Wang-Long Li

A new modified Reynolds equation for ultrathin film gas lubrication

A new modified Reynolds equation for solving the ultrathin film gas lubrication is proposed to overcome the complicated and time-consuming difficulties of solving the linearized Boltzmann equation. The model equation is based on modified high-order slip-flow velocity distribution with three adjustable coefficients, which are corrected according to the Boltzmann model. The results are compared to those obtained using other kinds of currently employed modified Reynolds equations. It shows that the present model produces a closer approximation to that of the exact Boltzmann model than do other models, in a wider range of inverse Knudsen number. In addition, the newly derived equation is widely applicable to practical use.

Effects of roughness on rarefied gas flow in long microtubes

In this paper, we propose a model that describes the behavior of rarefied gas flow in long microtubes. The inner surface is modeled as an annulus porous film pressed on an impermeable surface. The appropriate slip-flow boundary conditions (the high-order slip-flow model; Weng C-I et al 1999 Nanotechnology 10 373) and the proper porous flow model (the Brinkman-extended Darcy model; Li W-L and H Wang C-C 1999 J. Phys. D: Appl. Phys. 32 1421) are utilized in the core gas region and annulus porous region, respectively. Moreover, utilizing the matched conditions (velocity slip and stress continuity) at the gas/porous interface, we derive the governing equation of pressure distribution in long microtubes. We discuss the effects of pressure drop (Pin − Pout), roughness and gas rarefaction on the pressure distribution and velocity distributions of long microtubes. Moreover, the analytical solution of the pressure distribution for the first-order slip-flow model is obtained. The present results are valuable for the design and analysis of fluid flow in microelectromechanical systems.

An Average Reynolds Equation for Non-Newtonian Fluid with Application to the Lubrication of the Magnetic Head-Disk Interface©

A closed, form of the average Reynolds equation is derived for non-Newtonian inelastic fluids with roughness effects taken into consideration. The derivation of flow factors is carried out by means of the perturbation approach with Greens function technique. A coordinate transformation is also utilized to make the equations similar with the Newtonian ones. The results of flow factors are expressed as functions of the Peklenik numbers and the standard deviations of roughness heights of each surface, as well as functions of the film thickness ratio Final manuscript approved November 10, 1995 and the flow behavior index of the power-law fluid of the lubrication film. One can find a critical value for Peklenik number (γcr) from the expressions of pressure flow factors. When γ > γcr(γ < γcr), the pressure flow factors increase as n increases (decreases). A modified Peklenik number is defined to reveal the interactions between roughness orientations and the non-Newtonian flow. Furthermore, an appropriate combi...

Gaseous flow in microtubes at arbitrary Knudsen numbers

New models that describe gas flow behaviour in microtubes are presented. To avoid time-consuming calculations in solving the integral equation which is obtained from the microscopic point of view, the high-order slip-flow boundary condition is utilized to correct the gas flow in such a micron or submicron spacing. The proposed model can be applied to arbitrary Knudsen number conditions under the assumption that the bulk flow velocity is negligible compared with the sonic velocity of the gas. The analytical solution of the pressure distribution for the first-order slip-flow model is obtained. The results show that the first-order slip-flow model is in good agreement with this model. The nonlinear pressure distribution is due to gas compressibility. The dominant mechanism influencing the nonlinear pressure distribution comes from the rarefaction of gas and the inlet pressure. The rarefaction effect increases the pressure drop at the inlet region of the channel and decreases the pressure drop at the exit region of the channel. The decrease of inverse Knudsen number changes the pressure distribution from concave to almost linear and increases the mass flow.

