Non-Newtonian Thermal Elastohydrodynamic Lubrication

1991 ◽  
Vol 113 (2) ◽  
pp. 390-396 ◽  
Author(s):  
P. C. Sui ◽  
F. Sadeghi
Keyword(s):  
Film Thickness ◽  
Numerical Solution ◽  
Reynolds Equation ◽  
Fluid Model ◽  
Traction Force ◽  
Elastohydrodynamic Lubrication ◽  
Simultaneous System ◽  
Energy Equations ◽  
Rheology Model ◽  
Generalized Reynolds Equation

A numerical solution to the problem of thermal and non-Newtonian fluid model in elastohydrodynamic lubrication is presented. The generalized Reynolds equation was modified by the Eyring rheology model to incorporate the non-Newtonian effects of the fluid. The simultaneous system of modified Reynolds, elasticity and energy equations were numerically solved for the pressure, temperature and film thickness. Results have been presented for loads ranging from W = 7 × 10−5 to W = 2.3 × 10−4 and the speeds ranging from U* = 2 × 10−11 to U* = 6 × 10−11 at various slip conditions. Comparison between the isothermal and thermal non-Newtonian traction force has also been presented.

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.

scholarly journals Non-Newtonian Fluid Model Incorporated Into Elastohydrodynamic Lubrication of Rectangular Contacts

1984 ◽  
Vol 106 (2) ◽  
pp. 275-282 ◽  
Author(s):  
B. O. Jacobson ◽  
B. J. Hamrock
Keyword(s):  
Shear Stress ◽  
Shear Strength ◽  
Film Thickness ◽  
Numerical Solution ◽  
Newtonian Fluid ◽  
Fluid Model ◽  
Elastohydrodynamic Lubrication ◽  
Sliding Velocity ◽  
Minimum Film Thickness ◽  
Limiting Value

A procedure is outlined for the numerical solution of the complete elastohydrodynamic lubrication of rectangular contacts incorporating a non-Newtonian fluid model. The approach uses a Newtonian model as long as the shear stress is less than a limiting shear stress. If the shear stress exceeds the limiting value, the shear stress is set equal to the limiting value. The numerical solution requires the coupled solution of the pressure, film shape, and fluid rheology equations from the inlet to the outlet. Isothermal and no-side-leakage assumptions were imposed in the analysis. The influence of dimensionless speed U, load W, materials G, and sliding velocity U* and limiting-shear-strength proportionality constant γ on dimensionless minimum film thickness Hmin was investigated. Fourteen cases were investigated for an elastohydrodynamically lubricated rectangular contact incorporating a non-Newtonian fluid model. The influence of sliding velocity (U*) and limiting shear strength (γ) on minimum film thickness was observed to be small. Hence the film thickness equation obtained for a Newtonian fluid is sufficient for calculations considering non-Newtonian effects. Computer plots are also presented that indicate in detail pressure distribution, film shape, shear stress at the surfaces, and flow throughout the conjunction.

Elastohydrodynamic Lubrication of Hypoid Gears

1981 ◽  
Vol 103 (1) ◽  
pp. 195-203 ◽  
Author(s):  
V. Simon
Keyword(s):  
Film Thickness ◽  
Numerical Solution ◽  
Elastohydrodynamic Lubrication ◽  
Operating Conditions ◽  
Performance Characteristics ◽  
Temperature Variations ◽  
Hypoid Gears ◽  
Oil Film ◽  
Gear Teeth ◽  
Energy Equations

The full thermal elastohydrodynamic analysis of the lubrication of hypoid gears is presented. A numerical solution of the coupled Reynolds, elasticity and energy equations for the pressure, temperature and film thickness is obtained. The temperature variations across the oil film and in the pinion and gear teeth are included. The real tooth geometry of the modified hypoid gears is treated. The effect of the operating conditions on the performance characteristics is discussed.

scholarly journals Power Law Fluid Model for Thermal Elastohydrodynamic Lubrication

