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.

State-of-the-art analyses for the rotordynamic assessment of pumps and specific requirements for the simulation tools are described. Examples are a horizontal multistage pump with two fluid film bearings in atmospheric pressure, a horizontal submerged multistage pump with many bearings, and a submerged vertical single-stage pump with water-lubricated bearings. The rotor of the horizontal pump on two bearings is statically overdetermined by the seals and the static bearing forces depend on the deflection in the seals and the bearings. The nonlinear force-displacement relation in the bearings is considered in this paper. The stability of pumps is assessed by Campbell diagrams considering linear seal and bearing properties. Cylindrical bearings can have a destabilizing effect in the case of low loads as in the examples of the submerged pumps. For the pump with many bearings, the influence of the bearing ambient pressure and the bearing specific load on the stability is analyzed. For the vertical pump, the limit cycle, i.e. the vibration level of stabilization, is determined with a nonlinear analysis. All examples have a practical background from engineering work, although they do not exactly correspond to real cases. Analyses were performed with the rotordynamic software MADYN 2000.