On the Physical Meanings of Λ/Q˜p0 and σ/Q˜p0 in Molecular Gas Film Lubrication Problems

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Abstract
To estimate molecular gas film lubrication (MGL) characteristics, we propose a modified bearing number Λ′ and a modified squeeze number σ′, which are, respectively, the conventional bearing Λ and squeeze number σ divided by the relative Poiseuille flow rate Q˜p0. Using Λ′ and σ′, the linearized MGL problem can be reduced to the continuum gas film lubrication problem and the MGL characteristics can be exactly estimated, if the characteristic flow rate corresponding to the spacing, Q˜p0, is known. For nonlinear MGL problems, the lubrication characteristics can be verified to be roughly estimated by Λ′ and σ′ both in rectangular slider bearings and in circular squeeze-film thrust bearings.