The Effect of Two Sided Surface Roughness on Ultra-Thin Gas Films

1983 ◽  
Vol 105 (1) ◽  
pp. 131-137 ◽  
Author(s):  
J. W. White
Keyword(s):  
Surface Roughness ◽  
Current Method ◽  
Solution Procedure ◽  
Lubrication Equation ◽  
Write Heads ◽  
Stationary Surface ◽  
Simple Geometry ◽  
Load Carrying ◽  
Bearing Number ◽  
Gas Bearing

The influence of two sided striated surface roughness on bearing load carrying capacity is analyzed for very low clearance gas films. As was done for the case of stationary surface roughness [1], a model lubrication equation appropriate for extremely high gas bearing number films is solved analytically for several simple geometry bearings. The analytic solution provides information on the exact relationship between pressure and roughness which makes it possible to ensemble average the lubrication equation before solution, greatly simplifying the solution procedure. It is found that the translating surface roughness has an influence on load similar to that caused by the stationary surface. Exact solutions with the current method are compared with those of the theory attributed to Christensen and To̸nder. The results are strikingly different and serve to bring attention to the fact that for high bearing number compressible lubrication, the Christensen-To̸nder theory is inappropriate. The results reported here should find application in the computer peripherals area where read/write heads now routinely hover over a spinning disk at clearances of 0.25 micron.

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.

Effect of a Rough Translating Surface on Gas Film Lubrication: A Numerical and Analytical Study

1987 ◽  
Vol 109 (2) ◽  
pp. 271-275 ◽  
Author(s):  
J. W. White ◽  
P. E. Raad
Keyword(s):  
Surface Roughness ◽  
Analytical Study ◽  
Surface Velocity ◽  
Flow Area ◽  
Inlet Flow ◽  
Stationary Surface ◽  
Symmetric Wave ◽  
Bearing Number ◽  
Gas Bearing ◽  
Film Lubrication

A thin gas film wide wedge bearing with rough translating surface is studied both numerically and analytically. The fluctuating inlet flow area causes a symmetric wave to be generated from the inlet boundary which travels at half the translating surface velocity, possesses a wavelength half that of the surface roughness, and which decays in amplitude in the direction of motion. Since the wave is out of phase with the surface roughness, it has essentially no influence on the load. The load generated varies monotonically with gas bearing number and at a finite bearing number is less than the load developed with the rough stationary surface bearing.

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.

An Averaging Technique for the Analysis of Rough Surface High Bearing Number Gas Flows

1999 ◽  
Vol 121 (2) ◽  
pp. 333-340 ◽  
Author(s):  
James W. White
Keyword(s):  
Surface Roughness ◽  
Rough Surface ◽  
Numerical Solutions ◽  
Scale Effects ◽  
Wavy Surface ◽  
Universal Property ◽  
Flying Height ◽  
Lubrication Equation ◽  
Product Term ◽  
Bearing Number

Earlier analytical solutions by White (1980, 1983, 1992, 1993) included Couette effects, transverse diffusion, and mass storage in a model lubrication equation for narrow width wavy surface high bearing number gas films. The model lubrication equation did not include longitudinal diffusion effects due to the high bearing number restriction. Crone et al. (1991), however, reported numerical solutions of the full Reynolds equation for a gimbal mounted slider subject to wavy surface roughness. The first objective of this work is to reconcile the differences observed between the reported results of White and those of Crone et al. for moving and stationary roughness. The second objective is to describe how to best apply what appears to be a universal property of a high bearing number gas film subjected to a rough surface. Each solution of the model lubrication equation by White (1980, 1983, 1992, 1993) produced a product term based on local gas pressure and clearance (Z = Ph) that is independent of roughness details but which is dependent on the statistical properties of the roughness. In the present work, this characteristic is treated as a universal property of all high bearing number rough surface gas films. The product variable Z = Ph is introduced into the generalized full lubrication equation, and the resulting lubrication equation is ensemble averaged before a solution is attempted. This removes the short length and time scale effects due to the surface roughness. Solution of the ensemble averaged equation for Z(x, y, t) then follows by standard analytical or numerical methods. The unaveraged pressure is then given by P(x, y, t) = Z(x, y, t)/h(x, y, t) and the ensemble averaged or mean pressure at a point is computed from Pm(x, y, t) = Z(x, y, t)E(1/h(x, y, t)), where E(1/h) represents the ensemble average of 1/h. Using this technique, numerical solutions of the full generalized lubrication equation based on kinetic theory were obtained for a low flying gimbal mounted slider. Results indicate that the nominal flying height increases and the minimum flying height decreases as surface roughness increases.

