On the oscillatory behaviours and rub-impact forces of a horizontally supported asymmetric rotor system under position-velocity feedback controller

Saeed, Nasser A.; Elbendary, Sherif; Sayed, M.; Mohamed, Mokhtar; Elagan, S. K.

doi:10.1590/1679-78256410

Cited by 13 publications

(18 citation statements)

References 25 publications

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“…It is worth mentioning that the numerical simulations in the whole article are performed utilizing MATLAB ODE45 solver to obtain the system the bifurcation diagrams, temporal oscillations, orbit plot, and frequency spectrum. e dynamical characteristics of the considered system are analyzed utilizing the dimensionless system parameters [26][27][28]:…”

Section: Resultsmentioning

confidence: 99%

“…e dynamical model of the horizontally suspended rotor system shown in Figure 1(a) is given as follows [26][27][28][29]:…”

Section: Mathematical Formulationmentioning

confidence: 99%

“…It is considered that the rotor system performs a planer vibration in the stationary U 1 − U 2 frame, while ς 1 − ς 2 is a rotational frame that rotates with angular speed ω. When the rotating shaft is displaced by small radial displacement s � �� u 2 1 + u 2 2 as shown in Figure 1(b), an exerted nonlinear restoring force is developed in U 1 and U 2 directions that can be expressed as follows [26][27][28][29]:…”

Section: Mathematical Formulationmentioning

confidence: 99%

“…For the asymmetric rotating machinery, the restoring force in ς 1 and ς 2 directions may be not symmetric due to the winding slots as in the case of 2-pole rotor generators [29] (see Figure 1(c)). erefore, the equations of motions for such asymmetric machines can be obtained via modifying equations (5a) and (5b) as follows: Vibration control of the rotating shafts (i) Symmetric rotating shaft with passive control (i) References [16][17][18] (ii) Symmetric rotating shaft with active control (ii) References [19][20][21][22] (iii) Asymmetric rotating shaft system with active control (iii) References [20,28] Active vibration control of asymmetric rotating shafts including the rub-impact forces (i) Nonlinear vertically supported rotor (i) Reference [25] (ii) Nonlinear horizontally supported rotor (ii) is work…”

Section: Mathematical Formulationmentioning

confidence: 99%

“…where ΔF V 1 and ΔF V 2 represent the asymmetry of the restoring forces in V 1 and V 2 directions. It is considered that the difference between the restoring force in ς 1 direction and in ς 2 is ΔF, where ΔF is given as follows [28]:…”

Section: Mathematical Formulationmentioning

confidence: 99%

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Rub‐Impact Force Induces Periodic, Quasiperiodic, and Chaotic Motions of a Controlled Asymmetric Rotor System

Saeed

Awwad

Maarouf

et al. 2021

Shock and Vibration

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This article aims to explore the oscillatory characteristics of a controlled asymmetric rotor system when subjected to rub and impact forces between the rotor and stator. Four electromagnetic poles are used to control the whirling motion of the rotor system through a linear proportional-derivative control law. The equations of motion that govern the whole system dynamics are derived including the rub and impact forces. The derived mathematical model is analyzed in two basic steps. Firstly, the obtained model is treated as a weakly nonlinear system using perturbation analysis to obtain the slow-flow modulating equations when neglecting the rub and impact forces. Depending on the obtained slow-flow equations, different response curves are plotted to explore the system’s periodic vibrations and determine the conditions at which the system can exhibit rub and impact force. Secondly, the whole system model including the rub and impact forces is investigated by using the bifurcation diagrams, Poincare map, frequency spectrums, and temporal oscillations. The obtained results revealed that the applied control law could mitigate the system whirling oscillations and prevent the rub and impact forces if the control gains are tuned properly. However, the system can perform period-n, quasiperiodic, or chaotic motion depending on the shaft spinning speed if the controller fails to eliminate the contact between the rotor and stator.

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Section: Resultsmentioning

confidence: 99%

“…e dynamical model of the horizontally suspended rotor system shown in Figure 1(a) is given as follows [26][27][28][29]:…”

Section: Mathematical Formulationmentioning

confidence: 99%

Section: Mathematical Formulationmentioning

confidence: 99%

Section: Mathematical Formulationmentioning

confidence: 99%

Section: Mathematical Formulationmentioning

confidence: 99%

See 3 more Smart Citations

Rub‐Impact Force Induces Periodic, Quasiperiodic, and Chaotic Motions of a Controlled Asymmetric Rotor System

Saeed

Awwad

Maarouf

et al. 2021

Shock and Vibration

Self Cite

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On $$\frac{1}{2}$$-DOF active dampers to suppress multistability vibration of a $$2$$-DOF rotor model subjected to simultaneous multiparametric and external harmonic excitations

Saeed,

Awrejcewicz,

Elashmawey

et al. 2024

Nonlinear Dyn

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This article addresses the bifurcation characteristics and vibration reduction of a $$2$$ 2 -DOF dynamical system simulating the nonlinear oscillation of an asymmetric rotor model subjected to simultaneous multiparametric and external excitations. To suppress the system's vibrations, two $$1/2$$ 1 / 2 -DOF active dampers are attached to the system in linear and cubic nonlinear forms via a magnetic coupling actuator. The closed-loop system model is derived as two differential equations with multi-control terms, including cubic, quantic, and septic, coupled nonlinearly to two first-order systems. Applying perturbation theory, the system model is solved, and the autonomous system describing the closed-loop slow-flow dynamics is obtained. Through numerical algorithms, the motion bifurcation is analyzed using various tools such as 2D and 3D bifurcation diagrams, two-parameter stability charts, basins of attraction, orbit plots, and time response profiles. The analytical investigations confirm that the uncontrolled model behaves like a hardening Duffing oscillator with multistability characteristics, displaying simultaneous mono-stable, bi-stable, tri-stable, or quadri-stable periodic oscillations depending on both the asymmetric nonlinearities and angular velocity. Subsequently, the influence of different control parameters is analyzed to determine the threshold between mono and multi-stability conditions. Finally, optimal control parameters are designed to eliminate multistability characteristics and achieve minimum and safe vibration levels.

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Semi-analytical predictions of multi-stable independent periodic motions and bifurcation evolution in a nonlinear bolted rotor system

Zhao,

Jiao,

et al. 2024

Communications in Nonlinear Science and Numerical Simulation

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On the oscillatory behaviours and rub-impact forces of a horizontally supported asymmetric rotor system under position-velocity feedback controller

Cited by 13 publications

References 25 publications

Rub‐Impact Force Induces Periodic, Quasiperiodic, and Chaotic Motions of a Controlled Asymmetric Rotor System

Rub‐Impact Force Induces Periodic, Quasiperiodic, and Chaotic Motions of a Controlled Asymmetric Rotor System

On $$\frac{1}{2}$$-DOF active dampers to suppress multistability vibration of a $$2$$-DOF rotor model subjected to simultaneous multiparametric and external harmonic excitations

Semi-analytical predictions of multi-stable independent periodic motions and bifurcation evolution in a nonlinear bolted rotor system

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