On The Role of a Non-Newtonian Fluid in Short Bearing Theory

Abstract

The importance of rheological properties of lubricants has arisen from the realization that non-Newtonian fluid effects are manifested over a broad range of lubrication applications. In this paper a theoretical investigation of short journal bearings performance characteristics for non-Newtonian power-law lubricants is given. A modified form of the Reynolds’ equation for hydrodynamic lubrication is studied in the asymptotic limit of small slenderness ratio (i.e., bearing length to diameter, L/D = λ→0). Fluid film pressure distributions in short bearings of arbitrary azimuthal length are studied using matched asymptotic expansions in the slenderness ratio. The merit of the short bearing approach used in solving a modified Reynolds’ equation by the method of matched asymptotic expansions is emphasized. Fluid film pressure distributions are determined without recourse to numerical solutions to a modified Reynolds’ equation. Power-law rheological exponents less than and equal to one are considered; power-law fluids exhibit reduced load capacities relative to the Newtonian fluid. The cavitation boundary shape is determined from Reynolds’ free surface condition; and the boundary shape is shown to be independent of the bearing eccentricity ratio.

Analysis of the Hydrodynamic Lubrication Characteristics of the External Return Spherical Bearing Pair of an Axial Piston Pump/Motor

“…Applying the velocity boundary conditions of equation (14) into equations (18) and (21), τ φ1 , τ θ1 , C 1 , and C 2 can be solved. And, the expression of u φ and u θ can be written as follows:…”

“…Meyer et al [13] deduced the Reynolds equation for a Newtonian fluid lubrication in spherical coordinates and solved the lubrication problem of artificial hip implantations under quasi-static conditions. Buckholz et al [14] obtained a modified Reynolds equation based on the power-law fluid model and calculated the lubrication performance of a short radial sliding bearing. Chinyoka et al [15] studied the influence of viscoelasticity under Arrhenius dynamics on the temperature of a lubricant subjected to simple shear in one-dimensional flow by the numerical simulation method and proved the advantages viscoelastic fluid (represented by Oldroyd-B liquid) over Newtonian fluid.…”

Effects of non-Newtonian rheology on the film-height history between non-parallel sliding-squeezing surfaces

“…When n = 1, the consistency index is equal to the fluid viscosity η, and the linear stress-strain law of a Newtonian fluid is recovered. On the basis of the power-law fluid model, the effects of non-Newtonian characteristics of different operating mechanisms have been analysed by a number of investigators [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. In hydrostatic thrust bearings, the pressure distribution and load capacity are predicted by Shukla and Prakash [1] and Singh et al [2].…”

“…In hydrostatic thrust bearings, the pressure distribution and load capacity are predicted by Shukla and Prakash [1] and Singh et al [2]. In squeezing-flow problems, the load capacity and approaching velocity for various squeezing geometries are examined by Sinha and Singh [3], Buckholz [4], and Oliver and Shahidullah [5]. For journal bearings, both the steadystate performance and the dynamic characteristics are calculated by Dien and Elrod [6], Buckholz [7], Lin and Wang [8], and Raghunandana and Majumdar [9].…”

“…In squeezing-flow problems, the load capacity and approaching velocity for various squeezing geometries are examined by Sinha and Singh [3], Buckholz [4], and Oliver and Shahidullah [5]. For journal bearings, both the steadystate performance and the dynamic characteristics are calculated by Dien and Elrod [6], Buckholz [7], Lin and Wang [8], and Raghunandana and Majumdar [9]. On the characteristics of slider bearings, the steadystate performance including the load and friction coefficient is evaluated by Safar and Shawki [10], Buckholz [11], Wang and Jin [12], and Johnson and Mangkoesoebroto [13].…”