Simplified molecular gas film lubrication equation and accommodation coefficient effects

2011 ◽  
Vol 17 (8) ◽  
pp. 1271-1282 ◽  
Author(s):  
Bao-Jun Shi ◽  
Jia-Dong Ji ◽  
Ting-Yi Yang
Keyword(s):  
Accommodation Coefficient ◽  
Molecular Gas ◽  
Lubrication Equation ◽  
Molecular Gas Film Lubrication ◽  
Film Lubrication

Ultra-Thin Gas Squeeze Film Characteristics for Finite Squeeze Numbers

1996 ◽  
Vol 118 (1) ◽  
pp. 201-205 ◽  
Author(s):  
R. Matsuda ◽  
S. Fukui
Keyword(s):  
Squeeze Film ◽  
Molecular Gas ◽  
Lubrication Equation ◽  
Flow Rate Coefficient ◽  
Load Carrying ◽  
Molecular Gas Film Lubrication ◽  
Squeeze Number ◽  
Film Characteristics ◽  
Gas Effect ◽  
Film Lubrication

Ultra-thin gas squeeze film characteristics for finite squeeze numbers are examined by solving the molecular gas film lubrication (MGL) equation, which has a similar form to the conventional Reynolds-type lubrication equation but contains a flow rate coefficient and is valid for arbitrarily small spacings or for arbitrary Knudsen number. We quantitatively clarify by numerical computations that at thin film conditions below several micrometers, pressures generated by squeeze motions are lower than those of continuum flow case and therefore load-carrying capacities are smaller and depend upon film thickness because of the molecular gas effect. For example when the squeeze number is 10 and excursion ratio is 0.5, the load-carrying capacity at 0.1 μm is about one tenth of that at 1 μm.

Asymptotic Analysis of Ultra-Thin Gas Squeeze Film Lubrication for Infinitely Large Squeeze Number (Extension of Pan’s Theory to the Molecular Gas Film Lubrication Equation)

1995 ◽  
Vol 117 (1) ◽  
pp. 9-15 ◽  
Author(s):  
R. Matsuda ◽  
S. Fukui
Keyword(s):  
Film Thickness ◽  
Squeeze Film ◽  
Molecular Gas ◽  
Lubrication Equation ◽  
Linearized Boltzmann Equation ◽  
Flow Rate Coefficient ◽  
Load Carrying ◽  
Molecular Gas Film Lubrication ◽  
Squeeze Number ◽  
Film Lubrication

Ultra-thin gas squeeze film characteristics are analyzed by extending Pan’s asymptotic theory for infinite squeeze number to the molecular gas film lubrication equation which was derived from the linearized Boltzmann equation and is valid for arbitrary Knudsen numbers. The generalized asymptotic method is shown to solve the boundary value equation which contains the flow rate coefficient as a function of the product of pressure P and film thickness H. Numerical results are obtained for a circular squeeze film. The PH ratio and the load carrying capacity ratio to those of continuum flow both decrease when the average film thickness is less than several microns because of molecular gas effects.

Ultra-Thin Gas Squeeze Film Characteristics for Infinitely Large Squeeze Number

1998 ◽  
Vol 120 (4) ◽  
pp. 750-757 ◽  
Author(s):  
Wang-Long Li
Keyword(s):  
Squeeze Film ◽  
Molecular Gas ◽  
Lubrication Equation ◽  
Operation Conditions ◽  
Matching Equation ◽  
Molecular Gas Film Lubrication ◽  
Squeeze Number ◽  
Film Characteristics ◽  
Film Lubrication ◽  
Rarefaction Effects

In this study, the characteristics of ultra-thin gas films are analyzed asymptotically for infinite squeeze number using the molecular gas film lubrication equation with coupled roughness and rarefaction effects taken into consideration. The governing equation of the internal region was obtained by a time averaged technique, and the boundary conditions were obtained numerically from the matching conditions near the boundaries. Two new functions, H and H−1 were proposed for deriving the matching equation near the boundary. Finally, the characteristics of squeeze film bearings with infinite width were analyzed for various roughness parameters (Peklenik number, standard deviations of the composite roughness, and roughness orientation angles), rarefaction parameter (Knudsen number), and operation conditions (excursion ratio).

