A new extended Reynolds equation for gas bearing lubrication based on the method of moments

Abstract

equation has been used to model slider bearings. In the theory of lubrication, the continuum description is assumed and inertial terms are negligible (Reynolds 1886). A pressure equation can then be obtained with one dimension less than the Navier-Stokes (NS) equations. However, as modern read-write heads are typically floating 50 nm or less above the moving disk, the characteristic length scale involved is comparable to the molecular mean free path, , and the continuum assumption is no longer considered to be valid. Any gas in such a narrow spacing will suffer from significant non-equilibrium effects, which can be measured by the Knudsen number, Kn, and relates the ratio of the mean free path, , to the characteristic length scale of the device. For convenience, it is possible to classify four distinct flow regimes based on the Knudsen number (Barber and Emerson 2006): (1) Kn < 10 −3 , represents the continuum flow regime where no-slip boundary conditions can generally be applied; (2) 10 −3 < Kn < 10 −1 , indicates that the flow is in the slip regime and boundary conditions need to account for velocity-slip and temperature-jump conditions; (3) 10 −1 < Kn < 10, represents the transition flow regime and results obtained using continuum-based equations are no longer considered reliable; and (4) Kn > 10, is the free molecular or collisionless flow regime and the continuum hypothesis is not valid.In the case of slider bearings operating in the slip-flow regime, it is usually adequate to modify the Reynolds equation with a velocity-slip boundary condition (Burgdorfer 1959;Hsia and Domoto 1983;Mitsuya 1993;Bahukudumbi and Beskok 2003;Chen and Bogy 2010). However, for many problems, especially those related to disk-drive heads, the operating conditions lie well within the transition regime. This is a region where non-equilibrium effects come not only from the wall but also from the Knudsen layer (Cercignani 2000; Lilley and Sader 2008; Gu et al. AbstractAn extended Reynolds equation based on the regularised 13 moment equations and lubrication theory is derived for gas slider bearings operating in the early to upper transition regime. The new formulation performs well beyond the capability of the conventional Reynolds equation modified with simple velocity-slip models. Both load capacity and pressure distribution can be reliably predicted by the extended Reynolds equation and are in good agreement with available direct simulation Monte Carlo data. In addition, the equations are able to provide both velocity and stress information, which is not conveniently recovered from available kinetic models. Tests indicate that the equations can provide accurate data for Knudsen numbers up to unity but, as expected, begin to deteriorate afterwards.

Non-equilibrium effects on flow past a circular cylinder in the slip and early transition regime

“…For all DSMC simulations in this study, the gas was assumed to be argon and the variable hard sphere (VHS) model was employed. Previous theoretical and numerical studies , 2011Gu et al 2010;Gu, Zhang & Emerson 2016) have indicated that the results from the R26 equations using Maxwell molecules and the DSMC simulations using a VHS model are in close agreement with each other. Bird's no-time-counter (NTC) scheme (Bird 1994) has been employed for calculating the collision probabilities in a cell.…”

Rarefaction cloaking: Influence of the fractal rough surface in gas slider bearings

“…Then, according to the analysis in Eq. (19), the pressure rise in the rough bearing is smaller than that in the smooth bearing. Meanwhile, the bearing load capacity becomes smaller in the rough bearing and the load center moves to the entrance of channel.…”

“…1 Recently, a new extended Reynolds equation based on the regularized 13 moment equations and the lubrication theory has been derived for gas slider bearings, but it can only be applied for the Knudsen number up to unity. 19 Therefore, it is essential to establish a generalized gas film lubrication equation derived from the Boltzmann equation for flows at arbitrary values of the Knudsen number. [20][21][22][23][24][25] The generalized Reynolds equation for rarefied gas flows has been established by Fukui and Kaneko 21 and Cercignani, Lampis, and Lorenzani, 25 where the mass flow rates (MFRs) of the fundamental Poiseuille and Couette flows in the lubrication film are obtained based on gas kinetic equations such as the linearized Bhatnager-Gross-Krook (BGK) kinetic equation 26 for arbitrary Knudsen numbers.…”

Numerical and experimental investigation on the performance of hybrid porous gas journal bearings

“…Early investigations on porous gas bearings were mainly focused on the bearing performance with neglecting the influence of shaft rotation 6‐8 . However, with the increasing in rotational speed, the aerodynamic effect in the gas film clearance becomes highly significant 9 . Then, the high‐speed porous gas bearings are often used as hybrid bearings whose operation not only depends on the aerostatic but also on the aerodynamic effect.…”

“…[6][7][8] However, with the increasing in rotational speed, the aerodynamic effect in the gas film clearance becomes highly significant. 9 Then, the high-speed porous gas bearings are often used as hybrid bearings whose operation not only depends on the aerostatic but also on the aerodynamic effect. Some researchers 10,11 have studied the characteristics of conventional orifice-restricted aerostatic bearings with the consideration of aerodynamic effect.…”