DOI: 10.1002/pamm.202300045 ISSN:

SBFEM with reduced modal basis for hydrodynamic bearings

Simon Pfeil, Chongmin Song, Elmar Woschke
  • Electrical and Electronic Engineering
  • Atomic and Molecular Physics, and Optics


The numerical effort of transient rotordynamic simulations is often dominated by the computation of nonlinear hydrodynamic bearing forces. These forces are described by the Reynolds equation and need to be computed at every time step. Usually, numerical models, analytical approximations, or look‐up table techniques are employed, depending on the desired tradeoff between accuracy and computational cost. In recent studies, a semi‐analytical approach based on the scaled boundary finite element method (SBFEM) has been developed as an efficient alternative to these methods. The partial differential equation is transformed into a system of ordinary differential equations, leading to an eigenvalue problem. Here, the numerical effort can be further decreased by means of a modal reduction, which is investigated in this study. The shaft eccentricity determines the smoothness of the hydrodynamic pressure field and is identified as an adequate indicator as to what subset of eigenvalues and eigenvectors should be considered in the solution.

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