A Comparison of the Roughness Regimes in Hydrodynamic Lubrication

2017 ◽  
Vol 139 (5) ◽  
Author(s):  
John Fabricius ◽  
Afonso Tsandzana ◽  
Francesc Perez-Rafols ◽  
Peter Wall
Keyword(s):  
Asymptotic Behavior ◽  
Stokes Flow ◽  
High Frequency ◽  
Reynolds Equation ◽  
Pressure Field ◽  
Hydrodynamic Lubrication ◽  
Narrow Gap ◽  
Surface Textures ◽  
Lubrication Regimes ◽  
Generalized Reynolds Equation

This work relates to previous studies concerning the asymptotic behavior of Stokes flow in a narrow gap between two surfaces in relative motion. It is assumed that one of the surfaces is rough, with small roughness wavelength μ, so that the film thickness h becomes rapidly oscillating. Depending on the limit of the ratio h/μ, denoted as λ, three different lubrication regimes exist: Reynolds roughness (λ = 0), Stokes roughness (0 < λ < ∞), and high-frequency roughness (λ = ∞). In each regime, the pressure field is governed by a generalized Reynolds equation, whose coefficients (so-called flow factors) depend on λ. To investigate the accuracy and applicability of the limit regimes, we compute the Stokes flow factors for various roughness patterns by varying the parameter λ. The results show that there are realistic surface textures for which the Reynolds roughness is not accurate and the Stokes roughness must be used instead.

ON A LUBRICATION PROBLEM WITH FOURIER AND TRESCA BOUNDARY CONDITIONS

2004 ◽  
Vol 14 (06) ◽  
pp. 913-941 ◽  
Author(s):  
MAHDI BOUKROUCHE ◽  
GRZEGORZ ŁUKASZEWICZ
Keyword(s):  
Boundary Condition ◽  
Asymptotic Behavior ◽  
Free Boundary ◽  
Stokes Flow ◽  
Reynolds Equation ◽  
Friction Condition ◽  
The Other ◽  
One Dimension ◽  
Limit Velocity ◽  
Pressure Distributions

The asymptotic behavior of a Stokes flow with Fourier boundary condition on one part on the boundary and Tresca free boundary friction condition on the other, when one dimension of the fluid domain tends to zero is studied. The strong convergence of the velocity is proved, a specific Reynolds equation is obtained, and the uniqueness of the limit velocity and pressure distributions is established.

scholarly journals The Non-Unicity of the Film Thickness in the Hydrodynamic Lubrication: Novel Approach Generating Equivalent Micro-Grooves and Roughness

2021 ◽  
Vol 26 (3) ◽  
pp. 44-61
Author(s):  
M. El Gadari ◽  
M. Hajjam
Keyword(s):  
Film Thickness ◽  
Reynolds Equation ◽  
Pressure Field ◽  
Hydrodynamic Lubrication ◽  
Hydrodynamic Pressure ◽  
New Approach ◽  
Initial Film ◽  
Surface Finishes ◽  
Novel Approach ◽  
The 1960S

Abstract Since the 1960s, all studies have assumed that a film thickness “h” provides a unique pressure field “p” by resolving the Reynolds equation. However, it is relevant to investigate the film thickness unicity under a given hydrodynamic pressure within the inverse theory. This paper presents a new approach to deduce from an initial film thickness a widespread number of thicknesses providing the same hydrodynamic pressure under a specific condition of gradient pressure. For this purpose, three steps were presented: 1) computing the hydrodynamic pressure from an initial film thickness by resolving the Reynolds equation with Gümbel’s cavitation model, 2) using a new algorithm to generate a second film thickness, 3) comparing and validating the hydrodynamic pressure produced by both thicknesses with the modified Reynolds equation. Throughout three surface finishes: the macro-shaped, micro-textured, and rough surfaces, it has been demonstrated that under a specific hydrodynamic pressure gradient, several film thicknesses could generate the same pressure field with a slight difference by considering cavitation. Besides, this paper confirms also that with different ratios of the averaged film thickness to the root mean square (RMS) similar hydrodynamic pressure could be generated, thereby the deficiency of this ratio to define the lubrication regime as commonly known from Patir and Cheng theory.

