A Note on Film Rupture in Hydrodynamic Lubrication

1987 ◽  
Vol 109 (3) ◽  
pp. 562-566 ◽  
Author(s):  
Terukazu Ota
Keyword(s):  
Experimental Data ◽  
Boundary Condition ◽  
Experimental Study ◽  
Boundary Conditions ◽  
Present Model ◽  
Hydrodynamic Lubrication ◽  
Correction Term ◽  
Plane Geometry ◽  
Separation Boundary ◽  
Film Rupture

A theoretical and experimental study has been made for a film repture in hydrodynamic lubrication. A model is proposed on boundary conditions at the film rupture point. It contains a pressure correction term as a parameter, which simplifies that derived by Coyne and Elrod, and the so-called separation boundary condition. Some experiments have been conducted for a flow in a cylinder-plane geometry. It is found that numerical results using the present model agree reasonably well with the present and previous experimental data.

Inertia Effects on Film Rupture in Hydrodynamic Lubrication

1995 ◽  
Vol 117 (4) ◽  
pp. 685-690
Author(s):  
Terukazu Ota ◽  
Hiroyuki Yoshikawa ◽  
Makoto Hamasuna ◽  
Takeshi Motohashi ◽  
Soshu Oi
Keyword(s):  
Experimental Data ◽  
Boundary Condition ◽  
Reynolds Equation ◽  
Hydrodynamic Lubrication ◽  
Numerical Data ◽  
Wave Number ◽  
Film Rupture ◽  
Rupture Surface ◽  
Inertia Effects ◽  
Good Agreement

A perturbation analysis was made to study the effect of inertia on the film rupture in hydrodynamic lubrication using a modified Reynolds equation. A simplified boundary condition at film rupture proposed by Ota (1987) was employed. The theory was extended to investigate the wave number of the film rupture surface and to investigate the effect of gas bubbles included in the lubricant. Numerical calculations were carried out for a cylinder-plane bearing and are compared with previous experimental and numerical data. The effects of inertia on film rupture characteristics are clarified and the present numerical results are found to be in good agreement with earlier experimental data.

Re-Examination of Film Rupture Boundary Condition in Hydrodynamic Lubrication Under Inertia Effect

1991 ◽  
Vol 113 (3) ◽  
pp. 604-608 ◽  
Author(s):  
A. Mori ◽  
H. Mori
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Pressure Distribution ◽  
Journal Bearing ◽  
Hydrodynamic Lubrication ◽  
Careful Consideration ◽  
Inertia Effect ◽  
Film Rupture ◽  
The Difference ◽  
Inertia Forces

This paper presents discussions on the choice and handling of film rupture boundary conditions for the hydrodynamic lubrication under the effect of lubricant inertia forces. Many researchers have analyzed this inertia effect in converging-diverging hydrodynamic wedge and squeeze films without careful consideration of the problem caused by the film rupture boundary conditions used. To reveal the importance of the problem, the marked difference in pressure distribution produced by the difference in boundary conditions is presented for an infinitely long, steadily loaded, cylindrical journal bearing.

A Theoretical Model of Striated Film-Rupture Applied to the Cylinder-Plane

1985 ◽  
Vol 107 (3) ◽  
pp. 419-422 ◽  
Author(s):  
C. Fall
Keyword(s):  
Experimental Data ◽  
Theoretical Model ◽  
Perturbation Analysis ◽  
Reynolds Equation ◽  
Plane Geometry ◽  
Time Dependent ◽  
Linear Perturbation ◽  
Film Rupture ◽  
Successful Prediction

The author has previously presented a theoretical model of striated film-rupture consisting of a time-dependent linear perturbation analysis applied to the Reynolds equation. After review this model is applied to the cylinder-plane geometry for comparison with theoretical and experimental data due to Savage. Successful prediction of the number of striations for varying (ηU/T) and (R/h0) is achieved.