Numerical Investigations of Various Surface Roughness Parameters on the Performance of Profiled Hydrostatic Thrust Bearing

2005 ◽  
Author(s):  
Kirat Shah ◽  
Robert E. Johnson ◽  
Harish P. Cherukuri
Keyword(s):  
Surface Roughness ◽  
Thrust Bearings ◽  
Lubrication Equation ◽  
Load Carrying ◽  
Minimum Film Thickness ◽  
Order Of Magnitude ◽  
Auto Correlation Function ◽  
Non Gaussian ◽  
Gaussian Surface ◽  
Lubrication Conditions

Measurements of surface roughness on hydrostatic bearing slipper indicate that the surfaces are not always Gaussian. Previous studies in this area were primarily concerned with Gaussian surfaces. In this research the effects of non-Gaussian surface roughness on the performance of profiled hydrostatic thrust bearings are analyzed. This study is applicable to the lubrication conditions where the surface roughness is of the same order of magnitude as the minimum film thickness. Surfaces with different skewness, kurtosis, mean, auto-correlation function and standard deviation are generated numerically using a combination of Fast Fourier Transform (FFT) and Johnson translatory system. The finite difference method is used to solve the Reynolds lubrication equation. The effect of roughness on the load carrying capacity is investigated and compared with the results for ideal smooth surfaces.

Combined Effects of Surface Roughness and Rarefaction in the Region Between High Wave Number-Limited and High Bearing Number-Limited Lubricant Flows

2014 ◽  
Vol 137 (1) ◽  
Author(s):  
James White
Keyword(s):  
Surface Roughness ◽  
Knudsen Number ◽  
Analytical Methods ◽  
Wave Number ◽  
Solution Technique ◽  
High Wave Number ◽  
High Wave ◽  
Lubrication Equation ◽  
Wide Range ◽  
Bearing Number

Analytical methods and techniques are required for design and analysis of low clearance gas-bearings that account for the combined influence of surface roughness and Knudsen number. Analytical methods for the lubrication equation are currently available for bearings that are either high wave number-limited or high bearing number-limited. There are few useful analytical methods in the range between these limiting extremes that account for the combined effect of roughness and rarefaction. That is the focus of this paper as it extends the work reported by White (2013, “Surface Roughness Effects in the Region Between High Wave Number and High Bearing Number-Limited Lubricant Flows,” ASME J. Tribol., 135(4), p. 041706) to include rarefaction effects. Results of an analytical study will be reported that investigates a wedge bearing geometry using perturbation methods and multiple-scale analysis over a wide range of Knudsen numbers for roughness on moving and stationary surfaces. The solution technique developed allows nonlinear aspects of the lubrication equation to be retained in the analysis. Solutions will be presented graphically and discussed. Results indicate that most of the bearing sensitivity to Knudsen number can be accounted for by a modified form of the bearing number.

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.

Two-Sided Texture Effects on Ultra-Thin Wide Wedge Gas Bearings

1989 ◽  
Vol 111 (4) ◽  
pp. 719-725 ◽  
Author(s):  
Peter E. Raad ◽  
Isaac M. Kuria
Keyword(s):  
Surface Roughness ◽  
Reynolds Equation ◽  
Disk Surface ◽  
Rapid Separation ◽  
Gas Bearings ◽  
Head Surface ◽  
Load Carrying ◽  
Roughness Amplitude ◽  
Magnetic Hard Disk ◽  
Bearing Number

