Analysis of Unbalance Vibration of Rotating Shaft System with Many Bearings and Disks

In a rotating shaft system carrying an unsymmetrical rotor, there is always one unstable region in the neighborhood of the rotating speed at which the sum of two natural frequencies of the system is equal to twice the rotating speed of the shaft. In this unstable region two unstable lateral vibrations with frequencies P1 and P2 take place simultaneously and grow up steadily. Generally, frequencies P1 and P2 are not equal to the rotating speed ω of the shaft and the sum of these P1 + P2 is always equal to 2ω. Of course there are other unstable regions which appear at the major critical speeds.

Download Full-text

On the Vibration of a Rotor-Shaft System With Viscoelastically Supported Bearings

Design Engineering, Volumes 1 and 2 ◽

10.1115/imece2003-43582 ◽

2003 ◽

Author(s):

N. Shabaneh

Keyword(s):

Nonlinear System ◽

Linear System ◽

Vibration Analysis ◽

Perturbation Expansion ◽

Free Vibration Analysis ◽

Rotating Shaft ◽

Rotor Shaft ◽

Model Free ◽

Shaft System ◽

Nonlinear Elastic

This paper investigates the dynamic behaviour of a single rotor-shaft system with nonlinear elastic bearings at the ends mounted on viscoelastic suspensions. A Timoshenko shaft model is utilized to incororate the flexibility of the shaft; the rotor is considered to be rigig and located at the mid-span of the shaft. A nonlinear bearing pedestal model is assumed which has a cubic nonlinear spring and linear damping characteristics. The viscoelastic supports of the bearings are modeled as Kelvin-Voigt model. Free vibration analysis is performed on the linear system including the damping of the bearings. Forced vibration analysis is performed on the nonlinear system. Equations of motion are derived for the nonlinear system based on the direct multiple scale method of one-to-one frequency-to-amplitude relationship using third order perturbation expansion. The effects of stiffness and loss coefficients of the viscoelastic supports on the complex natural frequencies are identified for the linear system. The results show that optimum values of the viscoelastic stiffness and loss coefficient can be achieved for a specific rotating shaft system to reduce vibrations and increase the operating regions. In addition, the frequency response of the nonlinear system indicates that a jump phenomenon takes place for high values of the bearing nonlinear elastic coefficient.

Download Full-text

A Variational Approach to the Analysis of Rotor Dynamics Problems

Journal of Lubrication Technology ◽

10.1115/1.3253167 ◽

1982 ◽

Vol 104 (1) ◽

pp. 76-83

Author(s):

R. A. Mayo

Keyword(s):

Cross Sections ◽

Lagrange Equations ◽

Rotatory Inertia ◽

Rotating Shaft ◽

Coriolis Forces ◽

System A ◽

Shaft System ◽

Bearing Stiffness ◽

Stiffness And Damping ◽

Dynamics Problems

The differential equations for a rotating shaft system are derived variationally by the use of the Lagrange equations, where the kinetic and potential energy terms are obtained by integration of differential volume expressions which are in turn derived from system displacements and strains. Included, as a result, are the effects of initial and dynamic shaft curvature, gyroscopic moments, Coriolis forces, unbalances, rotatory inertia, static weight, and varying shaft cross-sections. Shown to be insignificant are the interacting effects of transverse shear, extensional displacements (and therefore axial constraint), torsion, product of inertia (for most shaft elements). Bearing forces are included as generalized forces on the shaft system. A sample solution of the equations uses the short bearing approximation to model bearing forces and derives expressions for shaft critical speed, equivalent bearing stiffness, and damping constants as functions of bearing eccentricity.

Download Full-text