An Efficient Algorithm for Thermal Elastohydrodynamic Lubrication Under Rolling/Sliding Line Contacts

1994 ◽  
Vol 116 (4) ◽  
pp. 762-769 ◽  
Author(s):  
Chao-Ho Hsu ◽  
Rong-Tsong Lee
Keyword(s):  
Film Thickness ◽  
Thermal Loading ◽  
Reduction Factor ◽  
Difference Approximation ◽  
Central Difference ◽  
Integration Algorithm ◽  
Wide Range ◽  
Minimum Film Thickness ◽  
Line Contacts ◽  
Thermal Ehl

One of the most time-consuming routines in thermal EHL problem is the calculation of the surface temperature integral. Combining the multigrid technique and the Newton-Raphson method, a modified multilevel, multi-integration algorithm for this integral is developed that can reduce the computational complexity from O (n2) to O (n ln n) for the thermal EHL problem of rolling/sliding line contacts. The employed standard central difference approximation to the coupled Reynolds and energy equations can yield the maximum difference of mass flow flux within one percent. Effects of dimensionless load, dimensionless materials parameter, slip ratio, and thermal loading parameter on the minimum film thickness are investigated. Correlation formula of thermal reduction factor for the minimum film thickness is derived for a wide range of slip ratios, loads, thermal loading parameters, and materials parameters.

Thermal Elastohydrodynamic Lubrication of Heavily Loaded Line Contacts—An Efficient Inlet Zone Analysis

1998 ◽  
Vol 120 (1) ◽  
pp. 119-125 ◽  
Author(s):  
Mihir K. Ghosh ◽  
Raj K. Pandey
Keyword(s):  
Film Thickness ◽  
Thermal Loading ◽  
Elastohydrodynamic Lubrication ◽  
Thermal Reduction ◽  
Reduction Factor ◽  
Computationally Efficient ◽  
Rolling Velocity ◽  
Minimum Film Thickness ◽  
Line Contacts ◽  
Inlet Zone

An inlet zone analysis of TEHD lubrication of heavily loaded line contacts has been done using a computationally efficient and accurate numerical method based on Lobatto quadrature developed by Elrod and Brewe (1986). The results under extremely heavy conditions of dimensionless load W = 5.2*10−4 (pH = 2.0 GPa) and dimensionless rolling velocity U = 2.0*10−10(50 m/s) are presented. Significant reduction in thermal reduction factor (film thickness) at high rolling speeds relative to isothermal conditions have been observed. The results of the present work have been compared with the results of Wilson and Sheu (1983) and Hsu and Lee (1994). A correction formula of the thermal reduction factor for the minimum film thickness has been derived for a range of thermal loading parameters, loads, and slip ratios.

scholarly journals Analysis of Starvation Effects on Hydrodynamic Lubrication in Nonconforming Contacts

1982 ◽  
Vol 104 (3) ◽  
pp. 410-417 ◽  
Author(s):  
D. E. Brewe ◽  
B. J. Hamrock
Keyword(s):  
Film Thickness ◽  
Hydrodynamic Lubrication ◽  
Three Dimensional ◽  
Point Contact ◽  
Sharp Decrease ◽  
Reduction Factor ◽  
Wide Range ◽  
Minimum Film Thickness ◽  
Contour Plots ◽  
Starvation Effects

Numerical methods were used to determine the effects of lubricant starvation on the minimum film thickness under conditions of a hydrodynamic point contact. Starvation was effected by varying the fluid inlet level. The Reynolds boundary conditions were applied at the cavitation boundary and zero pressure was stipulated at the meniscus or inlet boundary. The analysis is considered valid for a range of speeds and loads for which thermal, piezoviscous, and deformation effects are negligible. It is applied to a wide range of geometries (i.e., from a ball-on-plate configuration to a ball in a conforming groove). Seventy-four cases were used to numerically determine a minimum-film-thickness equation as a function of the ratio of dimensionless load to dimensionless speed for varying degrees of starvation. From this, a film reduction factor was determined as a function of the fluid inlet level. Further, a starved fully flooded boundary was defined and an expression determining the onset of starvation was derived. As the degree of starvation was increased, the minimum film thickness decreased gradually until the fluid inlet level became critical. Reducing the fluid inlet level still further led to a sharp decrease in the minimum film thickness. An expression determining the critically starved fluid inlet level was derived. The changes in the inlet pressure buildup due to changing the available lubricant supply are presented in the form of three-dimensional isometric plots and also in the form of contour plots.