Separation Cavitation in Lightly Loaded Fluid Film Bearings with Both Surfaces in Motion

1974 ◽  
Vol 16 (3) ◽  
pp. 147-155 ◽  
Author(s):  
C. M. Taylor
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Experimental Work ◽  
Journal Bearing ◽  
Fluid Film ◽  
Operating Parameters ◽  
Separation Boundary ◽  
Fluid Film Bearings ◽  
Theoretical Predictions ◽  
Bounding Surfaces

For lightly loaded fluid film bearings in which gaseous cavitation occurs, application of the continuity boundary condition at the liquid-gas interface is not satisfactory. Two alternative boundary conditions have been postulated. The purpose of this paper is to examine the separation boundary condition; in particular, the effect of both bounding surfaces being in motion is studied. This situation might be used as a basis for experimental work designed to select the most appropriate boundary condition for lightly loaded bearings. In Part 2, the boundary condition is used to analyse the cylinder-plane and journal bearing configurations. The theoretical predictions for the operating parameters are examined to see if their magnitudes and/or trends could be used for comparing the available cavitation boundary conditions.

On the Performance of Journal Bearings Under Conditions of Film Rupture, Part II

1975 ◽  
Vol 97 (4) ◽  
pp. 591-598
Author(s):  
W. A. Crosby ◽  
E. M. Badawy
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Finite Length ◽  
Infinite Number ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Journal Bearings ◽  
Operating Characteristics ◽  
Film Rupture ◽  
Rupture Part

An analytical analysis of journal bearing performance under conditions of film rupture by separation and by cavitation is performed. The ruptured region is considered to have an infinite number of cavities. The boundary condition of Reynolds’ equation at the trailing edge is influenced by the bearing’s operating characteristics and the method of oil admission. A variational solution is given in order to extend the applicability of the boundary conditions to bearings of finite length.

Paper 14: Hydrodynamic Lubrication of Lightly Loaded Finite Cylinders

1966 ◽  
Vol 181 (15) ◽  
pp. 112-116
Author(s):  
R. J. Boness
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Velocity Gradient ◽  
Carrying Capacity ◽  
Hydrodynamic Lubrication ◽  
Load Carrying Capacity ◽  
Load Carrying ◽  
Fluid Properties ◽  
Theoretical Results ◽  
Finite Cylinders

Theoretical results of the load-carrying capacity of lightly loaded finite cylinders indicate that the effect of side leakage can be secondary to upstream boundary condition considerations. Neglecting side leakage the calculations are extended to cover the experimental results of Crook into the régime where the fluid properties are pressure dependent. The results support the adoption of the new velocity and velocity gradient boundary conditions suggested by Lauder.

Stoßbestimmte Grenzschicht in einem schwach ionisierten Plasma

1970 ◽  
Vol 25 (4) ◽  
pp. 525-541
Author(s):  
Karl Gerhard Müller ◽  
Peter Wahle
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Velocity Distribution ◽  
Specular Reflection ◽  
Correction Term ◽  
Charge Carriers ◽  
Macroscopic Models ◽  
Basic Set ◽  
Transfer Equations ◽  
Set Up

Abstract In this work we develop a collision-dominated sheath model which includes the well known macroscopic models as extreme cases. We set up a description of the charge carriers with the help of the velocity distribution. In order to fulfil the microscopic boundary conditions at the wall we split up the velocity distributions into two parts. A basic set of new transport equations arises which differ from the usual equations by a correction term in the momentum transfer equations. Because of this splitting up of the velocity distribution we are able to take into account exactly specular reflection of the electrons at the wall. In a good approximation our results can also be obtained from the usual equations, if a suitably fitted factor is introduced into the electron boundary condition. at the wall.

