Modal Characteristics Of Asymmetrical Rotor-bearing Systems

Journal of Vibration and Control

Magableh

2022

The presented work examines the stability of general rotors subject to harmonic follower force. The examined rotor consists of asymmetric Timoshenko shaft carrying asymmetric rigid disk and supported by anisotropic flexible bearings. The assumed modes method is combined with Lagrange’s equation to derive the governing equations of motion with the help of symbolic computation. The employed approach resulted in equations of motion with multi-frequency periodic coefficients, and Floquet’s method was used to determine stability boundaries of the considered rotors. After validation of the proposed mathematical model, it was employed to examine the combined effect of rotor asymmetry, support anisotropy, and rotor speed on its stability in the presence of harmonic follower force. The presented results show that the considered general rotor exhibits both subharmonic and combination instabilities, which were completely identified and investigated. Additional higher order subharmonic and combination instabilities are observed for general rotors only.

Section: Introductionmentioning

confidence: 99%

Stability of general asymmetric-anisotropic rotors subject to harmonic follower force

Journal of Vibration and Control

Magableh

2022

“…They examined the effects of deviatoric inertia and stiffness due to asymmetry of flexible shaft and disk and used Timoshenko beam element and accounted for rotary inertia, shear deformation, and gyroscopic moments. Jei and Lee (1993) used the complex modal displacements to identify the forward and backward modes for rotating asymmetric disk supported by massless rigid shaft, which is held by isotropic bearings at both ends of the shaft. Tyagi and Chouksey (2015) presented modal analysis study of asymmetric rotor system using simple model.…”

Section: Introductionmentioning

confidence: 99%

Stability of asymmetric rotors with asymmetric flexible disks

Journal of Vibration and Control

2021

The presented work examines the dynamic behavior of an asymmetric rotor with asymmetric flexible disk, contrary to previous works on the subject, where researchers examined the effect of either rigid disk asymmetry or disk flexibility at a time. Account for the asymmetry of flexible disk in rotors constitutes the new contribution in this work. The suggested mathematical model combines Lagrangian approach with Rayleigh–Ritz method to derive the governing equations of motion of the rotor. Account for asymmetry of the flexible disk results in complicated and lengthy expressions for the potential and kinetic energies of the rotor, required in the adopted Lagrangian approach. Using symbolic computation simplified the derivation of the governing equations of motion with constant coefficients in terms of rotating coordinate system. Solution of the resulting eigenvalue problem provided numerical results for rotors with symmetric and asymmetric flexible disks, required to assess the effect of disk flexibility and asymmetry on the resulting frequencies and stability boundaries of the examined rotor system.

“…They studied the effect of shaft and disk asymmetry on synchronous critical and subcritical speeds. Jei and Lee (1993) used the complex modal displacements to identify the forward and backward modes for rotating asymmetric disk supported by massless rigid shaft, which is held by isotropic bearings at both ends of the shaft. Also, they showed the effect of asymmetry on the mode shapes.…”

Section: Introductionmentioning

confidence: 99%

Stability Analysis for Unsymmetrical Shaft With Flexible Bladed-Disk

Masoud

Volume 4: Manufacturing Materials and Metallurgy; Ceramics; Structures and Dynamics; Controls, Diagnostics and Instrumentation;

1997

The governing equations of motion for a rotating flexible blade-rigid disk-flexible shaft system are derived. The bladed disk is attached at one end of an asymmetric shaft with uniformly distributed mass, mass moment of inertia, and stiffness. The shaft is held by two isotropic supports; one at the far end from the bladed disk, modeled by two translational and two rotational springs, and an intermediate support, modeled by two translational springs only. The effect of shaft asymmetry on the dynamics behavior of the rotating bladed disk shaft system is examined over a wide range of rotational speed, and for different combinations of springs’ stiffness, which determines the type of shaft supports. The cantilever, and the simply supported shaft with an over hang can be looked upon as special cases of the described above shaft configuration, since the former is obtained by assigning large stiffness for both translational and rotational springs at the end support, and zero spring stiffness at the intermediate one, whereas the latter is obtained by assigning large stiffness for the translational springs at both supports and zero stiffness for the rotational springs. Stability boundaries are calculated, and presented in terms of shaft asymmetry and rotor speed for given bearing stiffness.