Elastohydrodynamic analysis of one-layered journal bearings

Abstract

Steady state and dynamic solutions to the problem of isothermal elastohydrodynamic lubrication of single-layered journal bearings are derived and presented. The mathematical problem comprises two parts: fluid and elasticity. The elasticity problem is governed by the elastostatic equations which are solved by application of a complex variable approach using the complex Kolosov-Muskhelishvili potentials. The fluid problem is described by the two-dimensional Reynolds equation which is discretized using a finite difference approach and solved by application of the Gauss-Seidel scheme with the Swift-Stieber boundary conditions. The fluid-structure coupling is achieved by an iterative procedure with an under-relaxation algorithm. The dynamic coefficients are obtained by use of a first-order perturbation approach. The results obtained show that the proposed elasticity model permits a fast solution of the problem, particularly under dynamic conditions. They also show that, under the effect of coating elastic deformation, the contact geometry is modified and the load-carrying capacity decreases while the stability margin of the journal bearing system increases.

Elastohydrodynamic analysis of double-layered journal bearings lubricated with couple-stress fluids

“…Note that the cross-coupling damping coefficients B XY and B YX , unlike the corresponding stiffness coefficients, are equal. However, these coefficients become different when the dynamic deformation of the bearing-liner is considered in addition to the static deformation [29,34].…”

“…In an earlier work [29], we have demonstrated that the general solutions of planeelastostatics problems for a circular ring can be expressed in a complex Fourier series as given below.…”

“…In the present analysis, the journal is assumed rigid and its surface deformations are neglected. The semi-analytical elasticity approach, developed in an earlier work [29] for describing the EHD behaviour of single-layered journal bearings lubricated with a Newtonian fluid, is extended to solve the EHD lubrication problem of double-layered journal bearings for which the bearing is made of two distinct elastic layers: an inner liner with a backing metal (bush) of different elastic characteristics. In this approach, based on the variable complex theory, the stresses and the displacements are expressed as a complex Fourier series along the bearing circumference.…”

EHD Effects in Lubricated Journal Bearing

“…When the additional condition ε R << 1 is correct, then the displacement of the liner surface w can be defined as [7,8] …”

Combined Effect of Rarefaction and Effective Viscosity on Micro-Elasto-Aerodynamic Lubrication Performance of Gas Microbearings

“…Some studies have examined the effect of bearing liner deformation on the slider bearing characteristics (e.g., the pressure distribution, load carrying capacity, and frictional force) [16,17,18,19,20,21,22] and they indicated that the elastic parameter could strongly affect the friction coefficient and the flow rate. Others focused on the impact of the journal eccentricity perturbation or the journal misalignment and the rheological effects of couple stress fluids on stiffness and dynamic coefficients of finite journal bearing with the elastic bearing shell, such as gas foil bearing, offset-halves pressure dam bearing, coupled journal-thrust bearing [23,24,25,26,27,28,29]. Another aspect of the research of elastic bearing properties is that of viscoelasticity.…”