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A reduced-order method with PGD for the analysis of dynamically loaded journal bearing
Comptes Rendus. Mécanique, Volume 350 (2022), pp. 361-390.

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.

La conception des composants de machines est devenue un sujet de premier plan pour les chercheurs ces dernières années. L’analyse des palier a fait l’objet d’une attention considérable afin d’éviter tout contact préjudiciable. Parmi les études les plus importantes dans ce domaine figurent les problèmes transitoires des paliers lisses, qui sont généralement réalisés en couplant les équations de Reynolds avec les équations de mouvement. De nombreuses techniques ont été présentées dans la littérature et sont encore en cours d’exploration pour garantir des résultats précis et une prédiction efficace de la solution de l’équation de Reynolds à l’état instable. Dans cet article, l’approche PGD (Proper Generalized Decomposition) est étendue pour l’analyse du comportement du lubrifiant d’un palier lisse dynamiquement chargé en considérant les conditions limites de Swift-Stieber. Le modèle PGD est appliqué à ce problème, en recherchant la solution approximative sous sa forme séparée de l’équation aux dérivées partielles de Reynolds à chaque pas de temps pendant le cycle d’application de la charge en utilisant la stratégie de direction alternée. Par rapport à la résolution classique, la solution PGD a un coût de calcul considérablement faible. Pour vérifier l’exactitude et l’efficacité de cette approche, trois cas ont été considérés, palier infiniment court, infiniment long et de longueur finie soumis à une charge dynamique. Les résultats de la méthodologie suggérée comparés au modèle discrétisé complet (FDM) montrent que le nouveau schéma est plus efficace, converge rapidement, et donne des solutions précises avec une très faible consommation du temps CPU.

Received:
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Accepted:
Published online:
DOI: 10.5802/crmeca.124
Keywords: Hydrodynamic lubrication, Journal bearings, Dynamical behavior, Reynolds equation, Proper generalized decomposition, Full discretized model
Mot clés : Lubrification hydrodynamique, Palier lisse, Comportement dynamique, Équation de Reynolds, Décomposition propre généralisée, Modèle discrétisé complet

Abdelhak Megdoud 1; Belkacem Manser 1; Idir Belaidi 1; Farid Bakir 2; Sofiane Khelladi 2

1 LEMI., FT., University of M’hamed Bougara, Avenue de I’indépendance, 35000-Boumerdes, Algeria
2 Arts et Métiers Institute of Technology, CNAM, LIFSE, HESAM University, F-75013 Paris, France
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Abdelhak Megdoud; Belkacem Manser; Idir Belaidi; Farid Bakir; Sofiane Khelladi. A reduced-order method with PGD for the analysis of dynamically loaded journal bearing. Comptes Rendus. Mécanique, Volume 350 (2022), pp. 361-390. doi : 10.5802/crmeca.124. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.124/

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