Dynamic Characteristics of Rotor-Bearing System with a Labyrinth Seal

In this paper, the dynamic characteristics of rotor-bearing system with a labyrinth seal are investigated. The dynamic coefficients of labyrinth seal and the whirl speeds of rotor-bearing system are analyzed. The simplified rotor-bearing model consists of a rigid disk and a flexible shaft. The rotor-bearing system supported by two ball bearings, which are modeled as the spring-damper systems. A labyrinth seal supports one of the rigid disks. The perturbation approach has been applied to the governing equations of the bulk-flow model to calculate the dynamic coefficients of labyrinth seal. The Finite Element Method (FEM) is utilized to model the flexible-rotor system. The numerical results show the labyrinth seal effect on the dynamic characteristics of rotor-bearing system, which depend on a great variety of parameters such as geometry of the labyrinth seal.

Analytical Solution for Whirling Speeds and Mode Shapes of a Distributed-Mass Shaft With Arbitrary Rigid Disks

The purpose of this paper is to present an approach for replacing the effects of each rigid disk mounted on the spin shaft by a lumped mass together with a frequency-dependent equivalent mass moment of inertia so that the whirling motion of a rotating shaft-disk system is similar to the transverse free vibration of a stationary beam and the technique for the free vibration analysis of a stationary beam with multiple concentrated elements can be used to determine the forward and backward whirling speeds, along with mode shapes of a distributed-mass shaft carrying arbitrary rigid disks. Numerical results reveal that the characteristics of whirling motions are significantly dependent on the slopes of the associated natural mode shapes at the positions where the rigid disks are located. Furthermore, the results obtained from the presented analytical method and those obtained from existing literature or the finite element method (FEM) are in good agreement.

On the Choice of Shape Functions of Unsymmetrical Elastic Rotors

In this paper the effects of rotordynamics under the aspect of the choice of shape functions are discussed. For this purpose a rotor system which consists of a slim shaft and two rigid disks is modeled using the Projection Equation. The shaft is assumed as an elastic Euler-Bernoulli beam, supported by two bearings modeled as radial spring systems. The rotor is driven by a permanent-magnet synchronous motor whose torque is transmitted with a spur gear pair next to one of the bearings. A Ritz approach is used to separate the elastic displacements in position and time, thereby different shape functions are evaluated. Approximated eigenfunctions are computed and used as shape functions as well. For validation, the eigenfrequencies are compared with semi-analytical ones, calculated with the Transfer-Matrix-Method and experimental results. The insights obtained from this work should make it easier to choose the appropriate shape functions for such problems.