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

Abstract

Machine component design has become a prominent topic for researchers in recent years. The analysis of bearing systems has 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 equation 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, seeking 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 when 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.