scholarly journals Formulation of the Reynolds equation on a time-dependent lubrication surface

2016 ◽  
Vol 472 (2187) ◽  
pp. 20160032 ◽  
Author(s):  
İ. Temizer ◽  
S. Stupkiewicz
Keyword(s):  
Reynolds Equation ◽  
Large Deformations ◽  
A Priori ◽  
Elastohydrodynamic Lubrication ◽  
Time Dependent ◽  
Soft Interfaces ◽  
The Third ◽  
Curvilinear Coordinate ◽  
Thin Fluid Film ◽  
Lubrication Effect

The Reynolds equation, which describes the lubrication effect arising through the interaction of two physical surfaces that are separated by a thin fluid film, is formulated with respect to a continuously evolving third surface that is described by a time-dependent curvilinear coordinate system. The proposed formulation essentially addresses lubrication mechanics at interfaces undergoing large deformations and a priori satisfies all objectivity requirements, neither of which are features of the classical Reynolds equation. As such, this formulation may be particularly suitable for non-stationary elastohydrodynamic lubrication problems associated with soft interfaces. The ability of the formulation to capture finite-deformation effects and the influence of the choice of the third surface are illustrated through analytical examples.

scholarly journals A Modified k – ε Turbulence Model for a Wave Breaking Simulation

Water ◽  
2019 ◽  
Vol 11 (11) ◽  
pp. 2282
Author(s):  
Giovanni Cannata ◽  
Federica Palleschi ◽  
Benedetta Iele ◽  
Francesco Gallerano
Keyword(s):  
Energy Dissipation ◽  
Turbulence Model ◽  
Wave Breaking ◽  
A Priori ◽  
Time Dependent ◽  
Breaking Wave ◽  
Vertical Coordinate ◽  
Initial Wave ◽  
Proposed Model ◽  
Curvilinear Coordinate

We propose a two-equation turbulence model based on modification of the k − ε standard model, for simulation of a breaking wave. The proposed model is able to adequately simulate the energy dissipation due to the wave breaking and does not require any “a priori” criterion to locate the initial wave breaking point and the region in which the turbulence model has to be activated. In order to numerically simulate the wave propagation from deep water to the shoreline and the wave breaking, we use a model in which vector and tensor quantities are expressed in terms of Cartesian components, where only the vertical coordinate is expressed as a function of a time-dependent curvilinear coordinate that follows the free surface movements. A laboratory test is numerically reproduced with the aim of validating the turbulence modified k − ε model. The numerical results compared with the experimental measurements show that the proposed turbulence model is capable of correctly estimating the energy dissipation induced by the wave breaking, in order to avoid any underestimation of the wave height.

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]

Amplitude Effects on the Dynamic Performance of Hydrostatic Gas Thrust Bearings

1979 ◽  
Vol 101 (4) ◽  
pp. 437-443 ◽  
Author(s):  
A. Kent Stiffler ◽  
R. R. Tapia
Keyword(s):  
Fourier Series ◽  
Finite Difference ◽  
Reynolds Equation ◽  
Load Capacity ◽  
Dynamic Performance ◽  
Time Dependent ◽  
Thrust Bearings ◽  
The Third ◽  
Linear Damping ◽  
Finite Difference Techniques

A strip gas film bearing with inherently compensated inlets is analyzed to determine the effect of disturbance amplitude on its dynamic performance. The governing Reynolds’ equation is solved using finite-difference techniques. The time dependent load capacity is represented by a Fourier series up to and including the third harmonics. For the range of amplitudes investigated the linear stiffness was independent of the amplitude, and the linear damping was inversely proportional to (1 − ε2)1.5 where ε is the amplitude relative to the film thickness.

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.

Über Gewissen und Gewissheit

2016 ◽  
Vol 64 (4) ◽  
Author(s):  
Dina Emundts
Keyword(s):  
Immanuel Kant ◽  
A Priori ◽  
Categorical Imperative ◽  
Moral Principles ◽  
The Third ◽  
The Status

AbstractThis paper suggests an understanding of the concept of “Gewissen” (conscience) according to which Gewissen is best understood as a receptivity to moral principles that corresponds to certain moral feelings. In the first part of the paper this suggestion is spelled out and alternatives to it are discussed. As is shown in the second part, this suggestion goes back to the thought of Immanuel Kant, but it can be developed even if one does not follow Kant in his understanding of the categorical imperative as an a priori principle. However, if one does not follow Kant with respect to the status of the categorical imperative, there are some interesting consequences for our understanding of conscience and especially for our understanding of its relation to knowledge and certainty. These consequences are discussed in the third part of this paper.

