Issue 21

D. Benasciutti et alii, Frattura ed Integrità Strutturale, 21 (2012) 37-45; DOI: 10.3221/IGF-ESIS.21.05 42 In general, a non-zero viscosity-to-pressure sensitivity (α=0.01) determines a variation in the overall pressure distribution (change of attitude angle β ) and in its maximum value p max , depending on the general pressure levels attained. Limiting the attention to the case with T in - T out linear temperature variation, for peak pressures p max <100 MPa (case JB1), the pressure effect is actually negligible, as shown in Fig. 3(a)-(b), with only a small decrease of the maximum pressure of about 3.5%. For larger pressure levels (case JB2), an increment of p max of about 12% is observed, see Fig. 3(c)-(d). The minimum oil thickness increment ( h 0 = c - e ) produced by the pressure effect is relevant in both cases, with a variation respectively of 28% and 32%. The obtained results can be summarized by saying that, if the influence of pressure on viscosity is taken into consideration, when α increases the peak pressure p max increases, while the eccentricity e decreases. However, the pressure- to-viscosity effect is smaller compared to temperature influence, at least for the maximum pressure peaks encountered in the examples studied. Accordingly, pressure dependence will be intentionally neglected in the rest of this paper. Effect of component elastic deformation (with α =0, T linear) In the second part of this work, the pressure distribution will be calculated by considering the real geometry of lubrication gap resulting from component elastic deformation. The pressure values calculated by solving the Reynolds equation (1) are applied as input mechanical loads in a FE model to compute the real meatus after deformation, which is next used to solve again equation (1) with an iterative analysis scheme. A fluid-dynamic and structural coupled approach is developed in Matlab environment; the flow chart in Fig. 2 has been integrated with a structural FE analysis toolbox, see Fig. 4. For the structural analysis, the plane FE model and the global stiffness matrices for shaft and support, [ K shaft ] and [ K supp ], are first calculated once at the beginning of the analysis. YES Output p ( θ ) , e, h ( θ ) END h i ' ( θ )= c - e i ·cos( θ )+ g i ( θ ) FE model (mesh) [ K shaft ], [ K supp ] START Fluid-dynamic analysis (Reynolds eq.) e i , p i ( θ ) with p i (θ)>0  θ FE structural analysis u shaft - u supp = g i ( θ )     i max 1) (i max (i) max p p p h 0 ( θ )= c - e 0 ·cos( θ ) e i =e 0 p max,i =0 NO i=i+ 1 Input F, μ ( T,p ) , N, T in , R, r, α Figure 4 : Sketch of the numerical algorithm for fluid-dynamic and structural numerical analysis of journal bearing. At first iteration, a guess value of eccentricity e 0 is entered into Reynolds equation (1) to compute the pressure distribution p ( θ ) and the eccentricity e for the case of not deformable components (with the algorithm of Fig. 2). The calculated pressure distribution is next applied as a boundary load in FE model, to calculate components elastic deformations; the relative difference of radial displacements between shaft and support is used to define a nominal gap as g ( θ )= u shaft - u supp . A new oil film geometry h '( θ )= c - e · cos( θ )+ g ( θ ) that incorporates mechanical deformation (thus it differs from the case of perfectly rigid components) can thus be calculated. At second iteration step, this updated gap geometry h '( θ ) is entered again in Eq. (1) to get a new pressure distribution p '( θ ). This iterative procedure is repeated until convergence is achieved with respect to an imposed threshold tolerance on the maximum pressure, calculated at each iteration.