Resonance behavior of a rotor-active magnetic bearing with time-varying stiffness

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

doi:10.1016/j.chaos.2006.04.040

Cited by 53 publications

(16 citation statements)

References 22 publications

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“…Eissa et al [22,23] analyzed the nonlinear dynamic behaviors of a rotor-AMB system with the time-varying stiffness under combined excitations. Furthermore, Amer and Hegazy [24] investigated the nonlinear dynamic behaviors of a rotor-AMB system subjected to a periodically time-varying stiffness under the simultaneous primary resonance. Kamel and Bauomy [25] employed the method of multiple scales to analyze the nonlinear vibrations of a rotor-AMB system with the multiparametric excitations.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Vibrations of a Rotor-Active Magnetic Bearing System with 16-Pole Legs and Two Degrees of Freedom

Zhang

2020

Shock and Vibration

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The asymptotic perturbation method is used to analyze the nonlinear vibrations and chaotic dynamics of a rotor-active magnetic bearing (AMB) system with 16-pole legs and the time-varying stiffness. Based on the expressions of the electromagnetic force resultants, the influences of some parameters, such as the cross-sectional area Aα of one electromagnet and the number N of windings in each electromagnet coil, on the electromagnetic force resultants are considered for the rotor-AMB system with 16-pole legs. Based on the Newton law, the governing equation of motion for the rotor-AMB system with 16-pole legs is obtained and expressed as a two-degree-of-freedom system with the parametric excitation and the quadratic and cubic nonlinearities. According to the asymptotic perturbation method, the four-dimensional averaged equation of the rotor-AMB system is derived under the case of 1 : 1 internal resonance and 1 : 2 subharmonic resonances. Then, the frequency-response curves are employed to study the steady-state solutions of the modal amplitudes. From the analysis of the frequency responses, both the hardening-type nonlinearity and the softening-type nonlinearity are observed in the rotor-AMB system. Based on the numerical solutions of the averaged equation, the changed procedure of the nonlinear dynamic behaviors of the rotor-AMB system with the control parameter is described by the bifurcation diagram. From the numerical simulations, the periodic, quasiperiodic, and chaotic motions are observed in the rotor-active magnetic bearing (AMB) system with 16-pole legs, the time-varying stiffness, and the quadratic and cubic nonlinearities.

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Section: Introductionmentioning

confidence: 99%

Nonlinear Vibrations of a Rotor-Active Magnetic Bearing System with 16-Pole Legs and Two Degrees of Freedom

Zhang

2020

Shock and Vibration

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“…The method of multiple scales is applied to obtain a system of four first ordinary differential equations that describes the time variation of the amplitudes and phases of the vibration in the horizontal and vertical directions [17]. Introducing the small perturbation parameter e, Eqs.…”

Section: Perturbation Analysismentioning

confidence: 99%

“…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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“…It is assumed to be in periodic form for better stability and controllability of motion of the spindle AMB system Amer and Hegazy, 2007)…”

Section: Mechanical Model Of the Spindlementioning

confidence: 99%

Cutting parameters and vibrations analysis of magnetic bearing spindle in milling process

Bouaziz¹,

Barkallah²,

Bouaziz³

et al. 2016

jtam

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In modern production, milling is considered the widespread cutting process in the formatting field. It remains important to study this manufacturing process as it can be subject to some parasitic phenomena that can degrade surface roughness of the machined part, increase tool wear and reduce spindle life span. In fact, the best quality work piece is obtained with a suitable choice of parameters and cutting conditions. In another hand, the study of tool vibrations and the cutting force attitude is related to the study of bearings as they present an essential part in the spindle system. In this work, a modeling of a High Speed Milling (HSM) spindle supported by two pair of Active Magnetic Bearings (AMB) is presented. The spindle is modeled by Timoshenko beam finite elements where six degrees of freedom are taken into account. The rigid displacements are also introduced in the modeling. Gyroscopic and centrifugal terms are included in the general equation. The bearings reaction forces are modeled as linear functions of journal displacement and velocity in the bearing clearance. A cutting force model for peripheral milling is proposed to estimate the tool-tip dynamic responses as well as dynamic cutting forces which are also numerically investigated. The time history of response, orbit, FFT diagram at the tool-tip center and the bearings dynamic coefficients are plotted to analyze dynamic behavior of the spindle.

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Resonance behavior of a rotor-active magnetic bearing with time-varying stiffness

Cited by 53 publications

References 22 publications

Nonlinear Vibrations of a Rotor-Active Magnetic Bearing System with 16-Pole Legs and Two Degrees of Freedom

Nonlinear Vibrations of a Rotor-Active Magnetic Bearing System with 16-Pole Legs and Two Degrees of Freedom

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

Cutting parameters and vibrations analysis of magnetic bearing spindle in milling process

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