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Active magnetic bearing-based tuned controller to suppress lateral vibrations of a nonlinear Jeffcott rotor system

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Abstract

Active magnetic bearing system is an up-to-date technology that supports rotors without physical contacts and facilitates the vibration control in rotating machinery. Within this research, a tuned positive position feedback controller is proposed to control the lateral vibrations in a Jeffcott rotor system having cubic and quadratic nonlinearities. The controller is integrated into the system via four electromagnetic poles that act as actuators. The nonlinearity due to the electromagnetic coupling is included in the system model. A second-order approximate solution to the system governing equations is sought by utilizing asymptotic analyses. Bifurcation behaviours are investigated for both the system and controller parameters. The influence of the air-gap size, bias current, disc eccentricity, feedback gain, and control gain on the vibration amplitudes has been explored. The analytical results approved that the proposed controller can reduce the vibration amplitudes close to zero at any spinning speed even at large disc eccentricity. Then, numerical confirmations for the acquired analytical results have been performed that illustrated an excellent agreement with the analytical ones. Finally, a comparison with already published articles is included.

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Abbreviations

\(q_1 ,\dot{q}_1, \ddot{q}_1\) :

Dimensionless displacement, velocity and acceleration of oscillations in horizontal direction.

\(q_2 ,\dot{q}_, \ddot{q}_2\) :

Dimensionless displacement, velocity and acceleration of oscillations in vertical direction.

\(q_3 ,\dot{q}_2, \ddot{q}_3\) :

Dimensionless displacement, velocity and acceleration of the controller in horizontal direction.

\(q_4 ,\dot{q}_4, \ddot{q}_4\) :

Dimensionless displacement, velocity and acceleration of the controller in vertical direction.

\(\mu _1 ,\mu _2 \) :

Dimensionless linear damping coefficients of both the horizontal and vertical oscillation modes.

\(\mu _3 ,\mu _4 \) :

Dimensionless linear damping coefficients of the controller of both the horizontal and vertical vibration modes.

\(\omega _1 ,\omega _2 \) :

Normalized linear natural frequencies of both the horizontal and vertical oscillation modes.

\(\omega _3 ,\omega _4 \) :

Normalized linear natural frequencies of the controllers.

\(\delta \) :

Dimensionless quadratic and cubic nonlinearity coefficient.

\({\Omega }\) :

The normalized rotor spinning speed.

f :

Dimensionless disc eccentricity.

\(\alpha _j ,j=1,\ldots ,5\) :

Dimensionless control signal gains.

\(\gamma \) :

Dimensionless feedback signal gains.

\(I_0 ,i_u ,i_v \) :

Bias current \((I_0 )\), and control currents \((i_u ,i_v )\) at both the horizontal and vertical directions in ampere.

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Acknowledgements

This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.

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Authors and Affiliations

  1. Department of Physics and Engineering Mathematics, Faculty of Electronic Engineering, Menoufia University, Menouf, 32952, Egypt

    N. A. Saeed & M. Kamel

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  1. N. A. Saeed
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  2. M. Kamel
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Correspondence to N. A. Saeed.

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Saeed, N.A., Kamel, M. Active magnetic bearing-based tuned controller to suppress lateral vibrations of a nonlinear Jeffcott rotor system. Nonlinear Dyn 90, 457–478 (2017). https://doi.org/10.1007/s11071-017-3675-y

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