A Simplified Model for the Elastohydrodynamic Traction Between Rollers

1976 ◽  
Vol 98 (3) ◽  
pp. 357-361 ◽  
Author(s):  
Charles W. Allen
Keyword(s):  
Preliminary Analysis ◽  
High Pressures ◽  
Elastohydrodynamic Lubrication ◽  
Rolling Contact ◽  
Experimental Investigations ◽  
Pressure Dependent Viscosity ◽  
Linear Shear ◽  
Dependent Viscosity ◽  
Low Pressures ◽  
Good Agreement

The elastohydrodynamic lubrication of two rollers in combined rolling and sliding is considered. A simple rheological model to predict the traction is presented. The model is based upon an exponential pressure dependent viscosity at low pressures and a linear shear stress/pressure relationship at high pressures. The slope of the latter is assumed to be a function of the rolling and sliding velocities. The model is used to analyze the traction data of two recently published experimental investigations of other authors and good agreement is achieved in most cases. The model should be of considerable use to designers in the preliminary analysis of rolling contact systems in combined rolling and sliding.

Two Dimensional Modified Reynolds Equation Including Pressure Dependent Viscosity Effect

2012 ◽  
Author(s):  
Jung Gu Lee ◽  
Alan Palazzolo
Keyword(s):  
Reynolds Equation ◽  
Elastohydrodynamic Lubrication ◽  
Fluid Film ◽  
Maximum Pressure ◽  
Elastic Solids ◽  
Pressure Distributions ◽  
Pressure Dependent Viscosity ◽  
Modified Reynolds Equation ◽  
Dependent Viscosity ◽  
Modified Equation

The Reynolds equation plays an important role for predicting pressure distributions for fluid film bearing analysis, One of the assumptions on the Reynolds equation is that the viscosity is independent of pressure. This assumption is still valid for most fluid film bearing applications, in which the maximum pressure is less than 1 GPa. However, in elastohydrodynamic lubrication (EHL) where the lubricant is subjected to extremely high pressure, this assumption should be reconsidered. The 2D modified Reynolds equation is derived in this study including pressure-dependent viscosity, The solutions of 2D modified Reynolds equation is compared with that of the classical Reynolds equation for the ball bearing case (elastic solids). The pressure distribution obtained from modified equation is slightly higher pressures than the classical Reynolds equations.

Remarks on the Reynolds problem of elastohydrodynamic lubrication

1993 ◽  
Vol 4 (1) ◽  
pp. 83-96 ◽  
Author(s):  
José-Francisco Rodrigues
Keyword(s):  
Free Boundary ◽  
A Priori ◽  
Elastohydrodynamic Lubrication ◽  
Small Data ◽  
Existence Of A Solution ◽  
Pressure Dependent Viscosity ◽  
Uniqueness Of The Solution ◽  
Non Local ◽  
Dependent Viscosity ◽  
The Mathematical Model

The mathematical model of the flow of a viscous lubricant between elastic bearings leads to the study of a highly non-linear and non-local elliptic variational inequality. We discuss the existence of a solution by using an a prioriL∞-estimate. This method allows us to solve a large class of problems, including those arising from the linear Hertzian theory, and yields new existence results for the cases of a pressure-dependent viscosity or the inclusion of a load constraint. For small data the uniqueness of the solution holds, and we show that in the cylindrical journal bearing problem with small eccentricity ratio, the free boundary is given by two disjoint differentiable arcs close to the free boundary of the first-order approximate solution.

Oil Film Thickness and Shape for a Ball Sliding in a Grooved Raceway

1972 ◽  
Vol 94 (3) ◽  
pp. 199-208 ◽  
Author(s):  
N. Thorp ◽  
R. Gohar
Keyword(s):  
General Theory ◽  
Film Thickness ◽  
Contact Area ◽  
Elastohydrodynamic Lubrication ◽  
Surface Velocity ◽  
Oil Film ◽  
Pressure Dependent Viscosity ◽  
Ball Surface ◽  
Lubricated Contact ◽  
Dependent Viscosity

The behavior in the lubricated contact area of a driven ball sliding in a conforming glass groove, is studied. Interferometry is used to measure the oil film. Coupled ball surface velocity components are provided by angling the drive, while loads and speeds are varied in order to cover a range of conditions from undistorted surfaces to elastohydrodynamic lubrication. A general theory for lubrication with, no distortion and pressure-dependent viscosity, is developed and compared with experiment. Ball spin is found to have only a small effect on the oil film thickness.

