Improvement of the numerical efficiency of rotordynamic simulations by applying the Scaled Boundary Finite Element Method to compute the hydrodynamic bearings

• Applicant: Professor Dr.-Ing. Elmar Woschke
• Subject Area: Mechanics
• Term: since 2021
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 490625563

The rotordynamic properties of systems with hydrodynamic bearings are affected crucially by the nonlinear bearing forces. Regarding fast-rotating, lightly-loaded rotors, this causes subsynchronous self-excited oscillations with potentially high amplitudes, which can reduce the durability of the components, cause critical noise emissions, and affect the energy efficiency of the machine. To reduce expensive test bench experiments and time-consuming iterations in the product development process, the design has to be based on precise simulative analyses of the operating behavior under consideration of the nonlinear interactions between the bearing forces and the shaft vibrations. To this end, the equation of motion of the elastic shaft is incorporated into a time integration scheme and coupled with the Reynolds equation, which describes the pressure generation in hydrodynamic bearings. Hence, each time step of the simulation includes a solution of the Reynolds equation, for which numerical methods, analytical approximations, and look-up tables are employed. While numerical methods lead to considerable and often inacceptable computational times, analytical solutions are only possible in conjunction with substantial simplifications. The look-up table approach, to some extent, offers a tradeoff between these two extremes, while the modeling depth is usually limited, since the interpolation effort increases with every considered physical effect.A promising basis for the development of a novel, numerically efficient solution without the substantial limitations of analytical methods or look-up table techniques is the semi-analytical Scaled Boundary Finite Element Method (SBFEM). The fundamentals for solving the Reynolds equation with the SBFEM have been derived in preliminary work, but the potential of the approach has not been exploited yet, which is the objective of this project. In order to further reduce the numerical effort, high-order shape functions need to be employed in combination with an automatic, adaptive mesh refinement as well as coarsening and a transformation of the Reynolds equation in a manner that smoothens the solution is analyzed. Another strategy worth investigating is to avoid the repeated solution of eigenvalue problems within the time integration scheme. This requires that the eigenvalue problem is differentiated with respect to the parameters of the shaft displacement and developed into a series prior to the rotordynamic simulation. In order to improve the modeling depth of the SBFEM solution compared to the preliminary work, strategies for incorporating mass-conserving cavitation models as well as shaft tilting need to be investigated. In the last step, the developed methodology is to be verified and analyzed with regard to its efficiency. To ensure a realistic context, this is done within the framework of a rotor dynamics or MBS formulation, whereby complex technical overall systems can also be simulated.

• DFG Programme: Research Grants
• Co-Investigator: Dr.-Ing. Fabian Duvigneau