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.

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.

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.

Numerical Solution of Mixed Thermal Elastohydrodynamic Lubrication in Point Contacts With Three-Dimensional Surface Roughness

2016 ◽  
Vol 139 (1) ◽  
Author(s):  
Xiaopeng Wang ◽  
Yuchuan Liu ◽  
Dong Zhu
Keyword(s):  
Surface Roughness ◽  
Film Thickness ◽  
Three Dimensional ◽  
Point Contact ◽  
Elastohydrodynamic Lubrication ◽  
Lubricant Film ◽  
Operating Conditions ◽  
Thickness Variation ◽  
Wide Range ◽  
Film Lubrication

Elastohydrodynamic lubrication (EHL) is a common mode of fluid-film lubrication in which many machine elements operate. Its thermal behavior is an important concern especially for components working under extreme conditions such as high speeds, heavy loads, and surfaces with significant roughness. Previous thermal EHL (TEHL) studies focused only on the cases with smooth surfaces under the full-film lubrication condition. The present study intends to develop a more realistic unified TEHL model for point contact problems that is capable of simulating the entire transition of lubrication status from the full-film and mixed lubrication all the way down to boundary lubrication with real machined roughness. The model consists of the generalized Reynolds equation, elasticity equation, film thickness equation, and those for lubricant rheology in combination with the energy equation for the lubricant film and the surface temperature equations. The solution algorithms based on the improved semi-system approach have demonstrated a good ability to achieve stable solutions with fast convergence under severe operating conditions. Lubricant film thickness variation and temperature rises in the lubricant film and on the surfaces during the entire transition have been investigated. It appears that this model can be used to predict mixed TEHL characteristics in a wide range of operating conditions with or without three-dimensional (3D) surface roughness involved. Therefore, it can be employed as a useful tool in engineering analyses.

Effect of Stiff Coatings on EHL Film Thickness in Point Contacts

2008 ◽  
Vol 130 (3) ◽  
Author(s):  
Yuchuan Liu ◽  
Q. Jane Wang ◽  
Dong Zhu
Keyword(s):  
Film Thickness ◽  
Coating Thickness ◽  
Performance Enhancement ◽  
Point Contact ◽  
Elastohydrodynamic Lubrication ◽  
Thickness Variation ◽  
Grand Challenge ◽  
Maximum Increase ◽  
Wide Range ◽  
Minimum Film Thickness

Coatings are widely used for interface performance enhancement and component life improvement, as well as for corrosion prevention and surface decoration. More and more mechanical components, especially those working under severe conditions, are coated with stiff (hard) thin coatings. However, the effects of coatings on lubrication characteristics, such as film thickness and friction, have not been well understood, and designing coating for optimal tribological performance is a grand challenge. In this paper, the influences of coating material properties and coating thickness on lubricant film thickness are investigated based on a point-contact isothermal elastohydrodynamic lubrication (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. Curve fitting of numerical results indicates that the maximum increase in minimum film thickness, Imax, and the corresponding optimal dimensionless coating thickness, H2max, can be expressed in the following forms: Imax=0.769M0.0238R20.0297L0.1376exp(−0.0243ln2L) and H2max=0.049M0.4557R2−0.1722L0.7611exp(−0.0504ln2M−0.0921ln2L). These formulas can be used to estimate the effect of coatings on film thickness for EHL applications.

Numerical and Experimental Research of the Slurry Film in Chemical Mechanical Polishing (CMP)

2010 ◽  
Vol 102-104 ◽  
pp. 669-674
Author(s):  
Fei Yan Lou ◽  
Qian Fa Deng ◽  
Ju Long Yuan
Keyword(s):  
Film Thickness ◽  
Chemical Mechanical Polishing ◽  
Applied Load ◽  
Reynolds Equation ◽  
Rotation Speed ◽  
Hydrodynamic Lubrication ◽  
Three Dimensional ◽  
Mechanical Polishing ◽  
Film Pressure ◽  
Minimum Film Thickness

A three-dimensional hydrodynamic lubrication model for chemical-mechanical polishing is presented based on the Reynolds equation and Reynolds boundary condition. By solving the Reynolds equation, the slurry film pressure distribution has been obtained. The effects of minimum film thickness and the wafer tile angle on the film pressure are analyzed, and the influence of the polishing applied load and rotation speed on slurry film thickness and tilt angle are discussed. At last, by experiment, it is found that the simulation results are similar to experiment results which film thickness is increasing with the increasing of rotation speed, decreasing of the applied load. It is proved that the simulation is reliable.

