Uncertainty Quantification in Hydrodynamic Bearings

Although it is possible to imagine a strong sensitivity of hydrodynamic bearings performance to geometrical and fluid dynamic uncertainties, a small amount of scientific contributions have been found in literature about the use of uncertainty quantification techniques for the numerical modeling of bearings. In the present paper we aim at quantifying the effects of the aleatory uncertainty of some relevant input values on key parameters related to rotordynamic effects in turbomachinery, and in particular on the rotor thermal instability problem (e.g. the equilibrium position and the dynamic coefficients). A methodology is initially developed in order to study the propagation of the uncertainties in the numerical analysis of Tilting Pad Journal Bearings (TPJB). Due to the characteristics of the in-house finite element code TILTPAD considered for the UQ analysis, the Monte Carlo method has been selected among the possible approaches. The analysis here presented considers the effects of both manufacturing tolerances on the assembled bearing clearance and of the tolerances adopted for the characterization of the viscosity grade of the oil. The test case adopted for the analysis is the Kingsbury D-140 TPJB. Considering the individual variation of the selected parameters, it is possible to observe that the standard deviation (STD) of the the non-dimensional dynamic coefficients is up to 2.1% in case of viscosity variation and up to 9.1% in case of clearance variation. The STD of the frictional power losses is about 2.2% and 1.4% respectively. Considering the simultaneous variation of the selected parameters, it is possible to observe a STD of the non-dimensional dynamic coefficients comprised between 6.4% and 9.4%, while the STD of the frictional power losses is about 2.7%.