Large deflection model for nonlinear flexural vibration analysis of a highly flexible rotor-bearing system

Phadatare, Hanmant P.; Maheshwari, Vinay; Vaidya, Kedar S.; Pratiher, Barun

doi:10.1016/j.ijmecsci.2017.09.039

Cited by 27 publications

(10 citation statements)

References 15 publications

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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%

“…have derived the mathematical model of the rotor system with rigid disk considering large elastic deformations. 25 Influence of rotary inertia on the critical speed and linear and nonlinear natural frequencies have been presented. Kumar and Dasgupta have studied time response and frequency response of the modified Jeffcott rotor with a nonlinear hysteric damping based on Buoc-wen model and cubic spring at the supports.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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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Section: Introductionmentioning

confidence: 99%

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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“…19 investigated the vibration behavior of the rotating system comprising a nonlinear flexible shaft and a rigid disk under moving platform with an unbalance mass while in another study, Phadatare et al. 20 analyzed the free vibration behavior of the large deflection model of highly flexible rotating system. Sadath et al.…”

Section: Introductionmentioning

confidence: 99%

Dynamic stability and bifurcation phenomena of an axially loaded flexible shaft-disk system supported by flexible bearing

Phadatare

Pratiher

2020

Proceedings of the Institution of Mechanical Engineers, Part C:

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The present research studies the vibration and bifurcation analysis of a spinning rotor-disk-bearing system to carefully scrutinize the dynamic stability under extrinsic mass unbalance and pulsating axial load. The shaft is flexible and taken into account the geometrical nonlinearities due to large elastic deformation in bending. The rotor is supported by flexible bearings, which are modeled as an equivalent spring-damper system having linear and nonlinear stiffness elements. Equation of motion of the rotating system, which includes flexible shaft, rigid disk, and flexible bearing, is derived using extended Hamilton principle with the assumption of the Euler's beam theory. We studied initially the modal analysis to determine the modal parameters, i.e. natural frequency and mode shapes prior to the investigation of the dynamics of the system. Further, we developed the bifurcation diagram for steady-state solutions and to study the subsequent dynamic stability and verify with the findings solved numerically. The interactive behavior among the nonlinear shaft-bearing, axial load and an unbalance has been analyzed. Numerical simulation tools, i.e. frequency–response characteristics, time history, phase trajectories, and Poincaré map have been used to highlight the presence of nonlinear phenomena and its important role towards evaluating the system dynamics and subsequent stability. This current research showed that flexible bearings stabilize the system as a result of increasing the restoring force. Analyzing the bifurcation diagrams of pulsating axial load, we found that the system exhibits complex phenomena as multiple but stable periodic orbits leading to period doubling. The present system is highly vulnerable to catastrophic failure due to the S–N and Pitchfork bifurcation. The present research enables the notability of axial load and mechanical unbalance on the overall system behavior and stability in real working conditions.

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“…Therefore, despite being far more difficult compared to linear models, nonlinear solutions are subject of more interest and have been carried out in more detail in the past decade. Nonlinearity appears due to various causes, such as large deformations [6,7] complicated geometric models [8], the clearances in mechanical elements like tooth backlash in gears or journal bearings [9], the magnetic bearing loads [10], and the contact which creates rubbing forces [11]. In industry, there are rotary machines such as salient 2-pole generators in which the shaft cross section is not symmetric.…”

Section: Introductionmentioning

confidence: 99%

Analytical investigation on nonlinear vibration behavior of an unbalanced asymmetric rotor using the method of multiple scales

Jamshidi

Jafari

2019

J Braz. Soc. Mech. Sci. Eng.

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In this paper, the vibration behavior of a rotor with an asymmetric shaft subjected to unbalanced forces is analyzed theoretically. The model is a rotor composed of a rigid disk and a flexible shaft. The shaft is considered to be a beam with a rectangular cross section. The general equations of motion were first derived by considering the effect of high order large deformation in bending. In this process, a continuous shaft, gyroscopic effects, and rotor mass unbalance are taken into account to study the rotor's nonlinear vibratory behavior near the main resonances. The equations are discretized using the Rayleigh-Ritz method. The obtained equations are nonlinear coupled differential equations which are solved using the multiple-scales method. It can be concluded from the results that nonlinearity due to an asymmetric shaft severely affects the resonance behavior of the rotor. Keywords Rotor dynamics Á Nonlinear vibration Á Asymmetric shaft Á High order deformations List of symbols a 1 Amplitude at the equilibrium position (m) in x direction a 2 Amplitude at the equilibrium position (m) in z direction X Angular Velocity of the rotor (rad sec-1) x 1 , x 2 First and second critical speed of the rotor (rad sec-1) I Average area moment of inertia of shaft (m 4) c Coefficient of damping (N s m-1) R 1 Cross-sectional radius of shaft/internal radius of disk (m 2) A Cross-sectional area of shaft (m 2) q Density of material (kg m-3) r Detuning parameter (rad sec-1) u(y, t) Displacement along x-axis of rotor (m) w(y, t) Displacement along z-axis of rotor (m)

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Large deflection model for nonlinear flexural vibration analysis of a highly flexible rotor-bearing system

Cited by 27 publications

References 15 publications

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

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

Dynamic stability and bifurcation phenomena of an axially loaded flexible shaft-disk system supported by flexible bearing

Analytical investigation on nonlinear vibration behavior of an unbalanced asymmetric rotor using the method of multiple scales

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