An Average Lubrication Equation for Thin Film Grain Flow With Surface Roughness Effects

2002 ◽  
Vol 124 (4) ◽  
pp. 736-742 ◽  
Author(s):  
Hung-Jung Tsai ◽  
Yeau-Ren Jeng
Keyword(s):  
Thin Film ◽  
Surface Roughness ◽  
Particle Size ◽  
Coordinate Transformation ◽  
Surface Characteristics ◽  
Perturbation Approach ◽  
Roughness Effects ◽  
Lubrication Equation ◽  
Grain Flow ◽  
Standard Derivation

A closed-form average lubrication equation for thin film grain flow with the effects of surface roughness is derived. This equation is based on Haff’s grain flow theory and also the flow factors proposed by Patir and Cheng. The flow factors, derived by the perturbation approach and coordinate transformation, are expressed in terms of surface characteristics (three characteristics for each surface: roughness orientation, Peklenik number and standard derivation) and particle size. Finally, the flow factors under different surface characteristics and particle size are discussed.

Grain Flow for Rough Surfaces Considering Elastic/Inelastic Grain Collision

2004 ◽  
Author(s):  
Yeau-Ren Jeng ◽  
Hung-Jung Tsai
Keyword(s):  
Grain Size ◽  
Energy Loss ◽  
Rough Surface ◽  
Collision Energy ◽  
Rough Surfaces ◽  
Surface Characteristics ◽  
Flow Theory ◽  
Roughness Effects ◽  
Lubrication Equation ◽  
Grain Flow

Previous work by this group on an average lubrication equation for grain flow with roughness effects is extended to include grain-grain collision elasticity ranging from perfectly elastic to perfectly inelastic. The average lubrication equation is based on Haff’s grain flow theory, with flow factors from Patir and Cheng and Tripp’s use of perturbation. The derived flow factors are obtained as functions of rough surface characteristics, grain size and collision pattern. As collision energy loss approaches zero, the inelastic results approach those for perfectly elastic grain collision. The mathematical formulae for flow factors, grain/grain collision elasticity, grain size and roughness are presented, discussed. Predictions for the elastic and inelastic cases are graphically demonstrated and compared.

Grain Flow for Rough Surfaces Considering Grain/Grain Collision Elasticity

2005 ◽  
Vol 127 (4) ◽  
pp. 837-844 ◽  
Author(s):  
Yeau-Ren Jeng ◽  
Hung-Jung Tsai
Keyword(s):  
Experimental Data ◽  
Grain Size ◽  
Energy Loss ◽  
Collision Energy ◽  
Surface Characteristics ◽  
Roughness Effects ◽  
Lubrication Equation ◽  
Grain Flow ◽  
Mathematical Formulas ◽  
Good Agreement

Previous work by this group on an average lubrication equation for grain flow with roughness effects is extended to include grain-grain collision elasticity ranging from perfectly elastic to perfectly inelastic. The average lubrication equation is based on Haff’s grain flow theory, with flow factors from Patir and Cheng and Tripp’s use of perturbation. The derived flow factors are obtained as functions of rough surface characteristics, grain size, and collision pattern. As collision energy loss approaches zero, the inelastic results approach those for perfectly elastic grain collision. The mathematical formulas for flow factors, grain/grain collision elasticity, grain size, and roughness are presented and discussed. Predicitons for the elastic and inelastic cases are graphically demonstrated and compared. The derived average lubrication equation for grain flow shows good agreement with the theoretical and experimental data of Yu, Craig, and Tichy [J. Rheol., 38(4), 921 (1994)].

Theoretical Approach to Turbulent Lubrication Problems Including Surface Roughness Effects

1989 ◽  
Vol 111 (1) ◽  
pp. 17-22 ◽  
Author(s):  
H. Hashimoto ◽  
S. Wada
Keyword(s):  
Surface Roughness ◽  
Velocity Distribution ◽  
Boundary Layers ◽  
Theoretical Approach ◽  
Turbulent Boundary Layers ◽  
Distribution Law ◽  
Roughness Effects ◽  
Relative Roughness ◽  
Lubrication Equation ◽  
Lubrication Characteristics

A new theoretical approach to turbulent lubrication problems including the surface roughness effects is described. On the basis of a logarithmic velocity distribution law in the turbulent boundary layers, the resistance laws for pressure and shear flows in the lubricant film are formulated separately in both cases of smooth and homogeneous rough surfaces. Moreover, combining the bulk flow concept proposed by Hirs with the formulated resistance laws, the generalized turbulent lubrication equation including the surface roughness effects is derived. Some numerical results for the modified turbulence coefficients are presented in the graphic form for different values of relative roughness, and the effects of surface roughness on the turbulent lubrication characteristics are generally discussed.

