Analytical solution of Reynolds equation under dynamic conditions

Abstract

The flow in the clearance heavily influences the lubrication performance of journal bearing. Therefore, it is important to study the flow mechanism in journal bearing. As known, the pressure distribution in bearing clearance can be described with Reynolds equation. In this paper, unsteady form of Reynolds equation was simplified and nondimensionalized at first, based on certain assumptions. Then, the equation was solved with regular perturbation method, obtaining the analytical solution. At the end, the results of our work were compared with the results of “infinitely short journal bearing” model, Vignolo et al. (Approximate analytical solution to Reynolds equation for finite length journal bearings. Tribol Int 2011; 44: 1089–1099), and numerical simulations. The comparison implies that our results show more coincidence with the numerical results in a wider range.

Centering deep hole drilling system with three oil films like centering rotating journal with oil films in bearing

“…Formula (3) can be used to calculate the force of the oil film (Robert, 2004; Gao et al , 2016; Gong et al , 2016).…”

Experimental and Numerical Investigation of Static and Dynamic Characteristics of Bio-Oils and SAE40 in Fluid Film Journal Bearing

“…However, for journal bearings of finite length, researchers could not succeed in obtaining the general solution for the finite bearing problem. It has even been stated that the exact solution of the Reynolds equation is only possible if the viscosity is constant and the film thickness is a linear function of the variables [ 2 ]. The numerical analysis of a plain journal bearing with nanoparticles and lubricating oil added, which uses a modified Reynolds equation considering the time-dependent inertia effects at rotating speeds with turbulence effects, is also investigated.…”

A reduced-order method with PGD for the analysis of dynamically loaded journal bearing

“…On one hand, we have analytical models, which can produce some intriguing findings for very specific instances under certain assumptions and simplifications. We cite the following study examples: for long [4], finite [5,6] and short [7] journal bearings. On the other hand, various numerical methods for solving fluid film lubrication problems have been established.…”