A mathematical model for the third-body concept

2017 ◽  
Vol 23 (3) ◽  
pp. 420-432 ◽  
Author(s):  
Pavel Krejčí ◽  
Adrien Petrov
Keyword(s):  
Mathematical Model ◽  
A Priori Estimates ◽  
A Priori ◽  
Dynamical Problem ◽  
Sobolev Embedding ◽  
Third Body ◽  
Embedding Theory ◽  
The Third ◽  
Galerkin Approximations ◽  
Body Concept

The third-body concept is a pragmatic tool used to understand the friction and wear of sliding materials. The wear particles play a crucial role in this approach and constitute the main part of the third-body. This paper aims to introduce a mathematical model for the motion of a third-body interface separating two surfaces in contact. This model is written in accordance with the formalism of hysteresis operators as solution operators of the underlying variational inequalities. The existence result for this dynamical problem is obtained by using a priori estimates established for Faedo–Galerkin approximations, and some more specific techniques such as anisotropic Sobolev embedding theory.

Il buono, il brutto e il cattivo. Disambiguare il naturalismo di Quine

2009 ◽  
pp. 75-97
Author(s):  
Susan Haack
Keyword(s):  
Empirical Study ◽  
A Priori ◽  
Scientific Investigation ◽  
The Third ◽  
Epistemological Naturalism

- Quine's ‘epistemology naturalised' has been profoundly influential, but it is also highly ambiguous. Quine seems at times to claim only that epistemology is not a purely a priori enterprise but an empirical study, continuous with the sciences of cognition; at others, that epistemological questions can be turned over to the sciences to resolve; and on other occasions, that epistemological questions are misconceived and should be replaced by scientific investigation into cognition. What is argued here is that the first and most modest version of Quine's epistemological naturalism is potentially fruitful, the second and more ambitious indefensible, and the third and most ambitious not only false but disastrous.

The Impact of the Court of Justice of the European Union on Neighbouring Countries

2020 ◽  
pp. 349-396
Author(s):  
Arie Reich ◽  
Hans-W. Micklitz
Keyword(s):  
European Union ◽  
A Priori ◽  
Policy Recommendations ◽  
Eu Law ◽  
The European Union ◽  
The Third ◽  
Court Of Justice ◽  
The Many ◽  
The Impact ◽  
Legal Integration

The concluding chapter sums up the overall findings of the project through three different strands of analysis: the first breaks down the eleven jurisdictions into three groups based on the relative quantity and impact of Court of Justice of the European Union (CJEU) citations found in these jurisdictions. By drawing conclusions from all the country reports through a comparative and macro-perspective, the goal is to distil the insights of the entire project and formulate policy recommendations in the light of EU external policy and legal integration objectives vis-à-vis its neighbourhood; the second examines the many factors that a priori could have an impact on whether judges are likely to cite the CJEU in their judgments, and then discusses what the research has found in relation to the actual role played by these factors; the third tries to place the current project into the context of overall research on the global reach of EU law, which can be ‘exported’ to non-members of the EU through various mechanisms, such as mutual and formal agreement or through more unilateral and spontaneous forms. They include modes of extraterritorial application of EU law, territorial extension, and the so-called ‘Brussels Effect’. The chapter concludes with some general observations and thoughts and formulates possible policy recommendations.

scholarly journals Doubly Degenerate Parabolic Equation with Time-Dependent Gradient Source and Initial Data Measures

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Lihua Deng ◽  
Xianguang Shang
Keyword(s):  
Parabolic Equation ◽  
Initial Data ◽  
Degenerate Parabolic Equation ◽  
A Priori Estimates ◽  
A Priori ◽  
Local Existence ◽  
Time Dependent ◽  
Priori Estimates ◽  
The Cauchy Problem ◽  
Degenerate Parabolic

This paper is devoted to the Cauchy problem for a class of doubly degenerate parabolic equation with time-dependent gradient source, where the initial data are Radon measures. Using the delicate a priori estimates, we first establish two local existence results. Furthermore, we show that the existence of solutions is optimal in the class considered here.

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