Sommerfeld effect at forward and backward critical speeds in a rigid rotor shaft system with anisotropic supports

Bharti, Saurabh Kumar; Bisoi, Alfa; Sinha, Anubhab; Samantaray, Arun Kumar; Bhattacharyya, Ranjan

doi:10.1016/j.jsv.2018.11.002

Cited by 41 publications

(12 citation statements)

References 27 publications

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“…where the zeroth Fourier coefficient v o of the speed expansion in Equation ( 19) takes the role of the averaged speed v in Section 3. The insertion of the expansions ( 17) and (18) into Equation ( 15) and the coefficient comparison of the sinusoidal terms of cos ϕ and sin ϕ leads to the same result, already noted in Equations ( 10) and (11). All other terms are cutoff and can only be taken into account when higher expansions are introduced.…”

Section: Stable and Unstable Oscillation Amplitudes Of Vehicle Speedssupporting

confidence: 61%

“…Note that one finds the same behavior in rotor dynamics, where the Sommerfeld rotor leads to the same driving characteristic [2] when in Equation ( 12) the road factor z 0 Ω is replaced by the mass ratio of the unbalanced rotor, the translation velocity by the rotation speed ratio, and the driving force by the moment. More details on Sommerfeld effects in rotor dynamics are given in [16][17][18][19][20].…”

Section: Speed Driving Force Characteristic Of Traveling Vehiclesmentioning

confidence: 99%

“…All other terms are cutoff and can only be taken into account when higher expansions are introduced. The insertion of the expansions ( 17), (18), and ( 19) into the speed Equation ( 16) and the coefficient comparison leads to…”

Section: Stable and Unstable Oscillation Amplitudes Of Vehicle Speedsmentioning

confidence: 99%

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Speed Oscillations of a Vehicle Rolling on a Wavy Road

Wedig

2021

Applied Sciences

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Every driver knows that his car is slowing down or accelerating when driving up or down, respectively. The same happens on uneven roads with plastic wave deformations, e.g., in front of traffic lights or on nonpaved desert roads. This paper investigates the resulting travel speed oscillations of a quarter car model rolling in contact on a sinusoidal and stochastic road surface. The nonlinear equations of motion of the vehicle road system leads to ill-conditioned differential-algebraic equations. They are solved introducing polar coordinates into the sinusoidal road model. Numerical simulations show the Sommerfeld effect, in which the vehicle becomes stuck before the resonance speed, exhibiting limit cycles of oscillating acceleration and speed, which bifurcate from one-periodic limit cycle to one that is double periodic. Analytical approximations are derived by means of nonlinear Fourier expansions. Extensions to more realistic road models by means of noise perturbation show limit flows as bundles of nonperiodic trajectories with periodic side limits. Vehicles with higher degrees of freedom become stuck before the first speed resonance, as well as in between further resonance speeds with strong vertical vibrations and longitudinal speed oscillations. They need more power supply in order to overcome the resonance peak. For small damping, the speeds after resonance are unstable. They migrate to lower or supercritical speeds of operation. Stability in mean is investigated.

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Section: Stable and Unstable Oscillation Amplitudes Of Vehicle Speedssupporting

confidence: 61%

Section: Speed Driving Force Characteristic Of Traveling Vehiclesmentioning

confidence: 99%

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Speed Oscillations of a Vehicle Rolling on a Wavy Road

Wedig

2021

Applied Sciences

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“…The process of passing the rotor system through critical speeds, considering its interaction with the energy source, was considered in many studies. 1–11 In particular, it was found that under conditions when the power reserve of the energy source is small, the course of the process significantly depends on the characteristics of the energy source. Changes in the rotor speed turn out to be closely related to the change in vibration amplitude.…”

Section: Introductionmentioning

confidence: 99%

Dynamic modeling of a non-ideal gyroscopic rotor system with nonlinear damping and nonlinear rigidity of an elastic support

Iskakov¹,

Jamalov

Bissembayeb

et al. 2022

Advances in Mechanical Engineering

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The article considers the effect of joint linear and nonlinear cubic damping on dynamics of a gyroscopic rigid rotor interacting with an electric motor with a rectilinear characteristic, taking into account the nonlinear rigidity of the support material. The method of regulating the control parameter (voltage on the motor), the amplitude of vibration, and the angular velocity of the shaft in the frequency equation, depending on the value of the coefficient of nonlinear cubic damping of the support, offers the most effective options for controlling resonant oscillations of large amplitudes. It is shown that the greater the value of the coefficient of nonlinear cubic damping, the easier it is to control these oscillations. Moreover, it is proved that the Sommerfeld effect (of the first kind) can also be weakened and eliminate with the help of joint linear and nonlinear damping. To do this, in the case of a rigid characteristic of the nonlinear elasticity of the support material, in a rotor system with a nonideal energy source to eliminate the bistability region, that is, jumping effects, more nonlinear damping of support or energy from a nonideal energy source will be required than in the case of an ideal rotor system.

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“…Firouzi and Ghassemi 13 studied the effects of diameter and torsional stiffness on the whirling speed of the ship shafting system with GM of the rotors neglected by analytical method. Bharti et al 14 studied the Sommerfeld effect (the jump phenomenon) at forward and backward critical speeds in a (four degree of freedom) “rigid” rotor shaft system with anisotropic supports by using the analytical method. In addition to the above‐mentioned analytical methods or TMMs, Nelson and McVaugh 15 studied the dynamics of the rotor‐bearing systems with the finite element method (FEM).…”

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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Sommerfeld effect at forward and backward critical speeds in a rigid rotor shaft system with anisotropic supports

Cited by 41 publications

References 27 publications

Speed Oscillations of a Vehicle Rolling on a Wavy Road

Speed Oscillations of a Vehicle Rolling on a Wavy Road

Dynamic modeling of a non-ideal gyroscopic rotor system with nonlinear damping and nonlinear rigidity of an elastic support

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

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