2021 ◽  
pp. 56-71
Author(s):  
Samuel Macharia Karimi ◽  
Duncan Kioi Gathungu
Keyword(s):  
Film Thickness ◽  
Power Law ◽  
Thermal Effects ◽  
Fluid Model ◽  
Elastohydrodynamic Lubrication ◽  
Coupled System ◽  
Rolling Bearing ◽  
Governing Equations ◽  
The One ◽  
Energy Equations

The aim of this paper is to analyse thermal elastohydrodynamic lubrication (TEHL) line contact of rolling a bearing using a non-Newtonian uid that is described by the power law model. The performance characteristics of the rolling bearing are determined for various index for dilatant, Newtonian and pseudo plastic uids. The one-dimensional Reynolds and energy equations are both modied to incorporate the non-Newtonian nature of the lubricant. The coupled system of governing equations are discretized using the finite difference method and solved simultaneously. The results show that the pressure, film thickness and temperature for dilatant uids increased with increase in the ow index as compared to pseudo plastic uids. The in uence of thermal effects on pressure and lm thickness is more significant compared with that under isothermal elastohydrodynamic lubrication especially on the case of dilatant uids. The viscosity of the lubricant increases with increase in pressure and reduces with increment in temperature. The surface roughness in the bearing surface increases the lm thickness of the lubricant. The uid pressure, film thickness and temperature increases with increase in the bearing speed. To truly re ect the characteristics of EHL models, thermal effects should be considered.

Three-Dimensional Temperature Distribution in EHD Lubrication: Part I—Circular Contact

1992 ◽  
Vol 114 (1) ◽  
pp. 32-41 ◽  
Author(s):  
Kyung Hoon Kim ◽  
Farshid Sadeghi
Keyword(s):  
Temperature Distribution ◽  
Film Thickness ◽  
Temperature Rise ◽  
Thermal Effects ◽  
Three Dimensional ◽  
Elastohydrodynamic Lubrication ◽  
Simultaneous System ◽  
Ehd Lubrication ◽  
Energy Equations ◽  
Circular Contact

A complete numerical solution of Newtonian thermal compressible elastohydrodynamic lubrication of rolling/sliding point (circular) contact has been obtained. The multilevel multigrid technique was used to solve the simultaneous system of thermal Reynolds, elasticity and the energy equations with their boundary conditions. The effects of various loads, speeds, and slip conditions on the lubricant temperature, film thickness, and friction force have been investigated. The results indicate that the temperature rise in the contact is significant and thermal effects cannot be neglected.

scholarly journals Analysis of Line Contact Elastohydrodynamic Lubrication with the Particles under Rough Contact Surface

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Keying Chen ◽  
Liangcai Zeng ◽  
Juan Chen ◽  
Xianzhong Ding
Keyword(s):  
Film Thickness ◽  
Rough Surface ◽  
Thickness Distribution ◽  
Traction Force ◽  
Elastohydrodynamic Lubrication ◽  
Equation System ◽  
Line Contact ◽  
Equivalent Inclusion Method ◽  
Equivalent Inclusion ◽  
The Matrix

A numerical solution for line contact elastohydrodynamic lubrication (EHL) occurring on the rough surface of heterogeneous materials with a group of particles is presented in this study. The film thickness disturbance caused by particles and roughness is considered into the solution system, and the film pressure between the contact gap generated by the particles and the surface roughness is obtained through a unified Reynold equation system. The inclusions buried in the matrix are made equivalent to areas with the same material as that of the matrix through Eshelby’s equivalent inclusion method and the roughness is characterized by related functions. The results present the effects of different rough topographies combined with the related parameters of the particles on the EHL performance, and the minimum film thickness distribution under different loads, running speeds, and initial viscosities are also investigated. The results show that the roughness morphology and the particles can affect the behavior of the EHL, the traction force on a square rough surface is smaller, and the soft particles have more advantages for improving the EHL performance.

