A Reynolds-Eyring Equation for Elastohydrodynamic Lubrication in Line Contacts

1987 ◽  
Vol 109 (4) ◽  
pp. 648-654 ◽  
Author(s):  
T. F. Conry ◽  
S. Wang ◽  
C. Cusano
Keyword(s):  
Film Thickness ◽  
Reynolds Equation ◽  
Numerical Solutions ◽  
Elastohydrodynamic Lubrication ◽  
Newtonian Flow ◽  
Line Contacts ◽  
Different Temperatures ◽  
Eyring Model ◽  
Eyring Theory ◽  
New Equation

A new Reynolds equation, based on the Eyring theory of non-Newtonian flow, is derived for flow in one dimension. It is shown that this new equation reduces to the traditional Reynolds equation as the Eyring model approaches the Newtonian model in the limit. Numerical solutions are presented for a selected oil at two different temperatures. The central film thickness decreases with increasing dimensionless viscosity parameter and slide/roll ratios. A transition zone is noted through which the ratio of minimum to central film thickness passes as the pressure distribution goes from near Hertzian to a distribution that appreciably deviates from Hertzian.

Thermal Elastohydrodynamic Lubrication Analysis for Point Contact Transmission

2009 ◽  
Author(s):  
Hai-zhou Huang ◽  
Xi-chuan Niu ◽  
Xiao-yang Yuan
Keyword(s):  
Film Thickness ◽  
Numerical Solutions ◽  
Point Contact ◽  
Elastohydrodynamic Lubrication ◽  
Surface Velocity ◽  
Squeeze Film ◽  
Elastic Displacement ◽  
Circular Arc ◽  
Tooth Width ◽  
Contact Transmission

To investigate the thermal EHL (elastohydrodynamic lubrication) in point contact transmission, a model considering the two-dimensional surface velocity of tooth face and the running-in is proposed. The numerical solutions for pressure, temperature and film thickness distribution in the contact zone are obtained by solving equations including the Reynolds, Energy and the elastic displacement with variable dimension meshing method. The model was used to study the point contact transmission of the circular arc gear in a windlass. The main results show that it is pure rolling along the direction of tooth width, and the rolling speed plays a leading role in improving the lubricating performance and transmission efficiency of circular arc gear. The squeeze film effect makes the pressure peak tend to be gentle and the film thickness increase slightly.

Study on the Influence of Non-Newtonian Characteristics on Robots for Medical Application

2010 ◽  
Vol 29-32 ◽  
pp. 857-861
Author(s):  
Jian Ping Liu ◽  
Xin Yi Zhang ◽  
Qing Xuan Jia
Keyword(s):  
Film Thickness ◽  
Elastic Deformation ◽  
Reynolds Equation ◽  
Traction Force ◽  
Elastohydrodynamic Lubrication ◽  
Medical Application ◽  
Lubrication Theory ◽  
Newtonian Model

Considering lumen elastic deformation, Reynolds equation is deduced based on non-Newtonian model in this paper. Traction force and hydrodynamic mucus film thickness are calculated according to elastohydrodynamic lubrication theory. Compared with results based on Newtonian model and experiments, analysis based on non-Newtonian model reflects practical condition well. Lumen elastic deformation has some influence on traction force and mucus film thickness.

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.

The Effects of Surface Irregularities on the Elastohydrodynamic Lubrication of Sliding Line Contacts. Part II—Wavy Surfaces

1984 ◽  
Vol 106 (1) ◽  
pp. 113-119 ◽  
Author(s):  
P. R. Goglia ◽  
C. Cusano ◽  
T. F. Conry
Keyword(s):  
Shear Stress ◽  
Film Thickness ◽  
Smooth Surface ◽  
Wave Amplitude ◽  
Elastohydrodynamic Lubrication ◽  
Wavy Surface ◽  
Line Contacts ◽  
Surface Irregularities ◽  
Wavy Surfaces ◽  
Octahedral Shear Stress

The micro-EHD effects caused by wavy surfaces have been analytically investigated. The investigation includes the effects of phase, wavelength, and wave amplitude on film thickness, pressure distribution and subsurface octahedral shear stress field. The presence of a wavy surface with a given wavelength produces pressure oscillations of the same wavelength. With increasing wave amplitude and decreasing wavelength, the micro-EHD action increases. This results in a maximum value of the octahedral shear stress which is greater in magnitude and closer to the surface than the corresponding smooth surface case. The slope of the wavy surface in the inlet region determines whether the average film thickness is smaller or larger than the smooth surface value.

