DDC Lubrication: A New Concept in Tribology

1992 ◽  
Vol 114 (1) ◽  
pp. 181-185 ◽  
Author(s):  
K. To̸nder
Keyword(s):  
Film Thickness ◽  
Reynolds Equation ◽  
Gap Function ◽  
Upper And Lower Bounds ◽  
Roughness Effects ◽  
Cavity Depth ◽  
Roughness Amplitude ◽  
Previously Treated ◽  
The Mean ◽  
Expansion Scheme

A new lubrication concept is presented, Deep Disconnected Cavities. It differs from the lubrication of microcavities, previously treated by other authors, by the deepness of the cavities. The validity of Reynolds’ equation and nonturbulent conditions are assumed. By a Taylor expansion scheme, it is shown that the roughness effects are expressible in terms of roughness factors modifying the Reynolds equation, similar to those proposed by Patir and Cheng (1978). Unlike those established for ordinary roughness, the DDC factors are independent of local film thickness and roughness amplitude (cavity depth), and may therefore be used to modify standard hydro-dynamic parameters. By a different mathematical approach, involving upper and lower bounds on the various hydrodynamic quantities, it is found that Reynolds’ equation and all the other hydrodynamic expressions may be written just as for smooth surfaces, with the following modifications: 1. The film thickness should be expressed by the minimum gap function, and not by the mean gap function. 2. There are, in general, three effective viscosities, lower than the physical one, two of which are associated with the x and y directions respectively and appear in the modified Reynolds equation as well as in the flow terms. The third one appears only in the expression for shear stress.

Analysis of Oil Film Thickness on a Piston Ring of Diesel Engine: Effect of Oil Film Temperature

2001 ◽  
Author(s):  
Yasuo Harigaya ◽  
Michiyoshi Suzuki ◽  
Masaaki Takiguchi
Keyword(s):  
Diesel Engine ◽  
Temperature Distribution ◽  
Heat Flow ◽  
Film Thickness ◽  
Piston Ring ◽  
Reynolds Equation ◽  
Energy Equation ◽  
Two Dimensional ◽  
Oil Film ◽  
The Mean

Abstract This paper describes that an analysis of oil film thickness on a piston ring of diesel engine. The oil film thickness has been performed by using Reynolds equation and unsteady, two-dimensional (2-D) energy equation with a heat generated from viscous dissipation. The temperature distribution in the oil film is calculated by using the energy equation and the mean oil film temperature is computed. Then the viscosity of oil film is estimated by using the mean oil film temperature. The effect of oil film temperature on the oil film thickness of a piston ring was examined. This model has been verified with published experimental results. Moreover, the heat flow at ring and liner surfaces was examined. As a result, the oil film thickness could be calculated by using the viscosity estimated from the mean oil film temperature and the calculated value is agreement with the measured values.

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.

Effect of Liquid-Solid Lubricant on Mixed Lubrication in Line Contact

2011 ◽  
Vol 148-149 ◽  
pp. 778-784
Author(s):  
Rattapasakorn Sountaree ◽  
Panichakorn Jesda ◽  
Mongkolwongrojn Mongkol
Keyword(s):  
Friction Coefficient ◽  
Film Thickness ◽  
Solid Lubricant ◽  
Reynolds Equation ◽  
Contact Region ◽  
Mixed Lubrication ◽  
Line Contact ◽  
Load Carrying ◽  
Roughness Amplitude ◽  
Raphson Method

This paper presents the performance characteristics of two surfaces in line contact under isothermal mixed lubrication with non-Newtonian liquid–solid lubricant base on Power law viscosity model. The time dependent Reynolds equation, elastic equation and viscosity equation were formulated for compressible fluid. Newton-Raphson method and multigrid technique were implemented to obtain film thickness profiles, friction coefficient and load carrying in the contact region at various roughness amplitudes, applied loads, speeds and the concentration of solid lubricant. The simulation results showed that roughness amplitude has a significant effect on the film pressure, film thickness and surface contact pressure in the contact region. The film thickness decrease but friction coefficient and asperities load rapidly increases when surface roughness amplitude increases or surface speed decreases. When the concentration of solid lubricant increased, friction coefficient and asperities load decrease but traction and film thickness increase.

