Issue 21

D. Benasciutti et alii, Frattura ed Integrità Strutturale, 21 (2012) 37-45; DOI: 10.3221/IGF-ESIS.21.05 38 In light of the above considerations, the present paper aims to present a general numerical approach to study the behavior of hydrodynamic radial journal bearings, by including in the analysis the effect of the aforementioned aspects. Attention will focus on the computation of pressure distribution as a function of both temperature variation within lubrication gap and on viscosity-to-pressure sensitivity (according to the Vogel-Barus constitutive model [6]), as well as on components elastic flexibility. An iterative algorithm using a finite difference scheme will be developed to solve the Reynolds equation, based on the deformed lubrication gap calculated by a structural finite elements (FE) model coupled with the hydrodynamic equation. The numerical approach will be able to compute the pressure distribution and the local stress field by including shaft and support elastic deformation. Results will clearly emphasize the strong influence of component flexibility on journal bearing performance, with a significant reduction of the oil pressure distribution peak caused by components deformation, compared to the case of perfectly rigid elements. J OURNAL BEARING : BASIC CONCEPTS typical configuration of a radial journal bearing under a vertical load (see Fig. 1) consists of a shaft rotating inside a fixed support (choke), where it is usually fitted a bush. The nominal radial clearance between shaft (diameter d=2r ) and choke (diameter D=2R ) is c=R-r . The steady-state response of a journal bearing is governed by the fundamental equation of lubrication theory (Reynolds equation) [1]:      d d 6 1 3 3 2 h r U z p h z p h r                     (1) where h ( θ )= c − e · cos( θ ) is the oil film thickness as a function of angular coordinate θ , symbol e is the eccentricity, U = ωr is the tangential velocity of shaft, ω is its angular velocity, p ( θ ) is the resultant oil pressure distribution over angle β (attitude angle), μ is the oil dynamic viscosity. The numerical solution of Reynolds equation gives the pressure distribution p ( θ ) within the lubrication gap together with other system operating parameters (eccentricity, minimum lubrication gap, force resultant components, etc.), as summarized for example in R&B diagrams [3, 4]. Figure 1 : Sketch of a hydrodynamic journal bearing and parameters used in numerical simulations A