Surface Roughness Effects on Hydrodynamic Lubrication and Scuffing Failure Analysis of Axially Grooved Plunger of a Rotary Diesel Fuel Injection Pump

2004 ◽  
Author(s):  
M. Afzaal Malik ◽  
Badar Rashid ◽  
Shahab Khushnood ◽  
Raja Amer Azim
Keyword(s):  
Surface Roughness ◽  
Particle Size ◽  
Diesel Fuel ◽  
Fuel Injection ◽  
Hydrodynamic Lubrication ◽  
Roughness Effects ◽  
Injection Pump ◽  
Fuel Injection Pump ◽  
Scuffing Failure ◽  
Diesel Fuel Injection

The wear between the plunger and plunger sleeve of rotary diesel fuel injection pump causes considerable decrease in injection pressure and the quantity of fuel to combustion chamber of an engine, which ultimately leads to failure of engine assembly. This research investigates the cause of failure particularly focusing on surface roughness effects to hydrodynamic lubrication and scuffing failure due to abrasive contaminant. The surface roughness of plunger and plunger sleeve were measured and incorporated in Reynolds equation to analyze roughness effects on hydrodynamic lubrication. The critical particle size of the dust normally present in the diesel fuel is evaluated to determine which test dust sample could cause systems to fail. Based on this information, scuffing failure of pumps due to an abrasive contaminant partially penetrated in the plunger sleeve is analyzed. The abrasive contaminant is modeled as a spherical shaped rigid particle. Excessive temperature rise between the particle-plunger interface is used as an indication of whether scuffing would take place. Experiments were conducted to determine parameters such as particle size of dust samples, surface roughness of plunger and plunger sleeve, specific heat of diesel fuel, diesel fuel density, quantity of fuel flow and radial clearance. These experimentally determined parameters are then used as input in our computer program to lend more confidence to our predicted results.

Surface Roughness Effects on Air Bearing Performance Over a Wide Range of Knudsen and Wave Numbers

2010 ◽  
Vol 132 (3) ◽  
Author(s):  
James White
Keyword(s):  
Surface Roughness ◽  
Data Storage ◽  
Knudsen Number ◽  
Poiseuille Flow ◽  
Air Bearing ◽  
Roughness Effects ◽  
Averaging Methods ◽  
Lubrication Equation ◽  
Wide Range ◽  
Averaging Techniques

Design of a near contact air bearing interface such as that created by a recording head slider and data storage disk requires consideration of a lubrication equation that is appropriate for high Knudsen number flows. The Poiseuille flow database reported by Fukui and Kaneko, 1990 [“A Database for Interpolation of Poiseuille Flow Rates for High Knudsen Number Lubrication Problems,” ASME J. Tribol., 112, pp. 78–83] is appropriate over a wide range of Knudsen numbers and is used throughout the data storage industry for analysis of the low flying recording head slider air bearing. However, at such low clearances, the topography of the air bearing surfaces also comes into question, making it important to consider both rarefaction and surface roughness effects in the air bearing design. In order to simplify the air bearing analysis of rough surfaces, averaging techniques for the lubrication equation have been developed for situations where the number of roughness elements (or waves) is either much greater or much less than the gas bearing number. Between these two extremes there are currently no roughness averaging methods available. Although some analytical and numerical studies have been reported for continuum and first-order slip conditions with simple geometries, little or no results have appeared that include both surface roughness and high Knudsen number flows outside the limited ranges where surface averaging techniques are used. In order to better understand the influence of transverse surface roughness over a wide range of Knudsen numbers and the relationship of key parameters involved, this paper describes a primarily analytical air bearing study of a wide, rough surface slider bearing using the Poiseuille flow database reported by Fukui and Kaneko. The work is focused outside the limited ranges where current surface averaging methods for the lubrication equation are expected to be valid.

Surface Roughness Effects on the Load Carrying Capacity of Very Thin Compressible Lubricating Films

1980 ◽  
Vol 102 (4) ◽  
pp. 445-451 ◽  
Author(s):  
J. W. White
Keyword(s):  
Surface Roughness ◽  
Exact Solutions ◽  
Carrying Capacity ◽  
Current Method ◽  
Previous Method ◽  
Finite Width ◽  
Load Carrying Capacity ◽  
Roughness Effects ◽  
Lubrication Equation ◽  
Load Carrying

The effect of surface roughness on load carrying capacity of very low clearance gas bearings is analyzed. A model lubrication equation appropriate for high bearing number, finite width films is first derived. Then, by obtaining exact solutions to several simple geometry bearings, the “closure problem” or statistical relationship of pressure and spacing is revealed. The lubrication equation is then ensamble averaged and solved for several test cases. The seemingly subtle differences in ensamble averaging the transverse terms in the lubrication equation are compared for the current theory and a previous method and are shown to produce vast differences in load carrying capacity. The current method is expected to be the correct approach since it is based on a generalization of exact solutions.