Solution of the Non-Newtonian Elastohydrodynamic Problem for Circular Contacts Based on a Flow Continuity Method

1996 ◽  
Vol 210 (4) ◽  
pp. 247-258 ◽  
Author(s):  
C A Holt ◽  
H P Evans ◽  
R W Snidle
Keyword(s):  
Film Thickness ◽  
Numerical Solution ◽  
Control Volume ◽  
Point Contact ◽  
Elastohydrodynamic Lubrication ◽  
Theoretical Formulation ◽  
New Approach ◽  
Limiting Shear Stress ◽  
Pure Rolling ◽  
Stress Behaviour

The paper describes a numerical solution method for the point contact elastohydrodynamic lubrication (EHL) problem under non-Newtonian, isothermal conditions. The theoretical formulation of the non-Newtonian effect is general and may be applied to both shear thinning and limiting shear stress behaviour. The particular rheological model investigated in this work is the Eyring ‘sinh law’ relation. The numerical solution of the lubrication equations is based upon a control volume approach rather than the more usual methods that utilize a modified Reynolds equation. This new approach ensures that flow continuity is satisfied at the discretization level. Results are presented to show the effect of non-Newtonian behaviour on film thickness and pressure distribution in circular EHL contacts operating over a range of slide-roll ratios from 0 (pure rolling) to 1.5. Under conditions of pure rolling or low sliding there is found to be little effect of non-Newtonian behaviour, but at the highest degree of sliding the film thickness over the central, flattened area of the contact is reduced by up to 10 per cent at the highest rolling speed of 0.75 m/s.

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.

Effects of Surface Roughness and Additives in Lubrication: Generalized Reynolds Equation and its Application to Elastohydrodynamic Film

1987 ◽  
Vol 201 (1) ◽  
pp. 1-9 ◽  
Author(s):  
P Sinha ◽  
J S Kennedy ◽  
C M Rodkiewicz ◽  
P Chandra ◽  
R Sharma ◽  
...  
Keyword(s):  
Surface Roughness ◽  
Film Thickness ◽  
Reynolds Equation ◽  
Molecular Size ◽  
One Dimensional ◽  
Theoretical Investigations ◽  
Minimum Film Thickness ◽  
Porous Matrices ◽  
The Mean ◽  
Generalized Reynolds Equation

To study the effects of surface roughness and additives in lubrication, a generalized form of Reynolds equation is derived by taking into account the roughness interaction zones adjacent to the moving rough surfaces as sparsely porous matrices and purely hydrodynamic film of micropolar fluid characterizing the lubricant with additives. A particular, one-dimensional form of this equation is used to study these effects on the elastohydrodynamic (EHD) minimum film thickness at the inlet, between two rough rollers. It is shown that for the low permeability of the roughness zone, the EHD film thickness increases as the mean height of the asperities increases, whereas for the high permeability it decreases. The EHD film thickness is also found to increase with the concentration of the additives and the molecular size of the particles. These results are in conformity at least qualitatively, with various experimental and theoretical investigations, cited in the paper.

Effects of Differential Scheme and Mesh Density on EHL Film Thickness in Point Contacts

2006 ◽  
Vol 128 (3) ◽  
pp. 641-653 ◽  
Author(s):  
Yuchuan Liu ◽  
Q. Jane Wang ◽  
Wenzhong Wang ◽  
Yuanzhong Hu ◽  
Dong Zhu
Keyword(s):  
Film Thickness ◽  
Numerical Solution ◽  
System Approach ◽  
Elastohydrodynamic Lubrication ◽  
Mesh Size ◽  
Point Contacts ◽  
Wide Range ◽  
Mesh Density ◽  
Differential Scheme

This paper investigates the effects of differential scheme and mesh density on elastohydrodynamic lubrication (EHL) film thickness based on a full numerical solution with a semi-system approach. The solution variation with different schemes and mesh sizes is revealed based on a set of numerical cases in a wide range of central film thickness from several hundred nanometers down to a few nanometers. It is observed that when the film is thick, the effects of differential schemes and mesh density are not significant. However, if the film becomes ultra-thin, e.g., below 10–20 nanometers, the influence of mesh density and differential schemes becomes more significant, and a proper dense mesh and differential scheme may be highly desirable. The present study also indicates that the solutions from the 1st-order backward scheme give the largest film thickness among all the solutions from different schemes at the same mesh size.

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