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Open Access Research Article

Mathematical modeling and numerical analysis of dynamic behavior in lubricated mechanisms : Case of Reynolds equation

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pp. 1–31Online FirstMay 2026DOI: 10.47974/JIM-2335XML
Received:
01 Mar 2025
Published Online:
09 May 2026
Article type:
Research Article
Language:
EN
Article no.:
JIM-2335
Pages:
1–31

Abstract

In this paper, we investigate the dynamic behavior of a lubricated mechanism in the incompressible case. The goal is to develop a mathematical model that describes the motion of the upper surface, based on the quasi-stationary Reynolds equation and Newton’s second law. We also analyze the existence and uniqueness of solutions to the resulting differential equations, as well as the conditions under which global nonexistence of solutions may arise. Furthermore, we conduct a thorough numerical analysis of the parameters a and p, examining their influence on the system’s behavior. The results provide valuable insights into the dynamics of lubrication, enhancing the understanding of these mechanisms in practical applications.

Keywords

Subject Classifications

Primary 49M05Secondary 53C35

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