Analysis of misaligned hydrodynamic porous journal bearings in the steady-state condition with micropolar lubricant

Abstract

Impregnated porous bearings are used in different machines and other applications. In this work, an analytical work is investigated to evaluate the steady-state characteristics of such self-lubricated porous journal bearings in micropolar lubrication with misalignment. Bi-axial misalignments are considered, namely axial (along the vertical direction) and twisting (along the horizontal direction). Reynolds equation is modified to fit bearing misalignment, by incorporating the effects of micropolarity of the lubricant and porosity of the bush. Darcy’s equation that considers porosity and the misalignment Reynolds’s equation applicable for film region are numerically solved using finite difference method applying successive over-relaxation scheme employing appropriate boundary conditions to obtain the dimensionless fluid film pressure at steady state, which is used to get the steady-state characteristics e.g. load parameter, moment of misalignment, frictional force, and friction parameter.

Uniqueness of generalized solution to micropolar viscous real gas flow with homogeneous boundary conditions

“…where m is a positive constant, it was proven in Bašić-Šiško et al 25 that the generalized solution to Equations (11)(12)(13)(14)(15)(16) exists locally in time on a domain Q T , where T is small enough, and that absolute temperature has the positivity property, i.e.,…”

“…In this paper, our aim is to prove the uniqueness of the generalized solution to Equation (11-16) on Q T , that is: Theorem 1. Let v 0 , 0 , 0 , and 0 satisfy the condition (22), and let Q T be a domain on which there exists at least one generalized solution to the problem (11)(12)(13)(14)(15)(16). Then, such generalized solution is unique.…”

“…are two distinct generalized solutions to Equations (11)(12)(13)(14)(15)(16) satisfying Equation (23). Let us notice that the inequalities (6-8) hold for…”

“…In the last few years, a micropolar fluid flow model was applied across a variety of scientific fields, for example, for modeling of rotational waves in seismology in Abreu et al, 9 blood‐flow modeling in Mekheimer et al, 10 wave propagation modeling in mineralogy in Abreu et al, 11 modeling of biological flow in biomedicine in Akbar et al, 12 and modeling the behavior of lubricants in engineering in Baidya et al 13 …”

“…A spherically symmetric model was considered in Dražić. 4 For the overview of the results regarding spherically symmetric case, see Dražić et al 5 A model with cylindrical symmetry was studied in Huang and Dražić, 6 Dražić, 7 and Dražić et al 8 In the last few years, a micropolar fluid flow model was applied across a variety of scientific fields, for example, for modeling of rotational waves in seismology in Abreu et al, 9 blood-flow modeling in Mekheimer et al, 10 wave propagation modeling in mineralogy in Abreu et al, 11 modeling of biological flow in biomedicine in Akbar et al, 12 and modeling the behavior of lubricants in engineering in Baidya et al 13 Instead of an ideal gas model described with the Clapeyron equation of state in which pressure is given by P = R , we study a real gas model characterized by the generalized equation of state (1), which according to Feireisl and Novotný, 14 better captures the behavior of gases under extreme conditions.…”