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.

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.

An Inverse Solution to the Point Contact EHL Problem Under Heavy Loads

1987 ◽  
Vol 109 (3) ◽  
pp. 432-436 ◽  
Author(s):  
K. P. Hou ◽  
D. Zhu ◽  
S. Z. Wen
Keyword(s):  
Film Thickness ◽  
Numerical Scheme ◽  
Reynolds Equation ◽  
Point Contact ◽  
Inverse Solution ◽  
Computational Results ◽  
Heavy Load ◽  
Operating Region ◽  
Heavy Loads ◽  
The Stability

A set of computational results of the point contact EHL problem under heavily loaded condition is presented in this paper, and the numerical scheme for the inverse solution of the Reynolds Equation is developed. By using a deformation matrix to calculate the local elastic deformation and its inverse matrix to modify the pressure distribution, both the convergence and the stability of the numerical method are satisfactory. The examples of calculation adopted have been extended from Hamrock and Dowson’s cases into the operating region of heavy load. The results obtained have shown the effects of speed, load, and choice of materials on the film thickness, and have proved Hamrock and Dowson’s formulae for estimating film thicknesses to be accurate under heavily loaded condition.

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.

Study on Photoelastic Method for Measuring Elastohydrodynamic Lubrication Pressure in Line Contact

2013 ◽  
Vol 281 ◽  
pp. 329-334
Author(s):  
Jun He ◽  
Huang Ping ◽  
Qian Qian Yang
Keyword(s):  
Film Thickness ◽  
Pressure Distribution ◽  
Reynolds Equation ◽  
Friction Pair ◽  
Elastohydrodynamic Lubrication ◽  
Ccd Camera ◽  
Measuring System ◽  
Line Contact ◽  
Basic Equations ◽  
Plastic Disk

In the present paper, a new method for measuring elastohydrodynamic lubrication (EHL) pressure in line contact is proposed, which is based on the photoelastic technique. The pressure distribution of EHL film and the inner stresses in the friction pairs are fundamental issues to carry out EHL research. The film thickness, pressure and temperature have been successfully obtained with solving the basic equations such as Reynolds equation and energy equation simultaneously or separately, with numerical model of EHL problem. The film thickness can be also measured with the optical interference technique. However, the pressure measurement is still a problem which has not been well solved yet, so as the inner stresses inside the friction pairs. With the experimental mechanics, the photoelastic technique is a possible method to be used for measuring the pressure distribution of EHL film and inner friction pair in the line contact. Therefore, A flat plastic disk and a steel roller compose the frictional pairs of the photoelastic pressure measuring rig with combining the monochromatic LED light source, polarizer CCD camera and stereomicroscope to form the whole pressure measuring system of the line contact EHL. The experimental results with the rig display the typical features of EHL pressure. This shows that the method is feasible to be used for measuring the pressure of EHL film and the inner stresses of the friction pairs in the line contact.

Elastohydrodynamic Lubrication of Circumferentially Finished Rollers having Sinusoidal Roughness

1987 ◽  
Vol 201 (1) ◽  
pp. 29-36 ◽  
Author(s):  
G Karami ◽  
H P Evans ◽  
R W Snidle
Keyword(s):  
Film Thickness ◽  
Point Contact ◽  
Elastohydrodynamic Lubrication ◽  
Hydrodynamic Pressure ◽  
Axial Direction ◽  
Constant Load ◽  
Asperity Contact ◽  
Asperity Contacts ◽  
Roughness Amplitude ◽  
Large Roughness

The paper describes an isothermal elastohydrodynamic lubrication analysis of rollers having circumferential sinusoidal roughness. Theoretical results are shown which demonstrate the influence of roughness amplitude on the distribution of hydrodynamic pressure and film thickness at constant load and constant roughness wavelength. At a large roughness amplitude the hydrodynamic pressure in the valleys between asperity contacts is insignificant and each asperity contact behaves as an ‘isolated’ elastohydrodynamic point contact. As the roughness is reduced, however, the valley pressures build up, the pressure becomes more uniformly distributed in the axial direction and the minimum film thickness increases.

