Nonlinear dynamics of a statically misaligned flexible rotor in active magnetic bearings

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Abstract

The response of a statically misaligned flexible rotor mounted in active magnetic bearings is numerically investigated in this work. The mathematical model of the rotor-bearing system incorporates nonlinearity due to the geometric coupling of the magnetic actuators as well as that arising from the magnetic actuator forces that are nonlinear function of the coil current and the air gap between the rotor and the stator. The influence of the rotor's static misalignment, represented by the gravity parameter, W, on its response was found to be dependent on the magnitude of the geometric coupling parameter, α. Numerical results showed that for α = 0, the response of the rotor was always synchronous regardless of the values of W. For moderate values of α, nonsynchronous vibration was seen in the response of the rotor for the case of W ≠ 0. For large values of α, nonsynchronous vibration was observed in the response of the rotor irrespective of the values of W. For the values of design and operating parameters of the rotor-bearing system investigated in this work, the response of the rotor displayed a rich variety of nonlinear dynamical phenomena including sub-synchronous vibrations of period-2, -3, -4, -6, -8, -12, -14 and -16, quasi-periodicity and chaos. Numerical results further revealed the existence of multiple attractors within certain ranges of the speed parameter, Ω. Co-existence of attractors has serious implications on the safe operation of magnetically supported rotating machinery as synchronous response of the rotor may become nonsynchronous or even chaotic when excited by external forces that cause the rotor's position to move from one basin of attraction to another.

Original languageEnglish
Pages (from-to)764-777
Number of pages14
JournalCommunications in Nonlinear Science and Numerical Simulation
Volume15
Issue number3
DOIs
Publication statusPublished - 01 Mar 2010

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Active Magnetic Bearing
Magnetic bearings
Rotor
Nonlinear Dynamics
Rotors
Bearings (structural)
Magnetic actuators
Vibration
Attractor
Actuator
Rotating Machinery
Quasiperiodicity
Numerical Results
Rotating machinery
Basin of Attraction
Misalignment
Coil
Nonlinear Function
Coexistence
Chaos theory

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Modelling and Simulation
  • Applied Mathematics

Cite this

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title = "Nonlinear dynamics of a statically misaligned flexible rotor in active magnetic bearings",
abstract = "The response of a statically misaligned flexible rotor mounted in active magnetic bearings is numerically investigated in this work. The mathematical model of the rotor-bearing system incorporates nonlinearity due to the geometric coupling of the magnetic actuators as well as that arising from the magnetic actuator forces that are nonlinear function of the coil current and the air gap between the rotor and the stator. The influence of the rotor's static misalignment, represented by the gravity parameter, W, on its response was found to be dependent on the magnitude of the geometric coupling parameter, α. Numerical results showed that for α = 0, the response of the rotor was always synchronous regardless of the values of W. For moderate values of α, nonsynchronous vibration was seen in the response of the rotor for the case of W ≠ 0. For large values of α, nonsynchronous vibration was observed in the response of the rotor irrespective of the values of W. For the values of design and operating parameters of the rotor-bearing system investigated in this work, the response of the rotor displayed a rich variety of nonlinear dynamical phenomena including sub-synchronous vibrations of period-2, -3, -4, -6, -8, -12, -14 and -16, quasi-periodicity and chaos. Numerical results further revealed the existence of multiple attractors within certain ranges of the speed parameter, Ω. Co-existence of attractors has serious implications on the safe operation of magnetically supported rotating machinery as synchronous response of the rotor may become nonsynchronous or even chaotic when excited by external forces that cause the rotor's position to move from one basin of attraction to another.",
author = "{Inayat Hussain}, {Jawaid Iqbal}",
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AB - The response of a statically misaligned flexible rotor mounted in active magnetic bearings is numerically investigated in this work. The mathematical model of the rotor-bearing system incorporates nonlinearity due to the geometric coupling of the magnetic actuators as well as that arising from the magnetic actuator forces that are nonlinear function of the coil current and the air gap between the rotor and the stator. The influence of the rotor's static misalignment, represented by the gravity parameter, W, on its response was found to be dependent on the magnitude of the geometric coupling parameter, α. Numerical results showed that for α = 0, the response of the rotor was always synchronous regardless of the values of W. For moderate values of α, nonsynchronous vibration was seen in the response of the rotor for the case of W ≠ 0. For large values of α, nonsynchronous vibration was observed in the response of the rotor irrespective of the values of W. For the values of design and operating parameters of the rotor-bearing system investigated in this work, the response of the rotor displayed a rich variety of nonlinear dynamical phenomena including sub-synchronous vibrations of period-2, -3, -4, -6, -8, -12, -14 and -16, quasi-periodicity and chaos. Numerical results further revealed the existence of multiple attractors within certain ranges of the speed parameter, Ω. Co-existence of attractors has serious implications on the safe operation of magnetically supported rotating machinery as synchronous response of the rotor may become nonsynchronous or even chaotic when excited by external forces that cause the rotor's position to move from one basin of attraction to another.

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