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A common problem in transient rotordynamic simulations is the numerical effort necessary for the computation of hydrodynamic bearing forces. Due to the nonlinear interaction between the rotordynamic and hydrodynamic systems, an adequate prediction of shaft oscillations requires a solution of the Reynolds equation at every time step. Since closed-form analytical solutions are only known for highly simplified models, numerical methods or look-up table techniques are usually employed. Numerical solutions provide excellent accuracy and allow a consideration of various physical influences that may affect the pressure generation in the bearing (e.g., cavitation or shaft tilting), but they are computationally expensive. Look-up tables are less universal because the interpolation effort and the database size increase significantly with every considered physical effect that introduces additional independent variables. In recent studies, the Reynolds equation was solved semianalytically by means of the scaled boundary finite element method (SBFEM). Compared to the finite element method (FEM), this solution is relatively fast if a small discretization error is desired or if the slenderness ratio of the bearing is large. The accuracy and efficiency of this approach, which have already been investigated for single calls of the Reynolds equation, are now examined in the context of rotordynamic simulations. For comparison of the simulation results and the computational effort, two numerical reference solutions based on the FEM and the finite volume method (FVM) are also analyzed. [ABSTRACT FROM AUTHOR]

The numerical effort of rotordynamic simulations with hydrodynamic bearings is often dominated by the solution of the Reynolds equation. Because of the nonlinear fluid–structure interaction, this equation needs to be solved in every time step. Although computationally efficient analytical approximations and look-up table techniques exist, these approaches often do not provide the necessary modeling depth and accuracy. Thus, in many cases, numerical methods are preferred despite their computational cost. In recent studies, a semi-analytical solution of the Reynolds equation has been developed based on the scaled boundary finite element method (SBFEM) with the objective of improving the numerical efficiency. The developed approach assumed Gümbel conditions, which means that cavitation was handled in a highly simplified manner. In this work, the SBFEM solution is for the first time combined with a more complex, nonlinear cavitation model based on the Elrod algorithm. Because of the semi-analytical technique, this requires a simplification of the switch function that defines the locations of the pressure and cavitation zones. However, as demonstrated in this paper, the resulting bearing forces are still in good agreement with a standard numerical reference solution based on the finite volume method (FVM). Since the SBFEM model uses only a one-dimensional discretization, its high-order formulation is very straightforward, even in case of a non-equidistant grid with varying shape functions that take the smooth and non-smooth regions of the solution into account. As a result, the numerical effort is reduced significantly in comparison to the standard FVM. [Display omitted] • An SBFEM solution of the Reynolds equation is combined with an Elrod cavitation model. • The accuracy of the hydrodynamic forces computed with this approach is adequate. • The developed method is numerically efficient compared to the standard FVM. [ABSTRACT FROM AUTHOR]