Thermo-Molecular Gas-Film Lubrication (t-MGL) Analysis in the Free Molecular Limit: Effects of Accommodation Coefficients on Static Pressure

2016 ◽  
Author(s):  
Shigehisa Fukui ◽  
Yuki Okamura ◽  
Hiroshige Matsuoka
Keyword(s):  
Temperature Distribution ◽  
Specular Reflection ◽  
Boundary Surface ◽  
Accommodation Coefficient ◽  
Molecular Gas ◽  
Temperature Distributions ◽  
Accommodation Coefficients ◽  
Molecular Gas Film Lubrication ◽  
Wedge Effect ◽  
Film Lubrication

In order to examine thermo-molecular gas film lubrication (t-MGL) characteristics with a temperature distribution at the disk or slider surfaces for spacings of several nanometers, the free molecular t-MGL equation considering temperature distributions and accommodation coefficients at the boundaries was established. By analyzing pressure generated by the wedge effect (slider inclination) and the thermal wedge effect (boundary temperature distributions), it is revealed that, as the accommodation coefficient, α0, of the running disk or the boundary surface with a temperature distribution decreases, that is, as the ratio of specular reflection increases, the pressure generation decreases, whereas as the accommodation coefficient, α1, of the stationary slider surface or the boundary surface without a temperature distribution decreases, the pressure generation increases.

Effect of Configuration of Micro-∕Nanoscale Structure on Sliding Surface on Molecular Gas-Film Lubrication

2011 ◽  
Author(s):  
Susumu Isono ◽  
Masashi Yamaguchi ◽  
Shigeru Yonemura ◽  
Takanori Takeno ◽  
Hiroyuki Miki ◽  
...  
Keyword(s):  
Molecular Gas ◽  
Sliding Surface ◽  
Nanoscale Structure ◽  
Molecular Gas Film Lubrication ◽  
Film Lubrication

Adjoint Design Sensitivity Analysis of Molecular Gas Film Lubrication Sliders

2002 ◽  
Vol 125 (1) ◽  
pp. 145-151 ◽  
Author(s):  
Sang-Joon Yoon ◽  
Dong-Hoon Choi
Keyword(s):  
Sensitivity Analysis ◽  
Design Sensitivity ◽  
Design Sensitivity Analysis ◽  
Finite Difference Approximation ◽  
Molecular Gas ◽  
Air Bearings ◽  
Adjoint Variable ◽  
Topological Parameters ◽  
Molecular Gas Film Lubrication ◽  
Film Lubrication

This paper proposes an analytical design sensitivity analysis (DSA) to topological parameters of MGL (molecular gas film lubrication) sliders by introducing an adjoint variable method. For the analysis of slider air bearings, we used the spatial discretization of the generalized lubrication equation based on a control volume formulation. The residual functions for inverse analysis of the slider are considered as the equality constraint functions. The slider rail heights of all grid cells are chosen as design variables since they are the topological parameters determining air bearing surface (ABS). Then, a complicated adjoint variable equation is formulated to directly handle the highly nonlinear asymmetric coefficient matrix and vector in the discrete system equations of slider air bearings. An alternating direction implicit (ADI) scheme is utilized to efficiently solve large-scale problem in special band storage. The simulation results of DSA are directly compared with those of finite-difference approximation (FDA) to show the effectiveness and accuracy of the proposed approach. The overall sensitivity distribution over the ABS is reported, and clearly shows to which section of the ABS the special attention should be given during the manufacturing process. It is demonstrated that the proposed method can reduce more than 99 percent of the CPU time in comparison with FDA, even though both methods give the same results.

A Database for Couette Flow Rate Considering the Effects of Non-Symmetric Molecular Interactions

2002 ◽  
Vol 124 (4) ◽  
pp. 869-873 ◽  
Author(s):  
Wang-Long Li
Keyword(s):  
Couette Flow ◽  
Molecular Interactions ◽  
Flow Rate ◽  
Molecular Gas ◽  
Mems Devices ◽  
Magnetic Head ◽  
Linearized Boltzmann Equation ◽  
Accommodation Coefficients ◽  
Molecular Gas Film Lubrication ◽  
Film Lubrication

A complete database for Couette flow rate (QCD,α1,α2,0.1⩽α1,α2⩽1.0,0.01⩽D⩽100, where D=inverse Knudsen number) for ultra-thin gas film lubrication problems is advanced. When the accommodation coefficients (AC) of the two lubricating surfaces are different α1≠α2, the Couette flow rate in the modified molecular gas film lubrication (MMGL) equation should be corrected. The linearized Boltzmann equation (under small Mach number conditions) is solved numerically for the case of non-symmetric molecular interactions α1≠α2. The Couette flow rate is then calculated, and the database is constructed. The present database can be easily implemented in the MMGL equation. In addition, the present database extends the previously published results for 0.1⩽α1,α2⩽0.7. The database for low ACs is valuable in the analysis and applications of MEMS devices (bushings of electrostatic micro motors, micro bearings, magnetic head/disk interfaces, etc.), and their future development.

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