Analysis of couple‐stress effects in gas foil bearings using the V. K. Stokes micro‐continuum theory

Abstract

This paper presents an original theoretical investigation of the steady‐state and dynamic characteristics of foil journal bearings lubricated with contaminated air taking into account couple stresses because of the presence of pollutant substances. The substance can be solid particles (eg dust, ash, pollen, and smoke). In aerodynamic lubrication theory, a fluid with couple stresses so‐called couple stress or polar fluid may be considered as one characterised by the 2 physical constants μ and η, which are the absolute viscosity assumed to be independent of the particle volume fraction and the new material constant responsible for couple stress or polar property. The effects of couple stresses on the oil‐lubricated sliding bearings are usually studied by defining the parameter 0.25eml=η/μ12 or its normalised form truel~=l/C . The couple‐stress parameter l, which has the dimension of length, can be thought of as a fluid property depending on the size of the particle contained in the base fluid (solvent). To determine the aerodynamic pressure and the power loss, the governing modified Reynolds' equation and the viscous dissipation term appearing on the right‐hand side of the modified energy equation are derived by using the Vijay Kumar Stokes micro‐continuum theory. The system of partial differential equations resulting from analytical perturbation of the transient modified Reynolds' equation is solved for the steady‐state and dynamic pressures by means of the finite difference method considering both the static and dynamic deformations of the bump foil. Using the complex variable technique, the analytical perturbation process leads to 2 first‐order uncoupled partial differential equations instead of 4 coupled equations as it is usually found in the technical literature. On the other hand, the 2 Cartesian coordinates of the equilibrium position for a given applied static load are iteratively determined by solving the nonlinear equilibrium equations of the journal bearing system with the improved Newton‐Raphson method. According to the obtained results, the effects of couple stresses on the steady‐state and dynamic behaviour of foil self‐acting gas bearings are significant and cannot be overlooked. The results also show that the dynamic deformation of the bump foil should be included in calculating the dynamic performance characteristics of foil journal bearings.

An Assessment of Couple Stress Theories

“…The extension of the Stokes couple stress theory to anisotropic or non-Newtonian fluids would be especially problematic. Although the Stokes' theory requires two couple-stress viscous parameters  and  for linear isotropic fluids, it is not known why in very recent work Laouadi et al (2018) incorrectly state that this theory depends on one couple-stress viscous parameter  . As mentioned, the dependence of the velocity profile and stresses on both viscous parameters  and  is obviously seen for Poiseuille flow through circular pipes (Stokes, 1966(Stokes, , 1984.…”

The lubrication characteristics of magnetized journal bearings affected by magnetic fluids considering the elasticity of its liner

“…The modified Reynolds formulas on the lubrication characteristics of journal bearing affected by magnetic fluids have been derived on the basis of Stokes micro-continuum theory, 16 considering the couple action between the rotating action of journal bearing and its oil-film squeeze dynamic action based on Hu and Xu’s theoretical research. 14 On the basis of this, the impact of the magnetic supporting oil-film pressure due to the symmetric gradient magnetic field in axial and its lubrication characteristics have been analyzed.…”

Thermohydrodynamic lubrication analysis of misaligned journal bearing considering surface roughness and couple stress

“…Researchers have found that adding a small amount of long-chain polymer to the lubricant can effectively improve the load capacity performance of the friction pair. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15] A small amount of long-chain polymer changes the fluid characteristics of the lubricant, changing the lubricant fluid characteristics from Newtonian fluid to couple stress fluid. From the perspective of engineering applications, such measures are simple and effective.…”

“…The current couple stress fluid lubrication theory is relatively mature, and the mathematical model of couple stress fluid lubrication is derived based on Stokes' microcontinuum theory. Many scholars have applied the mathematical model of coupled stress fluid lubrication to study the static and dynamic performance of various types of friction pairs such as journal bearing, [1][2][3][4][5][6][7] porous journal bearing, 8 double-layered journal bearing, 9 two-lobe journal bearing, [10][11][12] three-lobe journal bearing, 13 gas foil bearing, 14 and sliding bearing. 15 Compared with Newtonian fluid, coupled stress fluid can effectively improve the load capacity of the friction pair.…”