Viscoelastic Lubrication With Phan-Thein-Tanner Fluid (PTT)

2004 ◽  
Vol 126 (2) ◽  
pp. 288-291 ◽  
Author(s):  
F. Talay Akyildiz ◽  
Hamid Bellout
Keyword(s):  
Relaxation Time ◽  
Velocity Field ◽  
Constitutive Equation ◽  
Explicit Expression ◽  
Reynolds Equation ◽  
Pressure Field ◽  
Deborah Number ◽  
Time Dependent ◽  
Newtonian Case ◽  
Generalized Reynolds Equation

We analyze the lubrication flow of a viscoelastic fluid to account for the time dependent nature of the lubricant. The material obeys the constitutive equation for Phan-Thein-Tanner fluid (PTT). An explicit expression of the velocity field is obtained. This expression shows the effect of the Deborah number (De=λU/L, λ is the relaxation time). Using this velocity field, we derive the generalized Reynolds equation for PTT fluids. This equation reduces to the Newtonian case as De→0. Finally, the effect of the Deborah number on the pressure field is explored numerically in detail and the results are documented graphically.

Analysis of the Lubrication Regimes at the Small End and Big End of a Connecting Rod of a High Performance Motorbike Engine

2012 ◽  
Author(s):  
Luca Bertocchi ◽  
Matteo Giacopini ◽  
Daniele Dini
Keyword(s):  
Rotational Speed ◽  
High Speed ◽  
High Performance ◽  
Hydrodynamic Lubrication ◽  
Vertical Axis ◽  
Connecting Rod ◽  
Lubrication Regimes ◽  
High Speed Rotation ◽  
Speed Rotation ◽  
Squeeze Effect

In the present paper, the algorithm proposed by Giacopini et. al. [1], based on a mass-conserving formulation of the Reynolds equation using the concept of complementarity is suitably extended to include the effects of compressibility, piezoviscosity and shear-thinning on the lubricant properties. This improved algorithm is employed to analyse the performance of the lubricated small end and big end bearings of a connecting rod of a high performance motorbike engine. The application of the algorithm proposed to both the small end and the big end of a con-rod is challenging because of the different causes that sustain the hydrodynamic lubrication in the two cases. In the con-rod big end, the fluid film is mainly generated by the relative high speed rotation between the rod and the crankshaft. The relative speed between the two races forms a wedge of fluid that assures appropriate lubrication and avoids undesired direct contacts. On the contrary, at the con-rod small end the relative rotational speed is low and a complete rotation between the mating surfaces does not occurs since the con-rod only oscillates around its vertical axis. Thus, at every revolution of the crankshaft, there are two different moments in which the relative rotational speed between the con-rod and the piston pin is null. Therefore, the dominant effect in the lubrication is the squeeze caused by the high loads transmitted through the piston pin. In particular both combustion forces and inertial forces contribute to the squeeze effect. This work shows how the formulation developed by the authors is capable of predicting the performance of journal bearings in the unsteady regime, where cavitation and reformation occur several times. Moreover, the effects of the pressure and the shear rate on the density and on the viscosity of the lubricant are taken into account.

Application Of Elastic Layers To Register Pressure Field On The Model Surface In Supersonic Flow

2016 ◽  
Vol 11 (1) ◽  
pp. 23-33
Author(s):  
Maxim Golubev ◽  
Andrey Shmakov
Keyword(s):  
Surface Waves ◽  
High Frequency ◽  
High Speed ◽  
Pressure Pulsation ◽  
Pressure Field ◽  
Leading Edge ◽  
Supersonic Wind Tunnel ◽  
Register Pressure ◽  
Elastic Layers ◽  
Sharp Leading Edge

The work presents the results of application of panoramic interferential technique which is based on elastic layers (sensors) usage to obtain pressure distribution on the flat plate having sharp leading edge. Experiments were done in supersonic wind tunnel at Mach number M = 4. Sensitivity and response time are shown to be enough to register pressure pulsation against standing and traveling sensor surface waves. Applying high-frequency image acquiring is demonstrated to make possible to distinguish at visualization images high-speed disturbances propagating in the boundary layer from low-speed surface waves

scholarly journals Limit Theory for High Frequency Sampled MCARMA Models

2014 ◽  
Vol 46 (3) ◽  
pp. 846-877 ◽  
Author(s):  
Vicky Fasen
Keyword(s):  
Asymptotic Behavior ◽  
High Frequency ◽  
Lévy Process ◽  
Asymptotic Properties ◽  
Domain Of Attraction ◽  
Levy Process ◽  
Sample Variance ◽  
Limit Theory ◽  
Second Moments ◽  
Time Grid