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.

Some Remarks on the Validity of Reynolds Equation in the Modeling of Lubricant Film Flows on the Surface Roughness Scale

2004 ◽  
Vol 126 (4) ◽  
pp. 703-710 ◽  
Author(s):  
T. Almqvist ◽  
R. Larsson
Keyword(s):  
Surface Roughness ◽  
Reynolds Equation ◽  
Numerical Solutions ◽  
Fluid Dynamic ◽  
Lubricant Film ◽  
Continuity Equations ◽  
Newtonian Case ◽  
Eyring Model ◽  
Wavelength Scale ◽  
Film Flows

The objective of this paper is to investigate the flow in a lubricant film on the surface roughness scale and to compare the numerical solutions obtained by two different solution approaches. This is accomplished firstly by the CFD-approach (computational fluid dynamic approach) where the momentum and continuity equations are solved separately, and secondly the Reynolds equation approach, which is a combination and a simplification of the above equations. The rheology is assumed to be both Newtonian and non-Newtonian. An Eyring model is used in the non-Newtonian case. The result shows that discrepancies between the two approaches may occur, primarily due to a singularity which appears in the momentum equations when the stresses in the lubricant attain magnitudes that are common in EHL. This singularity is not represented by the Reynolds equation. If, however, the rheology is shifted to a non-Newtonian Eyring model the deviations between the two solution approaches is removed or reduced. The second source of discrepancies between the two approaches is the film thickness to wavelength scale ω. It will be shown that the Reynolds equation is valid until this ratio is approximately O10−2.

The Elastohydrodynamic Lubrication of Heavily Loaded Point Contacts

1980 ◽  
Vol 22 (4) ◽  
pp. 183-187 ◽  
Author(s):  
C. J. Hooke
Keyword(s):  
Exact Solution ◽  
Film Thickness ◽  
Close Agreement ◽  
Numerical Solutions ◽  
Elastohydrodynamic Lubrication ◽  
Substantial Part ◽  
Line Contact ◽  
Point Contacts ◽  
Contact Width ◽  
Inlet Zone

It is shown that the film thickness in heavily loaded point contacts can be accurately calculated by comparing the inlet and exit zones of the contact with those of an equivalent line contact. The results become increasingly accurate as the extent of the inlet and exit regions is reduced and in the limit yields an exact solution. Even for moderately loaded contacts in which the inlet zone occupies a substantial part of the contact width the results are in close agreement with existing numerical solutions.

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]

Surface roughness modification in elastohydrodynamic line contacts operating in the elastic piezoviscous regime

1998 ◽  
Vol 212 (2) ◽  
pp. 145-162 ◽  
Author(s):  
C. J. Hooke
Keyword(s):  
Surface Roughness ◽  
Spatial Distribution ◽  
Analytical Solution ◽  
Film Thickness ◽  
Numerical Solutions ◽  
Entrainment Velocity ◽  
Original Surface ◽  
Ehd Lubrication ◽  
Line Contacts

In heavily loaded elastohydrodynamic (EHD) lubrication contacts operating in the piezoviscous regime, the original surface roughness is largely flattened as it enters the conjunction and is replaced by an inlet generated clearance variation. This clearance variation is convected through the contact at the entrainment velocity. It has a spatial distribution that differs (except for rolling without slip) from the original surface and a different amplitude. This amplitude may be smaller or greater than that of the original profile. An analytical solution of this behaviour is presented for contacts operating well inside the elastic piezoviscous regime for the situation where the roughness is relatively small compared with the film thickness. This solution allows the main features of surface roughness modification to be understood and produces results that compare well with the few numerical solutions available.

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