Nonlinear study of a rotor–AMB system under simultaneous primary-internal resonance

Kamel, M.; Bauomy, H. S.

doi:10.1016/j.apm.2009.12.011

Cited by 21 publications

(6 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…One-mode solution of Equation (15) with boundary conditions of Equations (16) and 17is written as sum of forward and backward whirling modes as:…”

Section: Application Of Rgmmentioning

confidence: 99%

“…Ji and Hansen [13,14] studied the frequency response of an unbalanced rotor-AMB system. Kamel et al [15][16][17] obtained the response of a rotor-AMB with time varying stiffness under additive and parametric excitations using multiple scales method. Dynamical behavior of a parametrically excited rotor-AMB system with time-varying stiffness was investigated in several papers by Zhang et al [18][19][20][21][22][23].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Primary resonance analysis of a nonlinear flexible shaft supported by active magnetic bearings using analytical method

Hosseini

Yektanezhad

2020

Z Angew Math Mech

View full text Add to dashboard Cite

In this paper, primary resonances of a flexible rotor suspended by active magnetic bearings are investigated. The rotor has large amplitude vibrations, which leads to nonlinearities in curvature and inertia. In addition, nonlinearity characteristics of active magnetic bearings are considered. In modeling of the shaft, rotary inertia and shear deformation are neglected but gyroscopic effect is included. Here, the equations of motion and related boundary conditions are both nonlinear. To analyze the dynamical behavior of the system, the renormalization group method is directly applied to the partial differential equations of motion and boundary conditions. The effects of different parameters of the shaft and active magnetic bearings on the frequency response of the system in the neighborhood of critical speeds are investigated, and it is shown that both hardening and softening nonlinearity behaviors are possible.

show abstract

“…One-mode solution of Equation (15) with boundary conditions of Equations (16) and 17is written as sum of forward and backward whirling modes as:…”

Section: Application Of Rgmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Primary resonance analysis of a nonlinear flexible shaft supported by active magnetic bearings using analytical method

Hosseini

Yektanezhad

2020

Z Angew Math Mech

View full text Add to dashboard Cite

show abstract

“…Furthermore, because of the strong nonlinearities in the AMB systems, nonperiodic vibration can occur in rotor. [2][3][4] So, how to increase range of periodic motion and avoid the appearance of nonperiodic motion becomes the major execution of this paper.…”

Section: Introductionmentioning

confidence: 99%

Experimental and theoretical investigations of unbalance flexible rotor in active magnetic bearings considering backup bearings contacts

Ebrahimi

2022

Noise & Vibration Worldwide

View full text Add to dashboard Cite

This paper describes the experimental verification of an unbalance flexible rotor model in active magnetic bearings. The dynamic modeling takes into account the gyroscopic moments of the disk, geometric coupling of the magnetic actuators, and contact forces of the backup bearings. The Rung–Kutta method is used to integrate the equations of motion. The nonlinear dynamic response is analyzed using bifurcation plots, disc center trajectories, Fast Fourier Transforms, Poincaré maps, and maximum Lyapunov exponent. The analysis is carried out for different values of rotating speed and unbalance eccentricity. In the unbalance test, a concentrated mass of 5 gr is attached in three radial position of the disk. The numerical simulations and experiments prove that a variety of nonlinear dynamical phenomena such as period -3, -4, -8, periodic, quasi-periodic, and chaotic motions occur in the system. The results indicate that the response of the rotor returns back to a regular motion by increasing the rotational speed. Also, by increasing the unbalance eccentricity, the first irregular motion initiates at much higher rotational speeds. Therefore, sufficient attention should be paid to these factors in design of a flexible rotor system equipped with both active magnetic bearings and backup bearings in order to ensure system reliability.

show abstract

“…Orbit plot, the bifurcation diagram, the power spectrum, and Poincaré mapping were used in [8] to identify the main factors a ecting the dynamic characteristics of an AMB system. Asymptotic perturbation method [10] and the multiple scales method [11] were used to study the dynamical response of the magnetic bearing system with time-varying sti ness. Nonlinear phenomena like period doubling, quasiperiodic motion, and chaos in the presence of geometrical coupling were observed in [12] with numerical simulation.…”

Section: Introductionmentioning

confidence: 99%

Hopf Bifurcation and Control of Magnetic Bearing System with Uncertain Parameter

Wang

Hao³

et al. 2019

Complexity

View full text Add to dashboard Cite

In this paper, the Hopf bifurcation and control of the magnetic bearing system under an uncertain parameter are investigated. Firstly, the two-degree-of-freedom magnetic bearing system model with uncertain parameter is established. The method of orthogonal polynomial approximation is used to obtain the equivalent magnetic bearing model which is deterministic. Secondly, combining mathematical analysis tools and numerical simulations, the Hopf bifurcation of the equivalent model is analyzed. Finally, a hybrid feedback control method (linear feedback control method combined with nonlinear stochastic feedback control method) is introduced to control the Hopf bifurcation behavior of the magnetic bearing system.

show abstract

Nonlinear study of a rotor–AMB system under simultaneous primary-internal resonance

Cited by 21 publications

References 23 publications

Primary resonance analysis of a nonlinear flexible shaft supported by active magnetic bearings using analytical method

Primary resonance analysis of a nonlinear flexible shaft supported by active magnetic bearings using analytical method

Experimental and theoretical investigations of unbalance flexible rotor in active magnetic bearings considering backup bearings contacts

Hopf Bifurcation and Control of Magnetic Bearing System with Uncertain Parameter

Contact Info

Product

Resources

About