Surface Roughness Effects on Fluid Flow between Two Rotating Cylinders

2015 ◽  
Vol 642 ◽  
pp. 275-280
Author(s):  
Sutthinan Srirattayawong ◽  
Shian Gao
Keyword(s):  
Surface Roughness ◽  
Film Thickness ◽  
Reynolds Equation ◽  
Surface Profile ◽  
Fluid Film ◽  
Real Surface ◽  
Contact Center ◽  
Roughness Effects ◽  
Fluid Film Thickness ◽  
Lubricant Viscosity

In general, the thin fluid film problems are explained by the classical Reynolds equation, but this approach has some limitations. To overcome them, the method of Computational Fluid Dynamics (CFD) is used in this study, as an alternative to solving the Reynolds equation. The characteristics of the two cylinders contact with real surface roughness are investigated. The CFD model has been used to simulate the behavior of the fluid flows at the conjunction between two different radius cylinders. The non-Newtonian fluid is employed to calculate the lubricant viscosity, and the thermal effect is also considered in the evaluation of the lubricant properties. The pressure distributions, the fluid film thickness and the temperature distributions are investigated. The obtained results show clearly the significance of the surface roughness on the lubricant flow at the contact center area. The fluctuated flow also affects the pressure distribution, the temperature and the lubricant viscosity in a similar pattern to the rough surface profile. The surface roughness effect will decrease when the film thickness is increased.

Averaged Reynolds Equation Extended to Gas Lubrication Possessing Surface Roughness in the Slip Flow Regime: Approximate Method and Confirmation Experiments

1989 ◽  
Vol 111 (3) ◽  
pp. 495-503 ◽  
Author(s):  
Y. Mitsuya ◽  
T. Ohkubo ◽  
H. Ota
Keyword(s):  
Surface Roughness ◽  
Film Thickness ◽  
Approximate Method ◽  
Flow Regime ◽  
Reynolds Equation ◽  
Slip Flow ◽  
Roughness Effects ◽  
Gas Lubrication ◽  
Slip Flow Regime ◽  
Average Film Thickness

The average film thickness theory is extended to gas lubrication possessing surface roughness in the slip flow regime. A simplified averaged Reynolds equation is derived and its applicability is confirmed through comparing with experiments. This averaging equation makes use of the mixed average film thickness defined as Havem = αHm + (1 − α)Hmˆ, where m = 1, 2 and 3; α indicates the mixing ratio; and H¯ and Hˆ denote the arithmetically and harmonically averaged film thicknesses. The experiments were performed using computer flying heads having precisely photolithography-fabricated longitudinal, transverse or checkered pattern roughnesses under submicron spacing conditions. From the excellent agreement obtained between the calculated and experimental results, it can be concluded that the assumption that velocity slippage occurs along the surface even if roughnes is present is justified, and that the approximate method is applicable for determining the surface roughness effects in the slip flow regime.

On the Mean Reynolds Equation in the Presence of Homogeneous Random Surface Roughness

1982 ◽  
Vol 49 (3) ◽  
pp. 476-480 ◽  
Author(s):  
N. Phan-Thien
Keyword(s):  
Surface Roughness ◽  
Film Thickness ◽  
Spectral Density ◽  
Small Amplitude ◽  
Random Function ◽  
Reynolds Equation ◽  
Random Surface ◽  
Dimensionless Amplitude ◽  
The Mean

Assuming that the surface roughness is of small amplitude and can be modeled by a homogeneous random function in space, the classical Reynolds equation is averaged using a method due to J. B. Keller. The mean Reynolds equation is accurate up to terms of 0(ε2), where ε is the dimensionless amplitude of the surface roughness and has a nonlocal character. Furthermore, by exploiting the slowly varying property of the mean film thickness, this nonlocal character is eliminated. The resulting mean Reynolds equation depends on the surface roughness via its spectral density and, in the limits of either parallel or transverse surface roughness, it reduces to Christensen’s theory.

Analysis of Oil Film Thickness on a Piston Ring of Diesel Engine: Effect of Oil Film Temperature

2003 ◽  
Vol 125 (2) ◽  
pp. 596-603 ◽  
Author(s):  
Y. Harigaya ◽  
M. Suzuki ◽  
M. Takiguchi
Keyword(s):  
Diesel Engine ◽  
Film Thickness ◽  
Piston Ring ◽  
Engine Speed ◽  
Reynolds Equation ◽  
Energy Equation ◽  
Oil Field ◽  
Two Dimensional ◽  
Oil Film ◽  
The Mean

This paper describes an analysis of oil film thickness on a piston ring of a diesel engine. The analysis of the oil film thickness has been performed by using Reynolds equation and unsteady, two-dimensional energy equation with heat generated from viscous dissipation. The mean oil film temperature was determined from the calculation of the temperature distribution in the oil field which was calculated using the energy equation. The oil film viscosity was then estimated using the mean oil film temperature. The effect of oil film temperature on the oil film thickness of a piston ring was examined. This model has been verified with published experimental results. Moreover, the heat flow at ring and liner surfaces was examined. Results show that the oil film thickness could be calculated using the viscosity estimated from the mean oil film temperature. The calculated values generally agree with the measured values. For higher engine speed conditions, the maximum values of the calculated oil film thickness are larger than the measured values.