Characteristics of Powder Lubricated Finite-Width Journal Bearings: A Hydrodynamic Analysis

2005 ◽  
Author(s):  
Hung-Jung Tsai ◽  
Yeau-Ren Jeng
Keyword(s):  
Particle Size ◽  
Control Volume ◽  
Particle Size Effect ◽  
Journal Bearings ◽  
Finite Width ◽  
Control Volume Method ◽  
Hydrodynamic Analysis ◽  
Lubrication Equation ◽  
Grain Flow ◽  
Volume Method

In this paper, the average lubrication equation for grain flow is solved using a control volume method to analyze the performance of hydrodynamic journal bearings. The grain particle size effect was investigated. The nondimensional load and friction coefficient are demonstrated in terms of eccentricity ratios under various diameter-to-width ratios. The results demonstrate the performance of powdered lubricated journal bearings, and also accord with the results experimented by Heshmat and Brewe.

Comparison of Moving and Stationary Surface Roughness Effects on Bearing Performance, With Emphasis on High Knudsen Number Flow

2012 ◽  
Vol 134 (3) ◽  
Author(s):  
James White
Keyword(s):  
Surface Roughness ◽  
Knudsen Number ◽  
Multiple Scale ◽  
Air Bearing ◽  
Roughness Effects ◽  
Lubrication Equation ◽  
Wide Range ◽  
Transverse Roughness ◽  
Number Flow ◽  
Gas Bearing

Low clearance gas bearing applications require an understanding of surface roughness effects at increased levels of Knudsen number. Because very little information has been reported on the relative air-bearing influence of roughness location, this paper is focused on a comparison of the effects of moving and stationary striated surface roughness under high Knudsen number conditions. First, an appropriate lubrication equation will be derived based on multiple-scale analysis that extends the work of White (2010, “A Gas Lubrication Equation for High Knudsen Number Flows and Striated Rough Surfaces,” ASME J. Tribol., 132, p. 021701). The resulting roughness averaged equation, applicable for both moving and stationary roughness over a wide range of Knudsen numbers, allows an arbitrary striated roughness orientation with regard to both (1) the direction of surface translation and (2) the bearing coordinates. Next, the derived lubrication equation is used to analyze and compare the influences produced by a stepped transverse roughness pattern located on the moving and the stationary bearing surface of a wedge bearing geometry of variable inclination. Computed results are obtained for both incompressible and compressible lubricants, but with an emphasis on high Knudsen number flow. Significant differences in air-bearing performance are found to occur for moving versus stationary roughness.

Surface Roughness Effects in the Region Between High Wave Number and High Bearing Number Limited Lubricant Flows

2013 ◽  
Vol 135 (4) ◽  
Author(s):  
James White
Keyword(s):  
Surface Roughness ◽  
Roughness Length ◽  
Wave Number ◽  
Roughness Effects ◽  
High Wave Number ◽  
High Wave ◽  
Lubrication Equation ◽  
Order Of Magnitude ◽  
Bearing Number ◽  
Gas Bearing

The ability to predict surface roughness effects is now well established for gas bearings that satisfy the requirements for either high wave number–limited or high bearing number–limited conditions. However, depending on the parameters involved, a given bearing configuration may not satisfy either of these limited requirements for analysis of roughness effects. Well-established methods for the analysis of surface roughness effects on gas lubrication are not yet available outside of these two limited regions. With that as motivation, this paper then reports an analytical investigation of rough surface gas-bearing effects for the region bounded on one side by high wave number–limited conditions and on the other by high bearing number–limited effects. It emphasizes the gas-bearing region, where shear-driven flow rate and pressure-driven flow rate due to surface roughness are of the same order of magnitude. This paper makes use of the compressible continuum form of the Reynolds equation of lubrication together with multiple-scale analysis to formulate a governing lubrication equation appropriate for the analysis of striated roughness effects collectively subject to high bearing number (Λ→∞), high inverse roughness length scale (β→∞), and unity order of magnitude-modified bearing number based on roughness length scale (Λ2=Λ/β=O(1)). The resulting lubrication equation is applicable for both moving and stationary roughness and can be applied in either averaged or un-averaged form. Several numerical examples and comparisons are presented. Among them are results that illustrate an increased sensitivity of bearing force to modified bearing number for Λ2=O(1). With Λ2 in this range, bearings with either moving or stationary roughness exhibit increased force sensitivities, but the effects act in opposite ways. That is, while an increase in modified bearing number causes a decrease in force for stationary roughness, the same increase in modified bearing number causes an increase in force for moving roughness.

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