Effect of Surface Roughness on Elastohydrodynamic Line Contact

1982 ◽  
Vol 104 (3) ◽  
pp. 401-407 ◽  
Author(s):  
B. C. Majumdar ◽  
B. J. Hamrock
Keyword(s):  
Surface Roughness ◽  
Film Thickness ◽  
Strain Analysis ◽  
Elastohydrodynamic Lubrication ◽  
Asperity Contact ◽  
Pressure Dependent Viscosity ◽  
Surface Irregularities ◽  
Dependent Viscosity ◽  
Contact Pressures ◽  
Effect Of Surface

A numerical solution of an elastohydrodynamic lubrication (EHL) contact between two long, rough surface cylinders is obtained. A theoretical solution of pressure distribution, elastohydrodynamic load, and film thickness for given speeds and for lubricants with pressure-dependent viscosity, material properties of cylinders, and surface roughness parameters is made by simultaneous solution of an elasticity equation and the Reynolds equation for two partially lubricated rough surfaces. The pressure due to asperity contact is calculated by assuming a Gaussian distribution of surface irregularities. The elastic deformation is found from hydrodynamic and contact pressures by using plane strain analysis. The effect of surface roughness on EHL loads, speeds, and central film thicknesses is studied. The results indicate that for a constant central film thickness (1) increasing the surface roughness decreases the EHL load and (2) there is little variation in minimum film thickness as the surface roughness is increased.

Nondimensional Presentation of Frictional Tractions in Elastohydrodynamic Lubrication—Part II: Starved Conditions

1975 ◽  
Vol 97 (3) ◽  
pp. 412-421 ◽  
Author(s):  
J. F. Archard ◽  
K. P. Baglin
Keyword(s):  
Elastic Modulus ◽  
Film Thickness ◽  
Sliding Friction ◽  
Elastohydrodynamic Lubrication ◽  
Rolling Friction ◽  
Analytic Treatment ◽  
Low Elastic Modulus ◽  
Pressure Dependent Viscosity ◽  
Dependent Viscosity ◽  
Negligible Influence

Part I of this paper presented a broad semi-analytic treatment of frictional tractions in nondimensional terms; this was confined to the fully flooded situation and the present paper extends the analysis to include starved conditions. As in Part I three major conditions are considered in detail: classical (isoviscous, undeformed) low elastic modulus (isoviscous, heavily deformed) and high elastic modulus (pressure dependent viscosity, heavily deformed). The influence of starvation is presented as a series of correction curves for the rolling and sliding friction derived for fully flooded conditions. Starvation influences friction both through the extent to which the gap between the surfaces is filled by lubricant and through its influence upon the film thickness. Both factors affect rolling friction which is therefore markedly reduced by starvation so mild that there is negligible influence upon the film thickness. In contrast, sliding friction (arising either in the main pressure zone or the cavitated region) is most strongly influenced by the film thickness and is therefore markedly affected only by relatively severe starvation.

The Short-Time Compressibility of Elastohydrodynamic Lubricants

1991 ◽  
Vol 113 (2) ◽  
pp. 361-370 ◽  
Author(s):  
K. T. Ramesh
Keyword(s):  
High Pressures ◽  
Elastohydrodynamic Lubrication ◽  
Deformation Analysis ◽  
Plate Impact ◽  
Wide Range ◽  
Density Relationship ◽  
Short Time ◽  
Impact Experiments ◽  
Low Pressures ◽  
Short Times

Elastohydrodynamic (EHD) lubricants are subjected to very large pressures (several GPa) for very short times (10−4 seconds) in typical EHD contacts. However, measurements of EHD lubricant compressibilities to date have primarily been made for quasistatic deformations and only for relatively low pressures. This paper presents some experimental results on the variation of the density of the lubricant 5P4E over a very wide range of pressures and over two distinct timescales, from 10−6 seconds to 10−4 seconds. The very short time (10−6 seconds) data are obtained from plate-impact experiments, and the data near 10−4 seconds are obtained with a new experimental technique using the compression Kolsky bar. It is observed that the commonly used Dowson-Higginson relationship represents too stiff a response at the high pressures for these short times, at least for this synthetic lubricant. A full finite deformation analysis of the plate impact problem is used to obtain the material response function for the large compressibilities observed. On the basis of these results, we suggest a new form of the pressure-density relationship for an elastohydrodynamic lubricant that appears to hold over the entire range of pressures and for time durations on the order of those actually occurring in elastohydrodynamic lubrication.

