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Short Paper Proc. of Int. Colloquiums on Computer Electronics Electrical Mechanical and Civil 2011

3D Surface Roughness and Fluid Inertia Effects on Steady State Characteristics of Hydrodynamic Journal Bearing: Model Formulation E. Sujith Prasad1, T. Nagaraju2, J. Prem Sagar2 1

Department of Mechanical Engineering, T.John institute of technology, Bangalore -560083. (India). Email: sujith35@gmail.com 2 Department of Mechanical Engineering, P.E.S. College of Engineering, Mandya-571401 (India) Email: tnagghally@yahoo.co.in, premsag.2386@gmail.com Majumdar and Hamrock [5] shown that the average Reynolds equation derived by Patir and Cheng for an incompressible lubricant can be used for a compressible lubricant if the surface structures in both cases are same. Tonder [6] proposed a perturbation technique to determine the flow factors. Lunde and Tonder [7] determine the pure pressure flow factors using finite element method. Li et al [8] modified the Patir and Cheng’s flow factors by using perturbation approach with Green’s function technique for Non-Newtonian lubricant. Nagaraju et al (9) developed a modified average Reynolds equation to include viscosity variation across and along fluid-film of rough bearings and investigated the combined influence of surface roughness and non-Newtonian behavior of the lubricant on hybrid journal bearing performance. However, all the above mentioned models have been confined to neglect the fluid inertia. Among the few studies related to the fluid inertia effect, Constantinescu and Galetuse [10] evaluated the momentum equations for laminar and turbulent flows by assuming that the shape of the velocity profiles is not strongly affected by the presence of inertia forces. Banerjee et al (11) introduced an extended form of the Reynolds equation to include the effect of fluid inertia, adopting an iteration scheme. Tichy and Bou-Said [12], Bou-Said and Ehret [13] and Kakoty and Majumdar [14, 15] used the method of averaged inertia in which the inertia terms are integrated over the film thickness to account for the inertia effect in their studies. The above studies [10-15] were mainly based on ideally smooth bearing and journal surfaces. To the best of the authors knowledge, no mathematical models have been developed to include the surface roughness effect along with fluid inertia effect in the analysis of journal bearing systems. In the present work, a modified average Reynolds equation and a solution algorithm are developed to include surface roughness and fluid inertia effects in the analysis of lubrication problems. The developed model is used to study the influence of fluid inertia and surface roughness effects on the steady state characteristics such as circumferential pressure, load carrying capacity and stability threshold speed of a hydrodynamic journal bearing system.

Abstract— In the present work, a modified form of average Reynolds equation is developed to include the combined influence of 3D surface roughness and fluid inertia in the analysis of journal bearings. The modified average Reynolds equation is derived starting from the Navier-Stokes equations and flow continuity equation using Patir and Cheng’s (2, 3) flow factors. The local velocity components are expressed in terms of Patir and Cheng’s flow factors and the velocity profiles are assumed to be change very little due to fluid inertia. The developed mathematical model and solution algorithm are expected to be quite useful to the bearing designer. Index Terms— Convective inertia, Surface roughness, Hydrodynamic lubrication.

I. INTRODUCTION Ever-increasing demand for the hydrodynamic journal bearing systems to operate under high speed and high eccentricity makes it imperative to design this class of bearings accurately. In such cases, the familiar assumptions of a smooth surface can no longer be employed to accurately predict the performance of journal bearing systems as no machining surfaces are perfectly smooth. When the bearings operating under high speed and low viscosity lubricants, the flow may become laminar but fluid inertia forces cannot be neglected. Therefore, it is imperative to include the influence of surface roughness and fluid inertia effects in the design and analysis of journal bearings. From past several years, several concepts and mathematical models have been developed by the various researchers to incorporate the surface roughness effects in the lubrication problems. Notably among these researchers, Christensen and Tonder [1] developed the average Reynolds equation to analyze the effects of surface roughness on the lubrication problems but this model is limited to one-dimensional roughness structures oriented either transversely or longitudinally and is not applicable to the 3D area distributed surface roughness. Later, Patir and Cheng [2, 3] introduced a new concept of flow factors for deriving an average Reynolds equation applicable for any general roughness structure and derived a n average Reynolds equation to include 3d surface roughness effects in the analysis. Teale and Lebeck [4] evaluated the Patir and Cheng’s flow model and derived some flow factors for truncated rough surfaces. These flow factors helps to study the effects of partially worn surface on lubrication problems. © 2011 AMAE DOI: 02.CEMC.2011.01. 519

II. ANALYSIS A. Average fluid-film thickness The geometry of the journal bearing system along with rough surface and co-ordinate system is shown in Fig.1 172


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