Issue 21

D. Benasciutti et alii, Frattura ed Integrità Strutturale, 21 (2012) 37-45 ; DOI: 10.3221/IGF-ESIS.21.05 39 During service, due to the relative velocity between shaft and support, the oil generates a pressure p ( θ ) over the attitude angle β , where p max is the peak pressure that occurs at angle θ pmax . The system moves in a new equilibrium configuration, where the eccentricity e characterizes the position of shaft axis with respect to the axis of fixed support, along the direction defined by the angle θ h0 (which also specify the direction of minimum oil thickness h 0 ). Several design charts are available in literature [3, 4], which provide journal bearing operation parameters as a function of Sommerfeld number S =( r / c ) 2 ( μN / p m ), defined in terms of shaft radius r and rotational speed N , while p m = F /( LD ) is the average (specific) pressure defined as the ratio of the applied radial force F and the nominal projected area ( L is the length of journal bearing). Such diagrams were determined by R&B through numerical solution of Reynolds equation under the hypothesis of constant temperature (and thus viscosity) of lubrication film and also under the assumption of perfectly rigid components (shaft and support). An improvement of the analysis can be obtained by including in the Reynolds equation a more sophisticated constitutive model for viscosity. As it is well known, viscosity of lubricating oils is very sensitive to the operating temperature, showing a quite rapid decrease with increasing temperature. In literature several viscosity-temperature equations are available (for example, the most commonly used are those by Reynolds, Slotte, Walther, Vogel, see [6]). While the most widely used viscosity-temperature chart is ASTM chart based on Walther’s equation, the most accurate model is that of Vogel, which can be written as μ = a · exp( b /( T - c )), where a, b, c are oil characteristic parameters. The lubricant viscosity also depends on pressure, especially for high pressures as in heavily loaded concentrated contacts (elastohydrodynamic lubrication). A number of attempts have been made to propose explicit formulae to synthesize lubricant pressure sensitivity. The best known equation for moderate pressures is the Barus equation μ = μ 0 · exp(α p ), in which μ 0 is the viscosity at ambient atmospheric pressure and α [MPa -1 ] is a pressure-viscosity coefficient related to oil film pressure (typical values are α=0.01÷0.02 MPa -1 ). In accordance to this constitutive model, an increase in dynamic viscosity occurs for high pressures, with a solid-like behavior for very high pressures. This effect, well-known in elastohydrodynamic studies (e.g. lubricated contacts), has not been investigated in the field of journal bearings. The simultaneous coupled effect of temperature and pressure can then be evaluated by combining two of the above mentioned relationships. For example, a very simple model is the Vogel-Barus equation μ = μ 0 · exp(α p ), where now the pressure-independent viscosity term μ 0 is only function of temperature according to the Vogel equation: μ 0 = a · exp( b /( T - c )). A further improvement in journal bearing study can be obtained by including in the numerical solution of Reynolds equation the deformed geometry of lubrication gap, caused by elastic deformation of shaft and support under the imposed oil pressure p ( θ ). This would allow a more realistic estimate of the overall stress distribution on journal bearing components (shaft and housing), compared to other approaches (see for example [7]) that are based on approximate analytical (asymptotic) solutions of Reynolds equation. Shaft diameter d [mm] 500 Support diameter D [mm] 500.5 Bearing length L [mm] 300 Load F [kN] 3600 Angular velocity N [rpm] 65 Mean pressure p m [MPa] 24 Table 1 : Parameters used in numerical simulations This paper will develop a general numerical approach to solve Reynolds equation and to compute the resultant oil pressure distribution by including both temperature and pressure effects on viscosity, as well as the effect of components elastic flexibility. A typical journal bearing configuration (see Tab. 1), operating at two different inlet oil temperatures ( T in =40 and 70 °C), will be investigated. A viscosity-temperature curve typical of oil ISO VG 680 will be used [6]. N UMERICAL SIMULATIONS n numerical simulations a plane model for the journal bearing is adopted. In the first part of this paper the hypotheses used are perfectly rigid components and viscosity function of both temperature and pressure according to the Vogel-Barus equation. In the second part of the paper, the pressure effect will be neglected, while shaft and I