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Quasi-analytical solutions for the whirling motion of multi-stepped rotors with arbitrarily distributed mass unbalance running in anisotropic linear bearings

Klanner Michael, Prem Marcel S., Ellermann Katrin

Bulletin of the Polish Academy of Sciences. Technical Sciences

2021

Vol. 69, nr 6

art. no. e138999

Vibration in rotating machinery leads to a series of undesired effects, e.g. noise, reduced service life or even machine failure. Even though there are many sources of vibrations in a rotating machine, the most common one is mass unbalance. Therefore, a detailed knowledge of the system behavior due to mass unbalance is crucial in the design phase of a rotor-bearing system. The modelling of the rotor and mass unbalance as a lumped system is a widely used approach to calculate the whirling motion of a rotor-bearing system. A more accurate representation of the real system can be found by a continuous model, especially if the mass unbalance is not constant and arbitrarily oriented in space. Therefore, a quasi-analytical method called Numerical Assembly Technique is extended in this paper, which allows for an efficient and accurate simulation of the unbalance response of a rotor-bearing system. The rotor shaft is modelled by the Rayleigh beam theory including rotatory inertia and gyroscopic effects. Rigid discs can be mounted onto the rotor and the bearings are modeled by linear translational/rotational springs/dampers, including cross-coupling effects. The effect of a constant axial force or torque on the system response is also examined in the simulation.

Processing Transient Response of a Flexible Rotor-Bearing System with Unbalanced Disk

Attia Hili M., Bouaziz S., Maatar M., Fakhfakh T., Haddar M.

Machine Dynamics Research

2010

Vol. 34, No. 1

23-37

Turbomachinery rotors are frequently supported on several oil lubricating bearings and so are statically indeterminate. In such cases, the bearings reaction forces and hence their stiffness and damping properties affect the relative location of the bearing centres, thereby significantly the vibration behaviour of the rotor bearing system. In this paper, the dynamic behaviour of symmetrical rotor bearing system with unbalanced disk is analyzed based on a continuum model. The finite difference method is employed with the successive over relaxation technique to solve the Reynolds equation. The finite element method with an iteration scheme is adopted in the analysis of the system state trajectories. Bearing's stiffness and damping are considered. The motions of journal and disk have been simulated with Newmark method. Linear transient simulation, with time integration procedure, and unbalanced responses are investigated. The present results provide a deeper understanding to predict undesirable behaviour of the rotor and bearings centres can be avoided.