scholarly journals Analytical Formula for the Ratio of Central to Minimum Film Thickness in a Circular EHL Contact

Lubricants ◽  
2018 ◽  
Vol 6 (3) ◽  
pp. 80 ◽  
Author(s):  
Petr Sperka ◽  
Ivan Krupka ◽  
Martin Hartl
Keyword(s):  
Experimental Data ◽  
Film Thickness ◽  
Analytical Formula ◽  
Numerical Calculations ◽  
Constant Ratio ◽  
Viscosity Coefficients ◽  
Wide Range ◽  
Minimum Film Thickness ◽  
Film Parameter ◽  
Ehl Contact

Prediction of minimum film thickness is often used in practice for calculation of film parameter to design machine operation in full film regime. It was reported several times that majority of prediction formulas cannot match experimental data in terms of minimum film thickness. These standard prediction formulas give almost constant ratio between central and minimum film thickness while numerical calculations show ratio which spans from 1 to more than 3 depending on M and L parameters. In this paper, an analytical formula of this ratio is presented for lubricants with various pressure–viscosity coefficients. The analytical formula is compared with optical interferometry measurements and differences are discussed. It allows better prediction, compared to standard formulas, of minimum film thickness for wide range of M and L parameters.

Thermal Non-Newtonian Elastohydrodynamic Lubrication of Line Contacts Under Simple Sliding Conditions

1992 ◽  
Vol 114 (2) ◽  
pp. 317-327 ◽  
Author(s):  
Shao Wang ◽  
T. F. Conry ◽  
C. Cusano
Keyword(s):  
Film Thickness ◽  
Surface Temperature ◽  
Thermal Effects ◽  
Elastohydrodynamic Lubrication ◽  
Reduction Factor ◽  
Simple Formulation ◽  
Maximum Surface ◽  
Line Contacts ◽  
Traction Coefficient ◽  
Maximum Surface Temperature

A computationally simple formulation for the stationary surface temperature is developed to examine the thermal non-Newtonian EHD problem for line contacts under simple sliding conditions. Numerical results obtained are used to develop a formula for a thermal and non-Newtonian (Ree-Eyring) film thickness reduction factor. Results for the maximum surface temperature and traction coefficient are also presented. The thermal effects on film thickness and traction are found to be more pronounced for simple sliding than for combined sliding and rolling conditions.

Effect of Stiff Coatings on EHL Film Thickness in Point Contacts

2007 ◽  
Author(s):  
Yuchuan Liu ◽  
Q. Jane Wang ◽  
Dong Zhu
Keyword(s):  
Film Thickness ◽  
Working Conditions ◽  
Coating Thickness ◽  
Point Contact ◽  
Thickness Variation ◽  
Point Contacts ◽  
Lubricant Film Thickness ◽  
Wide Range ◽  
Minimum Film Thickness ◽  
Coating Material Properties

This study investigates the influences of coating material properties and coating thickness on lubricant film thickness based on a point-contact isothermal EHL model developed recently by the authors. The results present the trend of minimum film thickness variation as a function of coating thickness and elastic modulus under a wide range of working conditions. Numerical results indicates that the increase in minimum film thickness, Imax, and the corresponding optimal dimensionless coating thickness, H2, can be expressed in the following formulas: Imax=0.766M0.0248R20.0296L0.1379exp(−0.0245ln2L)H2=0.049M0.4557R2−0.1722L0.7611exp(−0.0504ln2M−0.0921ln2L) These formulas can be used to estimate the effect of a coating on EHL film thickness.

scholarly journals Elastohydrodynamic Film Thickness Model for Heavily Loaded Contacts

