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.

scholarly journals A Quantitative Determination of Minimum Film Thickness in Elastohydrodynamic Circular Contacts

2021 ◽  
Author(s):  
Wassim Habchi ◽  
Philippe Vergne
Keyword(s):  
Experimental Data ◽  
Finite Element ◽  
Numerical Model ◽  
Film Thickness ◽  
Quantitative Determination ◽  
Excellent Agreement ◽  
Operating Conditions ◽  
Pure Rolling ◽  
Minimum Film Thickness

Abstract The current work presents a quantitative approach for the prediction of minimum film thickness in elastohydrodynamic lubricated (EHL) circular contacts. In contrast to central film thickness, minimum film thickness can be hard to accurately measure, and it is usually poorly estimated by classical analytical film thickness formulae. For this, an advanced finite-element-based numerical model is used to quantify variations of the central-to-minimum film thickness ratio with operating conditions, under isothermal Newtonian pure-rolling conditions. An ensuing analytical expression is then derived and compared to classical film thickness formulae and to more recent similar expressions. The comparisons confirmed the inability of the former to predict the minimum film thickness, and the limitations of the latter, which tend to overestimate the ratio of central-to-minimum film thickness. The proposed approach is validated against numerical results as well as experimental data from the literature, revealing an excellent agreement with both. This framework can be used to predict minimum film thickness in circular elastohydrodynamic contacts from knowledge of central film thickness, which can be either accurately measured or rather well estimated using classical film thickness formulae.

Roughness Amplitude Reduction Under Non-Newtonian EHL Conditions

2005 ◽  
Author(s):  
A. D. Chapkov ◽  
C. H. Venner ◽  
A. A. Lubrecht
Keyword(s):  
Film Thickness ◽  
Pressure Fluctuations ◽  
Elastohydrodynamic Lubrication ◽  
Operating Conditions ◽  
Quantitative Prediction ◽  
Point Contacts ◽  
Minimum Film Thickness ◽  
Roughness Amplitude ◽  
Average Film Thickness ◽  
Ehl Contact

The influence of surface roughness on the performance of bearings and gears operating under ElastoHydrodynamic Lubrication (EHL) conditions has become increasingly important over the last decade, as the average film thickness decreased due to various influences. Surface features can reduce the minimum film thickness and thus increase the wear. They can also increase the temperature and the pressure fluctuations, which directly affects the component life. In order to describe the roughness geometry inside an EHL contact, the amplitude reduction of harmonic waviness has been studied over the last ten years. This theory currently allows a quantitative prediction of the waviness amplitude and includes the influence of wavelength and contact operating conditions. However, the model assumes a Newtonian behaviour of the lubricant. The current paper makes a first contribution to the extension of the roughness amplitude reduction for EHL point contacts including non-Newtonian effects.

An Experimental Evaluation of the Hamrock and Dowson Minimum Film Thickness Equation for Fully Flooded EHD Point Contacts

1981 ◽  
Vol 103 (2) ◽  
pp. 284-294 ◽  
Author(s):  
K. A. Koye ◽  
W. O. Winer
Keyword(s):  
Experimental Data ◽  
Statistical Analysis ◽  
Film Thickness ◽  
Experimental Evaluation ◽  
Point Contact ◽  
Major Axis ◽  
Point Contacts ◽  
Lubricant Film Thickness ◽  
Minimum Film Thickness ◽  
Ellipticity Ratio

Fifty-seven measurements of the minimum lubricant film thickness separating the elastohydrodynamically lubricated point contact of a steel crowned roller and a flat sapphire disk were made by an optical interferometry technique. The data collected were used to evaluate the Hamrock and Dowson minimum EHD film thickness model over a practical range of contact ellipticity ratio where the major axis of the contact ellipse is aligned both parallel and perpendicular to the direction of motion. A statistical analysis of the measured film thickness data showed that the experimental data averaged 30 percent greater film thickness than the Hamrock and Dowson model predicts.

