Asymptotic Equations ◽  
Line Contacts ◽  
Steady Motions ◽  
Numerical Approaches

Heavily loaded point elastohydrodynamically lubricated (EHL) contacts involved in steady purely transitional, skewed transitional, and transitional with spinning motions are considered. It is shown that in the central parts of the inlet and exit zones of such heavily loaded point EHL contacts the asymptotic equations governing the EHL problem along the lubricant flow streamlines for the above types of contact motions can be reduced to two sets of asymptotic equations: one in the inlet and one in the exit zones. The latter sets of equations are identical to the asymptotic equations describing lubrication process in the inlet and exit zones of the corresponding heavily loaded line EHL contact (Kudish, I. I., 2013, Elastohydrodynamic Lubrication for Line and Point Contacts: Asymptotic and Numerical Approaches, Chapman and Hall/CRC). For each specific motion of a point contact, a separate set of formulas for the lubrication film thickness is obtained. For different types of contact motions, these film thickness formulas differ significantly (Kudish, I. I., 2013, Elastohydrodynamic Lubrication for Line and Point Contacts: Asymptotic and Numerical Approaches, Chapman and Hall/CRC). For heavily loaded contacts, the discovered relationship between point and line EHL problems allows to apply to point contacts most of the results obtained for line contacts (Kudish, I. I., 2013, Elastohydrodynamic Lubrication for Line and Point Contacts: Asymptotic and Numerical Approaches, Chapman and Hall/CRC; Kudish, I. I., and Covitch, M. J., 2010, Modeling and Analytical Methods in Tribology, Chapman and Hall/CRC).

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