Modified average Reynolds equation for ultra-thin film gas lubrication considering roughness orientations at arbitrary Knudsen numbers

Abstract In this paper, the effects of roughness orientations and molecular mean free path on the roughness-induced flows are discussed. Based on the newly-proposed modified Reynolds equation, the flow factors are derived in compact forms by using the perturbation approach and the coordinate transformation. The flow factors are expressed as functions of surface characteristics (roughness orientation angles, Peklenik numbers and standard deviations of bearing surfaces) and gas rarefraction parameters (inverse Knudsen numbers). In the result, a comparison of several approximations of the rarefied gas models is discussed. Finally, the static performance of a magnetic recording head under ultrathin spacing conditions with roughness and rarefraction effects taken into account is analyzed.

Surface Roughness Effects in Journal Bearings with Non-Newtonian Lubricants

The static performance of finite journal bearings lubricated with non-Newtonian power law fluids is analyzed by using a control volume method with an Elrod algorithm to solve the average Reynolds equation and determine the cavitation region accurately. The results show that the flow behavior index of power law fluids has an insignificant affect on the load ratios, side flow ratios and cavitation regions, while it significantly affects load capacities and side flow rates. Furthermore, the effects of film thickness ratios, pressure flow factors, shear flow factors, slenderness ratios, eccentricities and inlet pressures on the variations of cavitation regions are also discussed.

Stress-strain analysis for evaluating the effect of the orientation of dentin tubules on their mechanical properties and deformation behavior.

A model whose porosity does not vary with compression depth is developed for evaluating the mechanical properties of dentin tubules with various orientation angles from micro-pillar nanocompression tests. Experimental results for a range of loading rates indicate that the yielding parameters and the elastic modulus are little affected by the creep behavior. For a given compression depth, the hardness, elastic modulus, and yielding strength decrease with increasing orientation angle of dentin. The mechanical properties obtained using the proposed model are consistent with the reported data, and are actually more precise since they consider the orientation angle. The proposed testing method can be applied to materials that yield a negative value of the elastic modulus due to creep behavior.

Lubrication of journal bearings: influence of stress jump condition at the porous-media/fluid film interface

In this study, the microstructure of bearing surface is modeled as a thin porous film press-fitted on an impermeable surface. On the basis of the Brinkman-extended Darcy model with stress jump condition at the porous-media/fluid film interface, the effects of viscous shear stress and stress jump on the performance of finite journal bearings are examined. The Elrod algorithm as well as the successive over-relaxation method is utilized to solve the modified Reynolds equation and determine the accurate cavitation region. The results show that the increase in stress jump parameter (β) provides a decrease in the load capacity, an increase in the attitude angle, and an increase in the coefficient of friction.

Surface Roughness Effects in Hydrodynamic Lubrication Involving the Mixture of Two Fluids

In this paper, the relations expressing the effects of surface roughness and homogeneous mixture (the mixture of power-law fluid inserted into a Newtonian fluid) on the roughness-induced flow factor are derived. A coordinate transformation is utilized to simplify the derivation. By using the perturbation approach incorporated with Green function technique, the flow factors and shear stress factors are derived and expressed as functions of the volume fraction of the power-law fluid in the mixture (v p ), the viscosity ratio of the power-law fluid to that of the Newtonian fluid (N or μ p * ), the flow behavior index of the power-law fluid (n), the Peklenik numbers (γ i ) and the standard deviations (σ i ) of each surface. A form of the average Reynolds equation is then obtained. It is shown that a number of currently available models are special cases of the theory presented here. Finally, the performance of a journal bearing is discussed.

Estimation of surface absorptivity and surface temperature in laser surface hardening process

A two-dimensional, quasi-static, inverse heat conduction problem (IHCP) is implemented to investigate the absorption efficiency of surface coatings in laser surface hardening process. The analysis of IHCP includes the utilization of the method of direct sensitivity coefficient and the measurement of interior temperatures nearby the laser heating surface. The results shows that the estimation of surface absorptivity generally agrees with that observed by experimental works. It is realized that the different kinds of coating make influences on the surface absorptivity as well as surface temperature significantly. Furthermore, the power density and scanning speed of laser beam to control the quality of surface hardening may be determined based on the informations of heat flow in the workpiece.