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On the lubrication approximation for a class of viscoelastic fluids
Institution:1. Center for Mathematical Analysis, Geometry and Dynamical Systems, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais 1, 1049-001 Lisboa, Portugal;2. Instituto Superior de Engenharia de Lisboa, Instituto Politécnico de Lisboa, Rua Conselheiro Emídio Navarro, 1959-007 Lisboa, Portugal;3. Department of Mechanical Engineering, Texas A & M University, College Station, TX77843, USA;1. Department of Mechanical Engineering, Indian Institute of Technology Madras, Chennai 600036, India;2. Department of Mechanical Engineering, Texas A & M University, College Station, Texas 77840, United States;1. CMT-Motores Térmicos, Universitat Politècnica de València, Valencia 46022, Spain;2. Bioingeniería e Ingeniería Aeroespacial, Universidad Carlos III de Madrid, Leganés 28911, Spain;3. Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, Valencia 46022, Spain;1. Deepwater Technology Research Centre (DTRC), Bureau Veritas, Singapore;2. College of Shipbuilding Engineering, Harbin Engineering University, Harbin 150001, China
Abstract:We present a rigorous derivation of a dimensionally reduced Reynolds type equation for thin film flow lubrication of a class of viscoelastic fluids by employing a perturbation analysis on the upper-convected Maxwell model in natural orthogonal coordinates. This approximation accounts for the viscoelastic and curvature corrections to the classical Reynolds lubrication approximation. Comparison of our approximation with the classical Reynolds approximation suggests that viscoelasticity can have a significant influence on the lubrication characteristics, at least for certain values of the film thickness and of the eccentricity ratios of the journal bearing.
Keywords:Viscoelastic fluid  Hydrodynamic lubrication  Reynolds equation
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