Effects of location and aspect ratio of a flexible disk on natural frequencies and critical speeds of a rotating shaft-disk system

Heydari, Hassan; Khorram, Amir

doi:10.1016/j.ijmecsci.2019.01.022

Cited by 41 publications

(12 citation statements)

References 26 publications

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“…By this time, the elasticity of the disk cannot be ignored. [24][25][26] Eshleman et al 27 investigated the critical speeds and free vibrations of a flexible spinning shaft-disk assembly.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear forced vibration analysis of spinning shaft‐disk assemblies under sliding bearing supports

Zhao

Wang

Pan

et al. 2021

Math Methods in App Sciences

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This paper presents an investigation on nonlinear forced vibration characteristics of a spinning shaft-disk assembly resting on sliding bearing supports. Based on the Timoshenko beam theory and Kirchhoff plate theory, the coupled model of the rotor is established. The present model is validated through comparison with the experiment results for different structure parameters. Considering the gyroscopic effect and nonlinear oil film force, the equations of motion are derived by employing the Lagrange equation. Then, the modal synthesis method and the Runge-Kutta method are adopted to obtain forced vibration responses of the spinning assembly. Special attention is

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“…By this time, the elasticity of the disk cannot be ignored. [24][25][26] Eshleman et al 27 investigated the critical speeds and free vibrations of a flexible spinning shaft-disk assembly.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear forced vibration analysis of spinning shaft‐disk assemblies under sliding bearing supports

Zhao

Wang

Pan

et al. 2021

Math Methods in App Sciences

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“…In recent years, many researchers have investigated the influence of some parameters such flexible disc, cracks in a shaft, bearing or electromagnetic loads and rotary inertia of rotor shaft on the nonlinear response of the rotor supporting bearings. 4–29…”

Section: Introductionmentioning

confidence: 99%

“…Heydari and Khorram have investigated the disc flexibility on the natural frequency and critical speed of the rotor supported on bearings. 27 Location of the disc on the rotor shaft leads to change the flexibility effect of disk. Xu et al.…”

Section: Introductionmentioning

confidence: 99%

Stability analysis of rotating shaft under electromagnetic and bearing oil-film forces

Eftekhari

Rahmatabadi

2021

Proceedings of the Institution of Mechanical Engineers, Part K:

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The stability of the fixed pints of a flexible rotor supported by journal bearings is investigated through the Bifurcation diagrams. In this paper the effect of nonlinear electromagnetic harmonic force is added to the simultaneous consideration of the effects of the nonlinearity in curvature and inertia, mass eccentricity and hydrodynamic forces of the journal bearings. Solution of the Reynolds equation renders the pressure distribution in the bearings. The bearing forces are found from integrating the pressure distribution on the surface of bearings. Derivation of the equations is performed using the Hamilton's principle and the nonlinearity terms are related to the eccentricity and the curvature of shaft. Primary and combination resonances are imposed to the rotor-bearing system and steady state responses show the effects of magnetic and bearing forces on the stability of amplitudes. In combination resonance, frequency of the electromagnetic load is tuned as the average of the forward and backward natural frequencies of the rotor. Existence of unstable Hopf points demonstrates that periodic, quasi-periodic and chaotic motions may be arisen in the nonlinear behavior of rotor.

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“…She et al 25 investigated the coupled vibration in a flexible-disk blades system with the influence of shaft bending vibration considered. Heydari and Khorram 26 studied the effects of location and aspect ratio of a flexible disk on the natural frequencies and critical speeds of a rotating shaft-disk system. Zhang et al 27 developed a mathematical model of a rotating shaft with centrifugal terms by using Hamilton's principle and Euler's angles based on the Timoshenko beam theory.…”

Section: Introductionmentioning

confidence: 99%

“…Afshari et al 23 studied the influence of lumped masses on the whirling speeds of a rotating Timoshenko shaft carrying multiple concentrated masses and found that: the influence of a concentrated mass on the forward and backward frequencies is nil if it is located at the “nodal points” of that natural mode shape and is highest when it is located at an “antinode” of that mode. By the way, the following References 24‐28, may be useful for some readers. Huang et al 24 studied the free vibration of an axially functionally graded beam spinning with constant angular speed about its longitudinal axis.…”

Section: Introductionmentioning

confidence: 99%

An efficient approach for whirling speeds and mode shapes of uniform and nonuniform Timoshenko shafts mounted by arbitrary rigid disks

Hsu

2020

Engineering Reports

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In theory, the whirling motion of a shaft-disk system is three-dimensional (3D), however, if the transverse displacement in the vertical principal xy-plane and that in the horizontal principal xz-plane for the cross-section of the shaft located at the axial coordinate x are represented by a complex number, then the mass moment of inertia for unit shaft length (at x) and that for each rigid disk i can be combined with their associated gyroscopic moments (GMs) to form the frequency-dependent equivalent mass moments of inertia, respectively, in the equations of motion for the rotating Timoshenko shaft carrying arbitrary rigid disks. It is found that the above-mentioned equations for the rotating 3D shaft-disk system take the same forms as the corresponding ones for the associated stationary two-dimensional (2D) Timoshenko beam carrying the same number of disks, so that the approaches for the free vibration analyses of the stationary 2D beam-disk system can be used to solve the title problem for obtaining the whirling speeds and mode shapes of a rotating 3D shaft-disk system. Since the order of the eigenproblem equation derived from the presented approach is much smaller than that derived from the conventional finite element method (FEM), the computer time consumed by the former is much less than that by the latter. In addition, the solutions obtained from the presented approach are exact and may be the benchmark for evaluating the accuracy of solutions of the other approximate methods. Numerical examples reveal that the presented approach is available for the uniform or nonuniform shaft-disk system, and the obtained results are very close to those obtained from existing literature or the FEM. The formulation of this article is available for a shaft-disk system with various boundary conditions (BCs), to save space, only the cases with pinned-pinned BCs are illustrated. K E Y W O R D S Timoshenko shaft, gyroscopic moment, equivalent mass moment of inertia, whirling speeds and mode shapes This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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Effects of location and aspect ratio of a flexible disk on natural frequencies and critical speeds of a rotating shaft-disk system

Cited by 41 publications

References 26 publications

Nonlinear forced vibration analysis of spinning shaft‐disk assemblies under sliding bearing supports

Nonlinear forced vibration analysis of spinning shaft‐disk assemblies under sliding bearing supports

Stability analysis of rotating shaft under electromagnetic and bearing oil-film forces

An efficient approach for whirling speeds and mode shapes of uniform and nonuniform Timoshenko shafts mounted by arbitrary rigid disks

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