Nondimensional Presentation of Frictional Tractions in Elastohydrodynamic Lubrication—Part I: Fully Flooded Conditions

1975 ◽  
Vol 97 (3) ◽  
pp. 398-410 ◽  
Author(s):  
J. F. Archard ◽  
K. P. Baglin
Keyword(s):  
Elastic Modulus ◽  
Elastohydrodynamic Lubrication ◽  
Analytic Solutions ◽  
Glassy Polymers ◽  
Exponential Relationship ◽  
Low Elastic Modulus ◽  
Pressure Dependent Viscosity ◽  
Wide Range ◽  
Computer Based ◽  
Dependent Viscosity

Using several sources, analytic and semi-analytic solutions for frictional tractions of a lubricated line contact are presented in the appropriate non-dimensional form which is similar to that previously used by Moes for film thickness. A Newtonian lubricant with an exponential relationship between viscosity and pressure is assumed and, at this stage, the treatment is confined to fully flooded conditions. The components of frictional tractions arising from rolling (Poisseiulle) and sliding (Couette) flows are distinguished and sliding tractions in the outlet cavitated region are separated from those in the main pressure zone. Three main regimes of lubrication are studied: classical (isoviscous, undeformed), low elastic modulus (isoviscous, heavily deformed) and high elastic modulus (pressure dependent viscosity, heavily deformed). The results presented here provide a broad background of approximate results, covering a very wide range of conditions against which the results of more precise computer-based analyses can be judged. Thus the treatment reveals the existence of a range of conditions (typical of the lubrication of glassy polymers by hydrocarbon lubricants) which has been little studied and is, as yet, imperfectly understood.

Packing Effect on the Transfer Integrals and Mobility in α,α′-bis(dithieno[3,2-b:2′,3′-d]thiophene) (BDT) and its Heteroatom-Substituted Analogues

2011 ◽  
Vol 64 (12) ◽  
pp. 1587 ◽  
Author(s):  
Ahmad Irfan ◽  
Abdullah G. Al-Sehemi ◽  
Shabbir Muhammad ◽  
Jingping Zhang
Keyword(s):  
Electron Transfer ◽  
Electron Mobility ◽  
Hole Mobility ◽  
Experimental Investigations ◽  
Hole Transfer ◽  
Space Group ◽  
Space Groups ◽  
Transfer Integrals ◽  
Packing Effect ◽  
Good Agreement

Theoretically calculated mobility has revealed that BDT is a hole transfer material, which is in good agreement with experimental investigations. The BDT, NHBDT, and OBDT are predicted to be hole transfer materials in the C2/c space group. Comparatively, hole mobility of BHBDT is 7 times while electron mobility is 20 times higher than the BDT. The packing effect for BDT and designed crystals was investigated by various space groups. Generally, mobility increases in BDT and its analogues by changing the packing from space group C2/c to space groups P1 or . In the designed ambipolar material, BHBDT hole mobility has been predicted 0.774 and 3.460 cm2 Vs–1 in space groups P1 and , which is 10 times and 48 times higher than BDT (0.075 and 0.072 cm2 Vs–1 in space groups P1 and ), respectively. Moreover, the BDT behaves as an electron transfer material by changing the packing from the C2/c space group to P1 and .

scholarly journals Validation of MATLAB algorithm to implement a two-step parallel pyrolysis model for the prediction of maximum %char yield

2021 ◽  
Vol 1 (1) ◽  
Author(s):  
Ibiba Taiwo Horsfall ◽  
Macmanus Chinenye Ndukwu ◽  
Fidelis Ibiang Abam ◽  
Ololade Moses Olatunji ◽  
Ojong Elias Ojong ◽  
...  
Keyword(s):  
Experimental Data ◽  
Isothermal Condition ◽  
Char Yield ◽  
Experimental Investigations ◽  
Time Saving ◽  
Pyrolysis Products ◽  
Pyrolysis Model ◽  
Experimental Yield ◽  
By Products ◽  
Good Agreement

AbstractNumerical modeling of biomass pyrolysis is becoming a cost and time-saving alternative for experimental investigations, also to predict the yield of the by-products of the entire process. In the present study, a two-step parallel kinetic model was used to predict char yield under isothermal condition. MATLAB ODE45 function codes were employed to solve a set of differential equations that predicts the %char at varying residence times and temperatures. The code shows how the various kinetic parameters and mass of pyrolysis products were determined. Nevertheless, the algorithm used for the prediction was validated with experimental data and results from past works. At 673.15 K, the numerical simulation using ODE45 function gives a char yield of 27.84%. From 573.15 K to 673.15 K, char yield ranges from 31.7 to 33.72% to 27.84% while experimental yield decreases from 44 to 22%. Hence, the error between algorithm prediction and experimental data from literature is − 0.26 and 0.22. Again, comparing the result of the present work with the analytical method from the literature showed a good agreement.

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