This work seeks to determine the effects of two-sided surface roughness amplitude on ultra-thin, compressible, isothermal, infinitely wide gas bearings. The transient Reynolds equation of lubrication is solved using a finite difference scheme that is second order accurate in space and time. Solutions of the Reynolds equation are presented for bearing numbers spanning seven orders of magnitude, including those experienced in magnetic hard disk recording. The results presented here show that introducing roughness on either bearing surface causes an increase in the load carrying capacity as compared to the smooth bearing case. However, when roughness is introduced on the stationary surface, the gas bearing generates higher loads which also exhibit a peak at finite bearing numbers. The load peaks increase quadratically with increasing stationary roughness amplitude. It is also demonstrated that at very high values of the bearing number, the load becomes dependent on the amplitude of the surface roughness and not its location. This suggests that a closer look at the possibility of roughening the head surface instead of the larger disk surface in order to cause a more rapid separation is warranted. Stiction resistance would still be achieved, but perhaps more economically, and wear to both surfaces would be minimized.

Recent Patents on Abnormal Hydrodynamic Thrust Slider Bearings: Part II-the Second Mode of the Bearings

2020 ◽  
Vol 13 (1) ◽  
pp. 35-40
Author(s):  
Yongbin Zhang ◽  
Huansheng Cheng ◽  
Junyan Wang
Keyword(s):  
Operating Conditions ◽  
Moving Surface ◽  
Friction Coefficients ◽  
Surface Separation ◽  
Slider Bearings ◽  
Stationary Surface ◽  
Boundary Slippage ◽  
Load Carrying ◽  
Second Mode ◽  
Inlet Zone

Background: As a successive part, the paper introduces the second mode of abnormal hydrodynamic thrust slider bearings with divergent surface separations registered in the patents, where the boundary slippage is artificially designed both on the stationary surface in the inlet zone and on the whole moving surface. Objective : To introduce a second method for artificially designing the boundary slippage for the formation of abnormal hydrodynamic thrust slider bearings. Methods: The analytical results are presented for the introduced bearings. The performances of the bearings are demonstrated. Result: : In appropriate operating conditions, the introduced bearings can have considerable loadcarrying capacities with low friction coefficients on the scales 10-3 or 10-4. With the weakening of the boundary slippage on the moving surface, the load-carrying capacities of the bearings are all increased, while the friction coefficients of the bearings are all reduced. Conclusion: When the boundary slippage is present both on the stationary surface in the bearing inlet zone and on the whole moving surface, abnormal hydrodynamic thrust slider bearings can be designed with the surface separation in the bearing inlet zone lower than that in the bearing outlet zone. The performances of these bearings are quite satisfactory.

scholarly journals Shear cutting induced residual stresses in involute gears and resulting tooth root bending strength of a fineblanked gear

2021 ◽  
Author(s):  
Daniel Müller ◽  
Jens Stahl ◽  
Anian Nürnberger ◽  
Roland Golle ◽  
Thomas Tobie ◽  
...  
Keyword(s):  
Surface Roughness ◽  
Residual Stresses ◽  
Carrying Capacity ◽  
Bending Strength ◽  
Tooth Root ◽  
Load Carrying Capacity ◽  
Near Surface ◽  
Load Carrying ◽  
Involute Gears ◽  
Cut Surface

AbstractThe manufacturing of case-hardened gears usually consists of several complex and expensive steps to ensure high load carrying capacity. The load carrying capacity for the main fatigue failure modes pitting and tooth root breakage can be increased significantly by increasing the near surface compressive residual stresses. In earlier publications, different shear cutting techniques, the near-net-shape-blanking processes (NNSBP’s), were investigated regarding a favorable residual stress state. The influence of the process parameters on the amount of clean cut, surface roughness, hardness and residual stresses was investigated. Furthermore, fatigue bending tests were carried out using C-shaped specimens. This paper reports about involute gears that are manufactured by fineblanking. This NNSBP was identified as suitable based on the previous research, because it led to a high amount of clean cut and favorable residual stresses. For the fineblanked gears of S355MC (1.0976), the die edge radii were varied and the effects on the cut surface geometry, hardness distribution, surface roughness and residual stresses are investigated. The accuracy of blanking the gear geometry is measured, and the tooth root bending strength is determined in a pulsating test rig according to standardized testing methods. It is shown that it is possible to manufacture gears by fineblanking with a high precision comparable to gear hobbing. Additionally, the cut surface properties lead to an increased tooth root bending strength.

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