1974 ◽  
Vol 96 (3) ◽  
pp. 472-479 ◽  
Author(s):  
S. H. Loewenthal ◽  
R. J. Parker ◽  
E. V. Zaretsky
Keyword(s):  
Film Thickness ◽  
Measured Data ◽  
Type Ii ◽  
X Ray ◽  
Polyphenyl Ether ◽  
Load Dependence ◽  
Test Conditions ◽  
Wide Range ◽  
Minimum Film Thickness ◽  
Thickness Measurements

An empirical elastohydrodynamic (EHD) film thickness formula for predicting the minimum film thickness occurring within heavily loaded contacts (maximum Hertz stresses above 1.04 × 109 N/m2 (150,000 psi)) was developed. The formula was based upon X-ray film thickness measurements made with synthetic paraffinic, fluorocarbon, Type II ester and polyphenyl ether fluids covering a wide range of test conditions. Comparisons were made between predictions from an isothermal EHD theory and the test data. The deduced relationship was found to adequately reflect the high-load dependence exhibited by the measured data. The effects of contact geometry, material and lubricant properties on the form of the empirical model are also discussed.

The Elastohydrodynamic Lubrication of Elliptical Point Contacts Operating in the Isoviscous Region

1995 ◽  
Vol 209 (4) ◽  
pp. 225-234 ◽  
Author(s):  
C J Hooke
Keyword(s):  
Film Thickness ◽  
Elastohydrodynamic Lubrication ◽  
Operating Conditions ◽  
Radius Ratio ◽  
Point Contacts ◽  
Reasonable Estimate ◽  
Wide Range ◽  
Minimum Film Thickness

The elastohydrodynamic lubrication of point contacts is examined and results for the minimum film thickness are presented for a wide range of radius ratios and operating conditions. The results are compared with the predictions of the appropriate regime formulae. Although these formulae give a reasonable estimate of the contact's behaviour, the actual clearances are often substantially different, particularly close to the regime boundaries. Interpolation equations for seven values of radius ratio are given and these should be sufficient to allow the minimum clearance to be estimated for most isoviscous point contacts.

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.

Multigrid, An Alternative Method for Calculating Film Thickness and Pressure Profiles in Elastohydrodynamically Lubricated Line Contacts

1986 ◽  
Vol 108 (4) ◽  
pp. 551-556 ◽  
Author(s):  
A. A. Lubrecht ◽  
W. E. ten Napel ◽  
R. Bosma
Keyword(s):  
Film Thickness ◽  
Multigrid Method ◽  
Computing Time ◽  
Alternative Method ◽  
Pressure Profiles ◽  
Minimum Film Thickness ◽  
Line Contacts ◽  
Pressure Spike ◽  
Order Of Magnitude

Film thickness and pressure profiles have been calculated for line contacts at moderate and high loads, using a Multigrid method. Influence of the compressibility of the lubricant on the minimum film thickness and on the pressure spike has been examined. The required computing time is an order of magnitude less than when using the previous methods.

The Minimum Film Thickness in Line Contacts During Reversal of Entrainment

1993 ◽  
Vol 115 (1) ◽  
pp. 191-199 ◽  
Author(s):  
C. J. Hooke
Keyword(s):  
Steady State ◽  
Film Thickness ◽  
Rate Of Change ◽  
Radius Of Curvature ◽  
Operating Cycle ◽  
Minimum Film Thickness ◽  
Line Contacts ◽  
Involute Gears ◽  
Shaft Seals ◽  
Steady State Predictions

In contacts, such as cams, non-involute gears and shaft seals, where the direction of entrainment reverses during the operating cycle, the minimum film thickness is typically found just after the reversal. This paper shows that this minimum film thickness is determined by the rate of change of the entraining velocity and by the fluid and surface properties. For line contacts, four regimes of lubrication are found—as for the steady-state situation—and expressions for the film thickness in each regime are developed. This enables an outline design chart for the minimum film thickness to be constructed. It is shown that this information, together with the steady-state predictions is sufficient to determine the variation of film thickness with time in most situations where load, radius of curvature, and entraining velocity vary.

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