Modified Reynolds Equations for Thin Film Lubrication with Saturated High-Viscosity Surface Layer and Lubrication Analysis of Tapered Pad Bearing

Abstract

This paper presents a modified Reynolds equation for analyzing thin film lubrication with a saturated high-viscosity surface layer on a solid surface. The saturated high-viscosity characteristics of engine oil blended with additives of metallic detergents and friction modifiers were expressed using new viscosity functions with various orders termed "viscosity model 2," which is different from the previous model, termed "viscosity model 1." The viscosity function was then incorporated on the moving surface, and the fluid flow in the bearing gap was determined in a closed-form solution for order numbers N of 2 to 5. Subsequently the modified Reynolds equation was formulated by numerically integrating the flow equation. The modified Reynolds equation was applied to analyze the tapered pad bearing, and different features of the load capacity and friction coefficients from those for viscosity model 1 were clarified. The effects of the order number N, viscosity ratio, bearing length, and high-viscosity layer thickness on the load capacity and friction coefficient were elucidated. It was found that when the order number N was increased to 5, the friction coefficient decreased to a minimal value, subsequently increased to the maximum value, and then decreased to the lowest value with a decrease in the trailing gap.

Modified Reynolds Equation for Thin Film Lubrication with Arbitrarily Enhanced Viscosity Surface Layers and Lubrication Analysis of Micro-Tapered Pad Bearing

“…The quantities Z c and z c are referenced film thicknesses close to the saturated viscosity film thickness when the viscosity at z = Z c and z c becomes (r 0 +1)/2 = ~r0 /2. Previous studies [16,18] demonstrated that the load capacity in the one-side model using Z c = 2z c was similar to that in the two-side model. The total saturated viscosity thickness of the effective viscosity measured by resonance shear force measurement system could correspond to Z c in Eq.…”

“…3.1 Viscosity function when the effective viscosity is saturated below a large film thickness A previous study [17,18] indicated that a high-viscosity surface layer on the moving surface could simulate the effective viscosity characteristics of engine oil comprising metallic detergent additive, which were measured by Shibasaki et al [11] and Tamura et al [12]. This high-viscosity surface layer for the one-side model is expressed by Eq.…”

“…where Q p1 and Q s2 are given by Thus, the one-dimensional Reynolds equation based on the wedge film effect is expressed as The shear stresses τ 0 and τ h at the moving and fixed surfaces, respectively, are given by From Eqs. (18) and (19), the theoretical value of the effective…”

“…where r 0 is the ratio of viscosity at the solid surface (µ 0 ) to bulk viscosity (µ b ). In a previous study [17,18], r 0 = 1000 and 100 were used for calculation examples, whereas r 0 = 500 was used in this study based on the effective viscosity measured by Tamura et al [12]. The quantities Z c and z c are referenced film thicknesses close to the saturated viscosity film thickness when the viscosity at z = Z c and z c becomes (r 0 +1)/2 = ~r0 /2.…”

“…The viscosity function was expressed by the saturated analytical function of the second to fifth order of the distance from the solid surface. Then, the modification coefficients of the Reynolds equation were obtained by numerically integrating the flow velocity, and the lubrication characteristics of a microtapered pad bearing were analyzed [17,18]. The load capacity increased at a rate similar to the rate of increase of the saturated viscosity relative to the bulk viscosity when the trailing gap of the bearing became smaller than the thickness of the saturated viscosity layer.…”