On the Mean Reynolds Equation in the Presence of Surface Roughness: Squeeze-Film Bearing

1981 ◽  
Vol 48 (4) ◽  
pp. 717-720 ◽  
Author(s):  
N. Phan-Thien
Keyword(s):  
Surface Roughness ◽  
Flow Field ◽  
Film Thickness ◽  
Reynolds Equation ◽  
Squeeze Film ◽  
Two Dimensional ◽  
Homogeneous Surface ◽  
Parallel Surface ◽  
Mean Pressure ◽  
The Mean

The mean Reynolds equation in the presence of surface roughness is derived using the techniques developed by Keller. This mean equation is nonlocal in the sense that the mean pressure at all points in the flow field has some effect on the mean pressure at any particular point. The performance of a two-dimensional squeeze film bearing with homogeneous surface roughness is considered next showing that the load is enhanced by a factor of 1 + ε2a2S/h2, where εa is the amplitude of the roughness, h is the film thickness, and S varies between −3 〈m2〉, for parallel surface roughness, to 6 〈m2〉 for transverse surface roughness. Here, the bearing surfaces are described by εam1 and h + εam2 and m = m2 − m1.

SET-VALUED PERFORMANCE APPROXIMATIONS FOR THE QUEUE GIVEN PARTIAL INFORMATION

2020 ◽  
pp. 1-23
Author(s):  
Yan Chen ◽  
Ward Whitt
Keyword(s):  
Steady State ◽  
Decay Rate ◽  
Waiting Time ◽  
Partial Information ◽  
Upper And Lower Bounds ◽  
Interarrival Time ◽  
Limited Information ◽  
Wide Range ◽  
The Mean ◽  
Third Moment

In order to understand queueing performance given only partial information about the model, we propose determining intervals of likely values of performance measures given that limited information. We illustrate this approach for the mean steady-state waiting time in the $GI/GI/K$ queue. We start by specifying the first two moments of the interarrival-time and service-time distributions, and then consider additional information about these underlying distributions, in particular, a third moment and a Laplace transform value. As a theoretical basis, we apply extremal models yielding tight upper and lower bounds on the asymptotic decay rate of the steady-state waiting-time tail probability. We illustrate by constructing the theoretically justified intervals of values for the decay rate and the associated heuristically determined interval of values for the mean waiting times. Without extra information, the extremal models involve two-point distributions, which yield a wide range for the mean. Adding constraints on the third moment and a transform value produces three-point extremal distributions, which significantly reduce the range, producing practical levels of accuracy.

The solution of theoretical seismic problems by best rational function approximations for Laplace transform inversion

1975 ◽  
Vol 65 (4) ◽  
pp. 927-935
Author(s):  
I. M. Longman ◽  
T. Beer
Keyword(s):  
Laplace Transform ◽  
Rational Function ◽  
High Accuracy ◽  
Time Variable ◽  
Inversion Method ◽  
The Laplace Transform ◽  
Previously Treated ◽  
The Mean ◽  
Function Approximations ◽  
Laplace Transform Inversion

Abstract In a recent paper, the first author has developed a method of computation of “best” rational function approximations ḡn(p) to a given function f̄(p) of the Laplace transform operator p. These approximations are best in the sense that analytic inversion of ḡn(p) gives a function gn(t) of the time variable t, which approximates the (generally unknown) inverse f(t) of f̄(p in a minimum least-squares manner. Only f̄(p) but not f(t) is required to be known in order to carry out this process. n is the “order” of the approximation, and it can be shown that as n tends to infinity gn(t) tends to f(t) in the mean. Under suitable conditions on f(t) the convergence is extremely rapid, and quite low values of n (four or five, say) are sufficient to give high accuracy for all t ≧ 0. For seismological applications, we use geometrical optics to subtract out of f(t) its discontinuities, and bring it to a form in which the above inversion method is very rapidly convergent. This modification is of course carried out (suitably transformed) on f̄(p), and the discontinuities are restored to f(t) after the inversion. An application is given to an example previously treated by the first author by a different method, and it is a certain vindication of the present method that an error in the previously given solution is brought to light. The paper also presents a new analytical method for handling the Bessel function integrals that occur in theoretical seismic problems related to layered media.

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