Mathematical Model of the Cooling of a Plastic, Thermoformed Part

2010 ◽  
Author(s):  
Thomas M. Aidich ◽  
Tien-Chien Jen ◽  
Yi-Hsin Yen
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Boundary Condition ◽  
Heat Flux ◽  
Boundary Conditions ◽  
Surface Temperature ◽  
Surface Heat Flux ◽  
Surface Heat ◽  
Cooling Cycle ◽  
Transient Conduction

This paper presents research into the mechanism involved in the cooling of a plastic thermoformed part after it is formed onto a mold. The intent of this research is to develop a simple and practical mathematical model useful to small thermoforming companies without a large engineering staff that describes the transient heat conduction of the cooling process. The model should also be able to predict the temperature distribution within the thickness of the part during the cooling. This mathematical model, which began with simplified boundary conditions, was then compared to experimental cooling data and modified accordingly to properly fit that data and the actual boundary conditions of the cooling part. The research began by examining the cooling of a series of high molecular weight polyethylene thermoformed side panels for plastic, portable restrooms. These parts where chosen for this preliminary research because of their very simple, flat geometric shape that lends them to being modeled as simple plane walls in transient conduction. The shape of the parts also leads to near constant thickness over the vast majority of the part. Using the model of a plane wall in transient conduction, the governing partial differential equation was solved for two possible boundary conditions on the mold side of the part: constant imposed surface temperature and constant imposed surface heat flux. These two solutions were then compared to experimental data gathered on the temperature profile of the free surface of the part during a production environment. After the experimental data and simple mathematical models were compared the necessary changes to the assumed mold side boundary condition was made to adjust the mathematical model to the experimental data. The research found that the use of simple boundary conditions at the mold side of the part is incorrect. Neither the constant imposed surface temperature nor the imposed surface heat flux boundary conditions fit the data. Initial analysis of the experimental data showed that a time of 30 seconds into the cooling cycle an apparent change in that boundary condition occurs for the part and mold used to gather the data. Further analysis showed that the boundary condition begins as a constant surface heat flux and then changes to an imposed surface temperature that decays exponentially to the initial mold surface temperature. Using this boundary condition, a revised mathematical was developed that match the experimental data very well. The error of the new model compared to the experimental was less than 1.5% for all times during the cooling cycle.

An Experimental Study of Hydrodynamic Film Rupture in a Steadily-Loaded, Non-Conformal Contact

1980 ◽  
Vol 22 (2) ◽  
pp. 71-78 ◽  
Author(s):  
D. Dowson ◽  
E. H. Smith ◽  
C. M. Taylor
Keyword(s):  
Experimental Study ◽  
Boundary Conditions ◽  
Film Rupture ◽  
Experimental Conditions ◽  
Pressure Distributions ◽  
Experimental Programme ◽  
Industrial Coating ◽  
Conformal Contact ◽  
Photographic Studies

A study of ventilated gaseous cavitation in a steadily-loaded, non-conformal contact has been undertaken. The work is particularly appropriate to what can be called ‘lightly loaded’ situations such as those occurring in radial race seals and certain industrial coating processes. A wide-ranging experimental programme has been carried out and measurements of film rupture location and pressure distributions compared to computer predictions obtained using the cavitation boundary conditions of Coyne and Elrod. Photographic studies are also reported. The boundary conditions due to Coyne and Elrod have been confirmed as appropriate for the experimental conditions studied.

Sturm-Liouville Problem for Stationary Differential Operator with Nonlocal Two-Point Boundary Conditions

2006 ◽  
Vol 11 (1) ◽  
pp. 47-78 ◽  
Author(s):  
S. Pečiulytė ◽  
A. Štikonas
Keyword(s):  
Boundary Condition ◽  
Differential Operator ◽  
Boundary Conditions ◽  
Nonlocal Boundary Condition ◽  
Nonlocal Boundary ◽  
Liouville Problem ◽  
Complex Case ◽  
Qualitative Behavior ◽  
Point Boundary ◽  
Sturm Liouville

The Sturm-Liouville problem with various types of two-point boundary conditions is considered in this paper. In the first part of the paper, we investigate the Sturm-Liouville problem in three cases of nonlocal two-point boundary conditions. We prove general properties of the eigenfunctions and eigenvalues for such a problem in the complex case. In the second part, we investigate the case of real eigenvalues. It is analyzed how the spectrum of these problems depends on the boundary condition parameters. Qualitative behavior of all eigenvalues subject to the nonlocal boundary condition parameters is described.

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