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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 precise calculation of drag forces in the technical application of automatic balancing of rotating machinery provides important information about efficiency and stability. With increasing geometric complexity of the design, this poses a challenge that can be solved with computer-aided fluid dynamic approaches. In rolling element bearings, the influence of drag induced by the lubricant is predominantly considered in the context of efficiency loss estimations, whereas the movement of the rolling elements is mainly constrained by the contact with the bearing rings and, if present, the cage. Automatic ball balancers, which are installed in rotating machinery to reduce unbalance excitation, are in design very similar to fully lubricated ball bearings missing the cage, the inner ring and the majority of the balls. Inherent to the functional principle, the balancing efficiency and stability are significantly influenced by the choice of lubricant and resulting drag forces. Therefore, the estimation of the drag coefficient based on the geometry and lubrication of automatic ball balancers plays an important role in the engineering process. With a focus on the Stokes flow regime, the drag coefficient for a single sphere in an annular flow domain is determined numerically with finite volume discretization and the SIMPLE steady state solution scheme. Based on a parameter study utilizing the presented solution approach, a simple empirical relation between the design of the automatic ball balancer and resulting drag coefficients is derived. As a result, a drag force formulation based on the balancer geometry and the lubrication fluid properties is presented, which helps to supplement a large number of published kinetic models regarding the analysis of automatic ball balancer stability and transient behavior, giving a better understanding of the influences of design decisions regarding geometry and lubricant. [ABSTRACT FROM AUTHOR]

Squeeze film dampers (SFDs) are commonly used in turbomachinery in order to introduce external damping, thereby reducing rotor vibrations and acoustic emissions. Since SFDs are of similar geometry as hydrodynamic bearings, the REYNOLDS equation of lubrication can be utilised to predict their dynamic behaviour. However, under certain operating conditions, SFDs can experience significant fluid inertia effects, which are neglected in the usual REYNOLDS analysis. An algorithm for the prediction of these effects on the pressure build up inside a finite-length SFD is therefore presented. For this purpose, the REYNOLDS equation is extended with a first-order perturbation in the fluid velocities to account for the local and convective inertia terms of the NAVIER-STOKES equations. Cavitation is taken into account by means of a mass conserving two-phase model. The resulting equation is then discretized using the finite volume method and solved with an LU factorization. The developed algorithm is capable of calculating the pressure field, and thereby the damping force, inside an SFD for arbitrary operating points in a time-efficient manner. It is therefore suited for integration into transient simulations of turbo machinery without the need for bearing force coefficient maps, which are usually restricted to circular centralized orbits. The capabilities of the method are demonstrated on a transient run-up simulation of a turbocharger rotor with two semi-floating bearings. It can be shown that the consideration of fluid inertia effects introduces a significant shift of the pressure field inside the SFDs, and therefore the resulting damper force vector, at high oil temperatures and high rotational speeds. The effect of fluid inertia on the kinematic behaviour of the whole system on the other hand is rather limited for the examined rotor. [ABSTRACT FROM AUTHOR]

Full-floating ring between shaft and housing leading to two fluid films in serial arrangement. Analogously, a thrust bearing with an additional separating disk between journal collar and housing can be designed. The disk is allowed to rotate freely only driven by drag torques, while it is radially supported by a short bearing against the journal. This paper addresses this kind of thrust bearing and its implementation into a transient rotor dynamic simulation by solving the Reynolds PDE online during time integration. Special attention is given to the coupling between the different fluid films of this bearing type. Finally, the differences between a coupled and an uncoupled solution are discussed. [ABSTRACT FROM AUTHOR]