Dynamic behavior of an AMB supported rotor subject to harmonic excitation

Eissa, M.; Hegazy, Usama H.; Amer, Y. A.

doi:10.1016/j.apm.2007.04.005

Cited by 44 publications

(12 citation statements)

References 8 publications

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“…The change rule is fundamentally different to that of the linear model, which illustrates that the weak nonlinear stiffness can cause obvious nonlinear characteristics. In addition, the jump phenomenon occurs when the detuning parameter σ changes and the jump points do not overlap in the case of different changing orders; these results are consistent with those calculated by Eissa [30]. Figure 4a and Figure 4b show the effects of k s and ω 0 on analytic responses for different σ.…”

Section: Resultssupporting

confidence: 86%

Research on Steady-State Characteristics of Centrifugal Pump Rotor System with Weak Nonlinear Stiffness

Zhou

Qiu

Zhang

et al. 2018

TFAMENA

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Steady-state vibration response characteristics of a motion model of a centrifugal pump rotor system with weak nonlinear stiffness have been calculated by using the multiple scale method (MSM). The theoretical results were in good agreement with the numerical results. Based on the MSM and the numerical method, the effects of detuning parameter, nonlinear stiffness parameter and natural frequency on steady-state amplitude were also investigated. Finally, Lyapunov's theorem on stability in the first approximation was applied for the determination of the system's stable and unstable solution regions. The calculated results imply that the centrifugal pump rotor system with weak nonlinear stiffness exhibits typical nonlinear vibration characteristics. The variation of detuning parameter, nonlinear stiffness parameter and natural frequency can result in a jump phenomenon, and their corresponding curves present 'hard spring', 'soft spring' and 'S'-shaped amplitude characteristic, respectively. Smaller detuning parameter and natural frequency or greater nonlinear stiffness parameter are beneficial to decreasing the steady-state response amplitude. The results can provide reference for an investigation into nonlinear vibration characteristics of a centrifugal pump rotor system.

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Section: Resultssupporting

confidence: 86%

Research on Steady-State Characteristics of Centrifugal Pump Rotor System with Weak Nonlinear Stiffness

Zhou

Qiu

Zhang

et al. 2018

TFAMENA

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“…Amer and co-workers [17][18][19][20][21] studied a rotor-active magnetic bearing with quadratic and cubic non-linearities and the time-varying stiffness under harmonic and parametric excitations. The steady state solution of a rotor system is studied under different resonance cases applying a perturbation technique.…”

Section: Introductionmentioning

confidence: 99%

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

Kamel

Bauomy

2010

Applied Mathematical Modelling

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a b s t r a c tA rotor-active magnetic bearing (AMB) system subjected to a periodically time-varying stiffness with quadratic and cubic non-linearities under multi-parametric excitations is studied and solved. The method of multiple scales is applied to analyze the response of two modes of a rotor-AMB system with multi-parametric excitations and time-varying stiffness near the simultaneous primary and internal resonance. The stability of the steady state solution for that resonance is determined and studied using Rung-Kutta method of fourth order. It is shown that the system exhibits many typical non-linear behaviors including multiple-valued solutions, jump phenomenon, hardening and softening non-linearities and chaos in the second mode of the system. The effects of the different parameters on the steady state solutions are investigated and discussed also. A comparison to published work is reported.

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“…Since magnetic levitation does not use long reaching and joint parts, wear and maintenance problem caused by friction are completely eliminated. Magnetic levitation has been used in magnetic bearings [1][2][3][4][5], vibration suspension [6][7][8][9] and position tracking [10]. Furthermore, different types of control techniques have been used in magnetic levitation systems.…”

Section: Introductionmentioning

confidence: 99%

Dual LQG-PID control of a highly nonlinear magnetic levitation system

El-Sinawi

Emam

2011

2011 Fourth International Conference on Modeling, Simulation and Applied Optimization

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A study of one-dimensional position control of a light iron ball levitated by one electromagnet is proposed in this work. The vertical position of the ball is the target of the proposed control strategy. It is assumed that the position measurement of the ball is inaccessible and thus, estimates of the position are utilized as the feedback signal to the controller. Control of the ball's position is carried out using LQG-based controller with the objective of manipulating the electromagnet current to drive the ball to steady state with minimal error. The integrity of the controller as well as accuracy of the system's model is evaluated via simulation.

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Dynamic behavior of an AMB supported rotor subject to harmonic excitation

Cited by 44 publications

References 8 publications

Research on Steady-State Characteristics of Centrifugal Pump Rotor System with Weak Nonlinear Stiffness

Research on Steady-State Characteristics of Centrifugal Pump Rotor System with Weak Nonlinear Stiffness

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

Dual LQG-PID control of a highly nonlinear magnetic levitation system

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