Influence of Laser Micro-Mesh Texturing on the Tribological Performance in an EHL Point Contact

2007 ◽  
Vol 353-358 ◽  
pp. 796-800
Author(s):  
Xiao Wang ◽  
Jian Li ◽  
Wei Chen ◽  
Lan Cai ◽  
Jian Ying Zhu
Keyword(s):  
Friction Coefficient ◽  
Film Thickness ◽  
Pressure Distribution ◽  
Reynolds Equation ◽  
Point Contact ◽  
Tribological Performance ◽  
Design And Optimization ◽  
Thickness Profile ◽  
Wide Range ◽  
Key Factor

Fabricating surfaces with controlled micro-geometry may be an effective approach to improved tribological performance. In this paper, the effect of laser surface micro-mesh texturing on the tribological performance is investigated theoretically with numerical solution of EHL point contact. In the theoretical model, the Reynolds equation is used as the governing equation. Well controlled micro-mesh texturing is described in film thickness equation. By Full Multi-Grid (FMG) method, the solutions of film thickness profile and pressure distribution map are present over a wide range of texturing parameters. The influence of width, depth and orientation of mesh texturing on the friction coefficient is analyzed. Result shows that, the film thickness profile and pressure distribution are sensitive to the parameters of micro-mesh texturing. The curve result of friction coefficient under two load conditions indicated that the parameters of mesh are key factor for texturing design. Solutions demonstrate the ability of numerical simulation on the design and optimization of surface mesh texturing.

Inverse approach for estimating pressure and viscosity in the elastohydrodynamic lubrication of circular contacts

2003 ◽  
Vol 217 (4) ◽  
pp. 277-288 ◽  
Author(s):  
Rong-Tsong Lee ◽  
Hsiao-Ming Chu ◽  
Yuang-Cherng Chiou
Keyword(s):  
Film Thickness ◽  
Pressure Distribution ◽  
Measurement Errors ◽  
Reynolds Equation ◽  
Least Squares Method ◽  
Viscosity Index ◽  
Elastohydrodynamic Lubrication ◽  
Force Balance ◽  
Measuring Point ◽  
Inverse Approach

The film thickness under steady state conditions can be measured by using an optical interferometer. An inverse approach is proposed for estimating the pressure distribution on the basis of film thickness measurement in elastohydrodynamic lubrication (EHL) circular contacts. This approach is constructed from the approximated model of elastic deformation and force balance equations. To obtain an accurate pressure, it is necessary to divide the domain into a few regions on account of the singularity at the pressure spike. The principle of measuring point selection is proposed, and the problem of pressure fluctuation is overcome. On the basis of the smoothed pressure distribution, the apparent viscosity of the film can be obtained from the Reynolds equation. The least-squares method is used to compute the optimum value of the pressure-viscosity index. Results show that the best region for estimating the pressure-viscosity index is along the x axis because the Poiseuille term becomes zero in the Reynolds equation on account of the symmetry. In this region, the estimated pressure-viscosity index shows very good agreement with the exact value when measurement errors are neglected. When measurement errors are taken into account, the close agreement shows the potential of the proposed approach in estimating accurate values of the pressure-viscosity index. Generally, the error in estimating the pressure-viscosity index increases with increasing standard deviation of the measurement error, load, speed, material parameter and absolute error of the measured film thickness. The inverse approach can also be used to estimate the pressure distribution on a film thickness map obtained from an optical EHL tester. Moreover, the agreement between the actual and the estimated values of z is quite good.

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.

Scale Effects in Generalized Newtonian Elastohydrodynamic Films

2008 ◽  
Author(s):  
I. I. Kudish ◽  
P. Kumar ◽  
M. M. Khonsary ◽  
S. Bair
Keyword(s):  
Film Thickness ◽  
Scale Effects ◽  
Point Contact ◽  
Elastohydrodynamic Lubrication ◽  
Viscosity Coefficient ◽  
Shear Thinning ◽  
Effective Pressure ◽  
Practical Advantage ◽  
Inlet Zone ◽  
Real Machine

The prediction of elastohydrodynamic lubrication (EHL) film thickness requires knowledge of the lubricant properties. Today, in many instances, the properties have been obtained from a measurement of the central film thickness in an optical EHL point contact simulator and the assumption of a classical Newtonian film thickness formula. This technique has the practical advantage of using an effective pressure-viscosity coefficient which compensates for shear-thinning. We have shown by a perturbation analysis and by a full EHL numerical solution that the practice of extrapolating from a laboratory scale measurement of film thickness to the film thickness of an operating contact within a real machine may substantially overestimate the film thickness in the real machine if the machine scale is smaller and the lubricant is shear-thinning in the inlet zone.

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