Experimental Studies of Leading Edge Contouring Influence on Secondary Losses in Transonic Turbines

2012 ◽  
Author(s):  
Ranjan Saha ◽  
Jens Fridh ◽  
Torsten Fransson ◽  
Boris I. Mamaev ◽  
Mats Annerfeldt
Keyword(s):  
Gas Turbine ◽  
Guide Vane ◽  
Experimental Studies ◽  
Three Dimensional ◽  
Leading Edge ◽  
Secondary Flows ◽  
Noticeable Effect ◽  
Flow Angle ◽  
Wide Range ◽  
Contour Plots

An experimental study of the hub leading edge contouring using fillets is performed in an annular sector cascade to observe the influence of secondary flows and aerodynamic losses. The investigated vane is a three dimensional gas turbine guide vane (geometrically similar) with a mid-span aspect ratio of 0.46. The measurements are carried out on the leading edge fillet and baseline cases using pneumatic probes. Significant precautions have been taken to increase the accuracy of the measurements. The investigations are performed for a wide range of operating exit Mach numbers from 0.5 to 0.9 at a design inlet flow angle of 90°. Data presented include the loading, fields of total pressures, exit flow angles, radial flow angles, as well as profile and secondary losses. The vane has a small profile loss of approximately 2.5% and secondary loss of about 1.1%. Contour plots of vorticity distributions and velocity vectors indicate there is a small influence of the vortex-structure in endwall regions when the leading edge fillet is used. Compared to the baseline case the loss for the filleted case is lower up to 13% of span and higher from 13% to 20% of the span for a reference condition with Mach no. of 0.9. For the filleted case, there is a small increase of turning up to 15% of the span and then a small decrease up to 35% of the span. Hence, there are no significant influences on the losses and turning for the filleted case. Results lead to the conclusion that one cannot expect a noticeable effect of leading edge contouring on the aerodynamic efficiency for the investigated 1st stage vane of a modern gas turbine.

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.

Lubrication at point contacts

1961 ◽  
Vol 261 (1307) ◽  
pp. 532-550 ◽  
Keyword(s):  
Film Thickness ◽  
Hydrodynamic Lubrication ◽  
Single Point ◽  
Applied Pressure ◽  
Hydrodynamic Theory ◽  
Radius Of Curvature ◽  
Point Contacts ◽  
Wide Range ◽  
Electrical Capacity ◽  
Classical Hydrodynamic

Measurements have been made of the friction, electrical resistance, and electrical capacity between rotating steel cylinders with their axes mutually at right angles. The lubricant was a plain hydrocarbon mineral oil. Nominally the surfaces come together at a single point and the apparatus is designed to ensure that this condition is maintained even if the cylinders wear. It is shown that hydrodynamic lubrication exists over a wide range of conditions. At loads of a few kilograms it persists even when the speed falls below 1 cm/s and at higher speeds (~ 100 cm/s) it is maintained even when the load becomes large enough to cause bulk plastic flow of hardened steel. Hitherto it has been considered that only boundary lubrication could occur under these extreme conditions. At very light loads classical hydrodynamic theory applies but as the load is increased a departure from classical theory occurs because the viscosity of the oil increases under the applied pressure. At heavier loads the pressures become large enough to cause appreciable elastic deformation of the surfaces and a state of elasto-hydrodynamic lubrication is achieved. Under elasto-hydrodynamic conditions the film thickness can be deduced from the measure­ments of electrical capacity. A simplified theory of elasto-hydrodynamic lubrication at point contacts is developed, and the measured values of film thickness are in fairly good agreement with those derived from the theory. However, the variations of film thick­ness with viscosity, speed and radius of curvature forecast by the theory differ significantly from those obtained experimentally. The values of the film thickness range from 2 x 10 -6 cm to more than 1 x 10 -4 cm. The results, over the whole range, conform to a regular pattern and there is no evidence of any disturbing influence of the surface molecular fields, even with the thinnest films.

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.

On Three-Dimensional Flat-Top Defects Passing Through an EHL Point Contact: A Comparison of Modeling with Experiments

2005 ◽  
Vol 127 (1) ◽  
pp. 51-60 ◽  
Author(s):  
A. Fe´lix-Quin˜onez ◽  
P. Ehret ◽  
J. L. Summers
Keyword(s):  
High Pressure ◽  
Film Thickness ◽  
Three Dimensional ◽  
Point Contact ◽  
Numerical Results ◽  
Shaped Surface ◽  
Pure Rolling ◽  
Pressure Region ◽  
Inlet Zone ◽  
High Pressure Region

A direct comparison between experimental and numerical results for the passage of an array of 3D flat-top, square shaped surface features through an EHL point contact is presented. Results for pure rolling conditions show that the features’ deformation in the high-pressure region is governed by their ability to entrap lubricant both underneath and in the grooves during their passage through the inlet zone. Film perturbations associated with each defect occur as locally enhanced regions of lubricant and film thickness micro-constrictions. Under sliding conditions the features sustain further deformations as they traverse the high-pressure conjunction and meet the highly viscous lubricant entrapped in the grooves, which moves at a different velocity. Lubricant is also seen to accumulate just in front or behind the features depending on the slide-to-roll ratio. Overall, the results highlight the importance of understanding the effects of the defects structure and the lubricant rheology on the film thickness to unravel the effects of real roughness patterns.

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