We consider a multivariate continuous-time ARMA (MCARMA) process sampled at a high-frequency time grid {hn, 2hn,…, nhn}, where hn ↓ 0 and nhn → ∞ as n → ∞, or at a constant time grid where hn = h. For this model, we present the asymptotic behavior of the properly normalized partial sum to a multivariate stable or a multivariate normal random vector depending on the domain of attraction of the driving Lévy process. Furthermore, we derive the asymptotic behavior of the sample variance. In the case of finite second moments of the driving Lévy process the sample variance is a consistent estimator. Moreover, we embed the MCARMA process in a cointegrated model. For this model, we propose a parameter estimator and derive its asymptotic behavior. The results are given for more general processes than MCARMA processes and contain some asymptotic properties of stochastic integrals.

Enhancing Tribological Conditions in Tube Hydroforming by Using Textured Tubes

2004 ◽  
Author(s):  
Gracious Ngaile ◽  
Mark Gariety ◽  
Taylan Altan
Keyword(s):  
Deformation Behavior ◽  
Hydrodynamic Lubrication ◽  
Tube Hydroforming ◽  
Great Influence ◽  
Tribological Performance ◽  
Tube Surface ◽  
Sliding Velocity ◽  
Textured Surfaces ◽  
Interface Pressure ◽  
Surface Textures

The effects of textured tubes on the tribological performance in Tube Hydroforming (THF) are discussed. Textured surfaces, namely sand blasted, knurled, and as rolled surfaces were tested under various interface pressure and sliding velocity conditions. Sand blasted textured tubes were found to have the best tribological performance. It was also found that the interface pressure has a great influence on the attainment of Micro-Plasto HydroDynamic Lubrication (MPHDL) and Micro-Plasto HydroStatic Lubrication (MPHSL) conditions at the tool-workpiece interface. Preliminary finite element simulations on the deformation behavior of tube surface shows that surface textures can be optimized to enhance tribological performance.

scholarly journals THE PROBABILITY CHARACTERISTICS OP WAVES AND WAVE PRESSURES AT A VERTICAL BREAKWATER

1984 ◽  
Vol 1 (19) ◽  
pp. 50
Author(s):  
Huang Peiji ◽  
Zhao Binglai
Keyword(s):  
Probability Distribution ◽  
High Frequency ◽  
Pressure Field ◽  
Spectral Component ◽  
High Frequency Band ◽  
Wave Pressure ◽  
Spectral Components ◽  
Wave Heights ◽  
Vertical Breakwater ◽  
Equilibrium Range

In this paper, under the condition of waves in front of a breakwater being not broken, studies were made on the characterises of probability distribution of waves and wave pressures, the regularity of the spectral component attenuation with depth and the constitution of the high frequency band of wave pressure spectrum. The distributions of wave heights in front of a vertical breakwater, the range of wave pressure fluctuation at different subsurface levels, and the wave periods have shown that they are practically invariable with depth and can be determined theoretically. The spectral constitution of wave pressure field and the regularity of attenuation of spectral components were analyzed at the vertical breakwater, and a new expression describing the equilibrium range of wave pressure spectrum was obtained.

On the effects of two-dimensional Reynolds roughness in hydrodynamic lubrication

1978 ◽  
Vol 364 (1716) ◽  
pp. 89-106 ◽  
Keyword(s):  
Surface Roughness ◽  
Numerical Computation ◽  
Autocorrelation Function ◽  
Reynolds Equation ◽  
Hydrodynamic Lubrication ◽  
The Other ◽  
Roughness Height ◽  
Two Dimensional ◽  
Roughness Effects ◽  
Dimensional Surface

The hydrodynamic lubrication of rough surfaces is analysed with the Reynolds equation, whose application requires the roughness spacing to be large, and the roughness height to be small, compared with the thick­ness of the fluid film. The general two-dimensional surface roughness is considered, and results applicable to any roughness structure are obtained. It is revealed analytically that two types of term contribute to roughness effects: one depends on the shape of the autocorrelation function and the other does not. The former contribution was neglected by previous workers. The numerical computation of an example shows that these two contributions are comparable in magnitude.

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