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loaded journal bearing
创建日期：2024-09-10 14:50:34
标签： PGD
loaded journal bearing
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A reduced-order method with PGD for the analysis of dynamically
loaded journal bearing
Machine component design has become a prominent topic for researchers in recent years. The analysis of bearing systems
has been received considerable attention in order to avoid detrimental contact. Among the most important studies in this
area are the transient problems of journal bearings, which are usually performed by coupling the Reynolds with the motion
equations. Many techniques have been presented in the literature and are still being explored to ensure the accurate findings
and efficient solution prediction of unsteady state Reynolds equation. In this paper, the Proper Generalized Decomposition
(PGD) approach is expanded for the analysis of the lubricant behavior of dynamically loaded journal bearing considering
Swift-Stieber boundary conditions. The PGD model is applied in this problem, looking for the approximate solution in its
separated form of the partial differential Reynolds equation at each time step during the load applied cycle employing the
alternating direction strategy. Compared to the classical resolution, the PGD solution has a considerably low computational
cost. To verify the accuracy and efficiency of this approach, three cases have been considered, infinitely short, infinitely long
and finite journal bearings under the dynamic load. The results of the suggested methodology compared to the full discretized
model (FDM) show that, the new scheme is more efficient, converges quickly, and gives the accurate solutions with a very
low CPU time consumption.
Keywords: Hydrodynamic lubrication ; Journal bearings ; Dynamical behavior ; Reynolds equation ; Proper Generalized
Decomposition ; Full Discretized Model.
1 Introduction
Hydrodynamic bearings are critical components of rotating machines, and are widely regarded as the best technological
solution currently available in a variety of industries, including thermal engines, turbo-machines, alternators, and compressors.
They offer a number of benefits like high efficiency and precision, minimal friction and effective heat dissipation. The journal
bearing transient analysis is frequently required in industrial applications. In engine bearings, for example, the variation of
the load pressing on the bearing, and in some circumstances of the bearing’s angular velocity, is so large that a static analysis
is useless.
The basics of hydrodynamic lubrication was firstly established by O. Reynolds in 1886 [1]. Reynolds research’s was
influenced by prior experimental results by N. P. Petrov [2] and B. Tower [3], where they showed that the viscosity is the most
essential characteristic in film lubrication and that the high pressures produced in the clearance space between the journal
and the sleeve determine a bearing’s load-carrying capacity. The so-called "Reynolds equation" which is derived from the
Navier–Stokes and the continuity equations for in-compressible flows, is an second-order partial differential equation witch
basically predicts the pressure distribution in thin film lubrication. To solve this equation, many methods have been presented.
On one hand, we have analytical models, which can produce some intriguing findings for very specific instances under certain
assumptions and simplifications. We may 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.
1We can quote the following research examples : [8], [9] and [10] where the finite volume method has been used to solve the
Reynolds equation under unsteady state conditions. In the works reported in [11] and [12] the finite element methods for the
dynamically loaded journal bearing analysis was employed. Furthermore, in the studies mentioned in [13], [14] and [15]] the
Gauss-Siedel iterative method using the finite difference discretization was applied to treat the transient problem of journal
bearing considering the Reynolds boundary conditions.
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