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.

Debris Effects on EHL Contact

2000 ◽  
Vol 122 (4) ◽  
pp. 711-720 ◽  
Author(s):  
Young S. Kang ◽  
Farshid Sadeghi ◽  
Xiaolan Ai
Keyword(s):  
Film Thickness ◽  
Reynolds Equation ◽  
Elastohydrodynamic Lubrication ◽  
Force Balance ◽  
Time Dependent ◽  
Elasticity Equations ◽  
Minimum Film Thickness ◽  
Bounding Surfaces ◽  
Force Balance Equation ◽  
Ehl Contact

A model was developed to study the effects of a rigid debris on elastohydrodynamic lubrication of rolling/sliding contacts. In order to achieve the objectives the time dependent Reynolds equation was modified to include the effects of an ellipsoidal shaped debris. The modified time dependent Reynolds and elasticity equations were simultaneously solved to determine the pressure and film thickness in EHL contacts. The debris force balance equation was solved to determine the debris velocity. The model was then used to obtain results for a variety of loads, speeds, and debris sizes. The results indicate that the debris has a significant effect on the pressure distribution and causes a dent on the rolling/sliding bounding surfaces. Depending on the size and location of the debris the pressure generated within the contact can be high enough to plastically deform the bounding surfaces. Debris smaller than the minimum film thickness do not enter the contact and only large and more spherical debris move toward the contact. [S0742-4787(11)00501-7]

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.

Design Optimization of Gas Foil Thrust Bearings for Maximum Load Capacity

2015 ◽  
Author(s):  
Tae Ho Kim ◽  
Tae Won Lee
Keyword(s):  
Experimental Data ◽  
Film Thickness ◽  
Load Capacity ◽  
Maximum Load ◽  
Drag Torque ◽  
Rotor Speed ◽  
Design Guideline ◽  
Film Pressure ◽  
Thrust Bearings ◽  
Minimum Film Thickness

Improvement of the load capacity of gas foil thrust bearings (GFTBs) is important to broadening their application in oil-free microturbomachinery (<250 kW) with high power density. Although GFTBs have the significant advantage of low friction without the use of lubrication systems compared to oil film thrust bearings, their inherently low load capacity has limited their application. The aim of the present study was to develop a design guideline for increasing the load capacity of GFTBs. The Reynolds equation for an isothermal isoviscous ideal gas was used to calculate the gas film pressure. To predict the ultimate load capacity of the GFTB, the pressure was averaged in the radial direction of the gas flow field used to deflect the foil structure. The load capacity, film pressure profile, and film thickness profile were predicted for a GFTB with an outer radius of 55 mm, inner radius of 30 mm, and eight foils each of arc length 45°. The predictions showed that the load capacity of the GFTB increased with increasing rotor speed and decreasing minimum film thickness, and was always lower than the analytically determined limit value for infinite rotor speed (obtained by simple algebraic equations). A parametric study in which the ramp extent (or inclined angle) was increased from 5° to 40°, and the ramp height from 0 to 0.320 mm, revealed that the GFTB had an optimal ramp extent of ∼22.5° and ramp height of ∼0.030 mm for maximum load capacity. Interestingly, the optimal values were also valid for a rigid-surface bearing. The predicted load capacities for a ramp extent of ∼22.5° and increasing ramp height from 0.030 to 0.320 mm were compared with experimental data obtained from a previous work. The predictions for a ramp height of 0.155 mm were in good agreement with the experimental data for all three test GFTBs with outer radii of 45, 50, and 55 mm, respectively. In addition, this paper shows that the predicted drag torque increases linearly with increasing rotor speed and decreasing minimum film thickness, and nonlinearly with decreasing ramp height. The drag torque significantly increased only for ramp heights below the optimal value. The predictions imply that the optimal ramp height improves the load capacity of the GFTB with little change in the drag torque.

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.

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